[{"data":1,"prerenderedAt":99978},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-imek-blok-01":1626,"course-stats-imek":1794,"course-topics-imek":1798,"backlinks-imek-blok-01":99948,"related-imek-blok-01":99972},{"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":1793},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":1129,"description":1637,"extension":661,"meta":1781,"navigation":664,"path":1782,"seo":1783,"sources":1784,"stem":1785,"tags":1786,"type":1791,"updated":677,"__hash__":1792},"summaries\u002Fsummaries\u002Fimek-blok-01.md","KS 1. blok — Kalkul a mikroekonomie",{"type":9,"value":1631,"toc":1776},[1632,1635,1638,1660,1664,1710,1714,1750,1754],[12,1633,1629],{"id":1634},"ks-1-blok-kalkul-a-mikroekonomie",[724,1636,1637],{},"Rozcestník prvního přednáškového bloku Mgr. Martiny Bobalové, Ph.D. (57 stran). Obsah byl rozdělen do menších tematických stránek, které lze studovat samostatně.",[1639,1640,1641],"blockquote",{},[724,1642,1643,1646,1647,1651,1652,1655,1656,1659],{},[38,1644,1645],{},"Konvence z přednášek:"," symbol ",[1648,1649,1650],"code",{},"≈"," pro přibližné rovnosti, výsledky ",[38,1653,1654],{},"na 3 desetinná místa",", pojem ",[614,1657,1658],{},"jednotková změna"," znamená změnu o 1.",[115,1661,1663],{"id":1662},"témata-bloku-doporučené-pořadí","Témata bloku — doporučené pořadí",[152,1665,1666,1672,1678,1685,1691,1696,1703],{},[123,1667,1668,1671],{},[207,1669,757],{"className":1670,"dataFsResolvedFilePath":755,"href":756},[210]," — model, endogenní\u002Fexogenní proměnné, ceteris paribus, komparativní statika, principy řešení",[123,1673,1674,1677],{},[207,1675,766],{"className":1676,"dataFsResolvedFilePath":764,"href":765},[210]," — funkce, polynomy, derivace (geom.\u002Finženýrská interpretace), tečna, diferenciál jako lineární odhad přírůstku, podmínky extrémů",[123,1679,1680,1684],{},[207,1681,1683],{"className":1682,"dataFsResolvedFilePath":773,"href":774},[210],"Integrál (neurčitý a určitý)"," — primitivní funkce, určitý integrál jako plocha, rekonstrukce TR z MR a TC z MC",[123,1686,1687,1690],{},[207,1688,784],{"className":1689,"dataFsResolvedFilePath":782,"href":783},[210]," — parciální derivace, diferenciál 2D, implicitní funkce, volné extrémy 2D, indiferenční křivky \u002F izokvanty",[123,1692,1693,794],{},[207,1694,793],{"className":1695,"dataFsResolvedFilePath":791,"href":792},[210],[123,1697,1698,1702],{},[207,1699,1701],{"className":1700,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka"," — modely D, S, tržní rovnováha, multiplikátory, přebytky, zdanění",[123,1704,1705,1709],{},[207,1706,1708],{"className":1707,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," — TR\u002FAR\u002FMR, TC\u002FAC\u002FMC\u002FAVC\u002FAFC, body zvratu, maximalizace zisku, konstrukce nabídky firmy",[115,1711,1713],{"id":1712},"vazby-do-dalších-bloků","Vazby do dalších bloků",[120,1715,1716,1723,1735],{},[123,1717,1718,1722],{},[207,1719,1721],{"className":1720,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (Blok 2) — navazuje na příjem (vliv elasticity na TR) a využívá derivace.",[123,1724,1725,1729,1730,1734],{},[207,1726,1728],{"className":1727,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (Blok 2) — využívá ",[207,1731,1733],{"className":1732,"dataFsResolvedFilePath":782,"href":783},[210],"parciální derivace",".",[123,1736,1737,1740,1741,1745,1746,1734],{},[207,1738,880],{"className":1739,"dataFsResolvedFilePath":878,"href":879},[210]," (Blok 3) — využívá ",[207,1742,1744],{"className":1743,"dataFsResolvedFilePath":791,"href":792},[210],"Lagrange"," a ",[207,1747,1749],{"className":1748,"dataFsResolvedFilePath":782,"href":783},[210],"2D kalkul",[115,1751,1753],{"id":1752},"související","Související",[120,1755,1756,1764,1770],{},[123,1757,1758],{},[207,1759,1763],{"className":1760,"dataFsResolvedFilePath":1761,"href":1762},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","Kurz ImeK",[123,1765,1766,1769],{},[207,1767,1094],{"className":1768,"dataFsResolvedFilePath":838,"href":839},[210]," — Elasticita a produkce",[123,1771,1772,1775],{},[207,1773,1101],{"className":1774,"dataFsResolvedFilePath":868,"href":869},[210]," — Užitečnost a národní důchod",{"title":641,"searchDepth":642,"depth":642,"links":1777},[1778,1779,1780],{"id":1662,"depth":642,"text":1663},{"id":1712,"depth":642,"text":1713},{"id":1752,"depth":642,"text":1753},{},"\u002Fsummaries\u002Fimek-blok-01",{"title":1629,"description":1637},[1135],"summaries\u002Fimek-blok-01",[1128,1787,1145,1788,1144,1789,1790,1142],"kalkul","integral","poptavka-nabidka","prijem-naklady-zisk","summary","L44rKXw_S6gzhoDZz59NET2mlCeh4JKwVNZq9bCCveU","summaries",{"zapisku":1625,"topics":1795,"summaries":1796,"outputs":1797},15,5,1,[1799,3705,9414,10970,11840,16123,17730,27610,36604,50671,54963,74307,86419,95378,95663],{"id":1800,"title":1801,"body":1802,"course":1128,"courses":659,"created":1129,"description":3693,"extension":661,"meta":3694,"navigation":664,"path":3695,"seo":3696,"sources":3697,"stem":3698,"tags":3699,"type":3703,"updated":677,"__hash__":3704},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":1803,"toc":3676},[1804,1807,1826,1830,1914,1917,2048,2205,2208,2291,2295,2356,2406,2415,2419,2555,2605,2609,2653,2722,2793,2800,2804,2843,2915,2919,3000,3049,3093,3097,3101,3171,3175,3225,3304,3311,3314,3367,3637,3641],[12,1805,1801],{"id":1806},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,1808,1809,1810,1814,1815,1818,1819,1822,1823,1734],{},"Matematický aparát kurzu ",[207,1811,1813],{"className":1812,"dataFsResolvedFilePath":1761,"href":1762},[210],"ImeK",". Bez derivace se neobejdou ",[38,1816,1817],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,1820,1821],{},"maximalizace zisku"," ani ",[38,1824,1825],{},"minimalizace nákladů",[115,1827,1829],{"id":1828},"funkce-a-polynomy","Funkce a polynomy",[724,1831,1832,1833,1865,1866,1879,1880,1893,1894,1734],{},"Funkce jedné proměnné ",[883,1834,1836],{"className":1835},[886],[888,1837,1838],{"xmlns":890},[892,1839,1840,1862],{},[895,1841,1842,1845,1849,1852,1856,1859],{},[898,1843,1844],{},"y",[1846,1847,1848],"mo",{},"=",[898,1850,1851],{},"f",[1846,1853,1855],{"stretchy":1854},"false","(",[898,1857,1858],{},"x",[1846,1860,1861],{"stretchy":1854},")",[902,1863,1864],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,1867,1869],{"className":1868},[886],[888,1870,1871],{"xmlns":890},[892,1872,1873,1877],{},[895,1874,1875],{},[898,1876,1858],{},[902,1878,1858],{"encoding":904}," (nezávislá) → ",[883,1881,1883],{"className":1882},[886],[888,1884,1885],{"xmlns":890},[892,1886,1887,1891],{},[895,1888,1889],{},[898,1890,1844],{},[902,1892,1844],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,1895,1897],{"className":1896},[886],[888,1898,1899],{"xmlns":890},[892,1900,1901,1911],{},[895,1902,1903,1905,1907,1909],{},[898,1904,1851],{},[1846,1906,1855],{"stretchy":1854},[898,1908,207],{},[1846,1910,1861],{"stretchy":1854},[902,1912,1913],{"encoding":904},"f(a)",[724,1915,1916],{},"Polynomy:",[120,1918,1919,1952,1996],{},[123,1920,1921],{},[152,1922,1923],{},[123,1924,1925,1926],{},"stupně: ",[883,1927,1929],{"className":1928},[886],[888,1930,1931],{"xmlns":890},[892,1932,1933,1949],{},[895,1934,1935,1937,1939,1941,1943,1946],{},[898,1936,1844],{},[1846,1938,1848],{},[898,1940,207],{},[898,1942,1858],{},[1846,1944,1945],{},"+",[898,1947,1948],{},"b",[902,1950,1951],{"encoding":904},"y = ax + b",[123,1953,1954],{},[152,1955,1956],{"start":642},[123,1957,1925,1958],{},[883,1959,1961],{"className":1960},[886],[888,1962,1963],{"xmlns":890},[892,1964,1965,1993],{},[895,1966,1967,1969,1971,1973,1982,1984,1986,1988,1990],{},[898,1968,1844],{},[1846,1970,1848],{},[898,1972,207],{},[1974,1975,1976,1978],"msup",{},[898,1977,1858],{},[1979,1980,1981],"mn",{},"2",[1846,1983,1945],{},[898,1985,1948],{},[898,1987,1858],{},[1846,1989,1945],{},[898,1991,1992],{},"c",[902,1994,1995],{"encoding":904},"y = ax^2 + bx + c",[123,1997,1998],{},[152,1999,2000],{"start":649},[123,2001,1925,2002],{},[883,2003,2005],{"className":2004},[886],[888,2006,2007],{"xmlns":890},[892,2008,2009,2045],{},[895,2010,2011,2013,2015,2017,2024,2026,2028,2034,2036,2038,2040,2042],{},[898,2012,1844],{},[1846,2014,1848],{},[898,2016,207],{},[1974,2018,2019,2021],{},[898,2020,1858],{},[1979,2022,2023],{},"3",[1846,2025,1945],{},[898,2027,1948],{},[1974,2029,2030,2032],{},[898,2031,1858],{},[1979,2033,1981],{},[1846,2035,1945],{},[898,2037,1992],{},[898,2039,1858],{},[1846,2041,1945],{},[898,2043,2044],{},"d",[902,2046,2047],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,2049,2050,2053,2054,2111,2112,2154,2155,1734],{},[38,2051,2052],{},"Příklad rozkladu:"," ",[883,2055,2057],{"className":2056},[886],[888,2058,2059],{"xmlns":890},[892,2060,2061,2108],{},[895,2062,2063,2065,2067,2073,2076,2079,2081,2083,2086,2088,2090,2092,2094,2096,2098,2100,2102,2104,2106],{},[898,2064,1844],{},[1846,2066,1848],{},[1974,2068,2069,2071],{},[898,2070,1858],{},[1979,2072,1981],{},[1846,2074,2075],{},"−",[1979,2077,2078],{},"5",[898,2080,1858],{},[1846,2082,1945],{},[1979,2084,2085],{},"6",[1846,2087,1848],{},[1846,2089,1855],{"stretchy":1854},[898,2091,1858],{},[1846,2093,2075],{},[1979,2095,1981],{},[1846,2097,1861],{"stretchy":1854},[1846,2099,1855],{"stretchy":1854},[898,2101,1858],{},[1846,2103,2075],{},[1979,2105,2023],{},[1846,2107,1861],{"stretchy":1854},[902,2109,2110],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,2113,2115],{"className":2114},[886],[888,2116,2117],{"xmlns":890},[892,2118,2119,2151],{},[895,2120,2121,2129,2131,2133,2137,2141,2147,2149],{},[2122,2123,2124,2126],"msub",{},[898,2125,1858],{},[1979,2127,2128],{},"1",[1846,2130,1848],{},[1979,2132,1981],{},[1846,2134,2136],{"separator":2135},"true",",",[2138,2139,2140],"mtext",{}," ",[2122,2142,2143,2145],{},[898,2144,1858],{},[1979,2146,1981],{},[1846,2148,1848],{},[1979,2150,2023],{},[902,2152,2153],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,2156,2158],{"className":2157},[886],[888,2159,2160],{"xmlns":890},[892,2161,2162,2202],{},[895,2163,2164,2166,2168,2170,2172,2174,2185,2191,2193],{},[898,2165,1844],{},[1846,2167,1848],{},[1846,2169,1855],{"stretchy":1854},[898,2171,1858],{},[1846,2173,2075],{},[2175,2176,2178],"mstyle",{"scriptlevel":2177,"displaystyle":1854},"0",[2179,2180,2181,2183],"mfrac",{},[1979,2182,2078],{},[1979,2184,1981],{},[1974,2186,2187,2189],{},[1846,2188,1861],{"stretchy":1854},[1979,2190,1981],{},[1846,2192,2075],{},[2175,2194,2195],{"scriptlevel":2177,"displaystyle":1854},[2179,2196,2197,2199],{},[1979,2198,2128],{},[1979,2200,2201],{},"4",[902,2203,2204],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,2206,2207],{"id":1145},"Derivace",[724,2209,2210,2211,1348,2238,2266,2267,1734],{},"Označení ",[883,2212,2214],{"className":2213},[886],[888,2215,2216],{"xmlns":890},[892,2217,2218,2235],{},[895,2219,2220,2229,2231,2233],{},[1974,2221,2222,2224],{},[898,2223,1851],{},[1846,2225,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},"normal","0em","′",[1846,2230,1855],{"stretchy":1854},[898,2232,1858],{},[1846,2234,1861],{"stretchy":1854},[902,2236,2237],{"encoding":904},"f'(x)",[883,2239,2241],{"className":2240},[886],[888,2242,2243],{"xmlns":890},[892,2244,2245,2263],{},[895,2246,2247],{},[2175,2248,2249],{"scriptlevel":2177,"displaystyle":2135},[2179,2250,2251,2257],{},[895,2252,2253,2255],{},[898,2254,2044],{},[898,2256,1844],{},[895,2258,2259,2261],{},[898,2260,2044],{},[898,2262,1858],{},[902,2264,2265],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,2268,2270],{"className":2269},[886],[888,2271,2272],{"xmlns":890},[892,2273,2274,2288],{},[895,2275,2276,2282,2284,2286],{},[1974,2277,2278,2280],{},[898,2279,1851],{},[1846,2281,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,2283,1855],{"stretchy":1854},[898,2285,207],{},[1846,2287,1861],{"stretchy":1854},[902,2289,2290],{"encoding":904},"f'(a)",[198,2292,2294],{"id":2293},"geometrická-interpretace","Geometrická interpretace",[724,2296,2297,2320,2321,2324,2325,2355],{},[883,2298,2300],{"className":2299},[886],[888,2301,2302],{"xmlns":890},[892,2303,2304,2318],{},[895,2305,2306,2312,2314,2316],{},[1974,2307,2308,2310],{},[898,2309,1851],{},[1846,2311,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,2313,1855],{"stretchy":1854},[898,2315,207],{},[1846,2317,1861],{"stretchy":1854},[902,2319,2290],{"encoding":904}," = ",[38,2322,2323],{},"sklon tečny"," ke grafu funkce v bodě ",[883,2326,2328],{"className":2327},[886],[888,2329,2330],{"xmlns":890},[892,2331,2332,2352],{},[895,2333,2334,2337,2339,2341,2343,2345,2347,2349],{},[1846,2335,2336],{"stretchy":1854},"[",[898,2338,207],{},[1846,2340,2136],{"separator":2135},[898,2342,1851],{},[1846,2344,1855],{"stretchy":1854},[898,2346,207],{},[1846,2348,1861],{"stretchy":1854},[1846,2350,2351],{"stretchy":1854},"]",[902,2353,2354],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,2357,2358],{},[883,2359,2361],{"className":2360},[886],[888,2362,2363],{"xmlns":890},[892,2364,2365,2403],{},[895,2366,2367,2369,2371,2373,2375,2377,2379,2381,2387,2389,2391,2393,2395,2397,2399,2401],{},[898,2368,1844],{},[1846,2370,2075],{},[898,2372,1851],{},[1846,2374,1855],{"stretchy":1854},[898,2376,207],{},[1846,2378,1861],{"stretchy":1854},[1846,2380,1848],{},[1974,2382,2383,2385],{},[898,2384,1851],{},[1846,2386,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,2388,1855],{"stretchy":1854},[898,2390,207],{},[1846,2392,1861],{"stretchy":1854},[1846,2394,1855],{"stretchy":1854},[898,2396,1858],{},[1846,2398,2075],{},[898,2400,207],{},[1846,2402,1861],{"stretchy":1854},[902,2404,2405],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,2407,2408],{},[2409,2410],"img",{"alt":2411,"className":2412,"src":2414},"imek-derivace-tecna",[210,2413],"wikilink-broken","\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,2416,2418],{"id":2417},"inženýrská-interpretace","Inženýrská interpretace",[724,2420,2421,2320,2444,2053,2447,2460,2461,2474,2475,2493,2494,2507,2508,2521,2522,2535,2536,2554],{},[883,2422,2424],{"className":2423},[886],[888,2425,2426],{"xmlns":890},[892,2427,2428,2442],{},[895,2429,2430,2436,2438,2440],{},[1974,2431,2432,2434],{},[898,2433,1851],{},[1846,2435,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,2437,1855],{"stretchy":1854},[898,2439,207],{},[1846,2441,1861],{"stretchy":1854},[902,2443,2290],{"encoding":904},[38,2445,2446],{},"rychlost změny",[883,2448,2450],{"className":2449},[886],[888,2451,2452],{"xmlns":890},[892,2453,2454,2458],{},[895,2455,2456],{},[898,2457,1844],{},[902,2459,1844],{"encoding":904}," vzhledem k ",[883,2462,2464],{"className":2463},[886],[888,2465,2466],{"xmlns":890},[892,2467,2468,2472],{},[895,2469,2470],{},[898,2471,1858],{},[902,2473,1858],{"encoding":904}," v bodě ",[883,2476,2478],{"className":2477},[886],[888,2479,2480],{"xmlns":890},[892,2481,2482,2490],{},[895,2483,2484,2486,2488],{},[898,2485,1858],{},[1846,2487,1848],{},[898,2489,207],{},[902,2491,2492],{"encoding":904},"x = a","; přibližná změna ",[883,2495,2497],{"className":2496},[886],[888,2498,2499],{"xmlns":890},[892,2500,2501,2505],{},[895,2502,2503],{},[898,2504,1844],{},[902,2506,1844],{"encoding":904}," při změně ",[883,2509,2511],{"className":2510},[886],[888,2512,2513],{"xmlns":890},[892,2514,2515,2519],{},[895,2516,2517],{},[898,2518,1858],{},[902,2520,1858],{"encoding":904}," z ",[883,2523,2525],{"className":2524},[886],[888,2526,2527],{"xmlns":890},[892,2528,2529,2533],{},[895,2530,2531],{},[898,2532,207],{},[902,2534,207],{"encoding":904}," na ",[883,2537,2539],{"className":2538},[886],[888,2540,2541],{"xmlns":890},[892,2542,2543,2551],{},[895,2544,2545,2547,2549],{},[898,2546,207],{},[1846,2548,1945],{},[1979,2550,2128],{},[902,2552,2553],{"encoding":904},"a+1",":",[724,2556,2557],{},[883,2558,2560],{"className":2559},[886],[888,2561,2562],{"xmlns":890},[892,2563,2564,2602],{},[895,2565,2566,2568,2570,2572,2574,2576,2578,2580,2582,2584,2586,2588,2590,2596,2598,2600],{},[898,2567,1851],{},[1846,2569,1855],{"stretchy":1854},[898,2571,207],{},[1846,2573,1945],{},[1979,2575,2128],{},[1846,2577,1861],{"stretchy":1854},[1846,2579,1650],{},[898,2581,1851],{},[1846,2583,1855],{"stretchy":1854},[898,2585,207],{},[1846,2587,1861],{"stretchy":1854},[1846,2589,1945],{},[1974,2591,2592,2594],{},[898,2593,1851],{},[1846,2595,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,2597,1855],{"stretchy":1854},[898,2599,207],{},[1846,2601,1861],{"stretchy":1854},[902,2603,2604],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,2606,2608],{"id":2607},"příklad-mezní-náklady","Příklad — mezní náklady",[724,2610,2611,2612,1734],{},"Celkové náklady ",[883,2613,2615],{"className":2614},[886],[888,2616,2617],{"xmlns":890},[892,2618,2619,2650],{},[895,2620,2621,2624,2627,2629,2632,2634,2636,2639,2641,2644],{},[898,2622,2623],{},"T",[898,2625,2626],{},"C",[1846,2628,1848],{},[1979,2630,2631],{},"1000",[1846,2633,1945],{},[1979,2635,1981],{},[898,2637,2638],{},"Q",[1846,2640,1945],{},[1979,2642,2643],{},"0,1",[1974,2645,2646,2648],{},[898,2647,2638],{},[1979,2649,1981],{},[902,2651,2652],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,2654,2655,2656,2694,2695,1734],{},"Mezní náklady: ",[883,2657,2659],{"className":2658},[886],[888,2660,2661],{"xmlns":890},[892,2662,2663,2691],{},[895,2664,2665,2668,2670,2672,2674,2680,2682,2684,2686,2689],{},[898,2666,2667],{},"M",[898,2669,2626],{},[1846,2671,1848],{},[898,2673,2623],{},[1974,2675,2676,2678],{},[898,2677,2626],{},[1846,2679,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,2681,1848],{},[1979,2683,1981],{},[1846,2685,1945],{},[1979,2687,2688],{},"0,2",[898,2690,2638],{},[902,2692,2693],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,2696,2698],{"className":2697},[886],[888,2699,2700],{"xmlns":890},[892,2701,2702,2719],{},[895,2703,2704,2706,2708,2710,2713,2715,2717],{},[898,2705,2667],{},[898,2707,2626],{},[1846,2709,1855],{"stretchy":1854},[1979,2711,2712],{},"10",[1846,2714,1861],{"stretchy":1854},[1846,2716,1848],{},[1979,2718,2201],{},[902,2720,2721],{"encoding":904},"MC(10) = 4",[724,2723,2724,2053,2727,2776,2777,2053,2780,1734],{},[38,2725,2726],{},"Skutečný přírůstek:",[883,2728,2730],{"className":2729},[886],[888,2731,2732],{"xmlns":890},[892,2733,2734,2773],{},[895,2735,2736,2739,2741,2743,2745,2747,2749,2751,2754,2756,2758,2760,2762,2764,2766,2768,2770],{},[898,2737,2738],{"mathvariant":2226},"Δ",[898,2740,2623],{},[898,2742,2626],{},[1846,2744,1848],{},[898,2746,2623],{},[898,2748,2626],{},[1846,2750,1855],{"stretchy":1854},[1979,2752,2753],{},"11",[1846,2755,1861],{"stretchy":1854},[1846,2757,2075],{},[898,2759,2623],{},[898,2761,2626],{},[1846,2763,1855],{"stretchy":1854},[1979,2765,2712],{},[1846,2767,1861],{"stretchy":1854},[1846,2769,1848],{},[1979,2771,2772],{},"4,2",[902,2774,2775],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[38,2778,2779],{},"Přibližný (lineární):",[883,2781,2783],{"className":2782},[886],[888,2784,2785],{"xmlns":890},[892,2786,2787,2791],{},[895,2788,2789],{},[1979,2790,2201],{},[902,2792,2201],{"encoding":904},[724,2794,2795,2796,2799],{},"(Viz aplikace v ",[207,2797,1790],{"className":2798,"dataFsResolvedFilePath":827,"href":828},[210],".)",[115,2801,2803],{"id":2802},"diferenciál","Diferenciál",[724,2805,2806],{},[883,2807,2809],{"className":2808},[886],[888,2810,2811],{"xmlns":890},[892,2812,2813,2840],{},[895,2814,2815,2817,2819,2821,2827,2829,2831,2833,2836,2838],{},[898,2816,2044],{},[898,2818,1851],{},[1846,2820,1848],{},[1974,2822,2823,2825],{},[898,2824,1851],{},[1846,2826,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,2828,1855],{"stretchy":1854},[898,2830,1858],{},[1846,2832,1861],{"stretchy":1854},[2138,2834,2835],{}," ",[898,2837,2044],{},[898,2839,1858],{},[902,2841,2842],{"encoding":904},"df = f'(x)\\, dx",[724,2844,2845,2846,2862,2863,2911,2912,1734],{},"Pro malá ",[883,2847,2849],{"className":2848},[886],[888,2850,2851],{"xmlns":890},[892,2852,2853,2859],{},[895,2854,2855,2857],{},[898,2856,2044],{},[898,2858,1858],{},[902,2860,2861],{"encoding":904},"dx"," platí: ",[883,2864,2866],{"className":2865},[886],[888,2867,2868],{"xmlns":890},[892,2869,2870,2908],{},[895,2871,2872,2874,2876,2878,2880,2882,2884,2886,2888,2890,2892,2894,2896,2898,2900,2902,2904,2906],{},[898,2873,2738],{"mathvariant":2226},[898,2875,1851],{},[1846,2877,1848],{},[898,2879,1851],{},[1846,2881,1855],{"stretchy":1854},[898,2883,1858],{},[1846,2885,1945],{},[898,2887,2044],{},[898,2889,1858],{},[1846,2891,1861],{"stretchy":1854},[1846,2893,2075],{},[898,2895,1851],{},[1846,2897,1855],{"stretchy":1854},[898,2899,1858],{},[1846,2901,1861],{"stretchy":1854},[1846,2903,1650],{},[898,2905,2044],{},[898,2907,1851],{},[902,2909,2910],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,2913,2914],{},"lineární odhad přírůstku",[198,2916,2918],{"id":2917},"příklad","Příklad",[724,2920,2921,2952,2953,2978,2979,2999],{},[883,2922,2924],{"className":2923},[886],[888,2925,2926],{"xmlns":890},[892,2927,2928,2949],{},[895,2929,2930,2932,2934,2936,2939,2941,2943],{},[898,2931,2623],{},[898,2933,2626],{},[1846,2935,1848],{},[1979,2937,2938],{},"100",[1846,2940,1945],{},[1979,2942,2643],{},[1974,2944,2945,2947],{},[898,2946,2638],{},[1979,2948,1981],{},[902,2950,2951],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,2954,2956],{"className":2955},[886],[888,2957,2958],{"xmlns":890},[892,2959,2960,2975],{},[895,2961,2962,2964,2966,2969,2972],{},[898,2963,2638],{},[1846,2965,2554],{},[1979,2967,2968],{},"50",[1846,2970,2971],{},"→",[1979,2973,2974],{},"60",[902,2976,2977],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,2980,2982],{"className":2981},[886],[888,2983,2984],{"xmlns":890},[892,2985,2986,2996],{},[895,2987,2988,2990,2992,2994],{},[898,2989,2044],{},[898,2991,2638],{},[1846,2993,1848],{},[1979,2995,2712],{},[902,2997,2998],{"encoding":904},"dQ = 10","):",[724,3001,3002],{},[883,3003,3005],{"className":3004},[886],[888,3006,3007],{"xmlns":890},[892,3008,3009,3046],{},[895,3010,3011,3013,3015,3017,3019,3021,3023,3026,3028,3030,3032,3034,3036,3038,3040,3042,3044],{},[898,3012,2044],{},[898,3014,2623],{},[898,3016,2626],{},[1846,3018,1848],{},[1979,3020,2688],{},[898,3022,2638],{},[1846,3024,3025],{},"⋅",[898,3027,2044],{},[898,3029,2638],{},[1846,3031,1848],{},[1979,3033,2688],{},[1846,3035,3025],{},[1979,3037,2968],{},[1846,3039,3025],{},[1979,3041,2712],{},[1846,3043,1848],{},[1979,3045,2938],{},[902,3047,3048],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,3050,3051,3052,3075,3076,3092],{},"Přesná změna: ",[883,3053,3055],{"className":3054},[886],[888,3056,3057],{"xmlns":890},[892,3058,3059,3072],{},[895,3060,3061,3063,3065,3067,3069],{},[898,3062,2738],{"mathvariant":2226},[898,3064,2623],{},[898,3066,2626],{},[1846,3068,1848],{},[1979,3070,3071],{},"110",[902,3073,3074],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,3077,3079],{"className":3078},[886],[888,3080,3081],{"xmlns":890},[892,3082,3083,3089],{},[895,3084,3085,3087],{},[898,3086,2623],{},[898,3088,2626],{},[902,3090,3091],{"encoding":904},"TC"," je konvexní.",[115,3094,3096],{"id":3095},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,3098,3100],{"id":3099},"nutná-podmínka","Nutná podmínka",[724,3102,3103,3104,2474,3124,3137,3138,3166,3167,3170],{},"Má-li ",[883,3105,3107],{"className":3106},[886],[888,3108,3109],{"xmlns":890},[892,3110,3111,3121],{},[895,3112,3113,3115,3117,3119],{},[898,3114,1851],{},[1846,3116,1855],{"stretchy":1854},[898,3118,1858],{},[1846,3120,1861],{"stretchy":1854},[902,3122,3123],{"encoding":904},"f(x)",[883,3125,3127],{"className":3126},[886],[888,3128,3129],{"xmlns":890},[892,3130,3131,3135],{},[895,3132,3133],{},[898,3134,207],{},[902,3136,207],{"encoding":904}," extrém, pak ",[883,3139,3141],{"className":3140},[886],[888,3142,3143],{"xmlns":890},[892,3144,3145,3163],{},[895,3146,3147,3153,3155,3157,3159,3161],{},[1974,3148,3149,3151],{},[898,3150,1851],{},[1846,3152,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,3154,1855],{"stretchy":1854},[898,3156,207],{},[1846,3158,1861],{"stretchy":1854},[1846,3160,1848],{},[1979,3162,2177],{},[902,3164,3165],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,3168,3169],{},"stacionární"," (podezřelé) body.",[198,3172,3174],{"id":3173},"postačující-podmínka","Postačující podmínka",[724,3176,3177,3178,3191,3192,2554],{},"Pro stacionární bod ",[883,3179,3181],{"className":3180},[886],[888,3182,3183],{"xmlns":890},[892,3184,3185,3189],{},[895,3186,3187],{},[898,3188,207],{},[902,3190,207],{"encoding":904},", je-li ",[883,3193,3195],{"className":3194},[886],[888,3196,3197],{"xmlns":890},[892,3198,3199,3222],{},[895,3200,3201,3211,3213,3215,3217,3220],{},[1974,3202,3203,3205],{},[898,3204,1851],{},[895,3206,3207,3209],{},[1846,3208,2228],{"mathvariant":2226},[1846,3210,2228],{"mathvariant":2226},[1846,3212,1855],{"stretchy":1854},[898,3214,207],{},[1846,3216,1861],{"stretchy":1854},[1846,3218,3219],{"mathvariant":2226},"≠",[1979,3221,2177],{},[902,3223,3224],{"encoding":904},"f''(a) \\neq 0",[120,3226,3227,3266],{},[123,3228,3229,3262,3263],{},[883,3230,3232],{"className":3231},[886],[888,3233,3234],{"xmlns":890},[892,3235,3236,3259],{},[895,3237,3238,3248,3250,3252,3254,3257],{},[1974,3239,3240,3242],{},[898,3241,1851],{},[895,3243,3244,3246],{},[1846,3245,2228],{"mathvariant":2226},[1846,3247,2228],{"mathvariant":2226},[1846,3249,1855],{"stretchy":1854},[898,3251,207],{},[1846,3253,1861],{"stretchy":1854},[1846,3255,3256],{},">",[1979,3258,2177],{},[902,3260,3261],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,3264,3265],{},"lokální minimum",[123,3267,3268,3262,3301],{},[883,3269,3271],{"className":3270},[886],[888,3272,3273],{"xmlns":890},[892,3274,3275,3298],{},[895,3276,3277,3287,3289,3291,3293,3296],{},[1974,3278,3279,3281],{},[898,3280,1851],{},[895,3282,3283,3285],{},[1846,3284,2228],{"mathvariant":2226},[1846,3286,2228],{"mathvariant":2226},[1846,3288,1855],{"stretchy":1854},[898,3290,207],{},[1846,3292,1861],{"stretchy":1854},[1846,3294,3295],{},"\u003C",[1979,3297,2177],{},[902,3299,3300],{"encoding":904},"f''(a) \u003C 0",[38,3302,3303],{},"lokální maximum",[724,3305,3306],{},[2409,3307],{"alt":3308,"className":3309,"src":3310},"imek-extremy-1d",[210,2413],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,3312,2918],{"id":3313},"příklad-1",[724,3315,3316],{},[883,3317,3319],{"className":3318},[886],[888,3320,3321],{"xmlns":890},[892,3322,3323,3364],{},[895,3324,3325,3327,3329,3331,3333,3335,3337,3343,3345,3347,3353,3355,3358,3360,3362],{},[898,3326,1851],{},[1846,3328,1855],{"stretchy":1854},[898,3330,1858],{},[1846,3332,1861],{"stretchy":1854},[1846,3334,1848],{},[1979,3336,1981],{},[1974,3338,3339,3341],{},[898,3340,1858],{},[1979,3342,2023],{},[1846,3344,2075],{},[1979,3346,2023],{},[1974,3348,3349,3351],{},[898,3350,1858],{},[1979,3352,1981],{},[1846,3354,2075],{},[1979,3356,3357],{},"12",[898,3359,1858],{},[1846,3361,1945],{},[1979,3363,2023],{},[902,3365,3366],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,3368,3369,3480,3520,3583],{},[123,3370,3371,3443,3444],{},[883,3372,3374],{"className":3373},[886],[888,3375,3376],{"xmlns":890},[892,3377,3378,3440],{},[895,3379,3380,3386,3388,3390,3392,3394,3396,3402,3404,3406,3408,3410,3412,3414,3416,3418,3420,3422,3424,3426,3428,3430,3432,3434,3436,3438],{},[1974,3381,3382,3384],{},[898,3383,1851],{},[1846,3385,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,3387,1855],{"stretchy":1854},[898,3389,1858],{},[1846,3391,1861],{"stretchy":1854},[1846,3393,1848],{},[1979,3395,2085],{},[1974,3397,3398,3400],{},[898,3399,1858],{},[1979,3401,1981],{},[1846,3403,2075],{},[1979,3405,2085],{},[898,3407,1858],{},[1846,3409,2075],{},[1979,3411,3357],{},[1846,3413,1848],{},[1979,3415,2085],{},[1846,3417,1855],{"stretchy":1854},[898,3419,1858],{},[1846,3421,1945],{},[1979,3423,2128],{},[1846,3425,1861],{"stretchy":1854},[1846,3427,1855],{"stretchy":1854},[898,3429,1858],{},[1846,3431,2075],{},[1979,3433,1981],{},[1846,3435,1861],{"stretchy":1854},[1846,3437,1848],{},[1979,3439,2177],{},[902,3441,3442],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,3445,3447],{"className":3446},[886],[888,3448,3449],{"xmlns":890},[892,3450,3451,3477],{},[895,3452,3453,3459,3461,3463,3465,3467,3473,3475],{},[2122,3454,3455,3457],{},[898,3456,1858],{},[1979,3458,2128],{},[1846,3460,1848],{},[1846,3462,2075],{},[1979,3464,2128],{},[1846,3466,2136],{"separator":2135},[2122,3468,3469,3471],{},[898,3470,1858],{},[1979,3472,1981],{},[1846,3474,1848],{},[1979,3476,1981],{},[902,3478,3479],{"encoding":904},"x_1 = -1, x_2 = 2",[123,3481,3482],{},[883,3483,3485],{"className":3484},[886],[888,3486,3487],{"xmlns":890},[892,3488,3489,3517],{},[895,3490,3491,3501,3503,3505,3507,3509,3511,3513,3515],{},[1974,3492,3493,3495],{},[898,3494,1851],{},[895,3496,3497,3499],{},[1846,3498,2228],{"mathvariant":2226},[1846,3500,2228],{"mathvariant":2226},[1846,3502,1855],{"stretchy":1854},[898,3504,1858],{},[1846,3506,1861],{"stretchy":1854},[1846,3508,1848],{},[1979,3510,3357],{},[898,3512,1858],{},[1846,3514,2075],{},[1979,3516,2085],{},[902,3518,3519],{"encoding":904},"f''(x) = 12x - 6",[123,3521,3522,3262,3563,3566,3567],{},[883,3523,3525],{"className":3524},[886],[888,3526,3527],{"xmlns":890},[892,3528,3529,3560],{},[895,3530,3531,3541,3543,3545,3547,3549,3551,3553,3556,3558],{},[1974,3532,3533,3535],{},[898,3534,1851],{},[895,3536,3537,3539],{},[1846,3538,2228],{"mathvariant":2226},[1846,3540,2228],{"mathvariant":2226},[1846,3542,1855],{"stretchy":1854},[1846,3544,2075],{},[1979,3546,2128],{},[1846,3548,1861],{"stretchy":1854},[1846,3550,1848],{},[1846,3552,2075],{},[1979,3554,3555],{},"18",[1846,3557,3295],{},[1979,3559,2177],{},[902,3561,3562],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,3564,3565],{},"maximum"," v ",[883,3568,3570],{"className":3569},[886],[888,3571,3572],{"xmlns":890},[892,3573,3574,3580],{},[895,3575,3576,3578],{},[1846,3577,2075],{},[1979,3579,2128],{},[902,3581,3582],{"encoding":904},"-1",[123,3584,3585,3262,3621,3566,3624],{},[883,3586,3588],{"className":3587},[886],[888,3589,3590],{"xmlns":890},[892,3591,3592,3618],{},[895,3593,3594,3604,3606,3608,3610,3612,3614,3616],{},[1974,3595,3596,3598],{},[898,3597,1851],{},[895,3599,3600,3602],{},[1846,3601,2228],{"mathvariant":2226},[1846,3603,2228],{"mathvariant":2226},[1846,3605,1855],{"stretchy":1854},[1979,3607,1981],{},[1846,3609,1861],{"stretchy":1854},[1846,3611,1848],{},[1979,3613,3555],{},[1846,3615,3256],{},[1979,3617,2177],{},[902,3619,3620],{"encoding":904},"f''(2) = 18 > 0",[38,3622,3623],{},"minimum",[883,3625,3627],{"className":3626},[886],[888,3628,3629],{"xmlns":890},[892,3630,3631,3635],{},[895,3632,3633],{},[1979,3634,1981],{},[902,3636,1981],{"encoding":904},[115,3638,3640],{"id":3639},"navigace","Navigace",[120,3642,3643,3651,3659],{},[123,3644,3645,2053,3648],{},[38,3646,3647],{},"Předchozí:",[207,3649,757],{"className":3650,"dataFsResolvedFilePath":755,"href":756},[210],[123,3652,3653,2053,3656],{},[38,3654,3655],{},"Navazující:",[207,3657,775],{"className":3658,"dataFsResolvedFilePath":773,"href":774},[210],[123,3660,3661,2053,3664,3667,3668,3671,3672,3675],{},[38,3662,3663],{},"Souvislosti:",[207,3665,784],{"className":3666,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,3669,1708],{"className":3670,"dataFsResolvedFilePath":827,"href":828},[210]," (aplikace mezních veličin), ",[207,3673,1721],{"className":3674,"dataFsResolvedFilePath":848,"href":849},[210]," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":3677},[3678,3679,3684,3687,3692],{"id":1828,"depth":642,"text":1829},{"id":1145,"depth":642,"text":2207,"children":3680},[3681,3682,3683],{"id":2293,"depth":649,"text":2294},{"id":2417,"depth":649,"text":2418},{"id":2607,"depth":649,"text":2608},{"id":2802,"depth":642,"text":2803,"children":3685},[3686],{"id":2917,"depth":649,"text":2918},{"id":3095,"depth":642,"text":3096,"children":3688},[3689,3690,3691],{"id":3099,"depth":649,"text":3100},{"id":3173,"depth":649,"text":3174},{"id":3313,"depth":649,"text":2918},{"id":3639,"depth":642,"text":3640},"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":1801,"description":3693},[1135],"topics\u002Fderivace",[1128,1145,3700,3701,3702],"diferencial","extremy","mezni-naklady","topic","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":3706,"title":3707,"body":3708,"course":1128,"courses":659,"created":9402,"description":641,"extension":661,"meta":9403,"navigation":664,"path":9404,"seo":9405,"sources":9406,"stem":9407,"tags":9408,"type":3703,"updated":677,"__hash__":9413},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":3709,"toc":9375},[3710,3713,3734,3738,3765,3769,3811,3902,3946,3950,3974,3981,3985,3995,4007,4011,4040,4049,4106,4112,4115,4121,4148,4154,4252,4412,4703,4707,4787,4793,4797,4895,4961,5129,5133,5211,5242,5269,5275,5307,5385,5472,5476,5539,5545,5548,5554,5668,5753,5797,5801,5847,5854,6171,6176,6200,6229,6296,6393,6397,6404,6411,6482,6602,6686,6689,6695,7022,7026,7189,7197,7333,7341,7579,7587,7590,7595,7851,7855,8029,8163,8200,8244,8247,8377,8467,8485,8489,8496,8502,8563,8566,8590,8593,8599,8602,8608,8611,8615,8653,8711,8900,8904,8977,8983,8990,8994,9000,9142,9146,9152,9188,9193,9370],[12,3711,3707],{"id":3712},"elasticita-poptávky-a-nabídky",[1639,3714,3715],{},[724,3716,3717,3720,3721,3723,3724,3727,3728,1745,3731,1734],{},[883,3718,3719],{},"!abstract"," TL;DR\n",[38,3722,1721],{}," 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: ",[38,3725,3726],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,3729,3730],{},"křížově-cenovou elasticitu",[38,3732,3733],{},"důchodovou elasticitu",[115,3735,3737],{"id":3736},"úvod-motivace","Úvod — motivace",[724,3739,3740,3741,3744,3745,3748,3749,3752,3753,3756,3757,3760,3761,3764],{},"Termín ",[614,3742,3743],{},"elasticita"," (alternativně ",[614,3746,3747],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,3750,3751],{},"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 ",[614,3754,3755],{},"cenové elasticity poptávky"," (resp. ",[614,3758,3759],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,3762,2207],{"className":3763,"dataFsResolvedFilePath":764,"href":765},[210],").",[198,3766,3768],{"id":3767},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,3770,3771,3772,3791,3792,3810],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,3773,3775],{"className":3774},[886],[888,3776,3777],{"xmlns":890},[892,3778,3779,3788],{},[895,3780,3781,3784,3786],{},[898,3782,3783],{},"P",[1846,3785,1848],{},[1979,3787,2712],{},[902,3789,3790],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,3793,3795],{"className":3794},[886],[888,3796,3797],{"xmlns":890},[892,3798,3799,3807],{},[895,3800,3801,3803,3805],{},[898,3802,2638],{},[1846,3804,1848],{},[1979,3806,2938],{},[902,3808,3809],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,3812,3813,3859],{},[123,3814,3815,3818,3819,3858],{},[38,3816,3817],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,3820,3822],{"className":3821},[886],[888,3823,3824],{"xmlns":890},[892,3825,3826,3855],{},[895,3827,3828,3831,3834,3836,3838,3841,3843,3846,3848,3850,3852],{},[2138,3829,3830],{},"  ",[1846,3832,3833],{},"⇒",[2138,3835,3830],{},[898,3837,2623],{},[898,3839,3840],{},"R",[1846,3842,1848],{},[1979,3844,3845],{},"9",[1846,3847,3025],{},[1979,3849,3071],{},[1846,3851,1848],{},[1979,3853,3854],{},"990",[902,3856,3857],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,3860,3861,3864,3865,3901],{},[38,3862,3863],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,3866,3868],{"className":3867},[886],[888,3869,3870],{"xmlns":890},[892,3871,3872,3898],{},[895,3873,3874,3876,3878,3880,3882,3884,3886,3888,3890,3893,3895],{},[2138,3875,3830],{},[1846,3877,3833],{},[2138,3879,3830],{},[898,3881,2623],{},[898,3883,3840],{},[1846,3885,1848],{},[1979,3887,3845],{},[1846,3889,3025],{},[1979,3891,3892],{},"120",[1846,3894,1848],{},[1979,3896,3897],{},"1080",[902,3899,3900],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,3903,3904,3905,3908,3909,3912,3913,3916,3917,3920,3921,3924,3925,3941,3942,3945],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,3906,3907],{},"nerozumné",", na Trhu 2 ",[38,3910,3911],{},"rozumné",". Trh 2 je ",[38,3914,3915],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,3918,3919],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,3922,3923],{},"neelastická"," a vyššího ",[883,3926,3928],{"className":3927},[886],[888,3929,3930],{"xmlns":890},[892,3931,3932,3938],{},[895,3933,3934,3936],{},[898,3935,2623],{},[898,3937,3840],{},[902,3939,3940],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,3943,3944],{},"zvýšením"," ceny.",[198,3947,3949],{"id":3948},"hypotéza-41","Hypotéza 4.1",[1639,3951,3952],{},[724,3953,3954,3955],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,3956,3958],{"className":3957},[886],[888,3959,3960],{"xmlns":890},[892,3961,3962,3971],{},[895,3963,3964,3966,3969],{},[1846,3965,1855],{"stretchy":1854},[1979,3967,3968],{},"4.1",[1846,3970,1861],{"stretchy":1854},[902,3972,3973],{"encoding":904},"(4.1)",[724,3975,3976,3977,3980],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,3978,3979],{},"procentní změny"," obou faktorů.",[115,3982,3984],{"id":3983},"pojem-elasticity","Pojem elasticity",[724,3986,3987,3988,3990,3991,3994],{},"Obecně ",[38,3989,3743],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,3992,3993],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[1639,3996,3997],{},[724,3998,3999,4002,4003,4006],{},[883,4000,4001],{},"!info"," Intuice\nElasticitu lze číst jako ",[38,4004,4005],{},"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.",[115,4008,4010],{"id":4009},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,4012,4013,4014,4039],{},"Nechť ",[883,4015,4017],{"className":4016},[886],[888,4018,4019],{"xmlns":890},[892,4020,4021,4036],{},[895,4022,4023,4025,4027,4030,4032,4034],{},[898,4024,2638],{},[1846,4026,1848],{},[898,4028,4029],{},"D",[1846,4031,1855],{"stretchy":1854},[898,4033,3783],{},[1846,4035,1861],{"stretchy":1854},[902,4037,4038],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,4041,4042],{},[883,4043,4048],{"className":4044,"title":4046,"style":4047},[4045],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,4050,4051,4052,1745,4068,4084,4085,4105],{},"Znaménko minus je korekce: změny ",[883,4053,4055],{"className":4054},[886],[888,4056,4057],{"xmlns":890},[892,4058,4059,4065],{},[895,4060,4061,4063],{},[898,4062,2738],{"mathvariant":2226},[898,4064,2638],{},[902,4066,4067],{"encoding":904},"\\Delta Q",[883,4069,4071],{"className":4070},[886],[888,4072,4073],{"xmlns":890},[892,4074,4075,4081],{},[895,4076,4077,4079],{},[898,4078,2738],{"mathvariant":2226},[898,4080,3783],{},[902,4082,4083],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,4086,4088],{"className":4087},[886],[888,4089,4090],{"xmlns":890},[892,4091,4092,4102],{},[895,4093,4094],{},[1974,4095,4096,4099],{},[898,4097,4098],{},"E",[898,4100,4101],{},"A",[902,4103,4104],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,4107,4108],{},[883,4109,4111],{"className":4110,"title":4046,"style":4047},[4045],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,4113,4114],{},"Po dosazení:",[724,4116,4117],{},[883,4118,4120],{"className":4119,"title":4046,"style":4047},[4045],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,4122,4123,4124,4144,4145,4147],{},"Limitním přechodem ",[883,4125,4127],{"className":4126},[886],[888,4128,4129],{"xmlns":890},[892,4130,4131,4141],{},[895,4132,4133,4135,4137,4139],{},[898,4134,2738],{"mathvariant":2226},[898,4136,3783],{},[1846,4138,2971],{},[1979,4140,2177],{},[902,4142,4143],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,4146,3755],{}," (price elasticity of demand):",[724,4149,4150],{},[883,4151,4153],{"className":4152,"title":4046,"style":4047},[4045],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,4155,4156,4157,4180,4181,4204,4205,4229,4230,4251],{},"kde ",[883,4158,4160],{"className":4159},[886],[888,4161,4162],{"xmlns":890},[892,4163,4164,4178],{},[895,4165,4166,4168,4170,4172,4174,4176],{},[898,4167,2638],{},[1846,4169,1848],{},[898,4171,4029],{},[1846,4173,1855],{"stretchy":1854},[898,4175,3783],{},[1846,4177,1861],{"stretchy":1854},[902,4179,4038],{"encoding":904},". Pro pevnou cenu ",[883,4182,4184],{"className":4183},[886],[888,4185,4186],{"xmlns":890},[892,4187,4188,4201],{},[895,4189,4190,4192,4194],{},[898,4191,3783],{},[1846,4193,1848],{},[1974,4195,4196,4198],{},[898,4197,3783],{},[1846,4199,4200],{},"∗",[902,4202,4203],{"encoding":904},"P = P^*"," se ",[883,4206,4208],{"className":4207},[886],[888,4209,4210],{"xmlns":890},[892,4211,4212,4226],{},[895,4213,4214,4216,4218,4224],{},[898,4215,4098],{},[1846,4217,1855],{"stretchy":1854},[1974,4219,4220,4222],{},[898,4221,3783],{},[1846,4223,4200],{},[1846,4225,1861],{"stretchy":1854},[902,4227,4228],{"encoding":904},"E(P^*)"," nazývá ",[614,4231,4232,4233],{},"elasticita poptávky při ceně ",[883,4234,4236],{"className":4235},[886],[888,4237,4238],{"xmlns":890},[892,4239,4240,4248],{},[895,4241,4242],{},[1974,4243,4244,4246],{},[898,4245,3783],{},[1846,4247,4200],{},[902,4249,4250],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[1639,4253,4254],{},[724,4255,4256,4259,4260,4278,4279,4307,4308,4337,4338,1343,4356,1343,4374,4392,4393,4408,4409,1734],{},[883,4257,4258],{},"!warning"," Pozor na znaménko\nV (4.5) je ",[38,4261,4262,4263],{},"explicitní ",[883,4264,4266],{"className":4265},[886],[888,4267,4268],{"xmlns":890},[892,4269,4270,4276],{},[895,4271,4272,4274],{},[1846,4273,2075],{},[1979,4275,2128],{},[902,4277,3582],{"encoding":904}," právě proto, že ",[883,4280,4282],{"className":4281},[886],[888,4283,4284],{"xmlns":890},[892,4285,4286,4304],{},[895,4287,4288,4294,4296,4298,4300,4302],{},[1974,4289,4290,4292],{},[898,4291,2638],{},[1846,4293,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,4295,1855],{"stretchy":1854},[898,4297,3783],{},[1846,4299,1861],{"stretchy":1854},[1846,4301,3295],{},[1979,4303,2177],{},[902,4305,4306],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,4309,4311],{"className":4310},[886],[888,4312,4313],{"xmlns":890},[892,4314,4315,4334],{},[895,4316,4317,4319,4321,4327,4329,4332],{},[898,4318,4098],{},[1846,4320,1855],{"stretchy":1854},[1974,4322,4323,4325],{},[898,4324,3783],{},[1846,4326,4200],{},[1846,4328,1861],{"stretchy":1854},[1846,4330,4331],{},"≥",[1979,4333,2177],{},[902,4335,4336],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,4339,4341],{"className":4340},[886],[888,4342,4343],{"xmlns":890},[892,4344,4345,4353],{},[895,4346,4347,4349,4351],{},[898,4348,4098],{},[1846,4350,3256],{},[1979,4352,2128],{},[902,4354,4355],{"encoding":904},"E > 1",[883,4357,4359],{"className":4358},[886],[888,4360,4361],{"xmlns":890},[892,4362,4363,4371],{},[895,4364,4365,4367,4369],{},[898,4366,4098],{},[1846,4368,3295],{},[1979,4370,2128],{},[902,4372,4373],{"encoding":904},"E \u003C 1",[883,4375,4377],{"className":4376},[886],[888,4378,4379],{"xmlns":890},[892,4380,4381,4389],{},[895,4382,4383,4385,4387],{},[898,4384,4098],{},[1846,4386,1848],{},[1979,4388,2128],{},[902,4390,4391],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,4394,4396],{"className":4395},[886],[888,4397,4398],{"xmlns":890},[892,4399,4400,4406],{},[895,4401,4402,4404],{},[1846,4403,2075],{},[1979,4405,2128],{},[902,4407,3582],{"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 ",[38,4410,4411],{},"absolutní hodnotou",[1639,4413,4414,4434],{},[724,4415,4416,4419,4420,4433],{},[883,4417,4418],{},"!tip"," Postup: jak spočítat ",[883,4421,4423],{"className":4422},[886],[888,4424,4425],{"xmlns":890},[892,4426,4427,4431],{},[895,4428,4429],{},[898,4430,4098],{},[902,4432,4098],{"encoding":904}," v bodě",[152,4435,4436,4488,4528,4581,4646],{},[123,4437,4438,4439,4462,4463,4487],{},"Zapište ",[883,4440,4442],{"className":4441},[886],[888,4443,4444],{"xmlns":890},[892,4445,4446,4460],{},[895,4447,4448,4450,4452,4454,4456,4458],{},[898,4449,2638],{},[1846,4451,1848],{},[898,4453,4029],{},[1846,4455,1855],{"stretchy":1854},[898,4457,3783],{},[1846,4459,1861],{"stretchy":1854},[902,4461,4038],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,4464,4466],{"className":4465},[886],[888,4467,4468],{"xmlns":890},[892,4469,4470,4484],{},[895,4471,4472,4474,4476,4478,4480,4482],{},[898,4473,3783],{},[1846,4475,1848],{},[898,4477,4029],{},[1846,4479,1855],{"stretchy":1854},[898,4481,2638],{},[1846,4483,1861],{"stretchy":1854},[902,4485,4486],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,4489,4490,4491,1734],{},"Spočítejte derivaci ",[883,4492,4494],{"className":4493},[886],[888,4495,4496],{"xmlns":890},[892,4497,4498,4525],{},[895,4499,4500,4506,4508,4510,4512,4514,4516,4518,4521,4523],{},[1974,4501,4502,4504],{},[898,4503,2638],{},[1846,4505,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,4507,1855],{"stretchy":1854},[898,4509,3783],{},[1846,4511,1861],{"stretchy":1854},[1846,4513,1848],{},[898,4515,2044],{"mathvariant":2226},[898,4517,2638],{},[898,4519,4520],{"mathvariant":2226},"\u002F",[898,4522,2044],{"mathvariant":2226},[898,4524,3783],{},[902,4526,4527],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,4529,4530,4531,4548,4549,1734],{},"Dosaďte zadanou cenu ",[883,4532,4534],{"className":4533},[886],[888,4535,4536],{"xmlns":890},[892,4537,4538,4546],{},[895,4539,4540],{},[1974,4541,4542,4544],{},[898,4543,3783],{},[1846,4545,4200],{},[902,4547,4250],{"encoding":904}," a dopočítejte odpovídající ",[883,4550,4552],{"className":4551},[886],[888,4553,4554],{"xmlns":890},[892,4555,4556,4578],{},[895,4557,4558,4564,4566,4568,4570,4576],{},[1974,4559,4560,4562],{},[898,4561,2638],{},[1846,4563,4200],{},[1846,4565,1848],{},[898,4567,4029],{},[1846,4569,1855],{"stretchy":1854},[1974,4571,4572,4574],{},[898,4573,3783],{},[1846,4575,4200],{},[1846,4577,1861],{"stretchy":1854},[902,4579,4580],{"encoding":904},"Q^* = D(P^*)",[123,4582,4583,4584,1734],{},"Dosaďte do (4.5): ",[883,4585,4587],{"className":4586},[886],[888,4588,4589],{"xmlns":890},[892,4590,4591,4643],{},[895,4592,4593,4595,4597,4603,4605,4607,4609,4625,4627,4633,4635,4641],{},[898,4594,4098],{},[1846,4596,1855],{"stretchy":1854},[1974,4598,4599,4601],{},[898,4600,3783],{},[1846,4602,4200],{},[1846,4604,1861],{"stretchy":1854},[1846,4606,1848],{},[1846,4608,2075],{},[2175,4610,4611],{"scriptlevel":2177,"displaystyle":2135},[2179,4612,4613,4619],{},[1974,4614,4615,4617],{},[898,4616,3783],{},[1846,4618,4200],{},[1974,4620,4621,4623],{},[898,4622,2638],{},[1846,4624,4200],{},[2138,4626,2835],{},[1974,4628,4629,4631],{},[898,4630,2638],{},[1846,4632,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,4634,1855],{"stretchy":1854},[1974,4636,4637,4639],{},[898,4638,3783],{},[1846,4640,4200],{},[1846,4642,1861],{"stretchy":1854},[902,4644,4645],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,4647,4648,4649,4666,4667,4684,4685,4702],{},"Klasifikujte: ",[883,4650,4652],{"className":4651},[886],[888,4653,4654],{"xmlns":890},[892,4655,4656,4664],{},[895,4657,4658,4660,4662],{},[898,4659,4098],{},[1846,4661,3256],{},[1979,4663,2128],{},[902,4665,4355],{"encoding":904}," elastická, ",[883,4668,4670],{"className":4669},[886],[888,4671,4672],{"xmlns":890},[892,4673,4674,4682],{},[895,4675,4676,4678,4680],{},[898,4677,4098],{},[1846,4679,1848],{},[1979,4681,2128],{},[902,4683,4391],{"encoding":904}," jednotková, ",[883,4686,4688],{"className":4687},[886],[888,4689,4690],{"xmlns":890},[892,4691,4692,4700],{},[895,4693,4694,4696,4698],{},[898,4695,4098],{},[1846,4697,3295],{},[1979,4699,2128],{},[902,4701,4373],{"encoding":904}," neelastická.",[198,4704,4706],{"id":4705},"interpretace-46","Interpretace (4.6)",[1639,4708,4709],{},[724,4710,4711,4712,4735,4736,4749,4750,4767,4768],{},"Číslo ",[883,4713,4715],{"className":4714},[886],[888,4716,4717],{"xmlns":890},[892,4718,4719,4733],{},[895,4720,4721,4723,4725,4731],{},[898,4722,4098],{},[1846,4724,1855],{"stretchy":1854},[1974,4726,4727,4729],{},[898,4728,3783],{},[1846,4730,4200],{},[1846,4732,1861],{"stretchy":1854},[902,4734,4228],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,4737,4739],{"className":4738},[886],[888,4740,4741],{"xmlns":890},[892,4742,4743,4747],{},[895,4744,4745],{},[898,4746,2638],{},[902,4748,2638],{"encoding":904},", jestliže se cena ",[883,4751,4753],{"className":4752},[886],[888,4754,4755],{"xmlns":890},[892,4756,4757,4765],{},[895,4758,4759],{},[1974,4760,4761,4763],{},[898,4762,3783],{},[1846,4764,4200],{},[902,4766,4250],{"encoding":904}," změní o 1 %. ",[883,4769,4771],{"className":4770},[886],[888,4772,4773],{"xmlns":890},[892,4774,4775,4784],{},[895,4776,4777,4779,4782],{},[1846,4778,1855],{"stretchy":1854},[1979,4780,4781],{},"4.6",[1846,4783,1861],{"stretchy":1854},[902,4785,4786],{"encoding":904},"(4.6)",[724,4788,4789,4792],{},[38,4790,4791],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,4794,4796],{"id":4795},"příklad-41","Příklad 4.1",[724,4798,4799,4800,4834,4835,1343,4861,2554],{},"Poptávka ",[883,4801,4803],{"className":4802},[886],[888,4804,4805],{"xmlns":890},[892,4806,4807,4831],{},[895,4808,4809,4811,4813,4815,4817,4819,4821,4823,4825,4827,4829],{},[898,4810,3783],{},[1846,4812,1848],{},[898,4814,4029],{},[1846,4816,1855],{"stretchy":1854},[898,4818,2638],{},[1846,4820,1861],{"stretchy":1854},[1846,4822,1848],{},[1979,4824,2968],{},[1846,4826,2075],{},[1979,4828,1981],{},[898,4830,2638],{},[902,4832,4833],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,4836,4838],{"className":4837},[886],[888,4839,4840],{"xmlns":890},[892,4841,4842,4858],{},[895,4843,4844,4846,4848,4851,4853,4856],{},[898,4845,2638],{},[1846,4847,1848],{},[1979,4849,4850],{},"25",[1846,4852,2075],{},[1979,4854,4855],{},"0,5",[898,4857,3783],{},[902,4859,4860],{"encoding":904},"Q = 25 - 0{,}5P",[883,4862,4864],{"className":4863},[886],[888,4865,4866],{"xmlns":890},[892,4867,4868,4892],{},[895,4869,4870,4886,4888,4890],{},[2175,4871,4872],{"scriptlevel":2177,"displaystyle":2135},[2179,4873,4874,4880],{},[895,4875,4876,4878],{},[898,4877,2044],{"mathvariant":2226},[898,4879,2638],{},[895,4881,4882,4884],{},[898,4883,2044],{"mathvariant":2226},[898,4885,3783],{},[1846,4887,1848],{},[1846,4889,2075],{},[1979,4891,4855],{},[902,4893,4894],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,4896,4897],{},[883,4898,4900],{"className":4899},[886],[888,4901,4902],{"xmlns":890},[892,4903,4904,4958],{},[895,4905,4906,4908,4910,4912,4926,4928,4930,4932,4934,4936,4938,4956],{},[898,4907,4098],{},[1846,4909,1848],{},[1846,4911,2075],{},[2179,4913,4914,4916],{},[898,4915,3783],{},[895,4917,4918,4920,4922,4924],{},[1979,4919,4850],{},[1846,4921,2075],{},[1979,4923,4855],{},[898,4925,3783],{},[1846,4927,3025],{},[1846,4929,1855],{"stretchy":1854},[1846,4931,2075],{},[1979,4933,4855],{},[1846,4935,1861],{"stretchy":1854},[1846,4937,1848],{},[2179,4939,4940,4946],{},[895,4941,4942,4944],{},[1979,4943,4855],{},[898,4945,3783],{},[895,4947,4948,4950,4952,4954],{},[1979,4949,4850],{},[1846,4951,2075],{},[1979,4953,4855],{},[898,4955,3783],{},[898,4957,1734],{"mathvariant":2226},[902,4959,4960],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,4962,4963,4964,1343,4988,1343,5018,1343,5042,5067,5068,5091,5092,2535,5110,3764],{},"Potom ",[883,4965,4967],{"className":4966},[886],[888,4968,4969],{"xmlns":890},[892,4970,4971,4985],{},[895,4972,4973,4975,4977,4979,4981,4983],{},[898,4974,4098],{},[1846,4976,1855],{"stretchy":1854},[1979,4978,2177],{},[1846,4980,1861],{"stretchy":1854},[1846,4982,1848],{},[1979,4984,2177],{},[902,4986,4987],{"encoding":904},"E(0)=0",[883,4989,4991],{"className":4990},[886],[888,4992,4993],{"xmlns":890},[892,4994,4995,5015],{},[895,4996,4997,4999,5001,5003,5005,5007],{},[898,4998,4098],{},[1846,5000,1855],{"stretchy":1854},[1979,5002,2712],{},[1846,5004,1861],{"stretchy":1854},[1846,5006,1848],{},[2175,5008,5009],{"scriptlevel":2177,"displaystyle":1854},[2179,5010,5011,5013],{},[1979,5012,2128],{},[1979,5014,2201],{},[902,5016,5017],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,5019,5021],{"className":5020},[886],[888,5022,5023],{"xmlns":890},[892,5024,5025,5039],{},[895,5026,5027,5029,5031,5033,5035,5037],{},[898,5028,4098],{},[1846,5030,1855],{"stretchy":1854},[1979,5032,4850],{},[1846,5034,1861],{"stretchy":1854},[1846,5036,1848],{},[1979,5038,2128],{},[902,5040,5041],{"encoding":904},"E(25)=1",[883,5043,5045],{"className":5044},[886],[888,5046,5047],{"xmlns":890},[892,5048,5049,5064],{},[895,5050,5051,5053,5055,5058,5060,5062],{},[898,5052,4098],{},[1846,5054,1855],{"stretchy":1854},[1979,5056,5057],{},"40",[1846,5059,1861],{"stretchy":1854},[1846,5061,1848],{},[1979,5063,2201],{},[902,5065,5066],{"encoding":904},"E(40)=4",". Např. ",[883,5069,5071],{"className":5070},[886],[888,5072,5073],{"xmlns":890},[892,5074,5075,5089],{},[895,5076,5077,5079,5081,5083,5085,5087],{},[898,5078,4098],{},[1846,5080,1855],{"stretchy":1854},[1979,5082,5057],{},[1846,5084,1861],{"stretchy":1854},[1846,5086,1848],{},[1979,5088,2201],{},[902,5090,5066],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,5093,5095],{"className":5094},[886],[888,5096,5097],{"xmlns":890},[892,5098,5099,5107],{},[895,5100,5101,5103,5105],{},[898,5102,2638],{},[1846,5104,1848],{},[1979,5106,2078],{},[902,5108,5109],{"encoding":904},"Q=5",[883,5111,5113],{"className":5112},[886],[888,5114,5115],{"xmlns":890},[892,5116,5117,5126],{},[895,5118,5119,5121,5123],{},[898,5120,2638],{},[1846,5122,1848],{},[1979,5124,5125],{},"4,8",[902,5127,5128],{"encoding":904},"Q=4{,}8",[198,5130,5132],{"id":5131},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,5134,5135,5191],{},[123,5136,5137,5140,5141,5158,5159,1734],{},[38,5138,5139],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,5142,5144],{"className":5143},[886],[888,5145,5146],{"xmlns":890},[892,5147,5148,5156],{},[895,5149,5150],{},[1974,5151,5152,5154],{},[898,5153,4098],{},[898,5155,4101],{},[902,5157,4104],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,5160,5162],{"className":5161},[886],[888,5163,5164],{"xmlns":890},[892,5165,5166,5188],{},[895,5167,5168,5171,5173,5175,5177,5179,5181,5183,5185],{},[1846,5169,5170],{"stretchy":1854},"⟨",[898,5172,3783],{},[1846,5174,2136],{"separator":2135},[2138,5176,2835],{},[898,5178,3783],{},[1846,5180,1945],{},[898,5182,2738],{"mathvariant":2226},[898,5184,3783],{},[1846,5186,5187],{"stretchy":1854},"⟩",[902,5189,5190],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,5192,5193,5196,5197,5210],{},[38,5194,5195],{},"Bodová"," (okamžitá) elasticita: ",[883,5198,5200],{"className":5199},[886],[888,5201,5202],{"xmlns":890},[892,5203,5204,5208],{},[895,5205,5206],{},[898,5207,4098],{},[902,5209,4098],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,5212,5214,5215,5228,5229],{"id":5213},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,5216,5218],{"className":5217},[886],[888,5219,5220],{"xmlns":890},[892,5221,5222,5226],{},[895,5223,5224],{},[898,5225,3783],{},[902,5227,3783],{"encoding":904}," jako funkce ",[883,5230,5232],{"className":5231},[886],[888,5233,5234],{"xmlns":890},[892,5235,5236,5240],{},[895,5237,5238],{},[898,5239,2638],{},[902,5241,2638],{"encoding":904},[724,5243,5244,5245,5268],{},"Pokud je poptávka zadaná ve tvaru ",[883,5246,5248],{"className":5247},[886],[888,5249,5250],{"xmlns":890},[892,5251,5252,5266],{},[895,5253,5254,5256,5258,5260,5262,5264],{},[898,5255,3783],{},[1846,5257,1848],{},[898,5259,4029],{},[1846,5261,1855],{"stretchy":1854},[898,5263,2638],{},[1846,5265,1861],{"stretchy":1854},[902,5267,4486],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,5270,5271],{},[883,5272,5274],{"className":5273,"title":4046,"style":4047},[4045],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,5276,5277,2053,5280,5306],{},[38,5278,5279],{},"Příklad 4.3.",[883,5281,5283],{"className":5282},[886],[888,5284,5285],{"xmlns":890},[892,5286,5287,5303],{},[895,5288,5289,5291,5293,5295,5297],{},[898,5290,3783],{},[1846,5292,1848],{},[1979,5294,2938],{},[1846,5296,2075],{},[1974,5298,5299,5301],{},[898,5300,2638],{},[1979,5302,1981],{},[902,5304,5305],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,5308,5309],{},[883,5310,5312],{"className":5311},[886],[888,5313,5314],{"xmlns":890},[892,5315,5316,5382],{},[895,5317,5318,5320,5322,5324,5340,5342,5354,5356,5380],{},[898,5319,4098],{},[1846,5321,1848],{},[1846,5323,2075],{},[2179,5325,5326,5338],{},[895,5327,5328,5330,5332],{},[1979,5329,2938],{},[1846,5331,2075],{},[1974,5333,5334,5336],{},[898,5335,2638],{},[1979,5337,1981],{},[898,5339,2638],{},[1846,5341,3025],{},[2179,5343,5344,5346],{},[1979,5345,2128],{},[895,5347,5348,5350,5352],{},[1846,5349,2075],{},[1979,5351,1981],{},[898,5353,2638],{},[1846,5355,1848],{},[2179,5357,5358,5370],{},[895,5359,5360,5362,5364],{},[1979,5361,2938],{},[1846,5363,2075],{},[1974,5365,5366,5368],{},[898,5367,2638],{},[1979,5369,1981],{},[895,5371,5372,5374],{},[1979,5373,1981],{},[1974,5375,5376,5378],{},[898,5377,2638],{},[1979,5379,1981],{},[898,5381,1734],{"mathvariant":2226},[902,5383,5384],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,5386,5387,5388,5415,5416,5435,5436,1734],{},"Z rovnice ",[883,5389,5391],{"className":5390},[886],[888,5392,5393],{"xmlns":890},[892,5394,5395,5412],{},[895,5396,5397,5399,5401,5407,5409],{},[1979,5398,2938],{},[1846,5400,2075],{},[1974,5402,5403,5405],{},[898,5404,2638],{},[1979,5406,1981],{},[1846,5408,1848],{},[1979,5410,5411],{},"36",[902,5413,5414],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,5417,5419],{"className":5418},[886],[888,5420,5421],{"xmlns":890},[892,5422,5423,5432],{},[895,5424,5425,5427,5429],{},[898,5426,2638],{},[1846,5428,1848],{},[1979,5430,5431],{},"8",[902,5433,5434],{"encoding":904},"Q = 8",", tedy ",[883,5437,5439],{"className":5438},[886],[888,5440,5441],{"xmlns":890},[892,5442,5443,5469],{},[895,5444,5445,5447,5449,5451,5453,5455,5464,5466],{},[898,5446,4098],{},[1846,5448,1855],{"stretchy":1854},[1979,5450,5431],{},[1846,5452,1861],{"stretchy":1854},[1846,5454,1848],{},[2175,5456,5457],{"scriptlevel":2177,"displaystyle":1854},[2179,5458,5459,5461],{},[1979,5460,5411],{},[1979,5462,5463],{},"128",[1846,5465,1848],{},[1979,5467,5468],{},"0,281",[902,5470,5471],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,5473,5475],{"id":5474},"přibližné-změny","Přibližné změny",[724,5477,5478,5479,5515,5516,5538],{},"Diferenciál ",[883,5480,5482],{"className":5481},[886],[888,5483,5484],{"xmlns":890},[892,5485,5486,5512],{},[895,5487,5488,5490,5492,5494,5500,5502,5504,5506,5508,5510],{},[898,5489,2044],{"mathvariant":2226},[898,5491,2638],{},[1846,5493,1848],{},[1974,5495,5496,5498],{},[898,5497,2638],{},[1846,5499,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,5501,1855],{"stretchy":1854},[898,5503,3783],{},[1846,5505,1861],{"stretchy":1854},[2138,5507,2835],{},[898,5509,2044],{"mathvariant":2226},[898,5511,3783],{},[902,5513,5514],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,5517,5519],{"className":5518},[886],[888,5520,5521],{"xmlns":890},[892,5522,5523,5535],{},[895,5524,5525,5527,5529,5531,5533],{},[898,5526,2044],{"mathvariant":2226},[898,5528,3783],{},[1846,5530,1848],{},[898,5532,2738],{"mathvariant":2226},[898,5534,3783],{},[902,5536,5537],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,5540,5541],{},[883,5542,5544],{"className":5543,"title":4046,"style":4047},[4045],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,5546,5547],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,5549,5550],{},[883,5551,5553],{"className":5552,"title":4046,"style":4047},[4045],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,5555,5556,2053,5559,5594,5595,5614,5615,5649,5650,5667],{},[38,5557,5558],{},"Příklad 4.5.",[883,5560,5562],{"className":5561},[886],[888,5563,5564],{"xmlns":890},[892,5565,5566,5591],{},[895,5567,5568,5570,5572,5574,5580,5582,5584,5586,5588],{},[898,5569,3783],{},[1846,5571,1848],{},[1846,5573,2075],{},[1974,5575,5576,5578],{},[898,5577,2638],{},[1979,5579,1981],{},[1846,5581,2075],{},[1979,5583,2201],{},[898,5585,2638],{},[1846,5587,1945],{},[1979,5589,5590],{},"96",[902,5592,5593],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,5596,5598],{"className":5597},[886],[888,5599,5600],{"xmlns":890},[892,5601,5602,5611],{},[895,5603,5604,5606,5608],{},[898,5605,3783],{},[1846,5607,1848],{},[1979,5609,5610],{},"51",[902,5612,5613],{"encoding":904},"P=51",". Z rovnice ",[883,5616,5618],{"className":5617},[886],[888,5619,5620],{"xmlns":890},[892,5621,5622,5646],{},[895,5623,5624,5626,5628,5630,5636,5638,5640,5642,5644],{},[1979,5625,5610],{},[1846,5627,1848],{},[1846,5629,2075],{},[1974,5631,5632,5634],{},[898,5633,2638],{},[1979,5635,1981],{},[1846,5637,2075],{},[1979,5639,2201],{},[898,5641,2638],{},[1846,5643,1945],{},[1979,5645,5590],{},[902,5647,5648],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,5651,5653],{"className":5652},[886],[888,5654,5655],{"xmlns":890},[892,5656,5657,5665],{},[895,5658,5659,5661,5663],{},[898,5660,2638],{},[1846,5662,1848],{},[1979,5664,2078],{},[902,5666,5109],{"encoding":904},". Elasticita:",[724,5669,5670],{},[883,5671,5673],{"className":5672},[886],[888,5674,5675],{"xmlns":890},[892,5676,5677,5750],{},[895,5678,5679,5681,5683,5721,5723,5727,5729,5731,5733,5735,5737,5744,5747],{},[898,5680,4098],{},[1846,5682,1848],{},[2179,5684,5685,5705],{},[895,5686,5687,5689,5695,5697,5699,5701,5703],{},[1846,5688,2075],{},[1974,5690,5691,5693],{},[898,5692,2638],{},[1979,5694,1981],{},[1846,5696,2075],{},[1979,5698,2201],{},[898,5700,2638],{},[1846,5702,1945],{},[1979,5704,5590],{},[895,5706,5707,5709,5711,5713,5715,5717,5719],{},[898,5708,2638],{},[1846,5710,1855],{"stretchy":1854},[1979,5712,1981],{},[898,5714,2638],{},[1846,5716,1945],{},[1979,5718,2201],{},[1846,5720,1861],{"stretchy":1854},[1846,5722,2136],{"separator":2135},[5724,5725],"mspace",{"width":5726},"2em",[898,5728,4098],{},[1846,5730,1855],{"stretchy":1854},[1979,5732,2078],{},[1846,5734,1861],{"stretchy":1854},[1846,5736,1848],{},[2179,5738,5739,5741],{},[1979,5740,5610],{},[1979,5742,5743],{},"70",[1846,5745,5746],{},"≐",[1979,5748,5749],{},"0,728.",[902,5751,5752],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,5754,5755,5756,1734],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,5757,5759],{"className":5758},[886],[888,5760,5761],{"xmlns":890},[892,5762,5763,5794],{},[895,5764,5765,5767,5769,5772,5774,5776,5779,5781,5783,5785,5787,5790,5792],{},[898,5766,2738],{"mathvariant":2226},[898,5768,2638],{},[898,5770,5771],{"mathvariant":2226},"%",[1846,5773,1650],{},[1846,5775,2075],{},[1979,5777,5778],{},"0,728",[1846,5780,3025],{},[1979,5782,1981],{},[1846,5784,1848],{},[1846,5786,2075],{},[1979,5788,5789],{},"1,456",[2138,5791,2835],{},[898,5793,5771],{"mathvariant":2226},[902,5795,5796],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,5798,5800],{"id":5799},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,5802,5803,5804,5827,5828,2554],{},"V závislosti na hodnotě ",[883,5805,5807],{"className":5806},[886],[888,5808,5809],{"xmlns":890},[892,5810,5811,5825],{},[895,5812,5813,5815,5817,5823],{},[898,5814,4098],{},[1846,5816,1855],{"stretchy":1854},[1974,5818,5819,5821],{},[898,5820,3783],{},[1846,5822,4200],{},[1846,5824,1861],{"stretchy":1854},[902,5826,4228],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,5829,5831],{"className":5830},[886],[888,5832,5833],{"xmlns":890},[892,5834,5835,5844],{},[895,5836,5837,5839,5842],{},[1846,5838,1855],{"stretchy":1854},[1979,5840,5841],{},"4.7",[1846,5843,1861],{"stretchy":1854},[902,5845,5846],{"encoding":904},"(4.7)",[724,5848,5849],{},[2409,5850],{"alt":5851,"className":5852,"src":5853},"imek-typy-elasticity-5panelu",[210,2413],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,5855,5856,5895],{},[19,5857,5858],{},[22,5859,5860,5886,5889,5892],{},[25,5861,5862,5863],{},"Hodnota ",[883,5864,5866],{"className":5865},[886],[888,5867,5868],{"xmlns":890},[892,5869,5870,5884],{},[895,5871,5872,5874,5876,5882],{},[898,5873,4098],{},[1846,5875,1855],{"stretchy":1854},[1974,5877,5878,5880],{},[898,5879,3783],{},[1846,5881,4200],{},[1846,5883,1861],{"stretchy":1854},[902,5885,4228],{"encoding":904},[25,5887,5888],{},"Typ poptávky",[25,5890,5891],{},"Termín",[25,5893,5894],{},"Význam",[30,5896,5897,5930,5992,6067,6124],{},[22,5898,5899,5919,5924,5927],{},[35,5900,5901],{},[883,5902,5904],{"className":5903},[886],[888,5905,5906],{"xmlns":890},[892,5907,5908,5916],{},[895,5909,5910,5912,5914],{},[898,5911,4098],{},[1846,5913,1848],{},[1979,5915,2177],{},[902,5917,5918],{"encoding":904},"E = 0",[35,5920,5921],{},[38,5922,5923],{},"dokonale neelastická",[35,5925,5926],{},"perfectly inelastic",[35,5928,5929],{},"množství se nemění bez ohledu na cenu",[22,5931,5932,5956,5960,5963],{},[35,5933,5934],{},[883,5935,5937],{"className":5936},[886],[888,5938,5939],{"xmlns":890},[892,5940,5941,5953],{},[895,5942,5943,5945,5947,5949,5951],{},[1979,5944,2177],{},[1846,5946,3295],{},[898,5948,4098],{},[1846,5950,3295],{},[1979,5952,2128],{},[902,5954,5955],{"encoding":904},"0 \u003C E \u003C 1",[35,5957,5958],{},[38,5959,3923],{},[35,5961,5962],{},"inelastic",[35,5964,5965,5978,5979],{},[883,5966,5968],{"className":5967},[886],[888,5969,5970],{"xmlns":890},[892,5971,5972,5976],{},[895,5973,5974],{},[898,5975,2638],{},[902,5977,2638],{"encoding":904}," se mění pomaleji než ",[883,5980,5982],{"className":5981},[886],[888,5983,5984],{"xmlns":890},[892,5985,5986,5990],{},[895,5987,5988],{},[898,5989,3783],{},[902,5991,3783],{"encoding":904},[22,5993,5994,6013,6018,6021],{},[35,5995,5996],{},[883,5997,5999],{"className":5998},[886],[888,6000,6001],{"xmlns":890},[892,6002,6003,6011],{},[895,6004,6005,6007,6009],{},[898,6006,4098],{},[1846,6008,1848],{},[1979,6010,2128],{},[902,6012,4391],{"encoding":904},[35,6014,6015],{},[38,6016,6017],{},"jednotkově elastická",[35,6019,6020],{},"unit elastic",[35,6022,6023,6036,6037,6050,6051,6066],{},[883,6024,6026],{"className":6025},[886],[888,6027,6028],{"xmlns":890},[892,6029,6030,6034],{},[895,6031,6032],{},[898,6033,2638],{},[902,6035,2638],{"encoding":904}," i ",[883,6038,6040],{"className":6039},[886],[888,6041,6042],{"xmlns":890},[892,6043,6044,6048],{},[895,6045,6046],{},[898,6047,3783],{},[902,6049,3783],{"encoding":904}," se mění stejně rychle; ",[883,6052,6054],{"className":6053},[886],[888,6055,6056],{"xmlns":890},[892,6057,6058,6064],{},[895,6059,6060,6062],{},[898,6061,2623],{},[898,6063,3840],{},[902,6065,3940],{"encoding":904}," má maximum",[22,6068,6069,6088,6092,6095],{},[35,6070,6071],{},[883,6072,6074],{"className":6073},[886],[888,6075,6076],{"xmlns":890},[892,6077,6078,6086],{},[895,6079,6080,6082,6084],{},[898,6081,4098],{},[1846,6083,3256],{},[1979,6085,2128],{},[902,6087,4355],{"encoding":904},[35,6089,6090],{},[38,6091,3919],{},[35,6093,6094],{},"elastic",[35,6096,6097,6110,6111],{},[883,6098,6100],{"className":6099},[886],[888,6101,6102],{"xmlns":890},[892,6103,6104,6108],{},[895,6105,6106],{},[898,6107,2638],{},[902,6109,2638],{"encoding":904}," se mění rychleji než ",[883,6112,6114],{"className":6113},[886],[888,6115,6116],{"xmlns":890},[892,6117,6118,6122],{},[895,6119,6120],{},[898,6121,3783],{},[902,6123,3783],{"encoding":904},[22,6125,6126,6147,6152,6155],{},[35,6127,6128],{},[883,6129,6131],{"className":6130},[886],[888,6132,6133],{"xmlns":890},[892,6134,6135,6144],{},[895,6136,6137,6139,6141],{},[898,6138,4098],{},[1846,6140,2971],{},[898,6142,6143],{"mathvariant":2226},"∞",[902,6145,6146],{"encoding":904},"E \\to \\infty",[35,6148,6149],{},[38,6150,6151],{},"dokonale elastická",[35,6153,6154],{},"perfectly elastic",[35,6156,6157,6158],{},"sebemenší změna ceny úplně mění ",[883,6159,6161],{"className":6160},[886],[888,6162,6163],{"xmlns":890},[892,6164,6165,6169],{},[895,6166,6167],{},[898,6168,2638],{},[902,6170,2638],{"encoding":904},[724,6172,6173],{},[38,6174,6175],{},"Pravidlo růstu elasticity s cenou:",[1639,6177,6178],{},[724,6179,6180,6181],{},"S rostoucí cenou elasticita poptávky roste. ",[883,6182,6184],{"className":6183},[886],[888,6185,6186],{"xmlns":890},[892,6187,6188,6197],{},[895,6189,6190,6192,6195],{},[1846,6191,1855],{"stretchy":1854},[1979,6193,6194],{},"4.8",[1846,6196,1861],{"stretchy":1854},[902,6198,6199],{"encoding":904},"(4.8)",[724,6201,6202,6203,6206,6207,6210,6211,6228],{},"Z toho plyne, že při ",[614,6204,6205],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,6208,6209],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,6212,6214],{"className":6213},[886],[888,6215,6216],{"xmlns":890},[892,6217,6218,6226],{},[895,6219,6220],{},[1974,6221,6222,6224],{},[898,6223,3783],{},[1846,6225,4200],{},[902,6227,4250],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[1639,6230,6231,6236],{},[724,6232,6233,6235],{},[883,6234,4418],{}," Postup: jak klasifikovat poptávku",[152,6237,6238,6265,6268],{},[123,6239,6240,6241,6264],{},"Spočítejte ",[883,6242,6244],{"className":6243},[886],[888,6245,6246],{"xmlns":890},[892,6247,6248,6262],{},[895,6249,6250,6252,6254,6260],{},[898,6251,4098],{},[1846,6253,1855],{"stretchy":1854},[1974,6255,6256,6258],{},[898,6257,3783],{},[1846,6259,4200],{},[1846,6261,1861],{"stretchy":1854},[902,6263,4228],{"encoding":904}," dle (4.5).",[123,6266,6267],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,6269,6270,6271,6295],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,6272,6274],{"className":6273},[886],[888,6275,6276],{"xmlns":890},[892,6277,6278,6292],{},[895,6279,6280,6282,6284,6286,6288,6290],{},[898,6281,4098],{},[1846,6283,1855],{"stretchy":1854},[898,6285,3783],{},[1846,6287,1861],{"stretchy":1854},[1846,6289,1848],{},[1979,6291,2128],{},[902,6293,6294],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,6297,6298,6301,6302,6319,6320,6338,6339,6366,6367,1734],{},[38,6299,6300],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,6303,6305],{"className":6304},[886],[888,6306,6307],{"xmlns":890},[892,6308,6309,6317],{},[895,6310,6311,6313,6315],{},[898,6312,4098],{},[1846,6314,1848],{},[1979,6316,2128],{},[902,6318,4391],{"encoding":904}," pro ",[883,6321,6323],{"className":6322},[886],[888,6324,6325],{"xmlns":890},[892,6326,6327,6335],{},[895,6328,6329,6331,6333],{},[898,6330,3783],{},[1846,6332,1848],{},[1979,6334,4850],{},[902,6336,6337],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,6340,6342],{"className":6341},[886],[888,6343,6344],{"xmlns":890},[892,6345,6346,6363],{},[895,6347,6348,6350,6353,6355,6357,6359,6361],{},[898,6349,3783],{},[1846,6351,6352],{},"∈",[1846,6354,5170],{"stretchy":1854},[1979,6356,2177],{},[1846,6358,2136],{"separator":2135},[1979,6360,4850],{},[1846,6362,1861],{"stretchy":1854},[902,6364,6365],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,6368,6370],{"className":6369},[886],[888,6371,6372],{"xmlns":890},[892,6373,6374,6390],{},[895,6375,6376,6378,6380,6382,6384,6386,6388],{},[898,6377,3783],{},[1846,6379,6352],{},[1846,6381,1855],{"stretchy":1854},[1979,6383,4850],{},[1846,6385,2136],{"separator":2135},[1979,6387,2968],{},[1846,6389,5187],{"stretchy":1854},[902,6391,6392],{"encoding":904},"P \\in (25, 50\\rangle",[115,6394,6396],{"id":6395},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,6398,6399],{},[2409,6400],{"alt":6401,"className":6402,"src":6403},"imek-elasticita-tr",[210,2413],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,6405,6406],{},[2409,6407],{"alt":6408,"className":6409,"src":6410},"imek-elasticita-podel-linearni-poptavky",[210,2413],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,6412,6413,6414,6464,6465,6481],{},"Pro celkový příjem platí ",[883,6415,6417],{"className":6416},[886],[888,6418,6419],{"xmlns":890},[892,6420,6421,6461],{},[895,6422,6423,6425,6427,6429,6431,6433,6435,6437,6439,6441,6443,6445,6447,6449,6451,6453,6455,6457,6459],{},[898,6424,2623],{},[898,6426,3840],{},[1846,6428,1848],{},[898,6430,2623],{},[898,6432,3840],{},[1846,6434,1855],{"stretchy":1854},[898,6436,2638],{},[1846,6438,1861],{"stretchy":1854},[1846,6440,1848],{},[898,6442,3783],{},[1846,6444,3025],{},[898,6446,2638],{},[1846,6448,1848],{},[898,6450,2638],{},[1846,6452,3025],{},[898,6454,4029],{},[1846,6456,1855],{"stretchy":1854},[898,6458,2638],{},[1846,6460,1861],{"stretchy":1854},[902,6462,6463],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,6466,6468],{"className":6467},[886],[888,6469,6470],{"xmlns":890},[892,6471,6472,6478],{},[895,6473,6474,6476],{},[898,6475,2667],{},[898,6477,3840],{},[902,6479,6480],{"encoding":904},"MR"," odvodíme:",[724,6483,6484],{},[883,6485,6487],{"className":6486},[886],[888,6488,6489],{"xmlns":890},[892,6490,6491,6599],{},[895,6492,6493,6495,6497,6499,6501,6507,6509,6511,6513,6515,6517,6519,6521,6523,6525,6527,6529,6535,6537,6539,6541,6543,6545,6547,6549,6563,6565,6567],{},[898,6494,2667],{},[898,6496,3840],{},[1846,6498,1848],{},[898,6500,2623],{},[1974,6502,6503,6505],{},[898,6504,3840],{},[1846,6506,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,6508,1855],{"stretchy":1854},[898,6510,2638],{},[1846,6512,1861],{"stretchy":1854},[1846,6514,1848],{},[898,6516,4029],{},[1846,6518,1855],{"stretchy":1854},[898,6520,2638],{},[1846,6522,1861],{"stretchy":1854},[1846,6524,1945],{},[898,6526,2638],{},[2138,6528,2835],{},[1974,6530,6531,6533],{},[898,6532,4029],{},[1846,6534,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,6536,1855],{"stretchy":1854},[898,6538,2638],{},[1846,6540,1861],{"stretchy":1854},[1846,6542,1848],{},[898,6544,3783],{},[1846,6546,1945],{},[898,6548,2638],{},[2179,6550,6551,6557],{},[895,6552,6553,6555],{},[898,6554,2044],{"mathvariant":2226},[898,6556,3783],{},[895,6558,6559,6561],{},[898,6560,2044],{"mathvariant":2226},[898,6562,2638],{},[1846,6564,1848],{},[898,6566,3783],{},[895,6568,6569,6571,6573,6575,6581,6583,6597],{},[1846,6570,1855],{"fence":2135},[1979,6572,2128],{},[1846,6574,1945],{},[2179,6576,6577,6579],{},[898,6578,2638],{},[898,6580,3783],{},[1846,6582,3025],{},[2179,6584,6585,6591],{},[895,6586,6587,6589],{},[898,6588,2044],{"mathvariant":2226},[898,6590,3783],{},[895,6592,6593,6595],{},[898,6594,2044],{"mathvariant":2226},[898,6596,2638],{},[1846,6598,1861],{"fence":2135},[902,6600,6601],{"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)",[724,6603,6604],{},[883,6605,6607],{"className":6606},[886],[888,6608,6609],{"xmlns":890},[892,6610,6611,6683],{},[895,6612,6613,6615,6617,6659,6661,6663],{},[1846,6614,1848],{},[898,6616,3783],{},[895,6618,6619,6621,6623,6625,6657],{},[1846,6620,1855],{"fence":2135},[1979,6622,2128],{},[1846,6624,1945],{},[2179,6626,6627,6629],{},[1979,6628,2128],{},[895,6630,6631,6639,6641],{},[2175,6632,6633],{"scriptlevel":2177,"displaystyle":1854},[2179,6634,6635,6637],{},[898,6636,3783],{},[898,6638,2638],{},[1846,6640,3025],{},[2175,6642,6643],{"scriptlevel":2177,"displaystyle":1854},[2179,6644,6645,6651],{},[895,6646,6647,6649],{},[898,6648,2044],{"mathvariant":2226},[898,6650,2638],{},[895,6652,6653,6655],{},[898,6654,2044],{"mathvariant":2226},[898,6656,3783],{},[1846,6658,1861],{"fence":2135},[1846,6660,1848],{},[898,6662,3783],{},[895,6664,6665,6667,6669,6671,6681],{},[1846,6666,1855],{"fence":2135},[1979,6668,2128],{},[1846,6670,1945],{},[2179,6672,6673,6675],{},[1979,6674,2128],{},[895,6676,6677,6679],{},[1846,6678,2075],{},[898,6680,4098],{},[1846,6682,1861],{"fence":2135},[902,6684,6685],{"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)",[724,6687,6688],{},"a tedy",[724,6690,6691],{},[883,6692,6694],{"className":6693,"title":4046,"style":4047},[4045],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[1639,6696,6697,6766,7016],{},[724,6698,6699,6701,6702,6736,6737,6752,6753,2554],{},[883,6700,4001],{}," Intuice: vztah ",[883,6703,6705],{"className":6704},[886],[888,6706,6707],{"xmlns":890},[892,6708,6709,6733],{},[895,6710,6711,6713,6715,6717,6719,6721,6723,6725,6727,6729,6731],{},[898,6712,2667],{},[898,6714,3840],{},[1846,6716,1848],{},[898,6718,3783],{},[1846,6720,1855],{"stretchy":1854},[1979,6722,2128],{},[1846,6724,2075],{},[1979,6726,2128],{},[898,6728,4520],{"mathvariant":2226},[898,6730,4098],{},[1846,6732,1861],{"stretchy":1854},[902,6734,6735],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,6738,6740],{"className":6739},[886],[888,6741,6742],{"xmlns":890},[892,6743,6744,6750],{},[895,6745,6746,6748],{},[898,6747,2667],{},[898,6749,3840],{},[902,6751,6480],{"encoding":904}," jednoznačně určuje hodnota ",[883,6754,6756],{"className":6755},[886],[888,6757,6758],{"xmlns":890},[892,6759,6760,6764],{},[895,6761,6762],{},[898,6763,4098],{},[902,6765,4098],{"encoding":904},[120,6767,6768,6878,6947],{},[123,6769,6770,6787,6788,2053,6802,2053,6828,2053,6841,6861,6862,6877],{},[883,6771,6773],{"className":6772},[886],[888,6774,6775],{"xmlns":890},[892,6776,6777,6785],{},[895,6778,6779,6781,6783],{},[898,6780,4098],{},[1846,6782,3256],{},[1979,6784,2128],{},[902,6786,4355],{"encoding":904}," (elastická) ",[883,6789,6791],{"className":6790},[886],[888,6792,6793],{"xmlns":890},[892,6794,6795,6799],{},[895,6796,6797],{},[1846,6798,3833],{},[902,6800,6801],{"encoding":904},"\\Rightarrow",[883,6803,6805],{"className":6804},[886],[888,6806,6807],{"xmlns":890},[892,6808,6809,6825],{},[895,6810,6811,6813,6815,6817,6819,6821,6823],{},[1979,6812,2128],{},[1846,6814,2075],{},[1979,6816,2128],{},[898,6818,4520],{"mathvariant":2226},[898,6820,4098],{},[1846,6822,3256],{},[1979,6824,2177],{},[902,6826,6827],{"encoding":904},"1 - 1\u002FE > 0",[883,6829,6831],{"className":6830},[886],[888,6832,6833],{"xmlns":890},[892,6834,6835,6839],{},[895,6836,6837],{},[1846,6838,3833],{},[902,6840,6801],{"encoding":904},[883,6842,6844],{"className":6843},[886],[888,6845,6846],{"xmlns":890},[892,6847,6848,6858],{},[895,6849,6850,6852,6854,6856],{},[898,6851,2667],{},[898,6853,3840],{},[1846,6855,3256],{},[1979,6857,2177],{},[902,6859,6860],{"encoding":904},"MR > 0"," — ",[883,6863,6865],{"className":6864},[886],[888,6866,6867],{"xmlns":890},[892,6868,6869,6875],{},[895,6870,6871,6873],{},[898,6872,2623],{},[898,6874,3840],{},[902,6876,3940],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,6879,6880,6897,6898,2053,6911,6861,6931,6946],{},[883,6881,6883],{"className":6882},[886],[888,6884,6885],{"xmlns":890},[892,6886,6887,6895],{},[895,6888,6889,6891,6893],{},[898,6890,4098],{},[1846,6892,1848],{},[1979,6894,2128],{},[902,6896,4391],{"encoding":904}," (jednotková) ",[883,6899,6901],{"className":6900},[886],[888,6902,6903],{"xmlns":890},[892,6904,6905,6909],{},[895,6906,6907],{},[1846,6908,3833],{},[902,6910,6801],{"encoding":904},[883,6912,6914],{"className":6913},[886],[888,6915,6916],{"xmlns":890},[892,6917,6918,6928],{},[895,6919,6920,6922,6924,6926],{},[898,6921,2667],{},[898,6923,3840],{},[1846,6925,1848],{},[1979,6927,2177],{},[902,6929,6930],{"encoding":904},"MR = 0",[883,6932,6934],{"className":6933},[886],[888,6935,6936],{"xmlns":890},[892,6937,6938,6944],{},[895,6939,6940,6942],{},[898,6941,2623],{},[898,6943,3840],{},[902,6945,3940],{"encoding":904}," je extrém (maximum).",[123,6948,6949,6966,6967,2053,6980,6861,7000,7015],{},[883,6950,6952],{"className":6951},[886],[888,6953,6954],{"xmlns":890},[892,6955,6956,6964],{},[895,6957,6958,6960,6962],{},[898,6959,4098],{},[1846,6961,3295],{},[1979,6963,2128],{},[902,6965,4373],{"encoding":904}," (neelastická) ",[883,6968,6970],{"className":6969},[886],[888,6971,6972],{"xmlns":890},[892,6973,6974,6978],{},[895,6975,6976],{},[1846,6977,3833],{},[902,6979,6801],{"encoding":904},[883,6981,6983],{"className":6982},[886],[888,6984,6985],{"xmlns":890},[892,6986,6987,6997],{},[895,6988,6989,6991,6993,6995],{},[898,6990,2667],{},[898,6992,3840],{},[1846,6994,3295],{},[1979,6996,2177],{},[902,6998,6999],{"encoding":904},"MR \u003C 0",[883,7001,7003],{"className":7002},[886],[888,7004,7005],{"xmlns":890},[892,7006,7007,7013],{},[895,7008,7009,7011],{},[898,7010,2623],{},[898,7012,3840],{},[902,7014,3940],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,7017,7018,7019,1734],{},"Viz také ",[207,7020,1708],{"className":7021,"dataFsResolvedFilePath":827,"href":828},[210],[198,7023,7025],{"id":7024},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,7027,7028,7048,7049,7075,7076,7091,7092,7105,7106,7119,7120,7133,7134,7150,7151,2053,7166,7169,7170,7150,7186,1734],{},[38,7029,7030,7031,3764],{},"(a) Poptávka elastická (",[883,7032,7034],{"className":7033},[886],[888,7035,7036],{"xmlns":890},[892,7037,7038,7046],{},[895,7039,7040,7042,7044],{},[898,7041,4098],{},[1846,7043,3256],{},[1979,7045,2128],{},[902,7047,4355],{"encoding":904}," Z (4.12) plyne ",[883,7050,7052],{"className":7051},[886],[888,7053,7054],{"xmlns":890},[892,7055,7056,7072],{},[895,7057,7058,7060,7062,7064,7066,7068,7070],{},[898,7059,2667],{},[898,7061,3840],{},[1846,7063,1855],{"stretchy":1854},[898,7065,2638],{},[1846,7067,1861],{"stretchy":1854},[1846,7069,3256],{},[1979,7071,2177],{},[902,7073,7074],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,7077,7079],{"className":7078},[886],[888,7080,7081],{"xmlns":890},[892,7082,7083,7089],{},[895,7084,7085,7087],{},[898,7086,2623],{},[898,7088,3840],{},[902,7090,3940],{"encoding":904}," je rostoucí funkcí ",[883,7093,7095],{"className":7094},[886],[888,7096,7097],{"xmlns":890},[892,7098,7099,7103],{},[895,7100,7101],{},[898,7102,2638],{},[902,7104,2638],{"encoding":904},". Avšak růst ",[883,7107,7109],{"className":7108},[886],[888,7110,7111],{"xmlns":890},[892,7112,7113,7117],{},[895,7114,7115],{},[898,7116,2638],{},[902,7118,2638],{"encoding":904}," je odezvou na pokles ceny ",[883,7121,7123],{"className":7122},[886],[888,7124,7125],{"xmlns":890},[892,7126,7127,7131],{},[895,7128,7129],{},[898,7130,3783],{},[902,7132,3783],{"encoding":904},". Tudíž s ",[614,7135,7136,7137],{},"poklesem ceny ",[883,7138,7140],{"className":7139},[886],[888,7141,7142],{"xmlns":890},[892,7143,7144,7148],{},[895,7145,7146],{},[898,7147,3783],{},[902,7149,3783],{"encoding":904}," celkový příjem ",[883,7152,7154],{"className":7153},[886],[888,7155,7156],{"xmlns":890},[892,7157,7158,7164],{},[895,7159,7160,7162],{},[898,7161,2623],{},[898,7163,3840],{},[902,7165,3940],{"encoding":904},[614,7167,7168],{},"roste"," a s ",[614,7171,7172,7173],{},"růstem ceny ",[883,7174,7176],{"className":7175},[886],[888,7177,7178],{"xmlns":890},[892,7179,7180,7184],{},[895,7181,7182],{},[898,7183,3783],{},[902,7185,3783],{"encoding":904},[614,7187,7188],{},"klesá",[1639,7190,7191],{},[724,7192,7193,7196],{},[38,7194,7195],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,7198,7199,7048,7219,1343,7245,7260,7261,7274,7275,7288,7289,7302,7303,7150,7316,2053,7331,1734],{},[38,7200,7201,7202,3764],{},"(b) Poptávka neelastická (",[883,7203,7205],{"className":7204},[886],[888,7206,7207],{"xmlns":890},[892,7208,7209,7217],{},[895,7210,7211,7213,7215],{},[898,7212,4098],{},[1846,7214,3295],{},[1979,7216,2128],{},[902,7218,4373],{"encoding":904},[883,7220,7222],{"className":7221},[886],[888,7223,7224],{"xmlns":890},[892,7225,7226,7242],{},[895,7227,7228,7230,7232,7234,7236,7238,7240],{},[898,7229,2667],{},[898,7231,3840],{},[1846,7233,1855],{"stretchy":1854},[898,7235,2638],{},[1846,7237,1861],{"stretchy":1854},[1846,7239,3295],{},[1979,7241,2177],{},[902,7243,7244],{"encoding":904},"MR(Q) \u003C 0",[883,7246,7248],{"className":7247},[886],[888,7249,7250],{"xmlns":890},[892,7251,7252,7258],{},[895,7253,7254,7256],{},[898,7255,2623],{},[898,7257,3840],{},[902,7259,3940],{"encoding":904}," je klesající funkce ",[883,7262,7264],{"className":7263},[886],[888,7265,7266],{"xmlns":890},[892,7267,7268,7272],{},[895,7269,7270],{},[898,7271,2638],{},[902,7273,2638],{"encoding":904},", tj. s růstem ",[883,7276,7278],{"className":7277},[886],[888,7279,7280],{"xmlns":890},[892,7281,7282,7286],{},[895,7283,7284],{},[898,7285,2638],{},[902,7287,2638],{"encoding":904}," (s poklesem ceny ",[883,7290,7292],{"className":7291},[886],[888,7293,7294],{"xmlns":890},[892,7295,7296,7300],{},[895,7297,7298],{},[898,7299,3783],{},[902,7301,3783],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,7304,7306],{"className":7305},[886],[888,7307,7308],{"xmlns":890},[892,7309,7310,7314],{},[895,7311,7312],{},[898,7313,3783],{},[902,7315,3783],{"encoding":904},[883,7317,7319],{"className":7318},[886],[888,7320,7321],{"xmlns":890},[892,7322,7323,7329],{},[895,7324,7325,7327],{},[898,7326,2623],{},[898,7328,3840],{},[902,7330,3940],{"encoding":904},[614,7332,7168],{},[1639,7334,7335],{},[724,7336,7337,7340],{},[38,7338,7339],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,7342,7343,7048,7363,7382,7383,7398,7399,7469,7470,1745,7498,7531,7532,5435,7560,7575,7576,1734],{},[38,7344,7345,7346,3764],{},"(c) Jednotková elasticita (",[883,7347,7349],{"className":7348},[886],[888,7350,7351],{"xmlns":890},[892,7352,7353,7361],{},[895,7354,7355,7357,7359],{},[898,7356,4098],{},[1846,7358,1848],{},[1979,7360,2128],{},[902,7362,4391],{"encoding":904},[883,7364,7366],{"className":7365},[886],[888,7367,7368],{"xmlns":890},[892,7369,7370,7380],{},[895,7371,7372,7374,7376,7378],{},[898,7373,2667],{},[898,7375,3840],{},[1846,7377,1848],{},[1979,7379,2177],{},[902,7381,6930],{"encoding":904}," — nutná podmínka extrému ",[883,7384,7386],{"className":7385},[886],[888,7387,7388],{"xmlns":890},[892,7389,7390,7396],{},[895,7391,7392,7394],{},[898,7393,2623],{},[898,7395,3840],{},[902,7397,3940],{"encoding":904},". Dále ",[883,7400,7402],{"className":7401},[886],[888,7403,7404],{"xmlns":890},[892,7405,7406,7466],{},[895,7407,7408,7410,7420,7422,7424,7430,7432,7438,7440,7442,7444,7446,7448,7450,7460,7462,7464],{},[898,7409,2623],{},[1974,7411,7412,7414],{},[898,7413,3840],{},[895,7415,7416,7418],{},[1846,7417,2228],{"mathvariant":2226},[1846,7419,2228],{"mathvariant":2226},[1846,7421,1848],{},[898,7423,2667],{},[1974,7425,7426,7428],{},[898,7427,3840],{},[1846,7429,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,7431,1848],{},[1974,7433,7434,7436],{},[898,7435,4029],{},[1846,7437,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,7439,1855],{"stretchy":1854},[898,7441,2638],{},[1846,7443,1861],{"stretchy":1854},[1846,7445,1945],{},[898,7447,2638],{},[2138,7449,2835],{},[1974,7451,7452,7454],{},[898,7453,4029],{},[895,7455,7456,7458],{},[1846,7457,2228],{"mathvariant":2226},[1846,7459,2228],{"mathvariant":2226},[1846,7461,1855],{"stretchy":1854},[898,7463,2638],{},[1846,7465,1861],{"stretchy":1854},[902,7467,7468],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,7471,7473],{"className":7472},[886],[888,7474,7475],{"xmlns":890},[892,7476,7477,7495],{},[895,7478,7479,7485,7487,7489,7491,7493],{},[1974,7480,7481,7483],{},[898,7482,4029],{},[1846,7484,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,7486,1855],{"stretchy":1854},[898,7488,2638],{},[1846,7490,1861],{"stretchy":1854},[1846,7492,3295],{},[1979,7494,2177],{},[902,7496,7497],{"encoding":904},"D'(Q) \u003C 0",[883,7499,7501],{"className":7500},[886],[888,7502,7503],{"xmlns":890},[892,7504,7505,7528],{},[895,7506,7507,7517,7519,7521,7523,7526],{},[1974,7508,7509,7511],{},[898,7510,4029],{},[895,7512,7513,7515],{},[1846,7514,2228],{"mathvariant":2226},[1846,7516,2228],{"mathvariant":2226},[1846,7518,1855],{"stretchy":1854},[898,7520,2638],{},[1846,7522,1861],{"stretchy":1854},[1846,7524,7525],{},"≤",[1979,7527,2177],{},[902,7529,7530],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,7533,7535],{"className":7534},[886],[888,7536,7537],{"xmlns":890},[892,7538,7539,7557],{},[895,7540,7541,7543,7553,7555],{},[898,7542,2623],{},[1974,7544,7545,7547],{},[898,7546,3840],{},[895,7548,7549,7551],{},[1846,7550,2228],{"mathvariant":2226},[1846,7552,2228],{"mathvariant":2226},[1846,7554,3295],{},[1979,7556,2177],{},[902,7558,7559],{"encoding":904},"TR'' \u003C 0",[883,7561,7563],{"className":7562},[886],[888,7564,7565],{"xmlns":890},[892,7566,7567,7573],{},[895,7568,7569,7571],{},[898,7570,2623],{},[898,7572,3840],{},[902,7574,3940],{"encoding":904}," nabývá ",[38,7577,7578],{},"maxima",[1639,7580,7581],{},[724,7582,7583,7586],{},[38,7584,7585],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,7588,7589],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,7591,7592],{},[38,7593,7594],{},"Souhrnná tabulka Pravidel 1–3:",[16,7596,7597,7701],{},[19,7598,7599],{},[22,7600,7601,7604,7619,7636,7667,7698],{},[25,7602,7603],{},"Charakter poptávky",[25,7605,7606],{},[883,7607,7609],{"className":7608},[886],[888,7610,7611],{"xmlns":890},[892,7612,7613,7617],{},[895,7614,7615],{},[898,7616,4098],{},[902,7618,4098],{"encoding":904},[25,7620,7621],{},[883,7622,7624],{"className":7623},[886],[888,7625,7626],{"xmlns":890},[892,7627,7628,7634],{},[895,7629,7630,7632],{},[898,7631,2667],{},[898,7633,3840],{},[902,7635,6480],{"encoding":904},[25,7637,7638,7639,2053,7652],{},"Pokles ceny ",[883,7640,7642],{"className":7641},[886],[888,7643,7644],{"xmlns":890},[892,7645,7646,7650],{},[895,7647,7648],{},[1846,7649,3833],{},[902,7651,6801],{"encoding":904},[883,7653,7655],{"className":7654},[886],[888,7656,7657],{"xmlns":890},[892,7658,7659,7665],{},[895,7660,7661,7663],{},[898,7662,2623],{},[898,7664,3840],{},[902,7666,3940],{"encoding":904},[25,7668,7669,7670,2053,7683],{},"Růst ceny ",[883,7671,7673],{"className":7672},[886],[888,7674,7675],{"xmlns":890},[892,7676,7677,7681],{},[895,7678,7679],{},[1846,7680,3833],{},[902,7682,6801],{"encoding":904},[883,7684,7686],{"className":7685},[886],[888,7687,7688],{"xmlns":890},[892,7689,7690,7696],{},[895,7691,7692,7694],{},[898,7693,2623],{},[898,7695,3840],{},[902,7697,3940],{"encoding":904},[25,7699,7700],{},"Doporučení",[30,7702,7703,7752,7802],{},[22,7704,7705,7707,7725,7743,7745,7747],{},[35,7706,3919],{},[35,7708,7709],{},[883,7710,7712],{"className":7711},[886],[888,7713,7714],{"xmlns":890},[892,7715,7716,7722],{},[895,7717,7718,7720],{},[1846,7719,3256],{},[1979,7721,2128],{},[902,7723,7724],{"encoding":904},"> 1",[35,7726,7727],{},[883,7728,7730],{"className":7729},[886],[888,7731,7732],{"xmlns":890},[892,7733,7734,7740],{},[895,7735,7736,7738],{},[1846,7737,3256],{},[1979,7739,2177],{},[902,7741,7742],{"encoding":904},"> 0",[35,7744,7168],{},[35,7746,7188],{},[35,7748,7749],{},[38,7750,7751],{},"snížit cenu",[22,7753,7754,7757,7775,7793,7795,7797],{},[35,7755,7756],{},"jednotková",[35,7758,7759],{},[883,7760,7762],{"className":7761},[886],[888,7763,7764],{"xmlns":890},[892,7765,7766,7772],{},[895,7767,7768,7770],{},[1846,7769,1848],{},[1979,7771,2128],{},[902,7773,7774],{"encoding":904},"= 1",[35,7776,7777],{},[883,7778,7780],{"className":7779},[886],[888,7781,7782],{"xmlns":890},[892,7783,7784,7790],{},[895,7785,7786,7788],{},[1846,7787,1848],{},[1979,7789,2177],{},[902,7791,7792],{"encoding":904},"= 0",[35,7794,3565],{},[35,7796,3565],{},[35,7798,7799],{},[38,7800,7801],{},"držet cenu",[22,7803,7804,7806,7824,7842,7844,7846],{},[35,7805,3923],{},[35,7807,7808],{},[883,7809,7811],{"className":7810},[886],[888,7812,7813],{"xmlns":890},[892,7814,7815,7821],{},[895,7816,7817,7819],{},[1846,7818,3295],{},[1979,7820,2128],{},[902,7822,7823],{"encoding":904},"\u003C 1",[35,7825,7826],{},[883,7827,7829],{"className":7828},[886],[888,7830,7831],{"xmlns":890},[892,7832,7833,7839],{},[895,7834,7835,7837],{},[1846,7836,3295],{},[1979,7838,2177],{},[902,7840,7841],{"encoding":904},"\u003C 0",[35,7843,7188],{},[35,7845,7168],{},[35,7847,7848],{},[38,7849,7850],{},"zvýšit cenu",[198,7852,7854],{"id":7853},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,7856,7857,7858,7883,7884,7906,7907,7920,7921,7934,7935,7948,7949,5435,7976,8028],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,7859,7861],{"className":7860},[886],[888,7862,7863],{"xmlns":890},[892,7864,7865,7881],{},[895,7866,7867,7869,7871,7873,7875],{},[898,7868,3783],{},[1846,7870,1848],{},[1979,7872,2938],{},[1846,7874,2075],{},[1974,7876,7877,7879],{},[898,7878,2638],{},[1979,7880,1981],{},[902,7882,5305],{"encoding":904},". Reálné cenové rozpětí je ",[883,7885,7887],{"className":7886},[886],[888,7888,7889],{"xmlns":890},[892,7890,7891,7903],{},[895,7892,7893,7895,7897,7899,7901],{},[1846,7894,5170],{"stretchy":1854},[1979,7896,2128],{},[1846,7898,2136],{"separator":2135},[1979,7900,2938],{},[1846,7902,5187],{"stretchy":1854},[902,7904,7905],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,7908,7910],{"className":7909},[886],[888,7911,7912],{"xmlns":890},[892,7913,7914,7918],{},[895,7915,7916],{},[898,7917,2638],{},[902,7919,2638],{"encoding":904}," jako funkci ",[883,7922,7924],{"className":7923},[886],[888,7925,7926],{"xmlns":890},[892,7927,7928,7932],{},[895,7929,7930],{},[898,7931,3783],{},[902,7933,3783],{"encoding":904},"; pro nezáporné ",[883,7936,7938],{"className":7937},[886],[888,7939,7940],{"xmlns":890},[892,7941,7942,7946],{},[895,7943,7944],{},[898,7945,2638],{},[902,7947,2638],{"encoding":904}," je ",[883,7950,7952],{"className":7951},[886],[888,7953,7954],{"xmlns":890},[892,7955,7956,7973],{},[895,7957,7958,7960,7962],{},[898,7959,2638],{},[1846,7961,1848],{},[7963,7964,7965],"msqrt",{},[895,7966,7967,7969,7971],{},[1979,7968,2938],{},[1846,7970,2075],{},[898,7972,3783],{},[902,7974,7975],{"encoding":904},"Q = \\sqrt{100 - P}",[883,7977,7979],{"className":7978},[886],[888,7980,7981],{"xmlns":890},[892,7982,7983,8025],{},[895,7984,7985,8001,8003,8005],{},[2175,7986,7987],{"scriptlevel":2177,"displaystyle":2135},[2179,7988,7989,7995],{},[895,7990,7991,7993],{},[898,7992,2044],{"mathvariant":2226},[898,7994,2638],{},[895,7996,7997,7999],{},[898,7998,2044],{"mathvariant":2226},[898,8000,3783],{},[1846,8002,1848],{},[1846,8004,2075],{},[2175,8006,8007],{"scriptlevel":2177,"displaystyle":2135},[2179,8008,8009,8011],{},[1979,8010,2128],{},[895,8012,8013,8015],{},[1979,8014,1981],{},[7963,8016,8017],{},[895,8018,8019,8021,8023],{},[1979,8020,2938],{},[1846,8022,2075],{},[898,8024,3783],{},[902,8026,8027],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,8030,8031],{},[883,8032,8034],{"className":8033},[886],[888,8035,8036],{"xmlns":890},[892,8037,8038,8160],{},[895,8039,8040,8042,8044,8046,8048,8050,8052,8058,8060,8074,8076,8078,8092,8094,8120,8122,8140,8142,8158],{},[898,8041,4098],{},[1846,8043,1855],{"stretchy":1854},[898,8045,3783],{},[1846,8047,1861],{"stretchy":1854},[1846,8049,1848],{},[1846,8051,2075],{},[2179,8053,8054,8056],{},[898,8055,3783],{},[898,8057,2638],{},[1846,8059,3025],{},[2179,8061,8062,8068],{},[895,8063,8064,8066],{},[898,8065,2044],{"mathvariant":2226},[898,8067,2638],{},[895,8069,8070,8072],{},[898,8071,2044],{"mathvariant":2226},[898,8073,3783],{},[1846,8075,1848],{},[1846,8077,2075],{},[2179,8079,8080,8082],{},[898,8081,3783],{},[7963,8083,8084],{},[895,8085,8086,8088,8090],{},[1979,8087,2938],{},[1846,8089,2075],{},[898,8091,3783],{},[1846,8093,3025],{},[895,8095,8096,8098,8100,8118],{},[1846,8097,1855],{"fence":2135},[1846,8099,2075],{},[2179,8101,8102,8104],{},[1979,8103,2128],{},[895,8105,8106,8108],{},[1979,8107,1981],{},[7963,8109,8110],{},[895,8111,8112,8114,8116],{},[1979,8113,2938],{},[1846,8115,2075],{},[898,8117,3783],{},[1846,8119,1861],{"fence":2135},[1846,8121,1848],{},[2179,8123,8124,8126],{},[898,8125,3783],{},[895,8127,8128,8130,8132,8134,8136,8138],{},[1979,8129,1981],{},[1846,8131,1855],{"stretchy":1854},[1979,8133,2938],{},[1846,8135,2075],{},[898,8137,3783],{},[1846,8139,1861],{"stretchy":1854},[1846,8141,1848],{},[2179,8143,8144,8150],{},[895,8145,8146,8148],{},[1979,8147,4855],{},[898,8149,3783],{},[895,8151,8152,8154,8156],{},[1979,8153,2938],{},[1846,8155,2075],{},[898,8157,3783],{},[898,8159,1734],{"mathvariant":2226},[902,8161,8162],{"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}.",[724,8164,8165,8166,2554],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,8167,8169],{"className":8168},[886],[888,8170,8171],{"xmlns":890},[892,8172,8173,8197],{},[895,8174,8175,8193,8195],{},[2175,8176,8177],{"scriptlevel":2177,"displaystyle":2135},[2179,8178,8179,8185],{},[895,8180,8181,8183],{},[1979,8182,4855],{},[898,8184,3783],{},[895,8186,8187,8189,8191],{},[1979,8188,2938],{},[1846,8190,2075],{},[898,8192,3783],{},[1846,8194,1848],{},[1979,8196,2128],{},[902,8198,8199],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,8201,8202],{},[883,8203,8205],{"className":8204},[886],[888,8206,8207],{"xmlns":890},[892,8208,8209,8241],{},[895,8210,8211,8217,8219,8226,8228,8231,8239],{},[1974,8212,8213,8215],{},[898,8214,3783],{},[1846,8216,4200],{},[1846,8218,1848],{},[2179,8220,8221,8224],{},[1979,8222,8223],{},"200",[1979,8225,2023],{},[1846,8227,5746],{},[1979,8229,8230],{},"66,",[8232,8233,8234,8236],"mover",{"accent":2135},[1979,8235,2085],{},[1846,8237,8238],{"stretchy":2135},"‾",[898,8240,1734],{"mathvariant":2226},[902,8242,8243],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,8245,8246],{},"S využitím vlastnosti (4.8):",[120,8248,8249,8295,8337],{},[123,8250,8251,8252,8287,8288,8290,8291,8294],{},"Při cenách ",[883,8253,8255],{"className":8254},[886],[888,8256,8257],{"xmlns":890},[892,8258,8259,8284],{},[895,8260,8261,8263,8265,8267,8269,8272,8274,8276,8282],{},[898,8262,3783],{},[1846,8264,6352],{},[1846,8266,5170],{"stretchy":1854},[1979,8268,2128],{},[1846,8270,8271],{"separator":2135},";",[2138,8273,2835],{},[1979,8275,8230],{},[8232,8277,8278,8280],{"accent":2135},[1979,8279,2085],{},[1846,8281,8238],{"stretchy":2135},[1846,8283,1861],{"stretchy":1854},[902,8285,8286],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,8289,3923],{}," — dle ",[614,8292,8293],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,8296,8251,8297,8287,8331,8290,8333,8336],{},[883,8298,8300],{"className":8299},[886],[888,8301,8302],{"xmlns":890},[892,8303,8304,8328],{},[895,8305,8306,8308,8310,8312,8314,8320,8322,8324,8326],{},[898,8307,3783],{},[1846,8309,6352],{},[1846,8311,1855],{"stretchy":1854},[1979,8313,8230],{},[8232,8315,8316,8318],{"accent":2135},[1979,8317,2085],{},[1846,8319,8238],{"stretchy":2135},[1846,8321,8271],{"separator":2135},[2138,8323,2835],{},[1979,8325,2938],{},[1846,8327,5187],{"stretchy":1854},[902,8329,8330],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,8332,3919],{},[614,8334,8335],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,8338,8339,8340,8343,8344,8372,8373,8376],{},"Dle ",[614,8341,8342],{},"Pravidla 3"," je při ceně ",[883,8345,8347],{"className":8346},[886],[888,8348,8349],{"xmlns":890},[892,8350,8351,8369],{},[895,8352,8353,8359,8361,8363],{},[1974,8354,8355,8357],{},[898,8356,3783],{},[1846,8358,4200],{},[1846,8360,1848],{},[1979,8362,8230],{},[8232,8364,8365,8367],{"accent":2135},[1979,8366,2085],{},[1846,8368,8238],{"stretchy":2135},[902,8370,8371],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,8374,8375],{},"maxima celkového příjmu"," ve výši",[724,8378,8379],{},[883,8380,8382],{"className":8381},[886],[888,8383,8384],{"xmlns":890},[892,8385,8386,8464],{},[895,8387,8388,8390,8392,8394,8400,8402,8404,8410,8412,8426,8428,8434,8436,8444,8446,8459,8461],{},[898,8389,2623],{},[898,8391,3840],{},[1846,8393,1855],{"stretchy":1854},[1974,8395,8396,8398],{},[898,8397,3783],{},[1846,8399,4200],{},[1846,8401,1861],{"stretchy":1854},[1846,8403,1848],{},[1974,8405,8406,8408],{},[898,8407,3783],{},[1846,8409,4200],{},[1846,8411,3025],{},[7963,8413,8414],{},[895,8415,8416,8418,8420],{},[1979,8417,2938],{},[1846,8419,2075],{},[1974,8421,8422,8424],{},[898,8423,3783],{},[1846,8425,4200],{},[1846,8427,1848],{},[2179,8429,8430,8432],{},[1979,8431,8223],{},[1979,8433,2023],{},[1846,8435,3025],{},[7963,8437,8438],{},[2179,8439,8440,8442],{},[1979,8441,2938],{},[1979,8443,2023],{},[1846,8445,1848],{},[2179,8447,8448,8451],{},[1979,8449,8450],{},"2000",[895,8452,8453,8455],{},[1979,8454,2023],{},[7963,8456,8457],{},[1979,8458,2023],{},[1846,8460,5746],{},[1979,8462,8463],{},"384,9.",[902,8465,8466],{"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.",[724,8468,8469,8470,1734],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,8471,8473],{"className":8472},[886],[888,8474,8475],{"xmlns":890},[892,8476,8477,8483],{},[895,8478,8479,8481],{},[898,8480,2623],{},[898,8482,3840],{},[902,8484,3940],{"encoding":904},[115,8486,8488],{"id":8487},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,8490,8491,8492,8495],{},"Analogicky se definuje ",[38,8493,8494],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,8497,8498],{},[883,8499,8501],{"className":8500,"title":4046,"style":4047},[4045],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,8503,4156,8504,8529,8530,8562],{},[883,8505,8507],{"className":8506},[886],[888,8508,8509],{"xmlns":890},[892,8510,8511,8526],{},[895,8512,8513,8515,8517,8520,8522,8524],{},[898,8514,2638],{},[1846,8516,1848],{},[898,8518,8519],{},"S",[1846,8521,1855],{"stretchy":1854},[898,8523,3783],{},[1846,8525,1861],{"stretchy":1854},[902,8527,8528],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,8531,8533],{"className":8532},[886],[888,8534,8535],{"xmlns":890},[892,8536,8537,8559],{},[895,8538,8539,8555,8557],{},[2175,8540,8541],{"scriptlevel":2177,"displaystyle":2135},[2179,8542,8543,8549],{},[895,8544,8545,8547],{},[898,8546,2044],{"mathvariant":2226},[898,8548,2638],{},[895,8550,8551,8553],{},[898,8552,2044],{"mathvariant":2226},[898,8554,3783],{},[1846,8556,3256],{},[1979,8558,2177],{},[902,8560,8561],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,8564,8565],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[1639,8567,8568],{},[724,8569,8570,8571],{},"S rostoucí cenou elasticita nabídky roste. ",[883,8572,8574],{"className":8573},[886],[888,8575,8576],{"xmlns":890},[892,8577,8578,8587],{},[895,8579,8580,8582,8585],{},[1846,8581,1855],{"stretchy":1854},[1979,8583,8584],{},"4.14",[1846,8586,1861],{"stretchy":1854},[902,8588,8589],{"encoding":904},"(4.14)",[724,8591,8592],{},"Pro nominální změny platí",[724,8594,8595],{},[883,8596,8598],{"className":8597,"title":4046,"style":4047},[4045],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,8600,8601],{},"a pro procentní změny",[724,8603,8604],{},[883,8605,8607],{"className":8606,"title":4046,"style":4047},[4045],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,8609,8610],{},"(bez znaménka minus).",[198,8612,8614],{"id":8613},"příklad-47","Příklad 4.7",[724,8616,8617,8618,2554],{},"Nabídka ",[883,8619,8621],{"className":8620},[886],[888,8622,8623],{"xmlns":890},[892,8624,8625,8650],{},[895,8626,8627,8629,8631,8633,8639,8641,8643,8645,8647],{},[898,8628,2638],{},[1846,8630,1848],{},[1979,8632,2643],{},[1974,8634,8635,8637],{},[898,8636,3783],{},[1979,8638,1981],{},[1846,8640,1945],{},[1979,8642,2078],{},[898,8644,3783],{},[1846,8646,1945],{},[1979,8648,8649],{},"150",[902,8651,8652],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,8654,8655],{},[883,8656,8658],{"className":8657},[886],[888,8659,8660],{"xmlns":890},[892,8661,8662,8708],{},[895,8663,8664,8666,8668,8692,8694,8696,8698,8700,8702,8704,8706],{},[898,8665,4098],{},[1846,8667,1848],{},[2179,8669,8670,8672],{},[898,8671,3783],{},[895,8673,8674,8676,8682,8684,8686,8688,8690],{},[1979,8675,2643],{},[1974,8677,8678,8680],{},[898,8679,3783],{},[1979,8681,1981],{},[1846,8683,1945],{},[1979,8685,2078],{},[898,8687,3783],{},[1846,8689,1945],{},[1979,8691,8649],{},[2138,8693,2835],{},[1846,8695,1855],{"stretchy":1854},[1979,8697,2688],{},[898,8699,3783],{},[1846,8701,1945],{},[1979,8703,2078],{},[1846,8705,1861],{"stretchy":1854},[898,8707,1734],{"mathvariant":2226},[902,8709,8710],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,8712,4963,8713,1343,8743,1343,8770,8806,8807,8832,8833,8851,8852,1734],{},[883,8714,8716],{"className":8715},[886],[888,8717,8718],{"xmlns":890},[892,8719,8720,8740],{},[895,8721,8722,8724,8726,8728,8730,8732],{},[898,8723,4098],{},[1846,8725,1855],{"stretchy":1854},[1979,8727,2712],{},[1846,8729,1861],{"stretchy":1854},[1846,8731,1848],{},[2175,8733,8734],{"scriptlevel":2177,"displaystyle":1854},[2179,8735,8736,8738],{},[1979,8737,2128],{},[1979,8739,2023],{},[902,8741,8742],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,8744,8746],{"className":8745},[886],[888,8747,8748],{"xmlns":890},[892,8749,8750,8767],{},[895,8751,8752,8754,8756,8761,8763,8765],{},[898,8753,4098],{},[1846,8755,1855],{"stretchy":1854},[7963,8757,8758],{},[1979,8759,8760],{},"1500",[1846,8762,1861],{"stretchy":1854},[1846,8764,1848],{},[1979,8766,2128],{},[902,8768,8769],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,8771,8773],{"className":8772},[886],[888,8774,8775],{"xmlns":890},[892,8776,8777,8803],{},[895,8778,8779,8781,8783,8785,8787,8789,8798,8800],{},[898,8780,4098],{},[1846,8782,1855],{"stretchy":1854},[1979,8784,2938],{},[1846,8786,1861],{"stretchy":1854},[1846,8788,1848],{},[2175,8790,8791],{"scriptlevel":2177,"displaystyle":1854},[2179,8792,8793,8795],{},[1979,8794,2968],{},[1979,8796,8797],{},"33",[1846,8799,5746],{},[1979,8801,8802],{},"1,515",[902,8804,8805],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,8808,8810],{"className":8809},[886],[888,8811,8812],{"xmlns":890},[892,8813,8814,8829],{},[895,8815,8816,8818,8820,8824,8826],{},[898,8817,3783],{},[1846,8819,3256],{},[7963,8821,8822],{},[1979,8823,8760],{},[1846,8825,1650],{},[1979,8827,8828],{},"38,7",[902,8830,8831],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,8834,8836],{"className":8835},[886],[888,8837,8838],{"xmlns":890},[892,8839,8840,8848],{},[895,8841,8842,8844,8846],{},[898,8843,3783],{},[1846,8845,3295],{},[1979,8847,8828],{},[902,8849,8850],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,8853,8855],{"className":8854},[886],[888,8856,8857],{"xmlns":890},[892,8858,8859,8897],{},[895,8860,8861,8863,8865,8867,8869,8877,8879,8882,8884,8887,8893,8895],{},[898,8862,2738],{"mathvariant":2226},[898,8864,2638],{},[898,8866,5771],{"mathvariant":2226},[1846,8868,1650],{},[2175,8870,8871],{"scriptlevel":2177,"displaystyle":1854},[2179,8872,8873,8875],{},[1979,8874,2128],{},[1979,8876,2023],{},[1846,8878,3025],{},[1979,8880,8881],{},"20",[1846,8883,1848],{},[1979,8885,8886],{},"6,",[8232,8888,8889,8891],{"accent":2135},[1979,8890,2085],{},[1846,8892,8238],{"stretchy":2135},[2138,8894,2835],{},[898,8896,5771],{"mathvariant":2226},[902,8898,8899],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,8901,8903],{"id":8902},"vícefaktorový-model","Vícefaktorový model",[724,8905,8906,8907,8920,8921,2053,8924,8937,8938,2053,8941,8959,8960,2053,8963,2554],{},"Předpokládejme, že poptávané množství ",[883,8908,8910],{"className":8909},[886],[888,8911,8912],{"xmlns":890},[892,8913,8914,8918],{},[895,8915,8916],{},[898,8917,2638],{},[902,8919,2638],{"encoding":904}," závisí na ",[38,8922,8923],{},"ceně základního zboží",[883,8925,8927],{"className":8926},[886],[888,8928,8929],{"xmlns":890},[892,8930,8931,8935],{},[895,8932,8933],{},[898,8934,3783],{},[902,8936,3783],{"encoding":904},", na ",[38,8939,8940],{},"ceně alternativního zboží",[883,8942,8944],{"className":8943},[886],[888,8945,8946],{"xmlns":890},[892,8947,8948,8956],{},[895,8949,8950],{},[2122,8951,8952,8954],{},[898,8953,3783],{},[898,8955,4101],{},[902,8957,8958],{"encoding":904},"P_A"," a na ",[38,8961,8962],{},"důchodu",[883,8964,8966],{"className":8965},[886],[888,8967,8968],{"xmlns":890},[892,8969,8970,8975],{},[895,8971,8972],{},[898,8973,8974],{},"Y",[902,8976,8974],{"encoding":904},[724,8978,8979],{},[883,8980,8982],{"className":8981,"title":4046,"style":4047},[4045],"Q = D(P, P_A, Y). \\tag{4.17}",[724,8984,8985,8986,8989],{},"V analogii jednofaktorového modelu pracujeme s ",[38,8987,8988],{},"parciálními derivacemi"," funkce poptávky.",[198,8991,8993],{"id":8992},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,8995,8996],{},[883,8997,8999],{"className":8998,"title":4046,"style":4047},[4045],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,9001,4156,9002,9023,9024,9037,9038,2776,9060,2053,9063,9109,9110,9123,9124,9141],{},[883,9003,9005],{"className":9004},[886],[888,9006,9007],{"xmlns":890},[892,9008,9009,9020],{},[895,9010,9011],{},[9012,9013,9014,9016,9018],"msubsup",{},[898,9015,2638],{},[898,9017,3783],{},[1846,9019,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,9021,9022],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,9025,9027],{"className":9026},[886],[888,9028,9029],{"xmlns":890},[892,9030,9031,9035],{},[895,9032,9033],{},[898,9034,3783],{},[902,9036,3783],{"encoding":904},". Vždy ",[883,9039,9041],{"className":9040},[886],[888,9042,9043],{"xmlns":890},[892,9044,9045,9057],{},[895,9046,9047,9053,9055],{},[2122,9048,9049,9051],{},[898,9050,4098],{},[898,9052,3783],{},[1846,9054,4331],{},[1979,9056,2177],{},[902,9058,9059],{"encoding":904},"E_P \\ge 0",[614,9061,9062],{},"Interpretace:",[883,9064,9066],{"className":9065},[886],[888,9067,9068],{"xmlns":890},[892,9069,9070,9106],{},[895,9071,9072,9078,9080,9086,9088,9096,9098,9104],{},[2122,9073,9074,9076],{},[898,9075,4098],{},[898,9077,3783],{},[1846,9079,1855],{"stretchy":1854},[1974,9081,9082,9084],{},[898,9083,3783],{},[1846,9085,4200],{},[1846,9087,2136],{"separator":2135},[9012,9089,9090,9092,9094],{},[898,9091,3783],{},[898,9093,4101],{},[1846,9095,4200],{},[1846,9097,2136],{"separator":2135},[1974,9099,9100,9102],{},[898,9101,8974],{},[1846,9103,4200],{},[1846,9105,1861],{"stretchy":1854},[902,9107,9108],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,9111,9113],{"className":9112},[886],[888,9114,9115],{"xmlns":890},[892,9116,9117,9121],{},[895,9118,9119],{},[898,9120,2638],{},[902,9122,2638],{"encoding":904}," při 1% změně ",[883,9125,9127],{"className":9126},[886],[888,9128,9129],{"xmlns":890},[892,9130,9131,9139],{},[895,9132,9133],{},[1974,9134,9135,9137],{},[898,9136,3783],{},[1846,9138,4200],{},[902,9140,4250],{"encoding":904},", ceteris paribus.",[198,9143,9145],{"id":9144},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,9147,9148],{},[883,9149,9151],{"className":9150,"title":4046,"style":4047},[4045],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,9153,9154,9109,9156,9169,9170,9187],{},[614,9155,9062],{},[883,9157,9159],{"className":9158},[886],[888,9160,9161],{"xmlns":890},[892,9162,9163,9167],{},[895,9164,9165],{},[898,9166,2638],{},[902,9168,2638],{"encoding":904}," základního zboží při 1% změně ceny ",[883,9171,9173],{"className":9172},[886],[888,9174,9175],{"xmlns":890},[892,9176,9177,9185],{},[895,9178,9179],{},[2122,9180,9181,9183],{},[898,9182,3783],{},[898,9184,4101],{},[902,9186,8958],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,9189,9190],{},[38,9191,9192],{},"Znaménko závisí na povaze alternativního zboží:",[120,9194,9195,9283],{},[123,9196,9197,9198,9201,9202,9219,9220,2053,9233,1734],{},"Je-li alternativní zboží ",[38,9199,9200],{},"komplement",", růst ",[883,9203,9205],{"className":9204},[886],[888,9206,9207],{"xmlns":890},[892,9208,9209,9217],{},[895,9210,9211],{},[2122,9212,9213,9215],{},[898,9214,3783],{},[898,9216,4101],{},[902,9218,8958],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,9221,9223],{"className":9222},[886],[888,9224,9225],{"xmlns":890},[892,9226,9227,9231],{},[895,9228,9229],{},[898,9230,2638],{},[902,9232,2638],{"encoding":904},[883,9234,9236],{"className":9235},[886],[888,9237,9238],{"xmlns":890},[892,9239,9240,9280],{},[895,9241,9242,9244,9246,9258,9260,9262,9264,9266,9276,9278],{},[1846,9243,3833],{},[2138,9245,3830],{},[9012,9247,9248,9250,9256],{},[898,9249,2638],{},[2122,9251,9252,9254],{},[898,9253,3783],{},[898,9255,4101],{},[1846,9257,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,9259,3295],{},[1979,9261,2177],{},[1846,9263,2136],{"separator":2135},[2138,9265,3830],{},[2122,9267,9268,9270],{},[898,9269,4098],{},[2122,9271,9272,9274],{},[898,9273,3783],{},[898,9275,4101],{},[1846,9277,3295],{},[1979,9279,2177],{},[902,9281,9282],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,9284,9197,9285,9201,9288,9305,9306,9319,9320,1734],{},[38,9286,9287],{},"substitut",[883,9289,9291],{"className":9290},[886],[888,9292,9293],{"xmlns":890},[892,9294,9295,9303],{},[895,9296,9297],{},[2122,9298,9299,9301],{},[898,9300,3783],{},[898,9302,4101],{},[902,9304,8958],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,9307,9309],{"className":9308},[886],[888,9310,9311],{"xmlns":890},[892,9312,9313,9317],{},[895,9314,9315],{},[898,9316,2638],{},[902,9318,2638],{"encoding":904}," roste ",[883,9321,9323],{"className":9322},[886],[888,9324,9325],{"xmlns":890},[892,9326,9327,9367],{},[895,9328,9329,9331,9333,9345,9347,9349,9351,9353,9363,9365],{},[1846,9330,3833],{},[2138,9332,3830],{},[9012,9334,9335,9337,9343],{},[898,9336,2638],{},[2122,9338,9339,9341],{},[898,9340,3783],{},[898,9342,4101],{},[1846,9344,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,9346,3256],{},[1979,9348,2177],{},[1846,9350,2136],{"separator":2135},[2138,9352,3830],{},[2122,9354,9355,9357],{},[898,9356,4098],{},[2122,9358,9359,9361],{},[898,9360,3783],{},[898,9362,4101],{},[1846,9364,3256],{},[1979,9366,2177],{},[902,9368,9369],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,9371,9374],{"className":9372,"title":9373,"style":4047},[4045],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":9376},[9377,9381,9382,9390,9391,9395,9398],{"id":3736,"depth":642,"text":3737,"children":9378},[9379,9380],{"id":3767,"depth":649,"text":3768},{"id":3948,"depth":649,"text":3949},{"id":3983,"depth":642,"text":3984},{"id":4009,"depth":642,"text":4010,"children":9383},[9384,9385,9386,9387,9389],{"id":4705,"depth":649,"text":4706},{"id":4795,"depth":649,"text":4796},{"id":5131,"depth":649,"text":5132},{"id":5213,"depth":649,"text":9388},"Výpočet, je-li dáno PP jako funkce QQ",{"id":5474,"depth":649,"text":5475},{"id":5799,"depth":642,"text":5800},{"id":6395,"depth":642,"text":6396,"children":9392},[9393,9394],{"id":7024,"depth":649,"text":7025},{"id":7853,"depth":649,"text":7854},{"id":8487,"depth":642,"text":8488,"children":9396},[9397],{"id":8613,"depth":649,"text":8614},{"id":8902,"depth":642,"text":8903,"children":9399},[9400,9401],{"id":8992,"depth":649,"text":8993},{"id":9144,"depth":649,"text":9145},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":3707,"description":641},[1138,1136],"topics\u002Felasticita",[1128,3743,9409,9410,9411,9412],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":9415,"title":9416,"body":9417,"course":1128,"courses":659,"created":1129,"description":10958,"extension":661,"meta":10959,"navigation":664,"path":10960,"seo":10961,"sources":10962,"stem":10963,"tags":10964,"type":3703,"updated":677,"__hash__":10969},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":9418,"toc":10943},[9419,9422,9496,9503,9507,9571,9660,9664,9691,9758,9813,9817,9844,9937,9939,9971,10142,10146,10216,10264,10268,10329,10435,10450,10454,10456,10484,10549,10551,10558,10646,10671,10869,10873,10909,10911],[12,9420,9416],{"id":9421},"kalkul-funkcí-více-proměnných",[724,9423,9424,9425,9428,9429,1343,9458,1734],{},"Většina ekonomických veličin závisí na ",[38,9426,9427],{},"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 ",[883,9430,9432],{"className":9431},[886],[888,9433,9434],{"xmlns":890},[892,9435,9436,9455],{},[895,9437,9438,9441,9443,9445,9447,9449,9451,9453],{},[898,9439,9440],{},"z",[1846,9442,1848],{},[898,9444,1851],{},[1846,9446,1855],{"stretchy":1854},[898,9448,1858],{},[1846,9450,2136],{"separator":2135},[898,9452,1844],{},[1846,9454,1861],{"stretchy":1854},[902,9456,9457],{"encoding":904},"z = f(x, y)",[883,9459,9461],{"className":9460},[886],[888,9462,9463],{"xmlns":890},[892,9464,9465,9493],{},[895,9466,9467,9470,9472,9474,9476,9478,9480,9482,9484,9486,9488,9490],{},[898,9468,9469],{},"w",[1846,9471,1848],{},[898,9473,1851],{},[1846,9475,1855],{"stretchy":1854},[898,9477,1858],{},[1846,9479,2136],{"separator":2135},[898,9481,1844],{},[1846,9483,2136],{"separator":2135},[898,9485,9440],{},[1846,9487,1861],{"stretchy":1854},[1846,9489,2136],{"separator":2135},[1846,9491,9492],{},"…",[902,9494,9495],{"encoding":904},"w = f(x, y, z), \\ldots",[724,9497,9498],{},[2409,9499],{"alt":9500,"className":9501,"src":9502},"imek-funkce-2d-vrstevnice",[210,2413],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,9504,9506],{"id":9505},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,9508,9509,9510,9537,9538,9566,9567,9570],{},"Pro ",[883,9511,9513],{"className":9512},[886],[888,9514,9515],{"xmlns":890},[892,9516,9517,9535],{},[895,9518,9519,9521,9523,9525,9527,9529,9531,9533],{},[898,9520,9440],{},[1846,9522,1848],{},[898,9524,1851],{},[1846,9526,1855],{"stretchy":1854},[898,9528,1858],{},[1846,9530,2136],{"separator":2135},[898,9532,1844],{},[1846,9534,1861],{"stretchy":1854},[902,9536,9457],{"encoding":904}," se křivkou s předpisem ",[883,9539,9541],{"className":9540},[886],[888,9542,9543],{"xmlns":890},[892,9544,9545,9563],{},[895,9546,9547,9549,9551,9553,9555,9557,9559,9561],{},[898,9548,1851],{},[1846,9550,1855],{"stretchy":1854},[898,9552,1858],{},[1846,9554,2136],{"separator":2135},[898,9556,1844],{},[1846,9558,1861],{"stretchy":1854},[1846,9560,1848],{},[898,9562,1992],{},[902,9564,9565],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,9568,9569],{},"vrstevnice"," funkce. V ekonomii:",[120,9572,9573,9620],{},[123,9574,9575,9578,9579,9615,9616,1734],{},[38,9576,9577],{},"Indiferenční křivky"," užitečnosti ",[883,9580,9582],{"className":9581},[886],[888,9583,9584],{"xmlns":890},[892,9585,9586,9612],{},[895,9587,9588,9590,9592,9598,9600,9606,9608,9610],{},[898,9589,900],{},[1846,9591,1855],{"stretchy":1854},[2122,9593,9594,9596],{},[898,9595,2638],{},[1979,9597,2128],{},[1846,9599,2136],{"separator":2135},[2122,9601,9602,9604],{},[898,9603,2638],{},[1979,9605,1981],{},[1846,9607,1861],{"stretchy":1854},[1846,9609,1848],{},[898,9611,1992],{},[902,9613,9614],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,9617,9619],{"className":9618,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,9621,9622,9625,9626,9615,9656,1734],{},[38,9623,9624],{},"Izokvanty"," produkce ",[883,9627,9629],{"className":9628},[886],[888,9630,9631],{"xmlns":890},[892,9632,9633,9653],{},[895,9634,9635,9637,9639,9642,9644,9647,9649,9651],{},[898,9636,2638],{},[1846,9638,1855],{"stretchy":1854},[898,9640,9641],{},"L",[1846,9643,2136],{"separator":2135},[898,9645,9646],{},"K",[1846,9648,1861],{"stretchy":1854},[1846,9650,1848],{},[898,9652,1992],{},[902,9654,9655],{"encoding":904},"Q(L, K) = c",[207,9657,9659],{"className":9658,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,9661,9663],{"id":9662},"parciální-derivace","Parciální derivace",[724,9665,9509,9666,9690],{},[883,9667,9669],{"className":9668},[886],[888,9670,9671],{"xmlns":890},[892,9672,9673,9687],{},[895,9674,9675,9677,9679,9681,9683,9685],{},[898,9676,1851],{},[1846,9678,1855],{"stretchy":1854},[898,9680,1858],{},[1846,9682,2136],{"separator":2135},[898,9684,1844],{},[1846,9686,1861],{"stretchy":1854},[902,9688,9689],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,9692,9693],{},[883,9694,9696],{"className":9695},[886],[888,9697,9698],{"xmlns":890},[892,9699,9700,9755],{},[895,9701,9702,9710,9712,9727,9729,9731,9739,9741],{},[9012,9703,9704,9706,9708],{},[898,9705,1851],{},[898,9707,1858],{},[1846,9709,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,9711,1848],{},[2179,9713,9714,9721],{},[895,9715,9716,9719],{},[898,9717,9718],{"mathvariant":2226},"∂",[898,9720,1851],{},[895,9722,9723,9725],{},[898,9724,9718],{"mathvariant":2226},[898,9726,1858],{},[1846,9728,2136],{"separator":2135},[5724,9730],{"width":5726},[9012,9732,9733,9735,9737],{},[898,9734,1851],{},[898,9736,1844],{},[1846,9738,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,9740,1848],{},[2179,9742,9743,9749],{},[895,9744,9745,9747],{},[898,9746,9718],{"mathvariant":2226},[898,9748,1851],{},[895,9750,9751,9753],{},[898,9752,9718],{"mathvariant":2226},[898,9754,1844],{},[902,9756,9757],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,9759,9760,9761,1734],{},"Hodnoty v bodě: ",[883,9762,9764],{"className":9763},[886],[888,9765,9766],{"xmlns":890},[892,9767,9768,9810],{},[895,9769,9770,9778,9780,9782,9784,9786,9788,9790,9792,9800,9802,9804,9806,9808],{},[9012,9771,9772,9774,9776],{},[898,9773,1851],{},[898,9775,1858],{},[1846,9777,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,9779,1855],{"stretchy":1854},[898,9781,207],{},[1846,9783,2136],{"separator":2135},[898,9785,1948],{},[1846,9787,1861],{"stretchy":1854},[1846,9789,2136],{"separator":2135},[2138,9791,2140],{},[9012,9793,9794,9796,9798],{},[898,9795,1851],{},[898,9797,1844],{},[1846,9799,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,9801,1855],{"stretchy":1854},[898,9803,207],{},[1846,9805,2136],{"separator":2135},[898,9807,1948],{},[1846,9809,1861],{"stretchy":1854},[902,9811,9812],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,9814,9816],{"id":9815},"ekonomické-značení","Ekonomické značení",[724,9818,9819,9820,2554],{},"Pro produkční funkci ",[883,9821,9823],{"className":9822},[886],[888,9824,9825],{"xmlns":890},[892,9826,9827,9841],{},[895,9828,9829,9831,9833,9835,9837,9839],{},[898,9830,2638],{},[1846,9832,1855],{"stretchy":1854},[898,9834,9641],{},[1846,9836,2136],{"separator":2135},[898,9838,9646],{},[1846,9840,1861],{"stretchy":1854},[902,9842,9843],{"encoding":904},"Q(L, K)",[120,9845,9846,9892],{},[123,9847,9848,2320,9868,9871,9872,1861],{},[883,9849,9851],{"className":9850},[886],[888,9852,9853],{"xmlns":890},[892,9854,9855,9865],{},[895,9856,9857],{},[9012,9858,9859,9861,9863],{},[898,9860,2638],{},[898,9862,9641],{},[1846,9864,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,9866,9867],{"encoding":904},"Q'_L",[38,9869,9870],{},"mezní produkt práce"," (",[883,9873,9875],{"className":9874},[886],[888,9876,9877],{"xmlns":890},[892,9878,9879,9889],{},[895,9880,9881,9883],{},[898,9882,2667],{},[2122,9884,9885,9887],{},[898,9886,3783],{},[898,9888,9641],{},[902,9890,9891],{"encoding":904},"MP_L",[123,9893,9894,2320,9914,9871,9917,1861],{},[883,9895,9897],{"className":9896},[886],[888,9898,9899],{"xmlns":890},[892,9900,9901,9911],{},[895,9902,9903],{},[9012,9904,9905,9907,9909],{},[898,9906,2638],{},[898,9908,9646],{},[1846,9910,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,9912,9913],{"encoding":904},"Q'_K",[38,9915,9916],{},"mezní produkt kapitálu",[883,9918,9920],{"className":9919},[886],[888,9921,9922],{"xmlns":890},[892,9923,9924,9934],{},[895,9925,9926,9928],{},[898,9927,2667],{},[2122,9929,9930,9932],{},[898,9931,3783],{},[898,9933,9646],{},[902,9935,9936],{"encoding":904},"MP_K",[198,9938,2418],{"id":2417},[724,9940,9941,2554],{},[883,9942,9944],{"className":9943},[886],[888,9945,9946],{"xmlns":890},[892,9947,9948,9968],{},[895,9949,9950,9958,9960,9962,9964,9966],{},[9012,9951,9952,9954,9956],{},[898,9953,1851],{},[898,9955,1858],{},[1846,9957,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,9959,1855],{"stretchy":1854},[898,9961,207],{},[1846,9963,2136],{"separator":2135},[898,9965,1948],{},[1846,9967,1861],{"stretchy":1854},[902,9969,9970],{"encoding":904},"f'_x(a, b)",[120,9972,9973,10031],{},[123,9974,9975,9976,9989,9990,10003,10004,10030],{},"rychlost změny ",[883,9977,9979],{"className":9978},[886],[888,9980,9981],{"xmlns":890},[892,9982,9983,9987],{},[895,9984,9985],{},[898,9986,1851],{},[902,9988,1851],{"encoding":904}," vůči ",[883,9991,9993],{"className":9992},[886],[888,9994,9995],{"xmlns":890},[892,9996,9997,10001],{},[895,9998,9999],{},[898,10000,1858],{},[902,10002,1858],{"encoding":904}," při ",[883,10005,10007],{"className":10006},[886],[888,10008,10009],{"xmlns":890},[892,10010,10011,10027],{},[895,10012,10013,10015,10017,10019,10021,10023,10025],{},[898,10014,1858],{},[1846,10016,1848],{},[898,10018,207],{},[1846,10020,2136],{"separator":2135},[898,10022,1844],{},[1846,10024,1848],{},[898,10026,1948],{},[902,10028,10029],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,10032,10033,10034,2507,10047,10060,10061,10079,10080,1734],{},"přibližná změna ",[883,10035,10037],{"className":10036},[886],[888,10038,10039],{"xmlns":890},[892,10040,10041,10045],{},[895,10042,10043],{},[898,10044,1851],{},[902,10046,1851],{"encoding":904},[883,10048,10050],{"className":10049},[886],[888,10051,10052],{"xmlns":890},[892,10053,10054,10058],{},[895,10055,10056],{},[898,10057,1858],{},[902,10059,1858],{"encoding":904}," o 1 (a pevném ",[883,10062,10064],{"className":10063},[886],[888,10065,10066],{"xmlns":890},[892,10067,10068,10076],{},[895,10069,10070,10072,10074],{},[898,10071,1844],{},[1846,10073,1848],{},[898,10075,1948],{},[902,10077,10078],{"encoding":904},"y = b","): ",[883,10081,10083],{"className":10082},[886],[888,10084,10085],{"xmlns":890},[892,10086,10087,10139],{},[895,10088,10089,10091,10093,10095,10097,10099,10101,10103,10105,10107,10109,10111,10113,10115,10117,10119,10121,10129,10131,10133,10135,10137],{},[898,10090,1851],{},[1846,10092,1855],{"stretchy":1854},[898,10094,207],{},[1846,10096,1945],{},[1979,10098,2128],{},[1846,10100,2136],{"separator":2135},[898,10102,1948],{},[1846,10104,1861],{"stretchy":1854},[1846,10106,1650],{},[898,10108,1851],{},[1846,10110,1855],{"stretchy":1854},[898,10112,207],{},[1846,10114,2136],{"separator":2135},[898,10116,1948],{},[1846,10118,1861],{"stretchy":1854},[1846,10120,1945],{},[9012,10122,10123,10125,10127],{},[898,10124,1851],{},[898,10126,1858],{},[1846,10128,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,10130,1855],{"stretchy":1854},[898,10132,207],{},[1846,10134,2136],{"separator":2135},[898,10136,1948],{},[1846,10138,1861],{"stretchy":1854},[902,10140,10141],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,10143,10145],{"id":10144},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,10147,10148],{},[883,10149,10151],{"className":10150},[886],[888,10152,10153],{"xmlns":890},[892,10154,10155,10213],{},[895,10156,10157,10159,10161,10163,10171,10173,10175,10177,10179,10181,10183,10185,10187,10189,10197,10199,10201,10203,10205,10207,10209,10211],{},[898,10158,2044],{},[898,10160,1851],{},[1846,10162,1848],{},[9012,10164,10165,10167,10169],{},[898,10166,1851],{},[898,10168,1858],{},[1846,10170,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,10172,1855],{"stretchy":1854},[898,10174,1858],{},[1846,10176,2136],{"separator":2135},[898,10178,1844],{},[1846,10180,1861],{"stretchy":1854},[2138,10182,2835],{},[898,10184,2044],{},[898,10186,1858],{},[1846,10188,1945],{},[9012,10190,10191,10193,10195],{},[898,10192,1851],{},[898,10194,1844],{},[1846,10196,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,10198,1855],{"stretchy":1854},[898,10200,1858],{},[1846,10202,2136],{"separator":2135},[898,10204,1844],{},[1846,10206,1861],{"stretchy":1854},[2138,10208,2835],{},[898,10210,2044],{},[898,10212,1844],{},[902,10214,10215],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,10217,2845,10218,10240,10241,10263],{},[883,10219,10221],{"className":10220},[886],[888,10222,10223],{"xmlns":890},[892,10224,10225,10237],{},[895,10226,10227,10229,10231,10233,10235],{},[898,10228,2044],{},[898,10230,1858],{},[1846,10232,2136],{"separator":2135},[898,10234,2044],{},[898,10236,1844],{},[902,10238,10239],{"encoding":904},"dx, dy"," platí ",[883,10242,10244],{"className":10243},[886],[888,10245,10246],{"xmlns":890},[892,10247,10248,10260],{},[895,10249,10250,10252,10254,10256,10258],{},[898,10251,2738],{"mathvariant":2226},[898,10253,1851],{},[1846,10255,1650],{},[898,10257,2044],{},[898,10259,1851],{},[902,10261,10262],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,10265,10267],{"id":10266},"implicitní-funkce","Implicitní funkce",[724,10269,10270,10271,10300,10301,10314,10315,10328],{},"Je-li vztah dán rovnicí ",[883,10272,10274],{"className":10273},[886],[888,10275,10276],{"xmlns":890},[892,10277,10278,10297],{},[895,10279,10280,10283,10285,10287,10289,10291,10293,10295],{},[898,10281,10282],{},"F",[1846,10284,1855],{"stretchy":1854},[898,10286,1858],{},[1846,10288,2136],{"separator":2135},[898,10290,1844],{},[1846,10292,1861],{"stretchy":1854},[1846,10294,1848],{},[1979,10296,2177],{},[902,10298,10299],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,10302,10304],{"className":10303},[886],[888,10305,10306],{"xmlns":890},[892,10307,10308,10312],{},[895,10309,10310],{},[898,10311,1844],{},[902,10313,1844],{"encoding":904}," podle ",[883,10316,10318],{"className":10317},[886],[888,10319,10320],{"xmlns":890},[892,10321,10322,10326],{},[895,10323,10324],{},[898,10325,1858],{},[902,10327,1858],{"encoding":904}," (nebo naopak):",[724,10330,10331],{},[883,10332,10334],{"className":10333},[886],[888,10335,10336],{"xmlns":890},[892,10337,10338,10432],{},[895,10339,10340,10346,10348,10362,10364,10366,10384,10386,10388,10394,10396,10410,10412,10414],{},[1974,10341,10342,10344],{},[898,10343,1844],{},[1846,10345,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,10347,1848],{},[2179,10349,10350,10356],{},[895,10351,10352,10354],{},[898,10353,2044],{},[898,10355,1844],{},[895,10357,10358,10360],{},[898,10359,2044],{},[898,10361,1858],{},[1846,10363,1848],{},[1846,10365,2075],{},[2179,10367,10368,10376],{},[9012,10369,10370,10372,10374],{},[898,10371,10282],{},[898,10373,1858],{},[1846,10375,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[9012,10377,10378,10380,10382],{},[898,10379,10282],{},[898,10381,1844],{},[1846,10383,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,10385,2136],{"separator":2135},[5724,10387],{"width":5726},[1974,10389,10390,10392],{},[898,10391,1858],{},[1846,10393,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,10395,1848],{},[2179,10397,10398,10404],{},[895,10399,10400,10402],{},[898,10401,2044],{},[898,10403,1858],{},[895,10405,10406,10408],{},[898,10407,2044],{},[898,10409,1844],{},[1846,10411,1848],{},[1846,10413,2075],{},[2179,10415,10416,10424],{},[9012,10417,10418,10420,10422],{},[898,10419,10282],{},[898,10421,1844],{},[1846,10423,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[9012,10425,10426,10428,10430],{},[898,10427,10282],{},[898,10429,1858],{},[1846,10431,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,10433,10434],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,10436,10437,10438,10441,10442,1745,10446,1734],{},"Tato vzorec dává ",[38,10439,10440],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,10443,10445],{"className":10444,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,10447,10449],{"className":10448,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,10451,10453],{"id":10452},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,10455,3100],{"id":3099},[724,10457,10458,10459,10483],{},"V bodě extrému ",[883,10460,10462],{"className":10461},[886],[888,10463,10464],{"xmlns":890},[892,10465,10466,10480],{},[895,10467,10468,10470,10472,10474,10476,10478],{},[898,10469,4101],{},[1846,10471,2336],{"stretchy":1854},[898,10473,207],{},[1846,10475,2136],{"separator":2135},[898,10477,1948],{},[1846,10479,2351],{"stretchy":1854},[902,10481,10482],{"encoding":904},"A[a, b]"," musí platit současně:",[724,10485,10486],{},[883,10487,10489],{"className":10488},[886],[888,10490,10491],{"xmlns":890},[892,10492,10493,10546],{},[895,10494,10495,10503,10505,10507,10509,10511,10513,10515,10517,10519,10522,10524,10532,10534,10536,10538,10540,10542,10544],{},[9012,10496,10497,10499,10501],{},[898,10498,1851],{},[898,10500,1858],{},[1846,10502,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,10504,1855],{"stretchy":1854},[898,10506,207],{},[1846,10508,2136],{"separator":2135},[898,10510,1948],{},[1846,10512,1861],{"stretchy":1854},[1846,10514,1848],{},[1979,10516,2177],{},[2138,10518,3830],{},[1846,10520,10521],{},"∧",[2138,10523,3830],{},[9012,10525,10526,10528,10530],{},[898,10527,1851],{},[898,10529,1844],{},[1846,10531,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,10533,1855],{"stretchy":1854},[898,10535,207],{},[1846,10537,2136],{"separator":2135},[898,10539,1948],{},[1846,10541,1861],{"stretchy":1854},[1846,10543,1848],{},[1979,10545,2177],{},[902,10547,10548],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,10550,3174],{"id":3173},[724,10552,10553,10554,10557],{},"Definujeme ",[38,10555,10556],{},"diskriminant"," (Hessián zjednodušeně):",[724,10559,10560],{},[883,10561,10563],{"className":10562},[886],[888,10564,10565],{"xmlns":890},[892,10566,10567,10643],{},[895,10568,10569,10571,10573,10575,10577,10579,10581,10583,10599,10601,10617,10619,10621,10637],{},[898,10570,4029],{},[1846,10572,1855],{"stretchy":1854},[898,10574,1858],{},[1846,10576,2136],{"separator":2135},[898,10578,1844],{},[1846,10580,1861],{"stretchy":1854},[1846,10582,1848],{},[9012,10584,10585,10587,10593],{},[898,10586,1851],{},[895,10588,10589,10591],{},[898,10590,1858],{},[898,10592,1858],{},[895,10594,10595,10597],{},[1846,10596,2228],{"mathvariant":2226},[1846,10598,2228],{"mathvariant":2226},[1846,10600,3025],{},[9012,10602,10603,10605,10611],{},[898,10604,1851],{},[895,10606,10607,10609],{},[898,10608,1844],{},[898,10610,1844],{},[895,10612,10613,10615],{},[1846,10614,2228],{"mathvariant":2226},[1846,10616,2228],{"mathvariant":2226},[1846,10618,2075],{},[1846,10620,1855],{"stretchy":1854},[9012,10622,10623,10625,10631],{},[898,10624,1851],{},[895,10626,10627,10629],{},[898,10628,1858],{},[898,10630,1844],{},[895,10632,10633,10635],{},[1846,10634,2228],{"mathvariant":2226},[1846,10636,2228],{"mathvariant":2226},[1974,10638,10639,10641],{},[1846,10640,1861],{"stretchy":1854},[1979,10642,1981],{},[902,10644,10645],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,10647,10648,10649,2554],{},"V podezřelém bodě ",[883,10650,10652],{"className":10651},[886],[888,10653,10654],{"xmlns":890},[892,10655,10656,10668],{},[895,10657,10658,10660,10662,10664,10666],{},[1846,10659,2336],{"stretchy":1854},[898,10661,207],{},[1846,10663,2136],{"separator":2135},[898,10665,1948],{},[1846,10667,2351],{"stretchy":1854},[902,10669,10670],{"encoding":904},"[a, b]",[152,10672,10673,10800,10836],{},[123,10674,10675,10705,10706],{},[38,10676,10677,2554],{},[883,10678,10680],{"className":10679},[886],[888,10681,10682],{"xmlns":890},[892,10683,10684,10702],{},[895,10685,10686,10688,10690,10692,10694,10696,10698,10700],{},[898,10687,4029],{},[1846,10689,1855],{"stretchy":1854},[898,10691,207],{},[1846,10693,2136],{"separator":2135},[898,10695,1948],{},[1846,10697,1861],{"stretchy":1854},[1846,10699,3256],{},[1979,10701,2177],{},[902,10703,10704],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,10707,10708,10754],{},[123,10709,10710,3262,10752],{},[883,10711,10713],{"className":10712},[886],[888,10714,10715],{"xmlns":890},[892,10716,10717,10749],{},[895,10718,10719,10735,10737,10739,10741,10743,10745,10747],{},[9012,10720,10721,10723,10729],{},[898,10722,1851],{},[895,10724,10725,10727],{},[898,10726,1858],{},[898,10728,1858],{},[895,10730,10731,10733],{},[1846,10732,2228],{"mathvariant":2226},[1846,10734,2228],{"mathvariant":2226},[1846,10736,1855],{"stretchy":1854},[898,10738,207],{},[1846,10740,2136],{"separator":2135},[898,10742,1948],{},[1846,10744,1861],{"stretchy":1854},[1846,10746,3256],{},[1979,10748,2177],{},[902,10750,10751],{"encoding":904},"f''_{xx}(a, b) > 0",[38,10753,3623],{},[123,10755,10756,3262,10798],{},[883,10757,10759],{"className":10758},[886],[888,10760,10761],{"xmlns":890},[892,10762,10763,10795],{},[895,10764,10765,10781,10783,10785,10787,10789,10791,10793],{},[9012,10766,10767,10769,10775],{},[898,10768,1851],{},[895,10770,10771,10773],{},[898,10772,1858],{},[898,10774,1858],{},[895,10776,10777,10779],{},[1846,10778,2228],{"mathvariant":2226},[1846,10780,2228],{"mathvariant":2226},[1846,10782,1855],{"stretchy":1854},[898,10784,207],{},[1846,10786,2136],{"separator":2135},[898,10788,1948],{},[1846,10790,1861],{"stretchy":1854},[1846,10792,3295],{},[1979,10794,2177],{},[902,10796,10797],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,10799,3565],{},[123,10801,10802,2053,10832,10835],{},[38,10803,10804,2554],{},[883,10805,10807],{"className":10806},[886],[888,10808,10809],{"xmlns":890},[892,10810,10811,10829],{},[895,10812,10813,10815,10817,10819,10821,10823,10825,10827],{},[898,10814,4029],{},[1846,10816,1855],{"stretchy":1854},[898,10818,207],{},[1846,10820,2136],{"separator":2135},[898,10822,1948],{},[1846,10824,1861],{"stretchy":1854},[1846,10826,3295],{},[1979,10828,2177],{},[902,10830,10831],{"encoding":904},"D(a, b) \u003C 0",[38,10833,10834],{},"sedlo"," (v daném bodě extrém není).",[123,10837,10838,10868],{},[38,10839,10840,2554],{},[883,10841,10843],{"className":10842},[886],[888,10844,10845],{"xmlns":890},[892,10846,10847,10865],{},[895,10848,10849,10851,10853,10855,10857,10859,10861,10863],{},[898,10850,4029],{},[1846,10852,1855],{"stretchy":1854},[898,10854,207],{},[1846,10856,2136],{"separator":2135},[898,10858,1948],{},[1846,10860,1861],{"stretchy":1854},[1846,10862,1848],{},[1979,10864,2177],{},[902,10866,10867],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,10870,10872],{"id":10871},"vázané-extrémy","Vázané extrémy",[724,10874,10875,10876,10905,10906,1734],{},"Pro extrémy s omezující podmínkou ",[883,10877,10879],{"className":10878},[886],[888,10880,10881],{"xmlns":890},[892,10882,10883,10902],{},[895,10884,10885,10888,10890,10892,10894,10896,10898,10900],{},[898,10886,10887],{},"g",[1846,10889,1855],{"stretchy":1854},[898,10891,1858],{},[1846,10893,2136],{"separator":2135},[898,10895,1844],{},[1846,10897,1861],{"stretchy":1854},[1846,10899,1848],{},[1979,10901,2177],{},[902,10903,10904],{"encoding":904},"g(x, y) = 0"," se používá ",[207,10907,793],{"className":10908,"dataFsResolvedFilePath":791,"href":792},[210],[115,10910,3640],{"id":3639},[120,10912,10913,10920,10927],{},[123,10914,10915,2053,10917],{},[38,10916,3647],{},[207,10918,775],{"className":10919,"dataFsResolvedFilePath":773,"href":774},[210],[123,10921,10922,2053,10924],{},[38,10923,3655],{},[207,10925,793],{"className":10926,"dataFsResolvedFilePath":791,"href":792},[210],[123,10928,10929,2053,10931,10934,10935,10938,10939,10942],{},[38,10930,3663],{},[207,10932,1728],{"className":10933,"dataFsResolvedFilePath":857,"href":858},[210]," (parciální derivace = mezní produkty), ",[207,10936,880],{"className":10937,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,10940,1721],{"className":10941,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":10944},[10945,10946,10950,10951,10952,10956,10957],{"id":9505,"depth":642,"text":9506},{"id":9662,"depth":642,"text":9663,"children":10947},[10948,10949],{"id":9815,"depth":649,"text":9816},{"id":2417,"depth":649,"text":2418},{"id":10144,"depth":642,"text":10145},{"id":10266,"depth":642,"text":10267},{"id":10452,"depth":642,"text":10453,"children":10953},[10954,10955],{"id":3099,"depth":649,"text":3100},{"id":3173,"depth":649,"text":3174},{"id":10871,"depth":642,"text":10872},{"id":3639,"depth":642,"text":3640},"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":9416,"description":10958},[1135],"topics\u002Ffunkce-vice-promennych",[1128,10965,3700,10966,10967,10968],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":10971,"title":775,"body":10972,"course":1128,"courses":659,"created":1129,"description":11827,"extension":661,"meta":11828,"navigation":664,"path":11829,"seo":11830,"sources":11831,"stem":11832,"tags":11833,"type":3703,"updated":677,"__hash__":11839},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":10973,"toc":11817},[10974,10977,10988,10992,11037,11117,11121,11197,11239,11246,11250,11254,11283,11341,11388,11426,11430,11480,11532,11584,11628,11631,11634,11706,11709,11781,11787,11789],[12,10975,775],{"id":10976},"integrál",[724,10978,10979,10980,10983,10984,10987],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,10981,10982],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,10985,10986],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,10989,10991],{"id":10990},"neurčitý-integrál","Neurčitý integrál",[724,10993,10994],{},[883,10995,10997],{"className":10996},[886],[888,10998,10999],{"xmlns":890},[892,11000,11001,11034],{},[895,11002,11003,11005,11007,11009,11011,11013,11016,11018,11020,11022,11024,11026,11028,11030,11032],{},[898,11004,10282],{},[1846,11006,1855],{"stretchy":1854},[898,11008,1858],{},[1846,11010,1861],{"stretchy":1854},[1846,11012,1848],{},[1846,11014,11015],{},"∫",[898,11017,1851],{},[1846,11019,1855],{"stretchy":1854},[898,11021,1858],{},[1846,11023,1861],{"stretchy":1854},[2138,11025,2835],{},[898,11027,2044],{},[898,11029,1858],{},[1846,11031,1945],{},[898,11033,2626],{},[902,11035,11036],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,11038,4156,11039,2776,11073,7948,11086,11089,11090,1343,11103,11116],{},[883,11040,11042],{"className":11041},[886],[888,11043,11044],{"xmlns":890},[892,11045,11046,11070],{},[895,11047,11048,11054,11056,11058,11060,11062,11064,11066,11068],{},[1974,11049,11050,11052],{},[898,11051,10282],{},[1846,11053,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,11055,1855],{"stretchy":1854},[898,11057,1858],{},[1846,11059,1861],{"stretchy":1854},[1846,11061,1848],{},[898,11063,1851],{},[1846,11065,1855],{"stretchy":1854},[898,11067,1858],{},[1846,11069,1861],{"stretchy":1854},[902,11071,11072],{"encoding":904},"F'(x) = f(x)",[883,11074,11076],{"className":11075},[886],[888,11077,11078],{"xmlns":890},[892,11079,11080,11084],{},[895,11081,11082],{},[898,11083,10282],{},[902,11085,10282],{"encoding":904},[38,11087,11088],{},"primitivní funkce"," k ",[883,11091,11093],{"className":11092},[886],[888,11094,11095],{"xmlns":890},[892,11096,11097,11101],{},[895,11098,11099],{},[898,11100,1851],{},[902,11102,1851],{"encoding":904},[883,11104,11106],{"className":11105},[886],[888,11107,11108],{"xmlns":890},[892,11109,11110,11114],{},[895,11111,11112],{},[898,11113,2626],{},[902,11115,2626],{"encoding":904}," konstanta.",[115,11118,11120],{"id":11119},"určitý-integrál","Určitý integrál",[724,11122,11123],{},[883,11124,11126],{"className":11125},[886],[888,11127,11128],{"xmlns":890},[892,11129,11130,11194],{},[895,11131,11132,11140,11142,11144,11146,11148,11150,11152,11154,11156,11158,11160,11162,11164,11166,11174,11176,11178,11180,11182,11184,11186,11188,11190,11192],{},[9012,11133,11134,11136,11138],{},[1846,11135,11015],{},[898,11137,207],{},[898,11139,1948],{},[898,11141,1851],{},[1846,11143,1855],{"stretchy":1854},[898,11145,1858],{},[1846,11147,1861],{"stretchy":1854},[2138,11149,2835],{},[898,11151,2044],{},[898,11153,1858],{},[1846,11155,1848],{},[1846,11157,2336],{"stretchy":1854},[898,11159,10282],{},[1846,11161,1855],{"stretchy":1854},[898,11163,1858],{},[1846,11165,1861],{"stretchy":1854},[9012,11167,11168,11170,11172],{},[1846,11169,2351],{"stretchy":1854},[898,11171,207],{},[898,11173,1948],{},[1846,11175,1848],{},[898,11177,10282],{},[1846,11179,1855],{"stretchy":1854},[898,11181,1948],{},[1846,11183,1861],{"stretchy":1854},[1846,11185,2075],{},[898,11187,10282],{},[1846,11189,1855],{"stretchy":1854},[898,11191,207],{},[1846,11193,1861],{"stretchy":1854},[902,11195,11196],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,11198,11199,11200,2053,11203,11216,11217,11238],{},"Geometricky ",[38,11201,11202],{},"plocha pod grafem",[883,11204,11206],{"className":11205},[886],[888,11207,11208],{"xmlns":890},[892,11209,11210,11214],{},[895,11211,11212],{},[898,11213,1851],{},[902,11215,1851],{"encoding":904}," na intervalu ",[883,11218,11220],{"className":11219},[886],[888,11221,11222],{"xmlns":890},[892,11223,11224,11236],{},[895,11225,11226,11228,11230,11232,11234],{},[1846,11227,2336],{"stretchy":1854},[898,11229,207],{},[1846,11231,2136],{"separator":2135},[898,11233,1948],{},[1846,11235,2351],{"stretchy":1854},[902,11237,10670],{"encoding":904}," (orientovaná).",[724,11240,11241],{},[2409,11242],{"alt":11243,"className":11244,"src":11245},"imek-integral-plocha",[210,2413],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,11247,11249],{"id":11248},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,11251,11253],{"id":11252},"příklad-tr-z-mr","Příklad — TR z MR",[724,11255,11256,11257,1734],{},"Mezní příjem ",[883,11258,11260],{"className":11259},[886],[888,11261,11262],{"xmlns":890},[892,11263,11264,11280],{},[895,11265,11266,11268,11270,11272,11274,11276,11278],{},[898,11267,2667],{},[898,11269,3840],{},[1846,11271,1848],{},[1979,11273,2938],{},[1846,11275,2075],{},[1979,11277,1981],{},[898,11279,2638],{},[902,11281,11282],{"encoding":904},"MR = 100 - 2Q",[724,11284,11285],{},[883,11286,11288],{"className":11287},[886],[888,11289,11290],{"xmlns":890},[892,11291,11292,11338],{},[895,11293,11294,11296,11298,11300,11302,11304,11306,11308,11310,11312,11314,11316,11318,11320,11322,11324,11326,11328,11334,11336],{},[898,11295,2623],{},[898,11297,3840],{},[1846,11299,1848],{},[1846,11301,11015],{},[1846,11303,1855],{"stretchy":1854},[1979,11305,2938],{},[1846,11307,2075],{},[1979,11309,1981],{},[898,11311,2638],{},[1846,11313,1861],{"stretchy":1854},[2138,11315,2835],{},[898,11317,2044],{},[898,11319,2638],{},[1846,11321,1848],{},[1979,11323,2938],{},[898,11325,2638],{},[1846,11327,2075],{},[1974,11329,11330,11332],{},[898,11331,2638],{},[1979,11333,1981],{},[1846,11335,1945],{},[898,11337,1992],{},[902,11339,11340],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,11342,11343,11344,3262,11370,2554],{},"Okrajová podmínka ",[883,11345,11347],{"className":11346},[886],[888,11348,11349],{"xmlns":890},[892,11350,11351,11367],{},[895,11352,11353,11355,11357,11359,11361,11363,11365],{},[898,11354,2623],{},[898,11356,3840],{},[1846,11358,1855],{"stretchy":1854},[1979,11360,2177],{},[1846,11362,1861],{"stretchy":1854},[1846,11364,1848],{},[1979,11366,2177],{},[902,11368,11369],{"encoding":904},"TR(0) = 0",[883,11371,11373],{"className":11372},[886],[888,11374,11375],{"xmlns":890},[892,11376,11377,11385],{},[895,11378,11379,11381,11383],{},[898,11380,1992],{},[1846,11382,1848],{},[1979,11384,2177],{},[902,11386,11387],{"encoding":904},"c = 0",[724,11389,11390],{},[883,11391,11393],{"className":11392},[886],[888,11394,11395],{"xmlns":890},[892,11396,11397,11423],{},[895,11398,11399,11401,11403,11405,11407,11409,11411,11413,11415,11417],{},[898,11400,2623],{},[898,11402,3840],{},[1846,11404,1855],{"stretchy":1854},[898,11406,2638],{},[1846,11408,1861],{"stretchy":1854},[1846,11410,1848],{},[1979,11412,2938],{},[898,11414,2638],{},[1846,11416,2075],{},[1974,11418,11419,11421],{},[898,11420,2638],{},[1979,11422,1981],{},[902,11424,11425],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,11427,11429],{"id":11428},"příklad-tc-z-mc","Příklad — TC z MC",[724,11431,11432,11433,11459,11460,1734],{},"Mezní náklady ",[883,11434,11436],{"className":11435},[886],[888,11437,11438],{"xmlns":890},[892,11439,11440,11456],{},[895,11441,11442,11444,11446,11448,11450,11452,11454],{},[898,11443,2667],{},[898,11445,2626],{},[1846,11447,1848],{},[1979,11449,1981],{},[1846,11451,1945],{},[1979,11453,2688],{},[898,11455,2638],{},[902,11457,11458],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,11461,11463],{"className":11462},[886],[888,11464,11465],{"xmlns":890},[892,11466,11467,11477],{},[895,11468,11469,11471,11473,11475],{},[898,11470,10282],{},[898,11472,2626],{},[1846,11474,1848],{},[1979,11476,2938],{},[902,11478,11479],{"encoding":904},"FC = 100",[724,11481,11482],{},[883,11483,11485],{"className":11484},[886],[888,11486,11487],{"xmlns":890},[892,11488,11489,11529],{},[895,11490,11491,11493,11495,11497,11499,11501,11503,11505,11507,11509,11511,11513,11515,11517,11519,11525,11527],{},[898,11492,2623],{},[898,11494,2626],{},[1846,11496,1848],{},[1846,11498,11015],{},[898,11500,2667],{},[898,11502,2626],{},[2138,11504,2835],{},[898,11506,2044],{},[898,11508,2638],{},[1846,11510,1848],{},[1979,11512,1981],{},[898,11514,2638],{},[1846,11516,1945],{},[1979,11518,2643],{},[1974,11520,11521,11523],{},[898,11522,2638],{},[1979,11524,1981],{},[1846,11526,1945],{},[898,11528,1992],{},[902,11530,11531],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,11533,11343,11534,3262,11566,2554],{},[883,11535,11537],{"className":11536},[886],[888,11538,11539],{"xmlns":890},[892,11540,11541,11563],{},[895,11542,11543,11545,11547,11549,11551,11553,11555,11557,11559,11561],{},[898,11544,2623],{},[898,11546,2626],{},[1846,11548,1855],{"stretchy":1854},[1979,11550,2177],{},[1846,11552,1861],{"stretchy":1854},[1846,11554,1848],{},[898,11556,10282],{},[898,11558,2626],{},[1846,11560,1848],{},[1979,11562,2938],{},[902,11564,11565],{"encoding":904},"TC(0) = FC = 100",[883,11567,11569],{"className":11568},[886],[888,11570,11571],{"xmlns":890},[892,11572,11573,11581],{},[895,11574,11575,11577,11579],{},[898,11576,1992],{},[1846,11578,1848],{},[1979,11580,2938],{},[902,11582,11583],{"encoding":904},"c = 100",[724,11585,11586],{},[883,11587,11589],{"className":11588},[886],[888,11590,11591],{"xmlns":890},[892,11592,11593,11625],{},[895,11594,11595,11597,11599,11601,11603,11605,11607,11609,11611,11613,11615,11617,11619],{},[898,11596,2623],{},[898,11598,2626],{},[1846,11600,1855],{"stretchy":1854},[898,11602,2638],{},[1846,11604,1861],{"stretchy":1854},[1846,11606,1848],{},[1979,11608,2938],{},[1846,11610,1945],{},[1979,11612,1981],{},[898,11614,2638],{},[1846,11616,1945],{},[1979,11618,2643],{},[1974,11620,11621,11623],{},[898,11622,2638],{},[1979,11624,1981],{},[902,11626,11627],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,11629,820],{"id":11630},"přebytek-spotřebitele-a-výrobce",[724,11632,11633],{},"Přebytek spotřebitele:",[724,11635,11636],{},[883,11637,11639],{"className":11638},[886],[888,11640,11641],{"xmlns":890},[892,11642,11643,11703],{},[895,11644,11645,11647,11649,11651,11657,11659,11661,11673,11675,11677,11679,11681,11683,11685,11687,11689,11695,11697],{},[898,11646,2626],{},[898,11648,8519],{},[1846,11650,1855],{"stretchy":1854},[2122,11652,11653,11655],{},[898,11654,2638],{},[1979,11656,2177],{},[1846,11658,1861],{"stretchy":1854},[1846,11660,1848],{},[9012,11662,11663,11665,11667],{},[1846,11664,11015],{},[1979,11666,2177],{},[2122,11668,11669,11671],{},[898,11670,2638],{},[1979,11672,2177],{},[898,11674,4029],{},[1846,11676,1855],{"stretchy":1854},[898,11678,2638],{},[1846,11680,1861],{"stretchy":1854},[2138,11682,2835],{},[898,11684,2044],{},[898,11686,2638],{},[1846,11688,2075],{},[2122,11690,11691,11693],{},[898,11692,3783],{},[1979,11694,2177],{},[2138,11696,2835],{},[2122,11698,11699,11701],{},[898,11700,2638],{},[1979,11702,2177],{},[902,11704,11705],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,11707,11708],{},"Přebytek výrobce:",[724,11710,11711],{},[883,11712,11714],{"className":11713},[886],[888,11715,11716],{"xmlns":890},[892,11717,11718,11778],{},[895,11719,11720,11722,11724,11726,11732,11734,11736,11742,11744,11750,11752,11764,11766,11768,11770,11772,11774,11776],{},[898,11721,3783],{},[898,11723,8519],{},[1846,11725,1855],{"stretchy":1854},[2122,11727,11728,11730],{},[898,11729,2638],{},[1979,11731,2177],{},[1846,11733,1861],{"stretchy":1854},[1846,11735,1848],{},[2122,11737,11738,11740],{},[898,11739,3783],{},[1979,11741,2177],{},[2138,11743,2835],{},[2122,11745,11746,11748],{},[898,11747,2638],{},[1979,11749,2177],{},[1846,11751,2075],{},[9012,11753,11754,11756,11758],{},[1846,11755,11015],{},[1979,11757,2177],{},[2122,11759,11760,11762],{},[898,11761,2638],{},[1979,11763,2177],{},[898,11765,8519],{},[1846,11767,1855],{"stretchy":1854},[898,11769,2638],{},[1846,11771,1861],{"stretchy":1854},[2138,11773,2835],{},[898,11775,2044],{},[898,11777,2638],{},[902,11779,11780],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,11782,11783,11784,1734],{},"Detailně viz ",[207,11785,1701],{"className":11786,"dataFsResolvedFilePath":800,"href":801},[210],[115,11788,3640],{"id":3639},[120,11790,11791,11798,11805],{},[123,11792,11793,2053,11795],{},[38,11794,3647],{},[207,11796,766],{"className":11797,"dataFsResolvedFilePath":764,"href":765},[210],[123,11799,11800,2053,11802],{},[38,11801,3655],{},[207,11803,784],{"className":11804,"dataFsResolvedFilePath":782,"href":783},[210],[123,11806,11807,2053,11809,11812,11813,11816],{},[38,11808,3663],{},[207,11810,1708],{"className":11811,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,11814,1701],{"className":11815,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":11818},[11819,11820,11821,11826],{"id":10990,"depth":642,"text":10991},{"id":11119,"depth":642,"text":11120},{"id":11248,"depth":642,"text":11249,"children":11822},[11823,11824,11825],{"id":11252,"depth":649,"text":11253},{"id":11428,"depth":649,"text":11429},{"id":11630,"depth":649,"text":820},{"id":3639,"depth":642,"text":3640},"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":11827},[1135],"topics\u002Fintegral",[1128,1788,11834,11835,11836,11837,11838],"neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":11841,"title":11842,"body":11843,"course":1128,"courses":659,"created":9402,"description":641,"extension":661,"meta":16111,"navigation":664,"path":16112,"seo":16113,"sources":16114,"stem":16115,"tags":16116,"type":3703,"updated":677,"__hash__":16122},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":11844,"toc":16099},[11845,11848,11852,11996,12003,12007,12077,12115,12218,12222,12252,12318,12365,12368,12437,12440,12475,12511,12515,12563,12570,12616,12662,12665,12744,12841,12924,12928,12972,13002,13008,13037,13059,13109,13162,13228,13231,13297,13326,13385,13401,13488,13586,13717,13721,13878,14027,14407,14411,14414,14473,14476,14562,14590,14628,14631,14668,14708,14742,14744,14781,14813,14911,14916,15040,15092,15174,15313,15317,15437,15444,15555,15562,15566,16041,16043],[12,11846,11842],{"id":11847},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,11849,11851],{"id":11850},"tldr","TL;DR",[724,11853,11854,11857,11858,9871,11861,11874,11875,11889,11890,11893,11894,1343,11897,11900,11901,1343,11904,11907,11908,2053,11911,11941,11942,11945,11946,1343,11960,11973,11974,11977,11978,3764],{},[38,11855,11856],{},"IS-LM"," je makroekonomický model se ",[38,11859,11860],{},"dvěma neznámými",[883,11862,11864],{"className":11863},[886],[888,11865,11866],{"xmlns":890},[892,11867,11868,11872],{},[895,11869,11870],{},[898,11871,8974],{},[902,11873,8974],{"encoding":904}," — národní důchod a ",[883,11876,11878],{"className":11877},[886],[888,11879,11880],{"xmlns":890},[892,11881,11882,11887],{},[895,11883,11884],{},[898,11885,11886],{},"r",[902,11888,11886],{"encoding":904}," — úroková míra) a ",[38,11891,11892],{},"dvěma trhy",": trhem zboží (křivka ",[38,11895,11896],{},"IS",[614,11898,11899],{},"Investment = Savings",") a trhem peněz (křivka ",[38,11902,11903],{},"LM",[614,11905,11906],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,11909,11910],{},"simultánní rovnováhu",[883,11912,11914],{"className":11913},[886],[888,11915,11916],{"xmlns":890},[892,11917,11918,11938],{},[895,11919,11920,11922,11928,11930,11936],{},[1846,11921,1855],{"stretchy":1854},[1974,11923,11924,11926],{},[898,11925,8974],{},[898,11927,4098],{},[1846,11929,2136],{"separator":2135},[1974,11931,11932,11934],{},[898,11933,11886],{},[898,11935,4098],{},[1846,11937,1861],{"stretchy":1854},[902,11939,11940],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,11943,11944],{},"fiskální politiky"," (posun IS změnou ",[883,11947,11949],{"className":11948},[886],[888,11950,11951],{"xmlns":890},[892,11952,11953,11958],{},[895,11954,11955],{},[898,11956,11957],{},"G",[902,11959,11957],{"encoding":904},[883,11961,11963],{"className":11962},[886],[888,11964,11965],{"xmlns":890},[892,11966,11967,11971],{},[895,11968,11969],{},[898,11970,2623],{},[902,11972,2623],{"encoding":904},") a ",[38,11975,11976],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,11979,11981],{"className":11980},[886],[888,11982,11983],{"xmlns":890},[892,11984,11985,11993],{},[895,11986,11987],{},[1974,11988,11989,11991],{},[898,11990,2667],{},[1846,11992,4200],{},[902,11994,11995],{"encoding":904},"M^*",[724,11997,11998],{},[2409,11999],{"alt":12000,"className":12001,"src":12002},"imek-is-lm-model",[210,2413],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,12004,12006],{"id":12005},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,12008,12009,12010,12014,12015,9871,12018,12041,12042,12045,12046,12062,12063,12076],{},"V modelech ",[207,12011,12013],{"className":12012,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,12016,12017],{},"investice pokládány za konstantní",[883,12019,12021],{"className":12020},[886],[888,12022,12023],{"xmlns":890},[892,12024,12025,12038],{},[895,12026,12027,12030,12032],{},[898,12028,12029],{},"I",[1846,12031,1848],{},[1974,12033,12034,12036],{},[898,12035,12029],{},[1846,12037,4200],{},[902,12039,12040],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,12043,12044],{},"ceně peněz",", tedy na ",[38,12047,12048,12049],{},"úrokové míře ",[883,12050,12052],{"className":12051},[886],[888,12053,12054],{"xmlns":890},[892,12055,12056,12060],{},[895,12057,12058],{},[898,12059,11886],{},[902,12061,11886],{"encoding":904},": čím vyšší ",[883,12064,12066],{"className":12065},[886],[888,12067,12068],{"xmlns":890},[892,12069,12070,12074],{},[895,12071,12072],{},[898,12073,11886],{},[902,12075,11886],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,12078,12079,12109],{},[123,12080,12081,2053,12084,12108],{},[38,12082,12083],{},"funkci investic",[883,12085,12087],{"className":12086},[886],[888,12088,12089],{"xmlns":890},[892,12090,12091,12105],{},[895,12092,12093,12095,12097,12099,12101,12103],{},[898,12094,12029],{},[1846,12096,1848],{},[898,12098,12029],{},[1846,12100,1855],{"stretchy":1854},[898,12102,11886],{},[1846,12104,1861],{"stretchy":1854},[902,12106,12107],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,12110,12111,12114],{},[38,12112,12113],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[1639,12116,12117],{},[724,12118,12119,12121,12122,12141,12142,12169,12170,12183,12184,12213,12214,12217],{},[883,12120,4258],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,12123,12125],{"className":12124},[886],[888,12126,12127],{"xmlns":890},[892,12128,12129,12138],{},[895,12130,12131,12133,12136],{},[898,12132,2626],{},[2138,12134,12135],{},"-",[898,12137,12029],{},[902,12139,12140],{"encoding":904},"C\\text{-}I"," až ",[883,12143,12145],{"className":12144},[886],[888,12146,12147],{"xmlns":890},[892,12148,12149,12166],{},[895,12150,12151,12153,12155,12157,12159,12161,12163],{},[898,12152,2626],{},[2138,12154,12135],{},[898,12156,12029],{},[2138,12158,12135],{},[898,12160,11957],{},[2138,12162,12135],{},[898,12164,12165],{},"X",[902,12167,12168],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,12171,12173],{"className":12172},[886],[888,12174,12175],{"xmlns":890},[892,12176,12177,12181],{},[895,12178,12179],{},[898,12180,8974],{},[902,12182,8974],{"encoding":904},". V IS-LM jsou ",[38,12185,12186,12187,1745,12200],{},"dvě neznámé ",[883,12188,12190],{"className":12189},[886],[888,12191,12192],{"xmlns":890},[892,12193,12194,12198],{},[895,12195,12196],{},[898,12197,8974],{},[902,12199,8974],{"encoding":904},[883,12201,12203],{"className":12202},[886],[888,12204,12205],{"xmlns":890},[892,12206,12207,12211],{},[895,12208,12209],{},[898,12210,11886],{},[902,12212,11886],{"encoding":904},", a proto potřebujeme ",[38,12215,12216],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,12219,12221],{"id":12220},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,12223,12224,12225,12238,12239,2554],{},"Lineární závislost investic ",[883,12226,12228],{"className":12227},[886],[888,12229,12230],{"xmlns":890},[892,12231,12232,12236],{},[895,12233,12234],{},[898,12235,12029],{},[902,12237,12029],{"encoding":904}," na úrokové míře ",[883,12240,12242],{"className":12241},[886],[888,12243,12244],{"xmlns":890},[892,12245,12246,12250],{},[895,12247,12248],{},[898,12249,11886],{},[902,12251,11886],{"encoding":904},[724,12253,12254],{},[883,12255,12257],{"className":12256},[886],[888,12258,12259],{"xmlns":890},[892,12260,12261,12315],{},[895,12262,12263,12265,12267,12269,12271,12273,12275,12277,12279,12281,12283,12285,12287,12289,12291,12293,12295,12297,12299,12301,12303,12306,12308,12310,12313],{},[898,12264,12029],{},[1846,12266,1848],{},[898,12268,12029],{},[1846,12270,1855],{"stretchy":1854},[898,12272,11886],{},[1846,12274,1861],{"stretchy":1854},[1846,12276,1848],{},[898,12278,1992],{},[898,12280,11886],{},[1846,12282,1945],{},[898,12284,2044],{},[1846,12286,2136],{"separator":2135},[5724,12288],{"width":5726},[898,12290,1992],{},[1846,12292,3295],{},[1979,12294,2177],{},[1846,12296,2136],{"separator":2135},[2138,12298,2140],{},[898,12300,2044],{},[1846,12302,3256],{},[1979,12304,12305],{},"0.",[5724,12307],{"width":5726},[1846,12309,1855],{"stretchy":1854},[1979,12311,12312],{},"7.11",[1846,12314,1861],{"stretchy":1854},[902,12316,12317],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,12319,12320,12341],{},[123,12321,12322,12340],{},[883,12323,12325],{"className":12324},[886],[888,12326,12327],{"xmlns":890},[892,12328,12329,12337],{},[895,12330,12331,12333,12335],{},[898,12332,2044],{},[1846,12334,3256],{},[1979,12336,2177],{},[902,12338,12339],{"encoding":904},"d > 0"," zřejmé,",[123,12342,12343,12361,12362,1734],{},[883,12344,12346],{"className":12345},[886],[888,12347,12348],{"xmlns":890},[892,12349,12350,12358],{},[895,12351,12352,12354,12356],{},[898,12353,1992],{},[1846,12355,3295],{},[1979,12357,2177],{},[902,12359,12360],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,12363,12364],{},"klesající",[724,12366,12367],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,12369,12370],{},[883,12371,12373],{"className":12372},[886],[888,12374,12375],{"xmlns":890},[892,12376,12377,12434],{},[895,12378,12379,12381,12383,12385,12387,12389,12391,12393,12395,12397,12399,12401,12403,12405,12407,12409,12411,12413,12415,12417,12419,12421,12423,12425,12427,12429,12432],{},[898,12380,2626],{},[1846,12382,1848],{},[898,12384,2626],{},[1846,12386,1855],{"stretchy":1854},[898,12388,8974],{},[1846,12390,1861],{"stretchy":1854},[1846,12392,1848],{},[898,12394,207],{},[898,12396,8974],{},[1846,12398,1945],{},[898,12400,1948],{},[1846,12402,2136],{"separator":2135},[5724,12404],{"width":5726},[1979,12406,2177],{},[1846,12408,3295],{},[898,12410,207],{},[1846,12412,3295],{},[1979,12414,2128],{},[1846,12416,2136],{"separator":2135},[2138,12418,2140],{},[898,12420,1948],{},[1846,12422,3256],{},[1979,12424,12305],{},[5724,12426],{"width":5726},[1846,12428,1855],{"stretchy":1854},[1979,12430,12431],{},"7.12",[1846,12433,1861],{"stretchy":1854},[902,12435,12436],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,12438,12439],{},"Podmínka rovnováhy na trhu zboží:",[724,12441,12442],{},[883,12443,12445],{"className":12444},[886],[888,12446,12447],{"xmlns":890},[892,12448,12449,12472],{},[895,12450,12451,12453,12455,12457,12459,12461,12463,12465,12467,12470],{},[898,12452,8974],{},[1846,12454,1848],{},[898,12456,2626],{},[1846,12458,1945],{},[898,12460,12029],{},[898,12462,1734],{"mathvariant":2226},[5724,12464],{"width":5726},[1846,12466,1855],{"stretchy":1854},[1979,12468,12469],{},"7.13",[1846,12471,1861],{"stretchy":1854},[902,12473,12474],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,12476,12477,12478,2053,12481,12507,12508,1734],{},"To dává ",[38,12479,12480],{},"tři rovnice o čtyřech neznámých",[883,12482,12484],{"className":12483},[886],[888,12485,12486],{"xmlns":890},[892,12487,12488,12504],{},[895,12489,12490,12492,12494,12496,12498,12500,12502],{},[898,12491,8974],{},[1846,12493,2136],{"separator":2135},[898,12495,2626],{},[1846,12497,2136],{"separator":2135},[898,12499,12029],{},[1846,12501,2136],{"separator":2135},[898,12503,11886],{},[902,12505,12506],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,12509,12510],{},"rovnováhy na trhu peněz",[115,12512,12514],{"id":12513},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,12516,12517,12518,5415,12540,12558,12559,12562],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,12519,12521],{"className":12520},[886],[888,12522,12523],{"xmlns":890},[892,12524,12525,12537],{},[895,12526,12527,12529,12531,12533,12535],{},[898,12528,8974],{},[1846,12530,1848],{},[898,12532,2626],{},[1846,12534,1945],{},[898,12536,8519],{},[902,12538,12539],{"encoding":904},"Y = C + S",[883,12541,12543],{"className":12542},[886],[888,12544,12545],{"xmlns":890},[892,12546,12547,12555],{},[895,12548,12549,12551,12553],{},[898,12550,12029],{},[1846,12552,1848],{},[898,12554,8519],{},[902,12556,12557],{"encoding":904},"I = S"," (plánované ",[38,12560,12561],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,12564,12565],{},[2409,12566],{"alt":12567,"className":12568,"src":12569},"imek-odvozeni-is-4panelu",[210,2413],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,12571,12572],{},[883,12573,12575],{"className":12574},[886],[888,12576,12577],{"xmlns":890},[892,12578,12579,12613],{},[895,12580,12581,12583,12585,12587,12589,12591,12593,12595,12597,12599,12601,12603,12605,12607,12609,12611],{},[898,12582,8974],{},[1846,12584,1848],{},[1846,12586,1855],{"stretchy":1854},[898,12588,207],{},[898,12590,8974],{},[1846,12592,1945],{},[898,12594,1948],{},[1846,12596,1861],{"stretchy":1854},[1846,12598,1945],{},[1846,12600,1855],{"stretchy":1854},[898,12602,1992],{},[898,12604,11886],{},[1846,12606,1945],{},[898,12608,2044],{},[1846,12610,1861],{"stretchy":1854},[1846,12612,2136],{"separator":2135},[902,12614,12615],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,12617,12618],{},[883,12619,12621],{"className":12620},[886],[888,12622,12623],{"xmlns":890},[892,12624,12625,12659],{},[895,12626,12627,12629,12631,12633,12635,12637,12639,12641,12643,12645,12647,12649,12651,12653,12655,12657],{},[1846,12628,1855],{"stretchy":1854},[1979,12630,2128],{},[1846,12632,2075],{},[898,12634,207],{},[1846,12636,1861],{"stretchy":1854},[898,12638,8974],{},[1846,12640,2075],{},[898,12642,1992],{},[898,12644,11886],{},[1846,12646,2075],{},[898,12648,1948],{},[1846,12650,2075],{},[898,12652,2044],{},[1846,12654,1848],{},[1979,12656,2177],{},[1846,12658,2136],{"separator":2135},[902,12660,12661],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,12663,12664],{},"odkud",[724,12666,12667],{},[883,12668,12670],{"className":12669},[886],[888,12671,12672],{"xmlns":890},[892,12673,12674,12741],{},[895,12675,12676,12732,12734,12736,12739],{},[12677,12678,12680],"menclose",{"notation":12679},"box",[2175,12681,12682],{"scriptlevel":2177,"displaystyle":1854},[2175,12683,12684],{"scriptlevel":2177,"displaystyle":1854},[2175,12685,12686],{"scriptlevel":2177,"displaystyle":2135},[895,12687,12688,12690,12692,12694,12706,12708,12710,12712,12730],{},[2138,12689,2835],{},[898,12691,8974],{},[1846,12693,1848],{},[2179,12695,12696,12698],{},[898,12697,1992],{},[895,12699,12700,12702,12704],{},[1979,12701,2128],{},[1846,12703,2075],{},[898,12705,207],{},[2138,12707,2835],{},[898,12709,11886],{},[1846,12711,1945],{},[2179,12713,12714,12722],{},[895,12715,12716,12718,12720],{},[898,12717,1948],{},[1846,12719,1945],{},[898,12721,2044],{},[895,12723,12724,12726,12728],{},[1979,12725,2128],{},[1846,12727,2075],{},[898,12729,207],{},[2138,12731,2835],{},[5724,12733],{"width":5726},[1846,12735,1855],{"stretchy":1854},[1979,12737,12738],{},"7.14",[1846,12740,1861],{"stretchy":1854},[902,12742,12743],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,12745,12746,12747,9871,12750,12753,12754,12757,12758,12760,12761,12783,12784,12812,12813,12834,12835,12837,12838,12840],{},"Tento vztah se nazývá ",[38,12748,12749],{},"funkce IS",[614,12751,12752],{},"IS schedule",") a její graf ",[38,12755,12756],{},"křivka IS",". Křivka je ",[38,12759,12364],{}," přímka v rovině ",[883,12762,12764],{"className":12763},[886],[888,12765,12766],{"xmlns":890},[892,12767,12768,12780],{},[895,12769,12770,12772,12774,12776,12778],{},[1846,12771,1855],{"stretchy":1854},[898,12773,11886],{},[1846,12775,2136],{"separator":2135},[898,12777,8974],{},[1846,12779,1861],{"stretchy":1854},[902,12781,12782],{"encoding":904},"(r, Y)",", neboť ",[883,12785,12787],{"className":12786},[886],[888,12788,12789],{"xmlns":890},[892,12790,12791,12809],{},[895,12792,12793,12805,12807],{},[2179,12794,12795,12797],{},[898,12796,1992],{},[895,12798,12799,12801,12803],{},[1979,12800,2128],{},[1846,12802,2075],{},[898,12804,207],{},[1846,12806,3295],{},[1979,12808,2177],{},[902,12810,12811],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,12814,12816],{"className":12815},[886],[888,12817,12818],{"xmlns":890},[892,12819,12820,12832],{},[895,12821,12822,12824,12826,12828,12830],{},[1846,12823,1855],{"stretchy":1854},[898,12825,11886],{},[1846,12827,2136],{"separator":2135},[898,12829,8974],{},[1846,12831,1861],{"stretchy":1854},[902,12833,12782],{"encoding":904},", pro které plánované ",[38,12836,12029],{},"nvestment = ",[38,12839,8519],{},"avings.",[1639,12842,12843],{},[724,12844,12845,12847,12848,12861,12862,2053,12865,12878,12879,12892,12893,1745,12906,12919,12920,12923],{},[883,12846,4001],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,12849,12851],{"className":12850},[886],[888,12852,12853],{"xmlns":890},[892,12854,12855,12859],{},[895,12856,12857],{},[898,12858,11886],{},[902,12860,11886],{"encoding":904}," → levnější úvěr → ",[38,12863,12864],{},"více investic",[883,12866,12868],{"className":12867},[886],[888,12869,12870],{"xmlns":890},[892,12871,12872,12876],{},[895,12873,12874],{},[898,12875,12029],{},[902,12877,12029],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,12880,12882],{"className":12881},[886],[888,12883,12884],{"xmlns":890},[892,12885,12886,12890],{},[895,12887,12888],{},[898,12889,8974],{},[902,12891,8974],{"encoding":904},". Vztah mezi ",[883,12894,12896],{"className":12895},[886],[888,12897,12898],{"xmlns":890},[892,12899,12900,12904],{},[895,12901,12902],{},[898,12903,11886],{},[902,12905,11886],{"encoding":904},[883,12907,12909],{"className":12908},[886],[888,12910,12911],{"xmlns":890},[892,12912,12913,12917],{},[895,12914,12915],{},[898,12916,8974],{},[902,12918,8974],{"encoding":904}," na trhu zboží je proto ",[38,12921,12922],{},"nepřímý"," (klesající křivka).",[115,12925,12927],{"id":12926},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,12929,12930,12931,12949,12950,2776,12968,12971],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,12932,12934],{"className":12933},[886],[888,12935,12936],{"xmlns":890},[892,12937,12938,12946],{},[895,12939,12940],{},[1974,12941,12942,12944],{},[898,12943,2667],{},[898,12945,4029],{},[902,12947,12948],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,12951,12953],{"className":12952},[886],[888,12954,12955],{"xmlns":890},[892,12956,12957,12965],{},[895,12958,12959],{},[1974,12960,12961,12963],{},[898,12962,2667],{},[898,12964,8519],{},[902,12966,12967],{"encoding":904},"M^S",[38,12969,12970],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,12973,12974],{},[883,12975,12977],{"className":12976},[886],[888,12978,12979],{"xmlns":890},[892,12980,12981,12999],{},[895,12982,12983,12989,12991,12997],{},[1974,12984,12985,12987],{},[898,12986,2667],{},[898,12988,8519],{},[1846,12990,1848],{},[1974,12992,12993,12995],{},[898,12994,2667],{},[1846,12996,4200],{},[898,12998,1734],{"mathvariant":2226},[902,13000,13001],{"encoding":904},"M^S = M^*.",[724,13003,13004,13007],{},[38,13005,13006],{},"Poptávka"," po penězích má tři zdroje:",[120,13009,13010,13019,13028],{},[123,13011,13012,9871,13015,13018],{},[38,13013,13014],{},"transakční poptávka",[614,13016,13017],{},"transactions demand",") — peníze pro nákup zboží,",[123,13020,13021,9871,13024,13027],{},[38,13022,13023],{},"opatrnostní poptávka",[614,13025,13026],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,13029,13030,9871,13033,13036],{},[38,13031,13032],{},"spekulační poptávka",[614,13034,13035],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,13038,13039,13040,13058],{},"Součet transakční a opatrnostní poptávky ",[883,13041,13043],{"className":13042},[886],[888,13044,13045],{"xmlns":890},[892,13046,13047,13055],{},[895,13048,13049],{},[2122,13050,13051,13053],{},[898,13052,9641],{},[1979,13054,2128],{},[902,13056,13057],{"encoding":904},"L_1"," je úměrný důchodu:",[724,13060,13061],{},[883,13062,13064],{"className":13063},[886],[888,13065,13066],{"xmlns":890},[892,13067,13068,13106],{},[895,13069,13070,13076,13078,13085,13087,13089,13091,13093,13095,13101,13103],{},[2122,13071,13072,13074],{},[898,13073,9641],{},[1979,13075,2128],{},[1846,13077,1848],{},[2122,13079,13080,13083],{},[898,13081,13082],{},"k",[1979,13084,2128],{},[898,13086,8974],{},[1846,13088,2136],{"separator":2135},[5724,13090],{"width":5726},[1979,13092,2177],{},[1846,13094,3295],{},[2122,13096,13097,13099],{},[898,13098,13082],{},[1979,13100,2128],{},[1846,13102,3295],{},[1979,13104,13105],{},"1.",[902,13107,13108],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,13110,13111,13112,13130,13131,1343,13144,13161],{},"Spekulační poptávka ",[883,13113,13115],{"className":13114},[886],[888,13116,13117],{"xmlns":890},[892,13118,13119,13127],{},[895,13120,13121],{},[2122,13122,13123,13125],{},[898,13124,9641],{},[1979,13126,1981],{},[902,13128,13129],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,13132,13134],{"className":13133},[886],[888,13135,13136],{"xmlns":890},[892,13137,13138,13142],{},[895,13139,13140],{},[898,13141,11886],{},[902,13143,11886],{"encoding":904},[883,13145,13147],{"className":13146},[886],[888,13148,13149],{"xmlns":890},[892,13150,13151,13159],{},[895,13152,13153],{},[2122,13154,13155,13157],{},[898,13156,9641],{},[1979,13158,1981],{},[902,13160,13129],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,13163,13164],{},[883,13165,13167],{"className":13166},[886],[888,13168,13169],{"xmlns":890},[892,13170,13171,13225],{},[895,13172,13173,13179,13181,13187,13189,13191,13197,13199,13201,13207,13209,13211,13213,13215,13221,13223],{},[2122,13174,13175,13177],{},[898,13176,9641],{},[1979,13178,1981],{},[1846,13180,1848],{},[2122,13182,13183,13185],{},[898,13184,13082],{},[1979,13186,1981],{},[898,13188,11886],{},[1846,13190,1945],{},[2122,13192,13193,13195],{},[898,13194,13082],{},[1979,13196,2023],{},[1846,13198,2136],{"separator":2135},[5724,13200],{"width":5726},[2122,13202,13203,13205],{},[898,13204,13082],{},[1979,13206,1981],{},[1846,13208,3295],{},[1979,13210,2177],{},[1846,13212,2136],{"separator":2135},[2138,13214,2140],{},[2122,13216,13217,13219],{},[898,13218,13082],{},[1979,13220,2023],{},[1846,13222,3256],{},[1979,13224,12305],{},[902,13226,13227],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,13229,13230],{},"Celková poptávka po penězích:",[724,13232,13233],{},[883,13234,13236],{"className":13235},[886],[888,13237,13238],{"xmlns":890},[892,13239,13240,13294],{},[895,13241,13242,13248,13250,13256,13258,13264,13266,13272,13274,13276,13282,13284,13286,13292],{},[1974,13243,13244,13246],{},[898,13245,2667],{},[898,13247,4029],{},[1846,13249,1848],{},[2122,13251,13252,13254],{},[898,13253,9641],{},[1979,13255,2128],{},[1846,13257,1945],{},[2122,13259,13260,13262],{},[898,13261,9641],{},[1979,13263,1981],{},[1846,13265,1848],{},[2122,13267,13268,13270],{},[898,13269,13082],{},[1979,13271,2128],{},[898,13273,8974],{},[1846,13275,1945],{},[2122,13277,13278,13280],{},[898,13279,13082],{},[1979,13281,1981],{},[898,13283,11886],{},[1846,13285,1945],{},[2122,13287,13288,13290],{},[898,13289,13082],{},[1979,13291,2023],{},[898,13293,1734],{"mathvariant":2226},[902,13295,13296],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,13298,13299,13300,2554],{},"Podmínka rovnováhy na trhu peněz ",[883,13301,13303],{"className":13302},[886],[888,13304,13305],{"xmlns":890},[892,13306,13307,13323],{},[895,13308,13309,13315,13317],{},[1974,13310,13311,13313],{},[898,13312,2667],{},[898,13314,4029],{},[1846,13316,1848],{},[1974,13318,13319,13321],{},[898,13320,2667],{},[1846,13322,4200],{},[902,13324,13325],{"encoding":904},"M^D = M^*",[724,13327,13328],{},[883,13329,13331],{"className":13330},[886],[888,13332,13333],{"xmlns":890},[892,13334,13335,13382],{},[895,13336,13337,13343,13345,13351,13353,13355,13361,13363,13365,13371,13373,13375,13377,13380],{},[1974,13338,13339,13341],{},[898,13340,2667],{},[1846,13342,4200],{},[1846,13344,1848],{},[2122,13346,13347,13349],{},[898,13348,13082],{},[1979,13350,2128],{},[898,13352,8974],{},[1846,13354,1945],{},[2122,13356,13357,13359],{},[898,13358,13082],{},[1979,13360,1981],{},[898,13362,11886],{},[1846,13364,1945],{},[2122,13366,13367,13369],{},[898,13368,13082],{},[1979,13370,2023],{},[1846,13372,2136],{"separator":2135},[5724,13374],{"width":5726},[1846,13376,1855],{"stretchy":1854},[1979,13378,13379],{},"7.15",[1846,13381,1861],{"stretchy":1854},[902,13383,13384],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,13386,13387,13388,2999],{},"po úpravě (vyjádření ",[883,13389,13391],{"className":13390},[886],[888,13392,13393],{"xmlns":890},[892,13394,13395,13399],{},[895,13396,13397],{},[898,13398,8974],{},[902,13400,8974],{"encoding":904},[724,13402,13403],{},[883,13404,13406],{"className":13405},[886],[888,13407,13408],{"xmlns":890},[892,13409,13410,13485],{},[895,13411,13412,13476,13478,13480,13483],{},[12677,13413,13414],{"notation":12679},[2175,13415,13416],{"scriptlevel":2177,"displaystyle":1854},[2175,13417,13418],{"scriptlevel":2177,"displaystyle":1854},[2175,13419,13420],{"scriptlevel":2177,"displaystyle":2135},[895,13421,13422,13424,13426,13428,13430,13444,13446,13448,13450,13474],{},[2138,13423,2835],{},[898,13425,8974],{},[1846,13427,1848],{},[1846,13429,2075],{},[2179,13431,13432,13438],{},[2122,13433,13434,13436],{},[898,13435,13082],{},[1979,13437,1981],{},[2122,13439,13440,13442],{},[898,13441,13082],{},[1979,13443,2128],{},[2138,13445,2835],{},[898,13447,11886],{},[1846,13449,1945],{},[2179,13451,13452,13468],{},[895,13453,13454,13460,13462],{},[1974,13455,13456,13458],{},[898,13457,2667],{},[1846,13459,4200],{},[1846,13461,2075],{},[2122,13463,13464,13466],{},[898,13465,13082],{},[1979,13467,2023],{},[2122,13469,13470,13472],{},[898,13471,13082],{},[1979,13473,2128],{},[2138,13475,2835],{},[5724,13477],{"width":5726},[1846,13479,1855],{"stretchy":1854},[1979,13481,13482],{},"7.16",[1846,13484,1861],{"stretchy":1854},[902,13486,13487],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,13489,12746,13490,9871,13493,13496,13497,12757,13500,12760,13503,12783,13524,13556,13557,13579,13580,13582,13583,13585],{},[38,13491,13492],{},"funkce LM",[614,13494,13495],{},"LM schedule","), její graf ",[38,13498,13499],{},"křivka LM",[38,13501,13502],{},"rostoucí",[883,13504,13506],{"className":13505},[886],[888,13507,13508],{"xmlns":890},[892,13509,13510,13522],{},[895,13511,13512,13514,13516,13518,13520],{},[1846,13513,1855],{"stretchy":1854},[898,13515,11886],{},[1846,13517,2136],{"separator":2135},[898,13519,8974],{},[1846,13521,1861],{"stretchy":1854},[902,13523,12782],{"encoding":904},[883,13525,13527],{"className":13526},[886],[888,13528,13529],{"xmlns":890},[892,13530,13531,13553],{},[895,13532,13533,13535,13549,13551],{},[1846,13534,2075],{},[2179,13536,13537,13543],{},[2122,13538,13539,13541],{},[898,13540,13082],{},[1979,13542,1981],{},[2122,13544,13545,13547],{},[898,13546,13082],{},[1979,13548,2128],{},[1846,13550,3256],{},[1979,13552,2177],{},[902,13554,13555],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,13558,13560],{"className":13559},[886],[888,13561,13562],{"xmlns":890},[892,13563,13564,13576],{},[895,13565,13566,13572,13574],{},[2122,13567,13568,13570],{},[898,13569,13082],{},[1979,13571,1981],{},[1846,13573,3295],{},[1979,13575,2177],{},[902,13577,13578],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,13581,9641],{},"iquidity of ",[38,13584,2667],{},"oney.",[1639,13587,13588],{},[724,13589,13590,13592,13593,13606,13607,13635,13636,13653,13654,13667,13668,13685,13686,1745,13699,13712,13713,13716],{},[883,13591,4001],{}," Intuice — proč LM roste\nVyšší důchod ",[883,13594,13596],{"className":13595},[886],[888,13597,13598],{"xmlns":890},[892,13599,13600,13604],{},[895,13601,13602],{},[898,13603,8974],{},[902,13605,8974],{"encoding":904}," → větší transakční poptávka po penězích ",[883,13608,13610],{"className":13609},[886],[888,13611,13612],{"xmlns":890},[892,13613,13614,13632],{},[895,13615,13616,13622,13624,13630],{},[2122,13617,13618,13620],{},[898,13619,9641],{},[1979,13621,2128],{},[1846,13623,1848],{},[2122,13625,13626,13628],{},[898,13627,13082],{},[1979,13629,2128],{},[898,13631,8974],{},[902,13633,13634],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,13637,13639],{"className":13638},[886],[888,13640,13641],{"xmlns":890},[892,13642,13643,13651],{},[895,13644,13645],{},[1974,13646,13647,13649],{},[898,13648,2667],{},[1846,13650,4200],{},[902,13652,11995],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,13655,13657],{"className":13656},[886],[888,13658,13659],{"xmlns":890},[892,13660,13661,13665],{},[895,13662,13663],{},[898,13664,11886],{},[902,13666,11886],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,13669,13671],{"className":13670},[886],[888,13672,13673],{"xmlns":890},[892,13674,13675,13683],{},[895,13676,13677],{},[2122,13678,13679,13681],{},[898,13680,9641],{},[1979,13682,1981],{},[902,13684,13129],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,13687,13689],{"className":13688},[886],[888,13690,13691],{"xmlns":890},[892,13692,13693,13697],{},[895,13694,13695],{},[898,13696,8974],{},[902,13698,8974],{"encoding":904},[883,13700,13702],{"className":13701},[886],[888,13703,13704],{"xmlns":890},[892,13705,13706,13710],{},[895,13707,13708],{},[898,13709,11886],{},[902,13711,11886],{"encoding":904}," na trhu peněz je proto ",[38,13714,13715],{},"přímý"," (rostoucí křivka).",[115,13718,13720],{"id":13719},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,13722,13723,13724,13727,13728,2053,13731,1745,13749,2053,13752,13770,13771,13789,13790,13808,13809,13825,13826,1745,13841,13856,13857,1734],{},"Řešením ",[38,13725,13726],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,13729,13730],{},"rovnovážný důchod",[883,13732,13734],{"className":13733},[886],[888,13735,13736],{"xmlns":890},[892,13737,13738,13746],{},[895,13739,13740],{},[1974,13741,13742,13744],{},[898,13743,8974],{},[898,13745,4098],{},[902,13747,13748],{"encoding":904},"Y^E",[38,13750,13751],{},"rovnovážnou úrokovou míru",[883,13753,13755],{"className":13754},[886],[888,13756,13757],{"xmlns":890},[892,13758,13759,13767],{},[895,13760,13761],{},[1974,13762,13763,13765],{},[898,13764,11886],{},[898,13766,4098],{},[902,13768,13769],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,13772,13774],{"className":13773},[886],[888,13775,13776],{"xmlns":890},[892,13777,13778,13786],{},[895,13779,13780],{},[1974,13781,13782,13784],{},[898,13783,12029],{},[898,13785,4098],{},[902,13787,13788],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,13791,13793],{"className":13792},[886],[888,13794,13795],{"xmlns":890},[892,13796,13797,13805],{},[895,13798,13799],{},[1974,13800,13801,13803],{},[898,13802,2626],{},[898,13804,4098],{},[902,13806,13807],{"encoding":904},"C^E",". Graficky jde o ",[38,13810,13811,13812],{},"průsečík ",[883,13813,13815],{"className":13814},[886],[888,13816,13817],{"xmlns":890},[892,13818,13819,13823],{},[895,13820,13821],{},[898,13822,4098],{},[902,13824,4098],{"encoding":904}," křivek ",[883,13827,13829],{"className":13828},[886],[888,13830,13831],{"xmlns":890},[892,13832,13833,13839],{},[895,13834,13835,13837],{},[898,13836,12029],{},[898,13838,8519],{},[902,13840,11896],{"encoding":904},[883,13842,13844],{"className":13843},[886],[888,13845,13846],{"xmlns":890},[892,13847,13848,13854],{},[895,13849,13850,13852],{},[898,13851,9641],{},[898,13853,2667],{},[902,13855,11903],{"encoding":904}," v rovině ",[883,13858,13860],{"className":13859},[886],[888,13861,13862],{"xmlns":890},[892,13863,13864,13876],{},[895,13865,13866,13868,13870,13872,13874],{},[1846,13867,1855],{"stretchy":1854},[898,13869,11886],{},[1846,13871,2136],{"separator":2135},[898,13873,8974],{},[1846,13875,1861],{"stretchy":1854},[902,13877,12782],{"encoding":904},[724,13879,13880],{},[614,13881,13882,13883,13904,13905,13920,13921,13936,13937,13950,13951,13968,13969,11973,13982,13968,13999,14012,14013,14026],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,13884,13886],{"className":13885},[886],[888,13887,13888],{"xmlns":890},[892,13889,13890,13902],{},[895,13891,13892,13894,13896,13898,13900],{},[1846,13893,1855],{"stretchy":1854},[898,13895,11886],{},[1846,13897,2136],{"separator":2135},[898,13899,8974],{},[1846,13901,1861],{"stretchy":1854},[902,13903,12782],{"encoding":904},". Rostoucí přímka ",[883,13906,13908],{"className":13907},[886],[888,13909,13910],{"xmlns":890},[892,13911,13912,13918],{},[895,13913,13914,13916],{},[898,13915,9641],{},[898,13917,2667],{},[902,13919,11903],{"encoding":904}," a klesající přímka ",[883,13922,13924],{"className":13923},[886],[888,13925,13926],{"xmlns":890},[892,13927,13928,13934],{},[895,13929,13930,13932],{},[898,13931,12029],{},[898,13933,8519],{},[902,13935,11896],{"encoding":904}," se protínají v bodě ",[883,13938,13940],{"className":13939},[886],[888,13941,13942],{"xmlns":890},[892,13943,13944,13948],{},[895,13945,13946],{},[898,13947,4098],{},[902,13949,4098],{"encoding":904}," se souřadnicemi ",[883,13952,13954],{"className":13953},[886],[888,13955,13956],{"xmlns":890},[892,13957,13958,13966],{},[895,13959,13960],{},[1974,13961,13962,13964],{},[898,13963,11886],{},[898,13965,4098],{},[902,13967,13769],{"encoding":904}," (na ose ",[883,13970,13972],{"className":13971},[886],[888,13973,13974],{"xmlns":890},[892,13975,13976,13980],{},[895,13977,13978],{},[898,13979,11886],{},[902,13981,11886],{"encoding":904},[883,13983,13985],{"className":13984},[886],[888,13986,13987],{"xmlns":890},[892,13988,13989,13997],{},[895,13990,13991],{},[1974,13992,13993,13995],{},[898,13994,8974],{},[898,13996,4098],{},[902,13998,13748],{"encoding":904},[883,14000,14002],{"className":14001},[886],[888,14003,14004],{"xmlns":890},[892,14005,14006,14010],{},[895,14007,14008],{},[898,14009,8974],{},[902,14011,8974],{"encoding":904},"); tečkované čáry z ",[883,14014,14016],{"className":14015},[886],[888,14017,14018],{"xmlns":890},[892,14019,14020,14024],{},[895,14021,14022],{},[898,14023,4098],{},[902,14025,4098],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[1639,14028,14029,14034],{},[724,14030,14031,14033],{},[883,14032,4418],{}," Postup — jak najít IS-LM rovnováhu",[152,14035,14036,14112,14180,14238,14311],{},[123,14037,14038,14041,14042,1745,14062,14082,14083,1745,14096,14109,14110,1734],{},[38,14039,14040],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,14043,14045],{"className":14044},[886],[888,14046,14047],{"xmlns":890},[892,14048,14049,14059],{},[895,14050,14051,14053,14055,14057],{},[898,14052,2626],{},[1846,14054,1855],{"stretchy":1854},[898,14056,8974],{},[1846,14058,1861],{"stretchy":1854},[902,14060,14061],{"encoding":904},"C(Y)",[883,14063,14065],{"className":14064},[886],[888,14066,14067],{"xmlns":890},[892,14068,14069,14079],{},[895,14070,14071,14073,14075,14077],{},[898,14072,12029],{},[1846,14074,1855],{"stretchy":1854},[898,14076,11886],{},[1846,14078,1861],{"stretchy":1854},[902,14080,14081],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,14084,14086],{"className":14085},[886],[888,14087,14088],{"xmlns":890},[892,14089,14090,14094],{},[895,14091,14092],{},[898,14093,8974],{},[902,14095,8974],{"encoding":904},[883,14097,14099],{"className":14098},[886],[888,14100,14101],{"xmlns":890},[892,14102,14103,14107],{},[895,14104,14105],{},[898,14106,11886],{},[902,14108,11886],{"encoding":904}," — dostaneš rovnici ",[38,14111,11896],{},[123,14113,14114,14117,14118,1745,14135,14152,14153,14109,14178,1734],{},[38,14115,14116],{},"Z trhu peněz (7.15)"," dosaď ",[883,14119,14121],{"className":14120},[886],[888,14122,14123],{"xmlns":890},[892,14124,14125,14133],{},[895,14126,14127],{},[2122,14128,14129,14131],{},[898,14130,9641],{},[1979,14132,2128],{},[902,14134,13057],{"encoding":904},[883,14136,14138],{"className":14137},[886],[888,14139,14140],{"xmlns":890},[892,14141,14142,14150],{},[895,14143,14144],{},[2122,14145,14146,14148],{},[898,14147,9641],{},[1979,14149,1981],{},[902,14151,13129],{"encoding":904}," a vztah ",[883,14154,14156],{"className":14155},[886],[888,14157,14158],{"xmlns":890},[892,14159,14160,14176],{},[895,14161,14162,14168,14170],{},[1974,14163,14164,14166],{},[898,14165,2667],{},[898,14167,4029],{},[1846,14169,1848],{},[1974,14171,14172,14174],{},[898,14173,2667],{},[1846,14175,4200],{},[902,14177,13325],{"encoding":904},[38,14179,11903],{},[123,14181,14182,14185,14186,1745,14199,14212,14213,14237],{},[38,14183,14184],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,14187,14189],{"className":14188},[886],[888,14190,14191],{"xmlns":890},[892,14192,14193,14197],{},[895,14194,14195],{},[898,14196,8974],{},[902,14198,8974],{"encoding":904},[883,14200,14202],{"className":14201},[886],[888,14203,14204],{"xmlns":890},[892,14205,14206,14210],{},[895,14207,14208],{},[898,14209,11886],{},[902,14211,11886],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,14214,14216],{"className":14215},[886],[888,14217,14218],{"xmlns":890},[892,14219,14220,14234],{},[895,14221,14222,14224,14226,14228,14230,14232],{},[898,14223,8974],{},[1846,14225,1848],{},[898,14227,1851],{},[1846,14229,1855],{"stretchy":1854},[898,14231,11886],{},[1846,14233,1861],{"stretchy":1854},[902,14235,14236],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,14239,14240,2053,14243,1745,14277,1734],{},[38,14241,14242],{},"Zpětně dopočítej",[883,14244,14246],{"className":14245},[886],[888,14247,14248],{"xmlns":890},[892,14249,14250,14274],{},[895,14251,14252,14258,14260,14262,14264,14270,14272],{},[1974,14253,14254,14256],{},[898,14255,2626],{},[898,14257,4098],{},[1846,14259,1848],{},[898,14261,207],{},[2138,14263,2835],{},[1974,14265,14266,14268],{},[898,14267,8974],{},[898,14269,4098],{},[1846,14271,1945],{},[898,14273,1948],{},[902,14275,14276],{"encoding":904},"C^E = a\\,Y^E + b",[883,14278,14280],{"className":14279},[886],[888,14281,14282],{"xmlns":890},[892,14283,14284,14308],{},[895,14285,14286,14292,14294,14296,14298,14304,14306],{},[1974,14287,14288,14290],{},[898,14289,12029],{},[898,14291,4098],{},[1846,14293,1848],{},[898,14295,1992],{},[2138,14297,2835],{},[1974,14299,14300,14302],{},[898,14301,11886],{},[898,14303,4098],{},[1846,14305,1945],{},[898,14307,2044],{},[902,14309,14310],{"encoding":904},"I^E = c\\,r^E + d",[123,14312,14313,14316,14317,14351,14352,14406],{},[38,14314,14315],{},"Ověř:"," musí platit ",[883,14318,14320],{"className":14319},[886],[888,14321,14322],{"xmlns":890},[892,14323,14324,14348],{},[895,14325,14326,14332,14334,14340,14342],{},[1974,14327,14328,14330],{},[898,14329,8974],{},[898,14331,4098],{},[1846,14333,1848],{},[1974,14335,14336,14338],{},[898,14337,2626],{},[898,14339,4098],{},[1846,14341,1945],{},[1974,14343,14344,14346],{},[898,14345,12029],{},[898,14347,4098],{},[902,14349,14350],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,14353,14355],{"className":14354},[886],[888,14356,14357],{"xmlns":890},[892,14358,14359,14403],{},[895,14360,14361,14367,14369,14375,14381,14383,14389,14395,14397],{},[1974,14362,14363,14365],{},[898,14364,2667],{},[1846,14366,4200],{},[1846,14368,1848],{},[2122,14370,14371,14373],{},[898,14372,13082],{},[1979,14374,2128],{},[1974,14376,14377,14379],{},[898,14378,8974],{},[898,14380,4098],{},[1846,14382,1945],{},[2122,14384,14385,14387],{},[898,14386,13082],{},[1979,14388,1981],{},[1974,14390,14391,14393],{},[898,14392,11886],{},[898,14394,4098],{},[1846,14396,1945],{},[2122,14398,14399,14401],{},[898,14400,13082],{},[1979,14402,2023],{},[902,14404,14405],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,14408,14410],{"id":14409},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,14412,14413],{},"Pro trh zboží jsou dány:",[120,14415,14416,14444],{},[123,14417,14418,14419,2136],{},"spotřeba ",[883,14420,14422],{"className":14421},[886],[888,14423,14424],{"xmlns":890},[892,14425,14426,14441],{},[895,14427,14428,14430,14432,14435,14437,14439],{},[898,14429,2626],{},[1846,14431,1848],{},[1979,14433,14434],{},"0,8",[898,14436,8974],{},[1846,14438,1945],{},[1979,14440,2938],{},[902,14442,14443],{"encoding":904},"C = 0{,}8Y + 100",[123,14445,14446,14447,1734],{},"investice ",[883,14448,14450],{"className":14449},[886],[888,14451,14452],{"xmlns":890},[892,14453,14454,14470],{},[895,14455,14456,14458,14460,14462,14464,14466,14468],{},[898,14457,12029],{},[1846,14459,1848],{},[1846,14461,2075],{},[1979,14463,8881],{},[898,14465,11886],{},[1846,14467,1945],{},[1979,14469,2631],{},[902,14471,14472],{"encoding":904},"I = -20r + 1000",[724,14474,14475],{},"Pro trh peněz:",[120,14477,14478,14504,14536],{},[123,14479,14480,2136],{},[883,14481,14483],{"className":14482},[886],[888,14484,14485],{"xmlns":890},[892,14486,14487,14501],{},[895,14488,14489,14495,14497,14499],{},[2122,14490,14491,14493],{},[898,14492,9641],{},[1979,14494,2128],{},[1846,14496,1848],{},[1979,14498,2643],{},[898,14500,8974],{},[902,14502,14503],{"encoding":904},"L_1 = 0{,}1Y",[123,14505,14506,2136],{},[883,14507,14509],{"className":14508},[886],[888,14510,14511],{"xmlns":890},[892,14512,14513,14533],{},[895,14514,14515,14521,14523,14525,14527,14529,14531],{},[2122,14516,14517,14519],{},[898,14518,9641],{},[1979,14520,1981],{},[1846,14522,1848],{},[1846,14524,2075],{},[1979,14526,4850],{},[898,14528,11886],{},[1846,14530,1945],{},[1979,14532,8450],{},[902,14534,14535],{"encoding":904},"L_2 = -25r + 2000",[123,14537,14538,14539,1734],{},"nabídka peněz ",[883,14540,14542],{"className":14541},[886],[888,14543,14544],{"xmlns":890},[892,14545,14546,14559],{},[895,14547,14548,14554,14556],{},[1974,14549,14550,14552],{},[898,14551,2667],{},[1846,14553,4200],{},[1846,14555,1848],{},[1979,14557,14558],{},"2375",[902,14560,14561],{"encoding":904},"M^* = 2375",[724,14563,14564,14567,14568,2554],{},[38,14565,14566],{},"Funkce IS"," — dosazením do (7.13) ",[883,14569,14571],{"className":14570},[886],[888,14572,14573],{"xmlns":890},[892,14574,14575,14587],{},[895,14576,14577,14579,14581,14583,14585],{},[898,14578,8974],{},[1846,14580,1848],{},[898,14582,2626],{},[1846,14584,1945],{},[898,14586,12029],{},[902,14588,14589],{"encoding":904},"Y = C + I",[724,14591,14592],{},[883,14593,14595],{"className":14594},[886],[888,14596,14597],{"xmlns":890},[892,14598,14599,14625],{},[895,14600,14601,14603,14605,14607,14609,14611,14613,14615,14617,14619,14621,14623],{},[898,14602,8974],{},[1846,14604,1848],{},[1979,14606,14434],{},[898,14608,8974],{},[1846,14610,1945],{},[1979,14612,2938],{},[1846,14614,2075],{},[1979,14616,8881],{},[898,14618,11886],{},[1846,14620,1945],{},[1979,14622,2631],{},[1846,14624,2136],{"separator":2135},[902,14626,14627],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,14629,14630],{},"tj.",[724,14632,14633],{},[883,14634,14636],{"className":14635},[886],[888,14637,14638],{"xmlns":890},[892,14639,14640,14665],{},[895,14641,14642,14644,14646,14648,14650,14652,14654,14657,14659,14661,14663],{},[1979,14643,2688],{},[898,14645,8974],{},[1846,14647,1945],{},[1979,14649,8881],{},[898,14651,11886],{},[1846,14653,1848],{},[1979,14655,14656],{},"1100.",[5724,14658],{"width":5726},[1846,14660,1855],{"stretchy":1854},[2138,14662,11896],{},[1846,14664,1861],{"stretchy":1854},[902,14666,14667],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,14669,14670,14673,14674,2554],{},[38,14671,14672],{},"Funkce LM"," — dosazením do (7.15) ",[883,14675,14677],{"className":14676},[886],[888,14678,14679],{"xmlns":890},[892,14680,14681,14705],{},[895,14682,14683,14689,14691,14697,14699],{},[1974,14684,14685,14687],{},[898,14686,2667],{},[1846,14688,4200],{},[1846,14690,1848],{},[2122,14692,14693,14695],{},[898,14694,9641],{},[1979,14696,2128],{},[1846,14698,1945],{},[2122,14700,14701,14703],{},[898,14702,9641],{},[1979,14704,1981],{},[902,14706,14707],{"encoding":904},"M^* = L_1 + L_2",[724,14709,14710],{},[883,14711,14713],{"className":14712},[886],[888,14714,14715],{"xmlns":890},[892,14716,14717,14739],{},[895,14718,14719,14721,14723,14725,14727,14729,14731,14733,14735,14737],{},[1979,14720,14558],{},[1846,14722,1848],{},[1979,14724,2643],{},[898,14726,8974],{},[1846,14728,2075],{},[1979,14730,4850],{},[898,14732,11886],{},[1846,14734,1945],{},[1979,14736,8450],{},[1846,14738,2136],{"separator":2135},[902,14740,14741],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,14743,14630],{},[724,14745,14746],{},[883,14747,14749],{"className":14748},[886],[888,14750,14751],{"xmlns":890},[892,14752,14753,14778],{},[895,14754,14755,14757,14759,14761,14763,14765,14767,14770,14772,14774,14776],{},[1979,14756,2643],{},[898,14758,8974],{},[1846,14760,2075],{},[1979,14762,4850],{},[898,14764,11886],{},[1846,14766,1848],{},[1979,14768,14769],{},"375.",[5724,14771],{"width":5726},[1846,14773,1855],{"stretchy":1854},[2138,14775,11903],{},[1846,14777,1861],{"stretchy":1854},[902,14779,14780],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,14782,14783,14786,14787,14812],{},[38,14784,14785],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,14788,14790],{"className":14789},[886],[888,14791,14792],{"xmlns":890},[892,14793,14794,14809],{},[895,14795,14796,14798,14800,14803,14805,14807],{},[898,14797,8974],{},[1846,14799,1848],{},[1979,14801,14802],{},"5500",[1846,14804,2075],{},[1979,14806,2938],{},[898,14808,11886],{},[902,14810,14811],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,14814,14815],{},[883,14816,14818],{"className":14817},[886],[888,14819,14820],{"xmlns":890},[892,14821,14822,14908],{},[895,14823,14824,14826,14828,14830,14832,14834,14836,14838,14840,14842,14844,14846,14849,14851,14854,14856,14859,14861,14863,14865,14867,14869,14871,14873,14875,14877,14879,14881,14884,14886,14888,14891,14893,14895,14897,14903,14905],{},[1979,14825,2643],{},[1846,14827,1855],{"stretchy":1854},[1979,14829,14802],{},[1846,14831,2075],{},[1979,14833,2938],{},[898,14835,11886],{},[1846,14837,1861],{"stretchy":1854},[1846,14839,2075],{},[1979,14841,4850],{},[898,14843,11886],{},[1846,14845,1848],{},[1979,14847,14848],{},"375",[2138,14850,3830],{},[1846,14852,14853],{},"⟹",[2138,14855,3830],{},[1979,14857,14858],{},"550",[1846,14860,2075],{},[1979,14862,2712],{},[898,14864,11886],{},[1846,14866,2075],{},[1979,14868,4850],{},[898,14870,11886],{},[1846,14872,1848],{},[1979,14874,14848],{},[2138,14876,3830],{},[1846,14878,14853],{},[2138,14880,3830],{},[1979,14882,14883],{},"35",[898,14885,11886],{},[1846,14887,1848],{},[1979,14889,14890],{},"175",[2138,14892,3830],{},[1846,14894,14853],{},[2138,14896,3830],{},[1974,14898,14899,14901],{},[898,14900,11886],{},[898,14902,4098],{},[1846,14904,1848],{},[1979,14906,14907],{},"5.",[902,14909,14910],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,14912,14913],{},[38,14914,14915],{},"Zpětné dosazení:",[120,14917,14918,14964,15001],{},[123,14919,14920,2136],{},[883,14921,14923],{"className":14922},[886],[888,14924,14925],{"xmlns":890},[892,14926,14927,14961],{},[895,14928,14929,14935,14937,14939,14941,14943,14945,14947,14949,14951,14953,14956,14958],{},[1974,14930,14931,14933],{},[898,14932,8974],{},[898,14934,4098],{},[1846,14936,1848],{},[1979,14938,14802],{},[1846,14940,2075],{},[1979,14942,2938],{},[1846,14944,3025],{},[1979,14946,2078],{},[1846,14948,1848],{},[1979,14950,14802],{},[1846,14952,2075],{},[1979,14954,14955],{},"500",[1846,14957,1848],{},[1979,14959,14960],{},"5000",[902,14962,14963],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,14965,14966,2136],{},[883,14967,14969],{"className":14968},[886],[888,14970,14971],{"xmlns":890},[892,14972,14973,14998],{},[895,14974,14975,14981,14983,14985,14987,14989,14991,14993,14995],{},[1974,14976,14977,14979],{},[898,14978,2626],{},[898,14980,4098],{},[1846,14982,1848],{},[1979,14984,14434],{},[1846,14986,3025],{},[1979,14988,14960],{},[1846,14990,1945],{},[1979,14992,2938],{},[1846,14994,1848],{},[1979,14996,14997],{},"4100",[902,14999,15000],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,15002,15003,1734],{},[883,15004,15006],{"className":15005},[886],[888,15007,15008],{"xmlns":890},[892,15009,15010,15037],{},[895,15011,15012,15018,15020,15022,15024,15026,15028,15030,15032,15034],{},[1974,15013,15014,15016],{},[898,15015,12029],{},[898,15017,4098],{},[1846,15019,1848],{},[1846,15021,2075],{},[1979,15023,8881],{},[1846,15025,3025],{},[1979,15027,2078],{},[1846,15029,1945],{},[1979,15031,2631],{},[1846,15033,1848],{},[1979,15035,15036],{},"900",[902,15038,15039],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,15041,15042,2053,15045,15091],{},[38,15043,15044],{},"Ověření:",[883,15046,15048],{"className":15047},[886],[888,15049,15050],{"xmlns":890},[892,15051,15052,15088],{},[895,15053,15054,15060,15062,15068,15070,15072,15074,15076,15078,15080,15082],{},[1974,15055,15056,15058],{},[898,15057,2626],{},[898,15059,4098],{},[1846,15061,1945],{},[1974,15063,15064,15066],{},[898,15065,12029],{},[898,15067,4098],{},[1846,15069,1848],{},[1979,15071,14997],{},[1846,15073,1945],{},[1979,15075,15036],{},[1846,15077,1848],{},[1979,15079,14960],{},[1846,15081,1848],{},[1974,15083,15084,15086],{},[898,15085,8974],{},[898,15087,4098],{},[902,15089,15090],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,15093,15094],{},[883,15095,15097],{"className":15096},[886],[888,15098,15099],{"xmlns":890},[892,15100,15101,15171],{},[895,15102,15103],{},[12677,15104,15105],{"notation":12679},[2175,15106,15107],{"scriptlevel":2177,"displaystyle":1854},[2175,15108,15109],{"scriptlevel":2177,"displaystyle":1854},[2175,15110,15111],{"scriptlevel":2177,"displaystyle":2135},[895,15112,15113,15115,15121,15123,15125,15127,15130,15136,15138,15140,15142,15144,15150,15152,15154,15156,15158,15164,15166,15169],{},[2138,15114,2835],{},[1974,15116,15117,15119],{},[898,15118,8974],{},[898,15120,4098],{},[1846,15122,1848],{},[1979,15124,14960],{},[1846,15126,2136],{"separator":2135},[5724,15128],{"width":15129},"1em",[1974,15131,15132,15134],{},[898,15133,11886],{},[898,15135,4098],{},[1846,15137,1848],{},[1979,15139,2078],{},[1846,15141,2136],{"separator":2135},[5724,15143],{"width":15129},[1974,15145,15146,15148],{},[898,15147,2626],{},[898,15149,4098],{},[1846,15151,1848],{},[1979,15153,14997],{},[1846,15155,2136],{"separator":2135},[5724,15157],{"width":15129},[1974,15159,15160,15162],{},[898,15161,12029],{},[898,15163,4098],{},[1846,15165,1848],{},[1979,15167,15168],{},"900.",[2138,15170,2835],{},[902,15172,15173],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,15175,15176],{},[614,15177,15178,15179,15192,15193,15206,15207,15222,15223,15236,15237,15252,15253,15266,15267,15280,15281,1734],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,15180,15182],{"className":15181},[886],[888,15183,15184],{"xmlns":890},[892,15185,15186,15190],{},[895,15187,15188],{},[898,15189,8974],{},[902,15191,8974],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,15194,15196],{"className":15195},[886],[888,15197,15198],{"xmlns":890},[892,15199,15200,15204],{},[895,15201,15202],{},[898,15203,11886],{},[902,15205,11886],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,15208,15210],{"className":15209},[886],[888,15211,15212],{"xmlns":890},[892,15213,15214,15220],{},[895,15215,15216,15218],{},[898,15217,9641],{},[898,15219,2667],{},[902,15221,11903],{"encoding":904}," stoupá z oblasti nízkých ",[883,15224,15226],{"className":15225},[886],[888,15227,15228],{"xmlns":890},[892,15229,15230,15234],{},[895,15231,15232],{},[898,15233,11886],{},[902,15235,11886],{"encoding":904},", přímka ",[883,15238,15240],{"className":15239},[886],[888,15241,15242],{"xmlns":890},[892,15243,15244,15250],{},[895,15245,15246,15248],{},[898,15247,12029],{},[898,15249,8519],{},[902,15251,11896],{"encoding":904}," klesá a protíná osu ",[883,15254,15256],{"className":15255},[886],[888,15257,15258],{"xmlns":890},[892,15259,15260,15264],{},[895,15261,15262],{},[898,15263,11886],{},[902,15265,11886],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,15268,15270],{"className":15269},[886],[888,15271,15272],{"xmlns":890},[892,15273,15274,15278],{},[895,15275,15276],{},[898,15277,4098],{},[902,15279,4098],{"encoding":904}," leží v bodě ",[883,15282,15284],{"className":15283},[886],[888,15285,15286],{"xmlns":890},[892,15287,15288,15310],{},[895,15289,15290,15292,15294,15296,15298,15300,15302,15304,15306,15308],{},[1846,15291,2336],{"stretchy":1854},[898,15293,11886],{},[1846,15295,1848],{},[1979,15297,2078],{},[1846,15299,2136],{"separator":2135},[2138,15301,2140],{},[898,15303,8974],{},[1846,15305,1848],{},[1979,15307,14960],{},[1846,15309,2351],{"stretchy":1854},[902,15311,15312],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,15314,15316],{"id":15315},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,15318,15319,15322,15323,15336,15337,6861,15350,15353,15354,15372,15373,15390,15391,15408,15409,15422,15423,15436],{},[38,15320,15321],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,15324,15326],{"className":15325},[886],[888,15327,15328],{"xmlns":890},[892,15329,15330,15334],{},[895,15331,15332],{},[898,15333,11957],{},[902,15335,11957],{"encoding":904}," nebo snížení daní ",[883,15338,15340],{"className":15339},[886],[888,15341,15342],{"xmlns":890},[892,15343,15344,15348],{},[895,15345,15346],{},[898,15347,2623],{},[902,15349,2623],{"encoding":904},[38,15351,15352],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,15355,15357],{"className":15356},[886],[888,15358,15359],{"xmlns":890},[892,15360,15361,15369],{},[895,15362,15363],{},[1974,15364,15365,15367],{},[898,15366,4098],{},[1846,15368,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,15370,15371],{"encoding":904},"E'"," má vyšší ",[883,15374,15376],{"className":15375},[886],[888,15377,15378],{"xmlns":890},[892,15379,15380,15388],{},[895,15381,15382],{},[1974,15383,15384,15386],{},[898,15385,8974],{},[898,15387,4098],{},[902,15389,13748],{"encoding":904}," i vyšší ",[883,15392,15394],{"className":15393},[886],[888,15395,15396],{"xmlns":890},[892,15397,15398,15406],{},[895,15399,15400],{},[1974,15401,15402,15404],{},[898,15403,11886],{},[898,15405,4098],{},[902,15407,13769],{"encoding":904}," (vyšší ",[883,15410,15412],{"className":15411},[886],[888,15413,15414],{"xmlns":890},[892,15415,15416,15420],{},[895,15417,15418],{},[898,15419,8974],{},[902,15421,8974],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,15424,15426],{"className":15425},[886],[888,15427,15428],{"xmlns":890},[892,15429,15430,15434],{},[895,15431,15432],{},[898,15433,11886],{},[902,15435,11886],{"encoding":904}," nahoru).",[724,15438,15439],{},[2409,15440],{"alt":15441,"className":15442,"src":15443},"imek-posun-is-lm-politiky",[210,2413],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,15445,15446,15449,15450,15467,15468,15471,15472,15489,15490,15507,15508,15521,15522,15541,15542,3764],{},[38,15447,15448],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,15451,15453],{"className":15452},[886],[888,15454,15455],{"xmlns":890},[892,15456,15457,15465],{},[895,15458,15459],{},[1974,15460,15461,15463],{},[898,15462,2667],{},[1846,15464,4200],{},[902,15466,11995],{"encoding":904}," národní bankou — ",[38,15469,15470],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,15473,15475],{"className":15474},[886],[888,15476,15477],{"xmlns":890},[892,15478,15479,15487],{},[895,15480,15481],{},[1974,15482,15483,15485],{},[898,15484,11886],{},[898,15486,4098],{},[902,15488,13769],{"encoding":904}," a vyšší ",[883,15491,15493],{"className":15492},[886],[888,15494,15495],{"xmlns":890},[892,15496,15497,15505],{},[895,15498,15499],{},[1974,15500,15501,15503],{},[898,15502,8974],{},[898,15504,4098],{},[902,15506,13748],{"encoding":904}," (nižší ",[883,15509,15511],{"className":15510},[886],[888,15512,15513],{"xmlns":890},[892,15514,15515,15519],{},[895,15516,15517],{},[898,15518,11886],{},[902,15520,11886],{"encoding":904}," povzbuzuje investice ",[883,15523,15525],{"className":15524},[886],[888,15526,15527],{"xmlns":890},[892,15528,15529,15539],{},[895,15530,15531,15533,15535,15537],{},[898,15532,12029],{},[1846,15534,1855],{"stretchy":1854},[898,15536,11886],{},[1846,15538,1861],{"stretchy":1854},[902,15540,14081],{"encoding":904},", ty zvedají ",[883,15543,15545],{"className":15544},[886],[888,15546,15547],{"xmlns":890},[892,15548,15549,15553],{},[895,15550,15551],{},[898,15552,8974],{},[902,15554,8974],{"encoding":904},[724,15556,15557,15558,15561],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,15559,15560],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,15563,15565],{"id":15564},"klíčové-pojmy","Klíčové pojmy",[120,15567,15568,15641,15687,15769,15819,15886,15943,15984,16017],{},[123,15569,15570,6861,15603,1343,15620,15637,15638,15640],{},[38,15571,15572,15573],{},"Funkce investic ",[883,15574,15576],{"className":15575},[886],[888,15577,15578],{"xmlns":890},[892,15579,15580,15600],{},[895,15581,15582,15584,15586,15588,15590,15592,15594,15596,15598],{},[898,15583,12029],{},[1846,15585,1855],{"stretchy":1854},[898,15587,11886],{},[1846,15589,1861],{"stretchy":1854},[1846,15591,1848],{},[898,15593,1992],{},[898,15595,11886],{},[1846,15597,1945],{},[898,15599,2044],{},[902,15601,15602],{"encoding":904},"I(r) = cr + d",[883,15604,15606],{"className":15605},[886],[888,15607,15608],{"xmlns":890},[892,15609,15610,15618],{},[895,15611,15612,15614,15616],{},[898,15613,1992],{},[1846,15615,3295],{},[1979,15617,2177],{},[902,15619,12360],{"encoding":904},[883,15621,15623],{"className":15622},[886],[888,15624,15625],{"xmlns":890},[892,15626,15627,15635],{},[895,15628,15629,15631,15633],{},[898,15630,2044],{},[1846,15632,3256],{},[1979,15634,2177],{},[902,15636,12339],{"encoding":904},"; ",[38,15639,12364],{}," funkce úrokové míry.",[123,15642,15643,15646,15647,15668,15669,15686],{},[38,15644,15645],{},"Trh zboží"," — rovnováha ",[883,15648,15650],{"className":15649},[886],[888,15651,15652],{"xmlns":890},[892,15653,15654,15666],{},[895,15655,15656,15658,15660,15662,15664],{},[898,15657,8974],{},[1846,15659,1848],{},[898,15661,2626],{},[1846,15663,1945],{},[898,15665,12029],{},[902,15667,14589],{"encoding":904},", ekvivalentně ",[883,15670,15672],{"className":15671},[886],[888,15673,15674],{"xmlns":890},[892,15675,15676,15684],{},[895,15677,15678,15680,15682],{},[898,15679,12029],{},[1846,15681,1848],{},[898,15683,8519],{},[902,15685,12557],{"encoding":904}," (investice = úspory).",[123,15688,15689,9871,15692,15694,15695,15745,15746,12760,15748,1734],{},[38,15690,15691],{},"Křivka IS",[614,15693,11899],{},") — ",[883,15696,15698],{"className":15697},[886],[888,15699,15700],{"xmlns":890},[892,15701,15702,15742],{},[895,15703,15704,15706,15708,15720,15722,15724],{},[898,15705,8974],{},[1846,15707,1848],{},[2179,15709,15710,15712],{},[898,15711,1992],{},[895,15713,15714,15716,15718],{},[1979,15715,2128],{},[1846,15717,2075],{},[898,15719,207],{},[898,15721,11886],{},[1846,15723,1945],{},[2179,15725,15726,15734],{},[895,15727,15728,15730,15732],{},[898,15729,1948],{},[1846,15731,1945],{},[898,15733,2044],{},[895,15735,15736,15738,15740],{},[1979,15737,2128],{},[1846,15739,2075],{},[898,15741,207],{},[902,15743,15744],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,15747,12364],{},[883,15749,15751],{"className":15750},[886],[888,15752,15753],{"xmlns":890},[892,15754,15755,15767],{},[895,15756,15757,15759,15761,15763,15765],{},[1846,15758,1855],{"stretchy":1854},[898,15760,11886],{},[1846,15762,2136],{"separator":2135},[898,15764,8974],{},[1846,15766,1861],{"stretchy":1854},[902,15768,12782],{"encoding":904},[123,15770,15771,15646,15774,15800,15801,1734],{},[38,15772,15773],{},"Trh peněz",[883,15775,15777],{"className":15776},[886],[888,15778,15779],{"xmlns":890},[892,15780,15781,15797],{},[895,15782,15783,15789,15791],{},[1974,15784,15785,15787],{},[898,15786,2667],{},[898,15788,4029],{},[1846,15790,1848],{},[1974,15792,15793,15795],{},[898,15794,2667],{},[898,15796,8519],{},[902,15798,15799],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,15802,15804],{"className":15803},[886],[888,15805,15806],{"xmlns":890},[892,15807,15808,15816],{},[895,15809,15810],{},[1974,15811,15812,15814],{},[898,15813,2667],{},[1846,15815,4200],{},[902,15817,15818],{"encoding":904},"M^* ",[123,15820,15821,6861,15824,1734],{},[38,15822,15823],{},"Transakční, opatrnostní, spekulační poptávka",[883,15825,15827],{"className":15826},[886],[888,15828,15829],{"xmlns":890},[892,15830,15831,15883],{},[895,15832,15833,15839,15841,15847,15849,15855,15857,15863,15865,15867,15873,15875,15877],{},[1974,15834,15835,15837],{},[898,15836,2667],{},[898,15838,4029],{},[1846,15840,1848],{},[2122,15842,15843,15845],{},[898,15844,9641],{},[1979,15846,2128],{},[1846,15848,1945],{},[2122,15850,15851,15853],{},[898,15852,9641],{},[1979,15854,1981],{},[1846,15856,1848],{},[2122,15858,15859,15861],{},[898,15860,13082],{},[1979,15862,2128],{},[898,15864,8974],{},[1846,15866,1945],{},[2122,15868,15869,15871],{},[898,15870,13082],{},[1979,15872,1981],{},[898,15874,11886],{},[1846,15876,1945],{},[2122,15878,15879,15881],{},[898,15880,13082],{},[1979,15882,2023],{},[902,15884,15885],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,15887,15888,9871,15891,15694,15893,15939,15940,15942],{},[38,15889,15890],{},"Křivka LM",[614,15892,11906],{},[883,15894,15896],{"className":15895},[886],[888,15897,15898],{"xmlns":890},[892,15899,15900,15936],{},[895,15901,15902,15908,15910,15916,15918,15920,15926,15928,15930],{},[1974,15903,15904,15906],{},[898,15905,2667],{},[1846,15907,4200],{},[1846,15909,1848],{},[2122,15911,15912,15914],{},[898,15913,13082],{},[1979,15915,2128],{},[898,15917,8974],{},[1846,15919,1945],{},[2122,15921,15922,15924],{},[898,15923,13082],{},[1979,15925,1981],{},[898,15927,11886],{},[1846,15929,1945],{},[2122,15931,15932,15934],{},[898,15933,13082],{},[1979,15935,2023],{},[902,15937,15938],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,15941,13502],{}," přímka.",[123,15944,15945,15948,15949,15983],{},[38,15946,15947],{},"Simultánní rovnováha"," — průsečík ",[883,15950,15952],{"className":15951},[886],[888,15953,15954],{"xmlns":890},[892,15955,15956,15980],{},[895,15957,15958,15960,15962,15964,15970,15972,15978],{},[898,15959,4098],{},[1846,15961,1848],{},[1846,15963,1855],{"stretchy":1854},[1974,15965,15966,15968],{},[898,15967,11886],{},[898,15969,4098],{},[1846,15971,2136],{"separator":2135},[1974,15973,15974,15976],{},[898,15975,8974],{},[898,15977,4098],{},[1846,15979,1861],{"stretchy":1854},[902,15981,15982],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,15985,15986,15989,15990,1343,16003,16016],{},[38,15987,15988],{},"Fiskální politika"," — nástroje ",[883,15991,15993],{"className":15992},[886],[888,15994,15995],{"xmlns":890},[892,15996,15997,16001],{},[895,15998,15999],{},[898,16000,11957],{},[902,16002,11957],{"encoding":904},[883,16004,16006],{"className":16005},[886],[888,16007,16008],{"xmlns":890},[892,16009,16010,16014],{},[895,16011,16012],{},[898,16013,2623],{},[902,16015,2623],{"encoding":904}," posouvající křivku IS.",[123,16018,16019,16022,16023,16040],{},[38,16020,16021],{},"Monetární politika"," — nástroj ",[883,16024,16026],{"className":16025},[886],[888,16027,16028],{"xmlns":890},[892,16029,16030,16038],{},[895,16031,16032],{},[1974,16033,16034,16036],{},[898,16035,2667],{},[1846,16037,4200],{},[902,16039,11995],{"encoding":904}," posouvající křivku LM.",[115,16042,3640],{"id":3639},[120,16044,16045,16054,16063,16073],{},[123,16046,16047,2053,16050],{},[38,16048,16049],{},"Kurz:",[207,16051,16053],{"className":16052,"dataFsResolvedFilePath":1761,"href":1762},[210],"Matematická ekonomie",[123,16055,16056,2053,16059],{},[38,16057,16058],{},"Přednáška:",[207,16060,16062],{"className":16061,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,16064,16065,2053,16068,16072],{},[38,16066,16067],{},"Nadřazené téma:",[207,16069,16071],{"className":16070,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,16074,16075,16078],{},[38,16076,16077],{},"Související:",[120,16079,16080,16086,16092],{},[123,16081,16082,16085],{},[207,16083,1789],{"className":16084,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,16087,16088,16091],{},[207,16089,1145],{"className":16090,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,16093,16094,16098],{},[207,16095,16097],{"className":16096,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":16100},[16101,16102,16103,16104,16105,16106,16107,16108,16109,16110],{"id":11850,"depth":642,"text":11851},{"id":12005,"depth":642,"text":12006},{"id":12220,"depth":642,"text":12221},{"id":12513,"depth":642,"text":12514},{"id":12926,"depth":642,"text":12927},{"id":13719,"depth":642,"text":13720},{"id":14409,"depth":642,"text":14410},{"id":15315,"depth":642,"text":15316},{"id":15564,"depth":642,"text":15565},{"id":3639,"depth":642,"text":3640},{},"\u002Ftopics\u002Fis-lm",{"title":11842,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,16117,1143,16118,16119,16120,16121,16071],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":16124,"title":16125,"body":16126,"course":659,"courses":17719,"created":1129,"description":17720,"extension":661,"meta":17721,"navigation":664,"path":17722,"seo":17723,"sources":17724,"stem":17725,"tags":17726,"type":3703,"updated":677,"__hash__":17729},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":16127,"toc":17707},[16128,16131,16227,16234,16254,16258,16263,16326,16345,16347,16350,16486,16488,16698,16732,16869,16873,16937,16953,16981,16985,17083,17087,17091,17144,17250,17464,17468,17511,17617,17669,17671],[12,16129,16125],{"id":16130},"lagrangeova-metoda-vázané-extrémy",[724,16132,16133,16134,3756,16157,16189,16190,16193,16194,16221,16222,16226],{},"Hledáme extrém funkce ",[883,16135,16137],{"className":16136},[886],[888,16138,16139],{"xmlns":890},[892,16140,16141,16155],{},[895,16142,16143,16145,16147,16149,16151,16153],{},[898,16144,1851],{},[1846,16146,1855],{"stretchy":1854},[898,16148,1858],{},[1846,16150,2136],{"separator":2135},[898,16152,1844],{},[1846,16154,1861],{"stretchy":1854},[902,16156,9689],{"encoding":904},[883,16158,16160],{"className":16159},[886],[888,16161,16162],{"xmlns":890},[892,16163,16164,16186],{},[895,16165,16166,16168,16170,16176,16178,16184],{},[898,16167,900],{},[1846,16169,1855],{"stretchy":1854},[2122,16171,16172,16174],{},[898,16173,2638],{},[1979,16175,2128],{},[1846,16177,2136],{"separator":2135},[2122,16179,16180,16182],{},[898,16181,2638],{},[1979,16183,1981],{},[1846,16185,1861],{"stretchy":1854},[902,16187,16188],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,16191,16192],{},"podmíněný"," rovnicí ",[883,16195,16197],{"className":16196},[886],[888,16198,16199],{"xmlns":890},[892,16200,16201,16219],{},[895,16202,16203,16205,16207,16209,16211,16213,16215,16217],{},[898,16204,10887],{},[1846,16206,1855],{"stretchy":1854},[898,16208,1858],{},[1846,16210,2136],{"separator":2135},[898,16212,1844],{},[1846,16214,1861],{"stretchy":1854},[1846,16216,1848],{},[1979,16218,2177],{},[902,16220,10904],{"encoding":904},". V ",[207,16223,16225],{"className":16224,"dataFsResolvedFilePath":1761,"href":1762},[210],"matematické ekonomii"," se používá pro:",[724,16228,16229],{},[2409,16230],{"alt":16231,"className":16232,"src":16233},"imek-lagrange-tecnost",[210,2413],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,16235,16236,16245,16251],{},[123,16237,16238,16241,16242,1861],{},[38,16239,16240],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,16243,9619],{"className":16244,"dataFsResolvedFilePath":878,"href":879},[210],[123,16246,16247,16250],{},[38,16248,16249],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,16252,16253],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,16255,16257],{"id":16256},"princip","Princip",[724,16259,10553,16260,2554],{},[38,16261,16262],{},"Lagrangeovu funkci",[724,16264,16265],{},[883,16266,16268],{"className":16267},[886],[888,16269,16270],{"xmlns":890},[892,16271,16272,16323],{},[895,16273,16274,16276,16278,16280,16282,16284,16286,16289,16291,16293,16295,16297,16299,16301,16303,16305,16307,16309,16311,16313,16315,16317,16319,16321],{},[898,16275,9641],{},[1846,16277,1855],{"stretchy":1854},[898,16279,1858],{},[1846,16281,2136],{"separator":2135},[898,16283,1844],{},[1846,16285,2136],{"separator":2135},[898,16287,16288],{},"λ",[1846,16290,1861],{"stretchy":1854},[1846,16292,1848],{},[898,16294,1851],{},[1846,16296,1855],{"stretchy":1854},[898,16298,1858],{},[1846,16300,2136],{"separator":2135},[898,16302,1844],{},[1846,16304,1861],{"stretchy":1854},[1846,16306,1945],{},[898,16308,16288],{},[2138,16310,2835],{},[898,16312,10887],{},[1846,16314,1855],{"stretchy":1854},[898,16316,1858],{},[1846,16318,2136],{"separator":2135},[898,16320,1844],{},[1846,16322,1861],{"stretchy":1854},[902,16324,16325],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,16327,4156,16328,7948,16342,1734],{},[883,16329,16331],{"className":16330},[886],[888,16332,16333],{"xmlns":890},[892,16334,16335,16339],{},[895,16336,16337],{},[898,16338,16288],{},[902,16340,16341],{"encoding":904},"\\lambda",[38,16343,16344],{},"Lagrangeův multiplikátor",[115,16346,3100],{"id":3099},[724,16348,16349],{},"Řešíme soustavu:",[724,16351,16352,16400,16448],{},[883,16353,16355],{"className":16354},[886],[888,16356,16357],{"xmlns":890},[892,16358,16359,16397],{},[895,16360,16361,16369,16371,16379,16381,16383,16385,16393,16395],{},[9012,16362,16363,16365,16367],{},[898,16364,9641],{},[898,16366,1858],{},[1846,16368,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,16370,1848],{},[9012,16372,16373,16375,16377],{},[898,16374,1851],{},[898,16376,1858],{},[1846,16378,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,16380,1945],{},[898,16382,16288],{},[2138,16384,2835],{},[9012,16386,16387,16389,16391],{},[898,16388,10887],{},[898,16390,1858],{},[1846,16392,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,16394,1848],{},[1979,16396,2177],{},[902,16398,16399],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,16401,16403],{"className":16402},[886],[888,16404,16405],{"xmlns":890},[892,16406,16407,16445],{},[895,16408,16409,16417,16419,16427,16429,16431,16433,16441,16443],{},[9012,16410,16411,16413,16415],{},[898,16412,9641],{},[898,16414,1844],{},[1846,16416,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,16418,1848],{},[9012,16420,16421,16423,16425],{},[898,16422,1851],{},[898,16424,1844],{},[1846,16426,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,16428,1945],{},[898,16430,16288],{},[2138,16432,2835],{},[9012,16434,16435,16437,16439],{},[898,16436,10887],{},[898,16438,1844],{},[1846,16440,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,16442,1848],{},[1979,16444,2177],{},[902,16446,16447],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,16449,16451],{"className":16450},[886],[888,16452,16453],{"xmlns":890},[892,16454,16455,16483],{},[895,16456,16457,16465,16467,16469,16471,16473,16475,16477,16479,16481],{},[9012,16458,16459,16461,16463],{},[898,16460,9641],{},[898,16462,16288],{},[1846,16464,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,16466,1848],{},[898,16468,10887],{},[1846,16470,1855],{"stretchy":1854},[898,16472,1858],{},[1846,16474,2136],{"separator":2135},[898,16476,1844],{},[1846,16478,1861],{"stretchy":1854},[1846,16480,1848],{},[1979,16482,2177],{},[902,16484,16485],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,16487,3174],{"id":3173},[724,16489,16490],{},[883,16491,16493],{"className":16492},[886],[888,16494,16495],{"xmlns":890},[892,16496,16497,16695],{},[895,16498,16499,16501,16503,16505,16507,16509,16511,16513,16515,16517,16519,16535,16537,16539,16555,16557,16559,16567,16573,16575,16577,16593,16595,16597,16613,16615,16617,16625,16631,16633,16635,16637,16653,16655,16657,16673,16675,16677,16685,16687],{},[898,16500,4029],{},[1846,16502,1855],{"stretchy":1854},[898,16504,1858],{},[1846,16506,2136],{"separator":2135},[898,16508,1844],{},[1846,16510,2136],{"separator":2135},[898,16512,16288],{},[1846,16514,1861],{"stretchy":1854},[1846,16516,1848],{},[1846,16518,1855],{"stretchy":1854},[9012,16520,16521,16523,16529],{},[898,16522,1851],{},[895,16524,16525,16527],{},[898,16526,1858],{},[898,16528,1858],{},[895,16530,16531,16533],{},[1846,16532,2228],{"mathvariant":2226},[1846,16534,2228],{"mathvariant":2226},[1846,16536,1945],{},[898,16538,16288],{},[9012,16540,16541,16543,16549],{},[898,16542,10887],{},[895,16544,16545,16547],{},[898,16546,1858],{},[898,16548,1858],{},[895,16550,16551,16553],{},[1846,16552,2228],{"mathvariant":2226},[1846,16554,2228],{"mathvariant":2226},[1846,16556,1861],{"stretchy":1854},[1846,16558,1855],{"stretchy":1854},[9012,16560,16561,16563,16565],{},[898,16562,10887],{},[898,16564,1844],{},[1846,16566,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1974,16568,16569,16571],{},[1846,16570,1861],{"stretchy":1854},[1979,16572,1981],{},[1846,16574,1945],{},[1846,16576,1855],{"stretchy":1854},[9012,16578,16579,16581,16587],{},[898,16580,1851],{},[895,16582,16583,16585],{},[898,16584,1844],{},[898,16586,1844],{},[895,16588,16589,16591],{},[1846,16590,2228],{"mathvariant":2226},[1846,16592,2228],{"mathvariant":2226},[1846,16594,1945],{},[898,16596,16288],{},[9012,16598,16599,16601,16607],{},[898,16600,10887],{},[895,16602,16603,16605],{},[898,16604,1844],{},[898,16606,1844],{},[895,16608,16609,16611],{},[1846,16610,2228],{"mathvariant":2226},[1846,16612,2228],{"mathvariant":2226},[1846,16614,1861],{"stretchy":1854},[1846,16616,1855],{"stretchy":1854},[9012,16618,16619,16621,16623],{},[898,16620,10887],{},[898,16622,1858],{},[1846,16624,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1974,16626,16627,16629],{},[1846,16628,1861],{"stretchy":1854},[1979,16630,1981],{},[1846,16632,2075],{},[1979,16634,1981],{},[1846,16636,1855],{"stretchy":1854},[9012,16638,16639,16641,16647],{},[898,16640,1851],{},[895,16642,16643,16645],{},[898,16644,1858],{},[898,16646,1844],{},[895,16648,16649,16651],{},[1846,16650,2228],{"mathvariant":2226},[1846,16652,2228],{"mathvariant":2226},[1846,16654,1945],{},[898,16656,16288],{},[9012,16658,16659,16661,16667],{},[898,16660,10887],{},[895,16662,16663,16665],{},[898,16664,1858],{},[898,16666,1844],{},[895,16668,16669,16671],{},[1846,16670,2228],{"mathvariant":2226},[1846,16672,2228],{"mathvariant":2226},[1846,16674,1861],{"stretchy":1854},[2138,16676,2835],{},[9012,16678,16679,16681,16683],{},[898,16680,10887],{},[898,16682,1858],{},[1846,16684,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[2138,16686,2835],{},[9012,16688,16689,16691,16693],{},[898,16690,10887],{},[898,16692,1844],{},[1846,16694,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,16696,16697],{"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",[724,16699,16700,16701,16731],{},"Je-li ",[883,16702,16704],{"className":16703},[886],[888,16705,16706],{"xmlns":890},[892,16707,16708,16728],{},[895,16709,16710,16712,16714,16716,16718,16720,16726],{},[1846,16711,2336],{"stretchy":1854},[898,16713,207],{},[1846,16715,2136],{"separator":2135},[898,16717,1948],{},[1846,16719,2136],{"separator":2135},[2122,16721,16722,16724],{},[898,16723,16288],{},[1979,16725,2177],{},[1846,16727,2351],{"stretchy":1854},[902,16729,16730],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,16733,16734,16802],{},[123,16735,16736,3262,16772,16774,16775],{},[883,16737,16739],{"className":16738},[886],[888,16740,16741],{"xmlns":890},[892,16742,16743,16769],{},[895,16744,16745,16747,16749,16751,16753,16755,16757,16763,16765,16767],{},[898,16746,4029],{},[1846,16748,1855],{"stretchy":1854},[898,16750,207],{},[1846,16752,2136],{"separator":2135},[898,16754,1948],{},[1846,16756,2136],{"separator":2135},[2122,16758,16759,16761],{},[898,16760,16288],{},[1979,16762,2177],{},[1846,16764,1861],{"stretchy":1854},[1846,16766,3295],{},[1979,16768,2177],{},[902,16770,16771],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,16773,3565],{}," vázané podmínkou ",[883,16776,16778],{"className":16777},[886],[888,16779,16780],{"xmlns":890},[892,16781,16782,16800],{},[895,16783,16784,16786,16788,16790,16792,16794,16796,16798],{},[898,16785,10887],{},[1846,16787,1855],{"stretchy":1854},[898,16789,1858],{},[1846,16791,2136],{"separator":2135},[898,16793,1844],{},[1846,16795,1861],{"stretchy":1854},[1846,16797,1848],{},[1979,16799,2177],{},[902,16801,10904],{"encoding":904},[123,16803,16804,3262,16840,16774,16842],{},[883,16805,16807],{"className":16806},[886],[888,16808,16809],{"xmlns":890},[892,16810,16811,16837],{},[895,16812,16813,16815,16817,16819,16821,16823,16825,16831,16833,16835],{},[898,16814,4029],{},[1846,16816,1855],{"stretchy":1854},[898,16818,207],{},[1846,16820,2136],{"separator":2135},[898,16822,1948],{},[1846,16824,2136],{"separator":2135},[2122,16826,16827,16829],{},[898,16828,16288],{},[1979,16830,2177],{},[1846,16832,1861],{"stretchy":1854},[1846,16834,3256],{},[1979,16836,2177],{},[902,16838,16839],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,16841,3623],{},[883,16843,16845],{"className":16844},[886],[888,16846,16847],{"xmlns":890},[892,16848,16849,16867],{},[895,16850,16851,16853,16855,16857,16859,16861,16863,16865],{},[898,16852,10887],{},[1846,16854,1855],{"stretchy":1854},[898,16856,1858],{},[1846,16858,2136],{"separator":2135},[898,16860,1844],{},[1846,16862,1861],{"stretchy":1854},[1846,16864,1848],{},[1979,16866,2177],{},[902,16868,10904],{"encoding":904},[115,16870,16872],{"id":16871},"význam-multiplikátoru","Význam multiplikátoru",[724,16874,16875],{},[883,16876,16878],{"className":16877},[886],[888,16879,16880],{"xmlns":890},[892,16881,16882,16934],{},[895,16883,16884,16886,16888,16910,16912],{},[898,16885,16288],{},[1846,16887,1848],{},[2179,16889,16890,16898],{},[9012,16891,16892,16894,16896],{},[898,16893,1851],{},[898,16895,1858],{},[1846,16897,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[895,16899,16900,16902],{},[1846,16901,2075],{},[9012,16903,16904,16906,16908],{},[898,16905,10887],{},[898,16907,1858],{},[1846,16909,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,16911,1848],{},[2179,16913,16914,16922],{},[9012,16915,16916,16918,16920],{},[898,16917,1851],{},[898,16919,1844],{},[1846,16921,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[895,16923,16924,16926],{},[1846,16925,2075],{},[9012,16927,16928,16930,16932],{},[898,16929,10887],{},[898,16931,1844],{},[1846,16933,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,16935,16936],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,16938,16939,16952],{},[883,16940,16942],{"className":16941},[886],[888,16943,16944],{"xmlns":890},[892,16945,16946,16950],{},[895,16947,16948],{},[898,16949,16288],{},[902,16951,16341],{"encoding":904}," udává:",[120,16954,16955,16961],{},[123,16956,16957,16958],{},"konstantní ",[38,16959,16960],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,16962,16963,16966,16967,16980],{},[38,16964,16965],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,16968,16970],{"className":16969},[886],[888,16971,16972],{"xmlns":890},[892,16973,16974,16978],{},[895,16975,16976],{},[898,16977,1851],{},[902,16979,1851],{"encoding":904},", uvolní-li se omezení o jednotku",[115,16982,16984],{"id":16983},"alternativní-postup","Alternativní postup",[724,16986,16987,16988,17015,17016,17040,17041,17065,17066,17079,17080,1734],{},"Lze-li z ",[883,16989,16991],{"className":16990},[886],[888,16992,16993],{"xmlns":890},[892,16994,16995,17013],{},[895,16996,16997,16999,17001,17003,17005,17007,17009,17011],{},[898,16998,10887],{},[1846,17000,1855],{"stretchy":1854},[898,17002,1858],{},[1846,17004,2136],{"separator":2135},[898,17006,1844],{},[1846,17008,1861],{"stretchy":1854},[1846,17010,1848],{},[1979,17012,2177],{},[902,17014,10904],{"encoding":904}," vyjádřit ",[883,17017,17019],{"className":17018},[886],[888,17020,17021],{"xmlns":890},[892,17022,17023,17037],{},[895,17024,17025,17027,17029,17031,17033,17035],{},[898,17026,1844],{},[1846,17028,1848],{},[898,17030,1844],{},[1846,17032,1855],{"stretchy":1854},[898,17034,1858],{},[1846,17036,1861],{"stretchy":1854},[902,17038,17039],{"encoding":904},"y = y(x)"," (nebo ",[883,17042,17044],{"className":17043},[886],[888,17045,17046],{"xmlns":890},[892,17047,17048,17062],{},[895,17049,17050,17052,17054,17056,17058,17060],{},[898,17051,1858],{},[1846,17053,1848],{},[898,17055,1858],{},[1846,17057,1855],{"stretchy":1854},[898,17059,1844],{},[1846,17061,1861],{"stretchy":1854},[902,17063,17064],{"encoding":904},"x = x(y)","), dosadíme do ",[883,17067,17069],{"className":17068},[886],[888,17070,17071],{"xmlns":890},[892,17072,17073,17077],{},[895,17074,17075],{},[898,17076,1851],{},[902,17078,1851],{"encoding":904}," a převedeme na ",[38,17081,17082],{},"extrém funkce jedné proměnné",[115,17084,17086],{"id":17085},"použití-v-imek","Použití v ImeK",[198,17088,17090],{"id":17089},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,17092,17093,17094,1734],{},"Rozpočtové omezení: ",[883,17095,17097],{"className":17096},[886],[888,17098,17099],{"xmlns":890},[892,17100,17101,17141],{},[895,17102,17103,17109,17111,17119,17125,17127,17135],{},[1974,17104,17105,17107],{},[898,17106,8974],{},[1846,17108,4200],{},[1846,17110,1848],{},[9012,17112,17113,17115,17117],{},[898,17114,3783],{},[1979,17116,2128],{},[1846,17118,4200],{},[2122,17120,17121,17123],{},[898,17122,2638],{},[1979,17124,2128],{},[1846,17126,1945],{},[9012,17128,17129,17131,17133],{},[898,17130,3783],{},[1979,17132,1981],{},[1846,17134,4200],{},[2122,17136,17137,17139],{},[898,17138,2638],{},[1979,17140,1981],{},[902,17142,17143],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,17145,17146],{},[883,17147,17149],{"className":17148},[886],[888,17150,17151],{"xmlns":890},[892,17152,17153,17247],{},[895,17154,17155,17157,17159,17165,17167,17173,17175,17177,17179,17181,17183,17185,17191,17193,17199,17201,17203,17205,17207,17213,17215,17223,17229,17231,17239,17245],{},[898,17156,9641],{},[1846,17158,1855],{"stretchy":1854},[2122,17160,17161,17163],{},[898,17162,2638],{},[1979,17164,2128],{},[1846,17166,2136],{"separator":2135},[2122,17168,17169,17171],{},[898,17170,2638],{},[1979,17172,1981],{},[1846,17174,2136],{"separator":2135},[898,17176,16288],{},[1846,17178,1861],{"stretchy":1854},[1846,17180,1848],{},[898,17182,900],{},[1846,17184,1855],{"stretchy":1854},[2122,17186,17187,17189],{},[898,17188,2638],{},[1979,17190,2128],{},[1846,17192,2136],{"separator":2135},[2122,17194,17195,17197],{},[898,17196,2638],{},[1979,17198,1981],{},[1846,17200,1861],{"stretchy":1854},[1846,17202,1945],{},[898,17204,16288],{},[1846,17206,1855],{"stretchy":1854},[1974,17208,17209,17211],{},[898,17210,8974],{},[1846,17212,4200],{},[1846,17214,2075],{},[9012,17216,17217,17219,17221],{},[898,17218,3783],{},[1979,17220,2128],{},[1846,17222,4200],{},[2122,17224,17225,17227],{},[898,17226,2638],{},[1979,17228,2128],{},[1846,17230,2075],{},[9012,17232,17233,17235,17237],{},[898,17234,3783],{},[1979,17236,1981],{},[1846,17238,4200],{},[2122,17240,17241,17243],{},[898,17242,2638],{},[1979,17244,1981],{},[1846,17246,1861],{"stretchy":1854},[902,17248,17249],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,17251,17252,17253,1343,17285,1343,17317,17366,17367,17421,17422,1734],{},"Soustava: ",[883,17254,17256],{"className":17255},[886],[888,17257,17258],{"xmlns":890},[892,17259,17260,17282],{},[895,17261,17262,17270,17272,17274],{},[9012,17263,17264,17266,17268],{},[898,17265,900],{},[1979,17267,2128],{},[1846,17269,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,17271,1848],{},[898,17273,16288],{},[9012,17275,17276,17278,17280],{},[898,17277,3783],{},[1979,17279,2128],{},[1846,17281,4200],{},[902,17283,17284],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,17286,17288],{"className":17287},[886],[888,17289,17290],{"xmlns":890},[892,17291,17292,17314],{},[895,17293,17294,17302,17304,17306],{},[9012,17295,17296,17298,17300],{},[898,17297,900],{},[1979,17299,1981],{},[1846,17301,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,17303,1848],{},[898,17305,16288],{},[9012,17307,17308,17310,17312],{},[898,17309,3783],{},[1979,17311,1981],{},[1846,17313,4200],{},[902,17315,17316],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,17318,17320],{"className":17319},[886],[888,17321,17322],{"xmlns":890},[892,17323,17324,17364],{},[895,17325,17326,17332,17334,17342,17348,17350,17358],{},[1974,17327,17328,17330],{},[898,17329,8974],{},[1846,17331,4200],{},[1846,17333,1848],{},[9012,17335,17336,17338,17340],{},[898,17337,3783],{},[1979,17339,2128],{},[1846,17341,4200],{},[2122,17343,17344,17346],{},[898,17345,2638],{},[1979,17347,2128],{},[1846,17349,1945],{},[9012,17351,17352,17354,17356],{},[898,17353,3783],{},[1979,17355,1981],{},[1846,17357,4200],{},[2122,17359,17360,17362],{},[898,17361,2638],{},[1979,17363,1981],{},[902,17365,17143],{"encoding":904},". Z prvních dvou: ",[883,17368,17370],{"className":17369},[886],[888,17371,17372],{"xmlns":890},[892,17373,17374,17418],{},[895,17375,17376,17396,17398],{},[2175,17377,17378],{"scriptlevel":2177,"displaystyle":1854},[2179,17379,17380,17388],{},[9012,17381,17382,17384,17386],{},[898,17383,900],{},[1979,17385,2128],{},[1846,17387,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[9012,17389,17390,17392,17394],{},[898,17391,900],{},[1979,17393,1981],{},[1846,17395,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,17397,1848],{},[2175,17399,17400],{"scriptlevel":2177,"displaystyle":1854},[2179,17401,17402,17410],{},[9012,17403,17404,17406,17408],{},[898,17405,3783],{},[1979,17407,2128],{},[1846,17409,4200],{},[9012,17411,17412,17414,17416],{},[898,17413,3783],{},[1979,17415,1981],{},[1846,17417,4200],{},[902,17419,17420],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,17423,17425],{"className":17424},[886],[888,17426,17427],{"xmlns":890},[892,17428,17429,17461],{},[895,17430,17431,17433,17435,17437,17439,17441],{},[898,17432,2667],{},[898,17434,3840],{},[898,17436,2626],{},[898,17438,8519],{},[1846,17440,1848],{},[2175,17442,17443],{"scriptlevel":2177,"displaystyle":1854},[2179,17444,17445,17453],{},[9012,17446,17447,17449,17451],{},[898,17448,3783],{},[1979,17450,2128],{},[1846,17452,4200],{},[9012,17454,17455,17457,17459],{},[898,17456,3783],{},[1979,17458,1981],{},[1846,17460,4200],{},[902,17462,17463],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,17465,17467],{"id":17466},"minimalizace-výdajů","Minimalizace výdajů",[724,17469,17470,17471,1734],{},"Podmínka dané užitečnosti ",[883,17472,17474],{"className":17473},[886],[888,17475,17476],{"xmlns":890},[892,17477,17478,17508],{},[895,17479,17480,17486,17488,17490,17492,17498,17500,17506],{},[1974,17481,17482,17484],{},[898,17483,900],{},[1846,17485,4200],{},[1846,17487,1848],{},[898,17489,900],{},[1846,17491,1855],{"stretchy":1854},[2122,17493,17494,17496],{},[898,17495,2638],{},[1979,17497,2128],{},[1846,17499,2136],{"separator":2135},[2122,17501,17502,17504],{},[898,17503,2638],{},[1979,17505,1981],{},[1846,17507,1861],{"stretchy":1854},[902,17509,17510],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,17512,17513],{},[883,17514,17516],{"className":17515},[886],[888,17517,17518],{"xmlns":890},[892,17519,17520,17614],{},[895,17521,17522,17524,17526,17532,17534,17540,17542,17544,17546,17548,17556,17562,17564,17572,17578,17580,17582,17584,17590,17592,17594,17596,17602,17604,17610,17612],{},[898,17523,9641],{},[1846,17525,1855],{"stretchy":1854},[2122,17527,17528,17530],{},[898,17529,2638],{},[1979,17531,2128],{},[1846,17533,2136],{"separator":2135},[2122,17535,17536,17538],{},[898,17537,2638],{},[1979,17539,1981],{},[1846,17541,2136],{"separator":2135},[898,17543,16288],{},[1846,17545,1861],{"stretchy":1854},[1846,17547,1848],{},[9012,17549,17550,17552,17554],{},[898,17551,3783],{},[1979,17553,2128],{},[1846,17555,4200],{},[2122,17557,17558,17560],{},[898,17559,2638],{},[1979,17561,2128],{},[1846,17563,1945],{},[9012,17565,17566,17568,17570],{},[898,17567,3783],{},[1979,17569,1981],{},[1846,17571,4200],{},[2122,17573,17574,17576],{},[898,17575,2638],{},[1979,17577,1981],{},[1846,17579,1945],{},[898,17581,16288],{},[1846,17583,1855],{"stretchy":1854},[1974,17585,17586,17588],{},[898,17587,900],{},[1846,17589,4200],{},[1846,17591,2075],{},[898,17593,900],{},[1846,17595,1855],{"stretchy":1854},[2122,17597,17598,17600],{},[898,17599,2638],{},[1979,17601,2128],{},[1846,17603,2136],{"separator":2135},[2122,17605,17606,17608],{},[898,17607,2638],{},[1979,17609,1981],{},[1846,17611,1861],{"stretchy":1854},[1846,17613,1861],{"stretchy":1854},[902,17615,17616],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,17618,17619,17620,1734],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,17621,17623],{"className":17622},[886],[888,17624,17625],{"xmlns":890},[892,17626,17627,17666],{},[895,17628,17629,17636,17638,17644,17646,17652,17654,17660,17662,17664],{},[2122,17630,17631,17633],{},[898,17632,2638],{},[898,17634,17635],{},"i",[1846,17637,1848],{},[2122,17639,17640,17642],{},[898,17641,4029],{},[898,17643,17635],{},[1846,17645,1855],{"stretchy":1854},[2122,17647,17648,17650],{},[898,17649,3783],{},[1979,17651,2128],{},[1846,17653,2136],{"separator":2135},[2122,17655,17656,17658],{},[898,17657,3783],{},[1979,17659,1981],{},[1846,17661,2136],{"separator":2135},[898,17663,900],{},[1846,17665,1861],{"stretchy":1854},[902,17667,17668],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,17670,3640],{"id":3639},[120,17672,17673,17680,17687,17696],{},[123,17674,17675,2053,17677],{},[38,17676,3647],{},[207,17678,784],{"className":17679,"dataFsResolvedFilePath":782,"href":783},[210],[123,17681,17682,2053,17684],{},[38,17683,3655],{},[207,17685,1701],{"className":17686,"dataFsResolvedFilePath":800,"href":801},[210],[123,17688,17689,2053,17692,17695],{},[38,17690,17691],{},"Aplikace v kurzu:",[207,17693,880],{"className":17694,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,17697,17698,2053,17700,1343,17703,17706],{},[38,17699,3663],{},[207,17701,936],{"className":17702,"dataFsResolvedFilePath":934,"href":935},[210],[207,17704,1400],{"className":17705,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":17708},[17709,17710,17711,17712,17713,17714,17718],{"id":16256,"depth":642,"text":16257},{"id":3099,"depth":642,"text":3100},{"id":3173,"depth":642,"text":3174},{"id":16871,"depth":642,"text":16872},{"id":16983,"depth":642,"text":16984},{"id":17085,"depth":642,"text":17086,"children":17715},[17716,17717],{"id":17089,"depth":649,"text":17090},{"id":17466,"depth":649,"text":17467},{"id":3639,"depth":642,"text":3640},[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":16125,"description":17720},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,17727,17728],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":17731,"title":936,"body":17732,"course":1128,"courses":659,"created":9402,"description":641,"extension":661,"meta":27600,"navigation":664,"path":27601,"seo":27602,"sources":27603,"stem":27604,"tags":27605,"type":3703,"updated":677,"__hash__":27609},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":17733,"toc":27562},[17734,17737,17739,17862,17997,18001,18004,18117,18121,18149,18196,18199,18265,18310,18313,18339,18370,18374,18378,18422,18466,18528,18583,18586,18590,18593,18640,18737,18843,18849,18926,18955,19094,19098,19127,19177,19324,19414,19418,19444,19482,19509,19547,19609,19684,19762,19820,19886,19930,19934,19992,20041,20086,20299,20419,20425,20429,20452,20456,20463,20467,20498,20533,20537,20587,20675,20717,20738,20800,20860,20864,20935,21003,21075,21190,21238,21242,21245,21286,21325,21348,21462,21626,21634,21661,21691,21694,21771,21924,22008,22347,22351,22475,22611,22747,22800,22803,23053,23134,23138,23141,23199,23231,23234,23283,23286,23357,23553,23557,23708,23938,23976,24029,24075,24078,24134,24183,24387,24477,24481,24497,24504,24673,24677,24748,24829,24910,24989,25135,25223,25227,25410,25541,25586,25683,25687,26426,26428,27479,27481],[12,17735,936],{"id":17736},"národní-důchod",[115,17738,11851],{"id":11850},[724,17740,17741,17742,2053,17746,17749,17750,2053,17753,17766,17767,17770,17771,17774,17775,17778,17779,17781,17782,2053,17784,17801,17802,17819,17820,17823,17824,3764],{},"Kapitola 7 ",[207,17743,17745],{"className":17744,"dataFsResolvedFilePath":1761,"href":1762},[210],"Matematické ekonomie",[38,17747,17748],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,17751,17752],{},"národním důchodem",[883,17754,17756],{"className":17755},[886],[888,17757,17758],{"xmlns":890},[892,17759,17760,17764],{},[895,17761,17762],{},[898,17763,8974],{},[902,17765,8974],{"encoding":904},". Budují se postupně bohatší modely — ",[38,17768,17769],{},"C-I"," (jen spotřeba a investice) → ",[38,17772,17773],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,17776,17777],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,17780,11856],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,17783,13730],{},[883,17785,17787],{"className":17786},[886],[888,17788,17789],{"xmlns":890},[892,17790,17791,17799],{},[895,17792,17793],{},[1974,17794,17795,17797],{},[898,17796,8974],{},[898,17798,4098],{},[902,17800,13748],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,17803,17805],{"className":17804},[886],[888,17806,17807],{"xmlns":890},[892,17808,17809,17817],{},[895,17810,17811],{},[1974,17812,17813,17815],{},[898,17814,8974],{},[898,17816,4098],{},[902,17818,13748],{"encoding":904}," na exogenní veličiny popisují ",[38,17821,17822],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,17825,17827],{"className":17826},[886],[888,17828,17829],{"xmlns":890},[892,17830,17831,17859],{},[895,17832,17833,17835,17837,17839,17841,17843,17845,17847,17849,17851,17853,17855,17857],{},[1979,17834,2128],{},[898,17836,4520],{"mathvariant":2226},[1846,17838,1855],{"stretchy":1854},[1979,17840,2128],{},[1846,17842,2075],{},[898,17844,207],{},[1846,17846,1861],{"stretchy":1854},[1846,17848,1848],{},[1979,17850,2128],{},[898,17852,4520],{"mathvariant":2226},[898,17854,2667],{},[898,17856,3783],{},[898,17858,8519],{},[902,17860,17861],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[1639,17863,17864],{},[724,17865,17866,17868,17869,17872,17873,17891,17892,17922,17923,17970,17971,17973,17974,17996],{},[883,17867,4001],{}," Intuice\n",[38,17870,17871],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,17874,17876],{"className":17875},[886],[888,17877,17878],{"xmlns":890},[892,17879,17880,17888],{},[895,17881,17882,17884,17886],{},[898,17883,2667],{},[898,17885,3783],{},[898,17887,2626],{},[902,17889,17890],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,17893,17895],{"className":17894},[886],[888,17896,17897],{"xmlns":890},[892,17898,17899,17919],{},[895,17900,17901,17903,17905,17907,17909,17911,17913,17915,17917],{},[898,17902,2667],{},[898,17904,3783],{},[898,17906,8519],{},[1846,17908,1848],{},[1979,17910,2128],{},[1846,17912,2075],{},[898,17914,2667],{},[898,17916,3783],{},[898,17918,2626],{},[902,17920,17921],{"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 ",[883,17924,17926],{"className":17925},[886],[888,17927,17928],{"xmlns":890},[892,17929,17930,17967],{},[895,17931,17932,17934,17936,17938,17940,17946,17948,17951,17953,17955,17957,17959,17961,17963,17965],{},[1979,17933,2128],{},[1846,17935,1945],{},[898,17937,207],{},[1846,17939,1945],{},[1974,17941,17942,17944],{},[898,17943,207],{},[1979,17945,1981],{},[1846,17947,1945],{},[1846,17949,17950],{},"⋯",[1846,17952,1848],{},[1979,17954,2128],{},[898,17956,4520],{"mathvariant":2226},[1846,17958,1855],{"stretchy":1854},[1979,17960,2128],{},[1846,17962,2075],{},[898,17964,207],{},[1846,17966,1861],{"stretchy":1854},[902,17968,17969],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,17972,11856],{}," 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 ",[883,17975,17977],{"className":17976},[886],[888,17978,17979],{"xmlns":890},[892,17980,17981,17993],{},[895,17982,17983,17985,17987,17989,17991],{},[1846,17984,1855],{"stretchy":1854},[898,17986,8974],{},[1846,17988,2136],{"separator":2135},[898,17990,11886],{},[1846,17992,1861],{"stretchy":1854},[902,17994,17995],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,17998,18000],{"id":17999},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,18002,18003],{},"Po prostudování kapitoly by čtenář měl umět:",[120,18005,18006,18009,18012,18015,18018,18021,18024,18114],{},[123,18007,18008],{},"popsat zjednodušený model národní ekonomiky,",[123,18010,18011],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,18013,18014],{},"popsat lineární model spotřeby a úspor,",[123,18016,18017],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,18019,18020],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,18022,18023],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,18025,18026,18027,1343,18044,1343,18066,1745,18091,18113],{},"popsat modely ",[883,18028,18030],{"className":18029},[886],[888,18031,18032],{"xmlns":890},[892,18033,18034,18042],{},[895,18035,18036,18038,18040],{},[898,18037,2626],{},[2138,18039,12135],{},[898,18041,12029],{},[902,18043,12140],{"encoding":904},[883,18045,18047],{"className":18046},[886],[888,18048,18049],{"xmlns":890},[892,18050,18051,18063],{},[895,18052,18053,18055,18057,18059,18061],{},[898,18054,2626],{},[2138,18056,12135],{},[898,18058,12029],{},[2138,18060,12135],{},[898,18062,11957],{},[902,18064,18065],{"encoding":904},"C\\text{-}I\\text{-}G",[883,18067,18069],{"className":18068},[886],[888,18070,18071],{"xmlns":890},[892,18072,18073,18089],{},[895,18074,18075,18077,18079,18081,18083,18085,18087],{},[898,18076,2626],{},[2138,18078,12135],{},[898,18080,12029],{},[2138,18082,12135],{},[898,18084,11957],{},[2138,18086,12135],{},[898,18088,12165],{},[902,18090,12168],{"encoding":904},[883,18092,18094],{"className":18093},[886],[888,18095,18096],{"xmlns":890},[892,18097,18098,18110],{},[895,18099,18100,18102,18104,18106,18108],{},[898,18101,12029],{},[898,18103,8519],{},[2138,18105,12135],{},[898,18107,9641],{},[898,18109,2667],{},[902,18111,18112],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,18115,18116],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,18118,18120],{"id":18119},"gnp-a-národní-důchod","GNP a národní důchod",[724,18122,18123,2053,18126,9871,18145,18148],{},[38,18124,18125],{},"Hrubý národní produkt",[883,18127,18129],{"className":18128},[886],[888,18130,18131],{"xmlns":890},[892,18132,18133,18142],{},[895,18134,18135,18137,18140],{},[898,18136,11957],{},[898,18138,18139],{},"N",[898,18141,3783],{},[902,18143,18144],{"encoding":904},"GNP",[614,18146,18147],{},"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:",[724,18150,18151],{},[883,18152,18154],{"className":18153},[886],[888,18155,18156],{"xmlns":890},[892,18157,18158,18193],{},[895,18159,18160,18162,18164,18166,18168,18170,18172,18174,18176,18178,18180,18182,18184,18186,18188,18191],{},[898,18161,11957],{},[898,18163,18139],{},[898,18165,3783],{},[1846,18167,1848],{},[898,18169,2626],{},[1846,18171,1945],{},[898,18173,12029],{},[1846,18175,1945],{},[898,18177,11957],{},[1846,18179,1945],{},[898,18181,12165],{},[1846,18183,2136],{"separator":2135},[5724,18185],{"width":5726},[1846,18187,1855],{"stretchy":1854},[1979,18189,18190],{},"7.1",[1846,18192,1861],{"stretchy":1854},[902,18194,18195],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,18197,18198],{},"kde",[120,18200,18201,18217,18233,18249],{},[123,18202,18203,18216],{},[883,18204,18206],{"className":18205},[886],[888,18207,18208],{"xmlns":890},[892,18209,18210,18214],{},[895,18211,18212],{},[898,18213,2626],{},[902,18215,2626],{"encoding":904}," — výdaje domácností na spotřebu,",[123,18218,18219,18232],{},[883,18220,18222],{"className":18221},[886],[888,18223,18224],{"xmlns":890},[892,18225,18226,18230],{},[895,18227,18228],{},[898,18229,12029],{},[902,18231,12029],{"encoding":904}," — hrubé domácí investice,",[123,18234,18235,18248],{},[883,18236,18238],{"className":18237},[886],[888,18239,18240],{"xmlns":890},[892,18241,18242,18246],{},[895,18243,18244],{},[898,18245,11957],{},[902,18247,11957],{"encoding":904}," — vládní výdaje,",[123,18250,18251,18264],{},[883,18252,18254],{"className":18253},[886],[888,18255,18256],{"xmlns":890},[892,18257,18258,18262],{},[895,18259,18260],{},[898,18261,12165],{},[902,18263,12165],{"encoding":904}," — čistý export.",[724,18266,18267,18268,18285,18286,18289,18290,2053,18293,9871,18306,18309],{},"K měření ",[883,18269,18271],{"className":18270},[886],[888,18272,18273],{"xmlns":890},[892,18274,18275,18283],{},[895,18276,18277,18279,18281],{},[898,18278,11957],{},[898,18280,18139],{},[898,18282,3783],{},[902,18284,18144],{"encoding":904}," se užívá ",[38,18287,18288],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,18291,18292],{},"národní důchod",[883,18294,18296],{"className":18295},[886],[888,18297,18298],{"xmlns":890},[892,18299,18300,18304],{},[895,18301,18302],{},[898,18303,8974],{},[902,18305,8974],{"encoding":904},[614,18307,18308],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,18311,18312],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,18314,18315],{},[883,18316,18318],{"className":18317},[886],[888,18319,18320],{"xmlns":890},[892,18321,18322,18336],{},[895,18323,18324,18326,18328,18330,18332,18334],{},[898,18325,11957],{},[898,18327,18139],{},[898,18329,3783],{},[1846,18331,1650],{},[898,18333,8974],{},[1846,18335,2136],{"separator":2135},[902,18337,18338],{"encoding":904},"GNP \\approx Y,",[724,18340,18341,18342,9871,18345,18348,18349,18362,18363,18366,18367,1734],{},"a užívá se společného názvu ",[38,18343,18344],{},"důchod",[614,18346,18347],{},"income",") s označením ",[883,18350,18352],{"className":18351},[886],[888,18353,18354],{"xmlns":890},[892,18355,18356,18360],{},[895,18357,18358],{},[898,18359,8974],{},[902,18361,8974],{"encoding":904},". Domácnosti důchod použijí ke ",[38,18364,18365],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,18368,18369],{},"úspor",[115,18371,18373],{"id":18372},"spotřeba-a-úspory","Spotřeba a úspory",[198,18375,18377],{"id":18376},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,18379,18380,18381,18394,18395,18408,18409,2554],{},"Jak spotřeba ",[883,18382,18384],{"className":18383},[886],[888,18385,18386],{"xmlns":890},[892,18387,18388,18392],{},[895,18389,18390],{},[898,18391,2626],{},[902,18393,2626],{"encoding":904},", tak úspory ",[883,18396,18398],{"className":18397},[886],[888,18399,18400],{"xmlns":890},[892,18401,18402,18406],{},[895,18403,18404],{},[898,18405,8519],{},[902,18407,8519],{"encoding":904}," závisejí na důchodu ",[883,18410,18412],{"className":18411},[886],[888,18413,18414],{"xmlns":890},[892,18415,18416,18420],{},[895,18417,18418],{},[898,18419,8974],{},[902,18421,8974],{"encoding":904},[724,18423,18424],{},[883,18425,18427],{"className":18426},[886],[888,18428,18429],{"xmlns":890},[892,18430,18431,18463],{},[895,18432,18433,18435,18437,18439,18441,18443,18445,18447,18449,18451,18453,18455,18457,18459,18461],{},[898,18434,2626],{},[1846,18436,1848],{},[898,18438,2626],{},[1846,18440,1855],{"stretchy":1854},[898,18442,8974],{},[1846,18444,1861],{"stretchy":1854},[1846,18446,2136],{"separator":2135},[5724,18448],{"width":5726},[898,18450,8519],{},[1846,18452,1848],{},[898,18454,8519],{},[1846,18456,1855],{"stretchy":1854},[898,18458,8974],{},[1846,18460,1861],{"stretchy":1854},[898,18462,1734],{"mathvariant":2226},[902,18464,18465],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,18467,18468,7948,18487,9871,18490,18493,18494,7948,18514,9871,18517,18520,18521,1745,18524,18527],{},[883,18469,18471],{"className":18470},[886],[888,18472,18473],{"xmlns":890},[892,18474,18475,18485],{},[895,18476,18477,18479,18481,18483],{},[898,18478,2626],{},[1846,18480,1855],{"stretchy":1854},[898,18482,8974],{},[1846,18484,1861],{"stretchy":1854},[902,18486,14061],{"encoding":904},[38,18488,18489],{},"funkce spotřeby",[614,18491,18492],{},"consumption function","), ",[883,18495,18497],{"className":18496},[886],[888,18498,18499],{"xmlns":890},[892,18500,18501,18511],{},[895,18502,18503,18505,18507,18509],{},[898,18504,8519],{},[1846,18506,1855],{"stretchy":1854},[898,18508,8974],{},[1846,18510,1861],{"stretchy":1854},[902,18512,18513],{"encoding":904},"S(Y)",[38,18515,18516],{},"funkce úspor",[614,18518,18519],{},"savings function","); jejich grafy se nazývají ",[38,18522,18523],{},"křivka spotřeby",[38,18525,18526],{},"křivka úspor",". Platí základní identita",[724,18529,18530],{},[883,18531,18533],{"className":18532},[886],[888,18534,18535],{"xmlns":890},[892,18536,18537,18580],{},[895,18538,18539,18541,18543,18545,18547,18549,18551,18553,18555,18557,18559,18561,18563,18565,18567,18569,18571,18573,18575,18578],{},[898,18540,8974],{},[1846,18542,1848],{},[898,18544,2626],{},[1846,18546,1945],{},[898,18548,8519],{},[1846,18550,1848],{},[898,18552,2626],{},[1846,18554,1855],{"stretchy":1854},[898,18556,8974],{},[1846,18558,1861],{"stretchy":1854},[1846,18560,1945],{},[898,18562,8519],{},[1846,18564,1855],{"stretchy":1854},[898,18566,8974],{},[1846,18568,1861],{"stretchy":1854},[898,18570,1734],{"mathvariant":2226},[5724,18572],{"width":5726},[1846,18574,1855],{"stretchy":1854},[1979,18576,18577],{},"7.2",[1846,18579,1861],{"stretchy":1854},[902,18581,18582],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,18584,18585],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,18587,18589],{"id":18588},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,18591,18592],{},"Nejjednodušší model předpokládá lineární tvar",[724,18594,18595],{},[883,18596,18598],{"className":18597},[886],[888,18599,18600],{"xmlns":890},[892,18601,18602,18637],{},[895,18603,18604,18606,18608,18610,18612,18614,18616,18618,18620,18622,18624,18626,18628,18630,18632,18635],{},[898,18605,2626],{},[1846,18607,1848],{},[898,18609,2626],{},[1846,18611,1855],{"stretchy":1854},[898,18613,8974],{},[1846,18615,1861],{"stretchy":1854},[1846,18617,1848],{},[898,18619,207],{},[898,18621,8974],{},[1846,18623,1945],{},[898,18625,1948],{},[1846,18627,2136],{"separator":2135},[5724,18629],{"width":5726},[1846,18631,1855],{"stretchy":1854},[1979,18633,18634],{},"7.3",[1846,18636,1861],{"stretchy":1854},[902,18638,18639],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,18641,4156,18642,1745,18660,18682,18683,18723,18724,1734],{},[883,18643,18645],{"className":18644},[886],[888,18646,18647],{"xmlns":890},[892,18648,18649,18657],{},[895,18650,18651,18653,18655],{},[898,18652,1948],{},[1846,18654,3256],{},[1979,18656,2177],{},[902,18658,18659],{"encoding":904},"b > 0",[883,18661,18663],{"className":18662},[886],[888,18664,18665],{"xmlns":890},[892,18666,18667,18679],{},[895,18668,18669,18671,18673,18675,18677],{},[1979,18670,2177],{},[1846,18672,3295],{},[898,18674,207],{},[1846,18676,3295],{},[1979,18678,2128],{},[902,18680,18681],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,18684,18686],{"className":18685},[886],[888,18687,18688],{"xmlns":890},[892,18689,18690,18720],{},[895,18691,18692,18694,18696,18703,18705,18708,18710,18712,18714,18716,18718],{},[898,18693,207],{},[1846,18695,1848],{},[895,18697,18698,18701],{},[898,18699,18700],{"mathvariant":2226},"t",[898,18702,10887],{"mathvariant":2226},[2138,18704,2835],{},[898,18706,18707],{},"α",[1846,18709,1848],{},[898,18711,2738],{"mathvariant":2226},[898,18713,2626],{},[898,18715,4520],{"mathvariant":2226},[898,18717,2738],{"mathvariant":2226},[898,18719,8974],{},[902,18721,18722],{"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 ",[883,18725,18727],{"className":18726},[886],[888,18728,18729],{"xmlns":890},[892,18730,18731,18735],{},[895,18732,18733],{},[898,18734,8974],{},[902,18736,8974],{"encoding":904},[724,18738,18739],{},[614,18740,18741,18742,18766,18767,18805,18806,18822,18823,1734],{},"Obrázek 7.1 — Přímka spotřeby ",[883,18743,18745],{"className":18744},[886],[888,18746,18747],{"xmlns":890},[892,18748,18749,18763],{},[895,18750,18751,18753,18755,18757,18759,18761],{},[898,18752,2626],{},[1846,18754,1848],{},[898,18756,207],{},[898,18758,8974],{},[1846,18760,1945],{},[898,18762,1948],{},[902,18764,18765],{"encoding":904},"C = aY + b"," se směrnicí ",[883,18768,18770],{"className":18769},[886],[888,18771,18772],{"xmlns":890},[892,18773,18774,18802],{},[895,18775,18776,18778,18780,18786,18788,18790,18792,18794,18796,18798,18800],{},[898,18777,207],{},[1846,18779,1848],{},[895,18781,18782,18784],{},[898,18783,18700],{"mathvariant":2226},[898,18785,10887],{"mathvariant":2226},[2138,18787,2835],{},[898,18789,18707],{},[1846,18791,1848],{},[898,18793,2738],{"mathvariant":2226},[898,18795,2626],{},[898,18797,4520],{"mathvariant":2226},[898,18799,2738],{"mathvariant":2226},[898,18801,8974],{},[902,18803,18804],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,18807,18809],{"className":18808},[886],[888,18810,18811],{"xmlns":890},[892,18812,18813,18819],{},[895,18814,18815,18817],{},[898,18816,2738],{"mathvariant":2226},[898,18818,2626],{},[902,18820,18821],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,18824,18826],{"className":18825},[886],[888,18827,18828],{"xmlns":890},[892,18829,18830,18840],{},[895,18831,18832,18834,18836,18838],{},[898,18833,2738],{"mathvariant":2226},[898,18835,8974],{},[1846,18837,1848],{},[1979,18839,2128],{},[902,18841,18842],{"encoding":904},"\\Delta Y = 1",[724,18844,18845,18846,2554],{},"Dosazením do (7.2) plyne ",[38,18847,18848],{},"lineární model úspor",[724,18850,18851],{},[883,18852,18854],{"className":18853},[886],[888,18855,18856],{"xmlns":890},[892,18857,18858,18923],{},[895,18859,18860,18862,18864,18866,18868,18870,18872,18874,18876,18878,18880,18882,18884,18886,18888,18890,18892,18894,18896,18898,18900,18902,18904,18906,18908,18910,18912,18914,18916,18918,18921],{},[898,18861,8519],{},[1846,18863,1848],{},[898,18865,8974],{},[1846,18867,2075],{},[898,18869,2626],{},[1846,18871,1855],{"stretchy":1854},[898,18873,8974],{},[1846,18875,1861],{"stretchy":1854},[1846,18877,1848],{},[898,18879,8974],{},[1846,18881,2075],{},[1846,18883,1855],{"stretchy":1854},[898,18885,207],{},[898,18887,8974],{},[1846,18889,1945],{},[898,18891,1948],{},[1846,18893,1861],{"stretchy":1854},[1846,18895,1848],{},[1846,18897,1855],{"stretchy":1854},[1979,18899,2128],{},[1846,18901,2075],{},[898,18903,207],{},[1846,18905,1861],{"stretchy":1854},[898,18907,8974],{},[1846,18909,2075],{},[898,18911,1948],{},[898,18913,1734],{"mathvariant":2226},[5724,18915],{"width":5726},[1846,18917,1855],{"stretchy":1854},[1979,18919,18920],{},"7.4",[1846,18922,1861],{"stretchy":1854},[902,18924,18925],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,18927,18928,18929,3764],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,18930,18932],{"className":18931},[886],[888,18933,18934],{"xmlns":890},[892,18935,18936,18952],{},[895,18937,18938,18940,18942,18944,18946,18948,18950],{},[1979,18939,2177],{},[1846,18941,3295],{},[1979,18943,2128],{},[1846,18945,2075],{},[898,18947,207],{},[1846,18949,3295],{},[1979,18951,2128],{},[902,18953,18954],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,18956,18957],{},[614,18958,18959,18960,1745,18983,19015,19016,2474,19029,19059,19060,2474,19078,1734],{},"Obrázek 7.2 — Přímky ",[883,18961,18963],{"className":18962},[886],[888,18964,18965],{"xmlns":890},[892,18966,18967,18981],{},[895,18968,18969,18971,18973,18975,18977,18979],{},[898,18970,2626],{},[1846,18972,1848],{},[898,18974,207],{},[898,18976,8974],{},[1846,18978,1945],{},[898,18980,1948],{},[902,18982,18765],{"encoding":904},[883,18984,18986],{"className":18985},[886],[888,18987,18988],{"xmlns":890},[892,18989,18990,19012],{},[895,18991,18992,18994,18996,18998,19000,19002,19004,19006,19008,19010],{},[898,18993,8519],{},[1846,18995,1848],{},[1846,18997,1855],{"stretchy":1854},[1979,18999,2128],{},[1846,19001,2075],{},[898,19003,207],{},[1846,19005,1861],{"stretchy":1854},[898,19007,8974],{},[1846,19009,2075],{},[898,19011,1948],{},[902,19013,19014],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,19017,19019],{"className":19018},[886],[888,19020,19021],{"xmlns":890},[892,19022,19023,19027],{},[895,19024,19025],{},[898,19026,8974],{},[902,19028,8974],{"encoding":904},[883,19030,19032],{"className":19031},[886],[888,19033,19034],{"xmlns":890},[892,19035,19036,19056],{},[895,19037,19038,19040,19042,19044,19046,19048,19050,19052,19054],{},[898,19039,8974],{},[1846,19041,1848],{},[898,19043,1948],{},[898,19045,4520],{"mathvariant":2226},[1846,19047,1855],{"stretchy":1854},[1979,19049,2128],{},[1846,19051,2075],{},[898,19053,207],{},[1846,19055,1861],{"stretchy":1854},[902,19057,19058],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,19061,19063],{"className":19062},[886],[888,19064,19065],{"xmlns":890},[892,19066,19067,19075],{},[895,19068,19069,19071,19073],{},[898,19070,2626],{},[1846,19072,2136],{"separator":2135},[898,19074,8519],{},[902,19076,19077],{"encoding":904},"C, S",[883,19079,19081],{"className":19080},[886],[888,19082,19083],{"xmlns":890},[892,19084,19085,19091],{},[895,19086,19087,19089],{},[1846,19088,2075],{},[898,19090,1948],{},[902,19092,19093],{"encoding":904},"-b",[198,19095,19097],{"id":19096},"příklad-71","Příklad 7.1",[724,19099,19100,19101,19126],{},"Pro spotřebu ",[883,19102,19104],{"className":19103},[886],[888,19105,19106],{"xmlns":890},[892,19107,19108,19123],{},[895,19109,19110,19112,19114,19117,19119,19121],{},[898,19111,2626],{},[1846,19113,1848],{},[1979,19115,19116],{},"0,4",[898,19118,8974],{},[1846,19120,1945],{},[1979,19122,2712],{},[902,19124,19125],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,19128,19129],{},[883,19130,19132],{"className":19131},[886],[888,19133,19134],{"xmlns":890},[892,19135,19136,19174],{},[895,19137,19138,19140,19142,19144,19146,19148,19150,19152,19154,19156,19158,19160,19162,19164,19167,19169,19171],{},[898,19139,8519],{},[1846,19141,1848],{},[898,19143,8974],{},[1846,19145,2075],{},[898,19147,2626],{},[1846,19149,1848],{},[898,19151,8974],{},[1846,19153,2075],{},[1979,19155,19116],{},[898,19157,8974],{},[1846,19159,2075],{},[1979,19161,2712],{},[1846,19163,1848],{},[1979,19165,19166],{},"0,6",[898,19168,8974],{},[1846,19170,2075],{},[1979,19172,19173],{},"10.",[902,19175,19176],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,19178,19179],{},[614,19180,19181,19182,1745,19205,19229,19230,7948,19243,19267,19268,7948,19285,19301,19302,1734],{},"Obrázek 7.3 — Přímky ",[883,19183,19185],{"className":19184},[886],[888,19186,19187],{"xmlns":890},[892,19188,19189,19203],{},[895,19190,19191,19193,19195,19197,19199,19201],{},[898,19192,2626],{},[1846,19194,1848],{},[1979,19196,19116],{},[898,19198,8974],{},[1846,19200,1945],{},[1979,19202,2712],{},[902,19204,19125],{"encoding":904},[883,19206,19208],{"className":19207},[886],[888,19209,19210],{"xmlns":890},[892,19211,19212,19226],{},[895,19213,19214,19216,19218,19220,19222,19224],{},[898,19215,8519],{},[1846,19217,1848],{},[1979,19219,19166],{},[898,19221,8974],{},[1846,19223,2075],{},[1979,19225,2712],{},[902,19227,19228],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,19231,19233],{"className":19232},[886],[888,19234,19235],{"xmlns":890},[892,19236,19237,19241],{},[895,19238,19239],{},[898,19240,8974],{},[902,19242,8974],{"encoding":904},[883,19244,19246],{"className":19245},[886],[888,19247,19248],{"xmlns":890},[892,19249,19250,19264],{},[895,19251,19252,19254,19257],{},[1846,19253,1650],{},[1979,19255,19256],{},"16,",[8232,19258,19259,19261],{"accent":2135},[1979,19260,2085],{},[1846,19262,19263],{},"ˉ",[902,19265,19266],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,19269,19271],{"className":19270},[886],[888,19272,19273],{"xmlns":890},[892,19274,19275,19283],{},[895,19276,19277,19279,19281],{},[898,19278,2626],{},[1846,19280,2136],{"separator":2135},[898,19282,8519],{},[902,19284,19077],{"encoding":904},[883,19286,19288],{"className":19287},[886],[888,19289,19290],{"xmlns":890},[892,19291,19292,19298],{},[895,19293,19294,19296],{},[1846,19295,2075],{},[1979,19297,2712],{},[902,19299,19300],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,19303,19305],{"className":19304},[886],[888,19306,19307],{"xmlns":890},[892,19308,19309,19321],{},[895,19310,19311,19313,19315,19317,19319],{},[1846,19312,1855],{"stretchy":1854},[1979,19314,2177],{},[1846,19316,2136],{"separator":2135},[1979,19318,2712],{},[1846,19320,1861],{"stretchy":1854},[902,19322,19323],{"encoding":904},"(0, 10)",[724,19325,19326,19327,7948,19345,19375,19376,9871,19379,19382,19383,7948,19407,9871,19410,19413],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,19328,19330],{"className":19329},[886],[888,19331,19332],{"xmlns":890},[892,19333,19334,19342],{},[895,19335,19336,19338,19340],{},[898,19337,8974],{},[1846,19339,1848],{},[1979,19341,2177],{},[902,19343,19344],{"encoding":904},"Y = 0",[883,19346,19348],{"className":19347},[886],[888,19349,19350],{"xmlns":890},[892,19351,19352,19372],{},[895,19353,19354,19356,19358,19360,19362,19364,19366,19368,19370],{},[898,19355,8519],{},[1846,19357,1855],{"stretchy":1854},[1979,19359,2177],{},[1846,19361,1861],{"stretchy":1854},[1846,19363,1848],{},[1846,19365,2075],{},[898,19367,1948],{},[1846,19369,3295],{},[1979,19371,2177],{},[902,19373,19374],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,19377,19378],{},"autonomních úsporách",[614,19380,19381],{},"autonomous savings","). Analogicky ",[883,19384,19386],{"className":19385},[886],[888,19387,19388],{"xmlns":890},[892,19389,19390,19404],{},[895,19391,19392,19394,19396,19398,19400,19402],{},[898,19393,2626],{},[1846,19395,1855],{"stretchy":1854},[1979,19397,2177],{},[1846,19399,1861],{"stretchy":1854},[1846,19401,1848],{},[898,19403,1948],{},[902,19405,19406],{"encoding":904},"C(0) = b",[38,19408,19409],{},"autonomní spotřeba",[614,19411,19412],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,19415,19417],{"id":19416},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,19419,19420,2053,19423,9871,19440,19443],{},[38,19421,19422],{},"Mezní sklon ke spotřebě",[883,19424,19426],{"className":19425},[886],[888,19427,19428],{"xmlns":890},[892,19429,19430,19438],{},[895,19431,19432,19434,19436],{},[898,19433,2667],{},[898,19435,3783],{},[898,19437,2626],{},[902,19439,17890],{"encoding":904},[614,19441,19442],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,19445,19446],{},[883,19447,19449],{"className":19448},[886],[888,19450,19451],{"xmlns":890},[892,19452,19453,19479],{},[895,19454,19455,19457,19459,19461,19463,19477],{},[898,19456,2667],{},[898,19458,3783],{},[898,19460,2626],{},[1846,19462,1848],{},[2179,19464,19465,19471],{},[895,19466,19467,19469],{},[898,19468,2044],{"mathvariant":2226},[898,19470,2626],{},[895,19472,19473,19475],{},[898,19474,2044],{"mathvariant":2226},[898,19476,8974],{},[898,19478,1734],{"mathvariant":2226},[902,19480,19481],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,19483,19484,2053,19487,9871,19505,19508],{},[38,19485,19486],{},"Mezní sklon k úsporám",[883,19488,19490],{"className":19489},[886],[888,19491,19492],{"xmlns":890},[892,19493,19494,19502],{},[895,19495,19496,19498,19500],{},[898,19497,2667],{},[898,19499,3783],{},[898,19501,8519],{},[902,19503,19504],{"encoding":904},"MPS",[614,19506,19507],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,19510,19511],{},[883,19512,19514],{"className":19513},[886],[888,19515,19516],{"xmlns":890},[892,19517,19518,19544],{},[895,19519,19520,19522,19524,19526,19528,19542],{},[898,19521,2667],{},[898,19523,3783],{},[898,19525,8519],{},[1846,19527,1848],{},[2179,19529,19530,19536],{},[895,19531,19532,19534],{},[898,19533,2044],{"mathvariant":2226},[898,19535,8519],{},[895,19537,19538,19540],{},[898,19539,2044],{"mathvariant":2226},[898,19541,8974],{},[898,19543,1734],{"mathvariant":2226},[902,19545,19546],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,19548,19549,19550,19608],{},"Z (7.2) plyne ",[883,19551,19553],{"className":19552},[886],[888,19554,19555],{"xmlns":890},[892,19556,19557,19605],{},[895,19558,19559,19573,19575,19589,19591],{},[2179,19560,19561,19567],{},[895,19562,19563,19565],{},[898,19564,2044],{"mathvariant":2226},[898,19566,8974],{},[895,19568,19569,19571],{},[898,19570,2044],{"mathvariant":2226},[898,19572,8974],{},[1846,19574,1848],{},[2179,19576,19577,19583],{},[895,19578,19579,19581],{},[898,19580,2044],{"mathvariant":2226},[898,19582,2626],{},[895,19584,19585,19587],{},[898,19586,2044],{"mathvariant":2226},[898,19588,8974],{},[1846,19590,1945],{},[2179,19592,19593,19599],{},[895,19594,19595,19597],{},[898,19596,2044],{"mathvariant":2226},[898,19598,8519],{},[895,19600,19601,19603],{},[898,19602,2044],{"mathvariant":2226},[898,19604,8974],{},[902,19606,19607],{"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",[724,19610,19611],{},[883,19612,19614],{"className":19613},[886],[888,19615,19616],{"xmlns":890},[892,19617,19618,19681],{},[895,19619,19620,19672,19674,19676,19679],{},[12677,19621,19622],{"notation":12679},[2175,19623,19624],{"scriptlevel":2177,"displaystyle":1854},[2175,19625,19626],{"scriptlevel":2177,"displaystyle":1854},[2175,19627,19628],{"scriptlevel":2177,"displaystyle":2135},[895,19629,19630,19632,19634,19636,19638,19640,19642,19644,19646,19648,19650,19652,19654,19656,19658,19660,19662,19664,19666,19668,19670],{},[898,19631,2667],{},[898,19633,3783],{},[898,19635,2626],{},[1846,19637,1945],{},[898,19639,2667],{},[898,19641,3783],{},[898,19643,8519],{},[1846,19645,1848],{},[1979,19647,2128],{},[1846,19649,2136],{"separator":2135},[5724,19651],{"width":5726},[898,19653,2667],{},[898,19655,3783],{},[898,19657,8519],{},[1846,19659,1848],{},[1979,19661,2128],{},[1846,19663,2075],{},[898,19665,2667],{},[898,19667,3783],{},[898,19669,2626],{},[898,19671,1734],{"mathvariant":2226},[5724,19673],{"width":5726},[1846,19675,1855],{"stretchy":1854},[1979,19677,19678],{},"7.5",[1846,19680,1861],{"stretchy":1854},[902,19682,19683],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,19685,19686,2053,19689,19712,19713,1745,19735,19761],{},[38,19687,19688],{},"Pro lineární model",[883,19690,19692],{"className":19691},[886],[888,19693,19694],{"xmlns":890},[892,19695,19696,19710],{},[895,19697,19698,19700,19702,19704,19706,19708],{},[898,19699,2626],{},[1846,19701,1848],{},[898,19703,207],{},[898,19705,8974],{},[1846,19707,1945],{},[898,19709,1948],{},[902,19711,18765],{"encoding":904}," vychází ",[883,19714,19716],{"className":19715},[886],[888,19717,19718],{"xmlns":890},[892,19719,19720,19732],{},[895,19721,19722,19724,19726,19728,19730],{},[898,19723,2667],{},[898,19725,3783],{},[898,19727,2626],{},[1846,19729,1848],{},[898,19731,207],{},[902,19733,19734],{"encoding":904},"MPC = a",[883,19736,19738],{"className":19737},[886],[888,19739,19740],{"xmlns":890},[892,19741,19742,19758],{},[895,19743,19744,19746,19748,19750,19752,19754,19756],{},[898,19745,2667],{},[898,19747,3783],{},[898,19749,8519],{},[1846,19751,1848],{},[1979,19753,2128],{},[1846,19755,2075],{},[898,19757,207],{},[902,19759,19760],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,19763,19764,19767,19768,19790,19791,19819],{},[38,19765,19766],{},"Interpretace diferenciálem."," Pro pevné ",[883,19769,19771],{"className":19770},[886],[888,19772,19773],{"xmlns":890},[892,19774,19775,19787],{},[895,19776,19777,19779,19781],{},[898,19778,8974],{},[1846,19780,1848],{},[1974,19782,19783,19785],{},[898,19784,8974],{},[1846,19786,4200],{},[902,19788,19789],{"encoding":904},"Y = Y^*"," udává ",[883,19792,19794],{"className":19793},[886],[888,19795,19796],{"xmlns":890},[892,19797,19798,19816],{},[895,19799,19800,19802,19804,19806,19808,19814],{},[898,19801,2667],{},[898,19803,3783],{},[898,19805,2626],{},[1846,19807,1855],{"stretchy":1854},[1974,19809,19810,19812],{},[898,19811,8974],{},[1846,19813,4200],{},[1846,19815,1861],{"stretchy":1854},[902,19817,19818],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,19821,19822],{},[883,19823,19825],{"className":19824},[886],[888,19826,19827],{"xmlns":890},[892,19828,19829,19883],{},[895,19830,19831,19833,19835,19837,19839,19841,19843,19849,19851,19853,19855,19857,19859,19861,19863,19865,19867,19869,19871,19873,19875,19877,19879,19881],{},[898,19832,2738],{"mathvariant":2226},[898,19834,2626],{},[1846,19836,1650],{},[898,19838,2044],{"mathvariant":2226},[898,19840,2626],{},[1846,19842,1848],{},[1974,19844,19845,19847],{},[898,19846,2626],{},[1846,19848,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,19850,1855],{"stretchy":1854},[898,19852,8974],{},[1846,19854,1861],{"stretchy":1854},[2138,19856,2835],{},[898,19858,2044],{"mathvariant":2226},[898,19860,8974],{},[1846,19862,1848],{},[898,19864,2667],{},[898,19866,3783],{},[898,19868,2626],{},[1846,19870,1855],{"stretchy":1854},[898,19872,8974],{},[1846,19874,1861],{"stretchy":1854},[2138,19876,2835],{},[898,19878,2044],{"mathvariant":2226},[898,19880,8974],{},[898,19882,1734],{"mathvariant":2226},[902,19884,19885],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,19887,19888,19889,19925,19926,19929],{},"Analogicky ",[883,19890,19892],{"className":19891},[886],[888,19893,19894],{"xmlns":890},[892,19895,19896,19922],{},[895,19897,19898,19900,19902,19904,19906,19908,19910,19912,19914,19916,19918,19920],{},[898,19899,2738],{"mathvariant":2226},[898,19901,8519],{},[1846,19903,1650],{},[898,19905,2667],{},[898,19907,3783],{},[898,19909,8519],{},[1846,19911,1855],{"stretchy":1854},[898,19913,8974],{},[1846,19915,1861],{"stretchy":1854},[2138,19917,2835],{},[898,19919,2044],{"mathvariant":2226},[898,19921,8974],{},[902,19923,19924],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,19927,1145],{"className":19928,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,19931,19933],{"id":19932},"příklad-72","Příklad 7.2",[724,19935,19100,19936,19971,19972,19991],{},[883,19937,19939],{"className":19938},[886],[888,19940,19941],{"xmlns":890},[892,19942,19943,19968],{},[895,19944,19945,19947,19949,19952,19958,19960,19962,19964,19966],{},[898,19946,2626],{},[1846,19948,1848],{},[1979,19950,19951],{},"0,001",[1974,19953,19954,19956],{},[898,19955,8974],{},[1979,19957,1981],{},[1846,19959,1945],{},[1979,19961,2688],{},[898,19963,8974],{},[1846,19965,1945],{},[1979,19967,2968],{},[902,19969,19970],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,19973,19975],{"className":19974},[886],[888,19976,19977],{"xmlns":890},[892,19978,19979,19988],{},[895,19980,19981,19983,19985],{},[898,19982,8974],{},[1846,19984,3295],{},[1979,19986,19987],{},"400",[902,19989,19990],{"encoding":904},"Y \u003C 400",") platí",[724,19993,19994],{},[883,19995,19997],{"className":19996},[886],[888,19998,19999],{"xmlns":890},[892,20000,20001,20038],{},[895,20002,20003,20005,20007,20009,20011,20025,20027,20030,20032,20034,20036],{},[898,20004,2667],{},[898,20006,3783],{},[898,20008,2626],{},[1846,20010,1848],{},[2179,20012,20013,20019],{},[895,20014,20015,20017],{},[898,20016,2044],{"mathvariant":2226},[898,20018,2626],{},[895,20020,20021,20023],{},[898,20022,2044],{"mathvariant":2226},[898,20024,8974],{},[1846,20026,1848],{},[1979,20028,20029],{},"0,002",[898,20031,8974],{},[1846,20033,1945],{},[1979,20035,2688],{},[1846,20037,2136],{"separator":2135},[902,20039,20040],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,20042,20043],{},[883,20044,20046],{"className":20045},[886],[888,20047,20048],{"xmlns":890},[892,20049,20050,20083],{},[895,20051,20052,20054,20056,20058,20060,20062,20064,20066,20068,20070,20072,20074,20076,20078,20080],{},[898,20053,2667],{},[898,20055,3783],{},[898,20057,8519],{},[1846,20059,1848],{},[1979,20061,2128],{},[1846,20063,2075],{},[898,20065,2667],{},[898,20067,3783],{},[898,20069,2626],{},[1846,20071,1848],{},[1846,20073,2075],{},[1979,20075,20029],{},[898,20077,8974],{},[1846,20079,1945],{},[1979,20081,20082],{},"0,8.",[902,20084,20085],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,20087,20088,20168,20247],{},[123,20089,20090,1343,20118,20146,20147,7948,20165,1734],{},[883,20091,20093],{"className":20092},[886],[888,20094,20095],{"xmlns":890},[892,20096,20097,20115],{},[895,20098,20099,20101,20103,20105,20107,20109,20111,20113],{},[898,20100,2667],{},[898,20102,3783],{},[898,20104,2626],{},[1846,20106,1855],{"stretchy":1854},[1979,20108,2938],{},[1846,20110,1861],{"stretchy":1854},[1846,20112,1848],{},[1979,20114,19116],{},[902,20116,20117],{"encoding":904},"MPC(100) = 0{,}4",[883,20119,20121],{"className":20120},[886],[888,20122,20123],{"xmlns":890},[892,20124,20125,20143],{},[895,20126,20127,20129,20131,20133,20135,20137,20139,20141],{},[898,20128,2667],{},[898,20130,3783],{},[898,20132,8519],{},[1846,20134,1855],{"stretchy":1854},[1979,20136,2938],{},[1846,20138,1861],{"stretchy":1854},[1846,20140,1848],{},[1979,20142,19166],{},[902,20144,20145],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,20148,20150],{"className":20149},[886],[888,20151,20152],{"xmlns":890},[892,20153,20154,20162],{},[895,20155,20156,20158,20160],{},[898,20157,8974],{},[1846,20159,1848],{},[1979,20161,2938],{},[902,20163,20164],{"encoding":904},"Y = 100",[38,20166,20167],{},"větší sklon k úsporám",[123,20169,20170,1343,20198,20146,20226,7948,20244,1734],{},[883,20171,20173],{"className":20172},[886],[888,20174,20175],{"xmlns":890},[892,20176,20177,20195],{},[895,20178,20179,20181,20183,20185,20187,20189,20191,20193],{},[898,20180,2667],{},[898,20182,3783],{},[898,20184,2626],{},[1846,20186,1855],{"stretchy":1854},[1979,20188,8223],{},[1846,20190,1861],{"stretchy":1854},[1846,20192,1848],{},[1979,20194,19166],{},[902,20196,20197],{"encoding":904},"MPC(200) = 0{,}6",[883,20199,20201],{"className":20200},[886],[888,20202,20203],{"xmlns":890},[892,20204,20205,20223],{},[895,20206,20207,20209,20211,20213,20215,20217,20219,20221],{},[898,20208,2667],{},[898,20210,3783],{},[898,20212,8519],{},[1846,20214,1855],{"stretchy":1854},[1979,20216,8223],{},[1846,20218,1861],{"stretchy":1854},[1846,20220,1848],{},[1979,20222,19116],{},[902,20224,20225],{"encoding":904},"MPS(200) = 0{,}4",[883,20227,20229],{"className":20228},[886],[888,20230,20231],{"xmlns":890},[892,20232,20233,20241],{},[895,20234,20235,20237,20239],{},[898,20236,8974],{},[1846,20238,1848],{},[1979,20240,8223],{},[902,20242,20243],{"encoding":904},"Y = 200",[38,20245,20246],{},"větší sklon ke spotřebě",[123,20248,20249,20250,20268,20269,3764],{},"Přesně při ",[883,20251,20253],{"className":20252},[886],[888,20254,20255],{"xmlns":890},[892,20256,20257,20265],{},[895,20258,20259,20261,20263],{},[898,20260,8974],{},[1846,20262,1848],{},[1979,20264,8649],{},[902,20266,20267],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,20270,20272],{"className":20271},[886],[888,20273,20274],{"xmlns":890},[892,20275,20276,20296],{},[895,20277,20278,20280,20282,20284,20286,20288,20290,20292,20294],{},[898,20279,2667],{},[898,20281,3783],{},[898,20283,2626],{},[1846,20285,1848],{},[898,20287,2667],{},[898,20289,3783],{},[898,20291,8519],{},[1846,20293,1848],{},[1979,20295,4855],{},[902,20297,20298],{"encoding":904},"MPC = MPS = 0{,}5",[724,20300,20301,20302,20319,20320,20334,20335,2535,20348,20362,20363,20376,20377,20418],{},"Interpretace: při ",[883,20303,20305],{"className":20304},[886],[888,20306,20307],{"xmlns":890},[892,20308,20309,20317],{},[895,20310,20311,20313,20315],{},[898,20312,8974],{},[1846,20314,1848],{},[1979,20316,2938],{},[902,20318,20164],{"encoding":904}," se spotřeba mění ",[883,20321,20323],{"className":20322},[886],[888,20324,20325],{"xmlns":890},[892,20326,20327,20331],{},[895,20328,20329],{},[1979,20330,19116],{},[902,20332,20333],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,20336,20338],{"className":20337},[886],[888,20339,20340],{"xmlns":890},[892,20341,20342,20346],{},[895,20343,20344],{},[1979,20345,2938],{},[902,20347,2938],{"encoding":904},[883,20349,20351],{"className":20350},[886],[888,20352,20353],{"xmlns":890},[892,20354,20355,20360],{},[895,20356,20357],{},[1979,20358,20359],{},"101",[902,20361,20359],{"encoding":904},", změní se spotřeba přibližně o ",[883,20364,20366],{"className":20365},[886],[888,20367,20368],{"xmlns":890},[892,20369,20370,20374],{},[895,20371,20372],{},[1979,20373,19116],{},[902,20375,20333],{"encoding":904},". Skutečná změna ",[883,20378,20380],{"className":20379},[886],[888,20381,20382],{"xmlns":890},[892,20383,20384,20415],{},[895,20385,20386,20388,20390,20392,20394,20396,20398,20400,20402,20404,20406,20408,20410,20412],{},[898,20387,2738],{"mathvariant":2226},[898,20389,2626],{},[1846,20391,1848],{},[898,20393,2626],{},[1846,20395,1855],{"stretchy":1854},[1979,20397,20359],{},[1846,20399,1861],{"stretchy":1854},[1846,20401,2075],{},[898,20403,2626],{},[1846,20405,1855],{"stretchy":1854},[1979,20407,2938],{},[1846,20409,1861],{"stretchy":1854},[1846,20411,1848],{},[1979,20413,20414],{},"0,401",[902,20416,20417],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,20420,20421,20422],{},"Obecný trend: ",[38,20423,20424],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,20426,20428],{"id":20427},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,20430,20431,20432,9871,20435,20438,20439,9871,20442,11973,20445,9871,20448,20451],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,20433,20434],{},"makroekonomická rovnováha",[614,20436,20437],{},"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 ",[38,20440,20441],{},"agregátní poptávky",[614,20443,20444],{},"aggregate demand",[38,20446,20447],{},"agregátní nabídky",[614,20449,20450],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,20453,20455],{"id":20454},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,20457,20458],{},[2409,20459],{"alt":20460,"className":20461,"src":20462},"imek-keynesian-kriz",[210,2413],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,20464,20466],{"id":20465},"zadání-modelu","Zadání modelu",[724,20468,20469,20470,20483,20484,20497],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,20471,20473],{"className":20472},[886],[888,20474,20475],{"xmlns":890},[892,20476,20477,20481],{},[895,20478,20479],{},[898,20480,2626],{},[902,20482,2626],{"encoding":904}," a investice ",[883,20485,20487],{"className":20486},[886],[888,20488,20489],{"xmlns":890},[892,20490,20491,20495],{},[895,20492,20493],{},[898,20494,12029],{},[902,20496,12029],{"encoding":904},". Podmínka rovnováhy:",[724,20499,20500],{},[883,20501,20503],{"className":20502},[886],[888,20504,20505],{"xmlns":890},[892,20506,20507,20530],{},[895,20508,20509,20511,20513,20515,20517,20519,20521,20523,20525,20528],{},[898,20510,8974],{},[1846,20512,1848],{},[898,20514,2626],{},[1846,20516,1945],{},[898,20518,12029],{},[898,20520,1734],{"mathvariant":2226},[5724,20522],{"width":5726},[1846,20524,1855],{"stretchy":1854},[1979,20526,20527],{},"7.6",[1846,20529,1861],{"stretchy":1854},[902,20531,20532],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,20534,20536],{"id":20535},"soustava-rovnic","Soustava rovnic",[724,20538,20539,20540,20561,20562,20586],{},"Pro pevně zadané (plánované) investice ",[883,20541,20543],{"className":20542},[886],[888,20544,20545],{"xmlns":890},[892,20546,20547,20559],{},[895,20548,20549,20551,20553],{},[898,20550,12029],{},[1846,20552,1848],{},[1974,20554,20555,20557],{},[898,20556,12029],{},[1846,20558,4200],{},[902,20560,12040],{"encoding":904}," a funkci spotřeby ",[883,20563,20565],{"className":20564},[886],[888,20566,20567],{"xmlns":890},[892,20568,20569,20583],{},[895,20570,20571,20573,20575,20577,20579,20581],{},[898,20572,2626],{},[1846,20574,1848],{},[898,20576,2626],{},[1846,20578,1855],{"stretchy":1854},[898,20580,8974],{},[1846,20582,1861],{"stretchy":1854},[902,20584,20585],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,20588,20589],{},[883,20590,20592],{"className":20591},[886],[888,20593,20594],{"xmlns":890},[892,20595,20596,20672],{},[895,20597,20598,20663,20665,20667,20670],{},[20599,20600,20603,20635],"mtable",{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},"0.25em","right left",[20604,20605,20606,20613],"mtr",{},[20607,20608,20609],"mtd",{},[2175,20610,20611],{"scriptlevel":2177,"displaystyle":2135},[898,20612,8974],{},[20607,20614,20615],{},[2175,20616,20617],{"scriptlevel":2177,"displaystyle":2135},[895,20618,20619,20621,20623,20625,20627,20633],{},[895,20620],{},[1846,20622,1848],{},[898,20624,2626],{},[1846,20626,1945],{},[1974,20628,20629,20631],{},[898,20630,12029],{},[1846,20632,4200],{},[1846,20634,2136],{"separator":2135},[20604,20636,20637,20643],{},[20607,20638,20639],{},[2175,20640,20641],{"scriptlevel":2177,"displaystyle":2135},[898,20642,2626],{},[20607,20644,20645],{},[2175,20646,20647],{"scriptlevel":2177,"displaystyle":2135},[895,20648,20649,20651,20653,20655,20657,20659,20661],{},[895,20650],{},[1846,20652,1848],{},[898,20654,2626],{},[1846,20656,1855],{"stretchy":1854},[898,20658,8974],{},[1846,20660,1861],{"stretchy":1854},[1846,20662,2136],{"separator":2135},[5724,20664],{"width":5726},[1846,20666,1855],{"stretchy":1854},[1979,20668,20669],{},"7.7",[1846,20671,1861],{"stretchy":1854},[902,20673,20674],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,20676,20677,20678,2053,20680,1745,20697,2053,20700,1734],{},"jejímž řešením jsou ",[38,20679,13730],{},[883,20681,20683],{"className":20682},[886],[888,20684,20685],{"xmlns":890},[892,20686,20687,20695],{},[895,20688,20689],{},[1974,20690,20691,20693],{},[898,20692,8974],{},[898,20694,4098],{},[902,20696,13748],{"encoding":904},[38,20698,20699],{},"rovnovážná spotřeba",[883,20701,20703],{"className":20702},[886],[888,20704,20705],{"xmlns":890},[892,20706,20707,20715],{},[895,20708,20709],{},[1974,20710,20711,20713],{},[898,20712,2626],{},[898,20714,4098],{},[902,20716,13807],{"encoding":904},[198,20718,20720,20721],{"id":20719},"výpočet-yeye","Výpočet ",[883,20722,20724],{"className":20723},[886],[888,20725,20726],{"xmlns":890},[892,20727,20728,20736],{},[895,20729,20730],{},[1974,20731,20732,20734],{},[898,20733,8974],{},[898,20735,4098],{},[902,20737,13748],{"encoding":904},[724,20739,20740,20741,20764,20765,7531,20797],{},"Pro lineární spotřebu ",[883,20742,20744],{"className":20743},[886],[888,20745,20746],{"xmlns":890},[892,20747,20748,20762],{},[895,20749,20750,20752,20754,20756,20758,20760],{},[898,20751,2626],{},[1846,20753,1848],{},[898,20755,207],{},[898,20757,8974],{},[1846,20759,1945],{},[898,20761,1948],{},[902,20763,18765],{"encoding":904}," plyne z (7.7) rovnice ",[883,20766,20768],{"className":20767},[886],[888,20769,20770],{"xmlns":890},[892,20771,20772,20794],{},[895,20773,20774,20776,20778,20780,20782,20784,20786,20788],{},[898,20775,8974],{},[1846,20777,1848],{},[898,20779,207],{},[898,20781,8974],{},[1846,20783,1945],{},[898,20785,1948],{},[1846,20787,1945],{},[1974,20789,20790,20792],{},[898,20791,12029],{},[1846,20793,4200],{},[902,20795,20796],{"encoding":904},"Y = aY + b + I^*",[38,20798,20799],{},"redukovaný tvar",[724,20801,20802],{},[883,20803,20805],{"className":20804},[886],[888,20806,20807],{"xmlns":890},[892,20808,20809,20857],{},[895,20810,20811],{},[12677,20812,20813],{"notation":12679},[2175,20814,20815],{"scriptlevel":2177,"displaystyle":1854},[2175,20816,20817],{"scriptlevel":2177,"displaystyle":1854},[2175,20818,20819],{"scriptlevel":2177,"displaystyle":2135},[895,20820,20821,20823,20829,20831,20853,20855],{},[2138,20822,2835],{},[1974,20824,20825,20827],{},[898,20826,8974],{},[898,20828,4098],{},[1846,20830,1848],{},[2179,20832,20833,20845],{},[895,20834,20835,20837,20839],{},[898,20836,1948],{},[1846,20838,1945],{},[1974,20840,20841,20843],{},[898,20842,12029],{},[1846,20844,4200],{},[895,20846,20847,20849,20851],{},[1979,20848,2128],{},[1846,20850,2075],{},[898,20852,207],{},[898,20854,1734],{"mathvariant":2226},[2138,20856,2835],{},[902,20858,20859],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,20861,20863],{"id":20862},"příklad-73","Příklad 7.3",[724,20865,20866,20867,7948,20884,1745,20908,20934],{},"V modelu ",[883,20868,20870],{"className":20869},[886],[888,20871,20872],{"xmlns":890},[892,20873,20874,20882],{},[895,20875,20876,20878,20880],{},[898,20877,2626],{},[2138,20879,12135],{},[898,20881,12029],{},[902,20883,12140],{"encoding":904},[883,20885,20887],{"className":20886},[886],[888,20888,20889],{"xmlns":890},[892,20890,20891,20905],{},[895,20892,20893,20895,20897,20899,20901,20903],{},[898,20894,2626],{},[1846,20896,1848],{},[1979,20898,19166],{},[898,20900,8974],{},[1846,20902,1945],{},[1979,20904,2712],{},[902,20906,20907],{"encoding":904},"C = 0{,}6Y + 10",[883,20909,20911],{"className":20910},[886],[888,20912,20913],{"xmlns":890},[892,20914,20915,20931],{},[895,20916,20917,20919,20921,20923,20925],{},[898,20918,12029],{},[1846,20920,1848],{},[1979,20922,3357],{},[1846,20924,1848],{},[1974,20926,20927,20929],{},[898,20928,12029],{},[1846,20930,4200],{},[902,20932,20933],{"encoding":904},"I = 12 = I^*",". Soustava",[724,20936,20937],{},[883,20938,20940],{"className":20939},[886],[888,20941,20942],{"xmlns":890},[892,20943,20944,21000],{},[20599,20945,20946,20972],{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},[20604,20947,20948,20954],{},[20607,20949,20950],{},[2175,20951,20952],{"scriptlevel":2177,"displaystyle":2135},[898,20953,8974],{},[20607,20955,20956],{},[2175,20957,20958],{"scriptlevel":2177,"displaystyle":2135},[895,20959,20960,20962,20964,20966,20968,20970],{},[895,20961],{},[1846,20963,1848],{},[898,20965,2626],{},[1846,20967,1945],{},[1979,20969,3357],{},[1846,20971,2136],{"separator":2135},[20604,20973,20974,20980],{},[20607,20975,20976],{},[2175,20977,20978],{"scriptlevel":2177,"displaystyle":2135},[898,20979,2626],{},[20607,20981,20982],{},[2175,20983,20984],{"scriptlevel":2177,"displaystyle":2135},[895,20985,20986,20988,20990,20992,20994,20996,20998],{},[895,20987],{},[1846,20989,1848],{},[1979,20991,19166],{},[898,20993,8974],{},[1846,20995,1945],{},[1979,20997,2712],{},[1846,20999,2136],{"separator":2135},[902,21001,21002],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,21004,21005,21006,1343,21029,21052,21053,3764],{},"má řešení ",[883,21007,21009],{"className":21008},[886],[888,21010,21011],{"xmlns":890},[892,21012,21013,21026],{},[895,21014,21015,21021,21023],{},[1974,21016,21017,21019],{},[898,21018,8974],{},[898,21020,4098],{},[1846,21022,1848],{},[1979,21024,21025],{},"55",[902,21027,21028],{"encoding":904},"Y^E = 55",[883,21030,21032],{"className":21031},[886],[888,21033,21034],{"xmlns":890},[892,21035,21036,21049],{},[895,21037,21038,21044,21046],{},[1974,21039,21040,21042],{},[898,21041,2626],{},[898,21043,4098],{},[1846,21045,1848],{},[1979,21047,21048],{},"43",[902,21050,21051],{"encoding":904},"C^E = 43"," (a ",[883,21054,21056],{"className":21055},[886],[888,21057,21058],{"xmlns":890},[892,21059,21060,21072],{},[895,21061,21062,21068,21070],{},[1974,21063,21064,21066],{},[898,21065,8519],{},[898,21067,4098],{},[1846,21069,1848],{},[1979,21071,3357],{},[902,21073,21074],{"encoding":904},"S^E = 12",[724,21076,21077],{},[614,21078,21079,21080,21102,21103,11973,21124,21147,21148,1734],{},"Obrázek 7.5 — Přímky ",[883,21081,21083],{"className":21082},[886],[888,21084,21085],{"xmlns":890},[892,21086,21087,21099],{},[895,21088,21089,21091,21093,21095,21097],{},[898,21090,2626],{},[1846,21092,1848],{},[898,21094,8974],{},[1846,21096,2075],{},[1979,21098,3357],{},[902,21100,21101],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,21104,21106],{"className":21105},[886],[888,21107,21108],{"xmlns":890},[892,21109,21110,21122],{},[895,21111,21112,21114,21116,21118,21120],{},[898,21113,8974],{},[1846,21115,1848],{},[898,21117,2626],{},[1846,21119,1945],{},[898,21121,12029],{},[902,21123,14589],{"encoding":904},[883,21125,21127],{"className":21126},[886],[888,21128,21129],{"xmlns":890},[892,21130,21131,21145],{},[895,21132,21133,21135,21137,21139,21141,21143],{},[898,21134,2626],{},[1846,21136,1848],{},[1979,21138,19166],{},[898,21140,8974],{},[1846,21142,1945],{},[1979,21144,2712],{},[902,21146,20907],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,21149,21151],{"className":21150},[886],[888,21152,21153],{"xmlns":890},[892,21154,21155,21187],{},[895,21156,21157,21159,21165,21167,21173,21175,21177,21179,21181,21183,21185],{},[1846,21158,2336],{"stretchy":1854},[1974,21160,21161,21163],{},[898,21162,8974],{},[898,21164,4098],{},[1846,21166,2136],{"separator":2135},[1974,21168,21169,21171],{},[898,21170,2626],{},[898,21172,4098],{},[1846,21174,2351],{"stretchy":1854},[1846,21176,1848],{},[1846,21178,2336],{"stretchy":1854},[1979,21180,21025],{},[1846,21182,2136],{"separator":2135},[1979,21184,21048],{},[1846,21186,2351],{"stretchy":1854},[902,21188,21189],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,21191,21192,21195,21196,21213,21214,1734],{},[38,21193,21194],{},"Komentář k přechodu."," Model ",[883,21197,21199],{"className":21198},[886],[888,21200,21201],{"xmlns":890},[892,21202,21203,21211],{},[895,21204,21205,21207,21209],{},[898,21206,2626],{},[2138,21208,12135],{},[898,21210,12029],{},[902,21212,12140],{"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 ",[38,21215,21216,21217],{},"model ",[883,21218,21220],{"className":21219},[886],[888,21221,21222],{"xmlns":890},[892,21223,21224,21236],{},[895,21225,21226,21228,21230,21232,21234],{},[898,21227,2626],{},[2138,21229,12135],{},[898,21231,12029],{},[2138,21233,12135],{},[898,21235,11957],{},[902,21237,18065],{"encoding":904},[115,21239,21241],{"id":21240},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,21243,20466],{"id":21244},"zadání-modelu-1",[724,21246,21247,21248,21265,21266,2053,21269,9871,21282,21285],{},"Rozšíření modelu ",[883,21249,21251],{"className":21250},[886],[888,21252,21253],{"xmlns":890},[892,21254,21255,21263],{},[895,21256,21257,21259,21261],{},[898,21258,2626],{},[2138,21260,12135],{},[898,21262,12029],{},[902,21264,12140],{"encoding":904}," o ",[38,21267,21268],{},"vládní výdaje",[883,21270,21272],{"className":21271},[886],[888,21273,21274],{"xmlns":890},[892,21275,21276,21280],{},[895,21277,21278],{},[898,21279,11957],{},[902,21281,11957],{"encoding":904},[614,21283,21284],{},"government expenditure","). Podmínka rovnováhy:",[724,21287,21288],{},[883,21289,21291],{"className":21290},[886],[888,21292,21293],{"xmlns":890},[892,21294,21295,21322],{},[895,21296,21297,21299,21301,21303,21305,21307,21309,21311,21313,21315,21317,21320],{},[898,21298,8974],{},[1846,21300,1848],{},[898,21302,2626],{},[1846,21304,1945],{},[898,21306,12029],{},[1846,21308,1945],{},[898,21310,11957],{},[898,21312,1734],{"mathvariant":2226},[5724,21314],{"width":5726},[1846,21316,1855],{"stretchy":1854},[1979,21318,21319],{},"7.8",[1846,21321,1861],{"stretchy":1854},[902,21323,21324],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,21326,21327,21328,2053,21331,9871,21344,21347],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,21329,21330],{},"zdaněním domácností",[883,21332,21334],{"className":21333},[886],[888,21335,21336],{"xmlns":890},[892,21337,21338,21342],{},[895,21339,21340],{},[898,21341,2623],{},[902,21343,2623],{"encoding":904},[614,21345,21346],{},"taxation","). Zdanění bývá:",[120,21349,21350,21383,21408],{},[123,21351,21352,21353,2136],{},"úměrné důchodu: ",[883,21354,21356],{"className":21355},[886],[888,21357,21358],{"xmlns":890},[892,21359,21360,21380],{},[895,21361,21362,21364,21366,21368,21370,21372,21374,21376,21378],{},[898,21363,2623],{},[1846,21365,1848],{},[898,21367,2623],{},[1846,21369,1855],{"stretchy":1854},[898,21371,8974],{},[1846,21373,1861],{"stretchy":1854},[1846,21375,1848],{},[898,21377,18700],{},[898,21379,8974],{},[902,21381,21382],{"encoding":904},"T = T(Y) = tY",[123,21384,21385,21386,2136],{},"fixní: ",[883,21387,21389],{"className":21388},[886],[888,21390,21391],{"xmlns":890},[892,21392,21393,21405],{},[895,21394,21395,21397,21399],{},[898,21396,2623],{},[1846,21398,1848],{},[1974,21400,21401,21403],{},[898,21402,2623],{},[1846,21404,4200],{},[902,21406,21407],{"encoding":904},"T = T^*",[123,21409,21410,21411,21439,21440,1734],{},"kombinované: ",[883,21412,21414],{"className":21413},[886],[888,21415,21416],{"xmlns":890},[892,21417,21418,21436],{},[895,21419,21420,21422,21424,21430,21432,21434],{},[898,21421,2623],{},[1846,21423,1848],{},[1974,21425,21426,21428],{},[898,21427,2623],{},[1846,21429,4200],{},[1846,21431,1945],{},[898,21433,18700],{},[898,21435,8974],{},[902,21437,21438],{"encoding":904},"T = T^* + tY",", kde ",[883,21441,21443],{"className":21442},[886],[888,21444,21445],{"xmlns":890},[892,21446,21447,21459],{},[895,21448,21449,21451,21453,21455,21457],{},[1979,21450,2177],{},[1846,21452,7525],{},[898,21454,18700],{},[1846,21456,3295],{},[1979,21458,2128],{},[902,21460,21461],{"encoding":904},"0 \\le t \u003C 1",[1639,21463,21464],{},[724,21465,21466,21468,21469,21490,21491,21494,21495,21508,21509,11973,21535,2053,21538,21564,21565,21593,21594,1745,21607,21625],{},[883,21467,4258],{}," Pozor na disponibilní důchod\nV modelu ",[883,21470,21472],{"className":21471},[886],[888,21473,21474],{"xmlns":890},[892,21475,21476,21488],{},[895,21477,21478,21480,21482,21484,21486],{},[898,21479,2626],{},[2138,21481,12135],{},[898,21483,12029],{},[2138,21485,12135],{},[898,21487,11957],{},[902,21489,18065],{"encoding":904}," je nutné ",[38,21492,21493],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,21496,21498],{"className":21497},[886],[888,21499,21500],{"xmlns":890},[892,21501,21502,21506],{},[895,21503,21504],{},[898,21505,8974],{},[902,21507,8974],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,21510,21512],{"className":21511},[886],[888,21513,21514],{"xmlns":890},[892,21515,21516,21532],{},[895,21517,21518,21520,21522,21524,21526,21528,21530],{},[898,21519,8974],{},[1846,21521,1848],{},[898,21523,2626],{},[1846,21525,1945],{},[898,21527,12029],{},[1846,21529,1945],{},[898,21531,11957],{},[902,21533,21534],{"encoding":904},"Y = C + I + G",[38,21536,21537],{},"disponibilní důchod",[883,21539,21541],{"className":21540},[886],[888,21542,21543],{"xmlns":890},[892,21544,21545,21561],{},[895,21546,21547,21553,21555,21557,21559],{},[2122,21548,21549,21551],{},[898,21550,8974],{},[898,21552,4029],{},[1846,21554,1848],{},[898,21556,8974],{},[1846,21558,2075],{},[898,21560,2623],{},[902,21562,21563],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,21566,21568],{"className":21567},[886],[888,21569,21570],{"xmlns":890},[892,21571,21572,21590],{},[895,21573,21574,21576,21578,21580,21582,21588],{},[898,21575,2626],{},[1846,21577,1848],{},[898,21579,2626],{},[1846,21581,1855],{"stretchy":1854},[2122,21583,21584,21586],{},[898,21585,8974],{},[898,21587,4029],{},[1846,21589,1861],{"stretchy":1854},[902,21591,21592],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,21595,21597],{"className":21596},[886],[888,21598,21599],{"xmlns":890},[892,21600,21601,21605],{},[895,21602,21603],{},[898,21604,8974],{},[902,21606,8974],{"encoding":904},[883,21608,21610],{"className":21609},[886],[888,21611,21612],{"xmlns":890},[892,21613,21614,21622],{},[895,21615,21616],{},[2122,21617,21618,21620],{},[898,21619,8974],{},[898,21621,4029],{},[902,21623,21624],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,21627,21628,9871,21631,1861],{},[38,21629,21630],{},"Disponibilní důchod",[614,21632,21633],{},"disposable income",[724,21635,21636],{},[883,21637,21639],{"className":21638},[886],[888,21640,21641],{"xmlns":890},[892,21642,21643,21659],{},[895,21644,21645,21651,21653,21655,21657],{},[2122,21646,21647,21649],{},[898,21648,8974],{},[898,21650,4029],{},[1846,21652,1848],{},[898,21654,8974],{},[1846,21656,2075],{},[898,21658,2623],{},[902,21660,21563],{"encoding":904},[724,21662,21663,21664,1734],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,21665,21667],{"className":21666},[886],[888,21668,21669],{"xmlns":890},[892,21670,21671,21689],{},[895,21672,21673,21675,21677,21679,21681,21687],{},[898,21674,2626],{},[1846,21676,1848],{},[898,21678,2626],{},[1846,21680,1855],{"stretchy":1854},[2122,21682,21683,21685],{},[898,21684,8974],{},[898,21686,4029],{},[1846,21688,1861],{"stretchy":1854},[902,21690,21592],{"encoding":904},[198,21692,20536],{"id":21693},"soustava-rovnic-1",[724,21695,21696,21697,1343,21718,21740,21741,2554],{},"Pro pevně zadané ",[883,21698,21700],{"className":21699},[886],[888,21701,21702],{"xmlns":890},[892,21703,21704,21716],{},[895,21705,21706,21708,21710],{},[898,21707,12029],{},[1846,21709,1848],{},[1974,21711,21712,21714],{},[898,21713,12029],{},[1846,21715,4200],{},[902,21717,12040],{"encoding":904},[883,21719,21721],{"className":21720},[886],[888,21722,21723],{"xmlns":890},[892,21724,21725,21737],{},[895,21726,21727,21729,21731],{},[898,21728,11957],{},[1846,21730,1848],{},[1974,21732,21733,21735],{},[898,21734,11957],{},[1846,21736,4200],{},[902,21738,21739],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,21742,21744],{"className":21743},[886],[888,21745,21746],{"xmlns":890},[892,21747,21748,21768],{},[895,21749,21750,21752,21754,21756,21758,21764,21766],{},[898,21751,8974],{},[1846,21753,2136],{"separator":2135},[898,21755,2626],{},[1846,21757,2136],{"separator":2135},[2122,21759,21760,21762],{},[898,21761,8974],{},[898,21763,4029],{},[1846,21765,2136],{"separator":2135},[898,21767,2623],{},[902,21769,21770],{"encoding":904},"Y, C, Y_D, T",[724,21772,21773],{},[883,21774,21776],{"className":21775},[886],[888,21777,21778],{"xmlns":890},[892,21779,21780,21921],{},[895,21781,21782,21912,21914,21916,21919],{},[20599,21783,21784,21822,21850,21882],{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},[20604,21785,21786,21792],{},[20607,21787,21788],{},[2175,21789,21790],{"scriptlevel":2177,"displaystyle":2135},[898,21791,8974],{},[20607,21793,21794],{},[2175,21795,21796],{"scriptlevel":2177,"displaystyle":2135},[895,21797,21798,21800,21802,21804,21806,21812,21814,21820],{},[895,21799],{},[1846,21801,1848],{},[898,21803,2626],{},[1846,21805,1945],{},[1974,21807,21808,21810],{},[898,21809,12029],{},[1846,21811,4200],{},[1846,21813,1945],{},[1974,21815,21816,21818],{},[898,21817,11957],{},[1846,21819,4200],{},[1846,21821,2136],{"separator":2135},[20604,21823,21824,21830],{},[20607,21825,21826],{},[2175,21827,21828],{"scriptlevel":2177,"displaystyle":2135},[898,21829,2623],{},[20607,21831,21832],{},[2175,21833,21834],{"scriptlevel":2177,"displaystyle":2135},[895,21835,21836,21838,21840,21842,21844,21846,21848],{},[895,21837],{},[1846,21839,1848],{},[898,21841,2623],{},[1846,21843,1855],{"stretchy":1854},[898,21845,8974],{},[1846,21847,1861],{"stretchy":1854},[1846,21849,2136],{"separator":2135},[20604,21851,21852,21858],{},[20607,21853,21854],{},[2175,21855,21856],{"scriptlevel":2177,"displaystyle":2135},[898,21857,2626],{},[20607,21859,21860],{},[2175,21861,21862],{"scriptlevel":2177,"displaystyle":2135},[895,21863,21864,21866,21868,21870,21872,21878,21880],{},[895,21865],{},[1846,21867,1848],{},[898,21869,2626],{},[1846,21871,1855],{"stretchy":1854},[2122,21873,21874,21876],{},[898,21875,8974],{},[898,21877,4029],{},[1846,21879,1861],{"stretchy":1854},[1846,21881,2136],{"separator":2135},[20604,21883,21884,21894],{},[20607,21885,21886],{},[2175,21887,21888],{"scriptlevel":2177,"displaystyle":2135},[2122,21889,21890,21892],{},[898,21891,8974],{},[898,21893,4029],{},[20607,21895,21896],{},[2175,21897,21898],{"scriptlevel":2177,"displaystyle":2135},[895,21899,21900,21902,21904,21906,21908,21910],{},[895,21901],{},[1846,21903,1848],{},[898,21905,8974],{},[1846,21907,2075],{},[898,21909,2623],{},[1846,21911,2136],{"separator":2135},[5724,21913],{"width":5726},[1846,21915,1855],{"stretchy":1854},[1979,21917,21918],{},"7.9",[1846,21920,1861],{"stretchy":1854},[902,21922,21923],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,21925,21926,21927,21971,21972,1734],{},"s řešeními ",[883,21928,21930],{"className":21929},[886],[888,21931,21932],{"xmlns":890},[892,21933,21934,21968],{},[895,21935,21936,21942,21944,21950,21952,21958,21960],{},[1974,21937,21938,21940],{},[898,21939,8974],{},[898,21941,4098],{},[1846,21943,2136],{"separator":2135},[1974,21945,21946,21948],{},[898,21947,2626],{},[898,21949,4098],{},[1846,21951,2136],{"separator":2135},[1974,21953,21954,21956],{},[898,21955,2623],{},[898,21957,4098],{},[1846,21959,2136],{"separator":2135},[9012,21961,21962,21964,21966],{},[898,21963,8974],{},[898,21965,4029],{},[898,21967,4098],{},[902,21969,21970],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,21973,21975],{"className":21974},[886],[888,21976,21977],{"xmlns":890},[892,21978,21979,22005],{},[895,21980,21981,21987,21989,21997,21999],{},[1974,21982,21983,21985],{},[898,21984,8519],{},[898,21986,4098],{},[1846,21988,1848],{},[9012,21990,21991,21993,21995],{},[898,21992,8974],{},[898,21994,4029],{},[898,21996,4098],{},[1846,21998,2075],{},[1974,22000,22001,22003],{},[898,22002,2626],{},[898,22004,4098],{},[902,22006,22007],{"encoding":904},"S^E = Y_D^E - C^E",[1639,22009,22010,22015],{},[724,22011,22012,22014],{},[883,22013,4418],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,22016,22017,22040,22123,22178,22268],{},[123,22018,22019,22022,22023,1734],{},[38,22020,22021],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,22024,22026],{"className":22025},[886],[888,22027,22028],{"xmlns":890},[892,22029,22030,22038],{},[895,22031,22032],{},[2122,22033,22034,22036],{},[898,22035,8974],{},[898,22037,4029],{},[902,22039,21624],{"encoding":904},[123,22041,22042,22091,22092,22109,22110,1734],{},[38,22043,22044,22045,22065,22066],{},"Dosaď ",[883,22046,22048],{"className":22047},[886],[888,22049,22050],{"xmlns":890},[892,22051,22052,22062],{},[895,22053,22054,22056,22058,22060],{},[898,22055,2623],{},[1846,22057,1855],{"stretchy":1854},[898,22059,8974],{},[1846,22061,1861],{"stretchy":1854},[902,22063,22064],{"encoding":904},"T(Y)"," do ",[883,22067,22069],{"className":22068},[886],[888,22070,22071],{"xmlns":890},[892,22072,22073,22089],{},[895,22074,22075,22081,22083,22085,22087],{},[2122,22076,22077,22079],{},[898,22078,8974],{},[898,22080,4029],{},[1846,22082,1848],{},[898,22084,8974],{},[1846,22086,2075],{},[898,22088,2623],{},[902,22090,21563],{"encoding":904}," — dostaneš ",[883,22093,22095],{"className":22094},[886],[888,22096,22097],{"xmlns":890},[892,22098,22099,22107],{},[895,22100,22101],{},[2122,22102,22103,22105],{},[898,22104,8974],{},[898,22106,4029],{},[902,22108,21624],{"encoding":904}," jako lineární funkci ",[883,22111,22113],{"className":22112},[886],[888,22114,22115],{"xmlns":890},[892,22116,22117,22121],{},[895,22118,22119],{},[898,22120,8974],{},[902,22122,8974],{"encoding":904},[123,22124,22125,22091,22152,22109,22165,1734],{},[38,22126,22044,22127,22151],{},[883,22128,22130],{"className":22129},[886],[888,22131,22132],{"xmlns":890},[892,22133,22134,22148],{},[895,22135,22136,22142,22144,22146],{},[2122,22137,22138,22140],{},[898,22139,8974],{},[898,22141,4029],{},[1846,22143,1855],{"stretchy":1854},[898,22145,8974],{},[1846,22147,1861],{"stretchy":1854},[902,22149,22150],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,22153,22155],{"className":22154},[886],[888,22156,22157],{"xmlns":890},[892,22158,22159,22163],{},[895,22160,22161],{},[898,22162,2626],{},[902,22164,2626],{"encoding":904},[883,22166,22168],{"className":22167},[886],[888,22169,22170],{"xmlns":890},[892,22171,22172,22176],{},[895,22173,22174],{},[898,22175,8974],{},[902,22177,8974],{"encoding":904},[123,22179,22180,2053,22202,22236,22237,22250,22251,1734],{},[38,22181,22044,22182,22201],{},[883,22183,22185],{"className":22184},[886],[888,22186,22187],{"xmlns":890},[892,22188,22189,22199],{},[895,22190,22191,22193,22195,22197],{},[898,22192,2626],{},[1846,22194,1855],{"stretchy":1854},[898,22196,8974],{},[1846,22198,1861],{"stretchy":1854},[902,22200,14061],{"encoding":904}," do podmínky rovnováhy",[883,22203,22205],{"className":22204},[886],[888,22206,22207],{"xmlns":890},[892,22208,22209,22233],{},[895,22210,22211,22213,22215,22217,22219,22225,22227],{},[898,22212,8974],{},[1846,22214,1848],{},[898,22216,2626],{},[1846,22218,1945],{},[1974,22220,22221,22223],{},[898,22222,12029],{},[1846,22224,4200],{},[1846,22226,1945],{},[1974,22228,22229,22231],{},[898,22230,11957],{},[1846,22232,4200],{},[902,22234,22235],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,22238,22240],{"className":22239},[886],[888,22241,22242],{"xmlns":890},[892,22243,22244,22248],{},[895,22245,22246],{},[898,22247,8974],{},[902,22249,8974],{"encoding":904},", odtud ",[883,22252,22254],{"className":22253},[886],[888,22255,22256],{"xmlns":890},[892,22257,22258,22266],{},[895,22259,22260],{},[1974,22261,22262,22264],{},[898,22263,8974],{},[898,22265,4098],{},[902,22267,13748],{"encoding":904},[123,22269,22270,22273,22274,1343,22292,1343,22312,1343,22329,1734],{},[38,22271,22272],{},"Zpětným dosazením"," dopočítej ",[883,22275,22277],{"className":22276},[886],[888,22278,22279],{"xmlns":890},[892,22280,22281,22289],{},[895,22282,22283],{},[1974,22284,22285,22287],{},[898,22286,2623],{},[898,22288,4098],{},[902,22290,22291],{"encoding":904},"T^E",[883,22293,22295],{"className":22294},[886],[888,22296,22297],{"xmlns":890},[892,22298,22299,22309],{},[895,22300,22301],{},[9012,22302,22303,22305,22307],{},[898,22304,8974],{},[898,22306,4029],{},[898,22308,4098],{},[902,22310,22311],{"encoding":904},"Y_D^E",[883,22313,22315],{"className":22314},[886],[888,22316,22317],{"xmlns":890},[892,22318,22319,22327],{},[895,22320,22321],{},[1974,22322,22323,22325],{},[898,22324,2626],{},[898,22326,4098],{},[902,22328,13807],{"encoding":904},[883,22330,22332],{"className":22331},[886],[888,22333,22334],{"xmlns":890},[892,22335,22336,22344],{},[895,22337,22338],{},[1974,22339,22340,22342],{},[898,22341,8519],{},[898,22343,4098],{},[902,22345,22346],{"encoding":904},"S^E",[198,22348,22350],{"id":22349},"příklad-74","Příklad 7.4",[724,22352,20866,22353,22374,22375,1343,22406,1343,22430,1343,22452,22474],{},[883,22354,22356],{"className":22355},[886],[888,22357,22358],{"xmlns":890},[892,22359,22360,22372],{},[895,22361,22362,22364,22366,22368,22370],{},[898,22363,2626],{},[2138,22365,12135],{},[898,22367,12029],{},[2138,22369,12135],{},[898,22371,11957],{},[902,22373,18065],{"encoding":904}," jsou dány ",[883,22376,22378],{"className":22377},[886],[888,22379,22380],{"xmlns":890},[892,22381,22382,22403],{},[895,22383,22384,22386,22388,22391,22393,22399,22401],{},[898,22385,2626],{},[1846,22387,1848],{},[1979,22389,22390],{},"0,9",[2138,22392,2835],{},[2122,22394,22395,22397],{},[898,22396,8974],{},[898,22398,4029],{},[1846,22400,1945],{},[1979,22402,5743],{},[902,22404,22405],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,22407,22409],{"className":22408},[886],[888,22410,22411],{"xmlns":890},[892,22412,22413,22427],{},[895,22414,22415,22417,22419,22421,22423,22425],{},[898,22416,2623],{},[1846,22418,1848],{},[1979,22420,2688],{},[898,22422,8974],{},[1846,22424,1945],{},[1979,22426,4850],{},[902,22428,22429],{"encoding":904},"T = 0{,}2Y + 25",[883,22431,22433],{"className":22432},[886],[888,22434,22435],{"xmlns":890},[892,22436,22437,22449],{},[895,22438,22439,22445,22447],{},[1974,22440,22441,22443],{},[898,22442,12029],{},[1846,22444,4200],{},[1846,22446,1848],{},[1979,22448,14883],{},[902,22450,22451],{"encoding":904},"I^* = 35",[883,22453,22455],{"className":22454},[886],[888,22456,22457],{"xmlns":890},[892,22458,22459,22471],{},[895,22460,22461,22467,22469],{},[1974,22462,22463,22465],{},[898,22464,11957],{},[1846,22466,4200],{},[1846,22468,1848],{},[1979,22470,8881],{},[902,22472,22473],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,22476,22477],{},[883,22478,22480],{"className":22479},[886],[888,22481,22482],{"xmlns":890},[892,22483,22484,22608],{},[20599,22485,22486,22516,22544,22578],{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},[20604,22487,22488,22494],{},[20607,22489,22490],{},[2175,22491,22492],{"scriptlevel":2177,"displaystyle":2135},[898,22493,8974],{},[20607,22495,22496],{},[2175,22497,22498],{"scriptlevel":2177,"displaystyle":2135},[895,22499,22500,22502,22504,22506,22508,22510,22512,22514],{},[895,22501],{},[1846,22503,1848],{},[898,22505,2626],{},[1846,22507,1945],{},[1979,22509,14883],{},[1846,22511,1945],{},[1979,22513,8881],{},[1846,22515,2136],{"separator":2135},[20604,22517,22518,22524],{},[20607,22519,22520],{},[2175,22521,22522],{"scriptlevel":2177,"displaystyle":2135},[898,22523,2623],{},[20607,22525,22526],{},[2175,22527,22528],{"scriptlevel":2177,"displaystyle":2135},[895,22529,22530,22532,22534,22536,22538,22540,22542],{},[895,22531],{},[1846,22533,1848],{},[1979,22535,2688],{},[898,22537,8974],{},[1846,22539,1945],{},[1979,22541,4850],{},[1846,22543,2136],{"separator":2135},[20604,22545,22546,22552],{},[20607,22547,22548],{},[2175,22549,22550],{"scriptlevel":2177,"displaystyle":2135},[898,22551,2626],{},[20607,22553,22554],{},[2175,22555,22556],{"scriptlevel":2177,"displaystyle":2135},[895,22557,22558,22560,22562,22564,22566,22572,22574,22576],{},[895,22559],{},[1846,22561,1848],{},[1979,22563,22390],{},[2138,22565,2835],{},[2122,22567,22568,22570],{},[898,22569,8974],{},[898,22571,4029],{},[1846,22573,1945],{},[1979,22575,5743],{},[1846,22577,2136],{"separator":2135},[20604,22579,22580,22590],{},[20607,22581,22582],{},[2175,22583,22584],{"scriptlevel":2177,"displaystyle":2135},[2122,22585,22586,22588],{},[898,22587,8974],{},[898,22589,4029],{},[20607,22591,22592],{},[2175,22593,22594],{"scriptlevel":2177,"displaystyle":2135},[895,22595,22596,22598,22600,22602,22604,22606],{},[895,22597],{},[1846,22599,1848],{},[898,22601,8974],{},[1846,22603,2075],{},[898,22605,2623],{},[898,22607,1734],{"mathvariant":2226},[902,22609,22610],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,22612,22613,22616,22617,22671,22672,22718,22719,2554],{},[38,22614,22615],{},"Řešení."," Z definice ",[883,22618,22620],{"className":22619},[886],[888,22621,22622],{"xmlns":890},[892,22623,22624,22668],{},[895,22625,22626,22632,22634,22636,22638,22640,22642,22644,22646,22648,22650,22652,22654,22656,22658,22660,22662,22664,22666],{},[2122,22627,22628,22630],{},[898,22629,8974],{},[898,22631,4029],{},[1846,22633,1848],{},[898,22635,8974],{},[1846,22637,2075],{},[898,22639,2623],{},[1846,22641,1848],{},[898,22643,8974],{},[1846,22645,2075],{},[1846,22647,1855],{"stretchy":1854},[1979,22649,2688],{},[898,22651,8974],{},[1846,22653,1945],{},[1979,22655,4850],{},[1846,22657,1861],{"stretchy":1854},[1846,22659,1848],{},[1979,22661,14434],{},[898,22663,8974],{},[1846,22665,2075],{},[1979,22667,4850],{},[902,22669,22670],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,22673,22675],{"className":22674},[886],[888,22676,22677],{"xmlns":890},[892,22678,22679,22715],{},[895,22680,22681,22683,22685,22687,22689,22691,22693,22695,22697,22699,22701,22703,22705,22708,22710,22712],{},[898,22682,2626],{},[1846,22684,1848],{},[1979,22686,22390],{},[1846,22688,1855],{"stretchy":1854},[1979,22690,14434],{},[898,22692,8974],{},[1846,22694,2075],{},[1979,22696,4850],{},[1846,22698,1861],{"stretchy":1854},[1846,22700,1945],{},[1979,22702,5743],{},[1846,22704,1848],{},[1979,22706,22707],{},"0,72",[898,22709,8974],{},[1846,22711,1945],{},[1979,22713,22714],{},"47,5",[902,22716,22717],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,22720,22722],{"className":22721},[886],[888,22723,22724],{"xmlns":890},[892,22725,22726,22744],{},[895,22727,22728,22730,22732,22734,22736,22738,22740,22742],{},[898,22729,8974],{},[1846,22731,1848],{},[1979,22733,22707],{},[898,22735,8974],{},[1846,22737,1945],{},[1979,22739,22714],{},[1846,22741,1945],{},[1979,22743,21025],{},[902,22745,22746],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,22748,22749],{},[883,22750,22752],{"className":22751},[886],[888,22753,22754],{"xmlns":890},[892,22755,22756,22797],{},[895,22757,22758,22761,22763,22765,22768,22770,22772,22774,22780,22782,22792,22794],{},[1979,22759,22760],{},"0,28",[898,22762,8974],{},[1846,22764,1848],{},[1979,22766,22767],{},"102,5",[2138,22769,3830],{},[1846,22771,14853],{},[2138,22773,3830],{},[1974,22775,22776,22778],{},[898,22777,8974],{},[898,22779,4098],{},[1846,22781,1848],{},[2175,22783,22784],{"scriptlevel":2177,"displaystyle":1854},[2179,22785,22786,22789],{},[1979,22787,22788],{},"5125",[1979,22790,22791],{},"14",[1846,22793,5746],{},[1979,22795,22796],{},"366,071.",[902,22798,22799],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,22801,22802],{},"Rovnovážné veličiny:",[120,22804,22805,22840,22892,22946,22994],{},[123,22806,22807,2136],{},[883,22808,22810],{"className":22809},[886],[888,22811,22812],{"xmlns":890},[892,22813,22814,22837],{},[895,22815,22816,22822,22824,22832,22834],{},[1974,22817,22818,22820],{},[898,22819,8974],{},[898,22821,4098],{},[1846,22823,1848],{},[2175,22825,22826],{"scriptlevel":2177,"displaystyle":1854},[2179,22827,22828,22830],{},[1979,22829,22788],{},[1979,22831,22791],{},[1846,22833,5746],{},[1979,22835,22836],{},"366,071",[902,22838,22839],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,22841,22842,2136],{},[883,22843,22845],{"className":22844},[886],[888,22846,22847],{"xmlns":890},[892,22848,22849,22889],{},[895,22850,22851,22857,22859,22861,22863,22869,22871,22873,22875,22884,22886],{},[1974,22852,22853,22855],{},[898,22854,2623],{},[898,22856,4098],{},[1846,22858,1848],{},[1979,22860,2688],{},[2138,22862,2835],{},[1974,22864,22865,22867],{},[898,22866,8974],{},[898,22868,4098],{},[1846,22870,1945],{},[1979,22872,4850],{},[1846,22874,1848],{},[2175,22876,22877],{"scriptlevel":2177,"displaystyle":1854},[2179,22878,22879,22882],{},[1979,22880,22881],{},"1375",[1979,22883,22791],{},[1846,22885,5746],{},[1979,22887,22888],{},"98,214",[902,22890,22891],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,22893,22894,2136],{},[883,22895,22897],{"className":22896},[886],[888,22898,22899],{"xmlns":890},[892,22900,22901,22943],{},[895,22902,22903,22911,22913,22919,22921,22927,22929,22938,22940],{},[9012,22904,22905,22907,22909],{},[898,22906,8974],{},[898,22908,4029],{},[898,22910,4098],{},[1846,22912,1848],{},[1974,22914,22915,22917],{},[898,22916,8974],{},[898,22918,4098],{},[1846,22920,2075],{},[1974,22922,22923,22925],{},[898,22924,2623],{},[898,22926,4098],{},[1846,22928,1848],{},[2175,22930,22931],{"scriptlevel":2177,"displaystyle":1854},[2179,22932,22933,22936],{},[1979,22934,22935],{},"3750",[1979,22937,22791],{},[1846,22939,5746],{},[1979,22941,22942],{},"267,857",[902,22944,22945],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,22947,22948,2136],{},[883,22949,22951],{"className":22950},[886],[888,22952,22953],{"xmlns":890},[892,22954,22955,22991],{},[895,22956,22957,22963,22965,22971,22973,22975,22977,22986,22988],{},[1974,22958,22959,22961],{},[898,22960,2626],{},[898,22962,4098],{},[1846,22964,1848],{},[1974,22966,22967,22969],{},[898,22968,8974],{},[898,22970,4098],{},[1846,22972,2075],{},[1979,22974,21025],{},[1846,22976,1848],{},[2175,22978,22979],{"scriptlevel":2177,"displaystyle":1854},[2179,22980,22981,22984],{},[1979,22982,22983],{},"4355",[1979,22985,22791],{},[1846,22987,5746],{},[1979,22989,22990],{},"311,071",[902,22992,22993],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,22995,22996,23052],{},[883,22997,22999],{"className":22998},[886],[888,23000,23001],{"xmlns":890},[892,23002,23003,23049],{},[895,23004,23005,23011,23013,23021,23023,23029,23031,23033,23042,23044,23046],{},[1974,23006,23007,23009],{},[898,23008,8519],{},[898,23010,4098],{},[1846,23012,1848],{},[9012,23014,23015,23017,23019],{},[898,23016,8974],{},[898,23018,4029],{},[898,23020,4098],{},[1846,23022,2075],{},[1974,23024,23025,23027],{},[898,23026,2626],{},[898,23028,4098],{},[1846,23030,1848],{},[1846,23032,2075],{},[2175,23034,23035],{"scriptlevel":2177,"displaystyle":1854},[2179,23036,23037,23040],{},[1979,23038,23039],{},"605",[1979,23041,22791],{},[1846,23043,5746],{},[1846,23045,2075],{},[1979,23047,23048],{},"43,214",[902,23050,23051],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,23054,23055,21195,23057,23078,23079,23082,23083,23106,23107,1734],{},[38,23056,21194],{},[883,23058,23060],{"className":23059},[886],[888,23061,23062],{"xmlns":890},[892,23063,23064,23076],{},[895,23065,23066,23068,23070,23072,23074],{},[898,23067,2626],{},[2138,23069,12135],{},[898,23071,12029],{},[2138,23073,12135],{},[898,23075,11957],{},[902,23077,18065],{"encoding":904}," stále uvažuje ",[38,23080,23081],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,23084,23086],{"className":23085},[886],[888,23087,23088],{"xmlns":890},[892,23089,23090,23103],{},[895,23091,23092,23094,23096,23099,23101],{},[898,23093,12165],{},[1846,23095,1848],{},[898,23097,23098],{},"B",[1846,23100,2075],{},[898,23102,2667],{},[902,23104,23105],{"encoding":904},"X = B - M"," dává ",[38,23108,21216,23109],{},[883,23110,23112],{"className":23111},[886],[888,23113,23114],{"xmlns":890},[892,23115,23116,23132],{},[895,23117,23118,23120,23122,23124,23126,23128,23130],{},[898,23119,2626],{},[2138,23121,12135],{},[898,23123,12029],{},[2138,23125,12135],{},[898,23127,11957],{},[2138,23129,12135],{},[898,23131,12165],{},[902,23133,12168],{"encoding":904},[115,23135,23137],{"id":23136},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,23139,20466],{"id":23140},"zadání-modelu-2",[724,23142,23143,23144,2053,23147,21439,23168,23181,23182,11973,23185,23198],{},"Rozšíření o ",[38,23145,23146],{},"čistý export",[883,23148,23150],{"className":23149},[886],[888,23151,23152],{"xmlns":890},[892,23153,23154,23166],{},[895,23155,23156,23158,23160,23162,23164],{},[898,23157,12165],{},[1846,23159,1848],{},[898,23161,23098],{},[1846,23163,2075],{},[898,23165,2667],{},[902,23167,23105],{"encoding":904},[883,23169,23171],{"className":23170},[886],[888,23172,23173],{"xmlns":890},[892,23174,23175,23179],{},[895,23176,23177],{},[898,23178,23098],{},[902,23180,23098],{"encoding":904}," je hrubý export (",[614,23183,23184],{},"brutto export",[883,23186,23188],{"className":23187},[886],[888,23189,23190],{"xmlns":890},[892,23191,23192,23196],{},[895,23193,23194],{},[898,23195,2667],{},[902,23197,2667],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,23200,23201],{},[883,23202,23204],{"className":23203},[886],[888,23205,23206],{"xmlns":890},[892,23207,23208,23228],{},[895,23209,23210,23212,23214,23216,23218,23224,23226],{},[898,23211,2667],{},[1846,23213,1848],{},[898,23215,2667],{},[1846,23217,1855],{"stretchy":1854},[2122,23219,23220,23222],{},[898,23221,8974],{},[898,23223,4029],{},[1846,23225,1861],{"stretchy":1854},[898,23227,1734],{"mathvariant":2226},[902,23229,23230],{"encoding":904},"M = M(Y_D).",[724,23232,23233],{},"Podmínka rovnováhy:",[724,23235,23236],{},[883,23237,23239],{"className":23238},[886],[888,23240,23241],{"xmlns":890},[892,23242,23243,23280],{},[895,23244,23245,23247,23249,23251,23253,23255,23257,23259,23261,23263,23265,23267,23269,23271,23273,23276,23278],{},[898,23246,8974],{},[1846,23248,1848],{},[898,23250,2626],{},[1846,23252,1945],{},[898,23254,12029],{},[1846,23256,1945],{},[898,23258,11957],{},[1846,23260,1945],{},[898,23262,23098],{},[1846,23264,2075],{},[898,23266,2667],{},[898,23268,1734],{"mathvariant":2226},[5724,23270],{"width":5726},[1846,23272,1855],{"stretchy":1854},[1979,23274,23275],{},"7.10",[2138,23277,207],{},[1846,23279,1861],{"stretchy":1854},[902,23281,23282],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,23284,20536],{"id":23285},"soustava-rovnic-2",[724,23287,21696,23288,23322,23323,2554],{},[883,23289,23291],{"className":23290},[886],[888,23292,23293],{"xmlns":890},[892,23294,23295,23319],{},[895,23296,23297,23303,23305,23311,23313],{},[1974,23298,23299,23301],{},[898,23300,12029],{},[1846,23302,4200],{},[1846,23304,2136],{"separator":2135},[1974,23306,23307,23309],{},[898,23308,11957],{},[1846,23310,4200],{},[1846,23312,2136],{"separator":2135},[1974,23314,23315,23317],{},[898,23316,23098],{},[1846,23318,4200],{},[902,23320,23321],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,23324,23326],{"className":23325},[886],[888,23327,23328],{"xmlns":890},[892,23329,23330,23354],{},[895,23331,23332,23334,23336,23338,23340,23342,23344,23350,23352],{},[898,23333,8974],{},[1846,23335,2136],{"separator":2135},[898,23337,2626],{},[1846,23339,2136],{"separator":2135},[898,23341,2623],{},[1846,23343,2136],{"separator":2135},[2122,23345,23346,23348],{},[898,23347,8974],{},[898,23349,4029],{},[1846,23351,2136],{"separator":2135},[898,23353,2667],{},[902,23355,23356],{"encoding":904},"Y, C, T, Y_D, M",[724,23358,23359],{},[883,23360,23362],{"className":23361},[886],[888,23363,23364],{"xmlns":890},[892,23365,23366,23550],{},[895,23367,23368,23542,23544,23546,23548],{},[20599,23369,23370,23402,23432,23460,23492],{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},[20604,23371,23372,23378],{},[20607,23373,23374],{},[2175,23375,23376],{"scriptlevel":2177,"displaystyle":2135},[898,23377,2626],{},[20607,23379,23380],{},[2175,23381,23382],{"scriptlevel":2177,"displaystyle":2135},[895,23383,23384,23386,23388,23390,23392,23398,23400],{},[895,23385],{},[1846,23387,1848],{},[898,23389,2626],{},[1846,23391,1855],{"stretchy":1854},[2122,23393,23394,23396],{},[898,23395,8974],{},[898,23397,4029],{},[1846,23399,1861],{"stretchy":1854},[1846,23401,2136],{"separator":2135},[20604,23403,23404,23414],{},[20607,23405,23406],{},[2175,23407,23408],{"scriptlevel":2177,"displaystyle":2135},[2122,23409,23410,23412],{},[898,23411,8974],{},[898,23413,4029],{},[20607,23415,23416],{},[2175,23417,23418],{"scriptlevel":2177,"displaystyle":2135},[895,23419,23420,23422,23424,23426,23428,23430],{},[895,23421],{},[1846,23423,1848],{},[898,23425,8974],{},[1846,23427,2075],{},[898,23429,2623],{},[1846,23431,2136],{"separator":2135},[20604,23433,23434,23440],{},[20607,23435,23436],{},[2175,23437,23438],{"scriptlevel":2177,"displaystyle":2135},[898,23439,2623],{},[20607,23441,23442],{},[2175,23443,23444],{"scriptlevel":2177,"displaystyle":2135},[895,23445,23446,23448,23450,23452,23454,23456,23458],{},[895,23447],{},[1846,23449,1848],{},[898,23451,2623],{},[1846,23453,1855],{"stretchy":1854},[898,23455,8974],{},[1846,23457,1861],{"stretchy":1854},[1846,23459,2136],{"separator":2135},[20604,23461,23462,23468],{},[20607,23463,23464],{},[2175,23465,23466],{"scriptlevel":2177,"displaystyle":2135},[898,23467,2667],{},[20607,23469,23470],{},[2175,23471,23472],{"scriptlevel":2177,"displaystyle":2135},[895,23473,23474,23476,23478,23480,23482,23488,23490],{},[895,23475],{},[1846,23477,1848],{},[898,23479,2667],{},[1846,23481,1855],{"stretchy":1854},[2122,23483,23484,23486],{},[898,23485,8974],{},[898,23487,4029],{},[1846,23489,1861],{"stretchy":1854},[1846,23491,2136],{"separator":2135},[20604,23493,23494,23500],{},[20607,23495,23496],{},[2175,23497,23498],{"scriptlevel":2177,"displaystyle":2135},[898,23499,8974],{},[20607,23501,23502],{},[2175,23503,23504],{"scriptlevel":2177,"displaystyle":2135},[895,23505,23506,23508,23510,23512,23514,23520,23522,23528,23530,23536,23538,23540],{},[895,23507],{},[1846,23509,1848],{},[898,23511,2626],{},[1846,23513,1945],{},[1974,23515,23516,23518],{},[898,23517,12029],{},[1846,23519,4200],{},[1846,23521,1945],{},[1974,23523,23524,23526],{},[898,23525,11957],{},[1846,23527,4200],{},[1846,23529,1945],{},[1974,23531,23532,23534],{},[898,23533,23098],{},[1846,23535,4200],{},[1846,23537,2075],{},[898,23539,2667],{},[898,23541,1734],{"mathvariant":2226},[5724,23543],{"width":5726},[1846,23545,1855],{"stretchy":1854},[1979,23547,23275],{},[1846,23549,1861],{"stretchy":1854},[902,23551,23552],{"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)",[198,23554,23556],{"id":23555},"příklad-75","Příklad 7.5",[724,23558,23559,23560,1343,23592,1343,23619,1343,23640,1343,23662,1343,23684,23707],{},"Dáno: ",[883,23561,23563],{"className":23562},[886],[888,23564,23565],{"xmlns":890},[892,23566,23567,23589],{},[895,23568,23569,23571,23573,23576,23578,23584,23586],{},[898,23570,2626],{},[1846,23572,1848],{},[1979,23574,23575],{},"0,75",[2138,23577,2835],{},[2122,23579,23580,23582],{},[898,23581,8974],{},[898,23583,4029],{},[1846,23585,1945],{},[1979,23587,23588],{},"750",[902,23590,23591],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,23593,23595],{"className":23594},[886],[888,23596,23597],{"xmlns":890},[892,23598,23599,23616],{},[895,23600,23601,23603,23605,23608,23610],{},[898,23602,2667],{},[1846,23604,1848],{},[1979,23606,23607],{},"0,15",[2138,23609,2835],{},[2122,23611,23612,23614],{},[898,23613,8974],{},[898,23615,4029],{},[902,23617,23618],{"encoding":904},"M = 0{,}15\\,Y_D",[883,23620,23622],{"className":23621},[886],[888,23623,23624],{"xmlns":890},[892,23625,23626,23637],{},[895,23627,23628,23630,23632,23635],{},[898,23629,2623],{},[1846,23631,1848],{},[1979,23633,23634],{},"0,25",[898,23636,8974],{},[902,23638,23639],{"encoding":904},"T = 0{,}25Y",[883,23641,23643],{"className":23642},[886],[888,23644,23645],{"xmlns":890},[892,23646,23647,23659],{},[895,23648,23649,23655,23657],{},[1974,23650,23651,23653],{},[898,23652,12029],{},[1846,23654,4200],{},[1846,23656,1848],{},[1979,23658,14955],{},[902,23660,23661],{"encoding":904},"I^* = 500",[883,23663,23665],{"className":23664},[886],[888,23666,23667],{"xmlns":890},[892,23668,23669,23681],{},[895,23670,23671,23677,23679],{},[1974,23672,23673,23675],{},[898,23674,11957],{},[1846,23676,4200],{},[1846,23678,1848],{},[1979,23680,8649],{},[902,23682,23683],{"encoding":904},"G^* = 150",[883,23685,23687],{"className":23686},[886],[888,23688,23689],{"xmlns":890},[892,23690,23691,23704],{},[895,23692,23693,23699,23701],{},[1974,23694,23695,23697],{},[898,23696,23098],{},[1846,23698,4200],{},[1846,23700,1848],{},[1979,23702,23703],{},"800",[902,23705,23706],{"encoding":904},"B^* = 800",". Soustava:",[724,23709,23710],{},[883,23711,23713],{"className":23712},[886],[888,23714,23715],{"xmlns":890},[892,23716,23717,23935],{},[20599,23718,23719,23765,23807,23843,23885],{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},[20604,23720,23721,23737],{},[20607,23722,23723],{},[2175,23724,23725],{"scriptlevel":2177,"displaystyle":2135},[895,23726,23727,23729,23731,23733,23735],{},[1846,23728,1855],{"stretchy":1854},[898,23730,11886],{},[1979,23732,2128],{},[1846,23734,1861],{"stretchy":1854},[2138,23736,2140],{},[20607,23738,23739],{},[2175,23740,23741],{"scriptlevel":2177,"displaystyle":2135},[895,23742,23743,23745,23747,23749,23751,23753,23759,23761,23763],{},[895,23744],{},[898,23746,2626],{},[1846,23748,1848],{},[1979,23750,23575],{},[2138,23752,2835],{},[2122,23754,23755,23757],{},[898,23756,8974],{},[898,23758,4029],{},[1846,23760,1945],{},[1979,23762,23588],{},[1846,23764,2136],{"separator":2135},[20604,23766,23767,23783],{},[20607,23768,23769],{},[2175,23770,23771],{"scriptlevel":2177,"displaystyle":2135},[895,23772,23773,23775,23777,23779,23781],{},[1846,23774,1855],{"stretchy":1854},[898,23776,11886],{},[1979,23778,1981],{},[1846,23780,1861],{"stretchy":1854},[2138,23782,2140],{},[20607,23784,23785],{},[2175,23786,23787],{"scriptlevel":2177,"displaystyle":2135},[895,23788,23789,23791,23797,23799,23801,23803,23805],{},[895,23790],{},[2122,23792,23793,23795],{},[898,23794,8974],{},[898,23796,4029],{},[1846,23798,1848],{},[898,23800,8974],{},[1846,23802,2075],{},[898,23804,2623],{},[1846,23806,2136],{"separator":2135},[20604,23808,23809,23825],{},[20607,23810,23811],{},[2175,23812,23813],{"scriptlevel":2177,"displaystyle":2135},[895,23814,23815,23817,23819,23821,23823],{},[1846,23816,1855],{"stretchy":1854},[898,23818,11886],{},[1979,23820,2023],{},[1846,23822,1861],{"stretchy":1854},[2138,23824,2140],{},[20607,23826,23827],{},[2175,23828,23829],{"scriptlevel":2177,"displaystyle":2135},[895,23830,23831,23833,23835,23837,23839,23841],{},[895,23832],{},[898,23834,2623],{},[1846,23836,1848],{},[1979,23838,23634],{},[898,23840,8974],{},[1846,23842,2136],{"separator":2135},[20604,23844,23845,23861],{},[20607,23846,23847],{},[2175,23848,23849],{"scriptlevel":2177,"displaystyle":2135},[895,23850,23851,23853,23855,23857,23859],{},[1846,23852,1855],{"stretchy":1854},[898,23854,11886],{},[1979,23856,2201],{},[1846,23858,1861],{"stretchy":1854},[2138,23860,2140],{},[20607,23862,23863],{},[2175,23864,23865],{"scriptlevel":2177,"displaystyle":2135},[895,23866,23867,23869,23871,23873,23875,23877,23883],{},[895,23868],{},[898,23870,2667],{},[1846,23872,1848],{},[1979,23874,23607],{},[2138,23876,2835],{},[2122,23878,23879,23881],{},[898,23880,8974],{},[898,23882,4029],{},[1846,23884,2136],{"separator":2135},[20604,23886,23887,23903],{},[20607,23888,23889],{},[2175,23890,23891],{"scriptlevel":2177,"displaystyle":2135},[895,23892,23893,23895,23897,23899,23901],{},[1846,23894,1855],{"stretchy":1854},[898,23896,11886],{},[1979,23898,2078],{},[1846,23900,1861],{"stretchy":1854},[2138,23902,2140],{},[20607,23904,23905],{},[2175,23906,23907],{"scriptlevel":2177,"displaystyle":2135},[895,23908,23909,23911,23913,23915,23917,23919,23921,23923,23925,23927,23929,23931,23933],{},[895,23910],{},[898,23912,8974],{},[1846,23914,1848],{},[898,23916,2626],{},[1846,23918,1945],{},[1979,23920,14955],{},[1846,23922,1945],{},[1979,23924,8649],{},[1846,23926,1945],{},[1979,23928,23703],{},[1846,23930,2075],{},[898,23932,2667],{},[898,23934,1734],{"mathvariant":2226},[902,23936,23937],{"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}",[724,23939,23940,23941,23975],{},"Postupná substituce — z (r3) do (r2): ",[883,23942,23944],{"className":23943},[886],[888,23945,23946],{"xmlns":890},[892,23947,23948,23972],{},[895,23949,23950,23956,23958,23960,23962,23964,23966,23968,23970],{},[2122,23951,23952,23954],{},[898,23953,8974],{},[898,23955,4029],{},[1846,23957,1848],{},[898,23959,8974],{},[1846,23961,2075],{},[1979,23963,23634],{},[898,23965,8974],{},[1846,23967,1848],{},[1979,23969,23575],{},[898,23971,8974],{},[902,23973,23974],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,23977,23978],{},[883,23979,23981],{"className":23980},[886],[888,23982,23983],{"xmlns":890},[892,23984,23985,24026],{},[895,23986,23987,23989,23991,23993,23995,23997,23999,24001,24003,24005,24007,24009,24011,24013,24015,24018,24020,24022,24024],{},[1846,23988,1855],{"stretchy":1854},[898,23990,11886],{},[1979,23992,2085],{},[1846,23994,1861],{"stretchy":1854},[2138,23996,2140],{},[898,23998,2626],{},[1846,24000,1848],{},[1979,24002,23575],{},[1846,24004,3025],{},[1979,24006,23575],{},[898,24008,8974],{},[1846,24010,1945],{},[1979,24012,23588],{},[1846,24014,1848],{},[1979,24016,24017],{},"0,5625",[898,24019,8974],{},[1846,24021,1945],{},[1979,24023,23588],{},[1846,24025,2136],{"separator":2135},[902,24027,24028],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,24030,24031],{},[883,24032,24034],{"className":24033},[886],[888,24035,24036],{"xmlns":890},[892,24037,24038,24072],{},[895,24039,24040,24042,24044,24047,24049,24051,24053,24055,24057,24059,24061,24063,24065,24068,24070],{},[1846,24041,1855],{"stretchy":1854},[898,24043,11886],{},[1979,24045,24046],{},"7",[1846,24048,1861],{"stretchy":1854},[2138,24050,2140],{},[898,24052,2667],{},[1846,24054,1848],{},[1979,24056,23607],{},[1846,24058,3025],{},[1979,24060,23575],{},[898,24062,8974],{},[1846,24064,1848],{},[1979,24066,24067],{},"0,1125",[898,24069,8974],{},[898,24071,1734],{"mathvariant":2226},[902,24073,24074],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,24076,24077],{},"Dosazením do (r5):",[724,24079,24080],{},[883,24081,24083],{"className":24082},[886],[888,24084,24085],{"xmlns":890},[892,24086,24087,24131],{},[895,24088,24089,24091,24093,24095,24097,24099,24101,24103,24105,24107,24109,24111,24113,24115,24117,24119,24121,24124,24126,24128],{},[898,24090,8974],{},[1846,24092,1848],{},[1979,24094,24017],{},[898,24096,8974],{},[1846,24098,1945],{},[1979,24100,23588],{},[1846,24102,1945],{},[1979,24104,14955],{},[1846,24106,1945],{},[1979,24108,8649],{},[1846,24110,1945],{},[1979,24112,23703],{},[1846,24114,2075],{},[1979,24116,24067],{},[898,24118,8974],{},[1846,24120,1848],{},[1979,24122,24123],{},"0,45",[898,24125,8974],{},[1846,24127,1945],{},[1979,24129,24130],{},"2200.",[902,24132,24133],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,24135,24136,24137,5435,24159,24182],{},"Odtud ",[883,24138,24140],{"className":24139},[886],[888,24141,24142],{"xmlns":890},[892,24143,24144,24156],{},[895,24145,24146,24149,24151,24153],{},[1979,24147,24148],{},"0,55",[898,24150,8974],{},[1846,24152,1848],{},[1979,24154,24155],{},"2200",[902,24157,24158],{"encoding":904},"0{,}55Y = 2200",[883,24160,24162],{"className":24161},[886],[888,24163,24164],{"xmlns":890},[892,24165,24166,24179],{},[895,24167,24168,24174,24176],{},[1974,24169,24170,24172],{},[898,24171,8974],{},[898,24173,4098],{},[1846,24175,1848],{},[1979,24177,24178],{},"4000",[902,24180,24181],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,24184,24185,24208,24240,24275,24308,24344],{},[123,24186,24187,2136],{},[883,24188,24190],{"className":24189},[886],[888,24191,24192],{"xmlns":890},[892,24193,24194,24206],{},[895,24195,24196,24202,24204],{},[1974,24197,24198,24200],{},[898,24199,8974],{},[898,24201,4098],{},[1846,24203,1848],{},[1979,24205,24178],{},[902,24207,24181],{"encoding":904},[123,24209,24210,2136],{},[883,24211,24213],{"className":24212},[886],[888,24214,24215],{"xmlns":890},[892,24216,24217,24237],{},[895,24218,24219,24225,24227,24229,24231,24233,24235],{},[1974,24220,24221,24223],{},[898,24222,2623],{},[898,24224,4098],{},[1846,24226,1848],{},[1979,24228,23634],{},[1846,24230,3025],{},[1979,24232,24178],{},[1846,24234,1848],{},[1979,24236,2631],{},[902,24238,24239],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,24241,24242,2136],{},[883,24243,24245],{"className":24244},[886],[888,24246,24247],{"xmlns":890},[892,24248,24249,24272],{},[895,24250,24251,24259,24261,24263,24265,24267,24269],{},[9012,24252,24253,24255,24257],{},[898,24254,8974],{},[898,24256,4029],{},[898,24258,4098],{},[1846,24260,1848],{},[1979,24262,23575],{},[1846,24264,3025],{},[1979,24266,24178],{},[1846,24268,1848],{},[1979,24270,24271],{},"3000",[902,24273,24274],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,24276,24277,2136],{},[883,24278,24280],{"className":24279},[886],[888,24281,24282],{"xmlns":890},[892,24283,24284,24305],{},[895,24285,24286,24292,24294,24296,24298,24300,24302],{},[1974,24287,24288,24290],{},[898,24289,2667],{},[898,24291,4098],{},[1846,24293,1848],{},[1979,24295,23607],{},[1846,24297,3025],{},[1979,24299,24271],{},[1846,24301,1848],{},[1979,24303,24304],{},"450",[902,24306,24307],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,24309,24310,2136],{},[883,24311,24313],{"className":24312},[886],[888,24314,24315],{"xmlns":890},[892,24316,24317,24341],{},[895,24318,24319,24325,24327,24329,24331,24333,24335,24337,24339],{},[1974,24320,24321,24323],{},[898,24322,2626],{},[898,24324,4098],{},[1846,24326,1848],{},[1979,24328,23575],{},[1846,24330,3025],{},[1979,24332,24271],{},[1846,24334,1945],{},[1979,24336,23588],{},[1846,24338,1848],{},[1979,24340,24271],{},[902,24342,24343],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,24345,24346,24386],{},[883,24347,24349],{"className":24348},[886],[888,24350,24351],{"xmlns":890},[892,24352,24353,24383],{},[895,24354,24355,24361,24363,24371,24373,24379,24381],{},[1974,24356,24357,24359],{},[898,24358,8519],{},[898,24360,4098],{},[1846,24362,1848],{},[9012,24364,24365,24367,24369],{},[898,24366,8974],{},[898,24368,4029],{},[898,24370,4098],{},[1846,24372,2075],{},[1974,24374,24375,24377],{},[898,24376,2626],{},[898,24378,4098],{},[1846,24380,1848],{},[1979,24382,2177],{},[902,24384,24385],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,24388,24389,24391,24392,1343,24409,1745,24430,24455,24456,24459,24460,24473,24474,1734],{},[38,24390,21194],{}," Modely ",[883,24393,24395],{"className":24394},[886],[888,24396,24397],{"xmlns":890},[892,24398,24399,24407],{},[895,24400,24401,24403,24405],{},[898,24402,2626],{},[2138,24404,12135],{},[898,24406,12029],{},[902,24408,12140],{"encoding":904},[883,24410,24412],{"className":24411},[886],[888,24413,24414],{"xmlns":890},[892,24415,24416,24428],{},[895,24417,24418,24420,24422,24424,24426],{},[898,24419,2626],{},[2138,24421,12135],{},[898,24423,12029],{},[2138,24425,12135],{},[898,24427,11957],{},[902,24429,18065],{"encoding":904},[883,24431,24433],{"className":24432},[886],[888,24434,24435],{"xmlns":890},[892,24436,24437,24453],{},[895,24438,24439,24441,24443,24445,24447,24449,24451],{},[898,24440,2626],{},[2138,24442,12135],{},[898,24444,12029],{},[2138,24446,12135],{},[898,24448,11957],{},[2138,24450,12135],{},[898,24452,12165],{},[902,24454,12168],{"encoding":904}," pokládají investice za ",[38,24457,24458],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,24461,24463],{"className":24462},[886],[888,24464,24465],{"xmlns":890},[892,24466,24467,24471],{},[895,24468,24469],{},[898,24470,11886],{},[902,24472,11886],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,24475,24476],{},"model IS-LM",[115,24478,24480],{"id":24479},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,24482,24483,24484,24488,24489,24492,24493,24496],{},"V článku ",[207,24485,24487],{"className":24486,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,24490,24491],{},"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 ",[38,24494,24495],{},"výraznější"," než v mikroekonomických modelech.",[724,24498,24499],{},[2409,24500],{"alt":24501,"className":24502,"src":24503},"imek-multiplikatorovy-efekt-chain",[210,2413],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,24505,12009,24506,1343,24523,1343,24544,24569,24570,24573,24574,24592,24593,24611,24612,24630,24631,24634,24635,1343,24652,24669,24670,24672],{},[883,24507,24509],{"className":24508},[886],[888,24510,24511],{"xmlns":890},[892,24512,24513,24521],{},[895,24514,24515,24517,24519],{},[898,24516,2626],{},[2138,24518,12135],{},[898,24520,12029],{},[902,24522,12140],{"encoding":904},[883,24524,24526],{"className":24525},[886],[888,24527,24528],{"xmlns":890},[892,24529,24530,24542],{},[895,24531,24532,24534,24536,24538,24540],{},[898,24533,2626],{},[2138,24535,12135],{},[898,24537,12029],{},[2138,24539,12135],{},[898,24541,11957],{},[902,24543,18065],{"encoding":904},[883,24545,24547],{"className":24546},[886],[888,24548,24549],{"xmlns":890},[892,24550,24551,24567],{},[895,24552,24553,24555,24557,24559,24561,24563,24565],{},[898,24554,2626],{},[2138,24556,12135],{},[898,24558,12029],{},[2138,24560,12135],{},[898,24562,11957],{},[2138,24564,12135],{},[898,24566,12165],{},[902,24568,12168],{"encoding":904}," se vyšetřuje vliv změn ",[38,24571,24572],{},"exogenních"," veličin (plánovaných investic ",[883,24575,24577],{"className":24576},[886],[888,24578,24579],{"xmlns":890},[892,24580,24581,24589],{},[895,24582,24583],{},[1974,24584,24585,24587],{},[898,24586,12029],{},[1846,24588,4200],{},[902,24590,24591],{"encoding":904},"I^*",", vládních výdajů ",[883,24594,24596],{"className":24595},[886],[888,24597,24598],{"xmlns":890},[892,24599,24600,24608],{},[895,24601,24602],{},[1974,24603,24604,24606],{},[898,24605,11957],{},[1846,24607,4200],{},[902,24609,24610],{"encoding":904},"G^*",", exportu ",[883,24613,24615],{"className":24614},[886],[888,24616,24617],{"xmlns":890},[892,24618,24619,24627],{},[895,24620,24621],{},[1974,24622,24623,24625],{},[898,24624,23098],{},[1846,24626,4200],{},[902,24628,24629],{"encoding":904},"B^*",") na změny ",[38,24632,24633],{},"endogenních"," rovnovážných veličin (",[883,24636,24638],{"className":24637},[886],[888,24639,24640],{"xmlns":890},[892,24641,24642,24650],{},[895,24643,24644],{},[1974,24645,24646,24648],{},[898,24647,8974],{},[898,24649,4098],{},[902,24651,13748],{"encoding":904},[883,24653,24655],{"className":24654},[886],[888,24656,24657],{"xmlns":890},[892,24658,24659,24667],{},[895,24660,24661],{},[1974,24662,24663,24665],{},[898,24664,2626],{},[898,24666,4098],{},[902,24668,13807],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,24671,17822],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,24674,24676],{"id":24675},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,24678,20740,24679,24702,24703,24747],{},[883,24680,24682],{"className":24681},[886],[888,24683,24684],{"xmlns":890},[892,24685,24686,24700],{},[895,24687,24688,24690,24692,24694,24696,24698],{},[898,24689,2626],{},[1846,24691,1848],{},[898,24693,207],{},[898,24695,8974],{},[1846,24697,1945],{},[898,24699,1948],{},[902,24701,18765],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,24704,24706],{"className":24705},[886],[888,24707,24708],{"xmlns":890},[892,24709,24710,24744],{},[895,24711,24712,24718,24720],{},[1974,24713,24714,24716],{},[898,24715,8974],{},[898,24717,4098],{},[1846,24719,1848],{},[2175,24721,24722],{"scriptlevel":2177,"displaystyle":2135},[2179,24723,24724,24736],{},[895,24725,24726,24728,24730],{},[898,24727,1948],{},[1846,24729,1945],{},[1974,24731,24732,24734],{},[898,24733,12029],{},[1846,24735,4200],{},[895,24737,24738,24740,24742],{},[1979,24739,2128],{},[1846,24741,2075],{},[898,24743,207],{},[902,24745,24746],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,24749,24750],{},[883,24751,24753],{"className":24752},[886],[888,24754,24755],{"xmlns":890},[892,24756,24757,24826],{},[895,24758,24759,24777,24779,24809,24811],{},[2179,24760,24761,24771],{},[895,24762,24763,24765],{},[898,24764,9718],{"mathvariant":2226},[1974,24766,24767,24769],{},[898,24768,8974],{},[898,24770,4098],{},[895,24772,24773,24775],{},[898,24774,9718],{"mathvariant":2226},[898,24776,207],{},[1846,24778,1848],{},[2179,24780,24781,24793],{},[895,24782,24783,24785,24787],{},[898,24784,1948],{},[1846,24786,1945],{},[1974,24788,24789,24791],{},[898,24790,12029],{},[1846,24792,4200],{},[895,24794,24795,24797,24799,24801,24803],{},[1846,24796,1855],{"stretchy":1854},[1979,24798,2128],{},[1846,24800,2075],{},[898,24802,207],{},[1974,24804,24805,24807],{},[1846,24806,1861],{"stretchy":1854},[1979,24808,1981],{},[5724,24810],{"width":5726},[895,24812,24813,24816,24823],{},[2138,24814,24815],{},"(multiplik",[8232,24817,24818,24820],{"accent":2135},[2138,24819,207],{},[1846,24821,24822],{},"ˊ",[2138,24824,24825],{},"tor MPC)",[902,24827,24828],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,24830,24831],{},[883,24832,24834],{"className":24833},[886],[888,24835,24836],{"xmlns":890},[892,24837,24838,24907],{},[895,24839,24840,24858,24860,24872,24874],{},[2179,24841,24842,24852],{},[895,24843,24844,24846],{},[898,24845,9718],{"mathvariant":2226},[1974,24847,24848,24850],{},[898,24849,8974],{},[898,24851,4098],{},[895,24853,24854,24856],{},[898,24855,9718],{"mathvariant":2226},[898,24857,1948],{},[1846,24859,1848],{},[2179,24861,24862,24864],{},[1979,24863,2128],{},[895,24865,24866,24868,24870],{},[1979,24867,2128],{},[1846,24869,2075],{},[898,24871,207],{},[5724,24873],{"width":5726},[895,24875,24876,24878,24884,24887,24894,24897,24904],{},[2138,24877,24815],{},[8232,24879,24880,24882],{"accent":2135},[2138,24881,207],{},[1846,24883,24822],{},[2138,24885,24886],{},"tor autonomn",[8232,24888,24889,24892],{"accent":2135},[2138,24890,24891],{},"ı",[1846,24893,24822],{},[2138,24895,24896],{}," spot",[8232,24898,24899,24901],{"accent":2135},[2138,24900,11886],{},[1846,24902,24903],{},"ˇ",[2138,24905,24906],{},"eby)",[902,24908,24909],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,24911,24912],{},[883,24913,24915],{"className":24914},[886],[888,24916,24917],{"xmlns":890},[892,24918,24919,24986],{},[895,24920,24921,24943,24945,24957,24959,24971,24973],{},[2179,24922,24923,24933],{},[895,24924,24925,24927],{},[898,24926,9718],{"mathvariant":2226},[1974,24928,24929,24931],{},[898,24930,8974],{},[898,24932,4098],{},[895,24934,24935,24937],{},[898,24936,9718],{"mathvariant":2226},[1974,24938,24939,24941],{},[898,24940,12029],{},[1846,24942,4200],{},[1846,24944,1848],{},[2179,24946,24947,24949],{},[1979,24948,2128],{},[895,24950,24951,24953,24955],{},[1979,24952,2128],{},[1846,24954,2075],{},[898,24956,207],{},[1846,24958,1848],{},[2179,24960,24961,24963],{},[1979,24962,2128],{},[895,24964,24965,24967,24969],{},[898,24966,2667],{},[898,24968,3783],{},[898,24970,8519],{},[5724,24972],{"width":5726},[895,24974,24975,24977,24983],{},[2138,24976,24815],{},[8232,24978,24979,24981],{"accent":2135},[2138,24980,207],{},[1846,24982,24822],{},[2138,24984,24985],{},"tor investic)",[902,24987,24988],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[1639,24990,24991],{},[724,24992,24993,24995,24996,24999,25000,25013,25014,25031,25032,25050,25051,25095,25096,21265,25113,25116,25117,25134],{},[883,24994,4001],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,24997,24998],{},"důchodem","; z něj se utratí ",[883,25001,25003],{"className":25002},[886],[888,25004,25005],{"xmlns":890},[892,25006,25007,25011],{},[895,25008,25009],{},[898,25010,207],{},[902,25012,207],{"encoding":904}," Kč (= ",[883,25015,25017],{"className":25016},[886],[888,25018,25019],{"xmlns":890},[892,25020,25021,25029],{},[895,25022,25023,25025,25027],{},[898,25024,2667],{},[898,25026,3783],{},[898,25028,2626],{},[902,25030,17890],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,25033,25035],{"className":25034},[886],[888,25036,25037],{"xmlns":890},[892,25038,25039,25047],{},[895,25040,25041],{},[1974,25042,25043,25045],{},[898,25044,207],{},[1979,25046,1981],{},[902,25048,25049],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,25052,25054],{"className":25053},[886],[888,25055,25056],{"xmlns":890},[892,25057,25058,25092],{},[895,25059,25060,25062,25064,25066,25068,25074,25076,25078,25080],{},[1979,25061,2128],{},[1846,25063,1945],{},[898,25065,207],{},[1846,25067,1945],{},[1974,25069,25070,25072],{},[898,25071,207],{},[1979,25073,1981],{},[1846,25075,1945],{},[1846,25077,17950],{},[1846,25079,1848],{},[2179,25081,25082,25084],{},[1979,25083,2128],{},[895,25085,25086,25088,25090],{},[1979,25087,2128],{},[1846,25089,2075],{},[898,25091,207],{},[902,25093,25094],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,25097,25099],{"className":25098},[886],[888,25100,25101],{"xmlns":890},[892,25102,25103,25111],{},[895,25104,25105],{},[1974,25106,25107,25109],{},[898,25108,8974],{},[898,25110,4098],{},[902,25112,13748],{"encoding":904},[38,25114,25115],{},"více"," než korunu — čím vyšší ",[883,25118,25120],{"className":25119},[886],[888,25121,25122],{"xmlns":890},[892,25123,25124,25132],{},[895,25125,25126,25128,25130],{},[898,25127,2667],{},[898,25129,3783],{},[898,25131,2626],{},[902,25133,17890],{"encoding":904},", tím silnější multiplikační efekt.",[724,25136,25137,25140,25141,25167,25168,25171,25172,1745,25193,25218,25219,1734],{},[38,25138,25139],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,25142,25144],{"className":25143},[886],[888,25145,25146],{"xmlns":890},[892,25147,25148,25164],{},[895,25149,25150],{},[2175,25151,25152],{"scriptlevel":2177,"displaystyle":1854},[2179,25153,25154,25156],{},[1979,25155,2128],{},[895,25157,25158,25160,25162],{},[1979,25159,2128],{},[1846,25161,2075],{},[898,25163,207],{},[902,25165,25166],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,25169,25170],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,25173,25175],{"className":25174},[886],[888,25176,25177],{"xmlns":890},[892,25178,25179,25191],{},[895,25180,25181,25183,25185,25187,25189],{},[898,25182,2626],{},[2138,25184,12135],{},[898,25186,12029],{},[2138,25188,12135],{},[898,25190,11957],{},[902,25192,18065],{"encoding":904},[883,25194,25196],{"className":25195},[886],[888,25197,25198],{"xmlns":890},[892,25199,25200,25216],{},[895,25201,25202,25204,25206,25208,25210,25212,25214],{},[898,25203,2626],{},[2138,25205,12135],{},[898,25207,12029],{},[2138,25209,12135],{},[898,25211,11957],{},[2138,25213,12135],{},[898,25215,12165],{},[902,25217,12168],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,25220,25222],{"className":25221,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,25224,25226],{"id":25225},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,25228,12009,25229,1343,25246,1745,25267,12014,25292,9871,25295,25316,25317,2053,25320,25333,25334,5515,25363,25380,25381,25384,25385,25387,25388,25409],{},[883,25230,25232],{"className":25231},[886],[888,25233,25234],{"xmlns":890},[892,25235,25236,25244],{},[895,25237,25238,25240,25242],{},[898,25239,2626],{},[2138,25241,12135],{},[898,25243,12029],{},[902,25245,12140],{"encoding":904},[883,25247,25249],{"className":25248},[886],[888,25250,25251],{"xmlns":890},[892,25252,25253,25265],{},[895,25254,25255,25257,25259,25261,25263],{},[898,25256,2626],{},[2138,25258,12135],{},[898,25260,12029],{},[2138,25262,12135],{},[898,25264,11957],{},[902,25266,18065],{"encoding":904},[883,25268,25270],{"className":25269},[886],[888,25271,25272],{"xmlns":890},[892,25273,25274,25290],{},[895,25275,25276,25278,25280,25282,25284,25286,25288],{},[898,25277,2626],{},[2138,25279,12135],{},[898,25281,12029],{},[2138,25283,12135],{},[898,25285,11957],{},[2138,25287,12135],{},[898,25289,12165],{},[902,25291,12168],{"encoding":904},[38,25293,25294],{},"investice konstantní",[883,25296,25298],{"className":25297},[886],[888,25299,25300],{"xmlns":890},[892,25301,25302,25314],{},[895,25303,25304,25306,25308],{},[898,25305,12029],{},[1846,25307,1848],{},[1974,25309,25310,25312],{},[898,25311,12029],{},[1846,25313,4200],{},[902,25315,12040],{"encoding":904},"). Reálnější je předpoklad, že ",[38,25318,25319],{},"investice závisejí na úrokové míře",[883,25321,25323],{"className":25322},[886],[888,25324,25325],{"xmlns":890},[892,25326,25327,25331],{},[895,25328,25329],{},[898,25330,11886],{},[902,25332,11886],{"encoding":904}," — klesající funkce ",[883,25335,25337],{"className":25336},[886],[888,25338,25339],{"xmlns":890},[892,25340,25341,25361],{},[895,25342,25343,25345,25347,25349,25351,25353,25355,25357,25359],{},[898,25344,12029],{},[1846,25346,1855],{"stretchy":1854},[898,25348,11886],{},[1846,25350,1861],{"stretchy":1854},[1846,25352,1848],{},[898,25354,1992],{},[898,25356,11886],{},[1846,25358,1945],{},[898,25360,2044],{},[902,25362,15602],{"encoding":904},[883,25364,25366],{"className":25365},[886],[888,25367,25368],{"xmlns":890},[892,25369,25370,25378],{},[895,25371,25372,25374,25376],{},[898,25373,1992],{},[1846,25375,3295],{},[1979,25377,2177],{},[902,25379,12360],{"encoding":904},". Přidáním ",[38,25382,25383],{},"trhu peněz"," k trhu zboží vzniká model ",[38,25386,11856],{}," se dvěma neznámými ",[883,25389,25391],{"className":25390},[886],[888,25392,25393],{"xmlns":890},[892,25394,25395,25407],{},[895,25396,25397,25399,25401,25403,25405],{},[1846,25398,1855],{"stretchy":1854},[898,25400,8974],{},[1846,25402,2136],{"separator":2135},[898,25404,11886],{},[1846,25406,1861],{"stretchy":1854},[902,25408,17995],{"encoding":904}," a dvěma rovnicemi:",[120,25411,25412,25462],{},[123,25413,25414,9871,25416,25418,25419,25440,25441,1734],{},[38,25415,15691],{},[614,25417,11899],{},") — klesající přímka v rovině ",[883,25420,25422],{"className":25421},[886],[888,25423,25424],{"xmlns":890},[892,25425,25426,25438],{},[895,25427,25428,25430,25432,25434,25436],{},[1846,25429,1855],{"stretchy":1854},[898,25431,11886],{},[1846,25433,2136],{"separator":2135},[898,25435,8974],{},[1846,25437,1861],{"stretchy":1854},[902,25439,12782],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,25442,25444],{"className":25443},[886],[888,25445,25446],{"xmlns":890},[892,25447,25448,25460],{},[895,25449,25450,25452,25454,25456,25458],{},[898,25451,8974],{},[1846,25453,1848],{},[898,25455,2626],{},[1846,25457,1945],{},[898,25459,12029],{},[902,25461,14589],{"encoding":904},[123,25463,25464,9871,25466,25468,25469,21439,25494,25540],{},[38,25465,15890],{},[614,25467,11906],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,25470,25472],{"className":25471},[886],[888,25473,25474],{"xmlns":890},[892,25475,25476,25492],{},[895,25477,25478,25484,25486],{},[1974,25479,25480,25482],{},[898,25481,2667],{},[898,25483,4029],{},[1846,25485,1848],{},[1974,25487,25488,25490],{},[898,25489,2667],{},[1846,25491,4200],{},[902,25493,13325],{"encoding":904},[883,25495,25497],{"className":25496},[886],[888,25498,25499],{"xmlns":890},[892,25500,25501,25537],{},[895,25502,25503,25509,25511,25517,25519,25521,25527,25529,25531],{},[1974,25504,25505,25507],{},[898,25506,2667],{},[898,25508,4029],{},[1846,25510,1848],{},[2122,25512,25513,25515],{},[898,25514,13082],{},[1979,25516,2128],{},[898,25518,8974],{},[1846,25520,1945],{},[2122,25522,25523,25525],{},[898,25524,13082],{},[1979,25526,1981],{},[898,25528,11886],{},[1846,25530,1945],{},[2122,25532,25533,25535],{},[898,25534,13082],{},[1979,25536,2023],{},[902,25538,25539],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,25542,25543,2053,25546,25579,25580,25582,25583,25585],{},[38,25544,25545],{},"Simultánní rovnovážný bod",[883,25547,25549],{"className":25548},[886],[888,25550,25551],{"xmlns":890},[892,25552,25553,25577],{},[895,25554,25555,25557,25559,25561,25567,25569,25575],{},[898,25556,4098],{},[1846,25558,1848],{},[1846,25560,1855],{"stretchy":1854},[1974,25562,25563,25565],{},[898,25564,11886],{},[898,25566,4098],{},[1846,25568,2136],{"separator":2135},[1974,25570,25571,25573],{},[898,25572,8974],{},[898,25574,4098],{},[1846,25576,1861],{"stretchy":1854},[902,25578,15982],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,25581,11944],{}," (posun IS) a ",[38,25584,11976],{}," (posun LM).",[724,25587,25588],{},[38,25589,25590,25591,1343,25613,1343,25635,1343,25657,25679,25680,1734],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,25592,25594],{"className":25593},[886],[888,25595,25596],{"xmlns":890},[892,25597,25598,25610],{},[895,25599,25600,25606,25608],{},[1974,25601,25602,25604],{},[898,25603,8974],{},[898,25605,4098],{},[1846,25607,1848],{},[1979,25609,14960],{},[902,25611,25612],{"encoding":904},"Y^E = 5000",[883,25614,25616],{"className":25615},[886],[888,25617,25618],{"xmlns":890},[892,25619,25620,25632],{},[895,25621,25622,25628,25630],{},[1974,25623,25624,25626],{},[898,25625,11886],{},[898,25627,4098],{},[1846,25629,1848],{},[1979,25631,2078],{},[902,25633,25634],{"encoding":904},"r^E = 5",[883,25636,25638],{"className":25637},[886],[888,25639,25640],{"xmlns":890},[892,25641,25642,25654],{},[895,25643,25644,25650,25652],{},[1974,25645,25646,25648],{},[898,25647,2626],{},[898,25649,4098],{},[1846,25651,1848],{},[1979,25653,14997],{},[902,25655,25656],{"encoding":904},"C^E = 4100",[883,25658,25660],{"className":25659},[886],[888,25661,25662],{"xmlns":890},[892,25663,25664,25676],{},[895,25665,25666,25672,25674],{},[1974,25667,25668,25670],{},[898,25669,12029],{},[898,25671,4098],{},[1846,25673,1848],{},[1979,25675,15036],{},[902,25677,25678],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,25681,945],{"className":25682,"dataFsResolvedFilePath":943,"href":944},[210],[115,25684,25686],{"id":25685},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,25688,25689,25753,25864,26007,26249,26317],{},[123,25690,25691,25694,25695,25717,25718,25752],{},[38,25692,25693],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,25696,25698],{"className":25697},[886],[888,25699,25700],{"xmlns":890},[892,25701,25702,25714],{},[895,25703,25704,25706,25708,25710,25712],{},[898,25705,11957],{},[898,25707,18139],{},[898,25709,3783],{},[1846,25711,1650],{},[898,25713,8974],{},[902,25715,25716],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,25719,25721],{"className":25720},[886],[888,25722,25723],{"xmlns":890},[892,25724,25725,25749],{},[895,25726,25727,25729,25731,25733,25735,25737,25739,25741,25743,25745,25747],{},[898,25728,11957],{},[898,25730,18139],{},[898,25732,3783],{},[1846,25734,1848],{},[898,25736,2626],{},[1846,25738,1945],{},[898,25740,12029],{},[1846,25742,1945],{},[898,25744,11957],{},[1846,25746,1945],{},[898,25748,12165],{},[902,25750,25751],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,25754,25755,25757,25758,25779,25780,1343,25803,25834,25835,25848,25849,1734],{},[38,25756,18373],{}," splňují ",[883,25759,25761],{"className":25760},[886],[888,25762,25763],{"xmlns":890},[892,25764,25765,25777],{},[895,25766,25767,25769,25771,25773,25775],{},[898,25768,8974],{},[1846,25770,1848],{},[898,25772,2626],{},[1846,25774,1945],{},[898,25776,8519],{},[902,25778,12539],{"encoding":904}," (7.2); lineární model ",[883,25781,25783],{"className":25782},[886],[888,25784,25785],{"xmlns":890},[892,25786,25787,25801],{},[895,25788,25789,25791,25793,25795,25797,25799],{},[898,25790,2626],{},[1846,25792,1848],{},[898,25794,207],{},[898,25796,8974],{},[1846,25798,1945],{},[898,25800,1948],{},[902,25802,18765],{"encoding":904},[883,25804,25806],{"className":25805},[886],[888,25807,25808],{"xmlns":890},[892,25809,25810,25832],{},[895,25811,25812,25814,25816,25818,25820,25822,25824,25826,25828,25830],{},[898,25813,8519],{},[1846,25815,1848],{},[1846,25817,1855],{"stretchy":1854},[1979,25819,2128],{},[1846,25821,2075],{},[898,25823,207],{},[1846,25825,1861],{"stretchy":1854},[898,25827,8974],{},[1846,25829,2075],{},[898,25831,1948],{},[902,25833,19014],{"encoding":904}," s autonomní spotřebou ",[883,25836,25838],{"className":25837},[886],[888,25839,25840],{"xmlns":890},[892,25841,25842,25846],{},[895,25843,25844],{},[898,25845,1948],{},[902,25847,1948],{"encoding":904}," a autonomními úsporami ",[883,25850,25852],{"className":25851},[886],[888,25853,25854],{"xmlns":890},[892,25855,25856,25862],{},[895,25857,25858,25860],{},[1846,25859,2075],{},[898,25861,1948],{},[902,25863,19093],{"encoding":904},[123,25865,25866,2053,25869,1343,25899,25929,25930,25960,25961,1343,25982,1734],{},[38,25867,25868],{},"Mezní sklony",[883,25870,25872],{"className":25871},[886],[888,25873,25874],{"xmlns":890},[892,25875,25876,25896],{},[895,25877,25878,25880,25882,25884,25886,25888,25890,25892,25894],{},[898,25879,2667],{},[898,25881,3783],{},[898,25883,2626],{},[1846,25885,1848],{},[898,25887,2044],{"mathvariant":2226},[898,25889,2626],{},[898,25891,4520],{"mathvariant":2226},[898,25893,2044],{"mathvariant":2226},[898,25895,8974],{},[902,25897,25898],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,25900,25902],{"className":25901},[886],[888,25903,25904],{"xmlns":890},[892,25905,25906,25926],{},[895,25907,25908,25910,25912,25914,25916,25918,25920,25922,25924],{},[898,25909,2667],{},[898,25911,3783],{},[898,25913,8519],{},[1846,25915,1848],{},[898,25917,2044],{"mathvariant":2226},[898,25919,8519],{},[898,25921,4520],{"mathvariant":2226},[898,25923,2044],{"mathvariant":2226},[898,25925,8974],{},[902,25927,25928],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,25931,25933],{"className":25932},[886],[888,25934,25935],{"xmlns":890},[892,25936,25937,25957],{},[895,25938,25939,25941,25943,25945,25947,25949,25951,25953,25955],{},[898,25940,2667],{},[898,25942,3783],{},[898,25944,2626],{},[1846,25946,1945],{},[898,25948,2667],{},[898,25950,3783],{},[898,25952,8519],{},[1846,25954,1848],{},[1979,25956,2128],{},[902,25958,25959],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,25962,25964],{"className":25963},[886],[888,25965,25966],{"xmlns":890},[892,25967,25968,25980],{},[895,25969,25970,25972,25974,25976,25978],{},[898,25971,2667],{},[898,25973,3783],{},[898,25975,2626],{},[1846,25977,1848],{},[898,25979,207],{},[902,25981,19734],{"encoding":904},[883,25983,25985],{"className":25984},[886],[888,25986,25987],{"xmlns":890},[892,25988,25989,26005],{},[895,25990,25991,25993,25995,25997,25999,26001,26003],{},[898,25992,2667],{},[898,25994,3783],{},[898,25996,8519],{},[1846,25998,1848],{},[1979,26000,2128],{},[1846,26002,2075],{},[898,26004,207],{},[902,26006,19760],{"encoding":904},[123,26008,26009,26012,26013],{},[38,26010,26011],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,26014,26015,26103,26172],{},[123,26016,26017,26034,26035,26056,26057,2136],{},[883,26018,26020],{"className":26019},[886],[888,26021,26022],{"xmlns":890},[892,26023,26024,26032],{},[895,26025,26026,26028,26030],{},[898,26027,2626],{},[2138,26029,12135],{},[898,26031,12029],{},[902,26033,12140],{"encoding":904},": ",[883,26036,26038],{"className":26037},[886],[888,26039,26040],{"xmlns":890},[892,26041,26042,26054],{},[895,26043,26044,26046,26048,26050,26052],{},[898,26045,8974],{},[1846,26047,1848],{},[898,26049,2626],{},[1846,26051,1945],{},[898,26053,12029],{},[902,26055,14589],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,26058,26060],{"className":26059},[886],[888,26061,26062],{"xmlns":890},[892,26063,26064,26100],{},[895,26065,26066,26072,26074,26076,26078,26080,26086,26088,26090,26092,26094,26096,26098],{},[1974,26067,26068,26070],{},[898,26069,8974],{},[898,26071,4098],{},[1846,26073,1848],{},[1846,26075,1855],{"stretchy":1854},[898,26077,1948],{},[1846,26079,1945],{},[1974,26081,26082,26084],{},[898,26083,12029],{},[1846,26085,4200],{},[1846,26087,1861],{"stretchy":1854},[898,26089,4520],{"mathvariant":2226},[1846,26091,1855],{"stretchy":1854},[1979,26093,2128],{},[1846,26095,2075],{},[898,26097,207],{},[1846,26099,1861],{"stretchy":1854},[902,26101,26102],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,26104,26105,26126,26127,26146,26147,2136],{},[883,26106,26108],{"className":26107},[886],[888,26109,26110],{"xmlns":890},[892,26111,26112,26124],{},[895,26113,26114,26116,26118,26120,26122],{},[898,26115,2626],{},[2138,26117,12135],{},[898,26119,12029],{},[2138,26121,12135],{},[898,26123,11957],{},[902,26125,18065],{"encoding":904},": přidává vládu, zdanění ",[883,26128,26130],{"className":26129},[886],[888,26131,26132],{"xmlns":890},[892,26133,26134,26144],{},[895,26135,26136,26138,26140,26142],{},[898,26137,2623],{},[1846,26139,1855],{"stretchy":1854},[898,26141,8974],{},[1846,26143,1861],{"stretchy":1854},[902,26145,22064],{"encoding":904}," a disponibilní důchod ",[883,26148,26150],{"className":26149},[886],[888,26151,26152],{"xmlns":890},[892,26153,26154,26170],{},[895,26155,26156,26162,26164,26166,26168],{},[2122,26157,26158,26160],{},[898,26159,8974],{},[898,26161,4029],{},[1846,26163,1848],{},[898,26165,8974],{},[1846,26167,2075],{},[898,26169,2623],{},[902,26171,21563],{"encoding":904},[123,26173,26174,26199,26200,21439,26221,1734],{},[883,26175,26177],{"className":26176},[886],[888,26178,26179],{"xmlns":890},[892,26180,26181,26197],{},[895,26182,26183,26185,26187,26189,26191,26193,26195],{},[898,26184,2626],{},[2138,26186,12135],{},[898,26188,12029],{},[2138,26190,12135],{},[898,26192,11957],{},[2138,26194,12135],{},[898,26196,12165],{},[902,26198,12168],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,26201,26203],{"className":26202},[886],[888,26204,26205],{"xmlns":890},[892,26206,26207,26219],{},[895,26208,26209,26211,26213,26215,26217],{},[898,26210,12165],{},[1846,26212,1848],{},[898,26214,23098],{},[1846,26216,2075],{},[898,26218,2667],{},[902,26220,23105],{"encoding":904},[883,26222,26224],{"className":26223},[886],[888,26225,26226],{"xmlns":890},[892,26227,26228,26246],{},[895,26229,26230,26232,26234,26236,26238,26244],{},[898,26231,2667],{},[1846,26233,1848],{},[898,26235,2667],{},[1846,26237,1855],{"stretchy":1854},[2122,26239,26240,26242],{},[898,26241,8974],{},[898,26243,4029],{},[1846,26245,1861],{"stretchy":1854},[902,26247,26248],{"encoding":904},"M = M(Y_D)",[123,26250,26251,26254,26255,2053,26258,26316],{},[38,26252,26253],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,26256,26257],{},"multiplikátor investic",[883,26259,26261],{"className":26260},[886],[888,26262,26263],{"xmlns":890},[892,26264,26265,26313],{},[895,26266,26267,26269,26275,26277,26279,26285,26287,26289,26291,26293,26295,26297,26299,26301,26303,26305,26307,26309,26311],{},[898,26268,9718],{"mathvariant":2226},[1974,26270,26271,26273],{},[898,26272,8974],{},[898,26274,4098],{},[898,26276,4520],{"mathvariant":2226},[898,26278,9718],{"mathvariant":2226},[1974,26280,26281,26283],{},[898,26282,12029],{},[1846,26284,4200],{},[1846,26286,1848],{},[1979,26288,2128],{},[898,26290,4520],{"mathvariant":2226},[1846,26292,1855],{"stretchy":1854},[1979,26294,2128],{},[1846,26296,2075],{},[898,26298,207],{},[1846,26300,1861],{"stretchy":1854},[1846,26302,1848],{},[1979,26304,2128],{},[898,26306,4520],{"mathvariant":2226},[898,26308,2667],{},[898,26310,3783],{},[898,26312,8519],{},[902,26314,26315],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,26318,26319,26321,26322,26337,26338,18493,26355,26370,26371,26396,26397,1734],{},[38,26320,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,26323,26325],{"className":26324},[886],[888,26326,26327],{"xmlns":890},[892,26328,26329,26335],{},[895,26330,26331,26333],{},[898,26332,12029],{},[898,26334,8519],{},[902,26336,11896],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,26339,26341],{"className":26340},[886],[888,26342,26343],{"xmlns":890},[892,26344,26345,26353],{},[895,26346,26347,26349,26351],{},[898,26348,12029],{},[1846,26350,1848],{},[898,26352,8519],{},[902,26354,12557],{"encoding":904},[883,26356,26358],{"className":26357},[886],[888,26359,26360],{"xmlns":890},[892,26361,26362,26368],{},[895,26363,26364,26366],{},[898,26365,9641],{},[898,26367,2667],{},[902,26369,11903],{"encoding":904}," rovnováhu trhu peněz (",[883,26372,26374],{"className":26373},[886],[888,26375,26376],{"xmlns":890},[892,26377,26378,26394],{},[895,26379,26380,26386,26388],{},[1974,26381,26382,26384],{},[898,26383,2667],{},[898,26385,4029],{},[1846,26387,1848],{},[1974,26389,26390,26392],{},[898,26391,2667],{},[1846,26393,4200],{},[902,26395,13325],{"encoding":904},"); průsečík dává ",[883,26398,26400],{"className":26399},[886],[888,26401,26402],{"xmlns":890},[892,26403,26404,26424],{},[895,26405,26406,26408,26414,26416,26422],{},[1846,26407,1855],{"stretchy":1854},[1974,26409,26410,26412],{},[898,26411,8974],{},[898,26413,4098],{},[1846,26415,2136],{"separator":2135},[1974,26417,26418,26420],{},[898,26419,11886],{},[898,26421,4098],{},[1846,26423,1861],{"stretchy":1854},[902,26425,11940],{"encoding":904},[115,26427,15565],{"id":15564},[120,26429,26430,26468,26508,26598,26680,26734,26790,26849,26884,26889,26961,27036,27122,27184,27252,27310,27363,27402],{},[123,26431,26432,6861,26435,25752],{},[38,26433,26434],{},"Hrubý národní produkt (GNP)",[883,26436,26438],{"className":26437},[886],[888,26439,26440],{"xmlns":890},[892,26441,26442,26466],{},[895,26443,26444,26446,26448,26450,26452,26454,26456,26458,26460,26462,26464],{},[898,26445,11957],{},[898,26447,18139],{},[898,26449,3783],{},[1846,26451,1848],{},[898,26453,2626],{},[1846,26455,1945],{},[898,26457,12029],{},[1846,26459,1945],{},[898,26461,11957],{},[1846,26463,1945],{},[898,26465,12165],{},[902,26467,25751],{"encoding":904},[123,26469,26470,26486,26487,1734],{},[38,26471,26472,26473],{},"Národní důchod ",[883,26474,26476],{"className":26475},[886],[888,26477,26478],{"xmlns":890},[892,26479,26480,26484],{},[895,26481,26482],{},[898,26483,8974],{},[902,26485,8974],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,26488,26490],{"className":26489},[886],[888,26491,26492],{"xmlns":890},[892,26493,26494,26506],{},[895,26495,26496,26498,26500,26502,26504],{},[898,26497,11957],{},[898,26499,18139],{},[898,26501,3783],{},[1846,26503,1650],{},[898,26505,8974],{},[902,26507,25716],{"encoding":904},[123,26509,26510,26536,26537,1343,26560,1343,26581,1734],{},[38,26511,26512,26513],{},"Funkce spotřeby ",[883,26514,26516],{"className":26515},[886],[888,26517,26518],{"xmlns":890},[892,26519,26520,26534],{},[895,26521,26522,26524,26526,26528,26530,26532],{},[898,26523,2626],{},[1846,26525,1848],{},[898,26527,2626],{},[1846,26529,1855],{"stretchy":1854},[898,26531,8974],{},[1846,26533,1861],{"stretchy":1854},[902,26535,20585],{"encoding":904}," — lineární model ",[883,26538,26540],{"className":26539},[886],[888,26541,26542],{"xmlns":890},[892,26543,26544,26558],{},[895,26545,26546,26548,26550,26552,26554,26556],{},[898,26547,2626],{},[1846,26549,1848],{},[898,26551,207],{},[898,26553,8974],{},[1846,26555,1945],{},[898,26557,1948],{},[902,26559,18765],{"encoding":904},[883,26561,26563],{"className":26562},[886],[888,26564,26565],{"xmlns":890},[892,26566,26567,26579],{},[895,26568,26569,26571,26573,26575,26577],{},[1979,26570,2177],{},[1846,26572,3295],{},[898,26574,207],{},[1846,26576,3295],{},[1979,26578,2128],{},[902,26580,18681],{"encoding":904},[883,26582,26584],{"className":26583},[886],[888,26585,26586],{"xmlns":890},[892,26587,26588,26596],{},[895,26589,26590,26592,26594],{},[898,26591,1948],{},[1846,26593,3256],{},[1979,26595,2177],{},[902,26597,18659],{"encoding":904},[123,26599,26600,6861,26627,26648,26649,1734],{},[38,26601,26602,26603],{},"Funkce úspor ",[883,26604,26606],{"className":26605},[886],[888,26607,26608],{"xmlns":890},[892,26609,26610,26624],{},[895,26611,26612,26614,26616,26618,26620,26622],{},[898,26613,8519],{},[1846,26615,1848],{},[898,26617,8519],{},[1846,26619,1855],{"stretchy":1854},[898,26621,8974],{},[1846,26623,1861],{"stretchy":1854},[902,26625,26626],{"encoding":904},"S = S(Y)",[883,26628,26630],{"className":26629},[886],[888,26631,26632],{"xmlns":890},[892,26633,26634,26646],{},[895,26635,26636,26638,26640,26642,26644],{},[898,26637,8974],{},[1846,26639,1848],{},[898,26641,2626],{},[1846,26643,1945],{},[898,26645,8519],{},[902,26647,12539],{"encoding":904},"; lineární ",[883,26650,26652],{"className":26651},[886],[888,26653,26654],{"xmlns":890},[892,26655,26656,26678],{},[895,26657,26658,26660,26662,26664,26666,26668,26670,26672,26674,26676],{},[898,26659,8519],{},[1846,26661,1848],{},[1846,26663,1855],{"stretchy":1854},[1979,26665,2128],{},[1846,26667,2075],{},[898,26669,207],{},[1846,26671,1861],{"stretchy":1854},[898,26673,8974],{},[1846,26675,2075],{},[898,26677,1948],{},[902,26679,19014],{"encoding":904},[123,26681,26682,6861,26685,1343,26708,1734],{},[38,26683,26684],{},"Autonomní spotřeba\u002Fúspory",[883,26686,26688],{"className":26687},[886],[888,26689,26690],{"xmlns":890},[892,26691,26692,26706],{},[895,26693,26694,26696,26698,26700,26702,26704],{},[898,26695,2626],{},[1846,26697,1855],{"stretchy":1854},[1979,26699,2177],{},[1846,26701,1861],{"stretchy":1854},[1846,26703,1848],{},[898,26705,1948],{},[902,26707,19406],{"encoding":904},[883,26709,26711],{"className":26710},[886],[888,26712,26713],{"xmlns":890},[892,26714,26715,26731],{},[895,26716,26717,26719,26721,26723,26725,26727,26729],{},[898,26718,8519],{},[1846,26720,1855],{"stretchy":1854},[1979,26722,2177],{},[1846,26724,1861],{"stretchy":1854},[1846,26726,1848],{},[1846,26728,2075],{},[898,26730,1948],{},[902,26732,26733],{"encoding":904},"S(0) = -b",[123,26735,26736,26768,26769,3764],{},[38,26737,26738,26739],{},"Mezní sklon ke spotřebě ",[883,26740,26742],{"className":26741},[886],[888,26743,26744],{"xmlns":890},[892,26745,26746,26766],{},[895,26747,26748,26750,26752,26754,26756,26758,26760,26762,26764],{},[898,26749,2667],{},[898,26751,3783],{},[898,26753,2626],{},[1846,26755,1848],{},[898,26757,2044],{"mathvariant":2226},[898,26759,2626],{},[898,26761,4520],{"mathvariant":2226},[898,26763,2044],{"mathvariant":2226},[898,26765,8974],{},[902,26767,25898],{"encoding":904}," (v lineárním modelu ",[883,26770,26772],{"className":26771},[886],[888,26773,26774],{"xmlns":890},[892,26775,26776,26788],{},[895,26777,26778,26780,26782,26784,26786],{},[898,26779,2667],{},[898,26781,3783],{},[898,26783,2626],{},[1846,26785,1848],{},[898,26787,207],{},[902,26789,19734],{"encoding":904},[123,26791,26792,26768,26824,3764],{},[38,26793,26794,26795],{},"Mezní sklon k úsporám ",[883,26796,26798],{"className":26797},[886],[888,26799,26800],{"xmlns":890},[892,26801,26802,26822],{},[895,26803,26804,26806,26808,26810,26812,26814,26816,26818,26820],{},[898,26805,2667],{},[898,26807,3783],{},[898,26809,8519],{},[1846,26811,1848],{},[898,26813,2044],{"mathvariant":2226},[898,26815,8519],{},[898,26817,4520],{"mathvariant":2226},[898,26819,2044],{"mathvariant":2226},[898,26821,8974],{},[902,26823,25928],{"encoding":904},[883,26825,26827],{"className":26826},[886],[888,26828,26829],{"xmlns":890},[892,26830,26831,26847],{},[895,26832,26833,26835,26837,26839,26841,26843,26845],{},[898,26834,2667],{},[898,26836,3783],{},[898,26838,8519],{},[1846,26840,1848],{},[1979,26842,2128],{},[1846,26844,2075],{},[898,26846,207],{},[902,26848,19760],{"encoding":904},[123,26850,26851,2053,26854,26883],{},[38,26852,26853],{},"Vztah",[883,26855,26857],{"className":26856},[886],[888,26858,26859],{"xmlns":890},[892,26860,26861,26881],{},[895,26862,26863,26865,26867,26869,26871,26873,26875,26877,26879],{},[898,26864,2667],{},[898,26866,3783],{},[898,26868,2626],{},[1846,26870,1945],{},[898,26872,2667],{},[898,26874,3783],{},[898,26876,8519],{},[1846,26878,1848],{},[1979,26880,2128],{},[902,26882,25959],{"encoding":904}," (7.5).",[123,26885,26886,26888],{},[38,26887,20428],{}," — rovnováha agregátní poptávky a nabídky.",[123,26890,26891,26894,26895,15637,26916,1734],{},[38,26892,26893],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,26896,26898],{"className":26897},[886],[888,26899,26900],{"xmlns":890},[892,26901,26902,26914],{},[895,26903,26904,26906,26908,26910,26912],{},[898,26905,8974],{},[1846,26907,1848],{},[898,26909,2626],{},[1846,26911,1945],{},[898,26913,12029],{},[902,26915,14589],{"encoding":904},[883,26917,26919],{"className":26918},[886],[888,26920,26921],{"xmlns":890},[892,26922,26923,26959],{},[895,26924,26925,26931,26933,26935,26937,26939,26945,26947,26949,26951,26953,26955,26957],{},[1974,26926,26927,26929],{},[898,26928,8974],{},[898,26930,4098],{},[1846,26932,1848],{},[1846,26934,1855],{"stretchy":1854},[898,26936,1948],{},[1846,26938,1945],{},[1974,26940,26941,26943],{},[898,26942,12029],{},[1846,26944,4200],{},[1846,26946,1861],{"stretchy":1854},[898,26948,4520],{"mathvariant":2226},[1846,26950,1855],{"stretchy":1854},[1979,26952,2128],{},[1846,26954,2075],{},[898,26956,207],{},[1846,26958,1861],{"stretchy":1854},[902,26960,26102],{"encoding":904},[123,26962,26963,26966,26967,1343,26986,15637,27011,1734],{},[38,26964,26965],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,26968,26970],{"className":26969},[886],[888,26971,26972],{"xmlns":890},[892,26973,26974,26984],{},[895,26975,26976,26978,26980,26982],{},[898,26977,2623],{},[1846,26979,1855],{"stretchy":1854},[898,26981,8974],{},[1846,26983,1861],{"stretchy":1854},[902,26985,22064],{"encoding":904},[883,26987,26989],{"className":26988},[886],[888,26990,26991],{"xmlns":890},[892,26992,26993,27009],{},[895,26994,26995,27001,27003,27005,27007],{},[2122,26996,26997,26999],{},[898,26998,8974],{},[898,27000,4029],{},[1846,27002,1848],{},[898,27004,8974],{},[1846,27006,2075],{},[898,27008,2623],{},[902,27010,21563],{"encoding":904},[883,27012,27014],{"className":27013},[886],[888,27015,27016],{"xmlns":890},[892,27017,27018,27034],{},[895,27019,27020,27022,27024,27026,27028,27030,27032],{},[898,27021,8974],{},[1846,27023,1848],{},[898,27025,2626],{},[1846,27027,1945],{},[898,27029,12029],{},[1846,27031,1945],{},[898,27033,11957],{},[902,27035,21534],{"encoding":904},[123,27037,27038,27041,27042,27063,27064,15637,27088,1734],{},[38,27039,27040],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,27043,27045],{"className":27044},[886],[888,27046,27047],{"xmlns":890},[892,27048,27049,27061],{},[895,27050,27051,27053,27055,27057,27059],{},[898,27052,12165],{},[1846,27054,1848],{},[898,27056,23098],{},[1846,27058,2075],{},[898,27060,2667],{},[902,27062,23105],{"encoding":904},", importem ",[883,27065,27067],{"className":27066},[886],[888,27068,27069],{"xmlns":890},[892,27070,27071,27085],{},[895,27072,27073,27075,27077,27083],{},[898,27074,2667],{},[1846,27076,1855],{"stretchy":1854},[2122,27078,27079,27081],{},[898,27080,8974],{},[898,27082,4029],{},[1846,27084,1861],{"stretchy":1854},[902,27086,27087],{"encoding":904},"M(Y_D)",[883,27089,27091],{"className":27090},[886],[888,27092,27093],{"xmlns":890},[892,27094,27095,27119],{},[895,27096,27097,27099,27101,27103,27105,27107,27109,27111,27113,27115,27117],{},[898,27098,8974],{},[1846,27100,1848],{},[898,27102,2626],{},[1846,27104,1945],{},[898,27106,12029],{},[1846,27108,1945],{},[898,27110,11957],{},[1846,27112,1945],{},[898,27114,23098],{},[1846,27116,2075],{},[898,27118,2667],{},[902,27120,27121],{"encoding":904},"Y = C + I + G + B - M",[123,27123,27124,6861,27127,26316],{},[38,27125,27126],{},"Multiplikátor investic",[883,27128,27130],{"className":27129},[886],[888,27131,27132],{"xmlns":890},[892,27133,27134,27182],{},[895,27135,27136,27138,27144,27146,27148,27154,27156,27158,27160,27162,27164,27166,27168,27170,27172,27174,27176,27178,27180],{},[898,27137,9718],{"mathvariant":2226},[1974,27139,27140,27142],{},[898,27141,8974],{},[898,27143,4098],{},[898,27145,4520],{"mathvariant":2226},[898,27147,9718],{"mathvariant":2226},[1974,27149,27150,27152],{},[898,27151,12029],{},[1846,27153,4200],{},[1846,27155,1848],{},[1979,27157,2128],{},[898,27159,4520],{"mathvariant":2226},[1846,27161,1855],{"stretchy":1854},[1979,27163,2128],{},[1846,27165,2075],{},[898,27167,207],{},[1846,27169,1861],{"stretchy":1854},[1846,27171,1848],{},[1979,27173,2128],{},[898,27175,4520],{"mathvariant":2226},[898,27177,2667],{},[898,27179,3783],{},[898,27181,8519],{},[902,27183,26315],{"encoding":904},[123,27185,27186,6861,27217,1343,27234,27251],{},[38,27187,15572,27188],{},[883,27189,27191],{"className":27190},[886],[888,27192,27193],{"xmlns":890},[892,27194,27195,27215],{},[895,27196,27197,27199,27201,27203,27205,27207,27209,27211,27213],{},[898,27198,12029],{},[1846,27200,1855],{"stretchy":1854},[898,27202,11886],{},[1846,27204,1861],{"stretchy":1854},[1846,27206,1848],{},[898,27208,1992],{},[898,27210,11886],{},[1846,27212,1945],{},[898,27214,2044],{},[902,27216,15602],{"encoding":904},[883,27218,27220],{"className":27219},[886],[888,27221,27222],{"xmlns":890},[892,27223,27224,27232],{},[895,27225,27226,27228,27230],{},[898,27227,1992],{},[1846,27229,3295],{},[1979,27231,2177],{},[902,27233,12360],{"encoding":904},[883,27235,27237],{"className":27236},[886],[888,27238,27239],{"xmlns":890},[892,27240,27241,27249],{},[895,27242,27243,27245,27247],{},[898,27244,2044],{},[1846,27246,3256],{},[1979,27248,2177],{},[902,27250,12339],{"encoding":904},"; klesající.",[123,27253,27254,27256,27257,27259,27260,27309],{},[38,27255,15691],{}," — rovnováha na trhu zboží (",[614,27258,11899],{},"); ",[883,27261,27263],{"className":27262},[886],[888,27264,27265],{"xmlns":890},[892,27266,27267,27307],{},[895,27268,27269,27271,27273,27285,27287,27289],{},[898,27270,8974],{},[1846,27272,1848],{},[2179,27274,27275,27277],{},[898,27276,1992],{},[895,27278,27279,27281,27283],{},[1979,27280,2128],{},[1846,27282,2075],{},[898,27284,207],{},[898,27286,11886],{},[1846,27288,1945],{},[2179,27290,27291,27299],{},[895,27292,27293,27295,27297],{},[898,27294,1948],{},[1846,27296,1945],{},[898,27298,2044],{},[895,27300,27301,27303,27305],{},[1979,27302,2128],{},[1846,27304,2075],{},[898,27306,207],{},[902,27308,15744],{"encoding":904}," (7.14); klesající.",[123,27311,27312,27314,27315,27259,27317,27362],{},[38,27313,15890],{}," — rovnováha na trhu peněz (",[614,27316,11906],{},[883,27318,27320],{"className":27319},[886],[888,27321,27322],{"xmlns":890},[892,27323,27324,27360],{},[895,27325,27326,27332,27334,27340,27342,27344,27350,27352,27354],{},[1974,27327,27328,27330],{},[898,27329,2667],{},[1846,27331,4200],{},[1846,27333,1848],{},[2122,27335,27336,27338],{},[898,27337,13082],{},[1979,27339,2128],{},[898,27341,8974],{},[1846,27343,1945],{},[2122,27345,27346,27348],{},[898,27347,13082],{},[1979,27349,1981],{},[898,27351,11886],{},[1846,27353,1945],{},[2122,27355,27356,27358],{},[898,27357,13082],{},[1979,27359,2023],{},[902,27361,15938],{"encoding":904}," (7.15); rostoucí.",[123,27364,27365,6861,27368,1734],{},[38,27366,27367],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,27369,27371],{"className":27370},[886],[888,27372,27373],{"xmlns":890},[892,27374,27375,27399],{},[895,27376,27377,27383,27385,27391,27393],{},[1974,27378,27379,27381],{},[898,27380,2667],{},[898,27382,4029],{},[1846,27384,1848],{},[2122,27386,27387,27389],{},[898,27388,9641],{},[1979,27390,2128],{},[1846,27392,1945],{},[2122,27394,27395,27397],{},[898,27396,9641],{},[1979,27398,1981],{},[902,27400,27401],{"encoding":904},"M^D = L_1 + L_2",[123,27403,27404,15948,27406,13825,27419,1745,27434,27449,27450,1734],{},[38,27405,945],{},[883,27407,27409],{"className":27408},[886],[888,27410,27411],{"xmlns":890},[892,27412,27413,27417],{},[895,27414,27415],{},[898,27416,4098],{},[902,27418,4098],{"encoding":904},[883,27420,27422],{"className":27421},[886],[888,27423,27424],{"xmlns":890},[892,27425,27426,27432],{},[895,27427,27428,27430],{},[898,27429,12029],{},[898,27431,8519],{},[902,27433,11896],{"encoding":904},[883,27435,27437],{"className":27436},[886],[888,27438,27439],{"xmlns":890},[892,27440,27441,27447],{},[895,27442,27443,27445],{},[898,27444,9641],{},[898,27446,2667],{},[902,27448,11903],{"encoding":904}," určuje ",[883,27451,27453],{"className":27452},[886],[888,27454,27455],{"xmlns":890},[892,27456,27457,27477],{},[895,27458,27459,27461,27467,27469,27475],{},[1846,27460,1855],{"stretchy":1854},[1974,27462,27463,27465],{},[898,27464,8974],{},[898,27466,4098],{},[1846,27468,2136],{"separator":2135},[1974,27470,27471,27473],{},[898,27472,11886],{},[898,27474,4098],{},[1846,27476,1861],{"stretchy":1854},[902,27478,11940],{"encoding":904},[115,27480,3640],{"id":3639},[120,27482,27483,27490,27497],{},[123,27484,27485,2053,27487],{},[38,27486,16049],{},[207,27488,16053],{"className":27489,"dataFsResolvedFilePath":1761,"href":1762},[210],[123,27491,27492,2053,27494],{},[38,27493,16058],{},[207,27495,16062],{"className":27496,"dataFsResolvedFilePath":868,"href":869},[210],[123,27498,27499,27501],{},[38,27500,16077],{},[120,27502,27503,27509,27515,27521],{},[123,27504,27505,27508],{},[207,27506,16117],{"className":27507,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,27510,27511,27514],{},[207,27512,1789],{"className":27513,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,27516,27517,27520],{},[207,27518,1790],{"className":27519,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,27522,27523,27526,27527,1343,27544,27561],{},[207,27524,1145],{"className":27525,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,27528,27530],{"className":27529},[886],[888,27531,27532],{"xmlns":890},[892,27533,27534,27542],{},[895,27535,27536,27538,27540],{},[898,27537,2667],{},[898,27539,3783],{},[898,27541,2626],{},[902,27543,17890],{"encoding":904},[883,27545,27547],{"className":27546},[886],[888,27548,27549],{"xmlns":890},[892,27550,27551,27559],{},[895,27552,27553,27555,27557],{},[898,27554,2667],{},[898,27556,3783],{},[898,27558,8519],{},[902,27560,19504],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":27563},[27564,27565,27566,27567,27572,27575,27576,27583,27588,27593,27596,27597,27598,27599],{"id":11850,"depth":642,"text":11851},{"id":17999,"depth":642,"text":18000},{"id":18119,"depth":642,"text":18120},{"id":18372,"depth":642,"text":18373,"children":27568},[27569,27570,27571],{"id":18376,"depth":649,"text":18377},{"id":18588,"depth":649,"text":18589},{"id":19096,"depth":649,"text":19097},{"id":19416,"depth":642,"text":19417,"children":27573},[27574],{"id":19932,"depth":649,"text":19933},{"id":20427,"depth":642,"text":20428},{"id":20454,"depth":642,"text":20455,"children":27577},[27578,27579,27580,27582],{"id":20465,"depth":649,"text":20466},{"id":20535,"depth":649,"text":20536},{"id":20719,"depth":649,"text":27581},"Výpočet YEY^E",{"id":20862,"depth":649,"text":20863},{"id":21240,"depth":642,"text":21241,"children":27584},[27585,27586,27587],{"id":21244,"depth":649,"text":20466},{"id":21693,"depth":649,"text":20536},{"id":22349,"depth":649,"text":22350},{"id":23136,"depth":642,"text":23137,"children":27589},[27590,27591,27592],{"id":23140,"depth":649,"text":20466},{"id":23285,"depth":649,"text":20536},{"id":23555,"depth":649,"text":23556},{"id":24479,"depth":642,"text":24480,"children":27594},[27595],{"id":24675,"depth":649,"text":24676},{"id":25225,"depth":642,"text":25226},{"id":25685,"depth":642,"text":25686},{"id":15564,"depth":642,"text":15565},{"id":3639,"depth":642,"text":3640},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,16071,1143,27606,27607,27608,16117,17728],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":27611,"title":27612,"body":27613,"course":1128,"courses":659,"created":9402,"description":641,"extension":661,"meta":36593,"navigation":664,"path":36594,"seo":36595,"sources":36596,"stem":36597,"tags":36598,"type":3703,"updated":677,"__hash__":36603},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":27614,"toc":36562},[27615,27618,27620,27849,27853,27906,27976,28088,28247,28251,28367,28371,28374,28496,28499,28692,28716,28784,28948,28966,29032,29410,29414,29421,29665,29721,29725,29790,29908,30040,30072,30192,30274,30277,30399,30592,30813,30817,30857,30962,31019,31119,31296,31426,31479,31482,31569,31573,31749,31753,31756,31841,31844,31901,32006,32010,32131,32134,32317,32320,32428,32637,32957,33005,33078,33152,33154,33378,33613,33881,33885,33888,33993,34050,34084,34131,34164,34248,34250,34482,34615,34692,34814,34969,34973,35114,35121,35345,35356,35360,35364,35469,35611,35721,35820,35824,35983,36093,36095,36488,36490],[12,27616,27612],{"id":27617},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,27619,11851],{"id":11850},[724,27621,27622,27624,27625,27659,27660,27663,27664,27695,27696,27742,27743,27746,27747,27789,27790,27808,27809,27813,27814,27844,27845,27848],{},[38,27623,913],{}," řeší, jaký svazek zboží ",[883,27626,27628],{"className":27627},[886],[888,27629,27630],{"xmlns":890},[892,27631,27632,27656],{},[895,27633,27634,27636,27644,27646,27654],{},[1846,27635,2336],{"stretchy":1854},[9012,27637,27638,27640,27642],{},[898,27639,2638],{},[1979,27641,2128],{},[1846,27643,4200],{},[1846,27645,2136],{"separator":2135},[9012,27647,27648,27650,27652],{},[898,27649,2638],{},[1979,27651,1981],{},[1846,27653,4200],{},[1846,27655,2351],{"stretchy":1854},[902,27657,27658],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,27661,27662],{},"primární úloha"," — maximalizace užitečnosti ",[883,27665,27667],{"className":27666},[886],[888,27668,27669],{"xmlns":890},[892,27670,27671,27693],{},[895,27672,27673,27675,27677,27683,27685,27691],{},[898,27674,900],{},[1846,27676,1855],{"stretchy":1854},[2122,27678,27679,27681],{},[898,27680,2638],{},[1979,27682,2128],{},[1846,27684,2136],{"separator":2135},[2122,27686,27687,27689],{},[898,27688,2638],{},[1979,27690,1981],{},[1846,27692,1861],{"stretchy":1854},[902,27694,16188],{"encoding":904}," při rozpočtovém omezení ",[883,27697,27699],{"className":27698},[886],[888,27700,27701],{"xmlns":890},[892,27702,27703,27739],{},[895,27704,27705,27711,27713,27719,27725,27727,27733],{},[1974,27706,27707,27709],{},[898,27708,8974],{},[1846,27710,4200],{},[1846,27712,1848],{},[2122,27714,27715,27717],{},[898,27716,3783],{},[1979,27718,2128],{},[2122,27720,27721,27723],{},[898,27722,2638],{},[1979,27724,2128],{},[1846,27726,1945],{},[2122,27728,27729,27731],{},[898,27730,3783],{},[1979,27732,1981],{},[2122,27734,27735,27737],{},[898,27736,2638],{},[1979,27738,1981],{},[902,27740,27741],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,27744,27745],{},"duální úloha"," — minimalizace výdajů ",[883,27748,27750],{"className":27749},[886],[888,27751,27752],{"xmlns":890},[892,27753,27754,27786],{},[895,27755,27756,27758,27760,27766,27772,27774,27780],{},[898,27757,4098],{},[1846,27759,1848],{},[2122,27761,27762,27764],{},[898,27763,3783],{},[1979,27765,2128],{},[2122,27767,27768,27770],{},[898,27769,2638],{},[1979,27771,2128],{},[1846,27773,1945],{},[2122,27775,27776,27778],{},[898,27777,3783],{},[1979,27779,1981],{},[2122,27781,27782,27784],{},[898,27783,2638],{},[1979,27785,1981],{},[902,27787,27788],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,27791,27793],{"className":27792},[886],[888,27794,27795],{"xmlns":890},[892,27796,27797,27805],{},[895,27798,27799],{},[1974,27800,27801,27803],{},[898,27802,900],{},[1846,27804,4200],{},[902,27806,27807],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,27810,27812],{"className":27811,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,27815,27817],{"className":27816},[886],[888,27818,27819],{"xmlns":890},[892,27820,27821,27841],{},[895,27822,27823,27825,27827,27833,27835],{},[2138,27824,10449],{},[1846,27826,1848],{},[2122,27828,27829,27831],{},[898,27830,3783],{},[1979,27832,2128],{},[898,27834,4520],{"mathvariant":2226},[2122,27836,27837,27839],{},[898,27838,3783],{},[1979,27840,1981],{},[902,27842,27843],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,27846,27847],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,27850,27852],{"id":27851},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,27854,27855,27856,27874,27875,27905],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,27857,27859],{"className":27858},[886],[888,27860,27861],{"xmlns":890},[892,27862,27863,27871],{},[895,27864,27865],{},[1974,27866,27867,27869],{},[898,27868,8974],{},[1846,27870,4200],{},[902,27872,27873],{"encoding":904},"Y^*"," a ceny ",[883,27876,27878],{"className":27877},[886],[888,27879,27880],{"xmlns":890},[892,27881,27882,27902],{},[895,27883,27884,27892,27894],{},[9012,27885,27886,27888,27890],{},[898,27887,3783],{},[1979,27889,2128],{},[1846,27891,4200],{},[1846,27893,2136],{"separator":2135},[9012,27895,27896,27898,27900],{},[898,27897,3783],{},[1979,27899,1981],{},[1846,27901,4200],{},[902,27903,27904],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,27907,27909],{"className":27908},[886],[888,27910,27912],{"xmlns":890,"display":27911},"block",[892,27913,27914,27973],{},[20599,27915,27917],{"width":27916},"100%",[20604,27918,27919,27922,27966,27968],{},[20607,27920],{"width":27921},"50%",[20607,27923,27924],{},[895,27925,27926,27932,27934,27942,27948,27950,27958,27964],{},[1974,27927,27928,27930],{},[898,27929,8974],{},[1846,27931,4200],{},[1846,27933,1848],{},[9012,27935,27936,27938,27940],{},[898,27937,3783],{},[1979,27939,2128],{},[1846,27941,4200],{},[2122,27943,27944,27946],{},[898,27945,2638],{},[1979,27947,2128],{},[1846,27949,1945],{},[9012,27951,27952,27954,27956],{},[898,27953,3783],{},[1979,27955,1981],{},[1846,27957,4200],{},[2122,27959,27960,27962],{},[898,27961,2638],{},[1979,27963,1981],{},[1846,27965,2136],{"separator":2135},[20607,27967],{"width":27921},[20607,27969,27970],{},[2138,27971,27972],{},"(6.12)",[902,27974,27975],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,27977,27978,27979,27982,27983,1745,28019,28055,28056,28069,28070,28084,28085,1734],{},"geometricky ",[38,27980,27981],{},"rozpočtová přímka (budget line)"," procházející body ",[883,27984,27986],{"className":27985},[886],[888,27987,27988],{"xmlns":890},[892,27989,27990,28016],{},[895,27991,27992,27994,28000,28002,28010,28012,28014],{},[1846,27993,2336],{"stretchy":1854},[1974,27995,27996,27998],{},[898,27997,8974],{},[1846,27999,4200],{},[898,28001,4520],{"mathvariant":2226},[9012,28003,28004,28006,28008],{},[898,28005,3783],{},[1979,28007,2128],{},[1846,28009,4200],{},[1846,28011,2136],{"separator":2135},[1979,28013,2177],{},[1846,28015,2351],{"stretchy":1854},[902,28017,28018],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,28020,28022],{"className":28021},[886],[888,28023,28024],{"xmlns":890},[892,28025,28026,28052],{},[895,28027,28028,28030,28032,28034,28040,28042,28050],{},[1846,28029,2336],{"stretchy":1854},[1979,28031,2177],{},[1846,28033,2136],{"separator":2135},[1974,28035,28036,28038],{},[898,28037,8974],{},[1846,28039,4200],{},[898,28041,4520],{"mathvariant":2226},[9012,28043,28044,28046,28048],{},[898,28045,3783],{},[1979,28047,1981],{},[1846,28049,4200],{},[1846,28051,2351],{"stretchy":1854},[902,28053,28054],{"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 ",[883,28057,28059],{"className":28058},[886],[888,28060,28061],{"xmlns":890},[892,28062,28063,28067],{},[895,28064,28065],{},[898,28066,900],{},[902,28068,900],{"encoding":904},", indiferenční křivky a ",[883,28071,28073],{"className":28072},[886],[888,28074,28075],{"xmlns":890},[892,28076,28077,28081],{},[895,28078,28079],{},[2138,28080,10449],{},[902,28082,28083],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,28086,880],{"className":28087,"dataFsResolvedFilePath":878,"href":879},[210],[1639,28089,28090],{},[724,28091,28092,28094,28095,28098,28099,28112,28113,28115,28116,28129,28130,2053,28133,28173,28174,28191,28192,28209,28210,28227,28228,28246],{},[883,28093,4258],{}," Pozor — dvě úlohy, totéž řešení\n",[38,28096,28097],{},"Primární úloha"," (max ",[883,28100,28102],{"className":28101},[886],[888,28103,28104],{"xmlns":890},[892,28105,28106,28110],{},[895,28107,28108],{},[898,28109,900],{},[902,28111,900],{"encoding":904}," při pevném rozpočtu) a ",[38,28114,27745],{}," (min ",[883,28117,28119],{"className":28118},[886],[888,28120,28121],{"xmlns":890},[892,28122,28123,28127],{},[895,28124,28125],{},[898,28126,4098],{},[902,28128,4098],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,28131,28132],{},"tentýž bod",[883,28134,28136],{"className":28135},[886],[888,28137,28138],{"xmlns":890},[892,28139,28140,28170],{},[895,28141,28142,28148,28150,28158,28160,28168],{},[1974,28143,28144,28146],{},[898,28145,2638],{},[1846,28147,4200],{},[1846,28149,2336],{"stretchy":1854},[9012,28151,28152,28154,28156],{},[898,28153,2638],{},[1979,28155,2128],{},[1846,28157,4200],{},[1846,28159,2136],{"separator":2135},[9012,28161,28162,28164,28166],{},[898,28163,2638],{},[1979,28165,1981],{},[1846,28167,4200],{},[1846,28169,2351],{"stretchy":1854},[902,28171,28172],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,28175,28177],{"className":28176},[886],[888,28178,28179],{"xmlns":890},[892,28180,28181,28189],{},[895,28182,28183],{},[1974,28184,28185,28187],{},[898,28186,8974],{},[1846,28188,4200],{},[902,28190,27873],{"encoding":904}," a hledáme maximální ",[883,28193,28195],{"className":28194},[886],[888,28196,28197],{"xmlns":890},[892,28198,28199,28207],{},[895,28200,28201],{},[1974,28202,28203,28205],{},[898,28204,900],{},[1846,28206,4200],{},[902,28208,27807],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,28211,28213],{"className":28212},[886],[888,28214,28215],{"xmlns":890},[892,28216,28217,28225],{},[895,28218,28219],{},[1974,28220,28221,28223],{},[898,28222,900],{},[1846,28224,4200],{},[902,28226,27807],{"encoding":904}," a hledáme minimální ",[883,28229,28231],{"className":28230},[886],[888,28232,28233],{"xmlns":890},[892,28234,28235,28243],{},[895,28236,28237],{},[1974,28238,28239,28241],{},[898,28240,4098],{},[1846,28242,4200],{},[902,28244,28245],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,28248,28250],{"id":28249},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,28252,28253,28254,28285,28286,28362,28363,1734],{},"Úlohou je najít maximum ",[883,28255,28257],{"className":28256},[886],[888,28258,28259],{"xmlns":890},[892,28260,28261,28283],{},[895,28262,28263,28265,28267,28273,28275,28281],{},[898,28264,900],{},[1846,28266,1855],{"stretchy":1854},[2122,28268,28269,28271],{},[898,28270,2638],{},[1979,28272,2128],{},[1846,28274,2136],{"separator":2135},[2122,28276,28277,28279],{},[898,28278,2638],{},[1979,28280,1981],{},[1846,28282,1861],{"stretchy":1854},[902,28284,16188],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,28287,28289],{"className":28288},[886],[888,28290,28291],{"xmlns":890},[892,28292,28293,28359],{},[895,28294,28295,28297,28299,28305,28307,28313,28315,28317,28323,28325,28333,28339,28341,28349,28355,28357],{},[898,28296,10887],{},[1846,28298,1855],{"stretchy":1854},[2122,28300,28301,28303],{},[898,28302,2638],{},[1979,28304,2128],{},[1846,28306,2136],{"separator":2135},[2122,28308,28309,28311],{},[898,28310,2638],{},[1979,28312,1981],{},[1846,28314,1861],{"stretchy":1854},[1846,28316,1848],{},[1974,28318,28319,28321],{},[898,28320,8974],{},[1846,28322,4200],{},[1846,28324,2075],{},[9012,28326,28327,28329,28331],{},[898,28328,3783],{},[1979,28330,2128],{},[1846,28332,4200],{},[2122,28334,28335,28337],{},[898,28336,2638],{},[1979,28338,2128],{},[1846,28340,2075],{},[9012,28342,28343,28345,28347],{},[898,28344,3783],{},[1979,28346,1981],{},[1846,28348,4200],{},[2122,28350,28351,28353],{},[898,28352,2638],{},[1979,28354,1981],{},[1846,28356,1848],{},[1979,28358,2177],{},[902,28360,28361],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,28364,28366],{"className":28365,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,28368,28370],{"id":28369},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,28372,28373],{},"Sestavíme",[883,28375,28377],{"className":28376},[886],[888,28378,28379],{"xmlns":890,"display":27911},[892,28380,28381,28493],{},[20599,28382,28383],{"width":27916},[20604,28384,28385,28387,28486,28488],{},[20607,28386],{"width":27921},[20607,28388,28389],{},[895,28390,28391,28394,28396,28402,28404,28410,28412,28414,28416,28418,28420,28422,28428,28430,28436,28438,28440,28442,28444,28450,28452,28460,28466,28468,28476,28482,28484],{},[898,28392,9641],{"mathvariant":28393},"script",[1846,28395,1855],{"stretchy":1854},[2122,28397,28398,28400],{},[898,28399,2638],{},[1979,28401,2128],{},[1846,28403,2136],{"separator":2135},[2122,28405,28406,28408],{},[898,28407,2638],{},[1979,28409,1981],{},[1846,28411,2136],{"separator":2135},[898,28413,16288],{},[1846,28415,1861],{"stretchy":1854},[1846,28417,1848],{},[898,28419,900],{},[1846,28421,1855],{"stretchy":1854},[2122,28423,28424,28426],{},[898,28425,2638],{},[1979,28427,2128],{},[1846,28429,2136],{"separator":2135},[2122,28431,28432,28434],{},[898,28433,2638],{},[1979,28435,1981],{},[1846,28437,1861],{"stretchy":1854},[1846,28439,1945],{},[898,28441,16288],{},[1846,28443,1855],{"stretchy":1854},[1974,28445,28446,28448],{},[898,28447,8974],{},[1846,28449,4200],{},[1846,28451,2075],{},[9012,28453,28454,28456,28458],{},[898,28455,3783],{},[1979,28457,2128],{},[1846,28459,4200],{},[2122,28461,28462,28464],{},[898,28463,2638],{},[1979,28465,2128],{},[1846,28467,2075],{},[9012,28469,28470,28472,28474],{},[898,28471,3783],{},[1979,28473,1981],{},[1846,28475,4200],{},[2122,28477,28478,28480],{},[898,28479,2638],{},[1979,28481,1981],{},[1846,28483,1861],{"stretchy":1854},[898,28485,1734],{"mathvariant":2226},[20607,28487],{"width":27921},[20607,28489,28490],{},[2138,28491,28492],{},"(6.13)",[902,28494,28495],{"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}",[724,28497,28498],{},"Soustava prvního řádu:",[883,28500,28502],{"className":28501},[886],[888,28503,28504],{"xmlns":890,"display":27911},[892,28505,28506,28689],{},[20599,28507,28508],{"width":27916},[20604,28509,28510,28512,28682,28684],{},[20607,28511],{"width":27921},[20607,28513,28514],{},[20599,28515,28516,28566,28616],{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},[20604,28517,28518,28530],{},[20607,28519,28520],{},[2175,28521,28522],{"scriptlevel":2177,"displaystyle":2135},[9012,28523,28524,28526,28528],{},[898,28525,9641],{"mathvariant":28393},[1979,28527,2128],{},[1846,28529,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,28531,28532],{},[2175,28533,28534],{"scriptlevel":2177,"displaystyle":2135},[895,28535,28536,28538,28540,28548,28550,28552,28560,28562,28564],{},[895,28537],{},[1846,28539,1848],{},[9012,28541,28542,28544,28546],{},[898,28543,900],{},[1979,28545,2128],{},[1846,28547,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,28549,2075],{},[898,28551,16288],{},[9012,28553,28554,28556,28558],{},[898,28555,3783],{},[1979,28557,2128],{},[1846,28559,4200],{},[1846,28561,1848],{},[1979,28563,2177],{},[1846,28565,2136],{"separator":2135},[20604,28567,28568,28580],{},[20607,28569,28570],{},[2175,28571,28572],{"scriptlevel":2177,"displaystyle":2135},[9012,28573,28574,28576,28578],{},[898,28575,9641],{"mathvariant":28393},[1979,28577,1981],{},[1846,28579,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,28581,28582],{},[2175,28583,28584],{"scriptlevel":2177,"displaystyle":2135},[895,28585,28586,28588,28590,28598,28600,28602,28610,28612,28614],{},[895,28587],{},[1846,28589,1848],{},[9012,28591,28592,28594,28596],{},[898,28593,900],{},[1979,28595,1981],{},[1846,28597,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,28599,2075],{},[898,28601,16288],{},[9012,28603,28604,28606,28608],{},[898,28605,3783],{},[1979,28607,1981],{},[1846,28609,4200],{},[1846,28611,1848],{},[1979,28613,2177],{},[1846,28615,2136],{"separator":2135},[20604,28617,28618,28630],{},[20607,28619,28620],{},[2175,28621,28622],{"scriptlevel":2177,"displaystyle":2135},[9012,28623,28624,28626,28628],{},[898,28625,9641],{"mathvariant":28393},[898,28627,16288],{},[1846,28629,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,28631,28632],{},[2175,28633,28634],{"scriptlevel":2177,"displaystyle":2135},[895,28635,28636,28638,28640,28646,28648,28656,28662,28664,28672,28678,28680],{},[895,28637],{},[1846,28639,1848],{},[1974,28641,28642,28644],{},[898,28643,8974],{},[1846,28645,4200],{},[1846,28647,2075],{},[9012,28649,28650,28652,28654],{},[898,28651,3783],{},[1979,28653,2128],{},[1846,28655,4200],{},[2122,28657,28658,28660],{},[898,28659,2638],{},[1979,28661,2128],{},[1846,28663,2075],{},[9012,28665,28666,28668,28670],{},[898,28667,3783],{},[1979,28669,1981],{},[1846,28671,4200],{},[2122,28673,28674,28676],{},[898,28675,2638],{},[1979,28677,1981],{},[1846,28679,1848],{},[1979,28681,12305],{},[20607,28683],{"width":27921},[20607,28685,28686],{},[2138,28687,28688],{},"(6.14)",[902,28690,28691],{"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}",[724,28693,28694,28695,28698,28699,28712,28713,2554],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,28696,28697],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,28700,28702],{"className":28701},[886],[888,28703,28704],{"xmlns":890},[892,28705,28706,28710],{},[895,28707,28708],{},[898,28709,16288],{},[902,28711,16341],{"encoding":904}," dostáváme ",[38,28714,28715],{},"podmínku optimality",[883,28717,28719],{"className":28718},[886],[888,28720,28721],{"xmlns":890,"display":27911},[892,28722,28723,28781],{},[895,28724,28725],{},[12677,28726,28727],{"notation":12679},[2175,28728,28729],{"scriptlevel":2177,"displaystyle":1854},[2175,28730,28731],{"scriptlevel":2177,"displaystyle":1854},[2175,28732,28733],{"scriptlevel":2177,"displaystyle":2135},[895,28734,28735,28737,28739,28741,28759,28761,28779],{},[2138,28736,3830],{},[2138,28738,10449],{},[1846,28740,1848],{},[2179,28742,28743,28751],{},[9012,28744,28745,28747,28749],{},[898,28746,900],{},[1979,28748,2128],{},[1846,28750,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[9012,28752,28753,28755,28757],{},[898,28754,900],{},[1979,28756,1981],{},[1846,28758,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,28760,1848],{},[2179,28762,28763,28771],{},[9012,28764,28765,28767,28769],{},[898,28766,3783],{},[1979,28768,2128],{},[1846,28770,4200],{},[9012,28772,28773,28775,28777],{},[898,28774,3783],{},[1979,28776,1981],{},[1846,28778,4200],{},[2138,28780,3830],{},[902,28782,28783],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[1639,28785,28786],{},[724,28787,28788,28790,28791,28825,28826,28829,28830,28848,28849,28867,28868,28898,28899,28916,28917,28947],{},[883,28789,4001],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,28792,28794],{"className":28793},[886],[888,28795,28796],{"xmlns":890},[892,28797,28798,28822],{},[895,28799,28800,28802,28804,28812,28814],{},[2138,28801,10449],{},[1846,28803,1848],{},[9012,28805,28806,28808,28810],{},[898,28807,3783],{},[1979,28809,2128],{},[1846,28811,4200],{},[898,28813,4520],{"mathvariant":2226},[9012,28815,28816,28818,28820],{},[898,28817,3783],{},[1979,28819,1981],{},[1846,28821,4200],{},[902,28823,28824],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,28827,28828],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,28831,28833],{"className":28832},[886],[888,28834,28835],{"xmlns":890},[892,28836,28837,28845],{},[895,28838,28839],{},[2122,28840,28841,28843],{},[898,28842,2638],{},[1979,28844,2128],{},[902,28846,28847],{"encoding":904},"Q_1"," za ",[883,28850,28852],{"className":28851},[886],[888,28853,28854],{"xmlns":890},[892,28855,28856,28864],{},[895,28857,28858],{},[2122,28859,28860,28862],{},[898,28861,2638],{},[1979,28863,1981],{},[902,28865,28866],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,28869,28871],{"className":28870},[886],[888,28872,28873],{"xmlns":890},[892,28874,28875,28895],{},[895,28876,28877,28879,28881,28887,28889],{},[2138,28878,10449],{},[1846,28880,3256],{},[2122,28882,28883,28885],{},[898,28884,3783],{},[1979,28886,2128],{},[898,28888,4520],{"mathvariant":2226},[2122,28890,28891,28893],{},[898,28892,3783],{},[1979,28894,1981],{},[902,28896,28897],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,28900,28902],{"className":28901},[886],[888,28903,28904],{"xmlns":890},[892,28905,28906,28914],{},[895,28907,28908],{},[2122,28909,28910,28912],{},[898,28911,2638],{},[1979,28913,2128],{},[902,28915,28847],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,28918,28920],{"className":28919},[886],[888,28921,28922],{"xmlns":890},[892,28923,28924,28944],{},[895,28925,28926,28928,28930,28936,28938],{},[2138,28927,10449],{},[1846,28929,3295],{},[2122,28931,28932,28934],{},[898,28933,3783],{},[1979,28935,2128],{},[898,28937,4520],{"mathvariant":2226},[2122,28939,28940,28942],{},[898,28941,3783],{},[1979,28943,1981],{},[902,28945,28946],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,28949,28951,28952,28965],{"id":28950},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,28953,28955],{"className":28954},[886],[888,28956,28957],{"xmlns":890},[892,28958,28959,28963],{},[895,28960,28961],{},[898,28962,16288],{},[902,28964,16341],{"encoding":904}," — mezní užitečnost důchodu",[724,28967,28968,28969,28987,28988,28991,28992,29009,29010,29027,29028,29031],{},"Lagrangeův multiplikátor ",[883,28970,28972],{"className":28971},[886],[888,28973,28974],{"xmlns":890},[892,28975,28976,28984],{},[895,28977,28978],{},[1974,28979,28980,28982],{},[898,28981,16288],{},[1846,28983,4200],{},[902,28985,28986],{"encoding":904},"\\lambda^*"," představuje ",[38,28989,28990],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,28993,28995],{"className":28994},[886],[888,28996,28997],{"xmlns":890},[892,28998,28999,29007],{},[895,29000,29001],{},[1974,29002,29003,29005],{},[898,29004,900],{},[1846,29006,4200],{},[902,29008,27807],{"encoding":904}," při jednotkové změně důchodu ",[883,29011,29013],{"className":29012},[886],[888,29014,29015],{"xmlns":890},[892,29016,29017,29025],{},[895,29018,29019],{},[1974,29020,29021,29023],{},[898,29022,8974],{},[1846,29024,4200],{},[902,29026,27873],{"encoding":904},". Je to ",[38,29029,29030],{},"stínová cena"," rozpočtového omezení.",[1639,29033,29034,29039],{},[724,29035,29036,29038],{},[883,29037,4418],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,29040,29041,29101,29188,29224,29311],{},[123,29042,29043,29046,29047,1734],{},[38,29044,29045],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,29048,29050],{"className":29049},[886],[888,29051,29052],{"xmlns":890},[892,29053,29054,29098],{},[895,29055,29056,29062,29064,29072,29078,29080,29088,29094,29096],{},[1974,29057,29058,29060],{},[898,29059,8974],{},[1846,29061,4200],{},[1846,29063,2075],{},[9012,29065,29066,29068,29070],{},[898,29067,3783],{},[1979,29069,2128],{},[1846,29071,4200],{},[2122,29073,29074,29076],{},[898,29075,2638],{},[1979,29077,2128],{},[1846,29079,2075],{},[9012,29081,29082,29084,29086],{},[898,29083,3783],{},[1979,29085,1981],{},[1846,29087,4200],{},[2122,29089,29090,29092],{},[898,29091,2638],{},[1979,29093,1981],{},[1846,29095,1848],{},[1979,29097,2177],{},[902,29099,29100],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,29102,29103,2053,29106,1734],{},[38,29104,29105],{},"Sestav Lagrangeovu funkci",[883,29107,29109],{"className":29108},[886],[888,29110,29111],{"xmlns":890},[892,29112,29113,29185],{},[895,29114,29115,29117,29119,29121,29123,29129,29131,29137,29139,29141,29143,29145,29151,29153,29161,29167,29169,29177,29183],{},[898,29116,9641],{"mathvariant":28393},[1846,29118,1848],{},[898,29120,900],{},[1846,29122,1855],{"stretchy":1854},[2122,29124,29125,29127],{},[898,29126,2638],{},[1979,29128,2128],{},[1846,29130,2136],{"separator":2135},[2122,29132,29133,29135],{},[898,29134,2638],{},[1979,29136,1981],{},[1846,29138,1861],{"stretchy":1854},[1846,29140,1945],{},[898,29142,16288],{},[1846,29144,1855],{"stretchy":1854},[1974,29146,29147,29149],{},[898,29148,8974],{},[1846,29150,4200],{},[1846,29152,2075],{},[9012,29154,29155,29157,29159],{},[898,29156,3783],{},[1979,29158,2128],{},[1846,29160,4200],{},[2122,29162,29163,29165],{},[898,29164,2638],{},[1979,29166,2128],{},[1846,29168,2075],{},[9012,29170,29171,29173,29175],{},[898,29172,3783],{},[1979,29174,1981],{},[1846,29176,4200],{},[2122,29178,29179,29181],{},[898,29180,2638],{},[1979,29182,1981],{},[1846,29184,1861],{"stretchy":1854},[902,29186,29187],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,29189,29190,10314,29193,29223],{},[38,29191,29192],{},"Spočítej parciální derivace",[883,29194,29196],{"className":29195},[886],[888,29197,29198],{"xmlns":890},[892,29199,29200,29220],{},[895,29201,29202,29208,29210,29216,29218],{},[2122,29203,29204,29206],{},[898,29205,2638],{},[1979,29207,2128],{},[1846,29209,2136],{"separator":2135},[2122,29211,29212,29214],{},[898,29213,2638],{},[1979,29215,1981],{},[1846,29217,2136],{"separator":2135},[898,29219,16288],{},[902,29221,29222],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,29225,29226,29242,29243,29276,29277,1745,29294,1734],{},[38,29227,29228,29229],{},"Vyluč ",[883,29230,29232],{"className":29231},[886],[888,29233,29234],{"xmlns":890},[892,29235,29236,29240],{},[895,29237,29238],{},[898,29239,16288],{},[902,29241,16341],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,29244,29246],{"className":29245},[886],[888,29247,29248],{"xmlns":890},[892,29249,29250,29274],{},[895,29251,29252,29254,29256,29264,29266],{},[2138,29253,10449],{},[1846,29255,1848],{},[9012,29257,29258,29260,29262],{},[898,29259,3783],{},[1979,29261,2128],{},[1846,29263,4200],{},[898,29265,4520],{"mathvariant":2226},[9012,29267,29268,29270,29272],{},[898,29269,3783],{},[1979,29271,1981],{},[1846,29273,4200],{},[902,29275,28824],{"encoding":904},", která dá vztah mezi ",[883,29278,29280],{"className":29279},[886],[888,29281,29282],{"xmlns":890},[892,29283,29284,29292],{},[895,29285,29286],{},[2122,29287,29288,29290],{},[898,29289,2638],{},[1979,29291,2128],{},[902,29293,28847],{"encoding":904},[883,29295,29297],{"className":29296},[886],[888,29298,29299],{"xmlns":890},[892,29300,29301,29309],{},[895,29302,29303],{},[2122,29304,29305,29307],{},[898,29306,2638],{},[1979,29308,1981],{},[902,29310,28866],{"encoding":904},[123,29312,29313,29316,29317,29347,29348,29365,29366,1734],{},[38,29314,29315],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,29318,29320],{"className":29319},[886],[888,29321,29322],{"xmlns":890},[892,29323,29324,29344],{},[895,29325,29326,29334,29336],{},[9012,29327,29328,29330,29332],{},[898,29329,2638],{},[1979,29331,2128],{},[1846,29333,4200],{},[1846,29335,2136],{"separator":2135},[9012,29337,29338,29340,29342],{},[898,29339,2638],{},[1979,29341,1981],{},[1846,29343,4200],{},[902,29345,29346],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,29349,29351],{"className":29350},[886],[888,29352,29353],{"xmlns":890},[892,29354,29355,29363],{},[895,29356,29357],{},[1974,29358,29359,29361],{},[898,29360,16288],{},[1846,29362,4200],{},[902,29364,28986],{"encoding":904}," a maximální užitečnost ",[883,29367,29369],{"className":29368},[886],[888,29370,29371],{"xmlns":890},[892,29372,29373,29407],{},[895,29374,29375,29381,29383,29385,29387,29395,29397,29405],{},[1974,29376,29377,29379],{},[898,29378,900],{},[1846,29380,4200],{},[1846,29382,1848],{},[898,29384,900],{},[1846,29386,1855],{"stretchy":1854},[9012,29388,29389,29391,29393],{},[898,29390,2638],{},[1979,29392,2128],{},[1846,29394,4200],{},[1846,29396,2136],{"separator":2135},[9012,29398,29399,29401,29403],{},[898,29400,2638],{},[1979,29402,1981],{},[1846,29404,4200],{},[1846,29406,1861],{"stretchy":1854},[902,29408,29409],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,29411,29413],{"id":29412},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,29415,29416],{},[2409,29417],{"alt":29418,"className":29419,"src":29420},"imek-uzitecnost-optimum",[210,2413],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,29422,29423],{},[614,29424,29425,29426,29475,29476,1745,29504,29532,29533,29567,29568,29607,29608,29626,29627,29645,29646,29664],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,29427,29429],{"className":29428},[886],[888,29430,29431],{"xmlns":890},[892,29432,29433,29473],{},[895,29434,29435,29441,29443,29451,29457,29459,29467],{},[1974,29436,29437,29439],{},[898,29438,8974],{},[1846,29440,4200],{},[1846,29442,1848],{},[9012,29444,29445,29447,29449],{},[898,29446,3783],{},[1979,29448,2128],{},[1846,29450,4200],{},[2122,29452,29453,29455],{},[898,29454,2638],{},[1979,29456,2128],{},[1846,29458,1945],{},[9012,29460,29461,29463,29465],{},[898,29462,3783],{},[1979,29464,1981],{},[1846,29466,4200],{},[2122,29468,29469,29471],{},[898,29470,2638],{},[1979,29472,1981],{},[902,29474,17143],{"encoding":904}," protíná osy v ",[883,29477,29479],{"className":29478},[886],[888,29480,29481],{"xmlns":890},[892,29482,29483,29501],{},[895,29484,29485,29491,29493],{},[1974,29486,29487,29489],{},[898,29488,8974],{},[1846,29490,4200],{},[898,29492,4520],{"mathvariant":2226},[9012,29494,29495,29497,29499],{},[898,29496,3783],{},[1979,29498,2128],{},[1846,29500,4200],{},[902,29502,29503],{"encoding":904},"Y^*\u002FP_1^*",[883,29505,29507],{"className":29506},[886],[888,29508,29509],{"xmlns":890},[892,29510,29511,29529],{},[895,29512,29513,29519,29521],{},[1974,29514,29515,29517],{},[898,29516,8974],{},[1846,29518,4200],{},[898,29520,4520],{"mathvariant":2226},[9012,29522,29523,29525,29527],{},[898,29524,3783],{},[1979,29526,1981],{},[1846,29528,4200],{},[902,29530,29531],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,29534,29536],{"className":29535},[886],[888,29537,29538],{"xmlns":890},[892,29539,29540,29564],{},[895,29541,29542,29548,29550,29556,29558],{},[2122,29543,29544,29546],{},[898,29545,1992],{},[1979,29547,2128],{},[1846,29549,3295],{},[1974,29551,29552,29554],{},[898,29553,1992],{},[1846,29555,4200],{},[1846,29557,3295],{},[2122,29559,29560,29562],{},[898,29561,1992],{},[1979,29563,1981],{},[902,29565,29566],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,29569,29571],{"className":29570},[886],[888,29572,29573],{"xmlns":890},[892,29574,29575,29605],{},[895,29576,29577,29583,29585,29593,29595,29603],{},[1974,29578,29579,29581],{},[898,29580,2638],{},[1846,29582,4200],{},[1846,29584,2336],{"stretchy":1854},[9012,29586,29587,29589,29591],{},[898,29588,2638],{},[1979,29590,2128],{},[1846,29592,4200],{},[1846,29594,2136],{"separator":2135},[9012,29596,29597,29599,29601],{},[898,29598,2638],{},[1979,29600,1981],{},[1846,29602,4200],{},[1846,29604,2351],{"stretchy":1854},[902,29606,28172],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,29609,29611],{"className":29610},[886],[888,29612,29613],{"xmlns":890},[892,29614,29615,29623],{},[895,29616,29617],{},[1974,29618,29619,29621],{},[898,29620,1992],{},[1846,29622,4200],{},[902,29624,29625],{"encoding":904},"c^*",". Křivka ",[883,29628,29630],{"className":29629},[886],[888,29631,29632],{"xmlns":890},[892,29633,29634,29642],{},[895,29635,29636],{},[2122,29637,29638,29640],{},[898,29639,1992],{},[1979,29641,2128],{},[902,29643,29644],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,29647,29649],{"className":29648},[886],[888,29650,29651],{"xmlns":890},[892,29652,29653,29661],{},[895,29654,29655],{},[2122,29656,29657,29659],{},[898,29658,1992],{},[1979,29660,1981],{},[902,29662,29663],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,29666,29667,29668,29671,29672,29690,29691,29720],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,29669,29670],{},"dotýkají",", tj. mají v bodě ",[883,29673,29675],{"className":29674},[886],[888,29676,29677],{"xmlns":890},[892,29678,29679,29687],{},[895,29680,29681],{},[1974,29682,29683,29685],{},[898,29684,2638],{},[1846,29686,4200],{},[902,29688,29689],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,29692,29694],{"className":29693},[886],[888,29695,29696],{"xmlns":890},[892,29697,29698,29718],{},[895,29699,29700,29702,29704,29710,29712],{},[2138,29701,10449],{},[1846,29703,1848],{},[2122,29705,29706,29708],{},[898,29707,3783],{},[1979,29709,2128],{},[898,29711,4520],{"mathvariant":2226},[2122,29713,29714,29716],{},[898,29715,3783],{},[1979,29717,1981],{},[902,29719,27843],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,29722,29724],{"id":29723},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,29726,9509,29727,29789],{},[883,29728,29730],{"className":29729},[886],[888,29731,29732],{"xmlns":890},[892,29733,29734,29786],{},[895,29735,29736,29738,29740,29746,29748,29754,29756,29758,29772],{},[898,29737,900],{},[1846,29739,1855],{"stretchy":1854},[2122,29741,29742,29744],{},[898,29743,2638],{},[1979,29745,2128],{},[1846,29747,2136],{"separator":2135},[2122,29749,29750,29752],{},[898,29751,2638],{},[1979,29753,1981],{},[1846,29755,1861],{"stretchy":1854},[1846,29757,1848],{},[9012,29759,29760,29762,29764],{},[898,29761,2638],{},[1979,29763,2128],{},[895,29765,29766,29768,29770],{},[1979,29767,2128],{},[898,29769,4520],{"mathvariant":2226},[1979,29771,1981],{},[9012,29773,29774,29776,29778],{},[898,29775,2638],{},[1979,29777,1981],{},[895,29779,29780,29782,29784],{},[1979,29781,2128],{},[898,29783,4520],{"mathvariant":2226},[1979,29785,1981],{},[902,29787,29788],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,29791,29792],{},[883,29793,29795],{"className":29794},[886],[888,29796,29797],{"xmlns":890},[892,29798,29799,29905],{},[895,29800,29801,29803,29805,29887,29889,29903],{},[2138,29802,10449],{},[1846,29804,1848],{},[2179,29806,29807,29847],{},[895,29808,29809,29817,29833],{},[2175,29810,29811],{"scriptlevel":2177,"displaystyle":1854},[2179,29812,29813,29815],{},[1979,29814,2128],{},[1979,29816,1981],{},[9012,29818,29819,29821,29823],{},[898,29820,2638],{},[1979,29822,2128],{},[895,29824,29825,29827,29829,29831],{},[1846,29826,2075],{},[1979,29828,2128],{},[898,29830,4520],{"mathvariant":2226},[1979,29832,1981],{},[9012,29834,29835,29837,29839],{},[898,29836,2638],{},[1979,29838,1981],{},[895,29840,29841,29843,29845],{},[1979,29842,2128],{},[898,29844,4520],{"mathvariant":2226},[1979,29846,1981],{},[895,29848,29849,29857,29871],{},[2175,29850,29851],{"scriptlevel":2177,"displaystyle":1854},[2179,29852,29853,29855],{},[1979,29854,2128],{},[1979,29856,1981],{},[9012,29858,29859,29861,29863],{},[898,29860,2638],{},[1979,29862,2128],{},[895,29864,29865,29867,29869],{},[1979,29866,2128],{},[898,29868,4520],{"mathvariant":2226},[1979,29870,1981],{},[9012,29872,29873,29875,29877],{},[898,29874,2638],{},[1979,29876,1981],{},[895,29878,29879,29881,29883,29885],{},[1846,29880,2075],{},[1979,29882,2128],{},[898,29884,4520],{"mathvariant":2226},[1979,29886,1981],{},[1846,29888,1848],{},[2179,29890,29891,29897],{},[2122,29892,29893,29895],{},[898,29894,2638],{},[1979,29896,1981],{},[2122,29898,29899,29901],{},[898,29900,2638],{},[1979,29902,2128],{},[898,29904,1734],{"mathvariant":2226},[902,29906,29907],{"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}.",[724,29909,29910,29911,2776,29956,29958,29959,29979,29980,30010,30011,1734],{},"Tedy ",[883,29912,29914],{"className":29913},[886],[888,29915,29916],{"xmlns":890},[892,29917,29918,29953],{},[895,29919,29920,29922,29924,29927,29929,29931,29933,29935,29943,29945],{},[2138,29921,10449],{},[1846,29923,1855],{"stretchy":1854},[1979,29925,29926],{},"300",[1846,29928,2136],{"separator":2135},[1979,29930,14955],{},[1846,29932,1861],{"stretchy":1854},[1846,29934,1848],{},[2175,29936,29937],{"scriptlevel":2177,"displaystyle":1854},[2179,29938,29939,29941],{},[1979,29940,14955],{},[1979,29942,29926],{},[1846,29944,1848],{},[2175,29946,29947],{"scriptlevel":2177,"displaystyle":1854},[2179,29948,29949,29951],{},[1979,29950,2078],{},[1979,29952,2023],{},[902,29954,29955],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,29957,9062],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,29960,29962],{"className":29961},[886],[888,29963,29964],{"xmlns":890},[892,29965,29966,29976],{},[895,29967,29968],{},[2175,29969,29970],{"scriptlevel":2177,"displaystyle":1854},[2179,29971,29972,29974],{},[1979,29973,2078],{},[1979,29975,2023],{},[902,29977,29978],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,29981,29983],{"className":29982},[886],[888,29984,29985],{"xmlns":890},[892,29986,29987,30007],{},[895,29988,29989,29991,29993,29999,30001],{},[2138,29990,10449],{},[1846,29992,1848],{},[2122,29994,29995,29997],{},[898,29996,2638],{},[1979,29998,1981],{},[898,30000,4520],{"mathvariant":2226},[2122,30002,30003,30005],{},[898,30004,2638],{},[1979,30006,2128],{},[902,30008,30009],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,30012,30014],{"className":30013},[886],[888,30015,30016],{"xmlns":890},[892,30017,30018,30038],{},[895,30019,30020,30022,30024,30030,30032],{},[2138,30021,10449],{},[1846,30023,1848],{},[2122,30025,30026,30028],{},[898,30027,3783],{},[1979,30029,2128],{},[898,30031,4520],{"mathvariant":2226},[2122,30033,30034,30036],{},[898,30035,3783],{},[1979,30037,1981],{},[902,30039,27843],{"encoding":904},[115,30041,30043,30044],{"id":30042},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,30045,30047],{"className":30046},[886],[888,30048,30049],{"xmlns":890},[892,30050,30051,30069],{},[895,30052,30053,30055,30057,30063],{},[898,30054,900],{},[1846,30056,1848],{},[2122,30058,30059,30061],{},[898,30060,2638],{},[1979,30062,2128],{},[2122,30064,30065,30067],{},[898,30066,2638],{},[1979,30068,1981],{},[902,30070,30071],{"encoding":904},"U = Q_1 Q_2",[724,30073,30074,30075,1343,30121,1343,30145,1343,30169,30191],{},"Je dána ",[883,30076,30078],{"className":30077},[886],[888,30079,30080],{"xmlns":890},[892,30081,30082,30118],{},[895,30083,30084,30086,30088,30094,30096,30102,30104,30106,30112],{},[898,30085,900],{},[1846,30087,1855],{"stretchy":1854},[2122,30089,30090,30092],{},[898,30091,2638],{},[1979,30093,2128],{},[1846,30095,2136],{"separator":2135},[2122,30097,30098,30100],{},[898,30099,2638],{},[1979,30101,1981],{},[1846,30103,1861],{"stretchy":1854},[1846,30105,1848],{},[2122,30107,30108,30110],{},[898,30109,2638],{},[1979,30111,2128],{},[2122,30113,30114,30116],{},[898,30115,2638],{},[1979,30117,1981],{},[902,30119,30120],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,30122,30124],{"className":30123},[886],[888,30125,30126],{"xmlns":890},[892,30127,30128,30142],{},[895,30129,30130,30138,30140],{},[9012,30131,30132,30134,30136],{},[898,30133,3783],{},[1979,30135,2128],{},[1846,30137,4200],{},[1846,30139,1848],{},[1979,30141,1981],{},[902,30143,30144],{"encoding":904},"P_1^* = 2",[883,30146,30148],{"className":30147},[886],[888,30149,30150],{"xmlns":890},[892,30151,30152,30166],{},[895,30153,30154,30162,30164],{},[9012,30155,30156,30158,30160],{},[898,30157,3783],{},[1979,30159,1981],{},[1846,30161,4200],{},[1846,30163,1848],{},[1979,30165,2078],{},[902,30167,30168],{"encoding":904},"P_2^* = 5",[883,30170,30172],{"className":30171},[886],[888,30173,30174],{"xmlns":890},[892,30175,30176,30188],{},[895,30177,30178,30184,30186],{},[1974,30179,30180,30182],{},[898,30181,8974],{},[1846,30183,4200],{},[1846,30185,1848],{},[1979,30187,2938],{},[902,30189,30190],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,30193,30195],{"className":30194},[886],[888,30196,30197],{"xmlns":890,"display":27911},[892,30198,30199,30271],{},[895,30200,30201,30203,30205,30211,30213,30219,30221,30223,30225,30227,30233,30239,30241,30243,30245,30247,30249,30251,30257,30259,30261,30267,30269],{},[898,30202,9641],{"mathvariant":28393},[1846,30204,1855],{"stretchy":1854},[2122,30206,30207,30209],{},[898,30208,2638],{},[1979,30210,2128],{},[1846,30212,2136],{"separator":2135},[2122,30214,30215,30217],{},[898,30216,2638],{},[1979,30218,1981],{},[1846,30220,2136],{"separator":2135},[898,30222,16288],{},[1846,30224,1861],{"stretchy":1854},[1846,30226,1848],{},[2122,30228,30229,30231],{},[898,30230,2638],{},[1979,30232,2128],{},[2122,30234,30235,30237],{},[898,30236,2638],{},[1979,30238,1981],{},[1846,30240,1945],{},[898,30242,16288],{},[1846,30244,1855],{"stretchy":1854},[1979,30246,2938],{},[1846,30248,2075],{},[1979,30250,1981],{},[2122,30252,30253,30255],{},[898,30254,2638],{},[1979,30256,2128],{},[1846,30258,2075],{},[1979,30260,2078],{},[2122,30262,30263,30265],{},[898,30264,2638],{},[1979,30266,1981],{},[1846,30268,1861],{"stretchy":1854},[898,30270,1734],{"mathvariant":2226},[902,30272,30273],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,30275,30276],{},"Soustava:",[883,30278,30280],{"className":30279},[886],[888,30281,30282],{"xmlns":890,"display":27911},[892,30283,30284,30396],{},[20599,30285,30286,30320,30354],{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},[20604,30287,30288,30306],{},[20607,30289,30290],{},[2175,30291,30292],{"scriptlevel":2177,"displaystyle":2135},[895,30293,30294,30300,30302,30304],{},[2122,30295,30296,30298],{},[898,30297,2638],{},[1979,30299,1981],{},[1846,30301,2075],{},[1979,30303,1981],{},[898,30305,16288],{},[20607,30307,30308],{},[2175,30309,30310],{"scriptlevel":2177,"displaystyle":2135},[895,30311,30312,30314,30316,30318],{},[895,30313],{},[1846,30315,1848],{},[1979,30317,2177],{},[1846,30319,2136],{"separator":2135},[20604,30321,30322,30340],{},[20607,30323,30324],{},[2175,30325,30326],{"scriptlevel":2177,"displaystyle":2135},[895,30327,30328,30334,30336,30338],{},[2122,30329,30330,30332],{},[898,30331,2638],{},[1979,30333,2128],{},[1846,30335,2075],{},[1979,30337,2078],{},[898,30339,16288],{},[20607,30341,30342],{},[2175,30343,30344],{"scriptlevel":2177,"displaystyle":2135},[895,30345,30346,30348,30350,30352],{},[895,30347],{},[1846,30349,1848],{},[1979,30351,2177],{},[1846,30353,2136],{"separator":2135},[20604,30355,30356,30384],{},[20607,30357,30358],{},[2175,30359,30360],{"scriptlevel":2177,"displaystyle":2135},[895,30361,30362,30364,30366,30368,30374,30376,30378],{},[1979,30363,2938],{},[1846,30365,2075],{},[1979,30367,1981],{},[2122,30369,30370,30372],{},[898,30371,2638],{},[1979,30373,2128],{},[1846,30375,2075],{},[1979,30377,2078],{},[2122,30379,30380,30382],{},[898,30381,2638],{},[1979,30383,1981],{},[20607,30385,30386],{},[2175,30387,30388],{"scriptlevel":2177,"displaystyle":2135},[895,30389,30390,30392,30394],{},[895,30391],{},[1846,30393,1848],{},[1979,30395,12305],{},[902,30397,30398],{"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}",[724,30400,30401,30402,1343,30426,30450,30451,5435,30491,30509,30510,30560,30561,1734],{},"Z prvních dvou rovnic ",[883,30403,30405],{"className":30404},[886],[888,30406,30407],{"xmlns":890},[892,30408,30409,30423],{},[895,30410,30411,30417,30419,30421],{},[2122,30412,30413,30415],{},[898,30414,2638],{},[1979,30416,1981],{},[1846,30418,1848],{},[1979,30420,1981],{},[898,30422,16288],{},[902,30424,30425],{"encoding":904},"Q_2 = 2\\lambda",[883,30427,30429],{"className":30428},[886],[888,30430,30431],{"xmlns":890},[892,30432,30433,30447],{},[895,30434,30435,30441,30443,30445],{},[2122,30436,30437,30439],{},[898,30438,2638],{},[1979,30440,2128],{},[1846,30442,1848],{},[1979,30444,2078],{},[898,30446,16288],{},[902,30448,30449],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,30452,30454],{"className":30453},[886],[888,30455,30456],{"xmlns":890},[892,30457,30458,30488],{},[895,30459,30460,30462,30464,30466,30468,30470,30472,30474,30476,30478,30480,30482,30484,30486],{},[1979,30461,2938],{},[1846,30463,1848],{},[1979,30465,1981],{},[1846,30467,3025],{},[1979,30469,2078],{},[898,30471,16288],{},[1846,30473,1945],{},[1979,30475,2078],{},[1846,30477,3025],{},[1979,30479,1981],{},[898,30481,16288],{},[1846,30483,1848],{},[1979,30485,8881],{},[898,30487,16288],{},[902,30489,30490],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,30492,30494],{"className":30493},[886],[888,30495,30496],{"xmlns":890},[892,30497,30498,30506],{},[895,30499,30500,30502,30504],{},[898,30501,16288],{},[1846,30503,1848],{},[1979,30505,2078],{},[902,30507,30508],{"encoding":904},"\\lambda = 5",". Odtud ",[38,30511,30512,1343,30536],{},[883,30513,30515],{"className":30514},[886],[888,30516,30517],{"xmlns":890},[892,30518,30519,30533],{},[895,30520,30521,30529,30531],{},[9012,30522,30523,30525,30527],{},[898,30524,2638],{},[1979,30526,2128],{},[1846,30528,4200],{},[1846,30530,1848],{},[1979,30532,4850],{},[902,30534,30535],{"encoding":904},"Q_1^* = 25",[883,30537,30539],{"className":30538},[886],[888,30540,30541],{"xmlns":890},[892,30542,30543,30557],{},[895,30544,30545,30553,30555],{},[9012,30546,30547,30549,30551],{},[898,30548,2638],{},[1979,30550,1981],{},[1846,30552,4200],{},[1846,30554,1848],{},[1979,30556,2712],{},[902,30558,30559],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,30562,30564],{"className":30563},[886],[888,30565,30566],{"xmlns":890},[892,30567,30568,30589],{},[895,30569,30570,30576,30578,30580,30582,30584,30586],{},[1974,30571,30572,30574],{},[898,30573,900],{},[1846,30575,4200],{},[1846,30577,1848],{},[1979,30579,4850],{},[1846,30581,3025],{},[1979,30583,2712],{},[1846,30585,1848],{},[1979,30587,30588],{},"250",[902,30590,30591],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,30593,30594],{},[614,30595,30596,30597,27982,30635,1745,30659,30683,30684,30714,30715,30739,30740,30762,30763,1734],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,30598,30600],{"className":30599},[886],[888,30601,30602],{"xmlns":890},[892,30603,30604,30632],{},[895,30605,30606,30608,30610,30612,30618,30620,30622,30628,30630],{},[1979,30607,2938],{},[1846,30609,2075],{},[1979,30611,1981],{},[2122,30613,30614,30616],{},[898,30615,2638],{},[1979,30617,2128],{},[1846,30619,2075],{},[1979,30621,2078],{},[2122,30623,30624,30626],{},[898,30625,2638],{},[1979,30627,1981],{},[1846,30629,1848],{},[1979,30631,2177],{},[902,30633,30634],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,30636,30638],{"className":30637},[886],[888,30639,30640],{"xmlns":890},[892,30641,30642,30656],{},[895,30643,30644,30646,30648,30650,30652,30654],{},[898,30645,4101],{},[1846,30647,2336],{"stretchy":1854},[1979,30649,2177],{},[1846,30651,2136],{"separator":2135},[1979,30653,8881],{},[1846,30655,2351],{"stretchy":1854},[902,30657,30658],{"encoding":904},"A[0, 20]",[883,30660,30662],{"className":30661},[886],[888,30663,30664],{"xmlns":890},[892,30665,30666,30680],{},[895,30667,30668,30670,30672,30674,30676,30678],{},[898,30669,23098],{},[1846,30671,2336],{"stretchy":1854},[1979,30673,2968],{},[1846,30675,2136],{"separator":2135},[1979,30677,2177],{},[1846,30679,2351],{"stretchy":1854},[902,30681,30682],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,30685,30687],{"className":30686},[886],[888,30688,30689],{"xmlns":890},[892,30690,30691,30711],{},[895,30692,30693,30699,30701,30703,30705],{},[2122,30694,30695,30697],{},[898,30696,2638],{},[1979,30698,1981],{},[1846,30700,1848],{},[1979,30702,30588],{},[898,30704,4520],{"mathvariant":2226},[2122,30706,30707,30709],{},[898,30708,2638],{},[1979,30710,2128],{},[902,30712,30713],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,30716,30718],{"className":30717},[886],[888,30719,30720],{"xmlns":890},[892,30721,30722,30736],{},[895,30723,30724,30726,30728,30730,30732,30734],{},[898,30725,4098],{},[1846,30727,2336],{"stretchy":1854},[1979,30729,4850],{},[1846,30731,2136],{"separator":2135},[1979,30733,2712],{},[1846,30735,2351],{"stretchy":1854},[902,30737,30738],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,30741,30743],{"className":30742},[886],[888,30744,30745],{"xmlns":890},[892,30746,30747,30759],{},[895,30748,30749,30751],{},[1846,30750,2075],{},[2175,30752,30753],{"scriptlevel":2177,"displaystyle":1854},[2179,30754,30755,30757],{},[1979,30756,1981],{},[1979,30758,2078],{},[902,30760,30761],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,30764,30766],{"className":30765},[886],[888,30767,30768],{"xmlns":890},[892,30769,30770,30810],{},[895,30771,30772,30774,30776,30778,30780,30782,30784,30786,30788,30790,30798,30800,30802],{},[1846,30773,2075],{},[2138,30775,10449],{},[1846,30777,1855],{"stretchy":1854},[1979,30779,4850],{},[1846,30781,2136],{"separator":2135},[1979,30783,2712],{},[1846,30785,1861],{"stretchy":1854},[1846,30787,1848],{},[1846,30789,2075],{},[2175,30791,30792],{"scriptlevel":2177,"displaystyle":1854},[2179,30793,30794,30796],{},[1979,30795,2712],{},[1979,30797,4850],{},[1846,30799,1848],{},[1846,30801,2075],{},[2175,30803,30804],{"scriptlevel":2177,"displaystyle":1854},[2179,30805,30806,30808],{},[1979,30807,1981],{},[1979,30809,2078],{},[902,30811,30812],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,30814,30816],{"id":30815},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,30818,30819,30820,28848,30850,30853,30854,2554],{},"Považujeme-li v úloze ",[883,30821,30823],{"className":30822},[886],[888,30824,30825],{"xmlns":890},[892,30826,30827,30847],{},[895,30828,30829,30835,30837,30843,30845],{},[2122,30830,30831,30833],{},[898,30832,3783],{},[1979,30834,2128],{},[1846,30836,2136],{"separator":2135},[2122,30838,30839,30841],{},[898,30840,3783],{},[1979,30842,1981],{},[1846,30844,2136],{"separator":2135},[898,30846,8974],{},[902,30848,30849],{"encoding":904},"P_1, P_2, Y",[38,30851,30852],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,30855,30856],{},"Marshallovy poptávkové funkce",[883,30858,30860],{"className":30859},[886],[888,30861,30862],{"xmlns":890,"display":27911},[892,30863,30864,30959],{},[20599,30865,30866],{"width":27916},[20604,30867,30868,30870,30952,30954],{},[20607,30869],{"width":27921},[20607,30871,30872],{},[895,30873,30874,30880,30882,30888,30890,30896,30898,30904,30906,30908,30910,30912,30914,30920,30922,30928,30930,30936,30938,30944,30946,30948,30950],{},[2122,30875,30876,30878],{},[898,30877,2638],{},[1979,30879,2128],{},[1846,30881,1848],{},[2122,30883,30884,30886],{},[898,30885,4029],{},[1979,30887,2128],{},[1846,30889,1855],{"stretchy":1854},[2122,30891,30892,30894],{},[898,30893,3783],{},[1979,30895,2128],{},[1846,30897,2136],{"separator":2135},[2122,30899,30900,30902],{},[898,30901,3783],{},[1979,30903,1981],{},[1846,30905,2136],{"separator":2135},[898,30907,8974],{},[1846,30909,1861],{"stretchy":1854},[1846,30911,2136],{"separator":2135},[5724,30913],{"width":15129},[2122,30915,30916,30918],{},[898,30917,2638],{},[1979,30919,1981],{},[1846,30921,1848],{},[2122,30923,30924,30926],{},[898,30925,4029],{},[1979,30927,1981],{},[1846,30929,1855],{"stretchy":1854},[2122,30931,30932,30934],{},[898,30933,3783],{},[1979,30935,2128],{},[1846,30937,2136],{"separator":2135},[2122,30939,30940,30942],{},[898,30941,3783],{},[1979,30943,1981],{},[1846,30945,2136],{"separator":2135},[898,30947,8974],{},[1846,30949,1861],{"stretchy":1854},[1846,30951,2136],{"separator":2135},[20607,30953],{"width":27921},[20607,30955,30956],{},[2138,30957,30958],{},"(6.15)",[902,30960,30961],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,30963,30965],{"className":30964},[886],[888,30966,30967],{"xmlns":890,"display":27911},[892,30968,30969,31016],{},[20599,30970,30971],{"width":27916},[20604,30972,30973,30975,31009,31011],{},[20607,30974],{"width":27921},[20607,30976,30977],{},[895,30978,30979,30981,30983,30985,30987,30993,30995,31001,31003,31005,31007],{},[898,30980,16288],{},[1846,30982,1848],{},[898,30984,16288],{},[1846,30986,1855],{"stretchy":1854},[2122,30988,30989,30991],{},[898,30990,3783],{},[1979,30992,2128],{},[1846,30994,2136],{"separator":2135},[2122,30996,30997,30999],{},[898,30998,3783],{},[1979,31000,1981],{},[1846,31002,2136],{"separator":2135},[898,31004,8974],{},[1846,31006,1861],{"stretchy":1854},[898,31008,1734],{"mathvariant":2226},[20607,31010],{"width":27921},[20607,31012,31013],{},[2138,31014,31015],{},"(6.16)",[902,31017,31018],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,31020,31021,31051,31052,31118],{},[38,31022,31023,31024,1734],{},"Odvození pro ",[883,31025,31027],{"className":31026},[886],[888,31028,31029],{"xmlns":890},[892,31030,31031,31049],{},[895,31032,31033,31035,31037,31043],{},[898,31034,900],{},[1846,31036,1848],{},[2122,31038,31039,31041],{},[898,31040,2638],{},[1979,31042,2128],{},[2122,31044,31045,31047],{},[898,31046,2638],{},[1979,31048,1981],{},[902,31050,30071],{"encoding":904}," Lagrangeova funkce ",[883,31053,31055],{"className":31054},[886],[888,31056,31057],{"xmlns":890},[892,31058,31059,31115],{},[895,31060,31061,31063,31065,31071,31077,31079,31081,31083,31085,31087,31093,31099,31101,31107,31113],{},[898,31062,9641],{"mathvariant":28393},[1846,31064,1848],{},[2122,31066,31067,31069],{},[898,31068,2638],{},[1979,31070,2128],{},[2122,31072,31073,31075],{},[898,31074,2638],{},[1979,31076,1981],{},[1846,31078,1945],{},[898,31080,16288],{},[1846,31082,1855],{"stretchy":1854},[898,31084,8974],{},[1846,31086,2075],{},[2122,31088,31089,31091],{},[898,31090,3783],{},[1979,31092,2128],{},[2122,31094,31095,31097],{},[898,31096,2638],{},[1979,31098,2128],{},[1846,31100,2075],{},[2122,31102,31103,31105],{},[898,31104,3783],{},[1979,31106,1981],{},[2122,31108,31109,31111],{},[898,31110,2638],{},[1979,31112,1981],{},[1846,31114,1861],{"stretchy":1854},[902,31116,31117],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,31120,31122],{"className":31121},[886],[888,31123,31124],{"xmlns":890,"display":27911},[892,31125,31126,31293],{},[20599,31127,31128],{"width":27916},[20604,31129,31130,31132,31286,31288],{},[20607,31131],{"width":27921},[20607,31133,31134],{},[20599,31135,31136,31182,31228],{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},[20604,31137,31138,31150],{},[20607,31139,31140],{},[2175,31141,31142],{"scriptlevel":2177,"displaystyle":2135},[9012,31143,31144,31146,31148],{},[898,31145,9641],{"mathvariant":28393},[1979,31147,2128],{},[1846,31149,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,31151,31152],{},[2175,31153,31154],{"scriptlevel":2177,"displaystyle":2135},[895,31155,31156,31158,31160,31166,31168,31170,31176,31178,31180],{},[895,31157],{},[1846,31159,1848],{},[2122,31161,31162,31164],{},[898,31163,2638],{},[1979,31165,1981],{},[1846,31167,2075],{},[898,31169,16288],{},[2122,31171,31172,31174],{},[898,31173,3783],{},[1979,31175,2128],{},[1846,31177,1848],{},[1979,31179,2177],{},[1846,31181,2136],{"separator":2135},[20604,31183,31184,31196],{},[20607,31185,31186],{},[2175,31187,31188],{"scriptlevel":2177,"displaystyle":2135},[9012,31189,31190,31192,31194],{},[898,31191,9641],{"mathvariant":28393},[1979,31193,1981],{},[1846,31195,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,31197,31198],{},[2175,31199,31200],{"scriptlevel":2177,"displaystyle":2135},[895,31201,31202,31204,31206,31212,31214,31216,31222,31224,31226],{},[895,31203],{},[1846,31205,1848],{},[2122,31207,31208,31210],{},[898,31209,2638],{},[1979,31211,2128],{},[1846,31213,2075],{},[898,31215,16288],{},[2122,31217,31218,31220],{},[898,31219,3783],{},[1979,31221,1981],{},[1846,31223,1848],{},[1979,31225,2177],{},[1846,31227,2136],{"separator":2135},[20604,31229,31230,31242],{},[20607,31231,31232],{},[2175,31233,31234],{"scriptlevel":2177,"displaystyle":2135},[9012,31235,31236,31238,31240],{},[898,31237,9641],{"mathvariant":28393},[898,31239,16288],{},[1846,31241,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,31243,31244],{},[2175,31245,31246],{"scriptlevel":2177,"displaystyle":2135},[895,31247,31248,31250,31252,31254,31256,31262,31268,31270,31276,31282,31284],{},[895,31249],{},[1846,31251,1848],{},[898,31253,8974],{},[1846,31255,2075],{},[2122,31257,31258,31260],{},[898,31259,3783],{},[1979,31261,2128],{},[2122,31263,31264,31266],{},[898,31265,2638],{},[1979,31267,2128],{},[1846,31269,2075],{},[2122,31271,31272,31274],{},[898,31273,3783],{},[1979,31275,1981],{},[2122,31277,31278,31280],{},[898,31279,2638],{},[1979,31281,1981],{},[1846,31283,1848],{},[1979,31285,12305],{},[20607,31287],{"width":27921},[20607,31289,31290],{},[2138,31291,31292],{},"(6.17)",[902,31294,31295],{"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}",[724,31297,31298,31299,31327,31328,31356,31357,31425],{},"Z prvních dvou: ",[883,31300,31302],{"className":31301},[886],[888,31303,31304],{"xmlns":890},[892,31305,31306,31324],{},[895,31307,31308,31314,31316,31322],{},[2122,31309,31310,31312],{},[898,31311,2638],{},[1979,31313,1981],{},[1846,31315,1848],{},[2122,31317,31318,31320],{},[898,31319,3783],{},[1979,31321,2128],{},[898,31323,16288],{},[902,31325,31326],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,31329,31331],{"className":31330},[886],[888,31332,31333],{"xmlns":890},[892,31334,31335,31353],{},[895,31336,31337,31343,31345,31351],{},[2122,31338,31339,31341],{},[898,31340,2638],{},[1979,31342,2128],{},[1846,31344,1848],{},[2122,31346,31347,31349],{},[898,31348,3783],{},[1979,31350,1981],{},[898,31352,16288],{},[902,31354,31355],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,31358,31360],{"className":31359},[886],[888,31361,31362],{"xmlns":890},[892,31363,31364,31422],{},[895,31365,31366,31368,31370,31376,31378,31384,31386,31388,31394,31396,31402,31404,31406,31408,31414,31420],{},[898,31367,8974],{},[1846,31369,1848],{},[2122,31371,31372,31374],{},[898,31373,3783],{},[1979,31375,2128],{},[1846,31377,3025],{},[2122,31379,31380,31382],{},[898,31381,3783],{},[1979,31383,1981],{},[898,31385,16288],{},[1846,31387,1945],{},[2122,31389,31390,31392],{},[898,31391,3783],{},[1979,31393,1981],{},[1846,31395,3025],{},[2122,31397,31398,31400],{},[898,31399,3783],{},[1979,31401,2128],{},[898,31403,16288],{},[1846,31405,1848],{},[1979,31407,1981],{},[2122,31409,31410,31412],{},[898,31411,3783],{},[1979,31413,2128],{},[2122,31415,31416,31418],{},[898,31417,3783],{},[1979,31419,1981],{},[898,31421,16288],{},[902,31423,31424],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,31427,31429],{"className":31428},[886],[888,31430,31431],{"xmlns":890,"display":27911},[892,31432,31433,31476],{},[20599,31434,31435],{"width":27916},[20604,31436,31437,31439,31469,31471],{},[20607,31438],{"width":27921},[20607,31440,31441],{},[895,31442,31443,31445,31447,31467],{},[898,31444,16288],{},[1846,31446,1848],{},[2179,31448,31449,31451],{},[898,31450,8974],{},[895,31452,31453,31455,31461],{},[1979,31454,1981],{},[2122,31456,31457,31459],{},[898,31458,3783],{},[1979,31460,2128],{},[2122,31462,31463,31465],{},[898,31464,3783],{},[1979,31466,1981],{},[898,31468,1734],{"mathvariant":2226},[20607,31470],{"width":27921},[20607,31472,31473],{},[2138,31474,31475],{},"(6.20)",[902,31477,31478],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,31480,31481],{},"Zpětně:",[883,31483,31485],{"className":31484},[886],[888,31486,31487],{"xmlns":890,"display":27911},[892,31488,31489,31566],{},[20599,31490,31491],{"width":27916},[20604,31492,31493,31495,31559,31561],{},[20607,31494],{"width":27921},[20607,31496,31497],{},[12677,31498,31499],{"notation":12679},[2175,31500,31501],{"scriptlevel":2177,"displaystyle":1854},[2175,31502,31503],{"scriptlevel":2177,"displaystyle":1854},[2175,31504,31505],{"scriptlevel":2177,"displaystyle":2135},[895,31506,31507,31509,31515,31517,31531,31533,31535,31541,31543,31557],{},[2138,31508,3830],{},[2122,31510,31511,31513],{},[898,31512,2638],{},[1979,31514,2128],{},[1846,31516,1848],{},[2179,31518,31519,31521],{},[898,31520,8974],{},[895,31522,31523,31525],{},[1979,31524,1981],{},[2122,31526,31527,31529],{},[898,31528,3783],{},[1979,31530,2128],{},[1846,31532,2136],{"separator":2135},[5724,31534],{"width":15129},[2122,31536,31537,31539],{},[898,31538,2638],{},[1979,31540,1981],{},[1846,31542,1848],{},[2179,31544,31545,31547],{},[898,31546,8974],{},[895,31548,31549,31551],{},[1979,31550,1981],{},[2122,31552,31553,31555],{},[898,31554,3783],{},[1979,31556,1981],{},[2138,31558,3830],{},[20607,31560],{"width":27921},[20607,31562,31563],{},[2138,31564,31565],{},"(6.21)",[902,31567,31568],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,31570,31572],{"id":31571},"engelova-funkce","Engelova funkce",[724,31574,9509,31575,31578,31579,31582,31583,19712,31600,1343,31630,31660,31661,31695,31696,1343,31722,31748],{},[38,31576,31577],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,31580,31581],{},"Engelovou funkcí",": pro ",[883,31584,31586],{"className":31585},[886],[888,31587,31588],{"xmlns":890},[892,31589,31590,31598],{},[895,31591,31592,31594,31596],{},[898,31593,8974],{},[1846,31595,1848],{},[1979,31597,2938],{},[902,31599,20164],{"encoding":904},[883,31601,31603],{"className":31602},[886],[888,31604,31605],{"xmlns":890},[892,31606,31607,31627],{},[895,31608,31609,31615,31617,31619,31621],{},[2122,31610,31611,31613],{},[898,31612,2638],{},[1979,31614,2128],{},[1846,31616,1848],{},[1979,31618,2968],{},[898,31620,4520],{"mathvariant":2226},[2122,31622,31623,31625],{},[898,31624,3783],{},[1979,31626,2128],{},[902,31628,31629],{"encoding":904},"Q_1 = 50\u002FP_1",[883,31631,31633],{"className":31632},[886],[888,31634,31635],{"xmlns":890},[892,31636,31637,31657],{},[895,31638,31639,31645,31647,31649,31651],{},[2122,31640,31641,31643],{},[898,31642,2638],{},[1979,31644,1981],{},[1846,31646,1848],{},[1979,31648,2968],{},[898,31650,4520],{"mathvariant":2226},[2122,31652,31653,31655],{},[898,31654,3783],{},[1979,31656,1981],{},[902,31658,31659],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,31662,31664],{"className":31663},[886],[888,31665,31666],{"xmlns":890},[892,31667,31668,31692],{},[895,31669,31670,31676,31678,31680,31682,31688,31690],{},[2122,31671,31672,31674],{},[898,31673,3783],{},[1979,31675,2128],{},[1846,31677,1848],{},[1979,31679,2712],{},[1846,31681,2136],{"separator":2135},[2122,31683,31684,31686],{},[898,31685,3783],{},[1979,31687,1981],{},[1846,31689,1848],{},[1979,31691,8881],{},[902,31693,31694],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,31697,31699],{"className":31698},[886],[888,31700,31701],{"xmlns":890},[892,31702,31703,31719],{},[895,31704,31705,31711,31713,31715,31717],{},[2122,31706,31707,31709],{},[898,31708,2638],{},[1979,31710,2128],{},[1846,31712,1848],{},[898,31714,8974],{},[898,31716,4520],{"mathvariant":2226},[1979,31718,8881],{},[902,31720,31721],{"encoding":904},"Q_1 = Y\u002F20",[883,31723,31725],{"className":31724},[886],[888,31726,31727],{"xmlns":890},[892,31728,31729,31745],{},[895,31730,31731,31737,31739,31741,31743],{},[2122,31732,31733,31735],{},[898,31734,2638],{},[1979,31736,1981],{},[1846,31738,1848],{},[898,31740,8974],{},[898,31742,4520],{"mathvariant":2226},[1979,31744,5057],{},[902,31746,31747],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,31750,31752],{"id":31751},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,31754,31755],{},"Výdaje spotřebitele jsou",[883,31757,31759],{"className":31758},[886],[888,31760,31761],{"xmlns":890,"display":27911},[892,31762,31763,31838],{},[20599,31764,31765],{"width":27916},[20604,31766,31767,31769,31831,31833],{},[20607,31768],{"width":27921},[20607,31770,31771],{},[895,31772,31773,31775,31777,31779,31781,31787,31789,31795,31797,31799,31807,31813,31815,31823,31829],{},[898,31774,4098],{},[1846,31776,1848],{},[898,31778,4098],{},[1846,31780,1855],{"stretchy":1854},[2122,31782,31783,31785],{},[898,31784,2638],{},[1979,31786,2128],{},[1846,31788,2136],{"separator":2135},[2122,31790,31791,31793],{},[898,31792,2638],{},[1979,31794,1981],{},[1846,31796,1861],{"stretchy":1854},[1846,31798,1848],{},[9012,31800,31801,31803,31805],{},[898,31802,3783],{},[1979,31804,2128],{},[1846,31806,4200],{},[2122,31808,31809,31811],{},[898,31810,2638],{},[1979,31812,2128],{},[1846,31814,1945],{},[9012,31816,31817,31819,31821],{},[898,31818,3783],{},[1979,31820,1981],{},[1846,31822,4200],{},[2122,31824,31825,31827],{},[898,31826,2638],{},[1979,31828,1981],{},[1846,31830,2136],{"separator":2135},[20607,31832],{"width":27921},[20607,31834,31835],{},[2138,31836,31837],{},"(6.22)",[902,31839,31840],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,31842,31843],{},"a je pevně zadána hladina užitečnosti",[883,31845,31847],{"className":31846},[886],[888,31848,31849],{"xmlns":890,"display":27911},[892,31850,31851,31898],{},[20599,31852,31853],{"width":27916},[20604,31854,31855,31857,31891,31893],{},[20607,31856],{"width":27921},[20607,31858,31859],{},[895,31860,31861,31867,31869,31871,31873,31879,31881,31887,31889],{},[1974,31862,31863,31865],{},[898,31864,900],{},[1846,31866,4200],{},[1846,31868,1848],{},[898,31870,900],{},[1846,31872,1855],{"stretchy":1854},[2122,31874,31875,31877],{},[898,31876,2638],{},[1979,31878,2128],{},[1846,31880,2136],{"separator":2135},[2122,31882,31883,31885],{},[898,31884,2638],{},[1979,31886,1981],{},[1846,31888,1861],{"stretchy":1854},[898,31890,1734],{"mathvariant":2226},[20607,31892],{"width":27921},[20607,31894,31895],{},[2138,31896,31897],{},"(6.23)",[902,31899,31900],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,31902,31903,31906,31907,31939,31940,1734],{},[38,31904,31905],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,31908,31910],{"className":31909},[886],[888,31911,31912],{"xmlns":890},[892,31913,31914,31936],{},[895,31915,31916,31918,31920,31926,31928,31934],{},[898,31917,4098],{},[1846,31919,1855],{"stretchy":1854},[2122,31921,31922,31924],{},[898,31923,2638],{},[1979,31925,2128],{},[1846,31927,2136],{"separator":2135},[2122,31929,31930,31932],{},[898,31931,2638],{},[1979,31933,1981],{},[1846,31935,1861],{"stretchy":1854},[902,31937,31938],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,31941,31943],{"className":31942},[886],[888,31944,31945],{"xmlns":890},[892,31946,31947,32003],{},[895,31948,31949,31951,31953,31959,31961,31967,31969,31971,31977,31979,31981,31983,31989,31991,31997,31999,32001],{},[898,31950,10887],{},[1846,31952,1855],{"stretchy":1854},[2122,31954,31955,31957],{},[898,31956,2638],{},[1979,31958,2128],{},[1846,31960,2136],{"separator":2135},[2122,31962,31963,31965],{},[898,31964,2638],{},[1979,31966,1981],{},[1846,31968,1861],{"stretchy":1854},[1846,31970,1848],{},[1974,31972,31973,31975],{},[898,31974,900],{},[1846,31976,4200],{},[1846,31978,2075],{},[898,31980,900],{},[1846,31982,1855],{"stretchy":1854},[2122,31984,31985,31987],{},[898,31986,2638],{},[1979,31988,2128],{},[1846,31990,2136],{"separator":2135},[2122,31992,31993,31995],{},[898,31994,2638],{},[1979,31996,1981],{},[1846,31998,1861],{"stretchy":1854},[1846,32000,1848],{},[1979,32002,2177],{},[902,32004,32005],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,32007,32009],{"id":32008},"lagrangeova-funkce","Lagrangeova funkce",[883,32011,32013],{"className":32012},[886],[888,32014,32015],{"xmlns":890,"display":27911},[892,32016,32017,32128],{},[20599,32018,32019],{"width":27916},[20604,32020,32021,32023,32121,32123],{},[20607,32022],{"width":27921},[20607,32024,32025],{},[895,32026,32027,32029,32031,32037,32039,32045,32047,32049,32051,32053,32061,32067,32069,32077,32083,32085,32087,32089,32095,32097,32099,32101,32107,32109,32115,32117,32119],{},[898,32028,9641],{"mathvariant":28393},[1846,32030,1855],{"stretchy":1854},[2122,32032,32033,32035],{},[898,32034,2638],{},[1979,32036,2128],{},[1846,32038,2136],{"separator":2135},[2122,32040,32041,32043],{},[898,32042,2638],{},[1979,32044,1981],{},[1846,32046,2136],{"separator":2135},[898,32048,16288],{},[1846,32050,1861],{"stretchy":1854},[1846,32052,1848],{},[9012,32054,32055,32057,32059],{},[898,32056,3783],{},[1979,32058,2128],{},[1846,32060,4200],{},[2122,32062,32063,32065],{},[898,32064,2638],{},[1979,32066,2128],{},[1846,32068,1945],{},[9012,32070,32071,32073,32075],{},[898,32072,3783],{},[1979,32074,1981],{},[1846,32076,4200],{},[2122,32078,32079,32081],{},[898,32080,2638],{},[1979,32082,1981],{},[1846,32084,1945],{},[898,32086,16288],{},[1846,32088,1855],{"stretchy":1854},[1974,32090,32091,32093],{},[898,32092,900],{},[1846,32094,4200],{},[1846,32096,2075],{},[898,32098,900],{},[1846,32100,1855],{"stretchy":1854},[2122,32102,32103,32105],{},[898,32104,2638],{},[1979,32106,2128],{},[1846,32108,2136],{"separator":2135},[2122,32110,32111,32113],{},[898,32112,2638],{},[1979,32114,1981],{},[1846,32116,1861],{"stretchy":1854},[1846,32118,1861],{"stretchy":1854},[898,32120,1734],{"mathvariant":2226},[20607,32122],{"width":27921},[20607,32124,32125],{},[2138,32126,32127],{},"(6.24)",[902,32129,32130],{"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}",[724,32132,32133],{},"Soustava podmínek prvního řádu:",[883,32135,32137],{"className":32136},[886],[888,32138,32139],{"xmlns":890,"display":27911},[892,32140,32141,32314],{},[20599,32142,32143],{"width":27916},[20604,32144,32145,32147,32307,32309],{},[20607,32146],{"width":27921},[20607,32148,32149],{},[20599,32150,32151,32201,32251],{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},[20604,32152,32153,32165],{},[20607,32154,32155],{},[2175,32156,32157],{"scriptlevel":2177,"displaystyle":2135},[9012,32158,32159,32161,32163],{},[898,32160,9641],{"mathvariant":28393},[1979,32162,2128],{},[1846,32164,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,32166,32167],{},[2175,32168,32169],{"scriptlevel":2177,"displaystyle":2135},[895,32170,32171,32173,32175,32183,32185,32187,32195,32197,32199],{},[895,32172],{},[1846,32174,1848],{},[9012,32176,32177,32179,32181],{},[898,32178,3783],{},[1979,32180,2128],{},[1846,32182,4200],{},[1846,32184,2075],{},[898,32186,16288],{},[9012,32188,32189,32191,32193],{},[898,32190,900],{},[1979,32192,2128],{},[1846,32194,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,32196,1848],{},[1979,32198,2177],{},[1846,32200,2136],{"separator":2135},[20604,32202,32203,32215],{},[20607,32204,32205],{},[2175,32206,32207],{"scriptlevel":2177,"displaystyle":2135},[9012,32208,32209,32211,32213],{},[898,32210,9641],{"mathvariant":28393},[1979,32212,1981],{},[1846,32214,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,32216,32217],{},[2175,32218,32219],{"scriptlevel":2177,"displaystyle":2135},[895,32220,32221,32223,32225,32233,32235,32237,32245,32247,32249],{},[895,32222],{},[1846,32224,1848],{},[9012,32226,32227,32229,32231],{},[898,32228,3783],{},[1979,32230,1981],{},[1846,32232,4200],{},[1846,32234,2075],{},[898,32236,16288],{},[9012,32238,32239,32241,32243],{},[898,32240,900],{},[1979,32242,1981],{},[1846,32244,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,32246,1848],{},[1979,32248,2177],{},[1846,32250,2136],{"separator":2135},[20604,32252,32253,32265],{},[20607,32254,32255],{},[2175,32256,32257],{"scriptlevel":2177,"displaystyle":2135},[9012,32258,32259,32261,32263],{},[898,32260,9641],{"mathvariant":28393},[898,32262,16288],{},[1846,32264,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,32266,32267],{},[2175,32268,32269],{"scriptlevel":2177,"displaystyle":2135},[895,32270,32271,32273,32275,32281,32283,32285,32287,32293,32295,32301,32303,32305],{},[895,32272],{},[1846,32274,1848],{},[1974,32276,32277,32279],{},[898,32278,900],{},[1846,32280,4200],{},[1846,32282,2075],{},[898,32284,900],{},[1846,32286,1855],{"stretchy":1854},[2122,32288,32289,32291],{},[898,32290,2638],{},[1979,32292,2128],{},[1846,32294,2136],{"separator":2135},[2122,32296,32297,32299],{},[898,32298,2638],{},[1979,32300,1981],{},[1846,32302,1861],{"stretchy":1854},[1846,32304,1848],{},[1979,32306,12305],{},[20607,32308],{"width":27921},[20607,32310,32311],{},[2138,32312,32313],{},"(6.25)",[902,32315,32316],{"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}",[724,32318,32319],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,32321,32323],{"className":32322},[886],[888,32324,32325],{"xmlns":890,"display":27911},[892,32326,32327,32425],{},[20599,32328,32329],{"width":27916},[20604,32330,32331,32333,32418,32420],{},[20607,32332],{"width":27921},[20607,32334,32335],{},[895,32336,32337,32339,32341,32347,32349,32355,32357,32359,32361,32363,32365,32367,32416],{},[898,32338,4029],{},[1846,32340,1855],{"stretchy":1854},[2122,32342,32343,32345],{},[898,32344,2638],{},[1979,32346,2128],{},[1846,32348,2136],{"separator":2135},[2122,32350,32351,32353],{},[898,32352,2638],{},[1979,32354,1981],{},[1846,32356,2136],{"separator":2135},[898,32358,16288],{},[1846,32360,1861],{"stretchy":1854},[1846,32362,1848],{},[1846,32364,2075],{},[898,32366,16288],{},[895,32368,32369,32371,32383,32385,32398,32400,32402,32414],{},[1846,32370,1855],{"fence":2135},[9012,32372,32373,32375,32377],{},[898,32374,900],{},[1979,32376,2753],{},[895,32378,32379,32381],{},[1846,32380,2228],{"mathvariant":2226},[1846,32382,2228],{"mathvariant":2226},[1846,32384,1945],{},[9012,32386,32387,32389,32392],{},[898,32388,900],{},[1979,32390,32391],{},"22",[895,32393,32394,32396],{},[1846,32395,2228],{"mathvariant":2226},[1846,32397,2228],{"mathvariant":2226},[1846,32399,1945],{},[1979,32401,1981],{},[9012,32403,32404,32406,32408],{},[898,32405,900],{},[1979,32407,3357],{},[895,32409,32410,32412],{},[1846,32411,2228],{"mathvariant":2226},[1846,32413,2228],{"mathvariant":2226},[1846,32415,1861],{"fence":2135},[898,32417,1734],{"mathvariant":2226},[20607,32419],{"width":27921},[20607,32421,32422],{},[2138,32423,32424],{},"(6.26)",[902,32426,32427],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,32429,32430,32433,32434,32473,32474,32513,32514,32564,32565,32591,32592,32609,32610,32636],{},[38,32431,32432],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,32435,32437],{"className":32436},[886],[888,32438,32439],{"xmlns":890},[892,32440,32441,32471],{},[895,32442,32443,32449,32451,32459,32461,32469],{},[1974,32444,32445,32447],{},[898,32446,2638],{},[1846,32448,4200],{},[1846,32450,2336],{"stretchy":1854},[9012,32452,32453,32455,32457],{},[898,32454,2638],{},[1979,32456,2128],{},[1846,32458,4200],{},[1846,32460,2136],{"separator":2135},[9012,32462,32463,32465,32467],{},[898,32464,2638],{},[1979,32466,1981],{},[1846,32468,4200],{},[1846,32470,2351],{"stretchy":1854},[902,32472,28172],{"encoding":904}," dotyku křivky užitečnosti ",[883,32475,32477],{"className":32476},[886],[888,32478,32479],{"xmlns":890},[892,32480,32481,32511],{},[895,32482,32483,32489,32491,32493,32495,32501,32503,32509],{},[1974,32484,32485,32487],{},[898,32486,900],{},[1846,32488,4200],{},[1846,32490,1848],{},[898,32492,900],{},[1846,32494,1855],{"stretchy":1854},[2122,32496,32497,32499],{},[898,32498,2638],{},[1979,32500,2128],{},[1846,32502,2136],{"separator":2135},[2122,32504,32505,32507],{},[898,32506,2638],{},[1979,32508,1981],{},[1846,32510,1861],{"stretchy":1854},[902,32512,17510],{"encoding":904}," s přímkou výdajů ",[883,32515,32517],{"className":32516},[886],[888,32518,32519],{"xmlns":890},[892,32520,32521,32561],{},[895,32522,32523,32529,32531,32539,32545,32547,32555],{},[1974,32524,32525,32527],{},[898,32526,4098],{},[1846,32528,4200],{},[1846,32530,1848],{},[9012,32532,32533,32535,32537],{},[898,32534,3783],{},[1979,32536,2128],{},[1846,32538,4200],{},[2122,32540,32541,32543],{},[898,32542,2638],{},[1979,32544,2128],{},[1846,32546,1945],{},[9012,32548,32549,32551,32553],{},[898,32550,3783],{},[1979,32552,1981],{},[1846,32554,4200],{},[2122,32556,32557,32559],{},[898,32558,2638],{},[1979,32560,1981],{},[902,32562,32563],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,32566,32568],{"className":32567},[886],[888,32569,32570],{"xmlns":890},[892,32571,32572,32588],{},[895,32573,32574,32580,32582],{},[2122,32575,32576,32578],{},[898,32577,4098],{},[1979,32579,2177],{},[1846,32581,3295],{},[1974,32583,32584,32586],{},[898,32585,4098],{},[1846,32587,4200],{},[902,32589,32590],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,32593,32595],{"className":32594},[886],[888,32596,32597],{"xmlns":890},[892,32598,32599,32607],{},[895,32600,32601],{},[1974,32602,32603,32605],{},[898,32604,900],{},[1846,32606,4200],{},[902,32608,27807],{"encoding":904},", hladina ",[883,32611,32613],{"className":32612},[886],[888,32614,32615],{"xmlns":890},[892,32616,32617,32633],{},[895,32618,32619,32625,32627],{},[2122,32620,32621,32623],{},[898,32622,4098],{},[1979,32624,2128],{},[1846,32626,3256],{},[1974,32628,32629,32631],{},[898,32630,4098],{},[1846,32632,4200],{},[902,32634,32635],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[1639,32638,32639,32644],{},[724,32640,32641,32643],{},[883,32642,4418],{}," Postup — duální úloha (minimalizace výdajů)",[152,32645,32646,32696,32782,32822,32897],{},[123,32647,32648,2053,32651,32695],{},[38,32649,32650],{},"Zapiš vazbu",[883,32652,32654],{"className":32653},[886],[888,32655,32656],{"xmlns":890},[892,32657,32658,32692],{},[895,32659,32660,32666,32668,32670,32672,32678,32680,32686,32688,32690],{},[1974,32661,32662,32664],{},[898,32663,900],{},[1846,32665,4200],{},[1846,32667,2075],{},[898,32669,900],{},[1846,32671,1855],{"stretchy":1854},[2122,32673,32674,32676],{},[898,32675,2638],{},[1979,32677,2128],{},[1846,32679,2136],{"separator":2135},[2122,32681,32682,32684],{},[898,32683,2638],{},[1979,32685,1981],{},[1846,32687,1861],{"stretchy":1854},[1846,32689,1848],{},[1979,32691,2177],{},[902,32693,32694],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,32697,32698,2053,32700,1734],{},[38,32699,29105],{},[883,32701,32703],{"className":32702},[886],[888,32704,32705],{"xmlns":890},[892,32706,32707,32779],{},[895,32708,32709,32711,32713,32721,32727,32729,32737,32743,32745,32747,32749,32755,32757,32759,32761,32767,32769,32775,32777],{},[898,32710,9641],{"mathvariant":28393},[1846,32712,1848],{},[9012,32714,32715,32717,32719],{},[898,32716,3783],{},[1979,32718,2128],{},[1846,32720,4200],{},[2122,32722,32723,32725],{},[898,32724,2638],{},[1979,32726,2128],{},[1846,32728,1945],{},[9012,32730,32731,32733,32735],{},[898,32732,3783],{},[1979,32734,1981],{},[1846,32736,4200],{},[2122,32738,32739,32741],{},[898,32740,2638],{},[1979,32742,1981],{},[1846,32744,1945],{},[898,32746,16288],{},[1846,32748,1855],{"stretchy":1854},[1974,32750,32751,32753],{},[898,32752,900],{},[1846,32754,4200],{},[1846,32756,2075],{},[898,32758,900],{},[1846,32760,1855],{"stretchy":1854},[2122,32762,32763,32765],{},[898,32764,2638],{},[1979,32766,2128],{},[1846,32768,2136],{"separator":2135},[2122,32770,32771,32773],{},[898,32772,2638],{},[1979,32774,1981],{},[1846,32776,1861],{"stretchy":1854},[1846,32778,1861],{"stretchy":1854},[902,32780,32781],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,32783,32784,32787,32788,32821],{},[38,32785,32786],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,32789,32791],{"className":32790},[886],[888,32792,32793],{"xmlns":890},[892,32794,32795,32819],{},[895,32796,32797,32799,32801,32809,32811],{},[2138,32798,10449],{},[1846,32800,1848],{},[9012,32802,32803,32805,32807],{},[898,32804,3783],{},[1979,32806,2128],{},[1846,32808,4200],{},[898,32810,4520],{"mathvariant":2226},[9012,32812,32813,32815,32817],{},[898,32814,3783],{},[1979,32816,1981],{},[1846,32818,4200],{},[902,32820,28824],{"encoding":904}," (stejná jako u maximalizace!).",[123,32823,32824,2053,32827,32867,32868,1734],{},[38,32825,32826],{},"Dosaď do vazby",[883,32828,32830],{"className":32829},[886],[888,32831,32832],{"xmlns":890},[892,32833,32834,32864],{},[895,32835,32836,32838,32840,32846,32848,32854,32856,32858],{},[898,32837,900],{},[1846,32839,1855],{"stretchy":1854},[2122,32841,32842,32844],{},[898,32843,2638],{},[1979,32845,2128],{},[1846,32847,2136],{"separator":2135},[2122,32849,32850,32852],{},[898,32851,2638],{},[1979,32853,1981],{},[1846,32855,1861],{"stretchy":1854},[1846,32857,1848],{},[1974,32859,32860,32862],{},[898,32861,900],{},[1846,32863,4200],{},[902,32865,32866],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,32869,32871],{"className":32870},[886],[888,32872,32873],{"xmlns":890},[892,32874,32875,32895],{},[895,32876,32877,32885,32887],{},[9012,32878,32879,32881,32883],{},[898,32880,2638],{},[1979,32882,2128],{},[1846,32884,4200],{},[1846,32886,2136],{"separator":2135},[9012,32888,32889,32891,32893],{},[898,32890,2638],{},[1979,32892,1981],{},[1846,32894,4200],{},[902,32896,29346],{"encoding":904},[123,32898,32899,2053,32902,32956],{},[38,32900,32901],{},"Vypočítej minimální výdaje",[883,32903,32905],{"className":32904},[886],[888,32906,32907],{"xmlns":890},[892,32908,32909,32953],{},[895,32910,32911,32917,32919,32927,32935,32937,32945],{},[1974,32912,32913,32915],{},[898,32914,4098],{},[1846,32916,4200],{},[1846,32918,1848],{},[9012,32920,32921,32923,32925],{},[898,32922,3783],{},[1979,32924,2128],{},[1846,32926,4200],{},[9012,32928,32929,32931,32933],{},[898,32930,2638],{},[1979,32932,2128],{},[1846,32934,4200],{},[1846,32936,1945],{},[9012,32938,32939,32941,32943],{},[898,32940,3783],{},[1979,32942,1981],{},[1846,32944,4200],{},[9012,32946,32947,32949,32951],{},[898,32948,2638],{},[1979,32950,1981],{},[1846,32952,4200],{},[902,32954,32955],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,32958,32960,32961],{"id":32959},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,32962,32964],{"className":32963},[886],[888,32965,32966],{"xmlns":890},[892,32967,32968,33002],{},[895,32969,32970,32972,32974,32988],{},[898,32971,900],{},[1846,32973,1848],{},[9012,32975,32976,32978,32980],{},[898,32977,2638],{},[1979,32979,2128],{},[895,32981,32982,32984,32986],{},[1979,32983,2128],{},[898,32985,4520],{"mathvariant":2226},[1979,32987,1981],{},[9012,32989,32990,32992,32994],{},[898,32991,2638],{},[1979,32993,1981],{},[895,32995,32996,32998,33000],{},[1979,32997,2128],{},[898,32999,4520],{"mathvariant":2226},[1979,33001,1981],{},[902,33003,33004],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,33006,33007,33008,1343,33030,1343,33054,30191],{},"Dáno ",[883,33009,33011],{"className":33010},[886],[888,33012,33013],{"xmlns":890},[892,33014,33015,33027],{},[895,33016,33017,33023,33025],{},[1974,33018,33019,33021],{},[898,33020,900],{},[1846,33022,4200],{},[1846,33024,1848],{},[1979,33026,1981],{},[902,33028,33029],{"encoding":904},"U^* = 2",[883,33031,33033],{"className":33032},[886],[888,33034,33035],{"xmlns":890},[892,33036,33037,33051],{},[895,33038,33039,33047,33049],{},[9012,33040,33041,33043,33045],{},[898,33042,3783],{},[1979,33044,2128],{},[1846,33046,4200],{},[1846,33048,1848],{},[1979,33050,23634],{},[902,33052,33053],{"encoding":904},"P_1^* = 0{,}25",[883,33055,33057],{"className":33056},[886],[888,33058,33059],{"xmlns":890},[892,33060,33061,33075],{},[895,33062,33063,33071,33073],{},[9012,33064,33065,33067,33069],{},[898,33066,3783],{},[1979,33068,1981],{},[1846,33070,4200],{},[1846,33072,1848],{},[1979,33074,2128],{},[902,33076,33077],{"encoding":904},"P_2^* = 1",[883,33079,33081],{"className":33080},[886],[888,33082,33083],{"xmlns":890,"display":27911},[892,33084,33085,33149],{},[895,33086,33087,33089,33091,33093,33099,33101,33107,33109,33111,33113,33115,33117,33131,33145,33147],{},[898,33088,9641],{"mathvariant":28393},[1846,33090,1848],{},[1979,33092,23634],{},[2122,33094,33095,33097],{},[898,33096,2638],{},[1979,33098,2128],{},[1846,33100,1945],{},[2122,33102,33103,33105],{},[898,33104,2638],{},[1979,33106,1981],{},[1846,33108,1945],{},[898,33110,16288],{},[1846,33112,1855],{"stretchy":1854},[1979,33114,1981],{},[1846,33116,2075],{},[9012,33118,33119,33121,33123],{},[898,33120,2638],{},[1979,33122,2128],{},[895,33124,33125,33127,33129],{},[1979,33126,2128],{},[898,33128,4520],{"mathvariant":2226},[1979,33130,1981],{},[9012,33132,33133,33135,33137],{},[898,33134,2638],{},[1979,33136,1981],{},[895,33138,33139,33141,33143],{},[1979,33140,2128],{},[898,33142,4520],{"mathvariant":2226},[1979,33144,1981],{},[1846,33146,1861],{"stretchy":1854},[898,33148,1734],{"mathvariant":2226},[902,33150,33151],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,33153,30276],{},[883,33155,33157],{"className":33156},[886],[888,33158,33159],{"xmlns":890,"display":27911},[892,33160,33161,33375],{},[20599,33162,33163,33239,33315],{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},[20604,33164,33165,33177],{},[20607,33166,33167],{},[2175,33168,33169],{"scriptlevel":2177,"displaystyle":2135},[9012,33170,33171,33173,33175],{},[898,33172,9641],{"mathvariant":28393},[1979,33174,2128],{},[1846,33176,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,33178,33179],{},[2175,33180,33181],{"scriptlevel":2177,"displaystyle":2135},[895,33182,33183,33185,33187,33189,33191,33193,33195,33203,33219,33233,33235,33237],{},[895,33184],{},[1846,33186,1848],{},[1979,33188,23634],{},[1846,33190,2075],{},[898,33192,16288],{},[1846,33194,3025],{},[2175,33196,33197],{"scriptlevel":2177,"displaystyle":1854},[2179,33198,33199,33201],{},[1979,33200,2128],{},[1979,33202,1981],{},[9012,33204,33205,33207,33209],{},[898,33206,2638],{},[1979,33208,2128],{},[895,33210,33211,33213,33215,33217],{},[1846,33212,2075],{},[1979,33214,2128],{},[898,33216,4520],{"mathvariant":2226},[1979,33218,1981],{},[9012,33220,33221,33223,33225],{},[898,33222,2638],{},[1979,33224,1981],{},[895,33226,33227,33229,33231],{},[1979,33228,2128],{},[898,33230,4520],{"mathvariant":2226},[1979,33232,1981],{},[1846,33234,1848],{},[1979,33236,2177],{},[1846,33238,2136],{"separator":2135},[20604,33240,33241,33253],{},[20607,33242,33243],{},[2175,33244,33245],{"scriptlevel":2177,"displaystyle":2135},[9012,33246,33247,33249,33251],{},[898,33248,9641],{"mathvariant":28393},[1979,33250,1981],{},[1846,33252,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,33254,33255],{},[2175,33256,33257],{"scriptlevel":2177,"displaystyle":2135},[895,33258,33259,33261,33263,33265,33267,33269,33271,33279,33293,33309,33311,33313],{},[895,33260],{},[1846,33262,1848],{},[1979,33264,2128],{},[1846,33266,2075],{},[898,33268,16288],{},[1846,33270,3025],{},[2175,33272,33273],{"scriptlevel":2177,"displaystyle":1854},[2179,33274,33275,33277],{},[1979,33276,2128],{},[1979,33278,1981],{},[9012,33280,33281,33283,33285],{},[898,33282,2638],{},[1979,33284,2128],{},[895,33286,33287,33289,33291],{},[1979,33288,2128],{},[898,33290,4520],{"mathvariant":2226},[1979,33292,1981],{},[9012,33294,33295,33297,33299],{},[898,33296,2638],{},[1979,33298,1981],{},[895,33300,33301,33303,33305,33307],{},[1846,33302,2075],{},[1979,33304,2128],{},[898,33306,4520],{"mathvariant":2226},[1979,33308,1981],{},[1846,33310,1848],{},[1979,33312,2177],{},[1846,33314,2136],{"separator":2135},[20604,33316,33317,33329],{},[20607,33318,33319],{},[2175,33320,33321],{"scriptlevel":2177,"displaystyle":2135},[9012,33322,33323,33325,33327],{},[898,33324,9641],{"mathvariant":28393},[898,33326,16288],{},[1846,33328,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,33330,33331],{},[2175,33332,33333],{"scriptlevel":2177,"displaystyle":2135},[895,33334,33335,33337,33339,33341,33343,33357,33371,33373],{},[895,33336],{},[1846,33338,1848],{},[1979,33340,1981],{},[1846,33342,2075],{},[9012,33344,33345,33347,33349],{},[898,33346,2638],{},[1979,33348,2128],{},[895,33350,33351,33353,33355],{},[1979,33352,2128],{},[898,33354,4520],{"mathvariant":2226},[1979,33356,1981],{},[9012,33358,33359,33361,33363],{},[898,33360,2638],{},[1979,33362,1981],{},[895,33364,33365,33367,33369],{},[1979,33366,2128],{},[898,33368,4520],{"mathvariant":2226},[1979,33370,1981],{},[1846,33372,1848],{},[1979,33374,12305],{},[902,33376,33377],{"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}",[724,33379,33380,33381,17421,33411,33439,33440,5435,33502,1343,33552,33574,33575,1734],{},"Podílem prvních dvou rovnic: ",[883,33382,33384],{"className":33383},[886],[888,33385,33386],{"xmlns":890},[892,33387,33388,33408],{},[895,33389,33390,33392,33394,33400,33402],{},[1979,33391,23634],{},[1846,33393,1848],{},[2122,33395,33396,33398],{},[898,33397,2638],{},[1979,33399,1981],{},[898,33401,4520],{"mathvariant":2226},[2122,33403,33404,33406],{},[898,33405,2638],{},[1979,33407,2128],{},[902,33409,33410],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,33412,33414],{"className":33413},[886],[888,33415,33416],{"xmlns":890},[892,33417,33418,33436],{},[895,33419,33420,33426,33428,33430],{},[2122,33421,33422,33424],{},[898,33423,2638],{},[1979,33425,1981],{},[1846,33427,1848],{},[1979,33429,23634],{},[2122,33431,33432,33434],{},[898,33433,2638],{},[1979,33435,2128],{},[902,33437,33438],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,33441,33443],{"className":33442},[886],[888,33444,33445],{"xmlns":890},[892,33446,33447,33499],{},[895,33448,33449,33463,33465,33467,33473,33485,33487,33489,33495,33497],{},[9012,33450,33451,33453,33455],{},[898,33452,2638],{},[1979,33454,2128],{},[895,33456,33457,33459,33461],{},[1979,33458,2128],{},[898,33460,4520],{"mathvariant":2226},[1979,33462,1981],{},[1846,33464,1855],{"stretchy":1854},[1979,33466,23634],{},[2122,33468,33469,33471],{},[898,33470,2638],{},[1979,33472,2128],{},[1974,33474,33475,33477],{},[1846,33476,1861],{"stretchy":1854},[895,33478,33479,33481,33483],{},[1979,33480,2128],{},[898,33482,4520],{"mathvariant":2226},[1979,33484,1981],{},[1846,33486,1848],{},[1979,33488,4855],{},[2122,33490,33491,33493],{},[898,33492,2638],{},[1979,33494,2128],{},[1846,33496,1848],{},[1979,33498,1981],{},[902,33500,33501],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,33503,33504,1343,33528],{},[883,33505,33507],{"className":33506},[886],[888,33508,33509],{"xmlns":890},[892,33510,33511,33525],{},[895,33512,33513,33521,33523],{},[9012,33514,33515,33517,33519],{},[898,33516,2638],{},[1979,33518,2128],{},[1846,33520,4200],{},[1846,33522,1848],{},[1979,33524,2201],{},[902,33526,33527],{"encoding":904},"Q_1^* = 4",[883,33529,33531],{"className":33530},[886],[888,33532,33533],{"xmlns":890},[892,33534,33535,33549],{},[895,33536,33537,33545,33547],{},[9012,33538,33539,33541,33543],{},[898,33540,2638],{},[1979,33542,1981],{},[1846,33544,4200],{},[1846,33546,1848],{},[1979,33548,2128],{},[902,33550,33551],{"encoding":904},"Q_2^* = 1",[883,33553,33555],{"className":33554},[886],[888,33556,33557],{"xmlns":890},[892,33558,33559,33571],{},[895,33560,33561,33567,33569],{},[1974,33562,33563,33565],{},[898,33564,16288],{},[1846,33566,4200],{},[1846,33568,1848],{},[1979,33570,2128],{},[902,33572,33573],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,33576,33578],{"className":33577},[886],[888,33579,33580],{"xmlns":890},[892,33581,33582,33610],{},[895,33583,33584,33590,33592,33594,33596,33598,33600,33602,33604,33606,33608],{},[1974,33585,33586,33588],{},[898,33587,4098],{},[1846,33589,4200],{},[1846,33591,1848],{},[1979,33593,23634],{},[1846,33595,3025],{},[1979,33597,2201],{},[1846,33599,1945],{},[1979,33601,2128],{},[1846,33603,3025],{},[1979,33605,2128],{},[1846,33607,1848],{},[1979,33609,1981],{},[902,33611,33612],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,33614,33615,33618,33619,1343,33685,1343,33751,33817,33818,33855,33856,33878,33879,1734],{},[614,33616,33617],{},"Ověření postačující podmínky"," (6.26): ",[883,33620,33622],{"className":33621},[886],[888,33623,33624],{"xmlns":890},[892,33625,33626,33682],{},[895,33627,33628,33640,33642,33644,33652,33668],{},[9012,33629,33630,33632,33634],{},[898,33631,900],{},[1979,33633,2753],{},[895,33635,33636,33638],{},[1846,33637,2228],{"mathvariant":2226},[1846,33639,2228],{"mathvariant":2226},[1846,33641,1848],{},[1846,33643,2075],{},[2175,33645,33646],{"scriptlevel":2177,"displaystyle":1854},[2179,33647,33648,33650],{},[1979,33649,2128],{},[1979,33651,2201],{},[9012,33653,33654,33656,33658],{},[898,33655,2638],{},[1979,33657,2128],{},[895,33659,33660,33662,33664,33666],{},[1846,33661,2075],{},[1979,33663,2023],{},[898,33665,4520],{"mathvariant":2226},[1979,33667,1981],{},[9012,33669,33670,33672,33674],{},[898,33671,2638],{},[1979,33673,1981],{},[895,33675,33676,33678,33680],{},[1979,33677,2128],{},[898,33679,4520],{"mathvariant":2226},[1979,33681,1981],{},[902,33683,33684],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,33686,33688],{"className":33687},[886],[888,33689,33690],{"xmlns":890},[892,33691,33692,33748],{},[895,33693,33694,33706,33708,33710,33718,33732],{},[9012,33695,33696,33698,33700],{},[898,33697,900],{},[1979,33699,32391],{},[895,33701,33702,33704],{},[1846,33703,2228],{"mathvariant":2226},[1846,33705,2228],{"mathvariant":2226},[1846,33707,1848],{},[1846,33709,2075],{},[2175,33711,33712],{"scriptlevel":2177,"displaystyle":1854},[2179,33713,33714,33716],{},[1979,33715,2128],{},[1979,33717,2201],{},[9012,33719,33720,33722,33724],{},[898,33721,2638],{},[1979,33723,2128],{},[895,33725,33726,33728,33730],{},[1979,33727,2128],{},[898,33729,4520],{"mathvariant":2226},[1979,33731,1981],{},[9012,33733,33734,33736,33738],{},[898,33735,2638],{},[1979,33737,1981],{},[895,33739,33740,33742,33744,33746],{},[1846,33741,2075],{},[1979,33743,2023],{},[898,33745,4520],{"mathvariant":2226},[1979,33747,1981],{},[902,33749,33750],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,33752,33754],{"className":33753},[886],[888,33755,33756],{"xmlns":890},[892,33757,33758,33814],{},[895,33759,33760,33772,33774,33782,33798],{},[9012,33761,33762,33764,33766],{},[898,33763,900],{},[1979,33765,3357],{},[895,33767,33768,33770],{},[1846,33769,2228],{"mathvariant":2226},[1846,33771,2228],{"mathvariant":2226},[1846,33773,1848],{},[2175,33775,33776],{"scriptlevel":2177,"displaystyle":1854},[2179,33777,33778,33780],{},[1979,33779,2128],{},[1979,33781,2201],{},[9012,33783,33784,33786,33788],{},[898,33785,2638],{},[1979,33787,2128],{},[895,33789,33790,33792,33794,33796],{},[1846,33791,2075],{},[1979,33793,2128],{},[898,33795,4520],{"mathvariant":2226},[1979,33797,1981],{},[9012,33799,33800,33802,33804],{},[898,33801,2638],{},[1979,33803,1981],{},[895,33805,33806,33808,33810,33812],{},[1846,33807,2075],{},[1979,33809,2128],{},[898,33811,4520],{"mathvariant":2226},[1979,33813,1981],{},[902,33815,33816],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,33819,33821],{"className":33820},[886],[888,33822,33823],{"xmlns":890},[892,33824,33825,33852],{},[895,33826,33827,33829,33831,33833,33835,33837,33839,33841,33843,33845,33848,33850],{},[898,33828,4029],{},[1846,33830,1855],{"stretchy":1854},[1979,33832,2201],{},[1846,33834,2136],{"separator":2135},[1979,33836,2128],{},[1846,33838,2136],{"separator":2135},[1979,33840,2128],{},[1846,33842,1861],{"stretchy":1854},[1846,33844,1848],{},[1979,33846,33847],{},"0,28125",[1846,33849,3256],{},[1979,33851,2177],{},[902,33853,33854],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,33857,33859],{"className":33858},[886],[888,33860,33861],{"xmlns":890},[892,33862,33863,33875],{},[895,33864,33865,33867,33869,33871,33873],{},[1846,33866,2336],{"stretchy":1854},[1979,33868,2201],{},[1846,33870,2136],{"separator":2135},[1979,33872,2128],{},[1846,33874,2351],{"stretchy":1854},[902,33876,33877],{"encoding":904},"[4, 1]"," je vázané ",[38,33880,3623],{},[115,33882,33884],{"id":33883},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,33886,33887],{},"Obecně:",[883,33889,33891],{"className":33890},[886],[888,33892,33893],{"xmlns":890,"display":27911},[892,33894,33895,33990],{},[20599,33896,33897],{"width":27916},[20604,33898,33899,33901,33983,33985],{},[20607,33900],{"width":27921},[20607,33902,33903],{},[895,33904,33905,33911,33913,33919,33921,33927,33929,33935,33937,33939,33941,33943,33945,33951,33953,33959,33961,33967,33969,33975,33977,33979,33981],{},[2122,33906,33907,33909],{},[898,33908,2638],{},[1979,33910,2128],{},[1846,33912,1848],{},[2122,33914,33915,33917],{},[898,33916,4029],{},[1979,33918,2128],{},[1846,33920,1855],{"stretchy":1854},[2122,33922,33923,33925],{},[898,33924,3783],{},[1979,33926,2128],{},[1846,33928,2136],{"separator":2135},[2122,33930,33931,33933],{},[898,33932,3783],{},[1979,33934,1981],{},[1846,33936,2136],{"separator":2135},[898,33938,900],{},[1846,33940,1861],{"stretchy":1854},[1846,33942,2136],{"separator":2135},[5724,33944],{"width":15129},[2122,33946,33947,33949],{},[898,33948,2638],{},[1979,33950,1981],{},[1846,33952,1848],{},[2122,33954,33955,33957],{},[898,33956,4029],{},[1979,33958,1981],{},[1846,33960,1855],{"stretchy":1854},[2122,33962,33963,33965],{},[898,33964,3783],{},[1979,33966,2128],{},[1846,33968,2136],{"separator":2135},[2122,33970,33971,33973],{},[898,33972,3783],{},[1979,33974,1981],{},[1846,33976,2136],{"separator":2135},[898,33978,900],{},[1846,33980,1861],{"stretchy":1854},[1846,33982,2136],{"separator":2135},[20607,33984],{"width":27921},[20607,33986,33987],{},[2138,33988,33989],{},"(6.27)",[902,33991,33992],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,33994,33996],{"className":33995},[886],[888,33997,33998],{"xmlns":890,"display":27911},[892,33999,34000,34047],{},[20599,34001,34002],{"width":27916},[20604,34003,34004,34006,34040,34042],{},[20607,34005],{"width":27921},[20607,34007,34008],{},[895,34009,34010,34012,34014,34016,34018,34024,34026,34032,34034,34036,34038],{},[898,34011,16288],{},[1846,34013,1848],{},[898,34015,16288],{},[1846,34017,1855],{"stretchy":1854},[2122,34019,34020,34022],{},[898,34021,3783],{},[1979,34023,2128],{},[1846,34025,2136],{"separator":2135},[2122,34027,34028,34030],{},[898,34029,3783],{},[1979,34031,1981],{},[1846,34033,2136],{"separator":2135},[898,34035,900],{},[1846,34037,1861],{"stretchy":1854},[898,34039,1734],{"mathvariant":2226},[20607,34041],{"width":27921},[20607,34043,34044],{},[2138,34045,34046],{},"(6.28)",[902,34048,34049],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,34051,34052,34053,2053,34056,34069,34070,34083],{},"Hicksova poptávka závisí na ",[38,34054,34055],{},"hladině užitečnosti",[883,34057,34059],{"className":34058},[886],[888,34060,34061],{"xmlns":890},[892,34062,34063,34067],{},[895,34064,34065],{},[898,34066,900],{},[902,34068,900],{"encoding":904}," (nikoli na důchodu ",[883,34071,34073],{"className":34072},[886],[888,34074,34075],{"xmlns":890},[892,34076,34077,34081],{},[895,34078,34079],{},[898,34080,8974],{},[902,34082,8974],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,34085,34087,34088],{"id":34086},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,34089,34091],{"className":34090},[886],[888,34092,34093],{"xmlns":890},[892,34094,34095,34129],{},[895,34096,34097,34099,34101,34115],{},[898,34098,900],{},[1846,34100,1848],{},[9012,34102,34103,34105,34107],{},[898,34104,2638],{},[1979,34106,2128],{},[895,34108,34109,34111,34113],{},[1979,34110,2128],{},[898,34112,4520],{"mathvariant":2226},[1979,34114,1981],{},[9012,34116,34117,34119,34121],{},[898,34118,2638],{},[1979,34120,1981],{},[895,34122,34123,34125,34127],{},[1979,34124,2128],{},[898,34126,4520],{"mathvariant":2226},[1979,34128,1981],{},[902,34130,33004],{"encoding":904},[724,34132,34133,34163],{},[883,34134,34136],{"className":34135},[886],[888,34137,34138],{"xmlns":890},[892,34139,34140,34160],{},[895,34141,34142,34148,34150,34156,34158],{},[2122,34143,34144,34146],{},[898,34145,3783],{},[1979,34147,2128],{},[1846,34149,2136],{"separator":2135},[2122,34151,34152,34154],{},[898,34153,3783],{},[1979,34155,1981],{},[1846,34157,2136],{"separator":2135},[898,34159,900],{},[902,34161,34162],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,34165,34167],{"className":34166},[886],[888,34168,34169],{"xmlns":890,"display":27911},[892,34170,34171,34245],{},[895,34172,34173,34175,34177,34183,34189,34191,34197,34203,34205,34207,34209,34211,34213,34227,34241,34243],{},[898,34174,9641],{"mathvariant":28393},[1846,34176,1848],{},[2122,34178,34179,34181],{},[898,34180,3783],{},[1979,34182,2128],{},[2122,34184,34185,34187],{},[898,34186,2638],{},[1979,34188,2128],{},[1846,34190,1945],{},[2122,34192,34193,34195],{},[898,34194,3783],{},[1979,34196,1981],{},[2122,34198,34199,34201],{},[898,34200,2638],{},[1979,34202,1981],{},[1846,34204,1945],{},[898,34206,16288],{},[1846,34208,1855],{"stretchy":1854},[898,34210,900],{},[1846,34212,2075],{},[9012,34214,34215,34217,34219],{},[898,34216,2638],{},[1979,34218,2128],{},[895,34220,34221,34223,34225],{},[1979,34222,2128],{},[898,34224,4520],{"mathvariant":2226},[1979,34226,1981],{},[9012,34228,34229,34231,34233],{},[898,34230,2638],{},[1979,34232,1981],{},[895,34234,34235,34237,34239],{},[1979,34236,2128],{},[898,34238,4520],{"mathvariant":2226},[1979,34240,1981],{},[1846,34242,1861],{"stretchy":1854},[898,34244,1734],{"mathvariant":2226},[902,34246,34247],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,34249,30276],{},[883,34251,34253],{"className":34252},[886],[888,34254,34255],{"xmlns":890,"display":27911},[892,34256,34257,34479],{},[20599,34258,34259,34339,34419],{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},[20604,34260,34261,34273],{},[20607,34262,34263],{},[2175,34264,34265],{"scriptlevel":2177,"displaystyle":2135},[9012,34266,34267,34269,34271],{},[898,34268,9641],{"mathvariant":28393},[1979,34270,2128],{},[1846,34272,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,34274,34275],{},[2175,34276,34277],{"scriptlevel":2177,"displaystyle":2135},[895,34278,34279,34281,34283,34289,34291,34293,34295,34303,34319,34333,34335,34337],{},[895,34280],{},[1846,34282,1848],{},[2122,34284,34285,34287],{},[898,34286,3783],{},[1979,34288,2128],{},[1846,34290,2075],{},[898,34292,16288],{},[1846,34294,3025],{},[2175,34296,34297],{"scriptlevel":2177,"displaystyle":1854},[2179,34298,34299,34301],{},[1979,34300,2128],{},[1979,34302,1981],{},[9012,34304,34305,34307,34309],{},[898,34306,2638],{},[1979,34308,2128],{},[895,34310,34311,34313,34315,34317],{},[1846,34312,2075],{},[1979,34314,2128],{},[898,34316,4520],{"mathvariant":2226},[1979,34318,1981],{},[9012,34320,34321,34323,34325],{},[898,34322,2638],{},[1979,34324,1981],{},[895,34326,34327,34329,34331],{},[1979,34328,2128],{},[898,34330,4520],{"mathvariant":2226},[1979,34332,1981],{},[1846,34334,1848],{},[1979,34336,2177],{},[1846,34338,2136],{"separator":2135},[20604,34340,34341,34353],{},[20607,34342,34343],{},[2175,34344,34345],{"scriptlevel":2177,"displaystyle":2135},[9012,34346,34347,34349,34351],{},[898,34348,9641],{"mathvariant":28393},[1979,34350,1981],{},[1846,34352,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,34354,34355],{},[2175,34356,34357],{"scriptlevel":2177,"displaystyle":2135},[895,34358,34359,34361,34363,34369,34371,34373,34375,34383,34397,34413,34415,34417],{},[895,34360],{},[1846,34362,1848],{},[2122,34364,34365,34367],{},[898,34366,3783],{},[1979,34368,1981],{},[1846,34370,2075],{},[898,34372,16288],{},[1846,34374,3025],{},[2175,34376,34377],{"scriptlevel":2177,"displaystyle":1854},[2179,34378,34379,34381],{},[1979,34380,2128],{},[1979,34382,1981],{},[9012,34384,34385,34387,34389],{},[898,34386,2638],{},[1979,34388,2128],{},[895,34390,34391,34393,34395],{},[1979,34392,2128],{},[898,34394,4520],{"mathvariant":2226},[1979,34396,1981],{},[9012,34398,34399,34401,34403],{},[898,34400,2638],{},[1979,34402,1981],{},[895,34404,34405,34407,34409,34411],{},[1846,34406,2075],{},[1979,34408,2128],{},[898,34410,4520],{"mathvariant":2226},[1979,34412,1981],{},[1846,34414,1848],{},[1979,34416,2177],{},[1846,34418,2136],{"separator":2135},[20604,34420,34421,34433],{},[20607,34422,34423],{},[2175,34424,34425],{"scriptlevel":2177,"displaystyle":2135},[9012,34426,34427,34429,34431],{},[898,34428,9641],{"mathvariant":28393},[898,34430,16288],{},[1846,34432,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[20607,34434,34435],{},[2175,34436,34437],{"scriptlevel":2177,"displaystyle":2135},[895,34438,34439,34441,34443,34445,34447,34461,34475,34477],{},[895,34440],{},[1846,34442,1848],{},[898,34444,900],{},[1846,34446,2075],{},[9012,34448,34449,34451,34453],{},[898,34450,2638],{},[1979,34452,2128],{},[895,34454,34455,34457,34459],{},[1979,34456,2128],{},[898,34458,4520],{"mathvariant":2226},[1979,34460,1981],{},[9012,34462,34463,34465,34467],{},[898,34464,2638],{},[1979,34466,1981],{},[895,34468,34469,34471,34473],{},[1979,34470,2128],{},[898,34472,4520],{"mathvariant":2226},[1979,34474,1981],{},[1846,34476,1848],{},[1979,34478,12305],{},[902,34480,34481],{"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}",[724,34483,34484,34485,34555,34556,34614],{},"Podílem rovnic: ",[883,34486,34488],{"className":34487},[886],[888,34489,34490],{"xmlns":890},[892,34491,34492,34552],{},[895,34493,34494,34500,34502,34508,34510,34516,34518,34524,34526,34532,34538,34540,34546],{},[2122,34495,34496,34498],{},[898,34497,3783],{},[1979,34499,2128],{},[898,34501,4520],{"mathvariant":2226},[2122,34503,34504,34506],{},[898,34505,3783],{},[1979,34507,1981],{},[1846,34509,1848],{},[2122,34511,34512,34514],{},[898,34513,2638],{},[1979,34515,1981],{},[898,34517,4520],{"mathvariant":2226},[2122,34519,34520,34522],{},[898,34521,2638],{},[1979,34523,2128],{},[1846,34525,3833],{},[2122,34527,34528,34530],{},[898,34529,3783],{},[1979,34531,2128],{},[2122,34533,34534,34536],{},[898,34535,2638],{},[1979,34537,2128],{},[1846,34539,1848],{},[2122,34541,34542,34544],{},[898,34543,3783],{},[1979,34545,1981],{},[2122,34547,34548,34550],{},[898,34549,2638],{},[1979,34551,1981],{},[902,34553,34554],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,34557,34559],{"className":34558},[886],[888,34560,34561],{"xmlns":890},[892,34562,34563,34611],{},[895,34564,34565,34567,34569,34575,34581,34583,34589,34595,34597,34599,34605],{},[898,34566,4098],{},[1846,34568,1848],{},[2122,34570,34571,34573],{},[898,34572,3783],{},[1979,34574,2128],{},[2122,34576,34577,34579],{},[898,34578,2638],{},[1979,34580,2128],{},[1846,34582,1945],{},[2122,34584,34585,34587],{},[898,34586,3783],{},[1979,34588,1981],{},[2122,34590,34591,34593],{},[898,34592,2638],{},[1979,34594,1981],{},[1846,34596,1848],{},[1979,34598,1981],{},[2122,34600,34601,34603],{},[898,34602,3783],{},[1979,34604,2128],{},[2122,34606,34607,34609],{},[898,34608,2638],{},[1979,34610,2128],{},[902,34612,34613],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,34616,34618],{"className":34617},[886],[888,34619,34620],{"xmlns":890,"display":27911},[892,34621,34622,34689],{},[20599,34623,34624],{"width":27916},[20604,34625,34626,34628,34682,34684],{},[20607,34627],{"width":27921},[20607,34629,34630],{},[895,34631,34632,34638,34640,34654,34656,34658,34664,34666,34680],{},[2122,34633,34634,34636],{},[898,34635,2638],{},[1979,34637,2128],{},[1846,34639,1848],{},[2179,34641,34642,34644],{},[898,34643,4098],{},[895,34645,34646,34648],{},[1979,34647,1981],{},[2122,34649,34650,34652],{},[898,34651,3783],{},[1979,34653,2128],{},[1846,34655,2136],{"separator":2135},[5724,34657],{"width":15129},[2122,34659,34660,34662],{},[898,34661,2638],{},[1979,34663,1981],{},[1846,34665,1848],{},[2179,34667,34668,34670],{},[898,34669,4098],{},[895,34671,34672,34674],{},[1979,34673,1981],{},[2122,34675,34676,34678],{},[898,34677,3783],{},[1979,34679,1981],{},[898,34681,1734],{"mathvariant":2226},[20607,34683],{"width":27921},[20607,34685,34686],{},[2138,34687,34688],{},"(6.29)",[902,34690,34691],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,34693,34694,34695,17421,34777,34813],{},"Ze třetí rovnice ",[883,34696,34698],{"className":34697},[886],[888,34699,34700],{"xmlns":890},[892,34701,34702,34774],{},[895,34703,34704,34706,34708,34746,34748],{},[898,34705,900],{},[1846,34707,1848],{},[7963,34709,34710],{},[895,34711,34712,34728,34730],{},[2175,34713,34714],{"scriptlevel":2177,"displaystyle":1854},[2179,34715,34716,34718],{},[898,34717,4098],{},[895,34719,34720,34722],{},[1979,34721,1981],{},[2122,34723,34724,34726],{},[898,34725,3783],{},[1979,34727,2128],{},[1846,34729,3025],{},[2175,34731,34732],{"scriptlevel":2177,"displaystyle":1854},[2179,34733,34734,34736],{},[898,34735,4098],{},[895,34737,34738,34740],{},[1979,34739,1981],{},[2122,34741,34742,34744],{},[898,34743,3783],{},[1979,34745,1981],{},[1846,34747,1848],{},[2175,34749,34750],{"scriptlevel":2177,"displaystyle":1854},[2179,34751,34752,34754],{},[898,34753,4098],{},[895,34755,34756,34758],{},[1979,34757,1981],{},[7963,34759,34760],{},[895,34761,34762,34768],{},[2122,34763,34764,34766],{},[898,34765,3783],{},[1979,34767,2128],{},[2122,34769,34770,34772],{},[898,34771,3783],{},[1979,34773,1981],{},[902,34775,34776],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,34778,34780],{"className":34779},[886],[888,34781,34782],{"xmlns":890},[892,34783,34784,34810],{},[895,34785,34786,34788,34790,34792,34794],{},[898,34787,4098],{},[1846,34789,1848],{},[1979,34791,1981],{},[898,34793,900],{},[7963,34795,34796],{},[895,34797,34798,34804],{},[2122,34799,34800,34802],{},[898,34801,3783],{},[1979,34803,2128],{},[2122,34805,34806,34808],{},[898,34807,3783],{},[1979,34809,1981],{},[902,34811,34812],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,34815,34817],{"className":34816},[886],[888,34818,34819],{"xmlns":890,"display":27911},[892,34820,34821,34966],{},[20599,34822,34823],{"width":27916},[20604,34824,34825,34827,34959,34961],{},[20607,34826],{"width":27921},[20607,34828,34829],{},[12677,34830,34831],{"notation":12679},[2175,34832,34833],{"scriptlevel":2177,"displaystyle":1854},[2175,34834,34835],{"scriptlevel":2177,"displaystyle":1854},[2175,34836,34837],{"scriptlevel":2177,"displaystyle":2135},[895,34838,34839,34841,34847,34849,34851,34867,34869,34875,34877,34883,34885,34891,34893,34895,34897,34899,34901,34907,34909,34911,34927,34929,34935,34937,34943,34945,34951,34953,34955,34957],{},[2138,34840,3830],{},[2122,34842,34843,34845],{},[898,34844,2638],{},[1979,34846,2128],{},[1846,34848,1848],{},[898,34850,900],{},[7963,34852,34853],{},[2179,34854,34855,34861],{},[2122,34856,34857,34859],{},[898,34858,3783],{},[1979,34860,1981],{},[2122,34862,34863,34865],{},[898,34864,3783],{},[1979,34866,2128],{},[1846,34868,1848],{},[2122,34870,34871,34873],{},[898,34872,4029],{},[1979,34874,2128],{},[1846,34876,1855],{"stretchy":1854},[2122,34878,34879,34881],{},[898,34880,3783],{},[1979,34882,2128],{},[1846,34884,2136],{"separator":2135},[2122,34886,34887,34889],{},[898,34888,3783],{},[1979,34890,1981],{},[1846,34892,2136],{"separator":2135},[898,34894,900],{},[1846,34896,1861],{"stretchy":1854},[1846,34898,2136],{"separator":2135},[5724,34900],{"width":15129},[2122,34902,34903,34905],{},[898,34904,2638],{},[1979,34906,1981],{},[1846,34908,1848],{},[898,34910,900],{},[7963,34912,34913],{},[2179,34914,34915,34921],{},[2122,34916,34917,34919],{},[898,34918,3783],{},[1979,34920,2128],{},[2122,34922,34923,34925],{},[898,34924,3783],{},[1979,34926,1981],{},[1846,34928,1848],{},[2122,34930,34931,34933],{},[898,34932,4029],{},[1979,34934,1981],{},[1846,34936,1855],{"stretchy":1854},[2122,34938,34939,34941],{},[898,34940,3783],{},[1979,34942,2128],{},[1846,34944,2136],{"separator":2135},[2122,34946,34947,34949],{},[898,34948,3783],{},[1979,34950,1981],{},[1846,34952,2136],{"separator":2135},[898,34954,900],{},[1846,34956,1861],{"stretchy":1854},[2138,34958,3830],{},[20607,34960],{"width":27921},[20607,34962,34963],{},[2138,34964,34965],{},"(6.30)",[902,34967,34968],{"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}",[115,34970,34972],{"id":34971},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,34974,34975,34976,34989,34990,35007,35008,35021,35022,35039,35040,35043,35044,35083,35084,35113],{},"Primární (max ",[883,34977,34979],{"className":34978},[886],[888,34980,34981],{"xmlns":890},[892,34982,34983,34987],{},[895,34984,34985],{},[898,34986,900],{},[902,34988,900],{"encoding":904}," při rozpočtu ",[883,34991,34993],{"className":34992},[886],[888,34994,34995],{"xmlns":890},[892,34996,34997,35005],{},[895,34998,34999],{},[1974,35000,35001,35003],{},[898,35002,8974],{},[1846,35004,4200],{},[902,35006,27873],{"encoding":904},") a duální (min ",[883,35009,35011],{"className":35010},[886],[888,35012,35013],{"xmlns":890},[892,35014,35015,35019],{},[895,35016,35017],{},[898,35018,4098],{},[902,35020,4098],{"encoding":904}," při užitečnosti ",[883,35023,35025],{"className":35024},[886],[888,35026,35027],{"xmlns":890},[892,35028,35029,35037],{},[895,35030,35031],{},[1974,35032,35033,35035],{},[898,35034,900],{},[1846,35036,4200],{},[902,35038,27807],{"encoding":904},") úloha jsou ",[38,35041,35042],{},"ekvivalentní",": mají tentýž bod optima ",[883,35045,35047],{"className":35046},[886],[888,35048,35049],{"xmlns":890},[892,35050,35051,35081],{},[895,35052,35053,35059,35061,35069,35071,35079],{},[1974,35054,35055,35057],{},[898,35056,2638],{},[1846,35058,4200],{},[1846,35060,2336],{"stretchy":1854},[9012,35062,35063,35065,35067],{},[898,35064,2638],{},[1979,35066,2128],{},[1846,35068,4200],{},[1846,35070,2136],{"separator":2135},[9012,35072,35073,35075,35077],{},[898,35074,2638],{},[1979,35076,1981],{},[1846,35078,4200],{},[1846,35080,2351],{"stretchy":1854},[902,35082,28172],{"encoding":904}," a v obou platí ",[883,35085,35087],{"className":35086},[886],[888,35088,35089],{"xmlns":890},[892,35090,35091,35111],{},[895,35092,35093,35095,35097,35103,35105],{},[2138,35094,10449],{},[1846,35096,1848],{},[2122,35098,35099,35101],{},[898,35100,3783],{},[1979,35102,2128],{},[898,35104,4520],{"mathvariant":2226},[2122,35106,35107,35109],{},[898,35108,3783],{},[1979,35110,1981],{},[902,35112,27843],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,35115,35116],{},[2409,35117],{"alt":35118,"className":35119,"src":35120},"imek-primarni-vs-dualni",[210,2413],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,35122,35123,35234],{},[123,35124,35125,35128,35129,35142,35143,35183,35184,1734],{},[38,35126,35127],{},"Primární"," (Marshall): zadáno ",[883,35130,35132],{"className":35131},[886],[888,35133,35134],{"xmlns":890},[892,35135,35136,35140],{},[895,35137,35138],{},[898,35139,8974],{},[902,35141,8974],{"encoding":904},", hledáme maximální ",[883,35144,35146],{"className":35145},[886],[888,35147,35148],{"xmlns":890},[892,35149,35150,35180],{},[895,35151,35152,35158,35160,35166,35168,35174,35176,35178],{},[1974,35153,35154,35156],{},[898,35155,900],{},[1846,35157,4200],{},[1846,35159,1855],{"stretchy":1854},[2122,35161,35162,35164],{},[898,35163,3783],{},[1979,35165,2128],{},[1846,35167,2136],{"separator":2135},[2122,35169,35170,35172],{},[898,35171,3783],{},[1979,35173,1981],{},[1846,35175,2136],{"separator":2135},[898,35177,8974],{},[1846,35179,1861],{"stretchy":1854},[902,35181,35182],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,35185,35187],{"className":35186},[886],[888,35188,35189],{"xmlns":890},[892,35190,35191,35231],{},[895,35192,35193,35199,35201,35209,35211,35217,35219,35225,35227,35229],{},[2122,35194,35195,35197],{},[898,35196,2638],{},[898,35198,17635],{},[1846,35200,1848],{},[9012,35202,35203,35205,35207],{},[898,35204,4029],{},[898,35206,17635],{},[898,35208,2667],{},[1846,35210,1855],{"stretchy":1854},[2122,35212,35213,35215],{},[898,35214,3783],{},[1979,35216,2128],{},[1846,35218,2136],{"separator":2135},[2122,35220,35221,35223],{},[898,35222,3783],{},[1979,35224,1981],{},[1846,35226,2136],{"separator":2135},[898,35228,8974],{},[1846,35230,1861],{"stretchy":1854},[902,35232,35233],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,35235,35236,35239,35240,35253,35254,35183,35294,1734],{},[38,35237,35238],{},"Duální"," (Hicks): zadáno ",[883,35241,35243],{"className":35242},[886],[888,35244,35245],{"xmlns":890},[892,35246,35247,35251],{},[895,35248,35249],{},[898,35250,900],{},[902,35252,900],{"encoding":904},", hledáme minimální ",[883,35255,35257],{"className":35256},[886],[888,35258,35259],{"xmlns":890},[892,35260,35261,35291],{},[895,35262,35263,35269,35271,35277,35279,35285,35287,35289],{},[1974,35264,35265,35267],{},[898,35266,4098],{},[1846,35268,4200],{},[1846,35270,1855],{"stretchy":1854},[2122,35272,35273,35275],{},[898,35274,3783],{},[1979,35276,2128],{},[1846,35278,2136],{"separator":2135},[2122,35280,35281,35283],{},[898,35282,3783],{},[1979,35284,1981],{},[1846,35286,2136],{"separator":2135},[898,35288,900],{},[1846,35290,1861],{"stretchy":1854},[902,35292,35293],{"encoding":904},"E^*(P_1, P_2, U)",[883,35295,35297],{"className":35296},[886],[888,35298,35299],{"xmlns":890},[892,35300,35301,35342],{},[895,35302,35303,35309,35311,35320,35322,35328,35330,35336,35338,35340],{},[2122,35304,35305,35307],{},[898,35306,2638],{},[898,35308,17635],{},[1846,35310,1848],{},[9012,35312,35313,35315,35317],{},[898,35314,4029],{},[898,35316,17635],{},[898,35318,35319],{},"H",[1846,35321,1855],{"stretchy":1854},[2122,35323,35324,35326],{},[898,35325,3783],{},[1979,35327,2128],{},[1846,35329,2136],{"separator":2135},[2122,35331,35332,35334],{},[898,35333,3783],{},[1979,35335,1981],{},[1846,35337,2136],{"separator":2135},[898,35339,900],{},[1846,35341,1861],{"stretchy":1854},[902,35343,35344],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,35346,35347,35348,35351,35352,35355],{},"Proč se studují obě? Marshallova poptávka je ",[38,35349,35350],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,35353,35354],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,35357,35359],{"id":35358},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,35361,35363],{"id":35362},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,35365,35366,35369,35370,35402,35403,35441,35442,35468],{},[38,35367,35368],{},"6.8"," Jsou dány užitečnost ",[883,35371,35373],{"className":35372},[886],[888,35374,35375],{"xmlns":890},[892,35376,35377,35399],{},[895,35378,35379,35381,35383,35391],{},[898,35380,900],{},[1846,35382,1848],{},[9012,35384,35385,35387,35389],{},[898,35386,2638],{},[1979,35388,2128],{},[1979,35390,4855],{},[9012,35392,35393,35395,35397],{},[898,35394,2638],{},[1979,35396,1981],{},[1979,35398,4855],{},[902,35400,35401],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,35404,35406],{"className":35405},[886],[888,35407,35408],{"xmlns":890},[892,35409,35410,35438],{},[895,35411,35412,35420,35422,35424,35426,35434,35436],{},[9012,35413,35414,35416,35418],{},[898,35415,3783],{},[1979,35417,2128],{},[1846,35419,4200],{},[1846,35421,1848],{},[1979,35423,2201],{},[1846,35425,2136],{"separator":2135},[9012,35427,35428,35430,35432],{},[898,35429,3783],{},[1979,35431,1981],{},[1846,35433,4200],{},[1846,35435,1848],{},[1979,35437,2712],{},[902,35439,35440],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,35443,35445],{"className":35444},[886],[888,35446,35447],{"xmlns":890},[892,35448,35449,35465],{},[895,35450,35451,35457,35459],{},[2122,35452,35453,35455],{},[898,35454,2638],{},[1979,35456,2128],{},[1846,35458,2136],{"separator":2135},[2122,35460,35461,35463],{},[898,35462,2638],{},[1979,35464,1981],{},[902,35466,35467],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,35470,35471,35474,35475,35517,35518,35549,35550,35572,35573,1734],{},[38,35472,35473],{},"6.9"," Jsou dány rozpočtové omezení ",[883,35476,35478],{"className":35477},[886],[888,35479,35480],{"xmlns":890},[892,35481,35482,35514],{},[895,35483,35484,35486,35488,35494,35500,35502,35508],{},[898,35485,8974],{},[1846,35487,1848],{},[2122,35489,35490,35492],{},[898,35491,3783],{},[1979,35493,2128],{},[2122,35495,35496,35498],{},[898,35497,2638],{},[1979,35499,2128],{},[1846,35501,1945],{},[2122,35503,35504,35506],{},[898,35505,3783],{},[1979,35507,1981],{},[2122,35509,35510,35512],{},[898,35511,2638],{},[1979,35513,1981],{},[902,35515,35516],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,35519,35521],{"className":35520},[886],[888,35522,35523],{"xmlns":890},[892,35524,35525,35547],{},[895,35526,35527,35529,35531,35539],{},[898,35528,900],{},[1846,35530,1848],{},[9012,35532,35533,35535,35537],{},[898,35534,2638],{},[1979,35536,2128],{},[1979,35538,4855],{},[9012,35540,35541,35543,35545],{},[898,35542,2638],{},[1979,35544,1981],{},[1979,35546,4855],{},[902,35548,35401],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,35551,35553],{"className":35552},[886],[888,35554,35555],{"xmlns":890},[892,35556,35557,35569],{},[895,35558,35559,35565,35567],{},[1974,35560,35561,35563],{},[898,35562,8974],{},[1846,35564,4200],{},[1846,35566,1848],{},[1979,35568,14955],{},[902,35570,35571],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,35574,35576],{"className":35575},[886],[888,35577,35578],{"xmlns":890},[892,35579,35580,35608],{},[895,35581,35582,35590,35592,35594,35596,35604,35606],{},[9012,35583,35584,35586,35588],{},[898,35585,3783],{},[1979,35587,2128],{},[1846,35589,4200],{},[1846,35591,1848],{},[1979,35593,2078],{},[1846,35595,2136],{"separator":2135},[9012,35597,35598,35600,35602],{},[898,35599,3783],{},[1979,35601,1981],{},[1846,35603,4200],{},[1846,35605,1848],{},[1979,35607,2712],{},[902,35609,35610],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,35612,35613,35616,35617,21439,35649,35679,35680,1734],{},[38,35614,35615],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,35618,35620],{"className":35619},[886],[888,35621,35622],{"xmlns":890},[892,35623,35624,35646],{},[895,35625,35626,35628,35630,35638],{},[898,35627,900],{},[1846,35629,1848],{},[9012,35631,35632,35634,35636],{},[898,35633,2638],{},[1979,35635,2128],{},[898,35637,207],{},[9012,35639,35640,35642,35644],{},[898,35641,2638],{},[1979,35643,1981],{},[898,35645,1948],{},[902,35647,35648],{"encoding":904},"U = Q_1^a Q_2^b",[883,35650,35652],{"className":35651},[886],[888,35653,35654],{"xmlns":890},[892,35655,35656,35676],{},[895,35657,35658,35660,35662,35664,35666,35668,35670,35672,35674],{},[898,35659,207],{},[1846,35661,2136],{"separator":2135},[898,35663,1948],{},[1846,35665,6352],{},[1846,35667,5170],{"stretchy":1854},[1979,35669,2177],{},[1846,35671,2136],{"separator":2135},[1979,35673,2128],{},[1846,35675,5187],{"stretchy":1854},[902,35677,35678],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,35681,35683],{"className":35682},[886],[888,35684,35685],{"xmlns":890},[892,35686,35687,35719],{},[895,35688,35689,35691,35693,35699,35705,35707,35713],{},[898,35690,8974],{},[1846,35692,1848],{},[2122,35694,35695,35697],{},[898,35696,3783],{},[1979,35698,2128],{},[2122,35700,35701,35703],{},[898,35702,2638],{},[1979,35704,2128],{},[1846,35706,1945],{},[2122,35708,35709,35711],{},[898,35710,3783],{},[1979,35712,1981],{},[2122,35714,35715,35717],{},[898,35716,2638],{},[1979,35718,1981],{},[902,35720,35516],{"encoding":904},[724,35722,35723,35726,35727,21439,35761,35679,35779,1734],{},[38,35724,35725],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,35728,35730],{"className":35729},[886],[888,35731,35732],{"xmlns":890},[892,35733,35734,35758],{},[895,35735,35736,35738,35740,35748,35750],{},[898,35737,900],{},[1846,35739,1848],{},[9012,35741,35742,35744,35746],{},[898,35743,2638],{},[1979,35745,2128],{},[898,35747,207],{},[1846,35749,1945],{},[9012,35751,35752,35754,35756],{},[898,35753,2638],{},[1979,35755,1981],{},[898,35757,207],{},[902,35759,35760],{"encoding":904},"U = Q_1^a + Q_2^a",[883,35762,35764],{"className":35763},[886],[888,35765,35766],{"xmlns":890},[892,35767,35768,35776],{},[895,35769,35770,35772,35774],{},[898,35771,207],{},[1846,35773,3219],{"mathvariant":2226},[1979,35775,2177],{},[902,35777,35778],{"encoding":904},"a \\neq 0",[883,35780,35782],{"className":35781},[886],[888,35783,35784],{"xmlns":890},[892,35785,35786,35818],{},[895,35787,35788,35790,35792,35798,35804,35806,35812],{},[898,35789,8974],{},[1846,35791,1848],{},[2122,35793,35794,35796],{},[898,35795,3783],{},[1979,35797,2128],{},[2122,35799,35800,35802],{},[898,35801,2638],{},[1979,35803,2128],{},[1846,35805,1945],{},[2122,35807,35808,35810],{},[898,35809,3783],{},[1979,35811,1981],{},[2122,35813,35814,35816],{},[898,35815,2638],{},[1979,35817,1981],{},[902,35819,35516],{"encoding":904},[198,35821,35823],{"id":35822},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,35825,35826,35369,35829,1343,35856,35878,35879,1343,35902,35926,35927,35952,35953,1734],{},[38,35827,35828],{},"6.12",[883,35830,35832],{"className":35831},[886],[888,35833,35834],{"xmlns":890},[892,35835,35836,35854],{},[895,35837,35838,35840,35842,35848],{},[898,35839,900],{},[1846,35841,1848],{},[2122,35843,35844,35846],{},[898,35845,2638],{},[1979,35847,2128],{},[2122,35849,35850,35852],{},[898,35851,2638],{},[1979,35853,1981],{},[902,35855,30071],{"encoding":904},[883,35857,35859],{"className":35858},[886],[888,35860,35861],{"xmlns":890},[892,35862,35863,35875],{},[895,35864,35865,35871,35873],{},[1974,35866,35867,35869],{},[898,35868,900],{},[1846,35870,4200],{},[1846,35872,1848],{},[1979,35874,2712],{},[902,35876,35877],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,35880,35882],{"className":35881},[886],[888,35883,35884],{"xmlns":890},[892,35885,35886,35900],{},[895,35887,35888,35896,35898],{},[9012,35889,35890,35892,35894],{},[898,35891,3783],{},[1979,35893,2128],{},[1846,35895,4200],{},[1846,35897,1848],{},[1979,35899,1981],{},[902,35901,30144],{"encoding":904},[883,35903,35905],{"className":35904},[886],[888,35906,35907],{"xmlns":890},[892,35908,35909,35923],{},[895,35910,35911,35919,35921],{},[9012,35912,35913,35915,35917],{},[898,35914,3783],{},[1979,35916,1981],{},[1846,35918,4200],{},[1846,35920,1848],{},[1979,35922,2201],{},[902,35924,35925],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,35928,35930],{"className":35929},[886],[888,35931,35932],{"xmlns":890},[892,35933,35934,35950],{},[895,35935,35936,35942,35944],{},[2122,35937,35938,35940],{},[898,35939,2638],{},[1979,35941,2128],{},[1846,35943,2136],{"separator":2135},[2122,35945,35946,35948],{},[898,35947,2638],{},[1979,35949,1981],{},[902,35951,35467],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,35954,35956],{"className":35955},[886],[888,35957,35958],{"xmlns":890},[892,35959,35960,35980],{},[895,35961,35962,35964,35966,35972,35974],{},[898,35963,900],{},[1846,35965,1848],{},[2122,35967,35968,35970],{},[898,35969,2638],{},[1979,35971,2128],{},[1846,35973,3025],{},[2122,35975,35976,35978],{},[898,35977,2638],{},[1979,35979,1981],{},[902,35981,35982],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,35984,35985,35988,35989,36030,36031,36053,36054,1734],{},[38,35986,35987],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,35990,35992],{"className":35991},[886],[888,35993,35994],{"xmlns":890},[892,35995,35996,36028],{},[895,35997,35998,36000,36002,36008,36014,36016,36022],{},[898,35999,4098],{},[1846,36001,1848],{},[2122,36003,36004,36006],{},[898,36005,3783],{},[1979,36007,2128],{},[2122,36009,36010,36012],{},[898,36011,2638],{},[1979,36013,2128],{},[1846,36015,1945],{},[2122,36017,36018,36020],{},[898,36019,3783],{},[1979,36021,1981],{},[2122,36023,36024,36026],{},[898,36025,2638],{},[1979,36027,1981],{},[902,36029,27788],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,36032,36034],{"className":36033},[886],[888,36035,36036],{"xmlns":890},[892,36037,36038,36050],{},[895,36039,36040,36046,36048],{},[1974,36041,36042,36044],{},[898,36043,900],{},[1846,36045,4200],{},[1846,36047,1848],{},[1979,36049,4850],{},[902,36051,36052],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,36055,36057],{"className":36056},[886],[888,36058,36059],{"xmlns":890},[892,36060,36061,36090],{},[895,36062,36063,36071,36073,36075,36077,36085,36087],{},[9012,36064,36065,36067,36069],{},[898,36066,3783],{},[1979,36068,2128],{},[1846,36070,4200],{},[1846,36072,1848],{},[1979,36074,8881],{},[1846,36076,2136],{"separator":2135},[9012,36078,36079,36081,36083],{},[898,36080,3783],{},[1979,36082,1981],{},[1846,36084,4200],{},[1846,36086,1848],{},[1979,36088,36089],{},"15",[902,36091,36092],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,36094,15565],{"id":15564},[120,36096,36097,36154,36193,36213,36248,36302,36307,36313,36409,36454],{},[123,36098,36099,2053,36102,36151,36152,1734],{},[38,36100,36101],{},"Rozpočtové omezení (budget constraint)",[883,36103,36105],{"className":36104},[886],[888,36106,36107],{"xmlns":890},[892,36108,36109,36149],{},[895,36110,36111,36117,36119,36127,36133,36135,36143],{},[1974,36112,36113,36115],{},[898,36114,8974],{},[1846,36116,4200],{},[1846,36118,1848],{},[9012,36120,36121,36123,36125],{},[898,36122,3783],{},[1979,36124,2128],{},[1846,36126,4200],{},[2122,36128,36129,36131],{},[898,36130,2638],{},[1979,36132,2128],{},[1846,36134,1945],{},[9012,36136,36137,36139,36141],{},[898,36138,3783],{},[1979,36140,1981],{},[1846,36142,4200],{},[2122,36144,36145,36147],{},[898,36146,2638],{},[1979,36148,1981],{},[902,36150,17143],{"encoding":904}," — (6.12); ",[38,36153,27981],{},[123,36155,36156,36159,36160,1734],{},[38,36157,36158],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,36161,36163],{"className":36162},[886],[888,36164,36165],{"xmlns":890},[892,36166,36167,36191],{},[895,36168,36169,36171,36173,36181,36183],{},[2138,36170,10449],{},[1846,36172,1848],{},[9012,36174,36175,36177,36179],{},[898,36176,3783],{},[1979,36178,2128],{},[1846,36180,4200],{},[898,36182,4520],{"mathvariant":2226},[9012,36184,36185,36187,36189],{},[898,36186,3783],{},[1979,36188,1981],{},[1846,36190,4200],{},[902,36192,28824],{"encoding":904},[123,36194,36195,36210,36211,1734],{},[38,36196,28968,36197],{},[883,36198,36200],{"className":36199},[886],[888,36201,36202],{"xmlns":890},[892,36203,36204,36208],{},[895,36205,36206],{},[898,36207,16288],{},[902,36209,16341],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,36212,28990],{},[123,36214,36215,36218,36219,1734],{},[38,36216,36217],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,36220,36222],{"className":36221},[886],[888,36223,36224],{"xmlns":890},[892,36225,36226,36246],{},[895,36227,36228,36230,36232,36238,36240],{},[2138,36229,10449],{},[1846,36231,1848],{},[2122,36233,36234,36236],{},[898,36235,3783],{},[1979,36237,2128],{},[898,36239,4520],{"mathvariant":2226},[2122,36241,36242,36244],{},[898,36243,3783],{},[1979,36245,1981],{},[902,36247,27843],{"encoding":904},[123,36249,36250,6861,36253,36301],{},[38,36251,36252],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,36254,36256],{"className":36255},[886],[888,36257,36258],{"xmlns":890},[892,36259,36260,36298],{},[895,36261,36262,36268,36270,36276,36278,36284,36286,36292,36294,36296],{},[2122,36263,36264,36266],{},[898,36265,2638],{},[898,36267,17635],{},[1846,36269,1848],{},[2122,36271,36272,36274],{},[898,36273,4029],{},[898,36275,17635],{},[1846,36277,1855],{"stretchy":1854},[2122,36279,36280,36282],{},[898,36281,3783],{},[1979,36283,2128],{},[1846,36285,2136],{"separator":2135},[2122,36287,36288,36290],{},[898,36289,3783],{},[1979,36291,1981],{},[1846,36293,2136],{"separator":2135},[898,36295,8974],{},[1846,36297,1861],{"stretchy":1854},[902,36299,36300],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,36303,36304,36306],{},[38,36305,31572],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,36308,36309,36312],{},[38,36310,36311],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,36314,36315,6861,36317,36364,36365,36408],{},[38,36316,33884],{},[883,36318,36320],{"className":36319},[886],[888,36321,36322],{"xmlns":890},[892,36323,36324,36362],{},[895,36325,36326,36332,36334,36340,36342,36348,36350,36356,36358,36360],{},[2122,36327,36328,36330],{},[898,36329,2638],{},[898,36331,17635],{},[1846,36333,1848],{},[2122,36335,36336,36338],{},[898,36337,4029],{},[898,36339,17635],{},[1846,36341,1855],{"stretchy":1854},[2122,36343,36344,36346],{},[898,36345,3783],{},[1979,36347,2128],{},[1846,36349,2136],{"separator":2135},[2122,36351,36352,36354],{},[898,36353,3783],{},[1979,36355,1981],{},[1846,36357,2136],{"separator":2135},[898,36359,900],{},[1846,36361,1861],{"stretchy":1854},[902,36363,17668],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,36366,36368],{"className":36367},[886],[888,36369,36370],{"xmlns":890},[892,36371,36372,36406],{},[895,36373,36374,36376,36378,36392],{},[898,36375,900],{},[1846,36377,1848],{},[9012,36379,36380,36382,36384],{},[898,36381,2638],{},[1979,36383,2128],{},[895,36385,36386,36388,36390],{},[1979,36387,2128],{},[898,36389,4520],{"mathvariant":2226},[1979,36391,1981],{},[9012,36393,36394,36396,36398],{},[898,36395,2638],{},[1979,36397,1981],{},[895,36399,36400,36402,36404],{},[1979,36401,2128],{},[898,36403,4520],{"mathvariant":2226},[1979,36405,1981],{},[902,36407,33004],{"encoding":904},": (6.30).",[123,36410,36411,36453],{},[38,36412,36413,36414],{},"Bod dotyku ",[883,36415,36417],{"className":36416},[886],[888,36418,36419],{"xmlns":890},[892,36420,36421,36451],{},[895,36422,36423,36429,36431,36439,36441,36449],{},[1974,36424,36425,36427],{},[898,36426,2638],{},[1846,36428,4200],{},[1846,36430,2336],{"stretchy":1854},[9012,36432,36433,36435,36437],{},[898,36434,2638],{},[1979,36436,2128],{},[1846,36438,4200],{},[1846,36440,2136],{"separator":2135},[9012,36442,36443,36445,36447],{},[898,36444,2638],{},[1979,36446,1981],{},[1846,36448,4200],{},[1846,36450,2351],{"stretchy":1854},[902,36452,28172],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,36455,36456,36459,36460,36473,36474,36487],{},[38,36457,36458],{},"Dualita"," — ekvivalence max ",[883,36461,36463],{"className":36462},[886],[888,36464,36465],{"xmlns":890},[892,36466,36467,36471],{},[895,36468,36469],{},[898,36470,900],{},[902,36472,900],{"encoding":904}," a min ",[883,36475,36477],{"className":36476},[886],[888,36478,36479],{"xmlns":890},[892,36480,36481,36485],{},[895,36482,36483],{},[898,36484,4098],{},[902,36486,4098],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,36489,3640],{"id":3639},[120,36491,36492,36515,36531,36544,36555],{},[123,36493,36494,2053,36497,36500,36501,36514],{},[38,36495,36496],{},"Teorie před optimalizací:",[207,36498,880],{"className":36499,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,36502,36504],{"className":36503},[886],[888,36505,36506],{"xmlns":890},[892,36507,36508,36512],{},[895,36509,36510],{},[898,36511,900],{},[902,36513,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,36516,36517,2053,36520,36523,36524,36527,36528,1734],{},[38,36518,36519],{},"Matematický aparát:",[207,36521,793],{"className":36522,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,36525,784],{"className":36526,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,36529,2207],{"className":36530,"dataFsResolvedFilePath":764,"href":765},[210],[123,36532,36533,2053,36536,36539,36540,36543],{},[38,36534,36535],{},"Paralely:",[207,36537,1728],{"className":36538,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,36541,1701],{"className":36542,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,36545,36546,2053,36549,1343,36552],{},[38,36547,36548],{},"Přednášky:",[207,36550,1094],{"className":36551,"dataFsResolvedFilePath":838,"href":839},[210],[207,36553,1101],{"className":36554,"dataFsResolvedFilePath":868,"href":869},[210],[123,36556,36557,2053,36559],{},[38,36558,16049],{},[207,36560,16053],{"className":36561,"dataFsResolvedFilePath":1761,"href":1762},[210],{"title":641,"searchDepth":642,"depth":642,"links":36563},[36564,36565,36566,36571,36572,36573,36575,36578,36581,36583,36584,36586,36587,36591,36592],{"id":11850,"depth":642,"text":11851},{"id":27851,"depth":642,"text":27852},{"id":28249,"depth":642,"text":28250,"children":36567},[36568,36569],{"id":28369,"depth":649,"text":28370},{"id":28950,"depth":649,"text":36570},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":29412,"depth":642,"text":29413},{"id":29723,"depth":642,"text":29724},{"id":30042,"depth":642,"text":36574},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":30815,"depth":642,"text":30816,"children":36576},[36577],{"id":31571,"depth":649,"text":31572},{"id":31751,"depth":642,"text":31752,"children":36579},[36580],{"id":32008,"depth":649,"text":32009},{"id":32959,"depth":642,"text":36582},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":33883,"depth":642,"text":33884},{"id":34086,"depth":642,"text":36585},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":34971,"depth":642,"text":34972},{"id":35358,"depth":642,"text":35359,"children":36588},[36589,36590],{"id":35362,"depth":649,"text":35363},{"id":35822,"depth":649,"text":35823},{"id":15564,"depth":642,"text":15565},{"id":3639,"depth":642,"text":3640},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":27612,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,36599,1144,9619,36600,36601,36602],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":36605,"title":802,"body":36606,"course":1128,"courses":659,"created":9402,"description":641,"extension":661,"meta":50659,"navigation":664,"path":50660,"seo":50661,"sources":50662,"stem":50663,"tags":50664,"type":3703,"updated":677,"__hash__":50670},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":36607,"toc":50615},[36608,36611,36637,36641,36648,36800,36814,36817,36819,36906,36910,36946,37019,37040,37165,37175,37188,37192,37197,37227,37289,37298,37302,37364,37371,37392,37510,37588,37592,37595,37654,37769,37774,37806,37868,37916,37971,37975,37996,38020,38068,38072,38084,38088,38198,38202,38218,38259,38270,38429,38439,38444,38448,38570,38580,38587,38591,38669,38680,38760,38766,38773,38912,38919,38922,38979,38983,39061,39107,39151,39157,39270,39274,39277,39472,39476,39713,39716,39870,40023,40025,40027,40107,40110,40215,40284,40293,40297,40300,40361,40370,40374,40407,40485,40524,40528,40577,40631,40635,40664,40693,40745,40752,40806,40884,40888,40931,40998,41042,41146,41165,41167,41171,41279,41283,41351,41400,41407,41492,41496,41568,41573,41621,41810,41814,41819,41995,42000,42059,42164,42168,42195,42199,42206,42370,42457,42462,42464,42467,42567,42717,42789,42863,42865,42869,42883,42887,43020,43075,43187,43264,43268,43325,43428,43487,43648,43652,43727,43799,43897,43955,44049,44102,44123,44177,44182,44260,44308,44395,44433,44521,44674,44710,44764,44767,44769,44771,44820,44827,44835,44922,44931,45018,45025,45027,45031,45256,45258,45262,45266,45335,45386,45589,45595,45606,45674,45680,46102,46106,46170,46194,46390,46396,46410,46478,46481,46521,46745,46813,47115,47524,47601,47767,47773,47776,47851,48304,48355,48761,48866,49529,49532,49609,49617,49691,49722,49724,49728,49772,49774,49776,49780,50010,50014,50105,50110,50204,50209,50382,50386,50504,50509,50558,50560,50562],[12,36609,802],{"id":36610},"poptávka-nabídka-a-tržní-rovnováha",[1639,36612,36613],{},[724,36614,36615,36617,36618,36621,36622,36625,36626,36629,36630,36632,36633,36636],{},[883,36616,4001],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,36619,36620],{},"poptávka",") a výrobce (",[38,36623,36624],{},"nabídka","), jejich interakci v ",[38,36627,36628],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,36631,17822],{},"). Uzavírá ji pojem ",[38,36634,36635],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,36638,36640],{"id":36639},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,36642,36643,36644,36647],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,36645,36646],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,36649,36650,36667,36709,36725],{},[123,36651,36652,36653,36666],{},"cena ",[883,36654,36656],{"className":36655},[886],[888,36657,36658],{"xmlns":890},[892,36659,36660,36664],{},[895,36661,36662],{},[898,36663,3783],{},[902,36665,3783],{"encoding":904}," zkoumaného zboží,",[123,36668,36669,36670,2136],{},"ceny alternativních zboží ",[883,36671,36673],{"className":36672},[886],[888,36674,36675],{"xmlns":890},[892,36676,36677,36706],{},[895,36678,36679,36685,36687,36693,36695,36697,36699],{},[2122,36680,36681,36683],{},[898,36682,3783],{},[1979,36684,2128],{},[1846,36686,2136],{"separator":2135},[2122,36688,36689,36691],{},[898,36690,3783],{},[1979,36692,1981],{},[1846,36694,2136],{"separator":2135},[1846,36696,9492],{},[1846,36698,2136],{"separator":2135},[2122,36700,36701,36703],{},[898,36702,3783],{},[898,36704,36705],{},"n",[902,36707,36708],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,36710,36711,36712,2136],{},"důchod ",[883,36713,36715],{"className":36714},[886],[888,36716,36717],{"xmlns":890},[892,36718,36719,36723],{},[895,36720,36721],{},[898,36722,8974],{},[902,36724,8974],{"encoding":904},[123,36726,36727,36728,36741,36742,36755,36756,36769,36770,36784,36785,36799],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,36729,36731],{"className":36730},[886],[888,36732,36733],{"xmlns":890},[892,36734,36735,36739],{},[895,36736,36737],{},[898,36738,9641],{},[902,36740,9641],{"encoding":904},", kapitál ",[883,36743,36745],{"className":36744},[886],[888,36746,36747],{"xmlns":890},[892,36748,36749,36753],{},[895,36750,36751],{},[898,36752,9646],{},[902,36754,9646],{"encoding":904},", půda ",[883,36757,36759],{"className":36758},[886],[888,36760,36761],{"xmlns":890},[892,36762,36763,36767],{},[895,36764,36765],{},[898,36766,4098],{},[902,36768,4098],{"encoding":904},"), technologie, počet výrobců ",[883,36771,36773],{"className":36772},[886],[888,36774,36775],{"xmlns":890},[892,36776,36777,36782],{},[895,36778,36779],{},[898,36780,36781],{},"O",[902,36783,36781],{"encoding":904},", počasí ",[883,36786,36788],{"className":36787},[886],[888,36789,36790],{"xmlns":890},[892,36791,36792,36797],{},[895,36793,36794],{},[898,36795,36796],{},"W",[902,36798,36796],{"encoding":904}," atd.",[724,36801,36802,36803,36806,36807,36810,36811,1734],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,36804,36805],{},"ceteris paribus","), hovoříme o ",[38,36808,36809],{},"jednofaktorovém modelu","; jinak jde o model ",[38,36812,36813],{},"vícefaktorový",[36815,36816],"hr",{},[115,36818,13006],{"id":36620},[1639,36820,36821],{},[724,36822,36823,36825,36826,36839,36840,36853,36854,36857,36858,36881,36882,1734],{},[883,36824,4001],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,36827,36829],{"className":36828},[886],[888,36830,36831],{"xmlns":890},[892,36832,36833,36837],{},[895,36834,36835],{},[898,36836,2638],{},[902,36838,2638],{"encoding":904}," na ceně ",[883,36841,36843],{"className":36842},[886],[888,36844,36845],{"xmlns":890},[892,36846,36847,36851],{},[895,36848,36849],{},[898,36850,3783],{},[902,36852,3783],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,36855,36856],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,36859,36861],{"className":36860},[886],[888,36862,36863],{"xmlns":890},[892,36864,36865,36879],{},[895,36866,36867,36869,36871,36873,36875,36877],{},[898,36868,2638],{},[1846,36870,1848],{},[898,36872,4029],{},[1846,36874,1855],{"stretchy":1854},[898,36876,3783],{},[1846,36878,1861],{"stretchy":1854},[902,36880,4038],{"encoding":904}," a jeho lineární verzí ",[883,36883,36885],{"className":36884},[886],[888,36886,36887],{"xmlns":890},[892,36888,36889,36903],{},[895,36890,36891,36893,36895,36897,36899,36901],{},[898,36892,3783],{},[1846,36894,1848],{},[898,36896,207],{},[898,36898,2638],{},[1846,36900,1945],{},[898,36902,1948],{},[902,36904,36905],{"encoding":904},"P = aQ + b",[198,36907,36909],{"id":36908},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,36911,36912,36913,36926,36927,36940,36941,9871,36943,2999],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,36914,36916],{"className":36915},[886],[888,36917,36918],{"xmlns":890},[892,36919,36920,36924],{},[895,36921,36922],{},[898,36923,2638],{},[902,36925,2638],{"encoding":904}," závisí na ceně ",[883,36928,36930],{"className":36929},[886],[888,36931,36932],{"xmlns":890},[892,36933,36934,36938],{},[895,36935,36936],{},[898,36937,3783],{},[902,36939,3783],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,36942,27847],{},[614,36944,36945],{},"demand function",[883,36947,36949],{"className":36948},[886],[888,36950,36951],{"xmlns":890,"display":27911},[892,36952,36953,37016],{},[20599,36954,36955],{"width":27916},[20604,36956,36957,36959,37009,37011],{},[20607,36958],{"width":27921},[20607,36960,36961],{},[895,36962,36963,36965,36967,36969,36971,36973,36975,36981,36983,36989,36991,36993,36995,37001,37003,37005,37007],{},[898,36964,2638],{},[1846,36966,1848],{},[898,36968,4029],{},[1846,36970,1855],{"stretchy":1854},[898,36972,3783],{},[1846,36974,2136],{"separator":2135},[2122,36976,36977,36979],{},[898,36978,3783],{},[1979,36980,2128],{},[1846,36982,2136],{"separator":2135},[2122,36984,36985,36987],{},[898,36986,3783],{},[1979,36988,1981],{},[1846,36990,2136],{"separator":2135},[1846,36992,9492],{},[1846,36994,2136],{"separator":2135},[2122,36996,36997,36999],{},[898,36998,3783],{},[898,37000,36705],{},[1846,37002,2136],{"separator":2135},[898,37004,8974],{},[1846,37006,1861],{"stretchy":1854},[898,37008,1734],{"mathvariant":2226},[20607,37010],{"width":27921},[20607,37012,37013],{},[2138,37014,37015],{},"(2.1)",[902,37017,37018],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,37020,37021,37022,37025,37026,37039],{},"Důležitou vlastností je ",[38,37023,37024],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,37027,37029],{"className":37028},[886],[888,37030,37031],{"xmlns":890},[892,37032,37033,37037],{},[895,37034,37035],{},[898,37036,11886],{},[902,37038,11886],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,37041,37043],{"className":37042},[886],[888,37044,37045],{"xmlns":890,"display":27911},[892,37046,37047,37162],{},[20599,37048,37049],{"width":27916},[20604,37050,37051,37053,37155,37157],{},[20607,37052],{"width":27921},[20607,37054,37055],{},[895,37056,37057,37059,37061,37063,37065,37067,37069,37071,37073,37079,37081,37083,37089,37091,37093,37095,37097,37103,37105,37107,37109,37111,37113,37115,37117,37119,37121,37127,37129,37135,37137,37139,37141,37147,37149,37151,37153],{},[898,37058,2638],{},[1846,37060,1848],{},[898,37062,4029],{},[1846,37064,1855],{"stretchy":1854},[898,37066,11886],{},[898,37068,3783],{},[1846,37070,2136],{"separator":2135},[898,37072,11886],{},[2122,37074,37075,37077],{},[898,37076,3783],{},[1979,37078,2128],{},[1846,37080,2136],{"separator":2135},[898,37082,11886],{},[2122,37084,37085,37087],{},[898,37086,3783],{},[1979,37088,1981],{},[1846,37090,2136],{"separator":2135},[1846,37092,9492],{},[1846,37094,2136],{"separator":2135},[898,37096,11886],{},[2122,37098,37099,37101],{},[898,37100,3783],{},[898,37102,36705],{},[1846,37104,2136],{"separator":2135},[898,37106,11886],{},[898,37108,8974],{},[1846,37110,1861],{"stretchy":1854},[1846,37112,1848],{},[898,37114,4029],{},[1846,37116,1855],{"stretchy":1854},[898,37118,3783],{},[1846,37120,2136],{"separator":2135},[2122,37122,37123,37125],{},[898,37124,3783],{},[1979,37126,2128],{},[1846,37128,2136],{"separator":2135},[2122,37130,37131,37133],{},[898,37132,3783],{},[1979,37134,1981],{},[1846,37136,2136],{"separator":2135},[1846,37138,9492],{},[1846,37140,2136],{"separator":2135},[2122,37142,37143,37145],{},[898,37144,3783],{},[898,37146,36705],{},[1846,37148,2136],{"separator":2135},[898,37150,8974],{},[1846,37152,1861],{"stretchy":1854},[898,37154,1734],{"mathvariant":2226},[20607,37156],{"width":27921},[20607,37158,37159],{},[2138,37160,37161],{},"(2.2)",[902,37163,37164],{"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}",[1639,37166,37167],{},[724,37168,37169,37171,37172,1734],{},[883,37170,4258],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,37173,37174],{},"v jednofaktorových modelech neplatí",[724,37176,37177,37178,1343,37181,1745,37184,37187],{},"Rozlišuje se poptávka ",[38,37179,37180],{},"individuální",[38,37182,37183],{},"tržní",[38,37185,37186],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,37189,37191],{"id":37190},"jednofaktorové-modely","Jednofaktorové modely",[37193,37194,37196],"h4",{"id":37195},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,37198,37199,37200,37213,37214,2554],{},"Poptávané množství ",[883,37201,37203],{"className":37202},[886],[888,37204,37205],{"xmlns":890},[892,37206,37207,37211],{},[895,37208,37209],{},[898,37210,2638],{},[902,37212,2638],{"encoding":904}," závisí pouze na ceně ",[883,37215,37217],{"className":37216},[886],[888,37218,37219],{"xmlns":890},[892,37220,37221,37225],{},[895,37222,37223],{},[898,37224,3783],{},[902,37226,3783],{"encoding":904},[883,37228,37230],{"className":37229},[886],[888,37231,37232],{"xmlns":890,"display":27911},[892,37233,37234,37286],{},[20599,37235,37236],{"width":27916},[20604,37237,37238,37240,37279,37281],{},[20607,37239],{"width":27921},[20607,37241,37242],{},[895,37243,37244,37246,37248,37250,37252,37254,37256,37258,37260,37263,37265,37267,37269,37271,37273,37275,37277],{},[898,37245,2638],{},[1846,37247,1848],{},[898,37249,4029],{},[1846,37251,1855],{"stretchy":1854},[898,37253,3783],{},[1846,37255,1861],{"stretchy":1854},[1846,37257,2136],{"separator":2135},[5724,37259],{"width":5726},[2138,37261,37262],{},"resp.",[5724,37264],{"width":5726},[898,37266,3783],{},[1846,37268,1848],{},[898,37270,4029],{},[1846,37272,1855],{"stretchy":1854},[898,37274,2638],{},[1846,37276,1861],{"stretchy":1854},[898,37278,1734],{"mathvariant":2226},[20607,37280],{"width":27921},[20607,37282,37283],{},[2138,37284,37285],{},"(2.3)",[902,37287,37288],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,37290,37291,37292,9871,37295,3764],{},"Graf této funkce se nazývá ",[38,37293,37294],{},"křivka poptávky",[614,37296,37297],{},"demand curve",[37193,37299,37301],{"id":37300},"zákon-klesající-poptávky","Zákon klesající poptávky",[1639,37303,37304],{},[724,37305,37306],{},[38,37307,37308,37309,37322,37323,37336,37337,37322,37350,37363],{},"Roste-li cena ",[883,37310,37312],{"className":37311},[886],[888,37313,37314],{"xmlns":890},[892,37315,37316,37320],{},[895,37317,37318],{},[898,37319,3783],{},[902,37321,3783],{"encoding":904},", pak množství ",[883,37324,37326],{"className":37325},[886],[888,37327,37328],{"xmlns":890},[892,37329,37330,37334],{},[895,37331,37332],{},[898,37333,2638],{},[902,37335,2638],{"encoding":904}," klesá; klesá-li cena ",[883,37338,37340],{"className":37339},[886],[888,37341,37342],{"xmlns":890},[892,37343,37344,37348],{},[895,37345,37346],{},[898,37347,3783],{},[902,37349,3783],{"encoding":904},[883,37351,37353],{"className":37352},[886],[888,37354,37355],{"xmlns":890},[892,37356,37357,37361],{},[895,37358,37359],{},[898,37360,2638],{},[902,37362,2638],{"encoding":904}," roste.",[724,37365,37366,37367,37370],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,37368,37369],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[1639,37372,37373,37378],{},[724,37374,37375,37377],{},[883,37376,4001],{}," Intuice — proč zákon platí",[120,37379,37380,37386],{},[123,37381,37382,37385],{},[38,37383,37384],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,37387,37388,37391],{},[38,37389,37390],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,37393,37394,37395,37408,37409,37422,37423,37449,37450,37476,37477,7948,37503,37506,37507,1734],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,37396,37398],{"className":37397},[886],[888,37399,37400],{"xmlns":890},[892,37401,37402,37406],{},[895,37403,37404],{},[898,37405,3783],{},[902,37407,3783],{"encoding":904}," se vynáší na svislou osu, množství ",[883,37410,37412],{"className":37411},[886],[888,37413,37414],{"xmlns":890},[892,37415,37416,37420],{},[895,37417,37418],{},[898,37419,2638],{},[902,37421,2638],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,37424,37426],{"className":37425},[886],[888,37427,37428],{"xmlns":890},[892,37429,37430,37446],{},[895,37431,37432,37434,37436,37438,37444],{},[1846,37433,2336],{"stretchy":1854},[1979,37435,2177],{},[1846,37437,2136],{"separator":2135},[2122,37439,37440,37442],{},[898,37441,3783],{},[1979,37443,2177],{},[1846,37445,2351],{"stretchy":1854},[902,37447,37448],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,37451,37453],{"className":37452},[886],[888,37454,37455],{"xmlns":890},[892,37456,37457,37473],{},[895,37458,37459,37461,37467,37469,37471],{},[1846,37460,2336],{"stretchy":1854},[2122,37462,37463,37465],{},[898,37464,2638],{},[1979,37466,2177],{},[1846,37468,2136],{"separator":2135},[1979,37470,2177],{},[1846,37472,2351],{"stretchy":1854},[902,37474,37475],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,37478,37480],{"className":37479},[886],[888,37481,37482],{"xmlns":890},[892,37483,37484,37500],{},[895,37485,37486,37488,37490,37492,37498],{},[1846,37487,1855],{"stretchy":1854},[1979,37489,2177],{},[1846,37491,2136],{"separator":2135},[2122,37493,37494,37496],{},[898,37495,3783],{},[1979,37497,2177],{},[1846,37499,1861],{"stretchy":1854},[902,37501,37502],{"encoding":904},"(0, P_0)",[38,37504,37505],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,37508,37509],{},"konvexní",[724,37511,37512],{},[614,37513,37514,37515,37537,37538,1745,37563,1734],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,37516,37518],{"className":37517},[886],[888,37519,37520],{"xmlns":890},[892,37521,37522,37534],{},[895,37523,37524,37526,37528,37530,37532],{},[1846,37525,1855],{"stretchy":1854},[898,37527,2638],{},[1846,37529,2136],{"separator":2135},[898,37531,3783],{},[1846,37533,1861],{"stretchy":1854},[902,37535,37536],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,37539,37541],{"className":37540},[886],[888,37542,37543],{"xmlns":890},[892,37544,37545,37561],{},[895,37546,37547,37549,37551,37553,37559],{},[1846,37548,2336],{"stretchy":1854},[1979,37550,2177],{},[1846,37552,2136],{"separator":2135},[2122,37554,37555,37557],{},[898,37556,3783],{},[1979,37558,2177],{},[1846,37560,2351],{"stretchy":1854},[902,37562,37448],{"encoding":904},[883,37564,37566],{"className":37565},[886],[888,37567,37568],{"xmlns":890},[892,37569,37570,37586],{},[895,37571,37572,37574,37580,37582,37584],{},[1846,37573,2336],{"stretchy":1854},[2122,37575,37576,37578],{},[898,37577,2638],{},[1979,37579,2177],{},[1846,37581,2136],{"separator":2135},[1979,37583,2177],{},[1846,37585,2351],{"stretchy":1854},[902,37587,37475],{"encoding":904},[37193,37589,37591],{"id":37590},"lineární-model-poptávky","Lineární model poptávky",[724,37593,37594],{},"Nejjednodušší závislostí je",[883,37596,37598],{"className":37597},[886],[888,37599,37600],{"xmlns":890,"display":27911},[892,37601,37602,37651],{},[20599,37603,37604],{"width":27916},[20604,37605,37606,37608,37644,37646],{},[20607,37607],{"width":27921},[20607,37609,37610],{},[895,37611,37612,37614,37616,37618,37620,37622,37624,37626,37628,37630,37632,37634,37636,37638,37640,37642],{},[898,37613,3783],{},[1846,37615,1848],{},[898,37617,207],{},[898,37619,2638],{},[1846,37621,1945],{},[898,37623,1948],{},[1846,37625,2136],{"separator":2135},[5724,37627],{"width":5726},[898,37629,207],{},[1846,37631,3295],{},[1979,37633,2177],{},[1846,37635,2136],{"separator":2135},[2138,37637,2140],{},[898,37639,1948],{},[1846,37641,3256],{},[1979,37643,12305],{},[20607,37645],{"width":27921},[20607,37647,37648],{},[2138,37649,37650],{},"(2.4)",[902,37652,37653],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,37655,37656,37657,21439,37693,1745,37717,7883,37743,37765,37766,1734],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,37658,37660],{"className":37659},[886],[888,37661,37662],{"xmlns":890},[892,37663,37664,37690],{},[895,37665,37666,37668,37670,37678,37680,37682],{},[898,37667,2638],{},[1846,37669,1848],{},[2175,37671,37672],{"scriptlevel":2177,"displaystyle":1854},[2179,37673,37674,37676],{},[1979,37675,2128],{},[898,37677,207],{},[898,37679,3783],{},[1846,37681,2075],{},[2175,37683,37684],{"scriptlevel":2177,"displaystyle":1854},[2179,37685,37686,37688],{},[898,37687,1948],{},[898,37689,207],{},[902,37691,37692],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,37694,37696],{"className":37695},[886],[888,37697,37698],{"xmlns":890},[892,37699,37700,37714],{},[895,37701,37702,37710,37712],{},[2175,37703,37704],{"scriptlevel":2177,"displaystyle":1854},[2179,37705,37706,37708],{},[1979,37707,2128],{},[898,37709,207],{},[1846,37711,3295],{},[1979,37713,2177],{},[902,37715,37716],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,37718,37720],{"className":37719},[886],[888,37721,37722],{"xmlns":890},[892,37723,37724,37740],{},[895,37725,37726,37728,37736,37738],{},[1846,37727,2075],{},[2175,37729,37730],{"scriptlevel":2177,"displaystyle":1854},[2179,37731,37732,37734],{},[898,37733,1948],{},[898,37735,207],{},[1846,37737,3256],{},[1979,37739,2177],{},[902,37741,37742],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,37744,37746],{"className":37745},[886],[888,37747,37748],{"xmlns":890},[892,37749,37750,37762],{},[895,37751,37752,37754,37756,37758,37760],{},[1846,37753,1855],{"stretchy":1854},[1979,37755,2177],{},[1846,37757,2136],{"separator":2135},[898,37759,1948],{},[1846,37761,1861],{"stretchy":1854},[902,37763,37764],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,37767,37768],{},"nedokonalé konkurenci",[37770,37771,37773],"h5",{"id":37772},"příklad-21","Příklad 2.1",[724,37775,37776,37779,37780,1734],{},[38,37777,37778],{},"Zadání:"," Lineární poptávka ",[883,37781,37783],{"className":37782},[886],[888,37784,37785],{"xmlns":890},[892,37786,37787,37803],{},[895,37788,37789,37791,37793,37795,37797,37799,37801],{},[898,37790,3783],{},[1846,37792,1848],{},[1846,37794,2075],{},[1979,37796,1981],{},[898,37798,2638],{},[1846,37800,1945],{},[1979,37802,2974],{},[902,37804,37805],{"encoding":904},"P = -2Q + 60",[724,37807,37808,37811,37812,37834,37835,1734],{},[38,37809,37810],{},"Řešení:"," Reálné cenové rozpětí je ",[883,37813,37815],{"className":37814},[886],[888,37816,37817],{"xmlns":890},[892,37818,37819,37831],{},[895,37820,37821,37823,37825,37827,37829],{},[1846,37822,1855],{"stretchy":1854},[1979,37824,2177],{},[1846,37826,2136],{"separator":2135},[1979,37828,2974],{},[1846,37830,1861],{"stretchy":1854},[902,37832,37833],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,37836,37838],{"className":37837},[886],[888,37839,37840],{"xmlns":890},[892,37841,37842,37865],{},[895,37843,37844,37846,37848,37850,37858,37860,37862],{},[898,37845,2638],{},[1846,37847,1848],{},[1846,37849,2075],{},[2175,37851,37852],{"scriptlevel":2177,"displaystyle":1854},[2179,37853,37854,37856],{},[1979,37855,2128],{},[1979,37857,1981],{},[898,37859,3783],{},[1846,37861,1945],{},[1979,37863,37864],{},"30",[902,37866,37867],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,37869,37870,37893],{},[19,37871,37872],{},[22,37873,37874,37889,37891],{},[25,37875,37876],{},[883,37877,37879],{"className":37878},[886],[888,37880,37881],{"xmlns":890},[892,37882,37883,37887],{},[895,37884,37885],{},[898,37886,3783],{},[902,37888,3783],{"encoding":904},[25,37890,5057],{},[25,37892,8881],{},[30,37894,37895],{},[22,37896,37897,37912,37914],{},[35,37898,37899],{},[883,37900,37902],{"className":37901},[886],[888,37903,37904],{"xmlns":890},[892,37905,37906,37910],{},[895,37907,37908],{},[898,37909,2638],{},[902,37911,2638],{"encoding":904},[35,37913,2712],{},[35,37915,8881],{},[724,37917,37918],{},[614,37919,37920,37921,1745,37943,1734],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,37922,37924],{"className":37923},[886],[888,37925,37926],{"xmlns":890},[892,37927,37928,37940],{},[895,37929,37930,37932,37934,37936,37938],{},[1846,37931,2336],{"stretchy":1854},[1979,37933,2177],{},[1846,37935,2136],{"separator":2135},[898,37937,1948],{},[1846,37939,2351],{"stretchy":1854},[902,37941,37942],{"encoding":904},"[0, b]",[883,37944,37946],{"className":37945},[886],[888,37947,37948],{"xmlns":890},[892,37949,37950,37968],{},[895,37951,37952,37954,37956,37958,37960,37962,37964,37966],{},[1846,37953,2336],{"stretchy":1854},[1846,37955,2075],{},[898,37957,1948],{},[898,37959,4520],{"mathvariant":2226},[898,37961,207],{},[1846,37963,2136],{"separator":2135},[1979,37965,2177],{},[1846,37967,2351],{"stretchy":1854},[902,37969,37970],{"encoding":904},"[-b\u002Fa, 0]",[37193,37972,37974],{"id":37973},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,37976,37977,37978,37995],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,37979,37981],{"className":37980},[886],[888,37982,37983],{"xmlns":890},[892,37984,37985,37993],{},[895,37986,37987],{},[1974,37988,37989,37991],{},[898,37990,3783],{},[1846,37992,4200],{},[902,37994,4250],{"encoding":904},", je funkce poptávky konstantní:",[883,37997,37999],{"className":37998},[886],[888,38000,38001],{"xmlns":890,"display":27911},[892,38002,38003,38017],{},[895,38004,38005,38007,38009,38015],{},[898,38006,3783],{},[1846,38008,1848],{},[1974,38010,38011,38013],{},[898,38012,3783],{},[1846,38014,4200],{},[898,38016,1734],{"mathvariant":2226},[902,38018,38019],{"encoding":904},"P = P^*.",[724,38021,38022],{},[614,38023,38024,38025,38046,38047,1734],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,38026,38028],{"className":38027},[886],[888,38029,38030],{"xmlns":890},[892,38031,38032,38044],{},[895,38033,38034,38036,38038,38040,38042],{},[1846,38035,1855],{"stretchy":1854},[898,38037,2638],{},[1846,38039,2136],{"separator":2135},[898,38041,3783],{},[1846,38043,1861],{"stretchy":1854},[902,38045,37536],{"encoding":904}," na úrovni ",[883,38048,38050],{"className":38049},[886],[888,38051,38052],{"xmlns":890},[892,38053,38054,38066],{},[895,38055,38056,38058,38060],{},[898,38057,3783],{},[1846,38059,1848],{},[1974,38061,38062,38064],{},[898,38063,3783],{},[1846,38065,4200],{},[902,38067,4203],{"encoding":904},[37193,38069,38071],{"id":38070},"giffenův-statek","Giffenův statek",[724,38073,38074,38075,38077,38078,38080,38081,1734],{},"Existují zboží, u nichž je křivka poptávky ",[38,38076,13502],{}," — tzv. ",[38,38079,38071],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,38082,38083],{},"podřadnému zboží",[37770,38085,38087],{"id":38086},"příklad-22","Příklad 2.2",[724,38089,38090,38093,38094,38112,38113,38135,38136,38154,38155,38173,38174,38197],{},[38,38091,38092],{},"Zadání a popis:"," Křivka ",[883,38095,38097],{"className":38096},[886],[888,38098,38099],{"xmlns":890},[892,38100,38101,38109],{},[895,38102,38103],{},[2122,38104,38105,38107],{},[898,38106,4029],{},[1979,38108,2128],{},[902,38110,38111],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,38114,38116],{"className":38115},[886],[888,38117,38118],{"xmlns":890},[892,38119,38120,38132],{},[895,38121,38122,38124,38126,38128,38130],{},[1846,38123,1855],{"stretchy":1854},[1979,38125,2177],{},[1846,38127,2136],{"separator":2135},[1979,38129,36089],{},[1846,38131,1861],{"stretchy":1854},[902,38133,38134],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,38137,38139],{"className":38138},[886],[888,38140,38141],{"xmlns":890},[892,38142,38143,38151],{},[895,38144,38145],{},[2122,38146,38147,38149],{},[898,38148,2638],{},[1979,38150,2177],{},[902,38152,38153],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,38156,38158],{"className":38157},[886],[888,38159,38160],{"xmlns":890},[892,38161,38162,38170],{},[895,38163,38164],{},[2122,38165,38166,38168],{},[898,38167,4029],{},[1979,38169,1981],{},[902,38171,38172],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,38175,38177],{"className":38176},[886],[888,38178,38179],{"xmlns":890},[892,38180,38181,38194],{},[895,38182,38183,38185,38187,38189,38192],{},[1846,38184,2336],{"stretchy":1854},[1979,38186,2177],{},[1846,38188,2136],{"separator":2135},[1979,38190,38191],{},"21",[1846,38193,2351],{"stretchy":1854},[902,38195,38196],{"encoding":904},"[0, 21]"," centů.",[198,38199,38201],{"id":38200},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,38203,38204,38205,2554],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,38206,38208],{"className":38207},[886],[888,38209,38210],{"xmlns":890},[892,38211,38212,38216],{},[895,38213,38214],{},[898,38215,8974],{},[902,38217,8974],{"encoding":904},[883,38219,38221],{"className":38220},[886],[888,38222,38223],{"xmlns":890,"display":27911},[892,38224,38225,38256],{},[20599,38226,38227],{"width":27916},[20604,38228,38229,38231,38249,38251],{},[20607,38230],{"width":27921},[20607,38232,38233],{},[895,38234,38235,38237,38239,38241,38243,38245,38247],{},[898,38236,2638],{},[1846,38238,1848],{},[898,38240,4098],{},[1846,38242,1855],{"stretchy":1854},[898,38244,8974],{},[1846,38246,1861],{"stretchy":1854},[898,38248,1734],{"mathvariant":2226},[20607,38250],{"width":27921},[20607,38252,38253],{},[2138,38254,38255],{},"(2.5)",[902,38257,38258],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,38260,38261,38262,38265,38266,38269],{},"Funkce se nazývá ",[38,38263,38264],{},"Engelova",", její graf ",[38,38267,38268],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,38271,38272,38404],{},[123,38273,38274,6861,38277,38290,38291,38304,38305,38322,38323],{},[38,38275,38276],{},"Normální (superior) zboží",[883,38278,38280],{"className":38279},[886],[888,38281,38282],{"xmlns":890},[892,38283,38284,38288],{},[895,38285,38286],{},[898,38287,2638],{},[902,38289,2638],{"encoding":904}," roste s ",[883,38292,38294],{"className":38293},[886],[888,38295,38296],{"xmlns":890},[892,38297,38298,38302],{},[895,38299,38300],{},[898,38301,8974],{},[902,38303,8974],{"encoding":904},", nepřesáhne hodnotu ",[883,38306,38308],{"className":38307},[886],[888,38309,38310],{"xmlns":890},[892,38311,38312,38320],{},[895,38313,38314],{},[2122,38315,38316,38318],{},[898,38317,2638],{},[1979,38319,2177],{},[902,38321,38153],{"encoding":904},":\n",[120,38324,38325,38357],{},[123,38326,38327,38330,38331,38334,38335,1734],{},[38,38328,38329],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,38332,38333],{},"konkávní"," křivka, autonomní spotřeba ",[883,38336,38338],{"className":38337},[886],[888,38339,38340],{"xmlns":890},[892,38341,38342,38354],{},[895,38343,38344,38350,38352],{},[2122,38345,38346,38348],{},[898,38347,2638],{},[1979,38349,2128],{},[1846,38351,3256],{},[1979,38353,2177],{},[902,38355,38356],{"encoding":904},"Q_1 > 0",[123,38358,38359,38362,38363,38381,38382,38384,38385,2053,38402,1734],{},[38,38360,38361],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,38364,38366],{"className":38365},[886],[888,38367,38368],{"xmlns":890},[892,38369,38370,38378],{},[895,38371,38372],{},[2122,38373,38374,38376],{},[898,38375,8974],{},[1979,38377,2128],{},[902,38379,38380],{"encoding":904},"Y_1",", křivka je nejprve ",[38,38383,37509],{}," a od ",[883,38386,38388],{"className":38387},[886],[888,38389,38390],{"xmlns":890},[892,38391,38392,38400],{},[895,38393,38394],{},[2122,38395,38396,38398],{},[898,38397,8974],{},[1979,38399,2128],{},[902,38401,38380],{"encoding":904},[38,38403,38333],{},[123,38405,38406,38409,38410,38428],{},[38,38407,38408],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,38411,38413],{"className":38412},[886],[888,38414,38415],{"xmlns":890},[892,38416,38417,38425],{},[895,38418,38419],{},[2122,38420,38421,38423],{},[898,38422,8974],{},[1979,38424,2177],{},[902,38426,38427],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,38430,38431,38432,38435,38436,3764],{},"Mírou citlivosti je ",[614,38433,38434],{},"důchodová elasticita"," (viz ",[207,38437,3743],{"className":38438,"dataFsResolvedFilePath":848,"href":849},[210],[724,38440,38441],{},[614,38442,38443],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[37193,38445,38447],{"id":38446},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[1639,38449,38450,38521,38564],{},[724,38451,38452,38454,38455,2053,38458,2053,38471,5515,38473,38486,38487,38490,38491,1734],{},[883,38453,4258],{}," Pozor — nezbytné ≠ podřadné\n",[38,38456,38457],{},"Nezbytné zboží:",[883,38459,38461],{"className":38460},[886],[888,38462,38463],{"xmlns":890},[892,38464,38465,38469],{},[895,38466,38467],{},[898,38468,2638],{},[902,38470,2638],{"encoding":904},[38,38472,7168],{},[883,38474,38476],{"className":38475},[886],[888,38477,38478],{"xmlns":890},[892,38479,38480,38484],{},[895,38481,38482],{},[898,38483,8974],{},[902,38485,8974],{"encoding":904},", ale ",[38,38488,38489],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,38492,38494],{"className":38493},[886],[888,38495,38496],{"xmlns":890},[892,38497,38498,38518],{},[895,38499,38500,38506,38508,38510,38512,38514,38516],{},[2122,38501,38502,38504],{},[898,38503,4098],{},[898,38505,8974],{},[1846,38507,6352],{},[1846,38509,1855],{"stretchy":1854},[1979,38511,2177],{},[1846,38513,2136],{"separator":2135},[1979,38515,2128],{},[1846,38517,1861],{"stretchy":1854},[902,38519,38520],{"encoding":904},"E_Y \\in (0, 1)",[724,38522,38523,2053,38526,2053,38539,38541,38542,1734],{},[38,38524,38525],{},"Podřadné zboží:",[883,38527,38529],{"className":38528},[886],[888,38530,38531],{"xmlns":890},[892,38532,38533,38537],{},[895,38534,38535],{},[898,38536,2638],{},[902,38538,2638],{"encoding":904},[38,38540,7188],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,38543,38545],{"className":38544},[886],[888,38546,38547],{"xmlns":890},[892,38548,38549,38561],{},[895,38550,38551,38557,38559],{},[2122,38552,38553,38555],{},[898,38554,4098],{},[898,38556,8974],{},[1846,38558,3295],{},[1979,38560,2177],{},[902,38562,38563],{"encoding":904},"E_Y \u003C 0",[724,38565,38566,38567,1734],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,38568,38569],{},"méně kusů, ne jen proporčně méně",[724,38571,38572,38575,38576,38579],{},[38,38573,38574],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,38577,38578],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,38581,38582],{},[2409,38583],{"alt":38584,"className":38585,"src":38586},"imek-engelovy-krivky-3typy",[210,2413],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[37770,38588,38590],{"id":38589},"české-příklady","České příklady",[16,38592,38593,38603],{},[19,38594,38595],{},[22,38596,38597,38600],{},[25,38598,38599],{},"Podřadné",[25,38601,38602],{},"Nahradí se za",[30,38604,38605,38613,38621,38629,38637,38645,38653,38661],{},[22,38606,38607,38610],{},[35,38608,38609],{},"Instantní polévky, ramen",[35,38611,38612],{},"Čerstvé jídlo, restaurace",[22,38614,38615,38618],{},[35,38616,38617],{},"MHD (autobus, tramvaj)",[35,38619,38620],{},"Vlastní auto, Uber, taxi",[22,38622,38623,38626],{},[35,38624,38625],{},"Mražené polotovary, pizza z mrazáku",[35,38627,38628],{},"Čerstvé suroviny, hotovky",[22,38630,38631,38634],{},[35,38632,38633],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,38635,38636],{},"Značkové produkty",[22,38638,38639,38642],{},[35,38640,38641],{},"Paštika Májka, obyčejný měkký salám",[35,38643,38644],{},"Kvalitní uzeniny, šunka od kosti",[22,38646,38647,38650],{},[35,38648,38649],{},"Second hand oblečení",[35,38651,38652],{},"Nové oblečení, značky",[22,38654,38655,38658],{},[35,38656,38657],{},"Krabicové víno, nejlevnější pivo",[35,38659,38660],{},"Lahvové víno, řemeslná piva",[22,38662,38663,38666],{},[35,38664,38665],{},"Ojetá auta nižších tříd",[35,38667,38668],{},"Nová auta, prémiové značky",[1639,38670,38671],{},[724,38672,38673,38675,38676,38679],{},[883,38674,4418],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,38677,38678],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,38681,38682,38685,38686,9871,38689,38711,38712,9871,38715,38736,38737,38755,38756,38759],{},[38,38683,38684],{},"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 ",[38,38687,38688],{},"luxus",[883,38690,38692],{"className":38691},[886],[888,38693,38694],{"xmlns":890},[892,38695,38696,38708],{},[895,38697,38698,38704,38706],{},[2122,38699,38700,38702],{},[898,38701,4098],{},[898,38703,8974],{},[1846,38705,3256],{},[1979,38707,2128],{},[902,38709,38710],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,38713,38714],{},"podřadné",[883,38716,38718],{"className":38717},[886],[888,38719,38720],{"xmlns":890},[892,38721,38722,38734],{},[895,38723,38724,38730,38732],{},[2122,38725,38726,38728],{},[898,38727,4098],{},[898,38729,8974],{},[1846,38731,3295],{},[1979,38733,2177],{},[902,38735,38563],{"encoding":904},"). Proto je ",[883,38738,38740],{"className":38739},[886],[888,38741,38742],{"xmlns":890},[892,38743,38744,38752],{},[895,38745,38746],{},[2122,38747,38748,38750],{},[898,38749,4098],{},[898,38751,8974],{},[902,38753,38754],{"encoding":904},"E_Y"," vždy ",[38,38757,38758],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,38761,38762,38763,38765],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,38764,38071],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,38767,38769,38770,1861],{"id":38768},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,38771,38772],{},"shift of demand",[724,38774,38775,38776,38794,38795,38812,38813,38826,38827,2535,38840,38862,38863,38880,38881,38907,38908,38911],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,38777,38779],{"className":38778},[886],[888,38780,38781],{"xmlns":890},[892,38782,38783,38791],{},[895,38784,38785],{},[2122,38786,38787,38789],{},[898,38788,3783],{},[1979,38790,2177],{},[902,38792,38793],{"encoding":904},"P_0"," odpovídá množství ",[883,38796,38798],{"className":38797},[886],[888,38799,38800],{"xmlns":890},[892,38801,38802,38810],{},[895,38803,38804],{},[2122,38805,38806,38808],{},[898,38807,2638],{},[1979,38809,2177],{},[902,38811,38153],{"encoding":904}," na křivce ",[883,38814,38816],{"className":38815},[886],[888,38817,38818],{"xmlns":890},[892,38819,38820,38824],{},[895,38821,38822],{},[898,38823,4029],{},[902,38825,4029],{"encoding":904},"; vzroste-li důchod z ",[883,38828,38830],{"className":38829},[886],[888,38831,38832],{"xmlns":890},[892,38833,38834,38838],{},[895,38835,38836],{},[898,38837,8974],{},[902,38839,8974],{"encoding":904},[883,38841,38843],{"className":38842},[886],[888,38844,38845],{"xmlns":890},[892,38846,38847,38859],{},[895,38848,38849,38855,38857],{},[2122,38850,38851,38853],{},[898,38852,8974],{},[1979,38854,2128],{},[1846,38856,3256],{},[898,38858,8974],{},[902,38860,38861],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,38864,38866],{"className":38865},[886],[888,38867,38868],{"xmlns":890},[892,38869,38870,38878],{},[895,38871,38872],{},[2122,38873,38874,38876],{},[898,38875,3783],{},[1979,38877,2177],{},[902,38879,38793],{"encoding":904}," odpovídá vyšší ",[883,38882,38884],{"className":38883},[886],[888,38885,38886],{"xmlns":890},[892,38887,38888,38904],{},[895,38889,38890,38896,38898],{},[2122,38891,38892,38894],{},[898,38893,2638],{},[1979,38895,2128],{},[1846,38897,3256],{},[2122,38899,38900,38902],{},[898,38901,2638],{},[1979,38903,2177],{},[902,38905,38906],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,38909,38910],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,38913,38914],{},[2409,38915],{"alt":38916,"className":38917,"src":38918},"imek-posun-vs-pohyb-po-krivce",[210,2413],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,38920,38921],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,38923,38924],{},[614,38925,38926,38927,13856,38957,38978],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,38928,38930],{"className":38929},[886],[888,38931,38932],{"xmlns":890},[892,38933,38934,38954],{},[895,38935,38936,38942,38944,38946,38948],{},[2122,38937,38938,38940],{},[898,38939,4029],{},[1979,38941,1981],{},[1846,38943,2136],{"separator":2135},[898,38945,4029],{},[1846,38947,2136],{"separator":2135},[2122,38949,38950,38952],{},[898,38951,4029],{},[1979,38953,2128],{},[902,38955,38956],{"encoding":904},"D_2, D, D_1",[883,38958,38960],{"className":38959},[886],[888,38961,38962],{"xmlns":890},[892,38963,38964,38976],{},[895,38965,38966,38968,38970,38972,38974],{},[1846,38967,1855],{"stretchy":1854},[898,38969,2638],{},[1846,38971,2136],{"separator":2135},[898,38973,3783],{},[1846,38975,1861],{"stretchy":1854},[902,38977,37536],{"encoding":904},", šipky naznačují posuny.",[37770,38980,38982],{"id":38981},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,38984,38985,38987,38988,39011,39012,39029,39030,39047,39048,1734],{},[38,38986,37778],{}," Poptávce ",[883,38989,38991],{"className":38990},[886],[888,38992,38993],{"xmlns":890},[892,38994,38995,39009],{},[895,38996,38997,38999,39001,39003,39005,39007],{},[898,38998,3783],{},[1846,39000,1848],{},[898,39002,4029],{},[1846,39004,1855],{"stretchy":1854},[898,39006,2638],{},[1846,39008,1861],{"stretchy":1854},[902,39010,4486],{"encoding":904}," odpovídá ceně ",[883,39013,39015],{"className":39014},[886],[888,39016,39017],{"xmlns":890},[892,39018,39019,39027],{},[895,39020,39021],{},[2122,39022,39023,39025],{},[898,39024,3783],{},[1979,39026,2177],{},[902,39028,38793],{"encoding":904}," množství ",[883,39031,39033],{"className":39032},[886],[888,39034,39035],{"xmlns":890},[892,39036,39037,39045],{},[895,39038,39039],{},[2122,39040,39041,39043],{},[898,39042,2638],{},[1979,39044,2177],{},[902,39046,38153],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,39049,39051],{"className":39050},[886],[888,39052,39053],{"xmlns":890},[892,39054,39055,39059],{},[895,39056,39057],{},[898,39058,2623],{},[902,39060,2623],{"encoding":904},[724,39062,39063,39065,39066,39083,39084,39106],{},[38,39064,37810],{}," Kupující nakupuje množství ",[883,39067,39069],{"className":39068},[886],[888,39070,39071],{"xmlns":890},[892,39072,39073,39081],{},[895,39074,39075],{},[2122,39076,39077,39079],{},[898,39078,2638],{},[1979,39080,2128],{},[902,39082,28847],{"encoding":904},", které odpovídá ceně ",[883,39085,39087],{"className":39086},[886],[888,39088,39089],{"xmlns":890},[892,39090,39091,39103],{},[895,39092,39093,39099,39101],{},[2122,39094,39095,39097],{},[898,39096,3783],{},[1979,39098,2177],{},[1846,39100,1945],{},[898,39102,2623],{},[902,39104,39105],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,39108,39110],{"className":39109},[886],[888,39111,39112],{"xmlns":890,"display":27911},[892,39113,39114,39148],{},[895,39115,39116,39118,39120,39126,39128,39130,39132,39134,39136,39138,39140,39142,39144,39146],{},[898,39117,3783],{},[1846,39119,1848],{},[2122,39121,39122,39124],{},[898,39123,4029],{},[1979,39125,2128],{},[1846,39127,1855],{"stretchy":1854},[898,39129,2638],{},[1846,39131,1861],{"stretchy":1854},[1846,39133,1848],{},[898,39135,4029],{},[1846,39137,1855],{"stretchy":1854},[898,39139,2638],{},[1846,39141,1861],{"stretchy":1854},[1846,39143,2075],{},[898,39145,2623],{},[1846,39147,2136],{"separator":2135},[902,39149,39150],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,39152,39153,39154,1734],{},"tj. dojde k ",[38,39155,39156],{},"posunu poptávky doleva",[724,39158,39159],{},[614,39160,39161,39162,39183,39184,1343,39201,1343,39214,39235,39236,1745,39253,1734],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,39163,39165],{"className":39164},[886],[888,39166,39167],{"xmlns":890},[892,39168,39169,39181],{},[895,39170,39171,39173,39175,39177,39179],{},[1846,39172,1855],{"stretchy":1854},[898,39174,2638],{},[1846,39176,2136],{"separator":2135},[898,39178,3783],{},[1846,39180,1861],{"stretchy":1854},[902,39182,37536],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,39185,39187],{"className":39186},[886],[888,39188,39189],{"xmlns":890},[892,39190,39191,39199],{},[895,39192,39193],{},[2122,39194,39195,39197],{},[898,39196,3783],{},[1979,39198,2177],{},[902,39200,38793],{"encoding":904},[883,39202,39204],{"className":39203},[886],[888,39205,39206],{"xmlns":890},[892,39207,39208,39212],{},[895,39209,39210],{},[898,39211,2623],{},[902,39213,2623],{"encoding":904},[883,39215,39217],{"className":39216},[886],[888,39218,39219],{"xmlns":890},[892,39220,39221,39233],{},[895,39222,39223,39229,39231],{},[2122,39224,39225,39227],{},[898,39226,3783],{},[1979,39228,2177],{},[1846,39230,1945],{},[898,39232,2623],{},[902,39234,39105],{"encoding":904},"; na vodorovné ",[883,39237,39239],{"className":39238},[886],[888,39240,39241],{"xmlns":890},[892,39242,39243,39251],{},[895,39244,39245],{},[2122,39246,39247,39249],{},[898,39248,2638],{},[1979,39250,2128],{},[902,39252,28847],{"encoding":904},[883,39254,39256],{"className":39255},[886],[888,39257,39258],{"xmlns":890},[892,39259,39260,39268],{},[895,39261,39262],{},[2122,39263,39264,39266],{},[898,39265,2638],{},[1979,39267,2177],{},[902,39269,38153],{"encoding":904},[198,39271,39273],{"id":39272},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,39275,39276],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,39278,39280],{"className":39279},[886],[888,39281,39282],{"xmlns":890,"display":27911},[892,39283,39284,39469],{},[20599,39285,39286],{"width":27916},[20604,39287,39288,39290,39462,39464],{},[20607,39289],{"width":27921},[20607,39291,39292],{},[20599,39293,39294,39378],{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},[20604,39295,39296,39306],{},[20607,39297,39298],{},[2175,39299,39300],{"scriptlevel":2177,"displaystyle":2135},[2122,39301,39302,39304],{},[898,39303,2638],{},[1979,39305,2128],{},[20607,39307,39308],{},[2175,39309,39310],{"scriptlevel":2177,"displaystyle":2135},[895,39311,39312,39314,39316,39322,39324,39330,39332,39338,39340,39342,39348,39350,39356,39362,39364,39370,39376],{},[895,39313],{},[1846,39315,1848],{},[2122,39317,39318,39320],{},[898,39319,4029],{},[1979,39321,2128],{},[1846,39323,1855],{"stretchy":1854},[2122,39325,39326,39328],{},[898,39327,3783],{},[1979,39329,2128],{},[1846,39331,2136],{"separator":2135},[2122,39333,39334,39336],{},[898,39335,3783],{},[1979,39337,1981],{},[1846,39339,1861],{"stretchy":1854},[1846,39341,1848],{},[2122,39343,39344,39346],{},[898,39345,207],{},[1979,39347,2128],{},[1846,39349,1945],{},[2122,39351,39352,39354],{},[898,39353,1948],{},[1979,39355,2128],{},[2122,39357,39358,39360],{},[898,39359,3783],{},[1979,39361,2128],{},[1846,39363,1945],{},[2122,39365,39366,39368],{},[898,39367,1992],{},[1979,39369,2128],{},[2122,39371,39372,39374],{},[898,39373,3783],{},[1979,39375,1981],{},[1846,39377,2136],{"separator":2135},[20604,39379,39380,39390],{},[20607,39381,39382],{},[2175,39383,39384],{"scriptlevel":2177,"displaystyle":2135},[2122,39385,39386,39388],{},[898,39387,2638],{},[1979,39389,1981],{},[20607,39391,39392],{},[2175,39393,39394],{"scriptlevel":2177,"displaystyle":2135},[895,39395,39396,39398,39400,39406,39408,39414,39416,39422,39424,39426,39432,39434,39440,39446,39448,39454,39460],{},[895,39397],{},[1846,39399,1848],{},[2122,39401,39402,39404],{},[898,39403,4029],{},[1979,39405,1981],{},[1846,39407,1855],{"stretchy":1854},[2122,39409,39410,39412],{},[898,39411,3783],{},[1979,39413,2128],{},[1846,39415,2136],{"separator":2135},[2122,39417,39418,39420],{},[898,39419,3783],{},[1979,39421,1981],{},[1846,39423,1861],{"stretchy":1854},[1846,39425,1848],{},[2122,39427,39428,39430],{},[898,39429,207],{},[1979,39431,1981],{},[1846,39433,1945],{},[2122,39435,39436,39438],{},[898,39437,1948],{},[1979,39439,1981],{},[2122,39441,39442,39444],{},[898,39443,3783],{},[1979,39445,2128],{},[1846,39447,1945],{},[2122,39449,39450,39452],{},[898,39451,1992],{},[1979,39453,1981],{},[2122,39455,39456,39458],{},[898,39457,3783],{},[1979,39459,1981],{},[898,39461,1734],{"mathvariant":2226},[20607,39463],{"width":27921},[20607,39465,39466],{},[2138,39467,39468],{},"(2.6)",[902,39470,39471],{"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}",[37193,39473,39475],{"id":39474},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,39477,39478,39525,39572],{},[123,39479,39480,1343,39502,39524],{},[883,39481,39483],{"className":39482},[886],[888,39484,39485],{"xmlns":890},[892,39486,39487,39499],{},[895,39488,39489,39495,39497],{},[2122,39490,39491,39493],{},[898,39492,207],{},[1979,39494,2128],{},[1846,39496,3256],{},[1979,39498,2177],{},[902,39500,39501],{"encoding":904},"a_1 > 0",[883,39503,39505],{"className":39504},[886],[888,39506,39507],{"xmlns":890},[892,39508,39509,39521],{},[895,39510,39511,39517,39519],{},[2122,39512,39513,39515],{},[898,39514,207],{},[1979,39516,1981],{},[1846,39518,3256],{},[1979,39520,2177],{},[902,39522,39523],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,39526,39527,1343,39549,39571],{},[883,39528,39530],{"className":39529},[886],[888,39531,39532],{"xmlns":890},[892,39533,39534,39546],{},[895,39535,39536,39542,39544],{},[2122,39537,39538,39540],{},[898,39539,1948],{},[1979,39541,2128],{},[1846,39543,3295],{},[1979,39545,2177],{},[902,39547,39548],{"encoding":904},"b_1 \u003C 0",[883,39550,39552],{"className":39551},[886],[888,39553,39554],{"xmlns":890},[892,39555,39556,39568],{},[895,39557,39558,39564,39566],{},[2122,39559,39560,39562],{},[898,39561,1992],{},[1979,39563,1981],{},[1846,39565,3295],{},[1979,39567,2177],{},[902,39569,39570],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,39573,39574,39575,1343,39592,39610,39611],{},"zkřížené koeficienty ",[883,39576,39578],{"className":39577},[886],[888,39579,39580],{"xmlns":890},[892,39581,39582,39590],{},[895,39583,39584],{},[2122,39585,39586,39588],{},[898,39587,1992],{},[1979,39589,2128],{},[902,39591,29644],{"encoding":904},[883,39593,39595],{"className":39594},[886],[888,39596,39597],{"xmlns":890},[892,39598,39599,39607],{},[895,39600,39601],{},[2122,39602,39603,39605],{},[898,39604,1948],{},[1979,39606,1981],{},[902,39608,39609],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,39612,39613,39663],{},[123,39614,39615,39618,39619,1343,39641,2136],{},[38,39616,39617],{},"substituty"," (máslo vs. margarín): ",[883,39620,39622],{"className":39621},[886],[888,39623,39624],{"xmlns":890},[892,39625,39626,39638],{},[895,39627,39628,39634,39636],{},[2122,39629,39630,39632],{},[898,39631,1992],{},[1979,39633,2128],{},[1846,39635,3256],{},[1979,39637,2177],{},[902,39639,39640],{"encoding":904},"c_1 > 0",[883,39642,39644],{"className":39643},[886],[888,39645,39646],{"xmlns":890},[892,39647,39648,39660],{},[895,39649,39650,39656,39658],{},[2122,39651,39652,39654],{},[898,39653,1948],{},[1979,39655,1981],{},[1846,39657,3256],{},[1979,39659,2177],{},[902,39661,39662],{"encoding":904},"b_2 > 0",[123,39664,39665,39668,39669,1343,39691,1734],{},[38,39666,39667],{},"komplementy"," (auto vs. benzín): ",[883,39670,39672],{"className":39671},[886],[888,39673,39674],{"xmlns":890},[892,39675,39676,39688],{},[895,39677,39678,39684,39686],{},[2122,39679,39680,39682],{},[898,39681,1992],{},[1979,39683,2128],{},[1846,39685,3295],{},[1979,39687,2177],{},[902,39689,39690],{"encoding":904},"c_1 \u003C 0",[883,39692,39694],{"className":39693},[886],[888,39695,39696],{"xmlns":890},[892,39697,39698,39710],{},[895,39699,39700,39706,39708],{},[2122,39701,39702,39704],{},[898,39703,1948],{},[1979,39705,1981],{},[1846,39707,3295],{},[1979,39709,2177],{},[902,39711,39712],{"encoding":904},"b_2 \u003C 0",[724,39714,39715],{},"Schematicky:",[724,39717,39718,39721],{},[38,39719,39720],{},"Substituty",[883,39722,39724],{"className":39723},[886],[888,39725,39726],{"xmlns":890},[892,39727,39728,39867],{},[895,39729,39730,39736,39738,39753,39755,39775,39777,39797,39799,39801,39807,39809,39823,39825,39845,39847],{},[2122,39731,39732,39734],{},[898,39733,2638],{},[1979,39735,2128],{},[1846,39737,1848],{},[898,39739,39740],{},[39741,39742,39743,39751],"munder",{},[1846,39744,39745],{},[2122,39746,39747,39749],{},[898,39748,207],{},[1979,39750,2128],{},[1846,39752,1945],{"lspace":2227,"rspace":2227},[1846,39754,1945],{},[898,39756,39757],{},[39741,39758,39759,39773],{},[1846,39760,39761,39767],{},[2122,39762,39763,39765],{},[898,39764,1948],{},[1979,39766,2128],{},[2122,39768,39769,39771],{},[898,39770,3783],{},[1979,39772,2128],{},[1846,39774,2075],{"lspace":2227,"rspace":2227},[1846,39776,1945],{},[898,39778,39779],{},[39741,39780,39781,39795],{},[1846,39782,39783,39789],{},[2122,39784,39785,39787],{},[898,39786,1992],{},[1979,39788,2128],{},[2122,39790,39791,39793],{},[898,39792,3783],{},[1979,39794,1981],{},[1846,39796,1945],{"lspace":2227,"rspace":2227},[1846,39798,2136],{"separator":2135},[5724,39800],{"width":5726},[2122,39802,39803,39805],{},[898,39804,2638],{},[1979,39806,1981],{},[1846,39808,1848],{},[898,39810,39811],{},[39741,39812,39813,39821],{},[1846,39814,39815],{},[2122,39816,39817,39819],{},[898,39818,207],{},[1979,39820,1981],{},[1846,39822,1945],{"lspace":2227,"rspace":2227},[1846,39824,1945],{},[898,39826,39827],{},[39741,39828,39829,39843],{},[1846,39830,39831,39837],{},[2122,39832,39833,39835],{},[898,39834,1948],{},[1979,39836,1981],{},[2122,39838,39839,39841],{},[898,39840,3783],{},[1979,39842,2128],{},[1846,39844,1945],{"lspace":2227,"rspace":2227},[1846,39846,1945],{},[898,39848,39849],{},[39741,39850,39851,39865],{},[1846,39852,39853,39859],{},[2122,39854,39855,39857],{},[898,39856,1992],{},[1979,39858,1981],{},[2122,39860,39861,39863],{},[898,39862,3783],{},[1979,39864,1981],{},[1846,39866,2075],{"lspace":2227,"rspace":2227},[902,39868,39869],{"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}",[724,39871,39872,39875],{},[38,39873,39874],{},"Komplementy",[883,39876,39878],{"className":39877},[886],[888,39879,39880],{"xmlns":890},[892,39881,39882,40020],{},[895,39883,39884,39890,39892,39906,39908,39928,39930,39950,39952,39954,39960,39962,39976,39978,39998,40000],{},[2122,39885,39886,39888],{},[898,39887,2638],{},[1979,39889,2128],{},[1846,39891,1848],{},[898,39893,39894],{},[39741,39895,39896,39904],{},[1846,39897,39898],{},[2122,39899,39900,39902],{},[898,39901,207],{},[1979,39903,2128],{},[1846,39905,1945],{"lspace":2227,"rspace":2227},[1846,39907,1945],{},[898,39909,39910],{},[39741,39911,39912,39926],{},[1846,39913,39914,39920],{},[2122,39915,39916,39918],{},[898,39917,1948],{},[1979,39919,2128],{},[2122,39921,39922,39924],{},[898,39923,3783],{},[1979,39925,2128],{},[1846,39927,2075],{"lspace":2227,"rspace":2227},[1846,39929,1945],{},[898,39931,39932],{},[39741,39933,39934,39948],{},[1846,39935,39936,39942],{},[2122,39937,39938,39940],{},[898,39939,1992],{},[1979,39941,2128],{},[2122,39943,39944,39946],{},[898,39945,3783],{},[1979,39947,1981],{},[1846,39949,2075],{"lspace":2227,"rspace":2227},[1846,39951,2136],{"separator":2135},[5724,39953],{"width":5726},[2122,39955,39956,39958],{},[898,39957,2638],{},[1979,39959,1981],{},[1846,39961,1848],{},[898,39963,39964],{},[39741,39965,39966,39974],{},[1846,39967,39968],{},[2122,39969,39970,39972],{},[898,39971,207],{},[1979,39973,1981],{},[1846,39975,1945],{"lspace":2227,"rspace":2227},[1846,39977,1945],{},[898,39979,39980],{},[39741,39981,39982,39996],{},[1846,39983,39984,39990],{},[2122,39985,39986,39988],{},[898,39987,1948],{},[1979,39989,1981],{},[2122,39991,39992,39994],{},[898,39993,3783],{},[1979,39995,2128],{},[1846,39997,2075],{"lspace":2227,"rspace":2227},[1846,39999,1945],{},[898,40001,40002],{},[39741,40003,40004,40018],{},[1846,40005,40006,40012],{},[2122,40007,40008,40010],{},[898,40009,1992],{},[1979,40011,1981],{},[2122,40013,40014,40016],{},[898,40015,3783],{},[1979,40017,1981],{},[1846,40019,2075],{"lspace":2227,"rspace":2227},[902,40021,40022],{"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}",[36815,40024],{},[115,40026,12970],{"id":36624},[1639,40028,40029],{},[724,40030,40031,40033,40034,36839,40047,36853,40060,40063,40064,5515,40088,40106],{},[883,40032,4001],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,40035,40037],{"className":40036},[886],[888,40038,40039],{"xmlns":890},[892,40040,40041,40045],{},[895,40042,40043],{},[898,40044,2638],{},[902,40046,2638],{"encoding":904},[883,40048,40050],{"className":40049},[886],[888,40051,40052],{"xmlns":890},[892,40053,40054,40058],{},[895,40055,40056],{},[898,40057,3783],{},[902,40059,3783],{"encoding":904},[38,40061,40062],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,40065,40067],{"className":40066},[886],[888,40068,40069],{"xmlns":890},[892,40070,40071,40085],{},[895,40072,40073,40075,40077,40079,40081,40083],{},[898,40074,3783],{},[1846,40076,1848],{},[898,40078,1992],{},[898,40080,2638],{},[1846,40082,1945],{},[898,40084,2044],{},[902,40086,40087],{"encoding":904},"P = cQ + d",[883,40089,40091],{"className":40090},[886],[888,40092,40093],{"xmlns":890},[892,40094,40095,40103],{},[895,40096,40097,40099,40101],{},[898,40098,1992],{},[1846,40100,3256],{},[1979,40102,2177],{},[902,40104,40105],{"encoding":904},"c > 0"," je standardní aproximací.",[198,40108,36909],{"id":40109},"obecný-vícefaktorový-model-1",[724,40111,40112,9871,40115,40118,40119,40132,40133,36741,40146,36755,40159,40172,40173,40187,40188,36784,40201,40214],{},[38,40113,40114],{},"Nabízené množství",[614,40116,40117],{},"quantity supplied",") závisí na ceně ",[883,40120,40122],{"className":40121},[886],[888,40123,40124],{"xmlns":890},[892,40125,40126,40130],{},[895,40127,40128],{},[898,40129,3783],{},[902,40131,3783],{"encoding":904},", cenách výrobních faktorů (práce ",[883,40134,40136],{"className":40135},[886],[888,40137,40138],{"xmlns":890},[892,40139,40140,40144],{},[895,40141,40142],{},[898,40143,9641],{},[902,40145,9641],{"encoding":904},[883,40147,40149],{"className":40148},[886],[888,40150,40151],{"xmlns":890},[892,40152,40153,40157],{},[895,40154,40155],{},[898,40156,9646],{},[902,40158,9646],{"encoding":904},[883,40160,40162],{"className":40161},[886],[888,40163,40164],{"xmlns":890},[892,40165,40166,40170],{},[895,40167,40168],{},[898,40169,4098],{},[902,40171,4098],{"encoding":904},"), očekávání ",[883,40174,40176],{"className":40175},[886],[888,40177,40178],{"xmlns":890},[892,40179,40180,40185],{},[895,40181,40182],{},[898,40183,40184],{},"V",[902,40186,40184],{"encoding":904},", počtu výrobců ",[883,40189,40191],{"className":40190},[886],[888,40192,40193],{"xmlns":890},[892,40194,40195,40199],{},[895,40196,40197],{},[898,40198,36781],{},[902,40200,36781],{"encoding":904},[883,40202,40204],{"className":40203},[886],[888,40205,40206],{"xmlns":890},[892,40207,40208,40212],{},[895,40209,40210],{},[898,40211,36796],{},[902,40213,36796],{"encoding":904}," a dalších:",[883,40216,40218],{"className":40217},[886],[888,40219,40220],{"xmlns":890,"display":27911},[892,40221,40222,40281],{},[20599,40223,40224],{"width":27916},[20604,40225,40226,40228,40274,40276],{},[20607,40227],{"width":27921},[20607,40229,40230],{},[895,40231,40232,40234,40236,40238,40240,40242,40244,40246,40248,40250,40252,40254,40256,40258,40260,40262,40264,40266,40268,40270,40272],{},[898,40233,2638],{},[1846,40235,1848],{},[898,40237,8519],{},[1846,40239,1855],{"stretchy":1854},[898,40241,3783],{},[1846,40243,2136],{"separator":2135},[898,40245,9641],{},[1846,40247,2136],{"separator":2135},[898,40249,9646],{},[1846,40251,2136],{"separator":2135},[898,40253,4098],{},[1846,40255,2136],{"separator":2135},[898,40257,40184],{},[1846,40259,2136],{"separator":2135},[898,40261,36781],{},[1846,40263,2136],{"separator":2135},[898,40265,36796],{},[1846,40267,2136],{"separator":2135},[1846,40269,9492],{},[1846,40271,1861],{"stretchy":1854},[898,40273,1734],{"mathvariant":2226},[20607,40275],{"width":27921},[20607,40277,40278],{},[2138,40279,40280],{},"(2.7)",[902,40282,40283],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,40285,38261,40286,9871,40289,40292],{},[38,40287,40288],{},"funkce nabídky",[614,40290,40291],{},"supply function",") v širším slova smyslu.",[198,40294,40296],{"id":40295},"jednofaktorový-model","Jednofaktorový model",[724,40298,40299],{},"V nejpřirozenějším jednofaktorovém modelu",[883,40301,40303],{"className":40302},[886],[888,40304,40305],{"xmlns":890,"display":27911},[892,40306,40307,40358],{},[20599,40308,40309],{"width":27916},[20604,40310,40311,40313,40351,40353],{},[20607,40312],{"width":27921},[20607,40314,40315],{},[895,40316,40317,40319,40321,40323,40325,40327,40329,40331,40333,40335,40337,40339,40341,40343,40345,40347,40349],{},[898,40318,2638],{},[1846,40320,1848],{},[898,40322,8519],{},[1846,40324,1855],{"stretchy":1854},[898,40326,3783],{},[1846,40328,1861],{"stretchy":1854},[1846,40330,2136],{"separator":2135},[5724,40332],{"width":5726},[2138,40334,37262],{},[5724,40336],{"width":5726},[898,40338,3783],{},[1846,40340,1848],{},[898,40342,8519],{},[1846,40344,1855],{"stretchy":1854},[898,40346,2638],{},[1846,40348,1861],{"stretchy":1854},[898,40350,1734],{"mathvariant":2226},[20607,40352],{"width":27921},[20607,40354,40355],{},[2138,40356,40357],{},"(2.8)",[902,40359,40360],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,40362,40363,40364,9871,40367,3764],{},"Graf je ",[38,40365,40366],{},"křivka nabídky",[614,40368,40369],{},"supply curve",[37193,40371,40373],{"id":40372},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[1639,40375,40376],{},[724,40377,40378],{},[38,40379,37308,40380,40393,40394,37363],{},[883,40381,40383],{"className":40382},[886],[888,40384,40385],{"xmlns":890},[892,40386,40387,40391],{},[895,40388,40389],{},[898,40390,3783],{},[902,40392,3783],{"encoding":904},", pak nabízené množství ",[883,40395,40397],{"className":40396},[886],[888,40398,40399],{"xmlns":890},[892,40400,40401,40405],{},[895,40402,40403],{},[898,40404,2638],{},[902,40406,2638],{"encoding":904},[724,40408,40409,40410,40435,40436,40466,40467,40484],{},"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 ",[883,40411,40413],{"className":40412},[886],[888,40414,40415],{"xmlns":890},[892,40416,40417,40433],{},[895,40418,40419,40421,40423,40425,40431],{},[1846,40420,2336],{"stretchy":1854},[1979,40422,2177],{},[1846,40424,2136],{"separator":2135},[2122,40426,40427,40429],{},[898,40428,3783],{},[1979,40430,2177],{},[1846,40432,2351],{"stretchy":1854},[902,40434,37448],{"encoding":904}," na svislé ose (případně z ",[883,40437,40439],{"className":40438},[886],[888,40440,40441],{"xmlns":890},[892,40442,40443,40463],{},[895,40444,40445,40447,40453,40455,40461],{},[1846,40446,2336],{"stretchy":1854},[2122,40448,40449,40451],{},[898,40450,2638],{},[1979,40452,2128],{},[1846,40454,2136],{"separator":2135},[2122,40456,40457,40459],{},[898,40458,3783],{},[1979,40460,2128],{},[1846,40462,2351],{"stretchy":1854},[902,40464,40465],{"encoding":904},"[Q_1, P_1]","), kde ",[883,40468,40470],{"className":40469},[886],[888,40471,40472],{"xmlns":890},[892,40473,40474,40482],{},[895,40475,40476],{},[2122,40477,40478,40480],{},[898,40479,3783],{},[1979,40481,2177],{},[902,40483,38793],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,40486,40487],{},[614,40488,40489,40490,3566,40503,1734],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,40491,40493],{"className":40492},[886],[888,40494,40495],{"xmlns":890},[892,40496,40497,40501],{},[895,40498,40499],{},[898,40500,8519],{},[902,40502,8519],{"encoding":904},[883,40504,40506],{"className":40505},[886],[888,40507,40508],{"xmlns":890},[892,40509,40510,40522],{},[895,40511,40512,40514,40516,40518,40520],{},[1846,40513,1855],{"stretchy":1854},[898,40515,2638],{},[1846,40517,2136],{"separator":2135},[898,40519,3783],{},[1846,40521,1861],{"stretchy":1854},[902,40523,37536],{"encoding":904},[37193,40525,40527],{"id":40526},"lineární-model-nabídky","Lineární model nabídky",[883,40529,40531],{"className":40530},[886],[888,40532,40533],{"xmlns":890,"display":27911},[892,40534,40535,40574],{},[20599,40536,40537],{"width":27916},[20604,40538,40539,40541,40567,40569],{},[20607,40540],{"width":27921},[20607,40542,40543],{},[895,40544,40545,40547,40549,40551,40553,40555,40557,40559,40561,40563,40565],{},[898,40546,3783],{},[1846,40548,1848],{},[898,40550,1992],{},[898,40552,2638],{},[1846,40554,1945],{},[898,40556,2044],{},[1846,40558,2136],{"separator":2135},[5724,40560],{"width":5726},[898,40562,1992],{},[1846,40564,3256],{},[1979,40566,12305],{},[20607,40568],{"width":27921},[20607,40570,40571],{},[2138,40572,40573],{},"(2.9)",[902,40575,40576],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,40578,40579,40580,40616,40617,40630],{},"Alternativně ",[883,40581,40583],{"className":40582},[886],[888,40584,40585],{"xmlns":890},[892,40586,40587,40613],{},[895,40588,40589,40591,40593,40601,40603,40605],{},[898,40590,2638],{},[1846,40592,1848],{},[2175,40594,40595],{"scriptlevel":2177,"displaystyle":1854},[2179,40596,40597,40599],{},[1979,40598,2128],{},[898,40600,1992],{},[898,40602,3783],{},[1846,40604,2075],{},[2175,40606,40607],{"scriptlevel":2177,"displaystyle":1854},[2179,40608,40609,40611],{},[898,40610,2044],{},[898,40612,1992],{},[902,40614,40615],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,40618,40620],{"className":40619},[886],[888,40621,40622],{"xmlns":890},[892,40623,40624,40628],{},[895,40625,40626],{},[898,40627,3783],{},[902,40629,3783],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[37770,40632,40634],{"id":40633},"příklad-25","Příklad 2.5",[724,40636,40637,40639,40640,1734],{},[38,40638,37778],{}," Lineární nabídka ",[883,40641,40643],{"className":40642},[886],[888,40644,40645],{"xmlns":890},[892,40646,40647,40661],{},[895,40648,40649,40651,40653,40655,40657,40659],{},[898,40650,3783],{},[1846,40652,1848],{},[1979,40654,4855],{},[898,40656,2638],{},[1846,40658,1945],{},[1979,40660,4850],{},[902,40662,40663],{"encoding":904},"P = 0{,}5Q + 25",[724,40665,40666,40668,40669,1734],{},[38,40667,37810],{}," Alternativní tvar ",[883,40670,40672],{"className":40671},[886],[888,40673,40674],{"xmlns":890},[892,40675,40676,40690],{},[895,40677,40678,40680,40682,40684,40686,40688],{},[898,40679,2638],{},[1846,40681,1848],{},[1979,40683,1981],{},[898,40685,3783],{},[1846,40687,2075],{},[1979,40689,2968],{},[902,40691,40692],{"encoding":904},"Q = 2P - 50",[16,40694,40695,40720],{},[19,40696,40697],{},[22,40698,40699,40714,40716,40718],{},[25,40700,40701],{},[883,40702,40704],{"className":40703},[886],[888,40705,40706],{"xmlns":890},[892,40707,40708,40712],{},[895,40709,40710],{},[898,40711,3783],{},[902,40713,3783],{"encoding":904},[25,40715,37864],{},[25,40717,14883],{},[25,40719,5057],{},[30,40721,40722],{},[22,40723,40724,40739,40741,40743],{},[35,40725,40726],{},[883,40727,40729],{"className":40728},[886],[888,40730,40731],{"xmlns":890},[892,40732,40733,40737],{},[895,40734,40735],{},[898,40736,2638],{},[902,40738,2638],{"encoding":904},[35,40740,2712],{},[35,40742,8881],{},[35,40744,37864],{},[198,40746,40748,40749,1861],{"id":40747},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,40750,40751],{},"shift of supply",[724,40753,40754,40755,40758,40759,40776,40777,40802,40803,1734],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,40756,40757],{},"doprava",": při stejné ceně ",[883,40760,40762],{"className":40761},[886],[888,40763,40764],{"xmlns":890},[892,40765,40766,40774],{},[895,40767,40768],{},[2122,40769,40770,40772],{},[898,40771,3783],{},[1979,40773,2177],{},[902,40775,38793],{"encoding":904}," vyrobí výrobce větší ",[883,40778,40780],{"className":40779},[886],[888,40781,40782],{"xmlns":890},[892,40783,40784,40800],{},[895,40785,40786,40792,40794],{},[2122,40787,40788,40790],{},[898,40789,2638],{},[1979,40791,2128],{},[1846,40793,3256],{},[2122,40795,40796,40798],{},[898,40797,2638],{},[1979,40799,2177],{},[902,40801,38906],{"encoding":904},"); zdražení vstupů posune křivku ",[38,40804,40805],{},"doleva",[724,40807,40808],{},[614,40809,40810,40811,40824,40825,40843,40844,40862,40863,1734],{},"Obrázek 2.11: Původní ",[883,40812,40814],{"className":40813},[886],[888,40815,40816],{"xmlns":890},[892,40817,40818,40822],{},[895,40819,40820],{},[898,40821,8519],{},[902,40823,8519],{"encoding":904},", posunuté ",[883,40826,40828],{"className":40827},[886],[888,40829,40830],{"xmlns":890},[892,40831,40832,40840],{},[895,40833,40834],{},[2122,40835,40836,40838],{},[898,40837,8519],{},[1979,40839,2128],{},[902,40841,40842],{"encoding":904},"S_1"," (doprava) a ",[883,40845,40847],{"className":40846},[886],[888,40848,40849],{"xmlns":890},[892,40850,40851,40859],{},[895,40852,40853],{},[2122,40854,40855,40857],{},[898,40856,8519],{},[1979,40858,1981],{},[902,40860,40861],{"encoding":904},"S_2"," (doleva) v ",[883,40864,40866],{"className":40865},[886],[888,40867,40868],{"xmlns":890},[892,40869,40870,40882],{},[895,40871,40872,40874,40876,40878,40880],{},[1846,40873,1855],{"stretchy":1854},[898,40875,2638],{},[1846,40877,2136],{"separator":2135},[898,40879,3783],{},[1846,40881,1861],{"stretchy":1854},[902,40883,37536],{"encoding":904},[37770,40885,40887],{"id":40886},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,40889,40890,40892,40893,40917,40918,1734],{},[38,40891,37778],{}," Nabídka ",[883,40894,40896],{"className":40895},[886],[888,40897,40898],{"xmlns":890},[892,40899,40900,40914],{},[895,40901,40902,40904,40906,40908,40910,40912],{},[898,40903,3783],{},[1846,40905,1848],{},[898,40907,8519],{},[1846,40909,1855],{"stretchy":1854},[898,40911,2638],{},[1846,40913,1861],{"stretchy":1854},[902,40915,40916],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,40919,40921],{"className":40920},[886],[888,40922,40923],{"xmlns":890},[892,40924,40925,40929],{},[895,40926,40927],{},[898,40928,2623],{},[902,40930,2623],{"encoding":904},[724,40932,40933,40935,40936,40949,40950,40968,40969,40997],{},[38,40934,37810],{}," Spotřebitel zaplatí ",[883,40937,40939],{"className":40938},[886],[888,40940,40941],{"xmlns":890},[892,40942,40943,40947],{},[895,40944,40945],{},[898,40946,3783],{},[902,40948,3783],{"encoding":904},", výrobce obdrží ",[883,40951,40953],{"className":40952},[886],[888,40954,40955],{"xmlns":890},[892,40956,40957,40965],{},[895,40958,40959,40961,40963],{},[898,40960,3783],{},[1846,40962,2075],{},[898,40964,2623],{},[902,40966,40967],{"encoding":904},"P - T",". Z podmínky ",[883,40970,40972],{"className":40971},[886],[888,40973,40974],{"xmlns":890},[892,40975,40976,40994],{},[895,40977,40978,40980,40982,40984,40986,40988,40990,40992],{},[898,40979,3783],{},[1846,40981,2075],{},[898,40983,2623],{},[1846,40985,1848],{},[898,40987,8519],{},[1846,40989,1855],{"stretchy":1854},[898,40991,2638],{},[1846,40993,1861],{"stretchy":1854},[902,40995,40996],{"encoding":904},"P - T = S(Q)"," plyne",[883,40999,41001],{"className":41000},[886],[888,41002,41003],{"xmlns":890,"display":27911},[892,41004,41005,41039],{},[895,41006,41007,41009,41011,41017,41019,41021,41023,41025,41027,41029,41031,41033,41035,41037],{},[898,41008,3783],{},[1846,41010,1848],{},[2122,41012,41013,41015],{},[898,41014,8519],{},[1979,41016,2128],{},[1846,41018,1855],{"stretchy":1854},[898,41020,2638],{},[1846,41022,1861],{"stretchy":1854},[1846,41024,1848],{},[898,41026,8519],{},[1846,41028,1855],{"stretchy":1854},[898,41030,2638],{},[1846,41032,1861],{"stretchy":1854},[1846,41034,1945],{},[898,41036,2623],{},[898,41038,1734],{"mathvariant":2226},[902,41040,41041],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,41043,41044,41045,41058,41059,2053,41072,41075,41076,1745,41096,7948,41114,1734],{},"Křivka ",[883,41046,41048],{"className":41047},[886],[888,41049,41050],{"xmlns":890},[892,41051,41052,41056],{},[895,41053,41054],{},[898,41055,8519],{},[902,41057,8519],{"encoding":904}," se tedy posune o ",[883,41060,41062],{"className":41061},[886],[888,41063,41064],{"xmlns":890},[892,41065,41066,41070],{},[895,41067,41068],{},[898,41069,2623],{},[902,41071,2623],{"encoding":904},[38,41073,41074],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,41077,41079],{"className":41078},[886],[888,41080,41081],{"xmlns":890},[892,41082,41083,41093],{},[895,41084,41085,41087,41089,41091],{},[898,41086,3783],{},[1846,41088,1848],{},[1979,41090,1981],{},[898,41092,2638],{},[902,41094,41095],{"encoding":904},"P = 2Q",[883,41097,41099],{"className":41098},[886],[888,41100,41101],{"xmlns":890},[892,41102,41103,41111],{},[895,41104,41105,41107,41109],{},[898,41106,2623],{},[1846,41108,1848],{},[1979,41110,2085],{},[902,41112,41113],{"encoding":904},"T = 6",[883,41115,41117],{"className":41116},[886],[888,41118,41119],{"xmlns":890},[892,41120,41121,41143],{},[895,41122,41123,41129,41131,41133,41135,41137,41139,41141],{},[2122,41124,41125,41127],{},[898,41126,8519],{},[1979,41128,2128],{},[1846,41130,2554],{},[898,41132,3783],{},[1846,41134,1848],{},[1979,41136,1981],{},[898,41138,2638],{},[1846,41140,1945],{},[1979,41142,2085],{},[902,41144,41145],{"encoding":904},"S_1: P = 2Q + 6",[724,41147,41148],{},[614,41149,41150,41151,41164],{},"Obrázek 2.12: Posun nabídky o ",[883,41152,41154],{"className":41153},[886],[888,41155,41156],{"xmlns":890},[892,41157,41158,41162],{},[895,41159,41160],{},[898,41161,2623],{},[902,41163,2623],{"encoding":904}," svisle nahoru.",[36815,41166],{},[115,41168,41170],{"id":41169},"tržní-rovnováha","Tržní rovnováha",[1639,41172,41173],{},[724,41174,41175,41177,41178,2053,41181,41213,41214,1343,41237,41260,41261,41264,41265,41278],{},[883,41176,4001],{}," TL;DR\nV ",[38,41179,41180],{},"rovnovážném bodě",[883,41182,41184],{"className":41183},[886],[888,41185,41186],{"xmlns":890},[892,41187,41188,41210],{},[895,41189,41190,41192,41194,41200,41202,41208],{},[898,41191,4098],{},[1846,41193,2336],{"stretchy":1854},[1974,41195,41196,41198],{},[898,41197,2638],{},[898,41199,4098],{},[1846,41201,2136],{"separator":2135},[1974,41203,41204,41206],{},[898,41205,3783],{},[898,41207,4098],{},[1846,41209,2351],{"stretchy":1854},[902,41211,41212],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,41215,41217],{"className":41216},[886],[888,41218,41219],{"xmlns":890},[892,41220,41221,41235],{},[895,41222,41223,41225,41227,41229,41231,41233],{},[898,41224,3783],{},[1846,41226,1848],{},[898,41228,4029],{},[1846,41230,1855],{"stretchy":1854},[898,41232,2638],{},[1846,41234,1861],{"stretchy":1854},[902,41236,4486],{"encoding":904},[883,41238,41240],{"className":41239},[886],[888,41241,41242],{"xmlns":890},[892,41243,41244,41258],{},[895,41245,41246,41248,41250,41252,41254,41256],{},[898,41247,3783],{},[1846,41249,1848],{},[898,41251,8519],{},[1846,41253,1855],{"stretchy":1854},[898,41255,2638],{},[1846,41257,1861],{"stretchy":1854},[902,41259,40916],{"encoding":904},". Čtyři ",[38,41262,41263],{},"pravidla komparativní statiky"," popisují, jak se ",[883,41266,41268],{"className":41267},[886],[888,41269,41270],{"xmlns":890},[892,41271,41272,41276],{},[895,41273,41274],{},[898,41275,4098],{},[902,41277,4098],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,41280,41282],{"id":41281},"definice","Definice",[724,41284,41285,9871,41287,41290,41291,2053,41294,41312,41313,41344,41345,9871,41348,3764],{},[38,41286,41170],{},[614,41288,41289],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,41292,41293],{},"rovnovážné ceně",[883,41295,41297],{"className":41296},[886],[888,41298,41299],{"xmlns":890},[892,41300,41301,41309],{},[895,41302,41303],{},[1974,41304,41305,41307],{},[898,41306,3783],{},[898,41308,4098],{},[902,41310,41311],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,41314,41316],{"className":41315},[886],[888,41317,41318],{"xmlns":890},[892,41319,41320,41342],{},[895,41321,41322,41324,41326,41332,41334,41340],{},[898,41323,4098],{},[1846,41325,2336],{"stretchy":1854},[1974,41327,41328,41330],{},[898,41329,2638],{},[898,41331,4098],{},[1846,41333,2136],{"separator":2135},[1974,41335,41336,41338],{},[898,41337,3783],{},[898,41339,4098],{},[1846,41341,2351],{"stretchy":1854},[902,41343,41212],{"encoding":904}," se nazývá ",[38,41346,41347],{},"rovnovážný bod",[614,41349,41350],{},"equilibrium point",[724,41352,41353,41354,1343,41377,1734],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,41355,41357],{"className":41356},[886],[888,41358,41359],{"xmlns":890},[892,41360,41361,41375],{},[895,41362,41363,41365,41367,41369,41371,41373],{},[898,41364,3783],{},[1846,41366,1848],{},[898,41368,4029],{},[1846,41370,1855],{"stretchy":1854},[898,41372,2638],{},[1846,41374,1861],{"stretchy":1854},[902,41376,4486],{"encoding":904},[883,41378,41380],{"className":41379},[886],[888,41381,41382],{"xmlns":890},[892,41383,41384,41398],{},[895,41385,41386,41388,41390,41392,41394,41396],{},[898,41387,3783],{},[1846,41389,1848],{},[898,41391,8519],{},[1846,41393,1855],{"stretchy":1854},[898,41395,2638],{},[1846,41397,1861],{"stretchy":1854},[902,41399,40916],{"encoding":904},[724,41401,41402],{},[2409,41403],{"alt":41404,"className":41405,"src":41406},"imek-poptavka-nabidka-rovnovaha",[210,2413],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,41408,41409],{},[614,41410,41411,41412,41425,41426,13856,41439,41460,41461,1734],{},"Obrázek 2.13: Klesající ",[883,41413,41415],{"className":41414},[886],[888,41416,41417],{"xmlns":890},[892,41418,41419,41423],{},[895,41420,41421],{},[898,41422,4029],{},[902,41424,4029],{"encoding":904}," a rostoucí ",[883,41427,41429],{"className":41428},[886],[888,41430,41431],{"xmlns":890},[892,41432,41433,41437],{},[895,41434,41435],{},[898,41436,8519],{},[902,41438,8519],{"encoding":904},[883,41440,41442],{"className":41441},[886],[888,41443,41444],{"xmlns":890},[892,41445,41446,41458],{},[895,41447,41448,41450,41452,41454,41456],{},[1846,41449,1855],{"stretchy":1854},[898,41451,2638],{},[1846,41453,2136],{"separator":2135},[898,41455,3783],{},[1846,41457,1861],{"stretchy":1854},[902,41459,37536],{"encoding":904}," protínající se v ",[883,41462,41464],{"className":41463},[886],[888,41465,41466],{"xmlns":890},[892,41467,41468,41490],{},[895,41469,41470,41472,41474,41480,41482,41488],{},[898,41471,4098],{},[1846,41473,2336],{"stretchy":1854},[1974,41475,41476,41478],{},[898,41477,2638],{},[898,41479,4098],{},[1846,41481,2136],{"separator":2135},[1974,41483,41484,41486],{},[898,41485,3783],{},[898,41487,4098],{},[1846,41489,2351],{"stretchy":1854},[902,41491,41212],{"encoding":904},[198,41493,41495],{"id":41494},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,41497,41498,41500,41501,41535,41536,1734],{},[38,41499,37778],{}," Poptávka ",[883,41502,41504],{"className":41503},[886],[888,41505,41506],{"xmlns":890},[892,41507,41508,41532],{},[895,41509,41510,41512,41514,41516,41522,41524,41526,41528,41530],{},[898,41511,3783],{},[1846,41513,1848],{},[1846,41515,2075],{},[1974,41517,41518,41520],{},[898,41519,2638],{},[1979,41521,1981],{},[1846,41523,2075],{},[1979,41525,2712],{},[898,41527,2638],{},[1846,41529,1945],{},[1979,41531,8649],{},[902,41533,41534],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,41537,41539],{"className":41538},[886],[888,41540,41541],{"xmlns":890},[892,41542,41543,41565],{},[895,41544,41545,41547,41549,41555,41557,41559,41561,41563],{},[898,41546,3783],{},[1846,41548,1848],{},[1974,41550,41551,41553],{},[898,41552,2638],{},[1979,41554,1981],{},[1846,41556,1945],{},[1979,41558,22791],{},[898,41560,2638],{},[1846,41562,1945],{},[1979,41564,32391],{},[902,41566,41567],{"encoding":904},"P = Q^2 + 14Q + 22",[724,41569,41570,41572],{},[38,41571,37810],{}," Z rovnosti",[883,41574,41576],{"className":41575},[886],[888,41577,41578],{"xmlns":890,"display":27911},[892,41579,41580,41618],{},[895,41581,41582,41584,41590,41592,41594,41596,41598,41600,41602,41608,41610,41612,41614,41616],{},[1846,41583,2075],{},[1974,41585,41586,41588],{},[898,41587,2638],{},[1979,41589,1981],{},[1846,41591,2075],{},[1979,41593,2712],{},[898,41595,2638],{},[1846,41597,1945],{},[1979,41599,8649],{},[1846,41601,1848],{},[1974,41603,41604,41606],{},[898,41605,2638],{},[1979,41607,1981],{},[1846,41609,1945],{},[1979,41611,22791],{},[898,41613,2638],{},[1846,41615,1945],{},[1979,41617,32391],{},[902,41619,41620],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,41622,41623,41624,41659,41660,41693,41694,41711,41712,41725,41726,1343,41748,41785,41786,1734],{},"dostaneme ",[883,41625,41627],{"className":41626},[886],[888,41628,41629],{"xmlns":890},[892,41630,41631,41656],{},[895,41632,41633,41635,41641,41643,41646,41648,41650,41652,41654],{},[1979,41634,1981],{},[1974,41636,41637,41639],{},[898,41638,2638],{},[1979,41640,1981],{},[1846,41642,1945],{},[1979,41644,41645],{},"24",[898,41647,2638],{},[1846,41649,2075],{},[1979,41651,5463],{},[1846,41653,1848],{},[1979,41655,2177],{},[902,41657,41658],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,41661,41663],{"className":41662},[886],[888,41664,41665],{"xmlns":890},[892,41666,41667,41690],{},[895,41668,41669,41675,41677,41679,41681,41683,41686,41688],{},[1974,41670,41671,41673],{},[898,41672,2638],{},[1979,41674,1981],{},[1846,41676,1945],{},[1979,41678,3357],{},[898,41680,2638],{},[1846,41682,2075],{},[1979,41684,41685],{},"64",[1846,41687,1848],{},[1979,41689,2177],{},[902,41691,41692],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,41695,41697],{"className":41696},[886],[888,41698,41699],{"xmlns":890},[892,41700,41701,41708],{},[895,41702,41703,41705],{},[1846,41704,2075],{},[1979,41706,41707],{},"16",[902,41709,41710],{"encoding":904},"-16"," (nevyhovuje) a ",[883,41713,41715],{"className":41714},[886],[888,41716,41717],{"xmlns":890},[892,41718,41719,41723],{},[895,41720,41721],{},[1979,41722,2201],{},[902,41724,2201],{"encoding":904},". Tedy ",[883,41727,41729],{"className":41728},[886],[888,41730,41731],{"xmlns":890},[892,41732,41733,41745],{},[895,41734,41735,41741,41743],{},[1974,41736,41737,41739],{},[898,41738,2638],{},[898,41740,4098],{},[1846,41742,1848],{},[1979,41744,2201],{},[902,41746,41747],{"encoding":904},"Q^E = 4",[883,41749,41751],{"className":41750},[886],[888,41752,41753],{"xmlns":890},[892,41754,41755,41782],{},[895,41756,41757,41763,41765,41767,41769,41771,41773,41775,41777,41779],{},[1974,41758,41759,41761],{},[898,41760,3783],{},[898,41762,4098],{},[1846,41764,1848],{},[1846,41766,2075],{},[1979,41768,41707],{},[1846,41770,2075],{},[1979,41772,5057],{},[1846,41774,1945],{},[1979,41776,8649],{},[1846,41778,1848],{},[1979,41780,41781],{},"94",[902,41783,41784],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,41787,41789],{"className":41788},[886],[888,41790,41791],{"xmlns":890},[892,41792,41793,41807],{},[895,41794,41795,41797,41799,41801,41803,41805],{},[898,41796,4098],{},[1846,41798,2336],{"stretchy":1854},[1979,41800,2201],{},[1846,41802,2136],{"separator":2135},[1979,41804,41781],{},[1846,41806,2351],{"stretchy":1854},[902,41808,41809],{"encoding":904},"E[4, 94]",[198,41811,41813],{"id":41812},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,41815,41816,41818],{},[38,41817,37778],{}," Poptávky a nabídky dvou zboží",[883,41820,41822],{"className":41821},[886],[888,41823,41824],{"xmlns":890,"display":27911},[892,41825,41826,41992],{},[20599,41827,41830,41918],{"rowspacing":20601,"columnalign":41828,"columnspacing":41829},"right left right left","0em 1em 0em",[20604,41831,41832,41842,41874,41884],{},[20607,41833,41834],{},[2175,41835,41836],{"scriptlevel":2177,"displaystyle":2135},[2122,41837,41838,41840],{},[898,41839,2638],{},[1979,41841,2128],{},[20607,41843,41844],{},[2175,41845,41846],{"scriptlevel":2177,"displaystyle":2135},[895,41847,41848,41850,41852,41854,41856,41858,41864,41866,41872],{},[895,41849],{},[1846,41851,1848],{},[1979,41853,5057],{},[1846,41855,2075],{},[1979,41857,2078],{},[2122,41859,41860,41862],{},[898,41861,3783],{},[1979,41863,2128],{},[1846,41865,2075],{},[2122,41867,41868,41870],{},[898,41869,3783],{},[1979,41871,1981],{},[1846,41873,2136],{"separator":2135},[20607,41875,41876],{},[2175,41877,41878],{"scriptlevel":2177,"displaystyle":2135},[2122,41879,41880,41882],{},[898,41881,2638],{},[1979,41883,1981],{},[20607,41885,41886],{},[2175,41887,41888],{"scriptlevel":2177,"displaystyle":2135},[895,41889,41890,41892,41894,41896,41898,41900,41906,41908,41910,41916],{},[895,41891],{},[1846,41893,1848],{},[1979,41895,2968],{},[1846,41897,2075],{},[1979,41899,1981],{},[2122,41901,41902,41904],{},[898,41903,3783],{},[1979,41905,2128],{},[1846,41907,2075],{},[1979,41909,2201],{},[2122,41911,41912,41914],{},[898,41913,3783],{},[1979,41915,1981],{},[1846,41917,2136],{"separator":2135},[20604,41919,41920,41930,41956,41966],{},[20607,41921,41922],{},[2175,41923,41924],{"scriptlevel":2177,"displaystyle":2135},[2122,41925,41926,41928],{},[898,41927,2638],{},[1979,41929,2128],{},[20607,41931,41932],{},[2175,41933,41934],{"scriptlevel":2177,"displaystyle":2135},[895,41935,41936,41938,41940,41942,41944,41946,41948,41954],{},[895,41937],{},[1846,41939,1848],{},[1846,41941,2075],{},[1979,41943,2023],{},[1846,41945,1945],{},[1979,41947,2201],{},[2122,41949,41950,41952],{},[898,41951,3783],{},[1979,41953,2128],{},[1846,41955,2136],{"separator":2135},[20607,41957,41958],{},[2175,41959,41960],{"scriptlevel":2177,"displaystyle":2135},[2122,41961,41962,41964],{},[898,41963,2638],{},[1979,41965,1981],{},[20607,41967,41968],{},[2175,41969,41970],{"scriptlevel":2177,"displaystyle":2135},[895,41971,41972,41974,41976,41978,41980,41982,41984,41990],{},[895,41973],{},[1846,41975,1848],{},[1846,41977,2075],{},[1979,41979,24046],{},[1846,41981,1945],{},[1979,41983,2023],{},[2122,41985,41986,41988],{},[898,41987,3783],{},[1979,41989,1981],{},[898,41991,1734],{"mathvariant":2226},[902,41993,41994],{"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}",[724,41996,41997,41999],{},[38,41998,37810],{}," Z rovností poptávek a nabídek dostaneme",[883,42001,42003],{"className":42002},[886],[888,42004,42005],{"xmlns":890,"display":27911},[892,42006,42007,42056],{},[895,42008,42009,42011,42017,42019,42025,42027,42029,42031,42033,42035,42041,42043,42045,42051,42053],{},[1979,42010,3845],{},[2122,42012,42013,42015],{},[898,42014,3783],{},[1979,42016,2128],{},[1846,42018,1945],{},[2122,42020,42021,42023],{},[898,42022,3783],{},[1979,42024,1981],{},[1846,42026,1848],{},[1979,42028,21048],{},[1846,42030,2136],{"separator":2135},[5724,42032],{"width":5726},[1979,42034,1981],{},[2122,42036,42037,42039],{},[898,42038,3783],{},[1979,42040,2128],{},[1846,42042,1945],{},[1979,42044,24046],{},[2122,42046,42047,42049],{},[898,42048,3783],{},[1979,42050,1981],{},[1846,42052,1848],{},[1979,42054,42055],{},"57.",[902,42057,42058],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,42060,42061,42062,1343,42086,42110,42111,1343,42136,42160,42161,42163],{},"Řešením je ",[883,42063,42065],{"className":42064},[886],[888,42066,42067],{"xmlns":890},[892,42068,42069,42083],{},[895,42070,42071,42079,42081],{},[9012,42072,42073,42075,42077],{},[898,42074,3783],{},[1979,42076,2128],{},[898,42078,4098],{},[1846,42080,1848],{},[1979,42082,2201],{},[902,42084,42085],{"encoding":904},"P_1^E = 4",[883,42087,42089],{"className":42088},[886],[888,42090,42091],{"xmlns":890},[892,42092,42093,42107],{},[895,42094,42095,42103,42105],{},[9012,42096,42097,42099,42101],{},[898,42098,3783],{},[1979,42100,1981],{},[898,42102,4098],{},[1846,42104,1848],{},[1979,42106,24046],{},[902,42108,42109],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,42112,42114],{"className":42113},[886],[888,42115,42116],{"xmlns":890},[892,42117,42118,42133],{},[895,42119,42120,42128,42130],{},[9012,42121,42122,42124,42126],{},[898,42123,2638],{},[1979,42125,2128],{},[898,42127,4098],{},[1846,42129,1848],{},[1979,42131,42132],{},"13",[902,42134,42135],{"encoding":904},"Q_1^E = 13",[883,42137,42139],{"className":42138},[886],[888,42140,42141],{"xmlns":890},[892,42142,42143,42157],{},[895,42144,42145,42153,42155],{},[9012,42146,42147,42149,42151],{},[898,42148,2638],{},[1979,42150,1981],{},[898,42152,4098],{},[1846,42154,1848],{},[1979,42156,22791],{},[902,42158,42159],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,42162,39667],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,42165,42167],{"id":42166},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,42169,42170,42171,42188,42189,9871,42192,3764],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,42172,42174],{"className":42173},[886],[888,42175,42176],{"xmlns":890},[892,42177,42178,42186],{},[895,42179,42180],{},[1974,42181,42182,42184],{},[898,42183,3783],{},[898,42185,4098],{},[902,42187,41311],{"encoding":904},"; mechanismus popisuje ",[38,42190,42191],{},"teorém pavučiny",[614,42193,42194],{},"cobweb model",[198,42196,42198],{"id":42197},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,42200,42201],{},[2409,42202],{"alt":42203,"className":42204,"src":42205},"imek-komparativni-statika-4pripady",[210,2413],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[1639,42207,42208,42249,42289,42329],{},[724,42209,42210,42213,42214,6036,42231,1734],{},[38,42211,42212],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,42215,42217],{"className":42216},[886],[888,42218,42219],{"xmlns":890},[892,42220,42221,42229],{},[895,42222,42223],{},[1974,42224,42225,42227],{},[898,42226,3783],{},[898,42228,4098],{},[902,42230,41311],{"encoding":904},[883,42232,42234],{"className":42233},[886],[888,42235,42236],{"xmlns":890},[892,42237,42238,42246],{},[895,42239,42240],{},[1974,42241,42242,42244],{},[898,42243,2638],{},[898,42245,4098],{},[902,42247,42248],{"encoding":904},"Q^E",[724,42250,42251,42254,42255,6036,42272,1734],{},[38,42252,42253],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,42256,42258],{"className":42257},[886],[888,42259,42260],{"xmlns":890},[892,42261,42262,42270],{},[895,42263,42264],{},[1974,42265,42266,42268],{},[898,42267,3783],{},[898,42269,4098],{},[902,42271,41311],{"encoding":904},[883,42273,42275],{"className":42274},[886],[888,42276,42277],{"xmlns":890},[892,42278,42279,42287],{},[895,42280,42281],{},[1974,42282,42283,42285],{},[898,42284,2638],{},[898,42286,4098],{},[902,42288,42248],{"encoding":904},[724,42290,42291,42294,42295,9201,42312,1734],{},[38,42292,42293],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,42296,42298],{"className":42297},[886],[888,42299,42300],{"xmlns":890},[892,42301,42302,42310],{},[895,42303,42304],{},[1974,42305,42306,42308],{},[898,42307,3783],{},[898,42309,4098],{},[902,42311,41311],{"encoding":904},[883,42313,42315],{"className":42314},[886],[888,42316,42317],{"xmlns":890},[892,42318,42319,42327],{},[895,42320,42321],{},[1974,42322,42323,42325],{},[898,42324,2638],{},[898,42326,4098],{},[902,42328,42248],{"encoding":904},[724,42330,42331,42334,42335,42352,42353,1734],{},[38,42332,42333],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,42336,42338],{"className":42337},[886],[888,42339,42340],{"xmlns":890},[892,42341,42342,42350],{},[895,42343,42344],{},[1974,42345,42346,42348],{},[898,42347,3783],{},[898,42349,4098],{},[902,42351,41311],{"encoding":904},", pokles ",[883,42354,42356],{"className":42355},[886],[888,42357,42358],{"xmlns":890},[892,42359,42360,42368],{},[895,42361,42362],{},[1974,42363,42364,42366],{},[898,42365,2638],{},[898,42367,4098],{},[902,42369,42248],{"encoding":904},[16,42371,42372,42417],{},[19,42373,42374],{},[22,42375,42376,42379,42398],{},[25,42377,42378],{},"Změna",[25,42380,42381],{},[883,42382,42384],{"className":42383},[886],[888,42385,42386],{"xmlns":890},[892,42387,42388,42396],{},[895,42389,42390],{},[1974,42391,42392,42394],{},[898,42393,3783],{},[898,42395,4098],{},[902,42397,41311],{"encoding":904},[25,42399,42400],{},[883,42401,42403],{"className":42402},[886],[888,42404,42405],{"xmlns":890},[892,42406,42407,42415],{},[895,42408,42409],{},[1974,42410,42411,42413],{},[898,42412,2638],{},[898,42414,4098],{},[902,42416,42248],{"encoding":904},[30,42418,42419,42429,42439,42448],{},[22,42420,42421,42424,42427],{},[35,42422,42423],{},"Růst poptávky",[35,42425,42426],{},"↑",[35,42428,42426],{},[22,42430,42431,42434,42437],{},[35,42432,42433],{},"Pokles poptávky",[35,42435,42436],{},"↓",[35,42438,42436],{},[22,42440,42441,42444,42446],{},[35,42442,42443],{},"Růst nabídky",[35,42445,42436],{},[35,42447,42426],{},[22,42449,42450,42453,42455],{},[35,42451,42452],{},"Pokles nabídky",[35,42454,42426],{},[35,42456,42436],{},[724,42458,42459],{},[614,42460,42461],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[36815,42463],{},[115,42465,811],{"id":42466},"zdanění-trhu",[1639,42468,42469,42558],{},[724,42470,42471,42473,42474,42487,42488,2776,42501,42504,42505,36621,42528,42553,42554,42557],{},[883,42472,4001],{}," TL;DR\nJednotková daň ",[883,42475,42477],{"className":42476},[886],[888,42478,42479],{"xmlns":890},[892,42480,42481,42485],{},[895,42482,42483],{},[898,42484,2623],{},[902,42486,2623],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,42489,42491],{"className":42490},[886],[888,42492,42493],{"xmlns":890},[892,42494,42495,42499],{},[895,42496,42497],{},[898,42498,2623],{},[902,42500,2623],{"encoding":904},[38,42502,42503],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,42506,42508],{"className":42507},[886],[888,42509,42510],{"xmlns":890},[892,42511,42512,42525],{},[895,42513,42514],{},[2122,42515,42516,42518],{},[898,42517,2623],{},[895,42519,42520,42523],{},[898,42521,42522],{},"s",[898,42524,724],{},[902,42526,42527],{"encoding":904},"T_{sp}",[883,42529,42531],{"className":42530},[886],[888,42532,42533],{"xmlns":890},[892,42534,42535,42550],{},[895,42536,42537],{},[2122,42538,42539,42541],{},[898,42540,2623],{},[895,42542,42543,42546,42548],{},[898,42544,42545],{},"v",[898,42547,1844],{},[898,42549,11886],{},[902,42551,42552],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,42555,42556],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,42559,42560],{},[614,42561,42562,42563,1734],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,42564,42566],{"className":42565,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,42568,42569,42570,42573,42574,42600,42601,42604,42605,42631,42632,42649,42650,42690,42691,1745,42704,1734],{},"Existují dvě formy zdanění — daň uložená ",[38,42571,42572],{},"výrobci"," (posun nabídky ",[883,42575,42577],{"className":42576},[886],[888,42578,42579],{"xmlns":890},[892,42580,42581,42597],{},[895,42582,42583,42589,42591,42593,42595],{},[2122,42584,42585,42587],{},[898,42586,8519],{},[1979,42588,2128],{},[1846,42590,1848],{},[898,42592,8519],{},[1846,42594,1945],{},[898,42596,2623],{},[902,42598,42599],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,42602,42603],{},"spotřebiteli"," (posun poptávky ",[883,42606,42608],{"className":42607},[886],[888,42609,42610],{"xmlns":890},[892,42611,42612,42628],{},[895,42613,42614,42620,42622,42624,42626],{},[2122,42615,42616,42618],{},[898,42617,4029],{},[1979,42619,1981],{},[1846,42621,1848],{},[898,42623,4029],{},[1846,42625,2075],{},[898,42627,2623],{},[902,42629,42630],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,42633,42635],{"className":42634},[886],[888,42636,42637],{"xmlns":890},[892,42638,42639,42647],{},[895,42640,42641],{},[1974,42642,42643,42645],{},[898,42644,2638],{},[898,42646,4098],{},[902,42648,42248],{"encoding":904}," klesá a vzniká rozklad daně ",[883,42651,42653],{"className":42652},[886],[888,42654,42655],{"xmlns":890},[892,42656,42657,42687],{},[895,42658,42659,42661,42663,42673,42675],{},[898,42660,2623],{},[1846,42662,1848],{},[2122,42664,42665,42667],{},[898,42666,2623],{},[895,42668,42669,42671],{},[898,42670,42522],{},[898,42672,724],{},[1846,42674,1945],{},[2122,42676,42677,42679],{},[898,42678,2623],{},[895,42680,42681,42683,42685],{},[898,42682,42545],{},[898,42684,1844],{},[898,42686,11886],{},[902,42688,42689],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,42692,42694],{"className":42693},[886],[888,42695,42696],{"xmlns":890},[892,42697,42698,42702],{},[895,42699,42700],{},[898,42701,4029],{},[902,42703,4029],{"encoding":904},[883,42705,42707],{"className":42706},[886],[888,42708,42709],{"xmlns":890},[892,42710,42711,42715],{},[895,42712,42713],{},[898,42714,8519],{},[902,42716,8519],{"encoding":904},[724,42718,42719,42720,42723,42724,1745,42754,42788],{},"Zásadním výsledkem kapitoly je ",[38,42721,42722],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,42725,42727],{"className":42726},[886],[888,42728,42729],{"xmlns":890},[892,42730,42731,42751],{},[895,42732,42733,42741,42743],{},[9012,42734,42735,42737,42739],{},[898,42736,2638],{},[1979,42738,2128],{},[898,42740,4098],{},[1846,42742,1848],{},[9012,42744,42745,42747,42749],{},[898,42746,2638],{},[1979,42748,1981],{},[898,42750,4098],{},[902,42752,42753],{"encoding":904},"Q_1^E = Q_2^E",[883,42755,42757],{"className":42756},[886],[888,42758,42759],{"xmlns":890},[892,42760,42761,42785],{},[895,42762,42763,42771,42773,42775,42777],{},[9012,42764,42765,42767,42769],{},[898,42766,3783],{},[1979,42768,2128],{},[898,42770,4098],{},[1846,42772,2075],{},[898,42774,2623],{},[1846,42776,1848],{},[9012,42778,42779,42781,42783],{},[898,42780,3783],{},[1979,42782,1981],{},[898,42784,4098],{},[902,42786,42787],{"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.",[724,42790,42791,42792,42795,42796,42822,42823,42851,42852,42855,42856,42859,42860,1734],{},"Podrobný výklad, Příklady ",[38,42793,42794],{},"2.9"," (daň výrobci, ",[883,42797,42799],{"className":42798},[886],[888,42800,42801],{"xmlns":890},[892,42802,42803,42819],{},[895,42804,42805,42815,42817],{},[2122,42806,42807,42809],{},[898,42808,2623],{},[895,42810,42811,42813],{},[898,42812,42522],{},[898,42814,724],{},[1846,42816,1848],{},[1979,42818,1981],{},[902,42820,42821],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,42824,42826],{"className":42825},[886],[888,42827,42828],{"xmlns":890},[892,42829,42830,42848],{},[895,42831,42832,42844,42846],{},[2122,42833,42834,42836],{},[898,42835,2623],{},[895,42837,42838,42840,42842],{},[898,42839,42545],{},[898,42841,1844],{},[898,42843,11886],{},[1846,42845,1848],{},[1979,42847,2201],{},[902,42849,42850],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,42853,42854],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,42857,42858],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,42861,42566],{"className":42862,"dataFsResolvedFilePath":809,"href":810},[210],[36815,42864],{},[115,42866,42868],{"id":42867},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[1639,42870,42871],{},[724,42872,42873,42875,42876,42879,42880,42882],{},[883,42874,4001],{}," TL;DR\nMultiplikátory jsou ",[38,42877,42878],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,42881,36805],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,42884,42886],{"id":42885},"redukovaný-tvar","Redukovaný tvar",[724,42888,42889,42890,9871,42913,1343,42931,11973,42948,9871,42971,42988,42989,43019],{},"Pro lineární model ",[883,42891,42893],{"className":42892},[886],[888,42894,42895],{"xmlns":890},[892,42896,42897,42911],{},[895,42898,42899,42901,42903,42905,42907,42909],{},[898,42900,3783],{},[1846,42902,1848],{},[898,42904,207],{},[898,42906,2638],{},[1846,42908,1945],{},[898,42910,1948],{},[902,42912,36905],{"encoding":904},[883,42914,42916],{"className":42915},[886],[888,42917,42918],{"xmlns":890},[892,42919,42920,42928],{},[895,42921,42922,42924,42926],{},[898,42923,207],{},[1846,42925,3295],{},[1979,42927,2177],{},[902,42929,42930],{"encoding":904},"a \u003C 0",[883,42932,42934],{"className":42933},[886],[888,42935,42936],{"xmlns":890},[892,42937,42938,42946],{},[895,42939,42940,42942,42944],{},[898,42941,1948],{},[1846,42943,3256],{},[1979,42945,2177],{},[902,42947,18659],{"encoding":904},[883,42949,42951],{"className":42950},[886],[888,42952,42953],{"xmlns":890},[892,42954,42955,42969],{},[895,42956,42957,42959,42961,42963,42965,42967],{},[898,42958,3783],{},[1846,42960,1848],{},[898,42962,1992],{},[898,42964,2638],{},[1846,42966,1945],{},[898,42968,2044],{},[902,42970,40087],{"encoding":904},[883,42972,42974],{"className":42973},[886],[888,42975,42976],{"xmlns":890},[892,42977,42978,42986],{},[895,42979,42980,42982,42984],{},[898,42981,1992],{},[1846,42983,3256],{},[1979,42985,2177],{},[902,42987,40105],{"encoding":904},") dává podmínka rovnováhy ",[883,42990,42992],{"className":42991},[886],[888,42993,42994],{"xmlns":890},[892,42995,42996,43016],{},[895,42997,42998,43000,43002,43004,43006,43008,43010,43012,43014],{},[898,42999,207],{},[898,43001,2638],{},[1846,43003,1945],{},[898,43005,1948],{},[1846,43007,1848],{},[898,43009,1992],{},[898,43011,2638],{},[1846,43013,1945],{},[898,43015,2044],{},[902,43017,43018],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,43021,43023],{"className":43022},[886],[888,43024,43025],{"xmlns":890,"display":27911},[892,43026,43027,43072],{},[20599,43028,43029],{"width":27916},[20604,43030,43031,43033,43065,43067],{},[20607,43032],{"width":27921},[20607,43034,43035],{},[895,43036,43037,43043,43045,43063],{},[1974,43038,43039,43041],{},[898,43040,2638],{},[898,43042,4098],{},[1846,43044,1848],{},[2179,43046,43047,43055],{},[895,43048,43049,43051,43053],{},[898,43050,1948],{},[1846,43052,2075],{},[898,43054,2044],{},[895,43056,43057,43059,43061],{},[898,43058,1992],{},[1846,43060,2075],{},[898,43062,207],{},[898,43064,1734],{"mathvariant":2226},[20607,43066],{"width":27921},[20607,43068,43069],{},[2138,43070,43071],{},"(2.10)",[902,43073,43074],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,43076,43077,43078,9871,43080,43083,43084,43101,43102,2053,43105,43131,43132,43145,43146,43164,43165,3764],{},"Vztah (2.10) je ",[38,43079,20799],{},[614,43081,43082],{},"reduced form",") pro ",[883,43085,43087],{"className":43086},[886],[888,43088,43089],{"xmlns":890},[892,43090,43091,43099],{},[895,43092,43093],{},[1974,43094,43095,43097],{},[898,43096,2638],{},[898,43098,4098],{},[902,43100,42248],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,43103,43104],{},"parametrů",[883,43106,43108],{"className":43107},[886],[888,43109,43110],{"xmlns":890},[892,43111,43112,43128],{},[895,43113,43114,43116,43118,43120,43122,43124,43126],{},[898,43115,207],{},[1846,43117,2136],{"separator":2135},[898,43119,1948],{},[1846,43121,2136],{"separator":2135},[898,43123,1992],{},[1846,43125,2136],{"separator":2135},[898,43127,2044],{},[902,43129,43130],{"encoding":904},"a, b, c, d",". Aby ",[883,43133,43135],{"className":43134},[886],[888,43136,43137],{"xmlns":890},[892,43138,43139,43143],{},[895,43140,43141],{},[898,43142,4098],{},[902,43144,4098],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,43147,43149],{"className":43148},[886],[888,43150,43151],{"xmlns":890},[892,43152,43153,43161],{},[895,43154,43155,43157,43159],{},[898,43156,1948],{},[1846,43158,3256],{},[898,43160,2044],{},[902,43162,43163],{"encoding":904},"b > d"," (neboť ",[883,43166,43168],{"className":43167},[886],[888,43169,43170],{"xmlns":890},[892,43171,43172,43184],{},[895,43173,43174,43176,43178,43180,43182],{},[898,43175,1992],{},[1846,43177,2075],{},[898,43179,207],{},[1846,43181,3256],{},[1979,43183,2177],{},[902,43185,43186],{"encoding":904},"c - a > 0",[724,43188,43189],{},[614,43190,43191,43192,43205,43206,43219,43220,18493,43233,41785,43250,43263],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,43193,43195],{"className":43194},[886],[888,43196,43197],{"xmlns":890},[892,43198,43199,43203],{},[895,43200,43201],{},[898,43202,1948],{},[902,43204,1948],{"encoding":904}," na ose ",[883,43207,43209],{"className":43208},[886],[888,43210,43211],{"xmlns":890},[892,43212,43213,43217],{},[895,43214,43215],{},[898,43216,3783],{},[902,43218,3783],{"encoding":904},") a nabídka (úsek ",[883,43221,43223],{"className":43222},[886],[888,43224,43225],{"xmlns":890},[892,43226,43227,43231],{},[895,43228,43229],{},[898,43230,2044],{},[902,43232,2044],{"encoding":904},[883,43234,43236],{"className":43235},[886],[888,43237,43238],{"xmlns":890},[892,43239,43240,43248],{},[895,43241,43242,43244,43246],{},[898,43243,1948],{},[1846,43245,3256],{},[898,43247,2044],{},[902,43249,43163],{"encoding":904},[883,43251,43253],{"className":43252},[886],[888,43254,43255],{"xmlns":890},[892,43256,43257,43261],{},[895,43258,43259],{},[898,43260,4098],{},[902,43262,4098],{"encoding":904}," v 1. kvadrantu.",[198,43265,43267],{"id":43266},"definice-multiplikátorů","Definice multiplikátorů",[724,43269,43270,43271,43296,43297,43310,43311,43324],{},"V komparativní statice jsou ",[883,43272,43274],{"className":43273},[886],[888,43275,43276],{"xmlns":890},[892,43277,43278,43294],{},[895,43279,43280,43282,43284,43286,43288,43290,43292],{},[898,43281,207],{},[1846,43283,2136],{"separator":2135},[898,43285,1948],{},[1846,43287,2136],{"separator":2135},[898,43289,1992],{},[1846,43291,2136],{"separator":2135},[898,43293,2044],{},[902,43295,43130],{"encoding":904}," exogenní proměnné a ",[883,43298,43300],{"className":43299},[886],[888,43301,43302],{"xmlns":890},[892,43303,43304,43308],{},[895,43305,43306],{},[898,43307,2638],{},[902,43309,2638],{"encoding":904}," endogenní. Přibližná změna ",[883,43312,43314],{"className":43313},[886],[888,43315,43316],{"xmlns":890},[892,43317,43318,43322],{},[895,43319,43320],{},[898,43321,2638],{},[902,43323,2638],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,43326,43328],{"className":43327},[886],[888,43329,43330],{"xmlns":890,"display":27911},[892,43331,43332,43425],{},[20599,43333,43334],{"width":27916},[20604,43335,43336,43338,43418,43420],{},[20607,43337],{"width":27921},[20607,43339,43340],{},[895,43341,43342,43344,43346,43348,43350,43352,43354,43362,43364,43366,43368,43370,43378,43380,43382,43384,43386,43394,43396,43398,43400,43402,43410,43412,43414,43416],{},[898,43343,2738],{"mathvariant":2226},[898,43345,2638],{},[1846,43347,1650],{},[898,43349,2044],{},[898,43351,2638],{},[1846,43353,1848],{},[9012,43355,43356,43358,43360],{},[898,43357,2638],{},[898,43359,207],{},[1846,43361,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[2138,43363,2835],{},[898,43365,2044],{},[898,43367,207],{},[1846,43369,1945],{},[9012,43371,43372,43374,43376],{},[898,43373,2638],{},[898,43375,1948],{},[1846,43377,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[2138,43379,2835],{},[898,43381,2044],{},[898,43383,1948],{},[1846,43385,1945],{},[9012,43387,43388,43390,43392],{},[898,43389,2638],{},[898,43391,1992],{},[1846,43393,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[2138,43395,2835],{},[898,43397,2044],{},[898,43399,1992],{},[1846,43401,1945],{},[9012,43403,43404,43406,43408],{},[898,43405,2638],{},[898,43407,2044],{},[1846,43409,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[2138,43411,2835],{},[898,43413,2044],{},[898,43415,2044],{},[898,43417,1734],{"mathvariant":2226},[20607,43419],{"width":27921},[20607,43421,43422],{},[2138,43423,43424],{},"(2.11)",[902,43426,43427],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,43429,43430,43431,43481,43482,9871,43484,2999],{},"Parciální derivace ",[883,43432,43434],{"className":43433},[886],[888,43435,43436],{"xmlns":890},[892,43437,43438,43478],{},[895,43439,43440,43448,43450,43458,43460,43468,43470],{},[9012,43441,43442,43444,43446],{},[898,43443,2638],{},[898,43445,207],{},[1846,43447,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,43449,2136],{"separator":2135},[9012,43451,43452,43454,43456],{},[898,43453,2638],{},[898,43455,1948],{},[1846,43457,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,43459,2136],{"separator":2135},[9012,43461,43462,43464,43466],{},[898,43463,2638],{},[898,43465,1992],{},[1846,43467,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,43469,2136],{"separator":2135},[9012,43471,43472,43474,43476],{},[898,43473,2638],{},[898,43475,2044],{},[1846,43477,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,43479,43480],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,43483,17822],{},[614,43485,43486],{},"multipliers",[883,43488,43490],{"className":43489},[886],[888,43491,43492],{"xmlns":890,"display":27911},[892,43493,43494,43645],{},[20599,43495,43496],{"width":27916},[20604,43497,43498,43500,43638,43640],{},[20607,43499],{"width":27921},[20607,43501,43502],{},[895,43503,43504,43512,43514,43540,43542,43544,43552,43554,43566,43568,43570,43578,43580,43582,43608,43610,43612,43620,43622,43624,43636],{},[9012,43505,43506,43508,43510],{},[898,43507,2638],{},[898,43509,207],{},[1846,43511,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,43513,1848],{},[2179,43515,43516,43524],{},[895,43517,43518,43520,43522],{},[898,43519,1948],{},[1846,43521,2075],{},[898,43523,2044],{},[895,43525,43526,43528,43530,43532,43534],{},[1846,43527,1855],{"stretchy":1854},[898,43529,1992],{},[1846,43531,2075],{},[898,43533,207],{},[1974,43535,43536,43538],{},[1846,43537,1861],{"stretchy":1854},[1979,43539,1981],{},[1846,43541,2136],{"separator":2135},[5724,43543],{"width":15129},[9012,43545,43546,43548,43550],{},[898,43547,2638],{},[898,43549,1948],{},[1846,43551,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,43553,1848],{},[2179,43555,43556,43558],{},[1979,43557,2128],{},[895,43559,43560,43562,43564],{},[898,43561,1992],{},[1846,43563,2075],{},[898,43565,207],{},[1846,43567,2136],{"separator":2135},[5724,43569],{"width":15129},[9012,43571,43572,43574,43576],{},[898,43573,2638],{},[898,43575,1992],{},[1846,43577,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,43579,1848],{},[1846,43581,2075],{},[2179,43583,43584,43592],{},[895,43585,43586,43588,43590],{},[898,43587,1948],{},[1846,43589,2075],{},[898,43591,2044],{},[895,43593,43594,43596,43598,43600,43602],{},[1846,43595,1855],{"stretchy":1854},[898,43597,1992],{},[1846,43599,2075],{},[898,43601,207],{},[1974,43603,43604,43606],{},[1846,43605,1861],{"stretchy":1854},[1979,43607,1981],{},[1846,43609,2136],{"separator":2135},[5724,43611],{"width":15129},[9012,43613,43614,43616,43618],{},[898,43615,2638],{},[898,43617,2044],{},[1846,43619,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,43621,1848],{},[1846,43623,2075],{},[2179,43625,43626,43628],{},[1979,43627,2128],{},[895,43629,43630,43632,43634],{},[898,43631,1992],{},[1846,43633,2075],{},[898,43635,207],{},[898,43637,1734],{"mathvariant":2226},[20607,43639],{"width":27921},[20607,43641,43642],{},[2138,43643,43644],{},"(2.12)",[902,43646,43647],{"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}",[198,43649,43651],{"id":43650},"znaménka-a-interpretace","Znaménka a interpretace",[724,43653,43654,43655,1343,43672,1343,43689,1343,43706,43723,43724,2999],{},"Za podmínek ",[883,43656,43658],{"className":43657},[886],[888,43659,43660],{"xmlns":890},[892,43661,43662,43670],{},[895,43663,43664,43666,43668],{},[898,43665,207],{},[1846,43667,3295],{},[1979,43669,2177],{},[902,43671,42930],{"encoding":904},[883,43673,43675],{"className":43674},[886],[888,43676,43677],{"xmlns":890},[892,43678,43679,43687],{},[895,43680,43681,43683,43685],{},[898,43682,1948],{},[1846,43684,3256],{},[1979,43686,2177],{},[902,43688,18659],{"encoding":904},[883,43690,43692],{"className":43691},[886],[888,43693,43694],{"xmlns":890},[892,43695,43696,43704],{},[895,43697,43698,43700,43702],{},[898,43699,1992],{},[1846,43701,3256],{},[1979,43703,2177],{},[902,43705,40105],{"encoding":904},[883,43707,43709],{"className":43708},[886],[888,43710,43711],{"xmlns":890},[892,43712,43713,43721],{},[895,43714,43715,43717,43719],{},[898,43716,1948],{},[1846,43718,3256],{},[898,43720,2044],{},[902,43722,43163],{"encoding":904}," platí (znaménka se ",[38,43725,43726],{},"nemění",[883,43728,43730],{"className":43729},[886],[888,43731,43732],{"xmlns":890,"display":27911},[892,43733,43734,43796],{},[895,43735,43736,43744,43746,43748,43750,43752,43760,43762,43764,43766,43768,43776,43778,43780,43782,43784,43792,43794],{},[9012,43737,43738,43740,43742],{},[898,43739,2638],{},[898,43741,207],{},[1846,43743,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,43745,3256],{},[1979,43747,2177],{},[1846,43749,2136],{"separator":2135},[5724,43751],{"width":5726},[9012,43753,43754,43756,43758],{},[898,43755,2638],{},[898,43757,1948],{},[1846,43759,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,43761,3256],{},[1979,43763,2177],{},[1846,43765,2136],{"separator":2135},[5724,43767],{"width":5726},[9012,43769,43770,43772,43774],{},[898,43771,2638],{},[898,43773,1992],{},[1846,43775,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,43777,3295],{},[1979,43779,2177],{},[1846,43781,2136],{"separator":2135},[5724,43783],{"width":5726},[9012,43785,43786,43788,43790],{},[898,43787,2638],{},[898,43789,2044],{},[1846,43791,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,43793,3295],{},[1979,43795,12305],{},[902,43797,43798],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,43800,43801,43860],{},[123,43802,43803,2053,43806,43826,43827,43844,43845,1343,43858,1734],{},[38,43804,43805],{},"Kvantitativní smysl:",[883,43807,43809],{"className":43808},[886],[888,43810,43811],{"xmlns":890},[892,43812,43813,43823],{},[895,43814,43815],{},[9012,43816,43817,43819,43821],{},[898,43818,2638],{},[898,43820,1858],{},[1846,43822,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,43824,43825],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,43828,43830],{"className":43829},[886],[888,43831,43832],{"xmlns":890},[892,43833,43834,43842],{},[895,43835,43836],{},[1974,43837,43838,43840],{},[898,43839,2638],{},[898,43841,4098],{},[902,43843,42248],{"encoding":904}," při jednotkové změně parametru ",[883,43846,43848],{"className":43847},[886],[888,43849,43850],{"xmlns":890},[892,43851,43852,43856],{},[895,43853,43854],{},[898,43855,1858],{},[902,43857,1858],{"encoding":904},[614,43859,36805],{},[123,43861,43862,43865,43866,43883,43884,1734],{},[38,43863,43864],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,43867,43869],{"className":43868},[886],[888,43870,43871],{"xmlns":890},[892,43872,43873,43881],{},[895,43874,43875],{},[1974,43876,43877,43879],{},[898,43878,2638],{},[898,43880,4098],{},[902,43882,42248],{"encoding":904}," na růst ",[883,43885,43887],{"className":43886},[886],[888,43888,43889],{"xmlns":890},[892,43890,43891,43895],{},[895,43892,43893],{},[898,43894,1858],{},[902,43896,1858],{"encoding":904},[724,43898,43899,43900,43913,43914,43164,43931,3764],{},"Např. růst ",[883,43901,43903],{"className":43902},[886],[888,43904,43905],{"xmlns":890},[892,43906,43907,43911],{},[895,43908,43909],{},[898,43910,1992],{},[902,43912,1992],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,43915,43917],{"className":43916},[886],[888,43918,43919],{"xmlns":890},[892,43920,43921,43929],{},[895,43922,43923],{},[1974,43924,43925,43927],{},[898,43926,2638],{},[898,43928,4098],{},[902,43930,42248],{"encoding":904},[883,43932,43934],{"className":43933},[886],[888,43935,43936],{"xmlns":890},[892,43937,43938,43952],{},[895,43939,43940,43948,43950],{},[9012,43941,43942,43944,43946],{},[898,43943,2638],{},[898,43945,1992],{},[1846,43947,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,43949,3295],{},[1979,43951,2177],{},[902,43953,43954],{"encoding":904},"Q'_c \u003C 0",[724,43956,43957],{},[614,43958,43959,43960,43980,43981,44005,44006,44028,44029,1734],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,43961,43963],{"className":43962},[886],[888,43964,43965],{"xmlns":890},[892,43966,43967,43977],{},[895,43968,43969,43971,43973,43975],{},[898,43970,1992],{},[898,43972,2638],{},[1846,43974,1945],{},[898,43976,2044],{},[902,43978,43979],{"encoding":904},"cQ + d"," na strmější ",[883,43982,43984],{"className":43983},[886],[888,43985,43986],{"xmlns":890},[892,43987,43988,44002],{},[895,43989,43990,43996,43998,44000],{},[2122,43991,43992,43994],{},[898,43993,1992],{},[1979,43995,2128],{},[898,43997,2638],{},[1846,43999,1945],{},[898,44001,2044],{},[902,44003,44004],{"encoding":904},"c_1 Q + d"," (při ",[883,44007,44009],{"className":44008},[886],[888,44010,44011],{"xmlns":890},[892,44012,44013,44025],{},[895,44014,44015,44021,44023],{},[2122,44016,44017,44019],{},[898,44018,1992],{},[1979,44020,2128],{},[1846,44022,3256],{},[898,44024,1992],{},[902,44026,44027],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,44030,44032],{"className":44031},[886],[888,44033,44034],{"xmlns":890},[892,44035,44036,44046],{},[895,44037,44038,44044],{},[1974,44039,44040,44042],{},[898,44041,2638],{},[898,44043,4098],{},[1846,44045,42436],{},[902,44047,44048],{"encoding":904},"Q^E \\downarrow",[724,44050,44051,44052,44084,44085,1734],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,44053,44055],{"className":44054},[886],[888,44056,44057],{"xmlns":890},[892,44058,44059,44081],{},[895,44060,44061,44063,44065,44067,44075,44077,44079],{},[898,44062,2738],{"mathvariant":2226},[898,44064,2638],{},[1846,44066,1650],{},[9012,44068,44069,44071,44073],{},[898,44070,2638],{},[898,44072,1948],{},[1846,44074,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[2138,44076,2835],{},[898,44078,2044],{},[898,44080,1948],{},[902,44082,44083],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,44086,44088],{"className":44087},[886],[888,44089,44090],{"xmlns":890},[892,44091,44092,44100],{},[895,44093,44094],{},[1974,44095,44096,44098],{},[898,44097,3783],{},[898,44099,4098],{},[902,44101,41311],{"encoding":904},[198,44103,44105,44106],{"id":44104},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,44107,44109],{"className":44108},[886],[888,44110,44111],{"xmlns":890},[892,44112,44113,44121],{},[895,44114,44115],{},[1974,44116,44117,44119],{},[898,44118,2638],{},[898,44120,4098],{},[902,44122,42248],{"encoding":904},[724,44124,44125,41500,44127,41535,44153,1734],{},[38,44126,37778],{},[883,44128,44130],{"className":44129},[886],[888,44131,44132],{"xmlns":890},[892,44133,44134,44150],{},[895,44135,44136,44138,44140,44142,44144,44146,44148],{},[898,44137,3783],{},[1846,44139,1848],{},[1846,44141,2075],{},[1979,44143,2023],{},[898,44145,2638],{},[1846,44147,1945],{},[1979,44149,5057],{},[902,44151,44152],{"encoding":904},"P = -3Q + 40",[883,44154,44156],{"className":44155},[886],[888,44157,44158],{"xmlns":890},[892,44159,44160,44174],{},[895,44161,44162,44164,44166,44168,44170,44172],{},[898,44163,3783],{},[1846,44165,1848],{},[1979,44167,4855],{},[898,44169,2638],{},[1846,44171,1945],{},[1979,44173,2712],{},[902,44175,44176],{"encoding":904},"P = 0{,}5Q + 10",[724,44178,44179,44181],{},[38,44180,37810],{}," Rovnovážné množství",[883,44183,44185],{"className":44184},[886],[888,44186,44187],{"xmlns":890,"display":27911},[892,44188,44189,44257],{},[895,44190,44191,44197,44199,44217,44219,44243,44245,44252,44254],{},[1974,44192,44193,44195],{},[898,44194,2638],{},[898,44196,4098],{},[1846,44198,1848],{},[2179,44200,44201,44209],{},[895,44202,44203,44205,44207],{},[898,44204,1948],{},[1846,44206,2075],{},[898,44208,2044],{},[895,44210,44211,44213,44215],{},[898,44212,1992],{},[1846,44214,2075],{},[898,44216,207],{},[1846,44218,1848],{},[2179,44220,44221,44229],{},[895,44222,44223,44225,44227],{},[1979,44224,5057],{},[1846,44226,2075],{},[1979,44228,2712],{},[895,44230,44231,44233,44235,44237,44239,44241],{},[1979,44232,4855],{},[1846,44234,2075],{},[1846,44236,1855],{"stretchy":1854},[1846,44238,2075],{},[1979,44240,2023],{},[1846,44242,1861],{"stretchy":1854},[1846,44244,1848],{},[2179,44246,44247,44249],{},[1979,44248,37864],{},[1979,44250,44251],{},"3,5",[1846,44253,1650],{},[1979,44255,44256],{},"8,571.",[902,44258,44259],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,44261,44262,44307],{},[38,44263,44264,44265,2521,44278,2535,44292,44306],{},"(a) Změna ",[883,44266,44268],{"className":44267},[886],[888,44269,44270],{"xmlns":890},[892,44271,44272,44276],{},[895,44273,44274],{},[898,44275,1992],{},[902,44277,1992],{"encoding":904},[883,44279,44281],{"className":44280},[886],[888,44282,44283],{"xmlns":890},[892,44284,44285,44289],{},[895,44286,44287],{},[1979,44288,4855],{},[902,44290,44291],{"encoding":904},"0{,}5",[883,44293,44295],{"className":44294},[886],[888,44296,44297],{"xmlns":890},[892,44298,44299,44303],{},[895,44300,44301],{},[1979,44302,19166],{},[902,44304,44305],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,44309,44311],{"className":44310},[886],[888,44312,44313],{"xmlns":890,"display":27911},[892,44314,44315,44392],{},[895,44316,44317,44325,44327,44329,44331,44333,44335,44361,44363,44365,44367,44369,44371,44381,44383,44385,44387,44389],{},[9012,44318,44319,44321,44323],{},[898,44320,2638],{},[898,44322,1992],{},[1846,44324,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[2138,44326,2835],{},[898,44328,2044],{},[898,44330,1992],{},[1846,44332,1848],{},[1846,44334,2075],{},[2179,44336,44337,44345],{},[895,44338,44339,44341,44343],{},[898,44340,1948],{},[1846,44342,2075],{},[898,44344,2044],{},[895,44346,44347,44349,44351,44353,44355],{},[1846,44348,1855],{"stretchy":1854},[898,44350,1992],{},[1846,44352,2075],{},[898,44354,207],{},[1974,44356,44357,44359],{},[1846,44358,1861],{"stretchy":1854},[1979,44360,1981],{},[2138,44362,2835],{},[898,44364,2044],{},[898,44366,1992],{},[1846,44368,1848],{},[1846,44370,2075],{},[2179,44372,44373,44375],{},[1979,44374,37864],{},[1974,44376,44377,44379],{},[1979,44378,44251],{},[1979,44380,1981],{},[1846,44382,3025],{},[1979,44384,2643],{},[1846,44386,1650],{},[1846,44388,2075],{},[1979,44390,44391],{},"0,245.",[902,44393,44394],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,44396,44397,44398,1734],{},"Nové rovnovážné množství ",[883,44399,44401],{"className":44400},[886],[888,44402,44403],{"xmlns":890},[892,44404,44405,44430],{},[895,44406,44407,44415,44417,44420,44422,44425,44427],{},[9012,44408,44409,44411,44413],{},[898,44410,2638],{},[1979,44412,2128],{},[898,44414,4098],{},[1846,44416,1650],{},[1979,44418,44419],{},"8,571",[1846,44421,2075],{},[1979,44423,44424],{},"0,245",[1846,44426,1848],{},[1979,44428,44429],{},"8,326",[902,44431,44432],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,44434,44435,44520],{},[38,44436,44437,44438,1343,44458,1343,44480,1343,44500,1734],{},"(b) Současné změny ",[883,44439,44441],{"className":44440},[886],[888,44442,44443],{"xmlns":890},[892,44444,44445,44455],{},[895,44446,44447,44449,44451,44453],{},[898,44448,2044],{},[898,44450,207],{},[1846,44452,1848],{},[1979,44454,4855],{},[902,44456,44457],{"encoding":904},"da = 0{,}5",[883,44459,44461],{"className":44460},[886],[888,44462,44463],{"xmlns":890},[892,44464,44465,44477],{},[895,44466,44467,44469,44471,44473,44475],{},[898,44468,2044],{},[898,44470,1948],{},[1846,44472,1848],{},[1846,44474,2075],{},[1979,44476,2078],{},[902,44478,44479],{"encoding":904},"db = -5",[883,44481,44483],{"className":44482},[886],[888,44484,44485],{"xmlns":890},[892,44486,44487,44497],{},[895,44488,44489,44491,44493,44495],{},[898,44490,2044],{},[898,44492,1992],{},[1846,44494,1848],{},[1979,44496,2643],{},[902,44498,44499],{"encoding":904},"dc = 0{,}1",[883,44501,44503],{"className":44502},[886],[888,44504,44505],{"xmlns":890},[892,44506,44507,44517],{},[895,44508,44509,44511,44513,44515],{},[898,44510,2044],{},[898,44512,2044],{},[1846,44514,1848],{},[1979,44516,2128],{},[902,44518,44519],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,44522,44524],{"className":44523},[886],[888,44525,44526],{"xmlns":890,"display":27911},[892,44527,44528,44671],{},[20599,44529,44530,44612,44648],{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},[20604,44531,44532,44542],{},[20607,44533,44534],{},[2175,44535,44536],{"scriptlevel":2177,"displaystyle":2135},[895,44537,44538,44540],{},[898,44539,2738],{"mathvariant":2226},[898,44541,2638],{},[20607,44543,44544],{},[2175,44545,44546],{"scriptlevel":2177,"displaystyle":2135},[895,44547,44548,44550,44552,44562,44564,44566,44568,44574,44576,44578,44580,44582,44584,44586,44596,44598,44600,44602,44608,44610],{},[895,44549],{},[1846,44551,1650],{},[2179,44553,44554,44556],{},[1979,44555,37864],{},[1974,44557,44558,44560],{},[1979,44559,44251],{},[1979,44561,1981],{},[1846,44563,3025],{},[1979,44565,4855],{},[1846,44567,1945],{},[2179,44569,44570,44572],{},[1979,44571,2128],{},[1979,44573,44251],{},[1846,44575,3025],{},[1846,44577,1855],{"stretchy":1854},[1846,44579,2075],{},[1979,44581,2078],{},[1846,44583,1861],{"stretchy":1854},[1846,44585,2075],{},[2179,44587,44588,44590],{},[1979,44589,37864],{},[1974,44591,44592,44594],{},[1979,44593,44251],{},[1979,44595,1981],{},[1846,44597,3025],{},[1979,44599,2643],{},[1846,44601,2075],{},[2179,44603,44604,44606],{},[1979,44605,2128],{},[1979,44607,44251],{},[1846,44609,3025],{},[1979,44611,2128],{},[20604,44613,44614,44620],{},[20607,44615,44616],{},[2175,44617,44618],{"scriptlevel":2177,"displaystyle":2135},[895,44619],{},[20607,44621,44622],{},[2175,44623,44624],{"scriptlevel":2177,"displaystyle":2135},[895,44625,44626,44628,44630,44633,44635,44638,44640,44643,44645],{},[895,44627],{},[1846,44629,1848],{},[1979,44631,44632],{},"1,2245",[1846,44634,2075],{},[1979,44636,44637],{},"1,4286",[1846,44639,2075],{},[1979,44641,44642],{},"0,2449",[1846,44644,2075],{},[1979,44646,44647],{},"0,2857",[20604,44649,44650,44656],{},[20607,44651,44652],{},[2175,44653,44654],{"scriptlevel":2177,"displaystyle":2135},[895,44655],{},[20607,44657,44658],{},[2175,44659,44660],{"scriptlevel":2177,"displaystyle":2135},[895,44661,44662,44664,44666,44668],{},[895,44663],{},[1846,44665,1650],{},[1846,44667,2075],{},[1979,44669,44670],{},"0,735.",[902,44672,44673],{"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}",[724,44675,29910,44676,1734],{},[883,44677,44679],{"className":44678},[886],[888,44680,44681],{"xmlns":890},[892,44682,44683,44707],{},[895,44684,44685,44693,44695,44697,44699,44702,44704],{},[9012,44686,44687,44689,44691],{},[898,44688,2638],{},[1979,44690,2128],{},[898,44692,4098],{},[1846,44694,1650],{},[1979,44696,44419],{},[1846,44698,2075],{},[1979,44700,44701],{},"0,735",[1846,44703,1848],{},[1979,44705,44706],{},"7,836",[902,44708,44709],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[1639,44711,44712],{},[724,44713,44714,44716,44717,44740,44741,44763],{},[883,44715,4258],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,44718,44720],{"className":44719},[886],[888,44721,44722],{"xmlns":890},[892,44723,44724,44737],{},[895,44725,44726,44728,44730,44732,44734],{},[898,44727,2738],{"mathvariant":2226},[898,44729,2638],{},[1846,44731,1650],{},[1846,44733,2075],{},[1979,44735,44736],{},"2,69",[902,44738,44739],{"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 ",[883,44742,44744],{"className":44743},[886],[888,44745,44746],{"xmlns":890},[892,44747,44748,44760],{},[895,44749,44750,44752,44754,44756,44758],{},[898,44751,2738],{"mathvariant":2226},[898,44753,2638],{},[1846,44755,1650],{},[1846,44757,2075],{},[1979,44759,44701],{},[902,44761,44762],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,44765,44766],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[36815,44768],{},[115,44770,820],{"id":11630},[1639,44772,44773],{},[724,44774,44775,3720,44777,9871,44780,11973,44796,9871,44799,44815,44816,1734],{},[883,44776,4001],{},[38,44778,44779],{},"Přebytek spotřebitele",[883,44781,44783],{"className":44782},[886],[888,44784,44785],{"xmlns":890},[892,44786,44787,44793],{},[895,44788,44789,44791],{},[898,44790,2626],{},[898,44792,8519],{},[902,44794,44795],{"encoding":904},"CS",[38,44797,44798],{},"přebytek výrobce",[883,44800,44802],{"className":44801},[886],[888,44803,44804],{"xmlns":890},[892,44805,44806,44812],{},[895,44807,44808,44810],{},[898,44809,3783],{},[898,44811,8519],{},[902,44813,44814],{"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 ",[207,44817,44819],{"className":44818,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,44821,44822],{},[2409,44823],{"alt":44824,"className":44825,"src":44826},"imek-prebytky-cs-ps",[210,2413],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,44828,44829,9871,44831,44834],{},[38,44830,44779],{},[614,44832,44833],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,44836,44838],{"className":44837},[886],[888,44839,44840],{"xmlns":890,"display":27911},[892,44841,44842,44919],{},[20599,44843,44844],{"width":27916},[20604,44845,44846,44848,44912,44914],{},[20607,44847],{"width":27921},[20607,44849,44850],{},[895,44851,44852,44854,44856,44858,44864,44866,44868,44880,44882,44884,44886,44888,44890,44892,44894,44896,44902,44904,44910],{},[898,44853,2626],{},[898,44855,8519],{},[1846,44857,1855],{"stretchy":1854},[2122,44859,44860,44862],{},[898,44861,2638],{},[1979,44863,2177],{},[1846,44865,1861],{"stretchy":1854},[1846,44867,1848],{},[9012,44869,44870,44872,44874],{},[1846,44871,11015],{},[1979,44873,2177],{},[2122,44875,44876,44878],{},[898,44877,2638],{},[1979,44879,2177],{},[898,44881,4029],{},[1846,44883,1855],{"stretchy":1854},[898,44885,2638],{},[1846,44887,1861],{"stretchy":1854},[2138,44889,2835],{},[898,44891,2044],{},[898,44893,2638],{},[1846,44895,2075],{},[2122,44897,44898,44900],{},[898,44899,3783],{},[1979,44901,2177],{},[2138,44903,2835],{},[2122,44905,44906,44908],{},[898,44907,2638],{},[1979,44909,2177],{},[898,44911,1734],{"mathvariant":2226},[20607,44913],{"width":27921},[20607,44915,44916],{},[2138,44917,44918],{},"(2.14)",[902,44920,44921],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,44923,44924,9871,44927,44930],{},[38,44925,44926],{},"Přebytek výrobce",[614,44928,44929],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,44932,44934],{"className":44933},[886],[888,44935,44936],{"xmlns":890,"display":27911},[892,44937,44938,45015],{},[20599,44939,44940],{"width":27916},[20604,44941,44942,44944,45008,45010],{},[20607,44943],{"width":27921},[20607,44945,44946],{},[895,44947,44948,44950,44952,44954,44960,44962,44964,44970,44972,44978,44980,44992,44994,44996,44998,45000,45002,45004,45006],{},[898,44949,3783],{},[898,44951,8519],{},[1846,44953,1855],{"stretchy":1854},[2122,44955,44956,44958],{},[898,44957,2638],{},[1979,44959,2177],{},[1846,44961,1861],{"stretchy":1854},[1846,44963,1848],{},[2122,44965,44966,44968],{},[898,44967,3783],{},[1979,44969,2177],{},[2138,44971,2835],{},[2122,44973,44974,44976],{},[898,44975,2638],{},[1979,44977,2177],{},[1846,44979,2075],{},[9012,44981,44982,44984,44986],{},[1846,44983,11015],{},[1979,44985,2177],{},[2122,44987,44988,44990],{},[898,44989,2638],{},[1979,44991,2177],{},[898,44993,8519],{},[1846,44995,1855],{"stretchy":1854},[898,44997,2638],{},[1846,44999,1861],{"stretchy":1854},[2138,45001,2835],{},[898,45003,2044],{},[898,45005,2638],{},[898,45007,1734],{"mathvariant":2226},[20607,45009],{"width":27921},[20607,45011,45012],{},[2138,45013,45014],{},"(2.15)",[902,45016,45017],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,45019,45020,45021,1734],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,45022,45024],{"className":45023,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[36815,45026],{},[115,45028,45030],{"id":45029},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,45032,45033,45064,45069,45075,45103,45109,45138,45144,45224,45250],{},[123,45034,45035,45037,45038,45063],{},[38,45036,37773],{}," — lineární poptávka ",[883,45039,45041],{"className":45040},[886],[888,45042,45043],{"xmlns":890},[892,45044,45045,45061],{},[895,45046,45047,45049,45051,45053,45055,45057,45059],{},[898,45048,3783],{},[1846,45050,1848],{},[1846,45052,2075],{},[1979,45054,1981],{},[898,45056,2638],{},[1846,45058,1945],{},[1979,45060,2974],{},[902,45062,37805],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,45065,45066,45068],{},[38,45067,38087],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,45070,45071,45074],{},[38,45072,45073],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,45076,45077,45079,45080,1734],{},[38,45078,40634],{}," — lineární nabídka ",[883,45081,45083],{"className":45082},[886],[888,45084,45085],{"xmlns":890},[892,45086,45087,45101],{},[895,45088,45089,45091,45093,45095,45097,45099],{},[898,45090,3783],{},[1846,45092,1848],{},[1979,45094,4855],{},[898,45096,2638],{},[1846,45098,1945],{},[1979,45100,4850],{},[902,45102,40663],{"encoding":904},[123,45104,45105,45108],{},[38,45106,45107],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,45110,45111,45114,45115,1734],{},[38,45112,45113],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,45116,45118],{"className":45117},[886],[888,45119,45120],{"xmlns":890},[892,45121,45122,45136],{},[895,45123,45124,45126,45128,45130,45132,45134],{},[898,45125,4098],{},[1846,45127,2336],{"stretchy":1854},[1979,45129,2201],{},[1846,45131,2136],{"separator":2135},[1979,45133,41781],{},[1846,45135,2351],{"stretchy":1854},[902,45137,41809],{"encoding":904},[123,45139,45140,45143],{},[38,45141,45142],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,45145,45146,45149,45150,45167,45168,1343,45193,45220,45221,2799],{},[38,45147,45148],{},"Příklad 2.9"," — daň ",[883,45151,45153],{"className":45152},[886],[888,45154,45155],{"xmlns":890},[892,45156,45157,45165],{},[895,45158,45159,45161,45163],{},[898,45160,2623],{},[1846,45162,1848],{},[1979,45164,2085],{},[902,45166,41113],{"encoding":904}," na výrobce; rozklad ",[883,45169,45171],{"className":45170},[886],[888,45172,45173],{"xmlns":890},[892,45174,45175,45191],{},[895,45176,45177,45187,45189],{},[2122,45178,45179,45181],{},[898,45180,2623],{},[895,45182,45183,45185],{},[898,45184,42522],{},[898,45186,724],{},[1846,45188,1848],{},[1979,45190,1981],{},[902,45192,42821],{"encoding":904},[883,45194,45196],{"className":45195},[886],[888,45197,45198],{"xmlns":890},[892,45199,45200,45218],{},[895,45201,45202,45214,45216],{},[2122,45203,45204,45206],{},[898,45205,2623],{},[895,45207,45208,45210,45212],{},[898,45209,42545],{},[898,45211,1844],{},[898,45213,11886],{},[1846,45215,1848],{},[1979,45217,2201],{},[902,45219,42850],{"encoding":904},". (Viz ",[207,45222,42566],{"className":45223,"dataFsResolvedFilePath":809,"href":810},[210],[123,45225,45226,45149,45229,45246,45247,2799],{},[38,45227,45228],{},"Příklad 2.10",[883,45230,45232],{"className":45231},[886],[888,45233,45234],{"xmlns":890},[892,45235,45236,45244],{},[895,45237,45238,45240,45242],{},[898,45239,2623],{},[1846,45241,1848],{},[1979,45243,2085],{},[902,45245,41113],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,45248,42566],{"className":45249,"dataFsResolvedFilePath":809,"href":810},[210],[123,45251,45252,45255],{},[38,45253,45254],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[36815,45257],{},[115,45259,45261],{"id":45260},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,45263,45265],{"id":45264},"základní-analýza-poptávky","Základní analýza poptávky",[724,45267,45268,45271,45272,45307,45308,45334],{},[38,45269,45270],{},"2.1"," Je dána poptávka ",[883,45273,45275],{"className":45274},[886],[888,45276,45277],{"xmlns":890},[892,45278,45279,45304],{},[895,45280,45281,45283,45285,45287,45289,45291,45293,45295,45298,45300,45302],{},[898,45282,2638],{},[1846,45284,1848],{},[898,45286,4029],{},[1846,45288,1855],{"stretchy":1854},[898,45290,3783],{},[1846,45292,1861],{"stretchy":1854},[1846,45294,1848],{},[1979,45296,45297],{},"75",[1846,45299,2075],{},[1979,45301,2078],{},[898,45303,3783],{},[902,45305,45306],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,45309,45311],{"className":45310},[886],[888,45312,45313],{"xmlns":890},[892,45314,45315,45331],{},[895,45316,45317,45319,45321,45323,45325,45327,45329],{},[1979,45318,2177],{},[1846,45320,2136],{"separator":2135},[1979,45322,2078],{},[1846,45324,2136],{"separator":2135},[1979,45326,2712],{},[1846,45328,2136],{"separator":2135},[1979,45330,36089],{},[902,45332,45333],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,45336,45337,45340,45341,45359,45360,2999],{},[38,45338,45339],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,45342,45344],{"className":45343},[886],[888,45345,45346],{"xmlns":890},[892,45347,45348,45356],{},[895,45349,45350,45352,45354],{},[898,45351,3783],{},[1846,45353,2136],{"separator":2135},[898,45355,2638],{},[902,45357,45358],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,45361,45363],{"className":45362},[886],[888,45364,45365],{"xmlns":890},[892,45366,45367,45383],{},[895,45368,45369,45371,45373,45375,45377,45379,45381],{},[898,45370,207],{},[1846,45372,2136],{"separator":2135},[898,45374,1948],{},[1846,45376,2136],{"separator":2135},[898,45378,1992],{},[1846,45380,3256],{},[1979,45382,2177],{},[902,45384,45385],{"encoding":904},"a, b, c > 0",[120,45387,45388,45421,45452,45487,45518,45553],{},[123,45389,45390,45391],{},"(a) ",[883,45392,45394],{"className":45393},[886],[888,45395,45396],{"xmlns":890},[892,45397,45398,45418],{},[895,45399,45400,45402,45404],{},[898,45401,2638],{},[1846,45403,1848],{},[2175,45405,45406],{"scriptlevel":2177,"displaystyle":2135},[2179,45407,45408,45410],{},[898,45409,207],{},[895,45411,45412,45414,45416],{},[898,45413,3783],{},[1846,45415,1945],{},[898,45417,1992],{},[902,45419,45420],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,45422,45423,45424],{},"(b) ",[883,45425,45427],{"className":45426},[886],[888,45428,45429],{"xmlns":890},[892,45430,45431,45449],{},[895,45432,45433,45435,45437],{},[898,45434,2638],{},[1846,45436,1848],{},[7963,45438,45439],{},[895,45440,45441,45443,45445,45447],{},[898,45442,207],{},[1846,45444,2075],{},[898,45446,1948],{},[898,45448,2638],{},[902,45450,45451],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,45453,45454,45455],{},"(c) ",[883,45456,45458],{"className":45457},[886],[888,45459,45460],{"xmlns":890},[892,45461,45462,45484],{},[895,45463,45464,45466,45468],{},[898,45465,2638],{},[1846,45467,1848],{},[2175,45469,45470],{"scriptlevel":2177,"displaystyle":2135},[2179,45471,45472,45482],{},[895,45473,45474,45476,45478],{},[898,45475,207],{},[1846,45477,2075],{},[7963,45479,45480],{},[898,45481,3783],{},[898,45483,1948],{},[902,45485,45486],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,45488,45489,45490],{},"(d) ",[883,45491,45493],{"className":45492},[886],[888,45494,45495],{"xmlns":890},[892,45496,45497,45515],{},[895,45498,45499,45501,45503,45505,45507,45509],{},[898,45500,3783],{},[1846,45502,1848],{},[898,45504,207],{},[1846,45506,2075],{},[898,45508,1948],{},[1974,45510,45511,45513],{},[898,45512,2638],{},[1979,45514,1981],{},[902,45516,45517],{"encoding":904},"P = a - bQ^2",[123,45519,45520,45521],{},"(e) ",[883,45522,45524],{"className":45523},[886],[888,45525,45526],{"xmlns":890},[892,45527,45528,45550],{},[895,45529,45530,45532,45534,45536,45546,45548],{},[898,45531,2638],{},[1846,45533,1848],{},[898,45535,1948],{},[1974,45537,45538,45540],{},[898,45539,3783],{},[895,45541,45542,45544],{},[1846,45543,2075],{},[898,45545,207],{},[1846,45547,1945],{},[898,45549,1992],{},[902,45551,45552],{"encoding":904},"Q = bP^{-a} + c",[123,45554,45555,45556],{},"(f) ",[883,45557,45559],{"className":45558},[886],[888,45560,45561],{"xmlns":890},[892,45562,45563,45586],{},[895,45564,45565,45567,45569,45571,45573],{},[898,45566,2638],{},[1846,45568,1848],{},[898,45570,207],{},[1846,45572,3025],{},[1974,45574,45575,45578],{},[898,45576,45577],{},"e",[895,45579,45580,45582,45584],{},[1846,45581,2075],{},[898,45583,1948],{},[898,45585,3783],{},[902,45587,45588],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,45590,45591,45594],{},[38,45592,45593],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,45596,45597,45600,45603],{},[123,45598,45599],{},"(a) Cena substitutu.",[123,45601,45602],{},"(b) Cena komplementu.",[123,45604,45605],{},"(c) Výdaje na reklamu.",[724,45607,45608,45271,45610,45644,45645,45673],{},[38,45609,24487],{},[883,45611,45613],{"className":45612},[886],[888,45614,45615],{"xmlns":890},[892,45616,45617,45641],{},[895,45618,45619,45621,45623,45625,45627,45629,45631,45633,45635,45637,45639],{},[898,45620,3783],{},[1846,45622,1848],{},[898,45624,4029],{},[1846,45626,1855],{"stretchy":1854},[898,45628,2638],{},[1846,45630,1861],{"stretchy":1854},[1846,45632,1848],{},[1979,45634,3357],{},[1846,45636,2075],{},[1979,45638,1981],{},[898,45640,2638],{},[902,45642,45643],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,45646,45648],{"className":45647},[886],[888,45649,45650],{"xmlns":890},[892,45651,45652,45670],{},[895,45653,45654,45656,45658,45664,45666,45668],{},[898,45655,3783],{},[1846,45657,1848],{},[1974,45659,45660,45662],{},[898,45661,4029],{},[1846,45663,4200],{},[1846,45665,1855],{"stretchy":1854},[898,45667,2638],{},[1846,45669,1861],{"stretchy":1854},[902,45671,45672],{"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.",[724,45675,45676,45679],{},[38,45677,45678],{},"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:",[120,45681,45682,45766,45842,45928,46016],{},[123,45683,45390,45684,1343,45724,1734],{},[883,45685,45687],{"className":45686},[886],[888,45688,45689],{"xmlns":890},[892,45690,45691,45721],{},[895,45692,45693,45699,45701,45703,45705,45707,45713,45715],{},[2122,45694,45695,45697],{},[898,45696,23098],{},[1979,45698,2128],{},[1846,45700,1848],{},[1979,45702,8881],{},[1846,45704,2075],{},[1979,45706,2201],{},[2122,45708,45709,45711],{},[898,45710,4101],{},[1979,45712,2128],{},[1846,45714,1945],{},[2122,45716,45717,45719],{},[898,45718,4101],{},[1979,45720,1981],{},[902,45722,45723],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,45725,45727],{"className":45726},[886],[888,45728,45729],{"xmlns":890},[892,45730,45731,45763],{},[895,45732,45733,45739,45741,45743,45745,45747,45753,45755,45757],{},[2122,45734,45735,45737],{},[898,45736,23098],{},[1979,45738,1981],{},[1846,45740,1848],{},[1979,45742,2712],{},[1846,45744,1945],{},[1979,45746,1981],{},[2122,45748,45749,45751],{},[898,45750,4101],{},[1979,45752,2128],{},[1846,45754,2075],{},[1979,45756,2201],{},[2122,45758,45759,45761],{},[898,45760,4101],{},[1979,45762,1981],{},[902,45764,45765],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,45767,45423,45768,1343,45810,1734],{},[883,45769,45771],{"className":45770},[886],[888,45772,45773],{"xmlns":890},[892,45774,45775,45807],{},[895,45776,45777,45783,45785,45787,45789,45791,45797,45799,45801],{},[2122,45778,45779,45781],{},[898,45780,23098],{},[1979,45782,2128],{},[1846,45784,1848],{},[1979,45786,2968],{},[1846,45788,2075],{},[1979,45790,2712],{},[2122,45792,45793,45795],{},[898,45794,4101],{},[1979,45796,2128],{},[1846,45798,2075],{},[1979,45800,2085],{},[2122,45802,45803,45805],{},[898,45804,4101],{},[1979,45806,1981],{},[902,45808,45809],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,45811,45813],{"className":45812},[886],[888,45814,45815],{"xmlns":890},[892,45816,45817,45839],{},[895,45818,45819,45825,45827,45829,45831,45833],{},[2122,45820,45821,45823],{},[898,45822,23098],{},[1979,45824,1981],{},[1846,45826,1848],{},[1979,45828,36089],{},[1846,45830,2075],{},[1979,45832,2712],{},[2122,45834,45835,45837],{},[898,45836,4101],{},[1979,45838,1981],{},[902,45840,45841],{"encoding":904},"B_2 = 15 - 10A_2",[123,45843,45454,45844,1343,45886,1734],{},[883,45845,45847],{"className":45846},[886],[888,45848,45849],{"xmlns":890},[892,45850,45851,45883],{},[895,45852,45853,45859,45861,45863,45865,45867,45873,45875,45877],{},[2122,45854,45855,45857],{},[898,45856,23098],{},[1979,45858,2128],{},[1846,45860,1848],{},[1979,45862,37864],{},[1846,45864,2075],{},[1979,45866,1981],{},[2122,45868,45869,45871],{},[898,45870,4101],{},[1979,45872,2128],{},[1846,45874,2075],{},[1979,45876,2201],{},[2122,45878,45879,45881],{},[898,45880,4101],{},[1979,45882,1981],{},[902,45884,45885],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,45887,45889],{"className":45888},[886],[888,45890,45891],{"xmlns":890},[892,45892,45893,45925],{},[895,45894,45895,45901,45903,45905,45907,45909,45915,45917,45919],{},[2122,45896,45897,45899],{},[898,45898,23098],{},[1979,45900,1981],{},[1846,45902,1848],{},[1979,45904,36089],{},[1846,45906,1945],{},[1979,45908,1981],{},[2122,45910,45911,45913],{},[898,45912,4101],{},[1979,45914,2128],{},[1846,45916,2075],{},[1979,45918,1981],{},[2122,45920,45921,45923],{},[898,45922,4101],{},[1979,45924,1981],{},[902,45926,45927],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,45929,45489,45930,1343,45974,1734],{},[883,45931,45933],{"className":45932},[886],[888,45934,45935],{"xmlns":890},[892,45936,45937,45971],{},[895,45938,45939,45945,45947,45949,45951,45953,45955,45961,45963,45965],{},[2122,45940,45941,45943],{},[898,45942,23098],{},[1979,45944,2128],{},[1846,45946,1848],{},[1846,45948,2075],{},[1979,45950,8881],{},[1846,45952,2075],{},[1979,45954,1981],{},[2122,45956,45957,45959],{},[898,45958,4101],{},[1979,45960,2128],{},[1846,45962,1945],{},[1979,45964,2023],{},[2122,45966,45967,45969],{},[898,45968,4101],{},[1979,45970,1981],{},[902,45972,45973],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,45975,45977],{"className":45976},[886],[888,45978,45979],{"xmlns":890},[892,45980,45981,46013],{},[895,45982,45983,45989,45991,45993,45995,45997,46003,46005,46007],{},[2122,45984,45985,45987],{},[898,45986,23098],{},[1979,45988,1981],{},[1846,45990,1848],{},[1979,45992,2712],{},[1846,45994,1945],{},[1979,45996,1981],{},[2122,45998,45999,46001],{},[898,46000,4101],{},[1979,46002,2128],{},[1846,46004,2075],{},[1979,46006,1981],{},[2122,46008,46009,46011],{},[898,46010,4101],{},[1979,46012,1981],{},[902,46014,46015],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,46017,45520,46018,1343,46060,1734],{},[883,46019,46021],{"className":46020},[886],[888,46022,46023],{"xmlns":890},[892,46024,46025,46057],{},[895,46026,46027,46033,46035,46037,46039,46041,46047,46049,46051],{},[2122,46028,46029,46031],{},[898,46030,23098],{},[1979,46032,2128],{},[1846,46034,1848],{},[1979,46036,8881],{},[1846,46038,1945],{},[1979,46040,1981],{},[2122,46042,46043,46045],{},[898,46044,4101],{},[1979,46046,2128],{},[1846,46048,1945],{},[1979,46050,2201],{},[2122,46052,46053,46055],{},[898,46054,4101],{},[1979,46056,1981],{},[902,46058,46059],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,46061,46063],{"className":46062},[886],[888,46064,46065],{"xmlns":890},[892,46066,46067,46099],{},[895,46068,46069,46075,46077,46079,46081,46083,46089,46091,46093],{},[2122,46070,46071,46073],{},[898,46072,23098],{},[1979,46074,1981],{},[1846,46076,1848],{},[1979,46078,5057],{},[1846,46080,2075],{},[1979,46082,2023],{},[2122,46084,46085,46087],{},[898,46086,4101],{},[1979,46088,2128],{},[1846,46090,1945],{},[1979,46092,2078],{},[2122,46094,46095,46097],{},[898,46096,4101],{},[1979,46098,1981],{},[902,46100,46101],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,46103,46105],{"id":46104},"základní-analýza-nabídky","Základní analýza nabídky",[724,46107,46108,46111,46112,46146,46147,46169],{},[38,46109,46110],{},"2.6"," Je dána nabídka ",[883,46113,46115],{"className":46114},[886],[888,46116,46117],{"xmlns":890},[892,46118,46119,46143],{},[895,46120,46121,46123,46125,46127,46129,46131,46133,46135,46137,46139,46141],{},[898,46122,3783],{},[1846,46124,1848],{},[898,46126,8519],{},[1846,46128,1855],{"stretchy":1854},[898,46130,2638],{},[1846,46132,1861],{"stretchy":1854},[1846,46134,1848],{},[1979,46136,8881],{},[1846,46138,1945],{},[1979,46140,2688],{},[898,46142,2638],{},[902,46144,46145],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,46148,46150],{"className":46149},[886],[888,46151,46152],{"xmlns":890},[892,46153,46154,46166],{},[895,46155,46156,46158,46160,46162,46164],{},[1979,46157,4850],{},[1846,46159,2136],{"separator":2135},[1979,46161,37864],{},[1846,46163,2136],{"separator":2135},[1979,46165,14883],{},[902,46167,46168],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,46171,46172,46175,46176,46193],{},[38,46173,46174],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,46177,46179],{"className":46178},[886],[888,46180,46181],{"xmlns":890},[892,46182,46183,46191],{},[895,46184,46185,46187,46189],{},[898,46186,3783],{},[1846,46188,2136],{"separator":2135},[898,46190,2638],{},[902,46192,45358],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,46195,46196,46222,46250,46283,46317,46353],{},[123,46197,45390,46198],{},[883,46199,46201],{"className":46200},[886],[888,46202,46203],{"xmlns":890},[892,46204,46205,46219],{},[895,46206,46207,46209,46211,46213,46215,46217],{},[898,46208,3783],{},[1846,46210,1848],{},[1979,46212,37864],{},[1846,46214,1945],{},[1979,46216,1981],{},[898,46218,2638],{},[902,46220,46221],{"encoding":904},"P = 30 + 2Q",[123,46223,45423,46224],{},[883,46225,46227],{"className":46226},[886],[888,46228,46229],{"xmlns":890},[892,46230,46231,46247],{},[895,46232,46233,46235,46237,46239,46241,46243,46245],{},[898,46234,2638],{},[1846,46236,1848],{},[1846,46238,2075],{},[1979,46240,2023],{},[1846,46242,1945],{},[1979,46244,3357],{},[898,46246,3783],{},[902,46248,46249],{"encoding":904},"Q = -3 + 12P",[123,46251,45454,46252],{},[883,46253,46255],{"className":46254},[886],[888,46256,46257],{"xmlns":890},[892,46258,46259,46281],{},[895,46260,46261,46263,46265,46271,46273,46275,46277,46279],{},[898,46262,3783],{},[1846,46264,1848],{},[1974,46266,46267,46269],{},[898,46268,2638],{},[1979,46270,1981],{},[1846,46272,1945],{},[1979,46274,22791],{},[898,46276,2638],{},[1846,46278,1945],{},[1979,46280,32391],{},[902,46282,41567],{"encoding":904},[123,46284,45489,46285],{},[883,46286,46288],{"className":46287},[886],[888,46289,46290],{"xmlns":890},[892,46291,46292,46314],{},[895,46293,46294,46296,46298,46304,46306,46308,46310,46312],{},[898,46295,3783],{},[1846,46297,1848],{},[1974,46299,46300,46302],{},[898,46301,2638],{},[1979,46303,1981],{},[1846,46305,1945],{},[1979,46307,1981],{},[898,46309,2638],{},[1846,46311,1945],{},[1979,46313,3357],{},[902,46315,46316],{"encoding":904},"P = Q^2 + 2Q + 12",[123,46318,45520,46319],{},[883,46320,46322],{"className":46321},[886],[888,46323,46324],{"xmlns":890},[892,46325,46326,46350],{},[895,46327,46328,46330,46332,46334,46336,46338,46340,46342,46344],{},[898,46329,2638],{},[1846,46331,1848],{},[1979,46333,8649],{},[1846,46335,1945],{},[1979,46337,2078],{},[898,46339,3783],{},[1846,46341,1945],{},[1979,46343,2643],{},[1974,46345,46346,46348],{},[898,46347,3783],{},[1979,46349,1981],{},[902,46351,46352],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,46354,45555,46355],{},[883,46356,46358],{"className":46357},[886],[888,46359,46360],{"xmlns":890},[892,46361,46362,46387],{},[895,46363,46364,46366,46368,46370,46372,46374,46376,46378,46381],{},[898,46365,2638],{},[1846,46367,1848],{},[1979,46369,24046],{},[1846,46371,1945],{},[1979,46373,2643],{},[898,46375,3783],{},[1846,46377,1945],{},[1979,46379,46380],{},"0,004",[1974,46382,46383,46385],{},[898,46384,3783],{},[1979,46386,1981],{},[902,46388,46389],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,46391,46392,46395],{},[38,46393,46394],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,46397,46398,46401,46404,46407],{},[123,46399,46400],{},"(a) Sníží ceny surovin — vstupů.",[123,46402,46403],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,46405,46406],{},"(c) Zvýší ceny všech energií.",[123,46408,46409],{},"(d) Sníží daňové odvody státu.",[724,46411,46412,46111,46414,46448,46449,46477],{},[38,46413,42794],{},[883,46415,46417],{"className":46416},[886],[888,46418,46419],{"xmlns":890},[892,46420,46421,46445],{},[895,46422,46423,46425,46427,46429,46431,46433,46435,46437,46439,46441,46443],{},[898,46424,3783],{},[1846,46426,1848],{},[898,46428,8519],{},[1846,46430,1855],{"stretchy":1854},[898,46432,2638],{},[1846,46434,1861],{"stretchy":1854},[1846,46436,1848],{},[1979,46438,4855],{},[898,46440,2638],{},[1846,46442,1945],{},[1979,46444,36089],{},[902,46446,46447],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,46450,46452],{"className":46451},[886],[888,46453,46454],{"xmlns":890},[892,46455,46456,46474],{},[895,46457,46458,46460,46462,46468,46470,46472],{},[898,46459,3783],{},[1846,46461,1848],{},[1974,46463,46464,46466],{},[898,46465,8519],{},[1846,46467,4200],{},[1846,46469,1855],{"stretchy":1854},[898,46471,2638],{},[1846,46473,1861],{"stretchy":1854},[902,46475,46476],{"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.",[198,46479,41170],{"id":46480},"tržní-rovnováha-1",[724,46482,46483,46485,46486,46503,46504,2554],{},[38,46484,42854],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,46487,46489],{"className":46488},[886],[888,46490,46491],{"xmlns":890},[892,46492,46493,46501],{},[895,46494,46495],{},[1974,46496,46497,46499],{},[898,46498,2638],{},[898,46500,4098],{},[902,46502,42248],{"encoding":904}," a rovnovážnou cenu ",[883,46505,46507],{"className":46506},[886],[888,46508,46509],{"xmlns":890},[892,46510,46511,46519],{},[895,46512,46513],{},[1974,46514,46515,46517],{},[898,46516,3783],{},[898,46518,4098],{},[902,46520,41311],{"encoding":904},[120,46522,46523,46576,46627,46686],{},[123,46524,45390,46525,1343,46552,1734],{},[883,46526,46528],{"className":46527},[886],[888,46529,46530],{"xmlns":890},[892,46531,46532,46549],{},[895,46533,46534,46536,46538,46540,46542,46544,46546],{},[898,46535,3783],{},[1846,46537,1848],{},[1846,46539,2075],{},[1979,46541,2078],{},[898,46543,2638],{},[1846,46545,1945],{},[1979,46547,46548],{},"80",[902,46550,46551],{"encoding":904},"P = -5Q + 80",[883,46553,46555],{"className":46554},[886],[888,46556,46557],{"xmlns":890},[892,46558,46559,46573],{},[895,46560,46561,46563,46565,46567,46569,46571],{},[898,46562,3783],{},[1846,46564,1848],{},[1979,46566,1981],{},[898,46568,2638],{},[1846,46570,1945],{},[1979,46572,2712],{},[902,46574,46575],{"encoding":904},"P = 2Q + 10",[123,46577,45423,46578,1343,46604,1734],{},[883,46579,46581],{"className":46580},[886],[888,46582,46583],{"xmlns":890},[892,46584,46585,46601],{},[895,46586,46587,46589,46591,46593,46595,46597,46599],{},[898,46588,2638],{},[1846,46590,1848],{},[1846,46592,2075],{},[1979,46594,4855],{},[898,46596,3783],{},[1846,46598,1945],{},[1979,46600,4850],{},[902,46602,46603],{"encoding":904},"Q = -0{,}5P + 25",[883,46605,46607],{"className":46606},[886],[888,46608,46609],{"xmlns":890},[892,46610,46611,46625],{},[895,46612,46613,46615,46617,46619,46621,46623],{},[898,46614,2638],{},[1846,46616,1848],{},[1979,46618,1981],{},[898,46620,3783],{},[1846,46622,2075],{},[1979,46624,2968],{},[902,46626,40692],{"encoding":904},[123,46628,45454,46629,1343,46655,1734],{},[883,46630,46632],{"className":46631},[886],[888,46633,46634],{"xmlns":890},[892,46635,46636,46652],{},[895,46637,46638,46640,46642,46644,46646,46648,46650],{},[898,46639,3783],{},[1846,46641,1848],{},[1846,46643,2075],{},[1979,46645,2201],{},[898,46647,2638],{},[1846,46649,1945],{},[1979,46651,3892],{},[902,46653,46654],{"encoding":904},"P = -4Q + 120",[883,46656,46658],{"className":46657},[886],[888,46659,46660],{"xmlns":890},[892,46661,46662,46683],{},[895,46663,46664,46666,46668,46676,46678,46680],{},[898,46665,3783],{},[1846,46667,1848],{},[2175,46669,46670],{"scriptlevel":2177,"displaystyle":1854},[2179,46671,46672,46674],{},[1979,46673,2128],{},[1979,46675,2023],{},[898,46677,2638],{},[1846,46679,1945],{},[1979,46681,46682],{},"29",[902,46684,46685],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,46687,45489,46688,1343,46717,1734],{},[883,46689,46691],{"className":46690},[886],[888,46692,46693],{"xmlns":890},[892,46694,46695,46714],{},[895,46696,46697,46699,46701,46703,46709,46711],{},[898,46698,3783],{},[1846,46700,1848],{},[1846,46702,2075],{},[1974,46704,46705,46707],{},[898,46706,2638],{},[1979,46708,1981],{},[1846,46710,1945],{},[1979,46712,46713],{},"52",[902,46715,46716],{"encoding":904},"P = -Q^2 + 52",[883,46718,46720],{"className":46719},[886],[888,46721,46722],{"xmlns":890},[892,46723,46724,46742],{},[895,46725,46726,46728,46730,46732,46738,46740],{},[898,46727,3783],{},[1846,46729,1848],{},[1979,46731,1981],{},[1974,46733,46734,46736],{},[898,46735,2638],{},[1979,46737,1981],{},[1846,46739,1945],{},[1979,46741,2712],{},[902,46743,46744],{"encoding":904},"P = 2Q^2 + 10",[724,46746,46747,46750,46751,46781,46782,46812],{},[38,46748,46749],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,46752,46754],{"className":46753},[886],[888,46755,46756],{"xmlns":890},[892,46757,46758,46778],{},[895,46759,46760,46768,46770],{},[9012,46761,46762,46764,46766],{},[898,46763,2638],{},[1979,46765,2128],{},[898,46767,4098],{},[1846,46769,2136],{"separator":2135},[9012,46771,46772,46774,46776],{},[898,46773,2638],{},[1979,46775,1981],{},[898,46777,4098],{},[902,46779,46780],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,46783,46785],{"className":46784},[886],[888,46786,46787],{"xmlns":890},[892,46788,46789,46809],{},[895,46790,46791,46799,46801],{},[9012,46792,46793,46795,46797],{},[898,46794,3783],{},[1979,46796,2128],{},[898,46798,4098],{},[1846,46800,2136],{"separator":2135},[9012,46802,46803,46805,46807],{},[898,46804,3783],{},[1979,46806,1981],{},[898,46808,4098],{},[902,46810,46811],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,46814,46815,46967],{},[123,46816,45390,46817,1343,46857,1343,46899,1343,46933,1734],{},[883,46818,46820],{"className":46819},[886],[888,46821,46822],{"xmlns":890},[892,46823,46824,46854],{},[895,46825,46826,46832,46834,46836,46838,46840,46846,46848],{},[2122,46827,46828,46830],{},[898,46829,2638],{},[1979,46831,2128],{},[1846,46833,1848],{},[1979,46835,2712],{},[1846,46837,2075],{},[1979,46839,1981],{},[2122,46841,46842,46844],{},[898,46843,3783],{},[1979,46845,2128],{},[1846,46847,1945],{},[2122,46849,46850,46852],{},[898,46851,3783],{},[1979,46853,1981],{},[902,46855,46856],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,46858,46860],{"className":46859},[886],[888,46861,46862],{"xmlns":890},[892,46863,46864,46896],{},[895,46865,46866,46872,46874,46876,46878,46880,46886,46888,46890],{},[2122,46867,46868,46870],{},[898,46869,2638],{},[1979,46871,1981],{},[1846,46873,1848],{},[1979,46875,2078],{},[1846,46877,1945],{},[1979,46879,1981],{},[2122,46881,46882,46884],{},[898,46883,3783],{},[1979,46885,2128],{},[1846,46887,2075],{},[1979,46889,1981],{},[2122,46891,46892,46894],{},[898,46893,3783],{},[1979,46895,1981],{},[902,46897,46898],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,46900,46902],{"className":46901},[886],[888,46903,46904],{"xmlns":890},[892,46905,46906,46930],{},[895,46907,46908,46914,46916,46918,46920,46922,46924],{},[2122,46909,46910,46912],{},[898,46911,2638],{},[1979,46913,2128],{},[1846,46915,1848],{},[1846,46917,2075],{},[1979,46919,2023],{},[1846,46921,1945],{},[1979,46923,1981],{},[2122,46925,46926,46928],{},[898,46927,3783],{},[1979,46929,2128],{},[902,46931,46932],{"encoding":904},"Q_1 = -3 + 2P_1",[883,46934,46936],{"className":46935},[886],[888,46937,46938],{"xmlns":890},[892,46939,46940,46964],{},[895,46941,46942,46948,46950,46952,46954,46956,46958],{},[2122,46943,46944,46946],{},[898,46945,2638],{},[1979,46947,1981],{},[1846,46949,1848],{},[1846,46951,2075],{},[1979,46953,1981],{},[1846,46955,1945],{},[1979,46957,2023],{},[2122,46959,46960,46962],{},[898,46961,3783],{},[1979,46963,1981],{},[902,46965,46966],{"encoding":904},"Q_2 = -2 + 3P_2",[123,46968,45423,46969,1343,47009,1343,47051,1343,47083,1734],{},[883,46970,46972],{"className":46971},[886],[888,46973,46974],{"xmlns":890},[892,46975,46976,47006],{},[895,46977,46978,46984,46986,46988,46990,46992,46998,47000],{},[2122,46979,46980,46982],{},[898,46981,2638],{},[1979,46983,2128],{},[1846,46985,1848],{},[1979,46987,2938],{},[1846,46989,2075],{},[1979,46991,1981],{},[2122,46993,46994,46996],{},[898,46995,3783],{},[1979,46997,2128],{},[1846,46999,1945],{},[2122,47001,47002,47004],{},[898,47003,3783],{},[1979,47005,1981],{},[902,47007,47008],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,47010,47012],{"className":47011},[886],[888,47013,47014],{"xmlns":890},[892,47015,47016,47048],{},[895,47017,47018,47024,47026,47028,47030,47032,47038,47040,47042],{},[2122,47019,47020,47022],{},[898,47021,2638],{},[1979,47023,1981],{},[1846,47025,1848],{},[1979,47027,2078],{},[1846,47029,1945],{},[1979,47031,1981],{},[2122,47033,47034,47036],{},[898,47035,3783],{},[1979,47037,2128],{},[1846,47039,2075],{},[1979,47041,2023],{},[2122,47043,47044,47046],{},[898,47045,3783],{},[1979,47047,1981],{},[902,47049,47050],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,47052,47054],{"className":47053},[886],[888,47055,47056],{"xmlns":890},[892,47057,47058,47080],{},[895,47059,47060,47066,47068,47070,47072,47074],{},[2122,47061,47062,47064],{},[898,47063,2638],{},[1979,47065,2128],{},[1846,47067,1848],{},[1846,47069,2075],{},[1979,47071,2712],{},[1846,47073,1945],{},[2122,47075,47076,47078],{},[898,47077,3783],{},[1979,47079,2128],{},[902,47081,47082],{"encoding":904},"Q_1 = -10 + P_1",[883,47084,47086],{"className":47085},[886],[888,47087,47088],{"xmlns":890},[892,47089,47090,47112],{},[895,47091,47092,47098,47100,47102,47104,47106],{},[2122,47093,47094,47096],{},[898,47095,2638],{},[1979,47097,1981],{},[1846,47099,1848],{},[1979,47101,2078],{},[1846,47103,1945],{},[1979,47105,2085],{},[2122,47107,47108,47110],{},[898,47109,3783],{},[1979,47111,1981],{},[902,47113,47114],{"encoding":904},"Q_2 = 5 + 6P_2",[724,47116,47117,47120,47121,1343,47169,1343,47215,47265,47266,1343,47298,1343,47332,21439,47366,1745,47384,47402,47403,47416,47417,47443,47444,46781,47484,1734],{},[38,47118,47119],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,47122,47124],{"className":47123},[886],[888,47125,47126],{"xmlns":890},[892,47127,47128,47166],{},[895,47129,47130,47136,47138,47140,47142,47148,47150,47152,47158,47160],{},[2122,47131,47132,47134],{},[898,47133,2638],{},[1979,47135,2128],{},[1846,47137,1848],{},[1979,47139,36089],{},[1846,47141,2075],{},[2122,47143,47144,47146],{},[898,47145,3783],{},[1979,47147,2128],{},[1846,47149,1945],{},[1979,47151,1981],{},[2122,47153,47154,47156],{},[898,47155,3783],{},[1979,47157,1981],{},[1846,47159,1945],{},[2122,47161,47162,47164],{},[898,47163,3783],{},[1979,47165,2023],{},[902,47167,47168],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,47170,47172],{"className":47171},[886],[888,47173,47174],{"xmlns":890},[892,47175,47176,47212],{},[895,47177,47178,47184,47186,47188,47190,47196,47198,47204,47206],{},[2122,47179,47180,47182],{},[898,47181,2638],{},[1979,47183,1981],{},[1846,47185,1848],{},[1979,47187,3845],{},[1846,47189,1945],{},[2122,47191,47192,47194],{},[898,47193,3783],{},[1979,47195,2128],{},[1846,47197,2075],{},[2122,47199,47200,47202],{},[898,47201,3783],{},[1979,47203,1981],{},[1846,47205,2075],{},[2122,47207,47208,47210],{},[898,47209,3783],{},[1979,47211,2023],{},[902,47213,47214],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,47216,47218],{"className":47217},[886],[888,47219,47220],{"xmlns":890},[892,47221,47222,47262],{},[895,47223,47224,47230,47232,47234,47236,47238,47244,47246,47252,47254,47256],{},[2122,47225,47226,47228],{},[898,47227,2638],{},[1979,47229,2023],{},[1846,47231,1848],{},[1979,47233,5431],{},[1846,47235,1945],{},[1979,47237,1981],{},[2122,47239,47240,47242],{},[898,47241,3783],{},[1979,47243,2128],{},[1846,47245,2075],{},[2122,47247,47248,47250],{},[898,47249,3783],{},[1979,47251,1981],{},[1846,47253,2075],{},[1979,47255,2201],{},[2122,47257,47258,47260],{},[898,47259,3783],{},[1979,47261,2023],{},[902,47263,47264],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,47267,47269],{"className":47268},[886],[888,47270,47271],{"xmlns":890},[892,47272,47273,47295],{},[895,47274,47275,47281,47283,47285,47287,47289],{},[2122,47276,47277,47279],{},[898,47278,2638],{},[1979,47280,2128],{},[1846,47282,1848],{},[1846,47284,2075],{},[1979,47286,24046],{},[1846,47288,1945],{},[2122,47290,47291,47293],{},[898,47292,3783],{},[1979,47294,2128],{},[902,47296,47297],{"encoding":904},"Q_1 = -7 + P_1",[883,47299,47301],{"className":47300},[886],[888,47302,47303],{"xmlns":890},[892,47304,47305,47329],{},[895,47306,47307,47313,47315,47317,47319,47321,47323],{},[2122,47308,47309,47311],{},[898,47310,2638],{},[1979,47312,1981],{},[1846,47314,1848],{},[1846,47316,2075],{},[1979,47318,2201],{},[1846,47320,1945],{},[1979,47322,2201],{},[2122,47324,47325,47327],{},[898,47326,3783],{},[1979,47328,1981],{},[902,47330,47331],{"encoding":904},"Q_2 = -4 + 4P_2",[883,47333,47335],{"className":47334},[886],[888,47336,47337],{"xmlns":890},[892,47338,47339,47363],{},[895,47340,47341,47347,47349,47351,47353,47355,47357],{},[2122,47342,47343,47345],{},[898,47344,2638],{},[1979,47346,2023],{},[1846,47348,1848],{},[1846,47350,2075],{},[1979,47352,2078],{},[1846,47354,1945],{},[1979,47356,1981],{},[2122,47358,47359,47361],{},[898,47360,3783],{},[1979,47362,2023],{},[902,47364,47365],{"encoding":904},"Q_3 = -5 + 2P_3",[883,47367,47369],{"className":47368},[886],[888,47370,47371],{"xmlns":890},[892,47372,47373,47381],{},[895,47374,47375],{},[2122,47376,47377,47379],{},[898,47378,2638],{},[898,47380,17635],{},[902,47382,47383],{"encoding":904},"Q_i",[883,47385,47387],{"className":47386},[886],[888,47388,47389],{"xmlns":890},[892,47390,47391,47399],{},[895,47392,47393],{},[2122,47394,47395,47397],{},[898,47396,3783],{},[898,47398,17635],{},[902,47400,47401],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,47404,47406],{"className":47405},[886],[888,47407,47408],{"xmlns":890},[892,47409,47410,47414],{},[895,47411,47412],{},[898,47413,17635],{},[902,47415,17635],{"encoding":904},"-tého zboží, ",[883,47418,47420],{"className":47419},[886],[888,47421,47422],{"xmlns":890},[892,47423,47424,47440],{},[895,47425,47426,47428,47430,47432,47434,47436,47438],{},[898,47427,17635],{},[1846,47429,1848],{},[1979,47431,2128],{},[1846,47433,2136],{"separator":2135},[1979,47435,1981],{},[1846,47437,2136],{"separator":2135},[1979,47439,2023],{},[902,47441,47442],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,47445,47447],{"className":47446},[886],[888,47448,47449],{"xmlns":890},[892,47450,47451,47481],{},[895,47452,47453,47461,47463,47471,47473],{},[9012,47454,47455,47457,47459],{},[898,47456,2638],{},[1979,47458,2128],{},[898,47460,4098],{},[1846,47462,2136],{"separator":2135},[9012,47464,47465,47467,47469],{},[898,47466,2638],{},[1979,47468,1981],{},[898,47470,4098],{},[1846,47472,2136],{"separator":2135},[9012,47474,47475,47477,47479],{},[898,47476,2638],{},[1979,47478,2023],{},[898,47480,4098],{},[902,47482,47483],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,47485,47487],{"className":47486},[886],[888,47488,47489],{"xmlns":890},[892,47490,47491,47521],{},[895,47492,47493,47501,47503,47511,47513],{},[9012,47494,47495,47497,47499],{},[898,47496,3783],{},[1979,47498,2128],{},[898,47500,4098],{},[1846,47502,2136],{"separator":2135},[9012,47504,47505,47507,47509],{},[898,47506,3783],{},[1979,47508,1981],{},[898,47510,4098],{},[1846,47512,2136],{"separator":2135},[9012,47514,47515,47517,47519],{},[898,47516,3783],{},[1979,47518,2023],{},[898,47520,4098],{},[902,47522,47523],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,47525,47526,47529,47530,47566,47567,1734],{},[38,47527,47528],{},"2.13"," Jsou dány poptávka ",[883,47531,47533],{"className":47532},[886],[888,47534,47535],{"xmlns":890},[892,47536,47537,47563],{},[895,47538,47539,47541,47543,47545,47547,47549,47551,47553,47555,47557,47559,47561],{},[898,47540,3783],{},[1846,47542,1848],{},[898,47544,4029],{},[1846,47546,1855],{"stretchy":1854},[898,47548,2638],{},[1846,47550,1861],{"stretchy":1854},[1846,47552,1848],{},[1846,47554,2075],{},[1979,47556,2201],{},[898,47558,2638],{},[1846,47560,1945],{},[1979,47562,46548],{},[902,47564,47565],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,47568,47570],{"className":47569},[886],[888,47571,47572],{"xmlns":890},[892,47573,47574,47598],{},[895,47575,47576,47578,47580,47582,47584,47586,47588,47590,47592,47594,47596],{},[898,47577,3783],{},[1846,47579,1848],{},[898,47581,8519],{},[1846,47583,1855],{"stretchy":1854},[898,47585,2638],{},[1846,47587,1861],{"stretchy":1854},[1846,47589,1848],{},[1979,47591,2023],{},[898,47593,2638],{},[1846,47595,1945],{},[1979,47597,2712],{},[902,47599,47600],{"encoding":904},"P = S(Q) = 3Q + 10",[120,47602,47603,47640,47704,47764],{},[123,47604,47605,47606,46503,47623,1734],{},"(a) Určete rovnovážné množství ",[883,47607,47609],{"className":47608},[886],[888,47610,47611],{"xmlns":890},[892,47612,47613,47621],{},[895,47614,47615],{},[1974,47616,47617,47619],{},[898,47618,2638],{},[898,47620,4098],{},[902,47622,42248],{"encoding":904},[883,47624,47626],{"className":47625},[886],[888,47627,47628],{"xmlns":890},[892,47629,47630,47638],{},[895,47631,47632],{},[1974,47633,47634,47636],{},[898,47635,3783],{},[898,47637,4098],{},[902,47639,41311],{"encoding":904},[123,47641,47642,47643,47661,47662,47682,47683,47703],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,47644,47646],{"className":47645},[886],[888,47647,47648],{"xmlns":890},[892,47649,47650,47658],{},[895,47651,47652,47654,47656],{},[898,47653,2623],{},[1846,47655,1848],{},[1979,47657,24046],{},[902,47659,47660],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,47663,47665],{"className":47664},[886],[888,47666,47667],{"xmlns":890},[892,47668,47669,47679],{},[895,47670,47671],{},[9012,47672,47673,47675,47677],{},[898,47674,2638],{},[1979,47676,2128],{},[898,47678,4098],{},[902,47680,47681],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,47684,47686],{"className":47685},[886],[888,47687,47688],{"xmlns":890},[892,47689,47690,47700],{},[895,47691,47692],{},[9012,47693,47694,47696,47698],{},[898,47695,3783],{},[1979,47697,2128],{},[898,47699,4098],{},[902,47701,47702],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,47705,47706,47707,47661,47724,47682,47744,47703],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,47708,47710],{"className":47709},[886],[888,47711,47712],{"xmlns":890},[892,47713,47714,47722],{},[895,47715,47716,47718,47720],{},[898,47717,2623],{},[1846,47719,1848],{},[1979,47721,24046],{},[902,47723,47660],{"encoding":904},[883,47725,47727],{"className":47726},[886],[888,47728,47729],{"xmlns":890},[892,47730,47731,47741],{},[895,47732,47733],{},[9012,47734,47735,47737,47739],{},[898,47736,2638],{},[1979,47738,1981],{},[898,47740,4098],{},[902,47742,47743],{"encoding":904},"Q_2^E",[883,47745,47747],{"className":47746},[886],[888,47748,47749],{"xmlns":890},[892,47750,47751,47761],{},[895,47752,47753],{},[9012,47754,47755,47757,47759],{},[898,47756,3783],{},[1979,47758,1981],{},[898,47760,4098],{},[902,47762,47763],{"encoding":904},"P_2^E",[123,47765,47766],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,47768,47769,47770,1734],{},"Viz též ",[207,47771,42566],{"className":47772,"dataFsResolvedFilePath":809,"href":810},[210],[198,47774,42868],{"id":47775},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,47777,47778,47529,47781,47566,47817,1734],{},[38,47779,47780],{},"2.14",[883,47782,47784],{"className":47783},[886],[888,47785,47786],{"xmlns":890},[892,47787,47788,47814],{},[895,47789,47790,47792,47794,47796,47798,47800,47802,47804,47806,47808,47810,47812],{},[898,47791,3783],{},[1846,47793,1848],{},[898,47795,207],{},[898,47797,2638],{},[1846,47799,1945],{},[898,47801,1948],{},[1846,47803,1848],{},[1846,47805,2075],{},[1979,47807,1981],{},[898,47809,2638],{},[1846,47811,1945],{},[1979,47813,2968],{},[902,47815,47816],{"encoding":904},"P = aQ + b = -2Q + 50",[883,47818,47820],{"className":47819},[886],[888,47821,47822],{"xmlns":890},[892,47823,47824,47848],{},[895,47825,47826,47828,47830,47832,47834,47836,47838,47840,47842,47844,47846],{},[898,47827,3783],{},[1846,47829,1848],{},[898,47831,1992],{},[898,47833,2638],{},[1846,47835,1945],{},[898,47837,2044],{},[1846,47839,1848],{},[1979,47841,19166],{},[898,47843,2638],{},[1846,47845,1945],{},[1979,47847,8881],{},[902,47849,47850],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,47852,47853,47889,47892,47978,48031,48111,48165],{},[123,47854,47605,47855,46503,47872,1734],{},[883,47856,47858],{"className":47857},[886],[888,47859,47860],{"xmlns":890},[892,47861,47862,47870],{},[895,47863,47864],{},[1974,47865,47866,47868],{},[898,47867,2638],{},[898,47869,4098],{},[902,47871,42248],{"encoding":904},[883,47873,47875],{"className":47874},[886],[888,47876,47877],{"xmlns":890},[892,47878,47879,47887],{},[895,47880,47881],{},[1974,47882,47883,47885],{},[898,47884,3783],{},[898,47886,4098],{},[902,47888,41311],{"encoding":904},[123,47890,47891],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,47893,47894,47895,47912,47913,2521,47926,2535,47942,47958,47959,1734],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,47896,47898],{"className":47897},[886],[888,47899,47900],{"xmlns":890},[892,47901,47902,47910],{},[895,47903,47904],{},[1974,47905,47906,47908],{},[898,47907,2638],{},[898,47909,4098],{},[902,47911,42248],{"encoding":904}," odpovídající změně ",[883,47914,47916],{"className":47915},[886],[888,47917,47918],{"xmlns":890},[892,47919,47920,47924],{},[895,47921,47922],{},[898,47923,207],{},[902,47925,207],{"encoding":904},[883,47927,47929],{"className":47928},[886],[888,47930,47931],{"xmlns":890},[892,47932,47933,47939],{},[895,47934,47935,47937],{},[1846,47936,2075],{},[1979,47938,1981],{},[902,47940,47941],{"encoding":904},"-2",[883,47943,47945],{"className":47944},[886],[888,47946,47947],{"xmlns":890},[892,47948,47949,47955],{},[895,47950,47951,47953],{},[1846,47952,2075],{},[1979,47954,2023],{},[902,47956,47957],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,47960,47962],{"className":47961},[886],[888,47963,47964],{"xmlns":890},[892,47965,47966,47976],{},[895,47967,47968],{},[9012,47969,47970,47972,47974],{},[898,47971,2638],{},[1979,47973,2128],{},[898,47975,4098],{},[902,47977,47681],{"encoding":904},[123,47979,47980,47981,47912,47998,48011,48012,1734],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,47982,47984],{"className":47983},[886],[888,47985,47986],{"xmlns":890},[892,47987,47988,47996],{},[895,47989,47990],{},[1974,47991,47992,47994],{},[898,47993,2638],{},[898,47995,4098],{},[902,47997,42248],{"encoding":904},[883,47999,48001],{"className":48000},[886],[888,48002,48003],{"xmlns":890},[892,48004,48005,48009],{},[895,48006,48007],{},[898,48008,1948],{},[902,48010,1948],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48013,48015],{"className":48014},[886],[888,48016,48017],{"xmlns":890},[892,48018,48019,48029],{},[895,48020,48021],{},[9012,48022,48023,48025,48027],{},[898,48024,2638],{},[1979,48026,1981],{},[898,48028,4098],{},[902,48030,47743],{"encoding":904},[123,48032,48033,48034,47912,48051,2521,48064,2535,48077,47958,48091,1734],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,48035,48037],{"className":48036},[886],[888,48038,48039],{"xmlns":890},[892,48040,48041,48049],{},[895,48042,48043],{},[1974,48044,48045,48047],{},[898,48046,2638],{},[898,48048,4098],{},[902,48050,42248],{"encoding":904},[883,48052,48054],{"className":48053},[886],[888,48055,48056],{"xmlns":890},[892,48057,48058,48062],{},[895,48059,48060],{},[898,48061,1992],{},[902,48063,1992],{"encoding":904},[883,48065,48067],{"className":48066},[886],[888,48068,48069],{"xmlns":890},[892,48070,48071,48075],{},[895,48072,48073],{},[1979,48074,19166],{},[902,48076,44305],{"encoding":904},[883,48078,48080],{"className":48079},[886],[888,48081,48082],{"xmlns":890},[892,48083,48084,48088],{},[895,48085,48086],{},[1979,48087,14434],{},[902,48089,48090],{"encoding":904},"0{,}8",[883,48092,48094],{"className":48093},[886],[888,48095,48096],{"xmlns":890},[892,48097,48098,48108],{},[895,48099,48100],{},[9012,48101,48102,48104,48106],{},[898,48103,2638],{},[1979,48105,2023],{},[898,48107,4098],{},[902,48109,48110],{"encoding":904},"Q_3^E",[123,48112,48113,48114,47912,48131,48144,48145,1734],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,48115,48117],{"className":48116},[886],[888,48118,48119],{"xmlns":890},[892,48120,48121,48129],{},[895,48122,48123],{},[1974,48124,48125,48127],{},[898,48126,2638],{},[898,48128,4098],{},[902,48130,42248],{"encoding":904},[883,48132,48134],{"className":48133},[886],[888,48135,48136],{"xmlns":890},[892,48137,48138,48142],{},[895,48139,48140],{},[898,48141,2044],{},[902,48143,2044],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48146,48148],{"className":48147},[886],[888,48149,48150],{"xmlns":890},[892,48151,48152,48162],{},[895,48153,48154],{},[9012,48155,48156,48158,48160],{},[898,48157,2638],{},[1979,48159,2201],{},[898,48161,4098],{},[902,48163,48164],{"encoding":904},"Q_4^E",[123,48166,48167,48168,48185,48186,48199,48200,21265,48213,1343,48228,21265,48241,1745,48255,21265,48268,48283,48284,1734],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,48169,48171],{"className":48170},[886],[888,48172,48173],{"xmlns":890},[892,48174,48175,48183],{},[895,48176,48177],{},[1974,48178,48179,48181],{},[898,48180,2638],{},[898,48182,4098],{},[902,48184,42248],{"encoding":904}," odpovídající změnám ",[883,48187,48189],{"className":48188},[886],[888,48190,48191],{"xmlns":890},[892,48192,48193,48197],{},[895,48194,48195],{},[898,48196,207],{},[902,48198,207],{"encoding":904}," o 1, ",[883,48201,48203],{"className":48202},[886],[888,48204,48205],{"xmlns":890},[892,48206,48207,48211],{},[895,48208,48209],{},[898,48210,1948],{},[902,48212,1948],{"encoding":904},[883,48214,48216],{"className":48215},[886],[888,48217,48218],{"xmlns":890},[892,48219,48220,48226],{},[895,48221,48222,48224],{},[1846,48223,2075],{},[1979,48225,2712],{},[902,48227,19300],{"encoding":904},[883,48229,48231],{"className":48230},[886],[888,48232,48233],{"xmlns":890},[892,48234,48235,48239],{},[895,48236,48237],{},[898,48238,1992],{},[902,48240,1992],{"encoding":904},[883,48242,48244],{"className":48243},[886],[888,48245,48246],{"xmlns":890},[892,48247,48248,48252],{},[895,48249,48250],{},[1979,48251,2643],{},[902,48253,48254],{"encoding":904},"0{,}1",[883,48256,48258],{"className":48257},[886],[888,48259,48260],{"xmlns":890},[892,48261,48262,48266],{},[895,48263,48264],{},[898,48265,2044],{},[902,48267,2044],{"encoding":904},[883,48269,48271],{"className":48270},[886],[888,48272,48273],{"xmlns":890},[892,48274,48275,48281],{},[895,48276,48277,48279],{},[1846,48278,2075],{},[1979,48280,2712],{},[902,48282,19300],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,48285,48287],{"className":48286},[886],[888,48288,48289],{"xmlns":890},[892,48290,48291,48301],{},[895,48292,48293],{},[9012,48294,48295,48297,48299],{},[898,48296,2638],{},[1979,48298,2078],{},[898,48300,4098],{},[902,48302,48303],{"encoding":904},"Q_5^E",[724,48305,48306,47529,48309,47566,48332,1734],{},[38,48307,48308],{},"2.15",[883,48310,48312],{"className":48311},[886],[888,48313,48314],{"xmlns":890},[892,48315,48316,48330],{},[895,48317,48318,48320,48322,48324,48326,48328],{},[898,48319,3783],{},[1846,48321,1848],{},[898,48323,207],{},[898,48325,2638],{},[1846,48327,1945],{},[898,48329,1948],{},[902,48331,36905],{"encoding":904},[883,48333,48335],{"className":48334},[886],[888,48336,48337],{"xmlns":890},[892,48338,48339,48353],{},[895,48340,48341,48343,48345,48347,48349,48351],{},[898,48342,3783],{},[1846,48344,1848],{},[898,48346,1992],{},[898,48348,2638],{},[1846,48350,1945],{},[898,48352,2044],{},[902,48354,40087],{"encoding":904},[120,48356,48357,48432,48449,48558,48611,48665],{},[123,48358,48359,48360,48373,48374,48399,48400,48431],{},"(a) Odvoďte redukovaný tvar pro ",[883,48361,48363],{"className":48362},[886],[888,48364,48365],{"xmlns":890},[892,48366,48367,48371],{},[895,48368,48369],{},[898,48370,3783],{},[902,48372,3783],{"encoding":904},". Stanovte podmínky pro ",[883,48375,48377],{"className":48376},[886],[888,48378,48379],{"xmlns":890},[892,48380,48381,48397],{},[895,48382,48383,48385,48387,48389,48391,48393,48395],{},[898,48384,207],{},[1846,48386,2136],{"separator":2135},[898,48388,1948],{},[1846,48390,2136],{"separator":2135},[898,48392,1992],{},[1846,48394,2136],{"separator":2135},[898,48396,2044],{},[902,48398,43130],{"encoding":904}," tak, aby rovnovážný bod ",[883,48401,48403],{"className":48402},[886],[888,48404,48405],{"xmlns":890},[892,48406,48407,48429],{},[895,48408,48409,48411,48413,48419,48421,48427],{},[898,48410,4098],{},[1846,48412,2336],{"stretchy":1854},[1974,48414,48415,48417],{},[898,48416,2638],{},[898,48418,4098],{},[1846,48420,2136],{"separator":2135},[1974,48422,48423,48425],{},[898,48424,3783],{},[898,48426,4098],{},[1846,48428,2351],{"stretchy":1854},[902,48430,41212],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,48433,48434,48435,48448],{},"(b) Vypočtěte multiplikátory pro ",[883,48436,48438],{"className":48437},[886],[888,48439,48440],{"xmlns":890},[892,48441,48442,48446],{},[895,48443,48444],{},[898,48445,3783],{},[902,48447,3783],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,48450,48451,48452,1343,48472,1343,48490,1343,48508,48526,48527,48544,48545,1734],{},"(c) Pro hodnoty parametrů ",[883,48453,48455],{"className":48454},[886],[888,48456,48457],{"xmlns":890},[892,48458,48459,48469],{},[895,48460,48461,48463,48465,48467],{},[898,48462,207],{},[1846,48464,1848],{},[1846,48466,2075],{},[1979,48468,1981],{},[902,48470,48471],{"encoding":904},"a = -2",[883,48473,48475],{"className":48474},[886],[888,48476,48477],{"xmlns":890},[892,48478,48479,48487],{},[895,48480,48481,48483,48485],{},[898,48482,1948],{},[1846,48484,1848],{},[1979,48486,5057],{},[902,48488,48489],{"encoding":904},"b = 40",[883,48491,48493],{"className":48492},[886],[888,48494,48495],{"xmlns":890},[892,48496,48497,48505],{},[895,48498,48499,48501,48503],{},[898,48500,1992],{},[1846,48502,1848],{},[1979,48504,4855],{},[902,48506,48507],{"encoding":904},"c = 0{,}5",[883,48509,48511],{"className":48510},[886],[888,48512,48513],{"xmlns":890},[892,48514,48515,48523],{},[895,48516,48517,48519,48521],{},[898,48518,2044],{},[1846,48520,1848],{},[1979,48522,2712],{},[902,48524,48525],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,48528,48530],{"className":48529},[886],[888,48531,48532],{"xmlns":890},[892,48533,48534,48542],{},[895,48535,48536],{},[1974,48537,48538,48540],{},[898,48539,3783],{},[898,48541,4098],{},[902,48543,41311],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,48546,48548],{"className":48547},[886],[888,48549,48550],{"xmlns":890},[892,48551,48552,48556],{},[895,48553,48554],{},[898,48555,3783],{},[902,48557,3783],{"encoding":904},[123,48559,48560,48561,47912,48578,48591,48592,1734],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,48562,48564],{"className":48563},[886],[888,48565,48566],{"xmlns":890},[892,48567,48568,48576],{},[895,48569,48570],{},[1974,48571,48572,48574],{},[898,48573,3783],{},[898,48575,4098],{},[902,48577,41311],{"encoding":904},[883,48579,48581],{"className":48580},[886],[888,48582,48583],{"xmlns":890},[892,48584,48585,48589],{},[895,48586,48587],{},[898,48588,207],{},[902,48590,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,48593,48595],{"className":48594},[886],[888,48596,48597],{"xmlns":890},[892,48598,48599,48609],{},[895,48600,48601],{},[9012,48602,48603,48605,48607],{},[898,48604,3783],{},[1979,48606,2128],{},[898,48608,4098],{},[902,48610,47702],{"encoding":904},[123,48612,48613,48614,48631,48632,48645,48646,1734],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,48615,48617],{"className":48616},[886],[888,48618,48619],{"xmlns":890},[892,48620,48621,48629],{},[895,48622,48623],{},[1974,48624,48625,48627],{},[898,48626,3783],{},[898,48628,4098],{},[902,48630,41311],{"encoding":904}," odpovídající poklesu ",[883,48633,48635],{"className":48634},[886],[888,48636,48637],{"xmlns":890},[892,48638,48639,48643],{},[895,48640,48641],{},[898,48642,207],{},[902,48644,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,48647,48649],{"className":48648},[886],[888,48650,48651],{"xmlns":890},[892,48652,48653,48663],{},[895,48654,48655],{},[9012,48656,48657,48659,48661],{},[898,48658,3783],{},[1979,48660,1981],{},[898,48662,4098],{},[902,48664,47763],{"encoding":904},[123,48666,48667,48668,48185,48685,48698,48699,2535,48712,1745,48727,48740,48741,1734],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,48669,48671],{"className":48670},[886],[888,48672,48673],{"xmlns":890},[892,48674,48675,48683],{},[895,48676,48677],{},[1974,48678,48679,48681],{},[898,48680,3783],{},[898,48682,4098],{},[902,48684,41311],{"encoding":904},[883,48686,48688],{"className":48687},[886],[888,48689,48690],{"xmlns":890},[892,48691,48692,48696],{},[895,48693,48694],{},[898,48695,207],{},[902,48697,207],{"encoding":904}," na 35, ",[883,48700,48702],{"className":48701},[886],[888,48703,48704],{"xmlns":890},[892,48705,48706,48710],{},[895,48707,48708],{},[898,48709,1992],{},[902,48711,1992],{"encoding":904},[883,48713,48715],{"className":48714},[886],[888,48716,48717],{"xmlns":890},[892,48718,48719,48724],{},[895,48720,48721],{},[1979,48722,48723],{},"0,7",[902,48725,48726],{"encoding":904},"0{,}7",[883,48728,48730],{"className":48729},[886],[888,48731,48732],{"xmlns":890},[892,48733,48734,48738],{},[895,48735,48736],{},[898,48737,2044],{},[902,48739,2044],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,48742,48744],{"className":48743},[886],[888,48745,48746],{"xmlns":890},[892,48747,48748,48758],{},[895,48749,48750],{},[9012,48751,48752,48754,48756],{},[898,48753,3783],{},[1979,48755,2023],{},[898,48757,4098],{},[902,48759,48760],{"encoding":904},"P_3^E",[724,48762,48763,47529,48766,47566,48794,21439,48822,1745,48848,1734],{},[38,48764,48765],{},"2.16",[883,48767,48769],{"className":48768},[886],[888,48770,48771],{"xmlns":890},[892,48772,48773,48791],{},[895,48774,48775,48777,48779,48781,48783,48785],{},[898,48776,3783],{},[1846,48778,1848],{},[898,48780,207],{},[1846,48782,1945],{},[898,48784,1948],{},[1974,48786,48787,48789],{},[898,48788,2638],{},[1979,48790,1981],{},[902,48792,48793],{"encoding":904},"P = a + bQ^2",[883,48795,48797],{"className":48796},[886],[888,48798,48799],{"xmlns":890},[892,48800,48801,48819],{},[895,48802,48803,48805,48807,48809,48811,48813],{},[898,48804,3783],{},[1846,48806,1848],{},[898,48808,1992],{},[1846,48810,1945],{},[898,48812,2044],{},[1974,48814,48815,48817],{},[898,48816,2638],{},[1979,48818,1981],{},[902,48820,48821],{"encoding":904},"P = c + dQ^2",[883,48823,48825],{"className":48824},[886],[888,48826,48827],{"xmlns":890},[892,48828,48829,48845],{},[895,48830,48831,48833,48835,48837,48839,48841,48843],{},[898,48832,207],{},[1846,48834,2136],{"separator":2135},[898,48836,1992],{},[1846,48838,2136],{"separator":2135},[898,48840,2044],{},[1846,48842,3256],{},[1979,48844,2177],{},[902,48846,48847],{"encoding":904},"a, c, d > 0",[883,48849,48851],{"className":48850},[886],[888,48852,48853],{"xmlns":890},[892,48854,48855,48863],{},[895,48856,48857,48859,48861],{},[898,48858,1948],{},[1846,48860,3295],{},[1979,48862,2177],{},[902,48864,48865],{"encoding":904},"b \u003C 0",[120,48867,48868,48916,48932,49039,49091,49143,49252,49268,49367,49420],{},[123,48869,48359,48870,48883,48884,48915],{},[883,48871,48873],{"className":48872},[886],[888,48874,48875],{"xmlns":890},[892,48876,48877,48881],{},[895,48878,48879],{},[898,48880,2638],{},[902,48882,2638],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,48885,48887],{"className":48886},[886],[888,48888,48889],{"xmlns":890},[892,48890,48891,48913],{},[895,48892,48893,48895,48897,48903,48905,48911],{},[898,48894,4098],{},[1846,48896,2336],{"stretchy":1854},[1974,48898,48899,48901],{},[898,48900,2638],{},[898,48902,4098],{},[1846,48904,2136],{"separator":2135},[1974,48906,48907,48909],{},[898,48908,3783],{},[898,48910,4098],{},[1846,48912,2351],{"stretchy":1854},[902,48914,41212],{"encoding":904}," patřil do 1. kvadrantu.",[123,48917,48434,48918,48931],{},[883,48919,48921],{"className":48920},[886],[888,48922,48923],{"xmlns":890},[892,48924,48925,48929],{},[895,48926,48927],{},[898,48928,2638],{},[902,48930,2638],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,48933,48451,48934,1343,48952,1343,48972,1343,48990,49008,49009,48544,49026,1734],{},[883,48935,48937],{"className":48936},[886],[888,48938,48939],{"xmlns":890},[892,48940,48941,48949],{},[895,48942,48943,48945,48947],{},[898,48944,207],{},[1846,48946,1848],{},[1979,48948,2938],{},[902,48950,48951],{"encoding":904},"a = 100",[883,48953,48955],{"className":48954},[886],[888,48956,48957],{"xmlns":890},[892,48958,48959,48969],{},[895,48960,48961,48963,48965,48967],{},[898,48962,1948],{},[1846,48964,1848],{},[1846,48966,2075],{},[1979,48968,2128],{},[902,48970,48971],{"encoding":904},"b = -1",[883,48973,48975],{"className":48974},[886],[888,48976,48977],{"xmlns":890},[892,48978,48979,48987],{},[895,48980,48981,48983,48985],{},[898,48982,1992],{},[1846,48984,1848],{},[1979,48986,8881],{},[902,48988,48989],{"encoding":904},"c = 20",[883,48991,48993],{"className":48992},[886],[888,48994,48995],{"xmlns":890},[892,48996,48997,49005],{},[895,48998,48999,49001,49003],{},[898,49000,2044],{},[1846,49002,1848],{},[1979,49004,2128],{},[902,49006,49007],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,49010,49012],{"className":49011},[886],[888,49013,49014],{"xmlns":890},[892,49015,49016,49024],{},[895,49017,49018],{},[1974,49019,49020,49022],{},[898,49021,2638],{},[898,49023,4098],{},[902,49025,42248],{"encoding":904},[883,49027,49029],{"className":49028},[886],[888,49030,49031],{"xmlns":890},[892,49032,49033,49037],{},[895,49034,49035],{},[898,49036,2638],{},[902,49038,2638],{"encoding":904},[123,49040,47980,49041,47912,49058,49071,49072,1734],{},[883,49042,49044],{"className":49043},[886],[888,49045,49046],{"xmlns":890},[892,49047,49048,49056],{},[895,49049,49050],{},[1974,49051,49052,49054],{},[898,49053,2638],{},[898,49055,4098],{},[902,49057,42248],{"encoding":904},[883,49059,49061],{"className":49060},[886],[888,49062,49063],{"xmlns":890},[892,49064,49065,49069],{},[895,49066,49067],{},[898,49068,207],{},[902,49070,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49073,49075],{"className":49074},[886],[888,49076,49077],{"xmlns":890},[892,49078,49079,49089],{},[895,49080,49081],{},[9012,49082,49083,49085,49087],{},[898,49084,2638],{},[1979,49086,2128],{},[898,49088,4098],{},[902,49090,47681],{"encoding":904},[123,49092,48033,49093,47912,49110,49123,49124,1734],{},[883,49094,49096],{"className":49095},[886],[888,49097,49098],{"xmlns":890},[892,49099,49100,49108],{},[895,49101,49102],{},[1974,49103,49104,49106],{},[898,49105,2638],{},[898,49107,4098],{},[902,49109,42248],{"encoding":904},[883,49111,49113],{"className":49112},[886],[888,49114,49115],{"xmlns":890},[892,49116,49117,49121],{},[895,49118,49119],{},[898,49120,1992],{},[902,49122,1992],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49125,49127],{"className":49126},[886],[888,49128,49129],{"xmlns":890},[892,49130,49131,49141],{},[895,49132,49133],{},[9012,49134,49135,49137,49139],{},[898,49136,2638],{},[1979,49138,1981],{},[898,49140,4098],{},[902,49142,47743],{"encoding":904},[123,49144,48113,49145,48185,49162,49175,49176,2535,49189,49204,49205,49218,49219,49232,49233,1734],{},[883,49146,49148],{"className":49147},[886],[888,49149,49150],{"xmlns":890},[892,49151,49152,49160],{},[895,49153,49154],{},[1974,49155,49156,49158],{},[898,49157,2638],{},[898,49159,4098],{},[902,49161,42248],{"encoding":904},[883,49163,49165],{"className":49164},[886],[888,49166,49167],{"xmlns":890},[892,49168,49169,49173],{},[895,49170,49171],{},[898,49172,207],{},[902,49174,207],{"encoding":904}," na 110, poklesu ",[883,49177,49179],{"className":49178},[886],[888,49180,49181],{"xmlns":890},[892,49182,49183,49187],{},[895,49184,49185],{},[898,49186,1948],{},[902,49188,1948],{"encoding":904},[883,49190,49192],{"className":49191},[886],[888,49193,49194],{"xmlns":890},[892,49195,49196,49202],{},[895,49197,49198,49200],{},[1846,49199,2075],{},[1979,49201,1981],{},[902,49203,47941],{"encoding":904},", růstu ",[883,49206,49208],{"className":49207},[886],[888,49209,49210],{"xmlns":890},[892,49211,49212,49216],{},[895,49213,49214],{},[898,49215,1992],{},[902,49217,1992],{"encoding":904}," na 25 a růstu ",[883,49220,49222],{"className":49221},[886],[888,49223,49224],{"xmlns":890},[892,49225,49226,49230],{},[895,49227,49228],{},[898,49229,2044],{},[902,49231,2044],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,49234,49236],{"className":49235},[886],[888,49237,49238],{"xmlns":890},[892,49239,49240,49250],{},[895,49241,49242],{},[9012,49243,49244,49246,49248],{},[898,49245,2638],{},[1979,49247,2023],{},[898,49249,4098],{},[902,49251,48110],{"encoding":904},[123,49253,49254,49255,48931],{},"(i) Vypočtěte multiplikátory pro ",[883,49256,49258],{"className":49257},[886],[888,49259,49260],{"xmlns":890},[892,49261,49262,49266],{},[895,49263,49264],{},[898,49265,3783],{},[902,49267,3783],{"encoding":904},[123,49269,49270,49271,48544,49288,49301,49302,47912,49319,2535,49332,49347,49348,1734],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,49272,49274],{"className":49273},[886],[888,49275,49276],{"xmlns":890},[892,49277,49278,49286],{},[895,49279,49280],{},[1974,49281,49282,49284],{},[898,49283,3783],{},[898,49285,4098],{},[902,49287,41311],{"encoding":904},[883,49289,49291],{"className":49290},[886],[888,49292,49293],{"xmlns":890},[892,49294,49295,49299],{},[895,49296,49297],{},[898,49298,3783],{},[902,49300,3783],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,49303,49305],{"className":49304},[886],[888,49306,49307],{"xmlns":890},[892,49308,49309,49317],{},[895,49310,49311],{},[1974,49312,49313,49315],{},[898,49314,3783],{},[898,49316,4098],{},[902,49318,41311],{"encoding":904},[883,49320,49322],{"className":49321},[886],[888,49323,49324],{"xmlns":890},[892,49325,49326,49330],{},[895,49327,49328],{},[898,49329,207],{},[902,49331,207],{"encoding":904},[883,49333,49335],{"className":49334},[886],[888,49336,49337],{"xmlns":890},[892,49338,49339,49345],{},[895,49340,49341,49343],{},[1846,49342,2075],{},[1979,49344,2023],{},[902,49346,47957],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49349,49351],{"className":49350},[886],[888,49352,49353],{"xmlns":890},[892,49354,49355,49365],{},[895,49356,49357],{},[9012,49358,49359,49361,49363],{},[898,49360,3783],{},[1979,49362,2128],{},[898,49364,4098],{},[902,49366,47702],{"encoding":904},[123,49368,49369,49370,47912,49387,49400,49401,1734],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,49371,49373],{"className":49372},[886],[888,49374,49375],{"xmlns":890},[892,49376,49377,49385],{},[895,49378,49379],{},[1974,49380,49381,49383],{},[898,49382,3783],{},[898,49384,4098],{},[902,49386,41311],{"encoding":904},[883,49388,49390],{"className":49389},[886],[888,49391,49392],{"xmlns":890},[892,49393,49394,49398],{},[895,49395,49396],{},[898,49397,207],{},[902,49399,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49402,49404],{"className":49403},[886],[888,49405,49406],{"xmlns":890},[892,49407,49408,49418],{},[895,49409,49410],{},[9012,49411,49412,49414,49416],{},[898,49413,3783],{},[1979,49415,1981],{},[898,49417,4098],{},[902,49419,47763],{"encoding":904},[123,49421,49422,49423,48631,49440,49453,49454,2535,49467,49204,49482,49495,49496,49509,49510,1734],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,49424,49426],{"className":49425},[886],[888,49427,49428],{"xmlns":890},[892,49429,49430,49438],{},[895,49431,49432],{},[1974,49433,49434,49436],{},[898,49435,3783],{},[898,49437,4098],{},[902,49439,41311],{"encoding":904},[883,49441,49443],{"className":49442},[886],[888,49444,49445],{"xmlns":890},[892,49446,49447,49451],{},[895,49448,49449],{},[898,49450,207],{},[902,49452,207],{"encoding":904}," na 90, poklesu ",[883,49455,49457],{"className":49456},[886],[888,49458,49459],{"xmlns":890},[892,49460,49461,49465],{},[895,49462,49463],{},[898,49464,1948],{},[902,49466,1948],{"encoding":904},[883,49468,49470],{"className":49469},[886],[888,49471,49472],{"xmlns":890},[892,49473,49474,49480],{},[895,49475,49476,49478],{},[1846,49477,2075],{},[1979,49479,2023],{},[902,49481,47957],{"encoding":904},[883,49483,49485],{"className":49484},[886],[888,49486,49487],{"xmlns":890},[892,49488,49489,49493],{},[895,49490,49491],{},[898,49492,1992],{},[902,49494,1992],{"encoding":904}," na 30 a růstu ",[883,49497,49499],{"className":49498},[886],[888,49500,49501],{"xmlns":890},[892,49502,49503,49507],{},[895,49504,49505],{},[898,49506,2044],{},[902,49508,2044],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49511,49513],{"className":49512},[886],[888,49514,49515],{"xmlns":890},[892,49516,49517,49527],{},[895,49518,49519],{},[9012,49520,49521,49523,49525],{},[898,49522,3783],{},[1979,49524,2023],{},[898,49526,4098],{},[902,49528,48760],{"encoding":904},[198,49530,820],{"id":49531},"přebytek-spotřebitele-a-výrobce-1",[724,49533,49534,47529,49537,47566,49573,1734],{},[38,49535,49536],{},"2.17",[883,49538,49540],{"className":49539},[886],[888,49541,49542],{"xmlns":890},[892,49543,49544,49570],{},[895,49545,49546,49548,49550,49552,49554,49556,49558,49560,49562,49564],{},[898,49547,3783],{},[1846,49549,1848],{},[898,49551,4029],{},[1846,49553,1855],{"stretchy":1854},[898,49555,2638],{},[1846,49557,1861],{"stretchy":1854},[1846,49559,1848],{},[1979,49561,14883],{},[1846,49563,2075],{},[1974,49565,49566,49568],{},[898,49567,2638],{},[1979,49569,1981],{},[902,49571,49572],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,49574,49576],{"className":49575},[886],[888,49577,49578],{"xmlns":890},[892,49579,49580,49606],{},[895,49581,49582,49584,49586,49588,49590,49592,49594,49596,49598,49600],{},[898,49583,3783],{},[1846,49585,1848],{},[898,49587,8519],{},[1846,49589,1855],{"stretchy":1854},[898,49591,2638],{},[1846,49593,1861],{"stretchy":1854},[1846,49595,1848],{},[1979,49597,2023],{},[1846,49599,1945],{},[1974,49601,49602,49604],{},[898,49603,2638],{},[1979,49605,1981],{},[902,49607,49608],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,49610,49611,49614],{},[123,49612,49613],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,49615,49616],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,49618,49619,47529,49622,47566,49656,1734],{},[38,49620,49621],{},"2.18",[883,49623,49625],{"className":49624},[886],[888,49626,49627],{"xmlns":890},[892,49628,49629,49653],{},[895,49630,49631,49633,49635,49637,49639,49641,49643,49645,49647,49649,49651],{},[898,49632,3783],{},[1846,49634,1848],{},[898,49636,4029],{},[1846,49638,1855],{"stretchy":1854},[898,49640,2638],{},[1846,49642,1861],{"stretchy":1854},[1846,49644,1848],{},[1979,49646,3555],{},[1846,49648,2075],{},[1979,49650,1981],{},[898,49652,2638],{},[902,49654,49655],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,49657,49659],{"className":49658},[886],[888,49660,49661],{"xmlns":890},[892,49662,49663,49689],{},[895,49664,49665,49667,49669,49671,49673,49675,49677,49679,49681,49683],{},[898,49666,3783],{},[1846,49668,1848],{},[898,49670,8519],{},[1846,49672,1855],{"stretchy":1854},[898,49674,2638],{},[1846,49676,1861],{"stretchy":1854},[1846,49678,1848],{},[1979,49680,2023],{},[1846,49682,1945],{},[1974,49684,49685,49687],{},[898,49686,2638],{},[1979,49688,1981],{},[902,49690,49608],{"encoding":904},[120,49692,49693,49713,49716,49719],{},[123,49694,49695,49696,1734],{},"(a) Vypočtěte rovnovážné množství ",[883,49697,49699],{"className":49698},[886],[888,49700,49701],{"xmlns":890},[892,49702,49703,49711],{},[895,49704,49705],{},[1974,49706,49707,49709],{},[898,49708,2638],{},[898,49710,4098],{},[902,49712,42248],{"encoding":904},[123,49714,49715],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,49717,49718],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,49720,49721],{},"(c) Graficky interpretujte.",[36815,49723],{},[115,49725,49727],{"id":49726},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,49729,49730,49733,49736,49739,49742,49745,49748,49751,49754,49757,49760,49763,49766,49769],{},[123,49731,49732],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,49734,49735],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,49737,49738],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,49740,49741],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,49743,49744],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,49746,49747],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,49749,49750],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,49752,49753],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,49755,49756],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,49758,49759],{},"K čemu slouží multiplikátory?",[123,49761,49762],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,49764,49765],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,49767,49768],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,49770,49771],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[36815,49773],{},[115,49775,15565],{"id":15564},[724,49777,49778],{},[38,49779,13006],{},[120,49781,49782,49817,49822,49852,49857,49920,49946,49951,49981,49990,49997,50003],{},[123,49783,49784,9871,49787,18493,49790,2053,49792,1343,49815],{},[38,49785,49786],{},"Poptávané množství",[614,49788,49789],{},"quantity demanded",[38,49791,27847],{},[883,49793,49795],{"className":49794},[886],[888,49796,49797],{"xmlns":890},[892,49798,49799,49813],{},[895,49800,49801,49803,49805,49807,49809,49811],{},[898,49802,2638],{},[1846,49804,1848],{},[898,49806,4029],{},[1846,49808,1855],{"stretchy":1854},[898,49810,3783],{},[1846,49812,1861],{"stretchy":1854},[902,49814,4038],{"encoding":904},[38,49816,37294],{},[123,49818,49819,49821],{},[38,49820,37301],{}," — substituční + důchodový efekt",[123,49823,49824,2053,49827],{},[38,49825,49826],{},"Reálné cenové rozpětí",[883,49828,49830],{"className":49829},[886],[888,49831,49832],{"xmlns":890},[892,49833,49834,49850],{},[895,49835,49836,49838,49840,49842,49848],{},[1846,49837,1855],{"stretchy":1854},[1979,49839,2177],{},[1846,49841,2136],{"separator":2135},[2122,49843,49844,49846],{},[898,49845,3783],{},[1979,49847,2177],{},[1846,49849,1861],{"stretchy":1854},[902,49851,37502],{"encoding":904},[123,49853,49854,10942],{},[38,49855,49856],{},"Homogenita poptávky",[123,49858,49859,2053,49862,1343,49885,1343,49902,49919],{},[38,49860,49861],{},"Lineární poptávka",[883,49863,49865],{"className":49864},[886],[888,49866,49867],{"xmlns":890},[892,49868,49869,49883],{},[895,49870,49871,49873,49875,49877,49879,49881],{},[898,49872,3783],{},[1846,49874,1848],{},[898,49876,207],{},[898,49878,2638],{},[1846,49880,1945],{},[898,49882,1948],{},[902,49884,36905],{"encoding":904},[883,49886,49888],{"className":49887},[886],[888,49889,49890],{"xmlns":890},[892,49891,49892,49900],{},[895,49893,49894,49896,49898],{},[898,49895,207],{},[1846,49897,3295],{},[1979,49899,2177],{},[902,49901,42930],{"encoding":904},[883,49903,49905],{"className":49904},[886],[888,49906,49907],{"xmlns":890},[892,49908,49909,49917],{},[895,49910,49911,49913,49915],{},[898,49912,1948],{},[1846,49914,3256],{},[1979,49916,2177],{},[902,49918,18659],{"encoding":904}," — nedokonalá konkurence",[123,49921,49922,6861,49925],{},[38,49923,49924],{},"Dokonalá konkurence",[883,49926,49928],{"className":49927},[886],[888,49929,49930],{"xmlns":890},[892,49931,49932,49944],{},[895,49933,49934,49936,49938],{},[898,49935,3783],{},[1846,49937,1848],{},[1974,49939,49940,49942],{},[898,49941,3783],{},[1846,49943,4200],{},[902,49945,4203],{"encoding":904},[123,49947,49948,49950],{},[38,49949,38071],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,49952,49953,2053,49955,1343,49979],{},[38,49954,31572],{},[883,49956,49958],{"className":49957},[886],[888,49959,49960],{"xmlns":890},[892,49961,49962,49976],{},[895,49963,49964,49966,49968,49970,49972,49974],{},[898,49965,2638],{},[1846,49967,1848],{},[898,49969,4098],{},[1846,49971,1855],{"stretchy":1854},[898,49973,8974],{},[1846,49975,1861],{"stretchy":1854},[902,49977,49978],{"encoding":904},"Q = E(Y)",[38,49980,38268],{},[123,49982,49983,49986,49987,49989],{},[38,49984,49985],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,49988,38714],{}," zboží",[123,49991,49992,1745,49994,49996],{},[38,49993,39720],{},[38,49995,39667],{}," — znaménka zkřížených koeficientů",[123,49998,49999,50002],{},[38,50000,50001],{},"Dvoukomoditní trh"," (2.6)",[123,50004,50005,9871,50008,1861],{},[38,50006,50007],{},"Posun poptávky",[614,50009,38772],{},[724,50011,50012],{},[38,50013,12970],{},[120,50015,50016,50049,50053,50098],{},[123,50017,50018,9871,50020,18493,50022,2053,50024,1343,50047],{},[38,50019,40114],{},[614,50021,40117],{},[38,50023,40288],{},[883,50025,50027],{"className":50026},[886],[888,50028,50029],{"xmlns":890},[892,50030,50031,50045],{},[895,50032,50033,50035,50037,50039,50041,50043],{},[898,50034,2638],{},[1846,50036,1848],{},[898,50038,8519],{},[1846,50040,1855],{"stretchy":1854},[898,50042,3783],{},[1846,50044,1861],{"stretchy":1854},[902,50046,8528],{"encoding":904},[38,50048,40366],{},[123,50050,50051],{},[38,50052,40373],{},[123,50054,50055,2053,50058,1343,50081],{},[38,50056,50057],{},"Lineární nabídka",[883,50059,50061],{"className":50060},[886],[888,50062,50063],{"xmlns":890},[892,50064,50065,50079],{},[895,50066,50067,50069,50071,50073,50075,50077],{},[898,50068,3783],{},[1846,50070,1848],{},[898,50072,1992],{},[898,50074,2638],{},[1846,50076,1945],{},[898,50078,2044],{},[902,50080,40087],{"encoding":904},[883,50082,50084],{"className":50083},[886],[888,50085,50086],{"xmlns":890},[892,50087,50088,50096],{},[895,50089,50090,50092,50094],{},[898,50091,1992],{},[1846,50093,3256],{},[1979,50095,2177],{},[902,50097,40105],{"encoding":904},[123,50099,50100,9871,50103,1861],{},[38,50101,50102],{},"Posun nabídky",[614,50104,40751],{},[724,50106,50107],{},[38,50108,50109],{},"Rovnováha a komparativní statika",[120,50111,50112,50191,50197],{},[123,50113,50114,9871,50116,18493,50118,2053,50121,1343,50138,2053,50141,1343,50158,2053,50160],{},[38,50115,41170],{},[614,50117,41289],{},[38,50119,50120],{},"rovnovážná cena",[883,50122,50124],{"className":50123},[886],[888,50125,50126],{"xmlns":890},[892,50127,50128,50136],{},[895,50129,50130],{},[1974,50131,50132,50134],{},[898,50133,3783],{},[898,50135,4098],{},[902,50137,41311],{"encoding":904},[38,50139,50140],{},"rovnovážné množství",[883,50142,50144],{"className":50143},[886],[888,50145,50146],{"xmlns":890},[892,50147,50148,50156],{},[895,50149,50150],{},[1974,50151,50152,50154],{},[898,50153,2638],{},[898,50155,4098],{},[902,50157,42248],{"encoding":904},[38,50159,41347],{},[883,50161,50163],{"className":50162},[886],[888,50164,50165],{"xmlns":890},[892,50166,50167,50189],{},[895,50168,50169,50171,50173,50179,50181,50187],{},[898,50170,4098],{},[1846,50172,2336],{"stretchy":1854},[1974,50174,50175,50177],{},[898,50176,2638],{},[898,50178,4098],{},[1846,50180,2136],{"separator":2135},[1974,50182,50183,50185],{},[898,50184,3783],{},[898,50186,4098],{},[1846,50188,2351],{"stretchy":1854},[902,50190,41212],{"encoding":904},[123,50192,50193,50196],{},[38,50194,50195],{},"Pravidla 1–4"," komparativní statiky",[123,50198,50199,9871,50202,1861],{},[38,50200,50201],{},"Teorém pavučiny",[614,50203,42194],{},[724,50205,50206],{},[38,50207,50208],{},"Zdanění",[120,50210,50211,50267,50315],{},[123,50212,50213,50215,50216,50241,50242,1861],{},[38,50214,50208],{}," — daň výrobci (",[883,50217,50219],{"className":50218},[886],[888,50220,50221],{"xmlns":890},[892,50222,50223,50239],{},[895,50224,50225,50231,50233,50235,50237],{},[2122,50226,50227,50229],{},[898,50228,8519],{},[1979,50230,2128],{},[1846,50232,1848],{},[898,50234,8519],{},[1846,50236,1945],{},[898,50238,2623],{},[902,50240,42599],{"encoding":904},") vs. daň spotřebiteli (",[883,50243,50245],{"className":50244},[886],[888,50246,50247],{"xmlns":890},[892,50248,50249,50265],{},[895,50250,50251,50257,50259,50261,50263],{},[2122,50252,50253,50255],{},[898,50254,4029],{},[1979,50256,1981],{},[1846,50258,1848],{},[898,50260,4029],{},[1846,50262,2075],{},[898,50264,2623],{},[902,50266,42630],{"encoding":904},[123,50268,50269,2053,50271,1343,50292],{},[38,50270,42503],{},[883,50272,50274],{"className":50273},[886],[888,50275,50276],{"xmlns":890},[892,50277,50278,50290],{},[895,50279,50280],{},[2122,50281,50282,50284],{},[898,50283,2623],{},[895,50285,50286,50288],{},[898,50287,42522],{},[898,50289,724],{},[902,50291,42527],{"encoding":904},[883,50293,50295],{"className":50294},[886],[888,50296,50297],{"xmlns":890},[892,50298,50299,50313],{},[895,50300,50301],{},[2122,50302,50303,50305],{},[898,50304,2623],{},[895,50306,50307,50309,50311],{},[898,50308,42545],{},[898,50310,1844],{},[898,50312,11886],{},[902,50314,42552],{"encoding":904},[123,50316,50317,2053,50320,1343,50349],{},[38,50318,50319],{},"Ekvivalence zdanění",[883,50321,50323],{"className":50322},[886],[888,50324,50325],{"xmlns":890},[892,50326,50327,50347],{},[895,50328,50329,50337,50339],{},[9012,50330,50331,50333,50335],{},[898,50332,2638],{},[1979,50334,2128],{},[898,50336,4098],{},[1846,50338,1848],{},[9012,50340,50341,50343,50345],{},[898,50342,2638],{},[1979,50344,1981],{},[898,50346,4098],{},[902,50348,42753],{"encoding":904},[883,50350,50352],{"className":50351},[886],[888,50353,50354],{"xmlns":890},[892,50355,50356,50380],{},[895,50357,50358,50366,50368,50370,50372],{},[9012,50359,50360,50362,50364],{},[898,50361,3783],{},[1979,50363,2128],{},[898,50365,4098],{},[1846,50367,2075],{},[898,50369,2623],{},[1846,50371,1848],{},[9012,50373,50374,50376,50378],{},[898,50375,3783],{},[1979,50377,1981],{},[898,50379,4098],{},[902,50381,42787],{"encoding":904},[724,50383,50384],{},[38,50385,26253],{},[120,50387,50388,50434,50465,50470,50476,50483],{},[123,50389,50390,2053,50392],{},[38,50391,42886],{},[883,50393,50395],{"className":50394},[886],[888,50396,50397],{"xmlns":890},[892,50398,50399,50431],{},[895,50400,50401,50407,50409,50411,50413,50415,50417,50419,50421,50423,50425,50427,50429],{},[1974,50402,50403,50405],{},[898,50404,2638],{},[898,50406,4098],{},[1846,50408,1848],{},[1846,50410,1855],{"stretchy":1854},[898,50412,1948],{},[1846,50414,2075],{},[898,50416,2044],{},[1846,50418,1861],{"stretchy":1854},[898,50420,4520],{"mathvariant":2226},[1846,50422,1855],{"stretchy":1854},[898,50424,1992],{},[1846,50426,2075],{},[898,50428,207],{},[1846,50430,1861],{"stretchy":1854},[902,50432,50433],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,50435,50436,2053,50439,50464],{},[38,50437,50438],{},"Parametry",[883,50440,50442],{"className":50441},[886],[888,50443,50444],{"xmlns":890},[892,50445,50446,50462],{},[895,50447,50448,50450,50452,50454,50456,50458,50460],{},[898,50449,207],{},[1846,50451,2136],{"separator":2135},[898,50453,1948],{},[1846,50455,2136],{"separator":2135},[898,50457,1992],{},[1846,50459,2136],{"separator":2135},[898,50461,2044],{},[902,50463,43130],{"encoding":904}," — exogenní proměnné",[123,50466,50467],{},[38,50468,50469],{},"Endogenní \u002F exogenní proměnná",[123,50471,50472,50475],{},[38,50473,50474],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,50477,50478,1343,50481],{},[38,50479,50480],{},"Komparativní statika",[38,50482,36805],{},[123,50484,50485,2053,50487,50503],{},[38,50486,2803],{},[883,50488,50490],{"className":50489},[886],[888,50491,50492],{"xmlns":890},[892,50493,50494,50500],{},[895,50495,50496,50498],{},[898,50497,2044],{},[898,50499,2638],{},[902,50501,50502],{"encoding":904},"dQ"," (2.11)",[724,50505,50506],{},[38,50507,50508],{},"Přebytky a ostatní",[120,50510,50511,50549],{},[123,50512,50513,2053,50515,50530,50531,2053,50533,50548],{},[38,50514,44779],{},[883,50516,50518],{"className":50517},[886],[888,50519,50520],{"xmlns":890},[892,50521,50522,50528],{},[895,50523,50524,50526],{},[898,50525,2626],{},[898,50527,8519],{},[902,50529,44795],{"encoding":904}," (2.14), ",[38,50532,44798],{},[883,50534,50536],{"className":50535},[886],[888,50537,50538],{"xmlns":890},[892,50539,50540,50546],{},[895,50541,50542,50544],{},[898,50543,3783],{},[898,50545,8519],{},[902,50547,44814],{"encoding":904}," (2.15)",[123,50550,50551,1343,50554,50557],{},[38,50552,50553],{},"Homo economicus",[38,50555,50556],{},"Marshallova formulace"," (1890)",[36815,50559],{},[115,50561,3640],{"id":3639},[120,50563,50564,50599,50608],{},[123,50565,50566,2053,50569,50572,50573,1343,50576,50579,50580,50583,50584,50587,50588,50591,50592,50595,50596],{},[38,50567,50568],{},"Související témata:",[207,50570,811],{"className":50571,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,50574,820],{"className":50575,"dataFsResolvedFilePath":818,"href":819},[210],[207,50577,2207],{"className":50578,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,50581,775],{"className":50582,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,50585,784],{"className":50586,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,50589,793],{"className":50590,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,50593,1721],{"className":50594,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,50597,1708],{"className":50598,"dataFsResolvedFilePath":827,"href":828},[210],[123,50600,50601,2053,50604],{},[38,50602,50603],{},"Shrnutí přednášek:",[207,50605,50607],{"className":50606,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,50609,50610,2053,50612],{},[38,50611,16049],{},[207,50613,16053],{"className":50614,"dataFsResolvedFilePath":1761,"href":1762},[210],{"title":641,"searchDepth":642,"depth":642,"links":50616},[50617,50618,50626,50632,50639,50640,50647,50648,50649,50656,50657,50658],{"id":36639,"depth":642,"text":36640},{"id":36620,"depth":642,"text":13006,"children":50619},[50620,50621,50622,50623,50625],{"id":36908,"depth":649,"text":36909},{"id":37190,"depth":649,"text":37191},{"id":38200,"depth":649,"text":38201},{"id":38768,"depth":649,"text":50624},"Posun poptávky (shift of demand)",{"id":39272,"depth":649,"text":39273},{"id":36624,"depth":642,"text":12970,"children":50627},[50628,50629,50630],{"id":40109,"depth":649,"text":36909},{"id":40295,"depth":649,"text":40296},{"id":40747,"depth":649,"text":50631},"Posun nabídky (shift of supply)",{"id":41169,"depth":642,"text":41170,"children":50633},[50634,50635,50636,50637,50638],{"id":41281,"depth":649,"text":41282},{"id":41494,"depth":649,"text":41495},{"id":41812,"depth":649,"text":41813},{"id":42166,"depth":649,"text":42167},{"id":42197,"depth":649,"text":42198},{"id":42466,"depth":642,"text":811},{"id":42867,"depth":642,"text":42868,"children":50641},[50642,50643,50644,50645],{"id":42885,"depth":649,"text":42886},{"id":43266,"depth":649,"text":43267},{"id":43650,"depth":649,"text":43651},{"id":44104,"depth":649,"text":50646},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":11630,"depth":642,"text":820},{"id":45029,"depth":642,"text":45030},{"id":45260,"depth":642,"text":45261,"children":50650},[50651,50652,50653,50654,50655],{"id":45264,"depth":649,"text":45265},{"id":46104,"depth":649,"text":46105},{"id":46480,"depth":649,"text":41170},{"id":47775,"depth":649,"text":42868},{"id":49531,"depth":649,"text":820},{"id":49726,"depth":642,"text":49727},{"id":15564,"depth":642,"text":15565},{"id":3639,"depth":642,"text":3640},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,50665,50666,50667,17728,50668,50669],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":50672,"title":820,"body":50673,"course":1128,"courses":659,"created":9402,"description":641,"extension":661,"meta":54952,"navigation":664,"path":54953,"seo":54954,"sources":54955,"stem":54956,"tags":54957,"type":3703,"updated":677,"__hash__":54962},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":50674,"toc":54930},[50675,50677,50745,50795,50797,50800,51058,51134,51139,51141,51160,51164,51240,51325,51327,51641,51734,51736,51755,51759,51833,51918,51921,52097,52102,52104,52524,52526,52530,52534,52770,52814,52914,52980,52983,53016,53192,53254,53384,53462,53573,53607,53805,53824,53843,53908,53912,53915,53960,53963,54081,54127,54129,54133,54481,54483,54485,54763,54765,54769,54804,54811,54884,54886,54888],[12,50676,820],{"id":11630},[1639,50678,50679],{},[724,50680,50681,3720,50683,9871,50685,50700,50701,9871,50703,50718,50719,50741,50742,1734],{},[883,50682,3719],{},[38,50684,44779],{},[883,50686,50688],{"className":50687},[886],[888,50689,50690],{"xmlns":890},[892,50691,50692,50698],{},[895,50693,50694,50696],{},[898,50695,2626],{},[898,50697,8519],{},[902,50699,44795],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,50702,44926],{},[883,50704,50706],{"className":50705},[886],[888,50707,50708],{"xmlns":890},[892,50709,50710,50716],{},[895,50711,50712,50714],{},[898,50713,3783],{},[898,50715,8519],{},[902,50717,44814],{"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 ",[883,50720,50722],{"className":50721},[886],[888,50723,50724],{"xmlns":890},[892,50725,50726,50738],{},[895,50727,50728,50730,50732,50734,50736],{},[898,50729,2626],{},[898,50731,8519],{},[1846,50733,1945],{},[898,50735,3783],{},[898,50737,8519],{},[902,50739,50740],{"encoding":904},"CS + PS"," měří ",[38,50743,50744],{},"celkový blahobyt trhu",[724,50746,50747,9871,50749,1343,50751,11973,50766,9871,50768,1343,50770,50785,50786,50790,50791,1734],{},[38,50748,44779],{},[614,50750,44833],{},[883,50752,50754],{"className":50753},[886],[888,50755,50756],{"xmlns":890},[892,50757,50758,50764],{},[895,50759,50760,50762],{},[898,50761,2626],{},[898,50763,8519],{},[902,50765,44795],{"encoding":904},[38,50767,44798],{},[614,50769,44929],{},[883,50771,50773],{"className":50772},[886],[888,50774,50775],{"xmlns":890},[892,50776,50777,50783],{},[895,50778,50779,50781],{},[898,50780,3783],{},[898,50782,8519],{},[902,50784,44814],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,50787,50789],{"className":50788,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,50792,50794],{"className":50793,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[36815,50796],{},[115,50798,1241],{"id":50799},"úvod",[724,50801,50802,50803,50826,50827,50850,50851,50868,50869,3756,50901,50933,50934,50960,50961,50964,50965,50968,50969,13856,51003,21439,51024,1734],{},"Je dána funkce poptávky ",[883,50804,50806],{"className":50805},[886],[888,50807,50808],{"xmlns":890},[892,50809,50810,50824],{},[895,50811,50812,50814,50816,50818,50820,50822],{},[898,50813,3783],{},[1846,50815,1848],{},[898,50817,4029],{},[1846,50819,1855],{"stretchy":1854},[898,50821,2638],{},[1846,50823,1861],{"stretchy":1854},[902,50825,4486],{"encoding":904},", resp. funkce nabídky ",[883,50828,50830],{"className":50829},[886],[888,50831,50832],{"xmlns":890},[892,50833,50834,50848],{},[895,50835,50836,50838,50840,50842,50844,50846],{},[898,50837,3783],{},[1846,50839,1848],{},[898,50841,8519],{},[1846,50843,1855],{"stretchy":1854},[898,50845,2638],{},[1846,50847,1861],{"stretchy":1854},[902,50849,40916],{"encoding":904},". Pro pevně zadané množství ",[883,50852,50854],{"className":50853},[886],[888,50855,50856],{"xmlns":890},[892,50857,50858,50866],{},[895,50859,50860],{},[2122,50861,50862,50864],{},[898,50863,2638],{},[1979,50865,2177],{},[902,50867,38153],{"encoding":904}," je odpovídající cena ",[883,50870,50872],{"className":50871},[886],[888,50873,50874],{"xmlns":890},[892,50875,50876,50898],{},[895,50877,50878,50884,50886,50888,50890,50896],{},[2122,50879,50880,50882],{},[898,50881,3783],{},[1979,50883,2177],{},[1846,50885,1848],{},[898,50887,4029],{},[1846,50889,1855],{"stretchy":1854},[2122,50891,50892,50894],{},[898,50893,2638],{},[1979,50895,2177],{},[1846,50897,1861],{"stretchy":1854},[902,50899,50900],{"encoding":904},"P_0 = D(Q_0)",[883,50902,50904],{"className":50903},[886],[888,50905,50906],{"xmlns":890},[892,50907,50908,50930],{},[895,50909,50910,50916,50918,50920,50922,50928],{},[2122,50911,50912,50914],{},[898,50913,3783],{},[1979,50915,2177],{},[1846,50917,1848],{},[898,50919,8519],{},[1846,50921,1855],{"stretchy":1854},[2122,50923,50924,50926],{},[898,50925,2638],{},[1979,50927,2177],{},[1846,50929,1861],{"stretchy":1854},[902,50931,50932],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,50935,50937],{"className":50936},[886],[888,50938,50939],{"xmlns":890},[892,50940,50941,50957],{},[895,50942,50943,50949,50951],{},[2122,50944,50945,50947],{},[898,50946,3783],{},[1979,50948,2177],{},[2138,50950,2835],{},[2122,50952,50953,50955],{},[898,50954,2638],{},[1979,50956,2177],{},[902,50958,50959],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,50962,50963],{},"výdaje spotřebitele",", nebo ",[38,50966,50967],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,50970,50972],{"className":50971},[886],[888,50973,50974],{"xmlns":890},[892,50975,50976,51000],{},[895,50977,50978,50980,50982,50988,50990,50992,50994],{},[1979,50979,2177],{},[2138,50981,2835],{},[2122,50983,50984,50986],{},[898,50985,2638],{},[1979,50987,2177],{},[2138,50989,2835],{},[898,50991,4101],{},[2138,50993,2835],{},[2122,50995,50996,50998],{},[898,50997,3783],{},[1979,50999,2177],{},[902,51001,51002],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,51004,51006],{"className":51005},[886],[888,51007,51008],{"xmlns":890},[892,51009,51010,51022],{},[895,51011,51012,51014,51016,51018,51020],{},[1846,51013,1855],{"stretchy":1854},[898,51015,2638],{},[1846,51017,2136],{"separator":2135},[898,51019,3783],{},[1846,51021,1861],{"stretchy":1854},[902,51023,37536],{"encoding":904},[883,51025,51027],{"className":51026},[886],[888,51028,51029],{"xmlns":890},[892,51030,51031,51055],{},[895,51032,51033,51035,51037,51039,51045,51047,51053],{},[898,51034,4101],{},[1846,51036,1848],{},[1846,51038,2336],{"stretchy":1854},[2122,51040,51041,51043],{},[898,51042,2638],{},[1979,51044,2177],{},[1846,51046,2136],{"separator":2135},[2122,51048,51049,51051],{},[898,51050,3783],{},[1979,51052,2177],{},[1846,51054,2351],{"stretchy":1854},[902,51056,51057],{"encoding":904},"A = [Q_0, P_0]",[1639,51059,51060,51065,51123],{},[724,51061,51062,51064],{},[883,51063,4001],{}," Intuice",[120,51066,51067,51095],{},[123,51068,51069,51070,51073,51074,51076,51077,51094],{},"Za jednotky zboží nakoupené ",[38,51071,51072],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,51075,25115],{}," než ",[883,51078,51080],{"className":51079},[886],[888,51081,51082],{"xmlns":890},[892,51083,51084,51092],{},[895,51085,51086],{},[2122,51087,51088,51090],{},[898,51089,3783],{},[1979,51091,2177],{},[902,51093,38793],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,51096,51097,51098,51100,51101,51104,51105,51122],{},"Za jednotky zboží prodané ",[38,51099,51072],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,51102,51103],{},"nižší"," cenu než ",[883,51106,51108],{"className":51107},[886],[888,51109,51110],{"xmlns":890},[892,51111,51112,51120],{},[895,51113,51114],{},[2122,51115,51116,51118],{},[898,51117,3783],{},[1979,51119,2177],{},[902,51121,38793],{"encoding":904}," — rozdíl je jeho přebytek.",[724,51124,51125,51126,51129,51130,51133],{},"Přebytek je tedy rozdíl mezi ",[614,51127,51128],{},"ochotou"," (platit \u002F prodávat) a ",[614,51131,51132],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,51135,51136],{},[2409,51137],{"alt":44824,"className":51138,"src":44826},[210,2413],[36815,51140],{},[115,51142,51144,51145,1861],{"id":51143},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,51146,51148],{"className":51147},[886],[888,51149,51150],{"xmlns":890},[892,51151,51152,51158],{},[895,51153,51154,51156],{},[898,51155,2626],{},[898,51157,8519],{},[902,51159,44795],{"encoding":904},[198,51161,51163],{"id":51162},"definice-vzorec-214","Definice (vzorec 2.14)",[724,51165,51166,51167,51190,51191,51208,51209,2554],{},"Pro poptávku ",[883,51168,51170],{"className":51169},[886],[888,51171,51172],{"xmlns":890},[892,51173,51174,51188],{},[895,51175,51176,51178,51180,51182,51184,51186],{},[898,51177,3783],{},[1846,51179,1848],{},[898,51181,4029],{},[1846,51183,1855],{"stretchy":1854},[898,51185,2638],{},[1846,51187,1861],{"stretchy":1854},[902,51189,4486],{"encoding":904}," a pevně zadané ",[883,51192,51194],{"className":51193},[886],[888,51195,51196],{"xmlns":890},[892,51197,51198,51206],{},[895,51199,51200],{},[2122,51201,51202,51204],{},[898,51203,2638],{},[1979,51205,2177],{},[902,51207,38153],{"encoding":904}," s cenou ",[883,51210,51212],{"className":51211},[886],[888,51213,51214],{"xmlns":890},[892,51215,51216,51238],{},[895,51217,51218,51224,51226,51228,51230,51236],{},[2122,51219,51220,51222],{},[898,51221,3783],{},[1979,51223,2177],{},[1846,51225,1848],{},[898,51227,4029],{},[1846,51229,1855],{"stretchy":1854},[2122,51231,51232,51234],{},[898,51233,2638],{},[1979,51235,2177],{},[1846,51237,1861],{"stretchy":1854},[902,51239,50900],{"encoding":904},[883,51241,51243],{"className":51242},[886],[888,51244,51245],{"xmlns":890,"display":27911},[892,51246,51247,51323],{},[20599,51248,51249],{"width":27916},[20604,51250,51251,51253,51317,51319],{},[20607,51252],{"width":27921},[20607,51254,51255],{},[895,51256,51257,51259,51261,51263,51269,51271,51273,51285,51287,51289,51291,51293,51295,51297,51299,51301,51307,51309,51315],{},[898,51258,2626],{},[898,51260,8519],{},[1846,51262,1855],{"stretchy":1854},[2122,51264,51265,51267],{},[898,51266,2638],{},[1979,51268,2177],{},[1846,51270,1861],{"stretchy":1854},[1846,51272,1848],{},[9012,51274,51275,51277,51279],{},[1846,51276,11015],{},[1979,51278,2177],{},[2122,51280,51281,51283],{},[898,51282,2638],{},[1979,51284,2177],{},[898,51286,4029],{},[1846,51288,1855],{"stretchy":1854},[898,51290,2638],{},[1846,51292,1861],{"stretchy":1854},[2138,51294,2835],{},[898,51296,2044],{},[898,51298,2638],{},[1846,51300,2075],{},[2122,51302,51303,51305],{},[898,51304,3783],{},[1979,51306,2177],{},[2138,51308,2835],{},[2122,51310,51311,51313],{},[898,51312,2638],{},[1979,51314,2177],{},[898,51316,1734],{"mathvariant":2226},[20607,51318],{"width":27921},[20607,51320,51321],{},[2138,51322,44918],{},[902,51324,44921],{"encoding":904},[198,51326,2294],{"id":2293},[120,51328,51329,51421,51483],{},[123,51330,51331,51371,51372,51398,51399,51402,51403,51420],{},[883,51332,51334],{"className":51333},[886],[888,51335,51336],{"xmlns":890},[892,51337,51338,51368],{},[895,51339,51340],{},[2175,51341,51342,51354,51356,51358,51360,51362,51364,51366],{"scriptlevel":2177,"displaystyle":2135},[9012,51343,51344,51346,51348],{},[1846,51345,11015],{},[1979,51347,2177],{},[2122,51349,51350,51352],{},[898,51351,2638],{},[1979,51353,2177],{},[898,51355,4029],{},[1846,51357,1855],{"stretchy":1854},[898,51359,2638],{},[1846,51361,1861],{"stretchy":1854},[2138,51363,2835],{},[898,51365,2044],{},[898,51367,2638],{},[902,51369,51370],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,51373,51375],{"className":51374},[886],[888,51376,51377],{"xmlns":890},[892,51378,51379,51395],{},[895,51380,51381,51383,51385,51387,51393],{},[1846,51382,2336],{"stretchy":1854},[1979,51384,2177],{},[1846,51386,2136],{"separator":2135},[2122,51388,51389,51391],{},[898,51390,2638],{},[1979,51392,2177],{},[1846,51394,2351],{"stretchy":1854},[902,51396,51397],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,51400,51401],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,51404,51406],{"className":51405},[886],[888,51407,51408],{"xmlns":890},[892,51409,51410,51418],{},[895,51411,51412],{},[2122,51413,51414,51416],{},[898,51415,2638],{},[1979,51417,2177],{},[902,51419,38153],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,51422,51423,51449,51450,3764],{},[883,51424,51426],{"className":51425},[886],[888,51427,51428],{"xmlns":890},[892,51429,51430,51446],{},[895,51431,51432,51438,51440],{},[2122,51433,51434,51436],{},[898,51435,3783],{},[1979,51437,2177],{},[2138,51439,2835],{},[2122,51441,51442,51444],{},[898,51443,2638],{},[1979,51445,2177],{},[902,51447,51448],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,51451,51453],{"className":51452},[886],[888,51454,51455],{"xmlns":890},[892,51456,51457,51481],{},[895,51458,51459,51461,51463,51469,51471,51473,51475],{},[1979,51460,2177],{},[2138,51462,2835],{},[2122,51464,51465,51467],{},[898,51466,2638],{},[1979,51468,2177],{},[2138,51470,2835],{},[898,51472,4101],{},[2138,51474,2835],{},[2122,51476,51477,51479],{},[898,51478,3783],{},[1979,51480,2177],{},[902,51482,51002],{"encoding":904},[123,51484,51485,51500,51501,51523,51524,51549,51550,21439,51576,1745,51608,1734],{},[883,51486,51488],{"className":51487},[886],[888,51489,51490],{"xmlns":890},[892,51491,51492,51498],{},[895,51493,51494,51496],{},[898,51495,2626],{},[898,51497,8519],{},[902,51499,44795],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,51502,51504],{"className":51503},[886],[888,51505,51506],{"xmlns":890},[892,51507,51508,51520],{},[895,51509,51510,51512,51514],{},[898,51511,3783],{},[1846,51513,1848],{},[2122,51515,51516,51518],{},[898,51517,3783],{},[1979,51519,2177],{},[902,51521,51522],{"encoding":904},"P = P_0"," v pásu ",[883,51525,51527],{"className":51526},[886],[888,51528,51529],{"xmlns":890},[892,51530,51531,51547],{},[895,51532,51533,51535,51537,51539,51545],{},[1846,51534,2336],{"stretchy":1854},[1979,51536,2177],{},[1846,51538,2136],{"separator":2135},[2122,51540,51541,51543],{},[898,51542,2638],{},[1979,51544,2177],{},[1846,51546,2351],{"stretchy":1854},[902,51548,51397],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,51551,51553],{"className":51552},[886],[888,51554,51555],{"xmlns":890},[892,51556,51557,51573],{},[895,51558,51559,51565,51567,51569,51571],{},[2122,51560,51561,51563],{},[898,51562,3783],{},[1979,51564,2177],{},[2138,51566,2835],{},[898,51568,23098],{},[2138,51570,2835],{},[898,51572,4101],{},[902,51574,51575],{"encoding":904},"P_0\\,B\\,A",[883,51577,51579],{"className":51578},[886],[888,51580,51581],{"xmlns":890},[892,51582,51583,51605],{},[895,51584,51585,51587,51589,51591,51593,51595,51597,51599,51601,51603],{},[898,51586,23098],{},[1846,51588,1848],{},[1846,51590,2336],{"stretchy":1854},[1979,51592,2177],{},[1846,51594,2136],{"separator":2135},[898,51596,4029],{},[1846,51598,1855],{"stretchy":1854},[1979,51600,2177],{},[1846,51602,1861],{"stretchy":1854},[1846,51604,2351],{"stretchy":1854},[902,51606,51607],{"encoding":904},"B = [0, D(0)]",[883,51609,51611],{"className":51610},[886],[888,51612,51613],{"xmlns":890},[892,51614,51615,51639],{},[895,51616,51617,51619,51621,51623,51629,51631,51637],{},[898,51618,4101],{},[1846,51620,1848],{},[1846,51622,2336],{"stretchy":1854},[2122,51624,51625,51627],{},[898,51626,2638],{},[1979,51628,2177],{},[1846,51630,2136],{"separator":2135},[2122,51632,51633,51635],{},[898,51634,3783],{},[1979,51636,2177],{},[1846,51638,2351],{"stretchy":1854},[902,51640,51057],{"encoding":904},[724,51642,51643],{},[614,51644,51645,51646,51659,51660,51693,51694,28987,51719,1734],{},"Obrázek 2.24: Křivka poptávky ",[883,51647,51649],{"className":51648},[886],[888,51650,51651],{"xmlns":890},[892,51652,51653,51657],{},[895,51654,51655],{},[898,51656,4029],{},[902,51658,4029],{"encoding":904},", bod ",[883,51661,51663],{"className":51662},[886],[888,51664,51665],{"xmlns":890},[892,51666,51667,51691],{},[895,51668,51669,51671,51673,51675,51681,51683,51689],{},[898,51670,4101],{},[1846,51672,1848],{},[1846,51674,2336],{"stretchy":1854},[2122,51676,51677,51679],{},[898,51678,2638],{},[1979,51680,2177],{},[1846,51682,2136],{"separator":2135},[2122,51684,51685,51687],{},[898,51686,3783],{},[1979,51688,2177],{},[1846,51690,2351],{"stretchy":1854},[902,51692,51057],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,51695,51697],{"className":51696},[886],[888,51698,51699],{"xmlns":890},[892,51700,51701,51717],{},[895,51702,51703,51709,51711,51713,51715],{},[2122,51704,51705,51707],{},[898,51706,3783],{},[1979,51708,2177],{},[2138,51710,2835],{},[898,51712,23098],{},[2138,51714,2835],{},[898,51716,4101],{},[902,51718,51575],{"encoding":904},[883,51720,51722],{"className":51721},[886],[888,51723,51724],{"xmlns":890},[892,51725,51726,51732],{},[895,51727,51728,51730],{},[898,51729,2626],{},[898,51731,8519],{},[902,51733,44795],{"encoding":904},[36815,51735],{},[115,51737,51739,51740,1861],{"id":51738},"přebytek-výrobce-psps","Přebytek výrobce (",[883,51741,51743],{"className":51742},[886],[888,51744,51745],{"xmlns":890},[892,51746,51747,51753],{},[895,51748,51749,51751],{},[898,51750,3783],{},[898,51752,8519],{},[902,51754,44814],{"encoding":904},[198,51756,51758],{"id":51757},"definice-vzorec-215","Definice (vzorec 2.15)",[724,51760,51761,51762,51190,51785,51208,51802,2554],{},"Analogicky — pro nabídku ",[883,51763,51765],{"className":51764},[886],[888,51766,51767],{"xmlns":890},[892,51768,51769,51783],{},[895,51770,51771,51773,51775,51777,51779,51781],{},[898,51772,3783],{},[1846,51774,1848],{},[898,51776,8519],{},[1846,51778,1855],{"stretchy":1854},[898,51780,2638],{},[1846,51782,1861],{"stretchy":1854},[902,51784,40916],{"encoding":904},[883,51786,51788],{"className":51787},[886],[888,51789,51790],{"xmlns":890},[892,51791,51792,51800],{},[895,51793,51794],{},[2122,51795,51796,51798],{},[898,51797,2638],{},[1979,51799,2177],{},[902,51801,38153],{"encoding":904},[883,51803,51805],{"className":51804},[886],[888,51806,51807],{"xmlns":890},[892,51808,51809,51831],{},[895,51810,51811,51817,51819,51821,51823,51829],{},[2122,51812,51813,51815],{},[898,51814,3783],{},[1979,51816,2177],{},[1846,51818,1848],{},[898,51820,8519],{},[1846,51822,1855],{"stretchy":1854},[2122,51824,51825,51827],{},[898,51826,2638],{},[1979,51828,2177],{},[1846,51830,1861],{"stretchy":1854},[902,51832,50932],{"encoding":904},[883,51834,51836],{"className":51835},[886],[888,51837,51838],{"xmlns":890,"display":27911},[892,51839,51840,51916],{},[20599,51841,51842],{"width":27916},[20604,51843,51844,51846,51910,51912],{},[20607,51845],{"width":27921},[20607,51847,51848],{},[895,51849,51850,51852,51854,51856,51862,51864,51866,51872,51874,51880,51882,51894,51896,51898,51900,51902,51904,51906,51908],{},[898,51851,3783],{},[898,51853,8519],{},[1846,51855,1855],{"stretchy":1854},[2122,51857,51858,51860],{},[898,51859,2638],{},[1979,51861,2177],{},[1846,51863,1861],{"stretchy":1854},[1846,51865,1848],{},[2122,51867,51868,51870],{},[898,51869,3783],{},[1979,51871,2177],{},[2138,51873,2835],{},[2122,51875,51876,51878],{},[898,51877,2638],{},[1979,51879,2177],{},[1846,51881,2075],{},[9012,51883,51884,51886,51888],{},[1846,51885,11015],{},[1979,51887,2177],{},[2122,51889,51890,51892],{},[898,51891,2638],{},[1979,51893,2177],{},[898,51895,8519],{},[1846,51897,1855],{"stretchy":1854},[898,51899,2638],{},[1846,51901,1861],{"stretchy":1854},[2138,51903,2835],{},[898,51905,2044],{},[898,51907,2638],{},[898,51909,1734],{"mathvariant":2226},[20607,51911],{"width":27921},[20607,51913,51914],{},[2138,51915,45014],{},[902,51917,45017],{"encoding":904},[198,51919,2294],{"id":51920},"geometrická-interpretace-1",[120,51922,51923,51971,52032],{},[123,51924,51925,6861,51950,51953,51954,1734],{},[883,51926,51928],{"className":51927},[886],[888,51929,51930],{"xmlns":890},[892,51931,51932,51948],{},[895,51933,51934,51940,51942],{},[2122,51935,51936,51938],{},[898,51937,3783],{},[1979,51939,2177],{},[2138,51941,2835],{},[2122,51943,51944,51946],{},[898,51945,2638],{},[1979,51947,2177],{},[902,51949,51448],{"encoding":904},[38,51951,51952],{},"tržba"," výrobce za prodané množství ",[883,51955,51957],{"className":51956},[886],[888,51958,51959],{"xmlns":890},[892,51960,51961,51969],{},[895,51962,51963],{},[2122,51964,51965,51967],{},[898,51966,2638],{},[1979,51968,2177],{},[902,51970,38153],{"encoding":904},[123,51972,51973,52013,52014,52031],{},[883,51974,51976],{"className":51975},[886],[888,51977,51978],{"xmlns":890},[892,51979,51980,52010],{},[895,51981,51982],{},[2175,51983,51984,51996,51998,52000,52002,52004,52006,52008],{"scriptlevel":2177,"displaystyle":2135},[9012,51985,51986,51988,51990],{},[1846,51987,11015],{},[1979,51989,2177],{},[2122,51991,51992,51994],{},[898,51993,2638],{},[1979,51995,2177],{},[898,51997,8519],{},[1846,51999,1855],{"stretchy":1854},[898,52001,2638],{},[1846,52003,1861],{"stretchy":1854},[2138,52005,2835],{},[898,52007,2044],{},[898,52009,2638],{},[902,52011,52012],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,52015,52017],{"className":52016},[886],[888,52018,52019],{"xmlns":890},[892,52020,52021,52029],{},[895,52022,52023],{},[2122,52024,52025,52027],{},[898,52026,2638],{},[1979,52028,2177],{},[902,52030,38153],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,52033,52034,52049,52050,52071,52072,1734],{},[883,52035,52037],{"className":52036},[886],[888,52038,52039],{"xmlns":890},[892,52040,52041,52047],{},[895,52042,52043,52045],{},[898,52044,3783],{},[898,52046,8519],{},[902,52048,44814],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,52051,52053],{"className":52052},[886],[888,52054,52055],{"xmlns":890},[892,52056,52057,52069],{},[895,52058,52059,52061,52063],{},[898,52060,3783],{},[1846,52062,1848],{},[2122,52064,52065,52067],{},[898,52066,3783],{},[1979,52068,2177],{},[902,52070,51522],{"encoding":904}," a křivkou nabídky v pásu ",[883,52073,52075],{"className":52074},[886],[888,52076,52077],{"xmlns":890},[892,52078,52079,52095],{},[895,52080,52081,52083,52085,52087,52093],{},[1846,52082,2336],{"stretchy":1854},[1979,52084,2177],{},[1846,52086,2136],{"separator":2135},[2122,52088,52089,52091],{},[898,52090,2638],{},[1979,52092,2177],{},[1846,52094,2351],{"stretchy":1854},[902,52096,51397],{"encoding":904},[724,52098,52099],{},[614,52100,52101],{},"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.",[36815,52103],{},[1639,52105,52106,52111],{},[724,52107,52108,52110],{},[883,52109,4418],{}," Postup výpočtu CS a PS",[152,52112,52113,52244,52354,52383,52517],{},[123,52114,52115,52116,52133,52134,52165,52166,52197,52198,1734],{},"Zjisti (nebo si zvol) množství ",[883,52117,52119],{"className":52118},[886],[888,52120,52121],{"xmlns":890},[892,52122,52123,52131],{},[895,52124,52125],{},[2122,52126,52127,52129],{},[898,52128,2638],{},[1979,52130,2177],{},[902,52132,38153],{"encoding":904}," a odpovídající cenu ",[883,52135,52137],{"className":52136},[886],[888,52138,52139],{"xmlns":890},[892,52140,52141,52163],{},[895,52142,52143,52149,52151,52153,52155,52161],{},[2122,52144,52145,52147],{},[898,52146,3783],{},[1979,52148,2177],{},[1846,52150,1848],{},[898,52152,4029],{},[1846,52154,1855],{"stretchy":1854},[2122,52156,52157,52159],{},[898,52158,2638],{},[1979,52160,2177],{},[1846,52162,1861],{"stretchy":1854},[902,52164,50900],{"encoding":904}," resp. ",[883,52167,52169],{"className":52168},[886],[888,52170,52171],{"xmlns":890},[892,52172,52173,52195],{},[895,52174,52175,52181,52183,52185,52187,52193],{},[2122,52176,52177,52179],{},[898,52178,3783],{},[1979,52180,2177],{},[1846,52182,1848],{},[898,52184,8519],{},[1846,52186,1855],{"stretchy":1854},[2122,52188,52189,52191],{},[898,52190,2638],{},[1979,52192,2177],{},[1846,52194,1861],{"stretchy":1854},[902,52196,50932],{"encoding":904},". V rovnováze platí ",[883,52199,52201],{"className":52200},[886],[888,52202,52203],{"xmlns":890},[892,52204,52205,52241],{},[895,52206,52207,52209,52211,52217,52219,52221,52223,52225,52231,52233,52235],{},[898,52208,4029],{},[1846,52210,1855],{"stretchy":1854},[1974,52212,52213,52215],{},[898,52214,2638],{},[898,52216,4098],{},[1846,52218,1861],{"stretchy":1854},[1846,52220,1848],{},[898,52222,8519],{},[1846,52224,1855],{"stretchy":1854},[1974,52226,52227,52229],{},[898,52228,2638],{},[898,52230,4098],{},[1846,52232,1861],{"stretchy":1854},[1846,52234,1848],{},[1974,52236,52237,52239],{},[898,52238,3783],{},[898,52240,4098],{},[902,52242,52243],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,52245,52246,52247,19971,52285,52300,52301,19971,52339,3764],{},"Spočti určitý integrál ",[883,52248,52250],{"className":52249},[886],[888,52251,52252],{"xmlns":890},[892,52253,52254,52282],{},[895,52255,52256,52268,52270,52272,52274,52276,52278,52280],{},[9012,52257,52258,52260,52262],{},[1846,52259,11015],{},[1979,52261,2177],{},[2122,52263,52264,52266],{},[898,52265,2638],{},[1979,52267,2177],{},[898,52269,4029],{},[1846,52271,1855],{"stretchy":1854},[898,52273,2638],{},[1846,52275,1861],{"stretchy":1854},[2138,52277,2835],{},[898,52279,2044],{},[898,52281,2638],{},[902,52283,52284],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,52286,52288],{"className":52287},[886],[888,52289,52290],{"xmlns":890},[892,52291,52292,52298],{},[895,52293,52294,52296],{},[898,52295,2626],{},[898,52297,8519],{},[902,52299,44795],{"encoding":904},") nebo ",[883,52302,52304],{"className":52303},[886],[888,52305,52306],{"xmlns":890},[892,52307,52308,52336],{},[895,52309,52310,52322,52324,52326,52328,52330,52332,52334],{},[9012,52311,52312,52314,52316],{},[1846,52313,11015],{},[1979,52315,2177],{},[2122,52317,52318,52320],{},[898,52319,2638],{},[1979,52321,2177],{},[898,52323,8519],{},[1846,52325,1855],{"stretchy":1854},[898,52327,2638],{},[1846,52329,1861],{"stretchy":1854},[2138,52331,2835],{},[898,52333,2044],{},[898,52335,2638],{},[902,52337,52338],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,52340,52342],{"className":52341},[886],[888,52343,52344],{"xmlns":890},[892,52345,52346,52352],{},[895,52347,52348,52350],{},[898,52349,3783],{},[898,52351,8519],{},[902,52353,44814],{"encoding":904},[123,52355,52356,52357,1734],{},"Sestav obdélník ",[883,52358,52360],{"className":52359},[886],[888,52361,52362],{"xmlns":890},[892,52363,52364,52380],{},[895,52365,52366,52372,52374],{},[2122,52367,52368,52370],{},[898,52369,3783],{},[1979,52371,2177],{},[1846,52373,3025],{},[2122,52375,52376,52378],{},[898,52377,2638],{},[1979,52379,2177],{},[902,52381,52382],{"encoding":904},"P_0 \\cdot Q_0",[123,52384,52385,52386],{},"Dosaď:\n",[120,52387,52388,52453],{},[123,52389,52390,52448,52449,52452],{},[883,52391,52393],{"className":52392},[886],[888,52394,52395],{"xmlns":890},[892,52396,52397,52445],{},[895,52398,52399,52401,52403,52405,52417,52419,52421,52423,52425,52427,52429,52431,52433,52439],{},[898,52400,2626],{},[898,52402,8519],{},[1846,52404,1848],{},[9012,52406,52407,52409,52411],{},[1846,52408,11015],{},[1979,52410,2177],{},[2122,52412,52413,52415],{},[898,52414,2638],{},[1979,52416,2177],{},[898,52418,4029],{},[1846,52420,1855],{"stretchy":1854},[898,52422,2638],{},[1846,52424,1861],{"stretchy":1854},[2138,52426,2835],{},[898,52428,2044],{},[898,52430,2638],{},[1846,52432,2075],{},[2122,52434,52435,52437],{},[898,52436,3783],{},[1979,52438,2177],{},[2122,52440,52441,52443],{},[898,52442,2638],{},[1979,52444,2177],{},[902,52446,52447],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,52450,52451],{},"mínus"," obdélník)",[123,52454,52455,52513,52514,52516],{},[883,52456,52458],{"className":52457},[886],[888,52459,52460],{"xmlns":890},[892,52461,52462,52510],{},[895,52463,52464,52466,52468,52470,52476,52482,52484,52496,52498,52500,52502,52504,52506,52508],{},[898,52465,3783],{},[898,52467,8519],{},[1846,52469,1848],{},[2122,52471,52472,52474],{},[898,52473,3783],{},[1979,52475,2177],{},[2122,52477,52478,52480],{},[898,52479,2638],{},[1979,52481,2177],{},[1846,52483,2075],{},[9012,52485,52486,52488,52490],{},[1846,52487,11015],{},[1979,52489,2177],{},[2122,52491,52492,52494],{},[898,52493,2638],{},[1979,52495,2177],{},[898,52497,8519],{},[1846,52499,1855],{"stretchy":1854},[898,52501,2638],{},[1846,52503,1861],{"stretchy":1854},[2138,52505,2835],{},[898,52507,2044],{},[898,52509,2638],{},[902,52511,52512],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,52515,52451],{}," integrál)",[123,52518,52519,52520,52523],{},"Kontrola znaménka: obě hodnoty musí být ",[38,52521,52522],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[36815,52525],{},[115,52527,52529],{"id":52528},"příklady","Příklady",[198,52531,52533],{"id":52532},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[1639,52535,52536],{},[724,52537,52538,52541,52542,47566,52565,52588,52589,1343,52609,1343,52626,1343,52643,52660,52661,52737,52738,52755,52756,52769],{},[883,52539,52540],{},"!example"," Zadání\nJsou dány poptávka ",[883,52543,52545],{"className":52544},[886],[888,52546,52547],{"xmlns":890},[892,52548,52549,52563],{},[895,52550,52551,52553,52555,52557,52559,52561],{},[898,52552,3783],{},[1846,52554,1848],{},[898,52556,207],{},[898,52558,2638],{},[1846,52560,1945],{},[898,52562,1948],{},[902,52564,36905],{"encoding":904},[883,52566,52568],{"className":52567},[886],[888,52569,52570],{"xmlns":890},[892,52571,52572,52586],{},[895,52573,52574,52576,52578,52580,52582,52584],{},[898,52575,3783],{},[1846,52577,1848],{},[898,52579,1992],{},[898,52581,2638],{},[1846,52583,1945],{},[898,52585,2044],{},[902,52587,40087],{"encoding":904}," s hodnotami ",[883,52590,52592],{"className":52591},[886],[888,52593,52594],{"xmlns":890},[892,52595,52596,52606],{},[895,52597,52598,52600,52602,52604],{},[898,52599,207],{},[1846,52601,1848],{},[1846,52603,2075],{},[1979,52605,2023],{},[902,52607,52608],{"encoding":904},"a = -3",[883,52610,52612],{"className":52611},[886],[888,52613,52614],{"xmlns":890},[892,52615,52616,52624],{},[895,52617,52618,52620,52622],{},[898,52619,1948],{},[1846,52621,1848],{},[1979,52623,5057],{},[902,52625,48489],{"encoding":904},[883,52627,52629],{"className":52628},[886],[888,52630,52631],{"xmlns":890},[892,52632,52633,52641],{},[895,52634,52635,52637,52639],{},[898,52636,1992],{},[1846,52638,1848],{},[1979,52640,4855],{},[902,52642,48507],{"encoding":904},[883,52644,52646],{"className":52645},[886],[888,52647,52648],{"xmlns":890},[892,52649,52650,52658],{},[895,52651,52652,52654,52656],{},[898,52653,2044],{},[1846,52655,1848],{},[1979,52657,2712],{},[902,52659,48525],{"encoding":904},".\nRovnovážné množství:\n",[883,52662,52664],{"className":52663},[886],[888,52665,52666],{"xmlns":890},[892,52667,52668,52734],{},[895,52669,52670,52676,52678,52696,52698,52722,52724,52730,52732],{},[1974,52671,52672,52674],{},[898,52673,2638],{},[898,52675,4098],{},[1846,52677,1848],{},[2179,52679,52680,52688],{},[895,52681,52682,52684,52686],{},[898,52683,1948],{},[1846,52685,2075],{},[898,52687,2044],{},[895,52689,52690,52692,52694],{},[898,52691,1992],{},[1846,52693,2075],{},[898,52695,207],{},[1846,52697,1848],{},[2179,52699,52700,52708],{},[895,52701,52702,52704,52706],{},[1979,52703,5057],{},[1846,52705,2075],{},[1979,52707,2712],{},[895,52709,52710,52712,52714,52716,52718,52720],{},[1979,52711,4855],{},[1846,52713,2075],{},[1846,52715,1855],{"stretchy":1854},[1846,52717,2075],{},[1979,52719,2023],{},[1846,52721,1861],{"stretchy":1854},[1846,52723,1848],{},[2179,52725,52726,52728],{},[1979,52727,37864],{},[1979,52729,44251],{},[1846,52731,5746],{},[1979,52733,44256],{},[902,52735,52736],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,52739,52741],{"className":52740},[886],[888,52742,52743],{"xmlns":890},[892,52744,52745,52753],{},[895,52746,52747],{},[1974,52748,52749,52751],{},[898,52750,2638],{},[898,52752,4098],{},[902,52754,42248],{"encoding":904}," (a) při změně samotného parametru ",[883,52757,52759],{"className":52758},[886],[888,52760,52761],{"xmlns":890},[892,52762,52763,52767],{},[895,52764,52765],{},[898,52766,1992],{},[902,52768,1992],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,52771,52772],{},[38,52773,52774,52775,2521,52788,2535,52801,9141],{},"Řešení (a) — změna ",[883,52776,52778],{"className":52777},[886],[888,52779,52780],{"xmlns":890},[892,52781,52782,52786],{},[895,52783,52784],{},[898,52785,1992],{},[902,52787,1992],{"encoding":904},[883,52789,52791],{"className":52790},[886],[888,52792,52793],{"xmlns":890},[892,52794,52795,52799],{},[895,52796,52797],{},[1979,52798,4855],{},[902,52800,44291],{"encoding":904},[883,52802,52804],{"className":52803},[886],[888,52805,52806],{"xmlns":890},[892,52807,52808,52812],{},[895,52809,52810],{},[1979,52811,19166],{},[902,52813,44305],{"encoding":904},[724,52815,52816,52817,52881,52882,2554],{},"Pomocí vzorce (2.13) pro ",[883,52818,52820],{"className":52819},[886],[888,52821,52822],{"xmlns":890},[892,52823,52824,52878],{},[895,52825,52826,52846,52848,52850],{},[2175,52827,52828],{"scriptlevel":2177,"displaystyle":2135},[2179,52829,52830,52840],{},[895,52831,52832,52834],{},[898,52833,9718],{"mathvariant":2226},[1974,52835,52836,52838],{},[898,52837,2638],{},[898,52839,4098],{},[895,52841,52842,52844],{},[898,52843,9718],{"mathvariant":2226},[898,52845,1992],{},[1846,52847,1848],{},[1846,52849,2075],{},[2175,52851,52852],{"scriptlevel":2177,"displaystyle":2135},[2179,52853,52854,52862],{},[895,52855,52856,52858,52860],{},[898,52857,1948],{},[1846,52859,2075],{},[898,52861,2044],{},[895,52863,52864,52866,52868,52870,52872],{},[1846,52865,1855],{"stretchy":1854},[898,52867,1992],{},[1846,52869,2075],{},[898,52871,207],{},[1974,52873,52874,52876],{},[1846,52875,1861],{"stretchy":1854},[1979,52877,1981],{},[902,52879,52880],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,52883,52885],{"className":52884},[886],[888,52886,52887],{"xmlns":890},[892,52888,52889,52911],{},[895,52890,52891,52893],{},[1846,52892,2075],{},[2175,52894,52895],{"scriptlevel":2177,"displaystyle":2135},[2179,52896,52897,52903],{},[1974,52898,52899,52901],{},[898,52900,2638],{},[898,52902,4098],{},[895,52904,52905,52907,52909],{},[898,52906,1992],{},[1846,52908,2075],{},[898,52910,207],{},[902,52912,52913],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,52915,52917],{"className":52916},[886],[888,52918,52919],{"xmlns":890,"display":27911},[892,52920,52921,52977],{},[895,52922,52923,52925,52931,52933,52935,52951,52953,52955,52957,52959,52961,52967,52969,52971,52973,52975],{},[898,52924,2044],{},[1974,52926,52927,52929],{},[898,52928,2638],{},[898,52930,4098],{},[1846,52932,1848],{},[1846,52934,2075],{},[2179,52936,52937,52943],{},[1974,52938,52939,52941],{},[898,52940,2638],{},[898,52942,4098],{},[895,52944,52945,52947,52949],{},[898,52946,1992],{},[1846,52948,2075],{},[898,52950,207],{},[2138,52952,2835],{},[898,52954,2044],{},[898,52956,1992],{},[1846,52958,1848],{},[1846,52960,2075],{},[2179,52962,52963,52965],{},[1979,52964,44419],{},[1979,52966,44251],{},[1846,52968,3025],{},[1979,52970,2643],{},[1846,52972,5746],{},[1846,52974,2075],{},[1979,52976,44391],{},[902,52978,52979],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,52981,52982],{},"Nové rovnovážné množství:",[883,52984,52986],{"className":52985},[886],[888,52987,52988],{"xmlns":890,"display":27911},[892,52989,52990,53013],{},[895,52991,52992,53000,53002,53004,53006,53008,53010],{},[9012,52993,52994,52996,52998],{},[898,52995,2638],{},[1979,52997,2128],{},[898,52999,4098],{},[1846,53001,1650],{},[1979,53003,44419],{},[1846,53005,2075],{},[1979,53007,44424],{},[1846,53009,1848],{},[1979,53011,53012],{},"8,326.",[902,53014,53015],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,53017,53018,2053,53021,1343,53048,1343,53070,1343,53092,5435,53114,1343,53133,1343,53154,1343,53173,1734],{},[38,53019,53020],{},"Řešení (b) — současná změna všech parametrů:",[883,53022,53024],{"className":53023},[886],[888,53025,53026],{"xmlns":890},[892,53027,53028,53045],{},[895,53029,53030,53032,53034,53036,53038,53040,53042],{},[898,53031,207],{},[1846,53033,2554],{},[1846,53035,2075],{},[1979,53037,2023],{},[1846,53039,2971],{},[1846,53041,2075],{},[1979,53043,53044],{},"2,5",[902,53046,53047],{"encoding":904},"a: -3 \\to -2{,}5",[883,53049,53051],{"className":53050},[886],[888,53052,53053],{"xmlns":890},[892,53054,53055,53067],{},[895,53056,53057,53059,53061,53063,53065],{},[898,53058,1948],{},[1846,53060,2554],{},[1979,53062,5057],{},[1846,53064,2971],{},[1979,53066,14883],{},[902,53068,53069],{"encoding":904},"b: 40 \\to 35",[883,53071,53073],{"className":53072},[886],[888,53074,53075],{"xmlns":890},[892,53076,53077,53089],{},[895,53078,53079,53081,53083,53085,53087],{},[898,53080,1992],{},[1846,53082,2554],{},[1979,53084,4855],{},[1846,53086,2971],{},[1979,53088,19166],{},[902,53090,53091],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,53093,53095],{"className":53094},[886],[888,53096,53097],{"xmlns":890},[892,53098,53099,53111],{},[895,53100,53101,53103,53105,53107,53109],{},[898,53102,2044],{},[1846,53104,2554],{},[1979,53106,2712],{},[1846,53108,2971],{},[1979,53110,2753],{},[902,53112,53113],{"encoding":904},"d: 10 \\to 11",[883,53115,53117],{"className":53116},[886],[888,53118,53119],{"xmlns":890},[892,53120,53121,53131],{},[895,53122,53123,53125,53127,53129],{},[898,53124,2044],{},[898,53126,207],{},[1846,53128,1848],{},[1979,53130,4855],{},[902,53132,44457],{"encoding":904},[883,53134,53136],{"className":53135},[886],[888,53137,53138],{"xmlns":890},[892,53139,53140,53152],{},[895,53141,53142,53144,53146,53148,53150],{},[898,53143,2044],{},[898,53145,1948],{},[1846,53147,1848],{},[1846,53149,2075],{},[1979,53151,2078],{},[902,53153,44479],{"encoding":904},[883,53155,53157],{"className":53156},[886],[888,53158,53159],{"xmlns":890},[892,53160,53161,53171],{},[895,53162,53163,53165,53167,53169],{},[898,53164,2044],{},[898,53166,1992],{},[1846,53168,1848],{},[1979,53170,2643],{},[902,53172,44499],{"encoding":904},[883,53174,53176],{"className":53175},[886],[888,53177,53178],{"xmlns":890},[892,53179,53180,53190],{},[895,53181,53182,53184,53186,53188],{},[898,53183,2044],{},[898,53185,2044],{},[1846,53187,1848],{},[1979,53189,2128],{},[902,53191,44519],{"encoding":904},[724,53193,53194,53195,53253],{},"Totální diferenciál ",[883,53196,53198],{"className":53197},[886],[888,53199,53200],{"xmlns":890},[892,53201,53202,53250],{},[895,53203,53204,53210,53212,53214,53216,53218,53220,53222,53224,53226,53228,53230],{},[1974,53205,53206,53208],{},[898,53207,2638],{},[898,53209,4098],{},[1846,53211,1855],{"stretchy":1854},[898,53213,207],{},[1846,53215,2136],{"separator":2135},[898,53217,1948],{},[1846,53219,2136],{"separator":2135},[898,53221,1992],{},[1846,53223,2136],{"separator":2135},[898,53225,2044],{},[1846,53227,1861],{"stretchy":1854},[1846,53229,1848],{},[2175,53231,53232],{"scriptlevel":2177,"displaystyle":2135},[2179,53233,53234,53242],{},[895,53235,53236,53238,53240],{},[898,53237,1948],{},[1846,53239,2075],{},[898,53241,2044],{},[895,53243,53244,53246,53248],{},[898,53245,1992],{},[1846,53247,2075],{},[898,53249,207],{},[902,53251,53252],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,53255,53257],{"className":53256},[886],[888,53258,53259],{"xmlns":890,"display":27911},[892,53260,53261,53381],{},[895,53262,53263,53265,53271,53273,53299,53301,53303,53305,53307,53319,53321,53323,53325,53327,53353,53355,53357,53359,53361,53373,53375,53377,53379],{},[898,53264,2044],{},[1974,53266,53267,53269],{},[898,53268,2638],{},[898,53270,4098],{},[1846,53272,1848],{},[2179,53274,53275,53283],{},[895,53276,53277,53279,53281],{},[898,53278,1948],{},[1846,53280,2075],{},[898,53282,2044],{},[895,53284,53285,53287,53289,53291,53293],{},[1846,53286,1855],{"stretchy":1854},[898,53288,1992],{},[1846,53290,2075],{},[898,53292,207],{},[1974,53294,53295,53297],{},[1846,53296,1861],{"stretchy":1854},[1979,53298,1981],{},[2138,53300,2835],{},[898,53302,2044],{},[898,53304,207],{},[1846,53306,1945],{},[2179,53308,53309,53311],{},[1979,53310,2128],{},[895,53312,53313,53315,53317],{},[898,53314,1992],{},[1846,53316,2075],{},[898,53318,207],{},[2138,53320,2835],{},[898,53322,2044],{},[898,53324,1948],{},[1846,53326,2075],{},[2179,53328,53329,53337],{},[895,53330,53331,53333,53335],{},[898,53332,1948],{},[1846,53334,2075],{},[898,53336,2044],{},[895,53338,53339,53341,53343,53345,53347],{},[1846,53340,1855],{"stretchy":1854},[898,53342,1992],{},[1846,53344,2075],{},[898,53346,207],{},[1974,53348,53349,53351],{},[1846,53350,1861],{"stretchy":1854},[1979,53352,1981],{},[2138,53354,2835],{},[898,53356,2044],{},[898,53358,1992],{},[1846,53360,2075],{},[2179,53362,53363,53365],{},[1979,53364,2128],{},[895,53366,53367,53369,53371],{},[898,53368,1992],{},[1846,53370,2075],{},[898,53372,207],{},[2138,53374,2835],{},[898,53376,2044],{},[898,53378,2044],{},[898,53380,1734],{"mathvariant":2226},[902,53382,53383],{"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.",[724,53385,53386,53387,1343,53409,1343,53440,2999],{},"Dosazením číselných hodnot (",[883,53388,53390],{"className":53389},[886],[888,53391,53392],{"xmlns":890},[892,53393,53394,53406],{},[895,53395,53396,53398,53400,53402,53404],{},[898,53397,1992],{},[1846,53399,2075],{},[898,53401,207],{},[1846,53403,1848],{},[1979,53405,44251],{},[902,53407,53408],{"encoding":904},"c - a = 3{,}5",[883,53410,53412],{"className":53411},[886],[888,53413,53414],{"xmlns":890},[892,53415,53416,53437],{},[895,53417,53418,53420,53422,53424,53426,53432,53434],{},[1846,53419,1855],{"stretchy":1854},[898,53421,1992],{},[1846,53423,2075],{},[898,53425,207],{},[1974,53427,53428,53430],{},[1846,53429,1861],{"stretchy":1854},[1979,53431,1981],{},[1846,53433,1848],{},[1979,53435,53436],{},"12,25",[902,53438,53439],{"encoding":904},"(c-a)^2 = 12{,}25",[883,53441,53443],{"className":53442},[886],[888,53444,53445],{"xmlns":890},[892,53446,53447,53459],{},[895,53448,53449,53451,53453,53455,53457],{},[898,53450,1948],{},[1846,53452,2075],{},[898,53454,2044],{},[1846,53456,1848],{},[1979,53458,37864],{},[902,53460,53461],{"encoding":904},"b - d = 30",[883,53463,53465],{"className":53464},[886],[888,53466,53467],{"xmlns":890,"display":27911},[892,53468,53469,53570],{},[895,53470,53471,53473,53479,53481,53489,53491,53493,53495,53497,53505,53507,53509,53511,53513,53515,53523,53525,53527,53529,53531,53539,53541,53543,53545,53547,53550,53552,53555,53557,53559,53561,53564,53566,53568],{},[898,53472,2044],{},[1974,53474,53475,53477],{},[898,53476,2638],{},[898,53478,4098],{},[1846,53480,1650],{},[2175,53482,53483],{"scriptlevel":2177,"displaystyle":1854},[2179,53484,53485,53487],{},[1979,53486,37864],{},[1979,53488,53436],{},[1846,53490,1855],{"stretchy":1854},[1979,53492,4855],{},[1846,53494,1861],{"stretchy":1854},[1846,53496,1945],{},[2175,53498,53499],{"scriptlevel":2177,"displaystyle":1854},[2179,53500,53501,53503],{},[1979,53502,2128],{},[1979,53504,44251],{},[1846,53506,1855],{"stretchy":1854},[1846,53508,2075],{},[1979,53510,2078],{},[1846,53512,1861],{"stretchy":1854},[1846,53514,2075],{},[2175,53516,53517],{"scriptlevel":2177,"displaystyle":1854},[2179,53518,53519,53521],{},[1979,53520,37864],{},[1979,53522,53436],{},[1846,53524,1855],{"stretchy":1854},[1979,53526,2643],{},[1846,53528,1861],{"stretchy":1854},[1846,53530,2075],{},[2175,53532,53533],{"scriptlevel":2177,"displaystyle":1854},[2179,53534,53535,53537],{},[1979,53536,2128],{},[1979,53538,44251],{},[1846,53540,1855],{"stretchy":1854},[1979,53542,2128],{},[1846,53544,1861],{"stretchy":1854},[1846,53546,5746],{},[1979,53548,53549],{},"1,224",[1846,53551,2075],{},[1979,53553,53554],{},"1,429",[1846,53556,2075],{},[1979,53558,44424],{},[1846,53560,2075],{},[1979,53562,53563],{},"0,286",[1846,53565,5746],{},[1846,53567,2075],{},[1979,53569,44670],{},[902,53571,53572],{"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.",[724,53574,29910,53575,1734],{},[883,53576,53578],{"className":53577},[886],[888,53579,53580],{"xmlns":890},[892,53581,53582,53604],{},[895,53583,53584,53592,53594,53596,53598,53600,53602],{},[9012,53585,53586,53588,53590],{},[898,53587,2638],{},[1979,53589,2128],{},[898,53591,4098],{},[1846,53593,1650],{},[1979,53595,44419],{},[1846,53597,2075],{},[1979,53599,44701],{},[1846,53601,5746],{},[1979,53603,44706],{},[902,53605,53606],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[1639,53608,53609],{},[724,53610,53611,53613,53614,53635,53636,53662,53663,53666,53667,53763,53764,53787,53788,53804],{},[883,53612,4258],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,53615,53617],{"className":53616},[886],[888,53618,53619],{"xmlns":890},[892,53620,53621,53633],{},[895,53622,53623,53625,53627,53629,53631],{},[898,53624,2738],{"mathvariant":2226},[898,53626,2638],{},[1846,53628,1650],{},[1846,53630,2075],{},[1979,53632,44736],{},[902,53634,44739],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,53637,53639],{"className":53638},[886],[888,53640,53641],{"xmlns":890},[892,53642,53643,53659],{},[895,53644,53645,53647,53653,53655,53657],{},[898,53646,2044],{},[1974,53648,53649,53651],{},[898,53650,2638],{},[898,53652,4098],{},[1846,53654,5746],{},[1846,53656,2075],{},[1979,53658,44701],{},[902,53660,53661],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,53664,53665],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,53668,53670],{"className":53669},[886],[888,53671,53672],{"xmlns":890},[892,53673,53674,53760],{},[895,53675,53676,53684,53686,53720,53722,53746,53748,53755,53757],{},[9012,53677,53678,53680,53682],{},[898,53679,2638],{},[1979,53681,2128],{},[898,53683,4098],{},[1846,53685,1848],{},[2179,53687,53688,53704],{},[895,53689,53690,53696,53698],{},[1974,53691,53692,53694],{},[898,53693,1948],{},[1846,53695,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,53697,2075],{},[1974,53699,53700,53702],{},[898,53701,2044],{},[1846,53703,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[895,53705,53706,53712,53714],{},[1974,53707,53708,53710],{},[898,53709,1992],{},[1846,53711,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,53713,2075],{},[1974,53715,53716,53718],{},[898,53717,207],{},[1846,53719,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,53721,1848],{},[2179,53723,53724,53732],{},[895,53725,53726,53728,53730],{},[1979,53727,14883],{},[1846,53729,2075],{},[1979,53731,2753],{},[895,53733,53734,53736,53738,53740,53742,53744],{},[1979,53735,19166],{},[1846,53737,2075],{},[1846,53739,1855],{"stretchy":1854},[1846,53741,2075],{},[1979,53743,53044],{},[1846,53745,1861],{"stretchy":1854},[1846,53747,1848],{},[2179,53749,53750,53752],{},[1979,53751,41645],{},[1979,53753,53754],{},"3,1",[1846,53756,5746],{},[1979,53758,53759],{},"7,742",[902,53761,53762],{"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 ",[883,53765,53767],{"className":53766},[886],[888,53768,53769],{"xmlns":890},[892,53770,53771,53784],{},[895,53772,53773,53775,53777,53779,53781],{},[898,53774,2738],{"mathvariant":2226},[898,53776,2638],{},[1846,53778,5746],{},[1846,53780,2075],{},[1979,53782,53783],{},"0,829",[902,53785,53786],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,53789,53791],{"className":53790},[886],[888,53792,53793],{"xmlns":890},[892,53794,53795,53801],{},[895,53796,53797,53799],{},[1846,53798,2075],{},[1979,53800,44736],{},[902,53802,53803],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,53806,53807],{},[614,53808,53809,53810,53823],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,53811,53813],{"className":53812},[886],[888,53814,53815],{"xmlns":890},[892,53816,53817,53821],{},[895,53818,53819],{},[898,53820,2638],{},[902,53822,2638],{"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.",[198,53825,53827,53828],{"id":53826},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,53829,53831],{"className":53830},[886],[888,53832,53833],{"xmlns":890},[892,53834,53835,53841],{},[895,53836,53837,53839],{},[898,53838,3783],{},[898,53840,8519],{},[902,53842,44814],{"encoding":904},[1639,53844,53845],{},[724,53846,53847,53849,53850,53884,53885,53907],{},[883,53848,52540],{}," Zadání\nPro nabídku ",[883,53851,53853],{"className":53852},[886],[888,53854,53855],{"xmlns":890},[892,53856,53857,53881],{},[895,53858,53859,53861,53863,53865,53867,53869,53871,53873,53875,53877,53879],{},[898,53860,3783],{},[1846,53862,1848],{},[898,53864,8519],{},[1846,53866,1855],{"stretchy":1854},[898,53868,2638],{},[1846,53870,1861],{"stretchy":1854},[1846,53872,1848],{},[1979,53874,2712],{},[1846,53876,1945],{},[1979,53878,1981],{},[898,53880,2638],{},[902,53882,53883],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,53886,53888],{"className":53887},[886],[888,53889,53890],{"xmlns":890},[892,53891,53892,53904],{},[895,53893,53894,53900,53902],{},[2122,53895,53896,53898],{},[898,53897,2638],{},[1979,53899,2177],{},[1846,53901,1848],{},[1979,53903,2712],{},[902,53905,53906],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,53909,53910],{},[38,53911,22615],{},[724,53913,53914],{},"Odpovídající cena:",[883,53916,53918],{"className":53917},[886],[888,53919,53920],{"xmlns":890,"display":27911},[892,53921,53922,53957],{},[895,53923,53924,53930,53932,53934,53936,53938,53940,53942,53944,53946,53948,53950,53952,53954],{},[2122,53925,53926,53928],{},[898,53927,3783],{},[1979,53929,2177],{},[1846,53931,1848],{},[898,53933,8519],{},[1846,53935,1855],{"stretchy":1854},[1979,53937,2712],{},[1846,53939,1861],{"stretchy":1854},[1846,53941,1848],{},[1979,53943,2712],{},[1846,53945,1945],{},[1979,53947,1981],{},[1846,53949,3025],{},[1979,53951,2712],{},[1846,53953,1848],{},[1979,53955,53956],{},"30.",[902,53958,53959],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,53961,53962],{},"Dle vzorce (2.15):",[883,53964,53966],{"className":53965},[886],[888,53967,53968],{"xmlns":890,"display":27911},[892,53969,53970,54078],{},[895,53971,53972,53974,53976,53978,53980,53982,53984,53990,53996,53998,54006,54008,54010,54012,54014,54016,54018,54020,54022,54024,54026,54028,54030,54032,54034,54037,54039,54041,54043,54049,54057,54059,54061,54063,54065,54067,54069,54071,54073,54075],{},[898,53973,3783],{},[898,53975,8519],{},[1846,53977,1855],{"stretchy":1854},[1979,53979,2712],{},[1846,53981,1861],{"stretchy":1854},[1846,53983,1848],{},[2122,53985,53986,53988],{},[898,53987,3783],{},[1979,53989,2177],{},[2122,53991,53992,53994],{},[898,53993,2638],{},[1979,53995,2177],{},[1846,53997,2075],{},[9012,53999,54000,54002,54004],{},[1846,54001,11015],{},[1979,54003,2177],{},[1979,54005,2712],{},[1846,54007,1855],{"stretchy":1854},[1979,54009,2712],{},[1846,54011,1945],{},[1979,54013,1981],{},[898,54015,2638],{},[1846,54017,1861],{"stretchy":1854},[2138,54019,2835],{},[898,54021,2044],{},[898,54023,2638],{},[1846,54025,1848],{},[1979,54027,2712],{},[1846,54029,3025],{},[1979,54031,37864],{},[1846,54033,2075],{},[1846,54035,2336],{"fence":1854,"stretchy":2135,"minsize":54036,"maxsize":54036},"1.8em",[1979,54038,2712],{},[898,54040,2638],{},[1846,54042,1945],{},[1974,54044,54045,54047],{},[898,54046,2638],{},[1979,54048,1981],{},[9012,54050,54051,54053,54055],{},[1846,54052,2351],{"fence":1854,"stretchy":2135,"minsize":54036,"maxsize":54036},[1979,54054,2177],{},[1979,54056,2712],{},[1846,54058,1848],{},[1979,54060,29926],{},[1846,54062,2075],{},[1846,54064,1855],{"stretchy":1854},[1979,54066,2938],{},[1846,54068,1945],{},[1979,54070,2938],{},[1846,54072,1861],{"stretchy":1854},[1846,54074,1848],{},[1979,54076,54077],{},"100.",[902,54079,54080],{"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.",[724,54082,54083,54084,54105,54106,54126],{},"Přebytek výrobce při množství ",[883,54085,54087],{"className":54086},[886],[888,54088,54089],{"xmlns":890},[892,54090,54091,54103],{},[895,54092,54093,54099,54101],{},[2122,54094,54095,54097],{},[898,54096,2638],{},[1979,54098,2177],{},[1846,54100,1848],{},[1979,54102,2712],{},[902,54104,53906],{"encoding":904}," je tedy ",[883,54107,54109],{"className":54108},[886],[888,54110,54111],{"xmlns":890},[892,54112,54113,54123],{},[895,54114,54115,54117,54119,54121],{},[898,54116,3783],{},[898,54118,8519],{},[1846,54120,1848],{},[1979,54122,2938],{},[902,54124,54125],{"encoding":904},"PS = 100"," (peněžních jednotek).",[36815,54128],{},[115,54130,54132],{"id":54131},"cheat-sheet","Cheat sheet",[16,54134,54135,54148],{},[19,54136,54137],{},[22,54138,54139,54142,54145],{},[25,54140,54141],{},"Veličina",[25,54143,54144],{},"Vzorec",[25,54146,54147],{},"Geometrie",[30,54149,54150,54268,54382,54450],{},[22,54151,54152,54180,54236],{},[35,54153,54154],{},[883,54155,54157],{"className":54156},[886],[888,54158,54159],{"xmlns":890},[892,54160,54161,54177],{},[895,54162,54163,54165,54167,54169,54175],{},[898,54164,2626],{},[898,54166,8519],{},[1846,54168,1855],{"stretchy":1854},[2122,54170,54171,54173],{},[898,54172,2638],{},[1979,54174,2177],{},[1846,54176,1861],{"stretchy":1854},[902,54178,54179],{"encoding":904},"CS(Q_0)",[35,54181,54182],{},[883,54183,54185],{"className":54184},[886],[888,54186,54187],{"xmlns":890},[892,54188,54189,54233],{},[895,54190,54191],{},[2175,54192,54193,54205,54207,54209,54211,54213,54215,54217,54219,54221,54227],{"scriptlevel":2177,"displaystyle":2135},[9012,54194,54195,54197,54199],{},[1846,54196,11015],{},[1979,54198,2177],{},[2122,54200,54201,54203],{},[898,54202,2638],{},[1979,54204,2177],{},[898,54206,4029],{},[1846,54208,1855],{"stretchy":1854},[898,54210,2638],{},[1846,54212,1861],{"stretchy":1854},[2138,54214,2835],{},[898,54216,2044],{},[898,54218,2638],{},[1846,54220,2075],{},[2122,54222,54223,54225],{},[898,54224,3783],{},[1979,54226,2177],{},[2122,54228,54229,54231],{},[898,54230,2638],{},[1979,54232,2177],{},[902,54234,54235],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,54237,54238,54239,54242,54243,54246,54247],{},"plocha ",[38,54240,54241],{},"pod"," křivkou poptávky, ",[38,54244,54245],{},"nad"," čárou ",[883,54248,54250],{"className":54249},[886],[888,54251,54252],{"xmlns":890},[892,54253,54254,54266],{},[895,54255,54256,54258,54260],{},[898,54257,3783],{},[1846,54259,1848],{},[2122,54261,54262,54264],{},[898,54263,3783],{},[1979,54265,2177],{},[902,54267,51522],{"encoding":904},[22,54269,54270,54298,54354],{},[35,54271,54272],{},[883,54273,54275],{"className":54274},[886],[888,54276,54277],{"xmlns":890},[892,54278,54279,54295],{},[895,54280,54281,54283,54285,54287,54293],{},[898,54282,3783],{},[898,54284,8519],{},[1846,54286,1855],{"stretchy":1854},[2122,54288,54289,54291],{},[898,54290,2638],{},[1979,54292,2177],{},[1846,54294,1861],{"stretchy":1854},[902,54296,54297],{"encoding":904},"PS(Q_0)",[35,54299,54300],{},[883,54301,54303],{"className":54302},[886],[888,54304,54305],{"xmlns":890},[892,54306,54307,54351],{},[895,54308,54309],{},[2175,54310,54311,54317,54323,54325,54337,54339,54341,54343,54345,54347,54349],{"scriptlevel":2177,"displaystyle":2135},[2122,54312,54313,54315],{},[898,54314,3783],{},[1979,54316,2177],{},[2122,54318,54319,54321],{},[898,54320,2638],{},[1979,54322,2177],{},[1846,54324,2075],{},[9012,54326,54327,54329,54331],{},[1846,54328,11015],{},[1979,54330,2177],{},[2122,54332,54333,54335],{},[898,54334,2638],{},[1979,54336,2177],{},[898,54338,8519],{},[1846,54340,1855],{"stretchy":1854},[898,54342,2638],{},[1846,54344,1861],{"stretchy":1854},[2138,54346,2835],{},[898,54348,2044],{},[898,54350,2638],{},[902,54352,54353],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,54355,54238,54356,54358,54359,54246,54361],{},[38,54357,54245],{}," křivkou nabídky, ",[38,54360,54241],{},[883,54362,54364],{"className":54363},[886],[888,54365,54366],{"xmlns":890},[892,54367,54368,54380],{},[895,54369,54370,54372,54374],{},[898,54371,3783],{},[1846,54373,1848],{},[2122,54375,54376,54378],{},[898,54377,3783],{},[1979,54379,2177],{},[902,54381,51522],{"encoding":904},[22,54383,54384,54387,54414],{},[35,54385,54386],{},"Výdaje \u002F tržby",[35,54388,54389],{},[883,54390,54392],{"className":54391},[886],[888,54393,54394],{"xmlns":890},[892,54395,54396,54412],{},[895,54397,54398,54404,54406],{},[2122,54399,54400,54402],{},[898,54401,3783],{},[1979,54403,2177],{},[1846,54405,3025],{},[2122,54407,54408,54410],{},[898,54409,2638],{},[1979,54411,2177],{},[902,54413,52382],{"encoding":904},[35,54415,54416,54417],{},"obdélník ",[883,54418,54420],{"className":54419},[886],[888,54421,54422],{"xmlns":890},[892,54423,54424,54448],{},[895,54425,54426,54428,54430,54436,54438,54440,54442],{},[1979,54427,2177],{},[2138,54429,2835],{},[2122,54431,54432,54434],{},[898,54433,2638],{},[1979,54435,2177],{},[2138,54437,2835],{},[898,54439,4101],{},[2138,54441,2835],{},[2122,54443,54444,54446],{},[898,54445,3783],{},[1979,54447,2177],{},[902,54449,51002],{"encoding":904},[22,54451,54452,54455,54478],{},[35,54453,54454],{},"Celkový přebytek",[35,54456,54457],{},[883,54458,54460],{"className":54459},[886],[888,54461,54462],{"xmlns":890},[892,54463,54464,54476],{},[895,54465,54466,54468,54470,54472,54474],{},[898,54467,2626],{},[898,54469,8519],{},[1846,54471,1945],{},[898,54473,3783],{},[898,54475,8519],{},[902,54477,50740],{"encoding":904},[35,54479,54480],{},"součet obou ploch v rovnováze",[36815,54482],{},[115,54484,15565],{"id":15564},[120,54486,54487,54509,54531,54575,54619,54682,54710],{},[123,54488,54489,9871,54491,1343,54506,54508],{},[38,54490,44779],{},[883,54492,54494],{"className":54493},[886],[888,54495,54496],{"xmlns":890},[892,54497,54498,54504],{},[895,54499,54500,54502],{},[898,54501,2626],{},[898,54503,8519],{},[902,54505,44795],{"encoding":904},[614,54507,44833],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,54510,54511,9871,54513,1343,54528,54530],{},[38,54512,44926],{},[883,54514,54516],{"className":54515},[886],[888,54517,54518],{"xmlns":890},[892,54519,54520,54526],{},[895,54521,54522,54524],{},[898,54523,3783],{},[898,54525,8519],{},[902,54527,44814],{"encoding":904},[614,54529,44929],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,54532,54533,6861,54536,1734],{},[38,54534,54535],{},"Ochota platit",[883,54537,54539],{"className":54538},[886],[888,54540,54541],{"xmlns":890},[892,54542,54543,54573],{},[895,54544,54545],{},[2175,54546,54547,54559,54561,54563,54565,54567,54569,54571],{"scriptlevel":2177,"displaystyle":2135},[9012,54548,54549,54551,54553],{},[1846,54550,11015],{},[1979,54552,2177],{},[2122,54554,54555,54557],{},[898,54556,2638],{},[1979,54558,2177],{},[898,54560,4029],{},[1846,54562,1855],{"stretchy":1854},[898,54564,2638],{},[1846,54566,1861],{"stretchy":1854},[2138,54568,2835],{},[898,54570,2044],{},[898,54572,2638],{},[902,54574,51370],{"encoding":904},[123,54576,54577,6861,54580,1734],{},[38,54578,54579],{},"Minimální cena výrobce",[883,54581,54583],{"className":54582},[886],[888,54584,54585],{"xmlns":890},[892,54586,54587,54617],{},[895,54588,54589],{},[2175,54590,54591,54603,54605,54607,54609,54611,54613,54615],{"scriptlevel":2177,"displaystyle":2135},[9012,54592,54593,54595,54597],{},[1846,54594,11015],{},[1979,54596,2177],{},[2122,54598,54599,54601],{},[898,54600,2638],{},[1979,54602,2177],{},[898,54604,8519],{},[1846,54606,1855],{"stretchy":1854},[898,54608,2638],{},[1846,54610,1861],{"stretchy":1854},[2138,54612,2835],{},[898,54614,2044],{},[898,54616,2638],{},[902,54618,52012],{"encoding":904},[123,54620,54621,6861,54624,52513,54649,3764],{},[38,54622,54623],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,54625,54627],{"className":54626},[886],[888,54628,54629],{"xmlns":890},[892,54630,54631,54647],{},[895,54632,54633,54639,54641],{},[2122,54634,54635,54637],{},[898,54636,3783],{},[1979,54638,2177],{},[2138,54640,2835],{},[2122,54642,54643,54645],{},[898,54644,2638],{},[1979,54646,2177],{},[902,54648,51448],{"encoding":904},[883,54650,54652],{"className":54651},[886],[888,54653,54654],{"xmlns":890},[892,54655,54656,54680],{},[895,54657,54658,54660,54662,54668,54670,54672,54674],{},[1979,54659,2177],{},[2138,54661,2835],{},[2122,54663,54664,54666],{},[898,54665,2638],{},[1979,54667,2177],{},[2138,54669,2835],{},[898,54671,4101],{},[2138,54673,2835],{},[2122,54675,54676,54678],{},[898,54677,3783],{},[1979,54679,2177],{},[902,54681,51002],{"encoding":904},[123,54683,54684,54687,54688,54709],{},[38,54685,54686],{},"Celkový přebytek trhu"," — součet ",[883,54689,54691],{"className":54690},[886],[888,54692,54693],{"xmlns":890},[892,54694,54695,54707],{},[895,54696,54697,54699,54701,54703,54705],{},[898,54698,2626],{},[898,54700,8519],{},[1846,54702,1945],{},[898,54704,3783],{},[898,54706,8519],{},[902,54708,50740],{"encoding":904}," v rovnovážném bodě.",[123,54711,54712,54714,54715,1343,54728,54741,54742,1734],{},[38,54713,2294],{}," — plochy ohraničené křivkami ",[883,54716,54718],{"className":54717},[886],[888,54719,54720],{"xmlns":890},[892,54721,54722,54726],{},[895,54723,54724],{},[898,54725,4029],{},[902,54727,4029],{"encoding":904},[883,54729,54731],{"className":54730},[886],[888,54732,54733],{"xmlns":890},[892,54734,54735,54739],{},[895,54736,54737],{},[898,54738,8519],{},[902,54740,8519],{"encoding":904}," a přímkou ",[883,54743,54745],{"className":54744},[886],[888,54746,54747],{"xmlns":890},[892,54748,54749,54761],{},[895,54750,54751,54753,54755],{},[898,54752,3783],{},[1846,54754,1848],{},[2122,54756,54757,54759],{},[898,54758,3783],{},[1979,54760,2177],{},[902,54762,51522],{"encoding":904},[36815,54764],{},[115,54766,54768],{"id":54767},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,54770,54771,54772,54785,54786,54803],{},"Uvalení jednotkové daně ",[883,54773,54775],{"className":54774},[886],[888,54776,54777],{"xmlns":890},[892,54778,54779,54783],{},[895,54780,54781],{},[898,54782,2623],{},[902,54784,2623],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,54787,54789],{"className":54788},[886],[888,54790,54791],{"xmlns":890},[892,54792,54793,54801],{},[895,54794,54795],{},[1974,54796,54797,54799],{},[898,54798,2638],{},[898,54800,4098],{},[902,54802,42248],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,54805,54806],{},[2409,54807],{"alt":54808,"className":54809,"src":54810},"imek-prebytky-s-dani-deadweight",[210,2413],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,54812,54813,54814,54829,54830,54845,54846,52513,54849,54873,54874,9871,54877,54880,54881,1734],{},"Přebytek spotřebitele ",[883,54815,54817],{"className":54816},[886],[888,54818,54819],{"xmlns":890},[892,54820,54821,54827],{},[895,54822,54823,54825],{},[898,54824,2626],{},[898,54826,8519],{},[902,54828,44795],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,54831,54833],{"className":54832},[886],[888,54834,54835],{"xmlns":890},[892,54836,54837,54843],{},[895,54838,54839,54841],{},[898,54840,3783],{},[898,54842,8519],{},[902,54844,44814],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,54847,54848],{},"daňový příjem",[883,54850,54852],{"className":54851},[886],[888,54853,54854],{"xmlns":890},[892,54855,54856,54870],{},[895,54857,54858,54860,54862],{},[898,54859,2623],{},[1846,54861,3025],{},[9012,54863,54864,54866,54868],{},[898,54865,2638],{},[1979,54867,2128],{},[898,54869,4098],{},[902,54871,54872],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,54875,54876],{},"mrtvá ztráta",[614,54878,54879],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,54882,811],{"className":54883,"dataFsResolvedFilePath":809,"href":810},[210],[36815,54885],{},[115,54887,3640],{"id":3639},[120,54889,54890,54897,54909,54916,54923],{},[123,54891,54892,2053,54894],{},[38,54893,16067],{},[207,54895,802],{"className":54896,"dataFsResolvedFilePath":800,"href":801},[210],[123,54898,54899,2053,54901,54904,54905,54908],{},[38,54900,36519],{},[207,54902,775],{"className":54903,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,54906,2207],{"className":54907,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,54910,54911,2053,54913],{},[38,54912,16077],{},[207,54914,1708],{"className":54915,"dataFsResolvedFilePath":827,"href":828},[210],[123,54917,54918,2053,54920],{},[38,54919,50603],{},[207,54921,50607],{"className":54922,"dataFsResolvedFilePath":745,"href":746},[210],[123,54924,54925,2053,54927],{},[38,54926,16049],{},[207,54928,16053],{"className":54929,"dataFsResolvedFilePath":1761,"href":1762},[210],{"title":641,"searchDepth":642,"depth":642,"links":54931},[54932,54933,54938,54943,54948,54949,54950,54951],{"id":50799,"depth":642,"text":1241},{"id":51143,"depth":642,"text":54934,"children":54935},"Přebytek spotřebitele (CSCS)",[54936,54937],{"id":51162,"depth":649,"text":51163},{"id":2293,"depth":649,"text":2294},{"id":51738,"depth":642,"text":54939,"children":54940},"Přebytek výrobce (PSPS)",[54941,54942],{"id":51757,"depth":649,"text":51758},{"id":51920,"depth":649,"text":2294},{"id":52528,"depth":642,"text":52529,"children":54944},[54945,54946],{"id":52532,"depth":649,"text":52533},{"id":53826,"depth":649,"text":54947},"Příklad 2.13 — numerický výpočet PSPS",{"id":54131,"depth":642,"text":54132},{"id":15564,"depth":642,"text":15565},{"id":54767,"depth":642,"text":54768},{"id":3639,"depth":642,"text":3640},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,50669,54958,54959,1788,1789,54960,54961],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":54964,"title":54965,"body":54966,"course":1128,"courses":659,"created":9402,"description":641,"extension":661,"meta":74295,"navigation":664,"path":74296,"seo":74297,"sources":74298,"stem":74299,"tags":74300,"type":3703,"updated":677,"__hash__":74306},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":54967,"toc":74259},[54968,54971,55157,55159,55250,55255,55581,55585,55592,55596,55641,55708,55739,55789,55824,55828,55887,55892,55958,56076,56178,56182,56205,56283,56326,56330,56359,56426,56432,56546,56550,56630,56667,56719,56917,56981,57068,57072,57075,57154,57157,57275,57294,57359,57363,57455,57523,57564,57618,57686,57723,57727,57785,57815,58026,58098,58150,58316,58409,58444,58448,58452,58489,58554,58609,58613,58636,58725,58829,58898,58902,58999,59112,59168,59222,59280,59341,59344,59380,59445,59475,59704,59762,59796,59800,59827,59906,60020,60041,60120,60122,60230,60234,60372,60694,60698,60701,60705,60754,60758,61012,61164,61171,61244,61428,61433,61776,61780,61803,61805,61826,61885,61895,61944,62086,62160,62255,62370,62468,62586,62590,62659,62664,62776,62921,62972,63084,63126,63130,63150,63211,63238,63300,63304,63326,63395,63675,63682,63712,63719,63912,63916,63994,63999,64075,64078,64166,64242,64309,64358,64461,64534,64655,65006,65119,65221,65225,65228,65235,65238,65274,65333,65342,65491,65715,65719,65782,65961,66053,66108,66112,66168,66238,66290,66311,66392,66395,66470,66514,66518,66559,66602,66628,66632,66703,66799,66861,66913,67016,67094,67117,67146,67150,67316,67433,67505,67820,67980,67984,68035,68097,68132,68162,68262,68304,68473,68478,68574,68612,68616,68735,69036,69038,69073,69077,69081,69209,69341,69663,69851,69929,69933,70238,70351,70497,70682,70788,71020,71135,71217,71336,71434,71475,71479,71534,71678,71832,71992,72085,72279,72591,72722,72851,72855,72927,72969,73020,73022,74217,74219],[12,54969,54965],{"id":54970},"příjem-náklady-zisk-a-nabídka-firmy",[1639,54972,54973],{},[724,54974,54975,3720,54977,2053,54980,54995,54996,2053,54999,55014,55015,2053,55018,55046,55047,55069,55070,55094,55095,55117,55118,55121,55122,55138,55139,1734],{},[883,54976,3719],{},[38,54978,54979],{},"Příjem",[883,54981,54983],{"className":54982},[886],[888,54984,54985],{"xmlns":890},[892,54986,54987,54993],{},[895,54988,54989,54991],{},[898,54990,2623],{},[898,54992,3840],{},[902,54994,3940],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,54997,54998],{},"náklady",[883,55000,55002],{"className":55001},[886],[888,55003,55004],{"xmlns":890},[892,55005,55006,55012],{},[895,55007,55008,55010],{},[898,55009,2623],{},[898,55011,2626],{},[902,55013,3091],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,55016,55017],{},"zisk",[883,55019,55021],{"className":55020},[886],[888,55022,55023],{"xmlns":890},[892,55024,55025,55043],{},[895,55026,55027,55029,55031,55033,55035,55037,55039,55041],{},[898,55028,3783],{},[898,55030,3840],{},[1846,55032,1848],{},[898,55034,2623],{},[898,55036,3840],{},[1846,55038,2075],{},[898,55040,2623],{},[898,55042,2626],{},[902,55044,55045],{"encoding":904},"PR = TR - TC"," jejich rozdíl. Kapitola pro každou ze tří veličin zavádí celkovou, průměrnou a mezní podobu, ukáže jejich grafický průběh (pro lineární poptávku a kubické náklady) a odvodí tři klíčové optimalizační principy: ",[883,55048,55050],{"className":55049},[886],[888,55051,55052],{"xmlns":890},[892,55053,55054,55066],{},[895,55055,55056,55058,55060,55062,55064],{},[898,55057,4101],{},[898,55059,2626],{},[1846,55061,1848],{},[898,55063,2667],{},[898,55065,2626],{},[902,55067,55068],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,55071,55073],{"className":55072},[886],[888,55074,55075],{"xmlns":890},[892,55076,55077,55091],{},[895,55078,55079,55081,55083,55085,55087,55089],{},[898,55080,4101],{},[898,55082,40184],{},[898,55084,2626],{},[1846,55086,1848],{},[898,55088,2667],{},[898,55090,2626],{},[902,55092,55093],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,55096,55098],{"className":55097},[886],[888,55099,55100],{"xmlns":890},[892,55101,55102,55114],{},[895,55103,55104,55106,55108,55110,55112],{},[898,55105,2667],{},[898,55107,3840],{},[1846,55109,1848],{},[898,55111,2667],{},[898,55113,2626],{},[902,55115,55116],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,55119,55120],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,55123,55125],{"className":55124},[886],[888,55126,55127],{"xmlns":890},[892,55128,55129,55135],{},[895,55130,55131,55133],{},[898,55132,2667],{},[898,55134,2626],{},[902,55136,55137],{"encoding":904},"MC"," nad bodem minima ",[883,55140,55142],{"className":55141},[886],[888,55143,55144],{"xmlns":890},[892,55145,55146,55154],{},[895,55147,55148,55150,55152],{},[898,55149,4101],{},[898,55151,40184],{},[898,55153,2626],{},[902,55155,55156],{"encoding":904},"AVC",[115,55158,1241],{"id":50799},[724,55160,55161,55162,55165,55166,55168,55169,1343,55172,1343,55175,55177,55178,55181,55182,55185,55186,55189,55190,2521,55205,1348,55220,2521,55235,3764],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,55163,55164],{},"příjmem"," (revenue) a ",[38,55167,54998],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,55170,55171],{},"zisku",[38,55173,55174],{},"bodů zvratu",[38,55176,1821],{}," a konstrukcí ",[38,55179,55180],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,55183,1145],{"className":55184,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,55187,10976],{"className":55188,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,55191,55193],{"className":55192},[886],[888,55194,55195],{"xmlns":890},[892,55196,55197,55203],{},[895,55198,55199,55201],{},[898,55200,2623],{},[898,55202,3840],{},[902,55204,3940],{"encoding":904},[883,55206,55208],{"className":55207},[886],[888,55209,55210],{"xmlns":890},[892,55211,55212,55218],{},[895,55213,55214,55216],{},[898,55215,2667],{},[898,55217,3840],{},[902,55219,6480],{"encoding":904},[883,55221,55223],{"className":55222},[886],[888,55224,55225],{"xmlns":890},[892,55226,55227,55233],{},[895,55228,55229,55231],{},[898,55230,2623],{},[898,55232,2626],{},[902,55234,3091],{"encoding":904},[883,55236,55238],{"className":55237},[886],[888,55239,55240],{"xmlns":890},[892,55241,55242,55248],{},[895,55243,55244,55246],{},[898,55245,2667],{},[898,55247,2626],{},[902,55249,55137],{"encoding":904},[724,55251,55252],{},[38,55253,55254],{},"Cílové znalosti:",[120,55256,55257,55421,55424,55427,55520,55567,55574],{},[123,55258,55259,55260,1343,55275,1343,55291,1745,55306,1343,55321,1343,55337,1343,55355,1343,55373,1343,55390,1343,55406,8271],{},"odvodit a interpretovat funkce ",[883,55261,55263],{"className":55262},[886],[888,55264,55265],{"xmlns":890},[892,55266,55267,55273],{},[895,55268,55269,55271],{},[898,55270,2623],{},[898,55272,3840],{},[902,55274,3940],{"encoding":904},[883,55276,55278],{"className":55277},[886],[888,55279,55280],{"xmlns":890},[892,55281,55282,55288],{},[895,55283,55284,55286],{},[898,55285,4101],{},[898,55287,3840],{},[902,55289,55290],{"encoding":904},"AR",[883,55292,55294],{"className":55293},[886],[888,55295,55296],{"xmlns":890},[892,55297,55298,55304],{},[895,55299,55300,55302],{},[898,55301,2667],{},[898,55303,3840],{},[902,55305,6480],{"encoding":904},[883,55307,55309],{"className":55308},[886],[888,55310,55311],{"xmlns":890},[892,55312,55313,55319],{},[895,55314,55315,55317],{},[898,55316,2623],{},[898,55318,2626],{},[902,55320,3091],{"encoding":904},[883,55322,55324],{"className":55323},[886],[888,55325,55326],{"xmlns":890},[892,55327,55328,55334],{},[895,55329,55330,55332],{},[898,55331,10282],{},[898,55333,2626],{},[902,55335,55336],{"encoding":904},"FC",[883,55338,55340],{"className":55339},[886],[888,55341,55342],{"xmlns":890},[892,55343,55344,55352],{},[895,55345,55346,55348,55350],{},[898,55347,2623],{},[898,55349,40184],{},[898,55351,2626],{},[902,55353,55354],{"encoding":904},"TVC",[883,55356,55358],{"className":55357},[886],[888,55359,55360],{"xmlns":890},[892,55361,55362,55370],{},[895,55363,55364,55366,55368],{},[898,55365,4101],{},[898,55367,10282],{},[898,55369,2626],{},[902,55371,55372],{"encoding":904},"AFC",[883,55374,55376],{"className":55375},[886],[888,55377,55378],{"xmlns":890},[892,55379,55380,55388],{},[895,55381,55382,55384,55386],{},[898,55383,4101],{},[898,55385,40184],{},[898,55387,2626],{},[902,55389,55156],{"encoding":904},[883,55391,55393],{"className":55392},[886],[888,55394,55395],{"xmlns":890},[892,55396,55397,55403],{},[895,55398,55399,55401],{},[898,55400,4101],{},[898,55402,2626],{},[902,55404,55405],{"encoding":904},"AC",[883,55407,55409],{"className":55408},[886],[888,55410,55411],{"xmlns":890},[892,55412,55413,55419],{},[895,55414,55415,55417],{},[898,55416,2667],{},[898,55418,2626],{},[902,55420,55137],{"encoding":904},[123,55422,55423],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,55425,55426],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,55428,55429,55430,55433,55434,41659,55476,8271],{},"osvojit si ",[38,55431,55432],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,55435,55437],{"className":55436},[886],[888,55438,55439],{"xmlns":890},[892,55440,55441,55473],{},[895,55442,55443,55445,55447,55449,55455,55457,55459,55461,55463,55465,55471],{},[898,55444,4101],{},[898,55446,2626],{},[1846,55448,1855],{"stretchy":1854},[2122,55450,55451,55453],{},[898,55452,2638],{},[1979,55454,2177],{},[1846,55456,1861],{"stretchy":1854},[1846,55458,1848],{},[898,55460,2667],{},[898,55462,2626],{},[1846,55464,1855],{"stretchy":1854},[2122,55466,55467,55469],{},[898,55468,2638],{},[1979,55470,2177],{},[1846,55472,1861],{"stretchy":1854},[902,55474,55475],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,55477,55479],{"className":55478},[886],[888,55480,55481],{"xmlns":890},[892,55482,55483,55517],{},[895,55484,55485,55487,55489,55491,55493,55499,55501,55503,55505,55507,55509,55515],{},[898,55486,4101],{},[898,55488,40184],{},[898,55490,2626],{},[1846,55492,1855],{"stretchy":1854},[2122,55494,55495,55497],{},[898,55496,2638],{},[1979,55498,2177],{},[1846,55500,1861],{"stretchy":1854},[1846,55502,1848],{},[898,55504,2667],{},[898,55506,2626],{},[1846,55508,1855],{"stretchy":1854},[2122,55510,55511,55513],{},[898,55512,2638],{},[1979,55514,2177],{},[1846,55516,1861],{"stretchy":1854},[902,55518,55519],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,55521,55429,55522,55433,55525,8271],{},[38,55523,55524],{},"princip maximalizace zisku",[883,55526,55528],{"className":55527},[886],[888,55529,55530],{"xmlns":890},[892,55531,55532,55564],{},[895,55533,55534,55536,55538,55540,55546,55548,55550,55552,55554,55556,55562],{},[898,55535,2667],{},[898,55537,3840],{},[1846,55539,1855],{"stretchy":1854},[2122,55541,55542,55544],{},[898,55543,2638],{},[1979,55545,2177],{},[1846,55547,1861],{"stretchy":1854},[1846,55549,1848],{},[898,55551,2667],{},[898,55553,2626],{},[1846,55555,1855],{"stretchy":1854},[2122,55557,55558,55560],{},[898,55559,2638],{},[1979,55561,2177],{},[1846,55563,1861],{"stretchy":1854},[902,55565,55566],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,55568,55569,55570,55573],{},"stanovit ",[38,55571,55572],{},"body zvratu"," a interval zisku;",[123,55575,55576,55577,55580],{},"zkonstruovat ",[38,55578,55579],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,55582,55584],{"id":55583},"příjem-firmy","Příjem firmy",[724,55586,55587],{},[2409,55588],{"alt":55589,"className":55590,"src":55591},"imek-ar-mr-dvojnasobny-sklon",[210,2413],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,55593,55595],{"id":55594},"celkový-příjem","Celkový příjem",[724,55597,55598,55599,9871,55614,55617,55618,29789],{},"Celkový příjem ",[883,55600,55602],{"className":55601},[886],[888,55603,55604],{"xmlns":890},[892,55605,55606,55612],{},[895,55607,55608,55610],{},[898,55609,2623],{},[898,55611,3840],{},[902,55613,3940],{"encoding":904},[38,55615,55616],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,55619,55621],{"className":55620},[886],[888,55622,55623],{"xmlns":890},[892,55624,55625,55639],{},[895,55626,55627,55629,55631,55633,55635,55637],{},[898,55628,3783],{},[1846,55630,1848],{},[898,55632,4029],{},[1846,55634,1855],{"stretchy":1854},[898,55636,2638],{},[1846,55638,1861],{"stretchy":1854},[902,55640,4486],{"encoding":904},[883,55642,55644],{"className":55643},[886],[888,55645,55646],{"xmlns":890,"display":27911},[892,55647,55648,55705],{},[20599,55649,55650],{"width":27916},[20604,55651,55652,55654,55698,55700],{},[20607,55653],{"width":27921},[20607,55655,55656],{},[895,55657,55658,55660,55662,55664,55666,55668,55670,55672,55674,55676,55678,55680,55682,55684,55686,55688,55690,55692,55694,55696],{},[898,55659,2623],{},[898,55661,3840],{},[1846,55663,1848],{},[898,55665,2623],{},[898,55667,3840],{},[1846,55669,1855],{"stretchy":1854},[898,55671,2638],{},[1846,55673,1861],{"stretchy":1854},[1846,55675,1848],{},[898,55677,3783],{},[1846,55679,3025],{},[898,55681,2638],{},[1846,55683,1848],{},[898,55685,4029],{},[1846,55687,1855],{"stretchy":1854},[898,55689,2638],{},[1846,55691,1861],{"stretchy":1854},[1846,55693,3025],{},[898,55695,2638],{},[898,55697,1734],{"mathvariant":2226},[20607,55699],{"width":27921},[20607,55701,55702],{},[2138,55703,55704],{},"(3.1)",[902,55706,55707],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,55709,55710,55711,55714,55715,55738],{},"Graf funkce se nazývá ",[38,55712,55713],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,55716,55718],{"className":55717},[886],[888,55719,55720],{"xmlns":890},[892,55721,55722,55736],{},[895,55723,55724,55726,55728,55730,55732,55734],{},[898,55725,3783],{},[1846,55727,1848],{},[898,55729,207],{},[898,55731,2638],{},[1846,55733,1945],{},[898,55735,1948],{},[902,55737,36905],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,55740,55742],{"className":55741},[886],[888,55743,55744],{"xmlns":890,"display":27911},[892,55745,55746,55786],{},[895,55747,55748,55750,55752,55754,55756,55758,55760,55762,55764,55766,55768,55770,55772,55778,55780,55782,55784],{},[898,55749,2623],{},[898,55751,3840],{},[1846,55753,1848],{},[898,55755,2638],{},[1846,55757,1855],{"stretchy":1854},[898,55759,207],{},[898,55761,2638],{},[1846,55763,1945],{},[898,55765,1948],{},[1846,55767,1861],{"stretchy":1854},[1846,55769,1848],{},[898,55771,207],{},[1974,55773,55774,55776],{},[898,55775,2638],{},[1979,55777,1981],{},[1846,55779,1945],{},[898,55781,1948],{},[898,55783,2638],{},[1846,55785,2136],{"separator":2135},[902,55787,55788],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,55790,55791,55792,55805,55806,55823],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,55793,55795],{"className":55794},[886],[888,55796,55797],{"xmlns":890},[892,55798,55799,55803],{},[895,55800,55801],{},[898,55802,900],{},[902,55804,900],{"encoding":904}," (jelikož ",[883,55807,55809],{"className":55808},[886],[888,55810,55811],{"xmlns":890},[892,55812,55813,55821],{},[895,55814,55815,55817,55819],{},[898,55816,207],{},[1846,55818,3295],{},[1979,55820,2177],{},[902,55822,42930],{"encoding":904},") procházející počátkem.",[37193,55825,55827],{"id":55826},"příklad-31","Příklad 3.1",[724,55829,55830,55833,55834,55870,55871,55886],{},[38,55831,55832],{},"Zadání."," Pro poptávku ",[883,55835,55837],{"className":55836},[886],[888,55838,55839],{"xmlns":890},[892,55840,55841,55867],{},[895,55842,55843,55845,55847,55849,55851,55853,55855,55857,55859,55861,55863,55865],{},[898,55844,3783],{},[1846,55846,1848],{},[898,55848,4029],{},[1846,55850,1855],{"stretchy":1854},[898,55852,2638],{},[1846,55854,1861],{"stretchy":1854},[1846,55856,1848],{},[1846,55858,2075],{},[1979,55860,1981],{},[898,55862,2638],{},[1846,55864,1945],{},[1979,55866,2938],{},[902,55868,55869],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,55872,55874],{"className":55873},[886],[888,55875,55876],{"xmlns":890},[892,55877,55878,55884],{},[895,55879,55880,55882],{},[898,55881,2623],{},[898,55883,3840],{},[902,55885,3940],{"encoding":904}," a charakterizujte jeho křivku.",[724,55888,55889,55891],{},[38,55890,22615],{}," Celkový příjem je",[883,55893,55895],{"className":55894},[886],[888,55896,55897],{"xmlns":890,"display":27911},[892,55898,55899,55955],{},[895,55900,55901,55903,55905,55907,55909,55911,55913,55915,55917,55919,55921,55923,55925,55927,55929,55931,55933,55935,55937,55939,55941,55947,55949,55951,55953],{},[898,55902,2623],{},[898,55904,3840],{},[1846,55906,1848],{},[898,55908,2623],{},[898,55910,3840],{},[1846,55912,1855],{"stretchy":1854},[898,55914,2638],{},[1846,55916,1861],{"stretchy":1854},[1846,55918,1848],{},[898,55920,2638],{},[1846,55922,1855],{"stretchy":1854},[1846,55924,2075],{},[1979,55926,1981],{},[898,55928,2638],{},[1846,55930,1945],{},[1979,55932,2938],{},[1846,55934,1861],{"stretchy":1854},[1846,55936,1848],{},[1846,55938,2075],{},[1979,55940,1981],{},[1974,55942,55943,55945],{},[898,55944,2638],{},[1979,55946,1981],{},[1846,55948,1945],{},[1979,55950,2938],{},[898,55952,2638],{},[898,55954,1734],{"mathvariant":2226},[902,55956,55957],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,55959,55960,55961,1745,55983,56005,56006,56024,56025,1734],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,55962,55964],{"className":55963},[886],[888,55965,55966],{"xmlns":890},[892,55967,55968,55980],{},[895,55969,55970,55976,55978],{},[2122,55971,55972,55974],{},[898,55973,2638],{},[1979,55975,2128],{},[1846,55977,1848],{},[1979,55979,2177],{},[902,55981,55982],{"encoding":904},"Q_1 = 0",[883,55984,55986],{"className":55985},[886],[888,55987,55988],{"xmlns":890},[892,55989,55990,56002],{},[895,55991,55992,55998,56000],{},[2122,55993,55994,55996],{},[898,55995,2638],{},[1979,55997,1981],{},[1846,55999,1848],{},[1979,56001,2968],{},[902,56003,56004],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,56007,56009],{"className":56008},[886],[888,56010,56011],{"xmlns":890},[892,56012,56013,56021],{},[895,56014,56015,56017,56019],{},[898,56016,2638],{},[1846,56018,1848],{},[1979,56020,4850],{},[902,56022,56023],{"encoding":904},"Q = 25"," ve výši ",[883,56026,56028],{"className":56027},[886],[888,56029,56030],{"xmlns":890},[892,56031,56032,56073],{},[895,56033,56034,56036,56046,56048,56050,56052,56054,56057,56059,56061,56063,56065,56067,56069,56071],{},[898,56035,2623],{},[2122,56037,56038,56040,56043],{},[898,56039,3840],{},[898,56041,56042],{},"max",[1846,56044,56045],{},"⁡",[1846,56047,1848],{},[1846,56049,2075],{},[1979,56051,1981],{},[1846,56053,3025],{},[1979,56055,56056],{},"625",[1846,56058,1945],{},[1979,56060,2938],{},[1846,56062,3025],{},[1979,56064,4850],{},[1846,56066,1848],{},[1979,56068,2128],{},[2138,56070,2835],{},[1979,56072,30588],{},[902,56074,56075],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,56077,56078],{},[614,56079,56080,56081,56115,56116,1745,56129,56142,56143,2474,56161,1734],{},"Obrázek 3.1: Parabola ",[883,56082,56084],{"className":56083},[886],[888,56085,56086],{"xmlns":890},[892,56087,56088,56112],{},[895,56089,56090,56092,56094,56096,56098,56100,56106,56108,56110],{},[898,56091,2623],{},[898,56093,3840],{},[1846,56095,1848],{},[1846,56097,2075],{},[1979,56099,1981],{},[1974,56101,56102,56104],{},[898,56103,2638],{},[1979,56105,1981],{},[1846,56107,1945],{},[1979,56109,2938],{},[898,56111,2638],{},[902,56113,56114],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,56117,56119],{"className":56118},[886],[888,56120,56121],{"xmlns":890},[892,56122,56123,56127],{},[895,56124,56125],{},[1979,56126,2177],{},[902,56128,2177],{"encoding":904},[883,56130,56132],{"className":56131},[886],[888,56133,56134],{"xmlns":890},[892,56135,56136,56140],{},[895,56137,56138],{},[1979,56139,2968],{},[902,56141,2968],{"encoding":904}," a maximem ",[883,56144,56146],{"className":56145},[886],[888,56147,56148],{"xmlns":890},[892,56149,56150,56158],{},[895,56151,56152,56154,56156],{},[1979,56153,2128],{},[2138,56155,2835],{},[1979,56157,30588],{},[902,56159,56160],{"encoding":904},"1\\,250",[883,56162,56164],{"className":56163},[886],[888,56165,56166],{"xmlns":890},[892,56167,56168,56176],{},[895,56169,56170,56172,56174],{},[898,56171,2638],{},[1846,56173,1848],{},[1979,56175,4850],{},[902,56177,56023],{"encoding":904},[198,56179,56181],{"id":56180},"průměrný-příjem","Průměrný příjem",[724,56183,56184,2053,56186,9871,56201,56204],{},[38,56185,56181],{},[883,56187,56189],{"className":56188},[886],[888,56190,56191],{"xmlns":890},[892,56192,56193,56199],{},[895,56194,56195,56197],{},[898,56196,4101],{},[898,56198,3840],{},[902,56200,55290],{"encoding":904},[38,56202,56203],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,56206,56208],{"className":56207},[886],[888,56209,56210],{"xmlns":890,"display":27911},[892,56211,56212,56280],{},[895,56213,56214,56216,56218,56220,56222,56224,56226,56228,56230,56232,56248,56250,56268,56270,56272,56274,56276,56278],{},[898,56215,4101],{},[898,56217,3840],{},[1846,56219,1848],{},[898,56221,4101],{},[898,56223,3840],{},[1846,56225,1855],{"stretchy":1854},[898,56227,2638],{},[1846,56229,1861],{"stretchy":1854},[1846,56231,1848],{},[2179,56233,56234,56246],{},[895,56235,56236,56238,56240,56242,56244],{},[898,56237,2623],{},[898,56239,3840],{},[1846,56241,1855],{"stretchy":1854},[898,56243,2638],{},[1846,56245,1861],{"stretchy":1854},[898,56247,2638],{},[1846,56249,1848],{},[2179,56251,56252,56266],{},[895,56253,56254,56256,56258,56260,56262,56264],{},[898,56255,2638],{},[2138,56257,2835],{},[898,56259,4029],{},[1846,56261,1855],{"stretchy":1854},[898,56263,2638],{},[1846,56265,1861],{"stretchy":1854},[898,56267,2638],{},[1846,56269,1848],{},[898,56271,4029],{},[1846,56273,1855],{"stretchy":1854},[898,56275,2638],{},[1846,56277,1861],{"stretchy":1854},[898,56279,1734],{"mathvariant":2226},[902,56281,56282],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[1639,56284,56285],{},[724,56286,56287,56290,56291,1343,56294,1734],{},[883,56288,56289],{},"!note"," Klíčové pozorování\n",[38,56292,56293],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,56295,56297],{"className":56296},[886],[888,56298,56299],{"xmlns":890},[892,56300,56301,56323],{},[895,56302,56303,56305,56307,56309,56311,56313,56315,56317,56319,56321],{},[898,56304,4101],{},[898,56306,3840],{},[1846,56308,1855],{"stretchy":1854},[898,56310,2638],{},[1846,56312,1861],{"stretchy":1854},[1846,56314,1848],{},[898,56316,4029],{},[1846,56318,1855],{"stretchy":1854},[898,56320,2638],{},[1846,56322,1861],{"stretchy":1854},[902,56324,56325],{"encoding":904},"AR(Q) = D(Q)",[198,56327,56329],{"id":56328},"mezní-příjem","Mezní příjem",[724,56331,56332,56333,2053,56336,9871,56351,56354,56355,56358],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,56334,56335],{},"mezní příjem",[883,56337,56339],{"className":56338},[886],[888,56340,56341],{"xmlns":890},[892,56342,56343,56349],{},[895,56344,56345,56347],{},[898,56346,2667],{},[898,56348,3840],{},[902,56350,6480],{"encoding":904},[38,56352,56353],{},"marginal revenue","), definovaný jako ",[207,56356,1145],{"className":56357,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,56360,56362],{"className":56361},[886],[888,56363,56364],{"xmlns":890,"display":27911},[892,56365,56366,56423],{},[20599,56367,56368],{"width":27916},[20604,56369,56370,56372,56416,56418],{},[20607,56371],{"width":27921},[20607,56373,56374],{},[895,56375,56376,56378,56380,56382,56398,56400,56402,56408,56410,56412,56414],{},[898,56377,2667],{},[898,56379,3840],{},[1846,56381,1848],{},[2179,56383,56384,56392],{},[895,56385,56386,56388,56390],{},[898,56387,2044],{"mathvariant":2226},[898,56389,2623],{},[898,56391,3840],{},[895,56393,56394,56396],{},[898,56395,2044],{"mathvariant":2226},[898,56397,2638],{},[1846,56399,1848],{},[898,56401,2623],{},[1974,56403,56404,56406],{},[898,56405,3840],{},[1846,56407,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,56409,1855],{"stretchy":1854},[898,56411,2638],{},[1846,56413,1861],{"stretchy":1854},[898,56415,1734],{"mathvariant":2226},[20607,56417],{"width":27921},[20607,56419,56420],{},[2138,56421,56422],{},"(3.2)",[902,56424,56425],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,56427,56428,56429,56431],{},"Mezní příjem udává ",[38,56430,2446],{}," celkového příjmu vzhledem k množství.",[1639,56433,56434],{},[724,56435,56436,56438,56439,56465,56466,56483,56484,1734],{},[883,56437,4001],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,56440,56442],{"className":56441},[886],[888,56443,56444],{"xmlns":890},[892,56445,56446,56462],{},[895,56447,56448,56450,56452,56454,56460],{},[898,56449,2667],{},[898,56451,3840],{},[1846,56453,1855],{"stretchy":1854},[1974,56455,56456,56458],{},[898,56457,2638],{},[1846,56459,4200],{},[1846,56461,1861],{"stretchy":1854},[902,56463,56464],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,56467,56469],{"className":56468},[886],[888,56470,56471],{"xmlns":890},[892,56472,56473,56481],{},[895,56474,56475],{},[1974,56476,56477,56479],{},[898,56478,2638],{},[1846,56480,4200],{},[902,56482,29689],{"encoding":904},". Jinak řečeno: ",[883,56485,56487],{"className":56486},[886],[888,56488,56489],{"xmlns":890},[892,56490,56491,56543],{},[895,56492,56493,56495,56497,56499,56505,56507,56509,56511,56513,56515,56521,56523,56525,56527,56529,56531,56533,56535,56541],{},[898,56494,2667],{},[898,56496,3840],{},[1846,56498,1855],{"stretchy":1854},[1974,56500,56501,56503],{},[898,56502,2638],{},[1846,56504,4200],{},[1846,56506,1861],{"stretchy":1854},[1846,56508,1650],{},[898,56510,2623],{},[898,56512,3840],{},[1846,56514,1855],{"stretchy":1854},[1974,56516,56517,56519],{},[898,56518,2638],{},[1846,56520,4200],{},[1846,56522,1945],{},[1979,56524,2128],{},[1846,56526,1861],{"stretchy":1854},[1846,56528,2075],{},[898,56530,2623],{},[898,56532,3840],{},[1846,56534,1855],{"stretchy":1854},[1974,56536,56537,56539],{},[898,56538,2638],{},[1846,56540,4200],{},[1846,56542,1861],{"stretchy":1854},[902,56544,56545],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[37193,56547,56549],{"id":56548},"příklad-32","Příklad 3.2",[724,56551,56552,55833,56554,55870,56588,56603,56604,1734],{},[38,56553,55832],{},[883,56555,56557],{"className":56556},[886],[888,56558,56559],{"xmlns":890},[892,56560,56561,56585],{},[895,56562,56563,56565,56567,56569,56571,56573,56575,56577,56579,56581,56583],{},[898,56564,3783],{},[1846,56566,1848],{},[898,56568,4029],{},[1846,56570,1855],{"stretchy":1854},[898,56572,2638],{},[1846,56574,1861],{"stretchy":1854},[1846,56576,1848],{},[1979,56578,2938],{},[1846,56580,2075],{},[1979,56582,1981],{},[898,56584,2638],{},[902,56586,56587],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,56589,56591],{"className":56590},[886],[888,56592,56593],{"xmlns":890},[892,56594,56595,56601],{},[895,56596,56597,56599],{},[898,56598,2667],{},[898,56600,3840],{},[902,56602,6480],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,56605,56607],{"className":56606},[886],[888,56608,56609],{"xmlns":890},[892,56610,56611,56627],{},[895,56612,56613,56615,56617,56619,56621,56623,56625],{},[898,56614,2638],{},[1846,56616,1848],{},[1979,56618,36089],{},[1846,56620,2136],{"separator":2135},[1979,56622,41707],{},[1846,56624,2136],{"separator":2135},[1979,56626,8881],{},[902,56628,56629],{"encoding":904},"Q = 15, 16, 20",[724,56631,56632,2053,56634,56666],{},[38,56633,22615],{},[883,56635,56637],{"className":56636},[886],[888,56638,56639],{"xmlns":890},[892,56640,56641,56663],{},[895,56642,56643,56645,56647,56649,56651,56653,56655,56657],{},[898,56644,2623],{},[898,56646,3840],{},[1846,56648,1848],{},[1979,56650,2938],{},[898,56652,2638],{},[1846,56654,2075],{},[1979,56656,1981],{},[1974,56658,56659,56661],{},[898,56660,2638],{},[1979,56662,1981],{},[902,56664,56665],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,56668,56670],{"className":56669},[886],[888,56671,56672],{"xmlns":890,"display":27911},[892,56673,56674,56716],{},[895,56675,56676,56678,56680,56682,56684,56686,56688,56690,56692,56698,56704,56706,56708,56710,56712,56714],{},[898,56677,2667],{},[898,56679,3840],{},[1846,56681,1848],{},[1846,56683,1855],{"stretchy":1854},[1979,56685,2938],{},[898,56687,2638],{},[1846,56689,2075],{},[1979,56691,1981],{},[1974,56693,56694,56696],{},[898,56695,2638],{},[1979,56697,1981],{},[1974,56699,56700,56702],{},[1846,56701,1861],{"stretchy":1854},[1846,56703,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,56705,1848],{},[1979,56707,2938],{},[1846,56709,2075],{},[1979,56711,2201],{},[898,56713,2638],{},[898,56715,1734],{"mathvariant":2226},[902,56717,56718],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,56720,9509,56721,7948,56739,56765,56766,4204,56779,56794,56795,56808,56809,21265,56822,4204,56835,56850,56851,56864,56865,56896,56897,56916],{},[883,56722,56724],{"className":56723},[886],[888,56725,56726],{"xmlns":890},[892,56727,56728,56736],{},[895,56729,56730,56732,56734],{},[898,56731,2638],{},[1846,56733,1848],{},[1979,56735,36089],{},[902,56737,56738],{"encoding":904},"Q = 15",[883,56740,56742],{"className":56741},[886],[888,56743,56744],{"xmlns":890},[892,56745,56746,56762],{},[895,56747,56748,56750,56752,56754,56756,56758,56760],{},[898,56749,2667],{},[898,56751,3840],{},[1846,56753,1855],{"stretchy":1854},[1979,56755,36089],{},[1846,56757,1861],{"stretchy":1854},[1846,56759,1848],{},[1979,56761,5057],{},[902,56763,56764],{"encoding":904},"MR(15) = 40",": při množství ",[883,56767,56769],{"className":56768},[886],[888,56770,56771],{"xmlns":890},[892,56772,56773,56777],{},[895,56774,56775],{},[1979,56776,36089],{},[902,56778,36089],{"encoding":904},[883,56780,56782],{"className":56781},[886],[888,56783,56784],{"xmlns":890},[892,56785,56786,56792],{},[895,56787,56788,56790],{},[898,56789,2623],{},[898,56791,3840],{},[902,56793,3940],{"encoding":904}," mění asi ",[883,56796,56798],{"className":56797},[886],[888,56799,56800],{"xmlns":890},[892,56801,56802,56806],{},[895,56803,56804],{},[1979,56805,5057],{},[902,56807,5057],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,56810,56812],{"className":56811},[886],[888,56813,56814],{"xmlns":890},[892,56815,56816,56820],{},[895,56817,56818],{},[898,56819,2638],{},[902,56821,2638],{"encoding":904},[883,56823,56825],{"className":56824},[886],[888,56826,56827],{"xmlns":890},[892,56828,56829,56833],{},[895,56830,56831],{},[1979,56832,2128],{},[902,56834,2128],{"encoding":904},[883,56836,56838],{"className":56837},[886],[888,56839,56840],{"xmlns":890},[892,56841,56842,56848],{},[895,56843,56844,56846],{},[898,56845,2623],{},[898,56847,3840],{},[902,56849,3940],{"encoding":904}," zvýší přibližně o ",[883,56852,56854],{"className":56853},[886],[888,56855,56856],{"xmlns":890},[892,56857,56858,56862],{},[895,56859,56860],{},[1979,56861,5057],{},[902,56863,5057],{"encoding":904},", tj. ze skutečné hodnoty ",[883,56866,56868],{"className":56867},[886],[888,56869,56870],{"xmlns":890},[892,56871,56872,56893],{},[895,56873,56874,56876,56878,56880,56882,56884,56886,56888,56890],{},[898,56875,2623],{},[898,56877,3840],{},[1846,56879,1855],{"stretchy":1854},[1979,56881,36089],{},[1846,56883,1861],{"stretchy":1854},[1846,56885,1848],{},[1979,56887,2128],{},[2138,56889,2835],{},[1979,56891,56892],{},"050",[902,56894,56895],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,56898,56900],{"className":56899},[886],[888,56901,56902],{"xmlns":890},[892,56903,56904,56913],{},[895,56905,56906,56908,56910],{},[1979,56907,2128],{},[2138,56909,2835],{},[1979,56911,56912],{},"090",[902,56914,56915],{"encoding":904},"1\\,090",". Skutečná změna je",[883,56918,56920],{"className":56919},[886],[888,56921,56922],{"xmlns":890,"display":27911},[892,56923,56924,56978],{},[895,56925,56926,56928,56930,56932,56934,56936,56938,56940,56942,56944,56946,56948,56950,56952,56954,56956,56958,56960,56962,56965,56967,56969,56971,56973,56975],{},[898,56927,2738],{"mathvariant":2226},[898,56929,2623],{},[898,56931,3840],{},[1846,56933,1848],{},[898,56935,2623],{},[898,56937,3840],{},[1846,56939,1855],{"stretchy":1854},[1979,56941,41707],{},[1846,56943,1861],{"stretchy":1854},[1846,56945,2075],{},[898,56947,2623],{},[898,56949,3840],{},[1846,56951,1855],{"stretchy":1854},[1979,56953,36089],{},[1846,56955,1861],{"stretchy":1854},[1846,56957,1848],{},[1979,56959,2128],{},[2138,56961,2835],{},[1979,56963,56964],{},"088",[1846,56966,2075],{},[1979,56968,2128],{},[2138,56970,2835],{},[1979,56972,56892],{},[1846,56974,1848],{},[1979,56976,56977],{},"38.",[902,56979,56980],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,56982,56983,56984,1343,57010,2776,57036,57051,57052,57067],{},"Podobně ",[883,56985,56987],{"className":56986},[886],[888,56988,56989],{"xmlns":890},[892,56990,56991,57007],{},[895,56992,56993,56995,56997,56999,57001,57003,57005],{},[898,56994,2667],{},[898,56996,3840],{},[1846,56998,1855],{"stretchy":1854},[1979,57000,41707],{},[1846,57002,1861],{"stretchy":1854},[1846,57004,1848],{},[1979,57006,5411],{},[902,57008,57009],{"encoding":904},"MR(16) = 36",[883,57011,57013],{"className":57012},[886],[888,57014,57015],{"xmlns":890},[892,57016,57017,57033],{},[895,57018,57019,57021,57023,57025,57027,57029,57031],{},[898,57020,2667],{},[898,57022,3840],{},[1846,57024,1855],{"stretchy":1854},[1979,57026,8881],{},[1846,57028,1861],{"stretchy":1854},[1846,57030,1848],{},[1979,57032,8881],{},[902,57034,57035],{"encoding":904},"MR(20) = 20",[883,57037,57039],{"className":57038},[886],[888,57040,57041],{"xmlns":890},[892,57042,57043,57049],{},[895,57044,57045,57047],{},[898,57046,2667],{},[898,57048,3840],{},[902,57050,6480],{"encoding":904}," je klesající funkce — rychlost změny ",[883,57053,57055],{"className":57054},[886],[888,57056,57057],{"xmlns":890},[892,57058,57059,57065],{},[895,57060,57061,57063],{},[898,57062,2623],{},[898,57064,3840],{},[902,57066,3940],{"encoding":904}," s růstem množství klesá.",[198,57069,57071],{"id":57070},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,57073,57074],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,57076,57078],{"className":57077},[886],[888,57079,57080],{"xmlns":890,"display":27911},[892,57081,57082,57151],{},[20599,57083,57084],{"width":27916},[20604,57085,57086,57088,57144,57146],{},[20607,57087],{"width":27921},[20607,57089,57090],{},[895,57091,57092,57094,57096,57098,57100,57102,57104,57106,57108,57110,57112,57114,57116,57118,57124,57126,57128,57130,57132,57134,57136,57138,57140,57142],{},[898,57093,2738],{"mathvariant":2226},[898,57095,2623],{},[898,57097,3840],{},[2138,57099,3830],{},[1846,57101,1650],{},[2138,57103,3830],{},[898,57105,2044],{"mathvariant":2226},[898,57107,2623],{},[898,57109,3840],{},[1846,57111,1848],{},[1846,57113,1855],{"stretchy":1854},[898,57115,2623],{},[898,57117,3840],{},[1974,57119,57120,57122],{},[1846,57121,1861],{"stretchy":1854},[1846,57123,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[2138,57125,2835],{},[898,57127,2044],{"mathvariant":2226},[898,57129,2638],{},[1846,57131,1848],{},[898,57133,2667],{},[898,57135,3840],{},[2138,57137,2835],{},[898,57139,2044],{"mathvariant":2226},[898,57141,2638],{},[1846,57143,2136],{"separator":2135},[20607,57145],{"width":27921},[20607,57147,57148],{},[2138,57149,57150],{},"(3.3)",[902,57152,57153],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,57155,57156],{},"schematicky:",[883,57158,57160],{"className":57159},[886],[888,57161,57162],{"xmlns":890,"display":27911},[892,57163,57164,57272],{},[895,57165,57166,57204,57206,57208,57210,57239,57242,57270],{},[895,57167,57168,57171,57177,57180,57186,57189,57195,57201],{},[2138,57169,57170],{},"zm",[8232,57172,57173,57175],{"accent":2135},[2138,57174,45577],{},[1846,57176,24903],{},[2138,57178,57179],{},"na celkov",[8232,57181,57182,57184],{"accent":2135},[2138,57183,45577],{},[1846,57185,24822],{},[2138,57187,57188],{},"ho p",[8232,57190,57191,57193],{"accent":2135},[2138,57192,11886],{},[1846,57194,24903],{},[8232,57196,57197,57199],{"accent":2135},[2138,57198,24891],{},[1846,57200,24822],{},[2138,57202,57203],{},"jmu",[2138,57205,3830],{},[1846,57207,1650],{},[2138,57209,3830],{},[895,57211,57212,57215,57221,57224,57230,57236],{},[2138,57213,57214],{},"mezn",[8232,57216,57217,57219],{"accent":2135},[2138,57218,24891],{},[1846,57220,24822],{},[2138,57222,57223],{}," p",[8232,57225,57226,57228],{"accent":2135},[2138,57227,11886],{},[1846,57229,24903],{},[8232,57231,57232,57234],{"accent":2135},[2138,57233,24891],{},[1846,57235,24822],{},[2138,57237,57238],{},"jem",[1846,57240,57241],{},"×",[895,57243,57244,57246,57252,57255,57261,57264],{},[2138,57245,57170],{},[8232,57247,57248,57250],{"accent":2135},[2138,57249,45577],{},[1846,57251,24903],{},[2138,57253,57254],{},"na mno",[8232,57256,57257,57259],{"accent":2135},[2138,57258,9440],{},[1846,57260,24903],{},[2138,57262,57263],{},"stv",[8232,57265,57266,57268],{"accent":2135},[2138,57267,24891],{},[1846,57269,24822],{},[898,57271,1734],{"mathvariant":2226},[902,57273,57274],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,57276,57277,57278,57293],{},"Pro porovnání skutečná změna ",[883,57279,57281],{"className":57280},[886],[888,57282,57283],{"xmlns":890},[892,57284,57285,57291],{},[895,57286,57287,57289],{},[898,57288,2623],{},[898,57290,3840],{},[902,57292,3940],{"encoding":904}," je",[883,57295,57297],{"className":57296},[886],[888,57298,57299],{"xmlns":890,"display":27911},[892,57300,57301,57356],{},[20599,57302,57303],{"width":27916},[20604,57304,57305,57307,57349,57351],{},[20607,57306],{"width":27921},[20607,57308,57309],{},[895,57310,57311,57313,57315,57317,57319,57321,57323,57325,57327,57329,57331,57333,57335,57337,57339,57341,57343,57345,57347],{},[898,57312,2738],{"mathvariant":2226},[898,57314,2623],{},[898,57316,3840],{},[1846,57318,1848],{},[898,57320,2623],{},[898,57322,3840],{},[1846,57324,1855],{"stretchy":1854},[898,57326,2638],{},[1846,57328,1945],{},[898,57330,2044],{"mathvariant":2226},[898,57332,2638],{},[1846,57334,1861],{"stretchy":1854},[1846,57336,2075],{},[898,57338,2623],{},[898,57340,3840],{},[1846,57342,1855],{"stretchy":1854},[898,57344,2638],{},[1846,57346,1861],{"stretchy":1854},[898,57348,1734],{"mathvariant":2226},[20607,57350],{"width":27921},[20607,57352,57353],{},[2138,57354,57355],{},"(3.4)",[902,57357,57358],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[37193,57360,57362],{"id":57361},"příklad-33","Příklad 3.3",[724,57364,57365,57367,57368,57398,57399,2507,57414,2521,57427,2535,57440,57454],{},[38,57366,55832],{}," Pro ",[883,57369,57371],{"className":57370},[886],[888,57372,57373],{"xmlns":890},[892,57374,57375,57395],{},[895,57376,57377,57379,57381,57383,57385,57387,57389],{},[898,57378,2623],{},[898,57380,3840],{},[1846,57382,1848],{},[1979,57384,2938],{},[898,57386,2638],{},[1846,57388,2075],{},[1974,57390,57391,57393],{},[898,57392,2638],{},[1979,57394,1981],{},[902,57396,57397],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,57400,57402],{"className":57401},[886],[888,57403,57404],{"xmlns":890},[892,57405,57406,57412],{},[895,57407,57408,57410],{},[898,57409,2623],{},[898,57411,3840],{},[902,57413,3940],{"encoding":904},[883,57415,57417],{"className":57416},[886],[888,57418,57419],{"xmlns":890},[892,57420,57421,57425],{},[895,57422,57423],{},[898,57424,2638],{},[902,57426,2638],{"encoding":904},[883,57428,57430],{"className":57429},[886],[888,57431,57432],{"xmlns":890},[892,57433,57434,57438],{},[895,57435,57436],{},[1979,57437,2974],{},[902,57439,2974],{"encoding":904},[883,57441,57443],{"className":57442},[886],[888,57444,57445],{"xmlns":890},[892,57446,57447,57452],{},[895,57448,57449],{},[1979,57450,57451],{},"63",[902,57453,57451],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,57456,57457,2053,57459,57484,57485,1343,57503,2554],{},[38,57458,22615],{},[883,57460,57462],{"className":57461},[886],[888,57463,57464],{"xmlns":890},[892,57465,57466,57482],{},[895,57467,57468,57470,57472,57474,57476,57478,57480],{},[898,57469,2667],{},[898,57471,3840],{},[1846,57473,1848],{},[1979,57475,2938],{},[1846,57477,2075],{},[1979,57479,1981],{},[898,57481,2638],{},[902,57483,11282],{"encoding":904},", tedy při ",[883,57486,57488],{"className":57487},[886],[888,57489,57490],{"xmlns":890},[892,57491,57492,57500],{},[895,57493,57494,57496,57498],{},[898,57495,2638],{},[1846,57497,1848],{},[1979,57499,2974],{},[902,57501,57502],{"encoding":904},"Q = 60",[883,57504,57506],{"className":57505},[886],[888,57507,57508],{"xmlns":890},[892,57509,57510,57520],{},[895,57511,57512,57514,57516,57518],{},[898,57513,2044],{"mathvariant":2226},[898,57515,2638],{},[1846,57517,1848],{},[1979,57519,2023],{},[902,57521,57522],{"encoding":904},"\\mathrm{d}Q = 3",[883,57524,57526],{"className":57525},[886],[888,57527,57528],{"xmlns":890,"display":27911},[892,57529,57530,57561],{},[895,57531,57532,57534,57536,57538,57540,57542,57544,57546,57548,57550,57552,57554,57556,57558],{},[898,57533,2044],{"mathvariant":2226},[898,57535,2623],{},[898,57537,3840],{},[1846,57539,1848],{},[1846,57541,1855],{"stretchy":1854},[1979,57543,2938],{},[1846,57545,2075],{},[1979,57547,3892],{},[1846,57549,1861],{"stretchy":1854},[1846,57551,3025],{},[1979,57553,2023],{},[1846,57555,1848],{},[1846,57557,2075],{},[1979,57559,57560],{},"60.",[902,57562,57563],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,57565,57566,57567,57597,57598,57617],{},"Celkový příjem klesne z ",[883,57568,57570],{"className":57569},[886],[888,57571,57572],{"xmlns":890},[892,57573,57574,57594],{},[895,57575,57576,57578,57580,57582,57584,57586,57588,57590,57592],{},[898,57577,2623],{},[898,57579,3840],{},[1846,57581,1855],{"stretchy":1854},[1979,57583,2974],{},[1846,57585,1861],{"stretchy":1854},[1846,57587,1848],{},[1979,57589,1981],{},[2138,57591,2835],{},[1979,57593,19987],{},[902,57595,57596],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,57599,57601],{"className":57600},[886],[888,57602,57603],{"xmlns":890},[892,57604,57605,57614],{},[895,57606,57607,57609,57611],{},[1979,57608,1981],{},[2138,57610,2835],{},[1979,57612,57613],{},"340",[902,57615,57616],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,57619,57621],{"className":57620},[886],[888,57622,57623],{"xmlns":890,"display":27911},[892,57624,57625,57683],{},[895,57626,57627,57629,57631,57633,57635,57637,57639,57641,57643,57645,57647,57649,57651,57653,57655,57657,57659,57661,57663,57666,57668,57670,57672,57674,57676,57678,57681],{},[898,57628,2738],{"mathvariant":2226},[898,57630,2623],{},[898,57632,3840],{},[1846,57634,1848],{},[898,57636,2623],{},[898,57638,3840],{},[1846,57640,1855],{"stretchy":1854},[1979,57642,57451],{},[1846,57644,1861],{"stretchy":1854},[1846,57646,2075],{},[898,57648,2623],{},[898,57650,3840],{},[1846,57652,1855],{"stretchy":1854},[1979,57654,2974],{},[1846,57656,1861],{"stretchy":1854},[1846,57658,1848],{},[1979,57660,1981],{},[2138,57662,2835],{},[1979,57664,57665],{},"331",[1846,57667,2075],{},[1979,57669,1981],{},[2138,57671,2835],{},[1979,57673,19987],{},[1846,57675,1848],{},[1846,57677,2075],{},[1979,57679,57680],{},"69",[1846,57682,2136],{"separator":2135},[902,57684,57685],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,57687,57688,57689,57704,57705,1734],{},"tj. ",[883,57690,57692],{"className":57691},[886],[888,57693,57694],{"xmlns":890},[892,57695,57696,57702],{},[895,57697,57698,57700],{},[898,57699,2623],{},[898,57701,3840],{},[902,57703,3940],{"encoding":904}," klesne na ",[883,57706,57708],{"className":57707},[886],[888,57709,57710],{"xmlns":890},[892,57711,57712,57720],{},[895,57713,57714,57716,57718],{},[1979,57715,1981],{},[2138,57717,2835],{},[1979,57719,57665],{},[902,57721,57722],{"encoding":904},"2\\,331",[198,57724,57726],{"id":57725},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,57728,57729,57730,10240,57753,31425],{},"Obecně pro lineární poptávku ",[883,57731,57733],{"className":57732},[886],[888,57734,57735],{"xmlns":890},[892,57736,57737,57751],{},[895,57738,57739,57741,57743,57745,57747,57749],{},[898,57740,3783],{},[1846,57742,1848],{},[898,57744,207],{},[898,57746,2638],{},[1846,57748,1945],{},[898,57750,1948],{},[902,57752,36905],{"encoding":904},[883,57754,57756],{"className":57755},[886],[888,57757,57758],{"xmlns":890},[892,57759,57760,57782],{},[895,57761,57762,57764,57766,57768,57770,57776,57778,57780],{},[898,57763,2623],{},[898,57765,3840],{},[1846,57767,1848],{},[898,57769,207],{},[1974,57771,57772,57774],{},[898,57773,2638],{},[1979,57775,1981],{},[1846,57777,1945],{},[898,57779,1948],{},[898,57781,2638],{},[902,57783,57784],{"encoding":904},"TR = aQ^2 + bQ",[883,57786,57788],{"className":57787},[886],[888,57789,57790],{"xmlns":890,"display":27911},[892,57791,57792,57812],{},[895,57793,57794,57796,57798,57800,57802,57804,57806,57808,57810],{},[898,57795,2667],{},[898,57797,3840],{},[1846,57799,1848],{},[1979,57801,1981],{},[898,57803,207],{},[898,57805,2638],{},[1846,57807,1945],{},[898,57809,1948],{},[898,57811,1734],{"mathvariant":2226},[902,57813,57814],{"encoding":904},"MR = 2aQ + b.",[724,57816,57817,57818,57833,57834,57849,57850,57863,57864,9871,57867,57883,57884,57897,57898,57913,57914,57929,57930,57945,57946,2474,57959,57989,57990,58009,58010,58025],{},"Křivky ",[883,57819,57821],{"className":57820},[886],[888,57822,57823],{"xmlns":890},[892,57824,57825,57831],{},[895,57826,57827,57829],{},[898,57828,2667],{},[898,57830,3840],{},[902,57832,6480],{"encoding":904}," a poptávky (resp. ",[883,57835,57837],{"className":57836},[886],[888,57838,57839],{"xmlns":890},[892,57840,57841,57847],{},[895,57842,57843,57845],{},[898,57844,4101],{},[898,57846,3840],{},[902,57848,55290],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,57851,57853],{"className":57852},[886],[888,57854,57855],{"xmlns":890},[892,57856,57857,57861],{},[895,57858,57859],{},[898,57860,1948],{},[902,57862,1948],{"encoding":904},", přičemž ",[38,57865,57866],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,57868,57870],{"className":57869},[886],[888,57871,57872],{"xmlns":890},[892,57873,57874,57880],{},[895,57875,57876,57878],{},[1979,57877,1981],{},[898,57879,207],{},[902,57881,57882],{"encoding":904},"2a"," vs. ",[883,57885,57887],{"className":57886},[886],[888,57888,57889],{"xmlns":890},[892,57890,57891,57895],{},[895,57892,57893],{},[898,57894,207],{},[902,57896,207],{"encoding":904},", obrázek 3.2). ",[883,57899,57901],{"className":57900},[886],[888,57902,57903],{"xmlns":890},[892,57904,57905,57911],{},[895,57906,57907,57909],{},[898,57908,2667],{},[898,57910,3840],{},[902,57912,6480],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,57915,57917],{"className":57916},[886],[888,57918,57919],{"xmlns":890},[892,57920,57921,57927],{},[895,57922,57923,57925],{},[898,57924,2623],{},[898,57926,3840],{},[902,57928,3940],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,57931,57933],{"className":57932},[886],[888,57934,57935],{"xmlns":890},[892,57936,57937,57943],{},[895,57938,57939,57941],{},[898,57940,2667],{},[898,57942,3840],{},[902,57944,6480],{"encoding":904}," osu ",[883,57947,57949],{"className":57948},[886],[888,57950,57951],{"xmlns":890},[892,57952,57953,57957],{},[895,57954,57955],{},[898,57956,2638],{},[902,57958,2638],{"encoding":904},[883,57960,57962],{"className":57961},[886],[888,57963,57964],{"xmlns":890},[892,57965,57966,57986],{},[895,57967,57968,57970,57972,57974],{},[898,57969,2638],{},[1846,57971,1848],{},[1846,57973,2075],{},[2175,57975,57976],{"scriptlevel":2177,"displaystyle":1854},[2179,57977,57978,57980],{},[898,57979,1948],{},[895,57981,57982,57984],{},[1979,57983,1981],{},[898,57985,207],{},[902,57987,57988],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,57991,57993],{"className":57992},[886],[888,57994,57995],{"xmlns":890},[892,57996,57997,58007],{},[895,57998,57999,58001,58003,58005],{},[898,58000,2667],{},[898,58002,3840],{},[1846,58004,1848],{},[1979,58006,2177],{},[902,58008,6930],{"encoding":904},", a dále ",[883,58011,58013],{"className":58012},[886],[888,58014,58015],{"xmlns":890},[892,58016,58017,58023],{},[895,58018,58019,58021],{},[898,58020,2623],{},[898,58022,3840],{},[902,58024,3940],{"encoding":904}," klesá.",[724,58027,58028,58029,58035,58036,58068,58069,58097],{},"V případě ",[38,58030,58031],{},[207,58032,58034],{"className":58033,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,58037,58039],{"className":58038},[886],[888,58040,58041],{"xmlns":890},[892,58042,58043,58065],{},[895,58044,58045,58047,58049,58051,58053,58055,58057,58059],{},[898,58046,3783],{},[1846,58048,1848],{},[898,58050,4029],{},[1846,58052,1855],{"stretchy":1854},[898,58054,2638],{},[1846,58056,1861],{"stretchy":1854},[1846,58058,1848],{},[1974,58060,58061,58063],{},[898,58062,3783],{},[1846,58064,4200],{},[902,58066,58067],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,58070,58072],{"className":58071},[886],[888,58073,58074],{"xmlns":890},[892,58075,58076,58094],{},[895,58077,58078,58080,58082,58084,58086,58088],{},[898,58079,2623],{},[898,58081,3840],{},[1846,58083,1848],{},[898,58085,2638],{},[1846,58087,3025],{},[1974,58089,58090,58092],{},[898,58091,3783],{},[1846,58093,4200],{},[902,58095,58096],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,58099,58101],{"className":58100},[886],[888,58102,58103],{"xmlns":890,"display":27911},[892,58104,58105,58147],{},[895,58106,58107,58109,58111,58113,58115,58117,58119,58125,58127,58129,58143,58145],{},[898,58108,2667],{},[898,58110,3840],{},[1846,58112,1848],{},[898,58114,4101],{},[898,58116,3840],{},[1846,58118,1848],{},[1974,58120,58121,58123],{},[898,58122,3783],{},[1846,58124,4200],{},[5724,58126],{"width":15129},[1846,58128,1855],{"stretchy":1854},[895,58130,58131,58134,58140],{},[2138,58132,58133],{},"obr",[8232,58135,58136,58138],{"accent":2135},[2138,58137,207],{},[1846,58139,24822],{},[2138,58141,58142],{},"zek 3.4",[1846,58144,1861],{"stretchy":1854},[898,58146,1734],{"mathvariant":2226},[902,58148,58149],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,58151,58152],{},[614,58153,58154,58155,1745,58181,58209,58210,58223,58224,58239,58240,3566,58253,1343,58279,3566,58294,1734],{},"Obrázek 3.2: Přímky ",[883,58156,58158],{"className":58157},[886],[888,58159,58160],{"xmlns":890},[892,58161,58162,58178],{},[895,58163,58164,58166,58168,58170,58172,58174,58176],{},[898,58165,4101],{},[898,58167,3840],{},[1846,58169,1848],{},[898,58171,207],{},[898,58173,2638],{},[1846,58175,1945],{},[898,58177,1948],{},[902,58179,58180],{"encoding":904},"AR = aQ + b",[883,58182,58184],{"className":58183},[886],[888,58185,58186],{"xmlns":890},[892,58187,58188,58206],{},[895,58189,58190,58192,58194,58196,58198,58200,58202,58204],{},[898,58191,2667],{},[898,58193,3840],{},[1846,58195,1848],{},[1979,58197,1981],{},[898,58199,207],{},[898,58201,2638],{},[1846,58203,1945],{},[898,58205,1948],{},[902,58207,58208],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,58211,58213],{"className":58212},[886],[888,58214,58215],{"xmlns":890},[892,58216,58217,58221],{},[895,58218,58219],{},[898,58220,1948],{},[902,58222,1948],{"encoding":904}," se svislou osou, ",[883,58225,58227],{"className":58226},[886],[888,58228,58229],{"xmlns":890},[892,58230,58231,58237],{},[895,58232,58233,58235],{},[898,58234,2667],{},[898,58236,3840],{},[902,58238,6480],{"encoding":904}," protíná osu ",[883,58241,58243],{"className":58242},[886],[888,58244,58245],{"xmlns":890},[892,58246,58247,58251],{},[895,58248,58249],{},[898,58250,2638],{},[902,58252,2638],{"encoding":904},[883,58254,58256],{"className":58255},[886],[888,58257,58258],{"xmlns":890},[892,58259,58260,58276],{},[895,58261,58262,58264],{},[1846,58263,2075],{},[2175,58265,58266],{"scriptlevel":2177,"displaystyle":1854},[2179,58267,58268,58270],{},[898,58269,1948],{},[895,58271,58272,58274],{},[1979,58273,1981],{},[898,58275,207],{},[902,58277,58278],{"encoding":904},"-\\tfrac{b}{2a}",[883,58280,58282],{"className":58281},[886],[888,58283,58284],{"xmlns":890},[892,58285,58286,58292],{},[895,58287,58288,58290],{},[898,58289,4101],{},[898,58291,3840],{},[902,58293,55290],{"encoding":904},[883,58295,58297],{"className":58296},[886],[888,58298,58299],{"xmlns":890},[892,58300,58301,58313],{},[895,58302,58303,58305],{},[1846,58304,2075],{},[2175,58306,58307],{"scriptlevel":2177,"displaystyle":1854},[2179,58308,58309,58311],{},[898,58310,1948],{},[898,58312,207],{},[902,58314,58315],{"encoding":904},"-\\tfrac{b}{a}",[724,58317,58318],{},[614,58319,58320,58321,58352,58353,58382,58383,1734],{},"Obrázek 3.3: Parabola ",[883,58322,58324],{"className":58323},[886],[888,58325,58326],{"xmlns":890},[892,58327,58328,58350],{},[895,58329,58330,58332,58334,58336,58338,58344,58346,58348],{},[898,58331,2623],{},[898,58333,3840],{},[1846,58335,1848],{},[898,58337,207],{},[1974,58339,58340,58342],{},[898,58341,2638],{},[1979,58343,1981],{},[1846,58345,1945],{},[898,58347,1948],{},[898,58349,2638],{},[902,58351,57784],{"encoding":904}," s maximem v ",[883,58354,58356],{"className":58355},[886],[888,58357,58358],{"xmlns":890},[892,58359,58360,58380],{},[895,58361,58362,58364,58366,58368],{},[898,58363,2638],{},[1846,58365,1848],{},[1846,58367,2075],{},[2175,58369,58370],{"scriptlevel":2177,"displaystyle":1854},[2179,58371,58372,58374],{},[898,58373,1948],{},[895,58375,58376,58378],{},[1979,58377,1981],{},[898,58379,207],{},[902,58381,57988],{"encoding":904}," a nulou v ",[883,58384,58386],{"className":58385},[886],[888,58387,58388],{"xmlns":890},[892,58389,58390,58406],{},[895,58391,58392,58394,58396,58398],{},[898,58393,2638],{},[1846,58395,1848],{},[1846,58397,2075],{},[2175,58399,58400],{"scriptlevel":2177,"displaystyle":1854},[2179,58401,58402,58404],{},[898,58403,1948],{},[898,58405,207],{},[902,58407,58408],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,58410,58411],{},[614,58412,58413,58414,1734],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,58415,58417],{"className":58416},[886],[888,58418,58419],{"xmlns":890},[892,58420,58421,58441],{},[895,58422,58423,58425,58427,58429,58431,58433,58435],{},[898,58424,4101],{},[898,58426,3840],{},[1846,58428,1848],{},[898,58430,2667],{},[898,58432,3840],{},[1846,58434,1848],{},[1974,58436,58437,58439],{},[898,58438,3783],{},[1846,58440,4200],{},[902,58442,58443],{"encoding":904},"AR = MR = P^*",[115,58445,58447],{"id":58446},"náklady-firmy","Náklady firmy",[198,58449,58451],{"id":58450},"celkové-náklady","Celkové náklady",[724,58453,58454,2053,58456,9871,58471,58474,58475,58488],{},[38,58455,58451],{},[883,58457,58459],{"className":58458},[886],[888,58460,58461],{"xmlns":890},[892,58462,58463,58469],{},[895,58464,58465,58467],{},[898,58466,2623],{},[898,58468,2626],{},[902,58470,3091],{"encoding":904},[38,58472,58473],{},"total cost",") jsou veškeré náklady na realizaci ",[883,58476,58478],{"className":58477},[886],[888,58479,58480],{"xmlns":890},[892,58481,58482,58486],{},[895,58483,58484],{},[898,58485,2638],{},[902,58487,2638],{"encoding":904}," jednotek produkce:",[883,58490,58492],{"className":58491},[886],[888,58493,58494],{"xmlns":890,"display":27911},[892,58495,58496,58551],{},[20599,58497,58498],{"width":27916},[20604,58499,58500,58502,58544,58546],{},[20607,58501],{"width":27921},[20607,58503,58504],{},[895,58505,58506,58508,58510,58512,58514,58516,58518,58520,58522,58524,58526,58528,58530,58532,58534,58536,58538,58540,58542],{},[898,58507,2623],{},[898,58509,2626],{},[1846,58511,1848],{},[898,58513,2623],{},[898,58515,2626],{},[1846,58517,1855],{"stretchy":1854},[898,58519,2638],{},[1846,58521,1861],{"stretchy":1854},[1846,58523,1848],{},[898,58525,10282],{},[898,58527,2626],{},[1846,58529,1945],{},[898,58531,2623],{},[898,58533,40184],{},[898,58535,2626],{},[1846,58537,1855],{"stretchy":1854},[898,58539,2638],{},[1846,58541,1861],{"stretchy":1854},[1846,58543,2136],{"separator":2135},[20607,58545],{"width":27921},[20607,58547,58548],{},[2138,58549,58550],{},"(3.5)",[902,58552,58553],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,58555,4156,58556,58571,58572,9871,58575,11973,58578,58571,58602,9871,58605,58608],{},[883,58557,58559],{"className":58558},[886],[888,58560,58561],{"xmlns":890},[892,58562,58563,58569],{},[895,58564,58565,58567],{},[898,58566,10282],{},[898,58568,2626],{},[902,58570,55336],{"encoding":904}," jsou ",[38,58573,58574],{},"fixní náklady",[38,58576,58577],{},"fixed cost",[883,58579,58581],{"className":58580},[886],[888,58582,58583],{"xmlns":890},[892,58584,58585,58599],{},[895,58586,58587,58589,58591,58593,58595,58597],{},[898,58588,2623],{},[898,58590,40184],{},[898,58592,2626],{},[1846,58594,1855],{"stretchy":1854},[898,58596,2638],{},[1846,58598,1861],{"stretchy":1854},[902,58600,58601],{"encoding":904},"TVC(Q)",[38,58603,58604],{},"celkové variabilní náklady",[38,58606,58607],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,58610,58612],{"id":58611},"průměrné-náklady","Průměrné náklady",[724,58614,58615,2053,58617,9871,58632,58635],{},[38,58616,58612],{},[883,58618,58620],{"className":58619},[886],[888,58621,58622],{"xmlns":890},[892,58623,58624,58630],{},[895,58625,58626,58628],{},[898,58627,4101],{},[898,58629,2626],{},[902,58631,55405],{"encoding":904},[38,58633,58634],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,58637,58639],{"className":58638},[886],[888,58640,58641],{"xmlns":890,"display":27911},[892,58642,58643,58722],{},[20599,58644,58645],{"width":27916},[20604,58646,58647,58649,58715,58717],{},[20607,58648],{"width":27921},[20607,58650,58651],{},[895,58652,58653,58655,58657,58659,58661,58663,58665,58667,58669,58671,58681,58683,58693,58695,58713],{},[898,58654,4101],{},[898,58656,2626],{},[1846,58658,1848],{},[898,58660,4101],{},[898,58662,2626],{},[1846,58664,1855],{"stretchy":1854},[898,58666,2638],{},[1846,58668,1861],{"stretchy":1854},[1846,58670,1848],{},[2179,58672,58673,58679],{},[895,58674,58675,58677],{},[898,58676,2623],{},[898,58678,2626],{},[898,58680,2638],{},[1846,58682,1848],{},[2179,58684,58685,58691],{},[895,58686,58687,58689],{},[898,58688,10282],{},[898,58690,2626],{},[898,58692,2638],{},[1846,58694,1945],{},[2179,58696,58697,58711],{},[895,58698,58699,58701,58703,58705,58707,58709],{},[898,58700,2623],{},[898,58702,40184],{},[898,58704,2626],{},[1846,58706,1855],{"stretchy":1854},[898,58708,2638],{},[1846,58710,1861],{"stretchy":1854},[898,58712,2638],{},[1846,58714,2136],{"separator":2135},[20607,58716],{"width":27921},[20607,58718,58719],{},[2138,58720,58721],{},"(3.6)",[902,58723,58724],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,58726,4156,58727,58571,58751,2053,58754,9871,58771,11973,58774,58571,58806,2053,58809,9871,58826,2999],{},[883,58728,58730],{"className":58729},[886],[888,58731,58732],{"xmlns":890},[892,58733,58734,58748],{},[895,58735,58736],{},[2175,58737,58738],{"scriptlevel":2177,"displaystyle":1854},[2179,58739,58740,58746],{},[895,58741,58742,58744],{},[898,58743,10282],{},[898,58745,2626],{},[898,58747,2638],{},[902,58749,58750],{"encoding":904},"\\tfrac{FC}{Q}",[38,58752,58753],{},"průměrné fixní náklady",[883,58755,58757],{"className":58756},[886],[888,58758,58759],{"xmlns":890},[892,58760,58761,58769],{},[895,58762,58763,58765,58767],{},[898,58764,4101],{},[898,58766,10282],{},[898,58768,2626],{},[902,58770,55372],{"encoding":904},[38,58772,58773],{},"average fixed cost",[883,58775,58777],{"className":58776},[886],[888,58778,58779],{"xmlns":890},[892,58780,58781,58803],{},[895,58782,58783],{},[2175,58784,58785],{"scriptlevel":2177,"displaystyle":1854},[2179,58786,58787,58801],{},[895,58788,58789,58791,58793,58795,58797,58799],{},[898,58790,2623],{},[898,58792,40184],{},[898,58794,2626],{},[1846,58796,1855],{"stretchy":1854},[898,58798,2638],{},[1846,58800,1861],{"stretchy":1854},[898,58802,2638],{},[902,58804,58805],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,58807,58808],{},"průměrné variabilní náklady",[883,58810,58812],{"className":58811},[886],[888,58813,58814],{"xmlns":890},[892,58815,58816,58824],{},[895,58817,58818,58820,58822],{},[898,58819,4101],{},[898,58821,40184],{},[898,58823,2626],{},[902,58825,55156],{"encoding":904},[38,58827,58828],{},"average variable cost",[883,58830,58832],{"className":58831},[886],[888,58833,58834],{"xmlns":890,"display":27911},[892,58835,58836,58895],{},[20599,58837,58838],{"width":27916},[20604,58839,58840,58842,58888,58890],{},[20607,58841],{"width":27921},[20607,58843,58844],{},[895,58845,58846,58848,58850,58852,58854,58856,58858,58860,58862,58864,58866,58868,58886],{},[898,58847,4101],{},[898,58849,40184],{},[898,58851,2626],{},[1846,58853,1848],{},[898,58855,4101],{},[898,58857,40184],{},[898,58859,2626],{},[1846,58861,1855],{"stretchy":1854},[898,58863,2638],{},[1846,58865,1861],{"stretchy":1854},[1846,58867,1848],{},[2179,58869,58870,58884],{},[895,58871,58872,58874,58876,58878,58880,58882],{},[898,58873,2623],{},[898,58875,40184],{},[898,58877,2626],{},[1846,58879,1855],{"stretchy":1854},[898,58881,2638],{},[1846,58883,1861],{"stretchy":1854},[898,58885,2638],{},[898,58887,1734],{"mathvariant":2226},[20607,58889],{"width":27921},[20607,58891,58892],{},[2138,58893,58894],{},"(3.7)",[902,58896,58897],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[37193,58899,58901],{"id":58900},"příklad-34","Příklad 3.4",[724,58903,58904,57367,58906,1745,58931,55870,58955,1745,58970,58985,58986,1734],{},[38,58905,55832],{},[883,58907,58909],{"className":58908},[886],[888,58910,58911],{"xmlns":890},[892,58912,58913,58928],{},[895,58914,58915,58917,58919,58921,58923,58925],{},[898,58916,10282],{},[898,58918,2626],{},[1846,58920,1848],{},[1979,58922,2128],{},[2138,58924,2835],{},[1979,58926,58927],{},"000",[902,58929,58930],{"encoding":904},"FC = 1\\,000",[883,58932,58934],{"className":58933},[886],[888,58935,58936],{"xmlns":890},[892,58937,58938,58952],{},[895,58939,58940,58942,58944,58946,58948,58950],{},[898,58941,2623],{},[898,58943,40184],{},[898,58945,2626],{},[1846,58947,1848],{},[1979,58949,2201],{},[898,58951,2638],{},[902,58953,58954],{"encoding":904},"TVC = 4Q",[883,58956,58958],{"className":58957},[886],[888,58959,58960],{"xmlns":890},[892,58961,58962,58968],{},[895,58963,58964,58966],{},[898,58965,2623],{},[898,58967,2626],{},[902,58969,3091],{"encoding":904},[883,58971,58973],{"className":58972},[886],[888,58974,58975],{"xmlns":890},[892,58976,58977,58983],{},[895,58978,58979,58981],{},[898,58980,4101],{},[898,58982,2626],{},[902,58984,55405],{"encoding":904}," a jejich chování s rostoucím ",[883,58987,58989],{"className":58988},[886],[888,58990,58991],{"xmlns":890},[892,58992,58993,58997],{},[895,58994,58995],{},[898,58996,2638],{},[902,58998,2638],{"encoding":904},[724,59000,59001,2053,59003,1745,59033,59069,59070,4204,59083,59098,59099,2554],{},[38,59002,22615],{},[883,59004,59006],{"className":59005},[886],[888,59007,59008],{"xmlns":890},[892,59009,59010,59030],{},[895,59011,59012,59014,59016,59018,59020,59022,59024,59026,59028],{},[898,59013,2623],{},[898,59015,2626],{},[1846,59017,1848],{},[1979,59019,2128],{},[2138,59021,2835],{},[1979,59023,58927],{},[1846,59025,1945],{},[1979,59027,2201],{},[898,59029,2638],{},[902,59031,59032],{"encoding":904},"TC = 1\\,000 + 4Q",[883,59034,59036],{"className":59035},[886],[888,59037,59038],{"xmlns":890},[892,59039,59040,59066],{},[895,59041,59042,59044,59046,59048,59062,59064],{},[898,59043,4101],{},[898,59045,2626],{},[1846,59047,1848],{},[2175,59049,59050],{"scriptlevel":2177,"displaystyle":1854},[2179,59051,59052,59060],{},[895,59053,59054,59056,59058],{},[1979,59055,2128],{},[2138,59057,2835],{},[1979,59059,58927],{},[898,59061,2638],{},[1846,59063,1945],{},[1979,59065,2201],{},[902,59067,59068],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,59071,59073],{"className":59072},[886],[888,59074,59075],{"xmlns":890},[892,59076,59077,59081],{},[895,59078,59079],{},[898,59080,2638],{},[902,59082,2638],{"encoding":904},[883,59084,59086],{"className":59085},[886],[888,59087,59088],{"xmlns":890},[892,59089,59090,59096],{},[895,59091,59092,59094],{},[898,59093,4101],{},[898,59095,2626],{},[902,59097,55405],{"encoding":904}," blíží ",[883,59100,59102],{"className":59101},[886],[888,59103,59104],{"xmlns":890},[892,59105,59106,59110],{},[895,59107,59108],{},[1979,59109,2201],{},[902,59111,2201],{"encoding":904},[883,59113,59115],{"className":59114},[886],[888,59116,59117],{"xmlns":890,"display":27911},[892,59118,59119,59165],{},[895,59120,59121,59138,59160,59162],{},[39741,59122,59123,59130],{},[895,59124,59125,59128],{},[898,59126,59127],{},"lim",[1846,59129,56045],{},[895,59131,59132,59134,59136],{},[898,59133,2638],{},[1846,59135,2971],{},[898,59137,6143],{"mathvariant":2226},[895,59139,59140,59142,59154,59156,59158],{},[1846,59141,1855],{"fence":2135},[2179,59143,59144,59152],{},[895,59145,59146,59148,59150],{},[1979,59147,2128],{},[2138,59149,2835],{},[1979,59151,58927],{},[898,59153,2638],{},[1846,59155,1945],{},[1979,59157,2201],{},[1846,59159,1861],{"fence":2135},[1846,59161,1848],{},[1979,59163,59164],{},"4.",[902,59166,59167],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,59169,59170,59208,59209,1734],{},[883,59171,59173],{"className":59172},[886],[888,59174,59175],{"xmlns":890},[892,59176,59177,59205],{},[895,59178,59179,59181,59183,59185,59187,59201,59203],{},[898,59180,4101],{},[898,59182,10282],{},[898,59184,2626],{},[1846,59186,1848],{},[2175,59188,59189],{"scriptlevel":2177,"displaystyle":1854},[2179,59190,59191,59199],{},[895,59192,59193,59195,59197],{},[1979,59194,2128],{},[2138,59196,2835],{},[1979,59198,58927],{},[898,59200,2638],{},[1846,59202,2971],{},[1979,59204,2177],{},[902,59206,59207],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,59210,59212],{"className":59211},[886],[888,59213,59214],{"xmlns":890},[892,59215,59216,59220],{},[895,59217,59218],{},[898,59219,2638],{},[902,59221,2638],{"encoding":904},[724,59223,59224],{},[614,59225,59226,59227,59256,59257,1734],{},"Obrázek 3.5: Přímka ",[883,59228,59230],{"className":59229},[886],[888,59231,59232],{"xmlns":890},[892,59233,59234,59254],{},[895,59235,59236,59238,59240,59242,59244,59246,59248,59250,59252],{},[898,59237,2623],{},[898,59239,2626],{},[1846,59241,1848],{},[1979,59243,2128],{},[2138,59245,2835],{},[1979,59247,58927],{},[1846,59249,1945],{},[1979,59251,2201],{},[898,59253,2638],{},[902,59255,59032],{"encoding":904}," protínající svislou osu ve výši ",[883,59258,59260],{"className":59259},[886],[888,59261,59262],{"xmlns":890},[892,59263,59264,59278],{},[895,59265,59266,59268,59270,59272,59274,59276],{},[898,59267,10282],{},[898,59269,2626],{},[1846,59271,1848],{},[1979,59273,2128],{},[2138,59275,2835],{},[1979,59277,58927],{},[902,59279,58930],{"encoding":904},[724,59281,59282],{},[614,59283,59284,59285,59320,59321,1734],{},"Obrázek 3.6: Hyperbola ",[883,59286,59288],{"className":59287},[886],[888,59289,59290],{"xmlns":890},[892,59291,59292,59318],{},[895,59293,59294,59296,59298,59300,59314,59316],{},[898,59295,4101],{},[898,59297,2626],{},[1846,59299,1848],{},[2175,59301,59302],{"scriptlevel":2177,"displaystyle":1854},[2179,59303,59304,59312],{},[895,59305,59306,59308,59310],{},[1979,59307,2128],{},[2138,59309,2835],{},[1979,59311,58927],{},[898,59313,2638],{},[1846,59315,1945],{},[1979,59317,2201],{},[902,59319,59068],{"encoding":904}," s vodorovnou asymptotou ",[883,59322,59324],{"className":59323},[886],[888,59325,59326],{"xmlns":890},[892,59327,59328,59338],{},[895,59329,59330,59332,59334,59336],{},[898,59331,4101],{},[898,59333,2626],{},[1846,59335,1848],{},[1979,59337,2201],{},[902,59339,59340],{"encoding":904},"AC = 4",[724,59342,59343],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,59345,59347],{"className":59346},[886],[888,59348,59349],{"xmlns":890,"display":27911},[892,59350,59351,59377],{},[895,59352,59353,59355,59357,59359,59361,59363,59365,59367,59369,59371,59373,59375],{},[898,59354,2623],{},[898,59356,40184],{},[898,59358,2626],{},[1846,59360,1848],{},[898,59362,2638],{},[1846,59364,3025],{},[898,59366,40184],{},[898,59368,2626],{},[1846,59370,1855],{"stretchy":1854},[898,59372,2638],{},[1846,59374,1861],{"stretchy":1854},[1846,59376,2136],{"separator":2135},[902,59378,59379],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,59381,4156,59382,58571,59410,59413,59414,59444],{},[883,59383,59385],{"className":59384},[886],[888,59386,59387],{"xmlns":890},[892,59388,59389,59407],{},[895,59390,59391,59393,59395,59397,59399,59401,59403,59405],{},[898,59392,40184],{},[898,59394,2626],{},[1846,59396,1848],{},[898,59398,40184],{},[898,59400,2626],{},[1846,59402,1855],{"stretchy":1854},[898,59404,2638],{},[1846,59406,1861],{"stretchy":1854},[902,59408,59409],{"encoding":904},"VC = VC(Q)",[38,59411,59412],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,59415,59417],{"className":59416},[886],[888,59418,59419],{"xmlns":890},[892,59420,59421,59441],{},[895,59422,59423,59425,59427,59429,59431,59433,59435,59437,59439],{},[898,59424,2623],{},[898,59426,40184],{},[898,59428,2626],{},[1846,59430,1855],{"stretchy":1854},[898,59432,2638],{},[1846,59434,1861],{"stretchy":1854},[1846,59436,1848],{},[898,59438,207],{},[898,59440,2638],{},[902,59442,59443],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,59446,59448],{"className":59447},[886],[888,59449,59450],{"xmlns":890,"display":27911},[892,59451,59452,59472],{},[895,59453,59454,59456,59458,59460,59462,59464,59466,59468,59470],{},[898,59455,2623],{},[898,59457,2626],{},[1846,59459,1848],{},[898,59461,10282],{},[898,59463,2626],{},[1846,59465,1945],{},[898,59467,207],{},[898,59469,2638],{},[898,59471,1734],{"mathvariant":2226},[902,59473,59474],{"encoding":904},"TC = FC + aQ.",[724,59476,59477,59478,59493,59494,59509,59510,59533,59534,59568,59569,59320,59582,59595,59596,1745,59644,59688,59689,1734],{},"Křivkou ",[883,59479,59481],{"className":59480},[886],[888,59482,59483],{"xmlns":890},[892,59484,59485,59491],{},[895,59486,59487,59489],{},[898,59488,2623],{},[898,59490,2626],{},[902,59492,3091],{"encoding":904}," je přímka se svislým průsečíkem ",[883,59495,59497],{"className":59496},[886],[888,59498,59499],{"xmlns":890},[892,59500,59501,59507],{},[895,59502,59503,59505],{},[898,59504,10282],{},[898,59506,2626],{},[902,59508,55336],{"encoding":904}," a sklonem ",[883,59511,59513],{"className":59512},[886],[888,59514,59515],{"xmlns":890},[892,59516,59517,59530],{},[895,59518,59519,59522,59524,59526,59528],{},[898,59520,59521],{},"tan",[1846,59523,56045],{},[898,59525,18707],{},[1846,59527,1848],{},[898,59529,207],{},[902,59531,59532],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,59535,59537],{"className":59536},[886],[888,59538,59539],{"xmlns":890},[892,59540,59541,59565],{},[895,59542,59543,59545,59547,59549,59561,59563],{},[898,59544,4101],{},[898,59546,2626],{},[1846,59548,1848],{},[2175,59550,59551],{"scriptlevel":2177,"displaystyle":1854},[2179,59552,59553,59559],{},[895,59554,59555,59557],{},[898,59556,10282],{},[898,59558,2626],{},[898,59560,2638],{},[1846,59562,1945],{},[898,59564,207],{},[902,59566,59567],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,59570,59572],{"className":59571},[886],[888,59573,59574],{"xmlns":890},[892,59575,59576,59580],{},[895,59577,59578],{},[898,59579,9641],{},[902,59581,9641],{"encoding":904},[883,59583,59585],{"className":59584},[886],[888,59586,59587],{"xmlns":890},[892,59588,59589,59593],{},[895,59590,59591],{},[898,59592,207],{},[902,59594,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,59597,59599],{"className":59598},[886],[888,59600,59601],{"xmlns":890},[892,59602,59603,59641],{},[895,59604,59605,59625,59637,59639],{},[2122,59606,59607,59613],{},[895,59608,59609,59611],{},[898,59610,59127],{},[1846,59612,56045],{},[895,59614,59615,59617,59619],{},[898,59616,2638],{},[1846,59618,2971],{},[1974,59620,59621,59623],{},[1979,59622,2177],{},[1846,59624,1945],{},[2175,59626,59627],{"scriptlevel":2177,"displaystyle":1854},[2179,59628,59629,59635],{},[895,59630,59631,59633],{},[898,59632,10282],{},[898,59634,2626],{},[898,59636,2638],{},[1846,59638,1848],{},[898,59640,6143],{"mathvariant":2226},[902,59642,59643],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,59645,59647],{"className":59646},[886],[888,59648,59649],{"xmlns":890},[892,59650,59651,59685],{},[895,59652,59653,59669,59681,59683],{},[2122,59654,59655,59661],{},[895,59656,59657,59659],{},[898,59658,59127],{},[1846,59660,56045],{},[895,59662,59663,59665,59667],{},[898,59664,2638],{},[1846,59666,2971],{},[898,59668,6143],{"mathvariant":2226},[2175,59670,59671],{"scriptlevel":2177,"displaystyle":1854},[2179,59672,59673,59679],{},[895,59674,59675,59677],{},[898,59676,10282],{},[898,59678,2626],{},[898,59680,2638],{},[1846,59682,1848],{},[1979,59684,2177],{},[902,59686,59687],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,59690,59692],{"className":59691},[886],[888,59693,59694],{"xmlns":890},[892,59695,59696,59702],{},[895,59697,59698,59700],{},[898,59699,4101],{},[898,59701,2626],{},[902,59703,55405],{"encoding":904},[724,59705,59706],{},[614,59707,59708,59709,59724,59725,59740,59741,1734],{},"Obrázek 3.7: Přímka ",[883,59710,59712],{"className":59711},[886],[888,59713,59714],{"xmlns":890},[892,59715,59716,59722],{},[895,59717,59718,59720],{},[898,59719,2623],{},[898,59721,2626],{},[902,59723,3091],{"encoding":904}," s osovým průsečíkem ve výši ",[883,59726,59728],{"className":59727},[886],[888,59729,59730],{"xmlns":890},[892,59731,59732,59738],{},[895,59733,59734,59736],{},[898,59735,10282],{},[898,59737,2626],{},[902,59739,55336],{"encoding":904}," a se sklonem ",[883,59742,59744],{"className":59743},[886],[888,59745,59746],{"xmlns":890},[892,59747,59748,59760],{},[895,59749,59750,59752,59754,59756,59758],{},[898,59751,59521],{},[1846,59753,56045],{},[898,59755,18707],{},[1846,59757,1848],{},[898,59759,207],{},[902,59761,59532],{"encoding":904},[724,59763,59764],{},[614,59765,59766,59767,59782,59783,1734],{},"Obrázek 3.8: Klesající hyperbola ",[883,59768,59770],{"className":59769},[886],[888,59771,59772],{"xmlns":890},[892,59773,59774,59780],{},[895,59775,59776,59778],{},[898,59777,4101],{},[898,59779,2626],{},[902,59781,55405],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,59784,59786],{"className":59785},[886],[888,59787,59788],{"xmlns":890},[892,59789,59790,59794],{},[895,59791,59792],{},[898,59793,207],{},[902,59795,207],{"encoding":904},[198,59797,59799],{"id":59798},"mezní-náklady","Mezní náklady",[724,59801,59802,2053,59804,9871,59819,59822,59823,59826],{},[38,59803,59799],{},[883,59805,59807],{"className":59806},[886],[888,59808,59809],{"xmlns":890},[892,59810,59811,59817],{},[895,59812,59813,59815],{},[898,59814,2667],{},[898,59816,2626],{},[902,59818,55137],{"encoding":904},[38,59820,59821],{},"marginal cost",") jsou ",[207,59824,1145],{"className":59825,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,59828,59830],{"className":59829},[886],[888,59831,59832],{"xmlns":890,"display":27911},[892,59833,59834,59903],{},[20599,59835,59836],{"width":27916},[20604,59837,59838,59840,59896,59898],{},[20607,59839],{"width":27921},[20607,59841,59842],{},[895,59843,59844,59846,59848,59850,59852,59854,59856,59858,59860,59862,59878,59880,59882,59888,59890,59892,59894],{},[898,59845,2667],{},[898,59847,2626],{},[1846,59849,1848],{},[898,59851,2667],{},[898,59853,2626],{},[1846,59855,1855],{"stretchy":1854},[898,59857,2638],{},[1846,59859,1861],{"stretchy":1854},[1846,59861,1848],{},[2179,59863,59864,59872],{},[895,59865,59866,59868,59870],{},[898,59867,2044],{"mathvariant":2226},[898,59869,2623],{},[898,59871,2626],{},[895,59873,59874,59876],{},[898,59875,2044],{"mathvariant":2226},[898,59877,2638],{},[1846,59879,1848],{},[898,59881,2623],{},[1974,59883,59884,59886],{},[898,59885,2626],{},[1846,59887,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,59889,1855],{"stretchy":1854},[898,59891,2638],{},[1846,59893,1861],{"stretchy":1854},[898,59895,1734],{"mathvariant":2226},[20607,59897],{"width":27921},[20607,59899,59900],{},[2138,59901,59902],{},"(3.8)",[902,59904,59905],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[1639,59907,59908],{},[724,59909,59910,59912,59913,59939,59940,59957,59958,1734],{},[883,59911,4001],{}," Intuice — „kolik stojí další kus\"\n",[883,59914,59916],{"className":59915},[886],[888,59917,59918],{"xmlns":890},[892,59919,59920,59936],{},[895,59921,59922,59924,59926,59928,59934],{},[898,59923,2667],{},[898,59925,2626],{},[1846,59927,1855],{"stretchy":1854},[1974,59929,59930,59932],{},[898,59931,2638],{},[1846,59933,4200],{},[1846,59935,1861],{"stretchy":1854},[902,59937,59938],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,59941,59943],{"className":59942},[886],[888,59944,59945],{"xmlns":890},[892,59946,59947,59955],{},[895,59948,59949],{},[1974,59950,59951,59953],{},[898,59952,2638],{},[1846,59954,4200],{},[902,59956,29689],{"encoding":904},". Formálně ",[883,59959,59961],{"className":59960},[886],[888,59962,59963],{"xmlns":890},[892,59964,59965,60017],{},[895,59966,59967,59969,59971,59973,59979,59981,59983,59985,59987,59989,59995,59997,59999,60001,60003,60005,60007,60009,60015],{},[898,59968,2667],{},[898,59970,2626],{},[1846,59972,1855],{"stretchy":1854},[1974,59974,59975,59977],{},[898,59976,2638],{},[1846,59978,4200],{},[1846,59980,1861],{"stretchy":1854},[1846,59982,1650],{},[898,59984,2623],{},[898,59986,2626],{},[1846,59988,1855],{"stretchy":1854},[1974,59990,59991,59993],{},[898,59992,2638],{},[1846,59994,4200],{},[1846,59996,1945],{},[1979,59998,2128],{},[1846,60000,1861],{"stretchy":1854},[1846,60002,2075],{},[898,60004,2623],{},[898,60006,2626],{},[1846,60008,1855],{"stretchy":1854},[1974,60010,60011,60013],{},[898,60012,2638],{},[1846,60014,4200],{},[1846,60016,1861],{"stretchy":1854},[902,60018,60019],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,60021,60022,60023,2554],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,60024,60026],{"className":60025},[886],[888,60027,60028],{"xmlns":890},[892,60029,60030,60038],{},[895,60031,60032,60034,60036],{},[898,60033,2738],{"mathvariant":2226},[898,60035,2623],{},[898,60037,2626],{},[902,60039,60040],{"encoding":904},"\\Delta TC",[883,60042,60044],{"className":60043},[886],[888,60045,60046],{"xmlns":890,"display":27911},[892,60047,60048,60117],{},[20599,60049,60050],{"width":27916},[20604,60051,60052,60054,60110,60112],{},[20607,60053],{"width":27921},[20607,60055,60056],{},[895,60057,60058,60060,60062,60064,60066,60068,60070,60072,60074,60076,60078,60080,60082,60084,60090,60092,60094,60096,60098,60100,60102,60104,60106,60108],{},[898,60059,2738],{"mathvariant":2226},[898,60061,2623],{},[898,60063,2626],{},[2138,60065,3830],{},[1846,60067,1650],{},[2138,60069,3830],{},[898,60071,2044],{"mathvariant":2226},[898,60073,2623],{},[898,60075,2626],{},[1846,60077,1848],{},[1846,60079,1855],{"stretchy":1854},[898,60081,2623],{},[898,60083,2626],{},[1974,60085,60086,60088],{},[1846,60087,1861],{"stretchy":1854},[1846,60089,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[2138,60091,2835],{},[898,60093,2044],{"mathvariant":2226},[898,60095,2638],{},[1846,60097,1848],{},[898,60099,2667],{},[898,60101,2626],{},[2138,60103,2835],{},[898,60105,2044],{"mathvariant":2226},[898,60107,2638],{},[1846,60109,2136],{"separator":2135},[20607,60111],{"width":27921},[20607,60113,60114],{},[2138,60115,60116],{},"(3.9)",[902,60118,60119],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,60121,57156],{},[883,60123,60125],{"className":60124},[886],[888,60126,60127],{"xmlns":890,"display":27911},[892,60128,60129,60227],{},[895,60130,60131,60169,60171,60173,60175,60197,60199,60225],{},[895,60132,60133,60135,60141,60143,60149,60152,60158,60161],{},[2138,60134,57170],{},[8232,60136,60137,60139],{"accent":2135},[2138,60138,45577],{},[1846,60140,24903],{},[2138,60142,57179],{},[8232,60144,60145,60147],{"accent":2135},[2138,60146,1844],{},[1846,60148,24822],{},[2138,60150,60151],{},"ch n",[8232,60153,60154,60156],{"accent":2135},[2138,60155,207],{},[1846,60157,24822],{},[2138,60159,60160],{},"klad",[8232,60162,60163,60166],{"accent":2135},[2138,60164,60165],{},"u",[1846,60167,60168],{},"˚",[2138,60170,3830],{},[1846,60172,1650],{},[2138,60174,3830],{},[895,60176,60177,60179,60185,60188,60194],{},[2138,60178,57214],{},[8232,60180,60181,60183],{"accent":2135},[2138,60182,24891],{},[1846,60184,24822],{},[2138,60186,60187],{}," n",[8232,60189,60190,60192],{"accent":2135},[2138,60191,207],{},[1846,60193,24822],{},[2138,60195,60196],{},"klady",[1846,60198,57241],{},[895,60200,60201,60203,60209,60211,60217,60219],{},[2138,60202,57170],{},[8232,60204,60205,60207],{"accent":2135},[2138,60206,45577],{},[1846,60208,24903],{},[2138,60210,57254],{},[8232,60212,60213,60215],{"accent":2135},[2138,60214,9440],{},[1846,60216,24903],{},[2138,60218,57263],{},[8232,60220,60221,60223],{"accent":2135},[2138,60222,24891],{},[1846,60224,24822],{},[898,60226,1734],{"mathvariant":2226},[902,60228,60229],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[37193,60231,60233],{"id":60232},"příklad-35","Příklad 3.5",[724,60235,60236,57367,60238,55870,60274,60289,60290,60305,60306,2521,60319,2535,60332,60345,60346,2535,60359,1734],{},[38,60237,55832],{},[883,60239,60241],{"className":60240},[886],[888,60242,60243],{"xmlns":890},[892,60244,60245,60271],{},[895,60246,60247,60249,60251,60253,60255,60257,60259,60261,60263,60265],{},[898,60248,2623],{},[898,60250,2626],{},[1846,60252,1848],{},[1979,60254,8223],{},[1846,60256,1945],{},[1979,60258,2085],{},[898,60260,2638],{},[1846,60262,1945],{},[1979,60264,1981],{},[1974,60266,60267,60269],{},[898,60268,2638],{},[1979,60270,1981],{},[902,60272,60273],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,60275,60277],{"className":60276},[886],[888,60278,60279],{"xmlns":890},[892,60280,60281,60287],{},[895,60282,60283,60285],{},[898,60284,2667],{},[898,60286,2626],{},[902,60288,55137],{"encoding":904}," a odhadněte změny ",[883,60291,60293],{"className":60292},[886],[888,60294,60295],{"xmlns":890},[892,60296,60297,60303],{},[895,60298,60299,60301],{},[898,60300,2623],{},[898,60302,2626],{},[902,60304,3091],{"encoding":904}," při změnách ",[883,60307,60309],{"className":60308},[886],[888,60310,60311],{"xmlns":890},[892,60312,60313,60317],{},[895,60314,60315],{},[898,60316,2638],{},[902,60318,2638],{"encoding":904},[883,60320,60322],{"className":60321},[886],[888,60323,60324],{"xmlns":890},[892,60325,60326,60330],{},[895,60327,60328],{},[1979,60329,36089],{},[902,60331,36089],{"encoding":904},[883,60333,60335],{"className":60334},[886],[888,60336,60337],{"xmlns":890},[892,60338,60339,60343],{},[895,60340,60341],{},[1979,60342,41707],{},[902,60344,41707],{"encoding":904}," a z ",[883,60347,60349],{"className":60348},[886],[888,60350,60351],{"xmlns":890},[892,60352,60353,60357],{},[895,60354,60355],{},[1979,60356,36089],{},[902,60358,36089],{"encoding":904},[883,60360,60362],{"className":60361},[886],[888,60363,60364],{"xmlns":890},[892,60365,60366,60370],{},[895,60367,60368],{},[1979,60369,3357],{},[902,60371,3357],{"encoding":904},[724,60373,60374,2053,60376,2776,60402,1343,60429,60456,60457,60472,60473,60488,60489,60516,60517,60537,60538,20376,60559,60615,60616,2521,60629,2535,60642,7948,60655,1734],{},[38,60375,22615],{},[883,60377,60379],{"className":60378},[886],[888,60380,60381],{"xmlns":890},[892,60382,60383,60399],{},[895,60384,60385,60387,60389,60391,60393,60395,60397],{},[898,60386,2667],{},[898,60388,2626],{},[1846,60390,1848],{},[1979,60392,2085],{},[1846,60394,1945],{},[1979,60396,2201],{},[898,60398,2638],{},[902,60400,60401],{"encoding":904},"MC = 6 + 4Q",[883,60403,60405],{"className":60404},[886],[888,60406,60407],{"xmlns":890},[892,60408,60409,60426],{},[895,60410,60411,60413,60415,60417,60419,60421,60423],{},[898,60412,2667],{},[898,60414,2626],{},[1846,60416,1855],{"stretchy":1854},[1979,60418,36089],{},[1846,60420,1861],{"stretchy":1854},[1846,60422,1848],{},[1979,60424,60425],{},"66",[902,60427,60428],{"encoding":904},"MC(15) = 66",[883,60430,60432],{"className":60431},[886],[888,60433,60434],{"xmlns":890},[892,60435,60436,60453],{},[895,60437,60438,60440,60442,60444,60446,60448,60450],{},[898,60439,2667],{},[898,60441,2626],{},[1846,60443,1855],{"stretchy":1854},[1979,60445,8881],{},[1846,60447,1861],{"stretchy":1854},[1846,60449,1848],{},[1979,60451,60452],{},"86",[902,60454,60455],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,60458,60460],{"className":60459},[886],[888,60461,60462],{"xmlns":890},[892,60463,60464,60470],{},[895,60465,60466,60468],{},[898,60467,2623],{},[898,60469,2626],{},[902,60471,3091],{"encoding":904}," zvyšuje (",[883,60474,60476],{"className":60475},[886],[888,60477,60478],{"xmlns":890},[892,60479,60480,60486],{},[895,60481,60482,60484],{},[898,60483,2667],{},[898,60485,2626],{},[902,60487,55137],{"encoding":904}," je rostoucí). Z ",[883,60490,60492],{"className":60491},[886],[888,60493,60494],{"xmlns":890},[892,60495,60496,60513],{},[895,60497,60498,60500,60502,60504,60506,60508,60510],{},[898,60499,2623],{},[898,60501,2626],{},[1846,60503,1855],{"stretchy":1854},[1979,60505,36089],{},[1846,60507,1861],{"stretchy":1854},[1846,60509,1848],{},[1979,60511,60512],{},"740",[902,60514,60515],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,60518,60520],{"className":60519},[886],[888,60521,60522],{"xmlns":890},[892,60523,60524,60534],{},[895,60525,60526,60528,60530,60532],{},[898,60527,2044],{"mathvariant":2226},[898,60529,2638],{},[1846,60531,1848],{},[1979,60533,2128],{},[902,60535,60536],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,60539,60541],{"className":60540},[886],[888,60542,60543],{"xmlns":890},[892,60544,60545,60556],{},[895,60546,60547,60549,60551,60553],{},[898,60548,2623],{},[898,60550,2626],{},[1846,60552,1650],{},[1979,60554,60555],{},"806",[902,60557,60558],{"encoding":904},"TC \\approx 806",[883,60560,60562],{"className":60561},[886],[888,60563,60564],{"xmlns":890},[892,60565,60566,60612],{},[895,60567,60568,60570,60572,60574,60576,60578,60580,60582,60584,60586,60588,60590,60592,60594,60596,60598,60600,60603,60605,60607,60609],{},[898,60569,2738],{"mathvariant":2226},[898,60571,2623],{},[898,60573,2626],{},[1846,60575,1848],{},[898,60577,2623],{},[898,60579,2626],{},[1846,60581,1855],{"stretchy":1854},[1979,60583,41707],{},[1846,60585,1861],{"stretchy":1854},[1846,60587,2075],{},[898,60589,2623],{},[898,60591,2626],{},[1846,60593,1855],{"stretchy":1854},[1979,60595,36089],{},[1846,60597,1861],{"stretchy":1854},[1846,60599,1848],{},[1979,60601,60602],{},"808",[1846,60604,2075],{},[1979,60606,60512],{},[1846,60608,1848],{},[1979,60610,60611],{},"68",[902,60613,60614],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,60617,60619],{"className":60618},[886],[888,60620,60621],{"xmlns":890},[892,60622,60623,60627],{},[895,60624,60625],{},[898,60626,2638],{},[902,60628,2638],{"encoding":904},[883,60630,60632],{"className":60631},[886],[888,60633,60634],{"xmlns":890},[892,60635,60636,60640],{},[895,60637,60638],{},[1979,60639,36089],{},[902,60641,36089],{"encoding":904},[883,60643,60645],{"className":60644},[886],[888,60646,60647],{"xmlns":890},[892,60648,60649,60653],{},[895,60650,60651],{},[1979,60652,3357],{},[902,60654,3357],{"encoding":904},[883,60656,60658],{"className":60657},[886],[888,60659,60660],{"xmlns":890},[892,60661,60662,60691],{},[895,60663,60664,60666,60668,60670,60672,60674,60676,60678,60680,60682,60684,60686,60688],{},[898,60665,2738],{"mathvariant":2226},[898,60667,2623],{},[898,60669,2626],{},[1846,60671,1650],{},[1979,60673,60425],{},[1846,60675,3025],{},[1846,60677,1855],{"stretchy":1854},[1846,60679,2075],{},[1979,60681,2023],{},[1846,60683,1861],{"stretchy":1854},[1846,60685,1848],{},[1846,60687,2075],{},[1979,60689,60690],{},"198",[902,60692,60693],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,60695,60697],{"id":60696},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,60699,60700],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[37193,60702,60704],{"id":60703},"příklad-36","Příklad 3.6",[724,60706,60707,57367,60709,60753],{},[38,60708,55832],{},[883,60710,60712],{"className":60711},[886],[888,60713,60714],{"xmlns":890},[892,60715,60716,60750],{},[895,60717,60718,60720,60722,60724,60726,60728,60730,60732,60734,60736,60742,60744],{},[898,60719,2623],{},[898,60721,2626],{},[1846,60723,1848],{},[1979,60725,2938],{},[1846,60727,1945],{},[1979,60729,4850],{},[898,60731,2638],{},[1846,60733,2075],{},[1979,60735,2078],{},[1974,60737,60738,60740],{},[898,60739,2638],{},[1979,60741,1981],{},[1846,60743,1945],{},[1974,60745,60746,60748],{},[898,60747,2638],{},[1979,60749,2023],{},[902,60751,60752],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,60755,60756],{},[38,60757,22615],{},[883,60759,60761],{"className":60760},[886],[888,60762,60763],{"xmlns":890,"display":27911},[892,60764,60765,61009],{},[20599,60766,60767,60793,60841,60875,60917,60967],{"rowspacing":20601,"columnalign":20602,"columnspacing":2227},[20604,60768,60769,60779],{},[20607,60770,60771],{},[2175,60772,60773],{"scriptlevel":2177,"displaystyle":2135},[895,60774,60775,60777],{},[898,60776,10282],{},[898,60778,2626],{},[20607,60780,60781],{},[2175,60782,60783],{"scriptlevel":2177,"displaystyle":2135},[895,60784,60785,60787,60789,60791],{},[895,60786],{},[1846,60788,1848],{},[1979,60790,2938],{},[1846,60792,2136],{"separator":2135},[20604,60794,60795,60807],{},[20607,60796,60797],{},[2175,60798,60799],{"scriptlevel":2177,"displaystyle":2135},[895,60800,60801,60803,60805],{},[898,60802,2623],{},[898,60804,40184],{},[898,60806,2626],{},[20607,60808,60809],{},[2175,60810,60811],{"scriptlevel":2177,"displaystyle":2135},[895,60812,60813,60815,60817,60819,60821,60823,60825,60831,60833,60839],{},[895,60814],{},[1846,60816,1848],{},[1979,60818,4850],{},[898,60820,2638],{},[1846,60822,2075],{},[1979,60824,2078],{},[1974,60826,60827,60829],{},[898,60828,2638],{},[1979,60830,1981],{},[1846,60832,1945],{},[1974,60834,60835,60837],{},[898,60836,2638],{},[1979,60838,2023],{},[1846,60840,2136],{"separator":2135},[20604,60842,60843,60855],{},[20607,60844,60845],{},[2175,60846,60847],{"scriptlevel":2177,"displaystyle":2135},[895,60848,60849,60851,60853],{},[898,60850,4101],{},[898,60852,10282],{},[898,60854,2626],{},[20607,60856,60857],{},[2175,60858,60859],{"scriptlevel":2177,"displaystyle":2135},[895,60860,60861,60863,60865,60873],{},[895,60862],{},[1846,60864,1848],{},[2175,60866,60867],{"scriptlevel":2177,"displaystyle":1854},[2179,60868,60869,60871],{},[1979,60870,2938],{},[898,60872,2638],{},[1846,60874,2136],{"separator":2135},[20604,60876,60877,60889],{},[20607,60878,60879],{},[2175,60880,60881],{"scriptlevel":2177,"displaystyle":2135},[895,60882,60883,60885,60887],{},[898,60884,4101],{},[898,60886,40184],{},[898,60888,2626],{},[20607,60890,60891],{},[2175,60892,60893],{"scriptlevel":2177,"displaystyle":2135},[895,60894,60895,60897,60899,60901,60903,60905,60907,60909,60915],{},[895,60896],{},[1846,60898,1848],{},[1979,60900,4850],{},[1846,60902,2075],{},[1979,60904,2078],{},[898,60906,2638],{},[1846,60908,1945],{},[1974,60910,60911,60913],{},[898,60912,2638],{},[1979,60914,1981],{},[1846,60916,2136],{"separator":2135},[20604,60918,60919,60929],{},[20607,60920,60921],{},[2175,60922,60923],{"scriptlevel":2177,"displaystyle":2135},[895,60924,60925,60927],{},[898,60926,4101],{},[898,60928,2626],{},[20607,60930,60931],{},[2175,60932,60933],{"scriptlevel":2177,"displaystyle":2135},[895,60934,60935,60937,60939,60947,60949,60951,60953,60955,60957,60959,60965],{},[895,60936],{},[1846,60938,1848],{},[2175,60940,60941],{"scriptlevel":2177,"displaystyle":1854},[2179,60942,60943,60945],{},[1979,60944,2938],{},[898,60946,2638],{},[1846,60948,1945],{},[1979,60950,4850],{},[1846,60952,2075],{},[1979,60954,2078],{},[898,60956,2638],{},[1846,60958,1945],{},[1974,60960,60961,60963],{},[898,60962,2638],{},[1979,60964,1981],{},[1846,60966,2136],{"separator":2135},[20604,60968,60969,60979],{},[20607,60970,60971],{},[2175,60972,60973],{"scriptlevel":2177,"displaystyle":2135},[895,60974,60975,60977],{},[898,60976,2667],{},[898,60978,2626],{},[20607,60980,60981],{},[2175,60982,60983],{"scriptlevel":2177,"displaystyle":2135},[895,60984,60985,60987,60989,60991,60993,60995,60997,60999,61001,61007],{},[895,60986],{},[1846,60988,1848],{},[1979,60990,4850],{},[1846,60992,2075],{},[1979,60994,2712],{},[898,60996,2638],{},[1846,60998,1945],{},[1979,61000,2023],{},[1974,61002,61003,61005],{},[898,61004,2638],{},[1979,61006,1981],{},[898,61008,1734],{"mathvariant":2226},[902,61010,61011],{"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}",[724,61013,61014,61015,15637,61030,15637,61045,61060,61061,61076,61077,1343,61095,61076,61112,1343,61130,61076,61145,61163],{},"Význačné body ",[883,61016,61018],{"className":61017},[886],[888,61019,61020],{"xmlns":890},[892,61021,61022,61027],{},[895,61023,61024],{},[1979,61025,61026],{},"1,67",[902,61028,61029],{"encoding":904},"1{,}67",[883,61031,61033],{"className":61032},[886],[888,61034,61035],{"xmlns":890},[892,61036,61037,61042],{},[895,61038,61039],{},[1979,61040,61041],{},"2,50",[902,61043,61044],{"encoding":904},"2{,}50",[883,61046,61048],{"className":61047},[886],[888,61049,61050],{"xmlns":890},[892,61051,61052,61057],{},[895,61053,61054],{},[1979,61055,61056],{},"4,73",[902,61058,61059],{"encoding":904},"4{,}73"," odpovídají: ",[883,61062,61064],{"className":61063},[886],[888,61065,61066],{"xmlns":890},[892,61067,61068,61074],{},[895,61069,61070,61072],{},[898,61071,2667],{},[898,61073,2626],{},[902,61075,55137],{"encoding":904}," minimum v ",[883,61078,61080],{"className":61079},[886],[888,61081,61082],{"xmlns":890},[892,61083,61084,61092],{},[895,61085,61086,61088,61090],{},[898,61087,2638],{},[1846,61089,5746],{},[1979,61091,61026],{},[902,61093,61094],{"encoding":904},"Q \\doteq 1{,}67",[883,61096,61098],{"className":61097},[886],[888,61099,61100],{"xmlns":890},[892,61101,61102,61110],{},[895,61103,61104,61106,61108],{},[898,61105,4101],{},[898,61107,40184],{},[898,61109,2626],{},[902,61111,55156],{"encoding":904},[883,61113,61115],{"className":61114},[886],[888,61116,61117],{"xmlns":890},[892,61118,61119,61127],{},[895,61120,61121,61123,61125],{},[898,61122,2638],{},[1846,61124,1848],{},[1979,61126,61041],{},[902,61128,61129],{"encoding":904},"Q = 2{,}50",[883,61131,61133],{"className":61132},[886],[888,61134,61135],{"xmlns":890},[892,61136,61137,61143],{},[895,61138,61139,61141],{},[898,61140,4101],{},[898,61142,2626],{},[902,61144,55405],{"encoding":904},[883,61146,61148],{"className":61147},[886],[888,61149,61150],{"xmlns":890},[892,61151,61152,61160],{},[895,61153,61154,61156,61158],{},[898,61155,2638],{},[1846,61157,5746],{},[1979,61159,61056],{},[902,61161,61162],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,61165,61166],{},[2409,61167],{"alt":61168,"className":61169,"src":61170},"imek-ac-avc-mc",[210,2413],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,61172,61173],{},[614,61174,61175,61176,1745,61191,61208,61209,15637,61228,61243],{},"Obrázek 3.9: Kubické křivky ",[883,61177,61179],{"className":61178},[886],[888,61180,61181],{"xmlns":890},[892,61182,61183,61189],{},[895,61184,61185,61187],{},[898,61186,2623],{},[898,61188,2626],{},[902,61190,3091],{"encoding":904},[883,61192,61194],{"className":61193},[886],[888,61195,61196],{"xmlns":890},[892,61197,61198,61206],{},[895,61199,61200,61202,61204],{},[898,61201,2623],{},[898,61203,40184],{},[898,61205,2626],{},[902,61207,55354],{"encoding":904}," rostoucí od bodu ",[883,61210,61212],{"className":61211},[886],[888,61213,61214],{"xmlns":890},[892,61215,61216,61226],{},[895,61217,61218,61220,61222,61224],{},[898,61219,10282],{},[898,61221,2626],{},[1846,61223,1848],{},[1979,61225,2938],{},[902,61227,11479],{"encoding":904},[883,61229,61231],{"className":61230},[886],[888,61232,61233],{"xmlns":890},[892,61234,61235,61241],{},[895,61236,61237,61239],{},[898,61238,10282],{},[898,61240,2626],{},[902,61242,55336],{"encoding":904}," je vodorovná přímka.",[724,61245,61246],{},[614,61247,61248,61249,1343,61264,1343,61281,29046,61296,61309,61310,2776,61327,61342,61343,6036,61360,61375,61376,26034,61389,1343,61402,1343,61415,1734],{},"Obrázek 3.10: Křivky ",[883,61250,61252],{"className":61251},[886],[888,61253,61254],{"xmlns":890},[892,61255,61256,61262],{},[895,61257,61258,61260],{},[898,61259,4101],{},[898,61261,2626],{},[902,61263,55405],{"encoding":904},[883,61265,61267],{"className":61266},[886],[888,61268,61269],{"xmlns":890},[892,61270,61271,61279],{},[895,61272,61273,61275,61277],{},[898,61274,4101],{},[898,61276,40184],{},[898,61278,2626],{},[902,61280,55156],{"encoding":904},[883,61282,61284],{"className":61283},[886],[888,61285,61286],{"xmlns":890},[892,61287,61288,61294],{},[895,61289,61290,61292],{},[898,61291,2667],{},[898,61293,2626],{},[902,61295,55137],{"encoding":904},[883,61297,61299],{"className":61298},[886],[888,61300,61301],{"xmlns":890},[892,61302,61303,61307],{},[895,61304,61305],{},[898,61306,900],{},[902,61308,900],{"encoding":904}," a klesající hyperbola ",[883,61311,61313],{"className":61312},[886],[888,61314,61315],{"xmlns":890},[892,61316,61317,61325],{},[895,61318,61319,61321,61323],{},[898,61320,4101],{},[898,61322,10282],{},[898,61324,2626],{},[902,61326,55372],{"encoding":904},[883,61328,61330],{"className":61329},[886],[888,61331,61332],{"xmlns":890},[892,61333,61334,61340],{},[895,61335,61336,61338],{},[898,61337,2667],{},[898,61339,2626],{},[902,61341,55137],{"encoding":904}," protíná ",[883,61344,61346],{"className":61345},[886],[888,61347,61348],{"xmlns":890},[892,61349,61350,61358],{},[895,61351,61352,61354,61356],{},[898,61353,4101],{},[898,61355,40184],{},[898,61357,2626],{},[902,61359,55156],{"encoding":904},[883,61361,61363],{"className":61362},[886],[888,61364,61365],{"xmlns":890},[892,61366,61367,61373],{},[895,61368,61369,61371],{},[898,61370,4101],{},[898,61372,2626],{},[902,61374,55405],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,61377,61379],{"className":61378},[886],[888,61380,61381],{"xmlns":890},[892,61382,61383,61387],{},[895,61384,61385],{},[898,61386,2638],{},[902,61388,2638],{"encoding":904},[883,61390,61392],{"className":61391},[886],[888,61393,61394],{"xmlns":890},[892,61395,61396,61400],{},[895,61397,61398],{},[1979,61399,61026],{},[902,61401,61029],{"encoding":904},[883,61403,61405],{"className":61404},[886],[888,61406,61407],{"xmlns":890},[892,61408,61409,61413],{},[895,61410,61411],{},[1979,61412,61041],{},[902,61414,61044],{"encoding":904},[883,61416,61418],{"className":61417},[886],[888,61419,61420],{"xmlns":890},[892,61421,61422,61426],{},[895,61423,61424],{},[1979,61425,61056],{},[902,61427,61059],{"encoding":904},[724,61429,61430],{},[38,61431,61432],{},"Standardní vlastnosti:",[120,61434,61435,61470,61534,61602,61652,61672],{},[123,61436,61437,1745,61452,61469],{},[883,61438,61440],{"className":61439},[886],[888,61441,61442],{"xmlns":890},[892,61443,61444,61450],{},[895,61445,61446,61448],{},[898,61447,2623],{},[898,61449,2626],{},[902,61451,3091],{"encoding":904},[883,61453,61455],{"className":61454},[886],[888,61456,61457],{"xmlns":890},[892,61458,61459,61467],{},[895,61460,61461,61463,61465],{},[898,61462,2623],{},[898,61464,40184],{},[898,61466,2626],{},[902,61468,55354],{"encoding":904}," jsou kubické funkce;",[123,61471,61472,1343,61487,1343,61504,61519,61520,61533],{},[883,61473,61475],{"className":61474},[886],[888,61476,61477],{"xmlns":890},[892,61478,61479,61485],{},[895,61480,61481,61483],{},[898,61482,4101],{},[898,61484,2626],{},[902,61486,55405],{"encoding":904},[883,61488,61490],{"className":61489},[886],[888,61491,61492],{"xmlns":890},[892,61493,61494,61502],{},[895,61495,61496,61498,61500],{},[898,61497,4101],{},[898,61499,40184],{},[898,61501,2626],{},[902,61503,55156],{"encoding":904},[883,61505,61507],{"className":61506},[886],[888,61508,61509],{"xmlns":890},[892,61510,61511,61517],{},[895,61512,61513,61515],{},[898,61514,2667],{},[898,61516,2626],{},[902,61518,55137],{"encoding":904}," jsou křivky tvaru ",[883,61521,61523],{"className":61522},[886],[888,61524,61525],{"xmlns":890},[892,61526,61527,61531],{},[895,61528,61529],{},[898,61530,900],{},[902,61532,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,61535,61536,61551,61552,1343,61569,61586,61587,8271],{},[883,61537,61539],{"className":61538},[886],[888,61540,61541],{"xmlns":890},[892,61542,61543,61549],{},[895,61544,61545,61547],{},[898,61546,2667],{},[898,61548,2626],{},[902,61550,55137],{"encoding":904}," nabývá minima před ",[883,61553,61555],{"className":61554},[886],[888,61556,61557],{"xmlns":890},[892,61558,61559,61567],{},[895,61560,61561,61563,61565],{},[898,61562,4101],{},[898,61564,40184],{},[898,61566,2626],{},[902,61568,55156],{"encoding":904},[883,61570,61572],{"className":61571},[886],[888,61573,61574],{"xmlns":890},[892,61575,61576,61584],{},[895,61577,61578,61580,61582],{},[898,61579,4101],{},[898,61581,40184],{},[898,61583,2626],{},[902,61585,55156],{"encoding":904}," před ",[883,61588,61590],{"className":61589},[886],[888,61591,61592],{"xmlns":890},[892,61593,61594,61600],{},[895,61595,61596,61598],{},[898,61597,4101],{},[898,61599,2626],{},[902,61601,55405],{"encoding":904},[123,61603,61604,61342,61619,1745,61634,61651],{},[883,61605,61607],{"className":61606},[886],[888,61608,61609],{"xmlns":890},[892,61610,61611,61617],{},[895,61612,61613,61615],{},[898,61614,2667],{},[898,61616,2626],{},[902,61618,55137],{"encoding":904},[883,61620,61622],{"className":61621},[886],[888,61623,61624],{"xmlns":890},[892,61625,61626,61632],{},[895,61627,61628,61630],{},[898,61629,4101],{},[898,61631,2626],{},[902,61633,55405],{"encoding":904},[883,61635,61637],{"className":61636},[886],[888,61638,61639],{"xmlns":890},[892,61640,61641,61649],{},[895,61642,61643,61645,61647],{},[898,61644,4101],{},[898,61646,40184],{},[898,61648,2626],{},[902,61650,55156],{"encoding":904}," zdola právě v jejich minimech;",[123,61653,61654,61671],{},[883,61655,61657],{"className":61656},[886],[888,61658,61659],{"xmlns":890},[892,61660,61661,61669],{},[895,61662,61663,61665,61667],{},[898,61664,4101],{},[898,61666,10282],{},[898,61668,2626],{},[902,61670,55372],{"encoding":904}," je hyperbola, stále klesající;",[123,61673,61674,61706,61707,1745,61722,61739,61740,61753,61754,3764],{},[883,61675,61677],{"className":61676},[886],[888,61678,61679],{"xmlns":890},[892,61680,61681,61703],{},[895,61682,61683,61685,61687,61689,61691,61693,61695,61697,61699,61701],{},[898,61684,4101],{},[898,61686,2626],{},[1846,61688,1848],{},[898,61690,4101],{},[898,61692,10282],{},[898,61694,2626],{},[1846,61696,1945],{},[898,61698,4101],{},[898,61700,40184],{},[898,61702,2626],{},[902,61704,61705],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,61708,61710],{"className":61709},[886],[888,61711,61712],{"xmlns":890},[892,61713,61714,61720],{},[895,61715,61716,61718],{},[898,61717,4101],{},[898,61719,2626],{},[902,61721,55405],{"encoding":904},[883,61723,61725],{"className":61724},[886],[888,61726,61727],{"xmlns":890},[892,61728,61729,61737],{},[895,61730,61731,61733,61735],{},[898,61732,4101],{},[898,61734,40184],{},[898,61736,2626],{},[902,61738,55156],{"encoding":904}," klesá s rostoucím ",[883,61741,61743],{"className":61742},[886],[888,61744,61745],{"xmlns":890},[892,61746,61747,61751],{},[895,61748,61749],{},[898,61750,2638],{},[902,61752,2638],{"encoding":904}," (protože ",[883,61755,61757],{"className":61756},[886],[888,61758,61759],{"xmlns":890},[892,61760,61761,61773],{},[895,61762,61763,61765,61767,61769,61771],{},[898,61764,4101],{},[898,61766,10282],{},[898,61768,2626],{},[1846,61770,2971],{},[1979,61772,2177],{},[902,61774,61775],{"encoding":904},"AFC \\to 0",[115,61777,61779],{"id":61778},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,61781,61782,61783,61786,61787,61802],{},"Častou optimalizační úlohou je ",[38,61784,61785],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,61788,61790],{"className":61789},[886],[888,61791,61792],{"xmlns":890},[892,61793,61794,61800],{},[895,61795,61796,61798],{},[898,61797,4101],{},[898,61799,2626],{},[902,61801,55405],{"encoding":904}," minimální.",[198,61804,16257],{"id":16256},[724,61806,61807,61808,61825],{},"Mají-li průměrné náklady minimum v bodě ",[883,61809,61811],{"className":61810},[886],[888,61812,61813],{"xmlns":890},[892,61814,61815,61823],{},[895,61816,61817],{},[2122,61818,61819,61821],{},[898,61820,2638],{},[1979,61822,2177],{},[902,61824,38153],{"encoding":904},", pak platí",[883,61827,61829],{"className":61828},[886],[888,61830,61831],{"xmlns":890,"display":27911},[892,61832,61833,61882],{},[20599,61834,61835],{"width":27916},[20604,61836,61837,61839,61875,61877],{},[20607,61838],{"width":27921},[20607,61840,61841],{},[895,61842,61843,61845,61847,61849,61855,61857,61859,61861,61863,61865,61871,61873],{},[898,61844,4101],{},[898,61846,2626],{},[1846,61848,1855],{"stretchy":1854},[2122,61850,61851,61853],{},[898,61852,2638],{},[1979,61854,2177],{},[1846,61856,1861],{"stretchy":1854},[1846,61858,1848],{},[898,61860,2667],{},[898,61862,2626],{},[1846,61864,1855],{"stretchy":1854},[2122,61866,61867,61869],{},[898,61868,2638],{},[1979,61870,2177],{},[1846,61872,1861],{"stretchy":1854},[898,61874,1734],{"mathvariant":2226},[20607,61876],{"width":27921},[20607,61878,61879],{},[2138,61880,61881],{},"(3.10)",[902,61883,61884],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[1639,61886,61887],{},[724,61888,61889,61891,61892],{},[883,61890,56289],{}," Princip\n",[38,61893,61894],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,61896,61897,61900,61901,61943],{},[38,61898,61899],{},"Odvození."," Z ",[883,61902,61904],{"className":61903},[886],[888,61905,61906],{"xmlns":890},[892,61907,61908,61940],{},[895,61909,61910,61912,61914,61916,61918,61920,61922],{},[898,61911,4101],{},[898,61913,2626],{},[1846,61915,1855],{"stretchy":1854},[898,61917,2638],{},[1846,61919,1861],{"stretchy":1854},[1846,61921,1848],{},[2175,61923,61924],{"scriptlevel":2177,"displaystyle":1854},[2179,61925,61926,61938],{},[895,61927,61928,61930,61932,61934,61936],{},[898,61929,2623],{},[898,61931,2626],{},[1846,61933,1855],{"stretchy":1854},[898,61935,2638],{},[1846,61937,1861],{"stretchy":1854},[898,61939,2638],{},[902,61941,61942],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,61945,61947],{"className":61946},[886],[888,61948,61949],{"xmlns":890,"display":27911},[892,61950,61951,62083],{},[895,61952,61953,61955,61961,61963,61965,61967,61969,62009,62011,62051,62053,62081],{},[898,61954,4101],{},[1974,61956,61957,61959],{},[898,61958,2626],{},[1846,61960,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,61962,1855],{"stretchy":1854},[898,61964,2638],{},[1846,61966,1861],{"stretchy":1854},[1846,61968,1848],{},[2179,61970,61971,62003],{},[895,61972,61973,61975,61981,61983,61985,61987,61989,61991,61993,61995,61997,61999,62001],{},[898,61974,2623],{},[1974,61976,61977,61979],{},[898,61978,2626],{},[1846,61980,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,61982,1855],{"stretchy":1854},[898,61984,2638],{},[1846,61986,1861],{"stretchy":1854},[1846,61988,3025],{},[898,61990,2638],{},[1846,61992,2075],{},[898,61994,2623],{},[898,61996,2626],{},[1846,61998,1855],{"stretchy":1854},[898,62000,2638],{},[1846,62002,1861],{"stretchy":1854},[1974,62004,62005,62007],{},[898,62006,2638],{},[1979,62008,1981],{},[1846,62010,1848],{},[2179,62012,62013,62045],{},[895,62014,62015,62017,62019,62021,62023,62025,62027,62029,62031,62033,62035,62037,62039,62041,62043],{},[898,62016,2667],{},[898,62018,2626],{},[1846,62020,1855],{"stretchy":1854},[898,62022,2638],{},[1846,62024,1861],{"stretchy":1854},[1846,62026,3025],{},[898,62028,2638],{},[1846,62030,2075],{},[898,62032,4101],{},[898,62034,2626],{},[1846,62036,1855],{"stretchy":1854},[898,62038,2638],{},[1846,62040,1861],{"stretchy":1854},[1846,62042,3025],{},[898,62044,2638],{},[1974,62046,62047,62049],{},[898,62048,2638],{},[1979,62050,1981],{},[1846,62052,1848],{},[2179,62054,62055,62079],{},[895,62056,62057,62059,62061,62063,62065,62067,62069,62071,62073,62075,62077],{},[898,62058,2667],{},[898,62060,2626],{},[1846,62062,1855],{"stretchy":1854},[898,62064,2638],{},[1846,62066,1861],{"stretchy":1854},[1846,62068,2075],{},[898,62070,4101],{},[898,62072,2626],{},[1846,62074,1855],{"stretchy":1854},[898,62076,2638],{},[1846,62078,1861],{"stretchy":1854},[898,62080,2638],{},[898,62082,1734],{"mathvariant":2226},[902,62084,62085],{"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}.",[724,62087,62088,62089,2474,62104,7948,62126,56666],{},"Nutnou podmínkou minima ",[883,62090,62092],{"className":62091},[886],[888,62093,62094],{"xmlns":890},[892,62095,62096,62102],{},[895,62097,62098,62100],{},[898,62099,4101],{},[898,62101,2626],{},[902,62103,55405],{"encoding":904},[883,62105,62107],{"className":62106},[886],[888,62108,62109],{"xmlns":890},[892,62110,62111,62123],{},[895,62112,62113,62119,62121],{},[2122,62114,62115,62117],{},[898,62116,2638],{},[1979,62118,2177],{},[1846,62120,3256],{},[1979,62122,2177],{},[902,62124,62125],{"encoding":904},"Q_0 > 0",[883,62127,62129],{"className":62128},[886],[888,62130,62131],{"xmlns":890},[892,62132,62133,62157],{},[895,62134,62135,62137,62143,62145,62151,62153,62155],{},[898,62136,4101],{},[1974,62138,62139,62141],{},[898,62140,2626],{},[1846,62142,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,62144,1855],{"stretchy":1854},[2122,62146,62147,62149],{},[898,62148,2638],{},[1979,62150,2177],{},[1846,62152,1861],{"stretchy":1854},[1846,62154,1848],{},[1979,62156,2177],{},[902,62158,62159],{"encoding":904},"AC'(Q_0) = 0",[883,62161,62163],{"className":62162},[886],[888,62164,62165],{"xmlns":890,"display":27911},[892,62166,62167,62252],{},[895,62168,62169,62209,62211,62213,62215,62218,62220,62222,62224,62226,62232,62234,62236,62238,62240,62242,62248,62250],{},[2179,62170,62171,62203],{},[895,62172,62173,62175,62177,62179,62185,62187,62189,62191,62193,62195,62201],{},[898,62174,2667],{},[898,62176,2626],{},[1846,62178,1855],{"stretchy":1854},[2122,62180,62181,62183],{},[898,62182,2638],{},[1979,62184,2177],{},[1846,62186,1861],{"stretchy":1854},[1846,62188,2075],{},[898,62190,4101],{},[898,62192,2626],{},[1846,62194,1855],{"stretchy":1854},[2122,62196,62197,62199],{},[898,62198,2638],{},[1979,62200,2177],{},[1846,62202,1861],{"stretchy":1854},[2122,62204,62205,62207],{},[898,62206,2638],{},[1979,62208,2177],{},[1846,62210,1848],{},[1979,62212,2177],{},[5724,62214],{"width":15129},[1846,62216,62217],{},"⟺",[5724,62219],{"width":15129},[898,62221,2667],{},[898,62223,2626],{},[1846,62225,1855],{"stretchy":1854},[2122,62227,62228,62230],{},[898,62229,2638],{},[1979,62231,2177],{},[1846,62233,1861],{"stretchy":1854},[1846,62235,1848],{},[898,62237,4101],{},[898,62239,2626],{},[1846,62241,1855],{"stretchy":1854},[2122,62243,62244,62246],{},[898,62245,2638],{},[1979,62247,2177],{},[1846,62249,1861],{"stretchy":1854},[898,62251,1734],{"mathvariant":2226},[902,62253,62254],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,62256,62257,2053,62260,61342,62275,62290,62291,62306,62307,7948,62324,62346,62347,62369],{},[38,62258,62259],{},"Geometrická interpretace.",[883,62261,62263],{"className":62262},[886],[888,62264,62265],{"xmlns":890},[892,62266,62267,62273],{},[895,62268,62269,62271],{},[898,62270,2667],{},[898,62272,2626],{},[902,62274,55137],{"encoding":904},[883,62276,62278],{"className":62277},[886],[888,62279,62280],{"xmlns":890},[892,62281,62282,62288],{},[895,62283,62284,62286],{},[898,62285,4101],{},[898,62287,2626],{},[902,62289,55405],{"encoding":904}," právě v bodě minima ",[883,62292,62294],{"className":62293},[886],[888,62295,62296],{"xmlns":890},[892,62297,62298,62304],{},[895,62299,62300,62302],{},[898,62301,4101],{},[898,62303,2626],{},[902,62305,55405],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,62308,62310],{"className":62309},[886],[888,62311,62312],{"xmlns":890},[892,62313,62314,62322],{},[895,62315,62316],{},[2122,62317,62318,62320],{},[898,62319,2638],{},[1979,62321,2177],{},[902,62323,38153],{"encoding":904},[883,62325,62327],{"className":62326},[886],[888,62328,62329],{"xmlns":890},[892,62330,62331,62343],{},[895,62332,62333,62335,62337,62339,62341],{},[898,62334,2667],{},[898,62336,2626],{},[1846,62338,3295],{},[898,62340,4101],{},[898,62342,2626],{},[902,62344,62345],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,62348,62350],{"className":62349},[886],[888,62351,62352],{"xmlns":890},[892,62353,62354,62366],{},[895,62355,62356,62358,62360,62362,62364],{},[898,62357,2667],{},[898,62359,2626],{},[1846,62361,3256],{},[898,62363,4101],{},[898,62365,2626],{},[902,62367,62368],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,62371,62372,62373,62415,62416,62433,62434,1734],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,62374,62376],{"className":62375},[886],[888,62377,62378],{"xmlns":890},[892,62379,62380,62412],{},[895,62381,62382,62384,62386,62388,62394,62396,62398,62400,62402,62404,62410],{},[898,62383,4101],{},[898,62385,2626],{},[1846,62387,1855],{"stretchy":1854},[2122,62389,62390,62392],{},[898,62391,2638],{},[1979,62393,2177],{},[1846,62395,1861],{"stretchy":1854},[1846,62397,1848],{},[898,62399,2667],{},[898,62401,2626],{},[1846,62403,1855],{"stretchy":1854},[2122,62405,62406,62408],{},[898,62407,2638],{},[1979,62409,2177],{},[1846,62411,1861],{"stretchy":1854},[902,62413,62414],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,62417,62419],{"className":62418},[886],[888,62420,62421],{"xmlns":890},[892,62422,62423,62431],{},[895,62424,62425],{},[2122,62426,62427,62429],{},[898,62428,2638],{},[1979,62430,2177],{},[902,62432,38153],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,62435,62437],{"className":62436},[886],[888,62438,62439],{"xmlns":890},[892,62440,62441,62465],{},[895,62442,62443,62445,62447,62449,62451,62453,62455,62457,62459,62461,62463],{},[898,62444,4101],{},[898,62446,2626],{},[1846,62448,1855],{"stretchy":1854},[898,62450,2638],{},[1846,62452,1861],{"stretchy":1854},[1846,62454,1848],{},[898,62456,2667],{},[898,62458,2626],{},[1846,62460,1855],{"stretchy":1854},[898,62462,2638],{},[1846,62464,1861],{"stretchy":1854},[902,62466,62467],{"encoding":904},"AC(Q) = MC(Q)",[1639,62469,62470],{},[724,62471,62472,62474,62475,10240,62493,62514,62515,10240,62518,62539,62540,62555,62556,57883,62571,3764],{},[883,62473,4258],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,62476,62477,62478],{},"minimum ",[883,62479,62481],{"className":62480},[886],[888,62482,62483],{"xmlns":890},[892,62484,62485,62491],{},[895,62486,62487,62489],{},[898,62488,4101],{},[898,62490,2626],{},[902,62492,55405],{"encoding":904},[883,62494,62496],{"className":62495},[886],[888,62497,62498],{"xmlns":890},[892,62499,62500,62512],{},[895,62501,62502,62504,62506,62508,62510],{},[898,62503,4101],{},[898,62505,2626],{},[1846,62507,1848],{},[898,62509,2667],{},[898,62511,2626],{},[902,62513,55068],{"encoding":904},", pro ",[38,62516,62517],{},"maximum zisku",[883,62519,62521],{"className":62520},[886],[888,62522,62523],{"xmlns":890},[892,62524,62525,62537],{},[895,62526,62527,62529,62531,62533,62535],{},[898,62528,2667],{},[898,62530,3840],{},[1846,62532,1848],{},[898,62534,2667],{},[898,62536,2626],{},[902,62538,55116],{"encoding":904},". Obě podmínky využívají ",[883,62541,62543],{"className":62542},[886],[888,62544,62545],{"xmlns":890},[892,62546,62547,62553],{},[895,62548,62549,62551],{},[898,62550,2667],{},[898,62552,2626],{},[902,62554,55137],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,62557,62559],{"className":62558},[886],[888,62560,62561],{"xmlns":890},[892,62562,62563,62569],{},[895,62564,62565,62567],{},[898,62566,4101],{},[898,62568,2626],{},[902,62570,55405],{"encoding":904},[883,62572,62574],{"className":62573},[886],[888,62575,62576],{"xmlns":890},[892,62577,62578,62584],{},[895,62579,62580,62582],{},[898,62581,2667],{},[898,62583,3840],{},[902,62585,6480],{"encoding":904},[37193,62587,62589],{"id":62588},"příklad-37","Příklad 3.7",[724,62591,62592,57367,62594,62628,62629,62642,62643,62658],{},[38,62593,55832],{},[883,62595,62597],{"className":62596},[886],[888,62598,62599],{"xmlns":890},[892,62600,62601,62625],{},[895,62602,62603,62605,62607,62609,62615,62617,62619,62621,62623],{},[898,62604,2623],{},[898,62606,2626],{},[1846,62608,1848],{},[1974,62610,62611,62613],{},[898,62612,2638],{},[1979,62614,1981],{},[1846,62616,1945],{},[1979,62618,2023],{},[898,62620,2638],{},[1846,62622,1945],{},[1979,62624,5411],{},[902,62626,62627],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,62630,62632],{"className":62631},[886],[888,62633,62634],{"xmlns":890},[892,62635,62636,62640],{},[895,62637,62638],{},[898,62639,2638],{},[902,62641,2638],{"encoding":904}," minimalizující ",[883,62644,62646],{"className":62645},[886],[888,62647,62648],{"xmlns":890},[892,62649,62650,62656],{},[895,62651,62652,62654],{},[898,62653,4101],{},[898,62655,2626],{},[902,62657,55405],{"encoding":904}," a ověřte princip (3.10).",[724,62660,62661,62663],{},[38,62662,22615],{}," Přímý výpočet:",[883,62665,62667],{"className":62666},[886],[888,62668,62669],{"xmlns":890,"display":27911},[892,62670,62671,62773],{},[895,62672,62673,62675,62677,62679,62701,62703,62705,62707,62709,62711,62717,62719,62721,62723,62725,62727,62733,62735,62737,62739,62749,62751,62771],{},[898,62674,4101],{},[898,62676,2626],{},[1846,62678,1848],{},[2179,62680,62681,62699],{},[895,62682,62683,62689,62691,62693,62695,62697],{},[1974,62684,62685,62687],{},[898,62686,2638],{},[1979,62688,1981],{},[1846,62690,1945],{},[1979,62692,2023],{},[898,62694,2638],{},[1846,62696,1945],{},[1979,62698,5411],{},[898,62700,2638],{},[1846,62702,1848],{},[898,62704,2638],{},[1846,62706,1945],{},[1979,62708,2023],{},[1846,62710,1945],{},[2179,62712,62713,62715],{},[1979,62714,5411],{},[898,62716,2638],{},[1846,62718,2136],{"separator":2135},[5724,62720],{"width":5726},[1846,62722,1855],{"stretchy":1854},[898,62724,4101],{},[898,62726,2626],{},[1974,62728,62729,62731],{},[1846,62730,1861],{"stretchy":1854},[1846,62732,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,62734,1848],{},[1979,62736,2128],{},[1846,62738,2075],{},[2179,62740,62741,62743],{},[1979,62742,5411],{},[1974,62744,62745,62747],{},[898,62746,2638],{},[1979,62748,1981],{},[1846,62750,1848],{},[2179,62752,62753,62765],{},[895,62754,62755,62761,62763],{},[1974,62756,62757,62759],{},[898,62758,2638],{},[1979,62760,1981],{},[1846,62762,2075],{},[1979,62764,5411],{},[1974,62766,62767,62769],{},[898,62768,2638],{},[1979,62770,1981],{},[898,62772,1734],{"mathvariant":2226},[902,62774,62775],{"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}.",[724,62777,62778,62818,62819,62843,62844,62894,62895,1734],{},[883,62779,62781],{"className":62780},[886],[888,62782,62783],{"xmlns":890},[892,62784,62785,62815],{},[895,62786,62787,62789,62791,62793,62799,62801,62803,62805,62811,62813],{},[1846,62788,1855],{"stretchy":1854},[898,62790,4101],{},[898,62792,2626],{},[1974,62794,62795,62797],{},[1846,62796,1861],{"stretchy":1854},[1846,62798,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,62800,1848],{},[1979,62802,2177],{},[1846,62804,3833],{},[2122,62806,62807,62809],{},[898,62808,2638],{},[1979,62810,2128],{},[1846,62812,1848],{},[1979,62814,2085],{},[902,62816,62817],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,62820,62822],{"className":62821},[886],[888,62823,62824],{"xmlns":890},[892,62825,62826,62840],{},[895,62827,62828,62834,62836,62838],{},[2122,62829,62830,62832],{},[898,62831,2638],{},[1979,62833,1981],{},[1846,62835,1848],{},[1846,62837,2075],{},[1979,62839,2085],{},[902,62841,62842],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,62845,62847],{"className":62846},[886],[888,62848,62849],{"xmlns":890},[892,62850,62851,62891],{},[895,62852,62853,62855,62857,62859,62869,62871,62873,62875,62877,62885,62887,62889],{},[1846,62854,1855],{"stretchy":1854},[898,62856,4101],{},[898,62858,2626],{},[1974,62860,62861,62863],{},[1846,62862,1861],{"stretchy":1854},[895,62864,62865,62867],{},[1846,62866,2228],{"mathvariant":2226},[1846,62868,2228],{"mathvariant":2226},[1846,62870,1855],{"stretchy":1854},[1979,62872,2085],{},[1846,62874,1861],{"stretchy":1854},[1846,62876,1848],{},[2175,62878,62879],{"scriptlevel":2177,"displaystyle":1854},[2179,62880,62881,62883],{},[1979,62882,2128],{},[1979,62884,2023],{},[1846,62886,3256],{},[1979,62888,2177],{},[1846,62890,3833],{},[902,62892,62893],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,62896,62898],{"className":62897},[886],[888,62899,62900],{"xmlns":890},[892,62901,62902,62918],{},[895,62903,62904,62906,62908,62910,62912,62914,62916],{},[898,62905,4101],{},[898,62907,2626],{},[1846,62909,1855],{"stretchy":1854},[1979,62911,2085],{},[1846,62913,1861],{"stretchy":1854},[1846,62915,1848],{},[1979,62917,36089],{},[902,62919,62920],{"encoding":904},"AC(6) = 15",[724,62922,62923,62924,62950,62951,2554],{},"Pomocí principu: ",[883,62925,62927],{"className":62926},[886],[888,62928,62929],{"xmlns":890},[892,62930,62931,62947],{},[895,62932,62933,62935,62937,62939,62941,62943,62945],{},[898,62934,2667],{},[898,62936,2626],{},[1846,62938,1848],{},[1979,62940,1981],{},[898,62942,2638],{},[1846,62944,1945],{},[1979,62946,2023],{},[902,62948,62949],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,62952,62954],{"className":62953},[886],[888,62955,62956],{"xmlns":890},[892,62957,62958,62970],{},[895,62959,62960,62962,62964,62966,62968],{},[898,62961,4101],{},[898,62963,2626],{},[1846,62965,1848],{},[898,62967,2667],{},[898,62969,2626],{},[902,62971,55068],{"encoding":904},[883,62973,62975],{"className":62974},[886],[888,62976,62977],{"xmlns":890,"display":27911},[892,62978,62979,63081],{},[895,62980,62981,63003,63005,63007,63009,63011,63013,63015,63017,63019,63025,63027,63029,63031,63033,63035,63037,63039,63045,63047,63049,63051,63053,63055,63057,63063,63065,63067,63069,63071,63073,63075,63077,63079],{},[2179,62982,62983,63001],{},[895,62984,62985,62991,62993,62995,62997,62999],{},[1974,62986,62987,62989],{},[898,62988,2638],{},[1979,62990,1981],{},[1846,62992,1945],{},[1979,62994,2023],{},[898,62996,2638],{},[1846,62998,1945],{},[1979,63000,5411],{},[898,63002,2638],{},[1846,63004,1848],{},[1979,63006,1981],{},[898,63008,2638],{},[1846,63010,1945],{},[1979,63012,2023],{},[2138,63014,3830],{},[1846,63016,3833],{},[2138,63018,3830],{},[1974,63020,63021,63023],{},[898,63022,2638],{},[1979,63024,1981],{},[1846,63026,1945],{},[1979,63028,2023],{},[898,63030,2638],{},[1846,63032,1945],{},[1979,63034,5411],{},[1846,63036,1848],{},[1979,63038,1981],{},[1974,63040,63041,63043],{},[898,63042,2638],{},[1979,63044,1981],{},[1846,63046,1945],{},[1979,63048,2023],{},[898,63050,2638],{},[2138,63052,3830],{},[1846,63054,3833],{},[2138,63056,3830],{},[1974,63058,63059,63061],{},[898,63060,2638],{},[1979,63062,1981],{},[1846,63064,1848],{},[1979,63066,5411],{},[2138,63068,3830],{},[1846,63070,3833],{},[2138,63072,3830],{},[898,63074,2638],{},[1846,63076,1848],{},[1979,63078,2085],{},[1846,63080,2136],{"separator":2135},[902,63082,63083],{"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,",[724,63085,63086,63087,63125],{},"a ",[883,63088,63090],{"className":63089},[886],[888,63091,63092],{"xmlns":890},[892,63093,63094,63122],{},[895,63095,63096,63098,63100,63102,63104,63106,63108,63110,63112,63114,63116,63118,63120],{},[898,63097,4101],{},[898,63099,2626],{},[1846,63101,1855],{"stretchy":1854},[1979,63103,2085],{},[1846,63105,1861],{"stretchy":1854},[1846,63107,1848],{},[898,63109,2667],{},[898,63111,2626],{},[1846,63113,1855],{"stretchy":1854},[1979,63115,2085],{},[1846,63117,1861],{"stretchy":1854},[1846,63119,1848],{},[1979,63121,36089],{},[902,63123,63124],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,63127,63129],{"id":63128},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,63131,63132,63133,2554],{},"Analogicky pro ",[883,63134,63136],{"className":63135},[886],[888,63137,63138],{"xmlns":890},[892,63139,63140,63148],{},[895,63141,63142,63144,63146],{},[898,63143,4101],{},[898,63145,40184],{},[898,63147,2626],{},[902,63149,55156],{"encoding":904},[883,63151,63153],{"className":63152},[886],[888,63154,63155],{"xmlns":890,"display":27911},[892,63156,63157,63208],{},[20599,63158,63159],{"width":27916},[20604,63160,63161,63163,63201,63203],{},[20607,63162],{"width":27921},[20607,63164,63165],{},[895,63166,63167,63169,63171,63173,63175,63181,63183,63185,63187,63189,63191,63197,63199],{},[898,63168,4101],{},[898,63170,40184],{},[898,63172,2626],{},[1846,63174,1855],{"stretchy":1854},[2122,63176,63177,63179],{},[898,63178,2638],{},[1979,63180,2177],{},[1846,63182,1861],{"stretchy":1854},[1846,63184,1848],{},[898,63186,2667],{},[898,63188,2626],{},[1846,63190,1855],{"stretchy":1854},[2122,63192,63193,63195],{},[898,63194,2638],{},[1979,63196,2177],{},[1846,63198,1861],{"stretchy":1854},[898,63200,1734],{"mathvariant":2226},[20607,63202],{"width":27921},[20607,63204,63205],{},[2138,63206,63207],{},"(3.11)",[902,63209,63210],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[1639,63212,63213],{},[724,63214,63215,61891,63217],{},[883,63216,56289],{},[38,63218,63219,63220,63237],{},"V bodě minima průměrných variabilních nákladů se ",[883,63221,63223],{"className":63222},[886],[888,63224,63225],{"xmlns":890},[892,63226,63227,63235],{},[895,63228,63229,63231,63233],{},[898,63230,4101],{},[898,63232,40184],{},[898,63234,2626],{},[902,63236,55156],{"encoding":904}," rovnají mezním nákladům.",[724,63239,63240,63241,63263,63264,1734],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,63242,63244],{"className":63243},[886],[888,63245,63246],{"xmlns":890},[892,63247,63248,63260],{},[895,63249,63250,63256,63258],{},[2122,63251,63252,63254],{},[898,63253,2638],{},[1979,63255,2177],{},[1846,63257,1848],{},[1979,63259,53044],{},[902,63261,63262],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,63265,63267],{"className":63266},[886],[888,63268,63269],{"xmlns":890},[892,63270,63271,63297],{},[895,63272,63273,63275,63277,63279,63281,63283,63285,63287,63289,63291,63293,63295],{},[898,63274,4101],{},[898,63276,40184],{},[898,63278,2626],{},[1846,63280,1855],{"stretchy":1854},[898,63282,2638],{},[1846,63284,1861],{"stretchy":1854},[1846,63286,1848],{},[898,63288,2667],{},[898,63290,2626],{},[1846,63292,1855],{"stretchy":1854},[898,63294,2638],{},[1846,63296,1861],{"stretchy":1854},[902,63298,63299],{"encoding":904},"AVC(Q) = MC(Q)",[115,63301,63303],{"id":63302},"zisk-a-body-zvratu","Zisk a body zvratu",[724,63305,63306,2053,63309,63325],{},[38,63307,63308],{},"Zisk",[883,63310,63312],{"className":63311},[886],[888,63313,63314],{"xmlns":890},[892,63315,63316,63322],{},[895,63317,63318,63320],{},[898,63319,3783],{},[898,63321,3840],{},[902,63323,63324],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,63327,63329],{"className":63328},[886],[888,63330,63331],{"xmlns":890,"display":27911},[892,63332,63333,63392],{},[20599,63334,63335],{"width":27916},[20604,63336,63337,63339,63385,63387],{},[20607,63338],{"width":27921},[20607,63340,63341],{},[895,63342,63343,63345,63347,63349,63351,63353,63355,63357,63359,63361,63363,63365,63367,63369,63371,63373,63375,63377,63379,63381,63383],{},[898,63344,3783],{},[898,63346,3840],{},[1846,63348,1848],{},[898,63350,3783],{},[898,63352,3840],{},[1846,63354,1855],{"stretchy":1854},[898,63356,2638],{},[1846,63358,1861],{"stretchy":1854},[1846,63360,1848],{},[898,63362,2623],{},[898,63364,3840],{},[1846,63366,1855],{"stretchy":1854},[898,63368,2638],{},[1846,63370,1861],{"stretchy":1854},[1846,63372,2075],{},[898,63374,2623],{},[898,63376,2626],{},[1846,63378,1855],{"stretchy":1854},[898,63380,2638],{},[1846,63382,1861],{"stretchy":1854},[898,63384,1734],{"mathvariant":2226},[20607,63386],{"width":27921},[20607,63388,63389],{},[2138,63390,63391],{},"(3.12)",[902,63393,63394],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,63396,63397,63398,1745,63413,43481,63428,63430,63431,63434,63435,63451,63452,63467,63468,63483,63484,1343,63497,63510,63511,1343,63529,63547,63548,9871,63551,63554,63555,1348,63577,7948,63599,63621,63622,7948,63652,63674],{},"Body rovnosti ",[883,63399,63401],{"className":63400},[886],[888,63402,63403],{"xmlns":890},[892,63404,63405,63411],{},[895,63406,63407,63409],{},[898,63408,2623],{},[898,63410,3840],{},[902,63412,3940],{"encoding":904},[883,63414,63416],{"className":63415},[886],[888,63417,63418],{"xmlns":890},[892,63419,63420,63426],{},[895,63421,63422,63424],{},[898,63423,2623],{},[898,63425,2626],{},[902,63427,3091],{"encoding":904},[38,63429,55572],{}," (též vyrovnání, ",[614,63432,63433],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,63436,63438],{"className":63437},[886],[888,63439,63440],{"xmlns":890},[892,63441,63442,63448],{},[895,63443,63444,63446],{},[898,63445,40184],{},[898,63447,2626],{},[902,63449,63450],{"encoding":904},"VC",") je ",[883,63453,63455],{"className":63454},[886],[888,63456,63457],{"xmlns":890},[892,63458,63459,63465],{},[895,63460,63461,63463],{},[898,63462,2623],{},[898,63464,3840],{},[902,63466,3940],{"encoding":904}," kvadratická a ",[883,63469,63471],{"className":63470},[886],[888,63472,63473],{"xmlns":890},[892,63474,63475,63481],{},[895,63476,63477,63479],{},[898,63478,2623],{},[898,63480,2626],{},[902,63482,3091],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,63485,63487],{"className":63486},[886],[888,63488,63489],{"xmlns":890},[892,63490,63491,63495],{},[895,63492,63493],{},[898,63494,4101],{},[902,63496,4101],{"encoding":904},[883,63498,63500],{"className":63499},[886],[888,63501,63502],{"xmlns":890},[892,63503,63504,63508],{},[895,63505,63506],{},[898,63507,23098],{},[902,63509,23098],{"encoding":904}," odpovídajících množstvím ",[883,63512,63514],{"className":63513},[886],[888,63515,63516],{"xmlns":890},[892,63517,63518,63526],{},[895,63519,63520],{},[2122,63521,63522,63524],{},[898,63523,2638],{},[898,63525,4101],{},[902,63527,63528],{"encoding":904},"Q_A",[883,63530,63532],{"className":63531},[886],[888,63533,63534],{"xmlns":890},[892,63535,63536,63544],{},[895,63537,63538],{},[2122,63539,63540,63542],{},[898,63541,2638],{},[898,63543,23098],{},[902,63545,63546],{"encoding":904},"Q_B"," — firma je na ",[38,63549,63550],{},"prahu rentability",[614,63552,63553],{},"break even","). Pro ",[883,63556,63558],{"className":63557},[886],[888,63559,63560],{"xmlns":890},[892,63561,63562,63574],{},[895,63563,63564,63566,63568],{},[898,63565,2638],{},[1846,63567,3295],{},[2122,63569,63570,63572],{},[898,63571,2638],{},[898,63573,4101],{},[902,63575,63576],{"encoding":904},"Q \u003C Q_A",[883,63578,63580],{"className":63579},[886],[888,63581,63582],{"xmlns":890},[892,63583,63584,63596],{},[895,63585,63586,63588,63590],{},[898,63587,2638],{},[1846,63589,3256],{},[2122,63591,63592,63594],{},[898,63593,2638],{},[898,63595,23098],{},[902,63597,63598],{"encoding":904},"Q > Q_B",[883,63600,63602],{"className":63601},[886],[888,63603,63604],{"xmlns":890},[892,63605,63606,63618],{},[895,63607,63608,63610,63612,63614,63616],{},[898,63609,2623],{},[898,63611,2626],{},[1846,63613,3256],{},[898,63615,2623],{},[898,63617,3840],{},[902,63619,63620],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,63623,63625],{"className":63624},[886],[888,63626,63627],{"xmlns":890},[892,63628,63629,63649],{},[895,63630,63631,63637,63639,63641,63643],{},[2122,63632,63633,63635],{},[898,63634,2638],{},[898,63636,4101],{},[1846,63638,3295],{},[898,63640,2638],{},[1846,63642,3295],{},[2122,63644,63645,63647],{},[898,63646,2638],{},[898,63648,23098],{},[902,63650,63651],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,63653,63655],{"className":63654},[886],[888,63656,63657],{"xmlns":890},[892,63658,63659,63671],{},[895,63660,63661,63663,63665,63667,63669],{},[898,63662,2623],{},[898,63664,3840],{},[1846,63666,3256],{},[898,63668,2623],{},[898,63670,2626],{},[902,63672,63673],{"encoding":904},"TR > TC"," (zisk).",[1639,63676,63677],{},[724,63678,63679,63681],{},[883,63680,4001],{}," 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.",[724,63683,63684,63685,63711],{},"Body zvratu jsou řešení rovnice ",[883,63686,63688],{"className":63687},[886],[888,63689,63690],{"xmlns":890},[892,63691,63692,63708],{},[895,63693,63694,63696,63698,63700,63702,63704,63706],{},[898,63695,3783],{},[898,63697,3840],{},[1846,63699,1855],{"stretchy":1854},[898,63701,2638],{},[1846,63703,1861],{"stretchy":1854},[1846,63705,1848],{},[1979,63707,2177],{},[902,63709,63710],{"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.",[724,63713,63714],{},[2409,63715],{"alt":63716,"className":63717,"src":63718},"imek-tr-tc-body-zvratu",[210,2413],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,63720,63721],{},[614,63722,63723,63724,63739,63740,63755,63756,1745,63769,43205,63782,63795,63796,1745,63813,63830,63831,63851,63852,1745,63867,6319,63882,63911],{},"Obrázek 3.11: Body zvratu — křivky ",[883,63725,63727],{"className":63726},[886],[888,63728,63729],{"xmlns":890},[892,63730,63731,63737],{},[895,63732,63733,63735],{},[898,63734,2623],{},[898,63736,3840],{},[902,63738,3940],{"encoding":904}," (obrácená parabola) a ",[883,63741,63743],{"className":63742},[886],[888,63744,63745],{"xmlns":890},[892,63746,63747,63753],{},[895,63748,63749,63751],{},[898,63750,2623],{},[898,63752,2626],{},[902,63754,3091],{"encoding":904}," (přímka) se protínají v bodech ",[883,63757,63759],{"className":63758},[886],[888,63760,63761],{"xmlns":890},[892,63762,63763,63767],{},[895,63764,63765],{},[898,63766,4101],{},[902,63768,4101],{"encoding":904},[883,63770,63772],{"className":63771},[886],[888,63773,63774],{"xmlns":890},[892,63775,63776,63780],{},[895,63777,63778],{},[898,63779,23098],{},[902,63781,23098],{"encoding":904},[883,63783,63785],{"className":63784},[886],[888,63786,63787],{"xmlns":890},[892,63788,63789,63793],{},[895,63790,63791],{},[898,63792,2638],{},[902,63794,2638],{"encoding":904}," v hodnotách ",[883,63797,63799],{"className":63798},[886],[888,63800,63801],{"xmlns":890},[892,63802,63803,63811],{},[895,63804,63805],{},[2122,63806,63807,63809],{},[898,63808,2638],{},[898,63810,4101],{},[902,63812,63528],{"encoding":904},[883,63814,63816],{"className":63815},[886],[888,63817,63818],{"xmlns":890},[892,63819,63820,63828],{},[895,63821,63822],{},[2122,63823,63824,63826],{},[898,63825,2638],{},[898,63827,23098],{},[902,63829,63546],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,63832,63834],{"className":63833},[886],[888,63835,63836],{"xmlns":890},[892,63837,63838,63848],{},[895,63839,63840],{},[2122,63841,63842,63844,63846],{},[898,63843,2638],{},[898,63845,56042],{},[1846,63847,56045],{},[902,63849,63850],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,63853,63855],{"className":63854},[886],[888,63856,63857],{"xmlns":890},[892,63858,63859,63865],{},[895,63860,63861,63863],{},[898,63862,2623],{},[898,63864,3840],{},[902,63866,3940],{"encoding":904},[883,63868,63870],{"className":63869},[886],[888,63871,63872],{"xmlns":890},[892,63873,63874,63880],{},[895,63875,63876,63878],{},[898,63877,2623],{},[898,63879,2626],{},[902,63881,3091],{"encoding":904},[883,63883,63885],{"className":63884},[886],[888,63886,63887],{"xmlns":890},[892,63888,63889,63909],{},[895,63890,63891,63897,63899,63901,63903],{},[2122,63892,63893,63895],{},[898,63894,2638],{},[898,63896,4101],{},[1846,63898,3295],{},[898,63900,2638],{},[1846,63902,3295],{},[2122,63904,63905,63907],{},[898,63906,2638],{},[898,63908,23098],{},[902,63910,63651],{"encoding":904}," vyznačuje zisk.",[37193,63913,63915],{"id":63914},"příklad-38","Příklad 3.8",[724,63917,63918,63920,63921,1343,63941,1343,63967,63993],{},[38,63919,55832],{}," Dáno ",[883,63922,63924],{"className":63923},[886],[888,63925,63926],{"xmlns":890},[892,63927,63928,63938],{},[895,63929,63930,63932,63934,63936],{},[898,63931,10282],{},[898,63933,2626],{},[1846,63935,1848],{},[1979,63937,2201],{},[902,63939,63940],{"encoding":904},"FC = 4",[883,63942,63944],{"className":63943},[886],[888,63945,63946],{"xmlns":890},[892,63947,63948,63964],{},[895,63949,63950,63952,63954,63956,63958],{},[898,63951,2623],{},[898,63953,40184],{},[898,63955,2626],{},[1846,63957,1848],{},[1974,63959,63960,63962],{},[898,63961,2638],{},[1979,63963,1981],{},[902,63965,63966],{"encoding":904},"TVC = Q^2",[883,63968,63970],{"className":63969},[886],[888,63971,63972],{"xmlns":890},[892,63973,63974,63990],{},[895,63975,63976,63978,63980,63982,63984,63986,63988],{},[898,63977,3783],{},[1846,63979,1848],{},[1846,63981,2075],{},[1979,63983,1981],{},[898,63985,2638],{},[1846,63987,1945],{},[1979,63989,3845],{},[902,63991,63992],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,63995,63996,63998],{},[38,63997,22615],{}," Celkové náklady a příjem:",[883,64000,64002],{"className":64001},[886],[888,64003,64004],{"xmlns":890,"display":27911},[892,64005,64006,64072],{},[895,64007,64008,64010,64012,64014,64016,64018,64024,64026,64028,64030,64032,64034,64036,64038,64040,64042,64044,64046,64048,64050,64052,64054,64056,64058,64064,64066,64068,64070],{},[898,64009,2623],{},[898,64011,2626],{},[1846,64013,1848],{},[1979,64015,2201],{},[1846,64017,1945],{},[1974,64019,64020,64022],{},[898,64021,2638],{},[1979,64023,1981],{},[1846,64025,2136],{"separator":2135},[5724,64027],{"width":5726},[898,64029,2623],{},[898,64031,3840],{},[1846,64033,1848],{},[898,64035,2638],{},[1846,64037,3025],{},[1846,64039,1855],{"stretchy":1854},[1846,64041,2075],{},[1979,64043,1981],{},[898,64045,2638],{},[1846,64047,1945],{},[1979,64049,3845],{},[1846,64051,1861],{"stretchy":1854},[1846,64053,1848],{},[1846,64055,2075],{},[1979,64057,1981],{},[1974,64059,64060,64062],{},[898,64061,2638],{},[1979,64063,1981],{},[1846,64065,1945],{},[1979,64067,3845],{},[898,64069,2638],{},[898,64071,1734],{"mathvariant":2226},[902,64073,64074],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,64076,64077],{},"Zisk dle (3.12):",[883,64079,64081],{"className":64080},[886],[888,64082,64083],{"xmlns":890,"display":27911},[892,64084,64085,64163],{},[895,64086,64087,64089,64091,64093,64095,64097,64099,64101,64103,64105,64107,64109,64111,64117,64119,64121,64123,64125,64127,64129,64131,64133,64139,64141,64143,64145,64147,64153,64155,64157,64159,64161],{},[898,64088,3783],{},[898,64090,3840],{},[1846,64092,1848],{},[898,64094,2623],{},[898,64096,3840],{},[1846,64098,2075],{},[898,64100,2623],{},[898,64102,2626],{},[1846,64104,1848],{},[1846,64106,1855],{"stretchy":1854},[1846,64108,2075],{},[1979,64110,1981],{},[1974,64112,64113,64115],{},[898,64114,2638],{},[1979,64116,1981],{},[1846,64118,1945],{},[1979,64120,3845],{},[898,64122,2638],{},[1846,64124,1861],{"stretchy":1854},[1846,64126,2075],{},[1846,64128,1855],{"stretchy":1854},[1979,64130,2201],{},[1846,64132,1945],{},[1974,64134,64135,64137],{},[898,64136,2638],{},[1979,64138,1981],{},[1846,64140,1861],{"stretchy":1854},[1846,64142,1848],{},[1846,64144,2075],{},[1979,64146,2023],{},[1974,64148,64149,64151],{},[898,64150,2638],{},[1979,64152,1981],{},[1846,64154,1945],{},[1979,64156,3845],{},[898,64158,2638],{},[1846,64160,2075],{},[1979,64162,59164],{},[902,64164,64165],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,64167,64168,64171,64172,17421,64208,2554],{},[38,64169,64170],{},"Body zvratu"," jsou kořeny rovnice ",[883,64173,64175],{"className":64174},[886],[888,64176,64177],{"xmlns":890},[892,64178,64179,64205],{},[895,64180,64181,64183,64185,64191,64193,64195,64197,64199,64201,64203],{},[1846,64182,2075],{},[1979,64184,2023],{},[1974,64186,64187,64189],{},[898,64188,2638],{},[1979,64190,1981],{},[1846,64192,1945],{},[1979,64194,3845],{},[898,64196,2638],{},[1846,64198,2075],{},[1979,64200,2201],{},[1846,64202,1848],{},[1979,64204,2177],{},[902,64206,64207],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,64209,64211],{"className":64210},[886],[888,64212,64213],{"xmlns":890},[892,64214,64215,64239],{},[895,64216,64217,64219,64225,64227,64229,64231,64233,64235,64237],{},[1979,64218,2023],{},[1974,64220,64221,64223],{},[898,64222,2638],{},[1979,64224,1981],{},[1846,64226,2075],{},[1979,64228,3845],{},[898,64230,2638],{},[1846,64232,1945],{},[1979,64234,2201],{},[1846,64236,1848],{},[1979,64238,2177],{},[902,64240,64241],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,64243,64245],{"className":64244},[886],[888,64246,64247],{"xmlns":890,"display":27911},[892,64248,64249,64306],{},[895,64250,64251,64263,64265,64288,64290,64304],{},[2122,64252,64253,64255],{},[898,64254,2638],{},[895,64256,64257,64259,64261],{},[1979,64258,2128],{},[1846,64260,2136],{"separator":2135},[1979,64262,1981],{},[1846,64264,1848],{},[2179,64266,64267,64286],{},[895,64268,64269,64271,64274],{},[1979,64270,3845],{},[1846,64272,64273],{},"±",[7963,64275,64276],{},[895,64277,64278,64281,64283],{},[1979,64279,64280],{},"81",[1846,64282,2075],{},[1979,64284,64285],{},"48",[1979,64287,2085],{},[1846,64289,1848],{},[2179,64291,64292,64302],{},[895,64293,64294,64296,64298],{},[1979,64295,3845],{},[1846,64297,64273],{},[7963,64299,64300],{},[1979,64301,8797],{},[1979,64303,2085],{},[1846,64305,2136],{"separator":2135},[902,64307,64308],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,64310,64311,64312,1745,64335,1734],{},"numericky ",[883,64313,64315],{"className":64314},[886],[888,64316,64317],{"xmlns":890},[892,64318,64319,64332],{},[895,64320,64321,64327,64329],{},[2122,64322,64323,64325],{},[898,64324,2638],{},[1979,64326,2128],{},[1846,64328,5746],{},[1979,64330,64331],{},"0,543",[902,64333,64334],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,64336,64338],{"className":64337},[886],[888,64339,64340],{"xmlns":890},[892,64341,64342,64355],{},[895,64343,64344,64350,64352],{},[2122,64345,64346,64348],{},[898,64347,2638],{},[1979,64349,1981],{},[1846,64351,5746],{},[1979,64353,64354],{},"2,457",[902,64356,64357],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,64359,64360,2053,64363,7398,64408,17421,64442,64460],{},[38,64361,64362],{},"Maximum zisku.",[883,64364,64366],{"className":64365},[886],[888,64367,64368],{"xmlns":890},[892,64369,64370,64405],{},[895,64371,64372,64374,64380,64382,64384,64386,64388,64390,64392,64394,64396,64398,64400,64402],{},[898,64373,3783],{},[1974,64375,64376,64378],{},[898,64377,3840],{},[1846,64379,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,64381,1848],{},[1846,64383,2075],{},[1979,64385,2085],{},[898,64387,2638],{},[1846,64389,1945],{},[1979,64391,3845],{},[1846,64393,1848],{},[1979,64395,2177],{},[1846,64397,3833],{},[898,64399,2638],{},[1846,64401,1848],{},[1979,64403,64404],{},"1,5",[902,64406,64407],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,64409,64411],{"className":64410},[886],[888,64412,64413],{"xmlns":890},[892,64414,64415,64439],{},[895,64416,64417,64419,64429,64431,64433,64435,64437],{},[898,64418,3783],{},[1974,64420,64421,64423],{},[898,64422,3840],{},[895,64424,64425,64427],{},[1846,64426,2228],{"mathvariant":2226},[1846,64428,2228],{"mathvariant":2226},[1846,64430,1848],{},[1846,64432,2075],{},[1979,64434,2085],{},[1846,64436,3295],{},[1979,64438,2177],{},[902,64440,64441],{"encoding":904},"PR'' = -6 \u003C 0",[883,64443,64445],{"className":64444},[886],[888,64446,64447],{"xmlns":890},[892,64448,64449,64457],{},[895,64450,64451,64453,64455],{},[898,64452,2638],{},[1846,64454,1848],{},[1979,64456,64404],{},[902,64458,64459],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,64462,64464],{"className":64463},[886],[888,64465,64466],{"xmlns":890,"display":27911},[892,64467,64468,64531],{},[895,64469,64470,64472,64474,64476,64478,64480,64482,64484,64486,64488,64490,64492,64498,64500,64502,64504,64506,64508,64510,64512,64514,64517,64519,64522,64524,64526,64528],{},[898,64471,3783],{},[898,64473,3840],{},[1846,64475,1855],{"stretchy":1854},[1979,64477,64404],{},[1846,64479,1861],{"stretchy":1854},[1846,64481,1848],{},[1846,64483,2075],{},[1979,64485,2023],{},[1846,64487,3025],{},[1846,64489,1855],{"stretchy":1854},[1979,64491,64404],{},[1974,64493,64494,64496],{},[1846,64495,1861],{"stretchy":1854},[1979,64497,1981],{},[1846,64499,1945],{},[1979,64501,3845],{},[1846,64503,3025],{},[1979,64505,64404],{},[1846,64507,2075],{},[1979,64509,2201],{},[1846,64511,1848],{},[1846,64513,2075],{},[1979,64515,64516],{},"6,75",[1846,64518,1945],{},[1979,64520,64521],{},"13,5",[1846,64523,2075],{},[1979,64525,2201],{},[1846,64527,1848],{},[1979,64529,64530],{},"2,75.",[902,64532,64533],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,64535,64536,64537,1343,64582,64635,64636,64654],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,64538,64540],{"className":64539},[886],[888,64541,64542],{"xmlns":890},[892,64543,64544,64579],{},[895,64545,64546,64548,64554,64556,64558,64560,64562,64564,64566,64568,64570,64572,64574,64576],{},[898,64547,2623],{},[1974,64549,64550,64552],{},[898,64551,3840],{},[1846,64553,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,64555,1848],{},[1846,64557,2075],{},[1979,64559,2201],{},[898,64561,2638],{},[1846,64563,1945],{},[1979,64565,3845],{},[1846,64567,1848],{},[1979,64569,2177],{},[1846,64571,3833],{},[898,64573,2638],{},[1846,64575,1848],{},[1979,64577,64578],{},"2,25",[902,64580,64581],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,64583,64585],{"className":64584},[886],[888,64586,64587],{"xmlns":890},[892,64588,64589,64632],{},[895,64590,64591,64593,64601,64603,64605,64607,64609,64611,64613,64619,64621,64623,64625,64627,64629],{},[898,64592,2623],{},[2122,64594,64595,64597,64599],{},[898,64596,3840],{},[898,64598,56042],{},[1846,64600,56045],{},[1846,64602,1848],{},[1846,64604,2075],{},[1979,64606,1981],{},[1846,64608,3025],{},[1846,64610,1855],{"stretchy":1854},[1979,64612,64578],{},[1974,64614,64615,64617],{},[1846,64616,1861],{"stretchy":1854},[1979,64618,1981],{},[1846,64620,1945],{},[1979,64622,3845],{},[1846,64624,3025],{},[1979,64626,64578],{},[1846,64628,1848],{},[1979,64630,64631],{},"10,125",[902,64633,64634],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,64637,64639],{"className":64638},[886],[888,64640,64641],{"xmlns":890},[892,64642,64643,64651],{},[895,64644,64645,64647,64649],{},[898,64646,2638],{},[1846,64648,1848],{},[1979,64650,64578],{},[902,64652,64653],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[1639,64656,64657],{},[724,64658,64659,64661,64662,1343,64684,64706,64707,1343,64724,64745,64746,64778,64779,64817,64818,2521,64836,64853,64854,1745,64882,64916,64917,7531,64955,1745,64979,1734],{},[883,64660,4258],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,64663,64665],{"className":64664},[886],[888,64666,64667],{"xmlns":890},[892,64668,64669,64681],{},[895,64670,64671,64677,64679],{},[2122,64672,64673,64675],{},[898,64674,2638],{},[1979,64676,2128],{},[1846,64678,1848],{},[1979,64680,4855],{},[902,64682,64683],{"encoding":904},"Q_1 = 0{,}5",[883,64685,64687],{"className":64686},[886],[888,64688,64689],{"xmlns":890},[892,64690,64691,64703],{},[895,64692,64693,64699,64701],{},[2122,64694,64695,64697],{},[898,64696,2638],{},[1979,64698,1981],{},[1846,64700,1848],{},[1979,64702,2201],{},[902,64704,64705],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,64708,64710],{"className":64709},[886],[888,64711,64712],{"xmlns":890},[892,64713,64714,64722],{},[895,64715,64716,64718,64720],{},[898,64717,2638],{},[1846,64719,1848],{},[1979,64721,64578],{},[902,64723,64653],{"encoding":904},[883,64725,64727],{"className":64726},[886],[888,64728,64729],{"xmlns":890},[892,64730,64731,64742],{},[895,64732,64733,64735,64737,64739],{},[898,64734,3783],{},[898,64736,3840],{},[1846,64738,1848],{},[1979,64740,64741],{},"6,125",[902,64743,64744],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,64747,64749],{"className":64748},[886],[888,64750,64751],{"xmlns":890},[892,64752,64753,64775],{},[895,64754,64755,64757,64763,64765,64767,64769,64771,64773],{},[898,64756,3783],{},[1974,64758,64759,64761],{},[898,64760,3840],{},[1846,64762,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,64764,1848],{},[1846,64766,2075],{},[1979,64768,2201],{},[898,64770,2638],{},[1846,64772,1945],{},[1979,64774,3845],{},[902,64776,64777],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,64780,64782],{"className":64781},[886],[888,64783,64784],{"xmlns":890},[892,64785,64786,64814],{},[895,64787,64788,64790,64792,64794,64796,64798,64804,64806,64808,64810,64812],{},[898,64789,3783],{},[898,64791,3840],{},[1846,64793,1848],{},[1846,64795,2075],{},[1979,64797,1981],{},[1974,64799,64800,64802],{},[898,64801,2638],{},[1979,64803,1981],{},[1846,64805,1945],{},[1979,64807,3845],{},[898,64809,2638],{},[1846,64811,2075],{},[1979,64813,2201],{},[902,64815,64816],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,64819,64821],{"className":64820},[886],[888,64822,64823],{"xmlns":890},[892,64824,64825,64833],{},[895,64826,64827],{},[1974,64828,64829,64831],{},[898,64830,2638],{},[1979,64832,1981],{},[902,64834,64835],{"encoding":904},"Q^2",[883,64837,64839],{"className":64838},[886],[888,64840,64841],{"xmlns":890},[892,64842,64843,64851],{},[895,64844,64845,64847,64849],{},[898,64846,2623],{},[898,64848,40184],{},[898,64850,2626],{},[902,64852,55354],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,64855,64857],{"className":64856},[886],[888,64858,64859],{"xmlns":890},[892,64860,64861,64879],{},[895,64862,64863,64865,64867,64869,64871,64873],{},[898,64864,2623],{},[898,64866,2626],{},[1846,64868,1848],{},[1979,64870,2201],{},[1846,64872,1945],{},[1974,64874,64875,64877],{},[898,64876,2638],{},[1979,64878,1981],{},[902,64880,64881],{"encoding":904},"TC = 4 + Q^2",[883,64883,64885],{"className":64884},[886],[888,64886,64887],{"xmlns":890},[892,64888,64889,64913],{},[895,64890,64891,64893,64895,64897,64899,64901,64907,64909,64911],{},[898,64892,2623],{},[898,64894,3840],{},[1846,64896,1848],{},[1846,64898,2075],{},[1979,64900,1981],{},[1974,64902,64903,64905],{},[898,64904,2638],{},[1979,64906,1981],{},[1846,64908,1945],{},[1979,64910,3845],{},[898,64912,2638],{},[902,64914,64915],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,64918,64920],{"className":64919},[886],[888,64921,64922],{"xmlns":890},[892,64923,64924,64952],{},[895,64925,64926,64928,64930,64932,64934,64936,64942,64944,64946,64948,64950],{},[898,64927,3783],{},[898,64929,3840],{},[1846,64931,1848],{},[1846,64933,2075],{},[1979,64935,2023],{},[1974,64937,64938,64940],{},[898,64939,2638],{},[1979,64941,1981],{},[1846,64943,1945],{},[1979,64945,3845],{},[898,64947,2638],{},[1846,64949,2075],{},[1979,64951,2201],{},[902,64953,64954],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,64956,64958],{"className":64957},[886],[888,64959,64960],{"xmlns":890},[892,64961,64962,64976],{},[895,64963,64964,64972,64974],{},[2122,64965,64966,64968,64970],{},[898,64967,2638],{},[898,64969,56042],{},[1846,64971,56045],{},[1846,64973,1848],{},[1979,64975,64404],{},[902,64977,64978],{"encoding":904},"Q_{\\max} = 1{,}5",[883,64980,64982],{"className":64981},[886],[888,64983,64984],{"xmlns":890},[892,64985,64986,65003],{},[895,64987,64988,64990,64998,65000],{},[898,64989,3783],{},[2122,64991,64992,64994,64996],{},[898,64993,3840],{},[898,64995,56042],{},[1846,64997,56045],{},[1846,64999,1848],{},[1979,65001,65002],{},"2,75",[902,65004,65005],{"encoding":904},"PR_{\\max} = 2{,}75",[724,65007,65008],{},[614,65009,65010,65011,65038,65039,65072,65073,1343,65096,1734],{},"Obrázek 3.12: Graf ",[883,65012,65014],{"className":65013},[886],[888,65015,65016],{"xmlns":890},[892,65017,65018,65036],{},[895,65019,65020,65022,65024,65026,65028,65030],{},[898,65021,2623],{},[898,65023,2626],{},[1846,65025,1848],{},[1979,65027,2201],{},[1846,65029,1945],{},[1974,65031,65032,65034],{},[898,65033,2638],{},[1979,65035,1981],{},[902,65037,64881],{"encoding":904}," (parabola) a ",[883,65040,65042],{"className":65041},[886],[888,65043,65044],{"xmlns":890},[892,65045,65046,65070],{},[895,65047,65048,65050,65052,65054,65056,65058,65064,65066,65068],{},[898,65049,2623],{},[898,65051,3840],{},[1846,65053,1848],{},[1846,65055,2075],{},[1979,65057,1981],{},[1974,65059,65060,65062],{},[898,65061,2638],{},[1979,65063,1981],{},[1846,65065,1945],{},[1979,65067,3845],{},[898,65069,2638],{},[902,65071,64915],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,65074,65076],{"className":65075},[886],[888,65077,65078],{"xmlns":890},[892,65079,65080,65093],{},[895,65081,65082,65088,65090],{},[2122,65083,65084,65086],{},[898,65085,2638],{},[1979,65087,2128],{},[1846,65089,5746],{},[1979,65091,65092],{},"0,54",[902,65094,65095],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,65097,65099],{"className":65098},[886],[888,65100,65101],{"xmlns":890},[892,65102,65103,65116],{},[895,65104,65105,65111,65113],{},[2122,65106,65107,65109],{},[898,65108,2638],{},[1979,65110,1981],{},[1846,65112,5746],{},[1979,65114,65115],{},"2,46",[902,65117,65118],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,65120,65121],{},[614,65122,65123,65124,58352,65161,65178,65179,1343,65200,1734],{},"Obrázek 3.13: Graf zisku ",[883,65125,65127],{"className":65126},[886],[888,65128,65129],{"xmlns":890},[892,65130,65131,65159],{},[895,65132,65133,65135,65137,65139,65141,65143,65149,65151,65153,65155,65157],{},[898,65134,3783],{},[898,65136,3840],{},[1846,65138,1848],{},[1846,65140,2075],{},[1979,65142,2023],{},[1974,65144,65145,65147],{},[898,65146,2638],{},[1979,65148,1981],{},[1846,65150,1945],{},[1979,65152,3845],{},[898,65154,2638],{},[1846,65156,2075],{},[1979,65158,2201],{},[902,65160,64954],{"encoding":904},[883,65162,65164],{"className":65163},[886],[888,65165,65166],{"xmlns":890},[892,65167,65168,65176],{},[895,65169,65170,65172,65174],{},[898,65171,2638],{},[1846,65173,1848],{},[1979,65175,64404],{},[902,65177,64459],{"encoding":904}," a nulami ",[883,65180,65182],{"className":65181},[886],[888,65183,65184],{"xmlns":890},[892,65185,65186,65198],{},[895,65187,65188,65194,65196],{},[2122,65189,65190,65192],{},[898,65191,2638],{},[1979,65193,2128],{},[1846,65195,5746],{},[1979,65197,65092],{},[902,65199,65095],{"encoding":904},[883,65201,65203],{"className":65202},[886],[888,65204,65205],{"xmlns":890},[892,65206,65207,65219],{},[895,65208,65209,65215,65217],{},[2122,65210,65211,65213],{},[898,65212,2638],{},[1979,65214,1981],{},[1846,65216,5746],{},[1979,65218,65115],{},[902,65220,65118],{"encoding":904},[115,65222,65224],{"id":65223},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,65226,65227],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,65229,65230],{},[2409,65231],{"alt":65232,"className":65233,"src":65234},"imek-max-zisku-dva-pohledy",[210,2413],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,65236,16257],{"id":65237},"princip-1",[724,65239,65240,65241,2474,65256,65273],{},"Má-li zisk ",[883,65242,65244],{"className":65243},[886],[888,65245,65246],{"xmlns":890},[892,65247,65248,65254],{},[895,65249,65250,65252],{},[898,65251,3783],{},[898,65253,3840],{},[902,65255,63324],{"encoding":904},[883,65257,65259],{"className":65258},[886],[888,65260,65261],{"xmlns":890},[892,65262,65263,65271],{},[895,65264,65265],{},[2122,65266,65267,65269],{},[898,65268,2638],{},[1979,65270,2177],{},[902,65272,38153],{"encoding":904}," maximum, pak platí",[883,65275,65277],{"className":65276},[886],[888,65278,65279],{"xmlns":890,"display":27911},[892,65280,65281,65330],{},[20599,65282,65283],{"width":27916},[20604,65284,65285,65287,65323,65325],{},[20607,65286],{"width":27921},[20607,65288,65289],{},[895,65290,65291,65293,65295,65297,65303,65305,65307,65309,65311,65313,65319,65321],{},[898,65292,2667],{},[898,65294,3840],{},[1846,65296,1855],{"stretchy":1854},[2122,65298,65299,65301],{},[898,65300,2638],{},[1979,65302,2177],{},[1846,65304,1861],{"stretchy":1854},[1846,65306,1848],{},[898,65308,2667],{},[898,65310,2626],{},[1846,65312,1855],{"stretchy":1854},[2122,65314,65315,65317],{},[898,65316,2638],{},[1979,65318,2177],{},[1846,65320,1861],{"stretchy":1854},[898,65322,1734],{"mathvariant":2226},[20607,65324],{"width":27921},[20607,65326,65327],{},[2138,65328,65329],{},"(3.13)",[902,65331,65332],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[1639,65334,65335],{},[724,65336,65337,61891,65339],{},[883,65338,56289],{},[38,65340,65341],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,65343,65344,65347,65348,7948,65375,17421,65449,1734],{},[38,65345,65346],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,65349,65351],{"className":65350},[886],[888,65352,65353],{"xmlns":890},[892,65354,65355,65373],{},[895,65356,65357,65359,65361,65363,65365,65367,65369,65371],{},[898,65358,3783],{},[898,65360,3840],{},[1846,65362,1848],{},[898,65364,2623],{},[898,65366,3840],{},[1846,65368,2075],{},[898,65370,2623],{},[898,65372,2626],{},[902,65374,55045],{"encoding":904},[883,65376,65378],{"className":65377},[886],[888,65379,65380],{"xmlns":890},[892,65381,65382,65446],{},[895,65383,65384,65386,65392,65394,65400,65402,65404,65406,65412,65414,65420,65422,65424,65426,65432,65434,65440,65442,65444],{},[898,65385,3783],{},[1974,65387,65388,65390],{},[898,65389,3840],{},[1846,65391,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,65393,1855],{"stretchy":1854},[2122,65395,65396,65398],{},[898,65397,2638],{},[1979,65399,2177],{},[1846,65401,1861],{"stretchy":1854},[1846,65403,1848],{},[898,65405,2623],{},[1974,65407,65408,65410],{},[898,65409,3840],{},[1846,65411,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,65413,1855],{"stretchy":1854},[2122,65415,65416,65418],{},[898,65417,2638],{},[1979,65419,2177],{},[1846,65421,1861],{"stretchy":1854},[1846,65423,2075],{},[898,65425,2623],{},[1974,65427,65428,65430],{},[898,65429,2626],{},[1846,65431,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,65433,1855],{"stretchy":1854},[2122,65435,65436,65438],{},[898,65437,2638],{},[1979,65439,2177],{},[1846,65441,1861],{"stretchy":1854},[1846,65443,1848],{},[1979,65445,2177],{},[902,65447,65448],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,65450,65452],{"className":65451},[886],[888,65453,65454],{"xmlns":890},[892,65455,65456,65488],{},[895,65457,65458,65460,65462,65464,65470,65472,65474,65476,65478,65480,65486],{},[898,65459,2667],{},[898,65461,3840],{},[1846,65463,1855],{"stretchy":1854},[2122,65465,65466,65468],{},[898,65467,2638],{},[1979,65469,2177],{},[1846,65471,1861],{"stretchy":1854},[1846,65473,1848],{},[898,65475,2667],{},[898,65477,2626],{},[1846,65479,1855],{"stretchy":1854},[2122,65481,65482,65484],{},[898,65483,2638],{},[1979,65485,2177],{},[1846,65487,1861],{"stretchy":1854},[902,65489,65490],{"encoding":904},"MR(Q_0) = MC(Q_0)",[1639,65492,65493,65498],{},[724,65494,65495,65497],{},[883,65496,4418],{}," Postup — jak najít maximum zisku",[152,65499,65500,65564,65619,65656,65684],{},[123,65501,65502,65503,1745,65518,65533,65534,3764],{},"Sestavte ",[883,65504,65506],{"className":65505},[886],[888,65507,65508],{"xmlns":890},[892,65509,65510,65516],{},[895,65511,65512,65514],{},[898,65513,2623],{},[898,65515,3840],{},[902,65517,3940],{"encoding":904},[883,65519,65521],{"className":65520},[886],[888,65522,65523],{"xmlns":890},[892,65524,65525,65531],{},[895,65526,65527,65529],{},[898,65528,2623],{},[898,65530,2626],{},[902,65532,3091],{"encoding":904}," ze zadání (typicky ",[883,65535,65537],{"className":65536},[886],[888,65538,65539],{"xmlns":890},[892,65540,65541,65561],{},[895,65542,65543,65545,65547,65549,65551,65553,65555,65557,65559],{},[898,65544,2623],{},[898,65546,3840],{},[1846,65548,1848],{},[898,65550,3783],{},[1846,65552,1855],{"stretchy":1854},[898,65554,2638],{},[1846,65556,1861],{"stretchy":1854},[1846,65558,3025],{},[898,65560,2638],{},[902,65562,65563],{"encoding":904},"TR = P(Q) \\cdot Q",[123,65565,65566,65567,1745,65593,1734],{},"Vypočtěte ",[883,65568,65570],{"className":65569},[886],[888,65571,65572],{"xmlns":890},[892,65573,65574,65590],{},[895,65575,65576,65578,65580,65582,65584],{},[898,65577,2667],{},[898,65579,3840],{},[1846,65581,1848],{},[898,65583,2623],{},[1974,65585,65586,65588],{},[898,65587,3840],{},[1846,65589,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,65591,65592],{"encoding":904},"MR = TR'",[883,65594,65596],{"className":65595},[886],[888,65597,65598],{"xmlns":890},[892,65599,65600,65616],{},[895,65601,65602,65604,65606,65608,65610],{},[898,65603,2667],{},[898,65605,2626],{},[1846,65607,1848],{},[898,65609,2623],{},[1974,65611,65612,65614],{},[898,65613,2626],{},[1846,65615,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,65617,65618],{"encoding":904},"MC = TC'",[123,65620,65621,65622,1734],{},"Řešte rovnici ",[883,65623,65625],{"className":65624},[886],[888,65626,65627],{"xmlns":890},[892,65628,65629,65653],{},[895,65630,65631,65633,65635,65637,65639,65641,65643,65645,65647,65649,65651],{},[898,65632,2667],{},[898,65634,3840],{},[1846,65636,1855],{"stretchy":1854},[898,65638,2638],{},[1846,65640,1861],{"stretchy":1854},[1846,65642,1848],{},[898,65644,2667],{},[898,65646,2626],{},[1846,65648,1855],{"stretchy":1854},[898,65650,2638],{},[1846,65652,1861],{"stretchy":1854},[902,65654,65655],{"encoding":904},"MR(Q) = MC(Q)",[123,65657,65658,65659,65683],{},"Ověřte druhou derivaci ",[883,65660,65662],{"className":65661},[886],[888,65663,65664],{"xmlns":890},[892,65665,65666,65680],{},[895,65667,65668,65670],{},[898,65669,3783],{},[1974,65671,65672,65674],{},[898,65673,3840],{},[895,65675,65676,65678],{},[1846,65677,2228],{"mathvariant":2226},[1846,65679,2228],{"mathvariant":2226},[902,65681,65682],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,65685,65686,65687,65714],{},"Dosaďte do ",[883,65688,65690],{"className":65689},[886],[888,65691,65692],{"xmlns":890},[892,65693,65694,65712],{},[895,65695,65696,65698,65700,65702,65704,65706,65708,65710],{},[898,65697,3783],{},[898,65699,3840],{},[1846,65701,1848],{},[898,65703,2623],{},[898,65705,3840],{},[1846,65707,2075],{},[898,65709,2623],{},[898,65711,2626],{},[902,65713,55045],{"encoding":904}," pro hodnotu maxima.",[37193,65716,65718],{"id":65717},"příklad-39","Příklad 3.9",[724,65720,65721,55833,65723,1745,65745,65781],{},[38,65722,55832],{},[883,65724,65726],{"className":65725},[886],[888,65727,65728],{"xmlns":890},[892,65729,65730,65742],{},[895,65731,65732,65734,65736,65738,65740],{},[898,65733,3783],{},[1846,65735,1848],{},[1979,65737,37864],{},[1846,65739,2075],{},[898,65741,2638],{},[902,65743,65744],{"encoding":904},"P = 30 - Q",[883,65746,65748],{"className":65747},[886],[888,65749,65750],{"xmlns":890},[892,65751,65752,65778],{},[895,65753,65754,65756,65758,65760,65762,65768,65770,65772,65774,65776],{},[898,65755,2623],{},[898,65757,2626],{},[1846,65759,1848],{},[1979,65761,4855],{},[1974,65763,65764,65766],{},[898,65765,2638],{},[1979,65767,1981],{},[1846,65769,1945],{},[1979,65771,2085],{},[898,65773,2638],{},[1846,65775,1945],{},[1979,65777,24046],{},[902,65779,65780],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,65783,65784,2053,65786,1343,65816,65854,65855,15637,65899,65933,65934,1734],{},[38,65785,22615],{},[883,65787,65789],{"className":65788},[886],[888,65790,65791],{"xmlns":890},[892,65792,65793,65813],{},[895,65794,65795,65797,65799,65801,65803,65805,65807],{},[898,65796,2623],{},[898,65798,3840],{},[1846,65800,1848],{},[1979,65802,37864],{},[898,65804,2638],{},[1846,65806,2075],{},[1974,65808,65809,65811],{},[898,65810,2638],{},[1979,65812,1981],{},[902,65814,65815],{"encoding":904},"TR = 30Q - Q^2",[883,65817,65819],{"className":65818},[886],[888,65820,65821],{"xmlns":890},[892,65822,65823,65851],{},[895,65824,65825,65827,65829,65831,65833,65835,65841,65843,65845,65847,65849],{},[898,65826,3783],{},[898,65828,3840],{},[1846,65830,1848],{},[1846,65832,2075],{},[1979,65834,64404],{},[1974,65836,65837,65839],{},[898,65838,2638],{},[1979,65840,1981],{},[1846,65842,1945],{},[1979,65844,41645],{},[898,65846,2638],{},[1846,65848,2075],{},[1979,65850,24046],{},[902,65852,65853],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,65856,65858],{"className":65857},[886],[888,65859,65860],{"xmlns":890},[892,65861,65862,65896],{},[895,65863,65864,65866,65872,65874,65876,65878,65880,65882,65884,65886,65888,65890,65892,65894],{},[898,65865,3783],{},[1974,65867,65868,65870],{},[898,65869,3840],{},[1846,65871,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,65873,1848],{},[1846,65875,2075],{},[1979,65877,2023],{},[898,65879,2638],{},[1846,65881,1945],{},[1979,65883,41645],{},[1846,65885,1848],{},[1979,65887,2177],{},[1846,65889,3833],{},[898,65891,2638],{},[1846,65893,1848],{},[1979,65895,5431],{},[902,65897,65898],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,65900,65902],{"className":65901},[886],[888,65903,65904],{"xmlns":890},[892,65905,65906,65930],{},[895,65907,65908,65910,65920,65922,65924,65926,65928],{},[898,65909,3783],{},[1974,65911,65912,65914],{},[898,65913,3840],{},[895,65915,65916,65918],{},[1846,65917,2228],{"mathvariant":2226},[1846,65919,2228],{"mathvariant":2226},[1846,65921,1848],{},[1846,65923,2075],{},[1979,65925,2023],{},[1846,65927,3295],{},[1979,65929,2177],{},[902,65931,65932],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,65935,65937],{"className":65936},[886],[888,65938,65939],{"xmlns":890},[892,65940,65941,65958],{},[895,65942,65943,65945,65947,65949,65951,65953,65955],{},[898,65944,3783],{},[898,65946,3840],{},[1846,65948,1855],{"stretchy":1854},[1979,65950,5431],{},[1846,65952,1861],{"stretchy":1854},[1846,65954,1848],{},[1979,65956,65957],{},"89",[902,65959,65960],{"encoding":904},"PR(8) = 89",[724,65962,65963,65964,1343,65990,15637,66014,66052],{},"Ověření principu: ",[883,65965,65967],{"className":65966},[886],[888,65968,65969],{"xmlns":890},[892,65970,65971,65987],{},[895,65972,65973,65975,65977,65979,65981,65983,65985],{},[898,65974,2667],{},[898,65976,3840],{},[1846,65978,1848],{},[1979,65980,37864],{},[1846,65982,2075],{},[1979,65984,1981],{},[898,65986,2638],{},[902,65988,65989],{"encoding":904},"MR = 30 - 2Q",[883,65991,65993],{"className":65992},[886],[888,65994,65995],{"xmlns":890},[892,65996,65997,66011],{},[895,65998,65999,66001,66003,66005,66007,66009],{},[898,66000,2667],{},[898,66002,2626],{},[1846,66004,1848],{},[898,66006,2638],{},[1846,66008,1945],{},[1979,66010,2085],{},[902,66012,66013],{"encoding":904},"MC = Q + 6",[883,66015,66017],{"className":66016},[886],[888,66018,66019],{"xmlns":890},[892,66020,66021,66049],{},[895,66022,66023,66025,66027,66029,66031,66033,66035,66037,66039,66041,66043,66045,66047],{},[898,66024,2667],{},[898,66026,3840],{},[1846,66028,1855],{"stretchy":1854},[1979,66030,5431],{},[1846,66032,1861],{"stretchy":1854},[1846,66034,1848],{},[1979,66036,22791],{},[1846,66038,1848],{},[898,66040,2667],{},[898,66042,2626],{},[1846,66044,1855],{"stretchy":1854},[1979,66046,5431],{},[1846,66048,1861],{"stretchy":1854},[902,66050,66051],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,66054,66055,66056,66089,66090,66107],{},"V řadě případů — má-li rovnice ",[883,66057,66059],{"className":66058},[886],[888,66060,66061],{"xmlns":890},[892,66062,66063,66087],{},[895,66064,66065,66067,66069,66071,66073,66075,66077,66079,66081,66083,66085],{},[898,66066,2667],{},[898,66068,3840],{},[1846,66070,1855],{"stretchy":1854},[898,66072,2638],{},[1846,66074,1861],{"stretchy":1854},[1846,66076,1848],{},[898,66078,2667],{},[898,66080,2626],{},[1846,66082,1855],{"stretchy":1854},[898,66084,2638],{},[1846,66086,1861],{"stretchy":1854},[902,66088,65655],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,66091,66093],{"className":66092},[886],[888,66094,66095],{"xmlns":890},[892,66096,66097,66105],{},[895,66098,66099],{},[2122,66100,66101,66103],{},[898,66102,2638],{},[1979,66104,2177],{},[902,66106,38153],{"encoding":904}," — není třeba provádět test druhé derivace.",[37193,66109,66111],{"id":66110},"příklad-310","Příklad 3.10",[724,66113,66114,66116,66117,66121,66122,66135,66136,66167],{},[38,66115,55832],{}," Firma vyrábí minipočítače v ",[207,66118,66120],{"className":66119,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,66123,66125],{"className":66124},[886],[888,66126,66127],{"xmlns":890},[892,66128,66129,66133],{},[895,66130,66131],{},[1979,66132,15036],{},[902,66134,15036],{"encoding":904}," EUR\u002Fks. ",[883,66137,66139],{"className":66138},[886],[888,66140,66141],{"xmlns":890},[892,66142,66143,66164],{},[895,66144,66145,66147,66149,66151,66153,66155,66158],{},[898,66146,2623],{},[898,66148,2626],{},[1846,66150,1848],{},[1979,66152,2968],{},[1846,66154,1945],{},[1979,66156,66157],{},"28",[1974,66159,66160,66162],{},[898,66161,2638],{},[1979,66163,1981],{},[902,66165,66166],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,66169,66170,2053,66172,1343,66194,1343,66214,66237],{},[38,66171,22615],{},[883,66173,66175],{"className":66174},[886],[888,66176,66177],{"xmlns":890},[892,66178,66179,66191],{},[895,66180,66181,66183,66185,66187,66189],{},[898,66182,2623],{},[898,66184,3840],{},[1846,66186,1848],{},[1979,66188,15036],{},[898,66190,2638],{},[902,66192,66193],{"encoding":904},"TR = 900Q",[883,66195,66197],{"className":66196},[886],[888,66198,66199],{"xmlns":890},[892,66200,66201,66211],{},[895,66202,66203,66205,66207,66209],{},[898,66204,2667],{},[898,66206,3840],{},[1846,66208,1848],{},[1979,66210,15036],{},[902,66212,66213],{"encoding":904},"MR = 900",[883,66215,66217],{"className":66216},[886],[888,66218,66219],{"xmlns":890},[892,66220,66221,66234],{},[895,66222,66223,66225,66227,66229,66232],{},[898,66224,2667],{},[898,66226,2626],{},[1846,66228,1848],{},[1979,66230,66231],{},"56",[898,66233,2638],{},[902,66235,66236],{"encoding":904},"MC = 56Q",". Z principu:",[883,66239,66241],{"className":66240},[886],[888,66242,66243],{"xmlns":890,"display":27911},[892,66244,66245,66287],{},[895,66246,66247,66249,66251,66253,66255,66257,66259,66261,66263,66265,66273,66275,66278,66280,66282,66284],{},[1979,66248,15036],{},[1846,66250,1848],{},[1979,66252,66231],{},[898,66254,2638],{},[2138,66256,3830],{},[1846,66258,3833],{},[2138,66260,3830],{},[898,66262,2638],{},[1846,66264,1848],{},[2175,66266,66267],{"scriptlevel":2177,"displaystyle":1854},[2179,66268,66269,66271],{},[1979,66270,15036],{},[1979,66272,66231],{},[1846,66274,5746],{},[1979,66276,66277],{},"16,07",[2138,66279,3830],{},[1846,66281,1650],{},[2138,66283,3830],{},[1979,66285,66286],{},"16.",[902,66288,66289],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,66291,66292,66293,2554],{},"Zisk při ",[883,66294,66296],{"className":66295},[886],[888,66297,66298],{"xmlns":890},[892,66299,66300,66308],{},[895,66301,66302,66304,66306],{},[898,66303,2638],{},[1846,66305,1848],{},[1979,66307,41707],{},[902,66309,66310],{"encoding":904},"Q = 16",[883,66312,66314],{"className":66313},[886],[888,66315,66316],{"xmlns":890,"display":27911},[892,66317,66318,66389],{},[895,66319,66320,66322,66324,66326,66328,66330,66332,66334,66336,66338,66340,66342,66344,66346,66348,66350,66356,66358,66360,66362,66364,66366,66368,66370,66372,66375,66377,66379,66381,66384,66387],{},[898,66321,3783],{},[898,66323,3840],{},[1846,66325,1855],{"stretchy":1854},[1979,66327,41707],{},[1846,66329,1861],{"stretchy":1854},[1846,66331,1848],{},[1979,66333,15036],{},[1846,66335,3025],{},[1979,66337,41707],{},[1846,66339,2075],{},[1846,66341,1855],{"stretchy":1854},[1979,66343,2968],{},[1846,66345,1945],{},[1979,66347,66157],{},[1846,66349,3025],{},[1974,66351,66352,66354],{},[1979,66353,41707],{},[1979,66355,1981],{},[1846,66357,1861],{"stretchy":1854},[1846,66359,1848],{},[1979,66361,22791],{},[2138,66363,2835],{},[1979,66365,19987],{},[1846,66367,2075],{},[1979,66369,24046],{},[2138,66371,2835],{},[1979,66373,66374],{},"218",[1846,66376,1848],{},[1979,66378,24046],{},[2138,66380,2835],{},[1979,66382,66383],{},"182",[2138,66385,66386],{}," EUR",[898,66388,1734],{"mathvariant":2226},[902,66390,66391],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,66393,66394],{},"Pro srovnání při původních 30 ks:",[883,66396,66398],{"className":66397},[886],[888,66399,66400],{"xmlns":890,"display":27911},[892,66401,66402,66467],{},[895,66403,66404,66406,66408,66410,66412,66414,66416,66418,66420,66422,66424,66426,66428,66430,66432,66434,66436,66438,66440,66443,66445,66447,66449,66451,66453,66455,66457,66459,66461,66463,66465],{},[898,66405,3783],{},[898,66407,3840],{},[1846,66409,1855],{"stretchy":1854},[1979,66411,37864],{},[1846,66413,1861],{"stretchy":1854},[1846,66415,1848],{},[1979,66417,15036],{},[1846,66419,3025],{},[1979,66421,37864],{},[1846,66423,2075],{},[1846,66425,1855],{"stretchy":1854},[1979,66427,2968],{},[1846,66429,1945],{},[1979,66431,66157],{},[1846,66433,3025],{},[1979,66435,15036],{},[1846,66437,1861],{"stretchy":1854},[1846,66439,1848],{},[1979,66441,66442],{},"27",[2138,66444,2835],{},[1979,66446,58927],{},[1846,66448,2075],{},[1979,66450,4850],{},[2138,66452,2835],{},[1979,66454,30588],{},[1846,66456,1848],{},[1979,66458,2128],{},[2138,66460,2835],{},[1979,66462,23588],{},[2138,66464,66386],{},[898,66466,1734],{"mathvariant":2226},[902,66468,66469],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,66471,66472,66475,66476,66494,66495,66513],{},[38,66473,66474],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,66477,66479],{"className":66478},[886],[888,66480,66481],{"xmlns":890},[892,66482,66483,66491],{},[895,66484,66485,66487,66489],{},[1979,66486,24046],{},[2138,66488,2835],{},[1979,66490,66383],{},[902,66492,66493],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,66496,66498],{"className":66497},[886],[888,66499,66500],{"xmlns":890},[892,66501,66502,66510],{},[895,66503,66504,66506,66508],{},[1979,66505,2128],{},[2138,66507,2835],{},[1979,66509,23588],{},[902,66511,66512],{"encoding":904},"1\\,750"," EUR.",[198,66515,66517],{"id":66516},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,66519,66520,66521,62415,66534,66558],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,66522,66524],{"className":66523},[886],[888,66525,66526],{"xmlns":890},[892,66527,66528,66532],{},[895,66529,66530],{},[898,66531,3783],{},[902,66533,3783],{"encoding":904},[883,66535,66537],{"className":66536},[886],[888,66538,66539],{"xmlns":890},[892,66540,66541,66555],{},[895,66542,66543,66545,66547,66549,66551,66553],{},[898,66544,2623],{},[898,66546,3840],{},[1846,66548,1848],{},[898,66550,3783],{},[1846,66552,3025],{},[898,66554,2638],{},[902,66556,66557],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,66560,66562],{"className":66561},[886],[888,66563,66564],{"xmlns":890,"display":27911},[892,66565,66566,66599],{},[20599,66567,66568],{"width":27916},[20604,66569,66570,66572,66592,66594],{},[20607,66571],{"width":27921},[20607,66573,66574],{},[895,66575,66576,66578,66580,66582,66584,66586,66588,66590],{},[898,66577,3783],{},[1846,66579,1848],{},[898,66581,2667],{},[898,66583,2626],{},[1846,66585,1855],{"stretchy":1854},[898,66587,2638],{},[1846,66589,1861],{"stretchy":1854},[898,66591,1734],{"mathvariant":2226},[20607,66593],{"width":27921},[20607,66595,66596],{},[2138,66597,66598],{},"(3.14)",[902,66600,66601],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,66603,66604,66605,1734],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,66606,66608],{"className":66607},[886],[888,66609,66610],{"xmlns":890},[892,66611,66612,66626],{},[895,66613,66614,66616],{},[898,66615,3783],{},[1974,66617,66618,66620],{},[898,66619,3840],{},[895,66621,66622,66624],{},[1846,66623,2228],{"mathvariant":2226},[1846,66625,2228],{"mathvariant":2226},[902,66627,65682],{"encoding":904},[37193,66629,66631],{"id":66630},"příklad-311","Příklad 3.11",[724,66633,66634,57367,66636,66683,66684,66702],{},[38,66635,55832],{},[883,66637,66639],{"className":66638},[886],[888,66640,66641],{"xmlns":890},[892,66642,66643,66680],{},[895,66644,66645,66647,66649,66651,66654,66660,66662,66664,66670,66672,66674,66676,66678],{},[898,66646,2623],{},[898,66648,2626],{},[1846,66650,1848],{},[1979,66652,66653],{},"0,04",[1974,66655,66656,66658],{},[898,66657,2638],{},[1979,66659,2023],{},[1846,66661,2075],{},[1979,66663,22390],{},[1974,66665,66666,66668],{},[898,66667,2638],{},[1979,66669,1981],{},[1846,66671,1945],{},[1979,66673,2712],{},[898,66675,2638],{},[1846,66677,1945],{},[1979,66679,2078],{},[902,66681,66682],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,66685,66687],{"className":66686},[886],[888,66688,66689],{"xmlns":890},[892,66690,66691,66699],{},[895,66692,66693,66695,66697],{},[898,66694,3783],{},[1846,66696,1848],{},[1979,66698,2201],{},[902,66700,66701],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,66704,66705,66707,66708,17421,66750,66784,66785,2554],{},[38,66706,22615],{}," Z (3.14): ",[883,66709,66711],{"className":66710},[886],[888,66712,66713],{"xmlns":890},[892,66714,66715,66747],{},[895,66716,66717,66719,66721,66723,66726,66732,66734,66737,66739,66741,66743,66745],{},[898,66718,2667],{},[898,66720,2626],{},[1846,66722,1848],{},[1979,66724,66725],{},"0,12",[1974,66727,66728,66730],{},[898,66729,2638],{},[1979,66731,1981],{},[1846,66733,2075],{},[1979,66735,66736],{},"1,8",[898,66738,2638],{},[1846,66740,1945],{},[1979,66742,2712],{},[1846,66744,1848],{},[1979,66746,2201],{},[902,66748,66749],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,66751,66753],{"className":66752},[886],[888,66754,66755],{"xmlns":890},[892,66756,66757,66781],{},[895,66758,66759,66761,66767,66769,66771,66773,66775,66777,66779],{},[1979,66760,66725],{},[1974,66762,66763,66765],{},[898,66764,2638],{},[1979,66766,1981],{},[1846,66768,2075],{},[1979,66770,66736],{},[898,66772,2638],{},[1846,66774,1945],{},[1979,66776,2085],{},[1846,66778,1848],{},[1979,66780,2177],{},[902,66782,66783],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,66786,66788],{"className":66787},[886],[888,66789,66790],{"xmlns":890},[892,66791,66792,66796],{},[895,66793,66794],{},[1979,66795,66725],{},[902,66797,66798],{"encoding":904},"0{,}12",[883,66800,66802],{"className":66801},[886],[888,66803,66804],{"xmlns":890,"display":27911},[892,66805,66806,66858],{},[895,66807,66808,66814,66816,66818,66820,66822,66824,66826,66828,66830,66832,66834,66840,66842,66844,66846,66848,66854,66856],{},[1974,66809,66810,66812],{},[898,66811,2638],{},[1979,66813,1981],{},[1846,66815,2075],{},[1979,66817,36089],{},[898,66819,2638],{},[1846,66821,1945],{},[1979,66823,2968],{},[1846,66825,1848],{},[1979,66827,2177],{},[2138,66829,3830],{},[1846,66831,3833],{},[2138,66833,3830],{},[2122,66835,66836,66838],{},[898,66837,2638],{},[1979,66839,2128],{},[1846,66841,1848],{},[1979,66843,2078],{},[1846,66845,2136],{"separator":2135},[2138,66847,3830],{},[2122,66849,66850,66852],{},[898,66851,2638],{},[1979,66853,1981],{},[1846,66855,1848],{},[1979,66857,19173],{},[902,66859,66860],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,66862,66863,66864,2554],{},"Dále ",[883,66865,66867],{"className":66866},[886],[888,66868,66869],{"xmlns":890},[892,66870,66871,66910],{},[895,66872,66873,66875,66885,66887,66889,66891,66897,66899,66901,66904,66906,66908],{},[898,66874,3783],{},[1974,66876,66877,66879],{},[898,66878,3840],{},[895,66880,66881,66883],{},[1846,66882,2228],{"mathvariant":2226},[1846,66884,2228],{"mathvariant":2226},[1846,66886,1848],{},[1846,66888,2075],{},[898,66890,2667],{},[1974,66892,66893,66895],{},[898,66894,2626],{},[1846,66896,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,66898,1848],{},[1846,66900,2075],{},[1979,66902,66903],{},"0,24",[898,66905,2638],{},[1846,66907,1945],{},[1979,66909,66736],{},[902,66911,66912],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,66914,66915,66965],{},[123,66916,66917,66961,66962,66964],{},[883,66918,66920],{"className":66919},[886],[888,66921,66922],{"xmlns":890},[892,66923,66924,66958],{},[895,66925,66926,66928,66938,66940,66942,66944,66946,66948,66950,66952,66954,66956],{},[898,66927,3783],{},[1974,66929,66930,66932],{},[898,66931,3840],{},[895,66933,66934,66936],{},[1846,66935,2228],{"mathvariant":2226},[1846,66937,2228],{"mathvariant":2226},[1846,66939,1855],{"stretchy":1854},[1979,66941,2078],{},[1846,66943,1861],{"stretchy":1854},[1846,66945,1848],{},[1979,66947,19166],{},[1846,66949,3256],{},[1979,66951,2177],{},[2138,66953,3830],{},[1846,66955,3833],{},[2138,66957,3830],{},[902,66959,66960],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,66963,3623],{}," zisku (minimalizace ztráty);",[123,66966,66967,66961,67013,67015],{},[883,66968,66970],{"className":66969},[886],[888,66971,66972],{"xmlns":890},[892,66973,66974,67010],{},[895,66975,66976,66978,66988,66990,66992,66994,66996,66998,67000,67002,67004,67006,67008],{},[898,66977,3783],{},[1974,66979,66980,66982],{},[898,66981,3840],{},[895,66983,66984,66986],{},[1846,66985,2228],{"mathvariant":2226},[1846,66987,2228],{"mathvariant":2226},[1846,66989,1855],{"stretchy":1854},[1979,66991,2712],{},[1846,66993,1861],{"stretchy":1854},[1846,66995,1848],{},[1846,66997,2075],{},[1979,66999,19166],{},[1846,67001,3295],{},[1979,67003,2177],{},[2138,67005,3830],{},[1846,67007,3833],{},[2138,67009,3830],{},[902,67011,67012],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,67014,3565],{}," zisku, avšak",[883,67017,67019],{"className":67018},[886],[888,67020,67021],{"xmlns":890,"display":27911},[892,67022,67023,67091],{},[895,67024,67025,67027,67029,67031,67033,67035,67037,67039,67041,67043,67045,67047,67049,67051,67053,67055,67057,67059,67061,67063,67065,67067,67069,67071,67073,67075,67077,67079,67081,67083,67085,67087,67089],{},[898,67026,3783],{},[898,67028,3840],{},[1846,67030,1855],{"stretchy":1854},[1979,67032,2712],{},[1846,67034,1861],{"stretchy":1854},[1846,67036,1848],{},[1979,67038,2201],{},[1846,67040,3025],{},[1979,67042,2712],{},[1846,67044,2075],{},[1846,67046,1855],{"stretchy":1854},[1979,67048,66653],{},[1846,67050,3025],{},[1979,67052,2128],{},[2138,67054,2835],{},[1979,67056,58927],{},[1846,67058,2075],{},[1979,67060,22390],{},[1846,67062,3025],{},[1979,67064,2938],{},[1846,67066,1945],{},[1979,67068,2938],{},[1846,67070,1945],{},[1979,67072,2078],{},[1846,67074,1861],{"stretchy":1854},[1846,67076,1848],{},[1979,67078,5057],{},[1846,67080,2075],{},[1979,67082,21025],{},[1846,67084,1848],{},[1846,67086,2075],{},[1979,67088,36089],{},[1846,67090,2136],{"separator":2135},[902,67092,67093],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,67095,67096,67097,1734],{},"tj. ztráta větší než ",[883,67098,67100],{"className":67099},[886],[888,67101,67102],{"xmlns":890},[892,67103,67104,67114],{},[895,67105,67106,67108,67110,67112],{},[898,67107,10282],{},[898,67109,2626],{},[1846,67111,1848],{},[1979,67113,2078],{},[902,67115,67116],{"encoding":904},"FC = 5",[724,67118,67119,67122,67123,67126,67127,1734],{},[38,67120,67121],{},"Závěr:"," firma by měla ",[38,67124,67125],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,67128,67130],{"className":67129},[886],[888,67131,67132],{"xmlns":890},[892,67133,67134,67144],{},[895,67135,67136,67138,67140,67142],{},[898,67137,10282],{},[898,67139,2626],{},[1846,67141,1848],{},[1979,67143,2078],{},[902,67145,67116],{"encoding":904},[115,67147,67149],{"id":67148},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,67151,67152,67153,67155,67156,67171,67172,67185,67186,67212,67213,67226,67227,67244,67245,2474,67262,67265,67266,67286,67287,67302,67303,2554],{},"Důležitým završením analýzy je konstrukce ",[38,67154,55120],{},". S nabízeným množstvím rostou mezní náklady ",[883,67157,67159],{"className":67158},[886],[888,67160,67161],{"xmlns":890},[892,67162,67163,67169],{},[895,67164,67165,67167],{},[898,67166,2667],{},[898,67168,2626],{},[902,67170,55137],{"encoding":904}," a tyto určují cenu ",[883,67173,67175],{"className":67174},[886],[888,67176,67177],{"xmlns":890},[892,67178,67179,67183],{},[895,67180,67181],{},[898,67182,3783],{},[902,67184,3783],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,67187,67189],{"className":67188},[886],[888,67190,67191],{"xmlns":890},[892,67192,67193,67209],{},[895,67194,67195,67197,67199,67201,67203,67205,67207],{},[898,67196,3783],{},[1846,67198,1848],{},[898,67200,2667],{},[898,67202,2626],{},[1846,67204,1855],{"stretchy":1854},[898,67206,2638],{},[1846,67208,1861],{"stretchy":1854},[902,67210,67211],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,67214,67216],{"className":67215},[886],[888,67217,67218],{"xmlns":890},[892,67219,67220,67224],{},[895,67221,67222],{},[898,67223,3783],{},[902,67225,3783],{"encoding":904}," však nemůže být nižší než ",[883,67228,67230],{"className":67229},[886],[888,67231,67232],{"xmlns":890},[892,67233,67234,67242],{},[895,67235,67236],{},[1974,67237,67238,67240],{},[898,67239,3783],{},[1846,67241,4200],{},[902,67243,4250],{"encoding":904}," odpovídající množství ",[883,67246,67248],{"className":67247},[886],[888,67249,67250],{"xmlns":890},[892,67251,67252,67260],{},[895,67253,67254],{},[1974,67255,67256,67258],{},[898,67257,2638],{},[1846,67259,4200],{},[902,67261,29689],{"encoding":904},[38,67263,67264],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,67267,67269],{"className":67268},[886],[888,67270,67271],{"xmlns":890},[892,67272,67273,67283],{},[895,67274,67275,67277],{},[1979,67276,2177],{},[1974,67278,67279,67281],{},[898,67280,2638],{},[1846,67282,4200],{},[902,67284,67285],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,67288,67290],{"className":67289},[886],[888,67291,67292],{"xmlns":890},[892,67293,67294,67300],{},[895,67295,67296,67298],{},[898,67297,2667],{},[898,67299,2626],{},[902,67301,55137],{"encoding":904}," nad bodem ",[883,67304,67306],{"className":67305},[886],[888,67307,67308],{"xmlns":890},[892,67309,67310,67314],{},[895,67311,67312],{},[898,67313,4101],{},[902,67315,4101],{"encoding":904},[883,67317,67319],{"className":67318},[886],[888,67320,67321],{"xmlns":890,"display":27911},[892,67322,67323,67430],{},[20599,67324,67325],{"width":27916},[20604,67326,67327,67329,67423,67425],{},[20607,67328],{"width":27921},[20607,67330,67331],{},[895,67332,67333,67335,67337,67339,67341,67343,67345,67347],{},[898,67334,3783],{},[1846,67336,1848],{},[898,67338,8519],{},[1846,67340,1855],{"stretchy":1854},[898,67342,2638],{},[1846,67344,1861],{"stretchy":1854},[1846,67346,1848],{},[895,67348,67349,67352],{},[1846,67350,67351],{"fence":2135},"{",[20599,67353,67356,67395],{"rowspacing":67354,"columnalign":67355,"columnspacing":15129},"0.36em","left left",[20604,67357,67358,67374],{},[20607,67359,67360],{},[2175,67361,67362],{"scriptlevel":2177,"displaystyle":1854},[895,67363,67364,67366,67368,67370,67372],{},[898,67365,2667],{},[898,67367,2626],{},[1846,67369,1855],{"stretchy":1854},[898,67371,2638],{},[1846,67373,1861],{"stretchy":1854},[20607,67375,67376],{},[2175,67377,67378],{"scriptlevel":2177,"displaystyle":1854},[895,67379,67380,67383,67385,67387,67393],{},[2138,67381,67382],{},"pro ",[898,67384,2638],{},[1846,67386,4331],{},[1974,67388,67389,67391],{},[898,67390,2638],{},[1846,67392,4200],{},[1846,67394,2136],{"separator":2135},[20604,67396,67397,67403],{},[20607,67398,67399],{},[2175,67400,67401],{"scriptlevel":2177,"displaystyle":1854},[1979,67402,2177],{},[20607,67404,67405],{},[2175,67406,67407],{"scriptlevel":2177,"displaystyle":1854},[895,67408,67409,67411,67413,67415,67421],{},[2138,67410,67382],{},[898,67412,2638],{},[1846,67414,3295],{},[1974,67416,67417,67419],{},[898,67418,2638],{},[1846,67420,4200],{},[1846,67422,2136],{"separator":2135},[20607,67424],{"width":27921},[20607,67426,67427],{},[2138,67428,67429],{},"(3.15)",[902,67431,67432],{"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}",[724,67434,4156,67435,67452,67453,67470,67471,41344,67501,67504],{},[883,67436,67438],{"className":67437},[886],[888,67439,67440],{"xmlns":890},[892,67441,67442,67450],{},[895,67443,67444],{},[1974,67445,67446,67448],{},[898,67447,2638],{},[1846,67449,4200],{},[902,67451,29689],{"encoding":904}," je bod minima ",[883,67454,67456],{"className":67455},[886],[888,67457,67458],{"xmlns":890},[892,67459,67460,67468],{},[895,67461,67462,67464,67466],{},[898,67463,4101],{},[898,67465,40184],{},[898,67467,2626],{},[902,67469,55156],{"encoding":904},". Bod ",[883,67472,67474],{"className":67473},[886],[888,67475,67476],{"xmlns":890},[892,67477,67478,67498],{},[895,67479,67480,67482,67488,67490,67496],{},[1846,67481,1855],{"stretchy":1854},[1974,67483,67484,67486],{},[898,67485,2638],{},[1846,67487,4200],{},[1846,67489,2136],{"separator":2135},[1974,67491,67492,67494],{},[898,67493,3783],{},[1846,67495,4200],{},[1846,67497,1861],{"stretchy":1854},[902,67499,67500],{"encoding":904},"(Q^*, P^*)",[38,67502,67503],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[1639,67506,67507,67512],{},[724,67508,67509,67511],{},[883,67510,4418],{}," Postup — jak odvodit nabídku firmy",[152,67513,67514,67563,67658,67713,67784],{},[123,67515,67516,67517,1745,67539,1734],{},"Ze zadaných nákladů určete ",[883,67518,67520],{"className":67519},[886],[888,67521,67522],{"xmlns":890},[892,67523,67524,67536],{},[895,67525,67526,67528,67530,67532,67534],{},[898,67527,2667],{},[898,67529,2626],{},[1846,67531,1855],{"stretchy":1854},[898,67533,2638],{},[1846,67535,1861],{"stretchy":1854},[902,67537,67538],{"encoding":904},"MC(Q)",[883,67540,67542],{"className":67541},[886],[888,67543,67544],{"xmlns":890},[892,67545,67546,67560],{},[895,67547,67548,67550,67552,67554,67556,67558],{},[898,67549,4101],{},[898,67551,40184],{},[898,67553,2626],{},[1846,67555,1855],{"stretchy":1854},[898,67557,2638],{},[1846,67559,1861],{"stretchy":1854},[902,67561,67562],{"encoding":904},"AVC(Q)",[123,67564,67565,67566,67583,67584,67601,67602,67634,67635,3764],{},"Najděte ",[883,67567,67569],{"className":67568},[886],[888,67570,67571],{"xmlns":890},[892,67572,67573,67581],{},[895,67574,67575],{},[1974,67576,67577,67579],{},[898,67578,2638],{},[1846,67580,4200],{},[902,67582,29689],{"encoding":904}," jako bod minima ",[883,67585,67587],{"className":67586},[886],[888,67588,67589],{"xmlns":890},[892,67590,67591,67599],{},[895,67592,67593,67595,67597],{},[898,67594,4101],{},[898,67596,40184],{},[898,67598,2626],{},[902,67600,55156],{"encoding":904}," (řešením ",[883,67603,67605],{"className":67604},[886],[888,67606,67607],{"xmlns":890},[892,67608,67609,67631],{},[895,67610,67611,67613,67615,67621,67623,67625,67627,67629],{},[898,67612,4101],{},[898,67614,40184],{},[1974,67616,67617,67619],{},[898,67618,2626],{},[1846,67620,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,67622,1855],{"stretchy":1854},[898,67624,2638],{},[1846,67626,1861],{"stretchy":1854},[1846,67628,1848],{},[1979,67630,2177],{},[902,67632,67633],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,67636,67638],{"className":67637},[886],[888,67639,67640],{"xmlns":890},[892,67641,67642,67656],{},[895,67643,67644,67646,67648,67650,67652,67654],{},[898,67645,4101],{},[898,67647,40184],{},[898,67649,2626],{},[1846,67651,1848],{},[898,67653,2667],{},[898,67655,2626],{},[902,67657,55093],{"encoding":904},[123,67659,65566,67660,67712],{},[883,67661,67663],{"className":67662},[886],[888,67664,67665],{"xmlns":890},[892,67666,67667,67709],{},[895,67668,67669,67675,67677,67679,67681,67683,67689,67691,67693,67695,67697,67699,67701,67707],{},[1974,67670,67671,67673],{},[898,67672,3783],{},[1846,67674,4200],{},[1846,67676,1848],{},[898,67678,2667],{},[898,67680,2626],{},[1846,67682,1855],{"stretchy":1854},[1974,67684,67685,67687],{},[898,67686,2638],{},[1846,67688,4200],{},[1846,67690,1861],{"stretchy":1854},[1846,67692,1848],{},[898,67694,4101],{},[898,67696,40184],{},[898,67698,2626],{},[1846,67700,1855],{"stretchy":1854},[1974,67702,67703,67705],{},[898,67704,2638],{},[1846,67706,4200],{},[1846,67708,1861],{"stretchy":1854},[902,67710,67711],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,67714,67715,67716,6319,67748,67770,67771,1734],{},"Zapište nabídku: ",[883,67717,67719],{"className":67718},[886],[888,67720,67721],{"xmlns":890},[892,67722,67723,67745],{},[895,67724,67725,67727,67729,67731,67733,67735,67737,67739,67741,67743],{},[898,67726,8519],{},[1846,67728,1855],{"stretchy":1854},[898,67730,2638],{},[1846,67732,1861],{"stretchy":1854},[1846,67734,1848],{},[898,67736,2667],{},[898,67738,2626],{},[1846,67740,1855],{"stretchy":1854},[898,67742,2638],{},[1846,67744,1861],{"stretchy":1854},[902,67746,67747],{"encoding":904},"S(Q) = MC(Q)",[883,67749,67751],{"className":67750},[886],[888,67752,67753],{"xmlns":890},[892,67754,67755,67767],{},[895,67756,67757,67759,67761],{},[898,67758,2638],{},[1846,67760,4331],{},[1974,67762,67763,67765],{},[898,67764,2638],{},[1846,67766,4200],{},[902,67768,67769],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,67772,67774],{"className":67773},[886],[888,67775,67776],{"xmlns":890},[892,67777,67778,67782],{},[895,67779,67780],{},[1979,67781,2177],{},[902,67783,2177],{"encoding":904},[123,67785,67786,67787,67819],{},"V případě potřeby vyjádřete inverzi ",[883,67788,67790],{"className":67789},[886],[888,67791,67792],{"xmlns":890},[892,67793,67794,67816],{},[895,67795,67796,67798,67800,67810,67812,67814],{},[898,67797,2638],{},[1846,67799,1848],{},[1974,67801,67802,67804],{},[898,67803,8519],{},[895,67805,67806,67808],{},[1846,67807,2075],{},[1979,67809,2128],{},[1846,67811,1855],{"stretchy":1854},[898,67813,3783],{},[1846,67815,1861],{"stretchy":1854},[902,67817,67818],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,67821,67822],{},[614,67823,67824,67825,1343,67840,1745,67857,29046,67872,67885,67886,67911,67912,67925,67926,67943,67944,67961,67962,67979],{},"Obrázek 3.14: Křivky ",[883,67826,67828],{"className":67827},[886],[888,67829,67830],{"xmlns":890},[892,67831,67832,67838],{},[895,67833,67834,67836],{},[898,67835,4101],{},[898,67837,2626],{},[902,67839,55405],{"encoding":904},[883,67841,67843],{"className":67842},[886],[888,67844,67845],{"xmlns":890},[892,67846,67847,67855],{},[895,67848,67849,67851,67853],{},[898,67850,4101],{},[898,67852,40184],{},[898,67854,2626],{},[902,67856,55156],{"encoding":904},[883,67858,67860],{"className":67859},[886],[888,67861,67862],{"xmlns":890},[892,67863,67864,67870],{},[895,67865,67866,67868],{},[898,67867,2667],{},[898,67869,2626],{},[902,67871,55137],{"encoding":904},[883,67873,67875],{"className":67874},[886],[888,67876,67877],{"xmlns":890},[892,67878,67879,67883],{},[895,67880,67881],{},[898,67882,900],{},[902,67884,900],{"encoding":904},"; křivka nabídky ",[883,67887,67889],{"className":67888},[886],[888,67890,67891],{"xmlns":890},[892,67892,67893,67909],{},[895,67894,67895,67897,67899,67901,67903,67905,67907],{},[898,67896,3783],{},[1846,67898,1848],{},[898,67900,2667],{},[898,67902,2626],{},[1846,67904,1855],{"stretchy":1854},[898,67906,2638],{},[1846,67908,1861],{"stretchy":1854},[902,67910,67211],{"encoding":904}," začíná v bodě ",[883,67913,67915],{"className":67914},[886],[888,67916,67917],{"xmlns":890},[892,67918,67919,67923],{},[895,67920,67921],{},[898,67922,4101],{},[902,67924,4101],{"encoding":904}," odpovídajícím minimu ",[883,67927,67929],{"className":67928},[886],[888,67930,67931],{"xmlns":890},[892,67932,67933,67941],{},[895,67934,67935,67937,67939],{},[898,67936,4101],{},[898,67938,40184],{},[898,67940,2626],{},[902,67942,55156],{"encoding":904}," při ceně ",[883,67945,67947],{"className":67946},[886],[888,67948,67949],{"xmlns":890},[892,67950,67951,67959],{},[895,67952,67953],{},[1974,67954,67955,67957],{},[898,67956,3783],{},[1846,67958,4200],{},[902,67960,4250],{"encoding":904}," (minimální cena nabídky); pod ",[883,67963,67965],{"className":67964},[886],[888,67966,67967],{"xmlns":890},[892,67968,67969,67977],{},[895,67970,67971],{},[1974,67972,67973,67975],{},[898,67974,2638],{},[1846,67976,4200],{},[902,67978,29689],{"encoding":904}," je nabídka nulová.",[37193,67981,67983],{"id":67982},"příklad-312","Příklad 3.12",[724,67985,67986,57367,67988,68034],{},[38,67987,55832],{},[883,67989,67991],{"className":67990},[886],[888,67992,67993],{"xmlns":890},[892,67994,67995,68031],{},[895,67996,67997,67999,68001,68003,68005,68011,68013,68015,68021,68023,68025,68027,68029],{},[898,67998,2623],{},[898,68000,2626],{},[1846,68002,1848],{},[1979,68004,2643],{},[1974,68006,68007,68009],{},[898,68008,2638],{},[1979,68010,2023],{},[1846,68012,2075],{},[1979,68014,1981],{},[1974,68016,68017,68019],{},[898,68018,2638],{},[1979,68020,1981],{},[1846,68022,1945],{},[1979,68024,36089],{},[898,68026,2638],{},[1846,68028,1945],{},[1979,68030,2712],{},[902,68032,68033],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,68036,68037,2053,68039,68076,68077,2554],{},[38,68038,22615],{},[883,68040,68042],{"className":68041},[886],[888,68043,68044],{"xmlns":890},[892,68045,68046,68073],{},[895,68047,68048,68050,68052,68054,68057,68063,68065,68067,68069,68071],{},[898,68049,2667],{},[898,68051,2626],{},[1846,68053,1848],{},[1979,68055,68056],{},"0,3",[1974,68058,68059,68061],{},[898,68060,2638],{},[1979,68062,1981],{},[1846,68064,2075],{},[1979,68066,2201],{},[898,68068,2638],{},[1846,68070,1945],{},[1979,68072,36089],{},[902,68074,68075],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,68078,68080],{"className":68079},[886],[888,68081,68082],{"xmlns":890},[892,68083,68084,68094],{},[895,68085,68086,68088,68090,68092],{},[898,68087,3783],{},[1846,68089,1848],{},[898,68091,2667],{},[898,68093,2626],{},[902,68095,68096],{"encoding":904},"P = MC",[883,68098,68100],{"className":68099},[886],[888,68101,68102],{"xmlns":890,"display":27911},[892,68103,68104,68129],{},[895,68105,68106,68108,68110,68112,68118,68120,68122,68124,68126],{},[898,68107,3783],{},[1846,68109,1848],{},[1979,68111,68056],{},[1974,68113,68114,68116],{},[898,68115,2638],{},[1979,68117,1981],{},[1846,68119,2075],{},[1979,68121,2201],{},[898,68123,2638],{},[1846,68125,1945],{},[1979,68127,68128],{},"15.",[902,68130,68131],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,68133,68134,68135,5228,68148,68161],{},"Vyjádření ",[883,68136,68138],{"className":68137},[886],[888,68139,68140],{"xmlns":890},[892,68141,68142,68146],{},[895,68143,68144],{},[898,68145,2638],{},[902,68147,2638],{"encoding":904},[883,68149,68151],{"className":68150},[886],[888,68152,68153],{"xmlns":890},[892,68154,68155,68159],{},[895,68156,68157],{},[898,68158,3783],{},[902,68160,3783],{"encoding":904}," doplněním na čtverec:",[883,68163,68165],{"className":68164},[886],[888,68166,68167],{"xmlns":890,"display":27911},[892,68168,68169,68259],{},[895,68170,68171,68173,68175,68177,68215,68217,68219,68241,68243,68257],{},[898,68172,3783],{},[1846,68174,1848],{},[1979,68176,68056],{},[895,68178,68179,68181,68203,68205,68213],{},[1846,68180,1855],{"fence":2135},[1974,68182,68183,68201],{},[895,68184,68185,68187,68189,68191,68199],{},[1846,68186,1855],{"fence":2135},[898,68188,2638],{},[1846,68190,2075],{},[2175,68192,68193],{"scriptlevel":2177,"displaystyle":1854},[2179,68194,68195,68197],{},[1979,68196,8881],{},[1979,68198,2023],{},[1846,68200,1861],{"fence":2135},[1979,68202,1981],{},[1846,68204,1945],{},[2175,68206,68207],{"scriptlevel":2177,"displaystyle":1854},[2179,68208,68209,68211],{},[1979,68210,2968],{},[1979,68212,3845],{},[1846,68214,1861],{"fence":2135},[1846,68216,2136],{"separator":2135},[5724,68218],{"width":5726},[1974,68220,68221,68239],{},[895,68222,68223,68225,68227,68229,68237],{},[1846,68224,1855],{"fence":2135},[898,68226,2638],{},[1846,68228,2075],{},[2175,68230,68231],{"scriptlevel":2177,"displaystyle":1854},[2179,68232,68233,68235],{},[1979,68234,8881],{},[1979,68236,2023],{},[1846,68238,1861],{"fence":2135},[1979,68240,1981],{},[1846,68242,1848],{},[2179,68244,68245,68255],{},[895,68246,68247,68249,68251,68253],{},[1979,68248,37864],{},[898,68250,3783],{},[1846,68252,2075],{},[1979,68254,2968],{},[1979,68256,3845],{},[1846,68258,2136],{"separator":2135},[902,68260,68261],{"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},",[883,68263,68265],{"className":68264},[886],[888,68266,68267],{"xmlns":890,"display":27911},[892,68268,68269,68301],{},[895,68270,68271,68273,68275,68281,68283,68299],{},[898,68272,2638],{},[1846,68274,1848],{},[2179,68276,68277,68279],{},[1979,68278,8881],{},[1979,68280,2023],{},[1846,68282,1945],{},[2179,68284,68285,68297],{},[7963,68286,68287],{},[895,68288,68289,68291,68293,68295],{},[1979,68290,37864],{},[898,68292,3783],{},[1846,68294,2075],{},[1979,68296,2968],{},[1979,68298,2023],{},[898,68300,1734],{"mathvariant":2226},[902,68302,68303],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,68305,66863,68306,1343,68344,1343,68392,68426,68427,1734],{},[883,68307,68309],{"className":68308},[886],[888,68310,68311],{"xmlns":890},[892,68312,68313,68341],{},[895,68314,68315,68317,68319,68321,68323,68325,68331,68333,68335,68337,68339],{},[898,68316,4101],{},[898,68318,40184],{},[898,68320,2626],{},[1846,68322,1848],{},[1979,68324,2643],{},[1974,68326,68327,68329],{},[898,68328,2638],{},[1979,68330,1981],{},[1846,68332,2075],{},[1979,68334,1981],{},[898,68336,2638],{},[1846,68338,1945],{},[1979,68340,36089],{},[902,68342,68343],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,68345,68347],{"className":68346},[886],[888,68348,68349],{"xmlns":890},[892,68350,68351,68389],{},[895,68352,68353,68355,68357,68363,68365,68367,68369,68371,68373,68375,68377,68379,68385,68387],{},[898,68354,4101],{},[898,68356,40184],{},[1974,68358,68359,68361],{},[898,68360,2626],{},[1846,68362,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,68364,1848],{},[1979,68366,2688],{},[898,68368,2638],{},[1846,68370,2075],{},[1979,68372,1981],{},[1846,68374,1848],{},[1979,68376,2177],{},[1846,68378,3833],{},[1974,68380,68381,68383],{},[898,68382,2638],{},[1846,68384,4200],{},[1846,68386,1848],{},[1979,68388,2712],{},[902,68390,68391],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,68393,68395],{"className":68394},[886],[888,68396,68397],{"xmlns":890},[892,68398,68399,68423],{},[895,68400,68401,68403,68405,68415,68417,68419,68421],{},[898,68402,4101],{},[898,68404,40184],{},[1974,68406,68407,68409],{},[898,68408,2626],{},[895,68410,68411,68413],{},[1846,68412,2228],{"mathvariant":2226},[1846,68414,2228],{"mathvariant":2226},[1846,68416,1848],{},[1979,68418,2688],{},[1846,68420,3256],{},[1979,68422,2177],{},[902,68424,68425],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,68428,68430],{"className":68429},[886],[888,68431,68432],{"xmlns":890},[892,68433,68434,68470],{},[895,68435,68436,68442,68444,68446,68448,68450,68452,68454,68456,68458,68460,68462,68464,68466,68468],{},[1974,68437,68438,68440],{},[898,68439,3783],{},[1846,68441,4200],{},[1846,68443,1848],{},[898,68445,2667],{},[898,68447,2626],{},[1846,68449,1855],{"stretchy":1854},[1979,68451,2712],{},[1846,68453,1861],{"stretchy":1854},[1846,68455,1848],{},[1979,68457,37864],{},[1846,68459,2075],{},[1979,68461,5057],{},[1846,68463,1945],{},[1979,68465,36089],{},[1846,68467,1848],{},[1979,68469,2078],{},[902,68471,68472],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,68474,68475],{},[38,68476,68477],{},"Závěr.",[883,68479,68481],{"className":68480},[886],[888,68482,68483],{"xmlns":890,"display":27911},[892,68484,68485,68571],{},[895,68486,68487,68489,68491,68493,68495,68497,68499,68501],{},[898,68488,3783],{},[1846,68490,1848],{},[898,68492,8519],{},[1846,68494,1855],{"stretchy":1854},[898,68496,2638],{},[1846,68498,1861],{"stretchy":1854},[1846,68500,1848],{},[895,68502,68503,68505],{},[1846,68504,67351],{"fence":2135},[20599,68506,68507,68549],{"rowspacing":67354,"columnalign":67355,"columnspacing":15129},[20604,68508,68509,68533],{},[20607,68510,68511],{},[2175,68512,68513],{"scriptlevel":2177,"displaystyle":1854},[895,68514,68515,68517,68523,68525,68527,68529,68531],{},[1979,68516,68056],{},[1974,68518,68519,68521],{},[898,68520,2638],{},[1979,68522,1981],{},[1846,68524,2075],{},[1979,68526,2201],{},[898,68528,2638],{},[1846,68530,1945],{},[1979,68532,36089],{},[20607,68534,68535],{},[2175,68536,68537],{"scriptlevel":2177,"displaystyle":1854},[895,68538,68539,68541,68543,68545,68547],{},[2138,68540,67382],{},[898,68542,2638],{},[1846,68544,4331],{},[1979,68546,2712],{},[1846,68548,2136],{"separator":2135},[20604,68550,68551,68557],{},[20607,68552,68553],{},[2175,68554,68555],{"scriptlevel":2177,"displaystyle":1854},[1979,68556,2177],{},[20607,68558,68559],{},[2175,68560,68561],{"scriptlevel":2177,"displaystyle":1854},[895,68562,68563,68565,68567,68569],{},[2138,68564,67382],{},[898,68566,2638],{},[1846,68568,3295],{},[1979,68570,19173],{},[902,68572,68573],{"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}",[724,68575,68576],{},[614,68577,68578,68579,68594,68595,1734],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,68580,68582],{"className":68581},[886],[888,68583,68584],{"xmlns":890},[892,68585,68586,68592],{},[895,68587,68588,68590],{},[898,68589,2667],{},[898,68591,2626],{},[902,68593,55137],{"encoding":904}," ležící nad minimem ",[883,68596,68598],{"className":68597},[886],[888,68599,68600],{"xmlns":890},[892,68601,68602,68610],{},[895,68603,68604,68606,68608],{},[898,68605,4101],{},[898,68607,40184],{},[898,68609,2626],{},[902,68611,55156],{"encoding":904},[115,68613,68615],{"id":68614},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,68617,68618,68619,68623,68624,68639,68640,68660,68661,1745,68664,68667,68668,68670,68671,19790,68693,68695,68696,1745,68698,58571,68701,2053,68704,41659,68719,68734],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,68620,68622],{"className":68621,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,68625,68627],{"className":68626},[886],[888,68628,68629],{"xmlns":890},[892,68630,68631,68637],{},[895,68632,68633,68635],{},[898,68634,2623],{},[898,68636,3840],{},[902,68638,3940],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,68641,68643],{"className":68642},[886],[888,68644,68645],{"xmlns":890},[892,68646,68647,68657],{},[895,68648,68649,68651,68653,68655],{},[898,68650,2623],{},[898,68652,3840],{},[898,68654,4520],{"mathvariant":2226},[898,68656,2638],{},[902,68658,68659],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,68662,68663],{},"fixních",[38,68665,68666],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,68669,64170],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,68672,68674],{"className":68673},[886],[888,68675,68676],{"xmlns":890},[892,68677,68678,68690],{},[895,68679,68680,68682,68684,68686,68688],{},[898,68681,2623],{},[898,68683,3840],{},[1846,68685,2075],{},[898,68687,2623],{},[898,68689,2626],{},[902,68691,68692],{"encoding":904},"TR - TC",[38,68694,55017],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,68697,56329],{},[38,68699,68700],{},"mezní náklady",[207,68702,1145],{"className":68703,"dataFsResolvedFilePath":764,"href":765},[210],[883,68705,68707],{"className":68706},[886],[888,68708,68709],{"xmlns":890},[892,68710,68711,68717],{},[895,68712,68713,68715],{},[898,68714,2623],{},[898,68716,3840],{},[902,68718,3940],{"encoding":904},[883,68720,68722],{"className":68721},[886],[888,68723,68724],{"xmlns":890},[892,68725,68726,68732],{},[895,68727,68728,68730],{},[898,68729,2623],{},[898,68731,2626],{},[902,68733,3091],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,68736,68737,68799,68865,68927],{},[123,68738,68739,68742,68743,10240,68758,1734],{},[38,68740,68741],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,68744,68746],{"className":68745},[886],[888,68747,68748],{"xmlns":890},[892,68749,68750,68756],{},[895,68751,68752,68754],{},[898,68753,4101],{},[898,68755,2626],{},[902,68757,55405],{"encoding":904},[883,68759,68761],{"className":68760},[886],[888,68762,68763],{"xmlns":890},[892,68764,68765,68797],{},[895,68766,68767,68769,68771,68773,68779,68781,68783,68785,68787,68789,68795],{},[898,68768,4101],{},[898,68770,2626],{},[1846,68772,1855],{"stretchy":1854},[2122,68774,68775,68777],{},[898,68776,2638],{},[1979,68778,2177],{},[1846,68780,1861],{"stretchy":1854},[1846,68782,1848],{},[898,68784,2667],{},[898,68786,2626],{},[1846,68788,1855],{"stretchy":1854},[2122,68790,68791,68793],{},[898,68792,2638],{},[1979,68794,2177],{},[1846,68796,1861],{"stretchy":1854},[902,68798,62414],{"encoding":904},[123,68800,68801,68742,68804,10240,68821,1734],{},[38,68802,68803],{},"Princip minimalizace průměrných variabilních nákladů:",[883,68805,68807],{"className":68806},[886],[888,68808,68809],{"xmlns":890},[892,68810,68811,68819],{},[895,68812,68813,68815,68817],{},[898,68814,4101],{},[898,68816,40184],{},[898,68818,2626],{},[902,68820,55156],{"encoding":904},[883,68822,68824],{"className":68823},[886],[888,68825,68826],{"xmlns":890},[892,68827,68828,68862],{},[895,68829,68830,68832,68834,68836,68838,68844,68846,68848,68850,68852,68854,68860],{},[898,68831,4101],{},[898,68833,40184],{},[898,68835,2626],{},[1846,68837,1855],{"stretchy":1854},[2122,68839,68840,68842],{},[898,68841,2638],{},[1979,68843,2177],{},[1846,68845,1861],{"stretchy":1854},[1846,68847,1848],{},[898,68849,2667],{},[898,68851,2626],{},[1846,68853,1855],{"stretchy":1854},[2122,68855,68856,68858],{},[898,68857,2638],{},[1979,68859,2177],{},[1846,68861,1861],{"stretchy":1854},[902,68863,68864],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,68866,68867,68870,68871,10240,68886,1734],{},[38,68868,68869],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,68872,68874],{"className":68873},[886],[888,68875,68876],{"xmlns":890},[892,68877,68878,68884],{},[895,68879,68880,68882],{},[898,68881,3783],{},[898,68883,3840],{},[902,68885,63324],{"encoding":904},[883,68887,68889],{"className":68888},[886],[888,68890,68891],{"xmlns":890},[892,68892,68893,68925],{},[895,68894,68895,68897,68899,68901,68907,68909,68911,68913,68915,68917,68923],{},[898,68896,2667],{},[898,68898,3840],{},[1846,68900,1855],{"stretchy":1854},[2122,68902,68903,68905],{},[898,68904,2638],{},[1979,68906,2177],{},[1846,68908,1861],{"stretchy":1854},[1846,68910,1848],{},[898,68912,2667],{},[898,68914,2626],{},[1846,68916,1855],{"stretchy":1854},[2122,68918,68919,68921],{},[898,68920,2638],{},[1979,68922,2177],{},[1846,68924,1861],{"stretchy":1854},[902,68926,65490],{"encoding":904},[123,68928,68929,2053,68932,6319,68968,67770,68989,21439,69002,67452,69019,1734],{},[38,68930,68931],{},"Funkce nabídky firmy:",[883,68933,68935],{"className":68934},[886],[888,68936,68937],{"xmlns":890},[892,68938,68939,68965],{},[895,68940,68941,68943,68945,68947,68949,68951,68953,68955,68957,68959,68961,68963],{},[898,68942,3783],{},[1846,68944,1848],{},[898,68946,8519],{},[1846,68948,1855],{"stretchy":1854},[898,68950,2638],{},[1846,68952,1861],{"stretchy":1854},[1846,68954,1848],{},[898,68956,2667],{},[898,68958,2626],{},[1846,68960,1855],{"stretchy":1854},[898,68962,2638],{},[1846,68964,1861],{"stretchy":1854},[902,68966,68967],{"encoding":904},"P = S(Q) = MC(Q)",[883,68969,68971],{"className":68970},[886],[888,68972,68973],{"xmlns":890},[892,68974,68975,68987],{},[895,68976,68977,68979,68981],{},[898,68978,2638],{},[1846,68980,4331],{},[1974,68982,68983,68985],{},[898,68984,2638],{},[1846,68986,4200],{},[902,68988,67769],{"encoding":904},[883,68990,68992],{"className":68991},[886],[888,68993,68994],{"xmlns":890},[892,68995,68996,69000],{},[895,68997,68998],{},[1979,68999,2177],{},[902,69001,2177],{"encoding":904},[883,69003,69005],{"className":69004},[886],[888,69006,69007],{"xmlns":890},[892,69008,69009,69017],{},[895,69010,69011],{},[1974,69012,69013,69015],{},[898,69014,2638],{},[1846,69016,4200],{},[902,69018,29689],{"encoding":904},[883,69020,69022],{"className":69021},[886],[888,69023,69024],{"xmlns":890},[892,69025,69026,69034],{},[895,69027,69028,69030,69032],{},[898,69029,4101],{},[898,69031,40184],{},[898,69033,2626],{},[902,69035,55156],{"encoding":904},[115,69037,49727],{"id":49726},[152,69039,69040,69043,69046,69049,69052,69055,69058,69061,69064,69067,69070],{},[123,69041,69042],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,69044,69045],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,69047,69048],{},"Jak se vypočte mezní příjem a co udává?",[123,69050,69051],{},"Z jakých složek se skládají celkové náklady?",[123,69053,69054],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,69056,69057],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,69059,69060],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,69062,69063],{},"Jak se vypočte zisk?",[123,69065,69066],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,69068,69069],{},"Co jsou body zvratu? Jak se najdou?",[123,69071,69072],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,69074,69076],{"id":69075},"úlohy-31328","Úlohy 3.1–3.28",[198,69078,69080],{"id":69079},"příjem-3135","Příjem (3.1–3.5)",[724,69082,69083,45271,69086,69114,69115,69130,69131,69146,69147,69162,69163,1343,69178,1343,69193,69208],{},[38,69084,69085],{},"3.1",[883,69087,69089],{"className":69088},[886],[888,69090,69091],{"xmlns":890},[892,69092,69093,69111],{},[895,69094,69095,69097,69099,69101,69103,69105,69107,69109],{},[898,69096,3783],{},[1846,69098,1848],{},[898,69100,4029],{},[1846,69102,1855],{"stretchy":1854},[898,69104,2638],{},[1846,69106,1861],{"stretchy":1854},[1846,69108,1848],{},[1979,69110,2938],{},[902,69112,69113],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,69116,69118],{"className":69117},[886],[888,69119,69120],{"xmlns":890},[892,69121,69122,69128],{},[895,69123,69124,69126],{},[898,69125,2623],{},[898,69127,3840],{},[902,69129,3940],{"encoding":904},", průměrný příjem ",[883,69132,69134],{"className":69133},[886],[888,69135,69136],{"xmlns":890},[892,69137,69138,69144],{},[895,69139,69140,69142],{},[898,69141,4101],{},[898,69143,3840],{},[902,69145,55290],{"encoding":904}," a mezní příjem ",[883,69148,69150],{"className":69149},[886],[888,69151,69152],{"xmlns":890},[892,69153,69154,69160],{},[895,69155,69156,69158],{},[898,69157,2667],{},[898,69159,3840],{},[902,69161,6480],{"encoding":904},". (c) Vypočtěte ",[883,69164,69166],{"className":69165},[886],[888,69167,69168],{"xmlns":890},[892,69169,69170,69176],{},[895,69171,69172,69174],{},[898,69173,2623],{},[898,69175,3840],{},[902,69177,3940],{"encoding":904},[883,69179,69181],{"className":69180},[886],[888,69182,69183],{"xmlns":890},[892,69184,69185,69191],{},[895,69186,69187,69189],{},[898,69188,4101],{},[898,69190,3840],{},[902,69192,55290],{"encoding":904},[883,69194,69196],{"className":69195},[886],[888,69197,69198],{"xmlns":890},[892,69199,69200,69206],{},[895,69201,69202,69204],{},[898,69203,2667],{},[898,69205,3840],{},[902,69207,6480],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,69210,69211,45271,69214,69114,69250,69130,69265,69146,69280,69162,69295,1343,69310,1343,69325,69340],{},[38,69212,69213],{},"3.2",[883,69215,69217],{"className":69216},[886],[888,69218,69219],{"xmlns":890},[892,69220,69221,69247],{},[895,69222,69223,69225,69227,69229,69231,69233,69235,69237,69239,69241,69243,69245],{},[898,69224,3783],{},[1846,69226,1848],{},[898,69228,4029],{},[1846,69230,1855],{"stretchy":1854},[898,69232,2638],{},[1846,69234,1861],{"stretchy":1854},[1846,69236,1848],{},[1846,69238,2075],{},[1979,69240,4855],{},[898,69242,2638],{},[1846,69244,1945],{},[1979,69246,8881],{},[902,69248,69249],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,69251,69253],{"className":69252},[886],[888,69254,69255],{"xmlns":890},[892,69256,69257,69263],{},[895,69258,69259,69261],{},[898,69260,2623],{},[898,69262,3840],{},[902,69264,3940],{"encoding":904},[883,69266,69268],{"className":69267},[886],[888,69269,69270],{"xmlns":890},[892,69271,69272,69278],{},[895,69273,69274,69276],{},[898,69275,4101],{},[898,69277,3840],{},[902,69279,55290],{"encoding":904},[883,69281,69283],{"className":69282},[886],[888,69284,69285],{"xmlns":890},[892,69286,69287,69293],{},[895,69288,69289,69291],{},[898,69290,2667],{},[898,69292,3840],{},[902,69294,6480],{"encoding":904},[883,69296,69298],{"className":69297},[886],[888,69299,69300],{"xmlns":890},[892,69301,69302,69308],{},[895,69303,69304,69306],{},[898,69305,2623],{},[898,69307,3840],{},[902,69309,3940],{"encoding":904},[883,69311,69313],{"className":69312},[886],[888,69314,69315],{"xmlns":890},[892,69316,69317,69323],{},[895,69318,69319,69321],{},[898,69320,4101],{},[898,69322,3840],{},[902,69324,55290],{"encoding":904},[883,69326,69328],{"className":69327},[886],[888,69329,69330],{"xmlns":890},[892,69331,69332,69338],{},[895,69333,69334,69336],{},[898,69335,2667],{},[898,69337,3840],{},[902,69339,6480],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,69342,69343,45271,69346,69383,69384,69130,69399,69146,69414,69429,69430,6319,69445,69471,69472,69487,69488,1343,69503,6319,69518,69471,69543,69558,69559,69572,69573,69588,69589,69604,69605,1343,69618,1343,69633,1343,69648,1734],{},[38,69344,69345],{},"3.3",[883,69347,69349],{"className":69348},[886],[888,69350,69351],{"xmlns":890},[892,69352,69353,69380],{},[895,69354,69355,69357,69359,69361,69363,69365,69367,69369,69372,69374],{},[898,69356,3783],{},[1846,69358,1848],{},[898,69360,4029],{},[1846,69362,1855],{"stretchy":1854},[898,69364,2638],{},[1846,69366,1861],{"stretchy":1854},[1846,69368,1848],{},[1979,69370,69371],{},"1200",[1846,69373,2075],{},[1974,69375,69376,69378],{},[898,69377,2638],{},[1979,69379,1981],{},[902,69381,69382],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,69385,69387],{"className":69386},[886],[888,69388,69389],{"xmlns":890},[892,69390,69391,69397],{},[895,69392,69393,69395],{},[898,69394,2623],{},[898,69396,3840],{},[902,69398,3940],{"encoding":904},[883,69400,69402],{"className":69401},[886],[888,69403,69404],{"xmlns":890},[892,69405,69406,69412],{},[895,69407,69408,69410],{},[898,69409,4101],{},[898,69411,3840],{},[902,69413,55290],{"encoding":904},[883,69415,69417],{"className":69416},[886],[888,69418,69419],{"xmlns":890},[892,69420,69421,69427],{},[895,69422,69423,69425],{},[898,69424,2667],{},[898,69426,3840],{},[902,69428,6480],{"encoding":904},". (b) Vypočtěte ",[883,69431,69433],{"className":69432},[886],[888,69434,69435],{"xmlns":890},[892,69436,69437,69443],{},[895,69438,69439,69441],{},[898,69440,2623],{},[898,69442,3840],{},[902,69444,3940],{"encoding":904},[883,69446,69448],{"className":69447},[886],[888,69449,69450],{"xmlns":890},[892,69451,69452,69468],{},[895,69453,69454,69456,69458,69460,69462,69464,69466],{},[898,69455,2638],{},[1846,69457,1848],{},[1979,69459,2712],{},[1846,69461,2136],{"separator":2135},[1979,69463,8881],{},[1846,69465,2136],{"separator":2135},[1979,69467,37864],{},[902,69469,69470],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,69473,69475],{"className":69474},[886],[888,69476,69477],{"xmlns":890},[892,69478,69479,69485],{},[895,69480,69481,69483],{},[898,69482,2623],{},[898,69484,3840],{},[902,69486,3940],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,69489,69491],{"className":69490},[886],[888,69492,69493],{"xmlns":890},[892,69494,69495,69501],{},[895,69496,69497,69499],{},[898,69498,4101],{},[898,69500,3840],{},[902,69502,55290],{"encoding":904},[883,69504,69506],{"className":69505},[886],[888,69507,69508],{"xmlns":890},[892,69509,69510,69516],{},[895,69511,69512,69514],{},[898,69513,2667],{},[898,69515,3840],{},[902,69517,6480],{"encoding":904},[883,69519,69521],{"className":69520},[886],[888,69522,69523],{"xmlns":890},[892,69524,69525,69541],{},[895,69526,69527,69529,69531,69533,69535,69537,69539],{},[898,69528,2638],{},[1846,69530,1848],{},[1979,69532,2712],{},[1846,69534,2136],{"separator":2135},[1979,69536,8881],{},[1846,69538,2136],{"separator":2135},[1979,69540,37864],{},[902,69542,69470],{"encoding":904},[883,69544,69546],{"className":69545},[886],[888,69547,69548],{"xmlns":890},[892,69549,69550,69556],{},[895,69551,69552,69554],{},[898,69553,2667],{},[898,69555,3840],{},[902,69557,6480],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,69560,69562],{"className":69561},[886],[888,69563,69564],{"xmlns":890},[892,69565,69566,69570],{},[895,69567,69568],{},[898,69569,2638],{},[902,69571,2638],{"encoding":904},", které maximalizuje ",[883,69574,69576],{"className":69575},[886],[888,69577,69578],{"xmlns":890},[892,69579,69580,69586],{},[895,69581,69582,69584],{},[898,69583,2623],{},[898,69585,3840],{},[902,69587,3940],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,69590,69592],{"className":69591},[886],[888,69593,69594],{"xmlns":890},[892,69595,69596,69602],{},[895,69597,69598,69600],{},[898,69599,2623],{},[898,69601,3840],{},[902,69603,3940],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,69606,69608],{"className":69607},[886],[888,69609,69610],{"xmlns":890},[892,69611,69612,69616],{},[895,69613,69614],{},[898,69615,4029],{},[902,69617,4029],{"encoding":904},[883,69619,69621],{"className":69620},[886],[888,69622,69623],{"xmlns":890},[892,69624,69625,69631],{},[895,69626,69627,69629],{},[898,69628,2623],{},[898,69630,3840],{},[902,69632,3940],{"encoding":904},[883,69634,69636],{"className":69635},[886],[888,69637,69638],{"xmlns":890},[892,69639,69640,69646],{},[895,69641,69642,69644],{},[898,69643,4101],{},[898,69645,3840],{},[902,69647,55290],{"encoding":904},[883,69649,69651],{"className":69650},[886],[888,69652,69653],{"xmlns":890},[892,69654,69655,69661],{},[895,69656,69657,69659],{},[898,69658,2667],{},[898,69660,3840],{},[902,69662,6480],{"encoding":904},[724,69664,69665,69668,69669,69699,69700,69715,69716,10003,69729,1343,69747,1343,69764,69782,69783,69805,69806,69821,69822,69835,69836,1734],{},[38,69666,69667],{},"3.4"," Je dán celkový příjem ",[883,69670,69672],{"className":69671},[886],[888,69673,69674],{"xmlns":890},[892,69675,69676,69696],{},[895,69677,69678,69680,69682,69684,69686,69688,69690],{},[898,69679,2623],{},[898,69681,3840],{},[1846,69683,1848],{},[1979,69685,69371],{},[898,69687,2638],{},[1846,69689,2075],{},[1974,69691,69692,69694],{},[898,69693,2638],{},[1979,69695,2023],{},[902,69697,69698],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,69701,69703],{"className":69702},[886],[888,69704,69705],{"xmlns":890},[892,69706,69707,69713],{},[895,69708,69709,69711],{},[898,69710,2623],{},[898,69712,3840],{},[902,69714,3940],{"encoding":904}," vzhledem ke ",[883,69717,69719],{"className":69718},[886],[888,69720,69721],{"xmlns":890},[892,69722,69723,69727],{},[895,69724,69725],{},[898,69726,2638],{},[902,69728,2638],{"encoding":904},[883,69730,69732],{"className":69731},[886],[888,69733,69734],{"xmlns":890},[892,69735,69736,69744],{},[895,69737,69738,69740,69742],{},[898,69739,2638],{},[1846,69741,1848],{},[1979,69743,2078],{},[902,69745,69746],{"encoding":904},"Q = 5",[883,69748,69750],{"className":69749},[886],[888,69751,69752],{"xmlns":890},[892,69753,69754,69762],{},[895,69755,69756,69758,69760],{},[898,69757,2638],{},[1846,69759,1848],{},[1979,69761,5431],{},[902,69763,5434],{"encoding":904},[883,69765,69767],{"className":69766},[886],[888,69768,69769],{"xmlns":890},[892,69770,69771,69779],{},[895,69772,69773,69775,69777],{},[898,69774,2638],{},[1846,69776,1848],{},[1979,69778,3357],{},[902,69780,69781],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,69784,69786],{"className":69785},[886],[888,69787,69788],{"xmlns":890},[892,69789,69790,69802],{},[895,69791,69792,69794,69796,69798,69800],{},[898,69793,2667],{},[898,69795,3840],{},[1846,69797,1855],{"stretchy":1854},[1979,69799,2712],{},[1846,69801,1861],{"stretchy":1854},[902,69803,69804],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,69807,69809],{"className":69808},[886],[888,69810,69811],{"xmlns":890},[892,69812,69813,69819],{},[895,69814,69815,69817],{},[898,69816,2623],{},[898,69818,3840],{},[902,69820,3940],{"encoding":904},", jestliže se ",[883,69823,69825],{"className":69824},[886],[888,69826,69827],{"xmlns":890},[892,69828,69829,69833],{},[895,69830,69831],{},[898,69832,2638],{},[902,69834,2638],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,69837,69839],{"className":69838},[886],[888,69840,69841],{"xmlns":890},[892,69842,69843,69849],{},[895,69844,69845,69847],{},[898,69846,2623],{},[898,69848,3840],{},[902,69850,3940],{"encoding":904},[724,69852,69853,69856,69857,69883,69884,69899,69900,69821,69915,69928],{},[38,69854,69855],{},"3.5"," Je dán mezní příjem ",[883,69858,69860],{"className":69859},[886],[888,69861,69862],{"xmlns":890},[892,69863,69864,69880],{},[895,69865,69866,69868,69870,69872,69874,69876,69878],{},[898,69867,2667],{},[898,69869,3840],{},[1846,69871,1848],{},[1846,69873,2075],{},[898,69875,2638],{},[1846,69877,1945],{},[1979,69879,8881],{},[902,69881,69882],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,69885,69887],{"className":69886},[886],[888,69888,69889],{"xmlns":890},[892,69890,69891,69897],{},[895,69892,69893,69895],{},[898,69894,2623],{},[898,69896,3840],{},[902,69898,3940],{"encoding":904},". (b) Vypočtěte změnu ",[883,69901,69903],{"className":69902},[886],[888,69904,69905],{"xmlns":890},[892,69906,69907,69913],{},[895,69908,69909,69911],{},[898,69910,2623],{},[898,69912,3840],{},[902,69914,3940],{"encoding":904},[883,69916,69918],{"className":69917},[886],[888,69919,69920],{"xmlns":890},[892,69921,69922,69926],{},[895,69923,69924],{},[898,69925,2638],{},[902,69927,2638],{"encoding":904}," změní z 8 na 12.",[198,69930,69932],{"id":69931},"náklady-36316","Náklady (3.6–3.16)",[724,69934,69935,69938,69939,69979,69980,69995,69996,70013,70014,70031,70032,70047,70048,70063,70064,69429,70079,1343,70094,1343,70111,1343,70128,1343,70143,1343,70158,6319,70173,70191,70192,1343,70207,1343,70222,70237],{},[38,69936,69937],{},"3.6"," Jsou dány celkové náklady ",[883,69940,69942],{"className":69941},[886],[888,69943,69944],{"xmlns":890},[892,69945,69946,69976],{},[895,69947,69948,69950,69952,69954,69956,69958,69960,69962,69964],{},[898,69949,2623],{},[898,69951,2626],{},[1846,69953,1848],{},[1979,69955,2938],{},[1846,69957,1945],{},[1979,69959,1981],{},[898,69961,2638],{},[1846,69963,1945],{},[2175,69965,69966],{"scriptlevel":2177,"displaystyle":1854},[2179,69967,69968,69974],{},[1974,69969,69970,69972],{},[898,69971,2638],{},[1979,69973,1981],{},[1979,69975,2712],{},[902,69977,69978],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,69981,69983],{"className":69982},[886],[888,69984,69985],{"xmlns":890},[892,69986,69987,69993],{},[895,69988,69989,69991],{},[898,69990,10282],{},[898,69992,2626],{},[902,69994,55336],{"encoding":904},", celkové variabilní náklady ",[883,69997,69999],{"className":69998},[886],[888,70000,70001],{"xmlns":890},[892,70002,70003,70011],{},[895,70004,70005,70007,70009],{},[898,70006,2623],{},[898,70008,40184],{},[898,70010,2626],{},[902,70012,55354],{"encoding":904},", průměrné variabilní náklady ",[883,70015,70017],{"className":70016},[886],[888,70018,70019],{"xmlns":890},[892,70020,70021,70029],{},[895,70022,70023,70025,70027],{},[898,70024,4101],{},[898,70026,40184],{},[898,70028,2626],{},[902,70030,55156],{"encoding":904},", variabilní náklady na jednotku ",[883,70033,70035],{"className":70034},[886],[888,70036,70037],{"xmlns":890},[892,70038,70039,70045],{},[895,70040,70041,70043],{},[898,70042,40184],{},[898,70044,2626],{},[902,70046,63450],{"encoding":904},", průměrné náklady ",[883,70049,70051],{"className":70050},[886],[888,70052,70053],{"xmlns":890},[892,70054,70055,70061],{},[895,70056,70057,70059],{},[898,70058,4101],{},[898,70060,2626],{},[902,70062,55405],{"encoding":904}," a mezní náklady ",[883,70065,70067],{"className":70066},[886],[888,70068,70069],{"xmlns":890},[892,70070,70071,70077],{},[895,70072,70073,70075],{},[898,70074,2667],{},[898,70076,2626],{},[902,70078,55137],{"encoding":904},[883,70080,70082],{"className":70081},[886],[888,70083,70084],{"xmlns":890},[892,70085,70086,70092],{},[895,70087,70088,70090],{},[898,70089,2623],{},[898,70091,2626],{},[902,70093,3091],{"encoding":904},[883,70095,70097],{"className":70096},[886],[888,70098,70099],{"xmlns":890},[892,70100,70101,70109],{},[895,70102,70103,70105,70107],{},[898,70104,2623],{},[898,70106,40184],{},[898,70108,2626],{},[902,70110,55354],{"encoding":904},[883,70112,70114],{"className":70113},[886],[888,70115,70116],{"xmlns":890},[892,70117,70118,70126],{},[895,70119,70120,70122,70124],{},[898,70121,4101],{},[898,70123,40184],{},[898,70125,2626],{},[902,70127,55156],{"encoding":904},[883,70129,70131],{"className":70130},[886],[888,70132,70133],{"xmlns":890},[892,70134,70135,70141],{},[895,70136,70137,70139],{},[898,70138,40184],{},[898,70140,2626],{},[902,70142,63450],{"encoding":904},[883,70144,70146],{"className":70145},[886],[888,70147,70148],{"xmlns":890},[892,70149,70150,70156],{},[895,70151,70152,70154],{},[898,70153,4101],{},[898,70155,2626],{},[902,70157,55405],{"encoding":904},[883,70159,70161],{"className":70160},[886],[888,70162,70163],{"xmlns":890},[892,70164,70165,70171],{},[895,70166,70167,70169],{},[898,70168,2667],{},[898,70170,2626],{},[902,70172,55137],{"encoding":904},[883,70174,70176],{"className":70175},[886],[888,70177,70178],{"xmlns":890},[892,70179,70180,70188],{},[895,70181,70182,70184,70186],{},[898,70183,2638],{},[1846,70185,1848],{},[1979,70187,2968],{},[902,70189,70190],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,70193,70195],{"className":70194},[886],[888,70196,70197],{"xmlns":890},[892,70198,70199,70205],{},[895,70200,70201,70203],{},[898,70202,2623],{},[898,70204,2626],{},[902,70206,3091],{"encoding":904},[883,70208,70210],{"className":70209},[886],[888,70211,70212],{"xmlns":890},[892,70213,70214,70220],{},[895,70215,70216,70218],{},[898,70217,4101],{},[898,70219,2626],{},[902,70221,55405],{"encoding":904},[883,70223,70225],{"className":70224},[886],[888,70226,70227],{"xmlns":890},[892,70228,70229,70235],{},[895,70230,70231,70233],{},[898,70232,2667],{},[898,70234,2626],{},[902,70236,55137],{"encoding":904}," rostou, resp. klesají.",[724,70239,70240,70243,70244,70063,70274,70289,70290,70305,70306,1343,70321,1343,70336,1734],{},[38,70241,70242],{},"3.7"," Jsou dány průměrné náklady ",[883,70245,70247],{"className":70246},[886],[888,70248,70249],{"xmlns":890},[892,70250,70251,70271],{},[895,70252,70253,70255,70257,70259,70267,70269],{},[898,70254,4101],{},[898,70256,2626],{},[1846,70258,1848],{},[2175,70260,70261],{"scriptlevel":2177,"displaystyle":1854},[2179,70262,70263,70265],{},[1979,70264,2938],{},[898,70266,2638],{},[1846,70268,1945],{},[1979,70270,8881],{},[902,70272,70273],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,70275,70277],{"className":70276},[886],[888,70278,70279],{"xmlns":890},[892,70280,70281,70287],{},[895,70282,70283,70285],{},[898,70284,2667],{},[898,70286,2626],{},[902,70288,55137],{"encoding":904},". (a) Určete celkové náklady ",[883,70291,70293],{"className":70292},[886],[888,70294,70295],{"xmlns":890},[892,70296,70297,70303],{},[895,70298,70299,70301],{},[898,70300,2623],{},[898,70302,2626],{},[902,70304,3091],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,70307,70309],{"className":70308},[886],[888,70310,70311],{"xmlns":890},[892,70312,70313,70319],{},[895,70314,70315,70317],{},[898,70316,4101],{},[898,70318,2626],{},[902,70320,55405],{"encoding":904},[883,70322,70324],{"className":70323},[886],[888,70325,70326],{"xmlns":890},[892,70327,70328,70334],{},[895,70329,70330,70332],{},[898,70331,2623],{},[898,70333,2626],{},[902,70335,3091],{"encoding":904},[883,70337,70339],{"className":70338},[886],[888,70340,70341],{"xmlns":890},[892,70342,70343,70349],{},[895,70344,70345,70347],{},[898,70346,2667],{},[898,70348,2626],{},[902,70350,55137],{"encoding":904},[724,70352,70353,69938,70356,70400,70401,1343,70418,1343,70433,1343,70450,1343,70465,1343,70482,1734],{},[38,70354,70355],{},"3.8",[883,70357,70359],{"className":70358},[886],[888,70360,70361],{"xmlns":890},[892,70362,70363,70397],{},[895,70364,70365,70367,70369,70371,70373,70375,70377,70379,70381,70383,70389,70391],{},[898,70366,2623],{},[898,70368,2626],{},[1846,70370,1848],{},[1979,70372,46548],{},[1846,70374,1945],{},[1979,70376,37864],{},[898,70378,2638],{},[1846,70380,2075],{},[1979,70382,2085],{},[1974,70384,70385,70387],{},[898,70386,2638],{},[1979,70388,1981],{},[1846,70390,1945],{},[1974,70392,70393,70395],{},[898,70394,2638],{},[1979,70396,2023],{},[902,70398,70399],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,70402,70404],{"className":70403},[886],[888,70405,70406],{"xmlns":890},[892,70407,70408,70416],{},[895,70409,70410,70412,70414],{},[898,70411,2623],{},[898,70413,40184],{},[898,70415,2626],{},[902,70417,55354],{"encoding":904},[883,70419,70421],{"className":70420},[886],[888,70422,70423],{"xmlns":890},[892,70424,70425,70431],{},[895,70426,70427,70429],{},[898,70428,10282],{},[898,70430,2626],{},[902,70432,55336],{"encoding":904},[883,70434,70436],{"className":70435},[886],[888,70437,70438],{"xmlns":890},[892,70439,70440,70448],{},[895,70441,70442,70444,70446],{},[898,70443,4101],{},[898,70445,40184],{},[898,70447,2626],{},[902,70449,55156],{"encoding":904},[883,70451,70453],{"className":70452},[886],[888,70454,70455],{"xmlns":890},[892,70456,70457,70463],{},[895,70458,70459,70461],{},[898,70460,4101],{},[898,70462,2626],{},[902,70464,55405],{"encoding":904},[883,70466,70468],{"className":70467},[886],[888,70469,70470],{"xmlns":890},[892,70471,70472,70480],{},[895,70473,70474,70476,70478],{},[898,70475,4101],{},[898,70477,10282],{},[898,70479,2626],{},[902,70481,55372],{"encoding":904},[883,70483,70485],{"className":70484},[886],[888,70486,70487],{"xmlns":890},[892,70488,70489,70495],{},[895,70490,70491,70493],{},[898,70492,2667],{},[898,70494,2626],{},[902,70496,55137],{"encoding":904},[724,70498,70499,69938,70502,70532,70533,69715,70548,6319,70561,1343,70579,1343,70597,69782,70615,69805,70637,70652,70653,70666,70667,1734],{},[38,70500,70501],{},"3.9",[883,70503,70505],{"className":70504},[886],[888,70506,70507],{"xmlns":890},[892,70508,70509,70529],{},[895,70510,70511,70513,70515,70517,70519,70521,70523],{},[898,70512,2623],{},[898,70514,2626],{},[1846,70516,1848],{},[1979,70518,14955],{},[1846,70520,1945],{},[1979,70522,19166],{},[1974,70524,70525,70527],{},[898,70526,2638],{},[1979,70528,1981],{},[902,70530,70531],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,70534,70536],{"className":70535},[886],[888,70537,70538],{"xmlns":890},[892,70539,70540,70546],{},[895,70541,70542,70544],{},[898,70543,2623],{},[898,70545,2626],{},[902,70547,3091],{"encoding":904},[883,70549,70551],{"className":70550},[886],[888,70552,70553],{"xmlns":890},[892,70554,70555,70559],{},[895,70556,70557],{},[898,70558,2638],{},[902,70560,2638],{"encoding":904},[883,70562,70564],{"className":70563},[886],[888,70565,70566],{"xmlns":890},[892,70567,70568,70576],{},[895,70569,70570,70572,70574],{},[898,70571,2638],{},[1846,70573,1848],{},[1979,70575,2712],{},[902,70577,70578],{"encoding":904},"Q = 10",[883,70580,70582],{"className":70581},[886],[888,70583,70584],{"xmlns":890},[892,70585,70586,70594],{},[895,70587,70588,70590,70592],{},[898,70589,2638],{},[1846,70591,1848],{},[1979,70593,8881],{},[902,70595,70596],{"encoding":904},"Q = 20",[883,70598,70600],{"className":70599},[886],[888,70601,70602],{"xmlns":890},[892,70603,70604,70612],{},[895,70605,70606,70608,70610],{},[898,70607,2638],{},[1846,70609,1848],{},[1979,70611,37864],{},[902,70613,70614],{"encoding":904},"Q = 30",[883,70616,70618],{"className":70617},[886],[888,70619,70620],{"xmlns":890},[892,70621,70622,70634],{},[895,70623,70624,70626,70628,70630,70632],{},[898,70625,2667],{},[898,70627,2626],{},[1846,70629,1855],{"stretchy":1854},[1979,70631,36089],{},[1846,70633,1861],{"stretchy":1854},[902,70635,70636],{"encoding":904},"MC(15)",[883,70638,70640],{"className":70639},[886],[888,70641,70642],{"xmlns":890},[892,70643,70644,70650],{},[895,70645,70646,70648],{},[898,70647,2623],{},[898,70649,2626],{},[902,70651,3091],{"encoding":904}," v důsledku změny ",[883,70654,70656],{"className":70655},[886],[888,70657,70658],{"xmlns":890},[892,70659,70660,70664],{},[895,70661,70662],{},[898,70663,2638],{},[902,70665,2638],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,70668,70670],{"className":70669},[886],[888,70671,70672],{"xmlns":890},[892,70673,70674,70680],{},[895,70675,70676,70678],{},[898,70677,2623],{},[898,70679,2626],{},[902,70681,3091],{"encoding":904},[724,70683,70684,70687,70688,70289,70724,70739,70740,69899,70759,70652,70774,70787],{},[38,70685,70686],{},"3.10"," Jsou dány mezní náklady ",[883,70689,70691],{"className":70690},[886],[888,70692,70693],{"xmlns":890},[892,70694,70695,70721],{},[895,70696,70697,70699,70701,70703,70705,70707,70709,70711,70713,70715],{},[898,70698,2667],{},[898,70700,2626],{},[1846,70702,1848],{},[1979,70704,2974],{},[1846,70706,2075],{},[1979,70708,41707],{},[898,70710,2638],{},[1846,70712,1945],{},[1979,70714,64404],{},[1974,70716,70717,70719],{},[898,70718,2638],{},[1979,70720,1981],{},[902,70722,70723],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,70725,70727],{"className":70726},[886],[888,70728,70729],{"xmlns":890},[892,70730,70731,70737],{},[895,70732,70733,70735],{},[898,70734,2623],{},[898,70736,2626],{},[902,70738,3091],{"encoding":904},", jestliže fixní náklady ",[883,70741,70743],{"className":70742},[886],[888,70744,70745],{"xmlns":890},[892,70746,70747,70757],{},[895,70748,70749,70751,70753,70755],{},[898,70750,10282],{},[898,70752,2626],{},[1846,70754,1848],{},[1979,70756,2938],{},[902,70758,11479],{"encoding":904},[883,70760,70762],{"className":70761},[886],[888,70763,70764],{"xmlns":890},[892,70765,70766,70772],{},[895,70767,70768,70770],{},[898,70769,2623],{},[898,70771,2626],{},[902,70773,3091],{"encoding":904},[883,70775,70777],{"className":70776},[886],[888,70778,70779],{"xmlns":890},[892,70780,70781,70785],{},[895,70782,70783],{},[898,70784,2638],{},[902,70786,2638],{"encoding":904}," z 15 na 20.",[724,70789,70790,69938,70793,70836,70837,70850,70851,70866,70867,70882,70883,70850,70896,70866,70913,70930,70931,70850,70944,70866,70959,70974,70975,70995,70996,71019],{},[38,70791,70792],{},"3.11",[883,70794,70796],{"className":70795},[886],[888,70797,70798],{"xmlns":890},[892,70799,70800,70834],{},[895,70801,70802,70804,70806,70808,70810,70812,70814,70816,70818,70820,70826,70828],{},[898,70803,2623],{},[898,70805,2626],{},[1846,70807,1848],{},[1979,70809,2938],{},[1846,70811,1945],{},[1979,70813,4850],{},[898,70815,2638],{},[1846,70817,2075],{},[1979,70819,2078],{},[1974,70821,70822,70824],{},[898,70823,2638],{},[1979,70825,1981],{},[1846,70827,1945],{},[1974,70829,70830,70832],{},[898,70831,2638],{},[1979,70833,2023],{},[902,70835,60752],{"encoding":904},". (a) Určete ",[883,70838,70840],{"className":70839},[886],[888,70841,70842],{"xmlns":890},[892,70843,70844,70848],{},[895,70845,70846],{},[898,70847,2638],{},[902,70849,2638],{"encoding":904},", které minimalizuje ",[883,70852,70854],{"className":70853},[886],[888,70855,70856],{"xmlns":890},[892,70857,70858,70864],{},[895,70859,70860,70862],{},[898,70861,2667],{},[898,70863,2626],{},[902,70865,55137],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,70868,70870],{"className":70869},[886],[888,70871,70872],{"xmlns":890},[892,70873,70874,70880],{},[895,70875,70876,70878],{},[898,70877,2667],{},[898,70879,2626],{},[902,70881,55137],{"encoding":904},". (b) Určete ",[883,70884,70886],{"className":70885},[886],[888,70887,70888],{"xmlns":890},[892,70889,70890,70894],{},[895,70891,70892],{},[898,70893,2638],{},[902,70895,2638],{"encoding":904},[883,70897,70899],{"className":70898},[886],[888,70900,70901],{"xmlns":890},[892,70902,70903,70911],{},[895,70904,70905,70907,70909],{},[898,70906,4101],{},[898,70908,40184],{},[898,70910,2626],{},[902,70912,55156],{"encoding":904},[883,70914,70916],{"className":70915},[886],[888,70917,70918],{"xmlns":890},[892,70919,70920,70928],{},[895,70921,70922,70924,70926],{},[898,70923,4101],{},[898,70925,40184],{},[898,70927,2626],{},[902,70929,55156],{"encoding":904},". (c) Určete ",[883,70932,70934],{"className":70933},[886],[888,70935,70936],{"xmlns":890},[892,70937,70938,70942],{},[895,70939,70940],{},[898,70941,2638],{},[902,70943,2638],{"encoding":904},[883,70945,70947],{"className":70946},[886],[888,70948,70949],{"xmlns":890},[892,70950,70951,70957],{},[895,70952,70953,70955],{},[898,70954,4101],{},[898,70956,2626],{},[902,70958,55405],{"encoding":904},[883,70960,70962],{"className":70961},[886],[888,70963,70964],{"xmlns":890},[892,70965,70966,70972],{},[895,70967,70968,70970],{},[898,70969,4101],{},[898,70971,2626],{},[902,70973,55405],{"encoding":904}," (rada: hledaný kořen ",[883,70976,70978],{"className":70977},[886],[888,70979,70980],{"xmlns":890},[892,70981,70982,70992],{},[895,70983,70984,70986],{},[898,70985,4101],{},[1974,70987,70988,70990],{},[898,70989,2626],{},[1846,70991,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,70993,70994],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,70997,70999],{"className":70998},[886],[888,71000,71001],{"xmlns":890},[892,71002,71003,71016],{},[895,71004,71005,71007,71010,71012,71014],{},[1846,71006,1855],{"stretchy":1854},[1979,71008,71009],{},"4,7",[1846,71011,8271],{"separator":2135},[1979,71013,5125],{},[1846,71015,1861],{"stretchy":1854},[902,71017,71018],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,71021,71022,71025,71026,2474,71054,71071,71072,21439,71113,71134],{},[38,71023,71024],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,71027,71029],{"className":71028},[886],[888,71030,71031],{"xmlns":890},[892,71032,71033,71051],{},[895,71034,71035,71037,71039,71041,71043,71045,71047,71049],{},[898,71036,4101],{},[898,71038,2626],{},[1846,71040,1848],{},[898,71042,4101],{},[898,71044,2626],{},[1846,71046,1855],{"stretchy":1854},[898,71048,2638],{},[1846,71050,1861],{"stretchy":1854},[902,71052,71053],{"encoding":904},"AC = AC(Q)",[883,71055,71057],{"className":71056},[886],[888,71058,71059],{"xmlns":890},[892,71060,71061,71069],{},[895,71062,71063],{},[2122,71064,71065,71067],{},[898,71066,2638],{},[1979,71068,2177],{},[902,71070,38153],{"encoding":904}," minimum, pak platí ",[883,71073,71075],{"className":71074},[886],[888,71076,71077],{"xmlns":890},[892,71078,71079,71111],{},[895,71080,71081,71083,71085,71087,71093,71095,71097,71099,71101,71103,71109],{},[898,71082,4101],{},[898,71084,2626],{},[1846,71086,1855],{"stretchy":1854},[2122,71088,71089,71091],{},[898,71090,2638],{},[1979,71092,2177],{},[1846,71094,1861],{"stretchy":1854},[1846,71096,1848],{},[898,71098,2667],{},[898,71100,2626],{},[1846,71102,1855],{"stretchy":1854},[2122,71104,71105,71107],{},[898,71106,2638],{},[1979,71108,2177],{},[1846,71110,1861],{"stretchy":1854},[902,71112,62414],{"encoding":904},[883,71114,71116],{"className":71115},[886],[888,71117,71118],{"xmlns":890},[892,71119,71120,71132],{},[895,71121,71122,71124,71126,71128,71130],{},[898,71123,2667],{},[898,71125,2626],{},[1846,71127,1855],{"stretchy":1854},[898,71129,2638],{},[1846,71131,1861],{"stretchy":1854},[902,71133,67538],{"encoding":904}," jsou mezní náklady.",[724,71136,71137,69938,71140,70400,71174,70850,71187,70866,71202,1734],{},[38,71138,71139],{},"3.13",[883,71141,71143],{"className":71142},[886],[888,71144,71145],{"xmlns":890},[892,71146,71147,71171],{},[895,71148,71149,71151,71153,71155,71161,71163,71165,71167,71169],{},[898,71150,2623],{},[898,71152,2626],{},[1846,71154,1848],{},[1974,71156,71157,71159],{},[898,71158,2638],{},[1979,71160,1981],{},[1846,71162,1945],{},[1979,71164,1981],{},[898,71166,2638],{},[1846,71168,1945],{},[1979,71170,4850],{},[902,71172,71173],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,71175,71177],{"className":71176},[886],[888,71178,71179],{"xmlns":890},[892,71180,71181,71185],{},[895,71182,71183],{},[898,71184,2638],{},[902,71186,2638],{"encoding":904},[883,71188,71190],{"className":71189},[886],[888,71191,71192],{"xmlns":890},[892,71193,71194,71200],{},[895,71195,71196,71198],{},[898,71197,4101],{},[898,71199,2626],{},[902,71201,55405],{"encoding":904},[883,71203,71205],{"className":71204},[886],[888,71206,71207],{"xmlns":890},[892,71208,71209,71215],{},[895,71210,71211,71213],{},[898,71212,4101],{},[898,71214,2626],{},[902,71216,55405],{"encoding":904},[724,71218,71219,71222,71223,2474,71255,71071,71272,21439,71315,71134],{},[38,71220,71221],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,71224,71226],{"className":71225},[886],[888,71227,71228],{"xmlns":890},[892,71229,71230,71252],{},[895,71231,71232,71234,71236,71238,71240,71242,71244,71246,71248,71250],{},[898,71233,4101],{},[898,71235,40184],{},[898,71237,2626],{},[1846,71239,1848],{},[898,71241,4101],{},[898,71243,40184],{},[898,71245,2626],{},[1846,71247,1855],{"stretchy":1854},[898,71249,2638],{},[1846,71251,1861],{"stretchy":1854},[902,71253,71254],{"encoding":904},"AVC = AVC(Q)",[883,71256,71258],{"className":71257},[886],[888,71259,71260],{"xmlns":890},[892,71261,71262,71270],{},[895,71263,71264],{},[2122,71265,71266,71268],{},[898,71267,2638],{},[1979,71269,2177],{},[902,71271,38153],{"encoding":904},[883,71273,71275],{"className":71274},[886],[888,71276,71277],{"xmlns":890},[892,71278,71279,71313],{},[895,71280,71281,71283,71285,71287,71289,71295,71297,71299,71301,71303,71305,71311],{},[898,71282,4101],{},[898,71284,40184],{},[898,71286,2626],{},[1846,71288,1855],{"stretchy":1854},[2122,71290,71291,71293],{},[898,71292,2638],{},[1979,71294,2177],{},[1846,71296,1861],{"stretchy":1854},[1846,71298,1848],{},[898,71300,2667],{},[898,71302,2626],{},[1846,71304,1855],{"stretchy":1854},[2122,71306,71307,71309],{},[898,71308,2638],{},[1979,71310,2177],{},[1846,71312,1861],{"stretchy":1854},[902,71314,68864],{"encoding":904},[883,71316,71318],{"className":71317},[886],[888,71319,71320],{"xmlns":890},[892,71321,71322,71334],{},[895,71323,71324,71326,71328,71330,71332],{},[898,71325,2667],{},[898,71327,2626],{},[1846,71329,1855],{"stretchy":1854},[898,71331,2638],{},[1846,71333,1861],{"stretchy":1854},[902,71335,67538],{"encoding":904},[724,71337,71338,69938,71341,70400,71387,70850,71400,70866,71417,1734],{},[38,71339,71340],{},"3.15",[883,71342,71344],{"className":71343},[886],[888,71345,71346],{"xmlns":890},[892,71347,71348,71384],{},[895,71349,71350,71352,71354,71356,71358,71360,71362,71364,71366,71368,71374,71376,71378],{},[898,71351,2623],{},[898,71353,2626],{},[1846,71355,1848],{},[1979,71357,2968],{},[1846,71359,1945],{},[1979,71361,36089],{},[898,71363,2638],{},[1846,71365,2075],{},[1979,71367,1981],{},[1974,71369,71370,71372],{},[898,71371,2638],{},[1979,71373,1981],{},[1846,71375,1945],{},[1979,71377,2688],{},[1974,71379,71380,71382],{},[898,71381,2638],{},[1979,71383,2023],{},[902,71385,71386],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,71388,71390],{"className":71389},[886],[888,71391,71392],{"xmlns":890},[892,71393,71394,71398],{},[895,71395,71396],{},[898,71397,2638],{},[902,71399,2638],{"encoding":904},[883,71401,71403],{"className":71402},[886],[888,71404,71405],{"xmlns":890},[892,71406,71407,71415],{},[895,71408,71409,71411,71413],{},[898,71410,4101],{},[898,71412,40184],{},[898,71414,2626],{},[902,71416,55156],{"encoding":904},[883,71418,71420],{"className":71419},[886],[888,71421,71422],{"xmlns":890},[892,71423,71424,71432],{},[895,71425,71426,71428,71430],{},[898,71427,4101],{},[898,71429,40184],{},[898,71431,2626],{},[902,71433,55156],{"encoding":904},[724,71435,71436,71439,71440,71453,71454,71474],{},[38,71437,71438],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,71441,71443],{"className":71442},[886],[888,71444,71445],{"xmlns":890},[892,71446,71447,71451],{},[895,71448,71449],{},[898,71450,1858],{},[902,71452,1858],{"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 ",[883,71455,71457],{"className":71456},[886],[888,71458,71459],{"xmlns":890},[892,71460,71461,71471],{},[895,71462,71463,71465,71467,71469],{},[1979,71464,2712],{},[2138,71466,2835],{},[1979,71468,58927],{},[898,71470,1858],{},[902,71472,71473],{"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.",[198,71476,71478],{"id":71477},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,71480,71481,71484,71485,1745,71507,71533],{},[38,71482,71483],{},"3.17"," Jsou dány ",[883,71486,71488],{"className":71487},[886],[888,71489,71490],{"xmlns":890},[892,71491,71492,71504],{},[895,71493,71494,71496,71498,71500,71502],{},[898,71495,2623],{},[898,71497,3840],{},[1846,71499,1848],{},[1979,71501,2712],{},[898,71503,2638],{},[902,71505,71506],{"encoding":904},"TR = 10Q",[883,71508,71510],{"className":71509},[886],[888,71511,71512],{"xmlns":890},[892,71513,71514,71530],{},[895,71515,71516,71518,71520,71522,71524,71526,71528],{},[898,71517,2623],{},[898,71519,2626],{},[1846,71521,1848],{},[1979,71523,2938],{},[1846,71525,1945],{},[1979,71527,2078],{},[898,71529,2638],{},[902,71531,71532],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,71535,71536,71539,71540,6036,71555,71570,71571,1343,71593,21439,71620,71642,71643,71677],{},[38,71537,71538],{},"3.18"," Odvoďte, že jestliže ",[883,71541,71543],{"className":71542},[886],[888,71544,71545],{"xmlns":890},[892,71546,71547,71553],{},[895,71548,71549,71551],{},[898,71550,2623],{},[898,71552,3840],{},[902,71554,3940],{"encoding":904},[883,71556,71558],{"className":71557},[886],[888,71559,71560],{"xmlns":890},[892,71561,71562,71568],{},[895,71563,71564,71566],{},[898,71565,2623],{},[898,71567,2626],{},[902,71569,3091],{"encoding":904}," jsou lineární tvaru ",[883,71572,71574],{"className":71573},[886],[888,71575,71576],{"xmlns":890},[892,71577,71578,71590],{},[895,71579,71580,71582,71584,71586,71588],{},[898,71581,2623],{},[898,71583,3840],{},[1846,71585,1848],{},[898,71587,724],{},[898,71589,2638],{},[902,71591,71592],{"encoding":904},"TR = pQ",[883,71594,71596],{"className":71595},[886],[888,71597,71598],{"xmlns":890},[892,71599,71600,71617],{},[895,71601,71602,71604,71606,71608,71611,71613,71615],{},[898,71603,2623],{},[898,71605,2626],{},[1846,71607,1848],{},[898,71609,71610],{},"m",[1846,71612,1945],{},[898,71614,36705],{},[898,71616,2638],{},[902,71618,71619],{"encoding":904},"TC = m + nQ",[883,71621,71623],{"className":71622},[886],[888,71624,71625],{"xmlns":890},[892,71626,71627,71639],{},[895,71628,71629,71631,71633,71635,71637],{},[898,71630,71610],{},[1846,71632,2136],{"separator":2135},[898,71634,36705],{},[1846,71636,2136],{"separator":2135},[898,71638,724],{},[902,71640,71641],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,71644,71646],{"className":71645},[886],[888,71647,71648],{"xmlns":890},[892,71649,71650,71674],{},[895,71651,71652,71658,71660],{},[1974,71653,71654,71656],{},[898,71655,2638],{},[1846,71657,4200],{},[1846,71659,1848],{},[2175,71661,71662],{"scriptlevel":2177,"displaystyle":1854},[2179,71663,71664,71666],{},[898,71665,71610],{},[895,71667,71668,71670,71672],{},[898,71669,724],{},[1846,71671,2075],{},[898,71673,36705],{},[902,71675,71676],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,71679,71680,71484,71683,1745,71717,70836,71743,71756,71757,69588,71772,71787,71788,69572,71801,69588,71816,71831],{},[38,71681,71682],{},"3.19",[883,71684,71686],{"className":71685},[886],[888,71687,71688],{"xmlns":890},[892,71689,71690,71714],{},[895,71691,71692,71694,71696,71698,71700,71702,71708,71710,71712],{},[898,71693,2623],{},[898,71695,3840],{},[1846,71697,1848],{},[1846,71699,2075],{},[1979,71701,1981],{},[1974,71703,71704,71706],{},[898,71705,2638],{},[1979,71707,1981],{},[1846,71709,1945],{},[1979,71711,22791],{},[898,71713,2638],{},[902,71715,71716],{"encoding":904},"TR = -2Q^2 + 14Q",[883,71718,71720],{"className":71719},[886],[888,71721,71722],{"xmlns":890},[892,71723,71724,71740],{},[895,71725,71726,71728,71730,71732,71734,71736,71738],{},[898,71727,2623],{},[898,71729,2626],{},[1846,71731,1848],{},[1979,71733,1981],{},[898,71735,2638],{},[1846,71737,1945],{},[1979,71739,2712],{},[902,71741,71742],{"encoding":904},"TC = 2Q + 10",[883,71744,71746],{"className":71745},[886],[888,71747,71748],{"xmlns":890},[892,71749,71750,71754],{},[895,71751,71752],{},[898,71753,2638],{},[902,71755,2638],{"encoding":904},", které maximalizuje zisk ",[883,71758,71760],{"className":71759},[886],[888,71761,71762],{"xmlns":890},[892,71763,71764,71770],{},[895,71765,71766,71768],{},[898,71767,3783],{},[898,71769,3840],{},[902,71771,63324],{"encoding":904},[883,71773,71775],{"className":71774},[886],[888,71776,71777],{"xmlns":890},[892,71778,71779,71785],{},[895,71780,71781,71783],{},[898,71782,3783],{},[898,71784,3840],{},[902,71786,63324],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,71789,71791],{"className":71790},[886],[888,71792,71793],{"xmlns":890},[892,71794,71795,71799],{},[895,71796,71797],{},[898,71798,2638],{},[902,71800,2638],{"encoding":904},[883,71802,71804],{"className":71803},[886],[888,71805,71806],{"xmlns":890},[892,71807,71808,71814],{},[895,71809,71810,71812],{},[898,71811,2623],{},[898,71813,3840],{},[902,71815,3940],{"encoding":904},[883,71817,71819],{"className":71818},[886],[888,71820,71821],{"xmlns":890},[892,71822,71823,71829],{},[895,71824,71825,71827],{},[898,71826,2623],{},[898,71828,3840],{},[902,71830,3940],{"encoding":904},". (d) Graficky interpretujte.",[724,71833,71834,47529,71837,1343,71863,1343,71882,70836,71902,71756,71915,69588,71930,71945,71946,71968,71969,71019],{},[38,71835,71836],{},"3.20",[883,71838,71840],{"className":71839},[886],[888,71841,71842],{"xmlns":890},[892,71843,71844,71860],{},[895,71845,71846,71848,71850,71852,71854],{},[898,71847,3783],{},[1846,71849,1848],{},[1979,71851,19987],{},[1846,71853,2075],{},[1974,71855,71856,71858],{},[898,71857,2638],{},[1979,71859,1981],{},[902,71861,71862],{"encoding":904},"P = 400 - Q^2",[883,71864,71866],{"className":71865},[886],[888,71867,71868],{"xmlns":890},[892,71869,71870,71880],{},[895,71871,71872,71874,71876,71878],{},[898,71873,10282],{},[898,71875,2626],{},[1846,71877,1848],{},[1979,71879,2938],{},[902,71881,11479],{"encoding":904},[883,71883,71885],{"className":71884},[886],[888,71886,71887],{"xmlns":890},[892,71888,71889,71899],{},[895,71890,71891,71893,71895,71897],{},[898,71892,2667],{},[898,71894,2626],{},[1846,71896,1848],{},[1979,71898,8881],{},[902,71900,71901],{"encoding":904},"MC = 20",[883,71903,71905],{"className":71904},[886],[888,71906,71907],{"xmlns":890},[892,71908,71909,71913],{},[895,71910,71911],{},[898,71912,2638],{},[902,71914,2638],{"encoding":904},[883,71916,71918],{"className":71917},[886],[888,71919,71920],{"xmlns":890},[892,71921,71922,71928],{},[895,71923,71924,71926],{},[898,71925,3783],{},[898,71927,3840],{},[902,71929,63324],{"encoding":904},[883,71931,71933],{"className":71932},[886],[888,71934,71935],{"xmlns":890},[892,71936,71937,71943],{},[895,71938,71939,71941],{},[898,71940,3783],{},[898,71942,3840],{},[902,71944,63324],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,71947,71949],{"className":71948},[886],[888,71950,71951],{"xmlns":890},[892,71952,71953,71965],{},[895,71954,71955,71957,71959,71961,71963],{},[1846,71956,1855],{"stretchy":1854},[1979,71958,2177],{},[1846,71960,2136],{"separator":2135},[1979,71962,2128],{},[1846,71964,1861],{"stretchy":1854},[902,71966,71967],{"encoding":904},"(0, 1)",", druhý do ",[883,71970,71972],{"className":71971},[886],[888,71973,71974],{"xmlns":890},[892,71975,71976,71989],{},[895,71977,71978,71980,71983,71985,71987],{},[1846,71979,1855],{"stretchy":1854},[1979,71981,71982],{},"19",[1846,71984,2136],{"separator":2135},[1979,71986,8881],{},[1846,71988,1861],{"stretchy":1854},[902,71990,71991],{"encoding":904},"(19, 20)",[724,71993,71994,71997,71998,2474,72026,72043,72044,1734],{},[38,71995,71996],{},"3.21"," Dokažte, že má-li zisk ",[883,71999,72001],{"className":72000},[886],[888,72002,72003],{"xmlns":890},[892,72004,72005,72023],{},[895,72006,72007,72009,72011,72013,72015,72017,72019,72021],{},[898,72008,3783],{},[898,72010,3840],{},[1846,72012,1848],{},[898,72014,3783],{},[898,72016,3840],{},[1846,72018,1855],{"stretchy":1854},[898,72020,2638],{},[1846,72022,1861],{"stretchy":1854},[902,72024,72025],{"encoding":904},"PR = PR(Q)",[883,72027,72029],{"className":72028},[886],[888,72030,72031],{"xmlns":890},[892,72032,72033,72041],{},[895,72034,72035],{},[2122,72036,72037,72039],{},[898,72038,2638],{},[1979,72040,2177],{},[902,72042,38153],{"encoding":904}," maximum, pak platí ",[883,72045,72047],{"className":72046},[886],[888,72048,72049],{"xmlns":890},[892,72050,72051,72083],{},[895,72052,72053,72055,72057,72059,72065,72067,72069,72071,72073,72075,72081],{},[898,72054,2667],{},[898,72056,3840],{},[1846,72058,1855],{"stretchy":1854},[2122,72060,72061,72063],{},[898,72062,2638],{},[1979,72064,2177],{},[1846,72066,1861],{"stretchy":1854},[1846,72068,1848],{},[898,72070,2667],{},[898,72072,2626],{},[1846,72074,1855],{"stretchy":1854},[2122,72076,72077,72079],{},[898,72078,2638],{},[1979,72080,2177],{},[1846,72082,1861],{"stretchy":1854},[902,72084,65490],{"encoding":904},[724,72086,72087,72090,72091,1745,72106,55870,72121,71756,72134,72149,72150,1343,72177,72214,72215,1343,72242,1734],{},[38,72088,72089],{},"3.22"," Pro zadané ",[883,72092,72094],{"className":72093},[886],[888,72095,72096],{"xmlns":890},[892,72097,72098,72104],{},[895,72099,72100,72102],{},[898,72101,2667],{},[898,72103,3840],{},[902,72105,6480],{"encoding":904},[883,72107,72109],{"className":72108},[886],[888,72110,72111],{"xmlns":890},[892,72112,72113,72119],{},[895,72114,72115,72117],{},[898,72116,2667],{},[898,72118,2626],{},[902,72120,55137],{"encoding":904},[883,72122,72124],{"className":72123},[886],[888,72125,72126],{"xmlns":890},[892,72127,72128,72132],{},[895,72129,72130],{},[898,72131,2638],{},[902,72133,2638],{"encoding":904},[883,72135,72137],{"className":72136},[886],[888,72138,72139],{"xmlns":890},[892,72140,72141,72147],{},[895,72142,72143,72145],{},[898,72144,3783],{},[898,72146,3840],{},[902,72148,63324],{"encoding":904},". (a) ",[883,72151,72153],{"className":72152},[886],[888,72154,72155],{"xmlns":890},[892,72156,72157,72174],{},[895,72158,72159,72161,72163,72165,72168,72170,72172],{},[898,72160,2667],{},[898,72162,3840],{},[1846,72164,1848],{},[1979,72166,72167],{},"236",[1846,72169,2075],{},[1979,72171,41707],{},[898,72173,2638],{},[902,72175,72176],{"encoding":904},"MR = 236 - 16Q",[883,72178,72180],{"className":72179},[886],[888,72181,72182],{"xmlns":890},[892,72183,72184,72211],{},[895,72185,72186,72188,72190,72192,72194,72200,72202,72205,72207,72209],{},[898,72187,2667],{},[898,72189,2626],{},[1846,72191,1848],{},[1979,72193,2023],{},[1974,72195,72196,72198],{},[898,72197,2638],{},[1979,72199,1981],{},[1846,72201,2075],{},[1979,72203,72204],{},"32",[898,72206,2638],{},[1846,72208,1945],{},[1979,72210,5590],{},[902,72212,72213],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,72216,72218],{"className":72217},[886],[888,72219,72220],{"xmlns":890},[892,72221,72222,72239],{},[895,72223,72224,72226,72228,72230,72233,72235,72237],{},[898,72225,2667],{},[898,72227,3840],{},[1846,72229,1848],{},[1979,72231,72232],{},"280",[1846,72234,2075],{},[1979,72236,8881],{},[898,72238,2638],{},[902,72240,72241],{"encoding":904},"MR = 280 - 20Q",[883,72243,72245],{"className":72244},[886],[888,72246,72247],{"xmlns":890},[892,72248,72249,72276],{},[895,72250,72251,72253,72255,72257,72260,72266,72268,72270,72272,72274],{},[898,72252,2667],{},[898,72254,2626],{},[1846,72256,1848],{},[1979,72258,72259],{},"1,6",[1974,72261,72262,72264],{},[898,72263,2638],{},[1979,72265,1981],{},[1846,72267,2075],{},[1979,72269,36089],{},[898,72271,2638],{},[1846,72273,1945],{},[1979,72275,2974],{},[902,72277,72278],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,72280,72281,72090,72284,1745,72299,55870,72314,69572,72327,69588,72342,72149,72357,1343,72388,72214,72424,1343,72456,72500,72501,1343,72533,1734],{},[38,72282,72283],{},"3.23",[883,72285,72287],{"className":72286},[886],[888,72288,72289],{"xmlns":890},[892,72290,72291,72297],{},[895,72292,72293,72295],{},[898,72294,2623],{},[898,72296,3840],{},[902,72298,3940],{"encoding":904},[883,72300,72302],{"className":72301},[886],[888,72303,72304],{"xmlns":890},[892,72305,72306,72312],{},[895,72307,72308,72310],{},[898,72309,2623],{},[898,72311,2626],{},[902,72313,3091],{"encoding":904},[883,72315,72317],{"className":72316},[886],[888,72318,72319],{"xmlns":890},[892,72320,72321,72325],{},[895,72322,72323],{},[898,72324,2638],{},[902,72326,2638],{"encoding":904},[883,72328,72330],{"className":72329},[886],[888,72331,72332],{"xmlns":890},[892,72333,72334,72340],{},[895,72335,72336,72338],{},[898,72337,3783],{},[898,72339,3840],{},[902,72341,63324],{"encoding":904},[883,72343,72345],{"className":72344},[886],[888,72346,72347],{"xmlns":890},[892,72348,72349,72355],{},[895,72350,72351,72353],{},[898,72352,3783],{},[898,72354,3840],{},[902,72356,63324],{"encoding":904},[883,72358,72360],{"className":72359},[886],[888,72361,72362],{"xmlns":890},[892,72363,72364,72385],{},[895,72365,72366,72368,72370,72372,72375,72377,72379],{},[898,72367,2623],{},[898,72369,3840],{},[1846,72371,1848],{},[1979,72373,72374],{},"125",[898,72376,2638],{},[1846,72378,2075],{},[1974,72380,72381,72383],{},[898,72382,2638],{},[1979,72384,1981],{},[902,72386,72387],{"encoding":904},"TR = 125Q - Q^2",[883,72389,72391],{"className":72390},[886],[888,72392,72393],{"xmlns":890},[892,72394,72395,72421],{},[895,72396,72397,72399,72401,72403,72405,72407,72409,72411,72413,72415],{},[898,72398,2623],{},[898,72400,2626],{},[1846,72402,1848],{},[1979,72404,14955],{},[1846,72406,1945],{},[1979,72408,2078],{},[898,72410,2638],{},[1846,72412,1945],{},[1979,72414,4855],{},[1974,72416,72417,72419],{},[898,72418,2638],{},[1979,72420,1981],{},[902,72422,72423],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,72425,72427],{"className":72426},[886],[888,72428,72429],{"xmlns":890},[892,72430,72431,72453],{},[895,72432,72433,72435,72437,72439,72441,72443,72445,72447],{},[898,72434,2623],{},[898,72436,3840],{},[1846,72438,1848],{},[1979,72440,8881],{},[898,72442,2638],{},[1846,72444,2075],{},[1979,72446,1981],{},[1974,72448,72449,72451],{},[898,72450,2638],{},[1979,72452,1981],{},[902,72454,72455],{"encoding":904},"TR = 20Q - 2Q^2",[883,72457,72459],{"className":72458},[886],[888,72460,72461],{"xmlns":890},[892,72462,72463,72497],{},[895,72464,72465,72467,72469,72471,72473,72475,72477,72479,72481,72483,72489,72491],{},[898,72466,2623],{},[898,72468,2626],{},[1846,72470,1848],{},[1979,72472,1981],{},[1846,72474,1945],{},[1979,72476,8881],{},[898,72478,2638],{},[1846,72480,2075],{},[1979,72482,5431],{},[1974,72484,72485,72487],{},[898,72486,2638],{},[1979,72488,1981],{},[1846,72490,1945],{},[1974,72492,72493,72495],{},[898,72494,2638],{},[1979,72496,2023],{},[902,72498,72499],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,72502,72504],{"className":72503},[886],[888,72505,72506],{"xmlns":890},[892,72507,72508,72530],{},[895,72509,72510,72512,72514,72516,72518,72520,72522,72524],{},[898,72511,2623],{},[898,72513,3840],{},[1846,72515,1848],{},[1979,72517,2201],{},[898,72519,2638],{},[1846,72521,2075],{},[1979,72523,23634],{},[1974,72525,72526,72528],{},[898,72527,2638],{},[1979,72529,1981],{},[902,72531,72532],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,72534,72536],{"className":72535},[886],[888,72537,72538],{"xmlns":890},[892,72539,72540,72588],{},[895,72541,72542,72544,72546,72548,72550,72552,72554,72556,72558,72574,72576],{},[898,72543,2623],{},[898,72545,2626],{},[1846,72547,1848],{},[1979,72549,2201],{},[1846,72551,1945],{},[1979,72553,1981],{},[898,72555,2638],{},[1846,72557,2075],{},[2175,72559,72560],{"scriptlevel":2177,"displaystyle":1854},[2179,72561,72562,72572],{},[895,72563,72564,72566],{},[1979,72565,2023],{},[1974,72567,72568,72570],{},[898,72569,2638],{},[1979,72571,1981],{},[1979,72573,2712],{},[1846,72575,1945],{},[2175,72577,72578],{"scriptlevel":2177,"displaystyle":1854},[2179,72579,72580,72586],{},[1974,72581,72582,72584],{},[898,72583,2638],{},[1979,72585,2023],{},[1979,72587,8881],{},[902,72589,72590],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,72592,72593,72596,72597,72627,72628,72660,72661,21439,72691,72721],{},[38,72594,72595],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,72598,72600],{"className":72599},[886],[888,72601,72602],{"xmlns":890},[892,72603,72604,72624],{},[895,72605,72606,72612,72614,72616,72618],{},[2122,72607,72608,72610],{},[898,72609,3783],{},[1979,72611,2128],{},[1846,72613,1848],{},[1979,72615,14955],{},[1846,72617,2075],{},[2122,72619,72620,72622],{},[898,72621,2638],{},[1979,72623,2128],{},[902,72625,72626],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,72629,72631],{"className":72630},[886],[888,72632,72633],{"xmlns":890},[892,72634,72635,72657],{},[895,72636,72637,72643,72645,72647,72649,72651],{},[2122,72638,72639,72641],{},[898,72640,3783],{},[1979,72642,1981],{},[1846,72644,1848],{},[1979,72646,29926],{},[1846,72648,2075],{},[1979,72650,64404],{},[2122,72652,72653,72655],{},[898,72654,2638],{},[1979,72656,1981],{},[902,72658,72659],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,72662,72664],{"className":72663},[886],[888,72665,72666],{"xmlns":890},[892,72667,72668,72688],{},[895,72669,72670,72672,72674,72676,72678,72680,72682,72684,72686],{},[898,72671,2623],{},[898,72673,2626],{},[1846,72675,1848],{},[1979,72677,2968],{},[2138,72679,2835],{},[1979,72681,58927],{},[1846,72683,1945],{},[1979,72685,8881],{},[898,72687,2638],{},[902,72689,72690],{"encoding":904},"TC = 50\\,000 + 20Q",[883,72692,72694],{"className":72693},[886],[888,72695,72696],{"xmlns":890},[892,72697,72698,72718],{},[895,72699,72700,72702,72704,72710,72712],{},[898,72701,2638],{},[1846,72703,1848],{},[2122,72705,72706,72708],{},[898,72707,2638],{},[1979,72709,2128],{},[1846,72711,1945],{},[2122,72713,72714,72716],{},[898,72715,2638],{},[1979,72717,1981],{},[902,72719,72720],{"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.",[724,72723,72724,72727,72728,72758,72759,72660,72791,21439,72821,72850],{},[38,72725,72726],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,72729,72731],{"className":72730},[886],[888,72732,72733],{"xmlns":890},[892,72734,72735,72755],{},[895,72736,72737,72743,72745,72747,72749],{},[2122,72738,72739,72741],{},[898,72740,3783],{},[1979,72742,2128],{},[1846,72744,1848],{},[1979,72746,29926],{},[1846,72748,2075],{},[2122,72750,72751,72753],{},[898,72752,2638],{},[1979,72754,2128],{},[902,72756,72757],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,72760,72762],{"className":72761},[886],[888,72763,72764],{"xmlns":890},[892,72765,72766,72788],{},[895,72767,72768,72774,72776,72778,72780,72782],{},[2122,72769,72770,72772],{},[898,72771,3783],{},[1979,72773,1981],{},[1846,72775,1848],{},[1979,72777,8223],{},[1846,72779,2075],{},[1979,72781,4855],{},[2122,72783,72784,72786],{},[898,72785,2638],{},[1979,72787,1981],{},[902,72789,72790],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,72792,72794],{"className":72793},[886],[888,72795,72796],{"xmlns":890},[892,72797,72798,72818],{},[895,72799,72800,72802,72804,72806,72808,72810,72812,72814,72816],{},[898,72801,2623],{},[898,72803,2626],{},[1846,72805,1848],{},[1979,72807,2078],{},[2138,72809,2835],{},[1979,72811,58927],{},[1846,72813,1945],{},[1979,72815,2938],{},[898,72817,2638],{},[902,72819,72820],{"encoding":904},"TC = 5\\,000 + 100Q",[883,72822,72824],{"className":72823},[886],[888,72825,72826],{"xmlns":890},[892,72827,72828,72848],{},[895,72829,72830,72832,72834,72840,72842],{},[898,72831,2638],{},[1846,72833,1848],{},[2122,72835,72836,72838],{},[898,72837,2638],{},[1979,72839,2128],{},[1846,72841,1945],{},[2122,72843,72844,72846],{},[898,72845,2638],{},[1979,72847,1981],{},[902,72849,72720],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,72852,72854],{"id":72853},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,72856,72857,72860,72861,72908,72909,72926],{},[38,72858,72859],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,72862,72864],{"className":72863},[886],[888,72865,72866],{"xmlns":890},[892,72867,72868,72905],{},[895,72869,72870,72872,72874,72876,72878,72881,72887,72889,72892,72898,72900,72903],{},[898,72871,2623],{},[898,72873,40184],{},[898,72875,2626],{},[1846,72877,1848],{},[1979,72879,72880],{},"0,85",[1974,72882,72883,72885],{},[898,72884,2638],{},[1979,72886,2023],{},[1846,72888,2075],{},[1979,72890,72891],{},"11,9",[1974,72893,72894,72896],{},[898,72895,2638],{},[1979,72897,1981],{},[1846,72899,1945],{},[1979,72901,72902],{},"102",[898,72904,2638],{},[902,72906,72907],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,72910,72912],{"className":72911},[886],[888,72913,72914],{"xmlns":890},[892,72915,72916,72924],{},[895,72917,72918],{},[1974,72919,72920,72922],{},[898,72921,3783],{},[1846,72923,4200],{},[902,72925,4250],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,72928,72929,70687,72932,72968],{},[38,72930,72931],{},"3.27",[883,72933,72935],{"className":72934},[886],[888,72936,72937],{"xmlns":890},[892,72938,72939,72965],{},[895,72940,72941,72943,72945,72947,72949,72955,72957,72959,72961,72963],{},[898,72942,2667],{},[898,72944,2626],{},[1846,72946,1848],{},[1979,72948,2772],{},[1974,72950,72951,72953],{},[898,72952,2638],{},[1979,72954,1981],{},[1846,72956,2075],{},[1979,72958,64285],{},[898,72960,2638],{},[1846,72962,1945],{},[1979,72964,30588],{},[902,72966,72967],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,72970,72971,69938,72974,72968],{},[38,72972,72973],{},"3.28",[883,72975,72977],{"className":72976},[886],[888,72978,72979],{"xmlns":890},[892,72980,72981,73017],{},[895,72982,72983,72985,72987,72989,72991,72997,72999,73001,73007,73009,73011,73013,73015],{},[898,72984,2623],{},[898,72986,2626],{},[1846,72988,1848],{},[1979,72990,4855],{},[1974,72992,72993,72995],{},[898,72994,2638],{},[1979,72996,2023],{},[1846,72998,2075],{},[1979,73000,24046],{},[1974,73002,73003,73005],{},[898,73004,2638],{},[1979,73006,1981],{},[1846,73008,1945],{},[1979,73010,2974],{},[898,73012,2638],{},[1846,73014,1945],{},[1979,73016,14955],{},[902,73018,73019],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,73021,15565],{"id":15564},[120,73023,73024,73052,73097,73169,73234,73274,73366,73472,73512,73626,73719,73783,73815,73875,73881,73945,73994,74048,74156,74211],{},[123,73025,73026,2053,73028,73051],{},[38,73027,55595],{},[883,73029,73031],{"className":73030},[886],[888,73032,73033],{"xmlns":890},[892,73034,73035,73049],{},[895,73036,73037,73039,73041,73043,73045,73047],{},[898,73038,2623],{},[898,73040,3840],{},[1846,73042,1848],{},[898,73044,3783],{},[1846,73046,3025],{},[898,73048,2638],{},[902,73050,66557],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,73053,73054,2053,73056,73096],{},[38,73055,56181],{},[883,73057,73059],{"className":73058},[886],[888,73060,73061],{"xmlns":890},[892,73062,73063,73093],{},[895,73064,73065,73067,73069,73071,73083,73085,73087,73089,73091],{},[898,73066,4101],{},[898,73068,3840],{},[1846,73070,1848],{},[2175,73072,73073],{"scriptlevel":2177,"displaystyle":1854},[2179,73074,73075,73081],{},[895,73076,73077,73079],{},[898,73078,2623],{},[898,73080,3840],{},[898,73082,2638],{},[1846,73084,1848],{},[898,73086,4029],{},[1846,73088,1855],{"stretchy":1854},[898,73090,2638],{},[1846,73092,1861],{"stretchy":1854},[902,73094,73095],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,73098,73099,2053,73101,73137,73138,73153,73154,1734],{},[38,73100,56329],{},[883,73102,73104],{"className":73103},[886],[888,73105,73106],{"xmlns":890},[892,73107,73108,73134],{},[895,73109,73110,73112,73114,73116],{},[898,73111,2667],{},[898,73113,3840],{},[1846,73115,1848],{},[2175,73117,73118],{"scriptlevel":2177,"displaystyle":1854},[2179,73119,73120,73128],{},[895,73121,73122,73124,73126],{},[898,73123,2044],{"mathvariant":2226},[898,73125,2623],{},[898,73127,3840],{},[895,73129,73130,73132],{},[898,73131,2044],{"mathvariant":2226},[898,73133,2638],{},[902,73135,73136],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,73139,73141],{"className":73140},[886],[888,73142,73143],{"xmlns":890},[892,73144,73145,73151],{},[895,73146,73147,73149],{},[898,73148,2623],{},[898,73150,3840],{},[902,73152,3940],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,73155,73157],{"className":73156},[886],[888,73158,73159],{"xmlns":890},[892,73160,73161,73167],{},[895,73162,73163,73165],{},[898,73164,4101],{},[898,73166,3840],{},[902,73168,55290],{"encoding":904},[123,73170,73171,2053,73174,1343,73204,1734],{},[38,73172,73173],{},"Diferenciál příjmu\u002Fnákladů",[883,73175,73177],{"className":73176},[886],[888,73178,73179],{"xmlns":890},[892,73180,73181,73201],{},[895,73182,73183,73185,73187,73189,73191,73193,73195,73197,73199],{},[898,73184,2738],{"mathvariant":2226},[898,73186,2623],{},[898,73188,3840],{},[1846,73190,1650],{},[898,73192,2667],{},[898,73194,3840],{},[2138,73196,2835],{},[898,73198,2044],{"mathvariant":2226},[898,73200,2638],{},[902,73202,73203],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,73205,73207],{"className":73206},[886],[888,73208,73209],{"xmlns":890},[892,73210,73211,73231],{},[895,73212,73213,73215,73217,73219,73221,73223,73225,73227,73229],{},[898,73214,2738],{"mathvariant":2226},[898,73216,2623],{},[898,73218,2626],{},[1846,73220,1650],{},[898,73222,2667],{},[898,73224,2626],{},[2138,73226,2835],{},[898,73228,2044],{"mathvariant":2226},[898,73230,2638],{},[902,73232,73233],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,73235,73236,2053,73238,1734],{},[38,73237,58451],{},[883,73239,73241],{"className":73240},[886],[888,73242,73243],{"xmlns":890},[892,73244,73245,73271],{},[895,73246,73247,73249,73251,73253,73255,73257,73259,73261,73263,73265,73267,73269],{},[898,73248,2623],{},[898,73250,2626],{},[1846,73252,1848],{},[898,73254,10282],{},[898,73256,2626],{},[1846,73258,1945],{},[898,73260,2623],{},[898,73262,40184],{},[898,73264,2626],{},[1846,73266,1855],{"stretchy":1854},[898,73268,2638],{},[1846,73270,1861],{"stretchy":1854},[902,73272,73273],{"encoding":904},"TC = FC + TVC(Q)",[123,73275,73276,2053,73279,1343,73294,2053,73296,1343,73319,2053,73322,1734],{},[38,73277,73278],{},"Fixní náklady",[883,73280,73282],{"className":73281},[886],[888,73283,73284],{"xmlns":890},[892,73285,73286,73292],{},[895,73287,73288,73290],{},[898,73289,10282],{},[898,73291,2626],{},[902,73293,55336],{"encoding":904},[38,73295,58604],{},[883,73297,73299],{"className":73298},[886],[888,73300,73301],{"xmlns":890},[892,73302,73303,73317],{},[895,73304,73305,73307,73309,73311,73313,73315],{},[898,73306,2623],{},[898,73308,40184],{},[898,73310,2626],{},[1846,73312,1855],{"stretchy":1854},[898,73314,2638],{},[1846,73316,1861],{"stretchy":1854},[902,73318,58601],{"encoding":904},[38,73320,73321],{},"variabilní náklady na jednotku",[883,73323,73325],{"className":73324},[886],[888,73326,73327],{"xmlns":890},[892,73328,73329,73363],{},[895,73330,73331,73333,73335,73337,73339,73341,73343],{},[898,73332,40184],{},[898,73334,2626],{},[1846,73336,1855],{"stretchy":1854},[898,73338,2638],{},[1846,73340,1861],{"stretchy":1854},[1846,73342,1848],{},[2175,73344,73345],{"scriptlevel":2177,"displaystyle":1854},[2179,73346,73347,73361],{},[895,73348,73349,73351,73353,73355,73357,73359],{},[898,73350,2623],{},[898,73352,40184],{},[898,73354,2626],{},[1846,73356,1855],{"stretchy":1854},[898,73358,2638],{},[1846,73360,1861],{"stretchy":1854},[898,73362,2638],{},[902,73364,73365],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,73367,73368,2053,73370,1343,73400,2053,73403,1343,73435,2053,73438,1734],{},[38,73369,58612],{},[883,73371,73373],{"className":73372},[886],[888,73374,73375],{"xmlns":890},[892,73376,73377,73397],{},[895,73378,73379,73381,73383,73385],{},[898,73380,4101],{},[898,73382,2626],{},[1846,73384,1848],{},[2175,73386,73387],{"scriptlevel":2177,"displaystyle":1854},[2179,73388,73389,73395],{},[895,73390,73391,73393],{},[898,73392,2623],{},[898,73394,2626],{},[898,73396,2638],{},[902,73398,73399],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,73401,73402],{},"průměrné fixní",[883,73404,73406],{"className":73405},[886],[888,73407,73408],{"xmlns":890},[892,73409,73410,73432],{},[895,73411,73412,73414,73416,73418,73420],{},[898,73413,4101],{},[898,73415,10282],{},[898,73417,2626],{},[1846,73419,1848],{},[2175,73421,73422],{"scriptlevel":2177,"displaystyle":1854},[2179,73423,73424,73430],{},[895,73425,73426,73428],{},[898,73427,10282],{},[898,73429,2626],{},[898,73431,2638],{},[902,73433,73434],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,73436,73437],{},"průměrné variabilní",[883,73439,73441],{"className":73440},[886],[888,73442,73443],{"xmlns":890},[892,73444,73445,73469],{},[895,73446,73447,73449,73451,73453,73455],{},[898,73448,4101],{},[898,73450,40184],{},[898,73452,2626],{},[1846,73454,1848],{},[2175,73456,73457],{"scriptlevel":2177,"displaystyle":1854},[2179,73458,73459,73467],{},[895,73460,73461,73463,73465],{},[898,73462,2623],{},[898,73464,40184],{},[898,73466,2626],{},[898,73468,2638],{},[902,73470,73471],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,73473,73474,2053,73476,1734],{},[38,73475,59799],{},[883,73477,73479],{"className":73478},[886],[888,73480,73481],{"xmlns":890},[892,73482,73483,73509],{},[895,73484,73485,73487,73489,73491],{},[898,73486,2667],{},[898,73488,2626],{},[1846,73490,1848],{},[2175,73492,73493],{"scriptlevel":2177,"displaystyle":1854},[2179,73494,73495,73503],{},[895,73496,73497,73499,73501],{},[898,73498,2044],{"mathvariant":2226},[898,73500,2623],{},[898,73502,2626],{},[895,73504,73505,73507],{},[898,73506,2044],{"mathvariant":2226},[898,73508,2638],{},[902,73510,73511],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,73513,73514,2053,73516,73564,73565,73578,73579,1343,73594,1343,73611,1734],{},[38,73515,60697],{},[883,73517,73519],{"className":73518},[886],[888,73520,73521],{"xmlns":890},[892,73522,73523,73561],{},[895,73524,73525,73527,73529,73531,73533,73535,73537,73539,73541,73543,73545,73551,73553,73555],{},[898,73526,2623],{},[898,73528,2626],{},[1846,73530,1848],{},[898,73532,10282],{},[898,73534,2626],{},[1846,73536,1945],{},[898,73538,207],{},[898,73540,2638],{},[1846,73542,1945],{},[898,73544,1948],{},[1974,73546,73547,73549],{},[898,73548,2638],{},[1979,73550,1981],{},[1846,73552,1945],{},[898,73554,1992],{},[1974,73556,73557,73559],{},[898,73558,2638],{},[1979,73560,2023],{},[902,73562,73563],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,73566,73568],{"className":73567},[886],[888,73569,73570],{"xmlns":890},[892,73571,73572,73576],{},[895,73573,73574],{},[898,73575,900],{},[902,73577,900],{"encoding":904},"-průběhem ",[883,73580,73582],{"className":73581},[886],[888,73583,73584],{"xmlns":890},[892,73585,73586,73592],{},[895,73587,73588,73590],{},[898,73589,4101],{},[898,73591,2626],{},[902,73593,55405],{"encoding":904},[883,73595,73597],{"className":73596},[886],[888,73598,73599],{"xmlns":890},[892,73600,73601,73609],{},[895,73602,73603,73605,73607],{},[898,73604,4101],{},[898,73606,40184],{},[898,73608,2626],{},[902,73610,55156],{"encoding":904},[883,73612,73614],{"className":73613},[886],[888,73615,73616],{"xmlns":890},[892,73617,73618,73624],{},[895,73619,73620,73622],{},[898,73621,2667],{},[898,73623,2626],{},[902,73625,55137],{"encoding":904},[123,73627,73628,73630,73631,10240,73646,73687,73688,61342,73703,73718],{},[38,73629,61779],{},": v bodě minima ",[883,73632,73634],{"className":73633},[886],[888,73635,73636],{"xmlns":890},[892,73637,73638,73644],{},[895,73639,73640,73642],{},[898,73641,4101],{},[898,73643,2626],{},[902,73645,55405],{"encoding":904},[883,73647,73649],{"className":73648},[886],[888,73650,73651],{"xmlns":890},[892,73652,73653,73685],{},[895,73654,73655,73657,73659,73661,73667,73669,73671,73673,73675,73677,73683],{},[898,73656,4101],{},[898,73658,2626],{},[1846,73660,1855],{"stretchy":1854},[2122,73662,73663,73665],{},[898,73664,2638],{},[1979,73666,2177],{},[1846,73668,1861],{"stretchy":1854},[1846,73670,1848],{},[898,73672,2667],{},[898,73674,2626],{},[1846,73676,1855],{"stretchy":1854},[2122,73678,73679,73681],{},[898,73680,2638],{},[1979,73682,2177],{},[1846,73684,1861],{"stretchy":1854},[902,73686,62414],{"encoding":904},"; geometricky ",[883,73689,73691],{"className":73690},[886],[888,73692,73693],{"xmlns":890},[892,73694,73695,73701],{},[895,73696,73697,73699],{},[898,73698,2667],{},[898,73700,2626],{},[902,73702,55137],{"encoding":904},[883,73704,73706],{"className":73705},[886],[888,73707,73708],{"xmlns":890},[892,73709,73710,73716],{},[895,73711,73712,73714],{},[898,73713,4101],{},[898,73715,2626],{},[902,73717,55405],{"encoding":904}," v jejím minimu.",[123,73720,73721,73630,73723,10240,73740,1734],{},[38,73722,63129],{},[883,73724,73726],{"className":73725},[886],[888,73727,73728],{"xmlns":890},[892,73729,73730,73738],{},[895,73731,73732,73734,73736],{},[898,73733,4101],{},[898,73735,40184],{},[898,73737,2626],{},[902,73739,55156],{"encoding":904},[883,73741,73743],{"className":73742},[886],[888,73744,73745],{"xmlns":890},[892,73746,73747,73781],{},[895,73748,73749,73751,73753,73755,73757,73763,73765,73767,73769,73771,73773,73779],{},[898,73750,4101],{},[898,73752,40184],{},[898,73754,2626],{},[1846,73756,1855],{"stretchy":1854},[2122,73758,73759,73761],{},[898,73760,2638],{},[1979,73762,2177],{},[1846,73764,1861],{"stretchy":1854},[1846,73766,1848],{},[898,73768,2667],{},[898,73770,2626],{},[1846,73772,1855],{"stretchy":1854},[2122,73774,73775,73777],{},[898,73776,2638],{},[1979,73778,2177],{},[1846,73780,1861],{"stretchy":1854},[902,73782,68864],{"encoding":904},[123,73784,73785,2053,73787,73814],{},[38,73786,63308],{},[883,73788,73790],{"className":73789},[886],[888,73791,73792],{"xmlns":890},[892,73793,73794,73812],{},[895,73795,73796,73798,73800,73802,73804,73806,73808,73810],{},[898,73797,3783],{},[898,73799,3840],{},[1846,73801,1848],{},[898,73803,2623],{},[898,73805,3840],{},[1846,73807,2075],{},[898,73809,2623],{},[898,73811,2626],{},[902,73813,55045],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,73816,73817,9871,73819,73821,73822,73848,73849,73874],{},[38,73818,64170],{},[614,73820,63433],{},") — hodnoty ",[883,73823,73825],{"className":73824},[886],[888,73826,73827],{"xmlns":890},[892,73828,73829,73845],{},[895,73830,73831,73837,73839],{},[2122,73832,73833,73835],{},[898,73834,2638],{},[898,73836,4101],{},[1846,73838,2136],{"separator":2135},[2122,73840,73841,73843],{},[898,73842,2638],{},[898,73844,23098],{},[902,73846,73847],{"encoding":904},"Q_A, Q_B"," splňující ",[883,73850,73852],{"className":73851},[886],[888,73853,73854],{"xmlns":890},[892,73855,73856,73872],{},[895,73857,73858,73860,73862,73864,73866,73868,73870],{},[898,73859,3783],{},[898,73861,3840],{},[1846,73863,1855],{"stretchy":1854},[898,73865,2638],{},[1846,73867,1861],{"stretchy":1854},[1846,73869,1848],{},[1979,73871,2177],{},[902,73873,63710],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,73876,73877,73880],{},[38,73878,73879],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,73882,73883,73885,73886,10240,73903,73944],{},[38,73884,65224],{}," — v bodě maxima zisku ",[883,73887,73889],{"className":73888},[886],[888,73890,73891],{"xmlns":890},[892,73892,73893,73901],{},[895,73894,73895],{},[2122,73896,73897,73899],{},[898,73898,2638],{},[1979,73900,2177],{},[902,73902,38153],{"encoding":904},[883,73904,73906],{"className":73905},[886],[888,73907,73908],{"xmlns":890},[892,73909,73910,73942],{},[895,73911,73912,73914,73916,73918,73924,73926,73928,73930,73932,73934,73940],{},[898,73913,2667],{},[898,73915,3840],{},[1846,73917,1855],{"stretchy":1854},[2122,73919,73920,73922],{},[898,73921,2638],{},[1979,73923,2177],{},[1846,73925,1861],{"stretchy":1854},[1846,73927,1848],{},[898,73929,2667],{},[898,73931,2626],{},[1846,73933,1855],{"stretchy":1854},[2122,73935,73936,73938],{},[898,73937,2638],{},[1979,73939,2177],{},[1846,73941,1861],{"stretchy":1854},[902,73943,65490],{"encoding":904}," (3.13).",[123,73946,73947,20146,73949,10240,73968,73993],{},[38,73948,66517],{},[883,73950,73952],{"className":73951},[886],[888,73953,73954],{"xmlns":890},[892,73955,73956,73965],{},[895,73957,73958,73960,73962],{},[898,73959,3783],{},[1846,73961,1848],{},[2138,73963,73964],{},"konst",[902,73966,73967],{"encoding":904},"P = \\text{konst}",[883,73969,73971],{"className":73970},[886],[888,73972,73973],{"xmlns":890},[892,73974,73975,73991],{},[895,73976,73977,73979,73981,73983,73985,73987,73989],{},[898,73978,3783],{},[1846,73980,1848],{},[898,73982,2667],{},[898,73984,2626],{},[1846,73986,1855],{"stretchy":1854},[898,73988,2638],{},[1846,73990,1861],{"stretchy":1854},[902,73992,67211],{"encoding":904}," (3.14).",[123,73995,73996,73999,74000,74029,74030,74047],{},[38,73997,73998],{},"Shutdown point"," — bod ",[883,74001,74003],{"className":74002},[886],[888,74004,74005],{"xmlns":890},[892,74006,74007,74027],{},[895,74008,74009,74011,74017,74019,74025],{},[1846,74010,1855],{"stretchy":1854},[1974,74012,74013,74015],{},[898,74014,2638],{},[1846,74016,4200],{},[1846,74018,2136],{"separator":2135},[1974,74020,74021,74023],{},[898,74022,3783],{},[1846,74024,4200],{},[1846,74026,1861],{"stretchy":1854},[902,74028,67500],{"encoding":904}," v minimu ",[883,74031,74033],{"className":74032},[886],[888,74034,74035],{"xmlns":890},[892,74036,74037,74045],{},[895,74038,74039,74041,74043],{},[898,74040,4101],{},[898,74042,40184],{},[898,74044,2626],{},[902,74046,55156],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,74049,74050,2053,74053,6319,74088,67770,74109,74122,74123,74138,74139,1734],{},[38,74051,74052],{},"Funkce nabídky firmy",[883,74054,74056],{"className":74055},[886],[888,74057,74058],{"xmlns":890},[892,74059,74060,74086],{},[895,74061,74062,74064,74066,74068,74070,74072,74074,74076,74078,74080,74082,74084],{},[898,74063,3783],{},[1846,74065,1848],{},[898,74067,8519],{},[1846,74069,1855],{"stretchy":1854},[898,74071,2638],{},[1846,74073,1861],{"stretchy":1854},[1846,74075,1848],{},[898,74077,2667],{},[898,74079,2626],{},[1846,74081,1855],{"stretchy":1854},[898,74083,2638],{},[1846,74085,1861],{"stretchy":1854},[902,74087,68967],{"encoding":904},[883,74089,74091],{"className":74090},[886],[888,74092,74093],{"xmlns":890},[892,74094,74095,74107],{},[895,74096,74097,74099,74101],{},[898,74098,2638],{},[1846,74100,4331],{},[1974,74102,74103,74105],{},[898,74104,2638],{},[1846,74106,4200],{},[902,74108,67769],{"encoding":904},[883,74110,74112],{"className":74111},[886],[888,74113,74114],{"xmlns":890},[892,74115,74116,74120],{},[895,74117,74118],{},[1979,74119,2177],{},[902,74121,2177],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,74124,74126],{"className":74125},[886],[888,74127,74128],{"xmlns":890},[892,74129,74130,74136],{},[895,74131,74132,74134],{},[898,74133,2667],{},[898,74135,2626],{},[902,74137,55137],{"encoding":904}," nad minimem ",[883,74140,74142],{"className":74141},[886],[888,74143,74144],{"xmlns":890},[892,74145,74146,74154],{},[895,74147,74148,74150,74152],{},[898,74149,4101],{},[898,74151,40184],{},[898,74153,2626],{},[902,74155,55156],{"encoding":904},[123,74157,74158,6861,74160,74181,74182,1734],{},[38,74159,49924],{},[883,74161,74163],{"className":74162},[886],[888,74164,74165],{"xmlns":890},[892,74166,74167,74179],{},[895,74168,74169,74171,74173],{},[898,74170,3783],{},[1846,74172,1848],{},[1974,74174,74175,74177],{},[898,74176,3783],{},[1846,74178,4200],{},[902,74180,4203],{"encoding":904}," konstantní ⇒ ",[883,74183,74185],{"className":74184},[886],[888,74186,74187],{"xmlns":890},[892,74188,74189,74209],{},[895,74190,74191,74193,74195,74197,74199,74201,74203],{},[898,74192,4101],{},[898,74194,3840],{},[1846,74196,1848],{},[898,74198,2667],{},[898,74200,3840],{},[1846,74202,1848],{},[1974,74204,74205,74207],{},[898,74206,3783],{},[1846,74208,4200],{},[902,74210,58443],{"encoding":904},[123,74212,74213,74216],{},[38,74214,74215],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,74218,3640],{"id":3639},[120,74220,74221,74240,74252],{},[123,74222,74223,2053,74225,1343,74228,1343,74231,1343,74234,1343,74237],{},[38,74224,50568],{},[207,74226,1701],{"className":74227,"dataFsResolvedFilePath":800,"href":801},[210],[207,74229,1721],{"className":74230,"dataFsResolvedFilePath":848,"href":849},[210],[207,74232,2207],{"className":74233,"dataFsResolvedFilePath":764,"href":765},[210],[207,74235,775],{"className":74236,"dataFsResolvedFilePath":773,"href":774},[210],[207,74238,859],{"className":74239,"dataFsResolvedFilePath":857,"href":858},[210],[123,74241,74242,2053,74244,1343,74248],{},[38,74243,36548],{},[207,74245,74247],{"className":74246,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,74249,74251],{"className":74250,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,74253,74254,2053,74256],{},[38,74255,16049],{},[207,74257,16053],{"className":74258,"dataFsResolvedFilePath":1761,"href":1762},[210],{"title":641,"searchDepth":642,"depth":642,"links":74260},[74261,74262,74269,74275,74279,74280,74284,74285,74286,74287,74293,74294],{"id":50799,"depth":642,"text":1241},{"id":55583,"depth":642,"text":55584,"children":74263},[74264,74265,74266,74267,74268],{"id":55594,"depth":649,"text":55595},{"id":56180,"depth":649,"text":56181},{"id":56328,"depth":649,"text":56329},{"id":57070,"depth":649,"text":57071},{"id":57725,"depth":649,"text":57726},{"id":58446,"depth":642,"text":58447,"children":74270},[74271,74272,74273,74274],{"id":58450,"depth":649,"text":58451},{"id":58611,"depth":649,"text":58612},{"id":59798,"depth":649,"text":59799},{"id":60696,"depth":649,"text":60697},{"id":61778,"depth":642,"text":61779,"children":74276},[74277,74278],{"id":16256,"depth":649,"text":16257},{"id":63128,"depth":649,"text":63129},{"id":63302,"depth":642,"text":63303},{"id":65223,"depth":642,"text":65224,"children":74281},[74282,74283],{"id":65237,"depth":649,"text":16257},{"id":66516,"depth":649,"text":66517},{"id":67148,"depth":642,"text":67149},{"id":68614,"depth":642,"text":68615},{"id":49726,"depth":642,"text":49727},{"id":69075,"depth":642,"text":69076,"children":74288},[74289,74290,74291,74292],{"id":69079,"depth":649,"text":69080},{"id":69931,"depth":649,"text":69932},{"id":71477,"depth":649,"text":71478},{"id":72853,"depth":649,"text":72854},{"id":15564,"depth":642,"text":15565},{"id":3639,"depth":642,"text":3640},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":54965,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,74301,74302,55017,74303,74304,74305],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":74308,"title":74309,"body":74310,"course":1128,"courses":659,"created":9402,"description":641,"extension":661,"meta":86407,"navigation":664,"path":86408,"seo":86409,"sources":86410,"stem":86411,"tags":86412,"type":3703,"updated":677,"__hash__":86418},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":74311,"toc":86364},[74312,74315,74671,74675,74678,74746,74798,74808,74812,74846,74887,74911,74934,74963,75030,75137,75180,75237,75312,75357,75361,75369,75377,75380,75645,75696,75776,75846,75869,75897,75942,75964,75968,75975,76024,76050,76201,76204,76241,76404,76512,76516,76553,76628,76697,76816,76938,77019,77025,77066,77139,77232,77236,77272,77360,77474,77579,77664,77804,77808,77856,77901,77907,77911,77914,77965,78015,78022,78088,78221,78266,78270,78291,78670,78765,78782,78836,78840,78922,79006,79176,79179,79222,79289,79363,79367,79372,79441,79449,79458,79536,79602,79607,79702,79745,79750,79798,79803,79851,79969,80052,80090,80193,80252,80393,80397,80440,80513,80537,80591,80598,80600,80645,80690,80701,80706,80742,80804,80827,80836,80937,81004,81077,81084,81175,81237,81273,81330,81389,81574,81670,81674,81678,81757,81762,81886,81972,81978,82088,82125,82216,82314,82317,82321,82387,82424,82546,82598,82602,82630,82682,82756,82861,82885,82944,82948,82966,83109,83257,83259,83294,83298,83300,83390,83520,83646,83738,83813,83817,83933,84037,84227,84263,84357,84363,84476,84779,84785,84903,85002,85078,85080,86242,86244],[12,74313,74309],{"id":74314},"produkce-produkční-funkce-cobb-douglas-mrts",[1639,74316,74317],{},[724,74318,74319,3720,74321,74323,74324,36741,74337,74350,74351,16221,74364,9871,74366,74390,74391,2053,74393,1745,74427,2053,74430,74458,74459,10240,74479,74509,74510,9871,74513,74541,74542,74545,74546,74576,74577,74607,74608,2053,74611,74651,74652,74670],{},[883,74320,3719],{},[38,74322,859],{}," popisuje vztah mezi vstupy (práce ",[883,74325,74327],{"className":74326},[886],[888,74328,74329],{"xmlns":890},[892,74330,74331,74335],{},[895,74332,74333],{},[898,74334,9641],{},[902,74336,9641],{"encoding":904},[883,74338,74340],{"className":74339},[886],[888,74341,74342],{"xmlns":890},[892,74343,74344,74348],{},[895,74345,74346],{},[898,74347,9646],{},[902,74349,9646],{"encoding":904},") a výstupem ",[883,74352,74354],{"className":74353},[886],[888,74355,74356],{"xmlns":890},[892,74357,74358,74362],{},[895,74359,74360],{},[898,74361,2638],{},[902,74363,2638],{"encoding":904},[38,74365,36809],{},[883,74367,74369],{"className":74368},[886],[888,74370,74371],{"xmlns":890},[892,74372,74373,74387],{},[895,74374,74375,74377,74379,74381,74383,74385],{},[898,74376,2638],{},[1846,74378,1848],{},[898,74380,2638],{},[1846,74382,1855],{"stretchy":1854},[898,74384,9641],{},[1846,74386,1861],{"stretchy":1854},[902,74388,74389],{"encoding":904},"Q = Q(L)",") studujeme ",[614,74392,9870],{},[883,74394,74396],{"className":74395},[886],[888,74397,74398],{"xmlns":890},[892,74399,74400,74424],{},[895,74401,74402,74404,74410,74412,74418,74420,74422],{},[898,74403,2667],{},[2122,74405,74406,74408],{},[898,74407,3783],{},[898,74409,9641],{},[1846,74411,1848],{},[1974,74413,74414,74416],{},[898,74415,2638],{},[1846,74417,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,74419,1855],{"stretchy":1854},[898,74421,9641],{},[1846,74423,1861],{"stretchy":1854},[902,74425,74426],{"encoding":904},"MP_L = Q'(L)",[614,74428,74429],{},"průměrný produkt",[883,74431,74433],{"className":74432},[886],[888,74434,74435],{"xmlns":890},[892,74436,74437,74455],{},[895,74438,74439,74441,74447,74449,74451,74453],{},[898,74440,4101],{},[2122,74442,74443,74445],{},[898,74444,3783],{},[898,74446,9641],{},[1846,74448,1848],{},[898,74450,2638],{},[898,74452,4520],{"mathvariant":2226},[898,74454,9641],{},[902,74456,74457],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,74460,74462],{"className":74461},[886],[888,74463,74464],{"xmlns":890},[892,74465,74466,74476],{},[895,74467,74468,74470],{},[898,74469,4101],{},[2122,74471,74472,74474],{},[898,74473,3783],{},[898,74475,9641],{},[902,74477,74478],{"encoding":904},"AP_L",[883,74480,74482],{"className":74481},[886],[888,74483,74484],{"xmlns":890},[892,74485,74486,74506],{},[895,74487,74488,74490,74496,74498,74500],{},[898,74489,2667],{},[2122,74491,74492,74494],{},[898,74493,3783],{},[898,74495,9641],{},[1846,74497,1848],{},[898,74499,4101],{},[2122,74501,74502,74504],{},[898,74503,3783],{},[898,74505,9641],{},[902,74507,74508],{"encoding":904},"MP_L = AP_L",". Ve ",[38,74511,74512],{},"dvoufaktorovém modelu",[883,74514,74516],{"className":74515},[886],[888,74517,74518],{"xmlns":890},[892,74519,74520,74538],{},[895,74521,74522,74524,74526,74528,74530,74532,74534,74536],{},[898,74523,2638],{},[1846,74525,1848],{},[898,74527,2638],{},[1846,74529,1855],{"stretchy":1854},[898,74531,9641],{},[1846,74533,2136],{"separator":2135},[898,74535,9646],{},[1846,74537,1861],{"stretchy":1854},[902,74539,74540],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,74543,74544],{},"Cobb-Douglasovy"," funkce ",[883,74547,74549],{"className":74548},[886],[888,74550,74551],{"xmlns":890},[892,74552,74553,74573],{},[895,74554,74555,74557,74559,74561,74567],{},[898,74556,2638],{},[1846,74558,1848],{},[898,74560,4101],{},[1974,74562,74563,74565],{},[898,74564,9641],{},[898,74566,207],{},[1974,74568,74569,74571],{},[898,74570,9646],{},[898,74572,1948],{},[902,74574,74575],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,74578,74580],{"className":74579},[886],[888,74581,74582],{"xmlns":890},[892,74583,74584,74604],{},[895,74585,74586,74588,74594,74596,74598],{},[898,74587,2667],{},[2122,74589,74590,74592],{},[898,74591,3783],{},[898,74593,9641],{},[1846,74595,2136],{"separator":2135},[898,74597,2667],{},[2122,74599,74600,74602],{},[898,74601,3783],{},[898,74603,9646],{},[902,74605,74606],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,74609,74610],{},"mezní míru technické substituce",[883,74612,74614],{"className":74613},[886],[888,74615,74616],{"xmlns":890},[892,74617,74618,74648],{},[895,74619,74620,74622,74624,74626,74628,74630,74632,74638,74640,74642],{},[898,74621,2667],{},[898,74623,3840],{},[898,74625,2623],{},[898,74627,8519],{},[1846,74629,1848],{},[898,74631,2667],{},[2122,74633,74634,74636],{},[898,74635,3783],{},[898,74637,9641],{},[898,74639,4520],{"mathvariant":2226},[898,74641,2667],{},[2122,74643,74644,74646],{},[898,74645,3783],{},[898,74647,9646],{},[902,74649,74650],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,74653,74655],{"className":74654},[886],[888,74656,74657],{"xmlns":890},[892,74658,74659,74667],{},[895,74660,74661,74663,74665],{},[898,74662,207],{},[1846,74664,1945],{},[898,74666,1948],{},[902,74668,74669],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,74672,74674],{"id":74673},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,74676,74677],{},"Po prostudování kapitoly 5 student umí:",[120,74679,74680,74686,74696,74702,74708,74713,74719,74729,74734,74740],{},[123,74681,74682,74683,2136],{},"popsat ",[38,74684,74685],{},"jednofaktorový model produkce",[123,74687,74688,74689,1745,74692,74695],{},"vypočítat ",[38,74690,74691],{},"mezní",[38,74693,74694],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,74697,74698,74699,2136],{},"charakterizovat průběh ",[38,74700,74701],{},"křivky produkce",[123,74703,74704,74705,2136],{},"formulovat ",[38,74706,74707],{},"princip maximalizace průměrného produktu práce",[123,74709,74682,74710,2136],{},[38,74711,74712],{},"dvoufaktorový model produkce",[123,74714,74715,74716,2136],{},"uvést tvar ",[38,74717,74718],{},"Cobb–Douglasových produkčních funkcí",[123,74720,74721,74722,1343,74724,1343,74726,2136],{},"vyložit, co jsou ",[38,74723,24458],{},[38,74725,13502],{},[38,74727,74728],{},"klesající výnosy z rozsahu",[123,74730,74688,74731,74695],{},[38,74732,74733],{},"mezní produkty práce a kapitálu",[123,74735,74736,74737,2136],{},"najít ",[38,74738,74739],{},"izokvanty",[123,74741,74688,74742,74745],{},[38,74743,74744],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,74747,74748,74749,74752,74753,74756,74757,2053,74760,1343,74773,2053,74776,1745,74789,74792,74793,74795,74796,1734],{},"Každý proces produkce je určován ",[38,74750,74751],{},"faktory"," (též ",[38,74754,74755],{},"vstupy",") produkce. K hlavním patří ",[38,74758,74759],{},"práce",[883,74761,74763],{"className":74762},[886],[888,74764,74765],{"xmlns":890},[892,74766,74767,74771],{},[895,74768,74769],{},[898,74770,9641],{},[902,74772,9641],{"encoding":904},[38,74774,74775],{},"kapitál",[883,74777,74779],{"className":74778},[886],[888,74780,74781],{"xmlns":890},[892,74782,74783,74787],{},[895,74784,74785],{},[898,74786,9646],{},[902,74788,9646],{"encoding":904},[38,74790,74791],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,74794,36809],{}," (produkce závisí jen na práci); v opačném případě o ",[38,74797,74512],{},[724,74799,74800,74801,1343,74804,74807],{},"Související matematický aparát: ",[207,74802,2207],{"className":74803,"dataFsResolvedFilePath":764,"href":765},[210],[207,74805,784],{"className":74806,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,74809,74811],{"id":74810},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,74813,74814,74815,74828,74829,74842,74843],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,74816,74818],{"className":74817},[886],[888,74819,74820],{"xmlns":890},[892,74821,74822,74826],{},[895,74823,74824],{},[898,74825,2638],{},[902,74827,2638],{"encoding":904}," na práci ",[883,74830,74832],{"className":74831},[886],[888,74833,74834],{"xmlns":890},[892,74835,74836,74840],{},[895,74837,74838],{},[898,74839,9641],{},[902,74841,9641],{"encoding":904}," vyjadřuje ",[38,74844,74845],{},"produkční funkce",[883,74847,74849],{"className":74848},[886],[888,74850,74851],{"xmlns":890,"display":27911},[892,74852,74853,74884],{},[20599,74854,74855],{"width":27916},[20604,74856,74857,74859,74877,74879],{},[20607,74858],{"width":27921},[20607,74860,74861],{},[895,74862,74863,74865,74867,74869,74871,74873,74875],{},[898,74864,2638],{},[1846,74866,1848],{},[898,74868,2638],{},[1846,74870,1855],{"stretchy":1854},[898,74872,9641],{},[1846,74874,1861],{"stretchy":1854},[1846,74876,2136],{"separator":2135},[20607,74878],{"width":27921},[20607,74880,74881],{},[2138,74882,74883],{},"(5.1)",[902,74885,74886],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,74888,74889,74890,9871,74893,74896,74897,74910],{},"jejíž graf se nazývá ",[38,74891,74892],{},"křivka produkce",[614,74894,74895],{},"production curve","). Práce ",[883,74898,74900],{"className":74899},[886],[888,74901,74902],{"xmlns":890},[892,74903,74904,74908],{},[895,74905,74906],{},[898,74907,9641],{},[902,74909,9641],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,74912,74914,74915,1861],{"id":74913},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,74916,74918],{"className":74917},[886],[888,74919,74920],{"xmlns":890},[892,74921,74922,74932],{},[895,74923,74924,74926],{},[898,74925,2667],{},[2122,74927,74928,74930],{},[898,74929,3783],{},[898,74931,9641],{},[902,74933,9891],{"encoding":904},[724,74935,74936,9871,74939,74942,74943,74962],{},[38,74937,74938],{},"Mezní produkt práce",[614,74940,74941],{},"marginal product of labour",") ",[883,74944,74946],{"className":74945},[886],[888,74947,74948],{"xmlns":890},[892,74949,74950,74960],{},[895,74951,74952,74954],{},[898,74953,2667],{},[2122,74955,74956,74958],{},[898,74957,3783],{},[898,74959,9641],{},[902,74961,9891],{"encoding":904}," je derivace produkce podle práce:",[883,74964,74966],{"className":74965},[886],[888,74967,74968],{"xmlns":890,"display":27911},[892,74969,74970,75027],{},[20599,74971,74972],{"width":27916},[20604,74973,74974,74976,75020,75022],{},[20607,74975],{"width":27921},[20607,74977,74978],{},[895,74979,74980,74982,74988,74990,75004,75006,75012,75014,75016,75018],{},[898,74981,2667],{},[2122,74983,74984,74986],{},[898,74985,3783],{},[898,74987,9641],{},[1846,74989,1848],{},[2179,74991,74992,74998],{},[895,74993,74994,74996],{},[898,74995,2044],{},[898,74997,2638],{},[895,74999,75000,75002],{},[898,75001,2044],{},[898,75003,9641],{},[1846,75005,1848],{},[1974,75007,75008,75010],{},[898,75009,2638],{},[1846,75011,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,75013,1855],{"stretchy":1854},[898,75015,9641],{},[1846,75017,1861],{"stretchy":1854},[898,75019,1734],{"mathvariant":2226},[20607,75021],{"width":27921},[20607,75023,75024],{},[2138,75025,75026],{},"(5.2)",[902,75028,75029],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,75031,75032,75033,19790,75051,75079,75080,75097,75098,2535,75115,3764],{},"Pro pevnou hodnotu ",[883,75034,75036],{"className":75035},[886],[888,75037,75038],{"xmlns":890},[892,75039,75040,75048],{},[895,75041,75042],{},[1974,75043,75044,75046],{},[898,75045,9641],{},[1846,75047,4200],{},[902,75049,75050],{"encoding":904},"L^*",[883,75052,75054],{"className":75053},[886],[888,75055,75056],{"xmlns":890},[892,75057,75058,75076],{},[895,75059,75060,75066,75068,75074],{},[1974,75061,75062,75064],{},[898,75063,2638],{},[1846,75065,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,75067,1855],{"stretchy":1854},[1974,75069,75070,75072],{},[898,75071,9641],{},[1846,75073,4200],{},[1846,75075,1861],{"stretchy":1854},[902,75077,75078],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,75081,75083],{"className":75082},[886],[888,75084,75085],{"xmlns":890},[892,75086,75087,75095],{},[895,75088,75089],{},[1974,75090,75091,75093],{},[898,75092,9641],{},[1846,75094,4200],{},[902,75096,75050],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,75099,75101],{"className":75100},[886],[888,75102,75103],{"xmlns":890},[892,75104,75105,75113],{},[895,75106,75107],{},[1974,75108,75109,75111],{},[898,75110,9641],{},[1846,75112,4200],{},[902,75114,75050],{"encoding":904},[883,75116,75118],{"className":75117},[886],[888,75119,75120],{"xmlns":890},[892,75121,75122,75134],{},[895,75123,75124,75130,75132],{},[1974,75125,75126,75128],{},[898,75127,9641],{},[1846,75129,4200],{},[1846,75131,1945],{},[1979,75133,2128],{},[902,75135,75136],{"encoding":904},"L^*+1",[1639,75138,75139],{},[724,75140,75141,17868,75143,75162,75163,75166,75167,1734],{},[883,75142,4001],{},[883,75144,75146],{"className":75145},[886],[888,75147,75148],{"xmlns":890},[892,75149,75150,75160],{},[895,75151,75152,75154],{},[898,75153,2667],{},[2122,75155,75156,75158],{},[898,75157,3783],{},[898,75159,9641],{},[902,75161,9891],{"encoding":904}," odpovídá na otázku „",[38,75164,75165],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,75168,75170],{"className":75169},[886],[888,75171,75172],{"xmlns":890},[892,75173,75174,75178],{},[895,75175,75176],{},[898,75177,9641],{},[902,75179,9641],{"encoding":904},[724,75181,75182,75185,75186,75202,75203,2535,75216,75236],{},[38,75183,75184],{},"Přibližná změna produkce"," pro změnu práce o ",[883,75187,75189],{"className":75188},[886],[888,75190,75191],{"xmlns":890},[892,75192,75193,75199],{},[895,75194,75195,75197],{},[898,75196,2044],{},[898,75198,9641],{},[902,75200,75201],{"encoding":904},"dL"," (z ",[883,75204,75206],{"className":75205},[886],[888,75207,75208],{"xmlns":890},[892,75209,75210,75214],{},[895,75211,75212],{},[898,75213,9641],{},[902,75215,9641],{"encoding":904},[883,75217,75219],{"className":75218},[886],[888,75220,75221],{"xmlns":890},[892,75222,75223,75233],{},[895,75224,75225,75227,75229,75231],{},[898,75226,9641],{},[1846,75228,1945],{},[898,75230,2044],{},[898,75232,9641],{},[902,75234,75235],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,75238,75240],{"className":75239},[886],[888,75241,75242],{"xmlns":890,"display":27911},[892,75243,75244,75309],{},[20599,75245,75246],{"width":27916},[20604,75247,75248,75250,75302,75304],{},[20607,75249],{"width":27921},[20607,75251,75252],{},[895,75253,75254,75256,75258,75260,75262,75264,75266,75272,75274,75276,75278,75280,75282,75284,75286,75288,75294,75296,75298,75300],{},[898,75255,2738],{"mathvariant":2226},[898,75257,2638],{},[1846,75259,1650],{},[898,75261,2044],{},[898,75263,2638],{},[1846,75265,1848],{},[1974,75267,75268,75270],{},[898,75269,2638],{},[1846,75271,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,75273,1855],{"stretchy":1854},[898,75275,9641],{},[1846,75277,1861],{"stretchy":1854},[2138,75279,2835],{},[898,75281,2044],{},[898,75283,9641],{},[1846,75285,1848],{},[898,75287,2667],{},[2122,75289,75290,75292],{},[898,75291,3783],{},[898,75293,9641],{},[2138,75295,2835],{},[898,75297,2044],{},[898,75299,9641],{},[898,75301,1734],{"mathvariant":2226},[20607,75303],{"width":27921},[20607,75305,75306],{},[2138,75307,75308],{},"(5.3)",[902,75310,75311],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,75313,75314,75315,1734],{},"Skutečná změna je ",[883,75316,75318],{"className":75317},[886],[888,75319,75320],{"xmlns":890},[892,75321,75322,75354],{},[895,75323,75324,75326,75328,75330,75332,75334,75336,75338,75340,75342,75344,75346,75348,75350,75352],{},[898,75325,2738],{"mathvariant":2226},[898,75327,2638],{},[1846,75329,1848],{},[898,75331,2638],{},[1846,75333,1855],{"stretchy":1854},[898,75335,9641],{},[1846,75337,1945],{},[898,75339,2044],{},[898,75341,9641],{},[1846,75343,1861],{"stretchy":1854},[1846,75345,2075],{},[898,75347,2638],{},[1846,75349,1855],{"stretchy":1854},[898,75351,9641],{},[1846,75353,1861],{"stretchy":1854},[902,75355,75356],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,75358,75360],{"id":75359},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,75362,75363,9871,75366,2999],{},[38,75364,75365],{},"Zákon klesajících výnosů",[614,75367,75368],{},"law of diminishing marginal productivity",[1639,75370,75371],{},[724,75372,75373,75374,75376],{},"Roste-li postupně některý ze vstupů (",[614,75375,36805],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,75378,75379],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,75381,75382,75383,2053,75404,75423,75424,75474,75475,75477,75478,2053,75498,75517,75518,75474,75550,2776,75552,75571,75572,21439,75589,75623,75624,7948,75641,75644],{},"1° ",[38,75384,75385,75386,2554],{},"Do bodu ",[883,75387,75389],{"className":75388},[886],[888,75390,75391],{"xmlns":890},[892,75392,75393,75401],{},[895,75394,75395],{},[2122,75396,75397,75399],{},[898,75398,9641],{},[1979,75400,2177],{},[902,75402,75403],{"encoding":904},"L_0",[883,75405,75407],{"className":75406},[886],[888,75408,75409],{"xmlns":890},[892,75410,75411,75421],{},[895,75412,75413,75415],{},[898,75414,2667],{},[2122,75416,75417,75419],{},[898,75418,3783],{},[898,75420,9641],{},[902,75422,9891],{"encoding":904}," roste, tj. ",[883,75425,75427],{"className":75426},[886],[888,75428,75429],{"xmlns":890},[892,75430,75431,75471],{},[895,75432,75433,75435,75437,75443,75449,75451,75461,75463,75465,75467,75469],{},[1846,75434,1855],{"stretchy":1854},[898,75436,2667],{},[2122,75438,75439,75441],{},[898,75440,3783],{},[898,75442,9641],{},[1974,75444,75445,75447],{},[1846,75446,1861],{"stretchy":1854},[1846,75448,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,75450,1848],{},[1974,75452,75453,75455],{},[898,75454,2638],{},[895,75456,75457,75459],{},[1846,75458,2228],{"mathvariant":2226},[1846,75460,2228],{"mathvariant":2226},[1846,75462,1855],{"stretchy":1854},[898,75464,9641],{},[1846,75466,1861],{"stretchy":1854},[1846,75468,3256],{},[1979,75470,2177],{},[902,75472,75473],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,75476,37509],{},".\n2° ",[38,75479,75480,75481,2554],{},"Od bodu ",[883,75482,75484],{"className":75483},[886],[888,75485,75486],{"xmlns":890},[892,75487,75488,75496],{},[895,75489,75490],{},[2122,75491,75492,75494],{},[898,75493,9641],{},[1979,75495,2177],{},[902,75497,75403],{"encoding":904},[883,75499,75501],{"className":75500},[886],[888,75502,75503],{"xmlns":890},[892,75504,75505,75515],{},[895,75506,75507,75509],{},[898,75508,2667],{},[2122,75510,75511,75513],{},[898,75512,3783],{},[898,75514,9641],{},[902,75516,9891],{"encoding":904}," klesá, ",[883,75519,75521],{"className":75520},[886],[888,75522,75523],{"xmlns":890},[892,75524,75525,75547],{},[895,75526,75527,75537,75539,75541,75543,75545],{},[1974,75528,75529,75531],{},[898,75530,2638],{},[895,75532,75533,75535],{},[1846,75534,2228],{"mathvariant":2226},[1846,75536,2228],{"mathvariant":2226},[1846,75538,1855],{"stretchy":1854},[898,75540,9641],{},[1846,75542,1861],{"stretchy":1854},[1846,75544,3295],{},[1979,75546,2177],{},[902,75548,75549],{"encoding":904},"Q''(L) \u003C 0",[38,75551,38333],{},[883,75553,75555],{"className":75554},[886],[888,75556,75557],{"xmlns":890},[892,75558,75559,75569],{},[895,75560,75561,75563],{},[898,75562,2667],{},[2122,75564,75565,75567],{},[898,75566,3783],{},[898,75568,9641],{},[902,75570,9891],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,75573,75575],{"className":75574},[886],[888,75576,75577],{"xmlns":890},[892,75578,75579,75587],{},[895,75580,75581],{},[2122,75582,75583,75585],{},[898,75584,9641],{},[1979,75586,2128],{},[902,75588,13057],{"encoding":904},[883,75590,75592],{"className":75591},[886],[888,75593,75594],{"xmlns":890},[892,75595,75596,75620],{},[895,75597,75598,75600,75606,75608,75614,75616,75618],{},[898,75599,2667],{},[2122,75601,75602,75604],{},[898,75603,3783],{},[898,75605,9641],{},[1846,75607,1855],{"stretchy":1854},[2122,75609,75610,75612],{},[898,75611,9641],{},[1979,75613,2128],{},[1846,75615,1861],{"stretchy":1854},[1846,75617,1848],{},[1979,75619,2177],{},[902,75621,75622],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,75625,75627],{"className":75626},[886],[888,75628,75629],{"xmlns":890},[892,75630,75631,75639],{},[895,75632,75633],{},[2122,75634,75635,75637],{},[898,75636,9641],{},[1979,75638,2177],{},[902,75640,75403],{"encoding":904},[38,75642,75643],{},"inflexním bodem"," produkční funkce.",[724,75646,75647,75648,10240,75665,1734],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,75649,75651],{"className":75650},[886],[888,75652,75653],{"xmlns":890},[892,75654,75655,75663],{},[895,75656,75657],{},[2122,75658,75659,75661],{},[898,75660,9641],{},[1979,75662,2177],{},[902,75664,75403],{"encoding":904},[883,75666,75668],{"className":75667},[886],[888,75669,75670],{"xmlns":890},[892,75671,75672,75694],{},[895,75673,75674,75684,75686,75688,75690,75692],{},[1974,75675,75676,75678],{},[898,75677,2638],{},[895,75679,75680,75682],{},[1846,75681,2228],{"mathvariant":2226},[1846,75683,2228],{"mathvariant":2226},[1846,75685,1855],{"stretchy":1854},[898,75687,9641],{},[1846,75689,1861],{"stretchy":1854},[1846,75691,3295],{},[1979,75693,2177],{},[902,75695,75549],{"encoding":904},[724,75697,75698,2053,75701,5515,75741,1343,75758,75775],{},[38,75699,75700],{},"Typický polynom třetího stupně:",[883,75702,75704],{"className":75703},[886],[888,75705,75706],{"xmlns":890},[892,75707,75708,75738],{},[895,75709,75710,75712,75714,75716,75718,75720,75722,75728,75730,75732],{},[898,75711,2638],{},[1846,75713,1855],{"stretchy":1854},[898,75715,9641],{},[1846,75717,1861],{"stretchy":1854},[1846,75719,1848],{},[898,75721,207],{},[1974,75723,75724,75726],{},[898,75725,9641],{},[1979,75727,2023],{},[1846,75729,1945],{},[898,75731,1948],{},[1974,75733,75734,75736],{},[898,75735,9641],{},[1979,75737,1981],{},[902,75739,75740],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,75742,75744],{"className":75743},[886],[888,75745,75746],{"xmlns":890},[892,75747,75748,75756],{},[895,75749,75750,75752,75754],{},[898,75751,207],{},[1846,75753,3295],{},[1979,75755,2177],{},[902,75757,42930],{"encoding":904},[883,75759,75761],{"className":75760},[886],[888,75762,75763],{"xmlns":890},[892,75764,75765,75773],{},[895,75766,75767,75769,75771],{},[898,75768,1948],{},[1846,75770,3256],{},[1979,75772,2177],{},[902,75774,18659],{"encoding":904},". Pak",[883,75777,75779],{"className":75778},[886],[888,75780,75781],{"xmlns":890,"display":27911},[892,75782,75783,75843],{},[895,75784,75785,75791,75793,75795,75803,75811,75813,75815,75821,75823,75825,75833,75841],{},[2122,75786,75787,75789],{},[898,75788,9641],{},[1979,75790,2177],{},[1846,75792,1848],{},[1846,75794,2075],{},[2175,75796,75797],{"scriptlevel":2177,"displaystyle":1854},[2179,75798,75799,75801],{},[1979,75800,2128],{},[1979,75802,2023],{},[2175,75804,75805],{"scriptlevel":2177,"displaystyle":1854},[2179,75806,75807,75809],{},[898,75808,1948],{},[898,75810,207],{},[1846,75812,2136],{"separator":2135},[5724,75814],{"width":5726},[2122,75816,75817,75819],{},[898,75818,9641],{},[1979,75820,2128],{},[1846,75822,1848],{},[1846,75824,2075],{},[2175,75826,75827],{"scriptlevel":2177,"displaystyle":1854},[2179,75828,75829,75831],{},[1979,75830,1981],{},[1979,75832,2023],{},[2175,75834,75835],{"scriptlevel":2177,"displaystyle":1854},[2179,75836,75837,75839],{},[898,75838,1948],{},[898,75840,207],{},[898,75842,1734],{"mathvariant":2226},[902,75844,75845],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,75847,75849,75850,1861],{"id":75848},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,75851,75853],{"className":75852},[886],[888,75854,75855],{"xmlns":890},[892,75856,75857,75867],{},[895,75858,75859,75861],{},[898,75860,4101],{},[2122,75862,75863,75865],{},[898,75864,3783],{},[898,75866,9641],{},[902,75868,74478],{"encoding":904},[724,75870,75871,9871,75874,74942,75877,75896],{},[38,75872,75873],{},"Průměrný produkt práce",[614,75875,75876],{},"average product of labour",[883,75878,75880],{"className":75879},[886],[888,75881,75882],{"xmlns":890},[892,75883,75884,75894],{},[895,75885,75886,75888],{},[898,75887,4101],{},[2122,75889,75890,75892],{},[898,75891,3783],{},[898,75893,9641],{},[902,75895,74478],{"encoding":904}," je podíl produkce a práce:",[883,75898,75900],{"className":75899},[886],[888,75901,75902],{"xmlns":890,"display":27911},[892,75903,75904,75939],{},[20599,75905,75906],{"width":27916},[20604,75907,75908,75910,75932,75934],{},[20607,75909],{"width":27921},[20607,75911,75912],{},[895,75913,75914,75916,75922,75924,75930],{},[898,75915,4101],{},[2122,75917,75918,75920],{},[898,75919,3783],{},[898,75921,9641],{},[1846,75923,1848],{},[2179,75925,75926,75928],{},[898,75927,2638],{},[898,75929,9641],{},[898,75931,1734],{"mathvariant":2226},[20607,75933],{"width":27921},[20607,75935,75936],{},[2138,75937,75938],{},"(5.4)",[902,75940,75941],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,75943,75944,75945,1734],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,75946,75948],{"className":75947},[886],[888,75949,75950],{"xmlns":890},[892,75951,75952,75962],{},[895,75953,75954,75956],{},[898,75955,4101],{},[2122,75957,75958,75960],{},[898,75959,3783],{},[898,75961,9641],{},[902,75963,74478],{"encoding":904},[115,75965,75967],{"id":75966},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,75969,75970],{},[2409,75971],{"alt":75972,"className":75973,"src":75974},"imek-q-mpl-apl-tripanel",[210,2413],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[1639,75976,75977],{},[724,75978,75979,75982,75983,2474,76002,76019,76020],{},[38,75980,75981],{},"Princip:"," Má-li ",[883,75984,75986],{"className":75985},[886],[888,75987,75988],{"xmlns":890},[892,75989,75990,76000],{},[895,75991,75992,75994],{},[898,75993,4101],{},[2122,75995,75996,75998],{},[898,75997,3783],{},[898,75999,9641],{},[902,76001,74478],{"encoding":904},[883,76003,76005],{"className":76004},[886],[888,76006,76007],{"xmlns":890},[892,76008,76009,76017],{},[895,76010,76011],{},[2122,76012,76013,76015],{},[898,76014,9641],{},[1979,76016,2177],{},[902,76018,75403],{"encoding":904}," maximum, pak platí\n",[883,76021,76023],{"className":76022,"title":4046,"style":4047},[4045],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,76025,76026,76027,76030,76031,2053,76035,1734],{},"Slovně: ",[38,76028,76029],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,76032,76034],{"className":76033,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,76036,76038],{"className":76037},[886],[888,76039,76040],{"xmlns":890},[892,76041,76042,76048],{},[895,76043,76044,76046],{},[898,76045,4101],{},[898,76047,2626],{},[902,76049,55405],{"encoding":904},[1639,76051,76052,76076],{},[724,76053,76054,76056,76057],{},[883,76055,4418],{}," Postup — jak najít max ",[883,76058,76060],{"className":76059},[886],[888,76061,76062],{"xmlns":890},[892,76063,76064,76074],{},[895,76065,76066,76068],{},[898,76067,4101],{},[2122,76069,76070,76072],{},[898,76071,3783],{},[898,76073,9641],{},[902,76075,74478],{"encoding":904},[152,76077,76078,76116,76198],{},[123,76079,76080,76081,76115],{},"Napište ",[883,76082,76084],{"className":76083},[886],[888,76085,76086],{"xmlns":890},[892,76087,76088,76112],{},[895,76089,76090,76092,76098,76100,76102,76104,76106,76108,76110],{},[898,76091,4101],{},[2122,76093,76094,76096],{},[898,76095,3783],{},[898,76097,9641],{},[1846,76099,1848],{},[898,76101,2638],{},[1846,76103,1855],{"stretchy":1854},[898,76105,9641],{},[1846,76107,1861],{"stretchy":1854},[898,76109,4520],{"mathvariant":2226},[898,76111,9641],{},[902,76113,76114],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,76117,76118,76119,76151,76152,76155,76156,1734],{},"Položte ",[883,76120,76122],{"className":76121},[886],[888,76123,76124],{"xmlns":890},[892,76125,76126,76148],{},[895,76127,76128,76130,76132,76138,76144,76146],{},[1846,76129,1855],{"stretchy":1854},[898,76131,4101],{},[2122,76133,76134,76136],{},[898,76135,3783],{},[898,76137,9641],{},[1974,76139,76140,76142],{},[1846,76141,1861],{"stretchy":1854},[1846,76143,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,76145,1848],{},[1979,76147,2177],{},[902,76149,76150],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,76153,76154],{},"Zkratka:"," můžete rovnou řešit ",[883,76157,76159],{"className":76158},[886],[888,76160,76161],{"xmlns":890},[892,76162,76163,76195],{},[895,76164,76165,76167,76173,76175,76177,76179,76181,76183,76189,76191,76193],{},[898,76166,2667],{},[2122,76168,76169,76171],{},[898,76170,3783],{},[898,76172,9641],{},[1846,76174,1855],{"stretchy":1854},[898,76176,9641],{},[1846,76178,1861],{"stretchy":1854},[1846,76180,1848],{},[898,76182,4101],{},[2122,76184,76185,76187],{},[898,76186,3783],{},[898,76188,9641],{},[1846,76190,1855],{"stretchy":1854},[898,76192,9641],{},[1846,76194,1861],{"stretchy":1854},[902,76196,76197],{"encoding":904},"MP_L(L) = AP_L(L)",[123,76199,76200],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,76202,65346],{"id":76203},"odvození",[724,76205,76206,76207,76240],{},"Z ",[883,76208,76210],{"className":76209},[886],[888,76211,76212],{"xmlns":890},[892,76213,76214,76238],{},[895,76215,76216,76218,76224,76226,76228,76230,76232,76234,76236],{},[898,76217,4101],{},[2122,76219,76220,76222],{},[898,76221,3783],{},[898,76223,9641],{},[1846,76225,1848],{},[898,76227,2638],{},[1846,76229,1855],{"stretchy":1854},[898,76231,9641],{},[1846,76233,1861],{"stretchy":1854},[898,76235,4520],{"mathvariant":2226},[898,76237,9641],{},[902,76239,76114],{"encoding":904}," a derivace podílu:",[883,76242,76244],{"className":76243},[886],[888,76245,76246],{"xmlns":890,"display":27911},[892,76247,76248,76401],{},[895,76249,76250,76252,76254,76260,76266,76268,76270,76272,76274,76314,76316,76322,76356,76358,76364,76367,76369,76375,76377,76379,76381,76383,76385,76391,76393,76395,76397,76399],{},[1846,76251,1855],{"stretchy":1854},[898,76253,4101],{},[2122,76255,76256,76258],{},[898,76257,3783],{},[898,76259,9641],{},[1974,76261,76262,76264],{},[1846,76263,1861],{"stretchy":1854},[1846,76265,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,76267,1855],{"stretchy":1854},[898,76269,9641],{},[1846,76271,1861],{"stretchy":1854},[1846,76273,1848],{},[2179,76275,76276,76308],{},[895,76277,76278,76284,76286,76288,76290,76292,76294,76296,76298,76300,76302,76304,76306],{},[1974,76279,76280,76282],{},[898,76281,2638],{},[1846,76283,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,76285,1855],{"stretchy":1854},[898,76287,9641],{},[1846,76289,1861],{"stretchy":1854},[1846,76291,3025],{},[898,76293,9641],{},[1846,76295,2075],{},[898,76297,2638],{},[1846,76299,1855],{"stretchy":1854},[898,76301,9641],{},[1846,76303,1861],{"stretchy":1854},[1846,76305,3025],{},[1979,76307,2128],{},[1974,76309,76310,76312],{},[898,76311,9641],{},[1979,76313,1981],{},[1846,76315,1848],{},[2179,76317,76318,76320],{},[1979,76319,2128],{},[898,76321,9641],{},[895,76323,76324,76326,76332,76334,76336,76338,76340,76354],{},[1846,76325,1855],{"fence":2135},[1974,76327,76328,76330],{},[898,76329,2638],{},[1846,76331,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,76333,1855],{"stretchy":1854},[898,76335,9641],{},[1846,76337,1861],{"stretchy":1854},[1846,76339,2075],{},[2179,76341,76342,76352],{},[895,76343,76344,76346,76348,76350],{},[898,76345,2638],{},[1846,76347,1855],{"stretchy":1854},[898,76349,9641],{},[1846,76351,1861],{"stretchy":1854},[898,76353,9641],{},[1846,76355,1861],{"fence":2135},[1846,76357,1848],{},[2179,76359,76360,76362],{},[1979,76361,2128],{},[898,76363,9641],{},[1846,76365,1855],{"fence":2135,"stretchy":2135,"minsize":76366,"maxsize":76366},"1.2em",[898,76368,2667],{},[2122,76370,76371,76373],{},[898,76372,3783],{},[898,76374,9641],{},[1846,76376,1855],{"stretchy":1854},[898,76378,9641],{},[1846,76380,1861],{"stretchy":1854},[1846,76382,2075],{},[898,76384,4101],{},[2122,76386,76387,76389],{},[898,76388,3783],{},[898,76390,9641],{},[1846,76392,1855],{"stretchy":1854},[898,76394,9641],{},[1846,76396,1861],{"stretchy":1854},[1846,76398,1861],{"fence":2135,"stretchy":2135,"minsize":76366,"maxsize":76366},[898,76400,1734],{"mathvariant":2226},[902,76402,76403],{"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).",[724,76405,9509,76406,7948,76428,76511],{},[883,76407,76409],{"className":76408},[886],[888,76410,76411],{"xmlns":890},[892,76412,76413,76425],{},[895,76414,76415,76421,76423],{},[2122,76416,76417,76419],{},[898,76418,9641],{},[1979,76420,2177],{},[1846,76422,3256],{},[1979,76424,2177],{},[902,76426,76427],{"encoding":904},"L_0 > 0",[883,76429,76431],{"className":76430},[886],[888,76432,76433],{"xmlns":890},[892,76434,76435,76508],{},[895,76436,76437,76439,76441,76447,76453,76455,76461,76463,76465,76467,76470,76472,76478,76480,76486,76488,76490,76492,76498,76500,76506],{},[1846,76438,1855],{"stretchy":1854},[898,76440,4101],{},[2122,76442,76443,76445],{},[898,76444,3783],{},[898,76446,9641],{},[1974,76448,76449,76451],{},[1846,76450,1861],{"stretchy":1854},[1846,76452,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,76454,1855],{"stretchy":1854},[2122,76456,76457,76459],{},[898,76458,9641],{},[1979,76460,2177],{},[1846,76462,1861],{"stretchy":1854},[1846,76464,1848],{},[1979,76466,2177],{},[1846,76468,76469],{},"⇔",[898,76471,2667],{},[2122,76473,76474,76476],{},[898,76475,3783],{},[898,76477,9641],{},[1846,76479,1855],{"stretchy":1854},[2122,76481,76482,76484],{},[898,76483,9641],{},[1979,76485,2177],{},[1846,76487,1861],{"stretchy":1854},[1846,76489,1848],{},[898,76491,4101],{},[2122,76493,76494,76496],{},[898,76495,3783],{},[898,76497,9641],{},[1846,76499,1855],{"stretchy":1854},[2122,76501,76502,76504],{},[898,76503,9641],{},[1979,76505,2177],{},[1846,76507,1861],{"stretchy":1854},[902,76509,76510],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,76513,76515],{"id":76514},"příklad-51","Příklad 5.1",[724,76517,76518,76519,1734],{},"Je dána produkce ",[883,76520,76522],{"className":76521},[886],[888,76523,76524],{"xmlns":890},[892,76525,76526,76550],{},[895,76527,76528,76530,76532,76534,76540,76542,76544],{},[898,76529,2638],{},[1846,76531,1848],{},[1979,76533,2085],{},[1974,76535,76536,76538],{},[898,76537,9641],{},[1979,76539,1981],{},[1846,76541,2075],{},[1979,76543,2688],{},[1974,76545,76546,76548],{},[898,76547,9641],{},[1979,76549,2023],{},[902,76551,76552],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,76554,76555,57367,76558,76608,76609,1734],{},[38,76556,76557],{},"(a)",[883,76559,76561],{"className":76560},[886],[888,76562,76563],{"xmlns":890},[892,76564,76565,76605],{},[895,76566,76567,76569,76571,76573,76575,76577,76579,76581,76583,76585,76587,76589,76591,76593,76595,76597,76599,76601,76603],{},[898,76568,9641],{},[1846,76570,1848],{},[1979,76572,1981],{},[1846,76574,2136],{"separator":2135},[1979,76576,2078],{},[1846,76578,2136],{"separator":2135},[1979,76580,5431],{},[1846,76582,2136],{"separator":2135},[1979,76584,2712],{},[1846,76586,2136],{"separator":2135},[1979,76588,22791],{},[1846,76590,2136],{"separator":2135},[1979,76592,3555],{},[1846,76594,2136],{"separator":2135},[1979,76596,8881],{},[1846,76598,2136],{"separator":2135},[1979,76600,38191],{},[1846,76602,2136],{"separator":2135},[1979,76604,4850],{},[902,76606,76607],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,76610,76612],{"className":76611},[886],[888,76613,76614],{"xmlns":890},[892,76615,76616,76626],{},[895,76617,76618,76620],{},[898,76619,2667],{},[2122,76621,76622,76624],{},[898,76623,3783],{},[898,76625,9641],{},[902,76627,9891],{"encoding":904},[724,76629,76630,76631,34813],{},"Podle (5.2): ",[883,76632,76634],{"className":76633},[886],[888,76635,76636],{"xmlns":890},[892,76637,76638,76694],{},[895,76639,76640,76642,76648,76650,76656,76658,76660,76662,76664,76666,76668,76670,76672,76678,76680,76682,76684,76686,76688,76690,76692],{},[898,76641,2667],{},[2122,76643,76644,76646],{},[898,76645,3783],{},[898,76647,9641],{},[1846,76649,1848],{},[1974,76651,76652,76654],{},[898,76653,2638],{},[1846,76655,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,76657,1855],{"stretchy":1854},[898,76659,9641],{},[1846,76661,1861],{"stretchy":1854},[1846,76663,1848],{},[1979,76665,3357],{},[898,76667,9641],{},[1846,76669,2075],{},[1979,76671,19166],{},[1974,76673,76674,76676],{},[898,76675,9641],{},[1979,76677,1981],{},[1846,76679,1848],{},[898,76681,9641],{},[1846,76683,1855],{"stretchy":1854},[1979,76685,3357],{},[1846,76687,2075],{},[1979,76689,19166],{},[898,76691,9641],{},[1846,76693,1861],{"stretchy":1854},[902,76695,76696],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,76698,76699,76736],{},[19,76700,76701],{},[22,76702,76703,76718,76720,76722,76724,76726,76728,76730,76732,76734],{},[25,76704,76705],{},[883,76706,76708],{"className":76707},[886],[888,76709,76710],{"xmlns":890},[892,76711,76712,76716],{},[895,76713,76714],{},[898,76715,9641],{},[902,76717,9641],{"encoding":904},[25,76719,1981],{},[25,76721,2078],{},[25,76723,5431],{},[25,76725,2712],{},[25,76727,22791],{},[25,76729,3555],{},[25,76731,8881],{},[25,76733,38191],{},[25,76735,4850],{},[30,76737,76738],{},[22,76739,76740,76761,76764,76767,76770,76772,76775,76777,76779,76798],{},[35,76741,76742],{},[883,76743,76745],{"className":76744},[886],[888,76746,76747],{"xmlns":890},[892,76748,76749,76759],{},[895,76750,76751,76753],{},[898,76752,2667],{},[2122,76754,76755,76757],{},[898,76756,3783],{},[898,76758,9641],{},[902,76760,9891],{"encoding":904},[35,76762,76763],{},"21,6",[35,76765,76766],{},"45",[35,76768,76769],{},"57,6",[35,76771,2974],{},[35,76773,76774],{},"50,4",[35,76776,76763],{},[35,76778,2177],{},[35,76780,76781],{},[883,76782,76784],{"className":76783},[886],[888,76785,76786],{"xmlns":890},[892,76787,76788,76795],{},[895,76789,76790,76792],{},[1846,76791,2075],{},[1979,76793,76794],{},"12,6",[902,76796,76797],{"encoding":904},"-12{,}6",[35,76799,76800],{},[883,76801,76803],{"className":76802},[886],[888,76804,76805],{"xmlns":890},[892,76806,76807,76813],{},[895,76808,76809,76811],{},[1846,76810,2075],{},[1979,76812,45297],{},[902,76814,76815],{"encoding":904},"-75",[724,76817,76818,76837,76838,76856,76857,76874,76875,76893,76894,76918,76919,76937],{},[883,76819,76821],{"className":76820},[886],[888,76822,76823],{"xmlns":890},[892,76824,76825,76835],{},[895,76826,76827,76829],{},[898,76828,2667],{},[2122,76830,76831,76833],{},[898,76832,3783],{},[898,76834,9641],{},[902,76836,9891],{"encoding":904}," nabývá maxima pro ",[883,76839,76841],{"className":76840},[886],[888,76842,76843],{"xmlns":890},[892,76844,76845,76853],{},[895,76846,76847,76849,76851],{},[898,76848,9641],{},[1846,76850,1848],{},[1979,76852,2712],{},[902,76854,76855],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,76858,76860],{"className":76859},[886],[888,76861,76862],{"xmlns":890},[892,76863,76864,76872],{},[895,76865,76866,76868,76870],{},[898,76867,9641],{},[1846,76869,1848],{},[1979,76871,2712],{},[902,76873,76855],{"encoding":904}," přírůstky klesají, v ",[883,76876,76878],{"className":76877},[886],[888,76879,76880],{"xmlns":890},[892,76881,76882,76890],{},[895,76883,76884,76886,76888],{},[898,76885,9641],{},[1846,76887,1848],{},[1979,76889,8881],{},[902,76891,76892],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,76895,76897],{"className":76896},[886],[888,76898,76899],{"xmlns":890},[892,76900,76901,76915],{},[895,76902,76903,76905,76907,76909,76911,76913],{},[898,76904,2638],{},[1846,76906,1855],{"stretchy":1854},[1979,76908,8881],{},[1846,76910,1861],{"stretchy":1854},[1846,76912,1848],{},[1979,76914,23703],{},[902,76916,76917],{"encoding":904},"Q(20) = 800","), od ",[883,76920,76922],{"className":76921},[886],[888,76923,76924],{"xmlns":890},[892,76925,76926,76934],{},[895,76927,76928,76930,76932],{},[898,76929,9641],{},[1846,76931,3256],{},[1979,76933,8881],{},[902,76935,76936],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,76939,76940],{},[614,76941,76942,76943,76983,76984,2474,77002,1734],{},"Obrázek 5.1 — graf produkce ",[883,76944,76946],{"className":76945},[886],[888,76947,76948],{"xmlns":890},[892,76949,76950,76980],{},[895,76951,76952,76954,76956,76958,76960,76962,76964,76970,76972,76974],{},[898,76953,2638],{},[1846,76955,1855],{"stretchy":1854},[898,76957,9641],{},[1846,76959,1861],{"stretchy":1854},[1846,76961,1848],{},[1979,76963,2085],{},[1974,76965,76966,76968],{},[898,76967,9641],{},[1979,76969,1981],{},[1846,76971,2075],{},[1979,76973,2688],{},[1974,76975,76976,76978],{},[898,76977,9641],{},[1979,76979,2023],{},[902,76981,76982],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,76985,76987],{"className":76986},[886],[888,76988,76989],{"xmlns":890},[892,76990,76991,76999],{},[895,76992,76993,76995,76997],{},[898,76994,2638],{},[1846,76996,1848],{},[1979,76998,23703],{},[902,77000,77001],{"encoding":904},"Q = 800",[883,77003,77005],{"className":77004},[886],[888,77006,77007],{"xmlns":890},[892,77008,77009,77017],{},[895,77010,77011,77013,77015],{},[898,77012,9641],{},[1846,77014,1848],{},[1979,77016,8881],{},[902,77018,76892],{"encoding":904},[724,77020,77021,77024],{},[38,77022,77023],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,77026,77027,77028,1343,77046,2554],{},"Podle (5.3) s ",[883,77029,77031],{"className":77030},[886],[888,77032,77033],{"xmlns":890},[892,77034,77035,77043],{},[895,77036,77037,77039,77041],{},[898,77038,9641],{},[1846,77040,1848],{},[1979,77042,2085],{},[902,77044,77045],{"encoding":904},"L = 6",[883,77047,77049],{"className":77048},[886],[888,77050,77051],{"xmlns":890},[892,77052,77053,77063],{},[895,77054,77055,77057,77059,77061],{},[898,77056,2044],{},[898,77058,9641],{},[1846,77060,1848],{},[1979,77062,2023],{},[902,77064,77065],{"encoding":904},"dL = 3",[883,77067,77069],{"className":77068},[886],[888,77070,77071],{"xmlns":890,"display":27911},[892,77072,77073,77136],{},[895,77074,77075,77077,77079,77081,77083,77089,77091,77093,77095,77097,77099,77101,77103,77105,77107,77109,77111,77113,77115,77117,77119,77121,77123,77125,77127,77129,77131,77133],{},[898,77076,2044],{},[898,77078,2638],{},[1846,77080,1848],{},[898,77082,2667],{},[2122,77084,77085,77087],{},[898,77086,3783],{},[898,77088,9641],{},[1846,77090,1855],{"stretchy":1854},[1979,77092,2085],{},[1846,77094,1861],{"stretchy":1854},[1846,77096,3025],{},[1979,77098,2023],{},[1846,77100,1848],{},[1846,77102,1855],{"stretchy":1854},[1979,77104,3357],{},[1846,77106,3025],{},[1979,77108,2085],{},[1846,77110,2075],{},[1979,77112,19166],{},[1846,77114,3025],{},[1979,77116,5411],{},[1846,77118,1861],{"stretchy":1854},[1846,77120,3025],{},[1979,77122,2023],{},[1846,77124,1848],{},[1979,77126,76774],{},[1846,77128,3025],{},[1979,77130,2023],{},[1846,77132,1848],{},[1979,77134,77135],{},"151,2.",[902,77137,77138],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,77140,77141,77142,57597,77167,77181,77182,1734],{},"Produkce vzroste z ",[883,77143,77145],{"className":77144},[886],[888,77146,77147],{"xmlns":890},[892,77148,77149,77164],{},[895,77150,77151,77153,77155,77157,77159,77161],{},[898,77152,2638],{},[1846,77154,1855],{"stretchy":1854},[1979,77156,2085],{},[1846,77158,1861],{"stretchy":1854},[1846,77160,1848],{},[1979,77162,77163],{},"172,8",[902,77165,77166],{"encoding":904},"Q(6) = 172{,}8",[883,77168,77170],{"className":77169},[886],[888,77171,77172],{"xmlns":890},[892,77173,77174,77179],{},[895,77175,77176],{},[1979,77177,77178],{},"324",[902,77180,77178],{"encoding":904},". Skutečná hodnota: ",[883,77183,77185],{"className":77184},[886],[888,77186,77187],{"xmlns":890},[892,77188,77189,77229],{},[895,77190,77191,77193,77195,77197,77199,77201,77203,77205,77207,77209,77211,77213,77215,77217,77220,77222,77224,77226],{},[898,77192,2738],{"mathvariant":2226},[898,77194,2638],{},[1846,77196,1848],{},[898,77198,2638],{},[1846,77200,1855],{"stretchy":1854},[1979,77202,3845],{},[1846,77204,1861],{"stretchy":1854},[1846,77206,2075],{},[898,77208,2638],{},[1846,77210,1855],{"stretchy":1854},[1979,77212,2085],{},[1846,77214,1861],{"stretchy":1854},[1846,77216,1848],{},[1979,77218,77219],{},"340,2",[1846,77221,2075],{},[1979,77223,77163],{},[1846,77225,1848],{},[1979,77227,77228],{},"167,4",[902,77230,77231],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,77233,77235],{"id":77234},"příklad-52","Příklad 5.2",[724,77237,77238,77239,1734],{},"Ověříme princip (5.5) pro ",[883,77240,77242],{"className":77241},[886],[888,77243,77244],{"xmlns":890},[892,77245,77246,77270],{},[895,77247,77248,77250,77252,77254,77260,77262,77264],{},[898,77249,2638],{},[1846,77251,1848],{},[1979,77253,2085],{},[1974,77255,77256,77258],{},[898,77257,9641],{},[1979,77259,1981],{},[1846,77261,2075],{},[1979,77263,2688],{},[1974,77265,77266,77268],{},[898,77267,9641],{},[1979,77269,2023],{},[902,77271,76552],{"encoding":904},[883,77273,77275],{"className":77274},[886],[888,77276,77277],{"xmlns":890,"display":27911},[892,77278,77279,77357],{},[895,77280,77281,77283,77289,77291,77297,77299,77301,77303,77305,77307,77313,77315,77317,77319,77327,77329,77331,77333,77335,77337,77339,77341,77343,77345,77347,77353,77355],{},[898,77282,4101],{},[2122,77284,77285,77287],{},[898,77286,3783],{},[898,77288,9641],{},[1846,77290,1848],{},[2179,77292,77293,77295],{},[898,77294,2638],{},[898,77296,9641],{},[1846,77298,1848],{},[1979,77300,2085],{},[898,77302,9641],{},[1846,77304,2075],{},[1979,77306,2688],{},[1974,77308,77309,77311],{},[898,77310,9641],{},[1979,77312,1981],{},[1846,77314,2136],{"separator":2135},[5724,77316],{"width":15129},[898,77318,4101],{},[9012,77320,77321,77323,77325],{},[898,77322,3783],{},[898,77324,9641],{},[1846,77326,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,77328,1848],{},[1979,77330,2085],{},[1846,77332,2075],{},[1979,77334,19116],{},[898,77336,9641],{},[1846,77338,1848],{},[1979,77340,2177],{},[2138,77342,3830],{},[1846,77344,3833],{},[2138,77346,3830],{},[2122,77348,77349,77351],{},[898,77350,9641],{},[1979,77352,2177],{},[1846,77354,1848],{},[1979,77356,68128],{},[902,77358,77359],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,77361,77362,77398,77399,77417,77418,1734],{},[883,77363,77365],{"className":77364},[886],[888,77366,77367],{"xmlns":890},[892,77368,77369,77395],{},[895,77370,77371,77373,77385,77387,77389,77391,77393],{},[898,77372,4101],{},[9012,77374,77375,77377,77379],{},[898,77376,3783],{},[898,77378,9641],{},[895,77380,77381,77383],{},[1846,77382,2228],{"mathvariant":2226},[1846,77384,2228],{"mathvariant":2226},[1846,77386,1848],{},[1846,77388,2075],{},[1979,77390,19116],{},[1846,77392,3295],{},[1979,77394,2177],{},[902,77396,77397],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,77400,77402],{"className":77401},[886],[888,77403,77404],{"xmlns":890},[892,77405,77406,77414],{},[895,77407,77408,77410,77412],{},[898,77409,9641],{},[1846,77411,1848],{},[1979,77413,36089],{},[902,77415,77416],{"encoding":904},"L = 15"," je maximum, ",[883,77419,77421],{"className":77420},[886],[888,77422,77423],{"xmlns":890},[892,77424,77425,77471],{},[895,77426,77427,77429,77435,77437,77439,77441,77443,77445,77447,77449,77451,77453,77455,77458,77460,77463,77465,77467,77469],{},[898,77428,4101],{},[2122,77430,77431,77433],{},[898,77432,3783],{},[898,77434,9641],{},[1846,77436,1855],{"stretchy":1854},[1979,77438,36089],{},[1846,77440,1861],{"stretchy":1854},[1846,77442,1848],{},[1979,77444,2085],{},[1846,77446,3025],{},[1979,77448,36089],{},[1846,77450,2075],{},[1979,77452,2688],{},[1846,77454,3025],{},[1979,77456,77457],{},"225",[1846,77459,1848],{},[1979,77461,77462],{},"90",[1846,77464,2075],{},[1979,77466,76766],{},[1846,77468,1848],{},[1979,77470,76766],{},[902,77472,77473],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,77475,77476,41725,77532,77578],{},[883,77477,77479],{"className":77478},[886],[888,77480,77481],{"xmlns":890},[892,77482,77483,77529],{},[895,77484,77485,77487,77493,77495,77497,77499,77501,77503,77505,77507,77509,77511,77513,77515,77517,77520,77522,77525,77527],{},[898,77486,2667],{},[2122,77488,77489,77491],{},[898,77490,3783],{},[898,77492,9641],{},[1846,77494,1855],{"stretchy":1854},[1979,77496,36089],{},[1846,77498,1861],{"stretchy":1854},[1846,77500,1848],{},[1979,77502,3357],{},[1846,77504,3025],{},[1979,77506,36089],{},[1846,77508,2075],{},[1979,77510,19166],{},[1846,77512,3025],{},[1979,77514,77457],{},[1846,77516,1848],{},[1979,77518,77519],{},"180",[1846,77521,2075],{},[1979,77523,77524],{},"135",[1846,77526,1848],{},[1979,77528,76766],{},[902,77530,77531],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,77533,77535],{"className":77534},[886],[888,77536,77537],{"xmlns":890},[892,77538,77539,77575],{},[895,77540,77541,77543,77549,77551,77553,77555,77557,77559,77565,77567,77569,77571,77573],{},[898,77542,2667],{},[2122,77544,77545,77547],{},[898,77546,3783],{},[898,77548,9641],{},[1846,77550,1855],{"stretchy":1854},[1979,77552,36089],{},[1846,77554,1861],{"stretchy":1854},[1846,77556,1848],{},[898,77558,4101],{},[2122,77560,77561,77563],{},[898,77562,3783],{},[898,77564,9641],{},[1846,77566,1855],{"stretchy":1854},[1979,77568,36089],{},[1846,77570,1861],{"stretchy":1854},[1846,77572,1848],{},[1979,77574,76766],{},[902,77576,77577],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,77580,77581,77584,77585,17421,77614,1734],{},[38,77582,77583],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,77586,77588],{"className":77587},[886],[888,77589,77590],{"xmlns":890},[892,77591,77592,77612],{},[895,77593,77594,77596,77602,77604,77606],{},[898,77595,2667],{},[2122,77597,77598,77600],{},[898,77599,3783],{},[898,77601,9641],{},[1846,77603,1848],{},[898,77605,4101],{},[2122,77607,77608,77610],{},[898,77609,3783],{},[898,77611,9641],{},[902,77613,74508],{"encoding":904},[883,77615,77617],{"className":77616},[886],[888,77618,77619],{"xmlns":890},[892,77620,77621,77661],{},[895,77622,77623,77625,77627,77629,77631,77637,77639,77641,77643,77645,77647,77653,77655,77657,77659],{},[1979,77624,3357],{},[898,77626,9641],{},[1846,77628,2075],{},[1979,77630,19166],{},[1974,77632,77633,77635],{},[898,77634,9641],{},[1979,77636,1981],{},[1846,77638,1848],{},[1979,77640,2085],{},[898,77642,9641],{},[1846,77644,2075],{},[1979,77646,2688],{},[1974,77648,77649,77651],{},[898,77650,9641],{},[1979,77652,1981],{},[1846,77654,3833],{},[898,77656,9641],{},[1846,77658,1848],{},[1979,77660,36089],{},[902,77662,77663],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,77665,77666],{},[614,77667,77668,77669,77688,77689,11973,77707,77726,77727,77745,77746,77763,77764,77783,77784,77803],{},"Obrázek 5.3 — křivky ",[883,77670,77672],{"className":77671},[886],[888,77673,77674],{"xmlns":890},[892,77675,77676,77686],{},[895,77677,77678,77680],{},[898,77679,2667],{},[2122,77681,77682,77684],{},[898,77683,3783],{},[898,77685,9641],{},[902,77687,9891],{"encoding":904}," (max 60 při ",[883,77690,77692],{"className":77691},[886],[888,77693,77694],{"xmlns":890},[892,77695,77696,77704],{},[895,77697,77698,77700,77702],{},[898,77699,9641],{},[1846,77701,1848],{},[1979,77703,2712],{},[902,77705,77706],{"encoding":904},"L=10",[883,77708,77710],{"className":77709},[886],[888,77711,77712],{"xmlns":890},[892,77713,77714,77724],{},[895,77715,77716,77718],{},[898,77717,4101],{},[2122,77719,77720,77722],{},[898,77721,3783],{},[898,77723,9641],{},[902,77725,74478],{"encoding":904}," (max 45 při ",[883,77728,77730],{"className":77729},[886],[888,77731,77732],{"xmlns":890},[892,77733,77734,77742],{},[895,77735,77736,77738,77740],{},[898,77737,9641],{},[1846,77739,1848],{},[1979,77741,36089],{},[902,77743,77744],{"encoding":904},"L=15","), průsečík v ",[883,77747,77749],{"className":77748},[886],[888,77750,77751],{"xmlns":890},[892,77752,77753,77761],{},[895,77754,77755,77757,77759],{},[898,77756,9641],{},[1846,77758,1848],{},[1979,77760,36089],{},[902,77762,77416],{"encoding":904},". Nalevo od 15 leží ",[883,77765,77767],{"className":77766},[886],[888,77768,77769],{"xmlns":890},[892,77770,77771,77781],{},[895,77772,77773,77775],{},[898,77774,2667],{},[2122,77776,77777,77779],{},[898,77778,3783],{},[898,77780,9641],{},[902,77782,9891],{"encoding":904}," nad ",[883,77785,77787],{"className":77786},[886],[888,77788,77789],{"xmlns":890},[892,77790,77791,77801],{},[895,77792,77793,77795],{},[898,77794,4101],{},[2122,77796,77797,77799],{},[898,77798,3783],{},[898,77800,9641],{},[902,77802,74478],{"encoding":904},", napravo pod ní.",[115,77805,77807],{"id":77806},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,77809,77810,77811,2535,77824,2053,77827,6036,77840,2053,77843,2554],{},"V dvoufaktorovém modelu závisí produkce ",[883,77812,77814],{"className":77813},[886],[888,77815,77816],{"xmlns":890},[892,77817,77818,77822],{},[895,77819,77820],{},[898,77821,2638],{},[902,77823,2638],{"encoding":904},[38,77825,77826],{},"práci",[883,77828,77830],{"className":77829},[886],[888,77831,77832],{"xmlns":890},[892,77833,77834,77838],{},[895,77835,77836],{},[898,77837,9641],{},[902,77839,9641],{"encoding":904},[38,77841,77842],{},"kapitálu",[883,77844,77846],{"className":77845},[886],[888,77847,77848],{"xmlns":890},[892,77849,77850,77854],{},[895,77851,77852],{},[898,77853,9646],{},[902,77855,9646],{"encoding":904},[883,77857,77859],{"className":77858},[886],[888,77860,77861],{"xmlns":890,"display":27911},[892,77862,77863,77898],{},[20599,77864,77865],{"width":27916},[20604,77866,77867,77869,77891,77893],{},[20607,77868],{"width":27921},[20607,77870,77871],{},[895,77872,77873,77875,77877,77879,77881,77883,77885,77887,77889],{},[898,77874,2638],{},[1846,77876,1848],{},[898,77878,2638],{},[1846,77880,1855],{"stretchy":1854},[898,77882,9641],{},[1846,77884,2136],{"separator":2135},[898,77886,9646],{},[1846,77888,1861],{"stretchy":1854},[898,77890,1734],{"mathvariant":2226},[20607,77892],{"width":27921},[20607,77894,77895],{},[2138,77896,77897],{},"(5.6)",[902,77899,77900],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,77902,77903,77904,77906],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,77905,74845],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,77908,77910],{"id":77909},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,77912,77913],{},"Široce používané produkční funkce mají tvar",[883,77915,77917],{"className":77916},[886],[888,77918,77919],{"xmlns":890,"display":27911},[892,77920,77921,77962],{},[20599,77922,77923],{"width":27916},[20604,77924,77925,77927,77955,77957],{},[20607,77926],{"width":27921},[20607,77928,77929],{},[895,77930,77931,77933,77935,77937,77939,77945,77947,77953],{},[898,77932,2638],{},[1846,77934,1848],{},[898,77936,4101],{},[2138,77938,2835],{},[1974,77940,77941,77943],{},[898,77942,9641],{},[898,77944,207],{},[2138,77946,2835],{},[1974,77948,77949,77951],{},[898,77950,9646],{},[898,77952,1948],{},[1846,77954,2136],{"separator":2135},[20607,77956],{"width":27921},[20607,77958,77959],{},[2138,77960,77961],{},"(5.7)",[902,77963,77964],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,77966,4156,77967,77989,77990,77992,77993,1734],{},[883,77968,77970],{"className":77969},[886],[888,77971,77972],{"xmlns":890},[892,77973,77974,77986],{},[895,77975,77976,77978,77980,77982,77984],{},[898,77977,4101],{},[1846,77979,2136],{"separator":2135},[898,77981,207],{},[1846,77983,2136],{"separator":2135},[898,77985,1948],{},[902,77987,77988],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,77991,74544],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,77994,77996],{"className":77995},[886],[888,77997,77998],{"xmlns":890},[892,77999,78000,78012],{},[895,78001,78002,78004,78006,78008,78010],{},[898,78003,207],{},[1846,78005,2136],{"separator":2135},[898,78007,1948],{},[1846,78009,3295],{},[1979,78011,2128],{},[902,78013,78014],{"encoding":904},"a, b \u003C 1",[724,78016,78017],{},[2409,78018],{"alt":78019,"className":78020,"src":78021},"imek-vynosy-z-rozsahu-3typy",[210,2413],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,78023,78024,78025,78028,78029,2535,78042,78058,78059,2535,78072,2554],{},"Reflektují ekonomickou zákonitost, že ",[38,78026,78027],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,78030,78032],{"className":78031},[886],[888,78033,78034],{"xmlns":890},[892,78035,78036,78040],{},[895,78037,78038],{},[898,78039,9641],{},[902,78041,9641],{"encoding":904},[883,78043,78045],{"className":78044},[886],[888,78046,78047],{"xmlns":890},[892,78048,78049,78055],{},[895,78050,78051,78053],{},[898,78052,11886],{},[898,78054,9641],{},[902,78056,78057],{"encoding":904},"rL"," a kapitál z ",[883,78060,78062],{"className":78061},[886],[888,78063,78064],{"xmlns":890},[892,78065,78066,78070],{},[895,78067,78068],{},[898,78069,9646],{},[902,78071,9646],{"encoding":904},[883,78073,78075],{"className":78074},[886],[888,78076,78077],{"xmlns":890},[892,78078,78079,78085],{},[895,78080,78081,78083],{},[898,78082,11886],{},[898,78084,9646],{},[902,78086,78087],{"encoding":904},"rK",[883,78089,78091],{"className":78090},[886],[888,78092,78093],{"xmlns":890,"display":27911},[892,78094,78095,78218],{},[20599,78096,78097],{"width":27916},[20604,78098,78099,78101,78211,78213],{},[20607,78100],{"width":27921},[20607,78102,78103],{},[895,78104,78105,78107,78109,78111,78113,78115,78117,78119,78121,78123,78125,78127,78129,78131,78137,78139,78141,78143,78149,78151,78153,78155,78167,78169,78175,78181,78183,78195,78197,78199,78201,78203,78205,78207,78209],{},[898,78106,2638],{},[1846,78108,1855],{"stretchy":1854},[898,78110,11886],{},[898,78112,9641],{},[1846,78114,2136],{"separator":2135},[898,78116,11886],{},[898,78118,9646],{},[1846,78120,1861],{"stretchy":1854},[1846,78122,1848],{},[898,78124,4101],{},[1846,78126,1855],{"stretchy":1854},[898,78128,11886],{},[898,78130,9641],{},[1974,78132,78133,78135],{},[1846,78134,1861],{"stretchy":1854},[898,78136,207],{},[1846,78138,1855],{"stretchy":1854},[898,78140,11886],{},[898,78142,9646],{},[1974,78144,78145,78147],{},[1846,78146,1861],{"stretchy":1854},[898,78148,1948],{},[1846,78150,1848],{},[898,78152,4101],{},[2138,78154,2835],{},[1974,78156,78157,78159],{},[898,78158,11886],{},[895,78160,78161,78163,78165],{},[898,78162,207],{},[1846,78164,1945],{},[898,78166,1948],{},[2138,78168,2835],{},[1974,78170,78171,78173],{},[898,78172,9641],{},[898,78174,207],{},[1974,78176,78177,78179],{},[898,78178,9646],{},[898,78180,1948],{},[1846,78182,1848],{},[1974,78184,78185,78187],{},[898,78186,11886],{},[895,78188,78189,78191,78193],{},[898,78190,207],{},[1846,78192,1945],{},[898,78194,1948],{},[2138,78196,2835],{},[898,78198,2638],{},[1846,78200,1855],{"stretchy":1854},[898,78202,9641],{},[1846,78204,2136],{"separator":2135},[898,78206,9646],{},[1846,78208,1861],{"stretchy":1854},[898,78210,1734],{"mathvariant":2226},[20607,78212],{"width":27921},[20607,78214,78215],{},[2138,78216,78217],{},"(5.8)",[902,78219,78220],{"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}",[724,78222,78223,78224],{},"Volně: ",[38,78225,78226,78227,78240,78241,78265],{},"změní-li se vstupy ",[883,78228,78230],{"className":78229},[886],[888,78231,78232],{"xmlns":890},[892,78233,78234,78238],{},[895,78235,78236],{},[898,78237,11886],{},[902,78239,11886],{"encoding":904},"-krát, změní se výstup ",[883,78242,78244],{"className":78243},[886],[888,78245,78246],{"xmlns":890},[892,78247,78248,78262],{},[895,78249,78250],{},[1974,78251,78252,78254],{},[898,78253,11886],{},[895,78255,78256,78258,78260],{},[898,78257,207],{},[1846,78259,1945],{},[898,78261,1948],{},[902,78263,78264],{"encoding":904},"r^{a+b}","-krát.",[198,78267,78269],{"id":78268},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,78271,78272,78273,78290],{},"Součet exponentů ",[883,78274,78276],{"className":78275},[886],[888,78277,78278],{"xmlns":890},[892,78279,78280,78288],{},[895,78281,78282,78284,78286],{},[898,78283,207],{},[1846,78285,1945],{},[898,78287,1948],{},[902,78289,74669],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,78292,78293,78322],{},[19,78294,78295],{},[22,78296,78297,78300,78303,78320],{},[25,78298,78299],{},"Typ",[25,78301,78302],{},"Podmínka",[25,78304,78305,78306,78319],{},"Chování produkce při ",[883,78307,78309],{"className":78308},[886],[888,78310,78311],{"xmlns":890},[892,78312,78313,78317],{},[895,78314,78315],{},[898,78316,11886],{},[902,78318,11886],{"encoding":904},"-násobném zvýšení vstupů",[25,78321,2918],{},[30,78323,78324,78435,78550],{},[22,78325,78326,78334,78358,78391],{},[35,78327,75382,78328,9871,78331,1861],{},[38,78329,78330],{},"Konstantní",[614,78332,78333],{},"constant returns",[35,78335,78336],{},[883,78337,78339],{"className":78338},[886],[888,78340,78341],{"xmlns":890},[892,78342,78343,78355],{},[895,78344,78345,78347,78349,78351,78353],{},[898,78346,207],{},[1846,78348,1945],{},[898,78350,1948],{},[1846,78352,1848],{},[1979,78354,2128],{},[902,78356,78357],{"encoding":904},"a+b = 1",[35,78359,78360,78373,78374,2053,78377,78390],{},[883,78361,78363],{"className":78362},[886],[888,78364,78365],{"xmlns":890},[892,78366,78367,78371],{},[895,78368,78369],{},[898,78370,2638],{},[902,78372,2638],{"encoding":904}," vzroste ",[38,78375,78376],{},"přesně",[883,78378,78380],{"className":78379},[886],[888,78381,78382],{"xmlns":890},[892,78383,78384,78388],{},[895,78385,78386],{},[898,78387,11886],{},[902,78389,11886],{"encoding":904},"-krát",[35,78392,78393],{},[883,78394,78396],{"className":78395},[886],[888,78397,78398],{"xmlns":890},[892,78399,78400,78432],{},[895,78401,78402,78404,78406,78408,78420],{},[898,78403,2638],{},[1846,78405,1848],{},[1979,78407,1981],{},[1974,78409,78410,78412],{},[898,78411,9641],{},[895,78413,78414,78416,78418],{},[1979,78415,2128],{},[898,78417,4520],{"mathvariant":2226},[1979,78419,2201],{},[1974,78421,78422,78424],{},[898,78423,9646],{},[895,78425,78426,78428,78430],{},[1979,78427,2023],{},[898,78429,4520],{"mathvariant":2226},[1979,78431,2201],{},[902,78433,78434],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,78436,78437,78446,78470,78500],{},[35,78438,78439,78440,9871,78443,1861],{},"2° ",[38,78441,78442],{},"Rostoucí",[614,78444,78445],{},"increasing returns",[35,78447,78448],{},[883,78449,78451],{"className":78450},[886],[888,78452,78453],{"xmlns":890},[892,78454,78455,78467],{},[895,78456,78457,78459,78461,78463,78465],{},[898,78458,207],{},[1846,78460,1945],{},[898,78462,1948],{},[1846,78464,3256],{},[1979,78466,2128],{},[902,78468,78469],{"encoding":904},"a+b > 1",[35,78471,78472,78373,78485,51076,78487,78390],{},[883,78473,78475],{"className":78474},[886],[888,78476,78477],{"xmlns":890},[892,78478,78479,78483],{},[895,78480,78481],{},[898,78482,2638],{},[902,78484,2638],{"encoding":904},[38,78486,25115],{},[883,78488,78490],{"className":78489},[886],[888,78491,78492],{"xmlns":890},[892,78493,78494,78498],{},[895,78495,78496],{},[898,78497,11886],{},[902,78499,11886],{"encoding":904},[35,78501,78502,9871,78528,1861],{},[883,78503,78505],{"className":78504},[886],[888,78506,78507],{"xmlns":890},[892,78508,78509,78525],{},[895,78510,78511,78513,78515,78517,78519],{},[898,78512,2638],{},[1846,78514,1848],{},[1979,78516,24046],{},[898,78518,9641],{},[1974,78520,78521,78523],{},[898,78522,9646],{},[1979,78524,1981],{},[902,78526,78527],{"encoding":904},"Q = 7LK^2",[883,78529,78531],{"className":78530},[886],[888,78532,78533],{"xmlns":890},[892,78534,78535,78547],{},[895,78536,78537,78539,78541,78543,78545],{},[898,78538,207],{},[1846,78540,1945],{},[898,78542,1948],{},[1846,78544,1848],{},[1979,78546,2023],{},[902,78548,78549],{"encoding":904},"a+b = 3",[22,78551,78552,78561,78585,78616],{},[35,78553,78554,78555,9871,78558,1861],{},"3° ",[38,78556,78557],{},"Klesající",[614,78559,78560],{},"decreasing returns",[35,78562,78563],{},[883,78564,78566],{"className":78565},[886],[888,78567,78568],{"xmlns":890},[892,78569,78570,78582],{},[895,78571,78572,78574,78576,78578,78580],{},[898,78573,207],{},[1846,78575,1945],{},[898,78577,1948],{},[1846,78579,3295],{},[1979,78581,2128],{},[902,78583,78584],{"encoding":904},"a+b \u003C 1",[35,78586,78587,78373,78600,51076,78603,78390],{},[883,78588,78590],{"className":78589},[886],[888,78591,78592],{"xmlns":890},[892,78593,78594,78598],{},[895,78595,78596],{},[898,78597,2638],{},[902,78599,2638],{"encoding":904},[38,78601,78602],{},"méně",[883,78604,78606],{"className":78605},[886],[888,78607,78608],{"xmlns":890},[892,78609,78610,78614],{},[895,78611,78612],{},[898,78613,11886],{},[902,78615,11886],{"encoding":904},[35,78617,78618,9871,78648,1861],{},[883,78619,78621],{"className":78620},[886],[888,78622,78623],{"xmlns":890},[892,78624,78625,78645],{},[895,78626,78627,78629,78631,78633,78639],{},[898,78628,2638],{},[1846,78630,1848],{},[1979,78632,2712],{},[1974,78634,78635,78637],{},[898,78636,9641],{},[1979,78638,68056],{},[1974,78640,78641,78643],{},[898,78642,9646],{},[1979,78644,4855],{},[902,78646,78647],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,78649,78651],{"className":78650},[886],[888,78652,78653],{"xmlns":890},[892,78654,78655,78667],{},[895,78656,78657,78659,78661,78663,78665],{},[898,78658,207],{},[1846,78660,1945],{},[898,78662,1948],{},[1846,78664,1848],{},[1979,78666,14434],{},[902,78668,78669],{"encoding":904},"a+b = 0{,}8",[1639,78671,78672],{},[724,78673,78674,78676,78677,78694,78695,78698,78699,2053,78702,78738,78739,78761,78762,1734],{},[883,78675,4258],{}," Pozor\nSoučet ",[883,78678,78680],{"className":78679},[886],[888,78681,78682],{"xmlns":890},[892,78683,78684,78692],{},[895,78685,78686,78688,78690],{},[898,78687,207],{},[1846,78689,1945],{},[898,78691,1948],{},[902,78693,74669],{"encoding":904}," neudává velikost produkce, ale ",[38,78696,78697],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,78700,78701],{},"ryzí Cobb-Douglas",[883,78703,78705],{"className":78704},[886],[888,78706,78707],{"xmlns":890},[892,78708,78709,78735],{},[895,78710,78711,78713,78715,78717,78723],{},[898,78712,2638],{},[1846,78714,1848],{},[898,78716,4101],{},[1974,78718,78719,78721],{},[898,78720,9641],{},[898,78722,207],{},[1974,78724,78725,78727],{},[898,78726,9646],{},[895,78728,78729,78731,78733],{},[1979,78730,2128],{},[1846,78732,2075],{},[898,78734,207],{},[902,78736,78737],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,78740,78742],{"className":78741},[886],[888,78743,78744],{"xmlns":890},[892,78745,78746,78758],{},[895,78747,78748,78750,78752,78754,78756],{},[898,78749,1948],{},[1846,78751,1848],{},[1979,78753,2128],{},[1846,78755,2075],{},[898,78757,207],{},[902,78759,78760],{"encoding":904},"b = 1-a",", tedy vždy ",[38,78763,78764],{},"konstantní výnosy z rozsahu",[198,78766,78768,78769],{"id":78767},"parametr-efektivity-aa","Parametr efektivity ",[883,78770,78772],{"className":78771},[886],[888,78773,78774],{"xmlns":890},[892,78775,78776,78780],{},[895,78777,78778],{},[898,78779,4101],{},[902,78781,4101],{"encoding":904},[724,78783,78784,78785,78798,78799,78812,78813,78831,78832,78835],{},"Konstanta ",[883,78786,78788],{"className":78787},[886],[888,78789,78790],{"xmlns":890},[892,78791,78792,78796],{},[895,78793,78794],{},[898,78795,4101],{},[902,78797,4101],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,78800,78802],{"className":78801},[886],[888,78803,78804],{"xmlns":890},[892,78805,78806,78810],{},[895,78807,78808],{},[898,78809,2638],{},[902,78811,2638],{"encoding":904}," při pevně zadaných ",[883,78814,78816],{"className":78815},[886],[888,78817,78818],{"xmlns":890},[892,78819,78820,78828],{},[895,78821,78822,78824,78826],{},[898,78823,9641],{},[1846,78825,2136],{"separator":2135},[898,78827,9646],{},[902,78829,78830],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,78833,78834],{},"parametr efektivity"," — indikátor stavu technologie.",[198,78837,78839],{"id":78838},"příklad-53","Příklad 5.3",[724,78841,78842,78843,78738,78885,78887,78888,1734],{},"Produkční funkce ",[883,78844,78846],{"className":78845},[886],[888,78847,78848],{"xmlns":890},[892,78849,78850,78882],{},[895,78851,78852,78854,78856,78858,78870],{},[898,78853,2638],{},[1846,78855,1848],{},[1979,78857,1981],{},[1974,78859,78860,78862],{},[898,78861,9641],{},[895,78863,78864,78866,78868],{},[1979,78865,2128],{},[898,78867,4520],{"mathvariant":2226},[1979,78869,2201],{},[1974,78871,78872,78874],{},[898,78873,9646],{},[895,78875,78876,78878,78880],{},[1979,78877,2023],{},[898,78879,4520],{"mathvariant":2226},[1979,78881,2201],{},[902,78883,78884],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,78886,24458],{}," výnosy z rozsahu, neboť ",[883,78889,78891],{"className":78890},[886],[888,78892,78893],{"xmlns":890},[892,78894,78895,78919],{},[895,78896,78897,78905,78907,78915,78917],{},[2175,78898,78899],{"scriptlevel":2177,"displaystyle":1854},[2179,78900,78901,78903],{},[1979,78902,2128],{},[1979,78904,2201],{},[1846,78906,1945],{},[2175,78908,78909],{"scriptlevel":2177,"displaystyle":1854},[2179,78910,78911,78913],{},[1979,78912,2023],{},[1979,78914,2201],{},[1846,78916,1848],{},[1979,78918,2128],{},[902,78920,78921],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,78923,78924,78925,6036,78938,78951,78952,2053,78965,79005],{},"Změní-li se ",[883,78926,78928],{"className":78927},[886],[888,78929,78930],{"xmlns":890},[892,78931,78932,78936],{},[895,78933,78934],{},[898,78935,9641],{},[902,78937,9641],{"encoding":904},[883,78939,78941],{"className":78940},[886],[888,78942,78943],{"xmlns":890},[892,78944,78945,78949],{},[895,78946,78947],{},[898,78948,9646],{},[902,78950,9646],{"encoding":904}," čtyřnásobně, změní se ",[883,78953,78955],{"className":78954},[886],[888,78956,78957],{"xmlns":890},[892,78958,78959,78963],{},[895,78960,78961],{},[898,78962,2638],{},[902,78964,2638],{"encoding":904},[883,78966,78968],{"className":78967},[886],[888,78969,78970],{"xmlns":890},[892,78971,78972,79002],{},[895,78973,78974,78994,78996],{},[1974,78975,78976,78978],{},[1979,78977,2201],{},[895,78979,78980,78982,78984,78986,78988,78990,78992],{},[1979,78981,2128],{},[898,78983,4520],{"mathvariant":2226},[1979,78985,2201],{},[1846,78987,1945],{},[1979,78989,2023],{},[898,78991,4520],{"mathvariant":2226},[1979,78993,2201],{},[1846,78995,1848],{},[1974,78997,78998,79000],{},[1979,78999,2201],{},[1979,79001,2128],{},[902,79003,79004],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,79007,79009],{"className":79008},[886],[888,79010,79011],{"xmlns":890,"display":27911},[892,79012,79013,79173],{},[895,79014,79015,79017,79019,79021,79023,79025,79027,79029,79031,79033,79035,79037,79039,79041,79053,79055,79057,79059,79071,79073,79075,79077,79097,79109,79121,79123,79125,79127,79129,79141,79153,79155,79157,79159,79161,79163,79165,79167,79169,79171],{},[898,79016,2638],{},[1846,79018,1855],{"stretchy":1854},[1979,79020,2201],{},[898,79022,9641],{},[1846,79024,2136],{"separator":2135},[1979,79026,2201],{},[898,79028,9646],{},[1846,79030,1861],{"stretchy":1854},[1846,79032,1848],{},[1979,79034,1981],{},[1846,79036,1855],{"stretchy":1854},[1979,79038,2201],{},[898,79040,9641],{},[1974,79042,79043,79045],{},[1846,79044,1861],{"stretchy":1854},[895,79046,79047,79049,79051],{},[1979,79048,2128],{},[898,79050,4520],{"mathvariant":2226},[1979,79052,2201],{},[1846,79054,1855],{"stretchy":1854},[1979,79056,2201],{},[898,79058,9646],{},[1974,79060,79061,79063],{},[1846,79062,1861],{"stretchy":1854},[895,79064,79065,79067,79069],{},[1979,79066,2023],{},[898,79068,4520],{"mathvariant":2226},[1979,79070,2201],{},[1846,79072,1848],{},[1979,79074,1981],{},[1846,79076,3025],{},[1974,79078,79079,79081],{},[1979,79080,2201],{},[895,79082,79083,79085,79087,79089,79091,79093,79095],{},[1979,79084,2128],{},[898,79086,4520],{"mathvariant":2226},[1979,79088,2201],{},[1846,79090,1945],{},[1979,79092,2023],{},[898,79094,4520],{"mathvariant":2226},[1979,79096,2201],{},[1974,79098,79099,79101],{},[898,79100,9641],{},[895,79102,79103,79105,79107],{},[1979,79104,2128],{},[898,79106,4520],{"mathvariant":2226},[1979,79108,2201],{},[1974,79110,79111,79113],{},[898,79112,9646],{},[895,79114,79115,79117,79119],{},[1979,79116,2023],{},[898,79118,4520],{"mathvariant":2226},[1979,79120,2201],{},[1846,79122,1848],{},[1979,79124,2201],{},[1846,79126,3025],{},[1979,79128,1981],{},[1974,79130,79131,79133],{},[898,79132,9641],{},[895,79134,79135,79137,79139],{},[1979,79136,2128],{},[898,79138,4520],{"mathvariant":2226},[1979,79140,2201],{},[1974,79142,79143,79145],{},[898,79144,9646],{},[895,79146,79147,79149,79151],{},[1979,79148,2023],{},[898,79150,4520],{"mathvariant":2226},[1979,79152,2201],{},[1846,79154,1848],{},[1979,79156,2201],{},[2138,79158,2835],{},[898,79160,2638],{},[1846,79162,1855],{"stretchy":1854},[898,79164,9641],{},[1846,79166,2136],{"separator":2135},[898,79168,9646],{},[1846,79170,1861],{"stretchy":1854},[898,79172,1734],{"mathvariant":2226},[902,79174,79175],{"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).",[198,79177,79178],{"id":37024},"Homogenita",[724,79180,79181,79182,7948,79205,79221],{},"Funkce ",[883,79183,79185],{"className":79184},[886],[888,79186,79187],{"xmlns":890},[892,79188,79189,79203],{},[895,79190,79191,79193,79195,79197,79199,79201],{},[898,79192,2638],{},[1846,79194,1855],{"stretchy":1854},[898,79196,9641],{},[1846,79198,2136],{"separator":2135},[898,79200,9646],{},[1846,79202,1861],{"stretchy":1854},[902,79204,9843],{"encoding":904},[38,79206,79207,79208],{},"homogenní stupně ",[883,79209,79211],{"className":79210},[886],[888,79212,79213],{"xmlns":890},[892,79214,79215,79219],{},[895,79216,79217],{},[898,79218,36705],{},[902,79220,36705],{"encoding":904},", jestliže",[883,79223,79225],{"className":79224},[886],[888,79226,79227],{"xmlns":890,"display":27911},[892,79228,79229,79286],{},[20599,79230,79231],{"width":27916},[20604,79232,79233,79235,79279,79281],{},[20607,79234],{"width":27921},[20607,79236,79237],{},[895,79238,79239,79241,79243,79245,79247,79249,79251,79253,79255,79257,79263,79265,79267,79269,79271,79273,79275,79277],{},[898,79240,2638],{},[1846,79242,1855],{"stretchy":1854},[898,79244,11886],{},[898,79246,9641],{},[1846,79248,2136],{"separator":2135},[898,79250,11886],{},[898,79252,9646],{},[1846,79254,1861],{"stretchy":1854},[1846,79256,1848],{},[1974,79258,79259,79261],{},[898,79260,11886],{},[898,79262,36705],{},[2138,79264,2835],{},[898,79266,2638],{},[1846,79268,1855],{"stretchy":1854},[898,79270,9641],{},[1846,79272,2136],{"separator":2135},[898,79274,9646],{},[1846,79276,1861],{"stretchy":1854},[1846,79278,2136],{"separator":2135},[20607,79280],{"width":27921},[20607,79282,79283],{},[2138,79284,79285],{},"(5.10)",[902,79287,79288],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,79290,4156,79291,79309,79310,79328,79329,43481,79342,79345,79346,1734],{},[883,79292,79294],{"className":79293},[886],[888,79295,79296],{"xmlns":890},[892,79297,79298,79306],{},[895,79299,79300,79302,79304],{},[898,79301,36705],{},[1846,79303,4331],{},[1979,79305,2177],{},[902,79307,79308],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,79311,79313],{"className":79312},[886],[888,79314,79315],{"xmlns":890},[892,79316,79317,79325],{},[895,79318,79319,79321,79323],{},[898,79320,11886],{},[1846,79322,3256],{},[1979,79324,2177],{},[902,79326,79327],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,79330,79332],{"className":79331},[886],[888,79333,79334],{"xmlns":890},[892,79335,79336,79340],{},[895,79337,79338],{},[1979,79339,2128],{},[902,79341,2128],{"encoding":904},[38,79343,79344],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,79347,79349],{"className":79348},[886],[888,79350,79351],{"xmlns":890},[892,79352,79353,79361],{},[895,79354,79355,79357,79359],{},[898,79356,207],{},[1846,79358,1945],{},[898,79360,1948],{},[902,79362,74669],{"encoding":904},[115,79364,79366],{"id":79365},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,79368,79369],{},[38,79370,79371],{},"Ryzí Cobb-Douglasovy funkce:",[883,79373,79375],{"className":79374},[886],[888,79376,79377],{"xmlns":890,"display":27911},[892,79378,79379,79438],{},[20599,79380,79381],{"width":27916},[20604,79382,79383,79385,79431,79433],{},[20607,79384],{"width":27921},[20607,79386,79387],{},[895,79388,79389,79391,79393,79395,79397,79403,79405,79417,79419,79421,79423,79425,79427,79429],{},[898,79390,2638],{},[1846,79392,1848],{},[898,79394,4101],{},[2138,79396,2835],{},[1974,79398,79399,79401],{},[898,79400,9641],{},[898,79402,207],{},[2138,79404,2835],{},[1974,79406,79407,79409],{},[898,79408,9646],{},[895,79410,79411,79413,79415],{},[1979,79412,2128],{},[1846,79414,2075],{},[898,79416,207],{},[1846,79418,2136],{"separator":2135},[5724,79420],{"width":15129},[1979,79422,2177],{},[1846,79424,3295],{},[898,79426,207],{},[1846,79428,3295],{},[1979,79430,13105],{},[20607,79432],{"width":27921},[20607,79434,79435],{},[2138,79436,79437],{},"(5.9)",[902,79439,79440],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,79442,79443,79444,79446,79447,1734],{},"Mají vždy ",[38,79445,78764],{}," a jsou ",[38,79448,79344],{},[724,79450,79451,9871,79454,79457],{},[38,79452,79453],{},"CES produkční funkce",[614,79455,79456],{},"Constant Elasticity of Substitution",", 1961):",[883,79459,79461],{"className":79460},[886],[888,79462,79463],{"xmlns":890,"display":27911},[892,79464,79465,79533],{},[895,79466,79467,79469,79471,79473,79531],{},[898,79468,2638],{},[1846,79470,1848],{},[898,79472,4101],{},[1974,79474,79475,79519],{},[895,79476,79477,79479,79481,79483,79485,79487,79489,79491,79501,79503,79505,79507,79517],{},[1846,79478,2336],{"fence":2135},[1846,79480,1855],{"stretchy":1854},[1979,79482,2128],{},[1846,79484,2075],{},[898,79486,207],{},[1846,79488,1861],{"stretchy":1854},[2138,79490,2835],{},[1974,79492,79493,79495],{},[898,79494,9641],{},[895,79496,79497,79499],{},[1846,79498,2075],{},[898,79500,1948],{},[1846,79502,1945],{},[898,79504,207],{},[2138,79506,2835],{},[1974,79508,79509,79511],{},[898,79510,9646],{},[895,79512,79513,79515],{},[1846,79514,2075],{},[898,79516,1948],{},[1846,79518,2351],{"fence":2135},[895,79520,79521,79523],{},[1846,79522,2075],{},[2175,79524,79525],{"scriptlevel":2177,"displaystyle":1854},[2179,79526,79527,79529],{},[1979,79528,2128],{},[898,79530,1948],{},[1846,79532,2136],{"separator":2135},[902,79534,79535],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,79537,4156,79538,1343,79556,1343,79577,79601],{},[883,79539,79541],{"className":79540},[886],[888,79542,79543],{"xmlns":890},[892,79544,79545,79553],{},[895,79546,79547,79549,79551],{},[898,79548,4101],{},[1846,79550,3256],{},[1979,79552,2177],{},[902,79554,79555],{"encoding":904},"A > 0",[883,79557,79559],{"className":79558},[886],[888,79560,79561],{"xmlns":890},[892,79562,79563,79575],{},[895,79564,79565,79567,79569,79571,79573],{},[1979,79566,2177],{},[1846,79568,3295],{},[898,79570,207],{},[1846,79572,3295],{},[1979,79574,2128],{},[902,79576,18681],{"encoding":904},[883,79578,79580],{"className":79579},[886],[888,79581,79582],{"xmlns":890},[892,79583,79584,79598],{},[895,79585,79586,79588,79590,79592,79594,79596],{},[1846,79587,2075],{},[1979,79589,2128],{},[1846,79591,3295],{},[898,79593,1948],{},[1846,79595,3219],{"mathvariant":2226},[1979,79597,2177],{},[902,79599,79600],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,79603,79604],{},[38,79605,79606],{},"Další typy:",[120,79608,79609,79651],{},[123,79610,79611,2053,79614,79650],{},[38,79612,79613],{},"Lineární:",[883,79615,79617],{"className":79616},[886],[888,79618,79619],{"xmlns":890},[892,79620,79621,79647],{},[895,79622,79623,79625,79627,79629,79631,79633,79635,79637,79639,79641,79643,79645],{},[898,79624,2638],{},[1846,79626,1855],{"stretchy":1854},[898,79628,9641],{},[1846,79630,2136],{"separator":2135},[898,79632,9646],{},[1846,79634,1861],{"stretchy":1854},[1846,79636,1848],{},[898,79638,207],{},[898,79640,9641],{},[1846,79642,1945],{},[898,79644,1948],{},[898,79646,9646],{},[902,79648,79649],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,79652,79653,2053,79656,79701],{},[38,79654,79655],{},"Leontiefova:",[883,79657,79659],{"className":79658},[886],[888,79660,79661],{"xmlns":890},[892,79662,79663,79698],{},[895,79664,79665,79667,79669,79671,79673,79675,79677,79679,79682,79684,79686,79688,79690,79692,79694,79696],{},[898,79666,2638],{},[1846,79668,1855],{"stretchy":1854},[898,79670,9641],{},[1846,79672,2136],{"separator":2135},[898,79674,9646],{},[1846,79676,1861],{"stretchy":1854},[1846,79678,1848],{},[898,79680,79681],{},"min",[1846,79683,56045],{},[1846,79685,1855],{"stretchy":1854},[898,79687,207],{},[898,79689,9641],{},[1846,79691,2136],{"separator":2135},[898,79693,1948],{},[898,79695,9646],{},[1846,79697,1861],{"stretchy":1854},[902,79699,79700],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,79703,79705,79706,1343,79725,79744],{"id":79704},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,79707,79709],{"className":79708},[886],[888,79710,79711],{"xmlns":890},[892,79712,79713,79723],{},[895,79714,79715,79717],{},[898,79716,2667],{},[2122,79718,79719,79721],{},[898,79720,3783],{},[898,79722,9641],{},[902,79724,9891],{"encoding":904},[883,79726,79728],{"className":79727},[886],[888,79729,79730],{"xmlns":890},[892,79731,79732,79742],{},[895,79733,79734,79736],{},[898,79735,2667],{},[2122,79737,79738,79740],{},[898,79739,3783],{},[898,79741,9646],{},[902,79743,9936],{"encoding":904}," a totální diferenciál",[724,79746,79747],{},[38,79748,79749],{},"Mezní produkt práce:",[883,79751,79753],{"className":79752},[886],[888,79754,79755],{"xmlns":890,"display":27911},[892,79756,79757,79795],{},[895,79758,79759,79761,79767,79769,79777,79779,79793],{},[898,79760,2667],{},[2122,79762,79763,79765],{},[898,79764,3783],{},[898,79766,9641],{},[1846,79768,1848],{},[9012,79770,79771,79773,79775],{},[898,79772,2638],{},[898,79774,9641],{},[1846,79776,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,79778,1848],{},[2179,79780,79781,79787],{},[895,79782,79783,79785],{},[898,79784,9718],{"mathvariant":2226},[898,79786,2638],{},[895,79788,79789,79791],{},[898,79790,9718],{"mathvariant":2226},[898,79792,9641],{},[898,79794,1734],{"mathvariant":2226},[902,79796,79797],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,79799,79800],{},[38,79801,79802],{},"Mezní produkt kapitálu:",[883,79804,79806],{"className":79805},[886],[888,79807,79808],{"xmlns":890,"display":27911},[892,79809,79810,79848],{},[895,79811,79812,79814,79820,79822,79830,79832,79846],{},[898,79813,2667],{},[2122,79815,79816,79818],{},[898,79817,3783],{},[898,79819,9646],{},[1846,79821,1848],{},[9012,79823,79824,79826,79828],{},[898,79825,2638],{},[898,79827,9646],{},[1846,79829,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,79831,1848],{},[2179,79833,79834,79840],{},[895,79835,79836,79838],{},[898,79837,9718],{"mathvariant":2226},[898,79839,2638],{},[895,79841,79842,79844],{},[898,79843,9718],{"mathvariant":2226},[898,79845,9646],{},[898,79847,1734],{"mathvariant":2226},[902,79849,79850],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,79852,79853,79883,79884,79905,79906,79924,79925,79938,79939,1734],{},[883,79854,79856],{"className":79855},[886],[888,79857,79858],{"xmlns":890},[892,79859,79860,79880],{},[895,79861,79862,79864,79870,79872,79874,79876,79878],{},[898,79863,2667],{},[2122,79865,79866,79868],{},[898,79867,3783],{},[898,79869,9641],{},[1846,79871,1855],{"stretchy":1854},[898,79873,207],{},[1846,79875,2136],{"separator":2135},[898,79877,1948],{},[1846,79879,1861],{"stretchy":1854},[902,79881,79882],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,79885,79887],{"className":79886},[886],[888,79888,79889],{"xmlns":890},[892,79890,79891,79903],{},[895,79892,79893,79895,79897,79899,79901],{},[1846,79894,2336],{"stretchy":1854},[898,79896,207],{},[1846,79898,2136],{"separator":2135},[898,79900,1948],{},[1846,79902,2351],{"stretchy":1854},[902,79904,10670],{"encoding":904}," (na hladině ",[883,79907,79909],{"className":79908},[886],[888,79910,79911],{"xmlns":890},[892,79912,79913,79921],{},[895,79914,79915,79917,79919],{},[898,79916,9646],{},[1846,79918,1848],{},[898,79920,1948],{},[902,79922,79923],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,79926,79928],{"className":79927},[886],[888,79929,79930],{"xmlns":890},[892,79931,79932,79936],{},[895,79933,79934],{},[898,79935,9641],{},[902,79937,9641],{"encoding":904},". Analogicky ",[883,79940,79942],{"className":79941},[886],[888,79943,79944],{"xmlns":890},[892,79945,79946,79966],{},[895,79947,79948,79950,79956,79958,79960,79962,79964],{},[898,79949,2667],{},[2122,79951,79952,79954],{},[898,79953,3783],{},[898,79955,9646],{},[1846,79957,1855],{"stretchy":1854},[898,79959,207],{},[1846,79961,2136],{"separator":2135},[898,79963,1948],{},[1846,79965,1861],{"stretchy":1854},[902,79967,79968],{"encoding":904},"MP_K(a, b)",[1639,79970,79971,79975],{},[724,79972,79973,51064],{},[883,79974,4001],{},[120,79976,79977,80015],{},[123,79978,79979,26034,79998],{},[883,79980,79982],{"className":79981},[886],[888,79983,79984],{"xmlns":890},[892,79985,79986,79996],{},[895,79987,79988,79990],{},[898,79989,2667],{},[2122,79991,79992,79994],{},[898,79993,3783],{},[898,79995,9641],{},[902,79997,9891],{"encoding":904},[614,79999,80000,80001,80014],{},"„o kolik vzroste ",[883,80002,80004],{"className":80003},[886],[888,80005,80006],{"xmlns":890},[892,80007,80008,80012],{},[895,80009,80010],{},[898,80011,2638],{},[902,80013,2638],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,80016,80017,26034,80036],{},[883,80018,80020],{"className":80019},[886],[888,80021,80022],{"xmlns":890},[892,80023,80024,80034],{},[895,80025,80026,80028],{},[898,80027,2667],{},[2122,80029,80030,80032],{},[898,80031,3783],{},[898,80033,9646],{},[902,80035,9936],{"encoding":904},[614,80037,80000,80038,80051],{},[883,80039,80041],{"className":80040},[886],[888,80042,80043],{"xmlns":890},[892,80044,80045,80049],{},[895,80046,80047],{},[898,80048,2638],{},[902,80050,2638],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,80053,80054,80057,80058,80073,80074,2554],{},[38,80055,80056],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,80059,80061],{"className":80060},[886],[888,80062,80063],{"xmlns":890},[892,80064,80065,80071],{},[895,80066,80067,80069],{},[898,80068,2044],{},[898,80070,9641],{},[902,80072,75201],{"encoding":904}," a kapitálu o ",[883,80075,80077],{"className":80076},[886],[888,80078,80079],{"xmlns":890},[892,80080,80081,80087],{},[895,80082,80083,80085],{},[898,80084,2044],{},[898,80086,9646],{},[902,80088,80089],{"encoding":904},"dK",[883,80091,80093],{"className":80092},[886],[888,80094,80095],{"xmlns":890,"display":27911},[892,80096,80097,80190],{},[20599,80098,80099],{"width":27916},[20604,80100,80101,80103,80183,80185],{},[20607,80102],{"width":27921},[20607,80104,80105],{},[895,80106,80107,80109,80111,80113,80115,80117,80119,80127,80129,80131,80133,80135,80143,80145,80147,80149,80151,80153,80159,80161,80163,80165,80167,80169,80175,80177,80179,80181],{},[898,80108,2738],{"mathvariant":2226},[898,80110,2638],{},[1846,80112,1650],{},[898,80114,2044],{},[898,80116,2638],{},[1846,80118,1848],{},[9012,80120,80121,80123,80125],{},[898,80122,2638],{},[898,80124,9641],{},[1846,80126,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[2138,80128,2835],{},[898,80130,2044],{},[898,80132,9641],{},[1846,80134,1945],{},[9012,80136,80137,80139,80141],{},[898,80138,2638],{},[898,80140,9646],{},[1846,80142,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[2138,80144,2835],{},[898,80146,2044],{},[898,80148,9646],{},[1846,80150,1848],{},[898,80152,2667],{},[2122,80154,80155,80157],{},[898,80156,3783],{},[898,80158,9641],{},[2138,80160,2835],{},[898,80162,2044],{},[898,80164,9641],{},[1846,80166,1945],{},[898,80168,2667],{},[2122,80170,80171,80173],{},[898,80172,3783],{},[898,80174,9646],{},[2138,80176,2835],{},[898,80178,2044],{},[898,80180,9646],{},[898,80182,1734],{"mathvariant":2226},[20607,80184],{"width":27921},[20607,80186,80187],{},[2138,80188,80189],{},"(5.11)",[902,80191,80192],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,80194,80195,80196,1734],{},"Skutečná změna: ",[883,80197,80199],{"className":80198},[886],[888,80200,80201],{"xmlns":890},[892,80202,80203,80249],{},[895,80204,80205,80207,80209,80211,80213,80215,80217,80219,80221,80223,80225,80227,80229,80231,80233,80235,80237,80239,80241,80243,80245,80247],{},[898,80206,2738],{"mathvariant":2226},[898,80208,2638],{},[1846,80210,1848],{},[898,80212,2638],{},[1846,80214,1855],{"stretchy":1854},[898,80216,9641],{},[1846,80218,1945],{},[898,80220,2044],{},[898,80222,9641],{},[1846,80224,2136],{"separator":2135},[898,80226,9646],{},[1846,80228,1945],{},[898,80230,2044],{},[898,80232,9646],{},[1846,80234,1861],{"stretchy":1854},[1846,80236,2075],{},[898,80238,2638],{},[1846,80240,1855],{"stretchy":1854},[898,80242,9641],{},[1846,80244,2136],{"separator":2135},[898,80246,9646],{},[1846,80248,1861],{"stretchy":1854},[902,80250,80251],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,80253,80254,80256,80257,80275,80276,80289,80290,80309,80310,80342,80343,80375,80376,1734],{},[38,80255,75365],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,80258,80260],{"className":80259},[886],[888,80261,80262],{"xmlns":890},[892,80263,80264,80272],{},[895,80265,80266],{},[2122,80267,80268,80270],{},[898,80269,9646],{},[1979,80271,2177],{},[902,80273,80274],{"encoding":904},"K_0"," se od jistého ",[883,80277,80279],{"className":80278},[886],[888,80280,80281],{"xmlns":890},[892,80282,80283,80287],{},[895,80284,80285],{},[898,80286,9641],{},[902,80288,9641],{"encoding":904}," stane ",[883,80291,80293],{"className":80292},[886],[888,80294,80295],{"xmlns":890},[892,80296,80297,80307],{},[895,80298,80299,80301],{},[898,80300,2667],{},[2122,80302,80303,80305],{},[898,80304,3783],{},[898,80306,9641],{},[902,80308,9891],{"encoding":904}," klesající (",[883,80311,80313],{"className":80312},[886],[888,80314,80315],{"xmlns":890},[892,80316,80317,80339],{},[895,80318,80319,80335,80337],{},[9012,80320,80321,80323,80329],{},[898,80322,2638],{},[895,80324,80325,80327],{},[898,80326,9641],{},[898,80328,9641],{},[895,80330,80331,80333],{},[1846,80332,2228],{"mathvariant":2226},[1846,80334,2228],{"mathvariant":2226},[1846,80336,3295],{},[1979,80338,2177],{},[902,80340,80341],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,80344,80346],{"className":80345},[886],[888,80347,80348],{"xmlns":890},[892,80349,80350,80372],{},[895,80351,80352,80368,80370],{},[9012,80353,80354,80356,80362],{},[898,80355,2638],{},[895,80357,80358,80360],{},[898,80359,9646],{},[898,80361,9646],{},[895,80363,80364,80366],{},[1846,80365,2228],{"mathvariant":2226},[1846,80367,2228],{"mathvariant":2226},[1846,80369,3295],{},[1979,80371,2177],{},[902,80373,80374],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,80377,80379],{"className":80378},[886],[888,80380,80381],{"xmlns":890},[892,80382,80383,80391],{},[895,80384,80385],{},[2122,80386,80387,80389],{},[898,80388,9641],{},[1979,80390,2177],{},[902,80392,75403],{"encoding":904},[115,80394,80396],{"id":80395},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,80398,80399,80402,80403,80426,80427,29789],{},[38,80400,80401],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,80404,80406],{"className":80405},[886],[888,80407,80408],{"xmlns":890},[892,80409,80410,80424],{},[895,80411,80412,80414,80416,80418,80420,80422],{},[898,80413,2638],{},[1846,80415,1855],{"stretchy":1854},[898,80417,9641],{},[1846,80419,2136],{"separator":2135},[898,80421,9646],{},[1846,80423,1861],{"stretchy":1854},[902,80425,9843],{"encoding":904}," stupně ",[883,80428,80430],{"className":80429},[886],[888,80431,80432],{"xmlns":890},[892,80433,80434,80438],{},[895,80435,80436],{},[898,80437,36705],{},[902,80439,36705],{"encoding":904},[883,80441,80443],{"className":80442},[886],[888,80444,80445],{"xmlns":890,"display":27911},[892,80446,80447,80510],{},[20599,80448,80449],{"width":27916},[20604,80450,80451,80453,80503,80505],{},[20607,80452],{"width":27921},[20607,80454,80455],{},[895,80456,80457,80459,80461,80469,80471,80473,80475,80483,80485,80487,80489,80491,80493,80495,80497,80499,80501],{},[898,80458,9641],{},[2138,80460,2835],{},[9012,80462,80463,80465,80467],{},[898,80464,2638],{},[898,80466,9641],{},[1846,80468,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,80470,1945],{},[898,80472,9646],{},[2138,80474,2835],{},[9012,80476,80477,80479,80481],{},[898,80478,2638],{},[898,80480,9646],{},[1846,80482,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,80484,1848],{},[898,80486,36705],{},[2138,80488,2835],{},[898,80490,2638],{},[1846,80492,1855],{"stretchy":1854},[898,80494,9641],{},[1846,80496,2136],{"separator":2135},[898,80498,9646],{},[1846,80500,1861],{"stretchy":1854},[898,80502,1734],{"mathvariant":2226},[20607,80504],{"width":27921},[20607,80506,80507],{},[2138,80508,80509],{},"(5.12)",[902,80511,80512],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,80514,80515,80536],{},[38,80516,80517,80518],{},"Speciální případ ",[883,80519,80521],{"className":80520},[886],[888,80522,80523],{"xmlns":890},[892,80524,80525,80533],{},[895,80526,80527,80529,80531],{},[898,80528,36705],{},[1846,80530,1848],{},[1979,80532,2128],{},[902,80534,80535],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,80538,80540],{"className":80539},[886],[888,80541,80542],{"xmlns":890,"display":27911},[892,80543,80544,80588],{},[895,80545,80546,80548,80550,80552,80558,80560,80562,80564,80566,80572,80574,80576,80578,80580,80582,80584,80586],{},[898,80547,9641],{},[1846,80549,3025],{},[898,80551,2667],{},[2122,80553,80554,80556],{},[898,80555,3783],{},[898,80557,9641],{},[1846,80559,1945],{},[898,80561,9646],{},[1846,80563,3025],{},[898,80565,2667],{},[2122,80567,80568,80570],{},[898,80569,3783],{},[898,80571,9646],{},[1846,80573,1848],{},[898,80575,2638],{},[1846,80577,1855],{"stretchy":1854},[898,80579,9641],{},[1846,80581,2136],{"separator":2135},[898,80583,9646],{},[1846,80585,1861],{"stretchy":1854},[898,80587,1734],{"mathvariant":2226},[902,80589,80590],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,80592,80593,80594,80597],{},"Slovně — ",[38,80595,80596],{},"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).",[115,80599,9624],{"id":74739},[724,80601,80602,9871,80604,80607,80608,80630,80631,2554],{},[38,80603,9624],{},[614,80605,80606],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,80609,80611],{"className":80610},[886],[888,80612,80613],{"xmlns":890},[892,80614,80615,80627],{},[895,80616,80617,80619,80621,80623,80625],{},[1846,80618,2336],{"stretchy":1854},[898,80620,9641],{},[1846,80622,2136],{"separator":2135},[898,80624,9646],{},[1846,80626,2351],{"stretchy":1854},[902,80628,80629],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,80632,80634],{"className":80633},[886],[888,80635,80636],{"xmlns":890},[892,80637,80638,80643],{},[895,80639,80640],{},[898,80641,80642],{},"q",[902,80644,80642],{"encoding":904},[883,80646,80648],{"className":80647},[886],[888,80649,80650],{"xmlns":890,"display":27911},[892,80651,80652,80687],{},[20599,80653,80654],{"width":27916},[20604,80655,80656,80658,80680,80682],{},[20607,80657],{"width":27921},[20607,80659,80660],{},[895,80661,80662,80664,80666,80668,80670,80672,80674,80676,80678],{},[898,80663,2638],{},[1846,80665,1855],{"stretchy":1854},[898,80667,9641],{},[1846,80669,2136],{"separator":2135},[898,80671,9646],{},[1846,80673,1861],{"stretchy":1854},[1846,80675,1848],{},[898,80677,80642],{},[898,80679,1734],{"mathvariant":2226},[20607,80681],{"width":27921},[20607,80683,80684],{},[2138,80685,80686],{},"(5.13)",[902,80688,80689],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,80691,80692,80693,80696,80697,3764],{},"Jsou to ",[38,80694,80695],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,80698,80700],{"className":80699,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,80702,80703],{},[38,80704,80705],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,80707,80708,80713,80718,80723],{},[123,80709,80710,80712],{},[38,80711,12364],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,80714,80715,80717],{},[38,80716,37509],{}," (úloha 5.14);",[123,80719,80720,8271],{},[38,80721,80722],{},"neprotínají se",[123,80724,80725,80726,4204,80739,1734],{},"s rostoucím ",[883,80727,80729],{"className":80728},[886],[888,80730,80731],{"xmlns":890},[892,80732,80733,80737],{},[895,80734,80735],{},[898,80736,80642],{},[902,80738,80642],{"encoding":904},[38,80740,80741],{},"vzdalují od počátku",[724,80743,80744],{},[614,80745,80746,80747,80769,80770,1734],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,80748,80750],{"className":80749},[886],[888,80751,80752],{"xmlns":890},[892,80753,80754,80766],{},[895,80755,80756,80758,80760,80762,80764],{},[1846,80757,1855],{"stretchy":1854},[898,80759,9641],{},[1846,80761,2136],{"separator":2135},[898,80763,9646],{},[1846,80765,1861],{"stretchy":1854},[902,80767,80768],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,80771,80773],{"className":80772},[886],[888,80774,80775],{"xmlns":890},[892,80776,80777,80801],{},[895,80778,80779,80785,80787,80793,80795],{},[2122,80780,80781,80783],{},[898,80782,80642],{},[1979,80784,2128],{},[1846,80786,3295],{},[2122,80788,80789,80791],{},[898,80790,80642],{},[1979,80792,2177],{},[1846,80794,3295],{},[2122,80796,80797,80799],{},[898,80798,80642],{},[1979,80800,1981],{},[902,80802,80803],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,80805,80807,80808,1861],{"id":80806},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,80809,80811],{"className":80810},[886],[888,80812,80813],{"xmlns":890},[892,80814,80815,80825],{},[895,80816,80817,80819,80821,80823],{},[898,80818,2667],{},[898,80820,3840],{},[898,80822,2623],{},[898,80824,8519],{},[902,80826,10445],{"encoding":904},[724,80828,80829,9871,80832,80835],{},[38,80830,80831],{},"Mezní míra technické substituce",[614,80833,80834],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,80837,80839],{"className":80838},[886],[888,80840,80841],{"xmlns":890,"display":27911},[892,80842,80843,80934],{},[20599,80844,80845],{"width":27916},[20604,80846,80847,80849,80927,80929],{},[20607,80848],{"width":27921},[20607,80850,80851],{},[895,80852,80853,80855,80857,80859,80861,80863,80865,80867,80869,80871,80873,80875,80877,80879,80881,80883,80905,80907,80925],{},[898,80854,2667],{},[898,80856,3840],{},[898,80858,2623],{},[898,80860,8519],{},[1846,80862,1848],{},[898,80864,2667],{},[898,80866,3840],{},[898,80868,2623],{},[898,80870,8519],{},[1846,80872,1855],{"stretchy":1854},[898,80874,9641],{},[1846,80876,2136],{"separator":2135},[898,80878,9646],{},[1846,80880,1861],{"stretchy":1854},[1846,80882,1848],{},[2179,80884,80885,80895],{},[895,80886,80887,80889],{},[898,80888,2667],{},[2122,80890,80891,80893],{},[898,80892,3783],{},[898,80894,9641],{},[895,80896,80897,80899],{},[898,80898,2667],{},[2122,80900,80901,80903],{},[898,80902,3783],{},[898,80904,9646],{},[1846,80906,1848],{},[2179,80908,80909,80917],{},[9012,80910,80911,80913,80915],{},[898,80912,2638],{},[898,80914,9641],{},[1846,80916,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[9012,80918,80919,80921,80923],{},[898,80920,2638],{},[898,80922,9646],{},[1846,80924,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[898,80926,1734],{"mathvariant":2226},[20607,80928],{"width":27921},[20607,80930,80931],{},[2138,80932,80933],{},"(5.14)",[902,80935,80936],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,80938,80939,2053,80941,80971,80972,81003],{},[38,80940,9062],{},[883,80942,80944],{"className":80943},[886],[888,80945,80946],{"xmlns":890},[892,80947,80948,80968],{},[895,80949,80950,80952,80954,80956,80958,80960,80962,80964,80966],{},[898,80951,2667],{},[898,80953,3840],{},[898,80955,2623],{},[898,80957,8519],{},[1846,80959,1855],{"stretchy":1854},[898,80961,9641],{},[1846,80963,2136],{"separator":2135},[898,80965,9646],{},[1846,80967,1861],{"stretchy":1854},[902,80969,80970],{"encoding":904},"MRTS(L, K)"," udává, ",[38,80973,80974,80975,80988,80989,81002],{},"o kolik se musí přibližně změnit kapitál ",[883,80976,80978],{"className":80977},[886],[888,80979,80980],{"xmlns":890},[892,80981,80982,80986],{},[895,80983,80984],{},[898,80985,9646],{},[902,80987,9646],{"encoding":904},", jestliže se práce ",[883,80990,80992],{"className":80991},[886],[888,80993,80994],{"xmlns":890},[892,80995,80996,81000],{},[895,80997,80998],{},[898,80999,9641],{},[902,81001,9641],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[1639,81005,81006],{},[724,81007,81008,17868,81010,81029,81030,81067,81068,81071,81072,81076],{},[883,81009,4001],{},[883,81011,81013],{"className":81012},[886],[888,81014,81015],{"xmlns":890},[892,81016,81017,81027],{},[895,81018,81019,81021,81023,81025],{},[898,81020,2667],{},[898,81022,3840],{},[898,81024,2623],{},[898,81026,8519],{},[902,81028,10445],{"encoding":904}," říká: ",[614,81031,81032,81033,81052,81053,81066],{},"„jednu jednotku práce musím nahradit přibližně ",[883,81034,81036],{"className":81035},[886],[888,81037,81038],{"xmlns":890},[892,81039,81040,81050],{},[895,81041,81042,81044,81046,81048],{},[898,81043,2667],{},[898,81045,3840],{},[898,81047,2623],{},[898,81049,8519],{},[902,81051,10445],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,81054,81056],{"className":81055},[886],[888,81057,81058],{"xmlns":890},[892,81059,81060,81064],{},[895,81061,81062],{},[898,81063,2638],{},[902,81065,2638],{"encoding":904}," zůstala stejná.\""," Je to ",[38,81069,81070],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,81073,81075],{"className":81074,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,81078,81079],{},[2409,81080],{"alt":81081,"className":81082,"src":81083},"imek-izokvanty-mrts",[210,2413],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,81085,81086,81089,81090,7948,81120,81142,81143,2999],{},[38,81087,81088],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,81091,81093],{"className":81092},[886],[888,81094,81095],{"xmlns":890},[892,81096,81097,81117],{},[895,81098,81099,81101,81107,81109,81115],{},[1846,81100,2336],{"stretchy":1854},[2122,81102,81103,81105],{},[898,81104,9641],{},[1979,81106,2177],{},[1846,81108,2136],{"separator":2135},[2122,81110,81111,81113],{},[898,81112,9646],{},[1979,81114,2177],{},[1846,81116,2351],{"stretchy":1854},[902,81118,81119],{"encoding":904},"[L_0, K_0]",[883,81121,81123],{"className":81122},[886],[888,81124,81125],{"xmlns":890},[892,81126,81127,81139],{},[895,81128,81129,81131,81133,81135,81137],{},[1846,81130,2075],{},[898,81132,2667],{},[898,81134,3840],{},[898,81136,2623],{},[898,81138,8519],{},[902,81140,81141],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,81144,81146],{"className":81145},[886],[888,81147,81148],{"xmlns":890},[892,81149,81150,81172],{},[895,81151,81152,81154,81156,81158,81160,81162,81164,81166],{},[898,81153,2638],{},[1846,81155,1855],{"stretchy":1854},[898,81157,9641],{},[1846,81159,2136],{"separator":2135},[898,81161,9646],{},[1846,81163,1861],{"stretchy":1854},[1846,81165,1848],{},[2122,81167,81168,81170],{},[898,81169,80642],{},[1979,81171,2177],{},[902,81173,81174],{"encoding":904},"Q(L,K) = q_0",[883,81176,81178],{"className":81177},[886],[888,81179,81180],{"xmlns":890,"display":27911},[892,81181,81182,81234],{},[895,81183,81184,81198,81200,81202,81220,81222,81224,81226,81228,81230,81232],{},[2179,81185,81186,81192],{},[895,81187,81188,81190],{},[898,81189,2044],{},[898,81191,9646],{},[895,81193,81194,81196],{},[898,81195,2044],{},[898,81197,9641],{},[1846,81199,1848],{},[1846,81201,2075],{},[2179,81203,81204,81212],{},[9012,81205,81206,81208,81210],{},[898,81207,2638],{},[898,81209,9641],{},[1846,81211,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[9012,81213,81214,81216,81218],{},[898,81215,2638],{},[898,81217,9646],{},[1846,81219,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,81221,1848],{},[1846,81223,2075],{},[898,81225,2667],{},[898,81227,3840],{},[898,81229,2623],{},[898,81231,8519],{},[898,81233,1734],{"mathvariant":2226},[902,81235,81236],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,81238,81239,81240,81255,81256,81272],{},"Změní-li se práce o ",[883,81241,81243],{"className":81242},[886],[888,81244,81245],{"xmlns":890},[892,81246,81247,81253],{},[895,81248,81249,81251],{},[898,81250,2044],{},[898,81252,9641],{},[902,81254,75201],{"encoding":904},", lze pro odhad změny kapitálu ",[883,81257,81259],{"className":81258},[886],[888,81260,81261],{"xmlns":890},[892,81262,81263,81269],{},[895,81264,81265,81267],{},[898,81266,2738],{"mathvariant":2226},[898,81268,9646],{},[902,81270,81271],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,81274,81276],{"className":81275},[886],[888,81277,81278],{"xmlns":890,"display":27911},[892,81279,81280,81327],{},[20599,81281,81282],{"width":27916},[20604,81283,81284,81286,81320,81322],{},[20607,81285],{"width":27921},[20607,81287,81288],{},[895,81289,81290,81292,81294,81296,81298,81300,81302,81304,81306,81308,81310,81312,81314,81316,81318],{},[898,81291,2738],{"mathvariant":2226},[898,81293,9646],{},[1846,81295,1650],{},[898,81297,2044],{},[898,81299,9646],{},[1846,81301,1848],{},[1846,81303,2075],{},[898,81305,2667],{},[898,81307,3840],{},[898,81309,2623],{},[898,81311,8519],{},[2138,81313,2835],{},[898,81315,2044],{},[898,81317,9641],{},[1846,81319,2136],{"separator":2135},[20607,81321],{"width":27921},[20607,81323,81324],{},[2138,81325,81326],{},"(5.15)",[902,81328,81329],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,81331,81333],{"className":81332},[886],[888,81334,81335],{"xmlns":890,"display":27911},[892,81336,81337,81386],{},[20599,81338,81339],{"width":27916},[20604,81340,81341,81343,81379,81381],{},[20607,81342],{"width":27921},[20607,81344,81345],{},[895,81346,81347,81349,81351,81353,81371,81373,81375,81377],{},[898,81348,2044],{},[898,81350,9641],{},[1846,81352,1848],{},[2179,81354,81355,81361],{},[895,81356,81357,81359],{},[1846,81358,2075],{},[1979,81360,2128],{},[895,81362,81363,81365,81367,81369],{},[898,81364,2667],{},[898,81366,3840],{},[898,81368,2623],{},[898,81370,8519],{},[2138,81372,2835],{},[898,81374,2044],{},[898,81376,9646],{},[898,81378,1734],{"mathvariant":2226},[20607,81380],{"width":27921},[20607,81382,81383],{},[2138,81384,81385],{},"(5.16)",[902,81387,81388],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[1639,81390,81391,81415],{},[724,81392,81393,81395,81396],{},[883,81394,4418],{}," Postup — jak spočítat ",[883,81397,81399],{"className":81398},[886],[888,81400,81401],{"xmlns":890},[892,81402,81403,81413],{},[895,81404,81405,81407,81409,81411],{},[898,81406,2667],{},[898,81408,3840],{},[898,81410,2623],{},[898,81412,8519],{},[902,81414,10445],{"encoding":904},[152,81416,81417,81458,81501,81533],{},[123,81418,81419,81420,1745,81439,1734],{},"Vypočtěte parciální derivace ",[883,81421,81423],{"className":81422},[886],[888,81424,81425],{"xmlns":890},[892,81426,81427,81437],{},[895,81428,81429],{},[9012,81430,81431,81433,81435],{},[898,81432,2638],{},[898,81434,9641],{},[1846,81436,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,81438,9867],{"encoding":904},[883,81440,81442],{"className":81441},[886],[888,81443,81444],{"xmlns":890},[892,81445,81446,81456],{},[895,81447,81448],{},[9012,81449,81450,81452,81454],{},[898,81451,2638],{},[898,81453,9646],{},[1846,81455,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,81457,9913],{"encoding":904},[123,81459,65686,81460,81500],{},[883,81461,81463],{"className":81462},[886],[888,81464,81465],{"xmlns":890},[892,81466,81467,81497],{},[895,81468,81469,81471,81473,81475,81477,81479,81487,81489],{},[898,81470,2667],{},[898,81472,3840],{},[898,81474,2623],{},[898,81476,8519],{},[1846,81478,1848],{},[9012,81480,81481,81483,81485],{},[898,81482,2638],{},[898,81484,9641],{},[1846,81486,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[898,81488,4520],{"mathvariant":2226},[9012,81490,81491,81493,81495],{},[898,81492,2638],{},[898,81494,9646],{},[1846,81496,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,81498,81499],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,81502,81503,81504,1734],{},"Případně dosaďte konkrétní ",[883,81505,81507],{"className":81506},[886],[888,81508,81509],{"xmlns":890},[892,81510,81511,81531],{},[895,81512,81513,81515,81521,81523,81529],{},[1846,81514,2336],{"stretchy":1854},[2122,81516,81517,81519],{},[898,81518,9641],{},[1979,81520,2177],{},[1846,81522,2136],{"separator":2135},[2122,81524,81525,81527],{},[898,81526,9646],{},[1979,81528,2177],{},[1846,81530,2351],{"stretchy":1854},[902,81532,81119],{"encoding":904},[123,81534,81535,81536,81570,81571,81573],{},"Pro odhad substituce použijte ",[883,81537,81539],{"className":81538},[886],[888,81540,81541],{"xmlns":890},[892,81542,81543,81567],{},[895,81544,81545,81547,81549,81551,81553,81555,81557,81559,81561,81563,81565],{},[898,81546,2738],{"mathvariant":2226},[898,81548,9646],{},[1846,81550,1650],{},[1846,81552,2075],{},[898,81554,2667],{},[898,81556,3840],{},[898,81558,2623],{},[898,81560,8519],{},[1846,81562,3025],{},[898,81564,2738],{"mathvariant":2226},[898,81566,9641],{},[902,81568,81569],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,81572,52451],{}," — substituce, ne doplnění).",[724,81575,81576],{},[614,81577,81578,81579,81611,81612,2474,81625,15637,81654,81669],{},"Obrázek 5.7 — izokvanta ",[883,81580,81582],{"className":81581},[886],[888,81583,81584],{"xmlns":890},[892,81585,81586,81608],{},[895,81587,81588,81594,81596,81598,81600,81602,81604,81606],{},[2122,81589,81590,81592],{},[898,81591,80642],{},[1979,81593,2177],{},[1846,81595,1848],{},[898,81597,2638],{},[1846,81599,1855],{"stretchy":1854},[898,81601,9641],{},[1846,81603,2136],{"separator":2135},[898,81605,9646],{},[1846,81607,1861],{"stretchy":1854},[902,81609,81610],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,81613,81615],{"className":81614},[886],[888,81616,81617],{"xmlns":890},[892,81618,81619,81623],{},[895,81620,81621],{},[898,81622,18700],{},[902,81624,18700],{"encoding":904},[883,81626,81628],{"className":81627},[886],[888,81629,81630],{"xmlns":890},[892,81631,81632,81652],{},[895,81633,81634,81636,81642,81644,81650],{},[1846,81635,2336],{"stretchy":1854},[2122,81637,81638,81640],{},[898,81639,9641],{},[1979,81641,2177],{},[1846,81643,2136],{"separator":2135},[2122,81645,81646,81648],{},[898,81647,9646],{},[1979,81649,2177],{},[1846,81651,2351],{"stretchy":1854},[902,81653,81119],{"encoding":904},[883,81655,81657],{"className":81656},[886],[888,81658,81659],{"xmlns":890},[892,81660,81661,81667],{},[895,81662,81663,81665],{},[898,81664,2738],{"mathvariant":2226},[898,81666,9646],{},[902,81668,81271],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,81671,81673],{"id":81672},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,81675,81677],{"id":81676},"příklad-54","Příklad 5.4",[724,81679,76518,81680,1343,81722,1343,81739,1734],{},[883,81681,81683],{"className":81682},[886],[888,81684,81685],{"xmlns":890},[892,81686,81687,81719],{},[895,81688,81689,81691,81693,81695,81707],{},[898,81690,2638],{},[1846,81692,1848],{},[1979,81694,36089],{},[1974,81696,81697,81699],{},[898,81698,9641],{},[895,81700,81701,81703,81705],{},[1979,81702,2128],{},[898,81704,4520],{"mathvariant":2226},[1979,81706,1981],{},[1974,81708,81709,81711],{},[898,81710,9646],{},[895,81712,81713,81715,81717],{},[1979,81714,2128],{},[898,81716,4520],{"mathvariant":2226},[1979,81718,2023],{},[902,81720,81721],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,81723,81725],{"className":81724},[886],[888,81726,81727],{"xmlns":890},[892,81728,81729,81737],{},[895,81730,81731,81733,81735],{},[898,81732,9641],{},[1846,81734,1848],{},[1979,81736,8881],{},[902,81738,76892],{"encoding":904},[883,81740,81742],{"className":81741},[886],[888,81743,81744],{"xmlns":890},[892,81745,81746,81754],{},[895,81747,81748,81750,81752],{},[898,81749,9646],{},[1846,81751,1848],{},[1979,81753,2938],{},[902,81755,81756],{"encoding":904},"K = 100",[724,81758,81759],{},[38,81760,81761],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,81763,81765],{"className":81764},[886],[888,81766,81767],{"xmlns":890,"display":27911},[892,81768,81769,81883],{},[895,81770,81771,81773,81779,81781,81789,81791,81799,81813,81825,81827,81829,81831,81837,81839,81841,81843,81845,81847,81849,81857,81859,81869,81871,81878,81880],{},[898,81772,2667],{},[2122,81774,81775,81777],{},[898,81776,3783],{},[898,81778,9641],{},[1846,81780,1848],{},[9012,81782,81783,81785,81787],{},[898,81784,2638],{},[898,81786,9641],{},[1846,81788,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,81790,1848],{},[2175,81792,81793],{"scriptlevel":2177,"displaystyle":1854},[2179,81794,81795,81797],{},[1979,81796,36089],{},[1979,81798,1981],{},[1974,81800,81801,81803],{},[898,81802,9641],{},[895,81804,81805,81807,81809,81811],{},[1846,81806,2075],{},[1979,81808,2128],{},[898,81810,4520],{"mathvariant":2226},[1979,81812,1981],{},[1974,81814,81815,81817],{},[898,81816,9646],{},[895,81818,81819,81821,81823],{},[1979,81820,2128],{},[898,81822,4520],{"mathvariant":2226},[1979,81824,2023],{},[1846,81826,2136],{"separator":2135},[5724,81828],{"width":15129},[898,81830,2667],{},[2122,81832,81833,81835],{},[898,81834,3783],{},[898,81836,9641],{},[1846,81838,1855],{"stretchy":1854},[1979,81840,8881],{},[1846,81842,2136],{"separator":2135},[1979,81844,2938],{},[1846,81846,1861],{"stretchy":1854},[1846,81848,1848],{},[2175,81850,81851],{"scriptlevel":2177,"displaystyle":1854},[2179,81852,81853,81855],{},[1979,81854,36089],{},[1979,81856,1981],{},[1846,81858,3025],{},[2175,81860,81861],{"scriptlevel":2177,"displaystyle":1854},[2179,81862,81863,81865],{},[1979,81864,2128],{},[7963,81866,81867],{},[1979,81868,8881],{},[1846,81870,3025],{},[81872,81873,81874,81876],"mroot",{},[1979,81875,2938],{},[1979,81877,2023],{},[1846,81879,1650],{},[1979,81881,81882],{},"7,153.",[902,81884,81885],{"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.",[724,81887,81888,81889,44005,81911,10079,81928,81949,81950,81971],{},"Přibližná změna při ",[883,81890,81892],{"className":81891},[886],[888,81893,81894],{"xmlns":890},[892,81895,81896,81908],{},[895,81897,81898,81900,81902,81904,81906],{},[898,81899,9641],{},[1846,81901,2554],{},[1979,81903,8881],{},[1846,81905,2971],{},[1979,81907,38191],{},[902,81909,81910],{"encoding":904},"L: 20 \\to 21",[883,81912,81914],{"className":81913},[886],[888,81915,81916],{"xmlns":890},[892,81917,81918,81926],{},[895,81919,81920,81922,81924],{},[898,81921,9646],{},[1846,81923,1848],{},[1979,81925,2938],{},[902,81927,81756],{"encoding":904},[883,81929,81931],{"className":81930},[886],[888,81932,81933],{"xmlns":890},[892,81934,81935,81946],{},[895,81936,81937,81939,81941,81943],{},[898,81938,2738],{"mathvariant":2226},[898,81940,2638],{},[1846,81942,1650],{},[1979,81944,81945],{},"7,153",[902,81947,81948],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,81951,81953],{"className":81952},[886],[888,81954,81955],{"xmlns":890},[892,81956,81957,81968],{},[895,81958,81959,81961,81963,81965],{},[898,81960,2738],{"mathvariant":2226},[898,81962,2638],{},[1846,81964,1650],{},[1979,81966,81967],{},"26,888",[902,81969,81970],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,81973,81974,81977],{},[38,81975,81976],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,81979,81981],{"className":81980},[886],[888,81982,81983],{"xmlns":890,"display":27911},[892,81984,81985,82085],{},[895,81986,81987,81989,81995,81997,82005,82007,82009,82021,82035,82037,82039,82041,82047,82049,82051,82053,82055,82057,82059,82061,82065,82067,82080,82082],{},[898,81988,2667],{},[2122,81990,81991,81993],{},[898,81992,3783],{},[898,81994,9646],{},[1846,81996,1848],{},[9012,81998,81999,82001,82003],{},[898,82000,2638],{},[898,82002,9646],{},[1846,82004,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,82006,1848],{},[1979,82008,2078],{},[1974,82010,82011,82013],{},[898,82012,9641],{},[895,82014,82015,82017,82019],{},[1979,82016,2128],{},[898,82018,4520],{"mathvariant":2226},[1979,82020,1981],{},[1974,82022,82023,82025],{},[898,82024,9646],{},[895,82026,82027,82029,82031,82033],{},[1846,82028,2075],{},[1979,82030,1981],{},[898,82032,4520],{"mathvariant":2226},[1979,82034,2023],{},[1846,82036,2136],{"separator":2135},[5724,82038],{"width":15129},[898,82040,2667],{},[2122,82042,82043,82045],{},[898,82044,3783],{},[898,82046,9646],{},[1846,82048,1855],{"stretchy":1854},[1979,82050,8881],{},[1846,82052,2136],{"separator":2135},[1979,82054,2938],{},[1846,82056,1861],{"stretchy":1854},[1846,82058,1848],{},[1979,82060,2078],{},[7963,82062,82063],{},[1979,82064,8881],{},[1846,82066,3025],{},[2175,82068,82069],{"scriptlevel":2177,"displaystyle":1854},[2179,82070,82071,82073],{},[1979,82072,2128],{},[81872,82074,82075,82078],{},[1979,82076,82077],{},"10000",[1979,82079,2023],{},[1846,82081,1650],{},[1979,82083,82084],{},"4,525.",[902,82086,82087],{"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.",[724,82089,82090,82091,2535,82108,3764],{},"Produkce poklesne přibližně o 4,525 (z ",[883,82092,82094],{"className":82093},[886],[888,82095,82096],{"xmlns":890},[892,82097,82098,82105],{},[895,82099,82100,82102],{},[1846,82101,1650],{},[1979,82103,82104],{},"905,126",[902,82106,82107],{"encoding":904},"\\approx 905{,}126",[883,82109,82111],{"className":82110},[886],[888,82112,82113],{"xmlns":890},[892,82114,82115,82122],{},[895,82116,82117,82119],{},[1846,82118,1650],{},[1979,82120,82121],{},"900,601",[902,82123,82124],{"encoding":904},"\\approx 900{,}601",[724,82126,82127,2978,82174,1343,82196,3764],{},[38,82128,82129,82130,1745,82152],{},"(c) Změna ",[883,82131,82133],{"className":82132},[886],[888,82134,82135],{"xmlns":890},[892,82136,82137,82149],{},[895,82138,82139,82141,82143,82145,82147],{},[898,82140,9641],{},[1846,82142,2554],{},[1979,82144,8881],{},[1846,82146,2971],{},[1979,82148,36089],{},[902,82150,82151],{"encoding":904},"L: 20 \\to 15",[883,82153,82155],{"className":82154},[886],[888,82156,82157],{"xmlns":890},[892,82158,82159,82171],{},[895,82160,82161,82163,82165,82167,82169],{},[898,82162,9646],{},[1846,82164,2554],{},[1979,82166,2938],{},[1846,82168,2971],{},[1979,82170,8649],{},[902,82172,82173],{"encoding":904},"K: 100 \\to 150",[883,82175,82177],{"className":82176},[886],[888,82178,82179],{"xmlns":890},[892,82180,82181,82193],{},[895,82182,82183,82185,82187,82189,82191],{},[898,82184,2044],{},[898,82186,9641],{},[1846,82188,1848],{},[1846,82190,2075],{},[1979,82192,2078],{},[902,82194,82195],{"encoding":904},"dL = -5",[883,82197,82199],{"className":82198},[886],[888,82200,82201],{"xmlns":890},[892,82202,82203,82213],{},[895,82204,82205,82207,82209,82211],{},[898,82206,2044],{},[898,82208,9646],{},[1846,82210,1848],{},[1979,82212,2968],{},[902,82214,82215],{"encoding":904},"dK = 50",[883,82217,82219],{"className":82218},[886],[888,82220,82221],{"xmlns":890,"display":27911},[892,82222,82223,82311],{},[895,82224,82225,82227,82229,82231,82233,82239,82241,82243,82245,82247,82249,82251,82253,82255,82257,82259,82261,82263,82269,82271,82273,82275,82277,82279,82281,82283,82285,82287,82289,82291,82293,82295,82297,82299,82302,82304,82306,82308],{},[898,82226,2044],{},[898,82228,2638],{},[1846,82230,1848],{},[898,82232,2667],{},[2122,82234,82235,82237],{},[898,82236,3783],{},[898,82238,9641],{},[1846,82240,1855],{"stretchy":1854},[1979,82242,8881],{},[1846,82244,2136],{"separator":2135},[1979,82246,2938],{},[1846,82248,1861],{"stretchy":1854},[1846,82250,3025],{},[1846,82252,1855],{"stretchy":1854},[1846,82254,2075],{},[1979,82256,2078],{},[1846,82258,1861],{"stretchy":1854},[1846,82260,1945],{},[898,82262,2667],{},[2122,82264,82265,82267],{},[898,82266,3783],{},[898,82268,9646],{},[1846,82270,1855],{"stretchy":1854},[1979,82272,8881],{},[1846,82274,2136],{"separator":2135},[1979,82276,2938],{},[1846,82278,1861],{"stretchy":1854},[1846,82280,3025],{},[1979,82282,2968],{},[1846,82284,1848],{},[1979,82286,81945],{},[1846,82288,3025],{},[1846,82290,1855],{"stretchy":1854},[1846,82292,2075],{},[1979,82294,2078],{},[1846,82296,1861],{"stretchy":1854},[1846,82298,1945],{},[1979,82300,82301],{},"4,525",[1846,82303,3025],{},[1979,82305,2968],{},[1846,82307,1650],{},[1979,82309,82310],{},"190,485.",[902,82312,82313],{"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.",[724,82315,82316],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,82318,82320],{"id":82319},"příklad-55","Příklad 5.5",[724,82322,82323,82324,82360,82361,1734],{},"Pro produkci ",[883,82325,82327],{"className":82326},[886],[888,82328,82329],{"xmlns":890},[892,82330,82331,82357],{},[895,82332,82333,82335,82337,82339,82341,82343,82345,82347,82353],{},[898,82334,2638],{},[1846,82336,1855],{"stretchy":1854},[898,82338,9641],{},[1846,82340,2136],{"separator":2135},[898,82342,9646],{},[1846,82344,1861],{"stretchy":1854},[1846,82346,1848],{},[81872,82348,82349,82351],{},[898,82350,9641],{},[1979,82352,2023],{},[7963,82354,82355],{},[898,82356,9646],{},[902,82358,82359],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,82362,82364],{"className":82363},[886],[888,82365,82366],{"xmlns":890},[892,82367,82368,82384],{},[895,82369,82370,82376,82380,82382],{},[81872,82371,82372,82374],{},[898,82373,9641],{},[1979,82375,2023],{},[7963,82377,82378],{},[898,82379,9646],{},[1846,82381,1848],{},[898,82383,80642],{},[902,82385,82386],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,82388,82389,82390,1734],{},"Umocněním na druhou: ",[883,82391,82393],{"className":82392},[886],[888,82394,82395],{"xmlns":890},[892,82396,82397,82421],{},[895,82398,82399,82401,82403,82409,82411],{},[898,82400,9646],{},[1846,82402,1848],{},[1974,82404,82405,82407],{},[898,82406,80642],{},[1979,82408,1981],{},[898,82410,4520],{"mathvariant":2226},[81872,82412,82413,82419],{},[1974,82414,82415,82417],{},[898,82416,9641],{},[1979,82418,1981],{},[1979,82420,2023],{},[902,82422,82423],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,82425,82426,82466,82506],{},[123,82427,82428],{},[883,82429,82431],{"className":82430},[886],[888,82432,82433],{"xmlns":890},[892,82434,82435,82463],{},[895,82436,82437,82439,82441,82443,82445,82447,82449,82451,82453],{},[898,82438,80642],{},[1846,82440,1848],{},[1979,82442,2128],{},[1846,82444,3833],{},[898,82446,9646],{},[1846,82448,1848],{},[1979,82450,2128],{},[898,82452,4520],{"mathvariant":2226},[81872,82454,82455,82461],{},[1974,82456,82457,82459],{},[898,82458,9641],{},[1979,82460,1981],{},[1979,82462,2023],{},[902,82464,82465],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,82467,82468],{},[883,82469,82471],{"className":82470},[886],[888,82472,82473],{"xmlns":890},[892,82474,82475,82503],{},[895,82476,82477,82479,82481,82483,82485,82487,82489,82491,82493],{},[898,82478,80642],{},[1846,82480,1848],{},[1979,82482,1981],{},[1846,82484,3833],{},[898,82486,9646],{},[1846,82488,1848],{},[1979,82490,2201],{},[898,82492,4520],{"mathvariant":2226},[81872,82494,82495,82501],{},[1974,82496,82497,82499],{},[898,82498,9641],{},[1979,82500,1981],{},[1979,82502,2023],{},[902,82504,82505],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,82507,82508],{},[883,82509,82511],{"className":82510},[886],[888,82512,82513],{"xmlns":890},[892,82514,82515,82543],{},[895,82516,82517,82519,82521,82523,82525,82527,82529,82531,82533],{},[898,82518,80642],{},[1846,82520,1848],{},[1979,82522,2023],{},[1846,82524,3833],{},[898,82526,9646],{},[1846,82528,1848],{},[1979,82530,3845],{},[898,82532,4520],{"mathvariant":2226},[81872,82534,82535,82541],{},[1974,82536,82537,82539],{},[898,82538,9641],{},[1979,82540,1981],{},[1979,82542,2023],{},[902,82544,82545],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,82547,82548],{},[614,82549,82550,82551,6319,82572,1734],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,82552,82554],{"className":82553},[886],[888,82555,82556],{"xmlns":890},[892,82557,82558,82570],{},[895,82559,82560,82562,82564,82566,82568],{},[1846,82561,1855],{"stretchy":1854},[898,82563,9641],{},[1846,82565,2136],{"separator":2135},[898,82567,9646],{},[1846,82569,1861],{"stretchy":1854},[902,82571,80768],{"encoding":904},[883,82573,82575],{"className":82574},[886],[888,82576,82577],{"xmlns":890},[892,82578,82579,82595],{},[895,82580,82581,82583,82585,82587,82589,82591,82593],{},[898,82582,80642],{},[1846,82584,1848],{},[1979,82586,2128],{},[1846,82588,2136],{"separator":2135},[1979,82590,1981],{},[1846,82592,2136],{"separator":2135},[1979,82594,2023],{},[902,82596,82597],{"encoding":904},"q = 1, 2, 3",[198,82599,82601],{"id":82600},"příklad-56","Příklad 5.6",[724,82603,76518,82604,1734],{},[883,82605,82607],{"className":82606},[886],[888,82608,82609],{"xmlns":890},[892,82610,82611,82627],{},[895,82612,82613,82615,82617,82619,82621,82623],{},[898,82614,2638],{},[1846,82616,1848],{},[1979,82618,1981],{},[898,82620,9641],{},[1846,82622,1945],{},[7963,82624,82625],{},[898,82626,9646],{},[902,82628,82629],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,82631,82633],{"className":82632},[886],[888,82634,82635],{"xmlns":890,"display":27911},[892,82636,82637,82679],{},[895,82638,82639,82641,82647,82649,82651,82653,82655,82657,82663,82665,82677],{},[898,82640,2667],{},[2122,82642,82643,82645],{},[898,82644,3783],{},[898,82646,9641],{},[1846,82648,1848],{},[1979,82650,1981],{},[1846,82652,2136],{"separator":2135},[5724,82654],{"width":5726},[898,82656,2667],{},[2122,82658,82659,82661],{},[898,82660,3783],{},[898,82662,9646],{},[1846,82664,1848],{},[2179,82666,82667,82669],{},[1979,82668,2128],{},[895,82670,82671,82673],{},[1979,82672,1981],{},[7963,82674,82675],{},[898,82676,9646],{},[898,82678,1734],{"mathvariant":2226},[902,82680,82681],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,82683,82685],{"className":82684},[886],[888,82686,82687],{"xmlns":890,"display":27911},[892,82688,82689,82753],{},[895,82690,82691,82693,82695,82697,82699,82701,82723,82725,82743,82745,82747,82751],{},[898,82692,2667],{},[898,82694,3840],{},[898,82696,2623],{},[898,82698,8519],{},[1846,82700,1848],{},[2179,82702,82703,82713],{},[895,82704,82705,82707],{},[898,82706,2667],{},[2122,82708,82709,82711],{},[898,82710,3783],{},[898,82712,9641],{},[895,82714,82715,82717],{},[898,82716,2667],{},[2122,82718,82719,82721],{},[898,82720,3783],{},[898,82722,9646],{},[1846,82724,1848],{},[2179,82726,82727,82729],{},[1979,82728,1981],{},[2175,82730,82731],{"scriptlevel":2177,"displaystyle":1854},[2179,82732,82733,82735],{},[1979,82734,2128],{},[895,82736,82737,82739],{},[1979,82738,1981],{},[7963,82740,82741],{},[898,82742,9646],{},[1846,82744,1848],{},[1979,82746,2201],{},[7963,82748,82749],{},[898,82750,9646],{},[898,82752,1734],{"mathvariant":2226},[902,82754,82755],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,82757,82758,82759,82802,82803,82842,82843,1734],{},"Například ",[883,82760,82762],{"className":82761},[886],[888,82763,82764],{"xmlns":890},[892,82765,82766,82799],{},[895,82767,82768,82770,82772,82774,82776,82778,82780,82782,82784,82786,82788,82790,82794,82796],{},[898,82769,2667],{},[898,82771,3840],{},[898,82773,2623],{},[898,82775,8519],{},[1846,82777,1855],{"stretchy":1854},[1979,82779,2201],{},[1846,82781,2136],{"separator":2135},[1979,82783,24046],{},[1846,82785,1861],{"stretchy":1854},[1846,82787,1848],{},[1979,82789,2201],{},[7963,82791,82792],{},[1979,82793,24046],{},[1846,82795,1650],{},[1979,82797,82798],{},"10,58",[902,82800,82801],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,82804,82806],{"className":82805},[886],[888,82807,82808],{"xmlns":890},[892,82809,82810,82839],{},[895,82811,82812,82814,82816,82818,82820,82822,82824,82826,82828,82830,82834,82836],{},[898,82813,2638],{},[1846,82815,1855],{"stretchy":1854},[1979,82817,2201],{},[1846,82819,2136],{"separator":2135},[1979,82821,24046],{},[1846,82823,1861],{"stretchy":1854},[1846,82825,1848],{},[1979,82827,5431],{},[1846,82829,1945],{},[7963,82831,82832],{},[1979,82833,24046],{},[1846,82835,1650],{},[1979,82837,82838],{},"10,646",[902,82840,82841],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,82844,82846],{"className":82845},[886],[888,82847,82848],{"xmlns":890},[892,82849,82850,82858],{},[895,82851,82852,82854],{},[1979,82853,2201],{},[7963,82855,82856],{},[1979,82857,24046],{},[902,82859,82860],{"encoding":904},"4\\sqrt{7}",[724,82862,82863,82864,82884],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,82865,82867],{"className":82866},[886],[888,82868,82869],{"xmlns":890},[892,82870,82871,82881],{},[895,82872,82873,82875,82877,82879],{},[898,82874,2044],{},[898,82876,9641],{},[1846,82878,1848],{},[1979,82880,1981],{},[902,82882,82883],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,82886,82888],{"className":82887},[886],[888,82889,82890],{"xmlns":890,"display":27911},[892,82891,82892,82941],{},[895,82893,82894,82896,82898,82900,82902,82904,82906,82908,82910,82912,82914,82916,82918,82920,82922,82924,82926,82928,82930,82934,82936,82938],{},[898,82895,2044],{},[898,82897,9646],{},[1846,82899,1848],{},[1846,82901,2075],{},[898,82903,2667],{},[898,82905,3840],{},[898,82907,2623],{},[898,82909,8519],{},[1846,82911,1855],{"stretchy":1854},[1979,82913,2201],{},[1846,82915,2136],{"separator":2135},[1979,82917,24046],{},[1846,82919,1861],{"stretchy":1854},[1846,82921,3025],{},[1979,82923,1981],{},[1846,82925,1848],{},[1846,82927,2075],{},[1979,82929,5431],{},[7963,82931,82932],{},[1979,82933,24046],{},[1846,82935,1650],{},[1846,82937,2075],{},[1979,82939,82940],{},"21,17.",[902,82942,82943],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,82945,82947],{"id":82946},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,82949,82950,82951,1343,82953,1745,82955,82957,82958,82961,82962,82965],{},"Hlavními faktory produkce jsou ",[38,82952,74759],{},[38,82954,74775],{},[38,82956,74791],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,82959,82960],{},"jednofaktorový"," (pouze práce) a ",[38,82963,82964],{},"dvoufaktorový"," (práce + kapitál) model.",[724,82967,82968,82969,82972,82973,82975,82976,82978,82979,26034,82982,83001,83002,83019,83020,83037,83038,83060,83061,4204,83080,1734],{},"V ",[38,82970,82971],{},"1F modelu"," se definuje ",[38,82974,9870],{}," (derivace produkce podle práce) a ",[38,82977,74694],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,82980,82981],{},"zákonu klesajících výnosů",[883,82983,82985],{"className":82984},[886],[888,82986,82987],{"xmlns":890},[892,82988,82989,82999],{},[895,82990,82991,82993],{},[898,82992,2667],{},[2122,82994,82995,82997],{},[898,82996,3783],{},[898,82998,9641],{},[902,83000,9891],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,83003,83005],{"className":83004},[886],[888,83006,83007],{"xmlns":890},[892,83008,83009,83017],{},[895,83010,83011],{},[2122,83012,83013,83015],{},[898,83014,9641],{},[1979,83016,2177],{},[902,83018,75403],{"encoding":904}," klesá a v bodě ",[883,83021,83023],{"className":83022},[886],[888,83024,83025],{"xmlns":890},[892,83026,83027,83035],{},[895,83028,83029],{},[2122,83030,83031,83033],{},[898,83032,9641],{},[1979,83034,2128],{},[902,83036,13057],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,83039,83040,83041],{},"princip maximalizace ",[883,83042,83044],{"className":83043},[886],[888,83045,83046],{"xmlns":890},[892,83047,83048,83058],{},[895,83049,83050,83052],{},[898,83051,4101],{},[2122,83053,83054,83056],{},[898,83055,3783],{},[898,83057,9641],{},[902,83059,74478],{"encoding":904},": v bodě maxima ",[883,83062,83064],{"className":83063},[886],[888,83065,83066],{"xmlns":890},[892,83067,83068,83078],{},[895,83069,83070,83072],{},[898,83071,4101],{},[2122,83073,83074,83076],{},[898,83075,3783],{},[898,83077,9641],{},[902,83079,74478],{"encoding":904},[883,83081,83083],{"className":83082},[886],[888,83084,83085],{"xmlns":890},[892,83086,83087,83107],{},[895,83088,83089,83091,83097,83099,83101],{},[898,83090,2667],{},[2122,83092,83093,83095],{},[898,83094,3783],{},[898,83096,9641],{},[1846,83098,1848],{},[898,83100,4101],{},[2122,83102,83103,83105],{},[898,83104,3783],{},[898,83106,9641],{},[902,83108,74508],{"encoding":904},[724,83110,83111,83112,83115,83116,2053,83119,83148,83149,83166,83167,83170,83171,83200,83201,83203,83204,7948,83234,83256],{},"Ve ",[38,83113,83114],{},"2F modelu"," se obvykle používají ",[38,83117,83118],{},"Cobb-Douglasovy funkce",[883,83120,83122],{"className":83121},[886],[888,83123,83124],{"xmlns":890},[892,83125,83126,83146],{},[895,83127,83128,83130,83132,83134,83140],{},[898,83129,2638],{},[1846,83131,1848],{},[898,83133,4101],{},[1974,83135,83136,83138],{},[898,83137,9641],{},[898,83139,207],{},[1974,83141,83142,83144],{},[898,83143,9646],{},[898,83145,1948],{},[902,83147,74575],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,83150,83152],{"className":83151},[886],[888,83153,83154],{"xmlns":890},[892,83155,83156,83164],{},[895,83157,83158,83160,83162],{},[898,83159,207],{},[1846,83161,1945],{},[898,83163,1948],{},[902,83165,74669],{"encoding":904}," rozlišujeme ",[38,83168,83169],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,83172,83174],{"className":83173},[886],[888,83175,83176],{"xmlns":890},[892,83177,83178,83198],{},[895,83179,83180,83182,83188,83190,83192],{},[898,83181,2667],{},[2122,83183,83184,83186],{},[898,83185,3783],{},[898,83187,9641],{},[1846,83189,2136],{"separator":2135},[898,83191,2667],{},[2122,83193,83194,83196],{},[898,83195,3783],{},[898,83197,9646],{},[902,83199,74606],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,83202,9624],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,83205,83207],{"className":83206},[886],[888,83208,83209],{"xmlns":890},[892,83210,83211,83231],{},[895,83212,83213,83215,83221,83223,83225],{},[898,83214,2667],{},[2122,83216,83217,83219],{},[898,83218,3783],{},[898,83220,9641],{},[898,83222,4520],{"mathvariant":2226},[898,83224,2667],{},[2122,83226,83227,83229],{},[898,83228,3783],{},[898,83230,9646],{},[902,83232,83233],{"encoding":904},"MP_L\u002FMP_K",[38,83235,83236,83237,1861],{},"mezní míra technické substituce (",[883,83238,83240],{"className":83239},[886],[888,83241,83242],{"xmlns":890},[892,83243,83244,83254],{},[895,83245,83246,83248,83250,83252],{},[898,83247,2667],{},[898,83249,3840],{},[898,83251,2623],{},[898,83253,8519],{},[902,83255,10445],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,83258,49727],{"id":49726},[152,83260,83261,83264,83267,83270,83273,83276,83279,83282,83285,83288,83291],{},[123,83262,83263],{},"Jaké jsou faktory produkce?",[123,83265,83266],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,83268,83269],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,83271,83272],{},"Co udává mezní produkt práce?",[123,83274,83275],{},"Co musí respektovat průběh křivky produkce?",[123,83277,83278],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,83280,83281],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,83283,83284],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,83286,83287],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,83289,83290],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,83292,83293],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,83295,83297],{"id":83296},"úlohy-51517","Úlohy 5.1–5.17",[198,83299,40296],{"id":40295},[724,83301,83302,83305,83306,83328,83329,1343,83349,1343,83369,83389],{},[38,83303,83304],{},"5.1"," Je dána produkce ",[883,83307,83309],{"className":83308},[886],[888,83310,83311],{"xmlns":890},[892,83312,83313,83325],{},[895,83314,83315,83317,83319,83321],{},[898,83316,2638],{},[1846,83318,1848],{},[1979,83320,2712],{},[7963,83322,83323],{},[898,83324,9641],{},[902,83326,83327],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,83330,83332],{"className":83331},[886],[888,83333,83334],{"xmlns":890},[892,83335,83336,83346],{},[895,83337,83338,83340,83342,83344],{},[898,83339,2638],{},[1846,83341,1855],{"stretchy":1854},[1979,83343,2128],{},[1846,83345,1861],{"stretchy":1854},[902,83347,83348],{"encoding":904},"Q(1)",[883,83350,83352],{"className":83351},[886],[888,83353,83354],{"xmlns":890},[892,83355,83356,83366],{},[895,83357,83358,83360,83362,83364],{},[898,83359,2638],{},[1846,83361,1855],{"stretchy":1854},[1979,83363,2201],{},[1846,83365,1861],{"stretchy":1854},[902,83367,83368],{"encoding":904},"Q(4)",[883,83370,83372],{"className":83371},[886],[888,83373,83374],{"xmlns":890},[892,83375,83376,83386],{},[895,83377,83378,83380,83382,83384],{},[898,83379,2638],{},[1846,83381,1855],{"stretchy":1854},[1979,83383,3845],{},[1846,83385,1861],{"stretchy":1854},[902,83387,83388],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,83391,83392,83305,83395,83431,83432,83445,83446,83465,83466,83492,83493,2535,83506,83519],{},[38,83393,83394],{},"5.2",[883,83396,83398],{"className":83397},[886],[888,83399,83400],{"xmlns":890},[892,83401,83402,83428],{},[895,83403,83404,83406,83408,83410,83412,83418,83420,83422],{},[898,83405,2638],{},[1846,83407,1848],{},[1846,83409,2075],{},[1979,83411,2643],{},[1974,83413,83414,83416],{},[898,83415,9641],{},[1979,83417,2023],{},[1846,83419,1945],{},[1979,83421,3845],{},[1974,83423,83424,83426],{},[898,83425,9641],{},[1979,83427,1981],{},[902,83429,83430],{"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 ",[883,83433,83435],{"className":83434},[886],[888,83436,83437],{"xmlns":890},[892,83438,83439,83443],{},[895,83440,83441],{},[898,83442,9641],{},[902,83444,9641],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,83447,83449],{"className":83448},[886],[888,83450,83451],{"xmlns":890},[892,83452,83453,83463],{},[895,83454,83455,83457],{},[898,83456,2667],{},[2122,83458,83459,83461],{},[898,83460,3783],{},[898,83462,9641],{},[902,83464,9891],{"encoding":904},". (f) Vypočtěte ",[883,83467,83469],{"className":83468},[886],[888,83470,83471],{"xmlns":890},[892,83472,83473,83489],{},[895,83474,83475,83477,83483,83485,83487],{},[898,83476,2667],{},[2122,83478,83479,83481],{},[898,83480,3783],{},[898,83482,9641],{},[1846,83484,1855],{"stretchy":1854},[1979,83486,2712],{},[1846,83488,1861],{"stretchy":1854},[902,83490,83491],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,83494,83496],{"className":83495},[886],[888,83497,83498],{"xmlns":890},[892,83499,83500,83504],{},[895,83501,83502],{},[1979,83503,2712],{},[902,83505,2712],{"encoding":904},[883,83507,83509],{"className":83508},[886],[888,83510,83511],{"xmlns":890},[892,83512,83513,83517],{},[895,83514,83515],{},[1979,83516,42132],{},[902,83518,42132],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,83521,83522,83525,83526,83548,83549,83577,83578,83609,83610,1734],{},[38,83523,83524],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,83527,83529],{"className":83528},[886],[888,83530,83531],{"xmlns":890},[892,83532,83533,83545],{},[895,83534,83535,83537,83539,83541],{},[898,83536,2638],{},[1846,83538,1848],{},[1979,83540,14955],{},[7963,83542,83543],{},[898,83544,9641],{},[902,83546,83547],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,83550,83552],{"className":83551},[886],[888,83553,83554],{"xmlns":890},[892,83555,83556,83574],{},[895,83557,83558,83560,83562,83564,83568,83570,83572],{},[898,83559,2638],{},[1846,83561,1848],{},[1979,83563,29926],{},[7963,83565,83566],{},[898,83567,9641],{},[1846,83569,2075],{},[1979,83571,2201],{},[898,83573,9641],{},[902,83575,83576],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,83579,83581],{"className":83580},[886],[888,83582,83583],{"xmlns":890},[892,83584,83585,83606],{},[895,83586,83587,83589,83591,83593,83595,83597,83600],{},[898,83588,2638],{},[1846,83590,1848],{},[1979,83592,2968],{},[898,83594,9641],{},[1846,83596,2075],{},[1979,83598,83599],{},"0,01",[1974,83601,83602,83604],{},[898,83603,9641],{},[1979,83605,1981],{},[902,83607,83608],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,83611,83613],{"className":83612},[886],[888,83614,83615],{"xmlns":890},[892,83616,83617,83643],{},[895,83618,83619,83621,83623,83625,83627,83633,83635,83637],{},[898,83620,2638],{},[1846,83622,1848],{},[1846,83624,2075],{},[1979,83626,68056],{},[1974,83628,83629,83631],{},[898,83630,9641],{},[1979,83632,2023],{},[1846,83634,1945],{},[1979,83636,3845],{},[1974,83638,83639,83641],{},[898,83640,9641],{},[1979,83642,1981],{},[902,83644,83645],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,83647,83648,83651,83652,2474,83671,72043,83688,1734],{},[38,83649,83650],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,83653,83655],{"className":83654},[886],[888,83656,83657],{"xmlns":890},[892,83658,83659,83669],{},[895,83660,83661,83663],{},[898,83662,4101],{},[2122,83664,83665,83667],{},[898,83666,3783],{},[898,83668,9641],{},[902,83670,74478],{"encoding":904},[883,83672,83674],{"className":83673},[886],[888,83675,83676],{"xmlns":890},[892,83677,83678,83686],{},[895,83679,83680],{},[2122,83681,83682,83684],{},[898,83683,9641],{},[1979,83685,2177],{},[902,83687,75403],{"encoding":904},[883,83689,83691],{"className":83690},[886],[888,83692,83693],{"xmlns":890},[892,83694,83695,83735],{},[895,83696,83697,83699,83705,83707,83713,83715,83717,83719,83725,83727,83733],{},[898,83698,4101],{},[2122,83700,83701,83703],{},[898,83702,3783],{},[898,83704,9641],{},[1846,83706,1855],{"stretchy":1854},[2122,83708,83709,83711],{},[898,83710,9641],{},[1979,83712,2177],{},[1846,83714,1861],{"stretchy":1854},[1846,83716,1848],{},[898,83718,2667],{},[2122,83720,83721,83723],{},[898,83722,3783],{},[898,83724,9641],{},[1846,83726,1855],{"stretchy":1854},[2122,83728,83729,83731],{},[898,83730,9641],{},[1979,83732,2177],{},[1846,83734,1861],{"stretchy":1854},[902,83736,83737],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,83739,83740,83305,83743,21439,83779,83792,83793,83812],{},[38,83741,83742],{},"5.5",[883,83744,83746],{"className":83745},[886],[888,83747,83748],{"xmlns":890},[892,83749,83750,83776],{},[895,83751,83752,83754,83756,83758,83760,83766,83768,83770],{},[898,83753,2638],{},[1846,83755,1848],{},[1846,83757,2075],{},[1979,83759,2688],{},[1974,83761,83762,83764],{},[898,83763,9641],{},[1979,83765,2023],{},[1846,83767,1945],{},[1979,83769,3357],{},[1974,83771,83772,83774],{},[898,83773,9641],{},[1979,83775,1981],{},[902,83777,83778],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,83780,83782],{"className":83781},[886],[888,83783,83784],{"xmlns":890},[892,83785,83786,83790],{},[895,83787,83788],{},[898,83789,9641],{},[902,83791,9641],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,83794,83796],{"className":83795},[886],[888,83797,83798],{"xmlns":890},[892,83799,83800,83810],{},[895,83801,83802,83804],{},[898,83803,4101],{},[2122,83805,83806,83808],{},[898,83807,3783],{},[898,83809,9641],{},[902,83811,74478],{"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.",[198,83814,83816],{"id":83815},"dvoufaktorový-model","Dvoufaktorový model",[724,83818,83819,83822,83823,83548,83849,83577,83891,1734],{},[38,83820,83821],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,83824,83826],{"className":83825},[886],[888,83827,83828],{"xmlns":890},[892,83829,83830,83846],{},[895,83831,83832,83834,83836,83838,83840],{},[898,83833,2638],{},[1846,83835,1848],{},[1979,83837,24046],{},[898,83839,9641],{},[1974,83841,83842,83844],{},[898,83843,9646],{},[1979,83845,1981],{},[902,83847,83848],{"encoding":904},"Q = 7 L K^{2}",[883,83850,83852],{"className":83851},[886],[888,83853,83854],{"xmlns":890},[892,83855,83856,83888],{},[895,83857,83858,83860,83862,83864,83876],{},[898,83859,2638],{},[1846,83861,1848],{},[1979,83863,2968],{},[1974,83865,83866,83868],{},[898,83867,9641],{},[895,83869,83870,83872,83874],{},[1979,83871,1981],{},[898,83873,4520],{"mathvariant":2226},[1979,83875,2023],{},[1974,83877,83878,83880],{},[898,83879,9646],{},[895,83881,83882,83884,83886],{},[1979,83883,2128],{},[898,83885,4520],{"mathvariant":2226},[1979,83887,2023],{},[902,83889,83890],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,83892,83894],{"className":83893},[886],[888,83895,83896],{"xmlns":890},[892,83897,83898,83930],{},[895,83899,83900,83902,83904,83906,83918],{},[898,83901,2638],{},[1846,83903,1848],{},[1979,83905,3555],{},[1974,83907,83908,83910],{},[898,83909,9641],{},[895,83911,83912,83914,83916],{},[1979,83913,2023],{},[898,83915,4520],{"mathvariant":2226},[1979,83917,2078],{},[1974,83919,83920,83922],{},[898,83921,9646],{},[895,83923,83924,83926,83928],{},[1979,83925,1981],{},[898,83927,4520],{"mathvariant":2226},[1979,83929,2078],{},[902,83931,83932],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,83934,83935,83305,83938,83980,83981,1343,83999,84018,84019,84036],{},[38,83936,83937],{},"5.7",[883,83939,83941],{"className":83940},[886],[888,83942,83943],{"xmlns":890},[892,83944,83945,83977],{},[895,83946,83947,83949,83951,83953,83965],{},[898,83948,2638],{},[1846,83950,1848],{},[1979,83952,2712],{},[1974,83954,83955,83957],{},[898,83956,9641],{},[895,83958,83959,83961,83963],{},[1979,83960,2128],{},[898,83962,4520],{"mathvariant":2226},[1979,83964,1981],{},[1974,83966,83967,83969],{},[898,83968,9646],{},[895,83970,83971,83973,83975],{},[1979,83972,2128],{},[898,83974,4520],{"mathvariant":2226},[1979,83976,1981],{},[902,83978,83979],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,83982,83984],{"className":83983},[886],[888,83985,83986],{"xmlns":890},[892,83987,83988,83996],{},[895,83989,83990,83992,83994],{},[898,83991,9641],{},[1846,83993,1848],{},[1979,83995,19987],{},[902,83997,83998],{"encoding":904},"L = 400",[883,84000,84002],{"className":84001},[886],[888,84003,84004],{"xmlns":890},[892,84005,84006,84015],{},[895,84007,84008,84010,84012],{},[898,84009,9646],{},[1846,84011,1848],{},[1979,84013,84014],{},"17576",[902,84016,84017],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,84020,84022],{"className":84021},[886],[888,84023,84024],{"xmlns":890},[892,84025,84026,84034],{},[895,84027,84028,84030,84032],{},[898,84029,9641],{},[1846,84031,2136],{"separator":2135},[898,84033,9646],{},[902,84035,78830],{"encoding":904}," zdvojnásobí.",[724,84038,84039,84042,84043,83980,84074,1343,84092,69429,84110,84140,84141,84171,84172,2535,84185,84199,84200,2535,84213,84226],{},[38,84040,84041],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,84044,84046],{"className":84045},[886],[888,84047,84048],{"xmlns":890},[892,84049,84050,84071],{},[895,84051,84052,84054,84056,84059,84065],{},[898,84053,2638],{},[1846,84055,1848],{},[1979,84057,84058],{},"1,01",[1974,84060,84061,84063],{},[898,84062,9641],{},[1979,84064,23575],{},[1974,84066,84067,84069],{},[898,84068,9646],{},[1979,84070,23634],{},[902,84072,84073],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,84075,84077],{"className":84076},[886],[888,84078,84079],{"xmlns":890},[892,84080,84081,84089],{},[895,84082,84083,84085,84087],{},[898,84084,9641],{},[1846,84086,1848],{},[1979,84088,30588],{},[902,84090,84091],{"encoding":904},"L = 250",[883,84093,84095],{"className":84094},[886],[888,84096,84097],{"xmlns":890},[892,84098,84099,84107],{},[895,84100,84101,84103,84105],{},[898,84102,9646],{},[1846,84104,1848],{},[1979,84106,2631],{},[902,84108,84109],{"encoding":904},"K = 1000",[883,84111,84113],{"className":84112},[886],[888,84114,84115],{"xmlns":890},[892,84116,84117,84137],{},[895,84118,84119,84121,84127,84129,84131,84133,84135],{},[898,84120,2667],{},[2122,84122,84123,84125],{},[898,84124,3783],{},[898,84126,9641],{},[1846,84128,1855],{"stretchy":1854},[1979,84130,30588],{},[1846,84132,2136],{"separator":2135},[1979,84134,2631],{},[1846,84136,1861],{"stretchy":1854},[902,84138,84139],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,84142,84144],{"className":84143},[886],[888,84145,84146],{"xmlns":890},[892,84147,84148,84168],{},[895,84149,84150,84152,84158,84160,84162,84164,84166],{},[898,84151,2667],{},[2122,84153,84154,84156],{},[898,84155,3783],{},[898,84157,9646],{},[1846,84159,1855],{"stretchy":1854},[1979,84161,30588],{},[1846,84163,2136],{"separator":2135},[1979,84165,2631],{},[1846,84167,1861],{"stretchy":1854},[902,84169,84170],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,84173,84175],{"className":84174},[886],[888,84176,84177],{"xmlns":890},[892,84178,84179,84183],{},[895,84180,84181],{},[898,84182,9641],{},[902,84184,9641],{"encoding":904},[883,84186,84188],{"className":84187},[886],[888,84189,84190],{"xmlns":890},[892,84191,84192,84197],{},[895,84193,84194],{},[1979,84195,84196],{},"260",[902,84198,84196],{"encoding":904}," a současném poklesu ",[883,84201,84203],{"className":84202},[886],[888,84204,84205],{"xmlns":890},[892,84206,84207,84211],{},[895,84208,84209],{},[898,84210,9646],{},[902,84212,9646],{"encoding":904},[883,84214,84216],{"className":84215},[886],[888,84217,84218],{"xmlns":890},[892,84219,84220,84224],{},[895,84221,84222],{},[1979,84223,15036],{},[902,84225,15036],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,84228,84229,84232,84233,1734],{},[38,84230,84231],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,84234,84236],{"className":84235},[886],[888,84237,84238],{"xmlns":890},[892,84239,84240,84260],{},[895,84241,84242,84244,84246,84248,84254],{},[898,84243,2638],{},[1846,84245,1848],{},[1979,84247,2712],{},[1974,84249,84250,84252],{},[898,84251,9641],{},[1979,84253,68056],{},[1974,84255,84256,84258],{},[898,84257,9646],{},[1979,84259,4855],{},[902,84261,84262],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,84264,84265,84268,84269,80426,84292,10240,84305,9871,84355,3764],{},[38,84266,84267],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,84270,84272],{"className":84271},[886],[888,84273,84274],{"xmlns":890},[892,84275,84276,84290],{},[895,84277,84278,84280,84282,84284,84286,84288],{},[898,84279,2638],{},[1846,84281,1855],{"stretchy":1854},[898,84283,9641],{},[1846,84285,2136],{"separator":2135},[898,84287,9646],{},[1846,84289,1861],{"stretchy":1854},[902,84291,9843],{"encoding":904},[883,84293,84295],{"className":84294},[886],[888,84296,84297],{"xmlns":890},[892,84298,84299,84303],{},[895,84300,84301],{},[898,84302,36705],{},[902,84304,36705],{"encoding":904},[883,84306,84308],{"className":84307},[886],[888,84309,84310],{"xmlns":890},[892,84311,84312,84352],{},[895,84313,84314,84316,84324,84326,84328,84336,84338,84340,84342,84344,84346,84348,84350],{},[898,84315,9641],{},[9012,84317,84318,84320,84322],{},[898,84319,2638],{},[898,84321,9641],{},[1846,84323,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,84325,1945],{},[898,84327,9646],{},[9012,84329,84330,84332,84334],{},[898,84331,2638],{},[898,84333,9646],{},[1846,84335,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,84337,1848],{},[898,84339,36705],{},[898,84341,2638],{},[1846,84343,1855],{"stretchy":1854},[898,84345,9641],{},[1846,84347,2136],{"separator":2135},[898,84349,9646],{},[1846,84351,1861],{"stretchy":1854},[902,84353,84354],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,84356,80401],{},[724,84358,84359,84362],{},[38,84360,84361],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,84364,84365,83305,84368,84408,84409,1343,84431,1343,84453,84475],{},[38,84366,84367],{},"5.12",[883,84369,84371],{"className":84370},[886],[888,84372,84373],{"xmlns":890},[892,84374,84375,84405],{},[895,84376,84377,84379,84381,84393],{},[898,84378,2638],{},[1846,84380,1848],{},[1974,84382,84383,84385],{},[898,84384,9641],{},[895,84386,84387,84389,84391],{},[1979,84388,2128],{},[898,84390,4520],{"mathvariant":2226},[1979,84392,2023],{},[1974,84394,84395,84397],{},[898,84396,9646],{},[895,84398,84399,84401,84403],{},[1979,84400,2128],{},[898,84402,4520],{"mathvariant":2226},[1979,84404,2201],{},[902,84406,84407],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,84410,84412],{"className":84411},[886],[888,84413,84414],{"xmlns":890},[892,84415,84416,84428],{},[895,84417,84418,84424,84426],{},[2122,84419,84420,84422],{},[898,84421,80642],{},[1979,84423,2177],{},[1846,84425,1848],{},[1979,84427,2128],{},[902,84429,84430],{"encoding":904},"q_0 = 1",[883,84432,84434],{"className":84433},[886],[888,84435,84436],{"xmlns":890},[892,84437,84438,84450],{},[895,84439,84440,84446,84448],{},[2122,84441,84442,84444],{},[898,84443,80642],{},[1979,84445,2128],{},[1846,84447,1848],{},[1979,84449,1981],{},[902,84451,84452],{"encoding":904},"q_1 = 2",[883,84454,84456],{"className":84455},[886],[888,84457,84458],{"xmlns":890},[892,84459,84460,84472],{},[895,84461,84462,84468,84470],{},[2122,84463,84464,84466],{},[898,84465,80642],{},[1979,84467,1981],{},[1846,84469,1848],{},[1979,84471,2023],{},[902,84473,84474],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,84477,84478,83305,84481,84521,84522,1343,84550,1343,84578,1343,84606,1343,84635,1343,84664,1343,84693,1343,84722,1343,84751,1734],{},[38,84479,84480],{},"5.13",[883,84482,84484],{"className":84483},[886],[888,84485,84486],{"xmlns":890},[892,84487,84488,84518],{},[895,84489,84490,84492,84494,84506],{},[898,84491,2638],{},[1846,84493,1848],{},[1974,84495,84496,84498],{},[898,84497,9641],{},[895,84499,84500,84502,84504],{},[1979,84501,2128],{},[898,84503,4520],{"mathvariant":2226},[1979,84505,2023],{},[1974,84507,84508,84510],{},[898,84509,9646],{},[895,84511,84512,84514,84516],{},[1979,84513,2128],{},[898,84515,4520],{"mathvariant":2226},[1979,84517,1981],{},[902,84519,84520],{"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): ",[883,84523,84525],{"className":84524},[886],[888,84526,84527],{"xmlns":890},[892,84528,84529,84547],{},[895,84530,84531,84537,84539,84541,84543,84545],{},[2122,84532,84533,84535],{},[898,84534,4101],{},[1979,84536,2128],{},[1846,84538,2336],{"stretchy":1854},[1979,84540,2128],{},[1846,84542,8271],{"separator":2135},[1979,84544,2128],{},[1846,84546,2351],{"stretchy":1854},[902,84548,84549],{"encoding":904},"A_1[1; 1]",[883,84551,84553],{"className":84552},[886],[888,84554,84555],{"xmlns":890},[892,84556,84557,84575],{},[895,84558,84559,84565,84567,84569,84571,84573],{},[2122,84560,84561,84563],{},[898,84562,4101],{},[1979,84564,1981],{},[1846,84566,2336],{"stretchy":1854},[1979,84568,2128],{},[1846,84570,8271],{"separator":2135},[1979,84572,5431],{},[1846,84574,2351],{"stretchy":1854},[902,84576,84577],{"encoding":904},"A_2[1; 8]",[883,84579,84581],{"className":84580},[886],[888,84582,84583],{"xmlns":890},[892,84584,84585,84603],{},[895,84586,84587,84593,84595,84597,84599,84601],{},[2122,84588,84589,84591],{},[898,84590,4101],{},[1979,84592,2023],{},[1846,84594,2336],{"stretchy":1854},[1979,84596,2128],{},[1846,84598,8271],{"separator":2135},[1979,84600,66442],{},[1846,84602,2351],{"stretchy":1854},[902,84604,84605],{"encoding":904},"A_3[1; 27]",[883,84607,84609],{"className":84608},[886],[888,84610,84611],{"xmlns":890},[892,84612,84613,84632],{},[895,84614,84615,84621,84623,84625,84627,84630],{},[2122,84616,84617,84619],{},[898,84618,4101],{},[1979,84620,2201],{},[1846,84622,2336],{"stretchy":1854},[1979,84624,1981],{},[1846,84626,8271],{"separator":2135},[1979,84628,84629],{},"0,353",[1846,84631,2351],{"stretchy":1854},[902,84633,84634],{"encoding":904},"A_4[2; 0{,}353]",[883,84636,84638],{"className":84637},[886],[888,84639,84640],{"xmlns":890},[892,84641,84642,84661],{},[895,84643,84644,84650,84652,84654,84656,84659],{},[2122,84645,84646,84648],{},[898,84647,4101],{},[1979,84649,2078],{},[1846,84651,2336],{"stretchy":1854},[1979,84653,1981],{},[1846,84655,8271],{"separator":2135},[1979,84657,84658],{},"2,828",[1846,84660,2351],{"stretchy":1854},[902,84662,84663],{"encoding":904},"A_5[2; 2{,}828]",[883,84665,84667],{"className":84666},[886],[888,84668,84669],{"xmlns":890},[892,84670,84671,84690],{},[895,84672,84673,84679,84681,84683,84685,84688],{},[2122,84674,84675,84677],{},[898,84676,4101],{},[1979,84678,2085],{},[1846,84680,2336],{"stretchy":1854},[1979,84682,1981],{},[1846,84684,8271],{"separator":2135},[1979,84686,84687],{},"9,545",[1846,84689,2351],{"stretchy":1854},[902,84691,84692],{"encoding":904},"A_6[2; 9{,}545]",[883,84694,84696],{"className":84695},[886],[888,84697,84698],{"xmlns":890},[892,84699,84700,84719],{},[895,84701,84702,84708,84710,84712,84714,84717],{},[2122,84703,84704,84706],{},[898,84705,4101],{},[1979,84707,24046],{},[1846,84709,2336],{"stretchy":1854},[1979,84711,64404],{},[1846,84713,8271],{"separator":2135},[1979,84715,84716],{},"0,544",[1846,84718,2351],{"stretchy":1854},[902,84720,84721],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,84723,84725],{"className":84724},[886],[888,84726,84727],{"xmlns":890},[892,84728,84729,84748],{},[895,84730,84731,84737,84739,84741,84743,84746],{},[2122,84732,84733,84735],{},[898,84734,4101],{},[1979,84736,5431],{},[1846,84738,2336],{"stretchy":1854},[1979,84740,64404],{},[1846,84742,8271],{"separator":2135},[1979,84744,84745],{},"14,696",[1846,84747,2351],{"stretchy":1854},[902,84749,84750],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,84752,84754],{"className":84753},[886],[888,84755,84756],{"xmlns":890},[892,84757,84758,84776],{},[895,84759,84760,84766,84768,84770,84772,84774],{},[2122,84761,84762,84764],{},[898,84763,4101],{},[1979,84765,3845],{},[1846,84767,2336],{"stretchy":1854},[1979,84769,1981],{},[1846,84771,8271],{"separator":2135},[1979,84773,2078],{},[1846,84775,2351],{"stretchy":1854},[902,84777,84778],{"encoding":904},"A_9[2; 5]",[724,84780,84781,84784],{},[38,84782,84783],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,84786,84787,84790,84791,84821,84822,84835,84836,84849,84850,69162,84869,84888,84889,1734],{},[38,84788,84789],{},"5.15"," Produkce firmy je dána vztahem ",[883,84792,84794],{"className":84793},[886],[888,84795,84796],{"xmlns":890},[892,84797,84798,84818],{},[895,84799,84800,84802,84804,84806,84812],{},[898,84801,2638],{},[1846,84803,1848],{},[1979,84805,1981],{},[1974,84807,84808,84810],{},[898,84809,9641],{},[1979,84811,4855],{},[1974,84813,84814,84816],{},[898,84815,9646],{},[1979,84817,23634],{},[902,84819,84820],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,84823,84825],{"className":84824},[886],[888,84826,84827],{"xmlns":890},[892,84828,84829,84833],{},[895,84830,84831],{},[1979,84832,2938],{},[902,84834,2938],{"encoding":904}," pracovníků a disponuje-li ",[883,84837,84839],{"className":84838},[886],[888,84840,84841],{"xmlns":890},[892,84842,84843,84847],{},[895,84844,84845],{},[1979,84846,64280],{},[902,84848,64280],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,84851,84853],{"className":84852},[886],[888,84854,84855],{"xmlns":890},[892,84856,84857,84867],{},[895,84858,84859,84861,84863,84865],{},[898,84860,2667],{},[898,84862,3840],{},[898,84864,2623],{},[898,84866,8519],{},[902,84868,10445],{"encoding":904},[883,84870,84872],{"className":84871},[886],[888,84873,84874],{"xmlns":890},[892,84875,84876,84886],{},[895,84877,84878,84880,84882,84884],{},[898,84879,2667],{},[898,84881,3840],{},[898,84883,2623],{},[898,84885,8519],{},[902,84887,10445],{"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 ",[883,84890,84892],{"className":84891},[886],[888,84893,84894],{"xmlns":890},[892,84895,84896,84901],{},[895,84897,84898],{},[1979,84899,84900],{},"95",[902,84902,84900],{"encoding":904},[724,84904,84905,83305,84908,70836,84940,84959,84960,84973,84974,84987,84988,85001],{},[38,84906,84907],{},"5.16",[883,84909,84911],{"className":84910},[886],[888,84912,84913],{"xmlns":890},[892,84914,84915,84937],{},[895,84916,84917,84919,84921,84927,84929,84931],{},[898,84918,2638],{},[1846,84920,1848],{},[1974,84922,84923,84925],{},[898,84924,9646],{},[1979,84926,1981],{},[1846,84928,1945],{},[1979,84930,1981],{},[1974,84932,84933,84935],{},[898,84934,9641],{},[1979,84936,1981],{},[902,84938,84939],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,84941,84943],{"className":84942},[886],[888,84944,84945],{"xmlns":890},[892,84946,84947,84957],{},[895,84948,84949,84951,84953,84955],{},[898,84950,2667],{},[898,84952,3840],{},[898,84954,2623],{},[898,84956,8519],{},[902,84958,10445],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,84961,84963],{"className":84962},[886],[888,84964,84965],{"xmlns":890},[892,84966,84967,84971],{},[895,84968,84969],{},[1979,84970,2968],{},[902,84972,2968],{"encoding":904}," pracovníky a ",[883,84975,84977],{"className":84976},[886],[888,84978,84979],{"xmlns":890},[892,84980,84981,84985],{},[895,84982,84983],{},[1979,84984,77462],{},[902,84986,77462],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,84989,84991],{"className":84990},[886],[888,84992,84993],{"xmlns":890},[892,84994,84995,84999],{},[895,84996,84997],{},[1979,84998,46548],{},[902,85000,46548],{"encoding":904}," jednotek.",[724,85003,85004,85007,85008,10240,85038,1734],{},[38,85005,85006],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,85009,85011],{"className":85010},[886],[888,85012,85013],{"xmlns":890},[892,85014,85015,85035],{},[895,85016,85017,85019,85021,85023,85029],{},[898,85018,2638],{},[1846,85020,1848],{},[898,85022,4101],{},[1974,85024,85025,85027],{},[898,85026,9641],{},[898,85028,207],{},[1974,85030,85031,85033],{},[898,85032,9646],{},[898,85034,1948],{},[902,85036,85037],{"encoding":904},"Q = A L^{a} K^{b}",[883,85039,85041],{"className":85040},[886],[888,85042,85043],{"xmlns":890},[892,85044,85045,85075],{},[895,85046,85047,85049,85051,85053,85055,85057,85065,85067],{},[898,85048,2667],{},[898,85050,3840],{},[898,85052,2623],{},[898,85054,8519],{},[1846,85056,1848],{},[2175,85058,85059],{"scriptlevel":2177,"displaystyle":1854},[2179,85060,85061,85063],{},[898,85062,207],{},[898,85064,1948],{},[1846,85066,3025],{},[2175,85068,85069],{"scriptlevel":2177,"displaystyle":1854},[2179,85070,85071,85073],{},[898,85072,9646],{},[898,85074,9641],{},[902,85076,85077],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,85079,15565],{"id":15564},[120,85081,85082,85115,85142,85151,85201,85232,85285,85308,85363,85436,85514,85557,85589,85622,85663,85735,85796,85862,85879,85952,86018,86070,86126,86160,86203],{},[123,85083,85084,85087,85088,36741,85101,85114],{},[38,85085,85086],{},"Faktory (vstupy) produkce:"," práce ",[883,85089,85091],{"className":85090},[886],[888,85092,85093],{"xmlns":890},[892,85094,85095,85099],{},[895,85096,85097],{},[898,85098,9641],{},[902,85100,9641],{"encoding":904},[883,85102,85104],{"className":85103},[886],[888,85105,85106],{"xmlns":890},[892,85107,85108,85112],{},[895,85109,85110],{},[898,85111,9646],{},[902,85113,9646],{"encoding":904},", půda.",[123,85116,85117,6861,85119,1734],{},[38,85118,40296],{},[883,85120,85122],{"className":85121},[886],[888,85123,85124],{"xmlns":890},[892,85125,85126,85140],{},[895,85127,85128,85130,85132,85134,85136,85138],{},[898,85129,2638],{},[1846,85131,1848],{},[898,85133,2638],{},[1846,85135,1855],{"stretchy":1854},[898,85137,9641],{},[1846,85139,1861],{"stretchy":1854},[902,85141,74389],{"encoding":904},[123,85143,85144,9871,85146,11973,85149,1734],{},[38,85145,859],{},[614,85147,85148],{},"production function",[38,85150,74892],{},[123,85152,85153,2053,85155,1734],{},[38,85154,74938],{},[883,85156,85158],{"className":85157},[886],[888,85159,85160],{"xmlns":890},[892,85161,85162,85198],{},[895,85163,85164,85166,85172,85174,85176,85178,85180,85182,85184,85186,85192,85194,85196],{},[898,85165,2667],{},[2122,85167,85168,85170],{},[898,85169,3783],{},[898,85171,9641],{},[1846,85173,1848],{},[898,85175,2044],{},[898,85177,2638],{},[898,85179,4520],{"mathvariant":2226},[898,85181,2044],{},[898,85183,9641],{},[1846,85185,1848],{},[1974,85187,85188,85190],{},[898,85189,2638],{},[1846,85191,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,85193,1855],{"stretchy":1854},[898,85195,9641],{},[1846,85197,1861],{"stretchy":1854},[902,85199,85200],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,85202,85203,2053,85205,1734],{},[38,85204,75873],{},[883,85206,85208],{"className":85207},[886],[888,85209,85210],{"xmlns":890},[892,85211,85212,85230],{},[895,85213,85214,85216,85222,85224,85226,85228],{},[898,85215,4101],{},[2122,85217,85218,85220],{},[898,85219,3783],{},[898,85221,9641],{},[1846,85223,1848],{},[898,85225,2638],{},[898,85227,4520],{"mathvariant":2226},[898,85229,9641],{},[902,85231,74457],{"encoding":904},[123,85233,85234,85236,85237,10240,85254,1734],{},[38,85235,75360],{}," — od určitého ",[883,85238,85240],{"className":85239},[886],[888,85241,85242],{"xmlns":890},[892,85243,85244,85252],{},[895,85245,85246],{},[2122,85247,85248,85250],{},[898,85249,9641],{},[1979,85251,2177],{},[902,85253,75403],{"encoding":904},[883,85255,85257],{"className":85256},[886],[888,85258,85259],{"xmlns":890},[892,85260,85261,85283],{},[895,85262,85263,85273,85275,85277,85279,85281],{},[1974,85264,85265,85267],{},[898,85266,2638],{},[895,85268,85269,85271],{},[1846,85270,2228],{"mathvariant":2226},[1846,85272,2228],{"mathvariant":2226},[1846,85274,1855],{"stretchy":1854},[898,85276,9641],{},[1846,85278,1861],{"stretchy":1854},[1846,85280,3295],{},[1979,85282,2177],{},[902,85284,75549],{"encoding":904},[123,85286,85287,2053,85290,85307],{},[38,85288,85289],{},"Inflexní bod",[883,85291,85293],{"className":85292},[886],[888,85294,85295],{"xmlns":890},[892,85296,85297,85305],{},[895,85298,85299],{},[2122,85300,85301,85303],{},[898,85302,9641],{},[1979,85304,2177],{},[902,85306,75403],{"encoding":904}," — přechod z konvexity do konkavity.",[123,85309,85310,2053,85313,6861,85330,1734],{},[38,85311,85312],{},"Bod maxima produkce",[883,85314,85316],{"className":85315},[886],[888,85317,85318],{"xmlns":890},[892,85319,85320,85328],{},[895,85321,85322],{},[2122,85323,85324,85326],{},[898,85325,9641],{},[1979,85327,2128],{},[902,85329,13057],{"encoding":904},[883,85331,85333],{"className":85332},[886],[888,85334,85335],{"xmlns":890},[892,85336,85337,85361],{},[895,85338,85339,85341,85347,85349,85355,85357,85359],{},[898,85340,2667],{},[2122,85342,85343,85345],{},[898,85344,3783],{},[898,85346,9641],{},[1846,85348,1855],{"stretchy":1854},[2122,85350,85351,85353],{},[898,85352,9641],{},[1979,85354,2128],{},[1846,85356,1861],{"stretchy":1854},[1846,85358,1848],{},[1979,85360,2177],{},[902,85362,75622],{"encoding":904},[123,85364,85365,85387,85388,10240,85407,1734],{},[38,85366,85367,85368],{},"Princip maximalizace ",[883,85369,85371],{"className":85370},[886],[888,85372,85373],{"xmlns":890},[892,85374,85375,85385],{},[895,85376,85377,85379],{},[898,85378,4101],{},[2122,85380,85381,85383],{},[898,85382,3783],{},[898,85384,9641],{},[902,85386,74478],{"encoding":904}," — v bodě maxima ",[883,85389,85391],{"className":85390},[886],[888,85392,85393],{"xmlns":890},[892,85394,85395,85405],{},[895,85396,85397,85399],{},[898,85398,4101],{},[2122,85400,85401,85403],{},[898,85402,3783],{},[898,85404,9641],{},[902,85406,74478],{"encoding":904},[883,85408,85410],{"className":85409},[886],[888,85411,85412],{"xmlns":890},[892,85413,85414,85434],{},[895,85415,85416,85418,85424,85426,85428],{},[898,85417,2667],{},[2122,85419,85420,85422],{},[898,85421,3783],{},[898,85423,9641],{},[1846,85425,1848],{},[898,85427,4101],{},[2122,85429,85430,85432],{},[898,85431,3783],{},[898,85433,9641],{},[902,85435,74508],{"encoding":904},[123,85437,85438,2053,85441,1343,85480,1343,85497,1734],{},[38,85439,85440],{},"Polynomiální produkční funkce",[883,85442,85444],{"className":85443},[886],[888,85445,85446],{"xmlns":890},[892,85447,85448,85478],{},[895,85449,85450,85452,85454,85456,85458,85460,85462,85468,85470,85472],{},[898,85451,2638],{},[1846,85453,1855],{"stretchy":1854},[898,85455,9641],{},[1846,85457,1861],{"stretchy":1854},[1846,85459,1848],{},[898,85461,207],{},[1974,85463,85464,85466],{},[898,85465,9641],{},[1979,85467,2023],{},[1846,85469,1945],{},[898,85471,1948],{},[1974,85473,85474,85476],{},[898,85475,9641],{},[1979,85477,1981],{},[902,85479,75740],{"encoding":904},[883,85481,85483],{"className":85482},[886],[888,85484,85485],{"xmlns":890},[892,85486,85487,85495],{},[895,85488,85489,85491,85493],{},[898,85490,207],{},[1846,85492,3295],{},[1979,85494,2177],{},[902,85496,42930],{"encoding":904},[883,85498,85500],{"className":85499},[886],[888,85501,85502],{"xmlns":890},[892,85503,85504,85512],{},[895,85505,85506,85508,85510],{},[898,85507,1948],{},[1846,85509,3256],{},[1979,85511,2177],{},[902,85513,18659],{"encoding":904},[123,85515,85516,2053,85519,1734],{},[38,85517,85518],{},"Diferenciál produkce",[883,85520,85522],{"className":85521},[886],[888,85523,85524],{"xmlns":890},[892,85525,85526,85554],{},[895,85527,85528,85530,85532,85534,85536,85538,85540,85542,85548,85550,85552],{},[898,85529,2738],{"mathvariant":2226},[898,85531,2638],{},[1846,85533,1650],{},[898,85535,2044],{},[898,85537,2638],{},[1846,85539,1848],{},[898,85541,2667],{},[2122,85543,85544,85546],{},[898,85545,3783],{},[898,85547,9641],{},[2138,85549,2835],{},[898,85551,2044],{},[898,85553,9641],{},[902,85555,85556],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,85558,85559,6861,85561,1734],{},[38,85560,83816],{},[883,85562,85564],{"className":85563},[886],[888,85565,85566],{"xmlns":890},[892,85567,85568,85586],{},[895,85569,85570,85572,85574,85576,85578,85580,85582,85584],{},[898,85571,2638],{},[1846,85573,1848],{},[898,85575,2638],{},[1846,85577,1855],{"stretchy":1854},[898,85579,9641],{},[1846,85581,2136],{"separator":2135},[898,85583,9646],{},[1846,85585,1861],{"stretchy":1854},[902,85587,85588],{"encoding":904},"Q = Q(L, K)",[123,85590,85591,6861,85593,1734],{},[38,85592,77910],{},[883,85594,85596],{"className":85595},[886],[888,85597,85598],{"xmlns":890},[892,85599,85600,85620],{},[895,85601,85602,85604,85606,85608,85614],{},[898,85603,2638],{},[1846,85605,1848],{},[898,85607,4101],{},[1974,85609,85610,85612],{},[898,85611,9641],{},[898,85613,207],{},[1974,85615,85616,85618],{},[898,85617,9646],{},[898,85619,1948],{},[902,85621,74575],{"encoding":904},[123,85623,85624,6861,85627,85662],{},[38,85625,85626],{},"Ryzí Cobb-Douglas",[883,85628,85630],{"className":85629},[886],[888,85631,85632],{"xmlns":890},[892,85633,85634,85660],{},[895,85635,85636,85638,85640,85642,85648],{},[898,85637,2638],{},[1846,85639,1848],{},[898,85641,4101],{},[1974,85643,85644,85646],{},[898,85645,9641],{},[898,85647,207],{},[1974,85649,85650,85652],{},[898,85651,9646],{},[895,85653,85654,85656,85658],{},[1979,85655,2128],{},[1846,85657,2075],{},[898,85659,207],{},[902,85661,78737],{"encoding":904}," (konstantní výnosy).",[123,85664,85665,6861,85667,1734],{},[38,85666,79453],{},[883,85668,85670],{"className":85669},[886],[888,85671,85672],{"xmlns":890},[892,85673,85674,85732],{},[895,85675,85676,85678,85680,85682,85684,85686,85688,85690,85692,85694,85704,85706,85708,85718],{},[898,85677,2638],{},[1846,85679,1848],{},[898,85681,4101],{},[1846,85683,2336],{"stretchy":1854},[1846,85685,1855],{"stretchy":1854},[1979,85687,2128],{},[1846,85689,2075],{},[898,85691,207],{},[1846,85693,1861],{"stretchy":1854},[1974,85695,85696,85698],{},[898,85697,9641],{},[895,85699,85700,85702],{},[1846,85701,2075],{},[898,85703,1948],{},[1846,85705,1945],{},[898,85707,207],{},[1974,85709,85710,85712],{},[898,85711,9646],{},[895,85713,85714,85716],{},[1846,85715,2075],{},[898,85717,1948],{},[1974,85719,85720,85722],{},[1846,85721,2351],{"stretchy":1854},[895,85723,85724,85726,85728,85730],{},[1846,85725,2075],{},[1979,85727,2128],{},[898,85729,4520],{"mathvariant":2226},[898,85731,1948],{},[902,85733,85734],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,85736,85737,9871,85740,11973,85762,9871,85765,85795],{},[38,85738,85739],{},"Lineární",[883,85741,85743],{"className":85742},[886],[888,85744,85745],{"xmlns":890},[892,85746,85747,85759],{},[895,85748,85749,85751,85753,85755,85757],{},[898,85750,207],{},[898,85752,9641],{},[1846,85754,1945],{},[898,85756,1948],{},[898,85758,9646],{},[902,85760,85761],{"encoding":904},"aL + bK",[38,85763,85764],{},"Leontiefova",[883,85766,85768],{"className":85767},[886],[888,85769,85770],{"xmlns":890},[892,85771,85772,85792],{},[895,85773,85774,85776,85778,85780,85782,85784,85786,85788,85790],{},[898,85775,79681],{},[1846,85777,56045],{},[1846,85779,1855],{"stretchy":1854},[898,85781,207],{},[898,85783,9641],{},[1846,85785,2136],{"separator":2135},[898,85787,1948],{},[898,85789,9646],{},[1846,85791,1861],{"stretchy":1854},[902,85793,85794],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,85797,85798,6861,85814,1734],{},[38,85799,85800,85801],{},"Homogenita stupně ",[883,85802,85804],{"className":85803},[886],[888,85805,85806],{"xmlns":890},[892,85807,85808,85812],{},[895,85809,85810],{},[898,85811,36705],{},[902,85813,36705],{"encoding":904},[883,85815,85817],{"className":85816},[886],[888,85818,85819],{"xmlns":890},[892,85820,85821,85859],{},[895,85822,85823,85825,85827,85829,85831,85833,85835,85837,85839,85841,85847,85849,85851,85853,85855,85857],{},[898,85824,2638],{},[1846,85826,1855],{"stretchy":1854},[898,85828,11886],{},[898,85830,9641],{},[1846,85832,2136],{"separator":2135},[898,85834,11886],{},[898,85836,9646],{},[1846,85838,1861],{"stretchy":1854},[1846,85840,1848],{},[1974,85842,85843,85845],{},[898,85844,11886],{},[898,85846,36705],{},[898,85848,2638],{},[1846,85850,1855],{"stretchy":1854},[898,85852,9641],{},[1846,85854,2136],{"separator":2135},[898,85856,9646],{},[1846,85858,1861],{"stretchy":1854},[902,85860,85861],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,85863,85864,78835],{},[38,85865,78768,85866],{},[883,85867,85869],{"className":85868},[886],[888,85870,85871],{"xmlns":890},[892,85872,85873,85877],{},[895,85874,85875],{},[898,85876,4101],{},[902,85878,4101],{"encoding":904},[123,85880,85881,85883,85884,85906,85907,85929,85930,3764],{},[38,85882,78269],{}," — konstantní (",[883,85885,85887],{"className":85886},[886],[888,85888,85889],{"xmlns":890},[892,85890,85891,85903],{},[895,85892,85893,85895,85897,85899,85901],{},[898,85894,207],{},[1846,85896,1945],{},[898,85898,1948],{},[1846,85900,1848],{},[1979,85902,2128],{},[902,85904,85905],{"encoding":904},"a+b=1","), rostoucí (",[883,85908,85910],{"className":85909},[886],[888,85911,85912],{"xmlns":890},[892,85913,85914,85926],{},[895,85915,85916,85918,85920,85922,85924],{},[898,85917,207],{},[1846,85919,1945],{},[898,85921,1948],{},[1846,85923,3256],{},[1979,85925,2128],{},[902,85927,85928],{"encoding":904},"a+b>1","), klesající (",[883,85931,85933],{"className":85932},[886],[888,85934,85935],{"xmlns":890},[892,85936,85937,85949],{},[895,85938,85939,85941,85943,85945,85947],{},[898,85940,207],{},[1846,85942,1945],{},[898,85944,1948],{},[1846,85946,3295],{},[1979,85948,2128],{},[902,85950,85951],{"encoding":904},"a+b\u003C1",[123,85953,85954,2053,85956,1343,85986,2053,85988,1734],{},[38,85955,74938],{},[883,85957,85959],{"className":85958},[886],[888,85960,85961],{"xmlns":890},[892,85962,85963,85983],{},[895,85964,85965,85967,85973,85975],{},[898,85966,2667],{},[2122,85968,85969,85971],{},[898,85970,3783],{},[898,85972,9641],{},[1846,85974,1848],{},[9012,85976,85977,85979,85981],{},[898,85978,2638],{},[898,85980,9641],{},[1846,85982,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,85984,85985],{"encoding":904},"MP_L = Q'_L",[38,85987,77842],{},[883,85989,85991],{"className":85990},[886],[888,85992,85993],{"xmlns":890},[892,85994,85995,86015],{},[895,85996,85997,85999,86005,86007],{},[898,85998,2667],{},[2122,86000,86001,86003],{},[898,86002,3783],{},[898,86004,9646],{},[1846,86006,1848],{},[9012,86008,86009,86011,86013],{},[898,86010,2638],{},[898,86012,9646],{},[1846,86014,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,86016,86017],{"encoding":904},"MP_K = Q'_K",[123,86019,86020,2053,86022,1734],{},[38,86021,80056],{},[883,86023,86025],{"className":86024},[886],[888,86026,86027],{"xmlns":890},[892,86028,86029,86067],{},[895,86030,86031,86033,86035,86037,86039,86045,86047,86049,86051,86053,86055,86061,86063,86065],{},[898,86032,2044],{},[898,86034,2638],{},[1846,86036,1848],{},[898,86038,2667],{},[2122,86040,86041,86043],{},[898,86042,3783],{},[898,86044,9641],{},[2138,86046,2835],{},[898,86048,2044],{},[898,86050,9641],{},[1846,86052,1945],{},[898,86054,2667],{},[2122,86056,86057,86059],{},[898,86058,3783],{},[898,86060,9646],{},[2138,86062,2835],{},[898,86064,2044],{},[898,86066,9646],{},[902,86068,86069],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,86071,86072,6861,86074,1734],{},[38,86073,80401],{},[883,86075,86077],{"className":86076},[886],[888,86078,86079],{"xmlns":890},[892,86080,86081,86123],{},[895,86082,86083,86085,86093,86095,86097,86105,86107,86109,86111,86113,86115,86117,86119,86121],{},[898,86084,9641],{},[9012,86086,86087,86089,86091],{},[898,86088,2638],{},[898,86090,9641],{},[1846,86092,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,86094,1945],{},[898,86096,9646],{},[9012,86098,86099,86101,86103],{},[898,86100,2638],{},[898,86102,9646],{},[1846,86104,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,86106,1848],{},[898,86108,36705],{},[2138,86110,2835],{},[898,86112,2638],{},[1846,86114,1855],{"stretchy":1854},[898,86116,9641],{},[1846,86118,2136],{"separator":2135},[898,86120,9646],{},[1846,86122,1861],{"stretchy":1854},[902,86124,86125],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,86127,86128,86131,86132,1734],{},[38,86129,86130],{},"Izokvanta"," — křivka ",[883,86133,86135],{"className":86134},[886],[888,86136,86137],{"xmlns":890},[892,86138,86139,86157],{},[895,86140,86141,86143,86145,86147,86149,86151,86153,86155],{},[898,86142,2638],{},[1846,86144,1855],{"stretchy":1854},[898,86146,9641],{},[1846,86148,2136],{"separator":2135},[898,86150,9646],{},[1846,86152,1861],{"stretchy":1854},[1846,86154,1848],{},[898,86156,80642],{},[902,86158,86159],{"encoding":904},"Q(L, K) = q",[123,86161,86162,2053,86164,1734],{},[38,86163,80831],{},[883,86165,86167],{"className":86166},[886],[888,86168,86169],{"xmlns":890},[892,86170,86171,86201],{},[895,86172,86173,86175,86177,86179,86181,86183,86185,86191,86193,86195],{},[898,86174,2667],{},[898,86176,3840],{},[898,86178,2623],{},[898,86180,8519],{},[1846,86182,1848],{},[898,86184,2667],{},[2122,86186,86187,86189],{},[898,86188,3783],{},[898,86190,9641],{},[898,86192,4520],{"mathvariant":2226},[898,86194,2667],{},[2122,86196,86197,86199],{},[898,86198,3783],{},[898,86200,9646],{},[902,86202,74650],{"encoding":904},[123,86204,86205,2053,86208,1734],{},[38,86206,86207],{},"Substituční vztah",[883,86209,86211],{"className":86210},[886],[888,86212,86213],{"xmlns":890},[892,86214,86215,86239],{},[895,86216,86217,86219,86221,86223,86225,86227,86229,86231,86233,86235,86237],{},[898,86218,2738],{"mathvariant":2226},[898,86220,9646],{},[1846,86222,1650],{},[1846,86224,2075],{},[898,86226,2667],{},[898,86228,3840],{},[898,86230,2623],{},[898,86232,8519],{},[2138,86234,2835],{},[898,86236,2044],{},[898,86238,9641],{},[902,86240,86241],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,86243,3640],{"id":3639},[120,86245,86246,86343,86350,86357],{},[123,86247,86248,2053,86250,86253,86254,1343,86257,86260,86261,86264,86265,86284,86285,18493,86304,86307,86308,86327,86328,3764],{},[38,86249,50568],{},[207,86251,784],{"className":86252,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,86255,2207],{"className":86256,"dataFsResolvedFilePath":764,"href":765},[210],[207,86258,793],{"className":86259,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,86262,880],{"className":86263,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,86266,86268],{"className":86267},[886],[888,86269,86270],{"xmlns":890},[892,86271,86272,86282],{},[895,86273,86274,86276,86278,86280],{},[898,86275,2667],{},[898,86277,3840],{},[898,86279,2623],{},[898,86281,8519],{},[902,86283,10445],{"encoding":904}," ↔ ",[883,86286,86288],{"className":86287},[886],[888,86289,86290],{"xmlns":890},[892,86291,86292,86302],{},[895,86293,86294,86296,86298,86300],{},[898,86295,2667],{},[898,86297,3840],{},[898,86299,2626],{},[898,86301,8519],{},[902,86303,10449],{"encoding":904},[207,86305,1708],{"className":86306,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,86309,86311],{"className":86310},[886],[888,86312,86313],{"xmlns":890},[892,86314,86315,86325],{},[895,86316,86317,86319],{},[898,86318,4101],{},[2122,86320,86321,86323],{},[898,86322,3783],{},[898,86324,9641],{},[902,86326,74478],{"encoding":904}," ↔ min ",[883,86329,86331],{"className":86330},[886],[888,86332,86333],{"xmlns":890},[892,86334,86335,86341],{},[895,86336,86337,86339],{},[898,86338,4101],{},[898,86340,2626],{},[902,86342,55405],{"encoding":904},[123,86344,86345,2053,86347,1734],{},[38,86346,3647],{},[207,86348,1721],{"className":86349,"dataFsResolvedFilePath":848,"href":849},[210],[123,86351,86352,2053,86354,1734],{},[38,86353,16058],{},[207,86355,1094],{"className":86356,"dataFsResolvedFilePath":838,"href":839},[210],[123,86358,86359,2053,86361,1734],{},[38,86360,16049],{},[207,86362,16053],{"className":86363,"dataFsResolvedFilePath":1761,"href":1762},[210],{"title":641,"searchDepth":642,"depth":642,"links":86365},[86366,86367,86368,86372,86374,86379,86380,86387,86388,86390,86391,86392,86394,86399,86400,86401,86405,86406],{"id":74673,"depth":642,"text":74674},{"id":74810,"depth":642,"text":74811},{"id":74913,"depth":642,"text":86369,"children":86370},"Mezní produkt práce (MPLMP_L)",[86371],{"id":75359,"depth":649,"text":75360},{"id":75848,"depth":642,"text":86373},"Průměrný produkt práce (APLAP_L)",{"id":75966,"depth":642,"text":75967,"children":86375},[86376,86377,86378],{"id":76203,"depth":649,"text":65346},{"id":76514,"depth":649,"text":76515},{"id":77234,"depth":649,"text":77235},{"id":77806,"depth":642,"text":77807},{"id":77909,"depth":642,"text":77910,"children":86381},[86382,86383,86385,86386],{"id":78268,"depth":649,"text":78269},{"id":78767,"depth":649,"text":86384},"Parametr efektivity AA",{"id":78838,"depth":649,"text":78839},{"id":37024,"depth":649,"text":79178},{"id":79365,"depth":642,"text":79366},{"id":79704,"depth":642,"text":86389},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":80395,"depth":642,"text":80396},{"id":74739,"depth":642,"text":9624},{"id":80806,"depth":642,"text":86393},"Mezní míra technické substituce (MRTSMRTS)",{"id":81672,"depth":642,"text":81673,"children":86395},[86396,86397,86398],{"id":81676,"depth":649,"text":81677},{"id":82319,"depth":649,"text":82320},{"id":82600,"depth":649,"text":82601},{"id":82946,"depth":642,"text":82947},{"id":49726,"depth":642,"text":49727},{"id":83296,"depth":642,"text":83297,"children":86402},[86403,86404],{"id":40295,"depth":649,"text":40296},{"id":83815,"depth":649,"text":83816},{"id":15564,"depth":642,"text":15565},{"id":3639,"depth":642,"text":3640},{},"\u002Ftopics\u002Fprodukce",{"title":74309,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,9659,86413,86414,86415,74739,86416,86417],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":86420,"title":86421,"body":86422,"course":1128,"courses":659,"created":9402,"description":641,"extension":661,"meta":95369,"navigation":664,"path":95370,"seo":95371,"sources":95372,"stem":95373,"tags":95374,"type":3703,"updated":677,"__hash__":95377},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":86423,"toc":95343},[86424,86427,86429,86626,86635,86639,86642,86695,86699,86711,86715,86718,86735,86858,86864,87008,87018,87022,87057,87095,87143,87200,87260,87302,87878,87882,87965,88074,88167,88425,88428,88481,88592,88674,88678,88689,88922,88977,88983,89023,89086,89097,89288,89394,89547,89595,89600,89714,89752,89878,89924,89951,90028,90103,90183,90313,90374,90462,90466,90469,90538,90621,90628,90688,90998,91002,91008,91061,91077,91128,91266,91342,91455,91772,91776,91783,91943,92002,92006,92028,92125,92246,92360,92383,92446,92503,92755,92763,92767,92774,93028,93078,93134,93137,93301,93305,93403,93405,93437,93441,93574,93816,94000,94168,94475,94608,94795,94807,94809,95244,95246],[12,86425,86421],{"id":86426},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,86428,11851],{"id":11850},[724,86430,86431,2053,86433,86464,86465,86468,86469,86499,86500,86518,86519,86559,86560,86563,86564,86577,86578,28098,86581,86594,86595,86608,86609,86622,86623,1734],{},[38,86432,880],{},[883,86434,86436],{"className":86435},[886],[888,86437,86438],{"xmlns":890},[892,86439,86440,86462],{},[895,86441,86442,86444,86446,86452,86454,86460],{},[898,86443,900],{},[1846,86445,1855],{"stretchy":1854},[2122,86447,86448,86450],{},[898,86449,2638],{},[1979,86451,2128],{},[1846,86453,2136],{"separator":2135},[2122,86455,86456,86458],{},[898,86457,2638],{},[1979,86459,1981],{},[1846,86461,1861],{"stretchy":1854},[902,86463,16188],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,86466,86467],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,86470,86472],{"className":86471},[886],[888,86473,86474],{"xmlns":890},[892,86475,86476,86496],{},[895,86477,86478,86480,86486,86488],{},[898,86479,2667],{},[2122,86481,86482,86484],{},[898,86483,900],{},[898,86485,17635],{},[1846,86487,1848],{},[9012,86489,86490,86492,86494],{},[898,86491,900],{},[898,86493,17635],{},[1846,86495,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,86497,86498],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,86501,86503],{"className":86502},[886],[888,86504,86505],{"xmlns":890},[892,86506,86507,86515],{},[895,86508,86509,86511,86513],{},[898,86510,900],{},[1846,86512,1848],{},[898,86514,1992],{},[902,86516,86517],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,86520,86522],{"className":86521},[886],[888,86523,86524],{"xmlns":890},[892,86525,86526,86556],{},[895,86527,86528,86530,86532,86534,86536,86538,86540,86546,86548,86550],{},[898,86529,2667],{},[898,86531,3840],{},[898,86533,2626],{},[898,86535,8519],{},[1846,86537,1848],{},[898,86539,2667],{},[2122,86541,86542,86544],{},[898,86543,900],{},[1979,86545,2128],{},[898,86547,4520],{"mathvariant":2226},[898,86549,2667],{},[2122,86551,86552,86554],{},[898,86553,900],{},[1979,86555,1981],{},[902,86557,86558],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,86561,86562],{},"teorii užitečnosti"," — funkce ",[883,86565,86567],{"className":86566},[886],[888,86568,86569],{"xmlns":890},[892,86570,86571,86575],{},[895,86572,86573],{},[898,86574,900],{},[902,86576,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,86579,86580],{},"Optimalizaci spotřebitele",[883,86582,86584],{"className":86583},[886],[888,86585,86586],{"xmlns":890},[892,86587,86588,86592],{},[895,86589,86590],{},[898,86591,900],{},[902,86593,900],{"encoding":904}," při rozpočtu, min ",[883,86596,86598],{"className":86597},[886],[888,86599,86600],{"xmlns":890},[892,86601,86602,86606],{},[895,86603,86604],{},[898,86605,4098],{},[902,86607,4098],{"encoding":904}," při dané ",[883,86610,86612],{"className":86611},[886],[888,86613,86614],{"xmlns":890},[892,86615,86616,86620],{},[895,86617,86618],{},[898,86619,900],{},[902,86621,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,86624,913],{"className":86625,"dataFsResolvedFilePath":911,"href":912},[210],[724,86627,86628,86629,86631,86632,1734],{},"Kapitola 6 knihy ",[614,86630,16053],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,86633,36599],{"className":86634,"dataFsResolvedFilePath":911,"href":912},[210],[115,86636,86638],{"id":86637},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,86640,86641],{},"Po prostudování této kapitoly byste měli umět:",[120,86643,86644,86650,86659,86664,86667,86673,86679,86682,86688],{},[123,86645,86646,86647,2136],{},"vyložit, co se rozumí termínem ",[38,86648,86649],{},"užitečnost",[123,86651,86652,86653,1745,86656,2136],{},"definovat pojmy ",[38,86654,86655],{},"svazek zboží",[38,86657,86658],{},"funkce užitečnosti",[123,86660,74688,86661,74695],{},[38,86662,86663],{},"mezní užitečnosti",[123,86665,86666],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,86668,74715,86669,86672],{},[38,86670,86671],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,86674,74736,86675,86678],{},[38,86676,86677],{},"křivky užitečnosti"," (indiferenční křivky),",[123,86680,86681],{},"vyjmenovat jejich základní vlastnosti,",[123,86683,74688,86684,86687],{},[38,86685,86686],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,86689,86690,86691,86694],{},"řešit ",[38,86692,86693],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,86696,86698],{"id":86697},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,86700,86701,86702,86706,86707,86710],{},"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 ",[207,86703,86705],{"className":86704,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,86708,86709],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,86712,86714],{"id":86713},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,86716,86717],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,86719,86720,86726],{},[123,86721,86722,86725],{},[38,86723,86724],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,86727,86728,86731,86732,86734],{},[38,86729,86730],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,86733,86467],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[1639,86736,86737],{},[724,86738,86739,86741,86742,86745,86746,2053,86759,86762,86763,1745,86776,86795,86796,1343,86822,86849,86850,86853,86854,86857],{},[883,86740,4258],{}," Pozor — ordinalisté užitečnost ",[38,86743,86744],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,86747,86749],{"className":86748},[886],[888,86750,86751],{"xmlns":890},[892,86752,86753,86757],{},[895,86754,86755],{},[898,86756,900],{},[902,86758,900],{"encoding":904},[38,86760,86761],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,86764,86766],{"className":86765},[886],[888,86767,86768],{"xmlns":890},[892,86769,86770,86774],{},[895,86771,86772],{},[898,86773,900],{},[902,86775,900],{"encoding":904},[883,86777,86779],{"className":86778},[886],[888,86780,86781],{"xmlns":890},[892,86782,86783,86792],{},[895,86784,86785],{},[8232,86786,86787,86789],{"accent":2135},[898,86788,900],{},[1846,86790,86791],{},"~",[902,86793,86794],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,86797,86799],{"className":86798},[886],[888,86800,86801],{"xmlns":890},[892,86802,86803,86819],{},[895,86804,86805,86811,86813],{},[8232,86806,86807,86809],{"accent":2135},[898,86808,900],{},[1846,86810,86791],{},[1846,86812,1848],{},[1974,86814,86815,86817],{},[898,86816,900],{},[1979,86818,1981],{},[902,86820,86821],{"encoding":904},"\\tilde U = U^2",[883,86823,86825],{"className":86824},[886],[888,86826,86827],{"xmlns":890},[892,86828,86829,86846],{},[895,86830,86831,86837,86839,86842,86844],{},[8232,86832,86833,86835],{"accent":2135},[898,86834,900],{},[1846,86836,86791],{},[1846,86838,1848],{},[898,86840,86841],{},"ln",[1846,86843,56045],{},[898,86845,900],{},[902,86847,86848],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,86851,86852],{},"porovnání"," mezi svazky a ",[38,86855,86856],{},"poměry"," mezních veličin.",[724,86859,86860,86861,2554],{},"Ordinalistický přístup vychází z ",[38,86862,86863],{},"pěti hlavních předpokladů",[152,86865,86866,86872,86878,86996,87002],{},[123,86867,86868,86871],{},[38,86869,86870],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,86873,86874,86877],{},[38,86875,86876],{},"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.",[123,86879,86880,86883,86884,61586,86897,86910,86911,61586,86924,2776,86937,86940,86941,1745,86960,62415,86978,1734],{},[38,86881,86882],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,86885,86887],{"className":86886},[886],[888,86888,86889],{"xmlns":890},[892,86890,86891,86895],{},[895,86892,86893],{},[898,86894,4101],{},[902,86896,4101],{"encoding":904},[883,86898,86900],{"className":86899},[886],[888,86901,86902],{"xmlns":890},[892,86903,86904,86908],{},[895,86905,86906],{},[898,86907,23098],{},[902,86909,23098],{"encoding":904},", nebude jindy preferovat ",[883,86912,86914],{"className":86913},[886],[888,86915,86916],{"xmlns":890},[892,86917,86918,86922],{},[895,86919,86920],{},[898,86921,23098],{},[902,86923,23098],{"encoding":904},[883,86925,86927],{"className":86926},[886],[888,86928,86929],{"xmlns":890},[892,86930,86931,86935],{},[895,86932,86933],{},[898,86934,4101],{},[902,86936,4101],{"encoding":904},[38,86938,86939],{},"Tranzitivita",": pokud ",[883,86942,86944],{"className":86943},[886],[888,86945,86946],{"xmlns":890},[892,86947,86948,86957],{},[895,86949,86950,86952,86955],{},[898,86951,4101],{},[1846,86953,86954],{},"≻",[898,86956,23098],{},[902,86958,86959],{"encoding":904},"A \\succ B",[883,86961,86963],{"className":86962},[886],[888,86964,86965],{"xmlns":890},[892,86966,86967,86975],{},[895,86968,86969,86971,86973],{},[898,86970,23098],{},[1846,86972,86954],{},[898,86974,2626],{},[902,86976,86977],{"encoding":904},"B \\succ C",[883,86979,86981],{"className":86980},[886],[888,86982,86983],{"xmlns":890},[892,86984,86985,86993],{},[895,86986,86987,86989,86991],{},[898,86988,4101],{},[1846,86990,86954],{},[898,86992,2626],{},[902,86994,86995],{"encoding":904},"A \\succ C",[123,86997,86998,87001],{},[38,86999,87000],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,87003,87004,87007],{},[38,87005,87006],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,87009,87010,87011,87014,87015,1734],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,87012,87013],{},"preference"," a na příbuzné ",[614,87016,87017],{},"funkci užitečnosti",[115,87019,87021],{"id":87020},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,87023,87024,87025,87038,87039,87042,87043,87056],{},"Uvažujme ",[883,87026,87028],{"className":87027},[886],[888,87029,87030],{"xmlns":890},[892,87031,87032,87036],{},[895,87033,87034],{},[898,87035,36705],{},[902,87037,36705],{"encoding":904}," různých zboží. ",[38,87040,87041],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,87044,87046],{"className":87045},[886],[888,87047,87048],{"xmlns":890},[892,87049,87050,87054],{},[895,87051,87052],{},[898,87053,36705],{},[902,87055,36705],{"encoding":904},"-tice",[724,87058,87059],{},[883,87060,87062],{"className":87061},[886],[888,87063,87064],{"xmlns":890},[892,87065,87066,87092],{},[895,87067,87068,87070,87076,87078,87080,87082,87088,87090],{},[1846,87069,1855],{"stretchy":1854},[2122,87071,87072,87074],{},[898,87073,2638],{},[1979,87075,2128],{},[1846,87077,2136],{"separator":2135},[1846,87079,9492],{},[1846,87081,2136],{"separator":2135},[2122,87083,87084,87086],{},[898,87085,2638],{},[898,87087,36705],{},[1846,87089,1861],{"stretchy":1854},[1846,87091,2136],{"separator":2135},[902,87093,87094],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,87096,4156,87097,87114,87115,87128,87129,87132,87133,87136,87137,87140,87141,2554],{},[883,87098,87100],{"className":87099},[886],[888,87101,87102],{"xmlns":890},[892,87103,87104,87112],{},[895,87105,87106],{},[2122,87107,87108,87110],{},[898,87109,2638],{},[898,87111,17635],{},[902,87113,47383],{"encoding":904}," značí množství ",[883,87116,87118],{"className":87117},[886],[888,87119,87120],{"xmlns":890},[892,87121,87122,87126],{},[895,87123,87124],{},[898,87125,17635],{},[902,87127,17635],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,87130,87131],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,87134,87135],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,87138,87139],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,87142,87017],{},[883,87144,87146],{"className":87145},[886],[888,87147,87148],{"xmlns":890,"display":27911},[892,87149,87150,87197],{},[20599,87151,87152],{"width":27916},[20604,87153,87154,87156,87190,87192],{},[20607,87155],{"width":27921},[20607,87157,87158],{},[895,87159,87160,87162,87164,87166,87168,87174,87176,87178,87180,87186,87188],{},[898,87161,900],{},[1846,87163,1848],{},[898,87165,900],{},[1846,87167,1855],{"stretchy":1854},[2122,87169,87170,87172],{},[898,87171,2638],{},[1979,87173,2128],{},[1846,87175,2136],{"separator":2135},[1846,87177,9492],{},[1846,87179,2136],{"separator":2135},[2122,87181,87182,87184],{},[898,87183,2638],{},[898,87185,36705],{},[1846,87187,1861],{"stretchy":1854},[1846,87189,2136],{"separator":2135},[20607,87191],{"width":27921},[20607,87193,87194],{},[2138,87195,87196],{},"(6.1)",[902,87198,87199],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,87201,4156,87202,87232,87233,87255,87256,87259],{},[883,87203,87205],{"className":87204},[886],[888,87206,87207],{"xmlns":890},[892,87208,87209,87229],{},[895,87210,87211,87217,87219,87221,87223],{},[2122,87212,87213,87215],{},[898,87214,2638],{},[1979,87216,2128],{},[1846,87218,2136],{"separator":2135},[1846,87220,9492],{},[1846,87222,2136],{"separator":2135},[2122,87224,87225,87227],{},[898,87226,2638],{},[898,87228,36705],{},[902,87230,87231],{"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 ",[883,87234,87236],{"className":87235},[886],[888,87237,87238],{"xmlns":890},[892,87239,87240,87252],{},[895,87241,87242,87244,87246],{},[898,87243,900],{},[1846,87245,2136],{"separator":2135},[8232,87247,87248,87250],{"accent":2135},[898,87249,900],{},[1846,87251,86791],{},[902,87253,87254],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,87257,87258],{},"monotónní transformace"," zachovávající pořadí.",[724,87261,87262,87263,6861,87266,1734],{},"Dále se omezíme na funkce pro ",[38,87264,87265],{},"dvě zboží",[883,87267,87269],{"className":87268},[886],[888,87270,87271],{"xmlns":890},[892,87272,87273,87299],{},[895,87274,87275,87277,87279,87281,87283,87289,87291,87297],{},[898,87276,900],{},[1846,87278,1848],{},[898,87280,900],{},[1846,87282,1855],{"stretchy":1854},[2122,87284,87285,87287],{},[898,87286,2638],{},[1979,87288,2128],{},[1846,87290,2136],{"separator":2135},[2122,87292,87293,87295],{},[898,87294,2638],{},[1979,87296,1981],{},[1846,87298,1861],{"stretchy":1854},[902,87300,87301],{"encoding":904},"U = U(Q_1, Q_2)",[1639,87303,87304,87379],{},[724,87305,87306,87308,87309,2554],{},[883,87307,52540],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,87310,87312],{"className":87311},[886],[888,87313,87314],{"xmlns":890},[892,87315,87316,87376],{},[895,87317,87318,87320,87322,87324,87326,87332,87334,87340,87342,87348,87350,87352,87354],{},[898,87319,900],{},[1846,87321,1848],{},[898,87323,900],{},[1846,87325,1855],{"stretchy":1854},[2122,87327,87328,87330],{},[898,87329,2638],{},[1979,87331,2128],{},[1846,87333,2136],{"separator":2135},[2122,87335,87336,87338],{},[898,87337,2638],{},[1979,87339,1981],{},[1846,87341,2136],{"separator":2135},[2122,87343,87344,87346],{},[898,87345,2638],{},[1979,87347,2023],{},[1846,87349,1861],{"stretchy":1854},[1846,87351,1848],{},[1979,87353,1981],{},[7963,87355,87356],{},[895,87357,87358,87364,87370],{},[2122,87359,87360,87362],{},[898,87361,2638],{},[1979,87363,2128],{},[2122,87365,87366,87368],{},[898,87367,2638],{},[1979,87369,1981],{},[2122,87371,87372,87374],{},[898,87373,2638],{},[1979,87375,2023],{},[902,87377,87378],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,87380,87381,87574],{},[123,87382,87383,87384,87410,87411,12783,87437,1745,87496,5435,87556,8271],{},"svazek ",[883,87385,87387],{"className":87386},[886],[888,87388,87389],{"xmlns":890},[892,87390,87391,87407],{},[895,87392,87393,87395,87397,87399,87401,87403,87405],{},[1846,87394,1855],{"stretchy":1854},[1979,87396,41707],{},[1846,87398,2136],{"separator":2135},[1979,87400,2201],{},[1846,87402,2136],{"separator":2135},[1979,87404,41685],{},[1846,87406,1861],{"stretchy":1854},[902,87408,87409],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,87412,87414],{"className":87413},[886],[888,87415,87416],{"xmlns":890},[892,87417,87418,87434],{},[895,87419,87420,87422,87424,87426,87428,87430,87432],{},[1846,87421,1855],{"stretchy":1854},[1979,87423,3845],{},[1846,87425,2136],{"separator":2135},[1979,87427,3845],{},[1846,87429,2136],{"separator":2135},[1979,87431,66442],{},[1846,87433,1861],{"stretchy":1854},[902,87435,87436],{"encoding":904},"(9, 9, 27)",[883,87438,87440],{"className":87439},[886],[888,87441,87442],{"xmlns":890},[892,87443,87444,87493],{},[895,87445,87446,87448,87450,87452,87454,87456,87458,87460,87462,87464,87466,87480,87482,87484,87489,87491],{},[898,87447,900],{},[1846,87449,1855],{"stretchy":1854},[1979,87451,41707],{},[1846,87453,2136],{"separator":2135},[1979,87455,2201],{},[1846,87457,2136],{"separator":2135},[1979,87459,41685],{},[1846,87461,1861],{"stretchy":1854},[1846,87463,1848],{},[1979,87465,1981],{},[7963,87467,87468],{},[895,87469,87470,87472,87474,87476,87478],{},[1979,87471,41707],{},[1846,87473,3025],{},[1979,87475,2201],{},[1846,87477,3025],{},[1979,87479,41685],{},[1846,87481,1848],{},[1979,87483,1981],{},[7963,87485,87486],{},[1979,87487,87488],{},"4096",[1846,87490,1848],{},[1979,87492,5463],{},[902,87494,87495],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,87497,87499],{"className":87498},[886],[888,87500,87501],{"xmlns":890},[892,87502,87503,87553],{},[895,87504,87505,87507,87509,87511,87513,87515,87517,87519,87521,87523,87525,87539,87541,87543,87548,87550],{},[898,87506,900],{},[1846,87508,1855],{"stretchy":1854},[1979,87510,3845],{},[1846,87512,2136],{"separator":2135},[1979,87514,3845],{},[1846,87516,2136],{"separator":2135},[1979,87518,66442],{},[1846,87520,1861],{"stretchy":1854},[1846,87522,1848],{},[1979,87524,1981],{},[7963,87526,87527],{},[895,87528,87529,87531,87533,87535,87537],{},[1979,87530,3845],{},[1846,87532,3025],{},[1979,87534,3845],{},[1846,87536,3025],{},[1979,87538,66442],{},[1846,87540,1848],{},[1979,87542,1981],{},[7963,87544,87545],{},[1979,87546,87547],{},"2187",[1846,87549,5746],{},[1979,87551,87552],{},"93,53",[902,87554,87555],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,87557,87559],{"className":87558},[886],[888,87560,87561],{"xmlns":890},[892,87562,87563,87571],{},[895,87564,87565,87567,87569],{},[1979,87566,5463],{},[1846,87568,3256],{},[1979,87570,87552],{},[902,87572,87573],{"encoding":904},"128 > 93{,}53",[123,87575,87576,87577,1745,87603,87629,87630,1745,87670,87711,87712,87758,87759,1745,87785,2694,87811,1745,87829,87847,87848,1734],{},"svazky ",[883,87578,87580],{"className":87579},[886],[888,87581,87582],{"xmlns":890},[892,87583,87584,87600],{},[895,87585,87586,87588,87590,87592,87594,87596,87598],{},[1846,87587,1855],{"stretchy":1854},[1979,87589,2201],{},[1846,87591,2136],{"separator":2135},[1979,87593,5431],{},[1846,87595,2136],{"separator":2135},[1979,87597,1981],{},[1846,87599,1861],{"stretchy":1854},[902,87601,87602],{"encoding":904},"(4, 8, 2)",[883,87604,87606],{"className":87605},[886],[888,87607,87608],{"xmlns":890},[892,87609,87610,87626],{},[895,87611,87612,87614,87616,87618,87620,87622,87624],{},[1846,87613,1855],{"stretchy":1854},[1979,87615,41685],{},[1846,87617,2136],{"separator":2135},[1979,87619,2128],{},[1846,87621,2136],{"separator":2135},[1979,87623,2201],{},[1846,87625,1861],{"stretchy":1854},[902,87627,87628],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,87631,87633],{"className":87632},[886],[888,87634,87635],{"xmlns":890},[892,87636,87637,87667],{},[895,87638,87639,87641,87643,87645,87647,87649,87651,87653,87655,87657,87659,87663,87665],{},[898,87640,900],{},[1846,87642,1855],{"stretchy":1854},[1979,87644,2201],{},[1846,87646,2136],{"separator":2135},[1979,87648,5431],{},[1846,87650,2136],{"separator":2135},[1979,87652,1981],{},[1846,87654,1861],{"stretchy":1854},[1846,87656,1848],{},[1979,87658,1981],{},[7963,87660,87661],{},[1979,87662,41685],{},[1846,87664,1848],{},[1979,87666,41707],{},[902,87668,87669],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,87671,87673],{"className":87672},[886],[888,87674,87675],{"xmlns":890},[892,87676,87677,87708],{},[895,87678,87679,87681,87683,87685,87687,87689,87691,87693,87695,87697,87699,87704,87706],{},[898,87680,900],{},[1846,87682,1855],{"stretchy":1854},[1979,87684,41685],{},[1846,87686,2136],{"separator":2135},[1979,87688,2128],{},[1846,87690,2136],{"separator":2135},[1979,87692,2201],{},[1846,87694,1861],{"stretchy":1854},[1846,87696,1848],{},[1979,87698,1981],{},[7963,87700,87701],{},[1979,87702,87703],{},"256",[1846,87705,1848],{},[1979,87707,72204],{},[902,87709,87710],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,87713,87715],{"className":87714},[886],[888,87716,87717],{"xmlns":890},[892,87718,87719,87755],{},[895,87720,87721,87723,87725,87727,87729,87731,87733,87735,87737,87739,87741,87743,87745,87747,87749,87751,87753],{},[898,87722,900],{},[1846,87724,1855],{"stretchy":1854},[1979,87726,2201],{},[1846,87728,2136],{"separator":2135},[1979,87730,5431],{},[1846,87732,2136],{"separator":2135},[1979,87734,1981],{},[1846,87736,1861],{"stretchy":1854},[1846,87738,1848],{},[898,87740,900],{},[1846,87742,1855],{"stretchy":1854},[1979,87744,41685],{},[1846,87746,2136],{"separator":2135},[1979,87748,2128],{},[1846,87750,2136],{"separator":2135},[1979,87752,2201],{},[1846,87754,1861],{"stretchy":1854},[902,87756,87757],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,87760,87762],{"className":87761},[886],[888,87763,87764],{"xmlns":890},[892,87765,87766,87782],{},[895,87767,87768,87770,87772,87774,87776,87778,87780],{},[1979,87769,2201],{},[1846,87771,3025],{},[1979,87773,5431],{},[1846,87775,3025],{},[1979,87777,1981],{},[1846,87779,1848],{},[1979,87781,41685],{},[902,87783,87784],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,87786,87788],{"className":87787},[886],[888,87789,87790],{"xmlns":890},[892,87791,87792,87808],{},[895,87793,87794,87796,87798,87800,87802,87804,87806],{},[1979,87795,41685],{},[1846,87797,3025],{},[1979,87799,2128],{},[1846,87801,3025],{},[1979,87803,2201],{},[1846,87805,1848],{},[1979,87807,87703],{},[902,87809,87810],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,87812,87814],{"className":87813},[886],[888,87815,87816],{"xmlns":890},[892,87817,87818,87826],{},[895,87819,87820,87822,87824],{},[898,87821,900],{},[1846,87823,1848],{},[1979,87825,41707],{},[902,87827,87828],{"encoding":904},"U = 16",[883,87830,87832],{"className":87831},[886],[888,87833,87834],{"xmlns":890},[892,87835,87836,87844],{},[895,87837,87838,87840,87842],{},[898,87839,900],{},[1846,87841,1848],{},[1979,87843,72204],{},[902,87845,87846],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,87849,87851],{"className":87850},[886],[888,87852,87853],{"xmlns":890},[892,87854,87855,87875],{},[895,87856,87857,87863,87869],{},[2122,87858,87859,87861],{},[898,87860,2638],{},[1979,87862,2128],{},[2122,87864,87865,87867],{},[898,87866,2638],{},[1979,87868,1981],{},[2122,87870,87871,87873],{},[898,87872,2638],{},[1979,87874,2023],{},[902,87876,87877],{"encoding":904},"Q_1 Q_2 Q_3",[115,87879,87881],{"id":87880},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,87883,87884,87885,7948,87920,2053,87923,41659,87940,9871,87957,87960,87961,87964],{},"Pro funkci užitečnosti ",[883,87886,87888],{"className":87887},[886],[888,87889,87890],{"xmlns":890},[892,87891,87892,87918],{},[895,87893,87894,87896,87898,87900,87902,87908,87910,87916],{},[898,87895,900],{},[1846,87897,1848],{},[898,87899,900],{},[1846,87901,1855],{"stretchy":1854},[2122,87903,87904,87906],{},[898,87905,2638],{},[1979,87907,2128],{},[1846,87909,2136],{"separator":2135},[2122,87911,87912,87914],{},[898,87913,2638],{},[1979,87915,1981],{},[1846,87917,1861],{"stretchy":1854},[902,87919,87301],{"encoding":904},[38,87921,87922],{},"mezní užitečnost",[883,87924,87926],{"className":87925},[886],[888,87927,87928],{"xmlns":890},[892,87929,87930,87938],{},[895,87931,87932],{},[2122,87933,87934,87936],{},[898,87935,2638],{},[1979,87937,2128],{},[902,87939,28847],{"encoding":904},[883,87941,87943],{"className":87942},[886],[888,87944,87945],{"xmlns":890},[892,87946,87947,87955],{},[895,87948,87949],{},[2122,87950,87951,87953],{},[898,87952,2638],{},[1979,87954,1981],{},[902,87956,28866],{"encoding":904},[38,87958,87959],{},"marginal utility",") parciální ",[207,87962,1145],{"className":87963,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,87966,87968],{"className":87967},[886],[888,87969,87970],{"xmlns":890,"display":27911},[892,87971,87972,88071],{},[20599,87973,87974],{"width":27916},[20604,87975,87976,87978,88064,88066],{},[20607,87977],{"width":27921},[20607,87979,87980],{},[895,87981,87982,87984,87990,87992,88000,88002,88020,88022,88024,88026,88032,88034,88042,88044,88062],{},[898,87983,2667],{},[2122,87985,87986,87988],{},[898,87987,900],{},[1979,87989,2128],{},[1846,87991,1848],{},[9012,87993,87994,87996,87998],{},[898,87995,900],{},[1979,87997,2128],{},[1846,87999,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,88001,1848],{},[2179,88003,88004,88010],{},[895,88005,88006,88008],{},[898,88007,9718],{"mathvariant":2226},[898,88009,900],{},[895,88011,88012,88014],{},[898,88013,9718],{"mathvariant":2226},[2122,88015,88016,88018],{},[898,88017,2638],{},[1979,88019,2128],{},[1846,88021,2136],{"separator":2135},[5724,88023],{"width":15129},[898,88025,2667],{},[2122,88027,88028,88030],{},[898,88029,900],{},[1979,88031,1981],{},[1846,88033,1848],{},[9012,88035,88036,88038,88040],{},[898,88037,900],{},[1979,88039,1981],{},[1846,88041,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,88043,1848],{},[2179,88045,88046,88052],{},[895,88047,88048,88050],{},[898,88049,9718],{"mathvariant":2226},[898,88051,900],{},[895,88053,88054,88056],{},[898,88055,9718],{"mathvariant":2226},[2122,88057,88058,88060],{},[898,88059,2638],{},[1979,88061,1981],{},[898,88063,1734],{"mathvariant":2226},[20607,88065],{"width":27921},[20607,88067,88068],{},[2138,88069,88070],{},"(6.2)",[902,88072,88073],{"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}",[724,88075,88076,88077,88111,88112,88142,88143,2053,88146,1734],{},"Pro pevné ",[883,88078,88080],{"className":88079},[886],[888,88081,88082],{"xmlns":890},[892,88083,88084,88108],{},[895,88085,88086,88092,88094,88096,88098,88104,88106],{},[2122,88087,88088,88090],{},[898,88089,2638],{},[1979,88091,2128],{},[1846,88093,1848],{},[898,88095,207],{},[1846,88097,2136],{"separator":2135},[2122,88099,88100,88102],{},[898,88101,2638],{},[1979,88103,1981],{},[1846,88105,1848],{},[898,88107,1948],{},[902,88109,88110],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,88113,88115],{"className":88114},[886],[888,88116,88117],{"xmlns":890},[892,88118,88119,88139],{},[895,88120,88121,88123,88129,88131,88133,88135,88137],{},[898,88122,2667],{},[2122,88124,88125,88127],{},[898,88126,900],{},[1979,88128,2128],{},[1846,88130,1855],{"stretchy":1854},[898,88132,207],{},[1846,88134,2136],{"separator":2135},[898,88136,1948],{},[1846,88138,1861],{"stretchy":1854},[902,88140,88141],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,88144,88145],{},"v bodě (na hladině)",[883,88147,88149],{"className":88148},[886],[888,88150,88151],{"xmlns":890},[892,88152,88153,88165],{},[895,88154,88155,88157,88159,88161,88163],{},[1846,88156,2336],{"stretchy":1854},[898,88158,207],{},[1846,88160,2136],{"separator":2135},[898,88162,1948],{},[1846,88164,2351],{"stretchy":1854},[902,88166,10670],{"encoding":904},[1639,88168,88169],{},[724,88170,88171,88173,88174,88204,88233,88234,2460,88247,2474,88264,88285,88286,2521,88303,2535,88316,88333,88334,88356,88357,88386,88387,6319,88407,88424],{},[883,88172,4001],{}," Intuice — co říká ",[883,88175,88177],{"className":88176},[886],[888,88178,88179],{"xmlns":890},[892,88180,88181,88201],{},[895,88182,88183,88185,88191,88193,88195,88197,88199],{},[898,88184,2667],{},[2122,88186,88187,88189],{},[898,88188,900],{},[1979,88190,2128],{},[1846,88192,1855],{"stretchy":1854},[898,88194,207],{},[1846,88196,2136],{"separator":2135},[898,88198,1948],{},[1846,88200,1861],{"stretchy":1854},[902,88202,88203],{"encoding":904},"MU_1(a,b)",[883,88205,88207],{"className":88206},[886],[888,88208,88209],{"xmlns":890},[892,88210,88211,88231],{},[895,88212,88213,88215,88221,88223,88225,88227,88229],{},[898,88214,2667],{},[2122,88216,88217,88219],{},[898,88218,900],{},[1979,88220,2128],{},[1846,88222,1855],{"stretchy":1854},[898,88224,207],{},[1846,88226,2136],{"separator":2135},[898,88228,1948],{},[1846,88230,1861],{"stretchy":1854},[902,88232,88141],{"encoding":904}," je rychlost změny ",[883,88235,88237],{"className":88236},[886],[888,88238,88239],{"xmlns":890},[892,88240,88241,88245],{},[895,88242,88243],{},[898,88244,900],{},[902,88246,900],{"encoding":904},[883,88248,88250],{"className":88249},[886],[888,88251,88252],{"xmlns":890},[892,88253,88254,88262],{},[895,88255,88256],{},[2122,88257,88258,88260],{},[898,88259,2638],{},[1979,88261,2128],{},[902,88263,28847],{"encoding":904},[883,88265,88267],{"className":88266},[886],[888,88268,88269],{"xmlns":890},[892,88270,88271,88283],{},[895,88272,88273,88275,88277,88279,88281],{},[1846,88274,2336],{"stretchy":1854},[898,88276,207],{},[1846,88278,2136],{"separator":2135},[898,88280,1948],{},[1846,88282,2351],{"stretchy":1854},[902,88284,10670],{"encoding":904},". Přibližně: změní-li se ",[883,88287,88289],{"className":88288},[886],[888,88290,88291],{"xmlns":890},[892,88292,88293,88301],{},[895,88294,88295],{},[2122,88296,88297,88299],{},[898,88298,2638],{},[1979,88300,2128],{},[902,88302,28847],{"encoding":904},[883,88304,88306],{"className":88305},[886],[888,88307,88308],{"xmlns":890},[892,88309,88310,88314],{},[895,88311,88312],{},[898,88313,207],{},[902,88315,207],{"encoding":904},[883,88317,88319],{"className":88318},[886],[888,88320,88321],{"xmlns":890},[892,88322,88323,88331],{},[895,88324,88325,88327,88329],{},[898,88326,207],{},[1846,88328,1945],{},[1979,88330,2128],{},[902,88332,2553],{"encoding":904}," při pevném ",[883,88335,88337],{"className":88336},[886],[888,88338,88339],{"xmlns":890},[892,88340,88341,88353],{},[895,88342,88343,88349,88351],{},[2122,88344,88345,88347],{},[898,88346,2638],{},[1979,88348,1981],{},[1846,88350,1848],{},[898,88352,1948],{},[902,88354,88355],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,88358,88360],{"className":88359},[886],[888,88361,88362],{"xmlns":890},[892,88363,88364,88384],{},[895,88365,88366,88368,88374,88376,88378,88380,88382],{},[898,88367,2667],{},[2122,88369,88370,88372],{},[898,88371,900],{},[1979,88373,2128],{},[1846,88375,1855],{"stretchy":1854},[898,88377,207],{},[1846,88379,2136],{"separator":2135},[898,88381,1948],{},[1846,88383,1861],{"stretchy":1854},[902,88385,88141],{"encoding":904},". Stejně tak ",[883,88388,88390],{"className":88389},[886],[888,88391,88392],{"xmlns":890},[892,88393,88394,88404],{},[895,88395,88396,88398],{},[898,88397,2667],{},[2122,88399,88400,88402],{},[898,88401,900],{},[1979,88403,1981],{},[902,88405,88406],{"encoding":904},"MU_2",[883,88408,88410],{"className":88409},[886],[888,88411,88412],{"xmlns":890},[892,88413,88414,88422],{},[895,88415,88416],{},[2122,88417,88418,88420],{},[898,88419,2638],{},[1979,88421,1981],{},[902,88423,28866],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,88426,80056],{"id":88427},"totální-diferenciál",[724,88429,88430,88431,48185,88447,88477,88478,2554],{},"Přibližnou změnu užitečnosti ",[883,88432,88434],{"className":88433},[886],[888,88435,88436],{"xmlns":890},[892,88437,88438,88444],{},[895,88439,88440,88442],{},[898,88441,2738],{"mathvariant":2226},[898,88443,900],{},[902,88445,88446],{"encoding":904},"\\Delta U",[883,88448,88450],{"className":88449},[886],[888,88451,88452],{"xmlns":890},[892,88453,88454,88474],{},[895,88455,88456,88458,88464,88466,88468],{},[898,88457,2044],{"mathvariant":2226},[2122,88459,88460,88462],{},[898,88461,2638],{},[1979,88463,2128],{},[1846,88465,2136],{"separator":2135},[898,88467,2044],{"mathvariant":2226},[2122,88469,88470,88472],{},[898,88471,2638],{},[1979,88473,1981],{},[902,88475,88476],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,88479,88480],{},"totálního diferenciálu",[883,88482,88484],{"className":88483},[886],[888,88485,88486],{"xmlns":890,"display":27911},[892,88487,88488,88589],{},[20599,88489,88490],{"width":27916},[20604,88491,88492,88494,88582,88584],{},[20607,88493],{"width":27921},[20607,88495,88496],{},[895,88497,88498,88500,88502,88504,88506,88508,88510,88518,88520,88526,88528,88536,88538,88544,88546,88548,88554,88556,88562,88564,88566,88572,88574,88580],{},[898,88499,2738],{"mathvariant":2226},[898,88501,900],{},[1846,88503,1650],{},[898,88505,2044],{"mathvariant":2226},[898,88507,900],{},[1846,88509,1848],{},[9012,88511,88512,88514,88516],{},[898,88513,900],{},[1979,88515,2128],{},[1846,88517,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[898,88519,2044],{"mathvariant":2226},[2122,88521,88522,88524],{},[898,88523,2638],{},[1979,88525,2128],{},[1846,88527,1945],{},[9012,88529,88530,88532,88534],{},[898,88531,900],{},[1979,88533,1981],{},[1846,88535,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[898,88537,2044],{"mathvariant":2226},[2122,88539,88540,88542],{},[898,88541,2638],{},[1979,88543,1981],{},[1846,88545,1848],{},[898,88547,2667],{},[2122,88549,88550,88552],{},[898,88551,900],{},[1979,88553,2128],{},[898,88555,2044],{"mathvariant":2226},[2122,88557,88558,88560],{},[898,88559,2638],{},[1979,88561,2128],{},[1846,88563,1945],{},[898,88565,2667],{},[2122,88567,88568,88570],{},[898,88569,900],{},[1979,88571,1981],{},[898,88573,2044],{"mathvariant":2226},[2122,88575,88576,88578],{},[898,88577,2638],{},[1979,88579,1981],{},[898,88581,1734],{"mathvariant":2226},[20607,88583],{"width":27921},[20607,88585,88586],{},[2138,88587,88588],{},"(6.3)",[902,88590,88591],{"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}",[724,88593,75314,88594,1734],{},[883,88595,88597],{"className":88596},[886],[888,88598,88599],{"xmlns":890},[892,88600,88601,88671],{},[895,88602,88603,88605,88607,88609,88611,88613,88619,88621,88623,88629,88631,88637,88639,88641,88647,88649,88651,88653,88655,88661,88663,88669],{},[898,88604,2738],{"mathvariant":2226},[898,88606,900],{},[1846,88608,1848],{},[898,88610,900],{},[1846,88612,1855],{"stretchy":1854},[2122,88614,88615,88617],{},[898,88616,2638],{},[1979,88618,2128],{},[1846,88620,1945],{},[898,88622,2044],{"mathvariant":2226},[2122,88624,88625,88627],{},[898,88626,2638],{},[1979,88628,2128],{},[1846,88630,2136],{"separator":2135},[2122,88632,88633,88635],{},[898,88634,2638],{},[1979,88636,1981],{},[1846,88638,1945],{},[898,88640,2044],{"mathvariant":2226},[2122,88642,88643,88645],{},[898,88644,2638],{},[1979,88646,1981],{},[1846,88648,1861],{"stretchy":1854},[1846,88650,2075],{},[898,88652,900],{},[1846,88654,1855],{"stretchy":1854},[2122,88656,88657,88659],{},[898,88658,2638],{},[1979,88660,2128],{},[1846,88662,2136],{"separator":2135},[2122,88664,88665,88667],{},[898,88666,2638],{},[1979,88668,1981],{},[1846,88670,1861],{"stretchy":1854},[902,88672,88673],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,88675,88677],{"id":88676},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,88679,88680,88681,88684,88685,88688],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,88682,88683],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,88686,88687],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,88690,88691,88694,88695,41659,88721,88747,88748,1343,88780,88812,88813,1745,88867,88921],{},[38,88692,88693],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,88696,88698],{"className":88697},[886],[888,88699,88700],{"xmlns":890},[892,88701,88702,88718],{},[895,88703,88704,88710,88712],{},[2122,88705,88706,88708],{},[898,88707,2638],{},[1979,88709,1981],{},[1846,88711,1848],{},[2122,88713,88714,88716],{},[898,88715,207],{},[1979,88717,2177],{},[902,88719,88720],{"encoding":904},"Q_2 = a_0",[883,88722,88724],{"className":88723},[886],[888,88725,88726],{"xmlns":890},[892,88727,88728,88744],{},[895,88729,88730,88736,88738],{},[2122,88731,88732,88734],{},[898,88733,2638],{},[1979,88735,2128],{},[1846,88737,1848],{},[2122,88739,88740,88742],{},[898,88741,1948],{},[1979,88743,2177],{},[902,88745,88746],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,88749,88751],{"className":88750},[886],[888,88752,88753],{"xmlns":890},[892,88754,88755,88777],{},[895,88756,88757,88759,88761,88767,88769,88775],{},[898,88758,900],{},[1846,88760,1855],{"stretchy":1854},[2122,88762,88763,88765],{},[898,88764,2638],{},[1979,88766,2128],{},[1846,88768,2136],{"separator":2135},[2122,88770,88771,88773],{},[898,88772,207],{},[1979,88774,2177],{},[1846,88776,1861],{"stretchy":1854},[902,88778,88779],{"encoding":904},"U(Q_1, a_0)",[883,88781,88783],{"className":88782},[886],[888,88784,88785],{"xmlns":890},[892,88786,88787,88809],{},[895,88788,88789,88791,88793,88799,88801,88807],{},[898,88790,900],{},[1846,88792,1855],{"stretchy":1854},[2122,88794,88795,88797],{},[898,88796,1948],{},[1979,88798,2177],{},[1846,88800,2136],{"separator":2135},[2122,88802,88803,88805],{},[898,88804,2638],{},[1979,88806,1981],{},[1846,88808,1861],{"stretchy":1854},[902,88810,88811],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,88814,88816],{"className":88815},[886],[888,88817,88818],{"xmlns":890},[892,88819,88820,88864],{},[895,88821,88822,88860,88862],{},[2175,88823,88824],{"scriptlevel":2177,"displaystyle":2135},[2179,88825,88826,88850],{},[895,88827,88828,88830,88832,88834,88840,88842,88848],{},[898,88829,2044],{"mathvariant":2226},[898,88831,900],{},[1846,88833,1855],{"stretchy":1854},[2122,88835,88836,88838],{},[898,88837,2638],{},[1979,88839,2128],{},[1846,88841,2136],{"separator":2135},[2122,88843,88844,88846],{},[898,88845,207],{},[1979,88847,2177],{},[1846,88849,1861],{"stretchy":1854},[895,88851,88852,88854],{},[898,88853,2044],{"mathvariant":2226},[2122,88855,88856,88858],{},[898,88857,2638],{},[1979,88859,2128],{},[1846,88861,3256],{},[1979,88863,2177],{},[902,88865,88866],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,88868,88870],{"className":88869},[886],[888,88871,88872],{"xmlns":890},[892,88873,88874,88918],{},[895,88875,88876,88914,88916],{},[2175,88877,88878],{"scriptlevel":2177,"displaystyle":2135},[2179,88879,88880,88904],{},[895,88881,88882,88884,88886,88888,88894,88896,88902],{},[898,88883,2044],{"mathvariant":2226},[898,88885,900],{},[1846,88887,1855],{"stretchy":1854},[2122,88889,88890,88892],{},[898,88891,1948],{},[1979,88893,2177],{},[1846,88895,2136],{"separator":2135},[2122,88897,88898,88900],{},[898,88899,2638],{},[1979,88901,1981],{},[1846,88903,1861],{"stretchy":1854},[895,88905,88906,88908],{},[898,88907,2044],{"mathvariant":2226},[2122,88909,88910,88912],{},[898,88911,2638],{},[1979,88913,1981],{},[1846,88915,3256],{},[1979,88917,2177],{},[902,88919,88920],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,88923,88925],{"className":88924},[886],[888,88926,88927],{"xmlns":890,"display":27911},[892,88928,88929,88974],{},[20599,88930,88931],{"width":27916},[20604,88932,88933,88935,88967,88969],{},[20607,88934],{"width":27921},[20607,88936,88937],{},[895,88938,88939,88947,88949,88951,88953,88955,88963,88965],{},[9012,88940,88941,88943,88945],{},[898,88942,900],{},[1979,88944,2128],{},[1846,88946,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,88948,3256],{},[1979,88950,2177],{},[1846,88952,2136],{"separator":2135},[5724,88954],{"width":15129},[9012,88956,88957,88959,88961],{},[898,88958,900],{},[1979,88960,1981],{},[1846,88962,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,88964,3256],{},[1979,88966,12305],{},[20607,88968],{"width":27921},[20607,88970,88971],{},[2138,88972,88973],{},"(6.4)",[902,88975,88976],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,88978,88979,88980,88982],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,88981,52522],{}," — užitečnost roste s množstvím každého zboží.",[724,88984,88985,88988,88989,89019,89020,2554],{},[38,88986,88987],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,88990,88992],{"className":88991},[886],[888,88993,88994],{"xmlns":890},[892,88995,88996,89016],{},[895,88997,88998,89006,89008],{},[9012,88999,89000,89002,89004],{},[898,89001,900],{},[1979,89003,2128],{},[1846,89005,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,89007,2136],{"separator":2135},[9012,89009,89010,89012,89014],{},[898,89011,900],{},[1979,89013,1981],{},[1846,89015,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,89017,89018],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,89021,89022],{},"záporné",[883,89024,89026],{"className":89025},[886],[888,89027,89028],{"xmlns":890,"display":27911},[892,89029,89030,89083],{},[20599,89031,89032],{"width":27916},[20604,89033,89034,89036,89076,89078],{},[20607,89035],{"width":27921},[20607,89037,89038],{},[895,89039,89040,89052,89054,89056,89058,89060,89072,89074],{},[9012,89041,89042,89044,89046],{},[898,89043,900],{},[1979,89045,2753],{},[895,89047,89048,89050],{},[1846,89049,2228],{"mathvariant":2226},[1846,89051,2228],{"mathvariant":2226},[1846,89053,3295],{},[1979,89055,2177],{},[1846,89057,2136],{"separator":2135},[5724,89059],{"width":15129},[9012,89061,89062,89064,89066],{},[898,89063,900],{},[1979,89065,32391],{},[895,89067,89068,89070],{},[1846,89069,2228],{"mathvariant":2226},[1846,89071,2228],{"mathvariant":2226},[1846,89073,3295],{},[1979,89075,12305],{},[20607,89077],{"width":27921},[20607,89079,89080],{},[2138,89081,89082],{},"(6.5)",[902,89084,89085],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,89087,89088,89089,89092,89093,1734],{},"Podmínka (6.5) je známa jako ",[38,89090,89091],{},"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 ",[207,89094,89096],{"className":89095,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,89098,89099,89100,1745,89132,89164,89165,1745,89191,89217,89218,89246,89247,1745,89249,89251,89252,89287],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,89101,89103],{"className":89102},[886],[888,89104,89105],{"xmlns":890},[892,89106,89107,89129],{},[895,89108,89109,89111,89113,89119,89121,89127],{},[898,89110,900],{},[1846,89112,1855],{"stretchy":1854},[2122,89114,89115,89117],{},[898,89116,2638],{},[1979,89118,2128],{},[1846,89120,2136],{"separator":2135},[2122,89122,89123,89125],{},[898,89124,1948],{},[1979,89126,2177],{},[1846,89128,1861],{"stretchy":1854},[902,89130,89131],{"encoding":904},"U(Q_1, b_0)",[883,89133,89135],{"className":89134},[886],[888,89136,89137],{"xmlns":890},[892,89138,89139,89161],{},[895,89140,89141,89143,89145,89151,89153,89159],{},[898,89142,900],{},[1846,89144,1855],{"stretchy":1854},[2122,89146,89147,89149],{},[898,89148,207],{},[1979,89150,2177],{},[1846,89152,2136],{"separator":2135},[2122,89154,89155,89157],{},[898,89156,2638],{},[1979,89158,1981],{},[1846,89160,1861],{"stretchy":1854},[902,89162,89163],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,89166,89168],{"className":89167},[886],[888,89169,89170],{"xmlns":890},[892,89171,89172,89188],{},[895,89173,89174,89176,89178,89180,89186],{},[1846,89175,1855],{"stretchy":1854},[898,89177,900],{},[1846,89179,2136],{"separator":2135},[2122,89181,89182,89184],{},[898,89183,2638],{},[1979,89185,2128],{},[1846,89187,1861],{"stretchy":1854},[902,89189,89190],{"encoding":904},"(U, Q_1)",[883,89192,89194],{"className":89193},[886],[888,89195,89196],{"xmlns":890},[892,89197,89198,89214],{},[895,89199,89200,89202,89204,89206,89212],{},[1846,89201,1855],{"stretchy":1854},[898,89203,900],{},[1846,89205,2136],{"separator":2135},[2122,89207,89208,89210],{},[898,89209,2638],{},[1979,89211,1981],{},[1846,89213,1861],{"stretchy":1854},[902,89215,89216],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,89219,89221],{"className":89220},[886],[888,89222,89223],{"xmlns":890},[892,89224,89225,89243],{},[895,89226,89227,89229,89231,89233,89235,89237,89239,89241],{},[898,89228,900],{},[1846,89230,1855],{"stretchy":1854},[1979,89232,2177],{},[1846,89234,2136],{"separator":2135},[1979,89236,2177],{},[1846,89238,1861],{"stretchy":1854},[1846,89240,1848],{},[1979,89242,2177],{},[902,89244,89245],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,89248,13502],{},[38,89250,38333],{},". Typický tvar grafu ",[883,89253,89255],{"className":89254},[886],[888,89256,89257],{"xmlns":890},[892,89258,89259,89285],{},[895,89260,89261,89263,89265,89267,89269,89275,89277,89283],{},[898,89262,900],{},[1846,89264,1848],{},[898,89266,900],{},[1846,89268,1855],{"stretchy":1854},[2122,89270,89271,89273],{},[898,89272,2638],{},[1979,89274,2128],{},[1846,89276,2136],{"separator":2135},[2122,89278,89279,89281],{},[898,89280,2638],{},[1979,89282,1981],{},[1846,89284,1861],{"stretchy":1854},[902,89286,87301],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,89289,89290],{},[614,89291,89292,89293,88333,89321,89342,89343,88333,89371,89393],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,89294,89296],{"className":89295},[886],[888,89297,89298],{"xmlns":890},[892,89299,89300,89318],{},[895,89301,89302,89304,89306,89312,89314,89316],{},[898,89303,900],{},[1846,89305,1855],{"stretchy":1854},[2122,89307,89308,89310],{},[898,89309,2638],{},[1979,89311,2128],{},[1846,89313,2136],{"separator":2135},[898,89315,1948],{},[1846,89317,1861],{"stretchy":1854},[902,89319,89320],{"encoding":904},"U(Q_1, b)",[883,89322,89324],{"className":89323},[886],[888,89325,89326],{"xmlns":890},[892,89327,89328,89340],{},[895,89329,89330,89336,89338],{},[2122,89331,89332,89334],{},[898,89333,2638],{},[1979,89335,1981],{},[1846,89337,1848],{},[898,89339,1948],{},[902,89341,88355],{"encoding":904}," (vlevo) a ",[883,89344,89346],{"className":89345},[886],[888,89347,89348],{"xmlns":890},[892,89349,89350,89368],{},[895,89351,89352,89354,89356,89358,89360,89366],{},[898,89353,900],{},[1846,89355,1855],{"stretchy":1854},[898,89357,207],{},[1846,89359,2136],{"separator":2135},[2122,89361,89362,89364],{},[898,89363,2638],{},[1979,89365,1981],{},[1846,89367,1861],{"stretchy":1854},[902,89369,89370],{"encoding":904},"U(a, Q_2)",[883,89372,89374],{"className":89373},[886],[888,89375,89376],{"xmlns":890},[892,89377,89378,89390],{},[895,89379,89380,89386,89388],{},[2122,89381,89382,89384],{},[898,89383,2638],{},[1979,89385,2128],{},[1846,89387,1848],{},[898,89389,207],{},[902,89391,89392],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,89395,89396],{},[614,89397,89398,89399,89434,89435,89465,89466,1745,89489,89511,89512,1734],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,89400,89402],{"className":89401},[886],[888,89403,89404],{"xmlns":890},[892,89405,89406,89432],{},[895,89407,89408,89410,89412,89414,89416,89422,89424,89430],{},[898,89409,900],{},[1846,89411,1848],{},[898,89413,900],{},[1846,89415,1855],{"stretchy":1854},[2122,89417,89418,89420],{},[898,89419,2638],{},[1979,89421,2128],{},[1846,89423,2136],{"separator":2135},[2122,89425,89426,89428],{},[898,89427,2638],{},[1979,89429,1981],{},[1846,89431,1861],{"stretchy":1854},[902,89433,87301],{"encoding":904}," nad rovinou ",[883,89436,89438],{"className":89437},[886],[888,89439,89440],{"xmlns":890},[892,89441,89442,89462],{},[895,89443,89444,89446,89452,89454,89460],{},[1846,89445,1855],{"stretchy":1854},[2122,89447,89448,89450],{},[898,89449,2638],{},[1979,89451,2128],{},[1846,89453,2136],{"separator":2135},[2122,89455,89456,89458],{},[898,89457,2638],{},[1979,89459,1981],{},[1846,89461,1861],{"stretchy":1854},[902,89463,89464],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,89467,89469],{"className":89468},[886],[888,89470,89471],{"xmlns":890},[892,89472,89473,89486],{},[895,89474,89475,89481,89483],{},[2122,89476,89477,89479],{},[898,89478,2638],{},[1979,89480,2128],{},[1846,89482,1848],{},[2138,89484,89485],{},"const",[902,89487,89488],{"encoding":904},"Q_1 = \\text{const}",[883,89490,89492],{"className":89491},[886],[888,89493,89494],{"xmlns":890},[892,89495,89496,89508],{},[895,89497,89498,89504,89506],{},[2122,89499,89500,89502],{},[898,89501,2638],{},[1979,89503,1981],{},[1846,89505,1848],{},[2138,89507,89485],{},[902,89509,89510],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,89513,89515],{"className":89514},[886],[888,89516,89517],{"xmlns":890},[892,89518,89519,89545],{},[895,89520,89521,89523,89525,89531,89533,89539,89541,89543],{},[898,89522,900],{},[1846,89524,1855],{"stretchy":1854},[2122,89526,89527,89529],{},[898,89528,2638],{},[1979,89530,2128],{},[1846,89532,2136],{"separator":2135},[2122,89534,89535,89537],{},[898,89536,2638],{},[1979,89538,1981],{},[1846,89540,1861],{"stretchy":1854},[1846,89542,1848],{},[898,89544,1992],{},[902,89546,9614],{"encoding":904},[198,89548,89550,89551],{"id":89549},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,89552,89554],{"className":89553},[886],[888,89555,89556],{"xmlns":890},[892,89557,89558,89592],{},[895,89559,89560,89562,89564,89578],{},[898,89561,900],{},[1846,89563,1848],{},[9012,89565,89566,89568,89570],{},[898,89567,2638],{},[1979,89569,2128],{},[895,89571,89572,89574,89576],{},[1979,89573,2128],{},[898,89575,4520],{"mathvariant":2226},[1979,89577,1981],{},[9012,89579,89580,89582,89584],{},[898,89581,2638],{},[1979,89583,1981],{},[895,89585,89586,89588,89590],{},[1979,89587,2128],{},[898,89589,4520],{"mathvariant":2226},[1979,89591,2023],{},[902,89593,89594],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,89596,89597],{},[38,89598,89599],{},"Ověření (6.4) a (6.5).",[883,89601,89603],{"className":89602},[886],[888,89604,89605],{"xmlns":890,"display":27911},[892,89606,89607,89711],{},[895,89608,89609,89617,89619,89627,89643,89657,89659,89661,89669,89671,89679,89693,89709],{},[9012,89610,89611,89613,89615],{},[898,89612,900],{},[1979,89614,2128],{},[1846,89616,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,89618,1848],{},[2175,89620,89621],{"scriptlevel":2177,"displaystyle":1854},[2179,89622,89623,89625],{},[1979,89624,2128],{},[1979,89626,1981],{},[9012,89628,89629,89631,89633],{},[898,89630,2638],{},[1979,89632,2128],{},[895,89634,89635,89637,89639,89641],{},[1846,89636,2075],{},[1979,89638,2128],{},[898,89640,4520],{"mathvariant":2226},[1979,89642,1981],{},[9012,89644,89645,89647,89649],{},[898,89646,2638],{},[1979,89648,1981],{},[895,89650,89651,89653,89655],{},[1979,89652,2128],{},[898,89654,4520],{"mathvariant":2226},[1979,89656,2023],{},[1846,89658,2136],{"separator":2135},[5724,89660],{"width":15129},[9012,89662,89663,89665,89667],{},[898,89664,900],{},[1979,89666,1981],{},[1846,89668,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,89670,1848],{},[2175,89672,89673],{"scriptlevel":2177,"displaystyle":1854},[2179,89674,89675,89677],{},[1979,89676,2128],{},[1979,89678,2023],{},[9012,89680,89681,89683,89685],{},[898,89682,2638],{},[1979,89684,2128],{},[895,89686,89687,89689,89691],{},[1979,89688,2128],{},[898,89690,4520],{"mathvariant":2226},[1979,89692,1981],{},[9012,89694,89695,89697,89699],{},[898,89696,2638],{},[1979,89698,1981],{},[895,89700,89701,89703,89705,89707],{},[1846,89702,2075],{},[1979,89704,1981],{},[898,89706,4520],{"mathvariant":2226},[1979,89708,2023],{},[1846,89710,2136],{"separator":2135},[902,89712,89713],{"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},",[724,89715,89716,89717,89751],{},"zřejmě ",[883,89718,89720],{"className":89719},[886],[888,89721,89722],{"xmlns":890},[892,89723,89724,89748],{},[895,89725,89726,89734,89736,89744,89746],{},[9012,89727,89728,89730,89732],{},[898,89729,900],{},[1979,89731,2128],{},[1846,89733,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,89735,2136],{"separator":2135},[9012,89737,89738,89740,89742],{},[898,89739,900],{},[1979,89741,1981],{},[1846,89743,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,89745,3256],{},[1979,89747,2177],{},[902,89749,89750],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,89753,89755],{"className":89754},[886],[888,89756,89757],{"xmlns":890,"display":27911},[892,89758,89759,89875],{},[895,89760,89761,89773,89775,89777,89785,89801,89815,89817,89819,89831,89833,89835,89843,89857,89873],{},[9012,89762,89763,89765,89767],{},[898,89764,900],{},[1979,89766,2753],{},[895,89768,89769,89771],{},[1846,89770,2228],{"mathvariant":2226},[1846,89772,2228],{"mathvariant":2226},[1846,89774,1848],{},[1846,89776,2075],{},[2175,89778,89779],{"scriptlevel":2177,"displaystyle":1854},[2179,89780,89781,89783],{},[1979,89782,2128],{},[1979,89784,2201],{},[9012,89786,89787,89789,89791],{},[898,89788,2638],{},[1979,89790,2128],{},[895,89792,89793,89795,89797,89799],{},[1846,89794,2075],{},[1979,89796,2023],{},[898,89798,4520],{"mathvariant":2226},[1979,89800,1981],{},[9012,89802,89803,89805,89807],{},[898,89804,2638],{},[1979,89806,1981],{},[895,89808,89809,89811,89813],{},[1979,89810,2128],{},[898,89812,4520],{"mathvariant":2226},[1979,89814,2023],{},[1846,89816,2136],{"separator":2135},[5724,89818],{"width":15129},[9012,89820,89821,89823,89825],{},[898,89822,900],{},[1979,89824,32391],{},[895,89826,89827,89829],{},[1846,89828,2228],{"mathvariant":2226},[1846,89830,2228],{"mathvariant":2226},[1846,89832,1848],{},[1846,89834,2075],{},[2175,89836,89837],{"scriptlevel":2177,"displaystyle":1854},[2179,89838,89839,89841],{},[1979,89840,1981],{},[1979,89842,3845],{},[9012,89844,89845,89847,89849],{},[898,89846,2638],{},[1979,89848,2128],{},[895,89850,89851,89853,89855],{},[1979,89852,2128],{},[898,89854,4520],{"mathvariant":2226},[1979,89856,1981],{},[9012,89858,89859,89861,89863],{},[898,89860,2638],{},[1979,89862,1981],{},[895,89864,89865,89867,89869,89871],{},[1846,89866,2075],{},[1979,89868,2078],{},[898,89870,4520],{"mathvariant":2226},[1979,89872,2023],{},[1846,89874,2136],{"separator":2135},[902,89876,89877],{"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},",[724,89879,89880,89881,89923],{},"opět ",[883,89882,89884],{"className":89883},[886],[888,89885,89886],{"xmlns":890},[892,89887,89888,89920],{},[895,89889,89890,89902,89904,89916,89918],{},[9012,89891,89892,89894,89896],{},[898,89893,900],{},[1979,89895,2753],{},[895,89897,89898,89900],{},[1846,89899,2228],{"mathvariant":2226},[1846,89901,2228],{"mathvariant":2226},[1846,89903,2136],{"separator":2135},[9012,89905,89906,89908,89910],{},[898,89907,900],{},[1979,89909,32391],{},[895,89911,89912,89914],{},[1846,89913,2228],{"mathvariant":2226},[1846,89915,2228],{"mathvariant":2226},[1846,89917,3295],{},[1979,89919,2177],{},[902,89921,89922],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,89925,89926],{},[38,89927,89928,89929,1734],{},"(a) Mezní užitečnosti v bodě ",[883,89930,89932],{"className":89931},[886],[888,89933,89934],{"xmlns":890},[892,89935,89936,89948],{},[895,89937,89938,89940,89942,89944,89946],{},[1846,89939,2336],{"stretchy":1854},[1979,89941,2938],{},[1846,89943,2136],{"separator":2135},[1979,89945,8223],{},[1846,89947,2351],{"stretchy":1854},[902,89949,89950],{"encoding":904},"[100, 200]",[883,89952,89954],{"className":89953},[886],[888,89955,89956],{"xmlns":890,"display":27911},[892,89957,89958,90025],{},[895,89959,89960,89962,89968,89970,89972,89974,89976,89978,89980,89988,89990,90004,90006,90018,90020,90023],{},[898,89961,2667],{},[2122,89963,89964,89966],{},[898,89965,900],{},[1979,89967,2128],{},[1846,89969,1855],{"stretchy":1854},[1979,89971,2938],{},[1846,89973,2136],{"separator":2135},[1979,89975,8223],{},[1846,89977,1861],{"stretchy":1854},[1846,89979,1848],{},[2175,89981,89982],{"scriptlevel":2177,"displaystyle":1854},[2179,89983,89984,89986],{},[1979,89985,2128],{},[1979,89987,1981],{},[1846,89989,3025],{},[1974,89991,89992,89994],{},[1979,89993,2938],{},[895,89995,89996,89998,90000,90002],{},[1846,89997,2075],{},[1979,89999,2128],{},[898,90001,4520],{"mathvariant":2226},[1979,90003,1981],{},[1846,90005,3025],{},[1974,90007,90008,90010],{},[1979,90009,8223],{},[895,90011,90012,90014,90016],{},[1979,90013,2128],{},[898,90015,4520],{"mathvariant":2226},[1979,90017,2023],{},[1846,90019,5746],{},[1979,90021,90022],{},"0,4204",[1846,90024,2136],{"separator":2135},[902,90026,90027],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,90029,90031],{"className":90030},[886],[888,90032,90033],{"xmlns":890,"display":27911},[892,90034,90035,90100],{},[895,90036,90037,90039,90045,90047,90049,90051,90053,90055,90057,90065,90067,90079,90081,90095,90097],{},[898,90038,2667],{},[2122,90040,90041,90043],{},[898,90042,900],{},[1979,90044,1981],{},[1846,90046,1855],{"stretchy":1854},[1979,90048,2938],{},[1846,90050,2136],{"separator":2135},[1979,90052,8223],{},[1846,90054,1861],{"stretchy":1854},[1846,90056,1848],{},[2175,90058,90059],{"scriptlevel":2177,"displaystyle":1854},[2179,90060,90061,90063],{},[1979,90062,2128],{},[1979,90064,2023],{},[1846,90066,3025],{},[1974,90068,90069,90071],{},[1979,90070,2938],{},[895,90072,90073,90075,90077],{},[1979,90074,2128],{},[898,90076,4520],{"mathvariant":2226},[1979,90078,1981],{},[1846,90080,3025],{},[1974,90082,90083,90085],{},[1979,90084,8223],{},[895,90086,90087,90089,90091,90093],{},[1846,90088,2075],{},[1979,90090,1981],{},[898,90092,4520],{"mathvariant":2226},[1979,90094,2023],{},[1846,90096,5746],{},[1979,90098,90099],{},"0,63067.",[902,90101,90102],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,90104,90105,2053,90107,90142,90143,90164,90165,90182],{},[614,90106,9062],{},[883,90108,90110],{"className":90109},[886],[888,90111,90112],{"xmlns":890},[892,90113,90114,90139],{},[895,90115,90116,90118,90124,90126,90128,90130,90132,90134,90136],{},[898,90117,2667],{},[2122,90119,90120,90122],{},[898,90121,900],{},[1979,90123,1981],{},[1846,90125,1855],{"stretchy":1854},[1979,90127,2938],{},[1846,90129,2136],{"separator":2135},[1979,90131,8223],{},[1846,90133,1861],{"stretchy":1854},[1846,90135,5746],{},[1979,90137,90138],{},"0,63067",[902,90140,90141],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,90144,90146],{"className":90145},[886],[888,90147,90148],{"xmlns":890},[892,90149,90150,90162],{},[895,90151,90152,90154,90156,90158,90160],{},[1846,90153,2336],{"stretchy":1854},[1979,90155,2938],{},[1846,90157,2136],{"separator":2135},[1979,90159,8223],{},[1846,90161,2351],{"stretchy":1854},[902,90163,89950],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,90166,90168],{"className":90167},[886],[888,90169,90170],{"xmlns":890},[892,90171,90172,90180],{},[895,90173,90174],{},[2122,90175,90176,90178],{},[898,90177,2638],{},[1979,90179,1981],{},[902,90181,28866],{"encoding":904}," přibližně o 0,63067.",[724,90184,90185,90204,90205,39029,90226,90243,90244,90270,90271,90288,90289,2999],{},[38,90186,90187,90188,90203],{},"(b) Odhad změny ",[883,90189,90191],{"className":90190},[886],[888,90192,90193],{"xmlns":890},[892,90194,90195,90201],{},[895,90196,90197,90199],{},[898,90198,2738],{"mathvariant":2226},[898,90200,900],{},[902,90202,88446],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,90206,90208],{"className":90207},[886],[888,90209,90210],{"xmlns":890},[892,90211,90212,90224],{},[895,90213,90214,90216,90218,90220,90222],{},[1846,90215,2336],{"stretchy":1854},[1979,90217,2938],{},[1846,90219,2136],{"separator":2135},[1979,90221,8223],{},[1846,90223,2351],{"stretchy":1854},[902,90225,89950],{"encoding":904},[883,90227,90229],{"className":90228},[886],[888,90230,90231],{"xmlns":890},[892,90232,90233,90241],{},[895,90234,90235],{},[2122,90236,90237,90239],{},[898,90238,2638],{},[1979,90240,2128],{},[902,90242,28847],{"encoding":904}," na 98 (tj. ",[883,90245,90247],{"className":90246},[886],[888,90248,90249],{"xmlns":890},[892,90250,90251,90267],{},[895,90252,90253,90255,90261,90263,90265],{},[898,90254,2044],{"mathvariant":2226},[2122,90256,90257,90259],{},[898,90258,2638],{},[1979,90260,2128],{},[1846,90262,1848],{},[1846,90264,2075],{},[1979,90266,1981],{},[902,90268,90269],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,90272,90274],{"className":90273},[886],[888,90275,90276],{"xmlns":890},[892,90277,90278,90286],{},[895,90279,90280],{},[2122,90281,90282,90284],{},[898,90283,2638],{},[1979,90285,1981],{},[902,90287,28866],{"encoding":904}," o 3 (tj. ",[883,90290,90292],{"className":90291},[886],[888,90293,90294],{"xmlns":890},[892,90295,90296,90310],{},[895,90297,90298,90300,90306,90308],{},[898,90299,2044],{"mathvariant":2226},[2122,90301,90302,90304],{},[898,90303,2638],{},[1979,90305,1981],{},[1846,90307,1848],{},[1979,90309,2023],{},[902,90311,90312],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,90314,90316],{"className":90315},[886],[888,90317,90318],{"xmlns":890,"display":27911},[892,90319,90320,90371],{},[895,90321,90322,90324,90326,90328,90330,90332,90334,90336,90338,90340,90342,90344,90346,90348,90350,90352,90354,90356,90358,90361,90363,90366,90368],{},[898,90323,2738],{"mathvariant":2226},[898,90325,900],{},[1846,90327,1650],{},[898,90329,2044],{"mathvariant":2226},[898,90331,900],{},[1846,90333,1848],{},[1979,90335,90022],{},[1846,90337,3025],{},[1846,90339,1855],{"stretchy":1854},[1846,90341,2075],{},[1979,90343,1981],{},[1846,90345,1861],{"stretchy":1854},[1846,90347,1945],{},[1979,90349,90138],{},[1846,90351,3025],{},[1979,90353,2023],{},[1846,90355,1848],{},[1846,90357,2075],{},[1979,90359,90360],{},"0,8408",[1846,90362,1945],{},[1979,90364,90365],{},"1,89201",[1846,90367,5746],{},[1979,90369,90370],{},"1,05.",[902,90372,90373],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,90375,90376,90377,90380,90381,90432,90433,1734],{},"Užitečnost se tedy zvýší přibližně o ",[38,90378,90379],{},"1,05",". Skutečná změna je ",[883,90382,90384],{"className":90383},[886],[888,90385,90386],{"xmlns":890},[892,90387,90388,90429],{},[895,90389,90390,90392,90394,90396,90398,90400,90403,90405,90408,90410,90412,90414,90416,90418,90420,90422,90424,90426],{},[898,90391,2738],{"mathvariant":2226},[898,90393,900],{},[1846,90395,1848],{},[898,90397,900],{},[1846,90399,1855],{"stretchy":1854},[1979,90401,90402],{},"98",[1846,90404,2136],{"separator":2135},[1979,90406,90407],{},"203",[1846,90409,1861],{"stretchy":1854},[1846,90411,2075],{},[898,90413,900],{},[1846,90415,1855],{"stretchy":1854},[1979,90417,2938],{},[1846,90419,2136],{"separator":2135},[1979,90421,8223],{},[1846,90423,1861],{"stretchy":1854},[1846,90425,5746],{},[1979,90427,90428],{},"1,031",[902,90430,90431],{"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 ",[883,90434,90436],{"className":90435},[886],[888,90437,90438],{"xmlns":890},[892,90439,90440,90460],{},[895,90441,90442,90444,90450,90452,90454],{},[898,90443,2044],{"mathvariant":2226},[2122,90445,90446,90448],{},[898,90447,2638],{},[1979,90449,2128],{},[1846,90451,2136],{"separator":2135},[898,90453,2044],{"mathvariant":2226},[2122,90455,90456,90458],{},[898,90457,2638],{},[1979,90459,1981],{},[902,90461,88476],{"encoding":904},[115,90463,90465],{"id":90464},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,90467,90468],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,90470,90472],{"className":90471},[886],[888,90473,90474],{"xmlns":890,"display":27911},[892,90475,90476,90535],{},[20599,90477,90478],{"width":27916},[20604,90479,90480,90482,90528,90530],{},[20607,90481],{"width":27921},[20607,90483,90484],{},[895,90485,90486,90488,90490,90496,90498,90504,90506,90508,90516,90518,90526],{},[898,90487,900],{},[1846,90489,1855],{"stretchy":1854},[2122,90491,90492,90494],{},[898,90493,2638],{},[1979,90495,2128],{},[1846,90497,2136],{"separator":2135},[2122,90499,90500,90502],{},[898,90501,2638],{},[1979,90503,1981],{},[1846,90505,1861],{"stretchy":1854},[1846,90507,1848],{},[9012,90509,90510,90512,90514],{},[898,90511,2638],{},[1979,90513,2128],{},[898,90515,207],{},[1846,90517,3025],{},[9012,90519,90520,90522,90524],{},[898,90521,2638],{},[1979,90523,1981],{},[898,90525,1948],{},[1846,90527,2136],{"separator":2135},[20607,90529],{"width":27921},[20607,90531,90532],{},[2138,90533,90534],{},"(6.6)",[902,90536,90537],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,90539,4156,90540,90558,90559,90561,90562,90566,90567,90597,90598,90620],{},[883,90541,90543],{"className":90542},[886],[888,90544,90545],{"xmlns":890},[892,90546,90547,90555],{},[895,90548,90549,90551,90553],{},[898,90550,207],{},[1846,90552,2136],{"separator":2135},[898,90554,1948],{},[902,90556,90557],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,90560,74544],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,90563,90565],{"className":90564,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,90568,90570],{"className":90569},[886],[888,90571,90572],{"xmlns":890},[892,90573,90574,90594],{},[895,90575,90576,90578,90580,90582,90584,90586,90588,90590,90592],{},[898,90577,207],{},[1846,90579,2136],{"separator":2135},[898,90581,1948],{},[1846,90583,6352],{},[1846,90585,1855],{"stretchy":1854},[1979,90587,2177],{},[1846,90589,2136],{"separator":2135},[1979,90591,2128],{},[1846,90593,1861],{"stretchy":1854},[902,90595,90596],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,90599,90601],{"className":90600},[886],[888,90602,90603],{"xmlns":890},[892,90604,90605,90617],{},[895,90606,90607,90609,90611,90613,90615],{},[898,90608,1948],{},[1846,90610,1848],{},[1979,90612,2128],{},[1846,90614,2075],{},[898,90616,207],{},[902,90618,90619],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,90622,90623],{},[2409,90624],{"alt":90625,"className":90626,"src":90627},"imek-cobb-douglas-3d-plus-ic",[210,2413],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,90629,90631],{"className":90630},[886],[888,90632,90633],{"xmlns":890,"display":27911},[892,90634,90635,90685],{},[895,90636,90637,90639,90641,90647,90649,90655,90657,90659,90667,90669,90683],{},[898,90638,900],{},[1846,90640,1855],{"stretchy":1854},[2122,90642,90643,90645],{},[898,90644,2638],{},[1979,90646,2128],{},[1846,90648,2136],{"separator":2135},[2122,90650,90651,90653],{},[898,90652,2638],{},[1979,90654,1981],{},[1846,90656,1861],{"stretchy":1854},[1846,90658,1848],{},[9012,90660,90661,90663,90665],{},[898,90662,2638],{},[1979,90664,2128],{},[898,90666,207],{},[1846,90668,3025],{},[9012,90670,90671,90673,90675],{},[898,90672,2638],{},[1979,90674,1981],{},[895,90676,90677,90679,90681],{},[1979,90678,2128],{},[1846,90680,2075],{},[898,90682,207],{},[898,90684,1734],{"mathvariant":2226},[902,90686,90687],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[1639,90689,90690,90739,90861,90995],{},[724,90691,90692,90694,90695],{},[883,90693,52540],{}," Příklad 6.3 — ověření vlastností pro ",[883,90696,90698],{"className":90697},[886],[888,90699,90700],{"xmlns":890},[892,90701,90702,90736],{},[895,90703,90704,90706,90708,90722],{},[898,90705,900],{},[1846,90707,1848],{},[9012,90709,90710,90712,90714],{},[898,90711,2638],{},[1979,90713,2128],{},[895,90715,90716,90718,90720],{},[1979,90717,2128],{},[898,90719,4520],{"mathvariant":2226},[1979,90721,2201],{},[9012,90723,90724,90726,90728],{},[898,90725,2638],{},[1979,90727,1981],{},[895,90729,90730,90732,90734],{},[1979,90731,2023],{},[898,90733,4520],{"mathvariant":2226},[1979,90735,2201],{},[902,90737,90738],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,90740,90742],{"className":90741},[886],[888,90743,90744],{"xmlns":890,"display":27911},[892,90745,90746,90858],{},[895,90747,90748,90756,90758,90766,90782,90796,90798,90800,90802,90804,90812,90814,90822,90836,90852,90854,90856],{},[9012,90749,90750,90752,90754],{},[898,90751,900],{},[1979,90753,2128],{},[1846,90755,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,90757,1848],{},[2175,90759,90760],{"scriptlevel":2177,"displaystyle":1854},[2179,90761,90762,90764],{},[1979,90763,2128],{},[1979,90765,2201],{},[9012,90767,90768,90770,90772],{},[898,90769,2638],{},[1979,90771,2128],{},[895,90773,90774,90776,90778,90780],{},[1846,90775,2075],{},[1979,90777,2023],{},[898,90779,4520],{"mathvariant":2226},[1979,90781,2201],{},[9012,90783,90784,90786,90788],{},[898,90785,2638],{},[1979,90787,1981],{},[895,90789,90790,90792,90794],{},[1979,90791,2023],{},[898,90793,4520],{"mathvariant":2226},[1979,90795,2201],{},[1846,90797,3256],{},[1979,90799,2177],{},[1846,90801,2136],{"separator":2135},[5724,90803],{"width":15129},[9012,90805,90806,90808,90810],{},[898,90807,900],{},[1979,90809,1981],{},[1846,90811,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,90813,1848],{},[2175,90815,90816],{"scriptlevel":2177,"displaystyle":1854},[2179,90817,90818,90820],{},[1979,90819,2023],{},[1979,90821,2201],{},[9012,90823,90824,90826,90828],{},[898,90825,2638],{},[1979,90827,2128],{},[895,90829,90830,90832,90834],{},[1979,90831,2128],{},[898,90833,4520],{"mathvariant":2226},[1979,90835,2201],{},[9012,90837,90838,90840,90842],{},[898,90839,2638],{},[1979,90841,1981],{},[895,90843,90844,90846,90848,90850],{},[1846,90845,2075],{},[1979,90847,2128],{},[898,90849,4520],{"mathvariant":2226},[1979,90851,2201],{},[1846,90853,3256],{},[1979,90855,2177],{},[1846,90857,2136],{"separator":2135},[902,90859,90860],{"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,",[883,90862,90864],{"className":90863},[886],[888,90865,90866],{"xmlns":890,"display":27911},[892,90867,90868,90992],{},[895,90869,90870,90882,90884,90886,90894,90910,90924,90926,90928,90930,90932,90944,90946,90948,90956,90970,90986,90988,90990],{},[9012,90871,90872,90874,90876],{},[898,90873,900],{},[1979,90875,2753],{},[895,90877,90878,90880],{},[1846,90879,2228],{"mathvariant":2226},[1846,90881,2228],{"mathvariant":2226},[1846,90883,1848],{},[1846,90885,2075],{},[2175,90887,90888],{"scriptlevel":2177,"displaystyle":1854},[2179,90889,90890,90892],{},[1979,90891,2023],{},[1979,90893,41707],{},[9012,90895,90896,90898,90900],{},[898,90897,2638],{},[1979,90899,2128],{},[895,90901,90902,90904,90906,90908],{},[1846,90903,2075],{},[1979,90905,24046],{},[898,90907,4520],{"mathvariant":2226},[1979,90909,2201],{},[9012,90911,90912,90914,90916],{},[898,90913,2638],{},[1979,90915,1981],{},[895,90917,90918,90920,90922],{},[1979,90919,2023],{},[898,90921,4520],{"mathvariant":2226},[1979,90923,2201],{},[1846,90925,3295],{},[1979,90927,2177],{},[1846,90929,2136],{"separator":2135},[5724,90931],{"width":15129},[9012,90933,90934,90936,90938],{},[898,90935,900],{},[1979,90937,32391],{},[895,90939,90940,90942],{},[1846,90941,2228],{"mathvariant":2226},[1846,90943,2228],{"mathvariant":2226},[1846,90945,1848],{},[1846,90947,2075],{},[2175,90949,90950],{"scriptlevel":2177,"displaystyle":1854},[2179,90951,90952,90954],{},[1979,90953,2023],{},[1979,90955,41707],{},[9012,90957,90958,90960,90962],{},[898,90959,2638],{},[1979,90961,2128],{},[895,90963,90964,90966,90968],{},[1979,90965,2128],{},[898,90967,4520],{"mathvariant":2226},[1979,90969,2201],{},[9012,90971,90972,90974,90976],{},[898,90973,2638],{},[1979,90975,1981],{},[895,90977,90978,90980,90982,90984],{},[1846,90979,2075],{},[1979,90981,2078],{},[898,90983,4520],{"mathvariant":2226},[1979,90985,2201],{},[1846,90987,3295],{},[1979,90989,2177],{},[1846,90991,2136],{"separator":2135},[902,90993,90994],{"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,",[724,90996,90997],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,90999,91001],{"id":91000},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,91003,91004,91007],{},[38,91005,91006],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,91009,91011],{"className":91010},[886],[888,91012,91013],{"xmlns":890,"display":27911},[892,91014,91015,91058],{},[20599,91016,91017],{"width":27916},[20604,91018,91019,91021,91051,91053],{},[20607,91020],{"width":27921},[20607,91022,91023],{},[895,91024,91025,91027,91029,91035,91037,91043,91045,91047,91049],{},[898,91026,900],{},[1846,91028,1855],{"stretchy":1854},[2122,91030,91031,91033],{},[898,91032,2638],{},[1979,91034,2128],{},[1846,91036,2136],{"separator":2135},[2122,91038,91039,91041],{},[898,91040,2638],{},[1979,91042,1981],{},[1846,91044,1861],{"stretchy":1854},[1846,91046,1848],{},[898,91048,1992],{},[1846,91050,2136],{"separator":2135},[20607,91052],{"width":27921},[20607,91054,91055],{},[2138,91056,91057],{},"(6.7)",[902,91059,91060],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,91062,4156,91063,91076],{},[883,91064,91066],{"className":91065},[886],[888,91067,91068],{"xmlns":890},[892,91069,91070,91074],{},[895,91071,91072],{},[898,91073,1992],{},[902,91075,1992],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,91078,91080],{"className":91079},[886],[888,91081,91082],{"xmlns":890,"display":27911},[892,91083,91084,91125],{},[20599,91085,91086],{"width":27916},[20604,91087,91088,91090,91118,91120],{},[20607,91089],{"width":27921},[20607,91091,91092],{},[895,91093,91094,91102,91104,91112,91114,91116],{},[9012,91095,91096,91098,91100],{},[898,91097,2638],{},[1979,91099,2128],{},[898,91101,207],{},[1846,91103,3025],{},[9012,91105,91106,91108,91110],{},[898,91107,2638],{},[1979,91109,1981],{},[898,91111,1948],{},[1846,91113,1848],{},[898,91115,1992],{},[898,91117,1734],{"mathvariant":2226},[20607,91119],{"width":27921},[20607,91121,91122],{},[2138,91123,91124],{},"(6.8)",[902,91126,91127],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,91129,91130,91131,4204,91161,2053,91164,91177,91178,91213,91214,91231,91232,91261,91262,91265],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,91132,91134],{"className":91133},[886],[888,91135,91136],{"xmlns":890},[892,91137,91138,91158],{},[895,91139,91140,91142,91148,91150,91156],{},[1846,91141,2336],{"stretchy":1854},[2122,91143,91144,91146],{},[898,91145,2638],{},[1979,91147,2128],{},[1846,91149,2136],{"separator":2135},[2122,91151,91152,91154],{},[898,91153,2638],{},[1979,91155,1981],{},[1846,91157,2351],{"stretchy":1854},[902,91159,91160],{"encoding":904},"[Q_1, Q_2]",[38,91162,91163],{},"stejnou úrovní uspokojení",[883,91165,91167],{"className":91166},[886],[888,91168,91169],{"xmlns":890},[892,91170,91171,91175],{},[895,91172,91173],{},[898,91174,1992],{},[902,91176,1992],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,91179,91181],{"className":91180},[886],[888,91182,91183],{"xmlns":890},[892,91184,91185,91211],{},[895,91186,91187,91189,91191,91193,91195,91201,91203,91209],{},[898,91188,900],{},[1846,91190,1848],{},[898,91192,900],{},[1846,91194,1855],{"stretchy":1854},[2122,91196,91197,91199],{},[898,91198,2638],{},[1979,91200,2128],{},[1846,91202,2136],{"separator":2135},[2122,91204,91205,91207],{},[898,91206,2638],{},[1979,91208,1981],{},[1846,91210,1861],{"stretchy":1854},[902,91212,87301],{"encoding":904}," s rovinami ",[883,91215,91217],{"className":91216},[886],[888,91218,91219],{"xmlns":890},[892,91220,91221,91229],{},[895,91222,91223,91225,91227],{},[898,91224,900],{},[1846,91226,1848],{},[898,91228,1992],{},[902,91230,86517],{"encoding":904}," rovnoběžnými s rovinou ",[883,91233,91235],{"className":91234},[886],[888,91236,91237],{"xmlns":890},[892,91238,91239,91259],{},[895,91240,91241,91243,91249,91251,91257],{},[1846,91242,1855],{"stretchy":1854},[2122,91244,91245,91247],{},[898,91246,2638],{},[1979,91248,2128],{},[1846,91250,2136],{"separator":2135},[2122,91252,91253,91255],{},[898,91254,2638],{},[1979,91256,1981],{},[1846,91258,1861],{"stretchy":1854},[902,91260,89464],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,91263,91264],{},"izokvantami"," produkčních funkcí.",[724,91267,91268],{},[614,91269,91270,91271,89342,91289,91307,91308,1734],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,91272,91274],{"className":91273},[886],[888,91275,91276],{"xmlns":890},[892,91277,91278,91286],{},[895,91279,91280,91282,91284],{},[898,91281,207],{},[1846,91283,3295],{},[898,91285,1948],{},[902,91287,91288],{"encoding":904},"a \u003C b",[883,91290,91292],{"className":91291},[886],[888,91293,91294],{"xmlns":890},[892,91295,91296,91304],{},[895,91297,91298,91300,91302],{},[898,91299,207],{},[1846,91301,3256],{},[898,91303,1948],{},[902,91305,91306],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,91309,91311],{"className":91310},[886],[888,91312,91313],{"xmlns":890},[892,91314,91315,91339],{},[895,91316,91317,91323,91325,91331,91333],{},[2122,91318,91319,91321],{},[898,91320,1992],{},[1979,91322,2177],{},[1846,91324,3295],{},[2122,91326,91327,91329],{},[898,91328,1992],{},[1979,91330,2128],{},[1846,91332,3295],{},[2122,91334,91335,91337],{},[898,91336,1992],{},[1979,91338,1981],{},[902,91340,91341],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,91343,91344],{},[614,91345,91346,91347,91376,91377,91435,91436,91454],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,91348,91350],{"className":91349},[886],[888,91351,91352],{"xmlns":890},[892,91353,91354,91374],{},[895,91355,91356,91358,91364,91366,91372],{},[1846,91357,1855],{"stretchy":1854},[2122,91359,91360,91362],{},[898,91361,2638],{},[1979,91363,2128],{},[1846,91365,2136],{"separator":2135},[2122,91367,91368,91370],{},[898,91369,2638],{},[1979,91371,1981],{},[1846,91373,1861],{"stretchy":1854},[902,91375,89464],{"encoding":904},"; body ",[883,91378,91380],{"className":91379},[886],[888,91381,91382],{"xmlns":890},[892,91383,91384,91432],{},[895,91385,91386,91388,91390,91392,91398,91400,91406,91408,91410,91412,91414,91416,91422,91424,91430],{},[898,91387,4101],{},[1846,91389,1848],{},[1846,91391,2336],{"stretchy":1854},[2122,91393,91394,91396],{},[898,91395,207],{},[1979,91397,2128],{},[1846,91399,2136],{"separator":2135},[2122,91401,91402,91404],{},[898,91403,207],{},[1979,91405,1981],{},[1846,91407,2351],{"stretchy":1854},[1846,91409,2136],{"separator":2135},[898,91411,23098],{},[1846,91413,1848],{},[1846,91415,2336],{"stretchy":1854},[2122,91417,91418,91420],{},[898,91419,1948],{},[1979,91421,2128],{},[1846,91423,2136],{"separator":2135},[2122,91425,91426,91428],{},[898,91427,1948],{},[1979,91429,1981],{},[1846,91431,2351],{"stretchy":1854},[902,91433,91434],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,91437,91439],{"className":91438},[886],[888,91440,91441],{"xmlns":890},[892,91442,91443,91451],{},[895,91444,91445,91447,91449],{},[898,91446,2626],{},[1846,91448,2136],{"separator":2135},[898,91450,4029],{},[902,91452,91453],{"encoding":904},"C, D"," na vyšší hladině.",[1639,91456,91457],{},[724,91458,91459,91461,91462,91524,91525,91569,91570,91604,91605,26034,91623,91604,91677,26034,91695,91771],{},[883,91460,52540],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,91463,91465],{"className":91464},[886],[888,91466,91467],{"xmlns":890},[892,91468,91469,91521],{},[895,91470,91471,91473,91475,91481,91483,91489,91491,91493,91507],{},[898,91472,900],{},[1846,91474,1855],{"stretchy":1854},[2122,91476,91477,91479],{},[898,91478,2638],{},[1979,91480,2128],{},[1846,91482,2136],{"separator":2135},[2122,91484,91485,91487],{},[898,91486,2638],{},[1979,91488,1981],{},[1846,91490,1861],{"stretchy":1854},[1846,91492,1848],{},[9012,91494,91495,91497,91499],{},[898,91496,2638],{},[1979,91498,2128],{},[895,91500,91501,91503,91505],{},[1979,91502,2128],{},[898,91504,4520],{"mathvariant":2226},[1979,91506,2201],{},[9012,91508,91509,91511,91513],{},[898,91510,2638],{},[1979,91512,1981],{},[895,91514,91515,91517,91519],{},[1979,91516,2023],{},[898,91518,4520],{"mathvariant":2226},[1979,91520,2201],{},[902,91522,91523],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,91526,91528],{"className":91527},[886],[888,91529,91530],{"xmlns":890},[892,91531,91532,91566],{},[895,91533,91534,91548,91562,91564],{},[9012,91535,91536,91538,91540],{},[898,91537,2638],{},[1979,91539,2128],{},[895,91541,91542,91544,91546],{},[1979,91543,2128],{},[898,91545,4520],{"mathvariant":2226},[1979,91547,2201],{},[9012,91549,91550,91552,91554],{},[898,91551,2638],{},[1979,91553,1981],{},[895,91555,91556,91558,91560],{},[1979,91557,2023],{},[898,91559,4520],{"mathvariant":2226},[1979,91561,2201],{},[1846,91563,1848],{},[898,91565,1992],{},[902,91567,91568],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,91571,91573],{"className":91572},[886],[888,91574,91575],{"xmlns":890},[892,91576,91577,91601],{},[895,91578,91579,91585,91593,91595],{},[2122,91580,91581,91583],{},[898,91582,2638],{},[1979,91584,2128],{},[9012,91586,91587,91589,91591],{},[898,91588,2638],{},[1979,91590,1981],{},[1979,91592,2023],{},[1846,91594,1848],{},[1974,91596,91597,91599],{},[898,91598,1992],{},[1979,91600,2201],{},[902,91602,91603],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,91606,91608],{"className":91607},[886],[888,91609,91610],{"xmlns":890},[892,91611,91612,91620],{},[895,91613,91614,91616,91618],{},[898,91615,1992],{},[1846,91617,1848],{},[1979,91619,2128],{},[902,91621,91622],{"encoding":904},"c = 1",[883,91624,91626],{"className":91625},[886],[888,91627,91628],{"xmlns":890},[892,91629,91630,91674],{},[895,91631,91632,91638,91640,91656,91658],{},[2122,91633,91634,91636],{},[898,91635,2638],{},[1979,91637,1981],{},[1846,91639,1848],{},[9012,91641,91642,91644,91646],{},[898,91643,2638],{},[1979,91645,2128],{},[895,91647,91648,91650,91652,91654],{},[1846,91649,2075],{},[1979,91651,2128],{},[898,91653,4520],{"mathvariant":2226},[1979,91655,2023],{},[1846,91657,1848],{},[2175,91659,91660],{"scriptlevel":2177,"displaystyle":2135},[2179,91661,91662,91664],{},[1979,91663,2128],{},[81872,91665,91666,91672],{},[2122,91667,91668,91670],{},[898,91669,2638],{},[1979,91671,2128],{},[1979,91673,2023],{},[902,91675,91676],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,91678,91680],{"className":91679},[886],[888,91681,91682],{"xmlns":890},[892,91683,91684,91692],{},[895,91685,91686,91688,91690],{},[898,91687,1992],{},[1846,91689,1848],{},[1979,91691,1981],{},[902,91693,91694],{"encoding":904},"c = 2",[883,91696,91698],{"className":91697},[886],[888,91699,91700],{"xmlns":890},[892,91701,91702,91768],{},[895,91703,91704,91710,91712,91724,91726,91742,91744],{},[2122,91705,91706,91708],{},[898,91707,2638],{},[1979,91709,1981],{},[1846,91711,1848],{},[1974,91713,91714,91716],{},[1979,91715,1981],{},[895,91717,91718,91720,91722],{},[1979,91719,2201],{},[898,91721,4520],{"mathvariant":2226},[1979,91723,2023],{},[1846,91725,3025],{},[9012,91727,91728,91730,91732],{},[898,91729,2638],{},[1979,91731,2128],{},[895,91733,91734,91736,91738,91740],{},[1846,91735,2075],{},[1979,91737,2128],{},[898,91739,4520],{"mathvariant":2226},[1979,91741,2023],{},[1846,91743,1848],{},[2175,91745,91746],{"scriptlevel":2177,"displaystyle":2135},[2179,91747,91748,91758],{},[895,91749,91750,91752],{},[1979,91751,1981],{},[81872,91753,91754,91756],{},[1979,91755,1981],{},[1979,91757,2023],{},[81872,91759,91760,91766],{},[2122,91761,91762,91764],{},[898,91763,2638],{},[1979,91765,2128],{},[1979,91767,2023],{},[902,91769,91770],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,91773,91775],{"id":91774},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,91777,91778],{},[2409,91779],{"alt":91780,"className":91781,"src":91782},"imek-ic-4vlastnosti-anotovane",[210,2413],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[1639,91784,91785,91794,91841,91885,91891,91897],{},[724,91786,91787,91789,91790,91793],{},[883,91788,4258],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,91791,91792],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,91795,91796],{},[883,91797,91799],{"className":91798},[886],[888,91800,91801],{"xmlns":890},[892,91802,91803,91838],{},[895,91804,91805,91808,91810,91812,91814,91816,91834,91836],{},[898,91806,91807],{"mathvariant":2226},"tg",[1846,91809,56045],{},[898,91811,18707],{},[1846,91813,1848],{},[1846,91815,2075],{},[2179,91817,91818,91826],{},[9012,91819,91820,91822,91824],{},[898,91821,900],{},[1979,91823,2128],{},[1846,91825,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[9012,91827,91828,91830,91832],{},[898,91829,900],{},[1979,91831,1981],{},[1846,91833,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,91835,3295],{},[1979,91837,2177],{},[902,91839,91840],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,91842,91843,91844,91884],{},"(derivace implicitně zadané funkce ",[883,91845,91847],{"className":91846},[886],[888,91848,91849],{"xmlns":890},[892,91850,91851,91881],{},[895,91852,91853,91855,91857,91863,91865,91871,91873,91875,91877,91879],{},[898,91854,900],{},[1846,91856,1855],{"stretchy":1854},[2122,91858,91859,91861],{},[898,91860,2638],{},[1979,91862,2128],{},[1846,91864,2136],{"separator":2135},[2122,91866,91867,91869],{},[898,91868,2638],{},[1979,91870,1981],{},[1846,91872,1861],{"stretchy":1854},[1846,91874,2075],{},[898,91876,1992],{},[1846,91878,1848],{},[1979,91880,2177],{},[902,91882,91883],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,91886,91887,91890],{},[38,91888,91889],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,91892,91893,91896],{},[38,91894,91895],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,91898,91899,91902,91903,91921,91922,91938,91939,91942],{},[38,91900,91901],{},"4° Konvexní."," Pro každé dva body ",[883,91904,91906],{"className":91905},[886],[888,91907,91908],{"xmlns":890},[892,91909,91910,91918],{},[895,91911,91912,91914,91916],{},[898,91913,4101],{},[1846,91915,2136],{"separator":2135},[898,91917,23098],{},[902,91919,91920],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,91923,91925],{"className":91924},[886],[888,91926,91927],{"xmlns":890},[892,91928,91929,91935],{},[895,91930,91931,91933],{},[898,91932,4101],{},[898,91934,23098],{},[902,91936,91937],{"encoding":904},"AB"," ve ",[38,91940,91941],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,91944,91945],{},[614,91946,91947,91948,91983,91984,1734],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,91949,91951],{"className":91950},[886],[888,91952,91953],{"xmlns":890},[892,91954,91955,91981],{},[895,91956,91957,91959,91961,91967,91969,91975,91977,91979],{},[898,91958,900],{},[1846,91960,1855],{"stretchy":1854},[2122,91962,91963,91965],{},[898,91964,2638],{},[1979,91966,2128],{},[1846,91968,2136],{"separator":2135},[2122,91970,91971,91973],{},[898,91972,2638],{},[1979,91974,1981],{},[1846,91976,1861],{"stretchy":1854},[1846,91978,1848],{},[898,91980,1992],{},[902,91982,9614],{"encoding":904}," s tečnou se sklonem ",[883,91985,91987],{"className":91986},[886],[888,91988,91989],{"xmlns":890},[892,91990,91991,91999],{},[895,91992,91993,91995,91997],{},[898,91994,91807],{"mathvariant":2226},[1846,91996,56045],{},[898,91998,18707],{},[902,92000,92001],{"encoding":904},"\\operatorname{tg}\\alpha",[115,92003,92005],{"id":92004},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,92007,92008,2053,92011,9871,92024,92027],{},[38,92009,92010],{},"Mezní míra komoditní substituce",[883,92012,92014],{"className":92013},[886],[888,92015,92016],{"xmlns":890},[892,92017,92018,92022],{},[895,92019,92020],{},[2138,92021,10449],{},[902,92023,28083],{"encoding":904},[38,92025,92026],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,92029,92031],{"className":92030},[886],[888,92032,92033],{"xmlns":890,"display":27911},[892,92034,92035,92122],{},[20599,92036,92037],{"width":27916},[20604,92038,92039,92041,92115,92117],{},[20607,92040],{"width":27921},[20607,92042,92043],{},[895,92044,92045,92047,92049,92051,92053,92059,92061,92067,92069,92071,92093,92095,92113],{},[2138,92046,10449],{},[1846,92048,1848],{},[2138,92050,10449],{},[1846,92052,1855],{"stretchy":1854},[2122,92054,92055,92057],{},[898,92056,2638],{},[1979,92058,2128],{},[1846,92060,2136],{"separator":2135},[2122,92062,92063,92065],{},[898,92064,2638],{},[1979,92066,1981],{},[1846,92068,1861],{"stretchy":1854},[1846,92070,1848],{},[2179,92072,92073,92083],{},[895,92074,92075,92077],{},[898,92076,2667],{},[2122,92078,92079,92081],{},[898,92080,900],{},[1979,92082,2128],{},[895,92084,92085,92087],{},[898,92086,2667],{},[2122,92088,92089,92091],{},[898,92090,900],{},[1979,92092,1981],{},[1846,92094,1848],{},[2179,92096,92097,92105],{},[9012,92098,92099,92101,92103],{},[898,92100,900],{},[1979,92102,2128],{},[1846,92104,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[9012,92106,92107,92109,92111],{},[898,92108,900],{},[1979,92110,1981],{},[1846,92112,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[898,92114,1734],{"mathvariant":2226},[20607,92116],{"width":27921},[20607,92118,92119],{},[2138,92120,92121],{},"(6.9)",[902,92123,92124],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,92126,92127,92128,92162,92163,92195,92196,92231,92232,92245],{},"Geometricky: ",[883,92129,92131],{"className":92130},[886],[888,92132,92133],{"xmlns":890},[892,92134,92135,92159],{},[895,92136,92137,92139],{},[1846,92138,2075],{},[2175,92140,92141],{"scriptlevel":2177,"displaystyle":1854},[2179,92142,92143,92151],{},[9012,92144,92145,92147,92149],{},[898,92146,900],{},[1979,92148,2128],{},[1846,92150,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[9012,92152,92153,92155,92157],{},[898,92154,900],{},[1979,92156,1981],{},[1846,92158,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,92160,92161],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,92164,92166],{"className":92165},[886],[888,92167,92168],{"xmlns":890},[892,92169,92170,92192],{},[895,92171,92172,92178,92180,92182,92184,92190],{},[2122,92173,92174,92176],{},[898,92175,2638],{},[1979,92177,1981],{},[1846,92179,1848],{},[898,92181,1851],{},[1846,92183,1855],{"stretchy":1854},[2122,92185,92186,92188],{},[898,92187,2638],{},[1979,92189,2128],{},[1846,92191,1861],{"stretchy":1854},[902,92193,92194],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,92197,92199],{"className":92198},[886],[888,92200,92201],{"xmlns":890},[892,92202,92203,92229],{},[895,92204,92205,92207,92209,92215,92217,92223,92225,92227],{},[898,92206,900],{},[1846,92208,1855],{"stretchy":1854},[2122,92210,92211,92213],{},[898,92212,2638],{},[1979,92214,2128],{},[1846,92216,2136],{"separator":2135},[2122,92218,92219,92221],{},[898,92220,2638],{},[1979,92222,1981],{},[1846,92224,1861],{"stretchy":1854},[1846,92226,1848],{},[898,92228,1992],{},[902,92230,9614],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,92233,92235],{"className":92234},[886],[888,92236,92237],{"xmlns":890},[892,92238,92239,92243],{},[895,92240,92241],{},[2138,92242,10449],{},[902,92244,28083],{"encoding":904}," chápeme jako velikost kompenzace.",[1639,92247,92248],{},[724,92249,92250,92252,92253,7948,92285,92323,92324,92341,92342,92359],{},[883,92251,4001],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,92254,92256],{"className":92255},[886],[888,92257,92258],{"xmlns":890},[892,92259,92260,92282],{},[895,92261,92262,92264,92266,92272,92274,92280],{},[2138,92263,10449],{},[1846,92265,1855],{"stretchy":1854},[2122,92267,92268,92270],{},[898,92269,2638],{},[1979,92271,2128],{},[1846,92273,2136],{"separator":2135},[2122,92275,92276,92278],{},[898,92277,2638],{},[1979,92279,1981],{},[1846,92281,1861],{"stretchy":1854},[902,92283,92284],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,92286,92287,92288,28848,92305,92322],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,92289,92291],{"className":92290},[886],[888,92292,92293],{"xmlns":890},[892,92294,92295,92303],{},[895,92296,92297],{},[2122,92298,92299,92301],{},[898,92300,2638],{},[1979,92302,2128],{},[902,92304,28847],{"encoding":904},[883,92306,92308],{"className":92307},[886],[888,92309,92310],{"xmlns":890},[892,92311,92312,92320],{},[895,92313,92314],{},[2122,92315,92316,92318],{},[898,92317,2638],{},[1979,92319,1981],{},[902,92321,28866],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,92325,92327],{"className":92326},[886],[888,92328,92329],{"xmlns":890},[892,92330,92331,92339],{},[895,92332,92333],{},[2122,92334,92335,92337],{},[898,92336,2638],{},[1979,92338,1981],{},[902,92340,28866],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,92343,92345],{"className":92344},[886],[888,92346,92347],{"xmlns":890},[892,92348,92349,92357],{},[895,92350,92351],{},[2122,92352,92353,92355],{},[898,92354,2638],{},[1979,92356,2128],{},[902,92358,28847],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,92361,92362,92363,29789],{},"Pro obecnou změnu ",[883,92364,92366],{"className":92365},[886],[888,92367,92368],{"xmlns":890},[892,92369,92370,92380],{},[895,92371,92372,92374],{},[898,92373,2044],{"mathvariant":2226},[2122,92375,92376,92378],{},[898,92377,2638],{},[1979,92379,2128],{},[902,92381,92382],{"encoding":904},"\\mathrm{d} Q_1",[883,92384,92386],{"className":92385},[886],[888,92387,92388],{"xmlns":890,"display":27911},[892,92389,92390,92443],{},[20599,92391,92392],{"width":27916},[20604,92393,92394,92396,92436,92438],{},[20607,92395],{"width":27921},[20607,92397,92398],{},[895,92399,92400,92402,92408,92410,92412,92418,92420,92422,92424,92426,92428,92434],{},[898,92401,2738],{"mathvariant":2226},[2122,92403,92404,92406],{},[898,92405,2638],{},[1979,92407,1981],{},[1846,92409,1650],{},[898,92411,2044],{"mathvariant":2226},[2122,92413,92414,92416],{},[898,92415,2638],{},[1979,92417,1981],{},[1846,92419,1848],{},[1846,92421,2075],{},[2138,92423,10449],{},[1846,92425,3025],{},[898,92427,2044],{"mathvariant":2226},[2122,92429,92430,92432],{},[898,92431,2638],{},[1979,92433,2128],{},[1846,92435,2136],{"separator":2135},[20607,92437],{"width":27921},[20607,92439,92440],{},[2138,92441,92442],{},"(6.10)",[902,92444,92445],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,92447,92449],{"className":92448},[886],[888,92450,92451],{"xmlns":890,"display":27911},[892,92452,92453,92500],{},[20599,92454,92455],{"width":27916},[20604,92456,92457,92459,92493,92495],{},[20607,92458],{"width":27921},[20607,92460,92461],{},[895,92462,92463,92465,92471,92473,92475,92481,92483,92485,92491],{},[898,92464,2044],{"mathvariant":2226},[2122,92466,92467,92469],{},[898,92468,2638],{},[1979,92470,2128],{},[1846,92472,1848],{},[1846,92474,2075],{},[2179,92476,92477,92479],{},[1979,92478,2128],{},[2138,92480,10449],{},[2138,92482,2835],{},[898,92484,2044],{"mathvariant":2226},[2122,92486,92487,92489],{},[898,92488,2638],{},[1979,92490,1981],{},[898,92492,1734],{"mathvariant":2226},[20607,92494],{"width":27921},[20607,92496,92497],{},[2138,92498,92499],{},"(6.11)",[902,92501,92502],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[1639,92504,92505,92571,92688],{},[724,92506,92507,92509,92510,29789],{},[883,92508,52540],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,92511,92513],{"className":92512},[886],[888,92514,92515],{"xmlns":890},[892,92516,92517,92569],{},[895,92518,92519,92521,92523,92529,92531,92537,92539,92541,92555],{},[898,92520,900],{},[1846,92522,1855],{"stretchy":1854},[2122,92524,92525,92527],{},[898,92526,2638],{},[1979,92528,2128],{},[1846,92530,2136],{"separator":2135},[2122,92532,92533,92535],{},[898,92534,2638],{},[1979,92536,1981],{},[1846,92538,1861],{"stretchy":1854},[1846,92540,1848],{},[9012,92542,92543,92545,92547],{},[898,92544,2638],{},[1979,92546,2128],{},[895,92548,92549,92551,92553],{},[1979,92550,2128],{},[898,92552,4520],{"mathvariant":2226},[1979,92554,1981],{},[9012,92556,92557,92559,92561],{},[898,92558,2638],{},[1979,92560,1981],{},[895,92562,92563,92565,92567],{},[1979,92564,2128],{},[898,92566,4520],{"mathvariant":2226},[1979,92568,1981],{},[902,92570,29788],{"encoding":904},[724,92572,92573],{},[883,92574,92576],{"className":92575},[886],[888,92577,92578],{"xmlns":890},[892,92579,92580,92686],{},[895,92581,92582,92584,92586,92668,92670,92684],{},[2138,92583,10449],{},[1846,92585,1848],{},[2179,92587,92588,92628],{},[895,92589,92590,92598,92614],{},[2175,92591,92592],{"scriptlevel":2177,"displaystyle":1854},[2179,92593,92594,92596],{},[1979,92595,2128],{},[1979,92597,1981],{},[9012,92599,92600,92602,92604],{},[898,92601,2638],{},[1979,92603,2128],{},[895,92605,92606,92608,92610,92612],{},[1846,92607,2075],{},[1979,92609,2128],{},[898,92611,4520],{"mathvariant":2226},[1979,92613,1981],{},[9012,92615,92616,92618,92620],{},[898,92617,2638],{},[1979,92619,1981],{},[895,92621,92622,92624,92626],{},[1979,92623,2128],{},[898,92625,4520],{"mathvariant":2226},[1979,92627,1981],{},[895,92629,92630,92638,92652],{},[2175,92631,92632],{"scriptlevel":2177,"displaystyle":1854},[2179,92633,92634,92636],{},[1979,92635,2128],{},[1979,92637,1981],{},[9012,92639,92640,92642,92644],{},[898,92641,2638],{},[1979,92643,2128],{},[895,92645,92646,92648,92650],{},[1979,92647,2128],{},[898,92649,4520],{"mathvariant":2226},[1979,92651,1981],{},[9012,92653,92654,92656,92658],{},[898,92655,2638],{},[1979,92657,1981],{},[895,92659,92660,92662,92664,92666],{},[1846,92661,2075],{},[1979,92663,2128],{},[898,92665,4520],{"mathvariant":2226},[1979,92667,1981],{},[1846,92669,1848],{},[2179,92671,92672,92678],{},[2122,92673,92674,92676],{},[898,92675,2638],{},[1979,92677,1981],{},[2122,92679,92680,92682],{},[898,92681,2638],{},[1979,92683,2128],{},[898,92685,1734],{"mathvariant":2226},[902,92687,29907],{"encoding":904},[724,92689,29910,92690,2776,92733,29958,92735,92754],{},[883,92691,92693],{"className":92692},[886],[888,92694,92695],{"xmlns":890},[892,92696,92697,92731],{},[895,92698,92699,92701,92703,92705,92707,92709,92711,92713,92721,92723],{},[2138,92700,10449],{},[1846,92702,1855],{"stretchy":1854},[1979,92704,29926],{},[1846,92706,2136],{"separator":2135},[1979,92708,14955],{},[1846,92710,1861],{"stretchy":1854},[1846,92712,1848],{},[2175,92714,92715],{"scriptlevel":2177,"displaystyle":1854},[2179,92716,92717,92719],{},[1979,92718,14955],{},[1979,92720,29926],{},[1846,92722,1848],{},[2175,92724,92725],{"scriptlevel":2177,"displaystyle":1854},[2179,92726,92727,92729],{},[1979,92728,2078],{},[1979,92730,2023],{},[902,92732,29955],{"encoding":904},[614,92734,9062],{},[883,92736,92738],{"className":92737},[886],[888,92739,92740],{"xmlns":890},[892,92741,92742,92752],{},[895,92743,92744],{},[2175,92745,92746],{"scriptlevel":2177,"displaystyle":1854},[2179,92747,92748,92750],{},[1979,92749,2078],{},[1979,92751,2023],{},[902,92753,29978],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,92756,92757,92758,92762],{},"(Paralelou je ",[207,92759,92761],{"className":92760,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,92764,92766],{"id":92765},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,92768,92769,92770,92773],{},"Rámcově se v kapitole 6 studují ",[38,92771,92772],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,92775,92776,92912],{},[123,92777,92778,92780,92781,10003,92812,2053,92815,92864,92865,1734],{},[38,92779,28097],{}," — maximalizace ",[883,92782,92784],{"className":92783},[886],[888,92785,92786],{"xmlns":890},[892,92787,92788,92810],{},[895,92789,92790,92792,92794,92800,92802,92808],{},[898,92791,900],{},[1846,92793,1855],{"stretchy":1854},[2122,92795,92796,92798],{},[898,92797,2638],{},[1979,92799,2128],{},[1846,92801,2136],{"separator":2135},[2122,92803,92804,92806],{},[898,92805,2638],{},[1979,92807,1981],{},[1846,92809,1861],{"stretchy":1854},[902,92811,16188],{"encoding":904},[38,92813,92814],{},"rozpočtovém omezení",[883,92816,92818],{"className":92817},[886],[888,92819,92820],{"xmlns":890},[892,92821,92822,92862],{},[895,92823,92824,92830,92832,92840,92846,92848,92856],{},[1974,92825,92826,92828],{},[898,92827,8974],{},[1846,92829,4200],{},[1846,92831,1848],{},[9012,92833,92834,92836,92838],{},[898,92835,3783],{},[1979,92837,2128],{},[1846,92839,4200],{},[2122,92841,92842,92844],{},[898,92843,2638],{},[1979,92845,2128],{},[1846,92847,1945],{},[9012,92849,92850,92852,92854],{},[898,92851,3783],{},[1979,92853,1981],{},[1846,92855,4200],{},[2122,92857,92858,92860],{},[898,92859,2638],{},[1979,92861,1981],{},[902,92863,17143],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,92866,92868],{"className":92867},[886],[888,92869,92870],{"xmlns":890},[892,92871,92872,92910],{},[895,92873,92874,92880,92882,92888,92890,92896,92898,92904,92906,92908],{},[2122,92875,92876,92878],{},[898,92877,2638],{},[898,92879,17635],{},[1846,92881,1848],{},[2122,92883,92884,92886],{},[898,92885,4029],{},[898,92887,17635],{},[1846,92889,1855],{"stretchy":1854},[2122,92891,92892,92894],{},[898,92893,3783],{},[1979,92895,2128],{},[1846,92897,2136],{"separator":2135},[2122,92899,92900,92902],{},[898,92901,3783],{},[1979,92903,1981],{},[1846,92905,2136],{"separator":2135},[898,92907,8974],{},[1846,92909,1861],{"stretchy":1854},[902,92911,36300],{"encoding":904},[123,92913,92914,27746,92917,27789,92963,92980,92981,1734],{},[38,92915,92916],{},"Duální úloha",[883,92918,92920],{"className":92919},[886],[888,92921,92922],{"xmlns":890},[892,92923,92924,92960],{},[895,92925,92926,92928,92930,92938,92944,92946,92954],{},[898,92927,4098],{},[1846,92929,1848],{},[9012,92931,92932,92934,92936],{},[898,92933,3783],{},[1979,92935,2128],{},[1846,92937,4200],{},[2122,92939,92940,92942],{},[898,92941,2638],{},[1979,92943,2128],{},[1846,92945,1945],{},[9012,92947,92948,92950,92952],{},[898,92949,3783],{},[1979,92951,1981],{},[1846,92953,4200],{},[2122,92955,92956,92958],{},[898,92957,2638],{},[1979,92959,1981],{},[902,92961,92962],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,92964,92966],{"className":92965},[886],[888,92967,92968],{"xmlns":890},[892,92969,92970,92978],{},[895,92971,92972],{},[1974,92973,92974,92976],{},[898,92975,900],{},[1846,92977,4200],{},[902,92979,27807],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,92982,92984],{"className":92983},[886],[888,92985,92986],{"xmlns":890},[892,92987,92988,93026],{},[895,92989,92990,92996,92998,93004,93006,93012,93014,93020,93022,93024],{},[2122,92991,92992,92994],{},[898,92993,2638],{},[898,92995,17635],{},[1846,92997,1848],{},[2122,92999,93000,93002],{},[898,93001,4029],{},[898,93003,17635],{},[1846,93005,1855],{"stretchy":1854},[2122,93007,93008,93010],{},[898,93009,3783],{},[1979,93011,2128],{},[1846,93013,2136],{"separator":2135},[2122,93015,93016,93018],{},[898,93017,3783],{},[1979,93019,1981],{},[1846,93021,2136],{"separator":2135},[898,93023,900],{},[1846,93025,1861],{"stretchy":1854},[902,93027,17668],{"encoding":904},[724,93029,93030,93031,93034,93035,2053,93038,93077],{},"Obě úlohy se řeší ",[207,93032,27812],{"className":93033,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,93036,93037],{},"tentýž bod dotyku",[883,93039,93041],{"className":93040},[886],[888,93042,93043],{"xmlns":890},[892,93044,93045,93075],{},[895,93046,93047,93053,93055,93063,93065,93073],{},[1974,93048,93049,93051],{},[898,93050,2638],{},[1846,93052,4200],{},[1846,93054,2336],{"stretchy":1854},[9012,93056,93057,93059,93061],{},[898,93058,2638],{},[1979,93060,2128],{},[1846,93062,4200],{},[1846,93064,2136],{"separator":2135},[9012,93066,93067,93069,93071],{},[898,93068,2638],{},[1979,93070,1981],{},[1846,93072,4200],{},[1846,93074,2351],{"stretchy":1854},[902,93076,28172],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,93079,93081],{"className":93080},[886],[888,93082,93083],{"xmlns":890,"display":27911},[892,93084,93085,93131],{},[895,93086,93087,93089,93091,93109,93111,93129],{},[2138,93088,10449],{},[1846,93090,1848],{},[2179,93092,93093,93101],{},[9012,93094,93095,93097,93099],{},[898,93096,900],{},[1979,93098,2128],{},[1846,93100,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[9012,93102,93103,93105,93107],{},[898,93104,900],{},[1979,93106,1981],{},[1846,93108,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,93110,1848],{},[2179,93112,93113,93121],{},[9012,93114,93115,93117,93119],{},[898,93116,3783],{},[1979,93118,2128],{},[1846,93120,4200],{},[9012,93122,93123,93125,93127],{},[898,93124,3783],{},[1979,93126,1981],{},[1846,93128,4200],{},[898,93130,1734],{"mathvariant":2226},[902,93132,93133],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,93135,93136],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[1639,93138,93139],{},[724,93140,93141,93143,93144,93147,93148,93151,93152,93179,93180,93214,93215,93249,93250,93293,93294,93297,93298,1734],{},[883,93142,4001],{}," Pro detailní postup viz ",[207,93145,36599],{"className":93146,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,93149,93150],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,93153,93155],{"className":93154},[886],[888,93156,93157],{"xmlns":890},[892,93158,93159,93177],{},[895,93160,93161,93163,93165,93171],{},[898,93162,900],{},[1846,93164,1848],{},[2122,93166,93167,93169],{},[898,93168,2638],{},[1979,93170,2128],{},[2122,93172,93173,93175],{},[898,93174,2638],{},[1979,93176,1981],{},[902,93178,30071],{"encoding":904}," s výsledkem ",[883,93181,93183],{"className":93182},[886],[888,93184,93185],{"xmlns":890},[892,93186,93187,93211],{},[895,93188,93189,93195,93197,93199,93201,93207,93209],{},[2122,93190,93191,93193],{},[898,93192,2638],{},[1979,93194,2128],{},[1846,93196,1848],{},[1979,93198,4850],{},[1846,93200,2136],{"separator":2135},[2122,93202,93203,93205],{},[898,93204,2638],{},[1979,93206,1981],{},[1846,93208,1848],{},[1979,93210,2712],{},[902,93212,93213],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,93216,93218],{"className":93217},[886],[888,93219,93220],{"xmlns":890},[892,93221,93222,93246],{},[895,93223,93224,93230,93232,93234,93236,93242,93244],{},[2122,93225,93226,93228],{},[898,93227,2638],{},[1979,93229,2128],{},[1846,93231,1848],{},[1979,93233,2201],{},[1846,93235,2136],{"separator":2135},[2122,93237,93238,93240],{},[898,93239,2638],{},[1979,93241,1981],{},[1846,93243,1848],{},[1979,93245,2128],{},[902,93247,93248],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,93251,93253],{"className":93252},[886],[888,93254,93255],{"xmlns":890},[892,93256,93257,93291],{},[895,93258,93259,93261,93263,93277],{},[898,93260,900],{},[1846,93262,1848],{},[9012,93264,93265,93267,93269],{},[898,93266,2638],{},[1979,93268,2128],{},[895,93270,93271,93273,93275],{},[1979,93272,2128],{},[898,93274,4520],{"mathvariant":2226},[1979,93276,1981],{},[9012,93278,93279,93281,93283],{},[898,93280,2638],{},[1979,93282,1981],{},[895,93284,93285,93287,93289],{},[1979,93286,2128],{},[898,93288,4520],{"mathvariant":2226},[1979,93290,1981],{},[902,93292,33004],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,93295,93296],{},"6.8–6.13"," jsou na stránce ",[207,93299,27612],{"className":93300,"dataFsResolvedFilePath":911,"href":912},[210],[115,93302,93304],{"id":93303},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,93306,93307,93308,93321,93322,93324,93325,93327,93328,93330,93331,93333,93334,93336,93337,93339,93340,2053,93342,93377,93378,93391,93392,93395,93396,93399,93400,1734],{},"Každá ",[883,93309,93311],{"className":93310},[886],[888,93312,93313],{"xmlns":890},[892,93314,93315,93319],{},[895,93316,93317],{},[898,93318,36705],{},[902,93320,36705],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,93323,86655],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,93326,87139],{}," a současně ",[38,93329,86658],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,93332,86663],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,93335,52522],{}," (6.4) a druhé parciální derivace ",[38,93338,89022],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,93341,9577],{},[883,93343,93345],{"className":93344},[886],[888,93346,93347],{"xmlns":890},[892,93348,93349,93375],{},[895,93350,93351,93353,93355,93361,93363,93369,93371,93373],{},[898,93352,900],{},[1846,93354,1855],{"stretchy":1854},[2122,93356,93357,93359],{},[898,93358,2638],{},[1979,93360,2128],{},[1846,93362,2136],{"separator":2135},[2122,93364,93365,93367],{},[898,93366,2638],{},[1979,93368,1981],{},[1846,93370,1861],{"stretchy":1854},[1846,93372,1848],{},[898,93374,1992],{},[902,93376,9614],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,93379,93381],{"className":93380},[886],[888,93382,93383],{"xmlns":890},[892,93384,93385,93389],{},[895,93386,93387],{},[2138,93388,10449],{},[902,93390,28083],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,93393,93394],{},"maximalizace užitečnosti"," a duální ",[38,93397,93398],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,93401,36599],{"className":93402,"dataFsResolvedFilePath":911,"href":912},[210],[115,93404,49727],{"id":49726},[152,93406,93407,93410,93413,93416,93419,93422,93425,93428,93431,93434],{},[123,93408,93409],{},"Co se zahrnuje pod termín užitečnost?",[123,93411,93412],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,93414,93415],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,93417,93418],{},"Jak se vypočítá mezní užitečnost?",[123,93420,93421],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,93423,93424],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,93426,93427],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,93429,93430],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,93432,93433],{},"Proč mají křivky užitečnosti záporný sklon?",[123,93435,93436],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,93438,93440],{"id":93439},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,93442,93443,93446,93447,83328,93489,1343,93517,1343,93545,93573],{},[38,93444,93445],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,93448,93450],{"className":93449},[886],[888,93451,93452],{"xmlns":890},[892,93453,93454,93486],{},[895,93455,93456,93458,93460,93466,93468,93470,93476,93478,93480],{},[898,93457,900],{},[1846,93459,1848],{},[2122,93461,93462,93464],{},[898,93463,2638],{},[1979,93465,2128],{},[1846,93467,1945],{},[1979,93469,64404],{},[2122,93471,93472,93474],{},[898,93473,2638],{},[1979,93475,1981],{},[1846,93477,1945],{},[1979,93479,1981],{},[2122,93481,93482,93484],{},[898,93483,2638],{},[1979,93485,2023],{},[902,93487,93488],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,93490,93492],{"className":93491},[886],[888,93493,93494],{"xmlns":890},[892,93495,93496,93514],{},[895,93497,93498,93500,93502,93504,93506,93508,93510,93512],{},[898,93499,900],{},[1846,93501,1855],{"stretchy":1854},[1979,93503,2201],{},[1846,93505,2136],{"separator":2135},[1979,93507,1981],{},[1846,93509,2136],{"separator":2135},[1979,93511,1981],{},[1846,93513,1861],{"stretchy":1854},[902,93515,93516],{"encoding":904},"U(4, 2, 2)",[883,93518,93520],{"className":93519},[886],[888,93521,93522],{"xmlns":890},[892,93523,93524,93542],{},[895,93525,93526,93528,93530,93532,93534,93536,93538,93540],{},[898,93527,900],{},[1846,93529,1855],{"stretchy":1854},[1979,93531,2128],{},[1846,93533,2136],{"separator":2135},[1979,93535,2201],{},[1846,93537,2136],{"separator":2135},[1979,93539,1981],{},[1846,93541,1861],{"stretchy":1854},[902,93543,93544],{"encoding":904},"U(1, 4, 2)",[883,93546,93548],{"className":93547},[886],[888,93549,93550],{"xmlns":890},[892,93551,93552,93570],{},[895,93553,93554,93556,93558,93560,93562,93564,93566,93568],{},[898,93555,900],{},[1846,93557,1855],{"stretchy":1854},[1979,93559,1981],{},[1846,93561,2136],{"separator":2135},[1979,93563,2023],{},[1846,93565,2136],{"separator":2135},[1979,93567,2128],{},[1846,93569,1861],{"stretchy":1854},[902,93571,93572],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,93575,93576,93579,93580,93632,93633,1343,93659,1343,93685,1343,93711,1343,93737,1343,93763,1343,93789,93815],{},[38,93577,93578],{},"6.2"," Je dána užitečnost ",[883,93581,93583],{"className":93582},[886],[888,93584,93585],{"xmlns":890},[892,93586,93587,93629],{},[895,93588,93589,93591,93593,93595,93609,93623],{},[898,93590,900],{},[1846,93592,1848],{},[1979,93594,1981],{},[9012,93596,93597,93599,93601],{},[898,93598,2638],{},[1979,93600,2128],{},[895,93602,93603,93605,93607],{},[1979,93604,2128],{},[898,93606,4520],{"mathvariant":2226},[1979,93608,2023],{},[9012,93610,93611,93613,93615],{},[898,93612,2638],{},[1979,93614,1981],{},[895,93616,93617,93619,93621],{},[1979,93618,2128],{},[898,93620,4520],{"mathvariant":2226},[1979,93622,1981],{},[2122,93624,93625,93627],{},[898,93626,2638],{},[1979,93628,2023],{},[902,93630,93631],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,93634,93636],{"className":93635},[886],[888,93637,93638],{"xmlns":890},[892,93639,93640,93656],{},[895,93641,93642,93644,93646,93648,93650,93652,93654],{},[1846,93643,1855],{"stretchy":1854},[1979,93645,5411],{},[1846,93647,2136],{"separator":2135},[1979,93649,66442],{},[1846,93651,2136],{"separator":2135},[1979,93653,2712],{},[1846,93655,1861],{"stretchy":1854},[902,93657,93658],{"encoding":904},"(36, 27, 10)",[883,93660,93662],{"className":93661},[886],[888,93663,93664],{"xmlns":890},[892,93665,93666,93682],{},[895,93667,93668,93670,93672,93674,93676,93678,93680],{},[1846,93669,1855],{"stretchy":1854},[1979,93671,41685],{},[1846,93673,2136],{"separator":2135},[1979,93675,5431],{},[1846,93677,2136],{"separator":2135},[1979,93679,8881],{},[1846,93681,1861],{"stretchy":1854},[902,93683,93684],{"encoding":904},"(64, 8, 20)",[883,93686,93688],{"className":93687},[886],[888,93689,93690],{"xmlns":890},[892,93691,93692,93708],{},[895,93693,93694,93696,93698,93700,93702,93704,93706],{},[1846,93695,1855],{"stretchy":1854},[1979,93697,4850],{},[1846,93699,2136],{"separator":2135},[1979,93701,41685],{},[1846,93703,2136],{"separator":2135},[1979,93705,5431],{},[1846,93707,1861],{"stretchy":1854},[902,93709,93710],{"encoding":904},"(25, 64, 8)",[883,93712,93714],{"className":93713},[886],[888,93715,93716],{"xmlns":890},[892,93717,93718,93734],{},[895,93719,93720,93722,93724,93726,93728,93730,93732],{},[1846,93721,1855],{"stretchy":1854},[1979,93723,2201],{},[1846,93725,2136],{"separator":2135},[1979,93727,72374],{},[1846,93729,2136],{"separator":2135},[1979,93731,2085],{},[1846,93733,1861],{"stretchy":1854},[902,93735,93736],{"encoding":904},"(4, 125, 6)",[883,93738,93740],{"className":93739},[886],[888,93741,93742],{"xmlns":890},[892,93743,93744,93760],{},[895,93745,93746,93748,93750,93752,93754,93756,93758],{},[1846,93747,1855],{"stretchy":1854},[1979,93749,3845],{},[1846,93751,2136],{"separator":2135},[1979,93753,5057],{},[1846,93755,2136],{"separator":2135},[1979,93757,3357],{},[1846,93759,1861],{"stretchy":1854},[902,93761,93762],{"encoding":904},"(9, 40, 12)",[883,93764,93766],{"className":93765},[886],[888,93767,93768],{"xmlns":890},[892,93769,93770,93786],{},[895,93771,93772,93774,93776,93778,93780,93782,93784],{},[1846,93773,1855],{"stretchy":1854},[1979,93775,3845],{},[1846,93777,2136],{"separator":2135},[1979,93779,41685],{},[1846,93781,2136],{"separator":2135},[1979,93783,2078],{},[1846,93785,1861],{"stretchy":1854},[902,93787,93788],{"encoding":904},"(9, 64, 5)",[883,93790,93792],{"className":93791},[886],[888,93793,93794],{"xmlns":890},[892,93795,93796,93812],{},[895,93797,93798,93800,93802,93804,93806,93808,93810],{},[1846,93799,1855],{"stretchy":1854},[1979,93801,41685],{},[1846,93803,2136],{"separator":2135},[1979,93805,5431],{},[1846,93807,2136],{"separator":2135},[1979,93809,2712],{},[1846,93811,1861],{"stretchy":1854},[902,93813,93814],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,93817,93818,93579,93821,93864,93865,93899,93900,6319,93930,93963,93964,93981,93982,93999],{},[38,93819,93820],{},"6.3",[883,93822,93824],{"className":93823},[886],[888,93825,93826],{"xmlns":890},[892,93827,93828,93862],{},[895,93829,93830,93832,93834,93848],{},[898,93831,900],{},[1846,93833,1848],{},[9012,93835,93836,93838,93840],{},[898,93837,2638],{},[1979,93839,2128],{},[895,93841,93842,93844,93846],{},[1979,93843,2128],{},[898,93845,4520],{"mathvariant":2226},[1979,93847,1981],{},[9012,93849,93850,93852,93854],{},[898,93851,2638],{},[1979,93853,1981],{},[895,93855,93856,93858,93860],{},[1979,93857,2128],{},[898,93859,4520],{"mathvariant":2226},[1979,93861,1981],{},[902,93863,33004],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,93866,93868],{"className":93867},[886],[888,93869,93870],{"xmlns":890},[892,93871,93872,93896],{},[895,93873,93874,93880,93882,93884,93886,93892,93894],{},[2122,93875,93876,93878],{},[898,93877,2638],{},[1979,93879,2128],{},[1846,93881,1848],{},[1979,93883,2968],{},[1846,93885,2136],{"separator":2135},[2122,93887,93888,93890],{},[898,93889,2638],{},[1979,93891,1981],{},[1846,93893,1848],{},[1979,93895,46548],{},[902,93897,93898],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,93901,93903],{"className":93902},[886],[888,93904,93905],{"xmlns":890},[892,93906,93907,93927],{},[895,93908,93909,93911,93917,93919,93921],{},[898,93910,2667],{},[2122,93912,93913,93915],{},[898,93914,900],{},[1979,93916,2128],{},[1846,93918,2136],{"separator":2135},[898,93920,2667],{},[2122,93922,93923,93925],{},[898,93924,900],{},[1979,93926,1981],{},[902,93928,93929],{"encoding":904},"MU_1, MU_2",[883,93931,93933],{"className":93932},[886],[888,93934,93935],{"xmlns":890},[892,93936,93937,93961],{},[895,93938,93939,93945,93947,93949,93951,93957,93959],{},[2122,93940,93941,93943],{},[898,93942,2638],{},[1979,93944,2128],{},[1846,93946,1848],{},[1979,93948,2968],{},[1846,93950,2136],{"separator":2135},[2122,93952,93953,93955],{},[898,93954,2638],{},[1979,93956,1981],{},[1846,93958,1848],{},[1979,93960,46548],{},[902,93962,93898],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,93965,93967],{"className":93966},[886],[888,93968,93969],{"xmlns":890},[892,93970,93971,93979],{},[895,93972,93973],{},[2122,93974,93975,93977],{},[898,93976,2638],{},[1979,93978,2128],{},[902,93980,28847],{"encoding":904}," na 60 a poklesu ",[883,93983,93985],{"className":93984},[886],[888,93986,93987],{"xmlns":890},[892,93988,93989,93997],{},[895,93990,93991],{},[2122,93992,93993,93995],{},[898,93994,2638],{},[1979,93996,1981],{},[902,93998,28866],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,94001,94002,94005,94006,94067,94068,1734],{},[38,94003,94004],{},"6.4"," Je dána funkce ",[883,94007,94009],{"className":94008},[886],[888,94010,94011],{"xmlns":890},[892,94012,94013,94065],{},[895,94014,94015,94017,94019,94025,94027,94033,94035,94037,94051],{},[898,94016,900],{},[1846,94018,1855],{"stretchy":1854},[2122,94020,94021,94023],{},[898,94022,2638],{},[1979,94024,2128],{},[1846,94026,2136],{"separator":2135},[2122,94028,94029,94031],{},[898,94030,2638],{},[1979,94032,1981],{},[1846,94034,1861],{"stretchy":1854},[1846,94036,1848],{},[9012,94038,94039,94041,94043],{},[898,94040,2638],{},[1979,94042,2128],{},[895,94044,94045,94047,94049],{},[1979,94046,2128],{},[898,94048,4520],{"mathvariant":2226},[1979,94050,1981],{},[9012,94052,94053,94055,94057],{},[898,94054,2638],{},[1979,94056,1981],{},[895,94058,94059,94061,94063],{},[1979,94060,2128],{},[898,94062,4520],{"mathvariant":2226},[1979,94064,1981],{},[902,94066,29788],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,94069,94071],{"className":94070},[886],[888,94072,94073],{"xmlns":890},[892,94074,94075,94165],{},[895,94076,94077,94079,94081,94087,94089,94091,94093,94095,94097,94099,94105,94107,94109,94111,94113,94115,94117,94119,94121,94127,94129,94131,94133,94135,94137,94139,94145,94147,94149,94151,94153,94155,94157,94163],{},[898,94078,900],{},[1846,94080,1855],{"stretchy":1854},[2122,94082,94083,94085],{},[898,94084,2638],{},[1979,94086,2128],{},[1846,94088,2136],{"separator":2135},[1979,94090,2128],{},[1846,94092,1861],{"stretchy":1854},[1846,94094,2136],{"separator":2135},[898,94096,900],{},[1846,94098,1855],{"stretchy":1854},[2122,94100,94101,94103],{},[898,94102,2638],{},[1979,94104,2128],{},[1846,94106,2136],{"separator":2135},[1979,94108,1981],{},[1846,94110,1861],{"stretchy":1854},[1846,94112,2136],{"separator":2135},[898,94114,900],{},[1846,94116,1855],{"stretchy":1854},[1979,94118,2128],{},[1846,94120,2136],{"separator":2135},[2122,94122,94123,94125],{},[898,94124,2638],{},[1979,94126,1981],{},[1846,94128,1861],{"stretchy":1854},[1846,94130,2136],{"separator":2135},[898,94132,900],{},[1846,94134,1855],{"stretchy":1854},[1979,94136,1981],{},[1846,94138,2136],{"separator":2135},[2122,94140,94141,94143],{},[898,94142,2638],{},[1979,94144,1981],{},[1846,94146,1861],{"stretchy":1854},[1846,94148,2136],{"separator":2135},[898,94150,900],{},[1846,94152,1855],{"stretchy":1854},[1979,94154,2023],{},[1846,94156,2136],{"separator":2135},[2122,94158,94159,94161],{},[898,94160,2638],{},[1979,94162,1981],{},[1846,94164,1861],{"stretchy":1854},[902,94166,94167],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,94169,94170,93579,94173,94217,94218,94326,94327,1343,94352,1343,94377,94419,94420,1343,94449,94474],{},[38,94171,94172],{},"6.5",[883,94174,94176],{"className":94175},[886],[888,94177,94178],{"xmlns":890},[892,94179,94180,94214],{},[895,94181,94182,94184,94186,94200],{},[898,94183,900],{},[1846,94185,1848],{},[9012,94187,94188,94190,94192],{},[898,94189,2638],{},[1979,94191,2128],{},[895,94193,94194,94196,94198],{},[1979,94195,1981],{},[898,94197,4520],{"mathvariant":2226},[1979,94199,2023],{},[9012,94201,94202,94204,94206],{},[898,94203,2638],{},[1979,94205,1981],{},[895,94207,94208,94210,94212],{},[1979,94209,2128],{},[898,94211,4520],{"mathvariant":2226},[1979,94213,2023],{},[902,94215,94216],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,94219,94221],{"className":94220},[886],[888,94222,94223],{"xmlns":890},[892,94224,94225,94323],{},[895,94226,94227,94229,94231,94237,94239,94245,94247,94249,94251,94253,94255,94257,94263,94265,94267,94269,94271,94273,94275,94281,94283,94285,94287,94289,94291,94293,94295,94297,94303,94305,94307,94309,94311,94313,94315,94321],{},[898,94228,900],{},[1846,94230,1855],{"stretchy":1854},[2122,94232,94233,94235],{},[898,94234,2638],{},[1979,94236,2128],{},[1846,94238,2136],{"separator":2135},[2122,94240,94241,94243],{},[898,94242,2638],{},[1979,94244,1981],{},[1846,94246,1861],{"stretchy":1854},[1846,94248,1848],{},[1979,94250,1981],{},[1846,94252,2136],{"separator":2135},[898,94254,900],{},[1846,94256,1855],{"stretchy":1854},[2122,94258,94259,94261],{},[898,94260,2638],{},[1979,94262,2128],{},[1846,94264,2136],{"separator":2135},[1979,94266,2023],{},[1846,94268,1861],{"stretchy":1854},[1846,94270,2136],{"separator":2135},[898,94272,900],{},[1846,94274,1855],{"stretchy":1854},[2122,94276,94277,94279],{},[898,94278,2638],{},[1979,94280,2128],{},[1846,94282,2136],{"separator":2135},[1979,94284,1981],{},[1846,94286,1861],{"stretchy":1854},[1846,94288,2136],{"separator":2135},[898,94290,900],{},[1846,94292,1855],{"stretchy":1854},[1979,94294,1981],{},[1846,94296,2136],{"separator":2135},[2122,94298,94299,94301],{},[898,94300,2638],{},[1979,94302,1981],{},[1846,94304,1861],{"stretchy":1854},[1846,94306,2136],{"separator":2135},[898,94308,900],{},[1846,94310,1855],{"stretchy":1854},[1979,94312,2023],{},[1846,94314,2136],{"separator":2135},[2122,94316,94317,94319],{},[898,94318,2638],{},[1979,94320,1981],{},[1846,94322,1861],{"stretchy":1854},[902,94324,94325],{"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 ",[883,94328,94330],{"className":94329},[886],[888,94331,94332],{"xmlns":890},[892,94333,94334,94349],{},[895,94335,94336,94338,94340,94342,94344,94347],{},[898,94337,4101],{},[1846,94339,2336],{"stretchy":1854},[1979,94341,64404],{},[1846,94343,8271],{"separator":2135},[1979,94345,94346],{},"3,555",[1846,94348,2351],{"stretchy":1854},[902,94350,94351],{"encoding":904},"A[1{,}5; 3{,}555]",[883,94353,94355],{"className":94354},[886],[888,94356,94357],{"xmlns":890},[892,94358,94359,94374],{},[895,94360,94361,94363,94365,94367,94369,94372],{},[898,94362,23098],{},[1846,94364,2336],{"stretchy":1854},[1979,94366,53044],{},[1846,94368,8271],{"separator":2135},[1979,94370,94371],{},"1,28",[1846,94373,2351],{"stretchy":1854},[902,94375,94376],{"encoding":904},"B[2{,}5; 1{,}28]",[883,94378,94380],{"className":94379},[886],[888,94381,94382],{"xmlns":890},[892,94383,94384,94416],{},[895,94385,94386,94388,94390,94392,94394,94396,94398,94404,94406,94408,94410,94412,94414],{},[898,94387,2626],{},[1846,94389,2336],{"stretchy":1854},[1979,94391,1981],{},[1846,94393,8271],{"separator":2135},[898,94395,900],{},[1846,94397,1855],{"stretchy":1854},[2122,94399,94400,94402],{},[898,94401,2638],{},[1979,94403,2128],{},[1846,94405,2136],{"separator":2135},[1979,94407,2023],{},[1846,94409,1861],{"stretchy":1854},[1846,94411,1848],{},[1979,94413,2023],{},[1846,94415,2351],{"stretchy":1854},[902,94417,94418],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,94421,94423],{"className":94422},[886],[888,94424,94425],{"xmlns":890},[892,94426,94427,94446],{},[895,94428,94429,94431,94433,94435,94437,94439,94441,94444],{},[898,94430,4029],{},[1846,94432,2336],{"stretchy":1854},[1979,94434,2023],{},[1846,94436,8271],{"separator":2135},[1979,94438,2128],{},[1846,94440,8271],{"separator":2135},[1979,94442,94443],{},"0,832",[1846,94445,2351],{"stretchy":1854},[902,94447,94448],{"encoding":904},"D[3; 1; 0{,}832]",[883,94450,94452],{"className":94451},[886],[888,94453,94454],{"xmlns":890},[892,94455,94456,94471],{},[895,94457,94458,94460,94462,94464,94466,94469],{},[898,94459,4098],{},[1846,94461,2336],{"stretchy":1854},[1979,94463,53044],{},[1846,94465,8271],{"separator":2135},[1979,94467,94468],{},"4,32",[1846,94470,2351],{"stretchy":1854},[902,94472,94473],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,94476,94477,93579,94480,94523,94524,6319,94537,94571,94572,94589,94590,94607],{},[38,94478,94479],{},"6.6",[883,94481,94483],{"className":94482},[886],[888,94484,94485],{"xmlns":890},[892,94486,94487,94521],{},[895,94488,94489,94491,94493,94507],{},[898,94490,900],{},[1846,94492,1848],{},[9012,94494,94495,94497,94499],{},[898,94496,2638],{},[1979,94498,2128],{},[895,94500,94501,94503,94505],{},[1979,94502,1981],{},[898,94504,4520],{"mathvariant":2226},[1979,94506,2023],{},[9012,94508,94509,94511,94513],{},[898,94510,2638],{},[1979,94512,1981],{},[895,94514,94515,94517,94519],{},[1979,94516,2128],{},[898,94518,4520],{"mathvariant":2226},[1979,94520,2023],{},[902,94522,94216],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,94525,94527],{"className":94526},[886],[888,94528,94529],{"xmlns":890},[892,94530,94531,94535],{},[895,94532,94533],{},[2138,94534,10449],{},[902,94536,28083],{"encoding":904},[883,94538,94540],{"className":94539},[886],[888,94541,94542],{"xmlns":890},[892,94543,94544,94568],{},[895,94545,94546,94552,94554,94556,94558,94564,94566],{},[2122,94547,94548,94550],{},[898,94549,2638],{},[1979,94551,2128],{},[1846,94553,1848],{},[1979,94555,2938],{},[1846,94557,2136],{"separator":2135},[2122,94559,94560,94562],{},[898,94561,2638],{},[1979,94563,1981],{},[1846,94565,1848],{},[1979,94567,8223],{},[902,94569,94570],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,94573,94575],{"className":94574},[886],[888,94576,94577],{"xmlns":890},[892,94578,94579,94587],{},[895,94580,94581],{},[2122,94582,94583,94585],{},[898,94584,2638],{},[1979,94586,2128],{},[902,94588,28847],{"encoding":904},", poklesne-li ",[883,94591,94593],{"className":94592},[886],[888,94594,94595],{"xmlns":890},[892,94596,94597,94605],{},[895,94598,94599],{},[2122,94600,94601,94603],{},[898,94602,2638],{},[1979,94604,1981],{},[902,94606,28866],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,94609,94610,94613,94614,94631,94632,94649,94650,94682,94683,94708,94709,94722,94723,1343,94747,1343,94771,1734],{},[38,94611,94612],{},"6.7"," Míra uspokojení z nákupu množství ",[883,94615,94617],{"className":94616},[886],[888,94618,94619],{"xmlns":890},[892,94620,94621,94629],{},[895,94622,94623],{},[2122,94624,94625,94627],{},[898,94626,2638],{},[1979,94628,2128],{},[902,94630,28847],{"encoding":904}," nealko nápojů a množství ",[883,94633,94635],{"className":94634},[886],[888,94636,94637],{"xmlns":890},[892,94638,94639,94647],{},[895,94640,94641],{},[2122,94642,94643,94645],{},[898,94644,2638],{},[1979,94646,1981],{},[902,94648,28866],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,94651,94653],{"className":94652},[886],[888,94654,94655],{"xmlns":890},[892,94656,94657,94679],{},[895,94658,94659,94661,94663],{},[898,94660,900],{},[1846,94662,1848],{},[7963,94664,94665],{},[895,94666,94667,94673],{},[2122,94668,94669,94671],{},[898,94670,2638],{},[1979,94672,2128],{},[2122,94674,94675,94677],{},[898,94676,2638],{},[1979,94678,1981],{},[902,94680,94681],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,94684,94686],{"className":94685},[886],[888,94687,94688],{"xmlns":890},[892,94689,94690,94706],{},[895,94691,94692,94698,94700],{},[2122,94693,94694,94696],{},[898,94695,2638],{},[1979,94697,2128],{},[1846,94699,2136],{"separator":2135},[2122,94701,94702,94704],{},[898,94703,2638],{},[1979,94705,1981],{},[902,94707,35467],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,94710,94712],{"className":94711},[886],[888,94713,94714],{"xmlns":890},[892,94715,94716,94720],{},[895,94717,94718],{},[2138,94719,10449],{},[902,94721,28083],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,94724,94726],{"className":94725},[886],[888,94727,94728],{"xmlns":890},[892,94729,94730,94744],{},[895,94731,94732,94734,94736,94738,94740,94742],{},[2138,94733,10449],{},[1846,94735,1855],{"stretchy":1854},[1979,94737,2078],{},[1846,94739,2136],{"separator":2135},[1979,94741,8881],{},[1846,94743,1861],{"stretchy":1854},[902,94745,94746],{"encoding":904},"\\text{MRCS}(5, 20)",[883,94748,94750],{"className":94749},[886],[888,94751,94752],{"xmlns":890},[892,94753,94754,94768],{},[895,94755,94756,94758,94760,94762,94764,94766],{},[2138,94757,10449],{},[1846,94759,1855],{"stretchy":1854},[1979,94761,8881],{},[1846,94763,2136],{"separator":2135},[1979,94765,2078],{},[1846,94767,1861],{"stretchy":1854},[902,94769,94770],{"encoding":904},"\\text{MRCS}(20, 5)",[883,94772,94774],{"className":94773},[886],[888,94775,94776],{"xmlns":890},[892,94777,94778,94792],{},[895,94779,94780,94782,94784,94786,94788,94790],{},[2138,94781,10449],{},[1846,94783,1855],{"stretchy":1854},[1979,94785,1981],{},[1846,94787,2136],{"separator":2135},[1979,94789,2968],{},[1846,94791,1861],{"stretchy":1854},[902,94793,94794],{"encoding":904},"\\text{MRCS}(2, 50)",[1639,94796,94797],{},[724,94798,94799,94801,94802,1734],{},[883,94800,4418],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,94803,94806],{"className":94804,"dataFsResolvedFilePath":911,"href":94805},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,94808,15565],{"id":15564},[120,94810,94811,94817,94822,94828,94881,94891,94937,94992,95055,95112,95167,95206],{},[123,94812,94813,94816],{},[38,94814,94815],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,94818,94819,94821],{},[38,94820,86714],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,94823,94824,94827],{},[38,94825,94826],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,94829,94830,94832,94833,94846,94847,1734],{},[38,94831,87041],{}," — uspořádaná ",[883,94834,94836],{"className":94835},[886],[888,94837,94838],{"xmlns":890},[892,94839,94840,94844],{},[895,94841,94842],{},[898,94843,36705],{},[902,94845,36705],{"encoding":904},"-tice ",[883,94848,94850],{"className":94849},[886],[888,94851,94852],{"xmlns":890},[892,94853,94854,94878],{},[895,94855,94856,94858,94864,94866,94868,94870,94876],{},[1846,94857,1855],{"stretchy":1854},[2122,94859,94860,94862],{},[898,94861,2638],{},[1979,94863,2128],{},[1846,94865,2136],{"separator":2135},[1846,94867,9492],{},[1846,94869,2136],{"separator":2135},[2122,94871,94872,94874],{},[898,94873,2638],{},[898,94875,36705],{},[1846,94877,1861],{"stretchy":1854},[902,94879,94880],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,94882,94883,94886,94887,94890],{},[38,94884,94885],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,94888,94889],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,94892,94893,2053,94896,94936],{},[38,94894,94895],{},"Funkce užitečnosti",[883,94897,94899],{"className":94898},[886],[888,94900,94901],{"xmlns":890},[892,94902,94903,94933],{},[895,94904,94905,94907,94909,94911,94913,94919,94921,94923,94925,94931],{},[898,94906,900],{},[1846,94908,1848],{},[898,94910,900],{},[1846,94912,1855],{"stretchy":1854},[2122,94914,94915,94917],{},[898,94916,2638],{},[1979,94918,2128],{},[1846,94920,2136],{"separator":2135},[1846,94922,9492],{},[1846,94924,2136],{"separator":2135},[2122,94926,94927,94929],{},[898,94928,2638],{},[898,94930,36705],{},[1846,94932,1861],{"stretchy":1854},[902,94934,94935],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,94938,94939,2053,94942,94971,94972,2053,94975,94991],{},[38,94940,94941],{},"Mezní užitečnost",[883,94943,94945],{"className":94944},[886],[888,94946,94947],{"xmlns":890},[892,94948,94949,94969],{},[895,94950,94951,94953,94959,94961],{},[898,94952,2667],{},[2122,94954,94955,94957],{},[898,94956,900],{},[898,94958,17635],{},[1846,94960,1848],{},[9012,94962,94963,94965,94967],{},[898,94964,900],{},[898,94966,17635],{},[1846,94968,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[902,94970,86498],{"encoding":904}," — vzorec (6.2); ",[38,94973,94974],{},"totální diferenciál",[883,94976,94978],{"className":94977},[886],[888,94979,94980],{"xmlns":890},[892,94981,94982,94988],{},[895,94983,94984,94986],{},[898,94985,2044],{"mathvariant":2226},[898,94987,900],{},[902,94989,94990],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,94993,94994,94996,94997,95021,95022,95054],{},[38,94995,88677],{}," — (6.4) ",[883,94998,95000],{"className":94999},[886],[888,95001,95002],{"xmlns":890},[892,95003,95004,95018],{},[895,95005,95006,95014,95016],{},[9012,95007,95008,95010,95012],{},[898,95009,900],{},[898,95011,17635],{},[1846,95013,2228],{"mathvariant":2226,"lspace":2227,"rspace":2227},[1846,95015,3256],{},[1979,95017,2177],{},[902,95019,95020],{"encoding":904},"U'_i > 0",", (6.5) ",[883,95023,95025],{"className":95024},[886],[888,95026,95027],{"xmlns":890},[892,95028,95029,95051],{},[895,95030,95031,95047,95049],{},[9012,95032,95033,95035,95041],{},[898,95034,900],{},[895,95036,95037,95039],{},[898,95038,17635],{},[898,95040,17635],{},[895,95042,95043,95045],{},[1846,95044,2228],{"mathvariant":2226},[1846,95046,2228],{"mathvariant":2226},[1846,95048,3295],{},[1979,95050,2177],{},[902,95052,95053],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,95056,95057,2053,95059,95090,95091,1734],{},[38,95058,90465],{},[883,95060,95062],{"className":95061},[886],[888,95063,95064],{"xmlns":890},[892,95065,95066,95088],{},[895,95067,95068,95070,95072,95080],{},[898,95069,900],{},[1846,95071,1848],{},[9012,95073,95074,95076,95078],{},[898,95075,2638],{},[1979,95077,2128],{},[898,95079,207],{},[9012,95081,95082,95084,95086],{},[898,95083,2638],{},[1979,95085,1981],{},[898,95087,1948],{},[902,95089,35648],{"encoding":904}," — (6.6), speciálně ",[883,95092,95094],{"className":95093},[886],[888,95095,95096],{"xmlns":890},[892,95097,95098,95110],{},[895,95099,95100,95102,95104,95106,95108],{},[898,95101,1948],{},[1846,95103,1848],{},[1979,95105,2128],{},[1846,95107,2075],{},[898,95109,207],{},[902,95111,90619],{"encoding":904},[123,95113,95114,2053,95117,95152,95153,95166],{},[38,95115,95116],{},"Křivky užitečnosti (indiferenční)",[883,95118,95120],{"className":95119},[886],[888,95121,95122],{"xmlns":890},[892,95123,95124,95150],{},[895,95125,95126,95128,95130,95136,95138,95144,95146,95148],{},[898,95127,900],{},[1846,95129,1855],{"stretchy":1854},[2122,95131,95132,95134],{},[898,95133,2638],{},[1979,95135,2128],{},[1846,95137,2136],{"separator":2135},[2122,95139,95140,95142],{},[898,95141,2638],{},[1979,95143,1981],{},[1846,95145,1861],{"stretchy":1854},[1846,95147,1848],{},[898,95149,1992],{},[902,95151,9614],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,95154,95156],{"className":95155},[886],[888,95157,95158],{"xmlns":890},[892,95159,95160,95164],{},[895,95161,95162],{},[898,95163,900],{},[902,95165,900],{"encoding":904},", konvexní.",[123,95168,95169,2053,95171,95205],{},[38,95170,92010],{},[883,95172,95174],{"className":95173},[886],[888,95175,95176],{"xmlns":890},[892,95177,95178,95202],{},[895,95179,95180,95182,95184,95186,95192,95194,95196],{},[2138,95181,10449],{},[1846,95183,1848],{},[898,95185,2667],{},[2122,95187,95188,95190],{},[898,95189,900],{},[1979,95191,2128],{},[898,95193,4520],{"mathvariant":2226},[898,95195,2667],{},[2122,95197,95198,95200],{},[898,95199,900],{},[1979,95201,1981],{},[902,95203,95204],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,95207,95208,2053,95211,9615,95240,95243],{},[38,95209,95210],{},"Podmínka optimality",[883,95212,95214],{"className":95213},[886],[888,95215,95216],{"xmlns":890},[892,95217,95218,95238],{},[895,95219,95220,95222,95224,95230,95232],{},[2138,95221,10449],{},[1846,95223,1848],{},[2122,95225,95226,95228],{},[898,95227,3783],{},[1979,95229,2128],{},[898,95231,4520],{"mathvariant":2226},[2122,95233,95234,95236],{},[898,95235,3783],{},[1979,95237,1981],{},[902,95239,27843],{"encoding":904},[207,95241,36599],{"className":95242,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,95245,3640],{"id":3639},[120,95247,95248,95285,95326,95336],{},[123,95249,95250,2053,95253,95256,95257,95270,95271,95284],{},[38,95251,95252],{},"Navazující téma:",[207,95254,913],{"className":95255,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,95258,95260],{"className":95259},[886],[888,95261,95262],{"xmlns":890},[892,95263,95264,95268],{},[895,95265,95266],{},[898,95267,900],{},[902,95269,900],{"encoding":904},", min ",[883,95272,95274],{"className":95273},[886],[888,95275,95276],{"xmlns":890},[892,95277,95278,95282],{},[895,95279,95280],{},[898,95281,4098],{},[902,95283,4098],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,95286,95287,2053,95290,10938,95293,86253,95296,95299,95300,95303,95304,18493,95322,95325],{},[38,95288,95289],{},"Související pojmy:",[207,95291,784],{"className":95292,"dataFsResolvedFilePath":782,"href":783},[210],[207,95294,2207],{"className":95295,"dataFsResolvedFilePath":764,"href":765},[210],[207,95297,1728],{"className":95298,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,95301,1701],{"className":95302,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,95305,95307],{"className":95306},[886],[888,95308,95309],{"xmlns":890},[892,95310,95311,95319],{},[895,95312,95313],{},[2122,95314,95315,95317],{},[898,95316,4029],{},[898,95318,17635],{},[902,95320,95321],{"encoding":904},"D_i",[207,95323,793],{"className":95324,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,95327,95328,2053,95330,1343,95333],{},[38,95329,36548],{},[207,95331,1094],{"className":95332,"dataFsResolvedFilePath":838,"href":839},[210],[207,95334,1101],{"className":95335,"dataFsResolvedFilePath":868,"href":869},[210],[123,95337,95338,2053,95340],{},[38,95339,16049],{},[207,95341,16053],{"className":95342,"dataFsResolvedFilePath":1761,"href":1762},[210],{"title":641,"searchDepth":642,"depth":642,"links":95344},[95345,95346,95347,95350,95351,95354,95358,95359,95362,95363,95364,95365,95366,95367,95368],{"id":11850,"depth":642,"text":11851},{"id":86637,"depth":642,"text":86638},{"id":86697,"depth":642,"text":86698,"children":95348},[95349],{"id":86713,"depth":649,"text":86714},{"id":87020,"depth":642,"text":87021},{"id":87880,"depth":642,"text":87881,"children":95352},[95353],{"id":88427,"depth":649,"text":80056},{"id":88676,"depth":642,"text":88677,"children":95355},[95356],{"id":89549,"depth":649,"text":95357},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":90464,"depth":642,"text":90465},{"id":91000,"depth":642,"text":91001,"children":95360},[95361],{"id":91774,"depth":649,"text":91775},{"id":92004,"depth":642,"text":92005},{"id":92765,"depth":642,"text":92766},{"id":93303,"depth":642,"text":93304},{"id":49726,"depth":642,"text":49727},{"id":93439,"depth":642,"text":93440},{"id":15564,"depth":642,"text":15565},{"id":3639,"depth":642,"text":3640},{},"\u002Ftopics\u002Fuzitecnost",{"title":86421,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,9619,95375,86415,10968,95376],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":95379,"title":757,"body":95380,"course":1128,"courses":659,"created":1129,"description":95650,"extension":661,"meta":95651,"navigation":664,"path":95652,"seo":95653,"sources":95654,"stem":95655,"tags":95656,"type":3703,"updated":677,"__hash__":95662},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":95381,"toc":95642},[95382,95385,95392,95399,95403,95413,95415,95449,95453,95496,95499,95557,95561,95591,95595,95613,95615],[12,95383,757],{"id":95384},"základy-matematické-ekonomie",[724,95386,95387,95388,95391],{},"Úvodní pojmy a princip modelování v ",[207,95389,16225],{"className":95390,"dataFsResolvedFilePath":1761,"href":1762},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,95393,95394],{},[2409,95395],{"alt":95396,"className":95397,"src":95398},"imek-model-promenne",[210,2413],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,95400,95402],{"id":95401},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,95404,95405,95408,95409,95412],{},[38,95406,95407],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,95410,95411],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,95414,15565],{"id":15564},[120,95416,95417,95423,95429,95435,95444],{},[123,95418,95419,95422],{},[38,95420,95421],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,95424,95425,95428],{},[38,95426,95427],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,95430,95431,95434],{},[38,95432,95433],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,95436,95437,6861,95440,95443],{},[38,95438,95439],{},"Ceteris paribus",[614,95441,95442],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,95445,95446,95448],{},[38,95447,50480],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,95450,95452],{"id":95451},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,95454,95455,95495],{},[883,95456,95458],{"className":95457},[886],[888,95459,95460],{"xmlns":890},[892,95461,95462,95492],{},[895,95463,95464,95466,95468,95470,95472,95474,95476,95478,95480,95482,95484,95486,95488,95490],{},[898,95465,2638],{},[1846,95467,1848],{},[898,95469,4029],{},[1846,95471,1855],{"stretchy":1854},[898,95473,3783],{},[1846,95475,2136],{"separator":2135},[898,95477,8974],{},[1846,95479,2136],{"separator":2135},[898,95481,18139],{},[1846,95483,2136],{"separator":2135},[898,95485,900],{},[1846,95487,2136],{"separator":2135},[1846,95489,9492],{},[1846,95491,1861],{"stretchy":1854},[902,95493,95494],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,95497,95498],{},"Zjednodušení:",[120,95500,95501,95529],{},[123,95502,95503,2053,95506],{},[38,95504,95505],{},"Jednofaktorový model:",[883,95507,95509],{"className":95508},[886],[888,95510,95511],{"xmlns":890},[892,95512,95513,95527],{},[895,95514,95515,95517,95519,95521,95523,95525],{},[898,95516,2638],{},[1846,95518,1848],{},[898,95520,4029],{},[1846,95522,1855],{"stretchy":1854},[898,95524,3783],{},[1846,95526,1861],{"stretchy":1854},[902,95528,4038],{"encoding":904},[123,95530,95531,2053,95534],{},[38,95532,95533],{},"Inverzní zápis:",[883,95535,95537],{"className":95536},[886],[888,95538,95539],{"xmlns":890},[892,95540,95541,95555],{},[895,95542,95543,95545,95547,95549,95551,95553],{},[898,95544,3783],{},[1846,95546,1848],{},[898,95548,4029],{},[1846,95550,1855],{"stretchy":1854},[898,95552,2638],{},[1846,95554,1861],{"stretchy":1854},[902,95556,4486],{"encoding":904},[115,95558,95560],{"id":95559},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,95562,95563,95572],{},[123,95564,95565,95568,95569,3764],{},[38,95566,95567],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,95570,1789],{"className":95571,"dataFsResolvedFilePath":800,"href":801},[210],[123,95573,95574,95577,95578,95581,95582,95585,95586,95590],{},[38,95575,95576],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,95579,1145],{"className":95580,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,95583,16097],{"className":95584,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,95587,95589],{"className":95588,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,95592,95594],{"id":95593},"konvence-z-přednášek","Konvence z přednášek",[120,95596,95597,95603,95608],{},[123,95598,95599,95600,95602],{},"Symbol ",[1648,95601,1650],{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,95604,95605,95606,1734],{},"Numerické výsledky ",[38,95607,1654],{},[123,95609,3740,95610,95612],{},[614,95611,1658],{}," má standardní význam (změna o 1).",[115,95614,3640],{"id":3639},[120,95616,95617,95622,95630],{},[123,95618,95619,95621],{},[38,95620,3647],{}," —",[123,95623,95624,2053,95626],{},[38,95625,3655],{},[207,95627,95629],{"className":95628,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,95631,95632,2053,95634,1343,95638],{},[38,95633,3663],{},[207,95635,95637],{"className":95636,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,95639,95641],{"className":95640,"dataFsResolvedFilePath":1761,"href":1762},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":95643},[95644,95645,95646,95647,95648,95649],{"id":95401,"depth":642,"text":95402},{"id":15564,"depth":642,"text":15565},{"id":95451,"depth":642,"text":95452},{"id":95559,"depth":642,"text":95560},{"id":95593,"depth":642,"text":95594},{"id":3639,"depth":642,"text":3640},"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":95650},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,95657,95658,95659,95660,95661],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":95664,"title":95665,"body":95666,"course":1128,"courses":659,"created":9402,"description":641,"extension":661,"meta":99938,"navigation":664,"path":99939,"seo":99940,"sources":99941,"stem":99942,"tags":99943,"type":3703,"updated":677,"__hash__":99947},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":95667,"toc":99921},[95668,95671,95765,95769,95791,95805,95857,95859,95863,95926,95969,95988,96151,96250,96253,96320,96324,96453,96492,96522,96634,96679,96745,96798,96874,96930,96932,96936,97000,97044,97064,97225,97228,97312,97409,97412,97478,97482,97531,97557,97662,97726,97731,97827,97874,97876,97879,97901,97943,97950,97983,97985,98056,98110,98219,98223,98312,98388,98652,98690,98692,98696,98699,98706,99017,99020,99078,99258,99287,99289,99293,99299,99437,99446,99448,99450,99875,99877,99879],[12,95669,95665],{"id":95670},"zdanění-trhu-dopady-daně-na-rovnováhu",[1639,95672,95673],{},[724,95674,95675,42473,95677,95690,95691,95694,95695,95697,95698,95701,95702,95723,95724,95747,95748,95751,95752,1734],{},[883,95676,4001],{},[883,95678,95680],{"className":95679},[886],[888,95681,95682],{"xmlns":890},[892,95683,95684,95688],{},[895,95685,95686],{},[898,95687,2623],{},[902,95689,2623],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,95692,95693],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,95696,86705],{}," (je-li uložena spotřebiteli). Výsledné ",[38,95699,95700],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,95703,95705],{"className":95704},[886],[888,95706,95707],{"xmlns":890},[892,95708,95709,95721],{},[895,95710,95711],{},[2122,95712,95713,95715],{},[898,95714,2623],{},[895,95716,95717,95719],{},[898,95718,42522],{},[898,95720,724],{},[902,95722,42527],{"encoding":904}," (spotřebitel) a ",[883,95725,95727],{"className":95726},[886],[888,95728,95729],{"xmlns":890},[892,95730,95731,95745],{},[895,95732,95733],{},[2122,95734,95735,95737],{},[898,95736,2623],{},[895,95738,95739,95741,95743],{},[898,95740,42545],{},[898,95742,1844],{},[898,95744,11886],{},[902,95746,42552],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,95749,95750],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,95753,95755],{"className":95754},[886],[888,95756,95757],{"xmlns":890},[892,95758,95759,95763],{},[895,95760,95761],{},[898,95762,2623],{},[902,95764,2623],{"encoding":904},[115,95766,95768],{"id":95767},"dvě-formy-zdanění","Dvě formy zdanění",[724,95770,95771,95772,95790],{},"Uvažujme jednotkovou daň ",[883,95773,95775],{"className":95774},[886],[888,95776,95777],{"xmlns":890},[892,95778,95779,95787],{},[895,95780,95781,95783,95785],{},[898,95782,2623],{},[1846,95784,3256],{},[1979,95786,2177],{},[902,95788,95789],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,95792,95793,95799],{},[123,95794,95795,95798],{},[38,95796,95797],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,95800,95801,95804],{},[38,95802,95803],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,95806,95807,95808,95821,95822,95825,95826,1734],{},"V obou případech dochází k posunu jedné z křivek o ",[883,95809,95811],{"className":95810},[886],[888,95812,95813],{"xmlns":890},[892,95814,95815,95819],{},[895,95816,95817],{},[898,95818,2623],{},[902,95820,2623],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,95823,95824],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,95827,95829],{"className":95828},[886],[888,95830,95831],{"xmlns":890},[892,95832,95833,95855],{},[895,95834,95835,95837,95839,95845,95847,95853],{},[898,95836,4098],{},[1846,95838,2336],{"stretchy":1854},[1974,95840,95841,95843],{},[898,95842,2638],{},[898,95844,4098],{},[1846,95846,2136],{"separator":2135},[1974,95848,95849,95851],{},[898,95850,3783],{},[898,95852,4098],{},[1846,95854,2351],{"stretchy":1854},[902,95856,41212],{"encoding":904},[36815,95858],{},[115,95860,95862],{"id":95861},"daň-uložená-výrobci","Daň uložená výrobci",[724,95864,95865,95866,95879,95880,95897,95898,95925],{},"Je-li daň ",[883,95867,95869],{"className":95868},[886],[888,95870,95871],{"xmlns":890},[892,95872,95873,95877],{},[895,95874,95875],{},[898,95876,2623],{},[902,95878,2623],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,95881,95883],{"className":95882},[886],[888,95884,95885],{"xmlns":890},[892,95886,95887,95895],{},[895,95888,95889,95891,95893],{},[898,95890,3783],{},[1846,95892,2075],{},[898,95894,2623],{},[902,95896,40967],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,95899,95901],{"className":95900},[886],[888,95902,95903],{"xmlns":890},[892,95904,95905,95923],{},[895,95906,95907,95909,95911,95913,95915,95917,95919,95921],{},[898,95908,3783],{},[1846,95910,2075],{},[898,95912,2623],{},[1846,95914,1848],{},[898,95916,8519],{},[1846,95918,1855],{"stretchy":1854},[898,95920,2638],{},[1846,95922,1861],{"stretchy":1854},[902,95924,40996],{"encoding":904}," nová funkce nabídky:",[883,95927,95929],{"className":95928},[886],[888,95930,95931],{"xmlns":890,"display":27911},[892,95932,95933,95967],{},[895,95934,95935,95937,95939,95945,95947,95949,95951,95953,95955,95957,95959,95961,95963,95965],{},[898,95936,3783],{},[1846,95938,1848],{},[2122,95940,95941,95943],{},[898,95942,8519],{},[1979,95944,2128],{},[1846,95946,1855],{"stretchy":1854},[898,95948,2638],{},[1846,95950,1861],{"stretchy":1854},[1846,95952,1848],{},[898,95954,8519],{},[1846,95956,1855],{"stretchy":1854},[898,95958,2638],{},[1846,95960,1861],{"stretchy":1854},[1846,95962,1945],{},[898,95964,2623],{},[898,95966,1734],{"mathvariant":2226},[902,95968,41041],{"encoding":904},[724,95970,95971,95972,2053,95985,95987],{},"Nabídka se tedy posouvá o ",[883,95973,95975],{"className":95974},[886],[888,95976,95977],{"xmlns":890},[892,95978,95979,95983],{},[895,95980,95981],{},[898,95982,2623],{},[902,95984,2623],{"encoding":904},[38,95986,41074],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,95989,95990,95991,96031,96032,1745,96060,96088,96089,96108,96109,96133,96134,3764],{},"Nový rovnovážný bod ",[883,95992,95994],{"className":95993},[886],[888,95995,95996],{"xmlns":890},[892,95997,95998,96028],{},[895,95999,96000,96006,96008,96016,96018,96026],{},[2122,96001,96002,96004],{},[898,96003,4098],{},[1979,96005,2128],{},[1846,96007,2336],{"stretchy":1854},[9012,96009,96010,96012,96014],{},[898,96011,2638],{},[1979,96013,2128],{},[898,96015,4098],{},[1846,96017,2136],{"separator":2135},[9012,96019,96020,96022,96024],{},[898,96021,3783],{},[1979,96023,2128],{},[898,96025,4098],{},[1846,96027,2351],{"stretchy":1854},[902,96029,96030],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,96033,96035],{"className":96034},[886],[888,96036,96037],{"xmlns":890},[892,96038,96039,96057],{},[895,96040,96041,96049,96051],{},[9012,96042,96043,96045,96047],{},[898,96044,2638],{},[1979,96046,2128],{},[898,96048,4098],{},[1846,96050,3295],{},[1974,96052,96053,96055],{},[898,96054,2638],{},[898,96056,4098],{},[902,96058,96059],{"encoding":904},"Q_1^E \u003C Q^E",[883,96061,96063],{"className":96062},[886],[888,96064,96065],{"xmlns":890},[892,96066,96067,96085],{},[895,96068,96069,96077,96079],{},[9012,96070,96071,96073,96075],{},[898,96072,3783],{},[1979,96074,2128],{},[898,96076,4098],{},[1846,96078,3256],{},[1974,96080,96081,96083],{},[898,96082,3783],{},[898,96084,4098],{},[902,96086,96087],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,96090,96092],{"className":96091},[886],[888,96093,96094],{"xmlns":890},[892,96095,96096,96106],{},[895,96097,96098],{},[9012,96099,96100,96102,96104],{},[898,96101,3783],{},[1979,96103,2128],{},[898,96105,4098],{},[902,96107,47702],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,96110,96112],{"className":96111},[886],[888,96113,96114],{"xmlns":890},[892,96115,96116,96130],{},[895,96117,96118,96126,96128],{},[9012,96119,96120,96122,96124],{},[898,96121,3783],{},[1979,96123,2128],{},[898,96125,4098],{},[1846,96127,2075],{},[898,96129,2623],{},[902,96131,96132],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,96135,96137],{"className":96136},[886],[888,96138,96139],{"xmlns":890},[892,96140,96141,96149],{},[895,96142,96143],{},[1974,96144,96145,96147],{},[898,96146,3783],{},[898,96148,4098],{},[902,96150,41311],{"encoding":904},[724,96152,96153],{},[614,96154,96155,96156,96186,96187,96200,96201,5515,96218,96231,96232,1734],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,96157,96159],{"className":96158},[886],[888,96160,96161],{"xmlns":890},[892,96162,96163,96183],{},[895,96164,96165,96167,96169,96175,96177,96179,96181],{},[898,96166,8519],{},[1846,96168,2971],{},[2122,96170,96171,96173],{},[898,96172,8519],{},[1979,96174,2128],{},[1846,96176,1848],{},[898,96178,8519],{},[1846,96180,1945],{},[898,96182,2623],{},[902,96184,96185],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,96188,96190],{"className":96189},[886],[888,96191,96192],{"xmlns":890},[892,96193,96194,96198],{},[895,96195,96196],{},[898,96197,2623],{},[902,96199,2623],{"encoding":904},". Průsečík ",[883,96202,96204],{"className":96203},[886],[888,96205,96206],{"xmlns":890},[892,96207,96208,96216],{},[895,96209,96210],{},[2122,96211,96212,96214],{},[898,96213,8519],{},[1979,96215,2128],{},[902,96217,40842],{"encoding":904},[883,96219,96221],{"className":96220},[886],[888,96222,96223],{"xmlns":890},[892,96224,96225,96229],{},[895,96226,96227],{},[898,96228,4029],{},[902,96230,4029],{"encoding":904}," je nový rovnovážný bod ",[883,96233,96235],{"className":96234},[886],[888,96236,96237],{"xmlns":890},[892,96238,96239,96247],{},[895,96240,96241],{},[2122,96242,96243,96245],{},[898,96244,4098],{},[1979,96246,2128],{},[902,96248,96249],{"encoding":904},"E_1",[198,96251,45148],{"id":96252},"příklad-29",[724,96254,96255,41500,96257,41535,96281,96301,96302,96319],{},[38,96256,37778],{},[883,96258,96260],{"className":96259},[886],[888,96261,96262],{"xmlns":890},[892,96263,96264,96278],{},[895,96265,96266,96268,96270,96272,96274,96276],{},[898,96267,3783],{},[1846,96269,1848],{},[1979,96271,3357],{},[1846,96273,2075],{},[1979,96275,1981],{},[898,96277,2638],{},[902,96279,96280],{"encoding":904},"P = 12 - 2Q",[883,96282,96284],{"className":96283},[886],[888,96285,96286],{"xmlns":890},[892,96287,96288,96298],{},[895,96289,96290,96292,96294,96296],{},[898,96291,3783],{},[1846,96293,1848],{},[1979,96295,2201],{},[898,96297,2638],{},[902,96299,96300],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,96303,96305],{"className":96304},[886],[888,96306,96307],{"xmlns":890},[892,96308,96309,96317],{},[895,96310,96311,96313,96315],{},[898,96312,2623],{},[1846,96314,1848],{},[1979,96316,2085],{},[902,96318,41113],{"encoding":904}," Kč.",[724,96321,96322],{},[38,96323,37810],{},[724,96325,96326,96329,96330,5415,96356,5435,96376,1343,96398,96428,96429,1734],{},[614,96327,96328],{},"Bez daně."," Z rovnosti ",[883,96331,96333],{"className":96332},[886],[888,96334,96335],{"xmlns":890},[892,96336,96337,96353],{},[895,96338,96339,96341,96343,96345,96347,96349,96351],{},[1979,96340,3357],{},[1846,96342,2075],{},[1979,96344,1981],{},[898,96346,2638],{},[1846,96348,1848],{},[1979,96350,2201],{},[898,96352,2638],{},[902,96354,96355],{"encoding":904},"12 - 2Q = 4Q",[883,96357,96359],{"className":96358},[886],[888,96360,96361],{"xmlns":890},[892,96362,96363,96373],{},[895,96364,96365,96367,96369,96371],{},[1979,96366,2085],{},[898,96368,2638],{},[1846,96370,1848],{},[1979,96372,3357],{},[902,96374,96375],{"encoding":904},"6Q = 12",[883,96377,96379],{"className":96378},[886],[888,96380,96381],{"xmlns":890},[892,96382,96383,96395],{},[895,96384,96385,96391,96393],{},[1974,96386,96387,96389],{},[898,96388,2638],{},[898,96390,4098],{},[1846,96392,1848],{},[1979,96394,1981],{},[902,96396,96397],{"encoding":904},"Q^E = 2",[883,96399,96401],{"className":96400},[886],[888,96402,96403],{"xmlns":890},[892,96404,96405,96425],{},[895,96406,96407,96413,96415,96417,96419,96421,96423],{},[1974,96408,96409,96411],{},[898,96410,3783],{},[898,96412,4098],{},[1846,96414,1848],{},[1979,96416,2201],{},[1846,96418,3025],{},[1979,96420,1981],{},[1846,96422,1848],{},[1979,96424,5431],{},[902,96426,96427],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,96430,96432],{"className":96431},[886],[888,96433,96434],{"xmlns":890},[892,96435,96436,96450],{},[895,96437,96438,96440,96442,96444,96446,96448],{},[898,96439,4098],{},[1846,96441,2336],{"stretchy":1854},[1979,96443,1981],{},[1846,96445,2136],{"separator":2135},[1979,96447,5431],{},[1846,96449,2351],{"stretchy":1854},[902,96451,96452],{"encoding":904},"E[2, 8]",[724,96454,96455,96458,96459,96491],{},[614,96456,96457],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,96460,96462],{"className":96461},[886],[888,96463,96464],{"xmlns":890},[892,96465,96466,96488],{},[895,96467,96468,96474,96476,96478,96480,96482,96484,96486],{},[2122,96469,96470,96472],{},[898,96471,8519],{},[1979,96473,2128],{},[1846,96475,2554],{},[898,96477,3783],{},[1846,96479,1848],{},[1979,96481,2201],{},[898,96483,2638],{},[1846,96485,1945],{},[1979,96487,2085],{},[902,96489,96490],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,96493,96495],{"className":96494},[886],[888,96496,96497],{"xmlns":890,"display":27911},[892,96498,96499,96519],{},[895,96500,96501,96503,96505,96507,96509,96511,96513,96515,96517],{},[1979,96502,3357],{},[1846,96504,2075],{},[1979,96506,1981],{},[898,96508,2638],{},[1846,96510,1848],{},[1979,96512,2201],{},[898,96514,2638],{},[1846,96516,1945],{},[1979,96518,2085],{},[902,96520,96521],{"encoding":904},"12 - 2Q = 4Q + 6",[724,96523,96524,96525,5435,96545,1343,96569,96605,96606,1734],{},"plyne ",[883,96526,96528],{"className":96527},[886],[888,96529,96530],{"xmlns":890},[892,96531,96532,96542],{},[895,96533,96534,96536,96538,96540],{},[1979,96535,2085],{},[898,96537,2638],{},[1846,96539,1848],{},[1979,96541,2085],{},[902,96543,96544],{"encoding":904},"6Q = 6",[883,96546,96548],{"className":96547},[886],[888,96549,96550],{"xmlns":890},[892,96551,96552,96566],{},[895,96553,96554,96562,96564],{},[9012,96555,96556,96558,96560],{},[898,96557,2638],{},[1979,96559,2128],{},[898,96561,4098],{},[1846,96563,1848],{},[1979,96565,2128],{},[902,96567,96568],{"encoding":904},"Q_1^E = 1",[883,96570,96572],{"className":96571},[886],[888,96573,96574],{"xmlns":890},[892,96575,96576,96602],{},[895,96577,96578,96586,96588,96590,96592,96594,96596,96598,96600],{},[9012,96579,96580,96582,96584],{},[898,96581,3783],{},[1979,96583,2128],{},[898,96585,4098],{},[1846,96587,1848],{},[1979,96589,2201],{},[1846,96591,3025],{},[1979,96593,2128],{},[1846,96595,1945],{},[1979,96597,2085],{},[1846,96599,1848],{},[1979,96601,2712],{},[902,96603,96604],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,96607,96609],{"className":96608},[886],[888,96610,96611],{"xmlns":890},[892,96612,96613,96631],{},[895,96614,96615,96621,96623,96625,96627,96629],{},[2122,96616,96617,96619],{},[898,96618,4098],{},[1979,96620,2128],{},[1846,96622,2336],{"stretchy":1854},[1979,96624,2128],{},[1846,96626,2136],{"separator":2135},[1979,96628,2712],{},[1846,96630,2351],{"stretchy":1854},[902,96632,96633],{"encoding":904},"E_1[1, 10]",[724,96635,96636,96639,96640,96664,96665,96678],{},[614,96637,96638],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,96641,96643],{"className":96642},[886],[888,96644,96645],{"xmlns":890},[892,96646,96647,96661],{},[895,96648,96649,96657,96659],{},[9012,96650,96651,96653,96655],{},[898,96652,3783],{},[1979,96654,2128],{},[898,96656,4098],{},[1846,96658,1848],{},[1979,96660,2712],{},[902,96662,96663],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,96666,96668],{"className":96667},[886],[888,96669,96670],{"xmlns":890},[892,96671,96672,96676],{},[895,96673,96674],{},[1979,96675,5431],{},[902,96677,5431],{"encoding":904},", navýšení je",[883,96680,96682],{"className":96681},[886],[888,96683,96684],{"xmlns":890,"display":27911},[892,96685,96686,96742],{},[895,96687,96688,96698,96700,96708,96710,96716,96718,96720,96722,96724,96726,96728,96730,96740],{},[2122,96689,96690,96692],{},[898,96691,2623],{},[895,96693,96694,96696],{},[898,96695,42522],{},[898,96697,724],{},[1846,96699,1848],{},[9012,96701,96702,96704,96706],{},[898,96703,3783],{},[1979,96705,2128],{},[898,96707,4098],{},[1846,96709,2075],{},[1974,96711,96712,96714],{},[898,96713,3783],{},[898,96715,4098],{},[1846,96717,1848],{},[1979,96719,2712],{},[1846,96721,2075],{},[1979,96723,5431],{},[1846,96725,1848],{},[1979,96727,1981],{},[2138,96729,2140],{},[895,96731,96732,96734],{},[2138,96733,9646],{},[8232,96735,96736,96738],{"accent":2135},[2138,96737,1992],{},[1846,96739,24903],{},[898,96741,1734],{"mathvariant":2226},[902,96743,96744],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,96746,96747,96748,96664,96784,96797],{},"Výrobci zůstává čistá cena ",[883,96749,96751],{"className":96750},[886],[888,96752,96753],{"xmlns":890},[892,96754,96755,96781],{},[895,96756,96757,96765,96767,96769,96771,96773,96775,96777,96779],{},[9012,96758,96759,96761,96763],{},[898,96760,3783],{},[1979,96762,2128],{},[898,96764,4098],{},[1846,96766,2075],{},[898,96768,2623],{},[1846,96770,1848],{},[1979,96772,2712],{},[1846,96774,2075],{},[1979,96776,2085],{},[1846,96778,1848],{},[1979,96780,2201],{},[902,96782,96783],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,96785,96787],{"className":96786},[886],[888,96788,96789],{"xmlns":890},[892,96790,96791,96795],{},[895,96792,96793],{},[1979,96794,5431],{},[902,96796,5431],{"encoding":904},", pokles je",[883,96799,96801],{"className":96800},[886],[888,96802,96803],{"xmlns":890,"display":27911},[892,96804,96805,96871],{},[895,96806,96807,96819,96821,96827,96829,96831,96839,96841,96843,96845,96847,96849,96851,96853,96855,96857,96859,96869],{},[2122,96808,96809,96811],{},[898,96810,2623],{},[895,96812,96813,96815,96817],{},[898,96814,42545],{},[898,96816,1844],{},[898,96818,11886],{},[1846,96820,1848],{},[1974,96822,96823,96825],{},[898,96824,3783],{},[898,96826,4098],{},[1846,96828,2075],{},[1846,96830,1855],{"stretchy":1854},[9012,96832,96833,96835,96837],{},[898,96834,3783],{},[1979,96836,2128],{},[898,96838,4098],{},[1846,96840,2075],{},[898,96842,2623],{},[1846,96844,1861],{"stretchy":1854},[1846,96846,1848],{},[1979,96848,5431],{},[1846,96850,2075],{},[1979,96852,2201],{},[1846,96854,1848],{},[1979,96856,2201],{},[2138,96858,2140],{},[895,96860,96861,96863],{},[2138,96862,9646],{},[8232,96864,96865,96867],{"accent":2135},[2138,96866,1992],{},[1846,96868,24903],{},[898,96870,1734],{"mathvariant":2226},[902,96872,96873],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,96875,96876,96877,96929],{},"Kontrola: ",[883,96878,96880],{"className":96879},[886],[888,96881,96882],{"xmlns":890},[892,96883,96884,96926],{},[895,96885,96886,96896,96898,96910,96912,96914,96916,96918,96920,96922,96924],{},[2122,96887,96888,96890],{},[898,96889,2623],{},[895,96891,96892,96894],{},[898,96893,42522],{},[898,96895,724],{},[1846,96897,1945],{},[2122,96899,96900,96902],{},[898,96901,2623],{},[895,96903,96904,96906,96908],{},[898,96905,42545],{},[898,96907,1844],{},[898,96909,11886],{},[1846,96911,1848],{},[1979,96913,1981],{},[1846,96915,1945],{},[1979,96917,2201],{},[1846,96919,1848],{},[1979,96921,2085],{},[1846,96923,1848],{},[898,96925,2623],{},[902,96927,96928],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[36815,96931],{},[115,96933,96935],{"id":96934},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,96937,95865,96938,96951,96952,96970,96971,96999],{},[883,96939,96941],{"className":96940},[886],[888,96942,96943],{"xmlns":890},[892,96944,96945,96949],{},[895,96946,96947],{},[898,96948,2623],{},[902,96950,2623],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,96953,96955],{"className":96954},[886],[888,96956,96957],{"xmlns":890},[892,96958,96959,96967],{},[895,96960,96961,96963,96965],{},[898,96962,3783],{},[1846,96964,1945],{},[898,96966,2623],{},[902,96968,96969],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,96972,96974],{"className":96973},[886],[888,96975,96976],{"xmlns":890},[892,96977,96978,96996],{},[895,96979,96980,96982,96984,96986,96988,96990,96992,96994],{},[898,96981,3783],{},[1846,96983,1945],{},[898,96985,2623],{},[1846,96987,1848],{},[898,96989,4029],{},[1846,96991,1855],{"stretchy":1854},[898,96993,2638],{},[1846,96995,1861],{"stretchy":1854},[902,96997,96998],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,97001,97003],{"className":97002},[886],[888,97004,97005],{"xmlns":890,"display":27911},[892,97006,97007,97041],{},[895,97008,97009,97011,97013,97019,97021,97023,97025,97027,97029,97031,97033,97035,97037,97039],{},[898,97010,3783],{},[1846,97012,1848],{},[2122,97014,97015,97017],{},[898,97016,4029],{},[1979,97018,1981],{},[1846,97020,1855],{"stretchy":1854},[898,97022,2638],{},[1846,97024,1861],{"stretchy":1854},[1846,97026,1848],{},[898,97028,4029],{},[1846,97030,1855],{"stretchy":1854},[898,97032,2638],{},[1846,97034,1861],{"stretchy":1854},[1846,97036,2075],{},[898,97038,2623],{},[898,97040,1734],{"mathvariant":2226},[902,97042,97043],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,97045,97046,97047,2053,97060,97063],{},"Poptávka se tedy posouvá o ",[883,97048,97050],{"className":97049},[886],[888,97051,97052],{"xmlns":890},[892,97053,97054,97058],{},[895,97055,97056],{},[898,97057,2623],{},[902,97059,2623],{"encoding":904},[38,97061,97062],{},"svisle dolů",". Nabídka se nemění.",[724,97065,95990,97066,96031,97106,1745,97134,97162,97163,97182,97183,97207,97208,3764],{},[883,97067,97069],{"className":97068},[886],[888,97070,97071],{"xmlns":890},[892,97072,97073,97103],{},[895,97074,97075,97081,97083,97091,97093,97101],{},[2122,97076,97077,97079],{},[898,97078,4098],{},[1979,97080,1981],{},[1846,97082,2336],{"stretchy":1854},[9012,97084,97085,97087,97089],{},[898,97086,2638],{},[1979,97088,1981],{},[898,97090,4098],{},[1846,97092,2136],{"separator":2135},[9012,97094,97095,97097,97099],{},[898,97096,3783],{},[1979,97098,1981],{},[898,97100,4098],{},[1846,97102,2351],{"stretchy":1854},[902,97104,97105],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,97107,97109],{"className":97108},[886],[888,97110,97111],{"xmlns":890},[892,97112,97113,97131],{},[895,97114,97115,97123,97125],{},[9012,97116,97117,97119,97121],{},[898,97118,2638],{},[1979,97120,1981],{},[898,97122,4098],{},[1846,97124,3295],{},[1974,97126,97127,97129],{},[898,97128,2638],{},[898,97130,4098],{},[902,97132,97133],{"encoding":904},"Q_2^E \u003C Q^E",[883,97135,97137],{"className":97136},[886],[888,97138,97139],{"xmlns":890},[892,97140,97141,97159],{},[895,97142,97143,97151,97153],{},[9012,97144,97145,97147,97149],{},[898,97146,3783],{},[1979,97148,1981],{},[898,97150,4098],{},[1846,97152,3295],{},[1974,97154,97155,97157],{},[898,97156,3783],{},[898,97158,4098],{},[902,97160,97161],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,97164,97166],{"className":97165},[886],[888,97167,97168],{"xmlns":890},[892,97169,97170,97180],{},[895,97171,97172],{},[9012,97173,97174,97176,97178],{},[898,97175,3783],{},[1979,97177,1981],{},[898,97179,4098],{},[902,97181,47763],{"encoding":904},", spotřebitel platí celkem ",[883,97184,97186],{"className":97185},[886],[888,97187,97188],{"xmlns":890},[892,97189,97190,97204],{},[895,97191,97192,97200,97202],{},[9012,97193,97194,97196,97198],{},[898,97195,3783],{},[1979,97197,1981],{},[898,97199,4098],{},[1846,97201,1945],{},[898,97203,2623],{},[902,97205,97206],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,97209,97211],{"className":97210},[886],[888,97212,97213],{"xmlns":890},[892,97214,97215,97223],{},[895,97216,97217],{},[1974,97218,97219,97221],{},[898,97220,3783],{},[898,97222,4098],{},[902,97224,41311],{"encoding":904},[724,97226,97227],{},"Daňové břemeno:",[883,97229,97231],{"className":97230},[886],[888,97232,97233],{"xmlns":890,"display":27911},[892,97234,97235,97309],{},[895,97236,97237,97247,97249,97251,97259,97261,97263,97265,97267,97273,97275,97277,97289,97291,97297,97299,97307],{},[2122,97238,97239,97241],{},[898,97240,2623],{},[895,97242,97243,97245],{},[898,97244,42522],{},[898,97246,724],{},[1846,97248,1848],{},[1846,97250,1855],{"stretchy":1854},[9012,97252,97253,97255,97257],{},[898,97254,3783],{},[1979,97256,1981],{},[898,97258,4098],{},[1846,97260,1945],{},[898,97262,2623],{},[1846,97264,1861],{"stretchy":1854},[1846,97266,2075],{},[1974,97268,97269,97271],{},[898,97270,3783],{},[898,97272,4098],{},[1846,97274,2136],{"separator":2135},[5724,97276],{"width":5726},[2122,97278,97279,97281],{},[898,97280,2623],{},[895,97282,97283,97285,97287],{},[898,97284,42545],{},[898,97286,1844],{},[898,97288,11886],{},[1846,97290,1848],{},[1974,97292,97293,97295],{},[898,97294,3783],{},[898,97296,4098],{},[1846,97298,2075],{},[9012,97300,97301,97303,97305],{},[898,97302,3783],{},[1979,97304,1981],{},[898,97306,4098],{},[898,97308,1734],{"mathvariant":2226},[902,97310,97311],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,97313,97314],{},[614,97315,97316,97317,97347,97348,96200,97361,5515,97378,96231,97391,1734],{},"Obrázek 2.19: Posun ",[883,97318,97320],{"className":97319},[886],[888,97321,97322],{"xmlns":890},[892,97323,97324,97344],{},[895,97325,97326,97328,97330,97336,97338,97340,97342],{},[898,97327,4029],{},[1846,97329,2971],{},[2122,97331,97332,97334],{},[898,97333,4029],{},[1979,97335,1981],{},[1846,97337,1848],{},[898,97339,4029],{},[1846,97341,2075],{},[898,97343,2623],{},[902,97345,97346],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,97349,97351],{"className":97350},[886],[888,97352,97353],{"xmlns":890},[892,97354,97355,97359],{},[895,97356,97357],{},[898,97358,2623],{},[902,97360,2623],{"encoding":904},[883,97362,97364],{"className":97363},[886],[888,97365,97366],{"xmlns":890},[892,97367,97368,97376],{},[895,97369,97370],{},[2122,97371,97372,97374],{},[898,97373,4029],{},[1979,97375,1981],{},[902,97377,38172],{"encoding":904},[883,97379,97381],{"className":97380},[886],[888,97382,97383],{"xmlns":890},[892,97384,97385,97389],{},[895,97386,97387],{},[898,97388,8519],{},[902,97390,8519],{"encoding":904},[883,97392,97394],{"className":97393},[886],[888,97395,97396],{"xmlns":890},[892,97397,97398,97406],{},[895,97399,97400],{},[2122,97401,97402,97404],{},[898,97403,4098],{},[1979,97405,1981],{},[902,97407,97408],{"encoding":904},"E_2",[198,97410,45228],{"id":97411},"příklad-210",[724,97413,97414,97416,97417,41535,97440,97459,97460,97477],{},[38,97415,37778],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,97418,97420],{"className":97419},[886],[888,97421,97422],{"xmlns":890},[892,97423,97424,97438],{},[895,97425,97426,97428,97430,97432,97434,97436],{},[898,97427,3783],{},[1846,97429,1848],{},[1979,97431,3357],{},[1846,97433,2075],{},[1979,97435,1981],{},[898,97437,2638],{},[902,97439,96280],{"encoding":904},[883,97441,97443],{"className":97442},[886],[888,97444,97445],{"xmlns":890},[892,97446,97447,97457],{},[895,97448,97449,97451,97453,97455],{},[898,97450,3783],{},[1846,97452,1848],{},[1979,97454,2201],{},[898,97456,2638],{},[902,97458,96300],{"encoding":904},". Daň ",[883,97461,97463],{"className":97462},[886],[888,97464,97465],{"xmlns":890},[892,97466,97467,97475],{},[895,97468,97469,97471,97473],{},[898,97470,2623],{},[1846,97472,1848],{},[1979,97474,2085],{},[902,97476,41113],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,97479,97480],{},[38,97481,37810],{},[724,97483,97484,97485,96491],{},"Nová poptávka je ",[883,97486,97488],{"className":97487},[886],[888,97489,97490],{"xmlns":890},[892,97491,97492,97528],{},[895,97493,97494,97500,97502,97504,97506,97508,97510,97512,97514,97516,97518,97520,97522,97524,97526],{},[2122,97495,97496,97498],{},[898,97497,4029],{},[1979,97499,1981],{},[1846,97501,2554],{},[898,97503,3783],{},[1846,97505,1848],{},[1979,97507,3357],{},[1846,97509,2075],{},[1979,97511,1981],{},[898,97513,2638],{},[1846,97515,2075],{},[1979,97517,2085],{},[1846,97519,1848],{},[1979,97521,2085],{},[1846,97523,2075],{},[1979,97525,1981],{},[898,97527,2638],{},[902,97529,97530],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,97532,97534],{"className":97533},[886],[888,97535,97536],{"xmlns":890,"display":27911},[892,97537,97538,97554],{},[895,97539,97540,97542,97544,97546,97548,97550,97552],{},[1979,97541,2085],{},[1846,97543,2075],{},[1979,97545,1981],{},[898,97547,2638],{},[1846,97549,1848],{},[1979,97551,2201],{},[898,97553,2638],{},[902,97555,97556],{"encoding":904},"6 - 2Q = 4Q",[724,97558,96524,97559,5435,97578,1343,97602,96605,97634,1734],{},[883,97560,97562],{"className":97561},[886],[888,97563,97564],{"xmlns":890},[892,97565,97566,97576],{},[895,97567,97568,97570,97572,97574],{},[1979,97569,2085],{},[898,97571,2638],{},[1846,97573,1848],{},[1979,97575,2085],{},[902,97577,96544],{"encoding":904},[883,97579,97581],{"className":97580},[886],[888,97582,97583],{"xmlns":890},[892,97584,97585,97599],{},[895,97586,97587,97595,97597],{},[9012,97588,97589,97591,97593],{},[898,97590,2638],{},[1979,97592,1981],{},[898,97594,4098],{},[1846,97596,1848],{},[1979,97598,2128],{},[902,97600,97601],{"encoding":904},"Q_2^E = 1",[883,97603,97605],{"className":97604},[886],[888,97606,97607],{"xmlns":890},[892,97608,97609,97631],{},[895,97610,97611,97619,97621,97623,97625,97627,97629],{},[9012,97612,97613,97615,97617],{},[898,97614,3783],{},[1979,97616,1981],{},[898,97618,4098],{},[1846,97620,1848],{},[1979,97622,2201],{},[1846,97624,3025],{},[1979,97626,2128],{},[1846,97628,1848],{},[1979,97630,2201],{},[902,97632,97633],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,97635,97637],{"className":97636},[886],[888,97638,97639],{"xmlns":890},[892,97640,97641,97659],{},[895,97642,97643,97649,97651,97653,97655,97657],{},[2122,97644,97645,97647],{},[898,97646,4098],{},[1979,97648,1981],{},[1846,97650,2336],{"stretchy":1854},[1979,97652,2128],{},[1846,97654,2136],{"separator":2135},[1979,97656,2201],{},[1846,97658,2351],{"stretchy":1854},[902,97660,97661],{"encoding":904},"E_2[1, 4]",[724,97663,97664,97665,97701,97702,96319],{},"Spotřebitel platí celkem ",[883,97666,97668],{"className":97667},[886],[888,97669,97670],{"xmlns":890},[892,97671,97672,97698],{},[895,97673,97674,97682,97684,97686,97688,97690,97692,97694,97696],{},[9012,97675,97676,97678,97680],{},[898,97677,3783],{},[1979,97679,1981],{},[898,97681,4098],{},[1846,97683,1945],{},[898,97685,2623],{},[1846,97687,1848],{},[1979,97689,2201],{},[1846,97691,1945],{},[1979,97693,2085],{},[1846,97695,1848],{},[1979,97697,2712],{},[902,97699,97700],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,97703,97705],{"className":97704},[886],[888,97706,97707],{"xmlns":890},[892,97708,97709,97723],{},[895,97710,97711,97719,97721],{},[9012,97712,97713,97715,97717],{},[898,97714,3783],{},[1979,97716,1981],{},[898,97718,4098],{},[1846,97720,1848],{},[1979,97722,2201],{},[902,97724,97725],{"encoding":904},"P_2^E = 4",[724,97727,97728],{},[614,97729,97730],{},"Rozklad daňového břemene:",[883,97732,97734],{"className":97733},[886],[888,97735,97736],{"xmlns":890,"display":27911},[892,97737,97738,97824],{},[895,97739,97740,97750,97752,97754,97756,97758,97760,97762,97764,97766,97768,97770,97772,97782,97784,97786,97798,97800,97802,97804,97806,97808,97810,97812,97822],{},[2122,97741,97742,97744],{},[898,97743,2623],{},[895,97745,97746,97748],{},[898,97747,42522],{},[898,97749,724],{},[1846,97751,1848],{},[1846,97753,1855],{"stretchy":1854},[1979,97755,2201],{},[1846,97757,1945],{},[1979,97759,2085],{},[1846,97761,1861],{"stretchy":1854},[1846,97763,2075],{},[1979,97765,5431],{},[1846,97767,1848],{},[1979,97769,1981],{},[2138,97771,2140],{},[895,97773,97774,97776],{},[2138,97775,9646],{},[8232,97777,97778,97780],{"accent":2135},[2138,97779,1992],{},[1846,97781,24903],{},[1846,97783,2136],{"separator":2135},[5724,97785],{"width":5726},[2122,97787,97788,97790],{},[898,97789,2623],{},[895,97791,97792,97794,97796],{},[898,97793,42545],{},[898,97795,1844],{},[898,97797,11886],{},[1846,97799,1848],{},[1979,97801,5431],{},[1846,97803,2075],{},[1979,97805,2201],{},[1846,97807,1848],{},[1979,97809,2201],{},[2138,97811,2140],{},[895,97813,97814,97816],{},[2138,97815,9646],{},[8232,97817,97818,97820],{"accent":2135},[2138,97819,1992],{},[1846,97821,24903],{},[898,97823,1734],{"mathvariant":2226},[902,97825,97826],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,97828,97829,97830,1734],{},"Opět ",[883,97831,97833],{"className":97832},[886],[888,97834,97835],{"xmlns":890},[892,97836,97837,97871],{},[895,97838,97839,97849,97851,97863,97865,97867,97869],{},[2122,97840,97841,97843],{},[898,97842,2623],{},[895,97844,97845,97847],{},[898,97846,42522],{},[898,97848,724],{},[1846,97850,1945],{},[2122,97852,97853,97855],{},[898,97854,2623],{},[895,97856,97857,97859,97861],{},[898,97858,42545],{},[898,97860,1844],{},[898,97862,11886],{},[1846,97864,1848],{},[1979,97866,2085],{},[1846,97868,1848],{},[898,97870,2623],{},[902,97872,97873],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[36815,97875],{},[115,97877,42503],{"id":97878},"daňové-břemeno",[724,97880,97881,9871,97883,97886,97887,97900],{},[38,97882,42503],{},[614,97884,97885],{},"tax burden",") je rozdělení zaplacené daně ",[883,97888,97890],{"className":97889},[886],[888,97891,97892],{"xmlns":890},[892,97893,97894,97898],{},[895,97895,97896],{},[898,97897,2623],{},[902,97899,2623],{"encoding":904}," mezi spotřebitele a výrobce:",[883,97902,97904],{"className":97903},[886],[888,97905,97906],{"xmlns":890,"display":27911},[892,97907,97908,97940],{},[895,97909,97910,97912,97914,97924,97926,97938],{},[898,97911,2623],{},[1846,97913,1848],{},[2122,97915,97916,97918],{},[898,97917,2623],{},[895,97919,97920,97922],{},[898,97921,42522],{},[898,97923,724],{},[1846,97925,1945],{},[2122,97927,97928,97930],{},[898,97929,2623],{},[895,97931,97932,97934,97936],{},[898,97933,42545],{},[898,97935,1844],{},[898,97937,11886],{},[898,97939,1734],{"mathvariant":2226},[902,97941,97942],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,97944,97945],{},[2409,97946],{"alt":97947,"className":97948,"src":97949},"imek-dan-rozklad-bremene-sklony",[210,2413],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[1639,97951,97952],{},[724,97953,97954,97956,97957,1745,97970,1734],{},[883,97955,4001],{}," 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 ",[883,97958,97960],{"className":97959},[886],[888,97961,97962],{"xmlns":890},[892,97963,97964,97968],{},[895,97965,97966],{},[898,97967,4029],{},[902,97969,4029],{"encoding":904},[883,97971,97973],{"className":97972},[886],[888,97974,97975],{"xmlns":890},[892,97976,97977,97981],{},[895,97978,97979],{},[898,97980,8519],{},[902,97982,8519],{"encoding":904},[198,97984,2294],{"id":2293},[724,97986,97987,97988,98009,98010,98023,98024,98041,98042,98055],{},"V grafu ",[883,97989,97991],{"className":97990},[886],[888,97992,97993],{"xmlns":890},[892,97994,97995,98007],{},[895,97996,97997,97999,98001,98003,98005],{},[1846,97998,1855],{"stretchy":1854},[898,98000,2638],{},[1846,98002,2136],{"separator":2135},[898,98004,3783],{},[1846,98006,1861],{"stretchy":1854},[902,98008,37536],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,98011,98013],{"className":98012},[886],[888,98014,98015],{"xmlns":890},[892,98016,98017,98021],{},[895,98018,98019],{},[898,98020,2623],{},[902,98022,2623],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,98025,98027],{"className":98026},[886],[888,98028,98029],{"xmlns":890},[892,98030,98031,98039],{},[895,98032,98033],{},[1974,98034,98035,98037],{},[898,98036,3783],{},[898,98038,4098],{},[902,98040,41311],{"encoding":904},", rozdělí se úsečka ",[883,98043,98045],{"className":98044},[886],[888,98046,98047],{"xmlns":890},[892,98048,98049,98053],{},[895,98050,98051],{},[898,98052,2623],{},[902,98054,2623],{"encoding":904}," na dvě části:",[120,98057,98058,98083],{},[123,98059,98060,98061,98082],{},"horní část odpovídá ",[883,98062,98064],{"className":98063},[886],[888,98065,98066],{"xmlns":890},[892,98067,98068,98080],{},[895,98069,98070],{},[2122,98071,98072,98074],{},[898,98073,2623],{},[895,98075,98076,98078],{},[898,98077,42522],{},[898,98079,724],{},[902,98081,42527],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,98084,98085,98086,98109],{},"dolní část odpovídá ",[883,98087,98089],{"className":98088},[886],[888,98090,98091],{"xmlns":890},[892,98092,98093,98107],{},[895,98094,98095],{},[2122,98096,98097,98099],{},[898,98098,2623],{},[895,98100,98101,98103,98105],{},[898,98102,42545],{},[898,98104,1844],{},[898,98106,11886],{},[902,98108,42552],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,98111,98112],{},[614,98113,98114,98115,2535,98128,98149,98150,98173,98174,1745,98195,98218],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,98116,98118],{"className":98117},[886],[888,98119,98120],{"xmlns":890},[892,98121,98122,98126],{},[895,98123,98124],{},[898,98125,2623],{},[902,98127,2623],{"encoding":904},[883,98129,98131],{"className":98130},[886],[888,98132,98133],{"xmlns":890},[892,98134,98135,98147],{},[895,98136,98137],{},[2122,98138,98139,98141],{},[898,98140,2623],{},[895,98142,98143,98145],{},[898,98144,42522],{},[898,98146,724],{},[902,98148,42527],{"encoding":904}," (nahoře) a ",[883,98151,98153],{"className":98152},[886],[888,98154,98155],{"xmlns":890},[892,98156,98157,98171],{},[895,98158,98159],{},[2122,98160,98161,98163],{},[898,98162,2623],{},[895,98164,98165,98167,98169],{},[898,98166,42545],{},[898,98168,1844],{},[898,98170,11886],{},[902,98172,42552],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,98175,98177],{"className":98176},[886],[888,98178,98179],{"xmlns":890},[892,98180,98181,98193],{},[895,98182,98183],{},[2122,98184,98185,98187],{},[898,98186,2623],{},[895,98188,98189,98191],{},[898,98190,42522],{},[898,98192,724],{},[902,98194,42527],{"encoding":904},[883,98196,98198],{"className":98197},[886],[888,98199,98200],{"xmlns":890},[892,98201,98202,98216],{},[895,98203,98204],{},[2122,98205,98206,98208],{},[898,98207,2623],{},[895,98209,98210,98212,98214],{},[898,98211,42545],{},[898,98213,1844],{},[898,98215,11886],{},[902,98217,42552],{"encoding":904}," je v obou případech stejná.",[198,98220,98222],{"id":98221},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,98224,98225,98226,98229,98230,9871,98253,98270,98271,9871,98294,98311],{},"Platí obecně: ",[38,98227,98228],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,98231,98233],{"className":98232},[886],[888,98234,98235],{"xmlns":890},[892,98236,98237,98251],{},[895,98238,98239,98241,98243,98245,98247,98249],{},[898,98240,3783],{},[1846,98242,1848],{},[898,98244,207],{},[898,98246,2638],{},[1846,98248,1945],{},[898,98250,1948],{},[902,98252,36905],{"encoding":904},[883,98254,98256],{"className":98255},[886],[888,98257,98258],{"xmlns":890},[892,98259,98260,98268],{},[895,98261,98262,98264,98266],{},[898,98263,207],{},[1846,98265,3295],{},[1979,98267,2177],{},[902,98269,42930],{"encoding":904},") a lineární nabídku ",[883,98272,98274],{"className":98273},[886],[888,98275,98276],{"xmlns":890},[892,98277,98278,98292],{},[895,98279,98280,98282,98284,98286,98288,98290],{},[898,98281,3783],{},[1846,98283,1848],{},[898,98285,1992],{},[898,98287,2638],{},[1846,98289,1945],{},[898,98291,2044],{},[902,98293,40087],{"encoding":904},[883,98295,98297],{"className":98296},[886],[888,98298,98299],{"xmlns":890},[892,98300,98301,98309],{},[895,98302,98303,98305,98307],{},[898,98304,1992],{},[1846,98306,3256],{},[1979,98308,2177],{},[902,98310,40105],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,98313,98315],{"className":98314},[886],[888,98316,98317],{"xmlns":890,"display":27911},[892,98318,98319,98385],{},[895,98320,98321,98345,98347,98357,98359,98383],{},[2179,98322,98323,98333],{},[2122,98324,98325,98327],{},[898,98326,2623],{},[895,98328,98329,98331],{},[898,98330,42522],{},[898,98332,724],{},[2122,98334,98335,98337],{},[898,98336,2623],{},[895,98338,98339,98341,98343],{},[898,98340,42545],{},[898,98342,1844],{},[898,98344,11886],{},[1846,98346,1848],{},[2179,98348,98349,98351],{},[898,98350,1992],{},[895,98352,98353,98355],{},[1846,98354,2075],{},[898,98356,207],{},[1846,98358,1848],{},[2179,98360,98361,98373],{},[895,98362,98363,98366,98369,98371],{},[898,98364,98365],{"mathvariant":2226},"∣",[2138,98367,98368],{},"sklon ",[898,98370,8519],{},[898,98372,98365],{"mathvariant":2226},[895,98374,98375,98377,98379,98381],{},[898,98376,98365],{"mathvariant":2226},[2138,98378,98368],{},[898,98380,4029],{},[898,98382,98365],{"mathvariant":2226},[898,98384,1734],{"mathvariant":2226},[902,98386,98387],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[1639,98389,98390,98395],{},[724,98391,98392,98394],{},[883,98393,4418],{}," Postup výpočtu rozkladu",[152,98396,98397,98432,98485,98564],{},[123,98398,98399,98400,98431],{},"Spočti rovnovážný bod ",[883,98401,98403],{"className":98402},[886],[888,98404,98405],{"xmlns":890},[892,98406,98407,98429],{},[895,98408,98409,98411,98413,98419,98421,98427],{},[898,98410,4098],{},[1846,98412,2336],{"stretchy":1854},[1974,98414,98415,98417],{},[898,98416,2638],{},[898,98418,4098],{},[1846,98420,2136],{"separator":2135},[1974,98422,98423,98425],{},[898,98424,3783],{},[898,98426,4098],{},[1846,98428,2351],{"stretchy":1854},[902,98430,41212],{"encoding":904}," bez daně.",[123,98433,98434,98435,1348,98460,3764],{},"Urči posunutou křivku (",[883,98436,98438],{"className":98437},[886],[888,98439,98440],{"xmlns":890},[892,98441,98442,98458],{},[895,98443,98444,98450,98452,98454,98456],{},[2122,98445,98446,98448],{},[898,98447,8519],{},[1979,98449,2128],{},[1846,98451,1848],{},[898,98453,8519],{},[1846,98455,1945],{},[898,98457,2623],{},[902,98459,42599],{"encoding":904},[883,98461,98463],{"className":98462},[886],[888,98464,98465],{"xmlns":890},[892,98466,98467,98483],{},[895,98468,98469,98475,98477,98479,98481],{},[2122,98470,98471,98473],{},[898,98472,4029],{},[1979,98474,1981],{},[1846,98476,1848],{},[898,98478,4029],{},[1846,98480,2075],{},[898,98482,2623],{},[902,98484,42630],{"encoding":904},[123,98486,98487,98488,3756,98507,11973,98526,3756,98545,3764],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,98489,98491],{"className":98490},[886],[888,98492,98493],{"xmlns":890},[892,98494,98495,98505],{},[895,98496,98497],{},[9012,98498,98499,98501,98503],{},[898,98500,2638],{},[1979,98502,2128],{},[898,98504,4098],{},[902,98506,47681],{"encoding":904},[883,98508,98510],{"className":98509},[886],[888,98511,98512],{"xmlns":890},[892,98513,98514,98524],{},[895,98515,98516],{},[9012,98517,98518,98520,98522],{},[898,98519,2638],{},[1979,98521,1981],{},[898,98523,4098],{},[902,98525,47743],{"encoding":904},[883,98527,98529],{"className":98528},[886],[888,98530,98531],{"xmlns":890},[892,98532,98533,98543],{},[895,98534,98535],{},[9012,98536,98537,98539,98541],{},[898,98538,3783],{},[1979,98540,2128],{},[898,98542,4098],{},[902,98544,47702],{"encoding":904},[883,98546,98548],{"className":98547},[886],[888,98549,98550],{"xmlns":890},[892,98551,98552,98562],{},[895,98553,98554],{},[9012,98555,98556,98558,98560],{},[898,98557,3783],{},[1979,98559,1981],{},[898,98561,4098],{},[902,98563,47763],{"encoding":904},[123,98565,98566,98567,1745,98588,98611,98612,1734],{},"Dopočítej ",[883,98568,98570],{"className":98569},[886],[888,98571,98572],{"xmlns":890},[892,98573,98574,98586],{},[895,98575,98576],{},[2122,98577,98578,98580],{},[898,98579,2623],{},[895,98581,98582,98584],{},[898,98583,42522],{},[898,98585,724],{},[902,98587,42527],{"encoding":904},[883,98589,98591],{"className":98590},[886],[888,98592,98593],{"xmlns":890},[892,98594,98595,98609],{},[895,98596,98597],{},[2122,98598,98599,98601],{},[898,98600,2623],{},[895,98602,98603,98605,98607],{},[898,98604,42545],{},[898,98606,1844],{},[898,98608,11886],{},[902,98610,42552],{"encoding":904}," z definice, vždy ověř ",[883,98613,98615],{"className":98614},[886],[888,98616,98617],{"xmlns":890},[892,98618,98619,98649],{},[895,98620,98621,98631,98633,98645,98647],{},[2122,98622,98623,98625],{},[898,98624,2623],{},[895,98626,98627,98629],{},[898,98628,42522],{},[898,98630,724],{},[1846,98632,1945],{},[2122,98634,98635,98637],{},[898,98636,2623],{},[895,98638,98639,98641,98643],{},[898,98640,42545],{},[898,98642,1844],{},[898,98644,11886],{},[1846,98646,1848],{},[898,98648,2623],{},[902,98650,98651],{"encoding":904},"T_{sp} + T_{vyr} = T",[1639,98653,98654],{},[724,98655,98656,98658,98659,98662,98663,1745,98676,98689],{},[883,98657,4258],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,98660,98661],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,98664,98666],{"className":98665},[886],[888,98667,98668],{"xmlns":890},[892,98669,98670,98674],{},[895,98671,98672],{},[898,98673,4029],{},[902,98675,4029],{"encoding":904},[883,98677,98679],{"className":98678},[886],[888,98680,98681],{"xmlns":890},[892,98682,98683,98687],{},[895,98684,98685],{},[898,98686,8519],{},[902,98688,8519],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[36815,98691],{},[115,98693,98695],{"id":98694},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,98697,98698],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,98700,98701],{},[2409,98702],{"alt":98703,"className":98704,"src":98705},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,2413],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,98707,98708,98720],{},[19,98709,98710],{},[22,98711,98712,98714,98717],{},[25,98713,54141],{},[25,98715,98716],{},"(a) daň výrobci",[25,98718,98719],{},"(b) daň spotřebiteli",[30,98721,98722,98777,98844,98904],{},[22,98723,98724,98727,98752],{},[35,98725,98726],{},"Rovnovážné množství",[35,98728,98729],{},[883,98730,98732],{"className":98731},[886],[888,98733,98734],{"xmlns":890},[892,98735,98736,98750],{},[895,98737,98738,98746,98748],{},[9012,98739,98740,98742,98744],{},[898,98741,2638],{},[1979,98743,2128],{},[898,98745,4098],{},[1846,98747,1848],{},[1979,98749,2128],{},[902,98751,96568],{"encoding":904},[35,98753,98754],{},[883,98755,98757],{"className":98756},[886],[888,98758,98759],{"xmlns":890},[892,98760,98761,98775],{},[895,98762,98763,98771,98773],{},[9012,98764,98765,98767,98769],{},[898,98766,2638],{},[1979,98768,1981],{},[898,98770,4098],{},[1846,98772,1848],{},[1979,98774,2128],{},[902,98776,97601],{"encoding":904},[22,98778,98779,98782,98807],{},[35,98780,98781],{},"Cena placená spotřebitelem",[35,98783,98784],{},[883,98785,98787],{"className":98786},[886],[888,98788,98789],{"xmlns":890},[892,98790,98791,98805],{},[895,98792,98793,98801,98803],{},[9012,98794,98795,98797,98799],{},[898,98796,3783],{},[1979,98798,2128],{},[898,98800,4098],{},[1846,98802,1848],{},[1979,98804,2712],{},[902,98806,96663],{"encoding":904},[35,98808,98809],{},[883,98810,98812],{"className":98811},[886],[888,98813,98814],{"xmlns":890},[892,98815,98816,98842],{},[895,98817,98818,98826,98828,98830,98832,98834,98836,98838,98840],{},[9012,98819,98820,98822,98824],{},[898,98821,3783],{},[1979,98823,1981],{},[898,98825,4098],{},[1846,98827,1945],{},[898,98829,2623],{},[1846,98831,1848],{},[1979,98833,2201],{},[1846,98835,1945],{},[1979,98837,2085],{},[1846,98839,1848],{},[1979,98841,2712],{},[902,98843,97700],{"encoding":904},[22,98845,98846,98849,98879],{},[35,98847,98848],{},"Cena přijímaná výrobcem",[35,98850,98851],{},[883,98852,98854],{"className":98853},[886],[888,98855,98856],{"xmlns":890},[892,98857,98858,98876],{},[895,98859,98860,98868,98870,98872,98874],{},[9012,98861,98862,98864,98866],{},[898,98863,3783],{},[1979,98865,2128],{},[898,98867,4098],{},[1846,98869,2075],{},[898,98871,2623],{},[1846,98873,1848],{},[1979,98875,2201],{},[902,98877,98878],{"encoding":904},"P_1^E - T = 4",[35,98880,98881],{},[883,98882,98884],{"className":98883},[886],[888,98885,98886],{"xmlns":890},[892,98887,98888,98902],{},[895,98889,98890,98898,98900],{},[9012,98891,98892,98894,98896],{},[898,98893,3783],{},[1979,98895,1981],{},[898,98897,4098],{},[1846,98899,1848],{},[1979,98901,2201],{},[902,98903,97725],{"encoding":904},[22,98905,98906,98909,98963],{},[35,98907,98908],{},"Rozklad břemene",[35,98910,98911,1343,98936],{},[883,98912,98914],{"className":98913},[886],[888,98915,98916],{"xmlns":890},[892,98917,98918,98934],{},[895,98919,98920,98930,98932],{},[2122,98921,98922,98924],{},[898,98923,2623],{},[895,98925,98926,98928],{},[898,98927,42522],{},[898,98929,724],{},[1846,98931,1848],{},[1979,98933,1981],{},[902,98935,42821],{"encoding":904},[883,98937,98939],{"className":98938},[886],[888,98940,98941],{"xmlns":890},[892,98942,98943,98961],{},[895,98944,98945,98957,98959],{},[2122,98946,98947,98949],{},[898,98948,2623],{},[895,98950,98951,98953,98955],{},[898,98952,42545],{},[898,98954,1844],{},[898,98956,11886],{},[1846,98958,1848],{},[1979,98960,2201],{},[902,98962,42850],{"encoding":904},[35,98964,98965,1343,98990],{},[883,98966,98968],{"className":98967},[886],[888,98969,98970],{"xmlns":890},[892,98971,98972,98988],{},[895,98973,98974,98984,98986],{},[2122,98975,98976,98978],{},[898,98977,2623],{},[895,98979,98980,98982],{},[898,98981,42522],{},[898,98983,724],{},[1846,98985,1848],{},[1979,98987,1981],{},[902,98989,42821],{"encoding":904},[883,98991,98993],{"className":98992},[886],[888,98994,98995],{"xmlns":890},[892,98996,98997,99015],{},[895,98998,98999,99011,99013],{},[2122,99000,99001,99003],{},[898,99002,2623],{},[895,99004,99005,99007,99009],{},[898,99006,42545],{},[898,99008,1844],{},[898,99010,11886],{},[1846,99012,1848],{},[1979,99014,2201],{},[902,99016,42850],{"encoding":904},[724,99018,99019],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,99021,99023],{"className":99022},[886],[888,99024,99025],{"xmlns":890,"display":27911},[892,99026,99027,99075],{},[895,99028,99029,99037,99039,99047,99049,99051,99059,99061,99063,99065,99073],{},[9012,99030,99031,99033,99035],{},[898,99032,2638],{},[1979,99034,2128],{},[898,99036,4098],{},[1846,99038,1848],{},[9012,99040,99041,99043,99045],{},[898,99042,2638],{},[1979,99044,1981],{},[898,99046,4098],{},[1846,99048,2136],{"separator":2135},[5724,99050],{"width":5726},[9012,99052,99053,99055,99057],{},[898,99054,3783],{},[1979,99056,2128],{},[898,99058,4098],{},[1846,99060,2075],{},[898,99062,2623],{},[1846,99064,1848],{},[9012,99066,99067,99069,99071],{},[898,99068,3783],{},[1979,99070,1981],{},[898,99072,4098],{},[898,99074,1734],{"mathvariant":2226},[902,99076,99077],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[1639,99079,99080,99099,99253],{},[724,99081,99082,99084,99085,99098],{},[883,99083,4418],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,99086,99088],{"className":99087},[886],[888,99089,99090],{"xmlns":890},[892,99091,99092,99096],{},[895,99093,99094],{},[898,99095,2623],{},[902,99097,2623],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,99100,99101,99133,99169,99206],{},[123,99102,99103,99104,2136],{},"rovnovážná množství obou režimů, ",[883,99105,99107],{"className":99106},[886],[888,99108,99109],{"xmlns":890},[892,99110,99111,99131],{},[895,99112,99113,99121,99123],{},[9012,99114,99115,99117,99119],{},[898,99116,2638],{},[1979,99118,2128],{},[898,99120,4098],{},[1846,99122,1848],{},[9012,99124,99125,99127,99129],{},[898,99126,2638],{},[1979,99128,1981],{},[898,99130,4098],{},[902,99132,42753],{"encoding":904},[123,99134,99135,99136,2136],{},"čistá cena přijímaná výrobcem, ",[883,99137,99139],{"className":99138},[886],[888,99140,99141],{"xmlns":890},[892,99142,99143,99167],{},[895,99144,99145,99153,99155,99157,99159],{},[9012,99146,99147,99149,99151],{},[898,99148,3783],{},[1979,99150,2128],{},[898,99152,4098],{},[1846,99154,2075],{},[898,99156,2623],{},[1846,99158,1848],{},[9012,99160,99161,99163,99165],{},[898,99162,3783],{},[1979,99164,1981],{},[898,99166,4098],{},[902,99168,42787],{"encoding":904},[123,99170,99171,99172,2136],{},"celková cena placená spotřebitelem, ",[883,99173,99175],{"className":99174},[886],[888,99176,99177],{"xmlns":890},[892,99178,99179,99203],{},[895,99180,99181,99189,99191,99199,99201],{},[9012,99182,99183,99185,99187],{},[898,99184,3783],{},[1979,99186,2128],{},[898,99188,4098],{},[1846,99190,1848],{},[9012,99192,99193,99195,99197],{},[898,99194,3783],{},[1979,99196,1981],{},[898,99198,4098],{},[1846,99200,1945],{},[898,99202,2623],{},[902,99204,99205],{"encoding":904},"P_1^E = P_2^E + T",[123,99207,99208,99209,1745,99230,1734],{},"rozklad daňového břemene ",[883,99210,99212],{"className":99211},[886],[888,99213,99214],{"xmlns":890},[892,99215,99216,99228],{},[895,99217,99218],{},[2122,99219,99220,99222],{},[898,99221,2623],{},[895,99223,99224,99226],{},[898,99225,42522],{},[898,99227,724],{},[902,99229,42527],{"encoding":904},[883,99231,99233],{"className":99232},[886],[888,99234,99235],{"xmlns":890},[892,99236,99237,99251],{},[895,99238,99239],{},[2122,99240,99241,99243],{},[898,99242,2623],{},[895,99244,99245,99247,99249],{},[898,99246,42545],{},[898,99248,1844],{},[898,99250,11886],{},[902,99252,42552],{"encoding":904},[724,99254,99255,99256,1734],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,99257,35042],{},[724,99259,99260,99261,1745,99274,3764],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,99262,99264],{"className":99263},[886],[888,99265,99266],{"xmlns":890},[892,99267,99268,99272],{},[895,99269,99270],{},[898,99271,4029],{},[902,99273,4029],{"encoding":904},[883,99275,99277],{"className":99276},[886],[888,99278,99279],{"xmlns":890},[892,99280,99281,99285],{},[895,99282,99283],{},[898,99284,8519],{},[902,99286,8519],{"encoding":904},[36815,99288],{},[115,99290,99292],{"id":99291},"úlohy","Úlohy",[724,99294,99295,99296,2999],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,99297,1789],{"className":99298,"dataFsResolvedFilePath":800,"href":801},[210],[120,99300,99301,99331,99362],{},[123,99302,99303,99306,99307,99330],{},[38,99304,99305],{},"Úloha 2.4"," — Poptávka ",[883,99308,99310],{"className":99309},[886],[888,99311,99312],{"xmlns":890},[892,99313,99314,99328],{},[895,99315,99316,99318,99320,99322,99324,99326],{},[898,99317,3783],{},[1846,99319,1848],{},[1979,99321,3357],{},[1846,99323,2075],{},[1979,99325,1981],{},[898,99327,2638],{},[902,99329,96280],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,99332,99333,99336,99337,99361],{},[38,99334,99335],{},"Úloha 2.9"," — Nabídka ",[883,99338,99340],{"className":99339},[886],[888,99341,99342],{"xmlns":890},[892,99343,99344,99358],{},[895,99345,99346,99348,99350,99352,99354,99356],{},[898,99347,3783],{},[1846,99349,1848],{},[1979,99351,4855],{},[898,99353,2638],{},[1846,99355,1945],{},[1979,99357,36089],{},[902,99359,99360],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,99363,99364,99367,99368,1745,99394,99418,99419,99436],{},[38,99365,99366],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,99369,99371],{"className":99370},[886],[888,99372,99373],{"xmlns":890},[892,99374,99375,99391],{},[895,99376,99377,99379,99381,99383,99385,99387,99389],{},[898,99378,3783],{},[1846,99380,1848],{},[1846,99382,2075],{},[1979,99384,2201],{},[898,99386,2638],{},[1846,99388,1945],{},[1979,99390,46548],{},[902,99392,99393],{"encoding":904},"P = -4Q + 80",[883,99395,99397],{"className":99396},[886],[888,99398,99399],{"xmlns":890},[892,99400,99401,99415],{},[895,99402,99403,99405,99407,99409,99411,99413],{},[898,99404,3783],{},[1846,99406,1848],{},[1979,99408,2023],{},[898,99410,2638],{},[1846,99412,1945],{},[1979,99414,2712],{},[902,99416,99417],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,99420,99422],{"className":99421},[886],[888,99423,99424],{"xmlns":890},[892,99425,99426,99434],{},[895,99427,99428,99430,99432],{},[898,99429,2623],{},[1846,99431,1848],{},[1979,99433,24046],{},[902,99435,47660],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,99438,99439,99440,99442,99443,99445],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,99441,45073],{}," (posun poptávky při zdanění kupujícího) a ",[38,99444,45107],{}," (posun nabídky při zdanění výrobce).",[36815,99447],{},[115,99449,15565],{"id":15564},[120,99451,99452,99471,99529,99586,99669,99715,99758,99803,99869],{},[123,99453,99454,2053,99457,99470],{},[38,99455,99456],{},"Jednotková daň",[883,99458,99460],{"className":99459},[886],[888,99461,99462],{"xmlns":890},[892,99463,99464,99468],{},[895,99465,99466],{},[898,99467,2623],{},[902,99469,2623],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,99472,99473,99475,99476,99514,99515,99528],{},[38,99474,95862],{}," — posun nabídky ",[883,99477,99479],{"className":99478},[886],[888,99480,99481],{"xmlns":890},[892,99482,99483,99511],{},[895,99484,99485,99491,99493,99495,99497,99499,99501,99503,99505,99507,99509],{},[2122,99486,99487,99489],{},[898,99488,8519],{},[1979,99490,2128],{},[1846,99492,1855],{"stretchy":1854},[898,99494,2638],{},[1846,99496,1861],{"stretchy":1854},[1846,99498,1848],{},[898,99500,8519],{},[1846,99502,1855],{"stretchy":1854},[898,99504,2638],{},[1846,99506,1861],{"stretchy":1854},[1846,99508,1945],{},[898,99510,2623],{},[902,99512,99513],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,99516,99518],{"className":99517},[886],[888,99519,99520],{"xmlns":890},[892,99521,99522,99526],{},[895,99523,99524],{},[898,99525,2623],{},[902,99527,2623],{"encoding":904}," svisle nahoru)",[123,99530,99531,99533,99534,99514,99572,99585],{},[38,99532,96935],{}," — posun poptávky ",[883,99535,99537],{"className":99536},[886],[888,99538,99539],{"xmlns":890},[892,99540,99541,99569],{},[895,99542,99543,99549,99551,99553,99555,99557,99559,99561,99563,99565,99567],{},[2122,99544,99545,99547],{},[898,99546,4029],{},[1979,99548,1981],{},[1846,99550,1855],{"stretchy":1854},[898,99552,2638],{},[1846,99554,1861],{"stretchy":1854},[1846,99556,1848],{},[898,99558,4029],{},[1846,99560,1855],{"stretchy":1854},[898,99562,2638],{},[1846,99564,1861],{"stretchy":1854},[1846,99566,2075],{},[898,99568,2623],{},[902,99570,99571],{"encoding":904},"D_2(Q) = D(Q) - T",[883,99573,99575],{"className":99574},[886],[888,99576,99577],{"xmlns":890},[892,99578,99579,99583],{},[895,99580,99581],{},[898,99582,2623],{},[902,99584,2623],{"encoding":904}," svisle dolů)",[123,99587,99588,6861,99591,41659,99630],{},[38,99589,99590],{},"Rovnovážný bod s daní",[883,99592,99594],{"className":99593},[886],[888,99595,99596],{"xmlns":890},[892,99597,99598,99628],{},[895,99599,99600,99606,99608,99616,99618,99626],{},[2122,99601,99602,99604],{},[898,99603,4098],{},[1979,99605,2128],{},[1846,99607,2336],{"stretchy":1854},[9012,99609,99610,99612,99614],{},[898,99611,2638],{},[1979,99613,2128],{},[898,99615,4098],{},[1846,99617,2136],{"separator":2135},[9012,99619,99620,99622,99624],{},[898,99621,3783],{},[1979,99623,2128],{},[898,99625,4098],{},[1846,99627,2351],{"stretchy":1854},[902,99629,96030],{"encoding":904},[883,99631,99633],{"className":99632},[886],[888,99634,99635],{"xmlns":890},[892,99636,99637,99667],{},[895,99638,99639,99645,99647,99655,99657,99665],{},[2122,99640,99641,99643],{},[898,99642,4098],{},[1979,99644,1981],{},[1846,99646,2336],{"stretchy":1854},[9012,99648,99649,99651,99653],{},[898,99650,2638],{},[1979,99652,1981],{},[898,99654,4098],{},[1846,99656,2136],{"separator":2135},[9012,99658,99659,99661,99663],{},[898,99660,3783],{},[1979,99662,1981],{},[898,99664,4098],{},[1846,99666,2351],{"stretchy":1854},[902,99668,97105],{"encoding":904},[123,99670,99671,9871,99673,99675,99676],{},[38,99672,42503],{},[614,99674,97885],{},") — rozklad ",[883,99677,99679],{"className":99678},[886],[888,99680,99681],{"xmlns":890},[892,99682,99683,99713],{},[895,99684,99685,99687,99689,99699,99701],{},[898,99686,2623],{},[1846,99688,1848],{},[2122,99690,99691,99693],{},[898,99692,2623],{},[895,99694,99695,99697],{},[898,99696,42522],{},[898,99698,724],{},[1846,99700,1945],{},[2122,99702,99703,99705],{},[898,99704,2623],{},[895,99706,99707,99709,99711],{},[898,99708,42545],{},[898,99710,1844],{},[898,99712,11886],{},[902,99714,42689],{"encoding":904},[123,99716,99717,99740,99741,1861],{},[38,99718,99719],{},[883,99720,99722],{"className":99721},[886],[888,99723,99724],{"xmlns":890},[892,99725,99726,99738],{},[895,99727,99728],{},[2122,99729,99730,99732],{},[898,99731,2623],{},[895,99733,99734,99736],{},[898,99735,42522],{},[898,99737,724],{},[902,99739,42527],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,99742,99744],{"className":99743},[886],[888,99745,99746],{"xmlns":890},[892,99747,99748,99756],{},[895,99749,99750],{},[1974,99751,99752,99754],{},[898,99753,3783],{},[898,99755,4098],{},[902,99757,41311],{"encoding":904},[123,99759,99760,99785,99786,1861],{},[38,99761,99762],{},[883,99763,99765],{"className":99764},[886],[888,99766,99767],{"xmlns":890},[892,99768,99769,99783],{},[895,99770,99771],{},[2122,99772,99773,99775],{},[898,99774,2623],{},[895,99776,99777,99779,99781],{},[898,99778,42545],{},[898,99780,1844],{},[898,99782,11886],{},[902,99784,42552],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,99787,99789],{"className":99788},[886],[888,99790,99791],{"xmlns":890},[892,99792,99793,99801],{},[895,99794,99795],{},[1974,99796,99797,99799],{},[898,99798,3783],{},[898,99800,4098],{},[902,99802,41311],{"encoding":904},[123,99804,99805,6861,99807,1343,99836],{},[38,99806,50319],{},[883,99808,99810],{"className":99809},[886],[888,99811,99812],{"xmlns":890},[892,99813,99814,99834],{},[895,99815,99816,99824,99826],{},[9012,99817,99818,99820,99822],{},[898,99819,2638],{},[1979,99821,2128],{},[898,99823,4098],{},[1846,99825,1848],{},[9012,99827,99828,99830,99832],{},[898,99829,2638],{},[1979,99831,1981],{},[898,99833,4098],{},[902,99835,42753],{"encoding":904},[883,99837,99839],{"className":99838},[886],[888,99840,99841],{"xmlns":890},[892,99842,99843,99867],{},[895,99844,99845,99853,99855,99857,99859],{},[9012,99846,99847,99849,99851],{},[898,99848,3783],{},[1979,99850,2128],{},[898,99852,4098],{},[1846,99854,2075],{},[898,99856,2623],{},[1846,99858,1848],{},[9012,99860,99861,99863,99865],{},[898,99862,3783],{},[1979,99864,1981],{},[898,99866,4098],{},[902,99868,42787],{"encoding":904},[123,99870,99871,99874],{},[38,99872,99873],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[36815,99876],{},[115,99878,3640],{"id":3639},[120,99880,99881,99889,99907,99914],{},[123,99882,99883,2053,99886],{},[38,99884,99885],{},"Kontext (hub):",[207,99887,802],{"className":99888,"dataFsResolvedFilePath":800,"href":801},[210],[123,99890,99891,2053,99893,99896,99897,18493,99899,99902,99903,99906],{},[38,99892,50568],{},[207,99894,820],{"className":99895,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,99898,54879],{},[207,99900,2207],{"className":99901,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,99904,1721],{"className":99905,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran 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