[{"data":1,"prerenderedAt":100315},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-imek-blok-02":1626,"course-stats-imek":2164,"course-topics-imek":2168,"backlinks-imek-blok-02":100287,"related-imek-blok-02":100311},{"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":2163},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":1129,"description":1637,"extension":661,"meta":2149,"navigation":664,"path":2150,"seo":2151,"sources":2152,"stem":2153,"tags":2154,"type":2161,"updated":677,"__hash__":2162},"summaries\u002Fsummaries\u002Fimek-blok-02.md","KS 2. blok — Elasticita a produkce",{"type":9,"value":1631,"toc":2143},[1632,1635,1638,1642,1742,1746,2095,2099,2129,2133],[12,1633,1629],{"id":1634},"ks-2-blok-elasticita-a-produkce",[724,1636,1637],{},"Rozcestník druhého přednáškového bloku (19 stran). Pokrývá dvě hlavní témata, každé se samostatnou stránkou.",[115,1639,1641],{"id":1640},"témata-bloku-doporučené-pořadí","Témata bloku — doporučené pořadí",[152,1643,1644,1681],{},[123,1645,1646,1650,1651,1665,1666,1680],{},[207,1647,1649],{"className":1648,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," — motivační hypotéza (procentní růst ",[883,1652,1654],{"className":1653},[886],[888,1655,1656],{"xmlns":890},[892,1657,1658,1663],{},[895,1659,1660],{},[898,1661,1662],{},"Q",[902,1664,1662],{"encoding":904}," ≥ procentní pokles ",[883,1667,1669],{"className":1668},[886],[888,1670,1671],{"xmlns":890},[892,1672,1673,1678],{},[895,1674,1675],{},[898,1676,1677],{},"P",[902,1679,1677],{"encoding":904},"), cenová\u002Fkřížová\u002Fdůchodová elasticita poptávky, cenová elasticita nabídky, vícefaktorový model, pravidla pro TR, klasifikace (elastická \u002F jednotkově elastická \u002F neelastická).",[123,1682,1683,1687,1688,1713,1714,1741],{},[207,1684,1686],{"className":1685,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce — produkční funkce"," — jednofaktorový a dvoufaktorový model ",[883,1689,1691],{"className":1690},[886],[888,1692,1693],{"xmlns":890},[892,1694,1695,1710],{},[895,1696,1697,1699,1704,1707],{},[898,1698,1662],{},[1700,1701,1703],"mo",{"stretchy":1702},"false","(",[898,1705,1706],{},"L",[1700,1708,1709],{"stretchy":1702},")",[902,1711,1712],{"encoding":904},"Q(L)"," resp. ",[883,1715,1717],{"className":1716},[886],[888,1718,1719],{"xmlns":890},[892,1720,1721,1738],{},[895,1722,1723,1725,1727,1729,1733,1736],{},[898,1724,1662],{},[1700,1726,1703],{"stretchy":1702},[898,1728,1706],{},[1700,1730,1732],{"separator":1731},"true",",",[898,1734,1735],{},"K",[1700,1737,1709],{"stretchy":1702},[902,1739,1740],{"encoding":904},"Q(L, K)",", Cobb-Douglas, CES, lineární, Leontiefova funkce, mezní produkty, izokvanty, MRTS, výnosy z rozsahu, Eulerova věta.",[115,1743,1745],{"id":1744},"klíčové-vzorce-na-jeden-pohled","Klíčové vzorce na jeden pohled",[120,1747,1748,1803,1844,1903,1985,2049],{},[123,1749,1750,1751],{},"Cenová elasticita poptávky: ",[883,1752,1754],{"className":1753},[886],[888,1755,1756],{"xmlns":890},[892,1757,1758,1800],{},[895,1759,1760,1763,1766,1769,1780,1784,1794,1796,1798],{},[898,1761,1762],{},"E",[1700,1764,1765],{},"=",[1700,1767,1768],{},"−",[1770,1771,1773],"mstyle",{"scriptlevel":1772,"displaystyle":1731},"0",[1774,1775,1776,1778],"mfrac",{},[898,1777,1677],{},[898,1779,1662],{},[1781,1782,1783],"mtext",{}," ",[1785,1786,1787,1789],"msup",{},[898,1788,1662],{},[1700,1790,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},"normal","0em","′",[1700,1795,1703],{"stretchy":1702},[898,1797,1677],{},[1700,1799,1709],{"stretchy":1702},[902,1801,1802],{"encoding":904},"E = -\\dfrac{P}{Q}\\, Q'(P)",[123,1804,1805,1806],{},"Cenová elasticita nabídky: ",[883,1807,1809],{"className":1808},[886],[888,1810,1811],{"xmlns":890},[892,1812,1813,1841],{},[895,1814,1815,1817,1819,1827,1829,1835,1837,1839],{},[898,1816,1762],{},[1700,1818,1765],{},[1770,1820,1821],{"scriptlevel":1772,"displaystyle":1731},[1774,1822,1823,1825],{},[898,1824,1677],{},[898,1826,1662],{},[1781,1828,1783],{},[1785,1830,1831,1833],{},[898,1832,1662],{},[1700,1834,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,1836,1703],{"stretchy":1702},[898,1838,1677],{},[1700,1840,1709],{"stretchy":1702},[902,1842,1843],{"encoding":904},"E = \\dfrac{P}{Q}\\, Q'(P)",[123,1845,1846,1847,1883,1884,1709],{},"Cobb-Douglas: ",[883,1848,1850],{"className":1849},[886],[888,1851,1852],{"xmlns":890},[892,1853,1854,1880],{},[895,1855,1856,1858,1860,1863,1865,1871,1873],{},[898,1857,1662],{},[1700,1859,1765],{},[898,1861,1862],{},"A",[1781,1864,1783],{},[1785,1866,1867,1869],{},[898,1868,1706],{},[898,1870,207],{},[1781,1872,1783],{},[1785,1874,1875,1877],{},[898,1876,1735],{},[898,1878,1879],{},"b",[902,1881,1882],{"encoding":904},"Q = A\\, L^a\\, K^b"," (rostoucí\u002Fkonstantní\u002Fklesající výnosy podle ",[883,1885,1887],{"className":1886},[886],[888,1888,1889],{"xmlns":890},[892,1890,1891,1900],{},[895,1892,1893,1895,1898],{},[898,1894,207],{},[1700,1896,1897],{},"+",[898,1899,1879],{},[902,1901,1902],{"encoding":904},"a + b",[123,1904,1905,1906],{},"CES: ",[883,1907,1909],{"className":1908},[886],[888,1910,1911],{"xmlns":890},[892,1912,1913,1982],{},[895,1914,1915,1917,1919,1921],{},[898,1916,1662],{},[1700,1918,1765],{},[898,1920,1862],{},[1785,1922,1923,1971],{},[895,1924,1925,1928,1930,1934,1936,1938,1940,1942,1952,1954,1956,1958,1968],{},[1700,1926,1927],{"fence":1731},"[",[1700,1929,1703],{"stretchy":1702},[1931,1932,1933],"mn",{},"1",[1700,1935,1768],{},[898,1937,207],{},[1700,1939,1709],{"stretchy":1702},[1781,1941,1783],{},[1785,1943,1944,1946],{},[898,1945,1706],{},[895,1947,1948,1950],{},[1700,1949,1768],{},[898,1951,1879],{},[1700,1953,1897],{},[898,1955,207],{},[1781,1957,1783],{},[1785,1959,1960,1962],{},[898,1961,1735],{},[895,1963,1964,1966],{},[1700,1965,1768],{},[898,1967,1879],{},[1700,1969,1970],{"fence":1731},"]",[895,1972,1973,1975,1977,1980],{},[1700,1974,1768],{},[1931,1976,1933],{},[898,1978,1979],{"mathvariant":1791},"\u002F",[898,1981,1879],{},[902,1983,1984],{"encoding":904},"Q = A \\left[(1-a)\\, L^{-b} + a\\, K^{-b}\\right]^{-1\u002Fb}",[123,1986,1987,1988],{},"MRTS: ",[883,1989,1991],{"className":1990},[886],[888,1992,1993],{"xmlns":890},[892,1994,1995,2046],{},[895,1996,1997,2023,2025],{},[1770,1998,1999],{"scriptlevel":1772,"displaystyle":1731},[1774,2000,2001,2013],{},[895,2002,2003,2006],{},[898,2004,2005],{},"M",[2007,2008,2009,2011],"msub",{},[898,2010,1677],{},[898,2012,1706],{},[895,2014,2015,2017],{},[898,2016,2005],{},[2007,2018,2019,2021],{},[898,2020,1677],{},[898,2022,1735],{},[1700,2024,1765],{},[1770,2026,2027],{"scriptlevel":1772,"displaystyle":1731},[1774,2028,2029,2038],{},[2030,2031,2032,2034,2036],"msubsup",{},[898,2033,1662],{},[898,2035,1706],{},[1700,2037,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[2030,2039,2040,2042,2044],{},[898,2041,1662],{},[898,2043,1735],{},[1700,2045,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,2047,2048],{"encoding":904},"\\dfrac{MP_L}{MP_K} = \\dfrac{Q'_L}{Q'_K}",[123,2050,2051,2052],{},"Eulerova věta (n = 1): ",[883,2053,2055],{"className":2054},[886],[888,2056,2057],{"xmlns":890},[892,2058,2059,2092],{},[895,2060,2061,2063,2066,2068,2074,2076,2078,2080,2082,2088,2090],{},[898,2062,1706],{},[1700,2064,2065],{},"⋅",[898,2067,2005],{},[2007,2069,2070,2072],{},[898,2071,1677],{},[898,2073,1706],{},[1700,2075,1897],{},[898,2077,1735],{},[1700,2079,2065],{},[898,2081,2005],{},[2007,2083,2084,2086],{},[898,2085,1677],{},[898,2087,1735],{},[1700,2089,1765],{},[898,2091,1662],{},[902,2093,2094],{"encoding":904},"L \\cdot MP_L + K \\cdot MP_K = Q",[115,2096,2098],{"id":2097},"vazby","Vazby",[120,2100,2101,2120],{},[123,2102,2103,2106,2107,2110,2111,2114,2115,2119],{},[38,2104,2105],{},"Předchozí blok:"," ",[207,2108,1087],{"className":2109,"dataFsResolvedFilePath":745,"href":746},[210]," — kalkul (zejm. ",[207,2112,1145],{"className":2113,"dataFsResolvedFilePath":764,"href":765},[210]," a ",[207,2116,2118],{"className":2117,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," je nutný předpoklad)",[123,2121,2122,2106,2125,2128],{},[38,2123,2124],{},"Navazující blok:",[207,2126,1101],{"className":2127,"dataFsResolvedFilePath":868,"href":869},[210]," — užitečnost (paralela izokvanty ↔ indiferenční křivky)",[115,2130,2132],{"id":2131},"související","Související",[120,2134,2135],{},[123,2136,2137],{},[207,2138,2142],{"className":2139,"dataFsResolvedFilePath":2140,"href":2141},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","Kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":2144},[2145,2146,2147,2148],{"id":1640,"depth":642,"text":1641},{"id":1744,"depth":642,"text":1745},{"id":2097,"depth":642,"text":2098},{"id":2131,"depth":642,"text":2132},{},"\u002Fsummaries\u002Fimek-blok-02",{"title":1629,"description":1637},[1136],"summaries\u002Fimek-blok-02",[1128,2155,2156,2157,2158,2159,2160],"elasticita","produkce","cobb-douglas","ces","izokvanty","mrts","summary","mb17Curl0KaUEMv7ngk7L4dH249715rS9GMlaUzLIdI","summaries",{"zapisku":1625,"topics":2165,"summaries":2166,"outputs":2167},15,5,1,[2169,4051,9755,11308,12180,16463,18070,27950,36944,51011,55302,74646,86755,95714,96002],{"id":2170,"title":2171,"body":2172,"course":1128,"courses":659,"created":1129,"description":4039,"extension":661,"meta":4040,"navigation":664,"path":4041,"seo":4042,"sources":4043,"stem":4044,"tags":4045,"type":4049,"updated":677,"__hash__":4050},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":2173,"toc":4022},[2174,2177,2197,2201,2280,2283,2410,2557,2560,2640,2644,2703,2753,2762,2766,2902,2953,2957,3000,3068,3139,3147,3151,3189,3261,3265,3346,3394,3438,3442,3446,3516,3520,3570,3649,3656,3659,3712,3982,3986],[12,2175,2171],{"id":2176},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,2178,2179,2180,2184,2185,2188,2189,2192,2193,2196],{},"Matematický aparát kurzu ",[207,2181,2183],{"className":2182,"dataFsResolvedFilePath":2140,"href":2141},[210],"ImeK",". Bez derivace se neobejdou ",[38,2186,2187],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,2190,2191],{},"maximalizace zisku"," ani ",[38,2194,2195],{},"minimalizace nákladů",".",[115,2198,2200],{"id":2199},"funkce-a-polynomy","Funkce a polynomy",[724,2202,2203,2204,2231,2232,2245,2246,2259,2260,2196],{},"Funkce jedné proměnné ",[883,2205,2207],{"className":2206},[886],[888,2208,2209],{"xmlns":890},[892,2210,2211,2228],{},[895,2212,2213,2216,2218,2221,2223,2226],{},[898,2214,2215],{},"y",[1700,2217,1765],{},[898,2219,2220],{},"f",[1700,2222,1703],{"stretchy":1702},[898,2224,2225],{},"x",[1700,2227,1709],{"stretchy":1702},[902,2229,2230],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,2233,2235],{"className":2234},[886],[888,2236,2237],{"xmlns":890},[892,2238,2239,2243],{},[895,2240,2241],{},[898,2242,2225],{},[902,2244,2225],{"encoding":904}," (nezávislá) → ",[883,2247,2249],{"className":2248},[886],[888,2250,2251],{"xmlns":890},[892,2252,2253,2257],{},[895,2254,2255],{},[898,2256,2215],{},[902,2258,2215],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,2261,2263],{"className":2262},[886],[888,2264,2265],{"xmlns":890},[892,2266,2267,2277],{},[895,2268,2269,2271,2273,2275],{},[898,2270,2220],{},[1700,2272,1703],{"stretchy":1702},[898,2274,207],{},[1700,2276,1709],{"stretchy":1702},[902,2278,2279],{"encoding":904},"f(a)",[724,2281,2282],{},"Polynomy:",[120,2284,2285,2316,2358],{},[123,2286,2287],{},[152,2288,2289],{},[123,2290,2291,2292],{},"stupně: ",[883,2293,2295],{"className":2294},[886],[888,2296,2297],{"xmlns":890},[892,2298,2299,2313],{},[895,2300,2301,2303,2305,2307,2309,2311],{},[898,2302,2215],{},[1700,2304,1765],{},[898,2306,207],{},[898,2308,2225],{},[1700,2310,1897],{},[898,2312,1879],{},[902,2314,2315],{"encoding":904},"y = ax + b",[123,2317,2318],{},[152,2319,2320],{"start":642},[123,2321,2291,2322],{},[883,2323,2325],{"className":2324},[886],[888,2326,2327],{"xmlns":890},[892,2328,2329,2355],{},[895,2330,2331,2333,2335,2337,2344,2346,2348,2350,2352],{},[898,2332,2215],{},[1700,2334,1765],{},[898,2336,207],{},[1785,2338,2339,2341],{},[898,2340,2225],{},[1931,2342,2343],{},"2",[1700,2345,1897],{},[898,2347,1879],{},[898,2349,2225],{},[1700,2351,1897],{},[898,2353,2354],{},"c",[902,2356,2357],{"encoding":904},"y = ax^2 + bx + c",[123,2359,2360],{},[152,2361,2362],{"start":649},[123,2363,2291,2364],{},[883,2365,2367],{"className":2366},[886],[888,2368,2369],{"xmlns":890},[892,2370,2371,2407],{},[895,2372,2373,2375,2377,2379,2386,2388,2390,2396,2398,2400,2402,2404],{},[898,2374,2215],{},[1700,2376,1765],{},[898,2378,207],{},[1785,2380,2381,2383],{},[898,2382,2225],{},[1931,2384,2385],{},"3",[1700,2387,1897],{},[898,2389,1879],{},[1785,2391,2392,2394],{},[898,2393,2225],{},[1931,2395,2343],{},[1700,2397,1897],{},[898,2399,2354],{},[898,2401,2225],{},[1700,2403,1897],{},[898,2405,2406],{},"d",[902,2408,2409],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,2411,2412,2106,2415,2471,2472,2509,2510,2196],{},[38,2413,2414],{},"Příklad rozkladu:",[883,2416,2418],{"className":2417},[886],[888,2419,2420],{"xmlns":890},[892,2421,2422,2468],{},[895,2423,2424,2426,2428,2434,2436,2439,2441,2443,2446,2448,2450,2452,2454,2456,2458,2460,2462,2464,2466],{},[898,2425,2215],{},[1700,2427,1765],{},[1785,2429,2430,2432],{},[898,2431,2225],{},[1931,2433,2343],{},[1700,2435,1768],{},[1931,2437,2438],{},"5",[898,2440,2225],{},[1700,2442,1897],{},[1931,2444,2445],{},"6",[1700,2447,1765],{},[1700,2449,1703],{"stretchy":1702},[898,2451,2225],{},[1700,2453,1768],{},[1931,2455,2343],{},[1700,2457,1709],{"stretchy":1702},[1700,2459,1703],{"stretchy":1702},[898,2461,2225],{},[1700,2463,1768],{},[1931,2465,2385],{},[1700,2467,1709],{"stretchy":1702},[902,2469,2470],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,2473,2475],{"className":2474},[886],[888,2476,2477],{"xmlns":890},[892,2478,2479,2506],{},[895,2480,2481,2487,2489,2491,2493,2496,2502,2504],{},[2007,2482,2483,2485],{},[898,2484,2225],{},[1931,2486,1933],{},[1700,2488,1765],{},[1931,2490,2343],{},[1700,2492,1732],{"separator":1731},[1781,2494,2495],{}," ",[2007,2497,2498,2500],{},[898,2499,2225],{},[1931,2501,2343],{},[1700,2503,1765],{},[1931,2505,2385],{},[902,2507,2508],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,2511,2513],{"className":2512},[886],[888,2514,2515],{"xmlns":890},[892,2516,2517,2554],{},[895,2518,2519,2521,2523,2525,2527,2529,2537,2543,2545],{},[898,2520,2215],{},[1700,2522,1765],{},[1700,2524,1703],{"stretchy":1702},[898,2526,2225],{},[1700,2528,1768],{},[1770,2530,2531],{"scriptlevel":1772,"displaystyle":1702},[1774,2532,2533,2535],{},[1931,2534,2438],{},[1931,2536,2343],{},[1785,2538,2539,2541],{},[1700,2540,1709],{"stretchy":1702},[1931,2542,2343],{},[1700,2544,1768],{},[1770,2546,2547],{"scriptlevel":1772,"displaystyle":1702},[1774,2548,2549,2551],{},[1931,2550,1933],{},[1931,2552,2553],{},"4",[902,2555,2556],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,2558,2559],{"id":1145},"Derivace",[724,2561,2562,2563,1348,2587,2615,2616,2196],{},"Označení ",[883,2564,2566],{"className":2565},[886],[888,2567,2568],{"xmlns":890},[892,2569,2570,2584],{},[895,2571,2572,2578,2580,2582],{},[1785,2573,2574,2576],{},[898,2575,2220],{},[1700,2577,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,2579,1703],{"stretchy":1702},[898,2581,2225],{},[1700,2583,1709],{"stretchy":1702},[902,2585,2586],{"encoding":904},"f'(x)",[883,2588,2590],{"className":2589},[886],[888,2591,2592],{"xmlns":890},[892,2593,2594,2612],{},[895,2595,2596],{},[1770,2597,2598],{"scriptlevel":1772,"displaystyle":1731},[1774,2599,2600,2606],{},[895,2601,2602,2604],{},[898,2603,2406],{},[898,2605,2215],{},[895,2607,2608,2610],{},[898,2609,2406],{},[898,2611,2225],{},[902,2613,2614],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,2617,2619],{"className":2618},[886],[888,2620,2621],{"xmlns":890},[892,2622,2623,2637],{},[895,2624,2625,2631,2633,2635],{},[1785,2626,2627,2629],{},[898,2628,2220],{},[1700,2630,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,2632,1703],{"stretchy":1702},[898,2634,207],{},[1700,2636,1709],{"stretchy":1702},[902,2638,2639],{"encoding":904},"f'(a)",[198,2641,2643],{"id":2642},"geometrická-interpretace","Geometrická interpretace",[724,2645,2646,2669,2670,2673,2674,2702],{},[883,2647,2649],{"className":2648},[886],[888,2650,2651],{"xmlns":890},[892,2652,2653,2667],{},[895,2654,2655,2661,2663,2665],{},[1785,2656,2657,2659],{},[898,2658,2220],{},[1700,2660,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,2662,1703],{"stretchy":1702},[898,2664,207],{},[1700,2666,1709],{"stretchy":1702},[902,2668,2639],{"encoding":904}," = ",[38,2671,2672],{},"sklon tečny"," ke grafu funkce v bodě ",[883,2675,2677],{"className":2676},[886],[888,2678,2679],{"xmlns":890},[892,2680,2681,2699],{},[895,2682,2683,2685,2687,2689,2691,2693,2695,2697],{},[1700,2684,1927],{"stretchy":1702},[898,2686,207],{},[1700,2688,1732],{"separator":1731},[898,2690,2220],{},[1700,2692,1703],{"stretchy":1702},[898,2694,207],{},[1700,2696,1709],{"stretchy":1702},[1700,2698,1970],{"stretchy":1702},[902,2700,2701],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,2704,2705],{},[883,2706,2708],{"className":2707},[886],[888,2709,2710],{"xmlns":890},[892,2711,2712,2750],{},[895,2713,2714,2716,2718,2720,2722,2724,2726,2728,2734,2736,2738,2740,2742,2744,2746,2748],{},[898,2715,2215],{},[1700,2717,1768],{},[898,2719,2220],{},[1700,2721,1703],{"stretchy":1702},[898,2723,207],{},[1700,2725,1709],{"stretchy":1702},[1700,2727,1765],{},[1785,2729,2730,2732],{},[898,2731,2220],{},[1700,2733,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,2735,1703],{"stretchy":1702},[898,2737,207],{},[1700,2739,1709],{"stretchy":1702},[1700,2741,1703],{"stretchy":1702},[898,2743,2225],{},[1700,2745,1768],{},[898,2747,207],{},[1700,2749,1709],{"stretchy":1702},[902,2751,2752],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,2754,2755],{},[2756,2757],"img",{"alt":2758,"className":2759,"src":2761},"imek-derivace-tecna",[210,2760],"wikilink-broken","\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,2763,2765],{"id":2764},"inženýrská-interpretace","Inženýrská interpretace",[724,2767,2768,2669,2791,2106,2794,2807,2808,2821,2822,2840,2841,2854,2855,2868,2869,2882,2883,2901],{},[883,2769,2771],{"className":2770},[886],[888,2772,2773],{"xmlns":890},[892,2774,2775,2789],{},[895,2776,2777,2783,2785,2787],{},[1785,2778,2779,2781],{},[898,2780,2220],{},[1700,2782,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,2784,1703],{"stretchy":1702},[898,2786,207],{},[1700,2788,1709],{"stretchy":1702},[902,2790,2639],{"encoding":904},[38,2792,2793],{},"rychlost změny",[883,2795,2797],{"className":2796},[886],[888,2798,2799],{"xmlns":890},[892,2800,2801,2805],{},[895,2802,2803],{},[898,2804,2215],{},[902,2806,2215],{"encoding":904}," vzhledem k ",[883,2809,2811],{"className":2810},[886],[888,2812,2813],{"xmlns":890},[892,2814,2815,2819],{},[895,2816,2817],{},[898,2818,2225],{},[902,2820,2225],{"encoding":904}," v bodě ",[883,2823,2825],{"className":2824},[886],[888,2826,2827],{"xmlns":890},[892,2828,2829,2837],{},[895,2830,2831,2833,2835],{},[898,2832,2225],{},[1700,2834,1765],{},[898,2836,207],{},[902,2838,2839],{"encoding":904},"x = a","; přibližná změna ",[883,2842,2844],{"className":2843},[886],[888,2845,2846],{"xmlns":890},[892,2847,2848,2852],{},[895,2849,2850],{},[898,2851,2215],{},[902,2853,2215],{"encoding":904}," při změně ",[883,2856,2858],{"className":2857},[886],[888,2859,2860],{"xmlns":890},[892,2861,2862,2866],{},[895,2863,2864],{},[898,2865,2225],{},[902,2867,2225],{"encoding":904}," z ",[883,2870,2872],{"className":2871},[886],[888,2873,2874],{"xmlns":890},[892,2875,2876,2880],{},[895,2877,2878],{},[898,2879,207],{},[902,2881,207],{"encoding":904}," na ",[883,2884,2886],{"className":2885},[886],[888,2887,2888],{"xmlns":890},[892,2889,2890,2898],{},[895,2891,2892,2894,2896],{},[898,2893,207],{},[1700,2895,1897],{},[1931,2897,1933],{},[902,2899,2900],{"encoding":904},"a+1",":",[724,2903,2904],{},[883,2905,2907],{"className":2906},[886],[888,2908,2909],{"xmlns":890},[892,2910,2911,2950],{},[895,2912,2913,2915,2917,2919,2921,2923,2925,2928,2930,2932,2934,2936,2938,2944,2946,2948],{},[898,2914,2220],{},[1700,2916,1703],{"stretchy":1702},[898,2918,207],{},[1700,2920,1897],{},[1931,2922,1933],{},[1700,2924,1709],{"stretchy":1702},[1700,2926,2927],{},"≈",[898,2929,2220],{},[1700,2931,1703],{"stretchy":1702},[898,2933,207],{},[1700,2935,1709],{"stretchy":1702},[1700,2937,1897],{},[1785,2939,2940,2942],{},[898,2941,2220],{},[1700,2943,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,2945,1703],{"stretchy":1702},[898,2947,207],{},[1700,2949,1709],{"stretchy":1702},[902,2951,2952],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,2954,2956],{"id":2955},"příklad-mezní-náklady","Příklad — mezní náklady",[724,2958,2959,2960,2196],{},"Celkové náklady ",[883,2961,2963],{"className":2962},[886],[888,2964,2965],{"xmlns":890},[892,2966,2967,2997],{},[895,2968,2969,2972,2975,2977,2980,2982,2984,2986,2988,2991],{},[898,2970,2971],{},"T",[898,2973,2974],{},"C",[1700,2976,1765],{},[1931,2978,2979],{},"1000",[1700,2981,1897],{},[1931,2983,2343],{},[898,2985,1662],{},[1700,2987,1897],{},[1931,2989,2990],{},"0,1",[1785,2992,2993,2995],{},[898,2994,1662],{},[1931,2996,2343],{},[902,2998,2999],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,3001,3002,3003,3040,3041,2196],{},"Mezní náklady: ",[883,3004,3006],{"className":3005},[886],[888,3007,3008],{"xmlns":890},[892,3009,3010,3037],{},[895,3011,3012,3014,3016,3018,3020,3026,3028,3030,3032,3035],{},[898,3013,2005],{},[898,3015,2974],{},[1700,3017,1765],{},[898,3019,2971],{},[1785,3021,3022,3024],{},[898,3023,2974],{},[1700,3025,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,3027,1765],{},[1931,3029,2343],{},[1700,3031,1897],{},[1931,3033,3034],{},"0,2",[898,3036,1662],{},[902,3038,3039],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,3042,3044],{"className":3043},[886],[888,3045,3046],{"xmlns":890},[892,3047,3048,3065],{},[895,3049,3050,3052,3054,3056,3059,3061,3063],{},[898,3051,2005],{},[898,3053,2974],{},[1700,3055,1703],{"stretchy":1702},[1931,3057,3058],{},"10",[1700,3060,1709],{"stretchy":1702},[1700,3062,1765],{},[1931,3064,2553],{},[902,3066,3067],{"encoding":904},"MC(10) = 4",[724,3069,3070,2106,3073,3122,3123,2106,3126,2196],{},[38,3071,3072],{},"Skutečný přírůstek:",[883,3074,3076],{"className":3075},[886],[888,3077,3078],{"xmlns":890},[892,3079,3080,3119],{},[895,3081,3082,3085,3087,3089,3091,3093,3095,3097,3100,3102,3104,3106,3108,3110,3112,3114,3116],{},[898,3083,3084],{"mathvariant":1791},"Δ",[898,3086,2971],{},[898,3088,2974],{},[1700,3090,1765],{},[898,3092,2971],{},[898,3094,2974],{},[1700,3096,1703],{"stretchy":1702},[1931,3098,3099],{},"11",[1700,3101,1709],{"stretchy":1702},[1700,3103,1768],{},[898,3105,2971],{},[898,3107,2974],{},[1700,3109,1703],{"stretchy":1702},[1931,3111,3058],{},[1700,3113,1709],{"stretchy":1702},[1700,3115,1765],{},[1931,3117,3118],{},"4,2",[902,3120,3121],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[38,3124,3125],{},"Přibližný (lineární):",[883,3127,3129],{"className":3128},[886],[888,3130,3131],{"xmlns":890},[892,3132,3133,3137],{},[895,3134,3135],{},[1931,3136,2553],{},[902,3138,2553],{"encoding":904},[724,3140,3141,3142,3146],{},"(Viz aplikace v ",[207,3143,3145],{"className":3144,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,3148,3150],{"id":3149},"diferenciál","Diferenciál",[724,3152,3153],{},[883,3154,3156],{"className":3155},[886],[888,3157,3158],{"xmlns":890},[892,3159,3160,3186],{},[895,3161,3162,3164,3166,3168,3174,3176,3178,3180,3182,3184],{},[898,3163,2406],{},[898,3165,2220],{},[1700,3167,1765],{},[1785,3169,3170,3172],{},[898,3171,2220],{},[1700,3173,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,3175,1703],{"stretchy":1702},[898,3177,2225],{},[1700,3179,1709],{"stretchy":1702},[1781,3181,1783],{},[898,3183,2406],{},[898,3185,2225],{},[902,3187,3188],{"encoding":904},"df = f'(x)\\, dx",[724,3190,3191,3192,3208,3209,3257,3258,2196],{},"Pro malá ",[883,3193,3195],{"className":3194},[886],[888,3196,3197],{"xmlns":890},[892,3198,3199,3205],{},[895,3200,3201,3203],{},[898,3202,2406],{},[898,3204,2225],{},[902,3206,3207],{"encoding":904},"dx"," platí: ",[883,3210,3212],{"className":3211},[886],[888,3213,3214],{"xmlns":890},[892,3215,3216,3254],{},[895,3217,3218,3220,3222,3224,3226,3228,3230,3232,3234,3236,3238,3240,3242,3244,3246,3248,3250,3252],{},[898,3219,3084],{"mathvariant":1791},[898,3221,2220],{},[1700,3223,1765],{},[898,3225,2220],{},[1700,3227,1703],{"stretchy":1702},[898,3229,2225],{},[1700,3231,1897],{},[898,3233,2406],{},[898,3235,2225],{},[1700,3237,1709],{"stretchy":1702},[1700,3239,1768],{},[898,3241,2220],{},[1700,3243,1703],{"stretchy":1702},[898,3245,2225],{},[1700,3247,1709],{"stretchy":1702},[1700,3249,2927],{},[898,3251,2406],{},[898,3253,2220],{},[902,3255,3256],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,3259,3260],{},"lineární odhad přírůstku",[198,3262,3264],{"id":3263},"příklad","Příklad",[724,3266,3267,3298,3299,3324,3325,3345],{},[883,3268,3270],{"className":3269},[886],[888,3271,3272],{"xmlns":890},[892,3273,3274,3295],{},[895,3275,3276,3278,3280,3282,3285,3287,3289],{},[898,3277,2971],{},[898,3279,2974],{},[1700,3281,1765],{},[1931,3283,3284],{},"100",[1700,3286,1897],{},[1931,3288,2990],{},[1785,3290,3291,3293],{},[898,3292,1662],{},[1931,3294,2343],{},[902,3296,3297],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,3300,3302],{"className":3301},[886],[888,3303,3304],{"xmlns":890},[892,3305,3306,3321],{},[895,3307,3308,3310,3312,3315,3318],{},[898,3309,1662],{},[1700,3311,2901],{},[1931,3313,3314],{},"50",[1700,3316,3317],{},"→",[1931,3319,3320],{},"60",[902,3322,3323],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,3326,3328],{"className":3327},[886],[888,3329,3330],{"xmlns":890},[892,3331,3332,3342],{},[895,3333,3334,3336,3338,3340],{},[898,3335,2406],{},[898,3337,1662],{},[1700,3339,1765],{},[1931,3341,3058],{},[902,3343,3344],{"encoding":904},"dQ = 10","):",[724,3347,3348],{},[883,3349,3351],{"className":3350},[886],[888,3352,3353],{"xmlns":890},[892,3354,3355,3391],{},[895,3356,3357,3359,3361,3363,3365,3367,3369,3371,3373,3375,3377,3379,3381,3383,3385,3387,3389],{},[898,3358,2406],{},[898,3360,2971],{},[898,3362,2974],{},[1700,3364,1765],{},[1931,3366,3034],{},[898,3368,1662],{},[1700,3370,2065],{},[898,3372,2406],{},[898,3374,1662],{},[1700,3376,1765],{},[1931,3378,3034],{},[1700,3380,2065],{},[1931,3382,3314],{},[1700,3384,2065],{},[1931,3386,3058],{},[1700,3388,1765],{},[1931,3390,3284],{},[902,3392,3393],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,3395,3396,3397,3420,3421,3437],{},"Přesná změna: ",[883,3398,3400],{"className":3399},[886],[888,3401,3402],{"xmlns":890},[892,3403,3404,3417],{},[895,3405,3406,3408,3410,3412,3414],{},[898,3407,3084],{"mathvariant":1791},[898,3409,2971],{},[898,3411,2974],{},[1700,3413,1765],{},[1931,3415,3416],{},"110",[902,3418,3419],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,3422,3424],{"className":3423},[886],[888,3425,3426],{"xmlns":890},[892,3427,3428,3434],{},[895,3429,3430,3432],{},[898,3431,2971],{},[898,3433,2974],{},[902,3435,3436],{"encoding":904},"TC"," je konvexní.",[115,3439,3441],{"id":3440},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,3443,3445],{"id":3444},"nutná-podmínka","Nutná podmínka",[724,3447,3448,3449,2821,3469,3482,3483,3511,3512,3515],{},"Má-li ",[883,3450,3452],{"className":3451},[886],[888,3453,3454],{"xmlns":890},[892,3455,3456,3466],{},[895,3457,3458,3460,3462,3464],{},[898,3459,2220],{},[1700,3461,1703],{"stretchy":1702},[898,3463,2225],{},[1700,3465,1709],{"stretchy":1702},[902,3467,3468],{"encoding":904},"f(x)",[883,3470,3472],{"className":3471},[886],[888,3473,3474],{"xmlns":890},[892,3475,3476,3480],{},[895,3477,3478],{},[898,3479,207],{},[902,3481,207],{"encoding":904}," extrém, pak ",[883,3484,3486],{"className":3485},[886],[888,3487,3488],{"xmlns":890},[892,3489,3490,3508],{},[895,3491,3492,3498,3500,3502,3504,3506],{},[1785,3493,3494,3496],{},[898,3495,2220],{},[1700,3497,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,3499,1703],{"stretchy":1702},[898,3501,207],{},[1700,3503,1709],{"stretchy":1702},[1700,3505,1765],{},[1931,3507,1772],{},[902,3509,3510],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,3513,3514],{},"stacionární"," (podezřelé) body.",[198,3517,3519],{"id":3518},"postačující-podmínka","Postačující podmínka",[724,3521,3522,3523,3536,3537,2901],{},"Pro stacionární bod ",[883,3524,3526],{"className":3525},[886],[888,3527,3528],{"xmlns":890},[892,3529,3530,3534],{},[895,3531,3532],{},[898,3533,207],{},[902,3535,207],{"encoding":904},", je-li ",[883,3538,3540],{"className":3539},[886],[888,3541,3542],{"xmlns":890},[892,3543,3544,3567],{},[895,3545,3546,3556,3558,3560,3562,3565],{},[1785,3547,3548,3550],{},[898,3549,2220],{},[895,3551,3552,3554],{},[1700,3553,1793],{"mathvariant":1791},[1700,3555,1793],{"mathvariant":1791},[1700,3557,1703],{"stretchy":1702},[898,3559,207],{},[1700,3561,1709],{"stretchy":1702},[1700,3563,3564],{"mathvariant":1791},"≠",[1931,3566,1772],{},[902,3568,3569],{"encoding":904},"f''(a) \\neq 0",[120,3571,3572,3611],{},[123,3573,3574,3607,3608],{},[883,3575,3577],{"className":3576},[886],[888,3578,3579],{"xmlns":890},[892,3580,3581,3604],{},[895,3582,3583,3593,3595,3597,3599,3602],{},[1785,3584,3585,3587],{},[898,3586,2220],{},[895,3588,3589,3591],{},[1700,3590,1793],{"mathvariant":1791},[1700,3592,1793],{"mathvariant":1791},[1700,3594,1703],{"stretchy":1702},[898,3596,207],{},[1700,3598,1709],{"stretchy":1702},[1700,3600,3601],{},">",[1931,3603,1772],{},[902,3605,3606],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,3609,3610],{},"lokální minimum",[123,3612,3613,3607,3646],{},[883,3614,3616],{"className":3615},[886],[888,3617,3618],{"xmlns":890},[892,3619,3620,3643],{},[895,3621,3622,3632,3634,3636,3638,3641],{},[1785,3623,3624,3626],{},[898,3625,2220],{},[895,3627,3628,3630],{},[1700,3629,1793],{"mathvariant":1791},[1700,3631,1793],{"mathvariant":1791},[1700,3633,1703],{"stretchy":1702},[898,3635,207],{},[1700,3637,1709],{"stretchy":1702},[1700,3639,3640],{},"\u003C",[1931,3642,1772],{},[902,3644,3645],{"encoding":904},"f''(a) \u003C 0",[38,3647,3648],{},"lokální maximum",[724,3650,3651],{},[2756,3652],{"alt":3653,"className":3654,"src":3655},"imek-extremy-1d",[210,2760],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,3657,3264],{"id":3658},"příklad-1",[724,3660,3661],{},[883,3662,3664],{"className":3663},[886],[888,3665,3666],{"xmlns":890},[892,3667,3668,3709],{},[895,3669,3670,3672,3674,3676,3678,3680,3682,3688,3690,3692,3698,3700,3703,3705,3707],{},[898,3671,2220],{},[1700,3673,1703],{"stretchy":1702},[898,3675,2225],{},[1700,3677,1709],{"stretchy":1702},[1700,3679,1765],{},[1931,3681,2343],{},[1785,3683,3684,3686],{},[898,3685,2225],{},[1931,3687,2385],{},[1700,3689,1768],{},[1931,3691,2385],{},[1785,3693,3694,3696],{},[898,3695,2225],{},[1931,3697,2343],{},[1700,3699,1768],{},[1931,3701,3702],{},"12",[898,3704,2225],{},[1700,3706,1897],{},[1931,3708,2385],{},[902,3710,3711],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,3713,3714,3825,3865,3928],{},[123,3715,3716,3788,3789],{},[883,3717,3719],{"className":3718},[886],[888,3720,3721],{"xmlns":890},[892,3722,3723,3785],{},[895,3724,3725,3731,3733,3735,3737,3739,3741,3747,3749,3751,3753,3755,3757,3759,3761,3763,3765,3767,3769,3771,3773,3775,3777,3779,3781,3783],{},[1785,3726,3727,3729],{},[898,3728,2220],{},[1700,3730,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,3732,1703],{"stretchy":1702},[898,3734,2225],{},[1700,3736,1709],{"stretchy":1702},[1700,3738,1765],{},[1931,3740,2445],{},[1785,3742,3743,3745],{},[898,3744,2225],{},[1931,3746,2343],{},[1700,3748,1768],{},[1931,3750,2445],{},[898,3752,2225],{},[1700,3754,1768],{},[1931,3756,3702],{},[1700,3758,1765],{},[1931,3760,2445],{},[1700,3762,1703],{"stretchy":1702},[898,3764,2225],{},[1700,3766,1897],{},[1931,3768,1933],{},[1700,3770,1709],{"stretchy":1702},[1700,3772,1703],{"stretchy":1702},[898,3774,2225],{},[1700,3776,1768],{},[1931,3778,2343],{},[1700,3780,1709],{"stretchy":1702},[1700,3782,1765],{},[1931,3784,1772],{},[902,3786,3787],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,3790,3792],{"className":3791},[886],[888,3793,3794],{"xmlns":890},[892,3795,3796,3822],{},[895,3797,3798,3804,3806,3808,3810,3812,3818,3820],{},[2007,3799,3800,3802],{},[898,3801,2225],{},[1931,3803,1933],{},[1700,3805,1765],{},[1700,3807,1768],{},[1931,3809,1933],{},[1700,3811,1732],{"separator":1731},[2007,3813,3814,3816],{},[898,3815,2225],{},[1931,3817,2343],{},[1700,3819,1765],{},[1931,3821,2343],{},[902,3823,3824],{"encoding":904},"x_1 = -1, x_2 = 2",[123,3826,3827],{},[883,3828,3830],{"className":3829},[886],[888,3831,3832],{"xmlns":890},[892,3833,3834,3862],{},[895,3835,3836,3846,3848,3850,3852,3854,3856,3858,3860],{},[1785,3837,3838,3840],{},[898,3839,2220],{},[895,3841,3842,3844],{},[1700,3843,1793],{"mathvariant":1791},[1700,3845,1793],{"mathvariant":1791},[1700,3847,1703],{"stretchy":1702},[898,3849,2225],{},[1700,3851,1709],{"stretchy":1702},[1700,3853,1765],{},[1931,3855,3702],{},[898,3857,2225],{},[1700,3859,1768],{},[1931,3861,2445],{},[902,3863,3864],{"encoding":904},"f''(x) = 12x - 6",[123,3866,3867,3607,3908,3911,3912],{},[883,3868,3870],{"className":3869},[886],[888,3871,3872],{"xmlns":890},[892,3873,3874,3905],{},[895,3875,3876,3886,3888,3890,3892,3894,3896,3898,3901,3903],{},[1785,3877,3878,3880],{},[898,3879,2220],{},[895,3881,3882,3884],{},[1700,3883,1793],{"mathvariant":1791},[1700,3885,1793],{"mathvariant":1791},[1700,3887,1703],{"stretchy":1702},[1700,3889,1768],{},[1931,3891,1933],{},[1700,3893,1709],{"stretchy":1702},[1700,3895,1765],{},[1700,3897,1768],{},[1931,3899,3900],{},"18",[1700,3902,3640],{},[1931,3904,1772],{},[902,3906,3907],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,3909,3910],{},"maximum"," v ",[883,3913,3915],{"className":3914},[886],[888,3916,3917],{"xmlns":890},[892,3918,3919,3925],{},[895,3920,3921,3923],{},[1700,3922,1768],{},[1931,3924,1933],{},[902,3926,3927],{"encoding":904},"-1",[123,3929,3930,3607,3966,3911,3969],{},[883,3931,3933],{"className":3932},[886],[888,3934,3935],{"xmlns":890},[892,3936,3937,3963],{},[895,3938,3939,3949,3951,3953,3955,3957,3959,3961],{},[1785,3940,3941,3943],{},[898,3942,2220],{},[895,3944,3945,3947],{},[1700,3946,1793],{"mathvariant":1791},[1700,3948,1793],{"mathvariant":1791},[1700,3950,1703],{"stretchy":1702},[1931,3952,2343],{},[1700,3954,1709],{"stretchy":1702},[1700,3956,1765],{},[1931,3958,3900],{},[1700,3960,3601],{},[1931,3962,1772],{},[902,3964,3965],{"encoding":904},"f''(2) = 18 > 0",[38,3967,3968],{},"minimum",[883,3970,3972],{"className":3971},[886],[888,3973,3974],{"xmlns":890},[892,3975,3976,3980],{},[895,3977,3978],{},[1931,3979,2343],{},[902,3981,2343],{"encoding":904},[115,3983,3985],{"id":3984},"navigace","Navigace",[120,3987,3988,3996,4004],{},[123,3989,3990,2106,3993],{},[38,3991,3992],{},"Předchozí:",[207,3994,757],{"className":3995,"dataFsResolvedFilePath":755,"href":756},[210],[123,3997,3998,2106,4001],{},[38,3999,4000],{},"Navazující:",[207,4002,775],{"className":4003,"dataFsResolvedFilePath":773,"href":774},[210],[123,4005,4006,2106,4009,4012,4013,4017,4018,4021],{},[38,4007,4008],{},"Souvislosti:",[207,4010,784],{"className":4011,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,4014,4016],{"className":4015,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,4019,1649],{"className":4020,"dataFsResolvedFilePath":848,"href":849},[210]," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":4023},[4024,4025,4030,4033,4038],{"id":2199,"depth":642,"text":2200},{"id":1145,"depth":642,"text":2559,"children":4026},[4027,4028,4029],{"id":2642,"depth":649,"text":2643},{"id":2764,"depth":649,"text":2765},{"id":2955,"depth":649,"text":2956},{"id":3149,"depth":642,"text":3150,"children":4031},[4032],{"id":3263,"depth":649,"text":3264},{"id":3440,"depth":642,"text":3441,"children":4034},[4035,4036,4037],{"id":3444,"depth":649,"text":3445},{"id":3518,"depth":649,"text":3519},{"id":3658,"depth":649,"text":3264},{"id":3984,"depth":642,"text":3985},"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":2171,"description":4039},[1135],"topics\u002Fderivace",[1128,1145,4046,4047,4048],"diferencial","extremy","mezni-naklady","topic","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":4052,"title":4053,"body":4054,"course":1128,"courses":659,"created":9743,"description":641,"extension":661,"meta":9744,"navigation":664,"path":9745,"seo":9746,"sources":9747,"stem":9748,"tags":9749,"type":4049,"updated":677,"__hash__":9754},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":4055,"toc":9716},[4056,4059,4081,4085,4111,4115,4156,4247,4291,4295,4319,4326,4330,4340,4352,4356,4385,4394,4449,4455,4458,4464,4491,4497,4595,4755,5045,5049,5129,5135,5139,5237,5303,5471,5475,5553,5584,5611,5617,5649,5727,5814,5818,5881,5887,5890,5896,6010,6095,6139,6143,6189,6196,6513,6518,6542,6571,6638,6735,6739,6746,6753,6824,6944,7028,7031,7037,7364,7368,7531,7539,7675,7683,7921,7929,7932,7937,8193,8197,8371,8505,8542,8586,8589,8719,8809,8827,8831,8838,8844,8905,8908,8932,8935,8941,8944,8950,8953,8957,8995,9053,9242,9246,9319,9325,9332,9336,9342,9483,9487,9493,9529,9534,9711],[12,4057,4053],{"id":4058},"elasticita-poptávky-a-nabídky",[4060,4061,4062],"blockquote",{},[724,4063,4064,4067,4068,4070,4071,4074,4075,2114,4078,2196],{},[883,4065,4066],{},"!abstract"," TL;DR\n",[38,4069,1649],{}," 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: ",[38,4072,4073],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,4076,4077],{},"křížově-cenovou elasticitu",[38,4079,4080],{},"důchodovou elasticitu",[115,4082,4084],{"id":4083},"úvod-motivace","Úvod — motivace",[724,4086,4087,4088,4090,4091,4094,4095,4098,4099,4102,4103,4106,4107,4110],{},"Termín ",[614,4089,2155],{}," (alternativně ",[614,4092,4093],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,4096,4097],{},"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 ",[614,4100,4101],{},"cenové elasticity poptávky"," (resp. ",[614,4104,4105],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,4108,2559],{"className":4109,"dataFsResolvedFilePath":764,"href":765},[210],").",[198,4112,4114],{"id":4113},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,4116,4117,4118,4136,4137,4155],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,4119,4121],{"className":4120},[886],[888,4122,4123],{"xmlns":890},[892,4124,4125,4133],{},[895,4126,4127,4129,4131],{},[898,4128,1677],{},[1700,4130,1765],{},[1931,4132,3058],{},[902,4134,4135],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,4138,4140],{"className":4139},[886],[888,4141,4142],{"xmlns":890},[892,4143,4144,4152],{},[895,4145,4146,4148,4150],{},[898,4147,1662],{},[1700,4149,1765],{},[1931,4151,3284],{},[902,4153,4154],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,4157,4158,4204],{},[123,4159,4160,4163,4164,4203],{},[38,4161,4162],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,4165,4167],{"className":4166},[886],[888,4168,4169],{"xmlns":890},[892,4170,4171,4200],{},[895,4172,4173,4176,4179,4181,4183,4186,4188,4191,4193,4195,4197],{},[1781,4174,4175],{},"  ",[1700,4177,4178],{},"⇒",[1781,4180,4175],{},[898,4182,2971],{},[898,4184,4185],{},"R",[1700,4187,1765],{},[1931,4189,4190],{},"9",[1700,4192,2065],{},[1931,4194,3416],{},[1700,4196,1765],{},[1931,4198,4199],{},"990",[902,4201,4202],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,4205,4206,4209,4210,4246],{},[38,4207,4208],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,4211,4213],{"className":4212},[886],[888,4214,4215],{"xmlns":890},[892,4216,4217,4243],{},[895,4218,4219,4221,4223,4225,4227,4229,4231,4233,4235,4238,4240],{},[1781,4220,4175],{},[1700,4222,4178],{},[1781,4224,4175],{},[898,4226,2971],{},[898,4228,4185],{},[1700,4230,1765],{},[1931,4232,4190],{},[1700,4234,2065],{},[1931,4236,4237],{},"120",[1700,4239,1765],{},[1931,4241,4242],{},"1080",[902,4244,4245],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,4248,4249,4250,4253,4254,4257,4258,4261,4262,4265,4266,4269,4270,4286,4287,4290],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,4251,4252],{},"nerozumné",", na Trhu 2 ",[38,4255,4256],{},"rozumné",". Trh 2 je ",[38,4259,4260],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,4263,4264],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,4267,4268],{},"neelastická"," a vyššího ",[883,4271,4273],{"className":4272},[886],[888,4274,4275],{"xmlns":890},[892,4276,4277,4283],{},[895,4278,4279,4281],{},[898,4280,2971],{},[898,4282,4185],{},[902,4284,4285],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,4288,4289],{},"zvýšením"," ceny.",[198,4292,4294],{"id":4293},"hypotéza-41","Hypotéza 4.1",[4060,4296,4297],{},[724,4298,4299,4300],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,4301,4303],{"className":4302},[886],[888,4304,4305],{"xmlns":890},[892,4306,4307,4316],{},[895,4308,4309,4311,4314],{},[1700,4310,1703],{"stretchy":1702},[1931,4312,4313],{},"4.1",[1700,4315,1709],{"stretchy":1702},[902,4317,4318],{"encoding":904},"(4.1)",[724,4320,4321,4322,4325],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,4323,4324],{},"procentní změny"," obou faktorů.",[115,4327,4329],{"id":4328},"pojem-elasticity","Pojem elasticity",[724,4331,4332,4333,4335,4336,4339],{},"Obecně ",[38,4334,2155],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,4337,4338],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[4060,4341,4342],{},[724,4343,4344,4347,4348,4351],{},[883,4345,4346],{},"!info"," Intuice\nElasticitu lze číst jako ",[38,4349,4350],{},"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.",[115,4353,4355],{"id":4354},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,4357,4358,4359,4384],{},"Nechť ",[883,4360,4362],{"className":4361},[886],[888,4363,4364],{"xmlns":890},[892,4365,4366,4381],{},[895,4367,4368,4370,4372,4375,4377,4379],{},[898,4369,1662],{},[1700,4371,1765],{},[898,4373,4374],{},"D",[1700,4376,1703],{"stretchy":1702},[898,4378,1677],{},[1700,4380,1709],{"stretchy":1702},[902,4382,4383],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,4386,4387],{},[883,4388,4393],{"className":4389,"title":4391,"style":4392},[4390],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,4395,4396,4397,2114,4413,4429,4430,4448],{},"Znaménko minus je korekce: změny ",[883,4398,4400],{"className":4399},[886],[888,4401,4402],{"xmlns":890},[892,4403,4404,4410],{},[895,4405,4406,4408],{},[898,4407,3084],{"mathvariant":1791},[898,4409,1662],{},[902,4411,4412],{"encoding":904},"\\Delta Q",[883,4414,4416],{"className":4415},[886],[888,4417,4418],{"xmlns":890},[892,4419,4420,4426],{},[895,4421,4422,4424],{},[898,4423,3084],{"mathvariant":1791},[898,4425,1677],{},[902,4427,4428],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,4431,4433],{"className":4432},[886],[888,4434,4435],{"xmlns":890},[892,4436,4437,4445],{},[895,4438,4439],{},[1785,4440,4441,4443],{},[898,4442,1762],{},[898,4444,1862],{},[902,4446,4447],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,4450,4451],{},[883,4452,4454],{"className":4453,"title":4391,"style":4392},[4390],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,4456,4457],{},"Po dosazení:",[724,4459,4460],{},[883,4461,4463],{"className":4462,"title":4391,"style":4392},[4390],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,4465,4466,4467,4487,4488,4490],{},"Limitním přechodem ",[883,4468,4470],{"className":4469},[886],[888,4471,4472],{"xmlns":890},[892,4473,4474,4484],{},[895,4475,4476,4478,4480,4482],{},[898,4477,3084],{"mathvariant":1791},[898,4479,1677],{},[1700,4481,3317],{},[1931,4483,1772],{},[902,4485,4486],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,4489,4101],{}," (price elasticity of demand):",[724,4492,4493],{},[883,4494,4496],{"className":4495,"title":4391,"style":4392},[4390],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,4498,4499,4500,4523,4524,4547,4548,4572,4573,4594],{},"kde ",[883,4501,4503],{"className":4502},[886],[888,4504,4505],{"xmlns":890},[892,4506,4507,4521],{},[895,4508,4509,4511,4513,4515,4517,4519],{},[898,4510,1662],{},[1700,4512,1765],{},[898,4514,4374],{},[1700,4516,1703],{"stretchy":1702},[898,4518,1677],{},[1700,4520,1709],{"stretchy":1702},[902,4522,4383],{"encoding":904},". Pro pevnou cenu ",[883,4525,4527],{"className":4526},[886],[888,4528,4529],{"xmlns":890},[892,4530,4531,4544],{},[895,4532,4533,4535,4537],{},[898,4534,1677],{},[1700,4536,1765],{},[1785,4538,4539,4541],{},[898,4540,1677],{},[1700,4542,4543],{},"∗",[902,4545,4546],{"encoding":904},"P = P^*"," se ",[883,4549,4551],{"className":4550},[886],[888,4552,4553],{"xmlns":890},[892,4554,4555,4569],{},[895,4556,4557,4559,4561,4567],{},[898,4558,1762],{},[1700,4560,1703],{"stretchy":1702},[1785,4562,4563,4565],{},[898,4564,1677],{},[1700,4566,4543],{},[1700,4568,1709],{"stretchy":1702},[902,4570,4571],{"encoding":904},"E(P^*)"," nazývá ",[614,4574,4575,4576],{},"elasticita poptávky při ceně ",[883,4577,4579],{"className":4578},[886],[888,4580,4581],{"xmlns":890},[892,4582,4583,4591],{},[895,4584,4585],{},[1785,4586,4587,4589],{},[898,4588,1677],{},[1700,4590,4543],{},[902,4592,4593],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[4060,4596,4597],{},[724,4598,4599,4602,4603,4621,4622,4650,4651,4680,4681,1343,4699,1343,4717,4735,4736,4751,4752,2196],{},[883,4600,4601],{},"!warning"," Pozor na znaménko\nV (4.5) je ",[38,4604,4605,4606],{},"explicitní ",[883,4607,4609],{"className":4608},[886],[888,4610,4611],{"xmlns":890},[892,4612,4613,4619],{},[895,4614,4615,4617],{},[1700,4616,1768],{},[1931,4618,1933],{},[902,4620,3927],{"encoding":904}," právě proto, že ",[883,4623,4625],{"className":4624},[886],[888,4626,4627],{"xmlns":890},[892,4628,4629,4647],{},[895,4630,4631,4637,4639,4641,4643,4645],{},[1785,4632,4633,4635],{},[898,4634,1662],{},[1700,4636,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,4638,1703],{"stretchy":1702},[898,4640,1677],{},[1700,4642,1709],{"stretchy":1702},[1700,4644,3640],{},[1931,4646,1772],{},[902,4648,4649],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,4652,4654],{"className":4653},[886],[888,4655,4656],{"xmlns":890},[892,4657,4658,4677],{},[895,4659,4660,4662,4664,4670,4672,4675],{},[898,4661,1762],{},[1700,4663,1703],{"stretchy":1702},[1785,4665,4666,4668],{},[898,4667,1677],{},[1700,4669,4543],{},[1700,4671,1709],{"stretchy":1702},[1700,4673,4674],{},"≥",[1931,4676,1772],{},[902,4678,4679],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,4682,4684],{"className":4683},[886],[888,4685,4686],{"xmlns":890},[892,4687,4688,4696],{},[895,4689,4690,4692,4694],{},[898,4691,1762],{},[1700,4693,3601],{},[1931,4695,1933],{},[902,4697,4698],{"encoding":904},"E > 1",[883,4700,4702],{"className":4701},[886],[888,4703,4704],{"xmlns":890},[892,4705,4706,4714],{},[895,4707,4708,4710,4712],{},[898,4709,1762],{},[1700,4711,3640],{},[1931,4713,1933],{},[902,4715,4716],{"encoding":904},"E \u003C 1",[883,4718,4720],{"className":4719},[886],[888,4721,4722],{"xmlns":890},[892,4723,4724,4732],{},[895,4725,4726,4728,4730],{},[898,4727,1762],{},[1700,4729,1765],{},[1931,4731,1933],{},[902,4733,4734],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,4737,4739],{"className":4738},[886],[888,4740,4741],{"xmlns":890},[892,4742,4743,4749],{},[895,4744,4745,4747],{},[1700,4746,1768],{},[1931,4748,1933],{},[902,4750,3927],{"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 ",[38,4753,4754],{},"absolutní hodnotou",[4060,4756,4757,4777],{},[724,4758,4759,4762,4763,4776],{},[883,4760,4761],{},"!tip"," Postup: jak spočítat ",[883,4764,4766],{"className":4765},[886],[888,4767,4768],{"xmlns":890},[892,4769,4770,4774],{},[895,4771,4772],{},[898,4773,1762],{},[902,4775,1762],{"encoding":904}," v bodě",[152,4778,4779,4831,4870,4923,4988],{},[123,4780,4781,4782,4805,4806,4830],{},"Zapište ",[883,4783,4785],{"className":4784},[886],[888,4786,4787],{"xmlns":890},[892,4788,4789,4803],{},[895,4790,4791,4793,4795,4797,4799,4801],{},[898,4792,1662],{},[1700,4794,1765],{},[898,4796,4374],{},[1700,4798,1703],{"stretchy":1702},[898,4800,1677],{},[1700,4802,1709],{"stretchy":1702},[902,4804,4383],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,4807,4809],{"className":4808},[886],[888,4810,4811],{"xmlns":890},[892,4812,4813,4827],{},[895,4814,4815,4817,4819,4821,4823,4825],{},[898,4816,1677],{},[1700,4818,1765],{},[898,4820,4374],{},[1700,4822,1703],{"stretchy":1702},[898,4824,1662],{},[1700,4826,1709],{"stretchy":1702},[902,4828,4829],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,4832,4833,4834,2196],{},"Spočítejte derivaci ",[883,4835,4837],{"className":4836},[886],[888,4838,4839],{"xmlns":890},[892,4840,4841,4867],{},[895,4842,4843,4849,4851,4853,4855,4857,4859,4861,4863,4865],{},[1785,4844,4845,4847],{},[898,4846,1662],{},[1700,4848,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,4850,1703],{"stretchy":1702},[898,4852,1677],{},[1700,4854,1709],{"stretchy":1702},[1700,4856,1765],{},[898,4858,2406],{"mathvariant":1791},[898,4860,1662],{},[898,4862,1979],{"mathvariant":1791},[898,4864,2406],{"mathvariant":1791},[898,4866,1677],{},[902,4868,4869],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,4871,4872,4873,4890,4891,2196],{},"Dosaďte zadanou cenu ",[883,4874,4876],{"className":4875},[886],[888,4877,4878],{"xmlns":890},[892,4879,4880,4888],{},[895,4881,4882],{},[1785,4883,4884,4886],{},[898,4885,1677],{},[1700,4887,4543],{},[902,4889,4593],{"encoding":904}," a dopočítejte odpovídající ",[883,4892,4894],{"className":4893},[886],[888,4895,4896],{"xmlns":890},[892,4897,4898,4920],{},[895,4899,4900,4906,4908,4910,4912,4918],{},[1785,4901,4902,4904],{},[898,4903,1662],{},[1700,4905,4543],{},[1700,4907,1765],{},[898,4909,4374],{},[1700,4911,1703],{"stretchy":1702},[1785,4913,4914,4916],{},[898,4915,1677],{},[1700,4917,4543],{},[1700,4919,1709],{"stretchy":1702},[902,4921,4922],{"encoding":904},"Q^* = D(P^*)",[123,4924,4925,4926,2196],{},"Dosaďte do (4.5): ",[883,4927,4929],{"className":4928},[886],[888,4930,4931],{"xmlns":890},[892,4932,4933,4985],{},[895,4934,4935,4937,4939,4945,4947,4949,4951,4967,4969,4975,4977,4983],{},[898,4936,1762],{},[1700,4938,1703],{"stretchy":1702},[1785,4940,4941,4943],{},[898,4942,1677],{},[1700,4944,4543],{},[1700,4946,1709],{"stretchy":1702},[1700,4948,1765],{},[1700,4950,1768],{},[1770,4952,4953],{"scriptlevel":1772,"displaystyle":1731},[1774,4954,4955,4961],{},[1785,4956,4957,4959],{},[898,4958,1677],{},[1700,4960,4543],{},[1785,4962,4963,4965],{},[898,4964,1662],{},[1700,4966,4543],{},[1781,4968,1783],{},[1785,4970,4971,4973],{},[898,4972,1662],{},[1700,4974,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,4976,1703],{"stretchy":1702},[1785,4978,4979,4981],{},[898,4980,1677],{},[1700,4982,4543],{},[1700,4984,1709],{"stretchy":1702},[902,4986,4987],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,4989,4990,4991,5008,5009,5026,5027,5044],{},"Klasifikujte: ",[883,4992,4994],{"className":4993},[886],[888,4995,4996],{"xmlns":890},[892,4997,4998,5006],{},[895,4999,5000,5002,5004],{},[898,5001,1762],{},[1700,5003,3601],{},[1931,5005,1933],{},[902,5007,4698],{"encoding":904}," elastická, ",[883,5010,5012],{"className":5011},[886],[888,5013,5014],{"xmlns":890},[892,5015,5016,5024],{},[895,5017,5018,5020,5022],{},[898,5019,1762],{},[1700,5021,1765],{},[1931,5023,1933],{},[902,5025,4734],{"encoding":904}," jednotková, ",[883,5028,5030],{"className":5029},[886],[888,5031,5032],{"xmlns":890},[892,5033,5034,5042],{},[895,5035,5036,5038,5040],{},[898,5037,1762],{},[1700,5039,3640],{},[1931,5041,1933],{},[902,5043,4716],{"encoding":904}," neelastická.",[198,5046,5048],{"id":5047},"interpretace-46","Interpretace (4.6)",[4060,5050,5051],{},[724,5052,5053,5054,5077,5078,5091,5092,5109,5110],{},"Číslo ",[883,5055,5057],{"className":5056},[886],[888,5058,5059],{"xmlns":890},[892,5060,5061,5075],{},[895,5062,5063,5065,5067,5073],{},[898,5064,1762],{},[1700,5066,1703],{"stretchy":1702},[1785,5068,5069,5071],{},[898,5070,1677],{},[1700,5072,4543],{},[1700,5074,1709],{"stretchy":1702},[902,5076,4571],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,5079,5081],{"className":5080},[886],[888,5082,5083],{"xmlns":890},[892,5084,5085,5089],{},[895,5086,5087],{},[898,5088,1662],{},[902,5090,1662],{"encoding":904},", jestliže se cena ",[883,5093,5095],{"className":5094},[886],[888,5096,5097],{"xmlns":890},[892,5098,5099,5107],{},[895,5100,5101],{},[1785,5102,5103,5105],{},[898,5104,1677],{},[1700,5106,4543],{},[902,5108,4593],{"encoding":904}," změní o 1 %. ",[883,5111,5113],{"className":5112},[886],[888,5114,5115],{"xmlns":890},[892,5116,5117,5126],{},[895,5118,5119,5121,5124],{},[1700,5120,1703],{"stretchy":1702},[1931,5122,5123],{},"4.6",[1700,5125,1709],{"stretchy":1702},[902,5127,5128],{"encoding":904},"(4.6)",[724,5130,5131,5134],{},[38,5132,5133],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,5136,5138],{"id":5137},"příklad-41","Příklad 4.1",[724,5140,5141,5142,5176,5177,1343,5203,2901],{},"Poptávka ",[883,5143,5145],{"className":5144},[886],[888,5146,5147],{"xmlns":890},[892,5148,5149,5173],{},[895,5150,5151,5153,5155,5157,5159,5161,5163,5165,5167,5169,5171],{},[898,5152,1677],{},[1700,5154,1765],{},[898,5156,4374],{},[1700,5158,1703],{"stretchy":1702},[898,5160,1662],{},[1700,5162,1709],{"stretchy":1702},[1700,5164,1765],{},[1931,5166,3314],{},[1700,5168,1768],{},[1931,5170,2343],{},[898,5172,1662],{},[902,5174,5175],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,5178,5180],{"className":5179},[886],[888,5181,5182],{"xmlns":890},[892,5183,5184,5200],{},[895,5185,5186,5188,5190,5193,5195,5198],{},[898,5187,1662],{},[1700,5189,1765],{},[1931,5191,5192],{},"25",[1700,5194,1768],{},[1931,5196,5197],{},"0,5",[898,5199,1677],{},[902,5201,5202],{"encoding":904},"Q = 25 - 0{,}5P",[883,5204,5206],{"className":5205},[886],[888,5207,5208],{"xmlns":890},[892,5209,5210,5234],{},[895,5211,5212,5228,5230,5232],{},[1770,5213,5214],{"scriptlevel":1772,"displaystyle":1731},[1774,5215,5216,5222],{},[895,5217,5218,5220],{},[898,5219,2406],{"mathvariant":1791},[898,5221,1662],{},[895,5223,5224,5226],{},[898,5225,2406],{"mathvariant":1791},[898,5227,1677],{},[1700,5229,1765],{},[1700,5231,1768],{},[1931,5233,5197],{},[902,5235,5236],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,5238,5239],{},[883,5240,5242],{"className":5241},[886],[888,5243,5244],{"xmlns":890},[892,5245,5246,5300],{},[895,5247,5248,5250,5252,5254,5268,5270,5272,5274,5276,5278,5280,5298],{},[898,5249,1762],{},[1700,5251,1765],{},[1700,5253,1768],{},[1774,5255,5256,5258],{},[898,5257,1677],{},[895,5259,5260,5262,5264,5266],{},[1931,5261,5192],{},[1700,5263,1768],{},[1931,5265,5197],{},[898,5267,1677],{},[1700,5269,2065],{},[1700,5271,1703],{"stretchy":1702},[1700,5273,1768],{},[1931,5275,5197],{},[1700,5277,1709],{"stretchy":1702},[1700,5279,1765],{},[1774,5281,5282,5288],{},[895,5283,5284,5286],{},[1931,5285,5197],{},[898,5287,1677],{},[895,5289,5290,5292,5294,5296],{},[1931,5291,5192],{},[1700,5293,1768],{},[1931,5295,5197],{},[898,5297,1677],{},[898,5299,2196],{"mathvariant":1791},[902,5301,5302],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,5304,5305,5306,1343,5330,1343,5360,1343,5384,5409,5410,5433,5434,2882,5452,4110],{},"Potom ",[883,5307,5309],{"className":5308},[886],[888,5310,5311],{"xmlns":890},[892,5312,5313,5327],{},[895,5314,5315,5317,5319,5321,5323,5325],{},[898,5316,1762],{},[1700,5318,1703],{"stretchy":1702},[1931,5320,1772],{},[1700,5322,1709],{"stretchy":1702},[1700,5324,1765],{},[1931,5326,1772],{},[902,5328,5329],{"encoding":904},"E(0)=0",[883,5331,5333],{"className":5332},[886],[888,5334,5335],{"xmlns":890},[892,5336,5337,5357],{},[895,5338,5339,5341,5343,5345,5347,5349],{},[898,5340,1762],{},[1700,5342,1703],{"stretchy":1702},[1931,5344,3058],{},[1700,5346,1709],{"stretchy":1702},[1700,5348,1765],{},[1770,5350,5351],{"scriptlevel":1772,"displaystyle":1702},[1774,5352,5353,5355],{},[1931,5354,1933],{},[1931,5356,2553],{},[902,5358,5359],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,5361,5363],{"className":5362},[886],[888,5364,5365],{"xmlns":890},[892,5366,5367,5381],{},[895,5368,5369,5371,5373,5375,5377,5379],{},[898,5370,1762],{},[1700,5372,1703],{"stretchy":1702},[1931,5374,5192],{},[1700,5376,1709],{"stretchy":1702},[1700,5378,1765],{},[1931,5380,1933],{},[902,5382,5383],{"encoding":904},"E(25)=1",[883,5385,5387],{"className":5386},[886],[888,5388,5389],{"xmlns":890},[892,5390,5391,5406],{},[895,5392,5393,5395,5397,5400,5402,5404],{},[898,5394,1762],{},[1700,5396,1703],{"stretchy":1702},[1931,5398,5399],{},"40",[1700,5401,1709],{"stretchy":1702},[1700,5403,1765],{},[1931,5405,2553],{},[902,5407,5408],{"encoding":904},"E(40)=4",". Např. ",[883,5411,5413],{"className":5412},[886],[888,5414,5415],{"xmlns":890},[892,5416,5417,5431],{},[895,5418,5419,5421,5423,5425,5427,5429],{},[898,5420,1762],{},[1700,5422,1703],{"stretchy":1702},[1931,5424,5399],{},[1700,5426,1709],{"stretchy":1702},[1700,5428,1765],{},[1931,5430,2553],{},[902,5432,5408],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,5435,5437],{"className":5436},[886],[888,5438,5439],{"xmlns":890},[892,5440,5441,5449],{},[895,5442,5443,5445,5447],{},[898,5444,1662],{},[1700,5446,1765],{},[1931,5448,2438],{},[902,5450,5451],{"encoding":904},"Q=5",[883,5453,5455],{"className":5454},[886],[888,5456,5457],{"xmlns":890},[892,5458,5459,5468],{},[895,5460,5461,5463,5465],{},[898,5462,1662],{},[1700,5464,1765],{},[1931,5466,5467],{},"4,8",[902,5469,5470],{"encoding":904},"Q=4{,}8",[198,5472,5474],{"id":5473},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,5476,5477,5533],{},[123,5478,5479,5482,5483,5500,5501,2196],{},[38,5480,5481],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,5484,5486],{"className":5485},[886],[888,5487,5488],{"xmlns":890},[892,5489,5490,5498],{},[895,5491,5492],{},[1785,5493,5494,5496],{},[898,5495,1762],{},[898,5497,1862],{},[902,5499,4447],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,5502,5504],{"className":5503},[886],[888,5505,5506],{"xmlns":890},[892,5507,5508,5530],{},[895,5509,5510,5513,5515,5517,5519,5521,5523,5525,5527],{},[1700,5511,5512],{"stretchy":1702},"⟨",[898,5514,1677],{},[1700,5516,1732],{"separator":1731},[1781,5518,1783],{},[898,5520,1677],{},[1700,5522,1897],{},[898,5524,3084],{"mathvariant":1791},[898,5526,1677],{},[1700,5528,5529],{"stretchy":1702},"⟩",[902,5531,5532],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,5534,5535,5538,5539,5552],{},[38,5536,5537],{},"Bodová"," (okamžitá) elasticita: ",[883,5540,5542],{"className":5541},[886],[888,5543,5544],{"xmlns":890},[892,5545,5546,5550],{},[895,5547,5548],{},[898,5549,1762],{},[902,5551,1762],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,5554,5556,5557,5570,5571],{"id":5555},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,5558,5560],{"className":5559},[886],[888,5561,5562],{"xmlns":890},[892,5563,5564,5568],{},[895,5565,5566],{},[898,5567,1677],{},[902,5569,1677],{"encoding":904}," jako funkce ",[883,5572,5574],{"className":5573},[886],[888,5575,5576],{"xmlns":890},[892,5577,5578,5582],{},[895,5579,5580],{},[898,5581,1662],{},[902,5583,1662],{"encoding":904},[724,5585,5586,5587,5610],{},"Pokud je poptávka zadaná ve tvaru ",[883,5588,5590],{"className":5589},[886],[888,5591,5592],{"xmlns":890},[892,5593,5594,5608],{},[895,5595,5596,5598,5600,5602,5604,5606],{},[898,5597,1677],{},[1700,5599,1765],{},[898,5601,4374],{},[1700,5603,1703],{"stretchy":1702},[898,5605,1662],{},[1700,5607,1709],{"stretchy":1702},[902,5609,4829],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,5612,5613],{},[883,5614,5616],{"className":5615,"title":4391,"style":4392},[4390],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,5618,5619,2106,5622,5648],{},[38,5620,5621],{},"Příklad 4.3.",[883,5623,5625],{"className":5624},[886],[888,5626,5627],{"xmlns":890},[892,5628,5629,5645],{},[895,5630,5631,5633,5635,5637,5639],{},[898,5632,1677],{},[1700,5634,1765],{},[1931,5636,3284],{},[1700,5638,1768],{},[1785,5640,5641,5643],{},[898,5642,1662],{},[1931,5644,2343],{},[902,5646,5647],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,5650,5651],{},[883,5652,5654],{"className":5653},[886],[888,5655,5656],{"xmlns":890},[892,5657,5658,5724],{},[895,5659,5660,5662,5664,5666,5682,5684,5696,5698,5722],{},[898,5661,1762],{},[1700,5663,1765],{},[1700,5665,1768],{},[1774,5667,5668,5680],{},[895,5669,5670,5672,5674],{},[1931,5671,3284],{},[1700,5673,1768],{},[1785,5675,5676,5678],{},[898,5677,1662],{},[1931,5679,2343],{},[898,5681,1662],{},[1700,5683,2065],{},[1774,5685,5686,5688],{},[1931,5687,1933],{},[895,5689,5690,5692,5694],{},[1700,5691,1768],{},[1931,5693,2343],{},[898,5695,1662],{},[1700,5697,1765],{},[1774,5699,5700,5712],{},[895,5701,5702,5704,5706],{},[1931,5703,3284],{},[1700,5705,1768],{},[1785,5707,5708,5710],{},[898,5709,1662],{},[1931,5711,2343],{},[895,5713,5714,5716],{},[1931,5715,2343],{},[1785,5717,5718,5720],{},[898,5719,1662],{},[1931,5721,2343],{},[898,5723,2196],{"mathvariant":1791},[902,5725,5726],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,5728,5729,5730,5757,5758,5777,5778,2196],{},"Z rovnice ",[883,5731,5733],{"className":5732},[886],[888,5734,5735],{"xmlns":890},[892,5736,5737,5754],{},[895,5738,5739,5741,5743,5749,5751],{},[1931,5740,3284],{},[1700,5742,1768],{},[1785,5744,5745,5747],{},[898,5746,1662],{},[1931,5748,2343],{},[1700,5750,1765],{},[1931,5752,5753],{},"36",[902,5755,5756],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,5759,5761],{"className":5760},[886],[888,5762,5763],{"xmlns":890},[892,5764,5765,5774],{},[895,5766,5767,5769,5771],{},[898,5768,1662],{},[1700,5770,1765],{},[1931,5772,5773],{},"8",[902,5775,5776],{"encoding":904},"Q = 8",", tedy ",[883,5779,5781],{"className":5780},[886],[888,5782,5783],{"xmlns":890},[892,5784,5785,5811],{},[895,5786,5787,5789,5791,5793,5795,5797,5806,5808],{},[898,5788,1762],{},[1700,5790,1703],{"stretchy":1702},[1931,5792,5773],{},[1700,5794,1709],{"stretchy":1702},[1700,5796,1765],{},[1770,5798,5799],{"scriptlevel":1772,"displaystyle":1702},[1774,5800,5801,5803],{},[1931,5802,5753],{},[1931,5804,5805],{},"128",[1700,5807,1765],{},[1931,5809,5810],{},"0,281",[902,5812,5813],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,5815,5817],{"id":5816},"přibližné-změny","Přibližné změny",[724,5819,5820,5821,5857,5858,5880],{},"Diferenciál ",[883,5822,5824],{"className":5823},[886],[888,5825,5826],{"xmlns":890},[892,5827,5828,5854],{},[895,5829,5830,5832,5834,5836,5842,5844,5846,5848,5850,5852],{},[898,5831,2406],{"mathvariant":1791},[898,5833,1662],{},[1700,5835,1765],{},[1785,5837,5838,5840],{},[898,5839,1662],{},[1700,5841,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,5843,1703],{"stretchy":1702},[898,5845,1677],{},[1700,5847,1709],{"stretchy":1702},[1781,5849,1783],{},[898,5851,2406],{"mathvariant":1791},[898,5853,1677],{},[902,5855,5856],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,5859,5861],{"className":5860},[886],[888,5862,5863],{"xmlns":890},[892,5864,5865,5877],{},[895,5866,5867,5869,5871,5873,5875],{},[898,5868,2406],{"mathvariant":1791},[898,5870,1677],{},[1700,5872,1765],{},[898,5874,3084],{"mathvariant":1791},[898,5876,1677],{},[902,5878,5879],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,5882,5883],{},[883,5884,5886],{"className":5885,"title":4391,"style":4392},[4390],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,5888,5889],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,5891,5892],{},[883,5893,5895],{"className":5894,"title":4391,"style":4392},[4390],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,5897,5898,2106,5901,5936,5937,5956,5957,5991,5992,6009],{},[38,5899,5900],{},"Příklad 4.5.",[883,5902,5904],{"className":5903},[886],[888,5905,5906],{"xmlns":890},[892,5907,5908,5933],{},[895,5909,5910,5912,5914,5916,5922,5924,5926,5928,5930],{},[898,5911,1677],{},[1700,5913,1765],{},[1700,5915,1768],{},[1785,5917,5918,5920],{},[898,5919,1662],{},[1931,5921,2343],{},[1700,5923,1768],{},[1931,5925,2553],{},[898,5927,1662],{},[1700,5929,1897],{},[1931,5931,5932],{},"96",[902,5934,5935],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,5938,5940],{"className":5939},[886],[888,5941,5942],{"xmlns":890},[892,5943,5944,5953],{},[895,5945,5946,5948,5950],{},[898,5947,1677],{},[1700,5949,1765],{},[1931,5951,5952],{},"51",[902,5954,5955],{"encoding":904},"P=51",". Z rovnice ",[883,5958,5960],{"className":5959},[886],[888,5961,5962],{"xmlns":890},[892,5963,5964,5988],{},[895,5965,5966,5968,5970,5972,5978,5980,5982,5984,5986],{},[1931,5967,5952],{},[1700,5969,1765],{},[1700,5971,1768],{},[1785,5973,5974,5976],{},[898,5975,1662],{},[1931,5977,2343],{},[1700,5979,1768],{},[1931,5981,2553],{},[898,5983,1662],{},[1700,5985,1897],{},[1931,5987,5932],{},[902,5989,5990],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,5993,5995],{"className":5994},[886],[888,5996,5997],{"xmlns":890},[892,5998,5999,6007],{},[895,6000,6001,6003,6005],{},[898,6002,1662],{},[1700,6004,1765],{},[1931,6006,2438],{},[902,6008,5451],{"encoding":904},". Elasticita:",[724,6011,6012],{},[883,6013,6015],{"className":6014},[886],[888,6016,6017],{"xmlns":890},[892,6018,6019,6092],{},[895,6020,6021,6023,6025,6063,6065,6069,6071,6073,6075,6077,6079,6086,6089],{},[898,6022,1762],{},[1700,6024,1765],{},[1774,6026,6027,6047],{},[895,6028,6029,6031,6037,6039,6041,6043,6045],{},[1700,6030,1768],{},[1785,6032,6033,6035],{},[898,6034,1662],{},[1931,6036,2343],{},[1700,6038,1768],{},[1931,6040,2553],{},[898,6042,1662],{},[1700,6044,1897],{},[1931,6046,5932],{},[895,6048,6049,6051,6053,6055,6057,6059,6061],{},[898,6050,1662],{},[1700,6052,1703],{"stretchy":1702},[1931,6054,2343],{},[898,6056,1662],{},[1700,6058,1897],{},[1931,6060,2553],{},[1700,6062,1709],{"stretchy":1702},[1700,6064,1732],{"separator":1731},[6066,6067],"mspace",{"width":6068},"2em",[898,6070,1762],{},[1700,6072,1703],{"stretchy":1702},[1931,6074,2438],{},[1700,6076,1709],{"stretchy":1702},[1700,6078,1765],{},[1774,6080,6081,6083],{},[1931,6082,5952],{},[1931,6084,6085],{},"70",[1700,6087,6088],{},"≐",[1931,6090,6091],{},"0,728.",[902,6093,6094],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,6096,6097,6098,2196],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,6099,6101],{"className":6100},[886],[888,6102,6103],{"xmlns":890},[892,6104,6105,6136],{},[895,6106,6107,6109,6111,6114,6116,6118,6121,6123,6125,6127,6129,6132,6134],{},[898,6108,3084],{"mathvariant":1791},[898,6110,1662],{},[898,6112,6113],{"mathvariant":1791},"%",[1700,6115,2927],{},[1700,6117,1768],{},[1931,6119,6120],{},"0,728",[1700,6122,2065],{},[1931,6124,2343],{},[1700,6126,1765],{},[1700,6128,1768],{},[1931,6130,6131],{},"1,456",[1781,6133,1783],{},[898,6135,6113],{"mathvariant":1791},[902,6137,6138],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,6140,6142],{"id":6141},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,6144,6145,6146,6169,6170,2901],{},"V závislosti na hodnotě ",[883,6147,6149],{"className":6148},[886],[888,6150,6151],{"xmlns":890},[892,6152,6153,6167],{},[895,6154,6155,6157,6159,6165],{},[898,6156,1762],{},[1700,6158,1703],{"stretchy":1702},[1785,6160,6161,6163],{},[898,6162,1677],{},[1700,6164,4543],{},[1700,6166,1709],{"stretchy":1702},[902,6168,4571],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,6171,6173],{"className":6172},[886],[888,6174,6175],{"xmlns":890},[892,6176,6177,6186],{},[895,6178,6179,6181,6184],{},[1700,6180,1703],{"stretchy":1702},[1931,6182,6183],{},"4.7",[1700,6185,1709],{"stretchy":1702},[902,6187,6188],{"encoding":904},"(4.7)",[724,6190,6191],{},[2756,6192],{"alt":6193,"className":6194,"src":6195},"imek-typy-elasticity-5panelu",[210,2760],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,6197,6198,6237],{},[19,6199,6200],{},[22,6201,6202,6228,6231,6234],{},[25,6203,6204,6205],{},"Hodnota ",[883,6206,6208],{"className":6207},[886],[888,6209,6210],{"xmlns":890},[892,6211,6212,6226],{},[895,6213,6214,6216,6218,6224],{},[898,6215,1762],{},[1700,6217,1703],{"stretchy":1702},[1785,6219,6220,6222],{},[898,6221,1677],{},[1700,6223,4543],{},[1700,6225,1709],{"stretchy":1702},[902,6227,4571],{"encoding":904},[25,6229,6230],{},"Typ poptávky",[25,6232,6233],{},"Termín",[25,6235,6236],{},"Význam",[30,6238,6239,6272,6334,6409,6466],{},[22,6240,6241,6261,6266,6269],{},[35,6242,6243],{},[883,6244,6246],{"className":6245},[886],[888,6247,6248],{"xmlns":890},[892,6249,6250,6258],{},[895,6251,6252,6254,6256],{},[898,6253,1762],{},[1700,6255,1765],{},[1931,6257,1772],{},[902,6259,6260],{"encoding":904},"E = 0",[35,6262,6263],{},[38,6264,6265],{},"dokonale neelastická",[35,6267,6268],{},"perfectly inelastic",[35,6270,6271],{},"množství se nemění bez ohledu na cenu",[22,6273,6274,6298,6302,6305],{},[35,6275,6276],{},[883,6277,6279],{"className":6278},[886],[888,6280,6281],{"xmlns":890},[892,6282,6283,6295],{},[895,6284,6285,6287,6289,6291,6293],{},[1931,6286,1772],{},[1700,6288,3640],{},[898,6290,1762],{},[1700,6292,3640],{},[1931,6294,1933],{},[902,6296,6297],{"encoding":904},"0 \u003C E \u003C 1",[35,6299,6300],{},[38,6301,4268],{},[35,6303,6304],{},"inelastic",[35,6306,6307,6320,6321],{},[883,6308,6310],{"className":6309},[886],[888,6311,6312],{"xmlns":890},[892,6313,6314,6318],{},[895,6315,6316],{},[898,6317,1662],{},[902,6319,1662],{"encoding":904}," se mění pomaleji než ",[883,6322,6324],{"className":6323},[886],[888,6325,6326],{"xmlns":890},[892,6327,6328,6332],{},[895,6329,6330],{},[898,6331,1677],{},[902,6333,1677],{"encoding":904},[22,6335,6336,6355,6360,6363],{},[35,6337,6338],{},[883,6339,6341],{"className":6340},[886],[888,6342,6343],{"xmlns":890},[892,6344,6345,6353],{},[895,6346,6347,6349,6351],{},[898,6348,1762],{},[1700,6350,1765],{},[1931,6352,1933],{},[902,6354,4734],{"encoding":904},[35,6356,6357],{},[38,6358,6359],{},"jednotkově elastická",[35,6361,6362],{},"unit elastic",[35,6364,6365,6378,6379,6392,6393,6408],{},[883,6366,6368],{"className":6367},[886],[888,6369,6370],{"xmlns":890},[892,6371,6372,6376],{},[895,6373,6374],{},[898,6375,1662],{},[902,6377,1662],{"encoding":904}," i ",[883,6380,6382],{"className":6381},[886],[888,6383,6384],{"xmlns":890},[892,6385,6386,6390],{},[895,6387,6388],{},[898,6389,1677],{},[902,6391,1677],{"encoding":904}," se mění stejně rychle; ",[883,6394,6396],{"className":6395},[886],[888,6397,6398],{"xmlns":890},[892,6399,6400,6406],{},[895,6401,6402,6404],{},[898,6403,2971],{},[898,6405,4185],{},[902,6407,4285],{"encoding":904}," má maximum",[22,6410,6411,6430,6434,6437],{},[35,6412,6413],{},[883,6414,6416],{"className":6415},[886],[888,6417,6418],{"xmlns":890},[892,6419,6420,6428],{},[895,6421,6422,6424,6426],{},[898,6423,1762],{},[1700,6425,3601],{},[1931,6427,1933],{},[902,6429,4698],{"encoding":904},[35,6431,6432],{},[38,6433,4264],{},[35,6435,6436],{},"elastic",[35,6438,6439,6452,6453],{},[883,6440,6442],{"className":6441},[886],[888,6443,6444],{"xmlns":890},[892,6445,6446,6450],{},[895,6447,6448],{},[898,6449,1662],{},[902,6451,1662],{"encoding":904}," se mění rychleji než ",[883,6454,6456],{"className":6455},[886],[888,6457,6458],{"xmlns":890},[892,6459,6460,6464],{},[895,6461,6462],{},[898,6463,1677],{},[902,6465,1677],{"encoding":904},[22,6467,6468,6489,6494,6497],{},[35,6469,6470],{},[883,6471,6473],{"className":6472},[886],[888,6474,6475],{"xmlns":890},[892,6476,6477,6486],{},[895,6478,6479,6481,6483],{},[898,6480,1762],{},[1700,6482,3317],{},[898,6484,6485],{"mathvariant":1791},"∞",[902,6487,6488],{"encoding":904},"E \\to \\infty",[35,6490,6491],{},[38,6492,6493],{},"dokonale elastická",[35,6495,6496],{},"perfectly elastic",[35,6498,6499,6500],{},"sebemenší změna ceny úplně mění ",[883,6501,6503],{"className":6502},[886],[888,6504,6505],{"xmlns":890},[892,6506,6507,6511],{},[895,6508,6509],{},[898,6510,1662],{},[902,6512,1662],{"encoding":904},[724,6514,6515],{},[38,6516,6517],{},"Pravidlo růstu elasticity s cenou:",[4060,6519,6520],{},[724,6521,6522,6523],{},"S rostoucí cenou elasticita poptávky roste. ",[883,6524,6526],{"className":6525},[886],[888,6527,6528],{"xmlns":890},[892,6529,6530,6539],{},[895,6531,6532,6534,6537],{},[1700,6533,1703],{"stretchy":1702},[1931,6535,6536],{},"4.8",[1700,6538,1709],{"stretchy":1702},[902,6540,6541],{"encoding":904},"(4.8)",[724,6543,6544,6545,6548,6549,6552,6553,6570],{},"Z toho plyne, že při ",[614,6546,6547],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,6550,6551],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,6554,6556],{"className":6555},[886],[888,6557,6558],{"xmlns":890},[892,6559,6560,6568],{},[895,6561,6562],{},[1785,6563,6564,6566],{},[898,6565,1677],{},[1700,6567,4543],{},[902,6569,4593],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[4060,6572,6573,6578],{},[724,6574,6575,6577],{},[883,6576,4761],{}," Postup: jak klasifikovat poptávku",[152,6579,6580,6607,6610],{},[123,6581,6582,6583,6606],{},"Spočítejte ",[883,6584,6586],{"className":6585},[886],[888,6587,6588],{"xmlns":890},[892,6589,6590,6604],{},[895,6591,6592,6594,6596,6602],{},[898,6593,1762],{},[1700,6595,1703],{"stretchy":1702},[1785,6597,6598,6600],{},[898,6599,1677],{},[1700,6601,4543],{},[1700,6603,1709],{"stretchy":1702},[902,6605,4571],{"encoding":904}," dle (4.5).",[123,6608,6609],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,6611,6612,6613,6637],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,6614,6616],{"className":6615},[886],[888,6617,6618],{"xmlns":890},[892,6619,6620,6634],{},[895,6621,6622,6624,6626,6628,6630,6632],{},[898,6623,1762],{},[1700,6625,1703],{"stretchy":1702},[898,6627,1677],{},[1700,6629,1709],{"stretchy":1702},[1700,6631,1765],{},[1931,6633,1933],{},[902,6635,6636],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,6639,6640,6643,6644,6661,6662,6680,6681,6708,6709,2196],{},[38,6641,6642],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,6645,6647],{"className":6646},[886],[888,6648,6649],{"xmlns":890},[892,6650,6651,6659],{},[895,6652,6653,6655,6657],{},[898,6654,1762],{},[1700,6656,1765],{},[1931,6658,1933],{},[902,6660,4734],{"encoding":904}," pro ",[883,6663,6665],{"className":6664},[886],[888,6666,6667],{"xmlns":890},[892,6668,6669,6677],{},[895,6670,6671,6673,6675],{},[898,6672,1677],{},[1700,6674,1765],{},[1931,6676,5192],{},[902,6678,6679],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,6682,6684],{"className":6683},[886],[888,6685,6686],{"xmlns":890},[892,6687,6688,6705],{},[895,6689,6690,6692,6695,6697,6699,6701,6703],{},[898,6691,1677],{},[1700,6693,6694],{},"∈",[1700,6696,5512],{"stretchy":1702},[1931,6698,1772],{},[1700,6700,1732],{"separator":1731},[1931,6702,5192],{},[1700,6704,1709],{"stretchy":1702},[902,6706,6707],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,6710,6712],{"className":6711},[886],[888,6713,6714],{"xmlns":890},[892,6715,6716,6732],{},[895,6717,6718,6720,6722,6724,6726,6728,6730],{},[898,6719,1677],{},[1700,6721,6694],{},[1700,6723,1703],{"stretchy":1702},[1931,6725,5192],{},[1700,6727,1732],{"separator":1731},[1931,6729,3314],{},[1700,6731,5529],{"stretchy":1702},[902,6733,6734],{"encoding":904},"P \\in (25, 50\\rangle",[115,6736,6738],{"id":6737},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,6740,6741],{},[2756,6742],{"alt":6743,"className":6744,"src":6745},"imek-elasticita-tr",[210,2760],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,6747,6748],{},[2756,6749],{"alt":6750,"className":6751,"src":6752},"imek-elasticita-podel-linearni-poptavky",[210,2760],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,6754,6755,6756,6806,6807,6823],{},"Pro celkový příjem platí ",[883,6757,6759],{"className":6758},[886],[888,6760,6761],{"xmlns":890},[892,6762,6763,6803],{},[895,6764,6765,6767,6769,6771,6773,6775,6777,6779,6781,6783,6785,6787,6789,6791,6793,6795,6797,6799,6801],{},[898,6766,2971],{},[898,6768,4185],{},[1700,6770,1765],{},[898,6772,2971],{},[898,6774,4185],{},[1700,6776,1703],{"stretchy":1702},[898,6778,1662],{},[1700,6780,1709],{"stretchy":1702},[1700,6782,1765],{},[898,6784,1677],{},[1700,6786,2065],{},[898,6788,1662],{},[1700,6790,1765],{},[898,6792,1662],{},[1700,6794,2065],{},[898,6796,4374],{},[1700,6798,1703],{"stretchy":1702},[898,6800,1662],{},[1700,6802,1709],{"stretchy":1702},[902,6804,6805],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,6808,6810],{"className":6809},[886],[888,6811,6812],{"xmlns":890},[892,6813,6814,6820],{},[895,6815,6816,6818],{},[898,6817,2005],{},[898,6819,4185],{},[902,6821,6822],{"encoding":904},"MR"," odvodíme:",[724,6825,6826],{},[883,6827,6829],{"className":6828},[886],[888,6830,6831],{"xmlns":890},[892,6832,6833,6941],{},[895,6834,6835,6837,6839,6841,6843,6849,6851,6853,6855,6857,6859,6861,6863,6865,6867,6869,6871,6877,6879,6881,6883,6885,6887,6889,6891,6905,6907,6909],{},[898,6836,2005],{},[898,6838,4185],{},[1700,6840,1765],{},[898,6842,2971],{},[1785,6844,6845,6847],{},[898,6846,4185],{},[1700,6848,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,6850,1703],{"stretchy":1702},[898,6852,1662],{},[1700,6854,1709],{"stretchy":1702},[1700,6856,1765],{},[898,6858,4374],{},[1700,6860,1703],{"stretchy":1702},[898,6862,1662],{},[1700,6864,1709],{"stretchy":1702},[1700,6866,1897],{},[898,6868,1662],{},[1781,6870,1783],{},[1785,6872,6873,6875],{},[898,6874,4374],{},[1700,6876,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,6878,1703],{"stretchy":1702},[898,6880,1662],{},[1700,6882,1709],{"stretchy":1702},[1700,6884,1765],{},[898,6886,1677],{},[1700,6888,1897],{},[898,6890,1662],{},[1774,6892,6893,6899],{},[895,6894,6895,6897],{},[898,6896,2406],{"mathvariant":1791},[898,6898,1677],{},[895,6900,6901,6903],{},[898,6902,2406],{"mathvariant":1791},[898,6904,1662],{},[1700,6906,1765],{},[898,6908,1677],{},[895,6910,6911,6913,6915,6917,6923,6925,6939],{},[1700,6912,1703],{"fence":1731},[1931,6914,1933],{},[1700,6916,1897],{},[1774,6918,6919,6921],{},[898,6920,1662],{},[898,6922,1677],{},[1700,6924,2065],{},[1774,6926,6927,6933],{},[895,6928,6929,6931],{},[898,6930,2406],{"mathvariant":1791},[898,6932,1677],{},[895,6934,6935,6937],{},[898,6936,2406],{"mathvariant":1791},[898,6938,1662],{},[1700,6940,1709],{"fence":1731},[902,6942,6943],{"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)",[724,6945,6946],{},[883,6947,6949],{"className":6948},[886],[888,6950,6951],{"xmlns":890},[892,6952,6953,7025],{},[895,6954,6955,6957,6959,7001,7003,7005],{},[1700,6956,1765],{},[898,6958,1677],{},[895,6960,6961,6963,6965,6967,6999],{},[1700,6962,1703],{"fence":1731},[1931,6964,1933],{},[1700,6966,1897],{},[1774,6968,6969,6971],{},[1931,6970,1933],{},[895,6972,6973,6981,6983],{},[1770,6974,6975],{"scriptlevel":1772,"displaystyle":1702},[1774,6976,6977,6979],{},[898,6978,1677],{},[898,6980,1662],{},[1700,6982,2065],{},[1770,6984,6985],{"scriptlevel":1772,"displaystyle":1702},[1774,6986,6987,6993],{},[895,6988,6989,6991],{},[898,6990,2406],{"mathvariant":1791},[898,6992,1662],{},[895,6994,6995,6997],{},[898,6996,2406],{"mathvariant":1791},[898,6998,1677],{},[1700,7000,1709],{"fence":1731},[1700,7002,1765],{},[898,7004,1677],{},[895,7006,7007,7009,7011,7013,7023],{},[1700,7008,1703],{"fence":1731},[1931,7010,1933],{},[1700,7012,1897],{},[1774,7014,7015,7017],{},[1931,7016,1933],{},[895,7018,7019,7021],{},[1700,7020,1768],{},[898,7022,1762],{},[1700,7024,1709],{"fence":1731},[902,7026,7027],{"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)",[724,7029,7030],{},"a tedy",[724,7032,7033],{},[883,7034,7036],{"className":7035,"title":4391,"style":4392},[4390],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[4060,7038,7039,7108,7358],{},[724,7040,7041,7043,7044,7078,7079,7094,7095,2901],{},[883,7042,4346],{}," Intuice: vztah ",[883,7045,7047],{"className":7046},[886],[888,7048,7049],{"xmlns":890},[892,7050,7051,7075],{},[895,7052,7053,7055,7057,7059,7061,7063,7065,7067,7069,7071,7073],{},[898,7054,2005],{},[898,7056,4185],{},[1700,7058,1765],{},[898,7060,1677],{},[1700,7062,1703],{"stretchy":1702},[1931,7064,1933],{},[1700,7066,1768],{},[1931,7068,1933],{},[898,7070,1979],{"mathvariant":1791},[898,7072,1762],{},[1700,7074,1709],{"stretchy":1702},[902,7076,7077],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,7080,7082],{"className":7081},[886],[888,7083,7084],{"xmlns":890},[892,7085,7086,7092],{},[895,7087,7088,7090],{},[898,7089,2005],{},[898,7091,4185],{},[902,7093,6822],{"encoding":904}," jednoznačně určuje hodnota ",[883,7096,7098],{"className":7097},[886],[888,7099,7100],{"xmlns":890},[892,7101,7102,7106],{},[895,7103,7104],{},[898,7105,1762],{},[902,7107,1762],{"encoding":904},[120,7109,7110,7220,7289],{},[123,7111,7112,7129,7130,2106,7144,2106,7170,2106,7183,7203,7204,7219],{},[883,7113,7115],{"className":7114},[886],[888,7116,7117],{"xmlns":890},[892,7118,7119,7127],{},[895,7120,7121,7123,7125],{},[898,7122,1762],{},[1700,7124,3601],{},[1931,7126,1933],{},[902,7128,4698],{"encoding":904}," (elastická) ",[883,7131,7133],{"className":7132},[886],[888,7134,7135],{"xmlns":890},[892,7136,7137,7141],{},[895,7138,7139],{},[1700,7140,4178],{},[902,7142,7143],{"encoding":904},"\\Rightarrow",[883,7145,7147],{"className":7146},[886],[888,7148,7149],{"xmlns":890},[892,7150,7151,7167],{},[895,7152,7153,7155,7157,7159,7161,7163,7165],{},[1931,7154,1933],{},[1700,7156,1768],{},[1931,7158,1933],{},[898,7160,1979],{"mathvariant":1791},[898,7162,1762],{},[1700,7164,3601],{},[1931,7166,1772],{},[902,7168,7169],{"encoding":904},"1 - 1\u002FE > 0",[883,7171,7173],{"className":7172},[886],[888,7174,7175],{"xmlns":890},[892,7176,7177,7181],{},[895,7178,7179],{},[1700,7180,4178],{},[902,7182,7143],{"encoding":904},[883,7184,7186],{"className":7185},[886],[888,7187,7188],{"xmlns":890},[892,7189,7190,7200],{},[895,7191,7192,7194,7196,7198],{},[898,7193,2005],{},[898,7195,4185],{},[1700,7197,3601],{},[1931,7199,1772],{},[902,7201,7202],{"encoding":904},"MR > 0"," — ",[883,7205,7207],{"className":7206},[886],[888,7208,7209],{"xmlns":890},[892,7210,7211,7217],{},[895,7212,7213,7215],{},[898,7214,2971],{},[898,7216,4185],{},[902,7218,4285],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,7221,7222,7239,7240,2106,7253,7203,7273,7288],{},[883,7223,7225],{"className":7224},[886],[888,7226,7227],{"xmlns":890},[892,7228,7229,7237],{},[895,7230,7231,7233,7235],{},[898,7232,1762],{},[1700,7234,1765],{},[1931,7236,1933],{},[902,7238,4734],{"encoding":904}," (jednotková) ",[883,7241,7243],{"className":7242},[886],[888,7244,7245],{"xmlns":890},[892,7246,7247,7251],{},[895,7248,7249],{},[1700,7250,4178],{},[902,7252,7143],{"encoding":904},[883,7254,7256],{"className":7255},[886],[888,7257,7258],{"xmlns":890},[892,7259,7260,7270],{},[895,7261,7262,7264,7266,7268],{},[898,7263,2005],{},[898,7265,4185],{},[1700,7267,1765],{},[1931,7269,1772],{},[902,7271,7272],{"encoding":904},"MR = 0",[883,7274,7276],{"className":7275},[886],[888,7277,7278],{"xmlns":890},[892,7279,7280,7286],{},[895,7281,7282,7284],{},[898,7283,2971],{},[898,7285,4185],{},[902,7287,4285],{"encoding":904}," je extrém (maximum).",[123,7290,7291,7308,7309,2106,7322,7203,7342,7357],{},[883,7292,7294],{"className":7293},[886],[888,7295,7296],{"xmlns":890},[892,7297,7298,7306],{},[895,7299,7300,7302,7304],{},[898,7301,1762],{},[1700,7303,3640],{},[1931,7305,1933],{},[902,7307,4716],{"encoding":904}," (neelastická) ",[883,7310,7312],{"className":7311},[886],[888,7313,7314],{"xmlns":890},[892,7315,7316,7320],{},[895,7317,7318],{},[1700,7319,4178],{},[902,7321,7143],{"encoding":904},[883,7323,7325],{"className":7324},[886],[888,7326,7327],{"xmlns":890},[892,7328,7329,7339],{},[895,7330,7331,7333,7335,7337],{},[898,7332,2005],{},[898,7334,4185],{},[1700,7336,3640],{},[1931,7338,1772],{},[902,7340,7341],{"encoding":904},"MR \u003C 0",[883,7343,7345],{"className":7344},[886],[888,7346,7347],{"xmlns":890},[892,7348,7349,7355],{},[895,7350,7351,7353],{},[898,7352,2971],{},[898,7354,4185],{},[902,7356,4285],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,7359,7360,7361,2196],{},"Viz také ",[207,7362,4016],{"className":7363,"dataFsResolvedFilePath":827,"href":828},[210],[198,7365,7367],{"id":7366},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,7369,7370,7390,7391,7417,7418,7433,7434,7447,7448,7461,7462,7475,7476,7492,7493,2106,7508,7511,7512,7492,7528,2196],{},[38,7371,7372,7373,4110],{},"(a) Poptávka elastická (",[883,7374,7376],{"className":7375},[886],[888,7377,7378],{"xmlns":890},[892,7379,7380,7388],{},[895,7381,7382,7384,7386],{},[898,7383,1762],{},[1700,7385,3601],{},[1931,7387,1933],{},[902,7389,4698],{"encoding":904}," Z (4.12) plyne ",[883,7392,7394],{"className":7393},[886],[888,7395,7396],{"xmlns":890},[892,7397,7398,7414],{},[895,7399,7400,7402,7404,7406,7408,7410,7412],{},[898,7401,2005],{},[898,7403,4185],{},[1700,7405,1703],{"stretchy":1702},[898,7407,1662],{},[1700,7409,1709],{"stretchy":1702},[1700,7411,3601],{},[1931,7413,1772],{},[902,7415,7416],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,7419,7421],{"className":7420},[886],[888,7422,7423],{"xmlns":890},[892,7424,7425,7431],{},[895,7426,7427,7429],{},[898,7428,2971],{},[898,7430,4185],{},[902,7432,4285],{"encoding":904}," je rostoucí funkcí ",[883,7435,7437],{"className":7436},[886],[888,7438,7439],{"xmlns":890},[892,7440,7441,7445],{},[895,7442,7443],{},[898,7444,1662],{},[902,7446,1662],{"encoding":904},". Avšak růst ",[883,7449,7451],{"className":7450},[886],[888,7452,7453],{"xmlns":890},[892,7454,7455,7459],{},[895,7456,7457],{},[898,7458,1662],{},[902,7460,1662],{"encoding":904}," je odezvou na pokles ceny ",[883,7463,7465],{"className":7464},[886],[888,7466,7467],{"xmlns":890},[892,7468,7469,7473],{},[895,7470,7471],{},[898,7472,1677],{},[902,7474,1677],{"encoding":904},". Tudíž s ",[614,7477,7478,7479],{},"poklesem ceny ",[883,7480,7482],{"className":7481},[886],[888,7483,7484],{"xmlns":890},[892,7485,7486,7490],{},[895,7487,7488],{},[898,7489,1677],{},[902,7491,1677],{"encoding":904}," celkový příjem ",[883,7494,7496],{"className":7495},[886],[888,7497,7498],{"xmlns":890},[892,7499,7500,7506],{},[895,7501,7502,7504],{},[898,7503,2971],{},[898,7505,4185],{},[902,7507,4285],{"encoding":904},[614,7509,7510],{},"roste"," a s ",[614,7513,7514,7515],{},"růstem ceny ",[883,7516,7518],{"className":7517},[886],[888,7519,7520],{"xmlns":890},[892,7521,7522,7526],{},[895,7523,7524],{},[898,7525,1677],{},[902,7527,1677],{"encoding":904},[614,7529,7530],{},"klesá",[4060,7532,7533],{},[724,7534,7535,7538],{},[38,7536,7537],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,7540,7541,7390,7561,1343,7587,7602,7603,7616,7617,7630,7631,7644,7645,7492,7658,2106,7673,2196],{},[38,7542,7543,7544,4110],{},"(b) Poptávka neelastická (",[883,7545,7547],{"className":7546},[886],[888,7548,7549],{"xmlns":890},[892,7550,7551,7559],{},[895,7552,7553,7555,7557],{},[898,7554,1762],{},[1700,7556,3640],{},[1931,7558,1933],{},[902,7560,4716],{"encoding":904},[883,7562,7564],{"className":7563},[886],[888,7565,7566],{"xmlns":890},[892,7567,7568,7584],{},[895,7569,7570,7572,7574,7576,7578,7580,7582],{},[898,7571,2005],{},[898,7573,4185],{},[1700,7575,1703],{"stretchy":1702},[898,7577,1662],{},[1700,7579,1709],{"stretchy":1702},[1700,7581,3640],{},[1931,7583,1772],{},[902,7585,7586],{"encoding":904},"MR(Q) \u003C 0",[883,7588,7590],{"className":7589},[886],[888,7591,7592],{"xmlns":890},[892,7593,7594,7600],{},[895,7595,7596,7598],{},[898,7597,2971],{},[898,7599,4185],{},[902,7601,4285],{"encoding":904}," je klesající funkce ",[883,7604,7606],{"className":7605},[886],[888,7607,7608],{"xmlns":890},[892,7609,7610,7614],{},[895,7611,7612],{},[898,7613,1662],{},[902,7615,1662],{"encoding":904},", tj. s růstem ",[883,7618,7620],{"className":7619},[886],[888,7621,7622],{"xmlns":890},[892,7623,7624,7628],{},[895,7625,7626],{},[898,7627,1662],{},[902,7629,1662],{"encoding":904}," (s poklesem ceny ",[883,7632,7634],{"className":7633},[886],[888,7635,7636],{"xmlns":890},[892,7637,7638,7642],{},[895,7639,7640],{},[898,7641,1677],{},[902,7643,1677],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,7646,7648],{"className":7647},[886],[888,7649,7650],{"xmlns":890},[892,7651,7652,7656],{},[895,7653,7654],{},[898,7655,1677],{},[902,7657,1677],{"encoding":904},[883,7659,7661],{"className":7660},[886],[888,7662,7663],{"xmlns":890},[892,7664,7665,7671],{},[895,7666,7667,7669],{},[898,7668,2971],{},[898,7670,4185],{},[902,7672,4285],{"encoding":904},[614,7674,7510],{},[4060,7676,7677],{},[724,7678,7679,7682],{},[38,7680,7681],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,7684,7685,7390,7705,7724,7725,7740,7741,7811,7812,2114,7840,7873,7874,5777,7902,7917,7918,2196],{},[38,7686,7687,7688,4110],{},"(c) Jednotková elasticita (",[883,7689,7691],{"className":7690},[886],[888,7692,7693],{"xmlns":890},[892,7694,7695,7703],{},[895,7696,7697,7699,7701],{},[898,7698,1762],{},[1700,7700,1765],{},[1931,7702,1933],{},[902,7704,4734],{"encoding":904},[883,7706,7708],{"className":7707},[886],[888,7709,7710],{"xmlns":890},[892,7711,7712,7722],{},[895,7713,7714,7716,7718,7720],{},[898,7715,2005],{},[898,7717,4185],{},[1700,7719,1765],{},[1931,7721,1772],{},[902,7723,7272],{"encoding":904}," — nutná podmínka extrému ",[883,7726,7728],{"className":7727},[886],[888,7729,7730],{"xmlns":890},[892,7731,7732,7738],{},[895,7733,7734,7736],{},[898,7735,2971],{},[898,7737,4185],{},[902,7739,4285],{"encoding":904},". Dále ",[883,7742,7744],{"className":7743},[886],[888,7745,7746],{"xmlns":890},[892,7747,7748,7808],{},[895,7749,7750,7752,7762,7764,7766,7772,7774,7780,7782,7784,7786,7788,7790,7792,7802,7804,7806],{},[898,7751,2971],{},[1785,7753,7754,7756],{},[898,7755,4185],{},[895,7757,7758,7760],{},[1700,7759,1793],{"mathvariant":1791},[1700,7761,1793],{"mathvariant":1791},[1700,7763,1765],{},[898,7765,2005],{},[1785,7767,7768,7770],{},[898,7769,4185],{},[1700,7771,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,7773,1765],{},[1785,7775,7776,7778],{},[898,7777,4374],{},[1700,7779,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,7781,1703],{"stretchy":1702},[898,7783,1662],{},[1700,7785,1709],{"stretchy":1702},[1700,7787,1897],{},[898,7789,1662],{},[1781,7791,1783],{},[1785,7793,7794,7796],{},[898,7795,4374],{},[895,7797,7798,7800],{},[1700,7799,1793],{"mathvariant":1791},[1700,7801,1793],{"mathvariant":1791},[1700,7803,1703],{"stretchy":1702},[898,7805,1662],{},[1700,7807,1709],{"stretchy":1702},[902,7809,7810],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,7813,7815],{"className":7814},[886],[888,7816,7817],{"xmlns":890},[892,7818,7819,7837],{},[895,7820,7821,7827,7829,7831,7833,7835],{},[1785,7822,7823,7825],{},[898,7824,4374],{},[1700,7826,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,7828,1703],{"stretchy":1702},[898,7830,1662],{},[1700,7832,1709],{"stretchy":1702},[1700,7834,3640],{},[1931,7836,1772],{},[902,7838,7839],{"encoding":904},"D'(Q) \u003C 0",[883,7841,7843],{"className":7842},[886],[888,7844,7845],{"xmlns":890},[892,7846,7847,7870],{},[895,7848,7849,7859,7861,7863,7865,7868],{},[1785,7850,7851,7853],{},[898,7852,4374],{},[895,7854,7855,7857],{},[1700,7856,1793],{"mathvariant":1791},[1700,7858,1793],{"mathvariant":1791},[1700,7860,1703],{"stretchy":1702},[898,7862,1662],{},[1700,7864,1709],{"stretchy":1702},[1700,7866,7867],{},"≤",[1931,7869,1772],{},[902,7871,7872],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,7875,7877],{"className":7876},[886],[888,7878,7879],{"xmlns":890},[892,7880,7881,7899],{},[895,7882,7883,7885,7895,7897],{},[898,7884,2971],{},[1785,7886,7887,7889],{},[898,7888,4185],{},[895,7890,7891,7893],{},[1700,7892,1793],{"mathvariant":1791},[1700,7894,1793],{"mathvariant":1791},[1700,7896,3640],{},[1931,7898,1772],{},[902,7900,7901],{"encoding":904},"TR'' \u003C 0",[883,7903,7905],{"className":7904},[886],[888,7906,7907],{"xmlns":890},[892,7908,7909,7915],{},[895,7910,7911,7913],{},[898,7912,2971],{},[898,7914,4185],{},[902,7916,4285],{"encoding":904}," nabývá ",[38,7919,7920],{},"maxima",[4060,7922,7923],{},[724,7924,7925,7928],{},[38,7926,7927],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,7930,7931],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,7933,7934],{},[38,7935,7936],{},"Souhrnná tabulka Pravidel 1–3:",[16,7938,7939,8043],{},[19,7940,7941],{},[22,7942,7943,7946,7961,7978,8009,8040],{},[25,7944,7945],{},"Charakter poptávky",[25,7947,7948],{},[883,7949,7951],{"className":7950},[886],[888,7952,7953],{"xmlns":890},[892,7954,7955,7959],{},[895,7956,7957],{},[898,7958,1762],{},[902,7960,1762],{"encoding":904},[25,7962,7963],{},[883,7964,7966],{"className":7965},[886],[888,7967,7968],{"xmlns":890},[892,7969,7970,7976],{},[895,7971,7972,7974],{},[898,7973,2005],{},[898,7975,4185],{},[902,7977,6822],{"encoding":904},[25,7979,7980,7981,2106,7994],{},"Pokles ceny ",[883,7982,7984],{"className":7983},[886],[888,7985,7986],{"xmlns":890},[892,7987,7988,7992],{},[895,7989,7990],{},[1700,7991,4178],{},[902,7993,7143],{"encoding":904},[883,7995,7997],{"className":7996},[886],[888,7998,7999],{"xmlns":890},[892,8000,8001,8007],{},[895,8002,8003,8005],{},[898,8004,2971],{},[898,8006,4185],{},[902,8008,4285],{"encoding":904},[25,8010,8011,8012,2106,8025],{},"Růst ceny ",[883,8013,8015],{"className":8014},[886],[888,8016,8017],{"xmlns":890},[892,8018,8019,8023],{},[895,8020,8021],{},[1700,8022,4178],{},[902,8024,7143],{"encoding":904},[883,8026,8028],{"className":8027},[886],[888,8029,8030],{"xmlns":890},[892,8031,8032,8038],{},[895,8033,8034,8036],{},[898,8035,2971],{},[898,8037,4185],{},[902,8039,4285],{"encoding":904},[25,8041,8042],{},"Doporučení",[30,8044,8045,8094,8144],{},[22,8046,8047,8049,8067,8085,8087,8089],{},[35,8048,4264],{},[35,8050,8051],{},[883,8052,8054],{"className":8053},[886],[888,8055,8056],{"xmlns":890},[892,8057,8058,8064],{},[895,8059,8060,8062],{},[1700,8061,3601],{},[1931,8063,1933],{},[902,8065,8066],{"encoding":904},"> 1",[35,8068,8069],{},[883,8070,8072],{"className":8071},[886],[888,8073,8074],{"xmlns":890},[892,8075,8076,8082],{},[895,8077,8078,8080],{},[1700,8079,3601],{},[1931,8081,1772],{},[902,8083,8084],{"encoding":904},"> 0",[35,8086,7510],{},[35,8088,7530],{},[35,8090,8091],{},[38,8092,8093],{},"snížit cenu",[22,8095,8096,8099,8117,8135,8137,8139],{},[35,8097,8098],{},"jednotková",[35,8100,8101],{},[883,8102,8104],{"className":8103},[886],[888,8105,8106],{"xmlns":890},[892,8107,8108,8114],{},[895,8109,8110,8112],{},[1700,8111,1765],{},[1931,8113,1933],{},[902,8115,8116],{"encoding":904},"= 1",[35,8118,8119],{},[883,8120,8122],{"className":8121},[886],[888,8123,8124],{"xmlns":890},[892,8125,8126,8132],{},[895,8127,8128,8130],{},[1700,8129,1765],{},[1931,8131,1772],{},[902,8133,8134],{"encoding":904},"= 0",[35,8136,3910],{},[35,8138,3910],{},[35,8140,8141],{},[38,8142,8143],{},"držet cenu",[22,8145,8146,8148,8166,8184,8186,8188],{},[35,8147,4268],{},[35,8149,8150],{},[883,8151,8153],{"className":8152},[886],[888,8154,8155],{"xmlns":890},[892,8156,8157,8163],{},[895,8158,8159,8161],{},[1700,8160,3640],{},[1931,8162,1933],{},[902,8164,8165],{"encoding":904},"\u003C 1",[35,8167,8168],{},[883,8169,8171],{"className":8170},[886],[888,8172,8173],{"xmlns":890},[892,8174,8175,8181],{},[895,8176,8177,8179],{},[1700,8178,3640],{},[1931,8180,1772],{},[902,8182,8183],{"encoding":904},"\u003C 0",[35,8185,7530],{},[35,8187,7510],{},[35,8189,8190],{},[38,8191,8192],{},"zvýšit cenu",[198,8194,8196],{"id":8195},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,8198,8199,8200,8225,8226,8248,8249,8262,8263,8276,8277,8290,8291,5777,8318,8370],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,8201,8203],{"className":8202},[886],[888,8204,8205],{"xmlns":890},[892,8206,8207,8223],{},[895,8208,8209,8211,8213,8215,8217],{},[898,8210,1677],{},[1700,8212,1765],{},[1931,8214,3284],{},[1700,8216,1768],{},[1785,8218,8219,8221],{},[898,8220,1662],{},[1931,8222,2343],{},[902,8224,5647],{"encoding":904},". Reálné cenové rozpětí je ",[883,8227,8229],{"className":8228},[886],[888,8230,8231],{"xmlns":890},[892,8232,8233,8245],{},[895,8234,8235,8237,8239,8241,8243],{},[1700,8236,5512],{"stretchy":1702},[1931,8238,1933],{},[1700,8240,1732],{"separator":1731},[1931,8242,3284],{},[1700,8244,5529],{"stretchy":1702},[902,8246,8247],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,8250,8252],{"className":8251},[886],[888,8253,8254],{"xmlns":890},[892,8255,8256,8260],{},[895,8257,8258],{},[898,8259,1662],{},[902,8261,1662],{"encoding":904}," jako funkci ",[883,8264,8266],{"className":8265},[886],[888,8267,8268],{"xmlns":890},[892,8269,8270,8274],{},[895,8271,8272],{},[898,8273,1677],{},[902,8275,1677],{"encoding":904},"; pro nezáporné ",[883,8278,8280],{"className":8279},[886],[888,8281,8282],{"xmlns":890},[892,8283,8284,8288],{},[895,8285,8286],{},[898,8287,1662],{},[902,8289,1662],{"encoding":904}," je ",[883,8292,8294],{"className":8293},[886],[888,8295,8296],{"xmlns":890},[892,8297,8298,8315],{},[895,8299,8300,8302,8304],{},[898,8301,1662],{},[1700,8303,1765],{},[8305,8306,8307],"msqrt",{},[895,8308,8309,8311,8313],{},[1931,8310,3284],{},[1700,8312,1768],{},[898,8314,1677],{},[902,8316,8317],{"encoding":904},"Q = \\sqrt{100 - P}",[883,8319,8321],{"className":8320},[886],[888,8322,8323],{"xmlns":890},[892,8324,8325,8367],{},[895,8326,8327,8343,8345,8347],{},[1770,8328,8329],{"scriptlevel":1772,"displaystyle":1731},[1774,8330,8331,8337],{},[895,8332,8333,8335],{},[898,8334,2406],{"mathvariant":1791},[898,8336,1662],{},[895,8338,8339,8341],{},[898,8340,2406],{"mathvariant":1791},[898,8342,1677],{},[1700,8344,1765],{},[1700,8346,1768],{},[1770,8348,8349],{"scriptlevel":1772,"displaystyle":1731},[1774,8350,8351,8353],{},[1931,8352,1933],{},[895,8354,8355,8357],{},[1931,8356,2343],{},[8305,8358,8359],{},[895,8360,8361,8363,8365],{},[1931,8362,3284],{},[1700,8364,1768],{},[898,8366,1677],{},[902,8368,8369],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,8372,8373],{},[883,8374,8376],{"className":8375},[886],[888,8377,8378],{"xmlns":890},[892,8379,8380,8502],{},[895,8381,8382,8384,8386,8388,8390,8392,8394,8400,8402,8416,8418,8420,8434,8436,8462,8464,8482,8484,8500],{},[898,8383,1762],{},[1700,8385,1703],{"stretchy":1702},[898,8387,1677],{},[1700,8389,1709],{"stretchy":1702},[1700,8391,1765],{},[1700,8393,1768],{},[1774,8395,8396,8398],{},[898,8397,1677],{},[898,8399,1662],{},[1700,8401,2065],{},[1774,8403,8404,8410],{},[895,8405,8406,8408],{},[898,8407,2406],{"mathvariant":1791},[898,8409,1662],{},[895,8411,8412,8414],{},[898,8413,2406],{"mathvariant":1791},[898,8415,1677],{},[1700,8417,1765],{},[1700,8419,1768],{},[1774,8421,8422,8424],{},[898,8423,1677],{},[8305,8425,8426],{},[895,8427,8428,8430,8432],{},[1931,8429,3284],{},[1700,8431,1768],{},[898,8433,1677],{},[1700,8435,2065],{},[895,8437,8438,8440,8442,8460],{},[1700,8439,1703],{"fence":1731},[1700,8441,1768],{},[1774,8443,8444,8446],{},[1931,8445,1933],{},[895,8447,8448,8450],{},[1931,8449,2343],{},[8305,8451,8452],{},[895,8453,8454,8456,8458],{},[1931,8455,3284],{},[1700,8457,1768],{},[898,8459,1677],{},[1700,8461,1709],{"fence":1731},[1700,8463,1765],{},[1774,8465,8466,8468],{},[898,8467,1677],{},[895,8469,8470,8472,8474,8476,8478,8480],{},[1931,8471,2343],{},[1700,8473,1703],{"stretchy":1702},[1931,8475,3284],{},[1700,8477,1768],{},[898,8479,1677],{},[1700,8481,1709],{"stretchy":1702},[1700,8483,1765],{},[1774,8485,8486,8492],{},[895,8487,8488,8490],{},[1931,8489,5197],{},[898,8491,1677],{},[895,8493,8494,8496,8498],{},[1931,8495,3284],{},[1700,8497,1768],{},[898,8499,1677],{},[898,8501,2196],{"mathvariant":1791},[902,8503,8504],{"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}.",[724,8506,8507,8508,2901],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,8509,8511],{"className":8510},[886],[888,8512,8513],{"xmlns":890},[892,8514,8515,8539],{},[895,8516,8517,8535,8537],{},[1770,8518,8519],{"scriptlevel":1772,"displaystyle":1731},[1774,8520,8521,8527],{},[895,8522,8523,8525],{},[1931,8524,5197],{},[898,8526,1677],{},[895,8528,8529,8531,8533],{},[1931,8530,3284],{},[1700,8532,1768],{},[898,8534,1677],{},[1700,8536,1765],{},[1931,8538,1933],{},[902,8540,8541],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,8543,8544],{},[883,8545,8547],{"className":8546},[886],[888,8548,8549],{"xmlns":890},[892,8550,8551,8583],{},[895,8552,8553,8559,8561,8568,8570,8573,8581],{},[1785,8554,8555,8557],{},[898,8556,1677],{},[1700,8558,4543],{},[1700,8560,1765],{},[1774,8562,8563,8566],{},[1931,8564,8565],{},"200",[1931,8567,2385],{},[1700,8569,6088],{},[1931,8571,8572],{},"66,",[8574,8575,8576,8578],"mover",{"accent":1731},[1931,8577,2445],{},[1700,8579,8580],{"stretchy":1731},"‾",[898,8582,2196],{"mathvariant":1791},[902,8584,8585],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,8587,8588],{},"S využitím vlastnosti (4.8):",[120,8590,8591,8637,8679],{},[123,8592,8593,8594,8629,8630,8632,8633,8636],{},"Při cenách ",[883,8595,8597],{"className":8596},[886],[888,8598,8599],{"xmlns":890},[892,8600,8601,8626],{},[895,8602,8603,8605,8607,8609,8611,8614,8616,8618,8624],{},[898,8604,1677],{},[1700,8606,6694],{},[1700,8608,5512],{"stretchy":1702},[1931,8610,1933],{},[1700,8612,8613],{"separator":1731},";",[1781,8615,1783],{},[1931,8617,8572],{},[8574,8619,8620,8622],{"accent":1731},[1931,8621,2445],{},[1700,8623,8580],{"stretchy":1731},[1700,8625,1709],{"stretchy":1702},[902,8627,8628],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,8631,4268],{}," — dle ",[614,8634,8635],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,8638,8593,8639,8629,8673,8632,8675,8678],{},[883,8640,8642],{"className":8641},[886],[888,8643,8644],{"xmlns":890},[892,8645,8646,8670],{},[895,8647,8648,8650,8652,8654,8656,8662,8664,8666,8668],{},[898,8649,1677],{},[1700,8651,6694],{},[1700,8653,1703],{"stretchy":1702},[1931,8655,8572],{},[8574,8657,8658,8660],{"accent":1731},[1931,8659,2445],{},[1700,8661,8580],{"stretchy":1731},[1700,8663,8613],{"separator":1731},[1781,8665,1783],{},[1931,8667,3284],{},[1700,8669,5529],{"stretchy":1702},[902,8671,8672],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,8674,4264],{},[614,8676,8677],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,8680,8681,8682,8685,8686,8714,8715,8718],{},"Dle ",[614,8683,8684],{},"Pravidla 3"," je při ceně ",[883,8687,8689],{"className":8688},[886],[888,8690,8691],{"xmlns":890},[892,8692,8693,8711],{},[895,8694,8695,8701,8703,8705],{},[1785,8696,8697,8699],{},[898,8698,1677],{},[1700,8700,4543],{},[1700,8702,1765],{},[1931,8704,8572],{},[8574,8706,8707,8709],{"accent":1731},[1931,8708,2445],{},[1700,8710,8580],{"stretchy":1731},[902,8712,8713],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,8716,8717],{},"maxima celkového příjmu"," ve výši",[724,8720,8721],{},[883,8722,8724],{"className":8723},[886],[888,8725,8726],{"xmlns":890},[892,8727,8728,8806],{},[895,8729,8730,8732,8734,8736,8742,8744,8746,8752,8754,8768,8770,8776,8778,8786,8788,8801,8803],{},[898,8731,2971],{},[898,8733,4185],{},[1700,8735,1703],{"stretchy":1702},[1785,8737,8738,8740],{},[898,8739,1677],{},[1700,8741,4543],{},[1700,8743,1709],{"stretchy":1702},[1700,8745,1765],{},[1785,8747,8748,8750],{},[898,8749,1677],{},[1700,8751,4543],{},[1700,8753,2065],{},[8305,8755,8756],{},[895,8757,8758,8760,8762],{},[1931,8759,3284],{},[1700,8761,1768],{},[1785,8763,8764,8766],{},[898,8765,1677],{},[1700,8767,4543],{},[1700,8769,1765],{},[1774,8771,8772,8774],{},[1931,8773,8565],{},[1931,8775,2385],{},[1700,8777,2065],{},[8305,8779,8780],{},[1774,8781,8782,8784],{},[1931,8783,3284],{},[1931,8785,2385],{},[1700,8787,1765],{},[1774,8789,8790,8793],{},[1931,8791,8792],{},"2000",[895,8794,8795,8797],{},[1931,8796,2385],{},[8305,8798,8799],{},[1931,8800,2385],{},[1700,8802,6088],{},[1931,8804,8805],{},"384,9.",[902,8807,8808],{"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.",[724,8810,8811,8812,2196],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,8813,8815],{"className":8814},[886],[888,8816,8817],{"xmlns":890},[892,8818,8819,8825],{},[895,8820,8821,8823],{},[898,8822,2971],{},[898,8824,4185],{},[902,8826,4285],{"encoding":904},[115,8828,8830],{"id":8829},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,8832,8833,8834,8837],{},"Analogicky se definuje ",[38,8835,8836],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,8839,8840],{},[883,8841,8843],{"className":8842,"title":4391,"style":4392},[4390],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,8845,4499,8846,8871,8872,8904],{},[883,8847,8849],{"className":8848},[886],[888,8850,8851],{"xmlns":890},[892,8852,8853,8868],{},[895,8854,8855,8857,8859,8862,8864,8866],{},[898,8856,1662],{},[1700,8858,1765],{},[898,8860,8861],{},"S",[1700,8863,1703],{"stretchy":1702},[898,8865,1677],{},[1700,8867,1709],{"stretchy":1702},[902,8869,8870],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,8873,8875],{"className":8874},[886],[888,8876,8877],{"xmlns":890},[892,8878,8879,8901],{},[895,8880,8881,8897,8899],{},[1770,8882,8883],{"scriptlevel":1772,"displaystyle":1731},[1774,8884,8885,8891],{},[895,8886,8887,8889],{},[898,8888,2406],{"mathvariant":1791},[898,8890,1662],{},[895,8892,8893,8895],{},[898,8894,2406],{"mathvariant":1791},[898,8896,1677],{},[1700,8898,3601],{},[1931,8900,1772],{},[902,8902,8903],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,8906,8907],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[4060,8909,8910],{},[724,8911,8912,8913],{},"S rostoucí cenou elasticita nabídky roste. ",[883,8914,8916],{"className":8915},[886],[888,8917,8918],{"xmlns":890},[892,8919,8920,8929],{},[895,8921,8922,8924,8927],{},[1700,8923,1703],{"stretchy":1702},[1931,8925,8926],{},"4.14",[1700,8928,1709],{"stretchy":1702},[902,8930,8931],{"encoding":904},"(4.14)",[724,8933,8934],{},"Pro nominální změny platí",[724,8936,8937],{},[883,8938,8940],{"className":8939,"title":4391,"style":4392},[4390],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,8942,8943],{},"a pro procentní změny",[724,8945,8946],{},[883,8947,8949],{"className":8948,"title":4391,"style":4392},[4390],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,8951,8952],{},"(bez znaménka minus).",[198,8954,8956],{"id":8955},"příklad-47","Příklad 4.7",[724,8958,8959,8960,2901],{},"Nabídka ",[883,8961,8963],{"className":8962},[886],[888,8964,8965],{"xmlns":890},[892,8966,8967,8992],{},[895,8968,8969,8971,8973,8975,8981,8983,8985,8987,8989],{},[898,8970,1662],{},[1700,8972,1765],{},[1931,8974,2990],{},[1785,8976,8977,8979],{},[898,8978,1677],{},[1931,8980,2343],{},[1700,8982,1897],{},[1931,8984,2438],{},[898,8986,1677],{},[1700,8988,1897],{},[1931,8990,8991],{},"150",[902,8993,8994],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,8996,8997],{},[883,8998,9000],{"className":8999},[886],[888,9001,9002],{"xmlns":890},[892,9003,9004,9050],{},[895,9005,9006,9008,9010,9034,9036,9038,9040,9042,9044,9046,9048],{},[898,9007,1762],{},[1700,9009,1765],{},[1774,9011,9012,9014],{},[898,9013,1677],{},[895,9015,9016,9018,9024,9026,9028,9030,9032],{},[1931,9017,2990],{},[1785,9019,9020,9022],{},[898,9021,1677],{},[1931,9023,2343],{},[1700,9025,1897],{},[1931,9027,2438],{},[898,9029,1677],{},[1700,9031,1897],{},[1931,9033,8991],{},[1781,9035,1783],{},[1700,9037,1703],{"stretchy":1702},[1931,9039,3034],{},[898,9041,1677],{},[1700,9043,1897],{},[1931,9045,2438],{},[1700,9047,1709],{"stretchy":1702},[898,9049,2196],{"mathvariant":1791},[902,9051,9052],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,9054,5305,9055,1343,9085,1343,9112,9148,9149,9174,9175,9193,9194,2196],{},[883,9056,9058],{"className":9057},[886],[888,9059,9060],{"xmlns":890},[892,9061,9062,9082],{},[895,9063,9064,9066,9068,9070,9072,9074],{},[898,9065,1762],{},[1700,9067,1703],{"stretchy":1702},[1931,9069,3058],{},[1700,9071,1709],{"stretchy":1702},[1700,9073,1765],{},[1770,9075,9076],{"scriptlevel":1772,"displaystyle":1702},[1774,9077,9078,9080],{},[1931,9079,1933],{},[1931,9081,2385],{},[902,9083,9084],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,9086,9088],{"className":9087},[886],[888,9089,9090],{"xmlns":890},[892,9091,9092,9109],{},[895,9093,9094,9096,9098,9103,9105,9107],{},[898,9095,1762],{},[1700,9097,1703],{"stretchy":1702},[8305,9099,9100],{},[1931,9101,9102],{},"1500",[1700,9104,1709],{"stretchy":1702},[1700,9106,1765],{},[1931,9108,1933],{},[902,9110,9111],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,9113,9115],{"className":9114},[886],[888,9116,9117],{"xmlns":890},[892,9118,9119,9145],{},[895,9120,9121,9123,9125,9127,9129,9131,9140,9142],{},[898,9122,1762],{},[1700,9124,1703],{"stretchy":1702},[1931,9126,3284],{},[1700,9128,1709],{"stretchy":1702},[1700,9130,1765],{},[1770,9132,9133],{"scriptlevel":1772,"displaystyle":1702},[1774,9134,9135,9137],{},[1931,9136,3314],{},[1931,9138,9139],{},"33",[1700,9141,6088],{},[1931,9143,9144],{},"1,515",[902,9146,9147],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,9150,9152],{"className":9151},[886],[888,9153,9154],{"xmlns":890},[892,9155,9156,9171],{},[895,9157,9158,9160,9162,9166,9168],{},[898,9159,1677],{},[1700,9161,3601],{},[8305,9163,9164],{},[1931,9165,9102],{},[1700,9167,2927],{},[1931,9169,9170],{},"38,7",[902,9172,9173],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,9176,9178],{"className":9177},[886],[888,9179,9180],{"xmlns":890},[892,9181,9182,9190],{},[895,9183,9184,9186,9188],{},[898,9185,1677],{},[1700,9187,3640],{},[1931,9189,9170],{},[902,9191,9192],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,9195,9197],{"className":9196},[886],[888,9198,9199],{"xmlns":890},[892,9200,9201,9239],{},[895,9202,9203,9205,9207,9209,9211,9219,9221,9224,9226,9229,9235,9237],{},[898,9204,3084],{"mathvariant":1791},[898,9206,1662],{},[898,9208,6113],{"mathvariant":1791},[1700,9210,2927],{},[1770,9212,9213],{"scriptlevel":1772,"displaystyle":1702},[1774,9214,9215,9217],{},[1931,9216,1933],{},[1931,9218,2385],{},[1700,9220,2065],{},[1931,9222,9223],{},"20",[1700,9225,1765],{},[1931,9227,9228],{},"6,",[8574,9230,9231,9233],{"accent":1731},[1931,9232,2445],{},[1700,9234,8580],{"stretchy":1731},[1781,9236,1783],{},[898,9238,6113],{"mathvariant":1791},[902,9240,9241],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,9243,9245],{"id":9244},"vícefaktorový-model","Vícefaktorový model",[724,9247,9248,9249,9262,9263,2106,9266,9279,9280,2106,9283,9301,9302,2106,9305,2901],{},"Předpokládejme, že poptávané množství ",[883,9250,9252],{"className":9251},[886],[888,9253,9254],{"xmlns":890},[892,9255,9256,9260],{},[895,9257,9258],{},[898,9259,1662],{},[902,9261,1662],{"encoding":904}," závisí na ",[38,9264,9265],{},"ceně základního zboží",[883,9267,9269],{"className":9268},[886],[888,9270,9271],{"xmlns":890},[892,9272,9273,9277],{},[895,9274,9275],{},[898,9276,1677],{},[902,9278,1677],{"encoding":904},", na ",[38,9281,9282],{},"ceně alternativního zboží",[883,9284,9286],{"className":9285},[886],[888,9287,9288],{"xmlns":890},[892,9289,9290,9298],{},[895,9291,9292],{},[2007,9293,9294,9296],{},[898,9295,1677],{},[898,9297,1862],{},[902,9299,9300],{"encoding":904},"P_A"," a na ",[38,9303,9304],{},"důchodu",[883,9306,9308],{"className":9307},[886],[888,9309,9310],{"xmlns":890},[892,9311,9312,9317],{},[895,9313,9314],{},[898,9315,9316],{},"Y",[902,9318,9316],{"encoding":904},[724,9320,9321],{},[883,9322,9324],{"className":9323,"title":4391,"style":4392},[4390],"Q = D(P, P_A, Y). \\tag{4.17}",[724,9326,9327,9328,9331],{},"V analogii jednofaktorového modelu pracujeme s ",[38,9329,9330],{},"parciálními derivacemi"," funkce poptávky.",[198,9333,9335],{"id":9334},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,9337,9338],{},[883,9339,9341],{"className":9340,"title":4391,"style":4392},[4390],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,9343,4499,9344,9364,9365,9378,9379,3122,9401,2106,9404,9450,9451,9464,9465,9482],{},[883,9345,9347],{"className":9346},[886],[888,9348,9349],{"xmlns":890},[892,9350,9351,9361],{},[895,9352,9353],{},[2030,9354,9355,9357,9359],{},[898,9356,1662],{},[898,9358,1677],{},[1700,9360,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,9362,9363],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,9366,9368],{"className":9367},[886],[888,9369,9370],{"xmlns":890},[892,9371,9372,9376],{},[895,9373,9374],{},[898,9375,1677],{},[902,9377,1677],{"encoding":904},". Vždy ",[883,9380,9382],{"className":9381},[886],[888,9383,9384],{"xmlns":890},[892,9385,9386,9398],{},[895,9387,9388,9394,9396],{},[2007,9389,9390,9392],{},[898,9391,1762],{},[898,9393,1677],{},[1700,9395,4674],{},[1931,9397,1772],{},[902,9399,9400],{"encoding":904},"E_P \\ge 0",[614,9402,9403],{},"Interpretace:",[883,9405,9407],{"className":9406},[886],[888,9408,9409],{"xmlns":890},[892,9410,9411,9447],{},[895,9412,9413,9419,9421,9427,9429,9437,9439,9445],{},[2007,9414,9415,9417],{},[898,9416,1762],{},[898,9418,1677],{},[1700,9420,1703],{"stretchy":1702},[1785,9422,9423,9425],{},[898,9424,1677],{},[1700,9426,4543],{},[1700,9428,1732],{"separator":1731},[2030,9430,9431,9433,9435],{},[898,9432,1677],{},[898,9434,1862],{},[1700,9436,4543],{},[1700,9438,1732],{"separator":1731},[1785,9440,9441,9443],{},[898,9442,9316],{},[1700,9444,4543],{},[1700,9446,1709],{"stretchy":1702},[902,9448,9449],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,9452,9454],{"className":9453},[886],[888,9455,9456],{"xmlns":890},[892,9457,9458,9462],{},[895,9459,9460],{},[898,9461,1662],{},[902,9463,1662],{"encoding":904}," při 1% změně ",[883,9466,9468],{"className":9467},[886],[888,9469,9470],{"xmlns":890},[892,9471,9472,9480],{},[895,9473,9474],{},[1785,9475,9476,9478],{},[898,9477,1677],{},[1700,9479,4543],{},[902,9481,4593],{"encoding":904},", ceteris paribus.",[198,9484,9486],{"id":9485},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,9488,9489],{},[883,9490,9492],{"className":9491,"title":4391,"style":4392},[4390],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,9494,9495,9450,9497,9510,9511,9528],{},[614,9496,9403],{},[883,9498,9500],{"className":9499},[886],[888,9501,9502],{"xmlns":890},[892,9503,9504,9508],{},[895,9505,9506],{},[898,9507,1662],{},[902,9509,1662],{"encoding":904}," základního zboží při 1% změně ceny ",[883,9512,9514],{"className":9513},[886],[888,9515,9516],{"xmlns":890},[892,9517,9518,9526],{},[895,9519,9520],{},[2007,9521,9522,9524],{},[898,9523,1677],{},[898,9525,1862],{},[902,9527,9300],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,9530,9531],{},[38,9532,9533],{},"Znaménko závisí na povaze alternativního zboží:",[120,9535,9536,9624],{},[123,9537,9538,9539,9542,9543,9560,9561,2106,9574,2196],{},"Je-li alternativní zboží ",[38,9540,9541],{},"komplement",", růst ",[883,9544,9546],{"className":9545},[886],[888,9547,9548],{"xmlns":890},[892,9549,9550,9558],{},[895,9551,9552],{},[2007,9553,9554,9556],{},[898,9555,1677],{},[898,9557,1862],{},[902,9559,9300],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,9562,9564],{"className":9563},[886],[888,9565,9566],{"xmlns":890},[892,9567,9568,9572],{},[895,9569,9570],{},[898,9571,1662],{},[902,9573,1662],{"encoding":904},[883,9575,9577],{"className":9576},[886],[888,9578,9579],{"xmlns":890},[892,9580,9581,9621],{},[895,9582,9583,9585,9587,9599,9601,9603,9605,9607,9617,9619],{},[1700,9584,4178],{},[1781,9586,4175],{},[2030,9588,9589,9591,9597],{},[898,9590,1662],{},[2007,9592,9593,9595],{},[898,9594,1677],{},[898,9596,1862],{},[1700,9598,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,9600,3640],{},[1931,9602,1772],{},[1700,9604,1732],{"separator":1731},[1781,9606,4175],{},[2007,9608,9609,9611],{},[898,9610,1762],{},[2007,9612,9613,9615],{},[898,9614,1677],{},[898,9616,1862],{},[1700,9618,3640],{},[1931,9620,1772],{},[902,9622,9623],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,9625,9538,9626,9542,9629,9646,9647,9660,9661,2196],{},[38,9627,9628],{},"substitut",[883,9630,9632],{"className":9631},[886],[888,9633,9634],{"xmlns":890},[892,9635,9636,9644],{},[895,9637,9638],{},[2007,9639,9640,9642],{},[898,9641,1677],{},[898,9643,1862],{},[902,9645,9300],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,9648,9650],{"className":9649},[886],[888,9651,9652],{"xmlns":890},[892,9653,9654,9658],{},[895,9655,9656],{},[898,9657,1662],{},[902,9659,1662],{"encoding":904}," roste ",[883,9662,9664],{"className":9663},[886],[888,9665,9666],{"xmlns":890},[892,9667,9668,9708],{},[895,9669,9670,9672,9674,9686,9688,9690,9692,9694,9704,9706],{},[1700,9671,4178],{},[1781,9673,4175],{},[2030,9675,9676,9678,9684],{},[898,9677,1662],{},[2007,9679,9680,9682],{},[898,9681,1677],{},[898,9683,1862],{},[1700,9685,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,9687,3601],{},[1931,9689,1772],{},[1700,9691,1732],{"separator":1731},[1781,9693,4175],{},[2007,9695,9696,9698],{},[898,9697,1762],{},[2007,9699,9700,9702],{},[898,9701,1677],{},[898,9703,1862],{},[1700,9705,3601],{},[1931,9707,1772],{},[902,9709,9710],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,9712,9715],{"className":9713,"title":9714,"style":4392},[4390],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":9717},[9718,9722,9723,9731,9732,9736,9739],{"id":4083,"depth":642,"text":4084,"children":9719},[9720,9721],{"id":4113,"depth":649,"text":4114},{"id":4293,"depth":649,"text":4294},{"id":4328,"depth":642,"text":4329},{"id":4354,"depth":642,"text":4355,"children":9724},[9725,9726,9727,9728,9730],{"id":5047,"depth":649,"text":5048},{"id":5137,"depth":649,"text":5138},{"id":5473,"depth":649,"text":5474},{"id":5555,"depth":649,"text":9729},"Výpočet, je-li dáno PP jako funkce QQ",{"id":5816,"depth":649,"text":5817},{"id":6141,"depth":642,"text":6142},{"id":6737,"depth":642,"text":6738,"children":9733},[9734,9735],{"id":7366,"depth":649,"text":7367},{"id":8195,"depth":649,"text":8196},{"id":8829,"depth":642,"text":8830,"children":9737},[9738],{"id":8955,"depth":649,"text":8956},{"id":9244,"depth":642,"text":9245,"children":9740},[9741,9742],{"id":9334,"depth":649,"text":9335},{"id":9485,"depth":649,"text":9486},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":4053,"description":641},[1138,1136],"topics\u002Felasticita",[1128,2155,9750,9751,9752,9753],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":9756,"title":9757,"body":9758,"course":1128,"courses":659,"created":1129,"description":11296,"extension":661,"meta":11297,"navigation":664,"path":11298,"seo":11299,"sources":11300,"stem":11301,"tags":11302,"type":4049,"updated":677,"__hash__":11307},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":9759,"toc":11281},[9760,9763,9837,9844,9848,9912,9998,10002,10029,10096,10151,10155,10181,10274,10276,10308,10479,10483,10553,10601,10605,10666,10772,10787,10791,10793,10821,10886,10888,10895,10983,11008,11206,11210,11246,11248],[12,9761,9757],{"id":9762},"kalkul-funkcí-více-proměnných",[724,9764,9765,9766,9769,9770,1343,9799,2196],{},"Většina ekonomických veličin závisí na ",[38,9767,9768],{},"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 ",[883,9771,9773],{"className":9772},[886],[888,9774,9775],{"xmlns":890},[892,9776,9777,9796],{},[895,9778,9779,9782,9784,9786,9788,9790,9792,9794],{},[898,9780,9781],{},"z",[1700,9783,1765],{},[898,9785,2220],{},[1700,9787,1703],{"stretchy":1702},[898,9789,2225],{},[1700,9791,1732],{"separator":1731},[898,9793,2215],{},[1700,9795,1709],{"stretchy":1702},[902,9797,9798],{"encoding":904},"z = f(x, y)",[883,9800,9802],{"className":9801},[886],[888,9803,9804],{"xmlns":890},[892,9805,9806,9834],{},[895,9807,9808,9811,9813,9815,9817,9819,9821,9823,9825,9827,9829,9831],{},[898,9809,9810],{},"w",[1700,9812,1765],{},[898,9814,2220],{},[1700,9816,1703],{"stretchy":1702},[898,9818,2225],{},[1700,9820,1732],{"separator":1731},[898,9822,2215],{},[1700,9824,1732],{"separator":1731},[898,9826,9781],{},[1700,9828,1709],{"stretchy":1702},[1700,9830,1732],{"separator":1731},[1700,9832,9833],{},"…",[902,9835,9836],{"encoding":904},"w = f(x, y, z), \\ldots",[724,9838,9839],{},[2756,9840],{"alt":9841,"className":9842,"src":9843},"imek-funkce-2d-vrstevnice",[210,2760],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,9845,9847],{"id":9846},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,9849,9850,9851,9878,9879,9907,9908,9911],{},"Pro ",[883,9852,9854],{"className":9853},[886],[888,9855,9856],{"xmlns":890},[892,9857,9858,9876],{},[895,9859,9860,9862,9864,9866,9868,9870,9872,9874],{},[898,9861,9781],{},[1700,9863,1765],{},[898,9865,2220],{},[1700,9867,1703],{"stretchy":1702},[898,9869,2225],{},[1700,9871,1732],{"separator":1731},[898,9873,2215],{},[1700,9875,1709],{"stretchy":1702},[902,9877,9798],{"encoding":904}," se křivkou s předpisem ",[883,9880,9882],{"className":9881},[886],[888,9883,9884],{"xmlns":890},[892,9885,9886,9904],{},[895,9887,9888,9890,9892,9894,9896,9898,9900,9902],{},[898,9889,2220],{},[1700,9891,1703],{"stretchy":1702},[898,9893,2225],{},[1700,9895,1732],{"separator":1731},[898,9897,2215],{},[1700,9899,1709],{"stretchy":1702},[1700,9901,1765],{},[898,9903,2354],{},[902,9905,9906],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,9909,9910],{},"vrstevnice"," funkce. V ekonomii:",[120,9913,9914,9961],{},[123,9915,9916,9919,9920,9956,9957,2196],{},[38,9917,9918],{},"Indiferenční křivky"," užitečnosti ",[883,9921,9923],{"className":9922},[886],[888,9924,9925],{"xmlns":890},[892,9926,9927,9953],{},[895,9928,9929,9931,9933,9939,9941,9947,9949,9951],{},[898,9930,900],{},[1700,9932,1703],{"stretchy":1702},[2007,9934,9935,9937],{},[898,9936,1662],{},[1931,9938,1933],{},[1700,9940,1732],{"separator":1731},[2007,9942,9943,9945],{},[898,9944,1662],{},[1931,9946,2343],{},[1700,9948,1709],{"stretchy":1702},[1700,9950,1765],{},[898,9952,2354],{},[902,9954,9955],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,9958,9960],{"className":9959,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,9962,9963,9966,9967,9956,9995,2196],{},[38,9964,9965],{},"Izokvanty"," produkce ",[883,9968,9970],{"className":9969},[886],[888,9971,9972],{"xmlns":890},[892,9973,9974,9992],{},[895,9975,9976,9978,9980,9982,9984,9986,9988,9990],{},[898,9977,1662],{},[1700,9979,1703],{"stretchy":1702},[898,9981,1706],{},[1700,9983,1732],{"separator":1731},[898,9985,1735],{},[1700,9987,1709],{"stretchy":1702},[1700,9989,1765],{},[898,9991,2354],{},[902,9993,9994],{"encoding":904},"Q(L, K) = c",[207,9996,2156],{"className":9997,"dataFsResolvedFilePath":857,"href":858},[210],[115,9999,10001],{"id":10000},"parciální-derivace","Parciální derivace",[724,10003,9850,10004,10028],{},[883,10005,10007],{"className":10006},[886],[888,10008,10009],{"xmlns":890},[892,10010,10011,10025],{},[895,10012,10013,10015,10017,10019,10021,10023],{},[898,10014,2220],{},[1700,10016,1703],{"stretchy":1702},[898,10018,2225],{},[1700,10020,1732],{"separator":1731},[898,10022,2215],{},[1700,10024,1709],{"stretchy":1702},[902,10026,10027],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,10030,10031],{},[883,10032,10034],{"className":10033},[886],[888,10035,10036],{"xmlns":890},[892,10037,10038,10093],{},[895,10039,10040,10048,10050,10065,10067,10069,10077,10079],{},[2030,10041,10042,10044,10046],{},[898,10043,2220],{},[898,10045,2225],{},[1700,10047,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,10049,1765],{},[1774,10051,10052,10059],{},[895,10053,10054,10057],{},[898,10055,10056],{"mathvariant":1791},"∂",[898,10058,2220],{},[895,10060,10061,10063],{},[898,10062,10056],{"mathvariant":1791},[898,10064,2225],{},[1700,10066,1732],{"separator":1731},[6066,10068],{"width":6068},[2030,10070,10071,10073,10075],{},[898,10072,2220],{},[898,10074,2215],{},[1700,10076,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,10078,1765],{},[1774,10080,10081,10087],{},[895,10082,10083,10085],{},[898,10084,10056],{"mathvariant":1791},[898,10086,2220],{},[895,10088,10089,10091],{},[898,10090,10056],{"mathvariant":1791},[898,10092,2215],{},[902,10094,10095],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,10097,10098,10099,2196],{},"Hodnoty v bodě: ",[883,10100,10102],{"className":10101},[886],[888,10103,10104],{"xmlns":890},[892,10105,10106,10148],{},[895,10107,10108,10116,10118,10120,10122,10124,10126,10128,10130,10138,10140,10142,10144,10146],{},[2030,10109,10110,10112,10114],{},[898,10111,2220],{},[898,10113,2225],{},[1700,10115,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,10117,1703],{"stretchy":1702},[898,10119,207],{},[1700,10121,1732],{"separator":1731},[898,10123,1879],{},[1700,10125,1709],{"stretchy":1702},[1700,10127,1732],{"separator":1731},[1781,10129,2495],{},[2030,10131,10132,10134,10136],{},[898,10133,2220],{},[898,10135,2215],{},[1700,10137,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,10139,1703],{"stretchy":1702},[898,10141,207],{},[1700,10143,1732],{"separator":1731},[898,10145,1879],{},[1700,10147,1709],{"stretchy":1702},[902,10149,10150],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,10152,10154],{"id":10153},"ekonomické-značení","Ekonomické značení",[724,10156,10157,10158,2901],{},"Pro produkční funkci ",[883,10159,10161],{"className":10160},[886],[888,10162,10163],{"xmlns":890},[892,10164,10165,10179],{},[895,10166,10167,10169,10171,10173,10175,10177],{},[898,10168,1662],{},[1700,10170,1703],{"stretchy":1702},[898,10172,1706],{},[1700,10174,1732],{"separator":1731},[898,10176,1735],{},[1700,10178,1709],{"stretchy":1702},[902,10180,1740],{"encoding":904},[120,10182,10183,10229],{},[123,10184,10185,2669,10205,10208,10209,1709],{},[883,10186,10188],{"className":10187},[886],[888,10189,10190],{"xmlns":890},[892,10191,10192,10202],{},[895,10193,10194],{},[2030,10195,10196,10198,10200],{},[898,10197,1662],{},[898,10199,1706],{},[1700,10201,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,10203,10204],{"encoding":904},"Q'_L",[38,10206,10207],{},"mezní produkt práce"," (",[883,10210,10212],{"className":10211},[886],[888,10213,10214],{"xmlns":890},[892,10215,10216,10226],{},[895,10217,10218,10220],{},[898,10219,2005],{},[2007,10221,10222,10224],{},[898,10223,1677],{},[898,10225,1706],{},[902,10227,10228],{"encoding":904},"MP_L",[123,10230,10231,2669,10251,10208,10254,1709],{},[883,10232,10234],{"className":10233},[886],[888,10235,10236],{"xmlns":890},[892,10237,10238,10248],{},[895,10239,10240],{},[2030,10241,10242,10244,10246],{},[898,10243,1662],{},[898,10245,1735],{},[1700,10247,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,10249,10250],{"encoding":904},"Q'_K",[38,10252,10253],{},"mezní produkt kapitálu",[883,10255,10257],{"className":10256},[886],[888,10258,10259],{"xmlns":890},[892,10260,10261,10271],{},[895,10262,10263,10265],{},[898,10264,2005],{},[2007,10266,10267,10269],{},[898,10268,1677],{},[898,10270,1735],{},[902,10272,10273],{"encoding":904},"MP_K",[198,10275,2765],{"id":2764},[724,10277,10278,2901],{},[883,10279,10281],{"className":10280},[886],[888,10282,10283],{"xmlns":890},[892,10284,10285,10305],{},[895,10286,10287,10295,10297,10299,10301,10303],{},[2030,10288,10289,10291,10293],{},[898,10290,2220],{},[898,10292,2225],{},[1700,10294,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,10296,1703],{"stretchy":1702},[898,10298,207],{},[1700,10300,1732],{"separator":1731},[898,10302,1879],{},[1700,10304,1709],{"stretchy":1702},[902,10306,10307],{"encoding":904},"f'_x(a, b)",[120,10309,10310,10368],{},[123,10311,10312,10313,10326,10327,10340,10341,10367],{},"rychlost změny ",[883,10314,10316],{"className":10315},[886],[888,10317,10318],{"xmlns":890},[892,10319,10320,10324],{},[895,10321,10322],{},[898,10323,2220],{},[902,10325,2220],{"encoding":904}," vůči ",[883,10328,10330],{"className":10329},[886],[888,10331,10332],{"xmlns":890},[892,10333,10334,10338],{},[895,10335,10336],{},[898,10337,2225],{},[902,10339,2225],{"encoding":904}," při ",[883,10342,10344],{"className":10343},[886],[888,10345,10346],{"xmlns":890},[892,10347,10348,10364],{},[895,10349,10350,10352,10354,10356,10358,10360,10362],{},[898,10351,2225],{},[1700,10353,1765],{},[898,10355,207],{},[1700,10357,1732],{"separator":1731},[898,10359,2215],{},[1700,10361,1765],{},[898,10363,1879],{},[902,10365,10366],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,10369,10370,10371,2854,10384,10397,10398,10416,10417,2196],{},"přibližná změna ",[883,10372,10374],{"className":10373},[886],[888,10375,10376],{"xmlns":890},[892,10377,10378,10382],{},[895,10379,10380],{},[898,10381,2220],{},[902,10383,2220],{"encoding":904},[883,10385,10387],{"className":10386},[886],[888,10388,10389],{"xmlns":890},[892,10390,10391,10395],{},[895,10392,10393],{},[898,10394,2225],{},[902,10396,2225],{"encoding":904}," o 1 (a pevném ",[883,10399,10401],{"className":10400},[886],[888,10402,10403],{"xmlns":890},[892,10404,10405,10413],{},[895,10406,10407,10409,10411],{},[898,10408,2215],{},[1700,10410,1765],{},[898,10412,1879],{},[902,10414,10415],{"encoding":904},"y = b","): ",[883,10418,10420],{"className":10419},[886],[888,10421,10422],{"xmlns":890},[892,10423,10424,10476],{},[895,10425,10426,10428,10430,10432,10434,10436,10438,10440,10442,10444,10446,10448,10450,10452,10454,10456,10458,10466,10468,10470,10472,10474],{},[898,10427,2220],{},[1700,10429,1703],{"stretchy":1702},[898,10431,207],{},[1700,10433,1897],{},[1931,10435,1933],{},[1700,10437,1732],{"separator":1731},[898,10439,1879],{},[1700,10441,1709],{"stretchy":1702},[1700,10443,2927],{},[898,10445,2220],{},[1700,10447,1703],{"stretchy":1702},[898,10449,207],{},[1700,10451,1732],{"separator":1731},[898,10453,1879],{},[1700,10455,1709],{"stretchy":1702},[1700,10457,1897],{},[2030,10459,10460,10462,10464],{},[898,10461,2220],{},[898,10463,2225],{},[1700,10465,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,10467,1703],{"stretchy":1702},[898,10469,207],{},[1700,10471,1732],{"separator":1731},[898,10473,1879],{},[1700,10475,1709],{"stretchy":1702},[902,10477,10478],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,10480,10482],{"id":10481},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,10484,10485],{},[883,10486,10488],{"className":10487},[886],[888,10489,10490],{"xmlns":890},[892,10491,10492,10550],{},[895,10493,10494,10496,10498,10500,10508,10510,10512,10514,10516,10518,10520,10522,10524,10526,10534,10536,10538,10540,10542,10544,10546,10548],{},[898,10495,2406],{},[898,10497,2220],{},[1700,10499,1765],{},[2030,10501,10502,10504,10506],{},[898,10503,2220],{},[898,10505,2225],{},[1700,10507,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,10509,1703],{"stretchy":1702},[898,10511,2225],{},[1700,10513,1732],{"separator":1731},[898,10515,2215],{},[1700,10517,1709],{"stretchy":1702},[1781,10519,1783],{},[898,10521,2406],{},[898,10523,2225],{},[1700,10525,1897],{},[2030,10527,10528,10530,10532],{},[898,10529,2220],{},[898,10531,2215],{},[1700,10533,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,10535,1703],{"stretchy":1702},[898,10537,2225],{},[1700,10539,1732],{"separator":1731},[898,10541,2215],{},[1700,10543,1709],{"stretchy":1702},[1781,10545,1783],{},[898,10547,2406],{},[898,10549,2215],{},[902,10551,10552],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,10554,3191,10555,10577,10578,10600],{},[883,10556,10558],{"className":10557},[886],[888,10559,10560],{"xmlns":890},[892,10561,10562,10574],{},[895,10563,10564,10566,10568,10570,10572],{},[898,10565,2406],{},[898,10567,2225],{},[1700,10569,1732],{"separator":1731},[898,10571,2406],{},[898,10573,2215],{},[902,10575,10576],{"encoding":904},"dx, dy"," platí ",[883,10579,10581],{"className":10580},[886],[888,10582,10583],{"xmlns":890},[892,10584,10585,10597],{},[895,10586,10587,10589,10591,10593,10595],{},[898,10588,3084],{"mathvariant":1791},[898,10590,2220],{},[1700,10592,2927],{},[898,10594,2406],{},[898,10596,2220],{},[902,10598,10599],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,10602,10604],{"id":10603},"implicitní-funkce","Implicitní funkce",[724,10606,10607,10608,10637,10638,10651,10652,10665],{},"Je-li vztah dán rovnicí ",[883,10609,10611],{"className":10610},[886],[888,10612,10613],{"xmlns":890},[892,10614,10615,10634],{},[895,10616,10617,10620,10622,10624,10626,10628,10630,10632],{},[898,10618,10619],{},"F",[1700,10621,1703],{"stretchy":1702},[898,10623,2225],{},[1700,10625,1732],{"separator":1731},[898,10627,2215],{},[1700,10629,1709],{"stretchy":1702},[1700,10631,1765],{},[1931,10633,1772],{},[902,10635,10636],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,10639,10641],{"className":10640},[886],[888,10642,10643],{"xmlns":890},[892,10644,10645,10649],{},[895,10646,10647],{},[898,10648,2215],{},[902,10650,2215],{"encoding":904}," podle ",[883,10653,10655],{"className":10654},[886],[888,10656,10657],{"xmlns":890},[892,10658,10659,10663],{},[895,10660,10661],{},[898,10662,2225],{},[902,10664,2225],{"encoding":904}," (nebo naopak):",[724,10667,10668],{},[883,10669,10671],{"className":10670},[886],[888,10672,10673],{"xmlns":890},[892,10674,10675,10769],{},[895,10676,10677,10683,10685,10699,10701,10703,10721,10723,10725,10731,10733,10747,10749,10751],{},[1785,10678,10679,10681],{},[898,10680,2215],{},[1700,10682,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,10684,1765],{},[1774,10686,10687,10693],{},[895,10688,10689,10691],{},[898,10690,2406],{},[898,10692,2215],{},[895,10694,10695,10697],{},[898,10696,2406],{},[898,10698,2225],{},[1700,10700,1765],{},[1700,10702,1768],{},[1774,10704,10705,10713],{},[2030,10706,10707,10709,10711],{},[898,10708,10619],{},[898,10710,2225],{},[1700,10712,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[2030,10714,10715,10717,10719],{},[898,10716,10619],{},[898,10718,2215],{},[1700,10720,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,10722,1732],{"separator":1731},[6066,10724],{"width":6068},[1785,10726,10727,10729],{},[898,10728,2225],{},[1700,10730,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,10732,1765],{},[1774,10734,10735,10741],{},[895,10736,10737,10739],{},[898,10738,2406],{},[898,10740,2225],{},[895,10742,10743,10745],{},[898,10744,2406],{},[898,10746,2215],{},[1700,10748,1765],{},[1700,10750,1768],{},[1774,10752,10753,10761],{},[2030,10754,10755,10757,10759],{},[898,10756,10619],{},[898,10758,2215],{},[1700,10760,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[2030,10762,10763,10765,10767],{},[898,10764,10619],{},[898,10766,2225],{},[1700,10768,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,10770,10771],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,10773,10774,10775,10778,10779,2114,10783,2196],{},"Tato vzorec dává ",[38,10776,10777],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,10780,10782],{"className":10781,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,10784,10786],{"className":10785,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,10788,10790],{"id":10789},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,10792,3445],{"id":3444},[724,10794,10795,10796,10820],{},"V bodě extrému ",[883,10797,10799],{"className":10798},[886],[888,10800,10801],{"xmlns":890},[892,10802,10803,10817],{},[895,10804,10805,10807,10809,10811,10813,10815],{},[898,10806,1862],{},[1700,10808,1927],{"stretchy":1702},[898,10810,207],{},[1700,10812,1732],{"separator":1731},[898,10814,1879],{},[1700,10816,1970],{"stretchy":1702},[902,10818,10819],{"encoding":904},"A[a, b]"," musí platit současně:",[724,10822,10823],{},[883,10824,10826],{"className":10825},[886],[888,10827,10828],{"xmlns":890},[892,10829,10830,10883],{},[895,10831,10832,10840,10842,10844,10846,10848,10850,10852,10854,10856,10859,10861,10869,10871,10873,10875,10877,10879,10881],{},[2030,10833,10834,10836,10838],{},[898,10835,2220],{},[898,10837,2225],{},[1700,10839,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,10841,1703],{"stretchy":1702},[898,10843,207],{},[1700,10845,1732],{"separator":1731},[898,10847,1879],{},[1700,10849,1709],{"stretchy":1702},[1700,10851,1765],{},[1931,10853,1772],{},[1781,10855,4175],{},[1700,10857,10858],{},"∧",[1781,10860,4175],{},[2030,10862,10863,10865,10867],{},[898,10864,2220],{},[898,10866,2215],{},[1700,10868,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,10870,1703],{"stretchy":1702},[898,10872,207],{},[1700,10874,1732],{"separator":1731},[898,10876,1879],{},[1700,10878,1709],{"stretchy":1702},[1700,10880,1765],{},[1931,10882,1772],{},[902,10884,10885],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,10887,3519],{"id":3518},[724,10889,10890,10891,10894],{},"Definujeme ",[38,10892,10893],{},"diskriminant"," (Hessián zjednodušeně):",[724,10896,10897],{},[883,10898,10900],{"className":10899},[886],[888,10901,10902],{"xmlns":890},[892,10903,10904,10980],{},[895,10905,10906,10908,10910,10912,10914,10916,10918,10920,10936,10938,10954,10956,10958,10974],{},[898,10907,4374],{},[1700,10909,1703],{"stretchy":1702},[898,10911,2225],{},[1700,10913,1732],{"separator":1731},[898,10915,2215],{},[1700,10917,1709],{"stretchy":1702},[1700,10919,1765],{},[2030,10921,10922,10924,10930],{},[898,10923,2220],{},[895,10925,10926,10928],{},[898,10927,2225],{},[898,10929,2225],{},[895,10931,10932,10934],{},[1700,10933,1793],{"mathvariant":1791},[1700,10935,1793],{"mathvariant":1791},[1700,10937,2065],{},[2030,10939,10940,10942,10948],{},[898,10941,2220],{},[895,10943,10944,10946],{},[898,10945,2215],{},[898,10947,2215],{},[895,10949,10950,10952],{},[1700,10951,1793],{"mathvariant":1791},[1700,10953,1793],{"mathvariant":1791},[1700,10955,1768],{},[1700,10957,1703],{"stretchy":1702},[2030,10959,10960,10962,10968],{},[898,10961,2220],{},[895,10963,10964,10966],{},[898,10965,2225],{},[898,10967,2215],{},[895,10969,10970,10972],{},[1700,10971,1793],{"mathvariant":1791},[1700,10973,1793],{"mathvariant":1791},[1785,10975,10976,10978],{},[1700,10977,1709],{"stretchy":1702},[1931,10979,2343],{},[902,10981,10982],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,10984,10985,10986,2901],{},"V podezřelém bodě ",[883,10987,10989],{"className":10988},[886],[888,10990,10991],{"xmlns":890},[892,10992,10993,11005],{},[895,10994,10995,10997,10999,11001,11003],{},[1700,10996,1927],{"stretchy":1702},[898,10998,207],{},[1700,11000,1732],{"separator":1731},[898,11002,1879],{},[1700,11004,1970],{"stretchy":1702},[902,11006,11007],{"encoding":904},"[a, b]",[152,11009,11010,11137,11173],{},[123,11011,11012,11042,11043],{},[38,11013,11014,2901],{},[883,11015,11017],{"className":11016},[886],[888,11018,11019],{"xmlns":890},[892,11020,11021,11039],{},[895,11022,11023,11025,11027,11029,11031,11033,11035,11037],{},[898,11024,4374],{},[1700,11026,1703],{"stretchy":1702},[898,11028,207],{},[1700,11030,1732],{"separator":1731},[898,11032,1879],{},[1700,11034,1709],{"stretchy":1702},[1700,11036,3601],{},[1931,11038,1772],{},[902,11040,11041],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,11044,11045,11091],{},[123,11046,11047,3607,11089],{},[883,11048,11050],{"className":11049},[886],[888,11051,11052],{"xmlns":890},[892,11053,11054,11086],{},[895,11055,11056,11072,11074,11076,11078,11080,11082,11084],{},[2030,11057,11058,11060,11066],{},[898,11059,2220],{},[895,11061,11062,11064],{},[898,11063,2225],{},[898,11065,2225],{},[895,11067,11068,11070],{},[1700,11069,1793],{"mathvariant":1791},[1700,11071,1793],{"mathvariant":1791},[1700,11073,1703],{"stretchy":1702},[898,11075,207],{},[1700,11077,1732],{"separator":1731},[898,11079,1879],{},[1700,11081,1709],{"stretchy":1702},[1700,11083,3601],{},[1931,11085,1772],{},[902,11087,11088],{"encoding":904},"f''_{xx}(a, b) > 0",[38,11090,3968],{},[123,11092,11093,3607,11135],{},[883,11094,11096],{"className":11095},[886],[888,11097,11098],{"xmlns":890},[892,11099,11100,11132],{},[895,11101,11102,11118,11120,11122,11124,11126,11128,11130],{},[2030,11103,11104,11106,11112],{},[898,11105,2220],{},[895,11107,11108,11110],{},[898,11109,2225],{},[898,11111,2225],{},[895,11113,11114,11116],{},[1700,11115,1793],{"mathvariant":1791},[1700,11117,1793],{"mathvariant":1791},[1700,11119,1703],{"stretchy":1702},[898,11121,207],{},[1700,11123,1732],{"separator":1731},[898,11125,1879],{},[1700,11127,1709],{"stretchy":1702},[1700,11129,3640],{},[1931,11131,1772],{},[902,11133,11134],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,11136,3910],{},[123,11138,11139,2106,11169,11172],{},[38,11140,11141,2901],{},[883,11142,11144],{"className":11143},[886],[888,11145,11146],{"xmlns":890},[892,11147,11148,11166],{},[895,11149,11150,11152,11154,11156,11158,11160,11162,11164],{},[898,11151,4374],{},[1700,11153,1703],{"stretchy":1702},[898,11155,207],{},[1700,11157,1732],{"separator":1731},[898,11159,1879],{},[1700,11161,1709],{"stretchy":1702},[1700,11163,3640],{},[1931,11165,1772],{},[902,11167,11168],{"encoding":904},"D(a, b) \u003C 0",[38,11170,11171],{},"sedlo"," (v daném bodě extrém není).",[123,11174,11175,11205],{},[38,11176,11177,2901],{},[883,11178,11180],{"className":11179},[886],[888,11181,11182],{"xmlns":890},[892,11183,11184,11202],{},[895,11185,11186,11188,11190,11192,11194,11196,11198,11200],{},[898,11187,4374],{},[1700,11189,1703],{"stretchy":1702},[898,11191,207],{},[1700,11193,1732],{"separator":1731},[898,11195,1879],{},[1700,11197,1709],{"stretchy":1702},[1700,11199,1765],{},[1931,11201,1772],{},[902,11203,11204],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,11207,11209],{"id":11208},"vázané-extrémy","Vázané extrémy",[724,11211,11212,11213,11242,11243,2196],{},"Pro extrémy s omezující podmínkou ",[883,11214,11216],{"className":11215},[886],[888,11217,11218],{"xmlns":890},[892,11219,11220,11239],{},[895,11221,11222,11225,11227,11229,11231,11233,11235,11237],{},[898,11223,11224],{},"g",[1700,11226,1703],{"stretchy":1702},[898,11228,2225],{},[1700,11230,1732],{"separator":1731},[898,11232,2215],{},[1700,11234,1709],{"stretchy":1702},[1700,11236,1765],{},[1931,11238,1772],{},[902,11240,11241],{"encoding":904},"g(x, y) = 0"," se používá ",[207,11244,793],{"className":11245,"dataFsResolvedFilePath":791,"href":792},[210],[115,11247,3985],{"id":3984},[120,11249,11250,11257,11264],{},[123,11251,11252,2106,11254],{},[38,11253,3992],{},[207,11255,775],{"className":11256,"dataFsResolvedFilePath":773,"href":774},[210],[123,11258,11259,2106,11261],{},[38,11260,4000],{},[207,11262,793],{"className":11263,"dataFsResolvedFilePath":791,"href":792},[210],[123,11265,11266,2106,11268,11272,11273,11276,11277,11280],{},[38,11267,4008],{},[207,11269,11271],{"className":11270,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,11274,880],{"className":11275,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,11278,1649],{"className":11279,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":11282},[11283,11284,11288,11289,11290,11294,11295],{"id":9846,"depth":642,"text":9847},{"id":10000,"depth":642,"text":10001,"children":11285},[11286,11287],{"id":10153,"depth":649,"text":10154},{"id":2764,"depth":649,"text":2765},{"id":10481,"depth":642,"text":10482},{"id":10603,"depth":642,"text":10604},{"id":10789,"depth":642,"text":10790,"children":11291},[11292,11293],{"id":3444,"depth":649,"text":3445},{"id":3518,"depth":649,"text":3519},{"id":11208,"depth":642,"text":11209},{"id":3984,"depth":642,"text":3985},"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":9757,"description":11296},[1135],"topics\u002Ffunkce-vice-promennych",[1128,11303,4046,11304,11305,11306],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":11309,"title":775,"body":11310,"course":1128,"courses":659,"created":1129,"description":12166,"extension":661,"meta":12167,"navigation":664,"path":12168,"seo":12169,"sources":12170,"stem":12171,"tags":12172,"type":4049,"updated":677,"__hash__":12179},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":11311,"toc":12156},[11312,11315,11326,11330,11375,11455,11459,11535,11577,11584,11588,11592,11621,11679,11726,11764,11768,11818,11870,11922,11966,11969,11972,12044,12047,12119,12126,12128],[12,11313,775],{"id":11314},"integrál",[724,11316,11317,11318,11321,11322,11325],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,11319,11320],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,11323,11324],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,11327,11329],{"id":11328},"neurčitý-integrál","Neurčitý integrál",[724,11331,11332],{},[883,11333,11335],{"className":11334},[886],[888,11336,11337],{"xmlns":890},[892,11338,11339,11372],{},[895,11340,11341,11343,11345,11347,11349,11351,11354,11356,11358,11360,11362,11364,11366,11368,11370],{},[898,11342,10619],{},[1700,11344,1703],{"stretchy":1702},[898,11346,2225],{},[1700,11348,1709],{"stretchy":1702},[1700,11350,1765],{},[1700,11352,11353],{},"∫",[898,11355,2220],{},[1700,11357,1703],{"stretchy":1702},[898,11359,2225],{},[1700,11361,1709],{"stretchy":1702},[1781,11363,1783],{},[898,11365,2406],{},[898,11367,2225],{},[1700,11369,1897],{},[898,11371,2974],{},[902,11373,11374],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,11376,4499,11377,3122,11411,8290,11424,11427,11428,1343,11441,11454],{},[883,11378,11380],{"className":11379},[886],[888,11381,11382],{"xmlns":890},[892,11383,11384,11408],{},[895,11385,11386,11392,11394,11396,11398,11400,11402,11404,11406],{},[1785,11387,11388,11390],{},[898,11389,10619],{},[1700,11391,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,11393,1703],{"stretchy":1702},[898,11395,2225],{},[1700,11397,1709],{"stretchy":1702},[1700,11399,1765],{},[898,11401,2220],{},[1700,11403,1703],{"stretchy":1702},[898,11405,2225],{},[1700,11407,1709],{"stretchy":1702},[902,11409,11410],{"encoding":904},"F'(x) = f(x)",[883,11412,11414],{"className":11413},[886],[888,11415,11416],{"xmlns":890},[892,11417,11418,11422],{},[895,11419,11420],{},[898,11421,10619],{},[902,11423,10619],{"encoding":904},[38,11425,11426],{},"primitivní funkce"," k ",[883,11429,11431],{"className":11430},[886],[888,11432,11433],{"xmlns":890},[892,11434,11435,11439],{},[895,11436,11437],{},[898,11438,2220],{},[902,11440,2220],{"encoding":904},[883,11442,11444],{"className":11443},[886],[888,11445,11446],{"xmlns":890},[892,11447,11448,11452],{},[895,11449,11450],{},[898,11451,2974],{},[902,11453,2974],{"encoding":904}," konstanta.",[115,11456,11458],{"id":11457},"určitý-integrál","Určitý integrál",[724,11460,11461],{},[883,11462,11464],{"className":11463},[886],[888,11465,11466],{"xmlns":890},[892,11467,11468,11532],{},[895,11469,11470,11478,11480,11482,11484,11486,11488,11490,11492,11494,11496,11498,11500,11502,11504,11512,11514,11516,11518,11520,11522,11524,11526,11528,11530],{},[2030,11471,11472,11474,11476],{},[1700,11473,11353],{},[898,11475,207],{},[898,11477,1879],{},[898,11479,2220],{},[1700,11481,1703],{"stretchy":1702},[898,11483,2225],{},[1700,11485,1709],{"stretchy":1702},[1781,11487,1783],{},[898,11489,2406],{},[898,11491,2225],{},[1700,11493,1765],{},[1700,11495,1927],{"stretchy":1702},[898,11497,10619],{},[1700,11499,1703],{"stretchy":1702},[898,11501,2225],{},[1700,11503,1709],{"stretchy":1702},[2030,11505,11506,11508,11510],{},[1700,11507,1970],{"stretchy":1702},[898,11509,207],{},[898,11511,1879],{},[1700,11513,1765],{},[898,11515,10619],{},[1700,11517,1703],{"stretchy":1702},[898,11519,1879],{},[1700,11521,1709],{"stretchy":1702},[1700,11523,1768],{},[898,11525,10619],{},[1700,11527,1703],{"stretchy":1702},[898,11529,207],{},[1700,11531,1709],{"stretchy":1702},[902,11533,11534],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,11536,11537,11538,2106,11541,11554,11555,11576],{},"Geometricky ",[38,11539,11540],{},"plocha pod grafem",[883,11542,11544],{"className":11543},[886],[888,11545,11546],{"xmlns":890},[892,11547,11548,11552],{},[895,11549,11550],{},[898,11551,2220],{},[902,11553,2220],{"encoding":904}," na intervalu ",[883,11556,11558],{"className":11557},[886],[888,11559,11560],{"xmlns":890},[892,11561,11562,11574],{},[895,11563,11564,11566,11568,11570,11572],{},[1700,11565,1927],{"stretchy":1702},[898,11567,207],{},[1700,11569,1732],{"separator":1731},[898,11571,1879],{},[1700,11573,1970],{"stretchy":1702},[902,11575,11007],{"encoding":904}," (orientovaná).",[724,11578,11579],{},[2756,11580],{"alt":11581,"className":11582,"src":11583},"imek-integral-plocha",[210,2760],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,11585,11587],{"id":11586},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,11589,11591],{"id":11590},"příklad-tr-z-mr","Příklad — TR z MR",[724,11593,11594,11595,2196],{},"Mezní příjem ",[883,11596,11598],{"className":11597},[886],[888,11599,11600],{"xmlns":890},[892,11601,11602,11618],{},[895,11603,11604,11606,11608,11610,11612,11614,11616],{},[898,11605,2005],{},[898,11607,4185],{},[1700,11609,1765],{},[1931,11611,3284],{},[1700,11613,1768],{},[1931,11615,2343],{},[898,11617,1662],{},[902,11619,11620],{"encoding":904},"MR = 100 - 2Q",[724,11622,11623],{},[883,11624,11626],{"className":11625},[886],[888,11627,11628],{"xmlns":890},[892,11629,11630,11676],{},[895,11631,11632,11634,11636,11638,11640,11642,11644,11646,11648,11650,11652,11654,11656,11658,11660,11662,11664,11666,11672,11674],{},[898,11633,2971],{},[898,11635,4185],{},[1700,11637,1765],{},[1700,11639,11353],{},[1700,11641,1703],{"stretchy":1702},[1931,11643,3284],{},[1700,11645,1768],{},[1931,11647,2343],{},[898,11649,1662],{},[1700,11651,1709],{"stretchy":1702},[1781,11653,1783],{},[898,11655,2406],{},[898,11657,1662],{},[1700,11659,1765],{},[1931,11661,3284],{},[898,11663,1662],{},[1700,11665,1768],{},[1785,11667,11668,11670],{},[898,11669,1662],{},[1931,11671,2343],{},[1700,11673,1897],{},[898,11675,2354],{},[902,11677,11678],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,11680,11681,11682,3607,11708,2901],{},"Okrajová podmínka ",[883,11683,11685],{"className":11684},[886],[888,11686,11687],{"xmlns":890},[892,11688,11689,11705],{},[895,11690,11691,11693,11695,11697,11699,11701,11703],{},[898,11692,2971],{},[898,11694,4185],{},[1700,11696,1703],{"stretchy":1702},[1931,11698,1772],{},[1700,11700,1709],{"stretchy":1702},[1700,11702,1765],{},[1931,11704,1772],{},[902,11706,11707],{"encoding":904},"TR(0) = 0",[883,11709,11711],{"className":11710},[886],[888,11712,11713],{"xmlns":890},[892,11714,11715,11723],{},[895,11716,11717,11719,11721],{},[898,11718,2354],{},[1700,11720,1765],{},[1931,11722,1772],{},[902,11724,11725],{"encoding":904},"c = 0",[724,11727,11728],{},[883,11729,11731],{"className":11730},[886],[888,11732,11733],{"xmlns":890},[892,11734,11735,11761],{},[895,11736,11737,11739,11741,11743,11745,11747,11749,11751,11753,11755],{},[898,11738,2971],{},[898,11740,4185],{},[1700,11742,1703],{"stretchy":1702},[898,11744,1662],{},[1700,11746,1709],{"stretchy":1702},[1700,11748,1765],{},[1931,11750,3284],{},[898,11752,1662],{},[1700,11754,1768],{},[1785,11756,11757,11759],{},[898,11758,1662],{},[1931,11760,2343],{},[902,11762,11763],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,11765,11767],{"id":11766},"příklad-tc-z-mc","Příklad — TC z MC",[724,11769,11770,11771,11797,11798,2196],{},"Mezní náklady ",[883,11772,11774],{"className":11773},[886],[888,11775,11776],{"xmlns":890},[892,11777,11778,11794],{},[895,11779,11780,11782,11784,11786,11788,11790,11792],{},[898,11781,2005],{},[898,11783,2974],{},[1700,11785,1765],{},[1931,11787,2343],{},[1700,11789,1897],{},[1931,11791,3034],{},[898,11793,1662],{},[902,11795,11796],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,11799,11801],{"className":11800},[886],[888,11802,11803],{"xmlns":890},[892,11804,11805,11815],{},[895,11806,11807,11809,11811,11813],{},[898,11808,10619],{},[898,11810,2974],{},[1700,11812,1765],{},[1931,11814,3284],{},[902,11816,11817],{"encoding":904},"FC = 100",[724,11819,11820],{},[883,11821,11823],{"className":11822},[886],[888,11824,11825],{"xmlns":890},[892,11826,11827,11867],{},[895,11828,11829,11831,11833,11835,11837,11839,11841,11843,11845,11847,11849,11851,11853,11855,11857,11863,11865],{},[898,11830,2971],{},[898,11832,2974],{},[1700,11834,1765],{},[1700,11836,11353],{},[898,11838,2005],{},[898,11840,2974],{},[1781,11842,1783],{},[898,11844,2406],{},[898,11846,1662],{},[1700,11848,1765],{},[1931,11850,2343],{},[898,11852,1662],{},[1700,11854,1897],{},[1931,11856,2990],{},[1785,11858,11859,11861],{},[898,11860,1662],{},[1931,11862,2343],{},[1700,11864,1897],{},[898,11866,2354],{},[902,11868,11869],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,11871,11681,11872,3607,11904,2901],{},[883,11873,11875],{"className":11874},[886],[888,11876,11877],{"xmlns":890},[892,11878,11879,11901],{},[895,11880,11881,11883,11885,11887,11889,11891,11893,11895,11897,11899],{},[898,11882,2971],{},[898,11884,2974],{},[1700,11886,1703],{"stretchy":1702},[1931,11888,1772],{},[1700,11890,1709],{"stretchy":1702},[1700,11892,1765],{},[898,11894,10619],{},[898,11896,2974],{},[1700,11898,1765],{},[1931,11900,3284],{},[902,11902,11903],{"encoding":904},"TC(0) = FC = 100",[883,11905,11907],{"className":11906},[886],[888,11908,11909],{"xmlns":890},[892,11910,11911,11919],{},[895,11912,11913,11915,11917],{},[898,11914,2354],{},[1700,11916,1765],{},[1931,11918,3284],{},[902,11920,11921],{"encoding":904},"c = 100",[724,11923,11924],{},[883,11925,11927],{"className":11926},[886],[888,11928,11929],{"xmlns":890},[892,11930,11931,11963],{},[895,11932,11933,11935,11937,11939,11941,11943,11945,11947,11949,11951,11953,11955,11957],{},[898,11934,2971],{},[898,11936,2974],{},[1700,11938,1703],{"stretchy":1702},[898,11940,1662],{},[1700,11942,1709],{"stretchy":1702},[1700,11944,1765],{},[1931,11946,3284],{},[1700,11948,1897],{},[1931,11950,2343],{},[898,11952,1662],{},[1700,11954,1897],{},[1931,11956,2990],{},[1785,11958,11959,11961],{},[898,11960,1662],{},[1931,11962,2343],{},[902,11964,11965],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,11967,820],{"id":11968},"přebytek-spotřebitele-a-výrobce",[724,11970,11971],{},"Přebytek spotřebitele:",[724,11973,11974],{},[883,11975,11977],{"className":11976},[886],[888,11978,11979],{"xmlns":890},[892,11980,11981,12041],{},[895,11982,11983,11985,11987,11989,11995,11997,11999,12011,12013,12015,12017,12019,12021,12023,12025,12027,12033,12035],{},[898,11984,2974],{},[898,11986,8861],{},[1700,11988,1703],{"stretchy":1702},[2007,11990,11991,11993],{},[898,11992,1662],{},[1931,11994,1772],{},[1700,11996,1709],{"stretchy":1702},[1700,11998,1765],{},[2030,12000,12001,12003,12005],{},[1700,12002,11353],{},[1931,12004,1772],{},[2007,12006,12007,12009],{},[898,12008,1662],{},[1931,12010,1772],{},[898,12012,4374],{},[1700,12014,1703],{"stretchy":1702},[898,12016,1662],{},[1700,12018,1709],{"stretchy":1702},[1781,12020,1783],{},[898,12022,2406],{},[898,12024,1662],{},[1700,12026,1768],{},[2007,12028,12029,12031],{},[898,12030,1677],{},[1931,12032,1772],{},[1781,12034,1783],{},[2007,12036,12037,12039],{},[898,12038,1662],{},[1931,12040,1772],{},[902,12042,12043],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,12045,12046],{},"Přebytek výrobce:",[724,12048,12049],{},[883,12050,12052],{"className":12051},[886],[888,12053,12054],{"xmlns":890},[892,12055,12056,12116],{},[895,12057,12058,12060,12062,12064,12070,12072,12074,12080,12082,12088,12090,12102,12104,12106,12108,12110,12112,12114],{},[898,12059,1677],{},[898,12061,8861],{},[1700,12063,1703],{"stretchy":1702},[2007,12065,12066,12068],{},[898,12067,1662],{},[1931,12069,1772],{},[1700,12071,1709],{"stretchy":1702},[1700,12073,1765],{},[2007,12075,12076,12078],{},[898,12077,1677],{},[1931,12079,1772],{},[1781,12081,1783],{},[2007,12083,12084,12086],{},[898,12085,1662],{},[1931,12087,1772],{},[1700,12089,1768],{},[2030,12091,12092,12094,12096],{},[1700,12093,11353],{},[1931,12095,1772],{},[2007,12097,12098,12100],{},[898,12099,1662],{},[1931,12101,1772],{},[898,12103,8861],{},[1700,12105,1703],{"stretchy":1702},[898,12107,1662],{},[1700,12109,1709],{"stretchy":1702},[1781,12111,1783],{},[898,12113,2406],{},[898,12115,1662],{},[902,12117,12118],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,12120,12121,12122,2196],{},"Detailně viz ",[207,12123,12125],{"className":12124,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,12127,3985],{"id":3984},[120,12129,12130,12137,12144],{},[123,12131,12132,2106,12134],{},[38,12133,3992],{},[207,12135,766],{"className":12136,"dataFsResolvedFilePath":764,"href":765},[210],[123,12138,12139,2106,12141],{},[38,12140,4000],{},[207,12142,784],{"className":12143,"dataFsResolvedFilePath":782,"href":783},[210],[123,12145,12146,2106,12148,12151,12152,12155],{},[38,12147,4008],{},[207,12149,4016],{"className":12150,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,12153,12125],{"className":12154,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":12157},[12158,12159,12160,12165],{"id":11328,"depth":642,"text":11329},{"id":11457,"depth":642,"text":11458},{"id":11586,"depth":642,"text":11587,"children":12161},[12162,12163,12164],{"id":11590,"depth":649,"text":11591},{"id":11766,"depth":649,"text":11767},{"id":11968,"depth":649,"text":820},{"id":3984,"depth":642,"text":3985},"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":12166},[1135],"topics\u002Fintegral",[1128,12173,12174,12175,12176,12177,12178],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":12181,"title":12182,"body":12183,"course":1128,"courses":659,"created":9743,"description":641,"extension":661,"meta":16451,"navigation":664,"path":16452,"seo":16453,"sources":16454,"stem":16455,"tags":16456,"type":4049,"updated":677,"__hash__":16462},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":12184,"toc":16439},[12185,12188,12192,12336,12343,12347,12417,12455,12558,12562,12592,12658,12705,12708,12777,12780,12815,12851,12855,12903,12910,12956,13002,13005,13084,13181,13264,13268,13312,13342,13348,13377,13399,13449,13502,13568,13571,13637,13666,13725,13741,13828,13926,14057,14061,14218,14367,14747,14751,14754,14813,14816,14902,14930,14968,14971,15008,15048,15082,15084,15121,15153,15251,15256,15380,15432,15514,15653,15657,15777,15784,15895,15902,15906,16381,16383],[12,12186,12182],{"id":12187},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,12189,12191],{"id":12190},"tldr","TL;DR",[724,12193,12194,12197,12198,10208,12201,12214,12215,12229,12230,12233,12234,1343,12237,12240,12241,1343,12244,12247,12248,2106,12251,12281,12282,12285,12286,1343,12300,12313,12314,12317,12318,4110],{},[38,12195,12196],{},"IS-LM"," je makroekonomický model se ",[38,12199,12200],{},"dvěma neznámými",[883,12202,12204],{"className":12203},[886],[888,12205,12206],{"xmlns":890},[892,12207,12208,12212],{},[895,12209,12210],{},[898,12211,9316],{},[902,12213,9316],{"encoding":904}," — národní důchod a ",[883,12216,12218],{"className":12217},[886],[888,12219,12220],{"xmlns":890},[892,12221,12222,12227],{},[895,12223,12224],{},[898,12225,12226],{},"r",[902,12228,12226],{"encoding":904}," — úroková míra) a ",[38,12231,12232],{},"dvěma trhy",": trhem zboží (křivka ",[38,12235,12236],{},"IS",[614,12238,12239],{},"Investment = Savings",") a trhem peněz (křivka ",[38,12242,12243],{},"LM",[614,12245,12246],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,12249,12250],{},"simultánní rovnováhu",[883,12252,12254],{"className":12253},[886],[888,12255,12256],{"xmlns":890},[892,12257,12258,12278],{},[895,12259,12260,12262,12268,12270,12276],{},[1700,12261,1703],{"stretchy":1702},[1785,12263,12264,12266],{},[898,12265,9316],{},[898,12267,1762],{},[1700,12269,1732],{"separator":1731},[1785,12271,12272,12274],{},[898,12273,12226],{},[898,12275,1762],{},[1700,12277,1709],{"stretchy":1702},[902,12279,12280],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,12283,12284],{},"fiskální politiky"," (posun IS změnou ",[883,12287,12289],{"className":12288},[886],[888,12290,12291],{"xmlns":890},[892,12292,12293,12298],{},[895,12294,12295],{},[898,12296,12297],{},"G",[902,12299,12297],{"encoding":904},[883,12301,12303],{"className":12302},[886],[888,12304,12305],{"xmlns":890},[892,12306,12307,12311],{},[895,12308,12309],{},[898,12310,2971],{},[902,12312,2971],{"encoding":904},") a ",[38,12315,12316],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,12319,12321],{"className":12320},[886],[888,12322,12323],{"xmlns":890},[892,12324,12325,12333],{},[895,12326,12327],{},[1785,12328,12329,12331],{},[898,12330,2005],{},[1700,12332,4543],{},[902,12334,12335],{"encoding":904},"M^*",[724,12337,12338],{},[2756,12339],{"alt":12340,"className":12341,"src":12342},"imek-is-lm-model",[210,2760],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,12344,12346],{"id":12345},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,12348,12349,12350,12354,12355,10208,12358,12381,12382,12385,12386,12402,12403,12416],{},"V modelech ",[207,12351,12353],{"className":12352,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,12356,12357],{},"investice pokládány za konstantní",[883,12359,12361],{"className":12360},[886],[888,12362,12363],{"xmlns":890},[892,12364,12365,12378],{},[895,12366,12367,12370,12372],{},[898,12368,12369],{},"I",[1700,12371,1765],{},[1785,12373,12374,12376],{},[898,12375,12369],{},[1700,12377,4543],{},[902,12379,12380],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,12383,12384],{},"ceně peněz",", tedy na ",[38,12387,12388,12389],{},"úrokové míře ",[883,12390,12392],{"className":12391},[886],[888,12393,12394],{"xmlns":890},[892,12395,12396,12400],{},[895,12397,12398],{},[898,12399,12226],{},[902,12401,12226],{"encoding":904},": čím vyšší ",[883,12404,12406],{"className":12405},[886],[888,12407,12408],{"xmlns":890},[892,12409,12410,12414],{},[895,12411,12412],{},[898,12413,12226],{},[902,12415,12226],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,12418,12419,12449],{},[123,12420,12421,2106,12424,12448],{},[38,12422,12423],{},"funkci investic",[883,12425,12427],{"className":12426},[886],[888,12428,12429],{"xmlns":890},[892,12430,12431,12445],{},[895,12432,12433,12435,12437,12439,12441,12443],{},[898,12434,12369],{},[1700,12436,1765],{},[898,12438,12369],{},[1700,12440,1703],{"stretchy":1702},[898,12442,12226],{},[1700,12444,1709],{"stretchy":1702},[902,12446,12447],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,12450,12451,12454],{},[38,12452,12453],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[4060,12456,12457],{},[724,12458,12459,12461,12462,12481,12482,12509,12510,12523,12524,12553,12554,12557],{},[883,12460,4601],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,12463,12465],{"className":12464},[886],[888,12466,12467],{"xmlns":890},[892,12468,12469,12478],{},[895,12470,12471,12473,12476],{},[898,12472,2974],{},[1781,12474,12475],{},"-",[898,12477,12369],{},[902,12479,12480],{"encoding":904},"C\\text{-}I"," až ",[883,12483,12485],{"className":12484},[886],[888,12486,12487],{"xmlns":890},[892,12488,12489,12506],{},[895,12490,12491,12493,12495,12497,12499,12501,12503],{},[898,12492,2974],{},[1781,12494,12475],{},[898,12496,12369],{},[1781,12498,12475],{},[898,12500,12297],{},[1781,12502,12475],{},[898,12504,12505],{},"X",[902,12507,12508],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,12511,12513],{"className":12512},[886],[888,12514,12515],{"xmlns":890},[892,12516,12517,12521],{},[895,12518,12519],{},[898,12520,9316],{},[902,12522,9316],{"encoding":904},". V IS-LM jsou ",[38,12525,12526,12527,2114,12540],{},"dvě neznámé ",[883,12528,12530],{"className":12529},[886],[888,12531,12532],{"xmlns":890},[892,12533,12534,12538],{},[895,12535,12536],{},[898,12537,9316],{},[902,12539,9316],{"encoding":904},[883,12541,12543],{"className":12542},[886],[888,12544,12545],{"xmlns":890},[892,12546,12547,12551],{},[895,12548,12549],{},[898,12550,12226],{},[902,12552,12226],{"encoding":904},", a proto potřebujeme ",[38,12555,12556],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,12559,12561],{"id":12560},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,12563,12564,12565,12578,12579,2901],{},"Lineární závislost investic ",[883,12566,12568],{"className":12567},[886],[888,12569,12570],{"xmlns":890},[892,12571,12572,12576],{},[895,12573,12574],{},[898,12575,12369],{},[902,12577,12369],{"encoding":904}," na úrokové míře ",[883,12580,12582],{"className":12581},[886],[888,12583,12584],{"xmlns":890},[892,12585,12586,12590],{},[895,12587,12588],{},[898,12589,12226],{},[902,12591,12226],{"encoding":904},[724,12593,12594],{},[883,12595,12597],{"className":12596},[886],[888,12598,12599],{"xmlns":890},[892,12600,12601,12655],{},[895,12602,12603,12605,12607,12609,12611,12613,12615,12617,12619,12621,12623,12625,12627,12629,12631,12633,12635,12637,12639,12641,12643,12646,12648,12650,12653],{},[898,12604,12369],{},[1700,12606,1765],{},[898,12608,12369],{},[1700,12610,1703],{"stretchy":1702},[898,12612,12226],{},[1700,12614,1709],{"stretchy":1702},[1700,12616,1765],{},[898,12618,2354],{},[898,12620,12226],{},[1700,12622,1897],{},[898,12624,2406],{},[1700,12626,1732],{"separator":1731},[6066,12628],{"width":6068},[898,12630,2354],{},[1700,12632,3640],{},[1931,12634,1772],{},[1700,12636,1732],{"separator":1731},[1781,12638,2495],{},[898,12640,2406],{},[1700,12642,3601],{},[1931,12644,12645],{},"0.",[6066,12647],{"width":6068},[1700,12649,1703],{"stretchy":1702},[1931,12651,12652],{},"7.11",[1700,12654,1709],{"stretchy":1702},[902,12656,12657],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,12659,12660,12681],{},[123,12661,12662,12680],{},[883,12663,12665],{"className":12664},[886],[888,12666,12667],{"xmlns":890},[892,12668,12669,12677],{},[895,12670,12671,12673,12675],{},[898,12672,2406],{},[1700,12674,3601],{},[1931,12676,1772],{},[902,12678,12679],{"encoding":904},"d > 0"," zřejmé,",[123,12682,12683,12701,12702,2196],{},[883,12684,12686],{"className":12685},[886],[888,12687,12688],{"xmlns":890},[892,12689,12690,12698],{},[895,12691,12692,12694,12696],{},[898,12693,2354],{},[1700,12695,3640],{},[1931,12697,1772],{},[902,12699,12700],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,12703,12704],{},"klesající",[724,12706,12707],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,12709,12710],{},[883,12711,12713],{"className":12712},[886],[888,12714,12715],{"xmlns":890},[892,12716,12717,12774],{},[895,12718,12719,12721,12723,12725,12727,12729,12731,12733,12735,12737,12739,12741,12743,12745,12747,12749,12751,12753,12755,12757,12759,12761,12763,12765,12767,12769,12772],{},[898,12720,2974],{},[1700,12722,1765],{},[898,12724,2974],{},[1700,12726,1703],{"stretchy":1702},[898,12728,9316],{},[1700,12730,1709],{"stretchy":1702},[1700,12732,1765],{},[898,12734,207],{},[898,12736,9316],{},[1700,12738,1897],{},[898,12740,1879],{},[1700,12742,1732],{"separator":1731},[6066,12744],{"width":6068},[1931,12746,1772],{},[1700,12748,3640],{},[898,12750,207],{},[1700,12752,3640],{},[1931,12754,1933],{},[1700,12756,1732],{"separator":1731},[1781,12758,2495],{},[898,12760,1879],{},[1700,12762,3601],{},[1931,12764,12645],{},[6066,12766],{"width":6068},[1700,12768,1703],{"stretchy":1702},[1931,12770,12771],{},"7.12",[1700,12773,1709],{"stretchy":1702},[902,12775,12776],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,12778,12779],{},"Podmínka rovnováhy na trhu zboží:",[724,12781,12782],{},[883,12783,12785],{"className":12784},[886],[888,12786,12787],{"xmlns":890},[892,12788,12789,12812],{},[895,12790,12791,12793,12795,12797,12799,12801,12803,12805,12807,12810],{},[898,12792,9316],{},[1700,12794,1765],{},[898,12796,2974],{},[1700,12798,1897],{},[898,12800,12369],{},[898,12802,2196],{"mathvariant":1791},[6066,12804],{"width":6068},[1700,12806,1703],{"stretchy":1702},[1931,12808,12809],{},"7.13",[1700,12811,1709],{"stretchy":1702},[902,12813,12814],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,12816,12817,12818,2106,12821,12847,12848,2196],{},"To dává ",[38,12819,12820],{},"tři rovnice o čtyřech neznámých",[883,12822,12824],{"className":12823},[886],[888,12825,12826],{"xmlns":890},[892,12827,12828,12844],{},[895,12829,12830,12832,12834,12836,12838,12840,12842],{},[898,12831,9316],{},[1700,12833,1732],{"separator":1731},[898,12835,2974],{},[1700,12837,1732],{"separator":1731},[898,12839,12369],{},[1700,12841,1732],{"separator":1731},[898,12843,12226],{},[902,12845,12846],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,12849,12850],{},"rovnováhy na trhu peněz",[115,12852,12854],{"id":12853},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,12856,12857,12858,5757,12880,12898,12899,12902],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,12859,12861],{"className":12860},[886],[888,12862,12863],{"xmlns":890},[892,12864,12865,12877],{},[895,12866,12867,12869,12871,12873,12875],{},[898,12868,9316],{},[1700,12870,1765],{},[898,12872,2974],{},[1700,12874,1897],{},[898,12876,8861],{},[902,12878,12879],{"encoding":904},"Y = C + S",[883,12881,12883],{"className":12882},[886],[888,12884,12885],{"xmlns":890},[892,12886,12887,12895],{},[895,12888,12889,12891,12893],{},[898,12890,12369],{},[1700,12892,1765],{},[898,12894,8861],{},[902,12896,12897],{"encoding":904},"I = S"," (plánované ",[38,12900,12901],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,12904,12905],{},[2756,12906],{"alt":12907,"className":12908,"src":12909},"imek-odvozeni-is-4panelu",[210,2760],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,12911,12912],{},[883,12913,12915],{"className":12914},[886],[888,12916,12917],{"xmlns":890},[892,12918,12919,12953],{},[895,12920,12921,12923,12925,12927,12929,12931,12933,12935,12937,12939,12941,12943,12945,12947,12949,12951],{},[898,12922,9316],{},[1700,12924,1765],{},[1700,12926,1703],{"stretchy":1702},[898,12928,207],{},[898,12930,9316],{},[1700,12932,1897],{},[898,12934,1879],{},[1700,12936,1709],{"stretchy":1702},[1700,12938,1897],{},[1700,12940,1703],{"stretchy":1702},[898,12942,2354],{},[898,12944,12226],{},[1700,12946,1897],{},[898,12948,2406],{},[1700,12950,1709],{"stretchy":1702},[1700,12952,1732],{"separator":1731},[902,12954,12955],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,12957,12958],{},[883,12959,12961],{"className":12960},[886],[888,12962,12963],{"xmlns":890},[892,12964,12965,12999],{},[895,12966,12967,12969,12971,12973,12975,12977,12979,12981,12983,12985,12987,12989,12991,12993,12995,12997],{},[1700,12968,1703],{"stretchy":1702},[1931,12970,1933],{},[1700,12972,1768],{},[898,12974,207],{},[1700,12976,1709],{"stretchy":1702},[898,12978,9316],{},[1700,12980,1768],{},[898,12982,2354],{},[898,12984,12226],{},[1700,12986,1768],{},[898,12988,1879],{},[1700,12990,1768],{},[898,12992,2406],{},[1700,12994,1765],{},[1931,12996,1772],{},[1700,12998,1732],{"separator":1731},[902,13000,13001],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,13003,13004],{},"odkud",[724,13006,13007],{},[883,13008,13010],{"className":13009},[886],[888,13011,13012],{"xmlns":890},[892,13013,13014,13081],{},[895,13015,13016,13072,13074,13076,13079],{},[13017,13018,13020],"menclose",{"notation":13019},"box",[1770,13021,13022],{"scriptlevel":1772,"displaystyle":1702},[1770,13023,13024],{"scriptlevel":1772,"displaystyle":1702},[1770,13025,13026],{"scriptlevel":1772,"displaystyle":1731},[895,13027,13028,13030,13032,13034,13046,13048,13050,13052,13070],{},[1781,13029,1783],{},[898,13031,9316],{},[1700,13033,1765],{},[1774,13035,13036,13038],{},[898,13037,2354],{},[895,13039,13040,13042,13044],{},[1931,13041,1933],{},[1700,13043,1768],{},[898,13045,207],{},[1781,13047,1783],{},[898,13049,12226],{},[1700,13051,1897],{},[1774,13053,13054,13062],{},[895,13055,13056,13058,13060],{},[898,13057,1879],{},[1700,13059,1897],{},[898,13061,2406],{},[895,13063,13064,13066,13068],{},[1931,13065,1933],{},[1700,13067,1768],{},[898,13069,207],{},[1781,13071,1783],{},[6066,13073],{"width":6068},[1700,13075,1703],{"stretchy":1702},[1931,13077,13078],{},"7.14",[1700,13080,1709],{"stretchy":1702},[902,13082,13083],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,13085,13086,13087,10208,13090,13093,13094,13097,13098,13100,13101,13123,13124,13152,13153,13174,13175,13177,13178,13180],{},"Tento vztah se nazývá ",[38,13088,13089],{},"funkce IS",[614,13091,13092],{},"IS schedule",") a její graf ",[38,13095,13096],{},"křivka IS",". Křivka je ",[38,13099,12704],{}," přímka v rovině ",[883,13102,13104],{"className":13103},[886],[888,13105,13106],{"xmlns":890},[892,13107,13108,13120],{},[895,13109,13110,13112,13114,13116,13118],{},[1700,13111,1703],{"stretchy":1702},[898,13113,12226],{},[1700,13115,1732],{"separator":1731},[898,13117,9316],{},[1700,13119,1709],{"stretchy":1702},[902,13121,13122],{"encoding":904},"(r, Y)",", neboť ",[883,13125,13127],{"className":13126},[886],[888,13128,13129],{"xmlns":890},[892,13130,13131,13149],{},[895,13132,13133,13145,13147],{},[1774,13134,13135,13137],{},[898,13136,2354],{},[895,13138,13139,13141,13143],{},[1931,13140,1933],{},[1700,13142,1768],{},[898,13144,207],{},[1700,13146,3640],{},[1931,13148,1772],{},[902,13150,13151],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,13154,13156],{"className":13155},[886],[888,13157,13158],{"xmlns":890},[892,13159,13160,13172],{},[895,13161,13162,13164,13166,13168,13170],{},[1700,13163,1703],{"stretchy":1702},[898,13165,12226],{},[1700,13167,1732],{"separator":1731},[898,13169,9316],{},[1700,13171,1709],{"stretchy":1702},[902,13173,13122],{"encoding":904},", pro které plánované ",[38,13176,12369],{},"nvestment = ",[38,13179,8861],{},"avings.",[4060,13182,13183],{},[724,13184,13185,13187,13188,13201,13202,2106,13205,13218,13219,13232,13233,2114,13246,13259,13260,13263],{},[883,13186,4346],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,13189,13191],{"className":13190},[886],[888,13192,13193],{"xmlns":890},[892,13194,13195,13199],{},[895,13196,13197],{},[898,13198,12226],{},[902,13200,12226],{"encoding":904}," → levnější úvěr → ",[38,13203,13204],{},"více investic",[883,13206,13208],{"className":13207},[886],[888,13209,13210],{"xmlns":890},[892,13211,13212,13216],{},[895,13213,13214],{},[898,13215,12369],{},[902,13217,12369],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,13220,13222],{"className":13221},[886],[888,13223,13224],{"xmlns":890},[892,13225,13226,13230],{},[895,13227,13228],{},[898,13229,9316],{},[902,13231,9316],{"encoding":904},". Vztah mezi ",[883,13234,13236],{"className":13235},[886],[888,13237,13238],{"xmlns":890},[892,13239,13240,13244],{},[895,13241,13242],{},[898,13243,12226],{},[902,13245,12226],{"encoding":904},[883,13247,13249],{"className":13248},[886],[888,13250,13251],{"xmlns":890},[892,13252,13253,13257],{},[895,13254,13255],{},[898,13256,9316],{},[902,13258,9316],{"encoding":904}," na trhu zboží je proto ",[38,13261,13262],{},"nepřímý"," (klesající křivka).",[115,13265,13267],{"id":13266},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,13269,13270,13271,13289,13290,3122,13308,13311],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,13272,13274],{"className":13273},[886],[888,13275,13276],{"xmlns":890},[892,13277,13278,13286],{},[895,13279,13280],{},[1785,13281,13282,13284],{},[898,13283,2005],{},[898,13285,4374],{},[902,13287,13288],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,13291,13293],{"className":13292},[886],[888,13294,13295],{"xmlns":890},[892,13296,13297,13305],{},[895,13298,13299],{},[1785,13300,13301,13303],{},[898,13302,2005],{},[898,13304,8861],{},[902,13306,13307],{"encoding":904},"M^S",[38,13309,13310],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,13313,13314],{},[883,13315,13317],{"className":13316},[886],[888,13318,13319],{"xmlns":890},[892,13320,13321,13339],{},[895,13322,13323,13329,13331,13337],{},[1785,13324,13325,13327],{},[898,13326,2005],{},[898,13328,8861],{},[1700,13330,1765],{},[1785,13332,13333,13335],{},[898,13334,2005],{},[1700,13336,4543],{},[898,13338,2196],{"mathvariant":1791},[902,13340,13341],{"encoding":904},"M^S = M^*.",[724,13343,13344,13347],{},[38,13345,13346],{},"Poptávka"," po penězích má tři zdroje:",[120,13349,13350,13359,13368],{},[123,13351,13352,10208,13355,13358],{},[38,13353,13354],{},"transakční poptávka",[614,13356,13357],{},"transactions demand",") — peníze pro nákup zboží,",[123,13360,13361,10208,13364,13367],{},[38,13362,13363],{},"opatrnostní poptávka",[614,13365,13366],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,13369,13370,10208,13373,13376],{},[38,13371,13372],{},"spekulační poptávka",[614,13374,13375],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,13378,13379,13380,13398],{},"Součet transakční a opatrnostní poptávky ",[883,13381,13383],{"className":13382},[886],[888,13384,13385],{"xmlns":890},[892,13386,13387,13395],{},[895,13388,13389],{},[2007,13390,13391,13393],{},[898,13392,1706],{},[1931,13394,1933],{},[902,13396,13397],{"encoding":904},"L_1"," je úměrný důchodu:",[724,13400,13401],{},[883,13402,13404],{"className":13403},[886],[888,13405,13406],{"xmlns":890},[892,13407,13408,13446],{},[895,13409,13410,13416,13418,13425,13427,13429,13431,13433,13435,13441,13443],{},[2007,13411,13412,13414],{},[898,13413,1706],{},[1931,13415,1933],{},[1700,13417,1765],{},[2007,13419,13420,13423],{},[898,13421,13422],{},"k",[1931,13424,1933],{},[898,13426,9316],{},[1700,13428,1732],{"separator":1731},[6066,13430],{"width":6068},[1931,13432,1772],{},[1700,13434,3640],{},[2007,13436,13437,13439],{},[898,13438,13422],{},[1931,13440,1933],{},[1700,13442,3640],{},[1931,13444,13445],{},"1.",[902,13447,13448],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,13450,13451,13452,13470,13471,1343,13484,13501],{},"Spekulační poptávka ",[883,13453,13455],{"className":13454},[886],[888,13456,13457],{"xmlns":890},[892,13458,13459,13467],{},[895,13460,13461],{},[2007,13462,13463,13465],{},[898,13464,1706],{},[1931,13466,2343],{},[902,13468,13469],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,13472,13474],{"className":13473},[886],[888,13475,13476],{"xmlns":890},[892,13477,13478,13482],{},[895,13479,13480],{},[898,13481,12226],{},[902,13483,12226],{"encoding":904},[883,13485,13487],{"className":13486},[886],[888,13488,13489],{"xmlns":890},[892,13490,13491,13499],{},[895,13492,13493],{},[2007,13494,13495,13497],{},[898,13496,1706],{},[1931,13498,2343],{},[902,13500,13469],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,13503,13504],{},[883,13505,13507],{"className":13506},[886],[888,13508,13509],{"xmlns":890},[892,13510,13511,13565],{},[895,13512,13513,13519,13521,13527,13529,13531,13537,13539,13541,13547,13549,13551,13553,13555,13561,13563],{},[2007,13514,13515,13517],{},[898,13516,1706],{},[1931,13518,2343],{},[1700,13520,1765],{},[2007,13522,13523,13525],{},[898,13524,13422],{},[1931,13526,2343],{},[898,13528,12226],{},[1700,13530,1897],{},[2007,13532,13533,13535],{},[898,13534,13422],{},[1931,13536,2385],{},[1700,13538,1732],{"separator":1731},[6066,13540],{"width":6068},[2007,13542,13543,13545],{},[898,13544,13422],{},[1931,13546,2343],{},[1700,13548,3640],{},[1931,13550,1772],{},[1700,13552,1732],{"separator":1731},[1781,13554,2495],{},[2007,13556,13557,13559],{},[898,13558,13422],{},[1931,13560,2385],{},[1700,13562,3601],{},[1931,13564,12645],{},[902,13566,13567],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,13569,13570],{},"Celková poptávka po penězích:",[724,13572,13573],{},[883,13574,13576],{"className":13575},[886],[888,13577,13578],{"xmlns":890},[892,13579,13580,13634],{},[895,13581,13582,13588,13590,13596,13598,13604,13606,13612,13614,13616,13622,13624,13626,13632],{},[1785,13583,13584,13586],{},[898,13585,2005],{},[898,13587,4374],{},[1700,13589,1765],{},[2007,13591,13592,13594],{},[898,13593,1706],{},[1931,13595,1933],{},[1700,13597,1897],{},[2007,13599,13600,13602],{},[898,13601,1706],{},[1931,13603,2343],{},[1700,13605,1765],{},[2007,13607,13608,13610],{},[898,13609,13422],{},[1931,13611,1933],{},[898,13613,9316],{},[1700,13615,1897],{},[2007,13617,13618,13620],{},[898,13619,13422],{},[1931,13621,2343],{},[898,13623,12226],{},[1700,13625,1897],{},[2007,13627,13628,13630],{},[898,13629,13422],{},[1931,13631,2385],{},[898,13633,2196],{"mathvariant":1791},[902,13635,13636],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,13638,13639,13640,2901],{},"Podmínka rovnováhy na trhu peněz ",[883,13641,13643],{"className":13642},[886],[888,13644,13645],{"xmlns":890},[892,13646,13647,13663],{},[895,13648,13649,13655,13657],{},[1785,13650,13651,13653],{},[898,13652,2005],{},[898,13654,4374],{},[1700,13656,1765],{},[1785,13658,13659,13661],{},[898,13660,2005],{},[1700,13662,4543],{},[902,13664,13665],{"encoding":904},"M^D = M^*",[724,13667,13668],{},[883,13669,13671],{"className":13670},[886],[888,13672,13673],{"xmlns":890},[892,13674,13675,13722],{},[895,13676,13677,13683,13685,13691,13693,13695,13701,13703,13705,13711,13713,13715,13717,13720],{},[1785,13678,13679,13681],{},[898,13680,2005],{},[1700,13682,4543],{},[1700,13684,1765],{},[2007,13686,13687,13689],{},[898,13688,13422],{},[1931,13690,1933],{},[898,13692,9316],{},[1700,13694,1897],{},[2007,13696,13697,13699],{},[898,13698,13422],{},[1931,13700,2343],{},[898,13702,12226],{},[1700,13704,1897],{},[2007,13706,13707,13709],{},[898,13708,13422],{},[1931,13710,2385],{},[1700,13712,1732],{"separator":1731},[6066,13714],{"width":6068},[1700,13716,1703],{"stretchy":1702},[1931,13718,13719],{},"7.15",[1700,13721,1709],{"stretchy":1702},[902,13723,13724],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,13726,13727,13728,3345],{},"po úpravě (vyjádření ",[883,13729,13731],{"className":13730},[886],[888,13732,13733],{"xmlns":890},[892,13734,13735,13739],{},[895,13736,13737],{},[898,13738,9316],{},[902,13740,9316],{"encoding":904},[724,13742,13743],{},[883,13744,13746],{"className":13745},[886],[888,13747,13748],{"xmlns":890},[892,13749,13750,13825],{},[895,13751,13752,13816,13818,13820,13823],{},[13017,13753,13754],{"notation":13019},[1770,13755,13756],{"scriptlevel":1772,"displaystyle":1702},[1770,13757,13758],{"scriptlevel":1772,"displaystyle":1702},[1770,13759,13760],{"scriptlevel":1772,"displaystyle":1731},[895,13761,13762,13764,13766,13768,13770,13784,13786,13788,13790,13814],{},[1781,13763,1783],{},[898,13765,9316],{},[1700,13767,1765],{},[1700,13769,1768],{},[1774,13771,13772,13778],{},[2007,13773,13774,13776],{},[898,13775,13422],{},[1931,13777,2343],{},[2007,13779,13780,13782],{},[898,13781,13422],{},[1931,13783,1933],{},[1781,13785,1783],{},[898,13787,12226],{},[1700,13789,1897],{},[1774,13791,13792,13808],{},[895,13793,13794,13800,13802],{},[1785,13795,13796,13798],{},[898,13797,2005],{},[1700,13799,4543],{},[1700,13801,1768],{},[2007,13803,13804,13806],{},[898,13805,13422],{},[1931,13807,2385],{},[2007,13809,13810,13812],{},[898,13811,13422],{},[1931,13813,1933],{},[1781,13815,1783],{},[6066,13817],{"width":6068},[1700,13819,1703],{"stretchy":1702},[1931,13821,13822],{},"7.16",[1700,13824,1709],{"stretchy":1702},[902,13826,13827],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,13829,13086,13830,10208,13833,13836,13837,13097,13840,13100,13843,13123,13864,13896,13897,13919,13920,13922,13923,13925],{},[38,13831,13832],{},"funkce LM",[614,13834,13835],{},"LM schedule","), její graf ",[38,13838,13839],{},"křivka LM",[38,13841,13842],{},"rostoucí",[883,13844,13846],{"className":13845},[886],[888,13847,13848],{"xmlns":890},[892,13849,13850,13862],{},[895,13851,13852,13854,13856,13858,13860],{},[1700,13853,1703],{"stretchy":1702},[898,13855,12226],{},[1700,13857,1732],{"separator":1731},[898,13859,9316],{},[1700,13861,1709],{"stretchy":1702},[902,13863,13122],{"encoding":904},[883,13865,13867],{"className":13866},[886],[888,13868,13869],{"xmlns":890},[892,13870,13871,13893],{},[895,13872,13873,13875,13889,13891],{},[1700,13874,1768],{},[1774,13876,13877,13883],{},[2007,13878,13879,13881],{},[898,13880,13422],{},[1931,13882,2343],{},[2007,13884,13885,13887],{},[898,13886,13422],{},[1931,13888,1933],{},[1700,13890,3601],{},[1931,13892,1772],{},[902,13894,13895],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,13898,13900],{"className":13899},[886],[888,13901,13902],{"xmlns":890},[892,13903,13904,13916],{},[895,13905,13906,13912,13914],{},[2007,13907,13908,13910],{},[898,13909,13422],{},[1931,13911,2343],{},[1700,13913,3640],{},[1931,13915,1772],{},[902,13917,13918],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,13921,1706],{},"iquidity of ",[38,13924,2005],{},"oney.",[4060,13927,13928],{},[724,13929,13930,13932,13933,13946,13947,13975,13976,13993,13994,14007,14008,14025,14026,2114,14039,14052,14053,14056],{},[883,13931,4346],{}," Intuice — proč LM roste\nVyšší důchod ",[883,13934,13936],{"className":13935},[886],[888,13937,13938],{"xmlns":890},[892,13939,13940,13944],{},[895,13941,13942],{},[898,13943,9316],{},[902,13945,9316],{"encoding":904}," → větší transakční poptávka po penězích ",[883,13948,13950],{"className":13949},[886],[888,13951,13952],{"xmlns":890},[892,13953,13954,13972],{},[895,13955,13956,13962,13964,13970],{},[2007,13957,13958,13960],{},[898,13959,1706],{},[1931,13961,1933],{},[1700,13963,1765],{},[2007,13965,13966,13968],{},[898,13967,13422],{},[1931,13969,1933],{},[898,13971,9316],{},[902,13973,13974],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,13977,13979],{"className":13978},[886],[888,13980,13981],{"xmlns":890},[892,13982,13983,13991],{},[895,13984,13985],{},[1785,13986,13987,13989],{},[898,13988,2005],{},[1700,13990,4543],{},[902,13992,12335],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,13995,13997],{"className":13996},[886],[888,13998,13999],{"xmlns":890},[892,14000,14001,14005],{},[895,14002,14003],{},[898,14004,12226],{},[902,14006,12226],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,14009,14011],{"className":14010},[886],[888,14012,14013],{"xmlns":890},[892,14014,14015,14023],{},[895,14016,14017],{},[2007,14018,14019,14021],{},[898,14020,1706],{},[1931,14022,2343],{},[902,14024,13469],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,14027,14029],{"className":14028},[886],[888,14030,14031],{"xmlns":890},[892,14032,14033,14037],{},[895,14034,14035],{},[898,14036,9316],{},[902,14038,9316],{"encoding":904},[883,14040,14042],{"className":14041},[886],[888,14043,14044],{"xmlns":890},[892,14045,14046,14050],{},[895,14047,14048],{},[898,14049,12226],{},[902,14051,12226],{"encoding":904}," na trhu peněz je proto ",[38,14054,14055],{},"přímý"," (rostoucí křivka).",[115,14058,14060],{"id":14059},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,14062,14063,14064,14067,14068,2106,14071,2114,14089,2106,14092,14110,14111,14129,14130,14148,14149,14165,14166,2114,14181,14196,14197,2196],{},"Řešením ",[38,14065,14066],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,14069,14070],{},"rovnovážný důchod",[883,14072,14074],{"className":14073},[886],[888,14075,14076],{"xmlns":890},[892,14077,14078,14086],{},[895,14079,14080],{},[1785,14081,14082,14084],{},[898,14083,9316],{},[898,14085,1762],{},[902,14087,14088],{"encoding":904},"Y^E",[38,14090,14091],{},"rovnovážnou úrokovou míru",[883,14093,14095],{"className":14094},[886],[888,14096,14097],{"xmlns":890},[892,14098,14099,14107],{},[895,14100,14101],{},[1785,14102,14103,14105],{},[898,14104,12226],{},[898,14106,1762],{},[902,14108,14109],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,14112,14114],{"className":14113},[886],[888,14115,14116],{"xmlns":890},[892,14117,14118,14126],{},[895,14119,14120],{},[1785,14121,14122,14124],{},[898,14123,12369],{},[898,14125,1762],{},[902,14127,14128],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,14131,14133],{"className":14132},[886],[888,14134,14135],{"xmlns":890},[892,14136,14137,14145],{},[895,14138,14139],{},[1785,14140,14141,14143],{},[898,14142,2974],{},[898,14144,1762],{},[902,14146,14147],{"encoding":904},"C^E",". Graficky jde o ",[38,14150,14151,14152],{},"průsečík ",[883,14153,14155],{"className":14154},[886],[888,14156,14157],{"xmlns":890},[892,14158,14159,14163],{},[895,14160,14161],{},[898,14162,1762],{},[902,14164,1762],{"encoding":904}," křivek ",[883,14167,14169],{"className":14168},[886],[888,14170,14171],{"xmlns":890},[892,14172,14173,14179],{},[895,14174,14175,14177],{},[898,14176,12369],{},[898,14178,8861],{},[902,14180,12236],{"encoding":904},[883,14182,14184],{"className":14183},[886],[888,14185,14186],{"xmlns":890},[892,14187,14188,14194],{},[895,14189,14190,14192],{},[898,14191,1706],{},[898,14193,2005],{},[902,14195,12243],{"encoding":904}," v rovině ",[883,14198,14200],{"className":14199},[886],[888,14201,14202],{"xmlns":890},[892,14203,14204,14216],{},[895,14205,14206,14208,14210,14212,14214],{},[1700,14207,1703],{"stretchy":1702},[898,14209,12226],{},[1700,14211,1732],{"separator":1731},[898,14213,9316],{},[1700,14215,1709],{"stretchy":1702},[902,14217,13122],{"encoding":904},[724,14219,14220],{},[614,14221,14222,14223,14244,14245,14260,14261,14276,14277,14290,14291,14308,14309,12313,14322,14308,14339,14352,14353,14366],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,14224,14226],{"className":14225},[886],[888,14227,14228],{"xmlns":890},[892,14229,14230,14242],{},[895,14231,14232,14234,14236,14238,14240],{},[1700,14233,1703],{"stretchy":1702},[898,14235,12226],{},[1700,14237,1732],{"separator":1731},[898,14239,9316],{},[1700,14241,1709],{"stretchy":1702},[902,14243,13122],{"encoding":904},". Rostoucí přímka ",[883,14246,14248],{"className":14247},[886],[888,14249,14250],{"xmlns":890},[892,14251,14252,14258],{},[895,14253,14254,14256],{},[898,14255,1706],{},[898,14257,2005],{},[902,14259,12243],{"encoding":904}," a klesající přímka ",[883,14262,14264],{"className":14263},[886],[888,14265,14266],{"xmlns":890},[892,14267,14268,14274],{},[895,14269,14270,14272],{},[898,14271,12369],{},[898,14273,8861],{},[902,14275,12236],{"encoding":904}," se protínají v bodě ",[883,14278,14280],{"className":14279},[886],[888,14281,14282],{"xmlns":890},[892,14283,14284,14288],{},[895,14285,14286],{},[898,14287,1762],{},[902,14289,1762],{"encoding":904}," se souřadnicemi ",[883,14292,14294],{"className":14293},[886],[888,14295,14296],{"xmlns":890},[892,14297,14298,14306],{},[895,14299,14300],{},[1785,14301,14302,14304],{},[898,14303,12226],{},[898,14305,1762],{},[902,14307,14109],{"encoding":904}," (na ose ",[883,14310,14312],{"className":14311},[886],[888,14313,14314],{"xmlns":890},[892,14315,14316,14320],{},[895,14317,14318],{},[898,14319,12226],{},[902,14321,12226],{"encoding":904},[883,14323,14325],{"className":14324},[886],[888,14326,14327],{"xmlns":890},[892,14328,14329,14337],{},[895,14330,14331],{},[1785,14332,14333,14335],{},[898,14334,9316],{},[898,14336,1762],{},[902,14338,14088],{"encoding":904},[883,14340,14342],{"className":14341},[886],[888,14343,14344],{"xmlns":890},[892,14345,14346,14350],{},[895,14347,14348],{},[898,14349,9316],{},[902,14351,9316],{"encoding":904},"); tečkované čáry z ",[883,14354,14356],{"className":14355},[886],[888,14357,14358],{"xmlns":890},[892,14359,14360,14364],{},[895,14361,14362],{},[898,14363,1762],{},[902,14365,1762],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[4060,14368,14369,14374],{},[724,14370,14371,14373],{},[883,14372,4761],{}," Postup — jak najít IS-LM rovnováhu",[152,14375,14376,14452,14520,14578,14651],{},[123,14377,14378,14381,14382,2114,14402,14422,14423,2114,14436,14449,14450,2196],{},[38,14379,14380],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,14383,14385],{"className":14384},[886],[888,14386,14387],{"xmlns":890},[892,14388,14389,14399],{},[895,14390,14391,14393,14395,14397],{},[898,14392,2974],{},[1700,14394,1703],{"stretchy":1702},[898,14396,9316],{},[1700,14398,1709],{"stretchy":1702},[902,14400,14401],{"encoding":904},"C(Y)",[883,14403,14405],{"className":14404},[886],[888,14406,14407],{"xmlns":890},[892,14408,14409,14419],{},[895,14410,14411,14413,14415,14417],{},[898,14412,12369],{},[1700,14414,1703],{"stretchy":1702},[898,14416,12226],{},[1700,14418,1709],{"stretchy":1702},[902,14420,14421],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,14424,14426],{"className":14425},[886],[888,14427,14428],{"xmlns":890},[892,14429,14430,14434],{},[895,14431,14432],{},[898,14433,9316],{},[902,14435,9316],{"encoding":904},[883,14437,14439],{"className":14438},[886],[888,14440,14441],{"xmlns":890},[892,14442,14443,14447],{},[895,14444,14445],{},[898,14446,12226],{},[902,14448,12226],{"encoding":904}," — dostaneš rovnici ",[38,14451,12236],{},[123,14453,14454,14457,14458,2114,14475,14492,14493,14449,14518,2196],{},[38,14455,14456],{},"Z trhu peněz (7.15)"," dosaď ",[883,14459,14461],{"className":14460},[886],[888,14462,14463],{"xmlns":890},[892,14464,14465,14473],{},[895,14466,14467],{},[2007,14468,14469,14471],{},[898,14470,1706],{},[1931,14472,1933],{},[902,14474,13397],{"encoding":904},[883,14476,14478],{"className":14477},[886],[888,14479,14480],{"xmlns":890},[892,14481,14482,14490],{},[895,14483,14484],{},[2007,14485,14486,14488],{},[898,14487,1706],{},[1931,14489,2343],{},[902,14491,13469],{"encoding":904}," a vztah ",[883,14494,14496],{"className":14495},[886],[888,14497,14498],{"xmlns":890},[892,14499,14500,14516],{},[895,14501,14502,14508,14510],{},[1785,14503,14504,14506],{},[898,14505,2005],{},[898,14507,4374],{},[1700,14509,1765],{},[1785,14511,14512,14514],{},[898,14513,2005],{},[1700,14515,4543],{},[902,14517,13665],{"encoding":904},[38,14519,12243],{},[123,14521,14522,14525,14526,2114,14539,14552,14553,14577],{},[38,14523,14524],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,14527,14529],{"className":14528},[886],[888,14530,14531],{"xmlns":890},[892,14532,14533,14537],{},[895,14534,14535],{},[898,14536,9316],{},[902,14538,9316],{"encoding":904},[883,14540,14542],{"className":14541},[886],[888,14543,14544],{"xmlns":890},[892,14545,14546,14550],{},[895,14547,14548],{},[898,14549,12226],{},[902,14551,12226],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,14554,14556],{"className":14555},[886],[888,14557,14558],{"xmlns":890},[892,14559,14560,14574],{},[895,14561,14562,14564,14566,14568,14570,14572],{},[898,14563,9316],{},[1700,14565,1765],{},[898,14567,2220],{},[1700,14569,1703],{"stretchy":1702},[898,14571,12226],{},[1700,14573,1709],{"stretchy":1702},[902,14575,14576],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,14579,14580,2106,14583,2114,14617,2196],{},[38,14581,14582],{},"Zpětně dopočítej",[883,14584,14586],{"className":14585},[886],[888,14587,14588],{"xmlns":890},[892,14589,14590,14614],{},[895,14591,14592,14598,14600,14602,14604,14610,14612],{},[1785,14593,14594,14596],{},[898,14595,2974],{},[898,14597,1762],{},[1700,14599,1765],{},[898,14601,207],{},[1781,14603,1783],{},[1785,14605,14606,14608],{},[898,14607,9316],{},[898,14609,1762],{},[1700,14611,1897],{},[898,14613,1879],{},[902,14615,14616],{"encoding":904},"C^E = a\\,Y^E + b",[883,14618,14620],{"className":14619},[886],[888,14621,14622],{"xmlns":890},[892,14623,14624,14648],{},[895,14625,14626,14632,14634,14636,14638,14644,14646],{},[1785,14627,14628,14630],{},[898,14629,12369],{},[898,14631,1762],{},[1700,14633,1765],{},[898,14635,2354],{},[1781,14637,1783],{},[1785,14639,14640,14642],{},[898,14641,12226],{},[898,14643,1762],{},[1700,14645,1897],{},[898,14647,2406],{},[902,14649,14650],{"encoding":904},"I^E = c\\,r^E + d",[123,14652,14653,14656,14657,14691,14692,14746],{},[38,14654,14655],{},"Ověř:"," musí platit ",[883,14658,14660],{"className":14659},[886],[888,14661,14662],{"xmlns":890},[892,14663,14664,14688],{},[895,14665,14666,14672,14674,14680,14682],{},[1785,14667,14668,14670],{},[898,14669,9316],{},[898,14671,1762],{},[1700,14673,1765],{},[1785,14675,14676,14678],{},[898,14677,2974],{},[898,14679,1762],{},[1700,14681,1897],{},[1785,14683,14684,14686],{},[898,14685,12369],{},[898,14687,1762],{},[902,14689,14690],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,14693,14695],{"className":14694},[886],[888,14696,14697],{"xmlns":890},[892,14698,14699,14743],{},[895,14700,14701,14707,14709,14715,14721,14723,14729,14735,14737],{},[1785,14702,14703,14705],{},[898,14704,2005],{},[1700,14706,4543],{},[1700,14708,1765],{},[2007,14710,14711,14713],{},[898,14712,13422],{},[1931,14714,1933],{},[1785,14716,14717,14719],{},[898,14718,9316],{},[898,14720,1762],{},[1700,14722,1897],{},[2007,14724,14725,14727],{},[898,14726,13422],{},[1931,14728,2343],{},[1785,14730,14731,14733],{},[898,14732,12226],{},[898,14734,1762],{},[1700,14736,1897],{},[2007,14738,14739,14741],{},[898,14740,13422],{},[1931,14742,2385],{},[902,14744,14745],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,14748,14750],{"id":14749},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,14752,14753],{},"Pro trh zboží jsou dány:",[120,14755,14756,14784],{},[123,14757,14758,14759,1732],{},"spotřeba ",[883,14760,14762],{"className":14761},[886],[888,14763,14764],{"xmlns":890},[892,14765,14766,14781],{},[895,14767,14768,14770,14772,14775,14777,14779],{},[898,14769,2974],{},[1700,14771,1765],{},[1931,14773,14774],{},"0,8",[898,14776,9316],{},[1700,14778,1897],{},[1931,14780,3284],{},[902,14782,14783],{"encoding":904},"C = 0{,}8Y + 100",[123,14785,14786,14787,2196],{},"investice ",[883,14788,14790],{"className":14789},[886],[888,14791,14792],{"xmlns":890},[892,14793,14794,14810],{},[895,14795,14796,14798,14800,14802,14804,14806,14808],{},[898,14797,12369],{},[1700,14799,1765],{},[1700,14801,1768],{},[1931,14803,9223],{},[898,14805,12226],{},[1700,14807,1897],{},[1931,14809,2979],{},[902,14811,14812],{"encoding":904},"I = -20r + 1000",[724,14814,14815],{},"Pro trh peněz:",[120,14817,14818,14844,14876],{},[123,14819,14820,1732],{},[883,14821,14823],{"className":14822},[886],[888,14824,14825],{"xmlns":890},[892,14826,14827,14841],{},[895,14828,14829,14835,14837,14839],{},[2007,14830,14831,14833],{},[898,14832,1706],{},[1931,14834,1933],{},[1700,14836,1765],{},[1931,14838,2990],{},[898,14840,9316],{},[902,14842,14843],{"encoding":904},"L_1 = 0{,}1Y",[123,14845,14846,1732],{},[883,14847,14849],{"className":14848},[886],[888,14850,14851],{"xmlns":890},[892,14852,14853,14873],{},[895,14854,14855,14861,14863,14865,14867,14869,14871],{},[2007,14856,14857,14859],{},[898,14858,1706],{},[1931,14860,2343],{},[1700,14862,1765],{},[1700,14864,1768],{},[1931,14866,5192],{},[898,14868,12226],{},[1700,14870,1897],{},[1931,14872,8792],{},[902,14874,14875],{"encoding":904},"L_2 = -25r + 2000",[123,14877,14878,14879,2196],{},"nabídka peněz ",[883,14880,14882],{"className":14881},[886],[888,14883,14884],{"xmlns":890},[892,14885,14886,14899],{},[895,14887,14888,14894,14896],{},[1785,14889,14890,14892],{},[898,14891,2005],{},[1700,14893,4543],{},[1700,14895,1765],{},[1931,14897,14898],{},"2375",[902,14900,14901],{"encoding":904},"M^* = 2375",[724,14903,14904,14907,14908,2901],{},[38,14905,14906],{},"Funkce IS"," — dosazením do (7.13) ",[883,14909,14911],{"className":14910},[886],[888,14912,14913],{"xmlns":890},[892,14914,14915,14927],{},[895,14916,14917,14919,14921,14923,14925],{},[898,14918,9316],{},[1700,14920,1765],{},[898,14922,2974],{},[1700,14924,1897],{},[898,14926,12369],{},[902,14928,14929],{"encoding":904},"Y = C + I",[724,14931,14932],{},[883,14933,14935],{"className":14934},[886],[888,14936,14937],{"xmlns":890},[892,14938,14939,14965],{},[895,14940,14941,14943,14945,14947,14949,14951,14953,14955,14957,14959,14961,14963],{},[898,14942,9316],{},[1700,14944,1765],{},[1931,14946,14774],{},[898,14948,9316],{},[1700,14950,1897],{},[1931,14952,3284],{},[1700,14954,1768],{},[1931,14956,9223],{},[898,14958,12226],{},[1700,14960,1897],{},[1931,14962,2979],{},[1700,14964,1732],{"separator":1731},[902,14966,14967],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,14969,14970],{},"tj.",[724,14972,14973],{},[883,14974,14976],{"className":14975},[886],[888,14977,14978],{"xmlns":890},[892,14979,14980,15005],{},[895,14981,14982,14984,14986,14988,14990,14992,14994,14997,14999,15001,15003],{},[1931,14983,3034],{},[898,14985,9316],{},[1700,14987,1897],{},[1931,14989,9223],{},[898,14991,12226],{},[1700,14993,1765],{},[1931,14995,14996],{},"1100.",[6066,14998],{"width":6068},[1700,15000,1703],{"stretchy":1702},[1781,15002,12236],{},[1700,15004,1709],{"stretchy":1702},[902,15006,15007],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,15009,15010,15013,15014,2901],{},[38,15011,15012],{},"Funkce LM"," — dosazením do (7.15) ",[883,15015,15017],{"className":15016},[886],[888,15018,15019],{"xmlns":890},[892,15020,15021,15045],{},[895,15022,15023,15029,15031,15037,15039],{},[1785,15024,15025,15027],{},[898,15026,2005],{},[1700,15028,4543],{},[1700,15030,1765],{},[2007,15032,15033,15035],{},[898,15034,1706],{},[1931,15036,1933],{},[1700,15038,1897],{},[2007,15040,15041,15043],{},[898,15042,1706],{},[1931,15044,2343],{},[902,15046,15047],{"encoding":904},"M^* = L_1 + L_2",[724,15049,15050],{},[883,15051,15053],{"className":15052},[886],[888,15054,15055],{"xmlns":890},[892,15056,15057,15079],{},[895,15058,15059,15061,15063,15065,15067,15069,15071,15073,15075,15077],{},[1931,15060,14898],{},[1700,15062,1765],{},[1931,15064,2990],{},[898,15066,9316],{},[1700,15068,1768],{},[1931,15070,5192],{},[898,15072,12226],{},[1700,15074,1897],{},[1931,15076,8792],{},[1700,15078,1732],{"separator":1731},[902,15080,15081],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,15083,14970],{},[724,15085,15086],{},[883,15087,15089],{"className":15088},[886],[888,15090,15091],{"xmlns":890},[892,15092,15093,15118],{},[895,15094,15095,15097,15099,15101,15103,15105,15107,15110,15112,15114,15116],{},[1931,15096,2990],{},[898,15098,9316],{},[1700,15100,1768],{},[1931,15102,5192],{},[898,15104,12226],{},[1700,15106,1765],{},[1931,15108,15109],{},"375.",[6066,15111],{"width":6068},[1700,15113,1703],{"stretchy":1702},[1781,15115,12243],{},[1700,15117,1709],{"stretchy":1702},[902,15119,15120],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,15122,15123,15126,15127,15152],{},[38,15124,15125],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,15128,15130],{"className":15129},[886],[888,15131,15132],{"xmlns":890},[892,15133,15134,15149],{},[895,15135,15136,15138,15140,15143,15145,15147],{},[898,15137,9316],{},[1700,15139,1765],{},[1931,15141,15142],{},"5500",[1700,15144,1768],{},[1931,15146,3284],{},[898,15148,12226],{},[902,15150,15151],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,15154,15155],{},[883,15156,15158],{"className":15157},[886],[888,15159,15160],{"xmlns":890},[892,15161,15162,15248],{},[895,15163,15164,15166,15168,15170,15172,15174,15176,15178,15180,15182,15184,15186,15189,15191,15194,15196,15199,15201,15203,15205,15207,15209,15211,15213,15215,15217,15219,15221,15224,15226,15228,15231,15233,15235,15237,15243,15245],{},[1931,15165,2990],{},[1700,15167,1703],{"stretchy":1702},[1931,15169,15142],{},[1700,15171,1768],{},[1931,15173,3284],{},[898,15175,12226],{},[1700,15177,1709],{"stretchy":1702},[1700,15179,1768],{},[1931,15181,5192],{},[898,15183,12226],{},[1700,15185,1765],{},[1931,15187,15188],{},"375",[1781,15190,4175],{},[1700,15192,15193],{},"⟹",[1781,15195,4175],{},[1931,15197,15198],{},"550",[1700,15200,1768],{},[1931,15202,3058],{},[898,15204,12226],{},[1700,15206,1768],{},[1931,15208,5192],{},[898,15210,12226],{},[1700,15212,1765],{},[1931,15214,15188],{},[1781,15216,4175],{},[1700,15218,15193],{},[1781,15220,4175],{},[1931,15222,15223],{},"35",[898,15225,12226],{},[1700,15227,1765],{},[1931,15229,15230],{},"175",[1781,15232,4175],{},[1700,15234,15193],{},[1781,15236,4175],{},[1785,15238,15239,15241],{},[898,15240,12226],{},[898,15242,1762],{},[1700,15244,1765],{},[1931,15246,15247],{},"5.",[902,15249,15250],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,15252,15253],{},[38,15254,15255],{},"Zpětné dosazení:",[120,15257,15258,15304,15341],{},[123,15259,15260,1732],{},[883,15261,15263],{"className":15262},[886],[888,15264,15265],{"xmlns":890},[892,15266,15267,15301],{},[895,15268,15269,15275,15277,15279,15281,15283,15285,15287,15289,15291,15293,15296,15298],{},[1785,15270,15271,15273],{},[898,15272,9316],{},[898,15274,1762],{},[1700,15276,1765],{},[1931,15278,15142],{},[1700,15280,1768],{},[1931,15282,3284],{},[1700,15284,2065],{},[1931,15286,2438],{},[1700,15288,1765],{},[1931,15290,15142],{},[1700,15292,1768],{},[1931,15294,15295],{},"500",[1700,15297,1765],{},[1931,15299,15300],{},"5000",[902,15302,15303],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,15305,15306,1732],{},[883,15307,15309],{"className":15308},[886],[888,15310,15311],{"xmlns":890},[892,15312,15313,15338],{},[895,15314,15315,15321,15323,15325,15327,15329,15331,15333,15335],{},[1785,15316,15317,15319],{},[898,15318,2974],{},[898,15320,1762],{},[1700,15322,1765],{},[1931,15324,14774],{},[1700,15326,2065],{},[1931,15328,15300],{},[1700,15330,1897],{},[1931,15332,3284],{},[1700,15334,1765],{},[1931,15336,15337],{},"4100",[902,15339,15340],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,15342,15343,2196],{},[883,15344,15346],{"className":15345},[886],[888,15347,15348],{"xmlns":890},[892,15349,15350,15377],{},[895,15351,15352,15358,15360,15362,15364,15366,15368,15370,15372,15374],{},[1785,15353,15354,15356],{},[898,15355,12369],{},[898,15357,1762],{},[1700,15359,1765],{},[1700,15361,1768],{},[1931,15363,9223],{},[1700,15365,2065],{},[1931,15367,2438],{},[1700,15369,1897],{},[1931,15371,2979],{},[1700,15373,1765],{},[1931,15375,15376],{},"900",[902,15378,15379],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,15381,15382,2106,15385,15431],{},[38,15383,15384],{},"Ověření:",[883,15386,15388],{"className":15387},[886],[888,15389,15390],{"xmlns":890},[892,15391,15392,15428],{},[895,15393,15394,15400,15402,15408,15410,15412,15414,15416,15418,15420,15422],{},[1785,15395,15396,15398],{},[898,15397,2974],{},[898,15399,1762],{},[1700,15401,1897],{},[1785,15403,15404,15406],{},[898,15405,12369],{},[898,15407,1762],{},[1700,15409,1765],{},[1931,15411,15337],{},[1700,15413,1897],{},[1931,15415,15376],{},[1700,15417,1765],{},[1931,15419,15300],{},[1700,15421,1765],{},[1785,15423,15424,15426],{},[898,15425,9316],{},[898,15427,1762],{},[902,15429,15430],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,15433,15434],{},[883,15435,15437],{"className":15436},[886],[888,15438,15439],{"xmlns":890},[892,15440,15441,15511],{},[895,15442,15443],{},[13017,15444,15445],{"notation":13019},[1770,15446,15447],{"scriptlevel":1772,"displaystyle":1702},[1770,15448,15449],{"scriptlevel":1772,"displaystyle":1702},[1770,15450,15451],{"scriptlevel":1772,"displaystyle":1731},[895,15452,15453,15455,15461,15463,15465,15467,15470,15476,15478,15480,15482,15484,15490,15492,15494,15496,15498,15504,15506,15509],{},[1781,15454,1783],{},[1785,15456,15457,15459],{},[898,15458,9316],{},[898,15460,1762],{},[1700,15462,1765],{},[1931,15464,15300],{},[1700,15466,1732],{"separator":1731},[6066,15468],{"width":15469},"1em",[1785,15471,15472,15474],{},[898,15473,12226],{},[898,15475,1762],{},[1700,15477,1765],{},[1931,15479,2438],{},[1700,15481,1732],{"separator":1731},[6066,15483],{"width":15469},[1785,15485,15486,15488],{},[898,15487,2974],{},[898,15489,1762],{},[1700,15491,1765],{},[1931,15493,15337],{},[1700,15495,1732],{"separator":1731},[6066,15497],{"width":15469},[1785,15499,15500,15502],{},[898,15501,12369],{},[898,15503,1762],{},[1700,15505,1765],{},[1931,15507,15508],{},"900.",[1781,15510,1783],{},[902,15512,15513],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,15515,15516],{},[614,15517,15518,15519,15532,15533,15546,15547,15562,15563,15576,15577,15592,15593,15606,15607,15620,15621,2196],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,15520,15522],{"className":15521},[886],[888,15523,15524],{"xmlns":890},[892,15525,15526,15530],{},[895,15527,15528],{},[898,15529,9316],{},[902,15531,9316],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,15534,15536],{"className":15535},[886],[888,15537,15538],{"xmlns":890},[892,15539,15540,15544],{},[895,15541,15542],{},[898,15543,12226],{},[902,15545,12226],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,15548,15550],{"className":15549},[886],[888,15551,15552],{"xmlns":890},[892,15553,15554,15560],{},[895,15555,15556,15558],{},[898,15557,1706],{},[898,15559,2005],{},[902,15561,12243],{"encoding":904}," stoupá z oblasti nízkých ",[883,15564,15566],{"className":15565},[886],[888,15567,15568],{"xmlns":890},[892,15569,15570,15574],{},[895,15571,15572],{},[898,15573,12226],{},[902,15575,12226],{"encoding":904},", přímka ",[883,15578,15580],{"className":15579},[886],[888,15581,15582],{"xmlns":890},[892,15583,15584,15590],{},[895,15585,15586,15588],{},[898,15587,12369],{},[898,15589,8861],{},[902,15591,12236],{"encoding":904}," klesá a protíná osu ",[883,15594,15596],{"className":15595},[886],[888,15597,15598],{"xmlns":890},[892,15599,15600,15604],{},[895,15601,15602],{},[898,15603,12226],{},[902,15605,12226],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,15608,15610],{"className":15609},[886],[888,15611,15612],{"xmlns":890},[892,15613,15614,15618],{},[895,15615,15616],{},[898,15617,1762],{},[902,15619,1762],{"encoding":904}," leží v bodě ",[883,15622,15624],{"className":15623},[886],[888,15625,15626],{"xmlns":890},[892,15627,15628,15650],{},[895,15629,15630,15632,15634,15636,15638,15640,15642,15644,15646,15648],{},[1700,15631,1927],{"stretchy":1702},[898,15633,12226],{},[1700,15635,1765],{},[1931,15637,2438],{},[1700,15639,1732],{"separator":1731},[1781,15641,2495],{},[898,15643,9316],{},[1700,15645,1765],{},[1931,15647,15300],{},[1700,15649,1970],{"stretchy":1702},[902,15651,15652],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,15654,15656],{"id":15655},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,15658,15659,15662,15663,15676,15677,7203,15690,15693,15694,15712,15713,15730,15731,15748,15749,15762,15763,15776],{},[38,15660,15661],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,15664,15666],{"className":15665},[886],[888,15667,15668],{"xmlns":890},[892,15669,15670,15674],{},[895,15671,15672],{},[898,15673,12297],{},[902,15675,12297],{"encoding":904}," nebo snížení daní ",[883,15678,15680],{"className":15679},[886],[888,15681,15682],{"xmlns":890},[892,15683,15684,15688],{},[895,15685,15686],{},[898,15687,2971],{},[902,15689,2971],{"encoding":904},[38,15691,15692],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,15695,15697],{"className":15696},[886],[888,15698,15699],{"xmlns":890},[892,15700,15701,15709],{},[895,15702,15703],{},[1785,15704,15705,15707],{},[898,15706,1762],{},[1700,15708,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,15710,15711],{"encoding":904},"E'"," má vyšší ",[883,15714,15716],{"className":15715},[886],[888,15717,15718],{"xmlns":890},[892,15719,15720,15728],{},[895,15721,15722],{},[1785,15723,15724,15726],{},[898,15725,9316],{},[898,15727,1762],{},[902,15729,14088],{"encoding":904}," i vyšší ",[883,15732,15734],{"className":15733},[886],[888,15735,15736],{"xmlns":890},[892,15737,15738,15746],{},[895,15739,15740],{},[1785,15741,15742,15744],{},[898,15743,12226],{},[898,15745,1762],{},[902,15747,14109],{"encoding":904}," (vyšší ",[883,15750,15752],{"className":15751},[886],[888,15753,15754],{"xmlns":890},[892,15755,15756,15760],{},[895,15757,15758],{},[898,15759,9316],{},[902,15761,9316],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,15764,15766],{"className":15765},[886],[888,15767,15768],{"xmlns":890},[892,15769,15770,15774],{},[895,15771,15772],{},[898,15773,12226],{},[902,15775,12226],{"encoding":904}," nahoru).",[724,15778,15779],{},[2756,15780],{"alt":15781,"className":15782,"src":15783},"imek-posun-is-lm-politiky",[210,2760],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,15785,15786,15789,15790,15807,15808,15811,15812,15829,15830,15847,15848,15861,15862,15881,15882,4110],{},[38,15787,15788],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,15791,15793],{"className":15792},[886],[888,15794,15795],{"xmlns":890},[892,15796,15797,15805],{},[895,15798,15799],{},[1785,15800,15801,15803],{},[898,15802,2005],{},[1700,15804,4543],{},[902,15806,12335],{"encoding":904}," národní bankou — ",[38,15809,15810],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,15813,15815],{"className":15814},[886],[888,15816,15817],{"xmlns":890},[892,15818,15819,15827],{},[895,15820,15821],{},[1785,15822,15823,15825],{},[898,15824,12226],{},[898,15826,1762],{},[902,15828,14109],{"encoding":904}," a vyšší ",[883,15831,15833],{"className":15832},[886],[888,15834,15835],{"xmlns":890},[892,15836,15837,15845],{},[895,15838,15839],{},[1785,15840,15841,15843],{},[898,15842,9316],{},[898,15844,1762],{},[902,15846,14088],{"encoding":904}," (nižší ",[883,15849,15851],{"className":15850},[886],[888,15852,15853],{"xmlns":890},[892,15854,15855,15859],{},[895,15856,15857],{},[898,15858,12226],{},[902,15860,12226],{"encoding":904}," povzbuzuje investice ",[883,15863,15865],{"className":15864},[886],[888,15866,15867],{"xmlns":890},[892,15868,15869,15879],{},[895,15870,15871,15873,15875,15877],{},[898,15872,12369],{},[1700,15874,1703],{"stretchy":1702},[898,15876,12226],{},[1700,15878,1709],{"stretchy":1702},[902,15880,14421],{"encoding":904},", ty zvedají ",[883,15883,15885],{"className":15884},[886],[888,15886,15887],{"xmlns":890},[892,15888,15889,15893],{},[895,15890,15891],{},[898,15892,9316],{},[902,15894,9316],{"encoding":904},[724,15896,15897,15898,15901],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,15899,15900],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,15903,15905],{"id":15904},"klíčové-pojmy","Klíčové pojmy",[120,15907,15908,15981,16027,16109,16159,16226,16283,16324,16357],{},[123,15909,15910,7203,15943,1343,15960,15977,15978,15980],{},[38,15911,15912,15913],{},"Funkce investic ",[883,15914,15916],{"className":15915},[886],[888,15917,15918],{"xmlns":890},[892,15919,15920,15940],{},[895,15921,15922,15924,15926,15928,15930,15932,15934,15936,15938],{},[898,15923,12369],{},[1700,15925,1703],{"stretchy":1702},[898,15927,12226],{},[1700,15929,1709],{"stretchy":1702},[1700,15931,1765],{},[898,15933,2354],{},[898,15935,12226],{},[1700,15937,1897],{},[898,15939,2406],{},[902,15941,15942],{"encoding":904},"I(r) = cr + d",[883,15944,15946],{"className":15945},[886],[888,15947,15948],{"xmlns":890},[892,15949,15950,15958],{},[895,15951,15952,15954,15956],{},[898,15953,2354],{},[1700,15955,3640],{},[1931,15957,1772],{},[902,15959,12700],{"encoding":904},[883,15961,15963],{"className":15962},[886],[888,15964,15965],{"xmlns":890},[892,15966,15967,15975],{},[895,15968,15969,15971,15973],{},[898,15970,2406],{},[1700,15972,3601],{},[1931,15974,1772],{},[902,15976,12679],{"encoding":904},"; ",[38,15979,12704],{}," funkce úrokové míry.",[123,15982,15983,15986,15987,16008,16009,16026],{},[38,15984,15985],{},"Trh zboží"," — rovnováha ",[883,15988,15990],{"className":15989},[886],[888,15991,15992],{"xmlns":890},[892,15993,15994,16006],{},[895,15995,15996,15998,16000,16002,16004],{},[898,15997,9316],{},[1700,15999,1765],{},[898,16001,2974],{},[1700,16003,1897],{},[898,16005,12369],{},[902,16007,14929],{"encoding":904},", ekvivalentně ",[883,16010,16012],{"className":16011},[886],[888,16013,16014],{"xmlns":890},[892,16015,16016,16024],{},[895,16017,16018,16020,16022],{},[898,16019,12369],{},[1700,16021,1765],{},[898,16023,8861],{},[902,16025,12897],{"encoding":904}," (investice = úspory).",[123,16028,16029,10208,16032,16034,16035,16085,16086,13100,16088,2196],{},[38,16030,16031],{},"Křivka IS",[614,16033,12239],{},") — ",[883,16036,16038],{"className":16037},[886],[888,16039,16040],{"xmlns":890},[892,16041,16042,16082],{},[895,16043,16044,16046,16048,16060,16062,16064],{},[898,16045,9316],{},[1700,16047,1765],{},[1774,16049,16050,16052],{},[898,16051,2354],{},[895,16053,16054,16056,16058],{},[1931,16055,1933],{},[1700,16057,1768],{},[898,16059,207],{},[898,16061,12226],{},[1700,16063,1897],{},[1774,16065,16066,16074],{},[895,16067,16068,16070,16072],{},[898,16069,1879],{},[1700,16071,1897],{},[898,16073,2406],{},[895,16075,16076,16078,16080],{},[1931,16077,1933],{},[1700,16079,1768],{},[898,16081,207],{},[902,16083,16084],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,16087,12704],{},[883,16089,16091],{"className":16090},[886],[888,16092,16093],{"xmlns":890},[892,16094,16095,16107],{},[895,16096,16097,16099,16101,16103,16105],{},[1700,16098,1703],{"stretchy":1702},[898,16100,12226],{},[1700,16102,1732],{"separator":1731},[898,16104,9316],{},[1700,16106,1709],{"stretchy":1702},[902,16108,13122],{"encoding":904},[123,16110,16111,15986,16114,16140,16141,2196],{},[38,16112,16113],{},"Trh peněz",[883,16115,16117],{"className":16116},[886],[888,16118,16119],{"xmlns":890},[892,16120,16121,16137],{},[895,16122,16123,16129,16131],{},[1785,16124,16125,16127],{},[898,16126,2005],{},[898,16128,4374],{},[1700,16130,1765],{},[1785,16132,16133,16135],{},[898,16134,2005],{},[898,16136,8861],{},[902,16138,16139],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,16142,16144],{"className":16143},[886],[888,16145,16146],{"xmlns":890},[892,16147,16148,16156],{},[895,16149,16150],{},[1785,16151,16152,16154],{},[898,16153,2005],{},[1700,16155,4543],{},[902,16157,16158],{"encoding":904},"M^* ",[123,16160,16161,7203,16164,2196],{},[38,16162,16163],{},"Transakční, opatrnostní, spekulační poptávka",[883,16165,16167],{"className":16166},[886],[888,16168,16169],{"xmlns":890},[892,16170,16171,16223],{},[895,16172,16173,16179,16181,16187,16189,16195,16197,16203,16205,16207,16213,16215,16217],{},[1785,16174,16175,16177],{},[898,16176,2005],{},[898,16178,4374],{},[1700,16180,1765],{},[2007,16182,16183,16185],{},[898,16184,1706],{},[1931,16186,1933],{},[1700,16188,1897],{},[2007,16190,16191,16193],{},[898,16192,1706],{},[1931,16194,2343],{},[1700,16196,1765],{},[2007,16198,16199,16201],{},[898,16200,13422],{},[1931,16202,1933],{},[898,16204,9316],{},[1700,16206,1897],{},[2007,16208,16209,16211],{},[898,16210,13422],{},[1931,16212,2343],{},[898,16214,12226],{},[1700,16216,1897],{},[2007,16218,16219,16221],{},[898,16220,13422],{},[1931,16222,2385],{},[902,16224,16225],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,16227,16228,10208,16231,16034,16233,16279,16280,16282],{},[38,16229,16230],{},"Křivka LM",[614,16232,12246],{},[883,16234,16236],{"className":16235},[886],[888,16237,16238],{"xmlns":890},[892,16239,16240,16276],{},[895,16241,16242,16248,16250,16256,16258,16260,16266,16268,16270],{},[1785,16243,16244,16246],{},[898,16245,2005],{},[1700,16247,4543],{},[1700,16249,1765],{},[2007,16251,16252,16254],{},[898,16253,13422],{},[1931,16255,1933],{},[898,16257,9316],{},[1700,16259,1897],{},[2007,16261,16262,16264],{},[898,16263,13422],{},[1931,16265,2343],{},[898,16267,12226],{},[1700,16269,1897],{},[2007,16271,16272,16274],{},[898,16273,13422],{},[1931,16275,2385],{},[902,16277,16278],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,16281,13842],{}," přímka.",[123,16284,16285,16288,16289,16323],{},[38,16286,16287],{},"Simultánní rovnováha"," — průsečík ",[883,16290,16292],{"className":16291},[886],[888,16293,16294],{"xmlns":890},[892,16295,16296,16320],{},[895,16297,16298,16300,16302,16304,16310,16312,16318],{},[898,16299,1762],{},[1700,16301,1765],{},[1700,16303,1703],{"stretchy":1702},[1785,16305,16306,16308],{},[898,16307,12226],{},[898,16309,1762],{},[1700,16311,1732],{"separator":1731},[1785,16313,16314,16316],{},[898,16315,9316],{},[898,16317,1762],{},[1700,16319,1709],{"stretchy":1702},[902,16321,16322],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,16325,16326,16329,16330,1343,16343,16356],{},[38,16327,16328],{},"Fiskální politika"," — nástroje ",[883,16331,16333],{"className":16332},[886],[888,16334,16335],{"xmlns":890},[892,16336,16337,16341],{},[895,16338,16339],{},[898,16340,12297],{},[902,16342,12297],{"encoding":904},[883,16344,16346],{"className":16345},[886],[888,16347,16348],{"xmlns":890},[892,16349,16350,16354],{},[895,16351,16352],{},[898,16353,2971],{},[902,16355,2971],{"encoding":904}," posouvající křivku IS.",[123,16358,16359,16362,16363,16380],{},[38,16360,16361],{},"Monetární politika"," — nástroj ",[883,16364,16366],{"className":16365},[886],[888,16367,16368],{"xmlns":890},[892,16369,16370,16378],{},[895,16371,16372],{},[1785,16373,16374,16376],{},[898,16375,2005],{},[1700,16377,4543],{},[902,16379,12335],{"encoding":904}," posouvající křivku LM.",[115,16382,3985],{"id":3984},[120,16384,16385,16394,16403,16413],{},[123,16386,16387,2106,16390],{},[38,16388,16389],{},"Kurz:",[207,16391,16393],{"className":16392,"dataFsResolvedFilePath":2140,"href":2141},[210],"Matematická ekonomie",[123,16395,16396,2106,16399],{},[38,16397,16398],{},"Přednáška:",[207,16400,16402],{"className":16401,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,16404,16405,2106,16408,16412],{},[38,16406,16407],{},"Nadřazené téma:",[207,16409,16411],{"className":16410,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,16414,16415,16418],{},[38,16416,16417],{},"Související:",[120,16419,16420,16427,16433],{},[123,16421,16422,16426],{},[207,16423,16425],{"className":16424,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,16428,16429,16432],{},[207,16430,1145],{"className":16431,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,16434,16435,16438],{},[207,16436,2118],{"className":16437,"dataFsResolvedFilePath":782,"href":783},[210]," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":16440},[16441,16442,16443,16444,16445,16446,16447,16448,16449,16450],{"id":12190,"depth":642,"text":12191},{"id":12345,"depth":642,"text":12346},{"id":12560,"depth":642,"text":12561},{"id":12853,"depth":642,"text":12854},{"id":13266,"depth":642,"text":13267},{"id":14059,"depth":642,"text":14060},{"id":14749,"depth":642,"text":14750},{"id":15655,"depth":642,"text":15656},{"id":15904,"depth":642,"text":15905},{"id":3984,"depth":642,"text":3985},{},"\u002Ftopics\u002Fis-lm",{"title":12182,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,16457,1143,16458,16459,16460,16461,16411],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":16464,"title":16465,"body":16466,"course":659,"courses":18059,"created":1129,"description":18060,"extension":661,"meta":18061,"navigation":664,"path":18062,"seo":18063,"sources":18064,"stem":18065,"tags":18066,"type":4049,"updated":677,"__hash__":18069},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":16467,"toc":18047},[16468,16471,16567,16574,16594,16598,16603,16666,16685,16687,16690,16826,16828,17038,17072,17209,17213,17277,17293,17321,17325,17423,17427,17431,17484,17590,17804,17808,17851,17957,18009,18011],[12,16469,16465],{"id":16470},"lagrangeova-metoda-vázané-extrémy",[724,16472,16473,16474,4102,16497,16529,16530,16533,16534,16561,16562,16566],{},"Hledáme extrém funkce ",[883,16475,16477],{"className":16476},[886],[888,16478,16479],{"xmlns":890},[892,16480,16481,16495],{},[895,16482,16483,16485,16487,16489,16491,16493],{},[898,16484,2220],{},[1700,16486,1703],{"stretchy":1702},[898,16488,2225],{},[1700,16490,1732],{"separator":1731},[898,16492,2215],{},[1700,16494,1709],{"stretchy":1702},[902,16496,10027],{"encoding":904},[883,16498,16500],{"className":16499},[886],[888,16501,16502],{"xmlns":890},[892,16503,16504,16526],{},[895,16505,16506,16508,16510,16516,16518,16524],{},[898,16507,900],{},[1700,16509,1703],{"stretchy":1702},[2007,16511,16512,16514],{},[898,16513,1662],{},[1931,16515,1933],{},[1700,16517,1732],{"separator":1731},[2007,16519,16520,16522],{},[898,16521,1662],{},[1931,16523,2343],{},[1700,16525,1709],{"stretchy":1702},[902,16527,16528],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,16531,16532],{},"podmíněný"," rovnicí ",[883,16535,16537],{"className":16536},[886],[888,16538,16539],{"xmlns":890},[892,16540,16541,16559],{},[895,16542,16543,16545,16547,16549,16551,16553,16555,16557],{},[898,16544,11224],{},[1700,16546,1703],{"stretchy":1702},[898,16548,2225],{},[1700,16550,1732],{"separator":1731},[898,16552,2215],{},[1700,16554,1709],{"stretchy":1702},[1700,16556,1765],{},[1931,16558,1772],{},[902,16560,11241],{"encoding":904},". V ",[207,16563,16565],{"className":16564,"dataFsResolvedFilePath":2140,"href":2141},[210],"matematické ekonomii"," se používá pro:",[724,16568,16569],{},[2756,16570],{"alt":16571,"className":16572,"src":16573},"imek-lagrange-tecnost",[210,2760],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,16575,16576,16585,16591],{},[123,16577,16578,16581,16582,1709],{},[38,16579,16580],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,16583,9960],{"className":16584,"dataFsResolvedFilePath":878,"href":879},[210],[123,16586,16587,16590],{},[38,16588,16589],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,16592,16593],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,16595,16597],{"id":16596},"princip","Princip",[724,16599,10890,16600,2901],{},[38,16601,16602],{},"Lagrangeovu funkci",[724,16604,16605],{},[883,16606,16608],{"className":16607},[886],[888,16609,16610],{"xmlns":890},[892,16611,16612,16663],{},[895,16613,16614,16616,16618,16620,16622,16624,16626,16629,16631,16633,16635,16637,16639,16641,16643,16645,16647,16649,16651,16653,16655,16657,16659,16661],{},[898,16615,1706],{},[1700,16617,1703],{"stretchy":1702},[898,16619,2225],{},[1700,16621,1732],{"separator":1731},[898,16623,2215],{},[1700,16625,1732],{"separator":1731},[898,16627,16628],{},"λ",[1700,16630,1709],{"stretchy":1702},[1700,16632,1765],{},[898,16634,2220],{},[1700,16636,1703],{"stretchy":1702},[898,16638,2225],{},[1700,16640,1732],{"separator":1731},[898,16642,2215],{},[1700,16644,1709],{"stretchy":1702},[1700,16646,1897],{},[898,16648,16628],{},[1781,16650,1783],{},[898,16652,11224],{},[1700,16654,1703],{"stretchy":1702},[898,16656,2225],{},[1700,16658,1732],{"separator":1731},[898,16660,2215],{},[1700,16662,1709],{"stretchy":1702},[902,16664,16665],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,16667,4499,16668,8290,16682,2196],{},[883,16669,16671],{"className":16670},[886],[888,16672,16673],{"xmlns":890},[892,16674,16675,16679],{},[895,16676,16677],{},[898,16678,16628],{},[902,16680,16681],{"encoding":904},"\\lambda",[38,16683,16684],{},"Lagrangeův multiplikátor",[115,16686,3445],{"id":3444},[724,16688,16689],{},"Řešíme soustavu:",[724,16691,16692,16740,16788],{},[883,16693,16695],{"className":16694},[886],[888,16696,16697],{"xmlns":890},[892,16698,16699,16737],{},[895,16700,16701,16709,16711,16719,16721,16723,16725,16733,16735],{},[2030,16702,16703,16705,16707],{},[898,16704,1706],{},[898,16706,2225],{},[1700,16708,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,16710,1765],{},[2030,16712,16713,16715,16717],{},[898,16714,2220],{},[898,16716,2225],{},[1700,16718,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,16720,1897],{},[898,16722,16628],{},[1781,16724,1783],{},[2030,16726,16727,16729,16731],{},[898,16728,11224],{},[898,16730,2225],{},[1700,16732,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,16734,1765],{},[1931,16736,1772],{},[902,16738,16739],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,16741,16743],{"className":16742},[886],[888,16744,16745],{"xmlns":890},[892,16746,16747,16785],{},[895,16748,16749,16757,16759,16767,16769,16771,16773,16781,16783],{},[2030,16750,16751,16753,16755],{},[898,16752,1706],{},[898,16754,2215],{},[1700,16756,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,16758,1765],{},[2030,16760,16761,16763,16765],{},[898,16762,2220],{},[898,16764,2215],{},[1700,16766,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,16768,1897],{},[898,16770,16628],{},[1781,16772,1783],{},[2030,16774,16775,16777,16779],{},[898,16776,11224],{},[898,16778,2215],{},[1700,16780,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,16782,1765],{},[1931,16784,1772],{},[902,16786,16787],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,16789,16791],{"className":16790},[886],[888,16792,16793],{"xmlns":890},[892,16794,16795,16823],{},[895,16796,16797,16805,16807,16809,16811,16813,16815,16817,16819,16821],{},[2030,16798,16799,16801,16803],{},[898,16800,1706],{},[898,16802,16628],{},[1700,16804,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,16806,1765],{},[898,16808,11224],{},[1700,16810,1703],{"stretchy":1702},[898,16812,2225],{},[1700,16814,1732],{"separator":1731},[898,16816,2215],{},[1700,16818,1709],{"stretchy":1702},[1700,16820,1765],{},[1931,16822,1772],{},[902,16824,16825],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,16827,3519],{"id":3518},[724,16829,16830],{},[883,16831,16833],{"className":16832},[886],[888,16834,16835],{"xmlns":890},[892,16836,16837,17035],{},[895,16838,16839,16841,16843,16845,16847,16849,16851,16853,16855,16857,16859,16875,16877,16879,16895,16897,16899,16907,16913,16915,16917,16933,16935,16937,16953,16955,16957,16965,16971,16973,16975,16977,16993,16995,16997,17013,17015,17017,17025,17027],{},[898,16840,4374],{},[1700,16842,1703],{"stretchy":1702},[898,16844,2225],{},[1700,16846,1732],{"separator":1731},[898,16848,2215],{},[1700,16850,1732],{"separator":1731},[898,16852,16628],{},[1700,16854,1709],{"stretchy":1702},[1700,16856,1765],{},[1700,16858,1703],{"stretchy":1702},[2030,16860,16861,16863,16869],{},[898,16862,2220],{},[895,16864,16865,16867],{},[898,16866,2225],{},[898,16868,2225],{},[895,16870,16871,16873],{},[1700,16872,1793],{"mathvariant":1791},[1700,16874,1793],{"mathvariant":1791},[1700,16876,1897],{},[898,16878,16628],{},[2030,16880,16881,16883,16889],{},[898,16882,11224],{},[895,16884,16885,16887],{},[898,16886,2225],{},[898,16888,2225],{},[895,16890,16891,16893],{},[1700,16892,1793],{"mathvariant":1791},[1700,16894,1793],{"mathvariant":1791},[1700,16896,1709],{"stretchy":1702},[1700,16898,1703],{"stretchy":1702},[2030,16900,16901,16903,16905],{},[898,16902,11224],{},[898,16904,2215],{},[1700,16906,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1785,16908,16909,16911],{},[1700,16910,1709],{"stretchy":1702},[1931,16912,2343],{},[1700,16914,1897],{},[1700,16916,1703],{"stretchy":1702},[2030,16918,16919,16921,16927],{},[898,16920,2220],{},[895,16922,16923,16925],{},[898,16924,2215],{},[898,16926,2215],{},[895,16928,16929,16931],{},[1700,16930,1793],{"mathvariant":1791},[1700,16932,1793],{"mathvariant":1791},[1700,16934,1897],{},[898,16936,16628],{},[2030,16938,16939,16941,16947],{},[898,16940,11224],{},[895,16942,16943,16945],{},[898,16944,2215],{},[898,16946,2215],{},[895,16948,16949,16951],{},[1700,16950,1793],{"mathvariant":1791},[1700,16952,1793],{"mathvariant":1791},[1700,16954,1709],{"stretchy":1702},[1700,16956,1703],{"stretchy":1702},[2030,16958,16959,16961,16963],{},[898,16960,11224],{},[898,16962,2225],{},[1700,16964,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1785,16966,16967,16969],{},[1700,16968,1709],{"stretchy":1702},[1931,16970,2343],{},[1700,16972,1768],{},[1931,16974,2343],{},[1700,16976,1703],{"stretchy":1702},[2030,16978,16979,16981,16987],{},[898,16980,2220],{},[895,16982,16983,16985],{},[898,16984,2225],{},[898,16986,2215],{},[895,16988,16989,16991],{},[1700,16990,1793],{"mathvariant":1791},[1700,16992,1793],{"mathvariant":1791},[1700,16994,1897],{},[898,16996,16628],{},[2030,16998,16999,17001,17007],{},[898,17000,11224],{},[895,17002,17003,17005],{},[898,17004,2225],{},[898,17006,2215],{},[895,17008,17009,17011],{},[1700,17010,1793],{"mathvariant":1791},[1700,17012,1793],{"mathvariant":1791},[1700,17014,1709],{"stretchy":1702},[1781,17016,1783],{},[2030,17018,17019,17021,17023],{},[898,17020,11224],{},[898,17022,2225],{},[1700,17024,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1781,17026,1783],{},[2030,17028,17029,17031,17033],{},[898,17030,11224],{},[898,17032,2215],{},[1700,17034,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,17036,17037],{"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",[724,17039,17040,17041,17071],{},"Je-li ",[883,17042,17044],{"className":17043},[886],[888,17045,17046],{"xmlns":890},[892,17047,17048,17068],{},[895,17049,17050,17052,17054,17056,17058,17060,17066],{},[1700,17051,1927],{"stretchy":1702},[898,17053,207],{},[1700,17055,1732],{"separator":1731},[898,17057,1879],{},[1700,17059,1732],{"separator":1731},[2007,17061,17062,17064],{},[898,17063,16628],{},[1931,17065,1772],{},[1700,17067,1970],{"stretchy":1702},[902,17069,17070],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,17073,17074,17142],{},[123,17075,17076,3607,17112,17114,17115],{},[883,17077,17079],{"className":17078},[886],[888,17080,17081],{"xmlns":890},[892,17082,17083,17109],{},[895,17084,17085,17087,17089,17091,17093,17095,17097,17103,17105,17107],{},[898,17086,4374],{},[1700,17088,1703],{"stretchy":1702},[898,17090,207],{},[1700,17092,1732],{"separator":1731},[898,17094,1879],{},[1700,17096,1732],{"separator":1731},[2007,17098,17099,17101],{},[898,17100,16628],{},[1931,17102,1772],{},[1700,17104,1709],{"stretchy":1702},[1700,17106,3640],{},[1931,17108,1772],{},[902,17110,17111],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,17113,3910],{}," vázané podmínkou ",[883,17116,17118],{"className":17117},[886],[888,17119,17120],{"xmlns":890},[892,17121,17122,17140],{},[895,17123,17124,17126,17128,17130,17132,17134,17136,17138],{},[898,17125,11224],{},[1700,17127,1703],{"stretchy":1702},[898,17129,2225],{},[1700,17131,1732],{"separator":1731},[898,17133,2215],{},[1700,17135,1709],{"stretchy":1702},[1700,17137,1765],{},[1931,17139,1772],{},[902,17141,11241],{"encoding":904},[123,17143,17144,3607,17180,17114,17182],{},[883,17145,17147],{"className":17146},[886],[888,17148,17149],{"xmlns":890},[892,17150,17151,17177],{},[895,17152,17153,17155,17157,17159,17161,17163,17165,17171,17173,17175],{},[898,17154,4374],{},[1700,17156,1703],{"stretchy":1702},[898,17158,207],{},[1700,17160,1732],{"separator":1731},[898,17162,1879],{},[1700,17164,1732],{"separator":1731},[2007,17166,17167,17169],{},[898,17168,16628],{},[1931,17170,1772],{},[1700,17172,1709],{"stretchy":1702},[1700,17174,3601],{},[1931,17176,1772],{},[902,17178,17179],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,17181,3968],{},[883,17183,17185],{"className":17184},[886],[888,17186,17187],{"xmlns":890},[892,17188,17189,17207],{},[895,17190,17191,17193,17195,17197,17199,17201,17203,17205],{},[898,17192,11224],{},[1700,17194,1703],{"stretchy":1702},[898,17196,2225],{},[1700,17198,1732],{"separator":1731},[898,17200,2215],{},[1700,17202,1709],{"stretchy":1702},[1700,17204,1765],{},[1931,17206,1772],{},[902,17208,11241],{"encoding":904},[115,17210,17212],{"id":17211},"význam-multiplikátoru","Význam multiplikátoru",[724,17214,17215],{},[883,17216,17218],{"className":17217},[886],[888,17219,17220],{"xmlns":890},[892,17221,17222,17274],{},[895,17223,17224,17226,17228,17250,17252],{},[898,17225,16628],{},[1700,17227,1765],{},[1774,17229,17230,17238],{},[2030,17231,17232,17234,17236],{},[898,17233,2220],{},[898,17235,2225],{},[1700,17237,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[895,17239,17240,17242],{},[1700,17241,1768],{},[2030,17243,17244,17246,17248],{},[898,17245,11224],{},[898,17247,2225],{},[1700,17249,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,17251,1765],{},[1774,17253,17254,17262],{},[2030,17255,17256,17258,17260],{},[898,17257,2220],{},[898,17259,2215],{},[1700,17261,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[895,17263,17264,17266],{},[1700,17265,1768],{},[2030,17267,17268,17270,17272],{},[898,17269,11224],{},[898,17271,2215],{},[1700,17273,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,17275,17276],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,17278,17279,17292],{},[883,17280,17282],{"className":17281},[886],[888,17283,17284],{"xmlns":890},[892,17285,17286,17290],{},[895,17287,17288],{},[898,17289,16628],{},[902,17291,16681],{"encoding":904}," udává:",[120,17294,17295,17301],{},[123,17296,17297,17298],{},"konstantní ",[38,17299,17300],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,17302,17303,17306,17307,17320],{},[38,17304,17305],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,17308,17310],{"className":17309},[886],[888,17311,17312],{"xmlns":890},[892,17313,17314,17318],{},[895,17315,17316],{},[898,17317,2220],{},[902,17319,2220],{"encoding":904},", uvolní-li se omezení o jednotku",[115,17322,17324],{"id":17323},"alternativní-postup","Alternativní postup",[724,17326,17327,17328,17355,17356,17380,17381,17405,17406,17419,17420,2196],{},"Lze-li z ",[883,17329,17331],{"className":17330},[886],[888,17332,17333],{"xmlns":890},[892,17334,17335,17353],{},[895,17336,17337,17339,17341,17343,17345,17347,17349,17351],{},[898,17338,11224],{},[1700,17340,1703],{"stretchy":1702},[898,17342,2225],{},[1700,17344,1732],{"separator":1731},[898,17346,2215],{},[1700,17348,1709],{"stretchy":1702},[1700,17350,1765],{},[1931,17352,1772],{},[902,17354,11241],{"encoding":904}," vyjádřit ",[883,17357,17359],{"className":17358},[886],[888,17360,17361],{"xmlns":890},[892,17362,17363,17377],{},[895,17364,17365,17367,17369,17371,17373,17375],{},[898,17366,2215],{},[1700,17368,1765],{},[898,17370,2215],{},[1700,17372,1703],{"stretchy":1702},[898,17374,2225],{},[1700,17376,1709],{"stretchy":1702},[902,17378,17379],{"encoding":904},"y = y(x)"," (nebo ",[883,17382,17384],{"className":17383},[886],[888,17385,17386],{"xmlns":890},[892,17387,17388,17402],{},[895,17389,17390,17392,17394,17396,17398,17400],{},[898,17391,2225],{},[1700,17393,1765],{},[898,17395,2225],{},[1700,17397,1703],{"stretchy":1702},[898,17399,2215],{},[1700,17401,1709],{"stretchy":1702},[902,17403,17404],{"encoding":904},"x = x(y)","), dosadíme do ",[883,17407,17409],{"className":17408},[886],[888,17410,17411],{"xmlns":890},[892,17412,17413,17417],{},[895,17414,17415],{},[898,17416,2220],{},[902,17418,2220],{"encoding":904}," a převedeme na ",[38,17421,17422],{},"extrém funkce jedné proměnné",[115,17424,17426],{"id":17425},"použití-v-imek","Použití v ImeK",[198,17428,17430],{"id":17429},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,17432,17433,17434,2196],{},"Rozpočtové omezení: ",[883,17435,17437],{"className":17436},[886],[888,17438,17439],{"xmlns":890},[892,17440,17441,17481],{},[895,17442,17443,17449,17451,17459,17465,17467,17475],{},[1785,17444,17445,17447],{},[898,17446,9316],{},[1700,17448,4543],{},[1700,17450,1765],{},[2030,17452,17453,17455,17457],{},[898,17454,1677],{},[1931,17456,1933],{},[1700,17458,4543],{},[2007,17460,17461,17463],{},[898,17462,1662],{},[1931,17464,1933],{},[1700,17466,1897],{},[2030,17468,17469,17471,17473],{},[898,17470,1677],{},[1931,17472,2343],{},[1700,17474,4543],{},[2007,17476,17477,17479],{},[898,17478,1662],{},[1931,17480,2343],{},[902,17482,17483],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,17485,17486],{},[883,17487,17489],{"className":17488},[886],[888,17490,17491],{"xmlns":890},[892,17492,17493,17587],{},[895,17494,17495,17497,17499,17505,17507,17513,17515,17517,17519,17521,17523,17525,17531,17533,17539,17541,17543,17545,17547,17553,17555,17563,17569,17571,17579,17585],{},[898,17496,1706],{},[1700,17498,1703],{"stretchy":1702},[2007,17500,17501,17503],{},[898,17502,1662],{},[1931,17504,1933],{},[1700,17506,1732],{"separator":1731},[2007,17508,17509,17511],{},[898,17510,1662],{},[1931,17512,2343],{},[1700,17514,1732],{"separator":1731},[898,17516,16628],{},[1700,17518,1709],{"stretchy":1702},[1700,17520,1765],{},[898,17522,900],{},[1700,17524,1703],{"stretchy":1702},[2007,17526,17527,17529],{},[898,17528,1662],{},[1931,17530,1933],{},[1700,17532,1732],{"separator":1731},[2007,17534,17535,17537],{},[898,17536,1662],{},[1931,17538,2343],{},[1700,17540,1709],{"stretchy":1702},[1700,17542,1897],{},[898,17544,16628],{},[1700,17546,1703],{"stretchy":1702},[1785,17548,17549,17551],{},[898,17550,9316],{},[1700,17552,4543],{},[1700,17554,1768],{},[2030,17556,17557,17559,17561],{},[898,17558,1677],{},[1931,17560,1933],{},[1700,17562,4543],{},[2007,17564,17565,17567],{},[898,17566,1662],{},[1931,17568,1933],{},[1700,17570,1768],{},[2030,17572,17573,17575,17577],{},[898,17574,1677],{},[1931,17576,2343],{},[1700,17578,4543],{},[2007,17580,17581,17583],{},[898,17582,1662],{},[1931,17584,2343],{},[1700,17586,1709],{"stretchy":1702},[902,17588,17589],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,17591,17592,17593,1343,17625,1343,17657,17706,17707,17761,17762,2196],{},"Soustava: ",[883,17594,17596],{"className":17595},[886],[888,17597,17598],{"xmlns":890},[892,17599,17600,17622],{},[895,17601,17602,17610,17612,17614],{},[2030,17603,17604,17606,17608],{},[898,17605,900],{},[1931,17607,1933],{},[1700,17609,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,17611,1765],{},[898,17613,16628],{},[2030,17615,17616,17618,17620],{},[898,17617,1677],{},[1931,17619,1933],{},[1700,17621,4543],{},[902,17623,17624],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,17626,17628],{"className":17627},[886],[888,17629,17630],{"xmlns":890},[892,17631,17632,17654],{},[895,17633,17634,17642,17644,17646],{},[2030,17635,17636,17638,17640],{},[898,17637,900],{},[1931,17639,2343],{},[1700,17641,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,17643,1765],{},[898,17645,16628],{},[2030,17647,17648,17650,17652],{},[898,17649,1677],{},[1931,17651,2343],{},[1700,17653,4543],{},[902,17655,17656],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,17658,17660],{"className":17659},[886],[888,17661,17662],{"xmlns":890},[892,17663,17664,17704],{},[895,17665,17666,17672,17674,17682,17688,17690,17698],{},[1785,17667,17668,17670],{},[898,17669,9316],{},[1700,17671,4543],{},[1700,17673,1765],{},[2030,17675,17676,17678,17680],{},[898,17677,1677],{},[1931,17679,1933],{},[1700,17681,4543],{},[2007,17683,17684,17686],{},[898,17685,1662],{},[1931,17687,1933],{},[1700,17689,1897],{},[2030,17691,17692,17694,17696],{},[898,17693,1677],{},[1931,17695,2343],{},[1700,17697,4543],{},[2007,17699,17700,17702],{},[898,17701,1662],{},[1931,17703,2343],{},[902,17705,17483],{"encoding":904},". Z prvních dvou: ",[883,17708,17710],{"className":17709},[886],[888,17711,17712],{"xmlns":890},[892,17713,17714,17758],{},[895,17715,17716,17736,17738],{},[1770,17717,17718],{"scriptlevel":1772,"displaystyle":1702},[1774,17719,17720,17728],{},[2030,17721,17722,17724,17726],{},[898,17723,900],{},[1931,17725,1933],{},[1700,17727,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[2030,17729,17730,17732,17734],{},[898,17731,900],{},[1931,17733,2343],{},[1700,17735,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,17737,1765],{},[1770,17739,17740],{"scriptlevel":1772,"displaystyle":1702},[1774,17741,17742,17750],{},[2030,17743,17744,17746,17748],{},[898,17745,1677],{},[1931,17747,1933],{},[1700,17749,4543],{},[2030,17751,17752,17754,17756],{},[898,17753,1677],{},[1931,17755,2343],{},[1700,17757,4543],{},[902,17759,17760],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,17763,17765],{"className":17764},[886],[888,17766,17767],{"xmlns":890},[892,17768,17769,17801],{},[895,17770,17771,17773,17775,17777,17779,17781],{},[898,17772,2005],{},[898,17774,4185],{},[898,17776,2974],{},[898,17778,8861],{},[1700,17780,1765],{},[1770,17782,17783],{"scriptlevel":1772,"displaystyle":1702},[1774,17784,17785,17793],{},[2030,17786,17787,17789,17791],{},[898,17788,1677],{},[1931,17790,1933],{},[1700,17792,4543],{},[2030,17794,17795,17797,17799],{},[898,17796,1677],{},[1931,17798,2343],{},[1700,17800,4543],{},[902,17802,17803],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,17805,17807],{"id":17806},"minimalizace-výdajů","Minimalizace výdajů",[724,17809,17810,17811,2196],{},"Podmínka dané užitečnosti ",[883,17812,17814],{"className":17813},[886],[888,17815,17816],{"xmlns":890},[892,17817,17818,17848],{},[895,17819,17820,17826,17828,17830,17832,17838,17840,17846],{},[1785,17821,17822,17824],{},[898,17823,900],{},[1700,17825,4543],{},[1700,17827,1765],{},[898,17829,900],{},[1700,17831,1703],{"stretchy":1702},[2007,17833,17834,17836],{},[898,17835,1662],{},[1931,17837,1933],{},[1700,17839,1732],{"separator":1731},[2007,17841,17842,17844],{},[898,17843,1662],{},[1931,17845,2343],{},[1700,17847,1709],{"stretchy":1702},[902,17849,17850],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,17852,17853],{},[883,17854,17856],{"className":17855},[886],[888,17857,17858],{"xmlns":890},[892,17859,17860,17954],{},[895,17861,17862,17864,17866,17872,17874,17880,17882,17884,17886,17888,17896,17902,17904,17912,17918,17920,17922,17924,17930,17932,17934,17936,17942,17944,17950,17952],{},[898,17863,1706],{},[1700,17865,1703],{"stretchy":1702},[2007,17867,17868,17870],{},[898,17869,1662],{},[1931,17871,1933],{},[1700,17873,1732],{"separator":1731},[2007,17875,17876,17878],{},[898,17877,1662],{},[1931,17879,2343],{},[1700,17881,1732],{"separator":1731},[898,17883,16628],{},[1700,17885,1709],{"stretchy":1702},[1700,17887,1765],{},[2030,17889,17890,17892,17894],{},[898,17891,1677],{},[1931,17893,1933],{},[1700,17895,4543],{},[2007,17897,17898,17900],{},[898,17899,1662],{},[1931,17901,1933],{},[1700,17903,1897],{},[2030,17905,17906,17908,17910],{},[898,17907,1677],{},[1931,17909,2343],{},[1700,17911,4543],{},[2007,17913,17914,17916],{},[898,17915,1662],{},[1931,17917,2343],{},[1700,17919,1897],{},[898,17921,16628],{},[1700,17923,1703],{"stretchy":1702},[1785,17925,17926,17928],{},[898,17927,900],{},[1700,17929,4543],{},[1700,17931,1768],{},[898,17933,900],{},[1700,17935,1703],{"stretchy":1702},[2007,17937,17938,17940],{},[898,17939,1662],{},[1931,17941,1933],{},[1700,17943,1732],{"separator":1731},[2007,17945,17946,17948],{},[898,17947,1662],{},[1931,17949,2343],{},[1700,17951,1709],{"stretchy":1702},[1700,17953,1709],{"stretchy":1702},[902,17955,17956],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,17958,17959,17960,2196],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,17961,17963],{"className":17962},[886],[888,17964,17965],{"xmlns":890},[892,17966,17967,18006],{},[895,17968,17969,17976,17978,17984,17986,17992,17994,18000,18002,18004],{},[2007,17970,17971,17973],{},[898,17972,1662],{},[898,17974,17975],{},"i",[1700,17977,1765],{},[2007,17979,17980,17982],{},[898,17981,4374],{},[898,17983,17975],{},[1700,17985,1703],{"stretchy":1702},[2007,17987,17988,17990],{},[898,17989,1677],{},[1931,17991,1933],{},[1700,17993,1732],{"separator":1731},[2007,17995,17996,17998],{},[898,17997,1677],{},[1931,17999,2343],{},[1700,18001,1732],{"separator":1731},[898,18003,900],{},[1700,18005,1709],{"stretchy":1702},[902,18007,18008],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,18010,3985],{"id":3984},[120,18012,18013,18020,18027,18036],{},[123,18014,18015,2106,18017],{},[38,18016,3992],{},[207,18018,784],{"className":18019,"dataFsResolvedFilePath":782,"href":783},[210],[123,18021,18022,2106,18024],{},[38,18023,4000],{},[207,18025,12125],{"className":18026,"dataFsResolvedFilePath":800,"href":801},[210],[123,18028,18029,2106,18032,18035],{},[38,18030,18031],{},"Aplikace v kurzu:",[207,18033,880],{"className":18034,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,18037,18038,2106,18040,1343,18043,18046],{},[38,18039,4008],{},[207,18041,936],{"className":18042,"dataFsResolvedFilePath":934,"href":935},[210],[207,18044,1400],{"className":18045,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":18048},[18049,18050,18051,18052,18053,18054,18058],{"id":16596,"depth":642,"text":16597},{"id":3444,"depth":642,"text":3445},{"id":3518,"depth":642,"text":3519},{"id":17211,"depth":642,"text":17212},{"id":17323,"depth":642,"text":17324},{"id":17425,"depth":642,"text":17426,"children":18055},[18056,18057],{"id":17429,"depth":649,"text":17430},{"id":17806,"depth":649,"text":17807},{"id":3984,"depth":642,"text":3985},[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":16465,"description":18060},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,18067,18068],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":18071,"title":936,"body":18072,"course":1128,"courses":659,"created":9743,"description":641,"extension":661,"meta":27940,"navigation":664,"path":27941,"seo":27942,"sources":27943,"stem":27944,"tags":27945,"type":4049,"updated":677,"__hash__":27949},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":18073,"toc":27902},[18074,18077,18079,18202,18337,18341,18344,18457,18461,18489,18536,18539,18605,18650,18653,18679,18710,18714,18718,18762,18806,18868,18923,18926,18930,18933,18980,19077,19183,19189,19266,19295,19434,19438,19467,19517,19664,19754,19758,19784,19822,19849,19887,19949,20024,20102,20160,20226,20270,20274,20332,20381,20426,20639,20759,20765,20769,20792,20796,20803,20807,20838,20873,20877,20927,21015,21057,21078,21140,21200,21204,21275,21343,21415,21530,21578,21582,21585,21626,21665,21688,21802,21966,21974,22001,22031,22034,22111,22264,22348,22687,22691,22815,22951,23087,23140,23143,23393,23474,23478,23481,23539,23571,23574,23623,23626,23697,23893,23897,24048,24278,24316,24369,24415,24418,24474,24523,24727,24817,24821,24837,24844,25013,25017,25088,25169,25250,25329,25475,25563,25567,25750,25881,25926,26023,26027,26766,26768,27819,27821],[12,18075,936],{"id":18076},"národní-důchod",[115,18078,12191],{"id":12190},[724,18080,18081,18082,2106,18086,18089,18090,2106,18093,18106,18107,18110,18111,18114,18115,18118,18119,18121,18122,2106,18124,18141,18142,18159,18160,18163,18164,4110],{},"Kapitola 7 ",[207,18083,18085],{"className":18084,"dataFsResolvedFilePath":2140,"href":2141},[210],"Matematické ekonomie",[38,18087,18088],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,18091,18092],{},"národním důchodem",[883,18094,18096],{"className":18095},[886],[888,18097,18098],{"xmlns":890},[892,18099,18100,18104],{},[895,18101,18102],{},[898,18103,9316],{},[902,18105,9316],{"encoding":904},". Budují se postupně bohatší modely — ",[38,18108,18109],{},"C-I"," (jen spotřeba a investice) → ",[38,18112,18113],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,18116,18117],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,18120,12196],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,18123,14070],{},[883,18125,18127],{"className":18126},[886],[888,18128,18129],{"xmlns":890},[892,18130,18131,18139],{},[895,18132,18133],{},[1785,18134,18135,18137],{},[898,18136,9316],{},[898,18138,1762],{},[902,18140,14088],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,18143,18145],{"className":18144},[886],[888,18146,18147],{"xmlns":890},[892,18148,18149,18157],{},[895,18150,18151],{},[1785,18152,18153,18155],{},[898,18154,9316],{},[898,18156,1762],{},[902,18158,14088],{"encoding":904}," na exogenní veličiny popisují ",[38,18161,18162],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,18165,18167],{"className":18166},[886],[888,18168,18169],{"xmlns":890},[892,18170,18171,18199],{},[895,18172,18173,18175,18177,18179,18181,18183,18185,18187,18189,18191,18193,18195,18197],{},[1931,18174,1933],{},[898,18176,1979],{"mathvariant":1791},[1700,18178,1703],{"stretchy":1702},[1931,18180,1933],{},[1700,18182,1768],{},[898,18184,207],{},[1700,18186,1709],{"stretchy":1702},[1700,18188,1765],{},[1931,18190,1933],{},[898,18192,1979],{"mathvariant":1791},[898,18194,2005],{},[898,18196,1677],{},[898,18198,8861],{},[902,18200,18201],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[4060,18203,18204],{},[724,18205,18206,18208,18209,18212,18213,18231,18232,18262,18263,18310,18311,18313,18314,18336],{},[883,18207,4346],{}," Intuice\n",[38,18210,18211],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,18214,18216],{"className":18215},[886],[888,18217,18218],{"xmlns":890},[892,18219,18220,18228],{},[895,18221,18222,18224,18226],{},[898,18223,2005],{},[898,18225,1677],{},[898,18227,2974],{},[902,18229,18230],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,18233,18235],{"className":18234},[886],[888,18236,18237],{"xmlns":890},[892,18238,18239,18259],{},[895,18240,18241,18243,18245,18247,18249,18251,18253,18255,18257],{},[898,18242,2005],{},[898,18244,1677],{},[898,18246,8861],{},[1700,18248,1765],{},[1931,18250,1933],{},[1700,18252,1768],{},[898,18254,2005],{},[898,18256,1677],{},[898,18258,2974],{},[902,18260,18261],{"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 ",[883,18264,18266],{"className":18265},[886],[888,18267,18268],{"xmlns":890},[892,18269,18270,18307],{},[895,18271,18272,18274,18276,18278,18280,18286,18288,18291,18293,18295,18297,18299,18301,18303,18305],{},[1931,18273,1933],{},[1700,18275,1897],{},[898,18277,207],{},[1700,18279,1897],{},[1785,18281,18282,18284],{},[898,18283,207],{},[1931,18285,2343],{},[1700,18287,1897],{},[1700,18289,18290],{},"⋯",[1700,18292,1765],{},[1931,18294,1933],{},[898,18296,1979],{"mathvariant":1791},[1700,18298,1703],{"stretchy":1702},[1931,18300,1933],{},[1700,18302,1768],{},[898,18304,207],{},[1700,18306,1709],{"stretchy":1702},[902,18308,18309],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,18312,12196],{}," 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 ",[883,18315,18317],{"className":18316},[886],[888,18318,18319],{"xmlns":890},[892,18320,18321,18333],{},[895,18322,18323,18325,18327,18329,18331],{},[1700,18324,1703],{"stretchy":1702},[898,18326,9316],{},[1700,18328,1732],{"separator":1731},[898,18330,12226],{},[1700,18332,1709],{"stretchy":1702},[902,18334,18335],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,18338,18340],{"id":18339},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,18342,18343],{},"Po prostudování kapitoly by čtenář měl umět:",[120,18345,18346,18349,18352,18355,18358,18361,18364,18454],{},[123,18347,18348],{},"popsat zjednodušený model národní ekonomiky,",[123,18350,18351],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,18353,18354],{},"popsat lineární model spotřeby a úspor,",[123,18356,18357],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,18359,18360],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,18362,18363],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,18365,18366,18367,1343,18384,1343,18406,2114,18431,18453],{},"popsat modely ",[883,18368,18370],{"className":18369},[886],[888,18371,18372],{"xmlns":890},[892,18373,18374,18382],{},[895,18375,18376,18378,18380],{},[898,18377,2974],{},[1781,18379,12475],{},[898,18381,12369],{},[902,18383,12480],{"encoding":904},[883,18385,18387],{"className":18386},[886],[888,18388,18389],{"xmlns":890},[892,18390,18391,18403],{},[895,18392,18393,18395,18397,18399,18401],{},[898,18394,2974],{},[1781,18396,12475],{},[898,18398,12369],{},[1781,18400,12475],{},[898,18402,12297],{},[902,18404,18405],{"encoding":904},"C\\text{-}I\\text{-}G",[883,18407,18409],{"className":18408},[886],[888,18410,18411],{"xmlns":890},[892,18412,18413,18429],{},[895,18414,18415,18417,18419,18421,18423,18425,18427],{},[898,18416,2974],{},[1781,18418,12475],{},[898,18420,12369],{},[1781,18422,12475],{},[898,18424,12297],{},[1781,18426,12475],{},[898,18428,12505],{},[902,18430,12508],{"encoding":904},[883,18432,18434],{"className":18433},[886],[888,18435,18436],{"xmlns":890},[892,18437,18438,18450],{},[895,18439,18440,18442,18444,18446,18448],{},[898,18441,12369],{},[898,18443,8861],{},[1781,18445,12475],{},[898,18447,1706],{},[898,18449,2005],{},[902,18451,18452],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,18455,18456],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,18458,18460],{"id":18459},"gnp-a-národní-důchod","GNP a národní důchod",[724,18462,18463,2106,18466,10208,18485,18488],{},[38,18464,18465],{},"Hrubý národní produkt",[883,18467,18469],{"className":18468},[886],[888,18470,18471],{"xmlns":890},[892,18472,18473,18482],{},[895,18474,18475,18477,18480],{},[898,18476,12297],{},[898,18478,18479],{},"N",[898,18481,1677],{},[902,18483,18484],{"encoding":904},"GNP",[614,18486,18487],{},"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:",[724,18490,18491],{},[883,18492,18494],{"className":18493},[886],[888,18495,18496],{"xmlns":890},[892,18497,18498,18533],{},[895,18499,18500,18502,18504,18506,18508,18510,18512,18514,18516,18518,18520,18522,18524,18526,18528,18531],{},[898,18501,12297],{},[898,18503,18479],{},[898,18505,1677],{},[1700,18507,1765],{},[898,18509,2974],{},[1700,18511,1897],{},[898,18513,12369],{},[1700,18515,1897],{},[898,18517,12297],{},[1700,18519,1897],{},[898,18521,12505],{},[1700,18523,1732],{"separator":1731},[6066,18525],{"width":6068},[1700,18527,1703],{"stretchy":1702},[1931,18529,18530],{},"7.1",[1700,18532,1709],{"stretchy":1702},[902,18534,18535],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,18537,18538],{},"kde",[120,18540,18541,18557,18573,18589],{},[123,18542,18543,18556],{},[883,18544,18546],{"className":18545},[886],[888,18547,18548],{"xmlns":890},[892,18549,18550,18554],{},[895,18551,18552],{},[898,18553,2974],{},[902,18555,2974],{"encoding":904}," — výdaje domácností na spotřebu,",[123,18558,18559,18572],{},[883,18560,18562],{"className":18561},[886],[888,18563,18564],{"xmlns":890},[892,18565,18566,18570],{},[895,18567,18568],{},[898,18569,12369],{},[902,18571,12369],{"encoding":904}," — hrubé domácí investice,",[123,18574,18575,18588],{},[883,18576,18578],{"className":18577},[886],[888,18579,18580],{"xmlns":890},[892,18581,18582,18586],{},[895,18583,18584],{},[898,18585,12297],{},[902,18587,12297],{"encoding":904}," — vládní výdaje,",[123,18590,18591,18604],{},[883,18592,18594],{"className":18593},[886],[888,18595,18596],{"xmlns":890},[892,18597,18598,18602],{},[895,18599,18600],{},[898,18601,12505],{},[902,18603,12505],{"encoding":904}," — čistý export.",[724,18606,18607,18608,18625,18626,18629,18630,2106,18633,10208,18646,18649],{},"K měření ",[883,18609,18611],{"className":18610},[886],[888,18612,18613],{"xmlns":890},[892,18614,18615,18623],{},[895,18616,18617,18619,18621],{},[898,18618,12297],{},[898,18620,18479],{},[898,18622,1677],{},[902,18624,18484],{"encoding":904}," se užívá ",[38,18627,18628],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,18631,18632],{},"národní důchod",[883,18634,18636],{"className":18635},[886],[888,18637,18638],{"xmlns":890},[892,18639,18640,18644],{},[895,18641,18642],{},[898,18643,9316],{},[902,18645,9316],{"encoding":904},[614,18647,18648],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,18651,18652],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,18654,18655],{},[883,18656,18658],{"className":18657},[886],[888,18659,18660],{"xmlns":890},[892,18661,18662,18676],{},[895,18663,18664,18666,18668,18670,18672,18674],{},[898,18665,12297],{},[898,18667,18479],{},[898,18669,1677],{},[1700,18671,2927],{},[898,18673,9316],{},[1700,18675,1732],{"separator":1731},[902,18677,18678],{"encoding":904},"GNP \\approx Y,",[724,18680,18681,18682,10208,18685,18688,18689,18702,18703,18706,18707,2196],{},"a užívá se společného názvu ",[38,18683,18684],{},"důchod",[614,18686,18687],{},"income",") s označením ",[883,18690,18692],{"className":18691},[886],[888,18693,18694],{"xmlns":890},[892,18695,18696,18700],{},[895,18697,18698],{},[898,18699,9316],{},[902,18701,9316],{"encoding":904},". Domácnosti důchod použijí ke ",[38,18704,18705],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,18708,18709],{},"úspor",[115,18711,18713],{"id":18712},"spotřeba-a-úspory","Spotřeba a úspory",[198,18715,18717],{"id":18716},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,18719,18720,18721,18734,18735,18748,18749,2901],{},"Jak spotřeba ",[883,18722,18724],{"className":18723},[886],[888,18725,18726],{"xmlns":890},[892,18727,18728,18732],{},[895,18729,18730],{},[898,18731,2974],{},[902,18733,2974],{"encoding":904},", tak úspory ",[883,18736,18738],{"className":18737},[886],[888,18739,18740],{"xmlns":890},[892,18741,18742,18746],{},[895,18743,18744],{},[898,18745,8861],{},[902,18747,8861],{"encoding":904}," závisejí na důchodu ",[883,18750,18752],{"className":18751},[886],[888,18753,18754],{"xmlns":890},[892,18755,18756,18760],{},[895,18757,18758],{},[898,18759,9316],{},[902,18761,9316],{"encoding":904},[724,18763,18764],{},[883,18765,18767],{"className":18766},[886],[888,18768,18769],{"xmlns":890},[892,18770,18771,18803],{},[895,18772,18773,18775,18777,18779,18781,18783,18785,18787,18789,18791,18793,18795,18797,18799,18801],{},[898,18774,2974],{},[1700,18776,1765],{},[898,18778,2974],{},[1700,18780,1703],{"stretchy":1702},[898,18782,9316],{},[1700,18784,1709],{"stretchy":1702},[1700,18786,1732],{"separator":1731},[6066,18788],{"width":6068},[898,18790,8861],{},[1700,18792,1765],{},[898,18794,8861],{},[1700,18796,1703],{"stretchy":1702},[898,18798,9316],{},[1700,18800,1709],{"stretchy":1702},[898,18802,2196],{"mathvariant":1791},[902,18804,18805],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,18807,18808,8290,18827,10208,18830,18833,18834,8290,18854,10208,18857,18860,18861,2114,18864,18867],{},[883,18809,18811],{"className":18810},[886],[888,18812,18813],{"xmlns":890},[892,18814,18815,18825],{},[895,18816,18817,18819,18821,18823],{},[898,18818,2974],{},[1700,18820,1703],{"stretchy":1702},[898,18822,9316],{},[1700,18824,1709],{"stretchy":1702},[902,18826,14401],{"encoding":904},[38,18828,18829],{},"funkce spotřeby",[614,18831,18832],{},"consumption function","), ",[883,18835,18837],{"className":18836},[886],[888,18838,18839],{"xmlns":890},[892,18840,18841,18851],{},[895,18842,18843,18845,18847,18849],{},[898,18844,8861],{},[1700,18846,1703],{"stretchy":1702},[898,18848,9316],{},[1700,18850,1709],{"stretchy":1702},[902,18852,18853],{"encoding":904},"S(Y)",[38,18855,18856],{},"funkce úspor",[614,18858,18859],{},"savings function","); jejich grafy se nazývají ",[38,18862,18863],{},"křivka spotřeby",[38,18865,18866],{},"křivka úspor",". Platí základní identita",[724,18869,18870],{},[883,18871,18873],{"className":18872},[886],[888,18874,18875],{"xmlns":890},[892,18876,18877,18920],{},[895,18878,18879,18881,18883,18885,18887,18889,18891,18893,18895,18897,18899,18901,18903,18905,18907,18909,18911,18913,18915,18918],{},[898,18880,9316],{},[1700,18882,1765],{},[898,18884,2974],{},[1700,18886,1897],{},[898,18888,8861],{},[1700,18890,1765],{},[898,18892,2974],{},[1700,18894,1703],{"stretchy":1702},[898,18896,9316],{},[1700,18898,1709],{"stretchy":1702},[1700,18900,1897],{},[898,18902,8861],{},[1700,18904,1703],{"stretchy":1702},[898,18906,9316],{},[1700,18908,1709],{"stretchy":1702},[898,18910,2196],{"mathvariant":1791},[6066,18912],{"width":6068},[1700,18914,1703],{"stretchy":1702},[1931,18916,18917],{},"7.2",[1700,18919,1709],{"stretchy":1702},[902,18921,18922],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,18924,18925],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,18927,18929],{"id":18928},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,18931,18932],{},"Nejjednodušší model předpokládá lineární tvar",[724,18934,18935],{},[883,18936,18938],{"className":18937},[886],[888,18939,18940],{"xmlns":890},[892,18941,18942,18977],{},[895,18943,18944,18946,18948,18950,18952,18954,18956,18958,18960,18962,18964,18966,18968,18970,18972,18975],{},[898,18945,2974],{},[1700,18947,1765],{},[898,18949,2974],{},[1700,18951,1703],{"stretchy":1702},[898,18953,9316],{},[1700,18955,1709],{"stretchy":1702},[1700,18957,1765],{},[898,18959,207],{},[898,18961,9316],{},[1700,18963,1897],{},[898,18965,1879],{},[1700,18967,1732],{"separator":1731},[6066,18969],{"width":6068},[1700,18971,1703],{"stretchy":1702},[1931,18973,18974],{},"7.3",[1700,18976,1709],{"stretchy":1702},[902,18978,18979],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,18981,4499,18982,2114,19000,19022,19023,19063,19064,2196],{},[883,18983,18985],{"className":18984},[886],[888,18986,18987],{"xmlns":890},[892,18988,18989,18997],{},[895,18990,18991,18993,18995],{},[898,18992,1879],{},[1700,18994,3601],{},[1931,18996,1772],{},[902,18998,18999],{"encoding":904},"b > 0",[883,19001,19003],{"className":19002},[886],[888,19004,19005],{"xmlns":890},[892,19006,19007,19019],{},[895,19008,19009,19011,19013,19015,19017],{},[1931,19010,1772],{},[1700,19012,3640],{},[898,19014,207],{},[1700,19016,3640],{},[1931,19018,1933],{},[902,19020,19021],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,19024,19026],{"className":19025},[886],[888,19027,19028],{"xmlns":890},[892,19029,19030,19060],{},[895,19031,19032,19034,19036,19043,19045,19048,19050,19052,19054,19056,19058],{},[898,19033,207],{},[1700,19035,1765],{},[895,19037,19038,19041],{},[898,19039,19040],{"mathvariant":1791},"t",[898,19042,11224],{"mathvariant":1791},[1781,19044,1783],{},[898,19046,19047],{},"α",[1700,19049,1765],{},[898,19051,3084],{"mathvariant":1791},[898,19053,2974],{},[898,19055,1979],{"mathvariant":1791},[898,19057,3084],{"mathvariant":1791},[898,19059,9316],{},[902,19061,19062],{"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 ",[883,19065,19067],{"className":19066},[886],[888,19068,19069],{"xmlns":890},[892,19070,19071,19075],{},[895,19072,19073],{},[898,19074,9316],{},[902,19076,9316],{"encoding":904},[724,19078,19079],{},[614,19080,19081,19082,19106,19107,19145,19146,19162,19163,2196],{},"Obrázek 7.1 — Přímka spotřeby ",[883,19083,19085],{"className":19084},[886],[888,19086,19087],{"xmlns":890},[892,19088,19089,19103],{},[895,19090,19091,19093,19095,19097,19099,19101],{},[898,19092,2974],{},[1700,19094,1765],{},[898,19096,207],{},[898,19098,9316],{},[1700,19100,1897],{},[898,19102,1879],{},[902,19104,19105],{"encoding":904},"C = aY + b"," se směrnicí ",[883,19108,19110],{"className":19109},[886],[888,19111,19112],{"xmlns":890},[892,19113,19114,19142],{},[895,19115,19116,19118,19120,19126,19128,19130,19132,19134,19136,19138,19140],{},[898,19117,207],{},[1700,19119,1765],{},[895,19121,19122,19124],{},[898,19123,19040],{"mathvariant":1791},[898,19125,11224],{"mathvariant":1791},[1781,19127,1783],{},[898,19129,19047],{},[1700,19131,1765],{},[898,19133,3084],{"mathvariant":1791},[898,19135,2974],{},[898,19137,1979],{"mathvariant":1791},[898,19139,3084],{"mathvariant":1791},[898,19141,9316],{},[902,19143,19144],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,19147,19149],{"className":19148},[886],[888,19150,19151],{"xmlns":890},[892,19152,19153,19159],{},[895,19154,19155,19157],{},[898,19156,3084],{"mathvariant":1791},[898,19158,2974],{},[902,19160,19161],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,19164,19166],{"className":19165},[886],[888,19167,19168],{"xmlns":890},[892,19169,19170,19180],{},[895,19171,19172,19174,19176,19178],{},[898,19173,3084],{"mathvariant":1791},[898,19175,9316],{},[1700,19177,1765],{},[1931,19179,1933],{},[902,19181,19182],{"encoding":904},"\\Delta Y = 1",[724,19184,19185,19186,2901],{},"Dosazením do (7.2) plyne ",[38,19187,19188],{},"lineární model úspor",[724,19190,19191],{},[883,19192,19194],{"className":19193},[886],[888,19195,19196],{"xmlns":890},[892,19197,19198,19263],{},[895,19199,19200,19202,19204,19206,19208,19210,19212,19214,19216,19218,19220,19222,19224,19226,19228,19230,19232,19234,19236,19238,19240,19242,19244,19246,19248,19250,19252,19254,19256,19258,19261],{},[898,19201,8861],{},[1700,19203,1765],{},[898,19205,9316],{},[1700,19207,1768],{},[898,19209,2974],{},[1700,19211,1703],{"stretchy":1702},[898,19213,9316],{},[1700,19215,1709],{"stretchy":1702},[1700,19217,1765],{},[898,19219,9316],{},[1700,19221,1768],{},[1700,19223,1703],{"stretchy":1702},[898,19225,207],{},[898,19227,9316],{},[1700,19229,1897],{},[898,19231,1879],{},[1700,19233,1709],{"stretchy":1702},[1700,19235,1765],{},[1700,19237,1703],{"stretchy":1702},[1931,19239,1933],{},[1700,19241,1768],{},[898,19243,207],{},[1700,19245,1709],{"stretchy":1702},[898,19247,9316],{},[1700,19249,1768],{},[898,19251,1879],{},[898,19253,2196],{"mathvariant":1791},[6066,19255],{"width":6068},[1700,19257,1703],{"stretchy":1702},[1931,19259,19260],{},"7.4",[1700,19262,1709],{"stretchy":1702},[902,19264,19265],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,19267,19268,19269,4110],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,19270,19272],{"className":19271},[886],[888,19273,19274],{"xmlns":890},[892,19275,19276,19292],{},[895,19277,19278,19280,19282,19284,19286,19288,19290],{},[1931,19279,1772],{},[1700,19281,3640],{},[1931,19283,1933],{},[1700,19285,1768],{},[898,19287,207],{},[1700,19289,3640],{},[1931,19291,1933],{},[902,19293,19294],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,19296,19297],{},[614,19298,19299,19300,2114,19323,19355,19356,2821,19369,19399,19400,2821,19418,2196],{},"Obrázek 7.2 — Přímky ",[883,19301,19303],{"className":19302},[886],[888,19304,19305],{"xmlns":890},[892,19306,19307,19321],{},[895,19308,19309,19311,19313,19315,19317,19319],{},[898,19310,2974],{},[1700,19312,1765],{},[898,19314,207],{},[898,19316,9316],{},[1700,19318,1897],{},[898,19320,1879],{},[902,19322,19105],{"encoding":904},[883,19324,19326],{"className":19325},[886],[888,19327,19328],{"xmlns":890},[892,19329,19330,19352],{},[895,19331,19332,19334,19336,19338,19340,19342,19344,19346,19348,19350],{},[898,19333,8861],{},[1700,19335,1765],{},[1700,19337,1703],{"stretchy":1702},[1931,19339,1933],{},[1700,19341,1768],{},[898,19343,207],{},[1700,19345,1709],{"stretchy":1702},[898,19347,9316],{},[1700,19349,1768],{},[898,19351,1879],{},[902,19353,19354],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,19357,19359],{"className":19358},[886],[888,19360,19361],{"xmlns":890},[892,19362,19363,19367],{},[895,19364,19365],{},[898,19366,9316],{},[902,19368,9316],{"encoding":904},[883,19370,19372],{"className":19371},[886],[888,19373,19374],{"xmlns":890},[892,19375,19376,19396],{},[895,19377,19378,19380,19382,19384,19386,19388,19390,19392,19394],{},[898,19379,9316],{},[1700,19381,1765],{},[898,19383,1879],{},[898,19385,1979],{"mathvariant":1791},[1700,19387,1703],{"stretchy":1702},[1931,19389,1933],{},[1700,19391,1768],{},[898,19393,207],{},[1700,19395,1709],{"stretchy":1702},[902,19397,19398],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,19401,19403],{"className":19402},[886],[888,19404,19405],{"xmlns":890},[892,19406,19407,19415],{},[895,19408,19409,19411,19413],{},[898,19410,2974],{},[1700,19412,1732],{"separator":1731},[898,19414,8861],{},[902,19416,19417],{"encoding":904},"C, S",[883,19419,19421],{"className":19420},[886],[888,19422,19423],{"xmlns":890},[892,19424,19425,19431],{},[895,19426,19427,19429],{},[1700,19428,1768],{},[898,19430,1879],{},[902,19432,19433],{"encoding":904},"-b",[198,19435,19437],{"id":19436},"příklad-71","Příklad 7.1",[724,19439,19440,19441,19466],{},"Pro spotřebu ",[883,19442,19444],{"className":19443},[886],[888,19445,19446],{"xmlns":890},[892,19447,19448,19463],{},[895,19449,19450,19452,19454,19457,19459,19461],{},[898,19451,2974],{},[1700,19453,1765],{},[1931,19455,19456],{},"0,4",[898,19458,9316],{},[1700,19460,1897],{},[1931,19462,3058],{},[902,19464,19465],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,19468,19469],{},[883,19470,19472],{"className":19471},[886],[888,19473,19474],{"xmlns":890},[892,19475,19476,19514],{},[895,19477,19478,19480,19482,19484,19486,19488,19490,19492,19494,19496,19498,19500,19502,19504,19507,19509,19511],{},[898,19479,8861],{},[1700,19481,1765],{},[898,19483,9316],{},[1700,19485,1768],{},[898,19487,2974],{},[1700,19489,1765],{},[898,19491,9316],{},[1700,19493,1768],{},[1931,19495,19456],{},[898,19497,9316],{},[1700,19499,1768],{},[1931,19501,3058],{},[1700,19503,1765],{},[1931,19505,19506],{},"0,6",[898,19508,9316],{},[1700,19510,1768],{},[1931,19512,19513],{},"10.",[902,19515,19516],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,19518,19519],{},[614,19520,19521,19522,2114,19545,19569,19570,8290,19583,19607,19608,8290,19625,19641,19642,2196],{},"Obrázek 7.3 — Přímky ",[883,19523,19525],{"className":19524},[886],[888,19526,19527],{"xmlns":890},[892,19528,19529,19543],{},[895,19530,19531,19533,19535,19537,19539,19541],{},[898,19532,2974],{},[1700,19534,1765],{},[1931,19536,19456],{},[898,19538,9316],{},[1700,19540,1897],{},[1931,19542,3058],{},[902,19544,19465],{"encoding":904},[883,19546,19548],{"className":19547},[886],[888,19549,19550],{"xmlns":890},[892,19551,19552,19566],{},[895,19553,19554,19556,19558,19560,19562,19564],{},[898,19555,8861],{},[1700,19557,1765],{},[1931,19559,19506],{},[898,19561,9316],{},[1700,19563,1768],{},[1931,19565,3058],{},[902,19567,19568],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,19571,19573],{"className":19572},[886],[888,19574,19575],{"xmlns":890},[892,19576,19577,19581],{},[895,19578,19579],{},[898,19580,9316],{},[902,19582,9316],{"encoding":904},[883,19584,19586],{"className":19585},[886],[888,19587,19588],{"xmlns":890},[892,19589,19590,19604],{},[895,19591,19592,19594,19597],{},[1700,19593,2927],{},[1931,19595,19596],{},"16,",[8574,19598,19599,19601],{"accent":1731},[1931,19600,2445],{},[1700,19602,19603],{},"ˉ",[902,19605,19606],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,19609,19611],{"className":19610},[886],[888,19612,19613],{"xmlns":890},[892,19614,19615,19623],{},[895,19616,19617,19619,19621],{},[898,19618,2974],{},[1700,19620,1732],{"separator":1731},[898,19622,8861],{},[902,19624,19417],{"encoding":904},[883,19626,19628],{"className":19627},[886],[888,19629,19630],{"xmlns":890},[892,19631,19632,19638],{},[895,19633,19634,19636],{},[1700,19635,1768],{},[1931,19637,3058],{},[902,19639,19640],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,19643,19645],{"className":19644},[886],[888,19646,19647],{"xmlns":890},[892,19648,19649,19661],{},[895,19650,19651,19653,19655,19657,19659],{},[1700,19652,1703],{"stretchy":1702},[1931,19654,1772],{},[1700,19656,1732],{"separator":1731},[1931,19658,3058],{},[1700,19660,1709],{"stretchy":1702},[902,19662,19663],{"encoding":904},"(0, 10)",[724,19665,19666,19667,8290,19685,19715,19716,10208,19719,19722,19723,8290,19747,10208,19750,19753],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,19668,19670],{"className":19669},[886],[888,19671,19672],{"xmlns":890},[892,19673,19674,19682],{},[895,19675,19676,19678,19680],{},[898,19677,9316],{},[1700,19679,1765],{},[1931,19681,1772],{},[902,19683,19684],{"encoding":904},"Y = 0",[883,19686,19688],{"className":19687},[886],[888,19689,19690],{"xmlns":890},[892,19691,19692,19712],{},[895,19693,19694,19696,19698,19700,19702,19704,19706,19708,19710],{},[898,19695,8861],{},[1700,19697,1703],{"stretchy":1702},[1931,19699,1772],{},[1700,19701,1709],{"stretchy":1702},[1700,19703,1765],{},[1700,19705,1768],{},[898,19707,1879],{},[1700,19709,3640],{},[1931,19711,1772],{},[902,19713,19714],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,19717,19718],{},"autonomních úsporách",[614,19720,19721],{},"autonomous savings","). Analogicky ",[883,19724,19726],{"className":19725},[886],[888,19727,19728],{"xmlns":890},[892,19729,19730,19744],{},[895,19731,19732,19734,19736,19738,19740,19742],{},[898,19733,2974],{},[1700,19735,1703],{"stretchy":1702},[1931,19737,1772],{},[1700,19739,1709],{"stretchy":1702},[1700,19741,1765],{},[898,19743,1879],{},[902,19745,19746],{"encoding":904},"C(0) = b",[38,19748,19749],{},"autonomní spotřeba",[614,19751,19752],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,19755,19757],{"id":19756},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,19759,19760,2106,19763,10208,19780,19783],{},[38,19761,19762],{},"Mezní sklon ke spotřebě",[883,19764,19766],{"className":19765},[886],[888,19767,19768],{"xmlns":890},[892,19769,19770,19778],{},[895,19771,19772,19774,19776],{},[898,19773,2005],{},[898,19775,1677],{},[898,19777,2974],{},[902,19779,18230],{"encoding":904},[614,19781,19782],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,19785,19786],{},[883,19787,19789],{"className":19788},[886],[888,19790,19791],{"xmlns":890},[892,19792,19793,19819],{},[895,19794,19795,19797,19799,19801,19803,19817],{},[898,19796,2005],{},[898,19798,1677],{},[898,19800,2974],{},[1700,19802,1765],{},[1774,19804,19805,19811],{},[895,19806,19807,19809],{},[898,19808,2406],{"mathvariant":1791},[898,19810,2974],{},[895,19812,19813,19815],{},[898,19814,2406],{"mathvariant":1791},[898,19816,9316],{},[898,19818,2196],{"mathvariant":1791},[902,19820,19821],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,19823,19824,2106,19827,10208,19845,19848],{},[38,19825,19826],{},"Mezní sklon k úsporám",[883,19828,19830],{"className":19829},[886],[888,19831,19832],{"xmlns":890},[892,19833,19834,19842],{},[895,19835,19836,19838,19840],{},[898,19837,2005],{},[898,19839,1677],{},[898,19841,8861],{},[902,19843,19844],{"encoding":904},"MPS",[614,19846,19847],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,19850,19851],{},[883,19852,19854],{"className":19853},[886],[888,19855,19856],{"xmlns":890},[892,19857,19858,19884],{},[895,19859,19860,19862,19864,19866,19868,19882],{},[898,19861,2005],{},[898,19863,1677],{},[898,19865,8861],{},[1700,19867,1765],{},[1774,19869,19870,19876],{},[895,19871,19872,19874],{},[898,19873,2406],{"mathvariant":1791},[898,19875,8861],{},[895,19877,19878,19880],{},[898,19879,2406],{"mathvariant":1791},[898,19881,9316],{},[898,19883,2196],{"mathvariant":1791},[902,19885,19886],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,19888,19889,19890,19948],{},"Z (7.2) plyne ",[883,19891,19893],{"className":19892},[886],[888,19894,19895],{"xmlns":890},[892,19896,19897,19945],{},[895,19898,19899,19913,19915,19929,19931],{},[1774,19900,19901,19907],{},[895,19902,19903,19905],{},[898,19904,2406],{"mathvariant":1791},[898,19906,9316],{},[895,19908,19909,19911],{},[898,19910,2406],{"mathvariant":1791},[898,19912,9316],{},[1700,19914,1765],{},[1774,19916,19917,19923],{},[895,19918,19919,19921],{},[898,19920,2406],{"mathvariant":1791},[898,19922,2974],{},[895,19924,19925,19927],{},[898,19926,2406],{"mathvariant":1791},[898,19928,9316],{},[1700,19930,1897],{},[1774,19932,19933,19939],{},[895,19934,19935,19937],{},[898,19936,2406],{"mathvariant":1791},[898,19938,8861],{},[895,19940,19941,19943],{},[898,19942,2406],{"mathvariant":1791},[898,19944,9316],{},[902,19946,19947],{"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",[724,19950,19951],{},[883,19952,19954],{"className":19953},[886],[888,19955,19956],{"xmlns":890},[892,19957,19958,20021],{},[895,19959,19960,20012,20014,20016,20019],{},[13017,19961,19962],{"notation":13019},[1770,19963,19964],{"scriptlevel":1772,"displaystyle":1702},[1770,19965,19966],{"scriptlevel":1772,"displaystyle":1702},[1770,19967,19968],{"scriptlevel":1772,"displaystyle":1731},[895,19969,19970,19972,19974,19976,19978,19980,19982,19984,19986,19988,19990,19992,19994,19996,19998,20000,20002,20004,20006,20008,20010],{},[898,19971,2005],{},[898,19973,1677],{},[898,19975,2974],{},[1700,19977,1897],{},[898,19979,2005],{},[898,19981,1677],{},[898,19983,8861],{},[1700,19985,1765],{},[1931,19987,1933],{},[1700,19989,1732],{"separator":1731},[6066,19991],{"width":6068},[898,19993,2005],{},[898,19995,1677],{},[898,19997,8861],{},[1700,19999,1765],{},[1931,20001,1933],{},[1700,20003,1768],{},[898,20005,2005],{},[898,20007,1677],{},[898,20009,2974],{},[898,20011,2196],{"mathvariant":1791},[6066,20013],{"width":6068},[1700,20015,1703],{"stretchy":1702},[1931,20017,20018],{},"7.5",[1700,20020,1709],{"stretchy":1702},[902,20022,20023],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,20025,20026,2106,20029,20052,20053,2114,20075,20101],{},[38,20027,20028],{},"Pro lineární model",[883,20030,20032],{"className":20031},[886],[888,20033,20034],{"xmlns":890},[892,20035,20036,20050],{},[895,20037,20038,20040,20042,20044,20046,20048],{},[898,20039,2974],{},[1700,20041,1765],{},[898,20043,207],{},[898,20045,9316],{},[1700,20047,1897],{},[898,20049,1879],{},[902,20051,19105],{"encoding":904}," vychází ",[883,20054,20056],{"className":20055},[886],[888,20057,20058],{"xmlns":890},[892,20059,20060,20072],{},[895,20061,20062,20064,20066,20068,20070],{},[898,20063,2005],{},[898,20065,1677],{},[898,20067,2974],{},[1700,20069,1765],{},[898,20071,207],{},[902,20073,20074],{"encoding":904},"MPC = a",[883,20076,20078],{"className":20077},[886],[888,20079,20080],{"xmlns":890},[892,20081,20082,20098],{},[895,20083,20084,20086,20088,20090,20092,20094,20096],{},[898,20085,2005],{},[898,20087,1677],{},[898,20089,8861],{},[1700,20091,1765],{},[1931,20093,1933],{},[1700,20095,1768],{},[898,20097,207],{},[902,20099,20100],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,20103,20104,20107,20108,20130,20131,20159],{},[38,20105,20106],{},"Interpretace diferenciálem."," Pro pevné ",[883,20109,20111],{"className":20110},[886],[888,20112,20113],{"xmlns":890},[892,20114,20115,20127],{},[895,20116,20117,20119,20121],{},[898,20118,9316],{},[1700,20120,1765],{},[1785,20122,20123,20125],{},[898,20124,9316],{},[1700,20126,4543],{},[902,20128,20129],{"encoding":904},"Y = Y^*"," udává ",[883,20132,20134],{"className":20133},[886],[888,20135,20136],{"xmlns":890},[892,20137,20138,20156],{},[895,20139,20140,20142,20144,20146,20148,20154],{},[898,20141,2005],{},[898,20143,1677],{},[898,20145,2974],{},[1700,20147,1703],{"stretchy":1702},[1785,20149,20150,20152],{},[898,20151,9316],{},[1700,20153,4543],{},[1700,20155,1709],{"stretchy":1702},[902,20157,20158],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,20161,20162],{},[883,20163,20165],{"className":20164},[886],[888,20166,20167],{"xmlns":890},[892,20168,20169,20223],{},[895,20170,20171,20173,20175,20177,20179,20181,20183,20189,20191,20193,20195,20197,20199,20201,20203,20205,20207,20209,20211,20213,20215,20217,20219,20221],{},[898,20172,3084],{"mathvariant":1791},[898,20174,2974],{},[1700,20176,2927],{},[898,20178,2406],{"mathvariant":1791},[898,20180,2974],{},[1700,20182,1765],{},[1785,20184,20185,20187],{},[898,20186,2974],{},[1700,20188,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,20190,1703],{"stretchy":1702},[898,20192,9316],{},[1700,20194,1709],{"stretchy":1702},[1781,20196,1783],{},[898,20198,2406],{"mathvariant":1791},[898,20200,9316],{},[1700,20202,1765],{},[898,20204,2005],{},[898,20206,1677],{},[898,20208,2974],{},[1700,20210,1703],{"stretchy":1702},[898,20212,9316],{},[1700,20214,1709],{"stretchy":1702},[1781,20216,1783],{},[898,20218,2406],{"mathvariant":1791},[898,20220,9316],{},[898,20222,2196],{"mathvariant":1791},[902,20224,20225],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,20227,20228,20229,20265,20266,20269],{},"Analogicky ",[883,20230,20232],{"className":20231},[886],[888,20233,20234],{"xmlns":890},[892,20235,20236,20262],{},[895,20237,20238,20240,20242,20244,20246,20248,20250,20252,20254,20256,20258,20260],{},[898,20239,3084],{"mathvariant":1791},[898,20241,8861],{},[1700,20243,2927],{},[898,20245,2005],{},[898,20247,1677],{},[898,20249,8861],{},[1700,20251,1703],{"stretchy":1702},[898,20253,9316],{},[1700,20255,1709],{"stretchy":1702},[1781,20257,1783],{},[898,20259,2406],{"mathvariant":1791},[898,20261,9316],{},[902,20263,20264],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,20267,1145],{"className":20268,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,20271,20273],{"id":20272},"příklad-72","Příklad 7.2",[724,20275,19440,20276,20311,20312,20331],{},[883,20277,20279],{"className":20278},[886],[888,20280,20281],{"xmlns":890},[892,20282,20283,20308],{},[895,20284,20285,20287,20289,20292,20298,20300,20302,20304,20306],{},[898,20286,2974],{},[1700,20288,1765],{},[1931,20290,20291],{},"0,001",[1785,20293,20294,20296],{},[898,20295,9316],{},[1931,20297,2343],{},[1700,20299,1897],{},[1931,20301,3034],{},[898,20303,9316],{},[1700,20305,1897],{},[1931,20307,3314],{},[902,20309,20310],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,20313,20315],{"className":20314},[886],[888,20316,20317],{"xmlns":890},[892,20318,20319,20328],{},[895,20320,20321,20323,20325],{},[898,20322,9316],{},[1700,20324,3640],{},[1931,20326,20327],{},"400",[902,20329,20330],{"encoding":904},"Y \u003C 400",") platí",[724,20333,20334],{},[883,20335,20337],{"className":20336},[886],[888,20338,20339],{"xmlns":890},[892,20340,20341,20378],{},[895,20342,20343,20345,20347,20349,20351,20365,20367,20370,20372,20374,20376],{},[898,20344,2005],{},[898,20346,1677],{},[898,20348,2974],{},[1700,20350,1765],{},[1774,20352,20353,20359],{},[895,20354,20355,20357],{},[898,20356,2406],{"mathvariant":1791},[898,20358,2974],{},[895,20360,20361,20363],{},[898,20362,2406],{"mathvariant":1791},[898,20364,9316],{},[1700,20366,1765],{},[1931,20368,20369],{},"0,002",[898,20371,9316],{},[1700,20373,1897],{},[1931,20375,3034],{},[1700,20377,1732],{"separator":1731},[902,20379,20380],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,20382,20383],{},[883,20384,20386],{"className":20385},[886],[888,20387,20388],{"xmlns":890},[892,20389,20390,20423],{},[895,20391,20392,20394,20396,20398,20400,20402,20404,20406,20408,20410,20412,20414,20416,20418,20420],{},[898,20393,2005],{},[898,20395,1677],{},[898,20397,8861],{},[1700,20399,1765],{},[1931,20401,1933],{},[1700,20403,1768],{},[898,20405,2005],{},[898,20407,1677],{},[898,20409,2974],{},[1700,20411,1765],{},[1700,20413,1768],{},[1931,20415,20369],{},[898,20417,9316],{},[1700,20419,1897],{},[1931,20421,20422],{},"0,8.",[902,20424,20425],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,20427,20428,20508,20587],{},[123,20429,20430,1343,20458,20486,20487,8290,20505,2196],{},[883,20431,20433],{"className":20432},[886],[888,20434,20435],{"xmlns":890},[892,20436,20437,20455],{},[895,20438,20439,20441,20443,20445,20447,20449,20451,20453],{},[898,20440,2005],{},[898,20442,1677],{},[898,20444,2974],{},[1700,20446,1703],{"stretchy":1702},[1931,20448,3284],{},[1700,20450,1709],{"stretchy":1702},[1700,20452,1765],{},[1931,20454,19456],{},[902,20456,20457],{"encoding":904},"MPC(100) = 0{,}4",[883,20459,20461],{"className":20460},[886],[888,20462,20463],{"xmlns":890},[892,20464,20465,20483],{},[895,20466,20467,20469,20471,20473,20475,20477,20479,20481],{},[898,20468,2005],{},[898,20470,1677],{},[898,20472,8861],{},[1700,20474,1703],{"stretchy":1702},[1931,20476,3284],{},[1700,20478,1709],{"stretchy":1702},[1700,20480,1765],{},[1931,20482,19506],{},[902,20484,20485],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,20488,20490],{"className":20489},[886],[888,20491,20492],{"xmlns":890},[892,20493,20494,20502],{},[895,20495,20496,20498,20500],{},[898,20497,9316],{},[1700,20499,1765],{},[1931,20501,3284],{},[902,20503,20504],{"encoding":904},"Y = 100",[38,20506,20507],{},"větší sklon k úsporám",[123,20509,20510,1343,20538,20486,20566,8290,20584,2196],{},[883,20511,20513],{"className":20512},[886],[888,20514,20515],{"xmlns":890},[892,20516,20517,20535],{},[895,20518,20519,20521,20523,20525,20527,20529,20531,20533],{},[898,20520,2005],{},[898,20522,1677],{},[898,20524,2974],{},[1700,20526,1703],{"stretchy":1702},[1931,20528,8565],{},[1700,20530,1709],{"stretchy":1702},[1700,20532,1765],{},[1931,20534,19506],{},[902,20536,20537],{"encoding":904},"MPC(200) = 0{,}6",[883,20539,20541],{"className":20540},[886],[888,20542,20543],{"xmlns":890},[892,20544,20545,20563],{},[895,20546,20547,20549,20551,20553,20555,20557,20559,20561],{},[898,20548,2005],{},[898,20550,1677],{},[898,20552,8861],{},[1700,20554,1703],{"stretchy":1702},[1931,20556,8565],{},[1700,20558,1709],{"stretchy":1702},[1700,20560,1765],{},[1931,20562,19456],{},[902,20564,20565],{"encoding":904},"MPS(200) = 0{,}4",[883,20567,20569],{"className":20568},[886],[888,20570,20571],{"xmlns":890},[892,20572,20573,20581],{},[895,20574,20575,20577,20579],{},[898,20576,9316],{},[1700,20578,1765],{},[1931,20580,8565],{},[902,20582,20583],{"encoding":904},"Y = 200",[38,20585,20586],{},"větší sklon ke spotřebě",[123,20588,20589,20590,20608,20609,4110],{},"Přesně při ",[883,20591,20593],{"className":20592},[886],[888,20594,20595],{"xmlns":890},[892,20596,20597,20605],{},[895,20598,20599,20601,20603],{},[898,20600,9316],{},[1700,20602,1765],{},[1931,20604,8991],{},[902,20606,20607],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,20610,20612],{"className":20611},[886],[888,20613,20614],{"xmlns":890},[892,20615,20616,20636],{},[895,20617,20618,20620,20622,20624,20626,20628,20630,20632,20634],{},[898,20619,2005],{},[898,20621,1677],{},[898,20623,2974],{},[1700,20625,1765],{},[898,20627,2005],{},[898,20629,1677],{},[898,20631,8861],{},[1700,20633,1765],{},[1931,20635,5197],{},[902,20637,20638],{"encoding":904},"MPC = MPS = 0{,}5",[724,20640,20641,20642,20659,20660,20674,20675,2882,20688,20702,20703,20716,20717,20758],{},"Interpretace: při ",[883,20643,20645],{"className":20644},[886],[888,20646,20647],{"xmlns":890},[892,20648,20649,20657],{},[895,20650,20651,20653,20655],{},[898,20652,9316],{},[1700,20654,1765],{},[1931,20656,3284],{},[902,20658,20504],{"encoding":904}," se spotřeba mění ",[883,20661,20663],{"className":20662},[886],[888,20664,20665],{"xmlns":890},[892,20666,20667,20671],{},[895,20668,20669],{},[1931,20670,19456],{},[902,20672,20673],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,20676,20678],{"className":20677},[886],[888,20679,20680],{"xmlns":890},[892,20681,20682,20686],{},[895,20683,20684],{},[1931,20685,3284],{},[902,20687,3284],{"encoding":904},[883,20689,20691],{"className":20690},[886],[888,20692,20693],{"xmlns":890},[892,20694,20695,20700],{},[895,20696,20697],{},[1931,20698,20699],{},"101",[902,20701,20699],{"encoding":904},", změní se spotřeba přibližně o ",[883,20704,20706],{"className":20705},[886],[888,20707,20708],{"xmlns":890},[892,20709,20710,20714],{},[895,20711,20712],{},[1931,20713,19456],{},[902,20715,20673],{"encoding":904},". Skutečná změna ",[883,20718,20720],{"className":20719},[886],[888,20721,20722],{"xmlns":890},[892,20723,20724,20755],{},[895,20725,20726,20728,20730,20732,20734,20736,20738,20740,20742,20744,20746,20748,20750,20752],{},[898,20727,3084],{"mathvariant":1791},[898,20729,2974],{},[1700,20731,1765],{},[898,20733,2974],{},[1700,20735,1703],{"stretchy":1702},[1931,20737,20699],{},[1700,20739,1709],{"stretchy":1702},[1700,20741,1768],{},[898,20743,2974],{},[1700,20745,1703],{"stretchy":1702},[1931,20747,3284],{},[1700,20749,1709],{"stretchy":1702},[1700,20751,1765],{},[1931,20753,20754],{},"0,401",[902,20756,20757],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,20760,20761,20762],{},"Obecný trend: ",[38,20763,20764],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,20766,20768],{"id":20767},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,20770,20771,20772,10208,20775,20778,20779,10208,20782,12313,20785,10208,20788,20791],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,20773,20774],{},"makroekonomická rovnováha",[614,20776,20777],{},"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 ",[38,20780,20781],{},"agregátní poptávky",[614,20783,20784],{},"aggregate demand",[38,20786,20787],{},"agregátní nabídky",[614,20789,20790],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,20793,20795],{"id":20794},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,20797,20798],{},[2756,20799],{"alt":20800,"className":20801,"src":20802},"imek-keynesian-kriz",[210,2760],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,20804,20806],{"id":20805},"zadání-modelu","Zadání modelu",[724,20808,20809,20810,20823,20824,20837],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,20811,20813],{"className":20812},[886],[888,20814,20815],{"xmlns":890},[892,20816,20817,20821],{},[895,20818,20819],{},[898,20820,2974],{},[902,20822,2974],{"encoding":904}," a investice ",[883,20825,20827],{"className":20826},[886],[888,20828,20829],{"xmlns":890},[892,20830,20831,20835],{},[895,20832,20833],{},[898,20834,12369],{},[902,20836,12369],{"encoding":904},". Podmínka rovnováhy:",[724,20839,20840],{},[883,20841,20843],{"className":20842},[886],[888,20844,20845],{"xmlns":890},[892,20846,20847,20870],{},[895,20848,20849,20851,20853,20855,20857,20859,20861,20863,20865,20868],{},[898,20850,9316],{},[1700,20852,1765],{},[898,20854,2974],{},[1700,20856,1897],{},[898,20858,12369],{},[898,20860,2196],{"mathvariant":1791},[6066,20862],{"width":6068},[1700,20864,1703],{"stretchy":1702},[1931,20866,20867],{},"7.6",[1700,20869,1709],{"stretchy":1702},[902,20871,20872],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,20874,20876],{"id":20875},"soustava-rovnic","Soustava rovnic",[724,20878,20879,20880,20901,20902,20926],{},"Pro pevně zadané (plánované) investice ",[883,20881,20883],{"className":20882},[886],[888,20884,20885],{"xmlns":890},[892,20886,20887,20899],{},[895,20888,20889,20891,20893],{},[898,20890,12369],{},[1700,20892,1765],{},[1785,20894,20895,20897],{},[898,20896,12369],{},[1700,20898,4543],{},[902,20900,12380],{"encoding":904}," a funkci spotřeby ",[883,20903,20905],{"className":20904},[886],[888,20906,20907],{"xmlns":890},[892,20908,20909,20923],{},[895,20910,20911,20913,20915,20917,20919,20921],{},[898,20912,2974],{},[1700,20914,1765],{},[898,20916,2974],{},[1700,20918,1703],{"stretchy":1702},[898,20920,9316],{},[1700,20922,1709],{"stretchy":1702},[902,20924,20925],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,20928,20929],{},[883,20930,20932],{"className":20931},[886],[888,20933,20934],{"xmlns":890},[892,20935,20936,21012],{},[895,20937,20938,21003,21005,21007,21010],{},[20939,20940,20943,20975],"mtable",{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},"0.25em","right left",[20944,20945,20946,20953],"mtr",{},[20947,20948,20949],"mtd",{},[1770,20950,20951],{"scriptlevel":1772,"displaystyle":1731},[898,20952,9316],{},[20947,20954,20955],{},[1770,20956,20957],{"scriptlevel":1772,"displaystyle":1731},[895,20958,20959,20961,20963,20965,20967,20973],{},[895,20960],{},[1700,20962,1765],{},[898,20964,2974],{},[1700,20966,1897],{},[1785,20968,20969,20971],{},[898,20970,12369],{},[1700,20972,4543],{},[1700,20974,1732],{"separator":1731},[20944,20976,20977,20983],{},[20947,20978,20979],{},[1770,20980,20981],{"scriptlevel":1772,"displaystyle":1731},[898,20982,2974],{},[20947,20984,20985],{},[1770,20986,20987],{"scriptlevel":1772,"displaystyle":1731},[895,20988,20989,20991,20993,20995,20997,20999,21001],{},[895,20990],{},[1700,20992,1765],{},[898,20994,2974],{},[1700,20996,1703],{"stretchy":1702},[898,20998,9316],{},[1700,21000,1709],{"stretchy":1702},[1700,21002,1732],{"separator":1731},[6066,21004],{"width":6068},[1700,21006,1703],{"stretchy":1702},[1931,21008,21009],{},"7.7",[1700,21011,1709],{"stretchy":1702},[902,21013,21014],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,21016,21017,21018,2106,21020,2114,21037,2106,21040,2196],{},"jejímž řešením jsou ",[38,21019,14070],{},[883,21021,21023],{"className":21022},[886],[888,21024,21025],{"xmlns":890},[892,21026,21027,21035],{},[895,21028,21029],{},[1785,21030,21031,21033],{},[898,21032,9316],{},[898,21034,1762],{},[902,21036,14088],{"encoding":904},[38,21038,21039],{},"rovnovážná spotřeba",[883,21041,21043],{"className":21042},[886],[888,21044,21045],{"xmlns":890},[892,21046,21047,21055],{},[895,21048,21049],{},[1785,21050,21051,21053],{},[898,21052,2974],{},[898,21054,1762],{},[902,21056,14147],{"encoding":904},[198,21058,21060,21061],{"id":21059},"výpočet-yeye","Výpočet ",[883,21062,21064],{"className":21063},[886],[888,21065,21066],{"xmlns":890},[892,21067,21068,21076],{},[895,21069,21070],{},[1785,21071,21072,21074],{},[898,21073,9316],{},[898,21075,1762],{},[902,21077,14088],{"encoding":904},[724,21079,21080,21081,21104,21105,7873,21137],{},"Pro lineární spotřebu ",[883,21082,21084],{"className":21083},[886],[888,21085,21086],{"xmlns":890},[892,21087,21088,21102],{},[895,21089,21090,21092,21094,21096,21098,21100],{},[898,21091,2974],{},[1700,21093,1765],{},[898,21095,207],{},[898,21097,9316],{},[1700,21099,1897],{},[898,21101,1879],{},[902,21103,19105],{"encoding":904}," plyne z (7.7) rovnice ",[883,21106,21108],{"className":21107},[886],[888,21109,21110],{"xmlns":890},[892,21111,21112,21134],{},[895,21113,21114,21116,21118,21120,21122,21124,21126,21128],{},[898,21115,9316],{},[1700,21117,1765],{},[898,21119,207],{},[898,21121,9316],{},[1700,21123,1897],{},[898,21125,1879],{},[1700,21127,1897],{},[1785,21129,21130,21132],{},[898,21131,12369],{},[1700,21133,4543],{},[902,21135,21136],{"encoding":904},"Y = aY + b + I^*",[38,21138,21139],{},"redukovaný tvar",[724,21141,21142],{},[883,21143,21145],{"className":21144},[886],[888,21146,21147],{"xmlns":890},[892,21148,21149,21197],{},[895,21150,21151],{},[13017,21152,21153],{"notation":13019},[1770,21154,21155],{"scriptlevel":1772,"displaystyle":1702},[1770,21156,21157],{"scriptlevel":1772,"displaystyle":1702},[1770,21158,21159],{"scriptlevel":1772,"displaystyle":1731},[895,21160,21161,21163,21169,21171,21193,21195],{},[1781,21162,1783],{},[1785,21164,21165,21167],{},[898,21166,9316],{},[898,21168,1762],{},[1700,21170,1765],{},[1774,21172,21173,21185],{},[895,21174,21175,21177,21179],{},[898,21176,1879],{},[1700,21178,1897],{},[1785,21180,21181,21183],{},[898,21182,12369],{},[1700,21184,4543],{},[895,21186,21187,21189,21191],{},[1931,21188,1933],{},[1700,21190,1768],{},[898,21192,207],{},[898,21194,2196],{"mathvariant":1791},[1781,21196,1783],{},[902,21198,21199],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,21201,21203],{"id":21202},"příklad-73","Příklad 7.3",[724,21205,21206,21207,8290,21224,2114,21248,21274],{},"V modelu ",[883,21208,21210],{"className":21209},[886],[888,21211,21212],{"xmlns":890},[892,21213,21214,21222],{},[895,21215,21216,21218,21220],{},[898,21217,2974],{},[1781,21219,12475],{},[898,21221,12369],{},[902,21223,12480],{"encoding":904},[883,21225,21227],{"className":21226},[886],[888,21228,21229],{"xmlns":890},[892,21230,21231,21245],{},[895,21232,21233,21235,21237,21239,21241,21243],{},[898,21234,2974],{},[1700,21236,1765],{},[1931,21238,19506],{},[898,21240,9316],{},[1700,21242,1897],{},[1931,21244,3058],{},[902,21246,21247],{"encoding":904},"C = 0{,}6Y + 10",[883,21249,21251],{"className":21250},[886],[888,21252,21253],{"xmlns":890},[892,21254,21255,21271],{},[895,21256,21257,21259,21261,21263,21265],{},[898,21258,12369],{},[1700,21260,1765],{},[1931,21262,3702],{},[1700,21264,1765],{},[1785,21266,21267,21269],{},[898,21268,12369],{},[1700,21270,4543],{},[902,21272,21273],{"encoding":904},"I = 12 = I^*",". Soustava",[724,21276,21277],{},[883,21278,21280],{"className":21279},[886],[888,21281,21282],{"xmlns":890},[892,21283,21284,21340],{},[20939,21285,21286,21312],{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},[20944,21287,21288,21294],{},[20947,21289,21290],{},[1770,21291,21292],{"scriptlevel":1772,"displaystyle":1731},[898,21293,9316],{},[20947,21295,21296],{},[1770,21297,21298],{"scriptlevel":1772,"displaystyle":1731},[895,21299,21300,21302,21304,21306,21308,21310],{},[895,21301],{},[1700,21303,1765],{},[898,21305,2974],{},[1700,21307,1897],{},[1931,21309,3702],{},[1700,21311,1732],{"separator":1731},[20944,21313,21314,21320],{},[20947,21315,21316],{},[1770,21317,21318],{"scriptlevel":1772,"displaystyle":1731},[898,21319,2974],{},[20947,21321,21322],{},[1770,21323,21324],{"scriptlevel":1772,"displaystyle":1731},[895,21325,21326,21328,21330,21332,21334,21336,21338],{},[895,21327],{},[1700,21329,1765],{},[1931,21331,19506],{},[898,21333,9316],{},[1700,21335,1897],{},[1931,21337,3058],{},[1700,21339,1732],{"separator":1731},[902,21341,21342],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,21344,21345,21346,1343,21369,21392,21393,4110],{},"má řešení ",[883,21347,21349],{"className":21348},[886],[888,21350,21351],{"xmlns":890},[892,21352,21353,21366],{},[895,21354,21355,21361,21363],{},[1785,21356,21357,21359],{},[898,21358,9316],{},[898,21360,1762],{},[1700,21362,1765],{},[1931,21364,21365],{},"55",[902,21367,21368],{"encoding":904},"Y^E = 55",[883,21370,21372],{"className":21371},[886],[888,21373,21374],{"xmlns":890},[892,21375,21376,21389],{},[895,21377,21378,21384,21386],{},[1785,21379,21380,21382],{},[898,21381,2974],{},[898,21383,1762],{},[1700,21385,1765],{},[1931,21387,21388],{},"43",[902,21390,21391],{"encoding":904},"C^E = 43"," (a ",[883,21394,21396],{"className":21395},[886],[888,21397,21398],{"xmlns":890},[892,21399,21400,21412],{},[895,21401,21402,21408,21410],{},[1785,21403,21404,21406],{},[898,21405,8861],{},[898,21407,1762],{},[1700,21409,1765],{},[1931,21411,3702],{},[902,21413,21414],{"encoding":904},"S^E = 12",[724,21416,21417],{},[614,21418,21419,21420,21442,21443,12313,21464,21487,21488,2196],{},"Obrázek 7.5 — Přímky ",[883,21421,21423],{"className":21422},[886],[888,21424,21425],{"xmlns":890},[892,21426,21427,21439],{},[895,21428,21429,21431,21433,21435,21437],{},[898,21430,2974],{},[1700,21432,1765],{},[898,21434,9316],{},[1700,21436,1768],{},[1931,21438,3702],{},[902,21440,21441],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,21444,21446],{"className":21445},[886],[888,21447,21448],{"xmlns":890},[892,21449,21450,21462],{},[895,21451,21452,21454,21456,21458,21460],{},[898,21453,9316],{},[1700,21455,1765],{},[898,21457,2974],{},[1700,21459,1897],{},[898,21461,12369],{},[902,21463,14929],{"encoding":904},[883,21465,21467],{"className":21466},[886],[888,21468,21469],{"xmlns":890},[892,21470,21471,21485],{},[895,21472,21473,21475,21477,21479,21481,21483],{},[898,21474,2974],{},[1700,21476,1765],{},[1931,21478,19506],{},[898,21480,9316],{},[1700,21482,1897],{},[1931,21484,3058],{},[902,21486,21247],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,21489,21491],{"className":21490},[886],[888,21492,21493],{"xmlns":890},[892,21494,21495,21527],{},[895,21496,21497,21499,21505,21507,21513,21515,21517,21519,21521,21523,21525],{},[1700,21498,1927],{"stretchy":1702},[1785,21500,21501,21503],{},[898,21502,9316],{},[898,21504,1762],{},[1700,21506,1732],{"separator":1731},[1785,21508,21509,21511],{},[898,21510,2974],{},[898,21512,1762],{},[1700,21514,1970],{"stretchy":1702},[1700,21516,1765],{},[1700,21518,1927],{"stretchy":1702},[1931,21520,21365],{},[1700,21522,1732],{"separator":1731},[1931,21524,21388],{},[1700,21526,1970],{"stretchy":1702},[902,21528,21529],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,21531,21532,21535,21536,21553,21554,2196],{},[38,21533,21534],{},"Komentář k přechodu."," Model ",[883,21537,21539],{"className":21538},[886],[888,21540,21541],{"xmlns":890},[892,21542,21543,21551],{},[895,21544,21545,21547,21549],{},[898,21546,2974],{},[1781,21548,12475],{},[898,21550,12369],{},[902,21552,12480],{"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 ",[38,21555,21556,21557],{},"model ",[883,21558,21560],{"className":21559},[886],[888,21561,21562],{"xmlns":890},[892,21563,21564,21576],{},[895,21565,21566,21568,21570,21572,21574],{},[898,21567,2974],{},[1781,21569,12475],{},[898,21571,12369],{},[1781,21573,12475],{},[898,21575,12297],{},[902,21577,18405],{"encoding":904},[115,21579,21581],{"id":21580},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,21583,20806],{"id":21584},"zadání-modelu-1",[724,21586,21587,21588,21605,21606,2106,21609,10208,21622,21625],{},"Rozšíření modelu ",[883,21589,21591],{"className":21590},[886],[888,21592,21593],{"xmlns":890},[892,21594,21595,21603],{},[895,21596,21597,21599,21601],{},[898,21598,2974],{},[1781,21600,12475],{},[898,21602,12369],{},[902,21604,12480],{"encoding":904}," o ",[38,21607,21608],{},"vládní výdaje",[883,21610,21612],{"className":21611},[886],[888,21613,21614],{"xmlns":890},[892,21615,21616,21620],{},[895,21617,21618],{},[898,21619,12297],{},[902,21621,12297],{"encoding":904},[614,21623,21624],{},"government expenditure","). Podmínka rovnováhy:",[724,21627,21628],{},[883,21629,21631],{"className":21630},[886],[888,21632,21633],{"xmlns":890},[892,21634,21635,21662],{},[895,21636,21637,21639,21641,21643,21645,21647,21649,21651,21653,21655,21657,21660],{},[898,21638,9316],{},[1700,21640,1765],{},[898,21642,2974],{},[1700,21644,1897],{},[898,21646,12369],{},[1700,21648,1897],{},[898,21650,12297],{},[898,21652,2196],{"mathvariant":1791},[6066,21654],{"width":6068},[1700,21656,1703],{"stretchy":1702},[1931,21658,21659],{},"7.8",[1700,21661,1709],{"stretchy":1702},[902,21663,21664],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,21666,21667,21668,2106,21671,10208,21684,21687],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,21669,21670],{},"zdaněním domácností",[883,21672,21674],{"className":21673},[886],[888,21675,21676],{"xmlns":890},[892,21677,21678,21682],{},[895,21679,21680],{},[898,21681,2971],{},[902,21683,2971],{"encoding":904},[614,21685,21686],{},"taxation","). Zdanění bývá:",[120,21689,21690,21723,21748],{},[123,21691,21692,21693,1732],{},"úměrné důchodu: ",[883,21694,21696],{"className":21695},[886],[888,21697,21698],{"xmlns":890},[892,21699,21700,21720],{},[895,21701,21702,21704,21706,21708,21710,21712,21714,21716,21718],{},[898,21703,2971],{},[1700,21705,1765],{},[898,21707,2971],{},[1700,21709,1703],{"stretchy":1702},[898,21711,9316],{},[1700,21713,1709],{"stretchy":1702},[1700,21715,1765],{},[898,21717,19040],{},[898,21719,9316],{},[902,21721,21722],{"encoding":904},"T = T(Y) = tY",[123,21724,21725,21726,1732],{},"fixní: ",[883,21727,21729],{"className":21728},[886],[888,21730,21731],{"xmlns":890},[892,21732,21733,21745],{},[895,21734,21735,21737,21739],{},[898,21736,2971],{},[1700,21738,1765],{},[1785,21740,21741,21743],{},[898,21742,2971],{},[1700,21744,4543],{},[902,21746,21747],{"encoding":904},"T = T^*",[123,21749,21750,21751,21779,21780,2196],{},"kombinované: ",[883,21752,21754],{"className":21753},[886],[888,21755,21756],{"xmlns":890},[892,21757,21758,21776],{},[895,21759,21760,21762,21764,21770,21772,21774],{},[898,21761,2971],{},[1700,21763,1765],{},[1785,21765,21766,21768],{},[898,21767,2971],{},[1700,21769,4543],{},[1700,21771,1897],{},[898,21773,19040],{},[898,21775,9316],{},[902,21777,21778],{"encoding":904},"T = T^* + tY",", kde ",[883,21781,21783],{"className":21782},[886],[888,21784,21785],{"xmlns":890},[892,21786,21787,21799],{},[895,21788,21789,21791,21793,21795,21797],{},[1931,21790,1772],{},[1700,21792,7867],{},[898,21794,19040],{},[1700,21796,3640],{},[1931,21798,1933],{},[902,21800,21801],{"encoding":904},"0 \\le t \u003C 1",[4060,21803,21804],{},[724,21805,21806,21808,21809,21830,21831,21834,21835,21848,21849,12313,21875,2106,21878,21904,21905,21933,21934,2114,21947,21965],{},[883,21807,4601],{}," Pozor na disponibilní důchod\nV modelu ",[883,21810,21812],{"className":21811},[886],[888,21813,21814],{"xmlns":890},[892,21815,21816,21828],{},[895,21817,21818,21820,21822,21824,21826],{},[898,21819,2974],{},[1781,21821,12475],{},[898,21823,12369],{},[1781,21825,12475],{},[898,21827,12297],{},[902,21829,18405],{"encoding":904}," je nutné ",[38,21832,21833],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,21836,21838],{"className":21837},[886],[888,21839,21840],{"xmlns":890},[892,21841,21842,21846],{},[895,21843,21844],{},[898,21845,9316],{},[902,21847,9316],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,21850,21852],{"className":21851},[886],[888,21853,21854],{"xmlns":890},[892,21855,21856,21872],{},[895,21857,21858,21860,21862,21864,21866,21868,21870],{},[898,21859,9316],{},[1700,21861,1765],{},[898,21863,2974],{},[1700,21865,1897],{},[898,21867,12369],{},[1700,21869,1897],{},[898,21871,12297],{},[902,21873,21874],{"encoding":904},"Y = C + I + G",[38,21876,21877],{},"disponibilní důchod",[883,21879,21881],{"className":21880},[886],[888,21882,21883],{"xmlns":890},[892,21884,21885,21901],{},[895,21886,21887,21893,21895,21897,21899],{},[2007,21888,21889,21891],{},[898,21890,9316],{},[898,21892,4374],{},[1700,21894,1765],{},[898,21896,9316],{},[1700,21898,1768],{},[898,21900,2971],{},[902,21902,21903],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,21906,21908],{"className":21907},[886],[888,21909,21910],{"xmlns":890},[892,21911,21912,21930],{},[895,21913,21914,21916,21918,21920,21922,21928],{},[898,21915,2974],{},[1700,21917,1765],{},[898,21919,2974],{},[1700,21921,1703],{"stretchy":1702},[2007,21923,21924,21926],{},[898,21925,9316],{},[898,21927,4374],{},[1700,21929,1709],{"stretchy":1702},[902,21931,21932],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,21935,21937],{"className":21936},[886],[888,21938,21939],{"xmlns":890},[892,21940,21941,21945],{},[895,21942,21943],{},[898,21944,9316],{},[902,21946,9316],{"encoding":904},[883,21948,21950],{"className":21949},[886],[888,21951,21952],{"xmlns":890},[892,21953,21954,21962],{},[895,21955,21956],{},[2007,21957,21958,21960],{},[898,21959,9316],{},[898,21961,4374],{},[902,21963,21964],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,21967,21968,10208,21971,1709],{},[38,21969,21970],{},"Disponibilní důchod",[614,21972,21973],{},"disposable income",[724,21975,21976],{},[883,21977,21979],{"className":21978},[886],[888,21980,21981],{"xmlns":890},[892,21982,21983,21999],{},[895,21984,21985,21991,21993,21995,21997],{},[2007,21986,21987,21989],{},[898,21988,9316],{},[898,21990,4374],{},[1700,21992,1765],{},[898,21994,9316],{},[1700,21996,1768],{},[898,21998,2971],{},[902,22000,21903],{"encoding":904},[724,22002,22003,22004,2196],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,22005,22007],{"className":22006},[886],[888,22008,22009],{"xmlns":890},[892,22010,22011,22029],{},[895,22012,22013,22015,22017,22019,22021,22027],{},[898,22014,2974],{},[1700,22016,1765],{},[898,22018,2974],{},[1700,22020,1703],{"stretchy":1702},[2007,22022,22023,22025],{},[898,22024,9316],{},[898,22026,4374],{},[1700,22028,1709],{"stretchy":1702},[902,22030,21932],{"encoding":904},[198,22032,20876],{"id":22033},"soustava-rovnic-1",[724,22035,22036,22037,1343,22058,22080,22081,2901],{},"Pro pevně zadané ",[883,22038,22040],{"className":22039},[886],[888,22041,22042],{"xmlns":890},[892,22043,22044,22056],{},[895,22045,22046,22048,22050],{},[898,22047,12369],{},[1700,22049,1765],{},[1785,22051,22052,22054],{},[898,22053,12369],{},[1700,22055,4543],{},[902,22057,12380],{"encoding":904},[883,22059,22061],{"className":22060},[886],[888,22062,22063],{"xmlns":890},[892,22064,22065,22077],{},[895,22066,22067,22069,22071],{},[898,22068,12297],{},[1700,22070,1765],{},[1785,22072,22073,22075],{},[898,22074,12297],{},[1700,22076,4543],{},[902,22078,22079],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,22082,22084],{"className":22083},[886],[888,22085,22086],{"xmlns":890},[892,22087,22088,22108],{},[895,22089,22090,22092,22094,22096,22098,22104,22106],{},[898,22091,9316],{},[1700,22093,1732],{"separator":1731},[898,22095,2974],{},[1700,22097,1732],{"separator":1731},[2007,22099,22100,22102],{},[898,22101,9316],{},[898,22103,4374],{},[1700,22105,1732],{"separator":1731},[898,22107,2971],{},[902,22109,22110],{"encoding":904},"Y, C, Y_D, T",[724,22112,22113],{},[883,22114,22116],{"className":22115},[886],[888,22117,22118],{"xmlns":890},[892,22119,22120,22261],{},[895,22121,22122,22252,22254,22256,22259],{},[20939,22123,22124,22162,22190,22222],{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},[20944,22125,22126,22132],{},[20947,22127,22128],{},[1770,22129,22130],{"scriptlevel":1772,"displaystyle":1731},[898,22131,9316],{},[20947,22133,22134],{},[1770,22135,22136],{"scriptlevel":1772,"displaystyle":1731},[895,22137,22138,22140,22142,22144,22146,22152,22154,22160],{},[895,22139],{},[1700,22141,1765],{},[898,22143,2974],{},[1700,22145,1897],{},[1785,22147,22148,22150],{},[898,22149,12369],{},[1700,22151,4543],{},[1700,22153,1897],{},[1785,22155,22156,22158],{},[898,22157,12297],{},[1700,22159,4543],{},[1700,22161,1732],{"separator":1731},[20944,22163,22164,22170],{},[20947,22165,22166],{},[1770,22167,22168],{"scriptlevel":1772,"displaystyle":1731},[898,22169,2971],{},[20947,22171,22172],{},[1770,22173,22174],{"scriptlevel":1772,"displaystyle":1731},[895,22175,22176,22178,22180,22182,22184,22186,22188],{},[895,22177],{},[1700,22179,1765],{},[898,22181,2971],{},[1700,22183,1703],{"stretchy":1702},[898,22185,9316],{},[1700,22187,1709],{"stretchy":1702},[1700,22189,1732],{"separator":1731},[20944,22191,22192,22198],{},[20947,22193,22194],{},[1770,22195,22196],{"scriptlevel":1772,"displaystyle":1731},[898,22197,2974],{},[20947,22199,22200],{},[1770,22201,22202],{"scriptlevel":1772,"displaystyle":1731},[895,22203,22204,22206,22208,22210,22212,22218,22220],{},[895,22205],{},[1700,22207,1765],{},[898,22209,2974],{},[1700,22211,1703],{"stretchy":1702},[2007,22213,22214,22216],{},[898,22215,9316],{},[898,22217,4374],{},[1700,22219,1709],{"stretchy":1702},[1700,22221,1732],{"separator":1731},[20944,22223,22224,22234],{},[20947,22225,22226],{},[1770,22227,22228],{"scriptlevel":1772,"displaystyle":1731},[2007,22229,22230,22232],{},[898,22231,9316],{},[898,22233,4374],{},[20947,22235,22236],{},[1770,22237,22238],{"scriptlevel":1772,"displaystyle":1731},[895,22239,22240,22242,22244,22246,22248,22250],{},[895,22241],{},[1700,22243,1765],{},[898,22245,9316],{},[1700,22247,1768],{},[898,22249,2971],{},[1700,22251,1732],{"separator":1731},[6066,22253],{"width":6068},[1700,22255,1703],{"stretchy":1702},[1931,22257,22258],{},"7.9",[1700,22260,1709],{"stretchy":1702},[902,22262,22263],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,22265,22266,22267,22311,22312,2196],{},"s řešeními ",[883,22268,22270],{"className":22269},[886],[888,22271,22272],{"xmlns":890},[892,22273,22274,22308],{},[895,22275,22276,22282,22284,22290,22292,22298,22300],{},[1785,22277,22278,22280],{},[898,22279,9316],{},[898,22281,1762],{},[1700,22283,1732],{"separator":1731},[1785,22285,22286,22288],{},[898,22287,2974],{},[898,22289,1762],{},[1700,22291,1732],{"separator":1731},[1785,22293,22294,22296],{},[898,22295,2971],{},[898,22297,1762],{},[1700,22299,1732],{"separator":1731},[2030,22301,22302,22304,22306],{},[898,22303,9316],{},[898,22305,4374],{},[898,22307,1762],{},[902,22309,22310],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,22313,22315],{"className":22314},[886],[888,22316,22317],{"xmlns":890},[892,22318,22319,22345],{},[895,22320,22321,22327,22329,22337,22339],{},[1785,22322,22323,22325],{},[898,22324,8861],{},[898,22326,1762],{},[1700,22328,1765],{},[2030,22330,22331,22333,22335],{},[898,22332,9316],{},[898,22334,4374],{},[898,22336,1762],{},[1700,22338,1768],{},[1785,22340,22341,22343],{},[898,22342,2974],{},[898,22344,1762],{},[902,22346,22347],{"encoding":904},"S^E = Y_D^E - C^E",[4060,22349,22350,22355],{},[724,22351,22352,22354],{},[883,22353,4761],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,22356,22357,22380,22463,22518,22608],{},[123,22358,22359,22362,22363,2196],{},[38,22360,22361],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,22364,22366],{"className":22365},[886],[888,22367,22368],{"xmlns":890},[892,22369,22370,22378],{},[895,22371,22372],{},[2007,22373,22374,22376],{},[898,22375,9316],{},[898,22377,4374],{},[902,22379,21964],{"encoding":904},[123,22381,22382,22431,22432,22449,22450,2196],{},[38,22383,22384,22385,22405,22406],{},"Dosaď ",[883,22386,22388],{"className":22387},[886],[888,22389,22390],{"xmlns":890},[892,22391,22392,22402],{},[895,22393,22394,22396,22398,22400],{},[898,22395,2971],{},[1700,22397,1703],{"stretchy":1702},[898,22399,9316],{},[1700,22401,1709],{"stretchy":1702},[902,22403,22404],{"encoding":904},"T(Y)"," do ",[883,22407,22409],{"className":22408},[886],[888,22410,22411],{"xmlns":890},[892,22412,22413,22429],{},[895,22414,22415,22421,22423,22425,22427],{},[2007,22416,22417,22419],{},[898,22418,9316],{},[898,22420,4374],{},[1700,22422,1765],{},[898,22424,9316],{},[1700,22426,1768],{},[898,22428,2971],{},[902,22430,21903],{"encoding":904}," — dostaneš ",[883,22433,22435],{"className":22434},[886],[888,22436,22437],{"xmlns":890},[892,22438,22439,22447],{},[895,22440,22441],{},[2007,22442,22443,22445],{},[898,22444,9316],{},[898,22446,4374],{},[902,22448,21964],{"encoding":904}," jako lineární funkci ",[883,22451,22453],{"className":22452},[886],[888,22454,22455],{"xmlns":890},[892,22456,22457,22461],{},[895,22458,22459],{},[898,22460,9316],{},[902,22462,9316],{"encoding":904},[123,22464,22465,22431,22492,22449,22505,2196],{},[38,22466,22384,22467,22491],{},[883,22468,22470],{"className":22469},[886],[888,22471,22472],{"xmlns":890},[892,22473,22474,22488],{},[895,22475,22476,22482,22484,22486],{},[2007,22477,22478,22480],{},[898,22479,9316],{},[898,22481,4374],{},[1700,22483,1703],{"stretchy":1702},[898,22485,9316],{},[1700,22487,1709],{"stretchy":1702},[902,22489,22490],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,22493,22495],{"className":22494},[886],[888,22496,22497],{"xmlns":890},[892,22498,22499,22503],{},[895,22500,22501],{},[898,22502,2974],{},[902,22504,2974],{"encoding":904},[883,22506,22508],{"className":22507},[886],[888,22509,22510],{"xmlns":890},[892,22511,22512,22516],{},[895,22513,22514],{},[898,22515,9316],{},[902,22517,9316],{"encoding":904},[123,22519,22520,2106,22542,22576,22577,22590,22591,2196],{},[38,22521,22384,22522,22541],{},[883,22523,22525],{"className":22524},[886],[888,22526,22527],{"xmlns":890},[892,22528,22529,22539],{},[895,22530,22531,22533,22535,22537],{},[898,22532,2974],{},[1700,22534,1703],{"stretchy":1702},[898,22536,9316],{},[1700,22538,1709],{"stretchy":1702},[902,22540,14401],{"encoding":904}," do podmínky rovnováhy",[883,22543,22545],{"className":22544},[886],[888,22546,22547],{"xmlns":890},[892,22548,22549,22573],{},[895,22550,22551,22553,22555,22557,22559,22565,22567],{},[898,22552,9316],{},[1700,22554,1765],{},[898,22556,2974],{},[1700,22558,1897],{},[1785,22560,22561,22563],{},[898,22562,12369],{},[1700,22564,4543],{},[1700,22566,1897],{},[1785,22568,22569,22571],{},[898,22570,12297],{},[1700,22572,4543],{},[902,22574,22575],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,22578,22580],{"className":22579},[886],[888,22581,22582],{"xmlns":890},[892,22583,22584,22588],{},[895,22585,22586],{},[898,22587,9316],{},[902,22589,9316],{"encoding":904},", odtud ",[883,22592,22594],{"className":22593},[886],[888,22595,22596],{"xmlns":890},[892,22597,22598,22606],{},[895,22599,22600],{},[1785,22601,22602,22604],{},[898,22603,9316],{},[898,22605,1762],{},[902,22607,14088],{"encoding":904},[123,22609,22610,22613,22614,1343,22632,1343,22652,1343,22669,2196],{},[38,22611,22612],{},"Zpětným dosazením"," dopočítej ",[883,22615,22617],{"className":22616},[886],[888,22618,22619],{"xmlns":890},[892,22620,22621,22629],{},[895,22622,22623],{},[1785,22624,22625,22627],{},[898,22626,2971],{},[898,22628,1762],{},[902,22630,22631],{"encoding":904},"T^E",[883,22633,22635],{"className":22634},[886],[888,22636,22637],{"xmlns":890},[892,22638,22639,22649],{},[895,22640,22641],{},[2030,22642,22643,22645,22647],{},[898,22644,9316],{},[898,22646,4374],{},[898,22648,1762],{},[902,22650,22651],{"encoding":904},"Y_D^E",[883,22653,22655],{"className":22654},[886],[888,22656,22657],{"xmlns":890},[892,22658,22659,22667],{},[895,22660,22661],{},[1785,22662,22663,22665],{},[898,22664,2974],{},[898,22666,1762],{},[902,22668,14147],{"encoding":904},[883,22670,22672],{"className":22671},[886],[888,22673,22674],{"xmlns":890},[892,22675,22676,22684],{},[895,22677,22678],{},[1785,22679,22680,22682],{},[898,22681,8861],{},[898,22683,1762],{},[902,22685,22686],{"encoding":904},"S^E",[198,22688,22690],{"id":22689},"příklad-74","Příklad 7.4",[724,22692,21206,22693,22714,22715,1343,22746,1343,22770,1343,22792,22814],{},[883,22694,22696],{"className":22695},[886],[888,22697,22698],{"xmlns":890},[892,22699,22700,22712],{},[895,22701,22702,22704,22706,22708,22710],{},[898,22703,2974],{},[1781,22705,12475],{},[898,22707,12369],{},[1781,22709,12475],{},[898,22711,12297],{},[902,22713,18405],{"encoding":904}," jsou dány ",[883,22716,22718],{"className":22717},[886],[888,22719,22720],{"xmlns":890},[892,22721,22722,22743],{},[895,22723,22724,22726,22728,22731,22733,22739,22741],{},[898,22725,2974],{},[1700,22727,1765],{},[1931,22729,22730],{},"0,9",[1781,22732,1783],{},[2007,22734,22735,22737],{},[898,22736,9316],{},[898,22738,4374],{},[1700,22740,1897],{},[1931,22742,6085],{},[902,22744,22745],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,22747,22749],{"className":22748},[886],[888,22750,22751],{"xmlns":890},[892,22752,22753,22767],{},[895,22754,22755,22757,22759,22761,22763,22765],{},[898,22756,2971],{},[1700,22758,1765],{},[1931,22760,3034],{},[898,22762,9316],{},[1700,22764,1897],{},[1931,22766,5192],{},[902,22768,22769],{"encoding":904},"T = 0{,}2Y + 25",[883,22771,22773],{"className":22772},[886],[888,22774,22775],{"xmlns":890},[892,22776,22777,22789],{},[895,22778,22779,22785,22787],{},[1785,22780,22781,22783],{},[898,22782,12369],{},[1700,22784,4543],{},[1700,22786,1765],{},[1931,22788,15223],{},[902,22790,22791],{"encoding":904},"I^* = 35",[883,22793,22795],{"className":22794},[886],[888,22796,22797],{"xmlns":890},[892,22798,22799,22811],{},[895,22800,22801,22807,22809],{},[1785,22802,22803,22805],{},[898,22804,12297],{},[1700,22806,4543],{},[1700,22808,1765],{},[1931,22810,9223],{},[902,22812,22813],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,22816,22817],{},[883,22818,22820],{"className":22819},[886],[888,22821,22822],{"xmlns":890},[892,22823,22824,22948],{},[20939,22825,22826,22856,22884,22918],{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},[20944,22827,22828,22834],{},[20947,22829,22830],{},[1770,22831,22832],{"scriptlevel":1772,"displaystyle":1731},[898,22833,9316],{},[20947,22835,22836],{},[1770,22837,22838],{"scriptlevel":1772,"displaystyle":1731},[895,22839,22840,22842,22844,22846,22848,22850,22852,22854],{},[895,22841],{},[1700,22843,1765],{},[898,22845,2974],{},[1700,22847,1897],{},[1931,22849,15223],{},[1700,22851,1897],{},[1931,22853,9223],{},[1700,22855,1732],{"separator":1731},[20944,22857,22858,22864],{},[20947,22859,22860],{},[1770,22861,22862],{"scriptlevel":1772,"displaystyle":1731},[898,22863,2971],{},[20947,22865,22866],{},[1770,22867,22868],{"scriptlevel":1772,"displaystyle":1731},[895,22869,22870,22872,22874,22876,22878,22880,22882],{},[895,22871],{},[1700,22873,1765],{},[1931,22875,3034],{},[898,22877,9316],{},[1700,22879,1897],{},[1931,22881,5192],{},[1700,22883,1732],{"separator":1731},[20944,22885,22886,22892],{},[20947,22887,22888],{},[1770,22889,22890],{"scriptlevel":1772,"displaystyle":1731},[898,22891,2974],{},[20947,22893,22894],{},[1770,22895,22896],{"scriptlevel":1772,"displaystyle":1731},[895,22897,22898,22900,22902,22904,22906,22912,22914,22916],{},[895,22899],{},[1700,22901,1765],{},[1931,22903,22730],{},[1781,22905,1783],{},[2007,22907,22908,22910],{},[898,22909,9316],{},[898,22911,4374],{},[1700,22913,1897],{},[1931,22915,6085],{},[1700,22917,1732],{"separator":1731},[20944,22919,22920,22930],{},[20947,22921,22922],{},[1770,22923,22924],{"scriptlevel":1772,"displaystyle":1731},[2007,22925,22926,22928],{},[898,22927,9316],{},[898,22929,4374],{},[20947,22931,22932],{},[1770,22933,22934],{"scriptlevel":1772,"displaystyle":1731},[895,22935,22936,22938,22940,22942,22944,22946],{},[895,22937],{},[1700,22939,1765],{},[898,22941,9316],{},[1700,22943,1768],{},[898,22945,2971],{},[898,22947,2196],{"mathvariant":1791},[902,22949,22950],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,22952,22953,22956,22957,23011,23012,23058,23059,2901],{},[38,22954,22955],{},"Řešení."," Z definice ",[883,22958,22960],{"className":22959},[886],[888,22961,22962],{"xmlns":890},[892,22963,22964,23008],{},[895,22965,22966,22972,22974,22976,22978,22980,22982,22984,22986,22988,22990,22992,22994,22996,22998,23000,23002,23004,23006],{},[2007,22967,22968,22970],{},[898,22969,9316],{},[898,22971,4374],{},[1700,22973,1765],{},[898,22975,9316],{},[1700,22977,1768],{},[898,22979,2971],{},[1700,22981,1765],{},[898,22983,9316],{},[1700,22985,1768],{},[1700,22987,1703],{"stretchy":1702},[1931,22989,3034],{},[898,22991,9316],{},[1700,22993,1897],{},[1931,22995,5192],{},[1700,22997,1709],{"stretchy":1702},[1700,22999,1765],{},[1931,23001,14774],{},[898,23003,9316],{},[1700,23005,1768],{},[1931,23007,5192],{},[902,23009,23010],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,23013,23015],{"className":23014},[886],[888,23016,23017],{"xmlns":890},[892,23018,23019,23055],{},[895,23020,23021,23023,23025,23027,23029,23031,23033,23035,23037,23039,23041,23043,23045,23048,23050,23052],{},[898,23022,2974],{},[1700,23024,1765],{},[1931,23026,22730],{},[1700,23028,1703],{"stretchy":1702},[1931,23030,14774],{},[898,23032,9316],{},[1700,23034,1768],{},[1931,23036,5192],{},[1700,23038,1709],{"stretchy":1702},[1700,23040,1897],{},[1931,23042,6085],{},[1700,23044,1765],{},[1931,23046,23047],{},"0,72",[898,23049,9316],{},[1700,23051,1897],{},[1931,23053,23054],{},"47,5",[902,23056,23057],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,23060,23062],{"className":23061},[886],[888,23063,23064],{"xmlns":890},[892,23065,23066,23084],{},[895,23067,23068,23070,23072,23074,23076,23078,23080,23082],{},[898,23069,9316],{},[1700,23071,1765],{},[1931,23073,23047],{},[898,23075,9316],{},[1700,23077,1897],{},[1931,23079,23054],{},[1700,23081,1897],{},[1931,23083,21365],{},[902,23085,23086],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,23088,23089],{},[883,23090,23092],{"className":23091},[886],[888,23093,23094],{"xmlns":890},[892,23095,23096,23137],{},[895,23097,23098,23101,23103,23105,23108,23110,23112,23114,23120,23122,23132,23134],{},[1931,23099,23100],{},"0,28",[898,23102,9316],{},[1700,23104,1765],{},[1931,23106,23107],{},"102,5",[1781,23109,4175],{},[1700,23111,15193],{},[1781,23113,4175],{},[1785,23115,23116,23118],{},[898,23117,9316],{},[898,23119,1762],{},[1700,23121,1765],{},[1770,23123,23124],{"scriptlevel":1772,"displaystyle":1702},[1774,23125,23126,23129],{},[1931,23127,23128],{},"5125",[1931,23130,23131],{},"14",[1700,23133,6088],{},[1931,23135,23136],{},"366,071.",[902,23138,23139],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,23141,23142],{},"Rovnovážné veličiny:",[120,23144,23145,23180,23232,23286,23334],{},[123,23146,23147,1732],{},[883,23148,23150],{"className":23149},[886],[888,23151,23152],{"xmlns":890},[892,23153,23154,23177],{},[895,23155,23156,23162,23164,23172,23174],{},[1785,23157,23158,23160],{},[898,23159,9316],{},[898,23161,1762],{},[1700,23163,1765],{},[1770,23165,23166],{"scriptlevel":1772,"displaystyle":1702},[1774,23167,23168,23170],{},[1931,23169,23128],{},[1931,23171,23131],{},[1700,23173,6088],{},[1931,23175,23176],{},"366,071",[902,23178,23179],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,23181,23182,1732],{},[883,23183,23185],{"className":23184},[886],[888,23186,23187],{"xmlns":890},[892,23188,23189,23229],{},[895,23190,23191,23197,23199,23201,23203,23209,23211,23213,23215,23224,23226],{},[1785,23192,23193,23195],{},[898,23194,2971],{},[898,23196,1762],{},[1700,23198,1765],{},[1931,23200,3034],{},[1781,23202,1783],{},[1785,23204,23205,23207],{},[898,23206,9316],{},[898,23208,1762],{},[1700,23210,1897],{},[1931,23212,5192],{},[1700,23214,1765],{},[1770,23216,23217],{"scriptlevel":1772,"displaystyle":1702},[1774,23218,23219,23222],{},[1931,23220,23221],{},"1375",[1931,23223,23131],{},[1700,23225,6088],{},[1931,23227,23228],{},"98,214",[902,23230,23231],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,23233,23234,1732],{},[883,23235,23237],{"className":23236},[886],[888,23238,23239],{"xmlns":890},[892,23240,23241,23283],{},[895,23242,23243,23251,23253,23259,23261,23267,23269,23278,23280],{},[2030,23244,23245,23247,23249],{},[898,23246,9316],{},[898,23248,4374],{},[898,23250,1762],{},[1700,23252,1765],{},[1785,23254,23255,23257],{},[898,23256,9316],{},[898,23258,1762],{},[1700,23260,1768],{},[1785,23262,23263,23265],{},[898,23264,2971],{},[898,23266,1762],{},[1700,23268,1765],{},[1770,23270,23271],{"scriptlevel":1772,"displaystyle":1702},[1774,23272,23273,23276],{},[1931,23274,23275],{},"3750",[1931,23277,23131],{},[1700,23279,6088],{},[1931,23281,23282],{},"267,857",[902,23284,23285],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,23287,23288,1732],{},[883,23289,23291],{"className":23290},[886],[888,23292,23293],{"xmlns":890},[892,23294,23295,23331],{},[895,23296,23297,23303,23305,23311,23313,23315,23317,23326,23328],{},[1785,23298,23299,23301],{},[898,23300,2974],{},[898,23302,1762],{},[1700,23304,1765],{},[1785,23306,23307,23309],{},[898,23308,9316],{},[898,23310,1762],{},[1700,23312,1768],{},[1931,23314,21365],{},[1700,23316,1765],{},[1770,23318,23319],{"scriptlevel":1772,"displaystyle":1702},[1774,23320,23321,23324],{},[1931,23322,23323],{},"4355",[1931,23325,23131],{},[1700,23327,6088],{},[1931,23329,23330],{},"311,071",[902,23332,23333],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,23335,23336,23392],{},[883,23337,23339],{"className":23338},[886],[888,23340,23341],{"xmlns":890},[892,23342,23343,23389],{},[895,23344,23345,23351,23353,23361,23363,23369,23371,23373,23382,23384,23386],{},[1785,23346,23347,23349],{},[898,23348,8861],{},[898,23350,1762],{},[1700,23352,1765],{},[2030,23354,23355,23357,23359],{},[898,23356,9316],{},[898,23358,4374],{},[898,23360,1762],{},[1700,23362,1768],{},[1785,23364,23365,23367],{},[898,23366,2974],{},[898,23368,1762],{},[1700,23370,1765],{},[1700,23372,1768],{},[1770,23374,23375],{"scriptlevel":1772,"displaystyle":1702},[1774,23376,23377,23380],{},[1931,23378,23379],{},"605",[1931,23381,23131],{},[1700,23383,6088],{},[1700,23385,1768],{},[1931,23387,23388],{},"43,214",[902,23390,23391],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,23394,23395,21535,23397,23418,23419,23422,23423,23446,23447,2196],{},[38,23396,21534],{},[883,23398,23400],{"className":23399},[886],[888,23401,23402],{"xmlns":890},[892,23403,23404,23416],{},[895,23405,23406,23408,23410,23412,23414],{},[898,23407,2974],{},[1781,23409,12475],{},[898,23411,12369],{},[1781,23413,12475],{},[898,23415,12297],{},[902,23417,18405],{"encoding":904}," stále uvažuje ",[38,23420,23421],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,23424,23426],{"className":23425},[886],[888,23427,23428],{"xmlns":890},[892,23429,23430,23443],{},[895,23431,23432,23434,23436,23439,23441],{},[898,23433,12505],{},[1700,23435,1765],{},[898,23437,23438],{},"B",[1700,23440,1768],{},[898,23442,2005],{},[902,23444,23445],{"encoding":904},"X = B - M"," dává ",[38,23448,21556,23449],{},[883,23450,23452],{"className":23451},[886],[888,23453,23454],{"xmlns":890},[892,23455,23456,23472],{},[895,23457,23458,23460,23462,23464,23466,23468,23470],{},[898,23459,2974],{},[1781,23461,12475],{},[898,23463,12369],{},[1781,23465,12475],{},[898,23467,12297],{},[1781,23469,12475],{},[898,23471,12505],{},[902,23473,12508],{"encoding":904},[115,23475,23477],{"id":23476},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,23479,20806],{"id":23480},"zadání-modelu-2",[724,23482,23483,23484,2106,23487,21779,23508,23521,23522,12313,23525,23538],{},"Rozšíření o ",[38,23485,23486],{},"čistý export",[883,23488,23490],{"className":23489},[886],[888,23491,23492],{"xmlns":890},[892,23493,23494,23506],{},[895,23495,23496,23498,23500,23502,23504],{},[898,23497,12505],{},[1700,23499,1765],{},[898,23501,23438],{},[1700,23503,1768],{},[898,23505,2005],{},[902,23507,23445],{"encoding":904},[883,23509,23511],{"className":23510},[886],[888,23512,23513],{"xmlns":890},[892,23514,23515,23519],{},[895,23516,23517],{},[898,23518,23438],{},[902,23520,23438],{"encoding":904}," je hrubý export (",[614,23523,23524],{},"brutto export",[883,23526,23528],{"className":23527},[886],[888,23529,23530],{"xmlns":890},[892,23531,23532,23536],{},[895,23533,23534],{},[898,23535,2005],{},[902,23537,2005],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,23540,23541],{},[883,23542,23544],{"className":23543},[886],[888,23545,23546],{"xmlns":890},[892,23547,23548,23568],{},[895,23549,23550,23552,23554,23556,23558,23564,23566],{},[898,23551,2005],{},[1700,23553,1765],{},[898,23555,2005],{},[1700,23557,1703],{"stretchy":1702},[2007,23559,23560,23562],{},[898,23561,9316],{},[898,23563,4374],{},[1700,23565,1709],{"stretchy":1702},[898,23567,2196],{"mathvariant":1791},[902,23569,23570],{"encoding":904},"M = M(Y_D).",[724,23572,23573],{},"Podmínka rovnováhy:",[724,23575,23576],{},[883,23577,23579],{"className":23578},[886],[888,23580,23581],{"xmlns":890},[892,23582,23583,23620],{},[895,23584,23585,23587,23589,23591,23593,23595,23597,23599,23601,23603,23605,23607,23609,23611,23613,23616,23618],{},[898,23586,9316],{},[1700,23588,1765],{},[898,23590,2974],{},[1700,23592,1897],{},[898,23594,12369],{},[1700,23596,1897],{},[898,23598,12297],{},[1700,23600,1897],{},[898,23602,23438],{},[1700,23604,1768],{},[898,23606,2005],{},[898,23608,2196],{"mathvariant":1791},[6066,23610],{"width":6068},[1700,23612,1703],{"stretchy":1702},[1931,23614,23615],{},"7.10",[1781,23617,207],{},[1700,23619,1709],{"stretchy":1702},[902,23621,23622],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,23624,20876],{"id":23625},"soustava-rovnic-2",[724,23627,22036,23628,23662,23663,2901],{},[883,23629,23631],{"className":23630},[886],[888,23632,23633],{"xmlns":890},[892,23634,23635,23659],{},[895,23636,23637,23643,23645,23651,23653],{},[1785,23638,23639,23641],{},[898,23640,12369],{},[1700,23642,4543],{},[1700,23644,1732],{"separator":1731},[1785,23646,23647,23649],{},[898,23648,12297],{},[1700,23650,4543],{},[1700,23652,1732],{"separator":1731},[1785,23654,23655,23657],{},[898,23656,23438],{},[1700,23658,4543],{},[902,23660,23661],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,23664,23666],{"className":23665},[886],[888,23667,23668],{"xmlns":890},[892,23669,23670,23694],{},[895,23671,23672,23674,23676,23678,23680,23682,23684,23690,23692],{},[898,23673,9316],{},[1700,23675,1732],{"separator":1731},[898,23677,2974],{},[1700,23679,1732],{"separator":1731},[898,23681,2971],{},[1700,23683,1732],{"separator":1731},[2007,23685,23686,23688],{},[898,23687,9316],{},[898,23689,4374],{},[1700,23691,1732],{"separator":1731},[898,23693,2005],{},[902,23695,23696],{"encoding":904},"Y, C, T, Y_D, M",[724,23698,23699],{},[883,23700,23702],{"className":23701},[886],[888,23703,23704],{"xmlns":890},[892,23705,23706,23890],{},[895,23707,23708,23882,23884,23886,23888],{},[20939,23709,23710,23742,23772,23800,23832],{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},[20944,23711,23712,23718],{},[20947,23713,23714],{},[1770,23715,23716],{"scriptlevel":1772,"displaystyle":1731},[898,23717,2974],{},[20947,23719,23720],{},[1770,23721,23722],{"scriptlevel":1772,"displaystyle":1731},[895,23723,23724,23726,23728,23730,23732,23738,23740],{},[895,23725],{},[1700,23727,1765],{},[898,23729,2974],{},[1700,23731,1703],{"stretchy":1702},[2007,23733,23734,23736],{},[898,23735,9316],{},[898,23737,4374],{},[1700,23739,1709],{"stretchy":1702},[1700,23741,1732],{"separator":1731},[20944,23743,23744,23754],{},[20947,23745,23746],{},[1770,23747,23748],{"scriptlevel":1772,"displaystyle":1731},[2007,23749,23750,23752],{},[898,23751,9316],{},[898,23753,4374],{},[20947,23755,23756],{},[1770,23757,23758],{"scriptlevel":1772,"displaystyle":1731},[895,23759,23760,23762,23764,23766,23768,23770],{},[895,23761],{},[1700,23763,1765],{},[898,23765,9316],{},[1700,23767,1768],{},[898,23769,2971],{},[1700,23771,1732],{"separator":1731},[20944,23773,23774,23780],{},[20947,23775,23776],{},[1770,23777,23778],{"scriptlevel":1772,"displaystyle":1731},[898,23779,2971],{},[20947,23781,23782],{},[1770,23783,23784],{"scriptlevel":1772,"displaystyle":1731},[895,23785,23786,23788,23790,23792,23794,23796,23798],{},[895,23787],{},[1700,23789,1765],{},[898,23791,2971],{},[1700,23793,1703],{"stretchy":1702},[898,23795,9316],{},[1700,23797,1709],{"stretchy":1702},[1700,23799,1732],{"separator":1731},[20944,23801,23802,23808],{},[20947,23803,23804],{},[1770,23805,23806],{"scriptlevel":1772,"displaystyle":1731},[898,23807,2005],{},[20947,23809,23810],{},[1770,23811,23812],{"scriptlevel":1772,"displaystyle":1731},[895,23813,23814,23816,23818,23820,23822,23828,23830],{},[895,23815],{},[1700,23817,1765],{},[898,23819,2005],{},[1700,23821,1703],{"stretchy":1702},[2007,23823,23824,23826],{},[898,23825,9316],{},[898,23827,4374],{},[1700,23829,1709],{"stretchy":1702},[1700,23831,1732],{"separator":1731},[20944,23833,23834,23840],{},[20947,23835,23836],{},[1770,23837,23838],{"scriptlevel":1772,"displaystyle":1731},[898,23839,9316],{},[20947,23841,23842],{},[1770,23843,23844],{"scriptlevel":1772,"displaystyle":1731},[895,23845,23846,23848,23850,23852,23854,23860,23862,23868,23870,23876,23878,23880],{},[895,23847],{},[1700,23849,1765],{},[898,23851,2974],{},[1700,23853,1897],{},[1785,23855,23856,23858],{},[898,23857,12369],{},[1700,23859,4543],{},[1700,23861,1897],{},[1785,23863,23864,23866],{},[898,23865,12297],{},[1700,23867,4543],{},[1700,23869,1897],{},[1785,23871,23872,23874],{},[898,23873,23438],{},[1700,23875,4543],{},[1700,23877,1768],{},[898,23879,2005],{},[898,23881,2196],{"mathvariant":1791},[6066,23883],{"width":6068},[1700,23885,1703],{"stretchy":1702},[1931,23887,23615],{},[1700,23889,1709],{"stretchy":1702},[902,23891,23892],{"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)",[198,23894,23896],{"id":23895},"příklad-75","Příklad 7.5",[724,23898,23899,23900,1343,23932,1343,23959,1343,23980,1343,24002,1343,24024,24047],{},"Dáno: ",[883,23901,23903],{"className":23902},[886],[888,23904,23905],{"xmlns":890},[892,23906,23907,23929],{},[895,23908,23909,23911,23913,23916,23918,23924,23926],{},[898,23910,2974],{},[1700,23912,1765],{},[1931,23914,23915],{},"0,75",[1781,23917,1783],{},[2007,23919,23920,23922],{},[898,23921,9316],{},[898,23923,4374],{},[1700,23925,1897],{},[1931,23927,23928],{},"750",[902,23930,23931],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,23933,23935],{"className":23934},[886],[888,23936,23937],{"xmlns":890},[892,23938,23939,23956],{},[895,23940,23941,23943,23945,23948,23950],{},[898,23942,2005],{},[1700,23944,1765],{},[1931,23946,23947],{},"0,15",[1781,23949,1783],{},[2007,23951,23952,23954],{},[898,23953,9316],{},[898,23955,4374],{},[902,23957,23958],{"encoding":904},"M = 0{,}15\\,Y_D",[883,23960,23962],{"className":23961},[886],[888,23963,23964],{"xmlns":890},[892,23965,23966,23977],{},[895,23967,23968,23970,23972,23975],{},[898,23969,2971],{},[1700,23971,1765],{},[1931,23973,23974],{},"0,25",[898,23976,9316],{},[902,23978,23979],{"encoding":904},"T = 0{,}25Y",[883,23981,23983],{"className":23982},[886],[888,23984,23985],{"xmlns":890},[892,23986,23987,23999],{},[895,23988,23989,23995,23997],{},[1785,23990,23991,23993],{},[898,23992,12369],{},[1700,23994,4543],{},[1700,23996,1765],{},[1931,23998,15295],{},[902,24000,24001],{"encoding":904},"I^* = 500",[883,24003,24005],{"className":24004},[886],[888,24006,24007],{"xmlns":890},[892,24008,24009,24021],{},[895,24010,24011,24017,24019],{},[1785,24012,24013,24015],{},[898,24014,12297],{},[1700,24016,4543],{},[1700,24018,1765],{},[1931,24020,8991],{},[902,24022,24023],{"encoding":904},"G^* = 150",[883,24025,24027],{"className":24026},[886],[888,24028,24029],{"xmlns":890},[892,24030,24031,24044],{},[895,24032,24033,24039,24041],{},[1785,24034,24035,24037],{},[898,24036,23438],{},[1700,24038,4543],{},[1700,24040,1765],{},[1931,24042,24043],{},"800",[902,24045,24046],{"encoding":904},"B^* = 800",". Soustava:",[724,24049,24050],{},[883,24051,24053],{"className":24052},[886],[888,24054,24055],{"xmlns":890},[892,24056,24057,24275],{},[20939,24058,24059,24105,24147,24183,24225],{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},[20944,24060,24061,24077],{},[20947,24062,24063],{},[1770,24064,24065],{"scriptlevel":1772,"displaystyle":1731},[895,24066,24067,24069,24071,24073,24075],{},[1700,24068,1703],{"stretchy":1702},[898,24070,12226],{},[1931,24072,1933],{},[1700,24074,1709],{"stretchy":1702},[1781,24076,2495],{},[20947,24078,24079],{},[1770,24080,24081],{"scriptlevel":1772,"displaystyle":1731},[895,24082,24083,24085,24087,24089,24091,24093,24099,24101,24103],{},[895,24084],{},[898,24086,2974],{},[1700,24088,1765],{},[1931,24090,23915],{},[1781,24092,1783],{},[2007,24094,24095,24097],{},[898,24096,9316],{},[898,24098,4374],{},[1700,24100,1897],{},[1931,24102,23928],{},[1700,24104,1732],{"separator":1731},[20944,24106,24107,24123],{},[20947,24108,24109],{},[1770,24110,24111],{"scriptlevel":1772,"displaystyle":1731},[895,24112,24113,24115,24117,24119,24121],{},[1700,24114,1703],{"stretchy":1702},[898,24116,12226],{},[1931,24118,2343],{},[1700,24120,1709],{"stretchy":1702},[1781,24122,2495],{},[20947,24124,24125],{},[1770,24126,24127],{"scriptlevel":1772,"displaystyle":1731},[895,24128,24129,24131,24137,24139,24141,24143,24145],{},[895,24130],{},[2007,24132,24133,24135],{},[898,24134,9316],{},[898,24136,4374],{},[1700,24138,1765],{},[898,24140,9316],{},[1700,24142,1768],{},[898,24144,2971],{},[1700,24146,1732],{"separator":1731},[20944,24148,24149,24165],{},[20947,24150,24151],{},[1770,24152,24153],{"scriptlevel":1772,"displaystyle":1731},[895,24154,24155,24157,24159,24161,24163],{},[1700,24156,1703],{"stretchy":1702},[898,24158,12226],{},[1931,24160,2385],{},[1700,24162,1709],{"stretchy":1702},[1781,24164,2495],{},[20947,24166,24167],{},[1770,24168,24169],{"scriptlevel":1772,"displaystyle":1731},[895,24170,24171,24173,24175,24177,24179,24181],{},[895,24172],{},[898,24174,2971],{},[1700,24176,1765],{},[1931,24178,23974],{},[898,24180,9316],{},[1700,24182,1732],{"separator":1731},[20944,24184,24185,24201],{},[20947,24186,24187],{},[1770,24188,24189],{"scriptlevel":1772,"displaystyle":1731},[895,24190,24191,24193,24195,24197,24199],{},[1700,24192,1703],{"stretchy":1702},[898,24194,12226],{},[1931,24196,2553],{},[1700,24198,1709],{"stretchy":1702},[1781,24200,2495],{},[20947,24202,24203],{},[1770,24204,24205],{"scriptlevel":1772,"displaystyle":1731},[895,24206,24207,24209,24211,24213,24215,24217,24223],{},[895,24208],{},[898,24210,2005],{},[1700,24212,1765],{},[1931,24214,23947],{},[1781,24216,1783],{},[2007,24218,24219,24221],{},[898,24220,9316],{},[898,24222,4374],{},[1700,24224,1732],{"separator":1731},[20944,24226,24227,24243],{},[20947,24228,24229],{},[1770,24230,24231],{"scriptlevel":1772,"displaystyle":1731},[895,24232,24233,24235,24237,24239,24241],{},[1700,24234,1703],{"stretchy":1702},[898,24236,12226],{},[1931,24238,2438],{},[1700,24240,1709],{"stretchy":1702},[1781,24242,2495],{},[20947,24244,24245],{},[1770,24246,24247],{"scriptlevel":1772,"displaystyle":1731},[895,24248,24249,24251,24253,24255,24257,24259,24261,24263,24265,24267,24269,24271,24273],{},[895,24250],{},[898,24252,9316],{},[1700,24254,1765],{},[898,24256,2974],{},[1700,24258,1897],{},[1931,24260,15295],{},[1700,24262,1897],{},[1931,24264,8991],{},[1700,24266,1897],{},[1931,24268,24043],{},[1700,24270,1768],{},[898,24272,2005],{},[898,24274,2196],{"mathvariant":1791},[902,24276,24277],{"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}",[724,24279,24280,24281,24315],{},"Postupná substituce — z (r3) do (r2): ",[883,24282,24284],{"className":24283},[886],[888,24285,24286],{"xmlns":890},[892,24287,24288,24312],{},[895,24289,24290,24296,24298,24300,24302,24304,24306,24308,24310],{},[2007,24291,24292,24294],{},[898,24293,9316],{},[898,24295,4374],{},[1700,24297,1765],{},[898,24299,9316],{},[1700,24301,1768],{},[1931,24303,23974],{},[898,24305,9316],{},[1700,24307,1765],{},[1931,24309,23915],{},[898,24311,9316],{},[902,24313,24314],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,24317,24318],{},[883,24319,24321],{"className":24320},[886],[888,24322,24323],{"xmlns":890},[892,24324,24325,24366],{},[895,24326,24327,24329,24331,24333,24335,24337,24339,24341,24343,24345,24347,24349,24351,24353,24355,24358,24360,24362,24364],{},[1700,24328,1703],{"stretchy":1702},[898,24330,12226],{},[1931,24332,2445],{},[1700,24334,1709],{"stretchy":1702},[1781,24336,2495],{},[898,24338,2974],{},[1700,24340,1765],{},[1931,24342,23915],{},[1700,24344,2065],{},[1931,24346,23915],{},[898,24348,9316],{},[1700,24350,1897],{},[1931,24352,23928],{},[1700,24354,1765],{},[1931,24356,24357],{},"0,5625",[898,24359,9316],{},[1700,24361,1897],{},[1931,24363,23928],{},[1700,24365,1732],{"separator":1731},[902,24367,24368],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,24370,24371],{},[883,24372,24374],{"className":24373},[886],[888,24375,24376],{"xmlns":890},[892,24377,24378,24412],{},[895,24379,24380,24382,24384,24387,24389,24391,24393,24395,24397,24399,24401,24403,24405,24408,24410],{},[1700,24381,1703],{"stretchy":1702},[898,24383,12226],{},[1931,24385,24386],{},"7",[1700,24388,1709],{"stretchy":1702},[1781,24390,2495],{},[898,24392,2005],{},[1700,24394,1765],{},[1931,24396,23947],{},[1700,24398,2065],{},[1931,24400,23915],{},[898,24402,9316],{},[1700,24404,1765],{},[1931,24406,24407],{},"0,1125",[898,24409,9316],{},[898,24411,2196],{"mathvariant":1791},[902,24413,24414],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,24416,24417],{},"Dosazením do (r5):",[724,24419,24420],{},[883,24421,24423],{"className":24422},[886],[888,24424,24425],{"xmlns":890},[892,24426,24427,24471],{},[895,24428,24429,24431,24433,24435,24437,24439,24441,24443,24445,24447,24449,24451,24453,24455,24457,24459,24461,24464,24466,24468],{},[898,24430,9316],{},[1700,24432,1765],{},[1931,24434,24357],{},[898,24436,9316],{},[1700,24438,1897],{},[1931,24440,23928],{},[1700,24442,1897],{},[1931,24444,15295],{},[1700,24446,1897],{},[1931,24448,8991],{},[1700,24450,1897],{},[1931,24452,24043],{},[1700,24454,1768],{},[1931,24456,24407],{},[898,24458,9316],{},[1700,24460,1765],{},[1931,24462,24463],{},"0,45",[898,24465,9316],{},[1700,24467,1897],{},[1931,24469,24470],{},"2200.",[902,24472,24473],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,24475,24476,24477,5777,24499,24522],{},"Odtud ",[883,24478,24480],{"className":24479},[886],[888,24481,24482],{"xmlns":890},[892,24483,24484,24496],{},[895,24485,24486,24489,24491,24493],{},[1931,24487,24488],{},"0,55",[898,24490,9316],{},[1700,24492,1765],{},[1931,24494,24495],{},"2200",[902,24497,24498],{"encoding":904},"0{,}55Y = 2200",[883,24500,24502],{"className":24501},[886],[888,24503,24504],{"xmlns":890},[892,24505,24506,24519],{},[895,24507,24508,24514,24516],{},[1785,24509,24510,24512],{},[898,24511,9316],{},[898,24513,1762],{},[1700,24515,1765],{},[1931,24517,24518],{},"4000",[902,24520,24521],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,24524,24525,24548,24580,24615,24648,24684],{},[123,24526,24527,1732],{},[883,24528,24530],{"className":24529},[886],[888,24531,24532],{"xmlns":890},[892,24533,24534,24546],{},[895,24535,24536,24542,24544],{},[1785,24537,24538,24540],{},[898,24539,9316],{},[898,24541,1762],{},[1700,24543,1765],{},[1931,24545,24518],{},[902,24547,24521],{"encoding":904},[123,24549,24550,1732],{},[883,24551,24553],{"className":24552},[886],[888,24554,24555],{"xmlns":890},[892,24556,24557,24577],{},[895,24558,24559,24565,24567,24569,24571,24573,24575],{},[1785,24560,24561,24563],{},[898,24562,2971],{},[898,24564,1762],{},[1700,24566,1765],{},[1931,24568,23974],{},[1700,24570,2065],{},[1931,24572,24518],{},[1700,24574,1765],{},[1931,24576,2979],{},[902,24578,24579],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,24581,24582,1732],{},[883,24583,24585],{"className":24584},[886],[888,24586,24587],{"xmlns":890},[892,24588,24589,24612],{},[895,24590,24591,24599,24601,24603,24605,24607,24609],{},[2030,24592,24593,24595,24597],{},[898,24594,9316],{},[898,24596,4374],{},[898,24598,1762],{},[1700,24600,1765],{},[1931,24602,23915],{},[1700,24604,2065],{},[1931,24606,24518],{},[1700,24608,1765],{},[1931,24610,24611],{},"3000",[902,24613,24614],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,24616,24617,1732],{},[883,24618,24620],{"className":24619},[886],[888,24621,24622],{"xmlns":890},[892,24623,24624,24645],{},[895,24625,24626,24632,24634,24636,24638,24640,24642],{},[1785,24627,24628,24630],{},[898,24629,2005],{},[898,24631,1762],{},[1700,24633,1765],{},[1931,24635,23947],{},[1700,24637,2065],{},[1931,24639,24611],{},[1700,24641,1765],{},[1931,24643,24644],{},"450",[902,24646,24647],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,24649,24650,1732],{},[883,24651,24653],{"className":24652},[886],[888,24654,24655],{"xmlns":890},[892,24656,24657,24681],{},[895,24658,24659,24665,24667,24669,24671,24673,24675,24677,24679],{},[1785,24660,24661,24663],{},[898,24662,2974],{},[898,24664,1762],{},[1700,24666,1765],{},[1931,24668,23915],{},[1700,24670,2065],{},[1931,24672,24611],{},[1700,24674,1897],{},[1931,24676,23928],{},[1700,24678,1765],{},[1931,24680,24611],{},[902,24682,24683],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,24685,24686,24726],{},[883,24687,24689],{"className":24688},[886],[888,24690,24691],{"xmlns":890},[892,24692,24693,24723],{},[895,24694,24695,24701,24703,24711,24713,24719,24721],{},[1785,24696,24697,24699],{},[898,24698,8861],{},[898,24700,1762],{},[1700,24702,1765],{},[2030,24704,24705,24707,24709],{},[898,24706,9316],{},[898,24708,4374],{},[898,24710,1762],{},[1700,24712,1768],{},[1785,24714,24715,24717],{},[898,24716,2974],{},[898,24718,1762],{},[1700,24720,1765],{},[1931,24722,1772],{},[902,24724,24725],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,24728,24729,24731,24732,1343,24749,2114,24770,24795,24796,24799,24800,24813,24814,2196],{},[38,24730,21534],{}," Modely ",[883,24733,24735],{"className":24734},[886],[888,24736,24737],{"xmlns":890},[892,24738,24739,24747],{},[895,24740,24741,24743,24745],{},[898,24742,2974],{},[1781,24744,12475],{},[898,24746,12369],{},[902,24748,12480],{"encoding":904},[883,24750,24752],{"className":24751},[886],[888,24753,24754],{"xmlns":890},[892,24755,24756,24768],{},[895,24757,24758,24760,24762,24764,24766],{},[898,24759,2974],{},[1781,24761,12475],{},[898,24763,12369],{},[1781,24765,12475],{},[898,24767,12297],{},[902,24769,18405],{"encoding":904},[883,24771,24773],{"className":24772},[886],[888,24774,24775],{"xmlns":890},[892,24776,24777,24793],{},[895,24778,24779,24781,24783,24785,24787,24789,24791],{},[898,24780,2974],{},[1781,24782,12475],{},[898,24784,12369],{},[1781,24786,12475],{},[898,24788,12297],{},[1781,24790,12475],{},[898,24792,12505],{},[902,24794,12508],{"encoding":904}," pokládají investice za ",[38,24797,24798],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,24801,24803],{"className":24802},[886],[888,24804,24805],{"xmlns":890},[892,24806,24807,24811],{},[895,24808,24809],{},[898,24810,12226],{},[902,24812,12226],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,24815,24816],{},"model IS-LM",[115,24818,24820],{"id":24819},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,24822,24823,24824,24828,24829,24832,24833,24836],{},"V článku ",[207,24825,24827],{"className":24826,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,24830,24831],{},"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 ",[38,24834,24835],{},"výraznější"," než v mikroekonomických modelech.",[724,24838,24839],{},[2756,24840],{"alt":24841,"className":24842,"src":24843},"imek-multiplikatorovy-efekt-chain",[210,2760],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,24845,12349,24846,1343,24863,1343,24884,24909,24910,24913,24914,24932,24933,24951,24952,24970,24971,24974,24975,1343,24992,25009,25010,25012],{},[883,24847,24849],{"className":24848},[886],[888,24850,24851],{"xmlns":890},[892,24852,24853,24861],{},[895,24854,24855,24857,24859],{},[898,24856,2974],{},[1781,24858,12475],{},[898,24860,12369],{},[902,24862,12480],{"encoding":904},[883,24864,24866],{"className":24865},[886],[888,24867,24868],{"xmlns":890},[892,24869,24870,24882],{},[895,24871,24872,24874,24876,24878,24880],{},[898,24873,2974],{},[1781,24875,12475],{},[898,24877,12369],{},[1781,24879,12475],{},[898,24881,12297],{},[902,24883,18405],{"encoding":904},[883,24885,24887],{"className":24886},[886],[888,24888,24889],{"xmlns":890},[892,24890,24891,24907],{},[895,24892,24893,24895,24897,24899,24901,24903,24905],{},[898,24894,2974],{},[1781,24896,12475],{},[898,24898,12369],{},[1781,24900,12475],{},[898,24902,12297],{},[1781,24904,12475],{},[898,24906,12505],{},[902,24908,12508],{"encoding":904}," se vyšetřuje vliv změn ",[38,24911,24912],{},"exogenních"," veličin (plánovaných investic ",[883,24915,24917],{"className":24916},[886],[888,24918,24919],{"xmlns":890},[892,24920,24921,24929],{},[895,24922,24923],{},[1785,24924,24925,24927],{},[898,24926,12369],{},[1700,24928,4543],{},[902,24930,24931],{"encoding":904},"I^*",", vládních výdajů ",[883,24934,24936],{"className":24935},[886],[888,24937,24938],{"xmlns":890},[892,24939,24940,24948],{},[895,24941,24942],{},[1785,24943,24944,24946],{},[898,24945,12297],{},[1700,24947,4543],{},[902,24949,24950],{"encoding":904},"G^*",", exportu ",[883,24953,24955],{"className":24954},[886],[888,24956,24957],{"xmlns":890},[892,24958,24959,24967],{},[895,24960,24961],{},[1785,24962,24963,24965],{},[898,24964,23438],{},[1700,24966,4543],{},[902,24968,24969],{"encoding":904},"B^*",") na změny ",[38,24972,24973],{},"endogenních"," rovnovážných veličin (",[883,24976,24978],{"className":24977},[886],[888,24979,24980],{"xmlns":890},[892,24981,24982,24990],{},[895,24983,24984],{},[1785,24985,24986,24988],{},[898,24987,9316],{},[898,24989,1762],{},[902,24991,14088],{"encoding":904},[883,24993,24995],{"className":24994},[886],[888,24996,24997],{"xmlns":890},[892,24998,24999,25007],{},[895,25000,25001],{},[1785,25002,25003,25005],{},[898,25004,2974],{},[898,25006,1762],{},[902,25008,14147],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,25011,18162],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,25014,25016],{"id":25015},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,25018,21080,25019,25042,25043,25087],{},[883,25020,25022],{"className":25021},[886],[888,25023,25024],{"xmlns":890},[892,25025,25026,25040],{},[895,25027,25028,25030,25032,25034,25036,25038],{},[898,25029,2974],{},[1700,25031,1765],{},[898,25033,207],{},[898,25035,9316],{},[1700,25037,1897],{},[898,25039,1879],{},[902,25041,19105],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,25044,25046],{"className":25045},[886],[888,25047,25048],{"xmlns":890},[892,25049,25050,25084],{},[895,25051,25052,25058,25060],{},[1785,25053,25054,25056],{},[898,25055,9316],{},[898,25057,1762],{},[1700,25059,1765],{},[1770,25061,25062],{"scriptlevel":1772,"displaystyle":1731},[1774,25063,25064,25076],{},[895,25065,25066,25068,25070],{},[898,25067,1879],{},[1700,25069,1897],{},[1785,25071,25072,25074],{},[898,25073,12369],{},[1700,25075,4543],{},[895,25077,25078,25080,25082],{},[1931,25079,1933],{},[1700,25081,1768],{},[898,25083,207],{},[902,25085,25086],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,25089,25090],{},[883,25091,25093],{"className":25092},[886],[888,25094,25095],{"xmlns":890},[892,25096,25097,25166],{},[895,25098,25099,25117,25119,25149,25151],{},[1774,25100,25101,25111],{},[895,25102,25103,25105],{},[898,25104,10056],{"mathvariant":1791},[1785,25106,25107,25109],{},[898,25108,9316],{},[898,25110,1762],{},[895,25112,25113,25115],{},[898,25114,10056],{"mathvariant":1791},[898,25116,207],{},[1700,25118,1765],{},[1774,25120,25121,25133],{},[895,25122,25123,25125,25127],{},[898,25124,1879],{},[1700,25126,1897],{},[1785,25128,25129,25131],{},[898,25130,12369],{},[1700,25132,4543],{},[895,25134,25135,25137,25139,25141,25143],{},[1700,25136,1703],{"stretchy":1702},[1931,25138,1933],{},[1700,25140,1768],{},[898,25142,207],{},[1785,25144,25145,25147],{},[1700,25146,1709],{"stretchy":1702},[1931,25148,2343],{},[6066,25150],{"width":6068},[895,25152,25153,25156,25163],{},[1781,25154,25155],{},"(multiplik",[8574,25157,25158,25160],{"accent":1731},[1781,25159,207],{},[1700,25161,25162],{},"ˊ",[1781,25164,25165],{},"tor MPC)",[902,25167,25168],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,25170,25171],{},[883,25172,25174],{"className":25173},[886],[888,25175,25176],{"xmlns":890},[892,25177,25178,25247],{},[895,25179,25180,25198,25200,25212,25214],{},[1774,25181,25182,25192],{},[895,25183,25184,25186],{},[898,25185,10056],{"mathvariant":1791},[1785,25187,25188,25190],{},[898,25189,9316],{},[898,25191,1762],{},[895,25193,25194,25196],{},[898,25195,10056],{"mathvariant":1791},[898,25197,1879],{},[1700,25199,1765],{},[1774,25201,25202,25204],{},[1931,25203,1933],{},[895,25205,25206,25208,25210],{},[1931,25207,1933],{},[1700,25209,1768],{},[898,25211,207],{},[6066,25213],{"width":6068},[895,25215,25216,25218,25224,25227,25234,25237,25244],{},[1781,25217,25155],{},[8574,25219,25220,25222],{"accent":1731},[1781,25221,207],{},[1700,25223,25162],{},[1781,25225,25226],{},"tor autonomn",[8574,25228,25229,25232],{"accent":1731},[1781,25230,25231],{},"ı",[1700,25233,25162],{},[1781,25235,25236],{}," spot",[8574,25238,25239,25241],{"accent":1731},[1781,25240,12226],{},[1700,25242,25243],{},"ˇ",[1781,25245,25246],{},"eby)",[902,25248,25249],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,25251,25252],{},[883,25253,25255],{"className":25254},[886],[888,25256,25257],{"xmlns":890},[892,25258,25259,25326],{},[895,25260,25261,25283,25285,25297,25299,25311,25313],{},[1774,25262,25263,25273],{},[895,25264,25265,25267],{},[898,25266,10056],{"mathvariant":1791},[1785,25268,25269,25271],{},[898,25270,9316],{},[898,25272,1762],{},[895,25274,25275,25277],{},[898,25276,10056],{"mathvariant":1791},[1785,25278,25279,25281],{},[898,25280,12369],{},[1700,25282,4543],{},[1700,25284,1765],{},[1774,25286,25287,25289],{},[1931,25288,1933],{},[895,25290,25291,25293,25295],{},[1931,25292,1933],{},[1700,25294,1768],{},[898,25296,207],{},[1700,25298,1765],{},[1774,25300,25301,25303],{},[1931,25302,1933],{},[895,25304,25305,25307,25309],{},[898,25306,2005],{},[898,25308,1677],{},[898,25310,8861],{},[6066,25312],{"width":6068},[895,25314,25315,25317,25323],{},[1781,25316,25155],{},[8574,25318,25319,25321],{"accent":1731},[1781,25320,207],{},[1700,25322,25162],{},[1781,25324,25325],{},"tor investic)",[902,25327,25328],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[4060,25330,25331],{},[724,25332,25333,25335,25336,25339,25340,25353,25354,25371,25372,25390,25391,25435,25436,21605,25453,25456,25457,25474],{},[883,25334,4346],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,25337,25338],{},"důchodem","; z něj se utratí ",[883,25341,25343],{"className":25342},[886],[888,25344,25345],{"xmlns":890},[892,25346,25347,25351],{},[895,25348,25349],{},[898,25350,207],{},[902,25352,207],{"encoding":904}," Kč (= ",[883,25355,25357],{"className":25356},[886],[888,25358,25359],{"xmlns":890},[892,25360,25361,25369],{},[895,25362,25363,25365,25367],{},[898,25364,2005],{},[898,25366,1677],{},[898,25368,2974],{},[902,25370,18230],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,25373,25375],{"className":25374},[886],[888,25376,25377],{"xmlns":890},[892,25378,25379,25387],{},[895,25380,25381],{},[1785,25382,25383,25385],{},[898,25384,207],{},[1931,25386,2343],{},[902,25388,25389],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,25392,25394],{"className":25393},[886],[888,25395,25396],{"xmlns":890},[892,25397,25398,25432],{},[895,25399,25400,25402,25404,25406,25408,25414,25416,25418,25420],{},[1931,25401,1933],{},[1700,25403,1897],{},[898,25405,207],{},[1700,25407,1897],{},[1785,25409,25410,25412],{},[898,25411,207],{},[1931,25413,2343],{},[1700,25415,1897],{},[1700,25417,18290],{},[1700,25419,1765],{},[1774,25421,25422,25424],{},[1931,25423,1933],{},[895,25425,25426,25428,25430],{},[1931,25427,1933],{},[1700,25429,1768],{},[898,25431,207],{},[902,25433,25434],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,25437,25439],{"className":25438},[886],[888,25440,25441],{"xmlns":890},[892,25442,25443,25451],{},[895,25444,25445],{},[1785,25446,25447,25449],{},[898,25448,9316],{},[898,25450,1762],{},[902,25452,14088],{"encoding":904},[38,25454,25455],{},"více"," než korunu — čím vyšší ",[883,25458,25460],{"className":25459},[886],[888,25461,25462],{"xmlns":890},[892,25463,25464,25472],{},[895,25465,25466,25468,25470],{},[898,25467,2005],{},[898,25469,1677],{},[898,25471,2974],{},[902,25473,18230],{"encoding":904},", tím silnější multiplikační efekt.",[724,25476,25477,25480,25481,25507,25508,25511,25512,2114,25533,25558,25559,2196],{},[38,25478,25479],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,25482,25484],{"className":25483},[886],[888,25485,25486],{"xmlns":890},[892,25487,25488,25504],{},[895,25489,25490],{},[1770,25491,25492],{"scriptlevel":1772,"displaystyle":1702},[1774,25493,25494,25496],{},[1931,25495,1933],{},[895,25497,25498,25500,25502],{},[1931,25499,1933],{},[1700,25501,1768],{},[898,25503,207],{},[902,25505,25506],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,25509,25510],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,25513,25515],{"className":25514},[886],[888,25516,25517],{"xmlns":890},[892,25518,25519,25531],{},[895,25520,25521,25523,25525,25527,25529],{},[898,25522,2974],{},[1781,25524,12475],{},[898,25526,12369],{},[1781,25528,12475],{},[898,25530,12297],{},[902,25532,18405],{"encoding":904},[883,25534,25536],{"className":25535},[886],[888,25537,25538],{"xmlns":890},[892,25539,25540,25556],{},[895,25541,25542,25544,25546,25548,25550,25552,25554],{},[898,25543,2974],{},[1781,25545,12475],{},[898,25547,12369],{},[1781,25549,12475],{},[898,25551,12297],{},[1781,25553,12475],{},[898,25555,12505],{},[902,25557,12508],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,25560,25562],{"className":25561,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,25564,25566],{"id":25565},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,25568,12349,25569,1343,25586,2114,25607,12354,25632,10208,25635,25656,25657,2106,25660,25673,25674,5857,25703,25720,25721,25724,25725,25727,25728,25749],{},[883,25570,25572],{"className":25571},[886],[888,25573,25574],{"xmlns":890},[892,25575,25576,25584],{},[895,25577,25578,25580,25582],{},[898,25579,2974],{},[1781,25581,12475],{},[898,25583,12369],{},[902,25585,12480],{"encoding":904},[883,25587,25589],{"className":25588},[886],[888,25590,25591],{"xmlns":890},[892,25592,25593,25605],{},[895,25594,25595,25597,25599,25601,25603],{},[898,25596,2974],{},[1781,25598,12475],{},[898,25600,12369],{},[1781,25602,12475],{},[898,25604,12297],{},[902,25606,18405],{"encoding":904},[883,25608,25610],{"className":25609},[886],[888,25611,25612],{"xmlns":890},[892,25613,25614,25630],{},[895,25615,25616,25618,25620,25622,25624,25626,25628],{},[898,25617,2974],{},[1781,25619,12475],{},[898,25621,12369],{},[1781,25623,12475],{},[898,25625,12297],{},[1781,25627,12475],{},[898,25629,12505],{},[902,25631,12508],{"encoding":904},[38,25633,25634],{},"investice konstantní",[883,25636,25638],{"className":25637},[886],[888,25639,25640],{"xmlns":890},[892,25641,25642,25654],{},[895,25643,25644,25646,25648],{},[898,25645,12369],{},[1700,25647,1765],{},[1785,25649,25650,25652],{},[898,25651,12369],{},[1700,25653,4543],{},[902,25655,12380],{"encoding":904},"). Reálnější je předpoklad, že ",[38,25658,25659],{},"investice závisejí na úrokové míře",[883,25661,25663],{"className":25662},[886],[888,25664,25665],{"xmlns":890},[892,25666,25667,25671],{},[895,25668,25669],{},[898,25670,12226],{},[902,25672,12226],{"encoding":904}," — klesající funkce ",[883,25675,25677],{"className":25676},[886],[888,25678,25679],{"xmlns":890},[892,25680,25681,25701],{},[895,25682,25683,25685,25687,25689,25691,25693,25695,25697,25699],{},[898,25684,12369],{},[1700,25686,1703],{"stretchy":1702},[898,25688,12226],{},[1700,25690,1709],{"stretchy":1702},[1700,25692,1765],{},[898,25694,2354],{},[898,25696,12226],{},[1700,25698,1897],{},[898,25700,2406],{},[902,25702,15942],{"encoding":904},[883,25704,25706],{"className":25705},[886],[888,25707,25708],{"xmlns":890},[892,25709,25710,25718],{},[895,25711,25712,25714,25716],{},[898,25713,2354],{},[1700,25715,3640],{},[1931,25717,1772],{},[902,25719,12700],{"encoding":904},". Přidáním ",[38,25722,25723],{},"trhu peněz"," k trhu zboží vzniká model ",[38,25726,12196],{}," se dvěma neznámými ",[883,25729,25731],{"className":25730},[886],[888,25732,25733],{"xmlns":890},[892,25734,25735,25747],{},[895,25736,25737,25739,25741,25743,25745],{},[1700,25738,1703],{"stretchy":1702},[898,25740,9316],{},[1700,25742,1732],{"separator":1731},[898,25744,12226],{},[1700,25746,1709],{"stretchy":1702},[902,25748,18335],{"encoding":904}," a dvěma rovnicemi:",[120,25751,25752,25802],{},[123,25753,25754,10208,25756,25758,25759,25780,25781,2196],{},[38,25755,16031],{},[614,25757,12239],{},") — klesající přímka v rovině ",[883,25760,25762],{"className":25761},[886],[888,25763,25764],{"xmlns":890},[892,25765,25766,25778],{},[895,25767,25768,25770,25772,25774,25776],{},[1700,25769,1703],{"stretchy":1702},[898,25771,12226],{},[1700,25773,1732],{"separator":1731},[898,25775,9316],{},[1700,25777,1709],{"stretchy":1702},[902,25779,13122],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,25782,25784],{"className":25783},[886],[888,25785,25786],{"xmlns":890},[892,25787,25788,25800],{},[895,25789,25790,25792,25794,25796,25798],{},[898,25791,9316],{},[1700,25793,1765],{},[898,25795,2974],{},[1700,25797,1897],{},[898,25799,12369],{},[902,25801,14929],{"encoding":904},[123,25803,25804,10208,25806,25808,25809,21779,25834,25880],{},[38,25805,16230],{},[614,25807,12246],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,25810,25812],{"className":25811},[886],[888,25813,25814],{"xmlns":890},[892,25815,25816,25832],{},[895,25817,25818,25824,25826],{},[1785,25819,25820,25822],{},[898,25821,2005],{},[898,25823,4374],{},[1700,25825,1765],{},[1785,25827,25828,25830],{},[898,25829,2005],{},[1700,25831,4543],{},[902,25833,13665],{"encoding":904},[883,25835,25837],{"className":25836},[886],[888,25838,25839],{"xmlns":890},[892,25840,25841,25877],{},[895,25842,25843,25849,25851,25857,25859,25861,25867,25869,25871],{},[1785,25844,25845,25847],{},[898,25846,2005],{},[898,25848,4374],{},[1700,25850,1765],{},[2007,25852,25853,25855],{},[898,25854,13422],{},[1931,25856,1933],{},[898,25858,9316],{},[1700,25860,1897],{},[2007,25862,25863,25865],{},[898,25864,13422],{},[1931,25866,2343],{},[898,25868,12226],{},[1700,25870,1897],{},[2007,25872,25873,25875],{},[898,25874,13422],{},[1931,25876,2385],{},[902,25878,25879],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,25882,25883,2106,25886,25919,25920,25922,25923,25925],{},[38,25884,25885],{},"Simultánní rovnovážný bod",[883,25887,25889],{"className":25888},[886],[888,25890,25891],{"xmlns":890},[892,25892,25893,25917],{},[895,25894,25895,25897,25899,25901,25907,25909,25915],{},[898,25896,1762],{},[1700,25898,1765],{},[1700,25900,1703],{"stretchy":1702},[1785,25902,25903,25905],{},[898,25904,12226],{},[898,25906,1762],{},[1700,25908,1732],{"separator":1731},[1785,25910,25911,25913],{},[898,25912,9316],{},[898,25914,1762],{},[1700,25916,1709],{"stretchy":1702},[902,25918,16322],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,25921,12284],{}," (posun IS) a ",[38,25924,12316],{}," (posun LM).",[724,25927,25928],{},[38,25929,25930,25931,1343,25953,1343,25975,1343,25997,26019,26020,2196],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,25932,25934],{"className":25933},[886],[888,25935,25936],{"xmlns":890},[892,25937,25938,25950],{},[895,25939,25940,25946,25948],{},[1785,25941,25942,25944],{},[898,25943,9316],{},[898,25945,1762],{},[1700,25947,1765],{},[1931,25949,15300],{},[902,25951,25952],{"encoding":904},"Y^E = 5000",[883,25954,25956],{"className":25955},[886],[888,25957,25958],{"xmlns":890},[892,25959,25960,25972],{},[895,25961,25962,25968,25970],{},[1785,25963,25964,25966],{},[898,25965,12226],{},[898,25967,1762],{},[1700,25969,1765],{},[1931,25971,2438],{},[902,25973,25974],{"encoding":904},"r^E = 5",[883,25976,25978],{"className":25977},[886],[888,25979,25980],{"xmlns":890},[892,25981,25982,25994],{},[895,25983,25984,25990,25992],{},[1785,25985,25986,25988],{},[898,25987,2974],{},[898,25989,1762],{},[1700,25991,1765],{},[1931,25993,15337],{},[902,25995,25996],{"encoding":904},"C^E = 4100",[883,25998,26000],{"className":25999},[886],[888,26001,26002],{"xmlns":890},[892,26003,26004,26016],{},[895,26005,26006,26012,26014],{},[1785,26007,26008,26010],{},[898,26009,12369],{},[898,26011,1762],{},[1700,26013,1765],{},[1931,26015,15376],{},[902,26017,26018],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,26021,945],{"className":26022,"dataFsResolvedFilePath":943,"href":944},[210],[115,26024,26026],{"id":26025},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,26028,26029,26093,26204,26347,26589,26657],{},[123,26030,26031,26034,26035,26057,26058,26092],{},[38,26032,26033],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,26036,26038],{"className":26037},[886],[888,26039,26040],{"xmlns":890},[892,26041,26042,26054],{},[895,26043,26044,26046,26048,26050,26052],{},[898,26045,12297],{},[898,26047,18479],{},[898,26049,1677],{},[1700,26051,2927],{},[898,26053,9316],{},[902,26055,26056],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,26059,26061],{"className":26060},[886],[888,26062,26063],{"xmlns":890},[892,26064,26065,26089],{},[895,26066,26067,26069,26071,26073,26075,26077,26079,26081,26083,26085,26087],{},[898,26068,12297],{},[898,26070,18479],{},[898,26072,1677],{},[1700,26074,1765],{},[898,26076,2974],{},[1700,26078,1897],{},[898,26080,12369],{},[1700,26082,1897],{},[898,26084,12297],{},[1700,26086,1897],{},[898,26088,12505],{},[902,26090,26091],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,26094,26095,26097,26098,26119,26120,1343,26143,26174,26175,26188,26189,2196],{},[38,26096,18713],{}," splňují ",[883,26099,26101],{"className":26100},[886],[888,26102,26103],{"xmlns":890},[892,26104,26105,26117],{},[895,26106,26107,26109,26111,26113,26115],{},[898,26108,9316],{},[1700,26110,1765],{},[898,26112,2974],{},[1700,26114,1897],{},[898,26116,8861],{},[902,26118,12879],{"encoding":904}," (7.2); lineární model ",[883,26121,26123],{"className":26122},[886],[888,26124,26125],{"xmlns":890},[892,26126,26127,26141],{},[895,26128,26129,26131,26133,26135,26137,26139],{},[898,26130,2974],{},[1700,26132,1765],{},[898,26134,207],{},[898,26136,9316],{},[1700,26138,1897],{},[898,26140,1879],{},[902,26142,19105],{"encoding":904},[883,26144,26146],{"className":26145},[886],[888,26147,26148],{"xmlns":890},[892,26149,26150,26172],{},[895,26151,26152,26154,26156,26158,26160,26162,26164,26166,26168,26170],{},[898,26153,8861],{},[1700,26155,1765],{},[1700,26157,1703],{"stretchy":1702},[1931,26159,1933],{},[1700,26161,1768],{},[898,26163,207],{},[1700,26165,1709],{"stretchy":1702},[898,26167,9316],{},[1700,26169,1768],{},[898,26171,1879],{},[902,26173,19354],{"encoding":904}," s autonomní spotřebou ",[883,26176,26178],{"className":26177},[886],[888,26179,26180],{"xmlns":890},[892,26181,26182,26186],{},[895,26183,26184],{},[898,26185,1879],{},[902,26187,1879],{"encoding":904}," a autonomními úsporami ",[883,26190,26192],{"className":26191},[886],[888,26193,26194],{"xmlns":890},[892,26195,26196,26202],{},[895,26197,26198,26200],{},[1700,26199,1768],{},[898,26201,1879],{},[902,26203,19433],{"encoding":904},[123,26205,26206,2106,26209,1343,26239,26269,26270,26300,26301,1343,26322,2196],{},[38,26207,26208],{},"Mezní sklony",[883,26210,26212],{"className":26211},[886],[888,26213,26214],{"xmlns":890},[892,26215,26216,26236],{},[895,26217,26218,26220,26222,26224,26226,26228,26230,26232,26234],{},[898,26219,2005],{},[898,26221,1677],{},[898,26223,2974],{},[1700,26225,1765],{},[898,26227,2406],{"mathvariant":1791},[898,26229,2974],{},[898,26231,1979],{"mathvariant":1791},[898,26233,2406],{"mathvariant":1791},[898,26235,9316],{},[902,26237,26238],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,26240,26242],{"className":26241},[886],[888,26243,26244],{"xmlns":890},[892,26245,26246,26266],{},[895,26247,26248,26250,26252,26254,26256,26258,26260,26262,26264],{},[898,26249,2005],{},[898,26251,1677],{},[898,26253,8861],{},[1700,26255,1765],{},[898,26257,2406],{"mathvariant":1791},[898,26259,8861],{},[898,26261,1979],{"mathvariant":1791},[898,26263,2406],{"mathvariant":1791},[898,26265,9316],{},[902,26267,26268],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,26271,26273],{"className":26272},[886],[888,26274,26275],{"xmlns":890},[892,26276,26277,26297],{},[895,26278,26279,26281,26283,26285,26287,26289,26291,26293,26295],{},[898,26280,2005],{},[898,26282,1677],{},[898,26284,2974],{},[1700,26286,1897],{},[898,26288,2005],{},[898,26290,1677],{},[898,26292,8861],{},[1700,26294,1765],{},[1931,26296,1933],{},[902,26298,26299],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,26302,26304],{"className":26303},[886],[888,26305,26306],{"xmlns":890},[892,26307,26308,26320],{},[895,26309,26310,26312,26314,26316,26318],{},[898,26311,2005],{},[898,26313,1677],{},[898,26315,2974],{},[1700,26317,1765],{},[898,26319,207],{},[902,26321,20074],{"encoding":904},[883,26323,26325],{"className":26324},[886],[888,26326,26327],{"xmlns":890},[892,26328,26329,26345],{},[895,26330,26331,26333,26335,26337,26339,26341,26343],{},[898,26332,2005],{},[898,26334,1677],{},[898,26336,8861],{},[1700,26338,1765],{},[1931,26340,1933],{},[1700,26342,1768],{},[898,26344,207],{},[902,26346,20100],{"encoding":904},[123,26348,26349,26352,26353],{},[38,26350,26351],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,26354,26355,26443,26512],{},[123,26356,26357,26374,26375,26396,26397,1732],{},[883,26358,26360],{"className":26359},[886],[888,26361,26362],{"xmlns":890},[892,26363,26364,26372],{},[895,26365,26366,26368,26370],{},[898,26367,2974],{},[1781,26369,12475],{},[898,26371,12369],{},[902,26373,12480],{"encoding":904},": ",[883,26376,26378],{"className":26377},[886],[888,26379,26380],{"xmlns":890},[892,26381,26382,26394],{},[895,26383,26384,26386,26388,26390,26392],{},[898,26385,9316],{},[1700,26387,1765],{},[898,26389,2974],{},[1700,26391,1897],{},[898,26393,12369],{},[902,26395,14929],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,26398,26400],{"className":26399},[886],[888,26401,26402],{"xmlns":890},[892,26403,26404,26440],{},[895,26405,26406,26412,26414,26416,26418,26420,26426,26428,26430,26432,26434,26436,26438],{},[1785,26407,26408,26410],{},[898,26409,9316],{},[898,26411,1762],{},[1700,26413,1765],{},[1700,26415,1703],{"stretchy":1702},[898,26417,1879],{},[1700,26419,1897],{},[1785,26421,26422,26424],{},[898,26423,12369],{},[1700,26425,4543],{},[1700,26427,1709],{"stretchy":1702},[898,26429,1979],{"mathvariant":1791},[1700,26431,1703],{"stretchy":1702},[1931,26433,1933],{},[1700,26435,1768],{},[898,26437,207],{},[1700,26439,1709],{"stretchy":1702},[902,26441,26442],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,26444,26445,26466,26467,26486,26487,1732],{},[883,26446,26448],{"className":26447},[886],[888,26449,26450],{"xmlns":890},[892,26451,26452,26464],{},[895,26453,26454,26456,26458,26460,26462],{},[898,26455,2974],{},[1781,26457,12475],{},[898,26459,12369],{},[1781,26461,12475],{},[898,26463,12297],{},[902,26465,18405],{"encoding":904},": přidává vládu, zdanění ",[883,26468,26470],{"className":26469},[886],[888,26471,26472],{"xmlns":890},[892,26473,26474,26484],{},[895,26475,26476,26478,26480,26482],{},[898,26477,2971],{},[1700,26479,1703],{"stretchy":1702},[898,26481,9316],{},[1700,26483,1709],{"stretchy":1702},[902,26485,22404],{"encoding":904}," a disponibilní důchod ",[883,26488,26490],{"className":26489},[886],[888,26491,26492],{"xmlns":890},[892,26493,26494,26510],{},[895,26495,26496,26502,26504,26506,26508],{},[2007,26497,26498,26500],{},[898,26499,9316],{},[898,26501,4374],{},[1700,26503,1765],{},[898,26505,9316],{},[1700,26507,1768],{},[898,26509,2971],{},[902,26511,21903],{"encoding":904},[123,26513,26514,26539,26540,21779,26561,2196],{},[883,26515,26517],{"className":26516},[886],[888,26518,26519],{"xmlns":890},[892,26520,26521,26537],{},[895,26522,26523,26525,26527,26529,26531,26533,26535],{},[898,26524,2974],{},[1781,26526,12475],{},[898,26528,12369],{},[1781,26530,12475],{},[898,26532,12297],{},[1781,26534,12475],{},[898,26536,12505],{},[902,26538,12508],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,26541,26543],{"className":26542},[886],[888,26544,26545],{"xmlns":890},[892,26546,26547,26559],{},[895,26548,26549,26551,26553,26555,26557],{},[898,26550,12505],{},[1700,26552,1765],{},[898,26554,23438],{},[1700,26556,1768],{},[898,26558,2005],{},[902,26560,23445],{"encoding":904},[883,26562,26564],{"className":26563},[886],[888,26565,26566],{"xmlns":890},[892,26567,26568,26586],{},[895,26569,26570,26572,26574,26576,26578,26584],{},[898,26571,2005],{},[1700,26573,1765],{},[898,26575,2005],{},[1700,26577,1703],{"stretchy":1702},[2007,26579,26580,26582],{},[898,26581,9316],{},[898,26583,4374],{},[1700,26585,1709],{"stretchy":1702},[902,26587,26588],{"encoding":904},"M = M(Y_D)",[123,26590,26591,26594,26595,2106,26598,26656],{},[38,26592,26593],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,26596,26597],{},"multiplikátor investic",[883,26599,26601],{"className":26600},[886],[888,26602,26603],{"xmlns":890},[892,26604,26605,26653],{},[895,26606,26607,26609,26615,26617,26619,26625,26627,26629,26631,26633,26635,26637,26639,26641,26643,26645,26647,26649,26651],{},[898,26608,10056],{"mathvariant":1791},[1785,26610,26611,26613],{},[898,26612,9316],{},[898,26614,1762],{},[898,26616,1979],{"mathvariant":1791},[898,26618,10056],{"mathvariant":1791},[1785,26620,26621,26623],{},[898,26622,12369],{},[1700,26624,4543],{},[1700,26626,1765],{},[1931,26628,1933],{},[898,26630,1979],{"mathvariant":1791},[1700,26632,1703],{"stretchy":1702},[1931,26634,1933],{},[1700,26636,1768],{},[898,26638,207],{},[1700,26640,1709],{"stretchy":1702},[1700,26642,1765],{},[1931,26644,1933],{},[898,26646,1979],{"mathvariant":1791},[898,26648,2005],{},[898,26650,1677],{},[898,26652,8861],{},[902,26654,26655],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,26658,26659,26661,26662,26677,26678,18833,26695,26710,26711,26736,26737,2196],{},[38,26660,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,26663,26665],{"className":26664},[886],[888,26666,26667],{"xmlns":890},[892,26668,26669,26675],{},[895,26670,26671,26673],{},[898,26672,12369],{},[898,26674,8861],{},[902,26676,12236],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,26679,26681],{"className":26680},[886],[888,26682,26683],{"xmlns":890},[892,26684,26685,26693],{},[895,26686,26687,26689,26691],{},[898,26688,12369],{},[1700,26690,1765],{},[898,26692,8861],{},[902,26694,12897],{"encoding":904},[883,26696,26698],{"className":26697},[886],[888,26699,26700],{"xmlns":890},[892,26701,26702,26708],{},[895,26703,26704,26706],{},[898,26705,1706],{},[898,26707,2005],{},[902,26709,12243],{"encoding":904}," rovnováhu trhu peněz (",[883,26712,26714],{"className":26713},[886],[888,26715,26716],{"xmlns":890},[892,26717,26718,26734],{},[895,26719,26720,26726,26728],{},[1785,26721,26722,26724],{},[898,26723,2005],{},[898,26725,4374],{},[1700,26727,1765],{},[1785,26729,26730,26732],{},[898,26731,2005],{},[1700,26733,4543],{},[902,26735,13665],{"encoding":904},"); průsečík dává ",[883,26738,26740],{"className":26739},[886],[888,26741,26742],{"xmlns":890},[892,26743,26744,26764],{},[895,26745,26746,26748,26754,26756,26762],{},[1700,26747,1703],{"stretchy":1702},[1785,26749,26750,26752],{},[898,26751,9316],{},[898,26753,1762],{},[1700,26755,1732],{"separator":1731},[1785,26757,26758,26760],{},[898,26759,12226],{},[898,26761,1762],{},[1700,26763,1709],{"stretchy":1702},[902,26765,12280],{"encoding":904},[115,26767,15905],{"id":15904},[120,26769,26770,26808,26848,26938,27020,27074,27130,27189,27224,27229,27301,27376,27462,27524,27592,27650,27703,27742],{},[123,26771,26772,7203,26775,26092],{},[38,26773,26774],{},"Hrubý národní produkt (GNP)",[883,26776,26778],{"className":26777},[886],[888,26779,26780],{"xmlns":890},[892,26781,26782,26806],{},[895,26783,26784,26786,26788,26790,26792,26794,26796,26798,26800,26802,26804],{},[898,26785,12297],{},[898,26787,18479],{},[898,26789,1677],{},[1700,26791,1765],{},[898,26793,2974],{},[1700,26795,1897],{},[898,26797,12369],{},[1700,26799,1897],{},[898,26801,12297],{},[1700,26803,1897],{},[898,26805,12505],{},[902,26807,26091],{"encoding":904},[123,26809,26810,26826,26827,2196],{},[38,26811,26812,26813],{},"Národní důchod ",[883,26814,26816],{"className":26815},[886],[888,26817,26818],{"xmlns":890},[892,26819,26820,26824],{},[895,26821,26822],{},[898,26823,9316],{},[902,26825,9316],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,26828,26830],{"className":26829},[886],[888,26831,26832],{"xmlns":890},[892,26833,26834,26846],{},[895,26835,26836,26838,26840,26842,26844],{},[898,26837,12297],{},[898,26839,18479],{},[898,26841,1677],{},[1700,26843,2927],{},[898,26845,9316],{},[902,26847,26056],{"encoding":904},[123,26849,26850,26876,26877,1343,26900,1343,26921,2196],{},[38,26851,26852,26853],{},"Funkce spotřeby ",[883,26854,26856],{"className":26855},[886],[888,26857,26858],{"xmlns":890},[892,26859,26860,26874],{},[895,26861,26862,26864,26866,26868,26870,26872],{},[898,26863,2974],{},[1700,26865,1765],{},[898,26867,2974],{},[1700,26869,1703],{"stretchy":1702},[898,26871,9316],{},[1700,26873,1709],{"stretchy":1702},[902,26875,20925],{"encoding":904}," — lineární model ",[883,26878,26880],{"className":26879},[886],[888,26881,26882],{"xmlns":890},[892,26883,26884,26898],{},[895,26885,26886,26888,26890,26892,26894,26896],{},[898,26887,2974],{},[1700,26889,1765],{},[898,26891,207],{},[898,26893,9316],{},[1700,26895,1897],{},[898,26897,1879],{},[902,26899,19105],{"encoding":904},[883,26901,26903],{"className":26902},[886],[888,26904,26905],{"xmlns":890},[892,26906,26907,26919],{},[895,26908,26909,26911,26913,26915,26917],{},[1931,26910,1772],{},[1700,26912,3640],{},[898,26914,207],{},[1700,26916,3640],{},[1931,26918,1933],{},[902,26920,19021],{"encoding":904},[883,26922,26924],{"className":26923},[886],[888,26925,26926],{"xmlns":890},[892,26927,26928,26936],{},[895,26929,26930,26932,26934],{},[898,26931,1879],{},[1700,26933,3601],{},[1931,26935,1772],{},[902,26937,18999],{"encoding":904},[123,26939,26940,7203,26967,26988,26989,2196],{},[38,26941,26942,26943],{},"Funkce úspor ",[883,26944,26946],{"className":26945},[886],[888,26947,26948],{"xmlns":890},[892,26949,26950,26964],{},[895,26951,26952,26954,26956,26958,26960,26962],{},[898,26953,8861],{},[1700,26955,1765],{},[898,26957,8861],{},[1700,26959,1703],{"stretchy":1702},[898,26961,9316],{},[1700,26963,1709],{"stretchy":1702},[902,26965,26966],{"encoding":904},"S = S(Y)",[883,26968,26970],{"className":26969},[886],[888,26971,26972],{"xmlns":890},[892,26973,26974,26986],{},[895,26975,26976,26978,26980,26982,26984],{},[898,26977,9316],{},[1700,26979,1765],{},[898,26981,2974],{},[1700,26983,1897],{},[898,26985,8861],{},[902,26987,12879],{"encoding":904},"; lineární ",[883,26990,26992],{"className":26991},[886],[888,26993,26994],{"xmlns":890},[892,26995,26996,27018],{},[895,26997,26998,27000,27002,27004,27006,27008,27010,27012,27014,27016],{},[898,26999,8861],{},[1700,27001,1765],{},[1700,27003,1703],{"stretchy":1702},[1931,27005,1933],{},[1700,27007,1768],{},[898,27009,207],{},[1700,27011,1709],{"stretchy":1702},[898,27013,9316],{},[1700,27015,1768],{},[898,27017,1879],{},[902,27019,19354],{"encoding":904},[123,27021,27022,7203,27025,1343,27048,2196],{},[38,27023,27024],{},"Autonomní spotřeba\u002Fúspory",[883,27026,27028],{"className":27027},[886],[888,27029,27030],{"xmlns":890},[892,27031,27032,27046],{},[895,27033,27034,27036,27038,27040,27042,27044],{},[898,27035,2974],{},[1700,27037,1703],{"stretchy":1702},[1931,27039,1772],{},[1700,27041,1709],{"stretchy":1702},[1700,27043,1765],{},[898,27045,1879],{},[902,27047,19746],{"encoding":904},[883,27049,27051],{"className":27050},[886],[888,27052,27053],{"xmlns":890},[892,27054,27055,27071],{},[895,27056,27057,27059,27061,27063,27065,27067,27069],{},[898,27058,8861],{},[1700,27060,1703],{"stretchy":1702},[1931,27062,1772],{},[1700,27064,1709],{"stretchy":1702},[1700,27066,1765],{},[1700,27068,1768],{},[898,27070,1879],{},[902,27072,27073],{"encoding":904},"S(0) = -b",[123,27075,27076,27108,27109,4110],{},[38,27077,27078,27079],{},"Mezní sklon ke spotřebě ",[883,27080,27082],{"className":27081},[886],[888,27083,27084],{"xmlns":890},[892,27085,27086,27106],{},[895,27087,27088,27090,27092,27094,27096,27098,27100,27102,27104],{},[898,27089,2005],{},[898,27091,1677],{},[898,27093,2974],{},[1700,27095,1765],{},[898,27097,2406],{"mathvariant":1791},[898,27099,2974],{},[898,27101,1979],{"mathvariant":1791},[898,27103,2406],{"mathvariant":1791},[898,27105,9316],{},[902,27107,26238],{"encoding":904}," (v lineárním modelu ",[883,27110,27112],{"className":27111},[886],[888,27113,27114],{"xmlns":890},[892,27115,27116,27128],{},[895,27117,27118,27120,27122,27124,27126],{},[898,27119,2005],{},[898,27121,1677],{},[898,27123,2974],{},[1700,27125,1765],{},[898,27127,207],{},[902,27129,20074],{"encoding":904},[123,27131,27132,27108,27164,4110],{},[38,27133,27134,27135],{},"Mezní sklon k úsporám ",[883,27136,27138],{"className":27137},[886],[888,27139,27140],{"xmlns":890},[892,27141,27142,27162],{},[895,27143,27144,27146,27148,27150,27152,27154,27156,27158,27160],{},[898,27145,2005],{},[898,27147,1677],{},[898,27149,8861],{},[1700,27151,1765],{},[898,27153,2406],{"mathvariant":1791},[898,27155,8861],{},[898,27157,1979],{"mathvariant":1791},[898,27159,2406],{"mathvariant":1791},[898,27161,9316],{},[902,27163,26268],{"encoding":904},[883,27165,27167],{"className":27166},[886],[888,27168,27169],{"xmlns":890},[892,27170,27171,27187],{},[895,27172,27173,27175,27177,27179,27181,27183,27185],{},[898,27174,2005],{},[898,27176,1677],{},[898,27178,8861],{},[1700,27180,1765],{},[1931,27182,1933],{},[1700,27184,1768],{},[898,27186,207],{},[902,27188,20100],{"encoding":904},[123,27190,27191,2106,27194,27223],{},[38,27192,27193],{},"Vztah",[883,27195,27197],{"className":27196},[886],[888,27198,27199],{"xmlns":890},[892,27200,27201,27221],{},[895,27202,27203,27205,27207,27209,27211,27213,27215,27217,27219],{},[898,27204,2005],{},[898,27206,1677],{},[898,27208,2974],{},[1700,27210,1897],{},[898,27212,2005],{},[898,27214,1677],{},[898,27216,8861],{},[1700,27218,1765],{},[1931,27220,1933],{},[902,27222,26299],{"encoding":904}," (7.5).",[123,27225,27226,27228],{},[38,27227,20768],{}," — rovnováha agregátní poptávky a nabídky.",[123,27230,27231,27234,27235,15977,27256,2196],{},[38,27232,27233],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,27236,27238],{"className":27237},[886],[888,27239,27240],{"xmlns":890},[892,27241,27242,27254],{},[895,27243,27244,27246,27248,27250,27252],{},[898,27245,9316],{},[1700,27247,1765],{},[898,27249,2974],{},[1700,27251,1897],{},[898,27253,12369],{},[902,27255,14929],{"encoding":904},[883,27257,27259],{"className":27258},[886],[888,27260,27261],{"xmlns":890},[892,27262,27263,27299],{},[895,27264,27265,27271,27273,27275,27277,27279,27285,27287,27289,27291,27293,27295,27297],{},[1785,27266,27267,27269],{},[898,27268,9316],{},[898,27270,1762],{},[1700,27272,1765],{},[1700,27274,1703],{"stretchy":1702},[898,27276,1879],{},[1700,27278,1897],{},[1785,27280,27281,27283],{},[898,27282,12369],{},[1700,27284,4543],{},[1700,27286,1709],{"stretchy":1702},[898,27288,1979],{"mathvariant":1791},[1700,27290,1703],{"stretchy":1702},[1931,27292,1933],{},[1700,27294,1768],{},[898,27296,207],{},[1700,27298,1709],{"stretchy":1702},[902,27300,26442],{"encoding":904},[123,27302,27303,27306,27307,1343,27326,15977,27351,2196],{},[38,27304,27305],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,27308,27310],{"className":27309},[886],[888,27311,27312],{"xmlns":890},[892,27313,27314,27324],{},[895,27315,27316,27318,27320,27322],{},[898,27317,2971],{},[1700,27319,1703],{"stretchy":1702},[898,27321,9316],{},[1700,27323,1709],{"stretchy":1702},[902,27325,22404],{"encoding":904},[883,27327,27329],{"className":27328},[886],[888,27330,27331],{"xmlns":890},[892,27332,27333,27349],{},[895,27334,27335,27341,27343,27345,27347],{},[2007,27336,27337,27339],{},[898,27338,9316],{},[898,27340,4374],{},[1700,27342,1765],{},[898,27344,9316],{},[1700,27346,1768],{},[898,27348,2971],{},[902,27350,21903],{"encoding":904},[883,27352,27354],{"className":27353},[886],[888,27355,27356],{"xmlns":890},[892,27357,27358,27374],{},[895,27359,27360,27362,27364,27366,27368,27370,27372],{},[898,27361,9316],{},[1700,27363,1765],{},[898,27365,2974],{},[1700,27367,1897],{},[898,27369,12369],{},[1700,27371,1897],{},[898,27373,12297],{},[902,27375,21874],{"encoding":904},[123,27377,27378,27381,27382,27403,27404,15977,27428,2196],{},[38,27379,27380],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,27383,27385],{"className":27384},[886],[888,27386,27387],{"xmlns":890},[892,27388,27389,27401],{},[895,27390,27391,27393,27395,27397,27399],{},[898,27392,12505],{},[1700,27394,1765],{},[898,27396,23438],{},[1700,27398,1768],{},[898,27400,2005],{},[902,27402,23445],{"encoding":904},", importem ",[883,27405,27407],{"className":27406},[886],[888,27408,27409],{"xmlns":890},[892,27410,27411,27425],{},[895,27412,27413,27415,27417,27423],{},[898,27414,2005],{},[1700,27416,1703],{"stretchy":1702},[2007,27418,27419,27421],{},[898,27420,9316],{},[898,27422,4374],{},[1700,27424,1709],{"stretchy":1702},[902,27426,27427],{"encoding":904},"M(Y_D)",[883,27429,27431],{"className":27430},[886],[888,27432,27433],{"xmlns":890},[892,27434,27435,27459],{},[895,27436,27437,27439,27441,27443,27445,27447,27449,27451,27453,27455,27457],{},[898,27438,9316],{},[1700,27440,1765],{},[898,27442,2974],{},[1700,27444,1897],{},[898,27446,12369],{},[1700,27448,1897],{},[898,27450,12297],{},[1700,27452,1897],{},[898,27454,23438],{},[1700,27456,1768],{},[898,27458,2005],{},[902,27460,27461],{"encoding":904},"Y = C + I + G + B - M",[123,27463,27464,7203,27467,26656],{},[38,27465,27466],{},"Multiplikátor investic",[883,27468,27470],{"className":27469},[886],[888,27471,27472],{"xmlns":890},[892,27473,27474,27522],{},[895,27475,27476,27478,27484,27486,27488,27494,27496,27498,27500,27502,27504,27506,27508,27510,27512,27514,27516,27518,27520],{},[898,27477,10056],{"mathvariant":1791},[1785,27479,27480,27482],{},[898,27481,9316],{},[898,27483,1762],{},[898,27485,1979],{"mathvariant":1791},[898,27487,10056],{"mathvariant":1791},[1785,27489,27490,27492],{},[898,27491,12369],{},[1700,27493,4543],{},[1700,27495,1765],{},[1931,27497,1933],{},[898,27499,1979],{"mathvariant":1791},[1700,27501,1703],{"stretchy":1702},[1931,27503,1933],{},[1700,27505,1768],{},[898,27507,207],{},[1700,27509,1709],{"stretchy":1702},[1700,27511,1765],{},[1931,27513,1933],{},[898,27515,1979],{"mathvariant":1791},[898,27517,2005],{},[898,27519,1677],{},[898,27521,8861],{},[902,27523,26655],{"encoding":904},[123,27525,27526,7203,27557,1343,27574,27591],{},[38,27527,15912,27528],{},[883,27529,27531],{"className":27530},[886],[888,27532,27533],{"xmlns":890},[892,27534,27535,27555],{},[895,27536,27537,27539,27541,27543,27545,27547,27549,27551,27553],{},[898,27538,12369],{},[1700,27540,1703],{"stretchy":1702},[898,27542,12226],{},[1700,27544,1709],{"stretchy":1702},[1700,27546,1765],{},[898,27548,2354],{},[898,27550,12226],{},[1700,27552,1897],{},[898,27554,2406],{},[902,27556,15942],{"encoding":904},[883,27558,27560],{"className":27559},[886],[888,27561,27562],{"xmlns":890},[892,27563,27564,27572],{},[895,27565,27566,27568,27570],{},[898,27567,2354],{},[1700,27569,3640],{},[1931,27571,1772],{},[902,27573,12700],{"encoding":904},[883,27575,27577],{"className":27576},[886],[888,27578,27579],{"xmlns":890},[892,27580,27581,27589],{},[895,27582,27583,27585,27587],{},[898,27584,2406],{},[1700,27586,3601],{},[1931,27588,1772],{},[902,27590,12679],{"encoding":904},"; klesající.",[123,27593,27594,27596,27597,27599,27600,27649],{},[38,27595,16031],{}," — rovnováha na trhu zboží (",[614,27598,12239],{},"); ",[883,27601,27603],{"className":27602},[886],[888,27604,27605],{"xmlns":890},[892,27606,27607,27647],{},[895,27608,27609,27611,27613,27625,27627,27629],{},[898,27610,9316],{},[1700,27612,1765],{},[1774,27614,27615,27617],{},[898,27616,2354],{},[895,27618,27619,27621,27623],{},[1931,27620,1933],{},[1700,27622,1768],{},[898,27624,207],{},[898,27626,12226],{},[1700,27628,1897],{},[1774,27630,27631,27639],{},[895,27632,27633,27635,27637],{},[898,27634,1879],{},[1700,27636,1897],{},[898,27638,2406],{},[895,27640,27641,27643,27645],{},[1931,27642,1933],{},[1700,27644,1768],{},[898,27646,207],{},[902,27648,16084],{"encoding":904}," (7.14); klesající.",[123,27651,27652,27654,27655,27599,27657,27702],{},[38,27653,16230],{}," — rovnováha na trhu peněz (",[614,27656,12246],{},[883,27658,27660],{"className":27659},[886],[888,27661,27662],{"xmlns":890},[892,27663,27664,27700],{},[895,27665,27666,27672,27674,27680,27682,27684,27690,27692,27694],{},[1785,27667,27668,27670],{},[898,27669,2005],{},[1700,27671,4543],{},[1700,27673,1765],{},[2007,27675,27676,27678],{},[898,27677,13422],{},[1931,27679,1933],{},[898,27681,9316],{},[1700,27683,1897],{},[2007,27685,27686,27688],{},[898,27687,13422],{},[1931,27689,2343],{},[898,27691,12226],{},[1700,27693,1897],{},[2007,27695,27696,27698],{},[898,27697,13422],{},[1931,27699,2385],{},[902,27701,16278],{"encoding":904}," (7.15); rostoucí.",[123,27704,27705,7203,27708,2196],{},[38,27706,27707],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,27709,27711],{"className":27710},[886],[888,27712,27713],{"xmlns":890},[892,27714,27715,27739],{},[895,27716,27717,27723,27725,27731,27733],{},[1785,27718,27719,27721],{},[898,27720,2005],{},[898,27722,4374],{},[1700,27724,1765],{},[2007,27726,27727,27729],{},[898,27728,1706],{},[1931,27730,1933],{},[1700,27732,1897],{},[2007,27734,27735,27737],{},[898,27736,1706],{},[1931,27738,2343],{},[902,27740,27741],{"encoding":904},"M^D = L_1 + L_2",[123,27743,27744,16288,27746,14165,27759,2114,27774,27789,27790,2196],{},[38,27745,945],{},[883,27747,27749],{"className":27748},[886],[888,27750,27751],{"xmlns":890},[892,27752,27753,27757],{},[895,27754,27755],{},[898,27756,1762],{},[902,27758,1762],{"encoding":904},[883,27760,27762],{"className":27761},[886],[888,27763,27764],{"xmlns":890},[892,27765,27766,27772],{},[895,27767,27768,27770],{},[898,27769,12369],{},[898,27771,8861],{},[902,27773,12236],{"encoding":904},[883,27775,27777],{"className":27776},[886],[888,27778,27779],{"xmlns":890},[892,27780,27781,27787],{},[895,27782,27783,27785],{},[898,27784,1706],{},[898,27786,2005],{},[902,27788,12243],{"encoding":904}," určuje ",[883,27791,27793],{"className":27792},[886],[888,27794,27795],{"xmlns":890},[892,27796,27797,27817],{},[895,27798,27799,27801,27807,27809,27815],{},[1700,27800,1703],{"stretchy":1702},[1785,27802,27803,27805],{},[898,27804,9316],{},[898,27806,1762],{},[1700,27808,1732],{"separator":1731},[1785,27810,27811,27813],{},[898,27812,12226],{},[898,27814,1762],{},[1700,27816,1709],{"stretchy":1702},[902,27818,12280],{"encoding":904},[115,27820,3985],{"id":3984},[120,27822,27823,27830,27837],{},[123,27824,27825,2106,27827],{},[38,27826,16389],{},[207,27828,16393],{"className":27829,"dataFsResolvedFilePath":2140,"href":2141},[210],[123,27831,27832,2106,27834],{},[38,27833,16398],{},[207,27835,16402],{"className":27836,"dataFsResolvedFilePath":868,"href":869},[210],[123,27838,27839,27841],{},[38,27840,16417],{},[120,27842,27843,27849,27855,27861],{},[123,27844,27845,27848],{},[207,27846,16457],{"className":27847,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,27850,27851,27854],{},[207,27852,16425],{"className":27853,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,27856,27857,27860],{},[207,27858,3145],{"className":27859,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,27862,27863,27866,27867,1343,27884,27901],{},[207,27864,1145],{"className":27865,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,27868,27870],{"className":27869},[886],[888,27871,27872],{"xmlns":890},[892,27873,27874,27882],{},[895,27875,27876,27878,27880],{},[898,27877,2005],{},[898,27879,1677],{},[898,27881,2974],{},[902,27883,18230],{"encoding":904},[883,27885,27887],{"className":27886},[886],[888,27888,27889],{"xmlns":890},[892,27890,27891,27899],{},[895,27892,27893,27895,27897],{},[898,27894,2005],{},[898,27896,1677],{},[898,27898,8861],{},[902,27900,19844],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":27903},[27904,27905,27906,27907,27912,27915,27916,27923,27928,27933,27936,27937,27938,27939],{"id":12190,"depth":642,"text":12191},{"id":18339,"depth":642,"text":18340},{"id":18459,"depth":642,"text":18460},{"id":18712,"depth":642,"text":18713,"children":27908},[27909,27910,27911],{"id":18716,"depth":649,"text":18717},{"id":18928,"depth":649,"text":18929},{"id":19436,"depth":649,"text":19437},{"id":19756,"depth":642,"text":19757,"children":27913},[27914],{"id":20272,"depth":649,"text":20273},{"id":20767,"depth":642,"text":20768},{"id":20794,"depth":642,"text":20795,"children":27917},[27918,27919,27920,27922],{"id":20805,"depth":649,"text":20806},{"id":20875,"depth":649,"text":20876},{"id":21059,"depth":649,"text":27921},"Výpočet YEY^E",{"id":21202,"depth":649,"text":21203},{"id":21580,"depth":642,"text":21581,"children":27924},[27925,27926,27927],{"id":21584,"depth":649,"text":20806},{"id":22033,"depth":649,"text":20876},{"id":22689,"depth":649,"text":22690},{"id":23476,"depth":642,"text":23477,"children":27929},[27930,27931,27932],{"id":23480,"depth":649,"text":20806},{"id":23625,"depth":649,"text":20876},{"id":23895,"depth":649,"text":23896},{"id":24819,"depth":642,"text":24820,"children":27934},[27935],{"id":25015,"depth":649,"text":25016},{"id":25565,"depth":642,"text":25566},{"id":26025,"depth":642,"text":26026},{"id":15904,"depth":642,"text":15905},{"id":3984,"depth":642,"text":3985},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,16411,1143,27946,27947,27948,16457,18068],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":27951,"title":27952,"body":27953,"course":1128,"courses":659,"created":9743,"description":641,"extension":661,"meta":36933,"navigation":664,"path":36934,"seo":36935,"sources":36936,"stem":36937,"tags":36938,"type":4049,"updated":677,"__hash__":36943},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":27954,"toc":36902},[27955,27958,27960,28189,28193,28246,28316,28428,28587,28591,28707,28711,28714,28836,28839,29032,29056,29124,29288,29306,29372,29750,29754,29761,30005,30061,30065,30130,30248,30380,30412,30532,30614,30617,30739,30932,31153,31157,31197,31302,31359,31459,31636,31766,31819,31822,31909,31913,32089,32093,32096,32181,32184,32241,32346,32350,32471,32474,32657,32660,32768,32977,33297,33345,33418,33492,33494,33718,33953,34221,34225,34228,34333,34390,34424,34471,34504,34588,34590,34822,34955,35032,35154,35309,35313,35454,35461,35685,35696,35700,35704,35809,35951,36061,36160,36164,36323,36433,36435,36828,36830],[12,27956,27952],{"id":27957},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,27959,12191],{"id":12190},[724,27961,27962,27964,27965,27999,28000,28003,28004,28035,28036,28082,28083,28086,28087,28129,28130,28148,28149,28153,28154,28184,28185,28188],{},[38,27963,913],{}," řeší, jaký svazek zboží ",[883,27966,27968],{"className":27967},[886],[888,27969,27970],{"xmlns":890},[892,27971,27972,27996],{},[895,27973,27974,27976,27984,27986,27994],{},[1700,27975,1927],{"stretchy":1702},[2030,27977,27978,27980,27982],{},[898,27979,1662],{},[1931,27981,1933],{},[1700,27983,4543],{},[1700,27985,1732],{"separator":1731},[2030,27987,27988,27990,27992],{},[898,27989,1662],{},[1931,27991,2343],{},[1700,27993,4543],{},[1700,27995,1970],{"stretchy":1702},[902,27997,27998],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,28001,28002],{},"primární úloha"," — maximalizace užitečnosti ",[883,28005,28007],{"className":28006},[886],[888,28008,28009],{"xmlns":890},[892,28010,28011,28033],{},[895,28012,28013,28015,28017,28023,28025,28031],{},[898,28014,900],{},[1700,28016,1703],{"stretchy":1702},[2007,28018,28019,28021],{},[898,28020,1662],{},[1931,28022,1933],{},[1700,28024,1732],{"separator":1731},[2007,28026,28027,28029],{},[898,28028,1662],{},[1931,28030,2343],{},[1700,28032,1709],{"stretchy":1702},[902,28034,16528],{"encoding":904}," při rozpočtovém omezení ",[883,28037,28039],{"className":28038},[886],[888,28040,28041],{"xmlns":890},[892,28042,28043,28079],{},[895,28044,28045,28051,28053,28059,28065,28067,28073],{},[1785,28046,28047,28049],{},[898,28048,9316],{},[1700,28050,4543],{},[1700,28052,1765],{},[2007,28054,28055,28057],{},[898,28056,1677],{},[1931,28058,1933],{},[2007,28060,28061,28063],{},[898,28062,1662],{},[1931,28064,1933],{},[1700,28066,1897],{},[2007,28068,28069,28071],{},[898,28070,1677],{},[1931,28072,2343],{},[2007,28074,28075,28077],{},[898,28076,1662],{},[1931,28078,2343],{},[902,28080,28081],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,28084,28085],{},"duální úloha"," — minimalizace výdajů ",[883,28088,28090],{"className":28089},[886],[888,28091,28092],{"xmlns":890},[892,28093,28094,28126],{},[895,28095,28096,28098,28100,28106,28112,28114,28120],{},[898,28097,1762],{},[1700,28099,1765],{},[2007,28101,28102,28104],{},[898,28103,1677],{},[1931,28105,1933],{},[2007,28107,28108,28110],{},[898,28109,1662],{},[1931,28111,1933],{},[1700,28113,1897],{},[2007,28115,28116,28118],{},[898,28117,1677],{},[1931,28119,2343],{},[2007,28121,28122,28124],{},[898,28123,1662],{},[1931,28125,2343],{},[902,28127,28128],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,28131,28133],{"className":28132},[886],[888,28134,28135],{"xmlns":890},[892,28136,28137,28145],{},[895,28138,28139],{},[1785,28140,28141,28143],{},[898,28142,900],{},[1700,28144,4543],{},[902,28146,28147],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,28150,28152],{"className":28151,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,28155,28157],{"className":28156},[886],[888,28158,28159],{"xmlns":890},[892,28160,28161,28181],{},[895,28162,28163,28165,28167,28173,28175],{},[1781,28164,10786],{},[1700,28166,1765],{},[2007,28168,28169,28171],{},[898,28170,1677],{},[1931,28172,1933],{},[898,28174,1979],{"mathvariant":1791},[2007,28176,28177,28179],{},[898,28178,1677],{},[1931,28180,2343],{},[902,28182,28183],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,28186,28187],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,28190,28192],{"id":28191},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,28194,28195,28196,28214,28215,28245],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,28197,28199],{"className":28198},[886],[888,28200,28201],{"xmlns":890},[892,28202,28203,28211],{},[895,28204,28205],{},[1785,28206,28207,28209],{},[898,28208,9316],{},[1700,28210,4543],{},[902,28212,28213],{"encoding":904},"Y^*"," a ceny ",[883,28216,28218],{"className":28217},[886],[888,28219,28220],{"xmlns":890},[892,28221,28222,28242],{},[895,28223,28224,28232,28234],{},[2030,28225,28226,28228,28230],{},[898,28227,1677],{},[1931,28229,1933],{},[1700,28231,4543],{},[1700,28233,1732],{"separator":1731},[2030,28235,28236,28238,28240],{},[898,28237,1677],{},[1931,28239,2343],{},[1700,28241,4543],{},[902,28243,28244],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,28247,28249],{"className":28248},[886],[888,28250,28252],{"xmlns":890,"display":28251},"block",[892,28253,28254,28313],{},[20939,28255,28257],{"width":28256},"100%",[20944,28258,28259,28262,28306,28308],{},[20947,28260],{"width":28261},"50%",[20947,28263,28264],{},[895,28265,28266,28272,28274,28282,28288,28290,28298,28304],{},[1785,28267,28268,28270],{},[898,28269,9316],{},[1700,28271,4543],{},[1700,28273,1765],{},[2030,28275,28276,28278,28280],{},[898,28277,1677],{},[1931,28279,1933],{},[1700,28281,4543],{},[2007,28283,28284,28286],{},[898,28285,1662],{},[1931,28287,1933],{},[1700,28289,1897],{},[2030,28291,28292,28294,28296],{},[898,28293,1677],{},[1931,28295,2343],{},[1700,28297,4543],{},[2007,28299,28300,28302],{},[898,28301,1662],{},[1931,28303,2343],{},[1700,28305,1732],{"separator":1731},[20947,28307],{"width":28261},[20947,28309,28310],{},[1781,28311,28312],{},"(6.12)",[902,28314,28315],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,28317,28318,28319,28322,28323,2114,28359,28395,28396,28409,28410,28424,28425,2196],{},"geometricky ",[38,28320,28321],{},"rozpočtová přímka (budget line)"," procházející body ",[883,28324,28326],{"className":28325},[886],[888,28327,28328],{"xmlns":890},[892,28329,28330,28356],{},[895,28331,28332,28334,28340,28342,28350,28352,28354],{},[1700,28333,1927],{"stretchy":1702},[1785,28335,28336,28338],{},[898,28337,9316],{},[1700,28339,4543],{},[898,28341,1979],{"mathvariant":1791},[2030,28343,28344,28346,28348],{},[898,28345,1677],{},[1931,28347,1933],{},[1700,28349,4543],{},[1700,28351,1732],{"separator":1731},[1931,28353,1772],{},[1700,28355,1970],{"stretchy":1702},[902,28357,28358],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,28360,28362],{"className":28361},[886],[888,28363,28364],{"xmlns":890},[892,28365,28366,28392],{},[895,28367,28368,28370,28372,28374,28380,28382,28390],{},[1700,28369,1927],{"stretchy":1702},[1931,28371,1772],{},[1700,28373,1732],{"separator":1731},[1785,28375,28376,28378],{},[898,28377,9316],{},[1700,28379,4543],{},[898,28381,1979],{"mathvariant":1791},[2030,28383,28384,28386,28388],{},[898,28385,1677],{},[1931,28387,2343],{},[1700,28389,4543],{},[1700,28391,1970],{"stretchy":1702},[902,28393,28394],{"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 ",[883,28397,28399],{"className":28398},[886],[888,28400,28401],{"xmlns":890},[892,28402,28403,28407],{},[895,28404,28405],{},[898,28406,900],{},[902,28408,900],{"encoding":904},", indiferenční křivky a ",[883,28411,28413],{"className":28412},[886],[888,28414,28415],{"xmlns":890},[892,28416,28417,28421],{},[895,28418,28419],{},[1781,28420,10786],{},[902,28422,28423],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,28426,880],{"className":28427,"dataFsResolvedFilePath":878,"href":879},[210],[4060,28429,28430],{},[724,28431,28432,28434,28435,28438,28439,28452,28453,28455,28456,28469,28470,2106,28473,28513,28514,28531,28532,28549,28550,28567,28568,28586],{},[883,28433,4601],{}," Pozor — dvě úlohy, totéž řešení\n",[38,28436,28437],{},"Primární úloha"," (max ",[883,28440,28442],{"className":28441},[886],[888,28443,28444],{"xmlns":890},[892,28445,28446,28450],{},[895,28447,28448],{},[898,28449,900],{},[902,28451,900],{"encoding":904}," při pevném rozpočtu) a ",[38,28454,28085],{}," (min ",[883,28457,28459],{"className":28458},[886],[888,28460,28461],{"xmlns":890},[892,28462,28463,28467],{},[895,28464,28465],{},[898,28466,1762],{},[902,28468,1762],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,28471,28472],{},"tentýž bod",[883,28474,28476],{"className":28475},[886],[888,28477,28478],{"xmlns":890},[892,28479,28480,28510],{},[895,28481,28482,28488,28490,28498,28500,28508],{},[1785,28483,28484,28486],{},[898,28485,1662],{},[1700,28487,4543],{},[1700,28489,1927],{"stretchy":1702},[2030,28491,28492,28494,28496],{},[898,28493,1662],{},[1931,28495,1933],{},[1700,28497,4543],{},[1700,28499,1732],{"separator":1731},[2030,28501,28502,28504,28506],{},[898,28503,1662],{},[1931,28505,2343],{},[1700,28507,4543],{},[1700,28509,1970],{"stretchy":1702},[902,28511,28512],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,28515,28517],{"className":28516},[886],[888,28518,28519],{"xmlns":890},[892,28520,28521,28529],{},[895,28522,28523],{},[1785,28524,28525,28527],{},[898,28526,9316],{},[1700,28528,4543],{},[902,28530,28213],{"encoding":904}," a hledáme maximální ",[883,28533,28535],{"className":28534},[886],[888,28536,28537],{"xmlns":890},[892,28538,28539,28547],{},[895,28540,28541],{},[1785,28542,28543,28545],{},[898,28544,900],{},[1700,28546,4543],{},[902,28548,28147],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,28551,28553],{"className":28552},[886],[888,28554,28555],{"xmlns":890},[892,28556,28557,28565],{},[895,28558,28559],{},[1785,28560,28561,28563],{},[898,28562,900],{},[1700,28564,4543],{},[902,28566,28147],{"encoding":904}," a hledáme minimální ",[883,28569,28571],{"className":28570},[886],[888,28572,28573],{"xmlns":890},[892,28574,28575,28583],{},[895,28576,28577],{},[1785,28578,28579,28581],{},[898,28580,1762],{},[1700,28582,4543],{},[902,28584,28585],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,28588,28590],{"id":28589},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,28592,28593,28594,28625,28626,28702,28703,2196],{},"Úlohou je najít maximum ",[883,28595,28597],{"className":28596},[886],[888,28598,28599],{"xmlns":890},[892,28600,28601,28623],{},[895,28602,28603,28605,28607,28613,28615,28621],{},[898,28604,900],{},[1700,28606,1703],{"stretchy":1702},[2007,28608,28609,28611],{},[898,28610,1662],{},[1931,28612,1933],{},[1700,28614,1732],{"separator":1731},[2007,28616,28617,28619],{},[898,28618,1662],{},[1931,28620,2343],{},[1700,28622,1709],{"stretchy":1702},[902,28624,16528],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,28627,28629],{"className":28628},[886],[888,28630,28631],{"xmlns":890},[892,28632,28633,28699],{},[895,28634,28635,28637,28639,28645,28647,28653,28655,28657,28663,28665,28673,28679,28681,28689,28695,28697],{},[898,28636,11224],{},[1700,28638,1703],{"stretchy":1702},[2007,28640,28641,28643],{},[898,28642,1662],{},[1931,28644,1933],{},[1700,28646,1732],{"separator":1731},[2007,28648,28649,28651],{},[898,28650,1662],{},[1931,28652,2343],{},[1700,28654,1709],{"stretchy":1702},[1700,28656,1765],{},[1785,28658,28659,28661],{},[898,28660,9316],{},[1700,28662,4543],{},[1700,28664,1768],{},[2030,28666,28667,28669,28671],{},[898,28668,1677],{},[1931,28670,1933],{},[1700,28672,4543],{},[2007,28674,28675,28677],{},[898,28676,1662],{},[1931,28678,1933],{},[1700,28680,1768],{},[2030,28682,28683,28685,28687],{},[898,28684,1677],{},[1931,28686,2343],{},[1700,28688,4543],{},[2007,28690,28691,28693],{},[898,28692,1662],{},[1931,28694,2343],{},[1700,28696,1765],{},[1931,28698,1772],{},[902,28700,28701],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,28704,28706],{"className":28705,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,28708,28710],{"id":28709},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,28712,28713],{},"Sestavíme",[883,28715,28717],{"className":28716},[886],[888,28718,28719],{"xmlns":890,"display":28251},[892,28720,28721,28833],{},[20939,28722,28723],{"width":28256},[20944,28724,28725,28727,28826,28828],{},[20947,28726],{"width":28261},[20947,28728,28729],{},[895,28730,28731,28734,28736,28742,28744,28750,28752,28754,28756,28758,28760,28762,28768,28770,28776,28778,28780,28782,28784,28790,28792,28800,28806,28808,28816,28822,28824],{},[898,28732,1706],{"mathvariant":28733},"script",[1700,28735,1703],{"stretchy":1702},[2007,28737,28738,28740],{},[898,28739,1662],{},[1931,28741,1933],{},[1700,28743,1732],{"separator":1731},[2007,28745,28746,28748],{},[898,28747,1662],{},[1931,28749,2343],{},[1700,28751,1732],{"separator":1731},[898,28753,16628],{},[1700,28755,1709],{"stretchy":1702},[1700,28757,1765],{},[898,28759,900],{},[1700,28761,1703],{"stretchy":1702},[2007,28763,28764,28766],{},[898,28765,1662],{},[1931,28767,1933],{},[1700,28769,1732],{"separator":1731},[2007,28771,28772,28774],{},[898,28773,1662],{},[1931,28775,2343],{},[1700,28777,1709],{"stretchy":1702},[1700,28779,1897],{},[898,28781,16628],{},[1700,28783,1703],{"stretchy":1702},[1785,28785,28786,28788],{},[898,28787,9316],{},[1700,28789,4543],{},[1700,28791,1768],{},[2030,28793,28794,28796,28798],{},[898,28795,1677],{},[1931,28797,1933],{},[1700,28799,4543],{},[2007,28801,28802,28804],{},[898,28803,1662],{},[1931,28805,1933],{},[1700,28807,1768],{},[2030,28809,28810,28812,28814],{},[898,28811,1677],{},[1931,28813,2343],{},[1700,28815,4543],{},[2007,28817,28818,28820],{},[898,28819,1662],{},[1931,28821,2343],{},[1700,28823,1709],{"stretchy":1702},[898,28825,2196],{"mathvariant":1791},[20947,28827],{"width":28261},[20947,28829,28830],{},[1781,28831,28832],{},"(6.13)",[902,28834,28835],{"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}",[724,28837,28838],{},"Soustava prvního řádu:",[883,28840,28842],{"className":28841},[886],[888,28843,28844],{"xmlns":890,"display":28251},[892,28845,28846,29029],{},[20939,28847,28848],{"width":28256},[20944,28849,28850,28852,29022,29024],{},[20947,28851],{"width":28261},[20947,28853,28854],{},[20939,28855,28856,28906,28956],{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},[20944,28857,28858,28870],{},[20947,28859,28860],{},[1770,28861,28862],{"scriptlevel":1772,"displaystyle":1731},[2030,28863,28864,28866,28868],{},[898,28865,1706],{"mathvariant":28733},[1931,28867,1933],{},[1700,28869,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,28871,28872],{},[1770,28873,28874],{"scriptlevel":1772,"displaystyle":1731},[895,28875,28876,28878,28880,28888,28890,28892,28900,28902,28904],{},[895,28877],{},[1700,28879,1765],{},[2030,28881,28882,28884,28886],{},[898,28883,900],{},[1931,28885,1933],{},[1700,28887,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,28889,1768],{},[898,28891,16628],{},[2030,28893,28894,28896,28898],{},[898,28895,1677],{},[1931,28897,1933],{},[1700,28899,4543],{},[1700,28901,1765],{},[1931,28903,1772],{},[1700,28905,1732],{"separator":1731},[20944,28907,28908,28920],{},[20947,28909,28910],{},[1770,28911,28912],{"scriptlevel":1772,"displaystyle":1731},[2030,28913,28914,28916,28918],{},[898,28915,1706],{"mathvariant":28733},[1931,28917,2343],{},[1700,28919,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,28921,28922],{},[1770,28923,28924],{"scriptlevel":1772,"displaystyle":1731},[895,28925,28926,28928,28930,28938,28940,28942,28950,28952,28954],{},[895,28927],{},[1700,28929,1765],{},[2030,28931,28932,28934,28936],{},[898,28933,900],{},[1931,28935,2343],{},[1700,28937,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,28939,1768],{},[898,28941,16628],{},[2030,28943,28944,28946,28948],{},[898,28945,1677],{},[1931,28947,2343],{},[1700,28949,4543],{},[1700,28951,1765],{},[1931,28953,1772],{},[1700,28955,1732],{"separator":1731},[20944,28957,28958,28970],{},[20947,28959,28960],{},[1770,28961,28962],{"scriptlevel":1772,"displaystyle":1731},[2030,28963,28964,28966,28968],{},[898,28965,1706],{"mathvariant":28733},[898,28967,16628],{},[1700,28969,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,28971,28972],{},[1770,28973,28974],{"scriptlevel":1772,"displaystyle":1731},[895,28975,28976,28978,28980,28986,28988,28996,29002,29004,29012,29018,29020],{},[895,28977],{},[1700,28979,1765],{},[1785,28981,28982,28984],{},[898,28983,9316],{},[1700,28985,4543],{},[1700,28987,1768],{},[2030,28989,28990,28992,28994],{},[898,28991,1677],{},[1931,28993,1933],{},[1700,28995,4543],{},[2007,28997,28998,29000],{},[898,28999,1662],{},[1931,29001,1933],{},[1700,29003,1768],{},[2030,29005,29006,29008,29010],{},[898,29007,1677],{},[1931,29009,2343],{},[1700,29011,4543],{},[2007,29013,29014,29016],{},[898,29015,1662],{},[1931,29017,2343],{},[1700,29019,1765],{},[1931,29021,12645],{},[20947,29023],{"width":28261},[20947,29025,29026],{},[1781,29027,29028],{},"(6.14)",[902,29030,29031],{"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}",[724,29033,29034,29035,29038,29039,29052,29053,2901],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,29036,29037],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,29040,29042],{"className":29041},[886],[888,29043,29044],{"xmlns":890},[892,29045,29046,29050],{},[895,29047,29048],{},[898,29049,16628],{},[902,29051,16681],{"encoding":904}," dostáváme ",[38,29054,29055],{},"podmínku optimality",[883,29057,29059],{"className":29058},[886],[888,29060,29061],{"xmlns":890,"display":28251},[892,29062,29063,29121],{},[895,29064,29065],{},[13017,29066,29067],{"notation":13019},[1770,29068,29069],{"scriptlevel":1772,"displaystyle":1702},[1770,29070,29071],{"scriptlevel":1772,"displaystyle":1702},[1770,29072,29073],{"scriptlevel":1772,"displaystyle":1731},[895,29074,29075,29077,29079,29081,29099,29101,29119],{},[1781,29076,4175],{},[1781,29078,10786],{},[1700,29080,1765],{},[1774,29082,29083,29091],{},[2030,29084,29085,29087,29089],{},[898,29086,900],{},[1931,29088,1933],{},[1700,29090,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[2030,29092,29093,29095,29097],{},[898,29094,900],{},[1931,29096,2343],{},[1700,29098,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,29100,1765],{},[1774,29102,29103,29111],{},[2030,29104,29105,29107,29109],{},[898,29106,1677],{},[1931,29108,1933],{},[1700,29110,4543],{},[2030,29112,29113,29115,29117],{},[898,29114,1677],{},[1931,29116,2343],{},[1700,29118,4543],{},[1781,29120,4175],{},[902,29122,29123],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[4060,29125,29126],{},[724,29127,29128,29130,29131,29165,29166,29169,29170,29188,29189,29207,29208,29238,29239,29256,29257,29287],{},[883,29129,4346],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,29132,29134],{"className":29133},[886],[888,29135,29136],{"xmlns":890},[892,29137,29138,29162],{},[895,29139,29140,29142,29144,29152,29154],{},[1781,29141,10786],{},[1700,29143,1765],{},[2030,29145,29146,29148,29150],{},[898,29147,1677],{},[1931,29149,1933],{},[1700,29151,4543],{},[898,29153,1979],{"mathvariant":1791},[2030,29155,29156,29158,29160],{},[898,29157,1677],{},[1931,29159,2343],{},[1700,29161,4543],{},[902,29163,29164],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,29167,29168],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,29171,29173],{"className":29172},[886],[888,29174,29175],{"xmlns":890},[892,29176,29177,29185],{},[895,29178,29179],{},[2007,29180,29181,29183],{},[898,29182,1662],{},[1931,29184,1933],{},[902,29186,29187],{"encoding":904},"Q_1"," za ",[883,29190,29192],{"className":29191},[886],[888,29193,29194],{"xmlns":890},[892,29195,29196,29204],{},[895,29197,29198],{},[2007,29199,29200,29202],{},[898,29201,1662],{},[1931,29203,2343],{},[902,29205,29206],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,29209,29211],{"className":29210},[886],[888,29212,29213],{"xmlns":890},[892,29214,29215,29235],{},[895,29216,29217,29219,29221,29227,29229],{},[1781,29218,10786],{},[1700,29220,3601],{},[2007,29222,29223,29225],{},[898,29224,1677],{},[1931,29226,1933],{},[898,29228,1979],{"mathvariant":1791},[2007,29230,29231,29233],{},[898,29232,1677],{},[1931,29234,2343],{},[902,29236,29237],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,29240,29242],{"className":29241},[886],[888,29243,29244],{"xmlns":890},[892,29245,29246,29254],{},[895,29247,29248],{},[2007,29249,29250,29252],{},[898,29251,1662],{},[1931,29253,1933],{},[902,29255,29187],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,29258,29260],{"className":29259},[886],[888,29261,29262],{"xmlns":890},[892,29263,29264,29284],{},[895,29265,29266,29268,29270,29276,29278],{},[1781,29267,10786],{},[1700,29269,3640],{},[2007,29271,29272,29274],{},[898,29273,1677],{},[1931,29275,1933],{},[898,29277,1979],{"mathvariant":1791},[2007,29279,29280,29282],{},[898,29281,1677],{},[1931,29283,2343],{},[902,29285,29286],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,29289,29291,29292,29305],{"id":29290},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,29293,29295],{"className":29294},[886],[888,29296,29297],{"xmlns":890},[892,29298,29299,29303],{},[895,29300,29301],{},[898,29302,16628],{},[902,29304,16681],{"encoding":904}," — mezní užitečnost důchodu",[724,29307,29308,29309,29327,29328,29331,29332,29349,29350,29367,29368,29371],{},"Lagrangeův multiplikátor ",[883,29310,29312],{"className":29311},[886],[888,29313,29314],{"xmlns":890},[892,29315,29316,29324],{},[895,29317,29318],{},[1785,29319,29320,29322],{},[898,29321,16628],{},[1700,29323,4543],{},[902,29325,29326],{"encoding":904},"\\lambda^*"," představuje ",[38,29329,29330],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,29333,29335],{"className":29334},[886],[888,29336,29337],{"xmlns":890},[892,29338,29339,29347],{},[895,29340,29341],{},[1785,29342,29343,29345],{},[898,29344,900],{},[1700,29346,4543],{},[902,29348,28147],{"encoding":904}," při jednotkové změně důchodu ",[883,29351,29353],{"className":29352},[886],[888,29354,29355],{"xmlns":890},[892,29356,29357,29365],{},[895,29358,29359],{},[1785,29360,29361,29363],{},[898,29362,9316],{},[1700,29364,4543],{},[902,29366,28213],{"encoding":904},". Je to ",[38,29369,29370],{},"stínová cena"," rozpočtového omezení.",[4060,29373,29374,29379],{},[724,29375,29376,29378],{},[883,29377,4761],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,29380,29381,29441,29528,29564,29651],{},[123,29382,29383,29386,29387,2196],{},[38,29384,29385],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,29388,29390],{"className":29389},[886],[888,29391,29392],{"xmlns":890},[892,29393,29394,29438],{},[895,29395,29396,29402,29404,29412,29418,29420,29428,29434,29436],{},[1785,29397,29398,29400],{},[898,29399,9316],{},[1700,29401,4543],{},[1700,29403,1768],{},[2030,29405,29406,29408,29410],{},[898,29407,1677],{},[1931,29409,1933],{},[1700,29411,4543],{},[2007,29413,29414,29416],{},[898,29415,1662],{},[1931,29417,1933],{},[1700,29419,1768],{},[2030,29421,29422,29424,29426],{},[898,29423,1677],{},[1931,29425,2343],{},[1700,29427,4543],{},[2007,29429,29430,29432],{},[898,29431,1662],{},[1931,29433,2343],{},[1700,29435,1765],{},[1931,29437,1772],{},[902,29439,29440],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,29442,29443,2106,29446,2196],{},[38,29444,29445],{},"Sestav Lagrangeovu funkci",[883,29447,29449],{"className":29448},[886],[888,29450,29451],{"xmlns":890},[892,29452,29453,29525],{},[895,29454,29455,29457,29459,29461,29463,29469,29471,29477,29479,29481,29483,29485,29491,29493,29501,29507,29509,29517,29523],{},[898,29456,1706],{"mathvariant":28733},[1700,29458,1765],{},[898,29460,900],{},[1700,29462,1703],{"stretchy":1702},[2007,29464,29465,29467],{},[898,29466,1662],{},[1931,29468,1933],{},[1700,29470,1732],{"separator":1731},[2007,29472,29473,29475],{},[898,29474,1662],{},[1931,29476,2343],{},[1700,29478,1709],{"stretchy":1702},[1700,29480,1897],{},[898,29482,16628],{},[1700,29484,1703],{"stretchy":1702},[1785,29486,29487,29489],{},[898,29488,9316],{},[1700,29490,4543],{},[1700,29492,1768],{},[2030,29494,29495,29497,29499],{},[898,29496,1677],{},[1931,29498,1933],{},[1700,29500,4543],{},[2007,29502,29503,29505],{},[898,29504,1662],{},[1931,29506,1933],{},[1700,29508,1768],{},[2030,29510,29511,29513,29515],{},[898,29512,1677],{},[1931,29514,2343],{},[1700,29516,4543],{},[2007,29518,29519,29521],{},[898,29520,1662],{},[1931,29522,2343],{},[1700,29524,1709],{"stretchy":1702},[902,29526,29527],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,29529,29530,10651,29533,29563],{},[38,29531,29532],{},"Spočítej parciální derivace",[883,29534,29536],{"className":29535},[886],[888,29537,29538],{"xmlns":890},[892,29539,29540,29560],{},[895,29541,29542,29548,29550,29556,29558],{},[2007,29543,29544,29546],{},[898,29545,1662],{},[1931,29547,1933],{},[1700,29549,1732],{"separator":1731},[2007,29551,29552,29554],{},[898,29553,1662],{},[1931,29555,2343],{},[1700,29557,1732],{"separator":1731},[898,29559,16628],{},[902,29561,29562],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,29565,29566,29582,29583,29616,29617,2114,29634,2196],{},[38,29567,29568,29569],{},"Vyluč ",[883,29570,29572],{"className":29571},[886],[888,29573,29574],{"xmlns":890},[892,29575,29576,29580],{},[895,29577,29578],{},[898,29579,16628],{},[902,29581,16681],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,29584,29586],{"className":29585},[886],[888,29587,29588],{"xmlns":890},[892,29589,29590,29614],{},[895,29591,29592,29594,29596,29604,29606],{},[1781,29593,10786],{},[1700,29595,1765],{},[2030,29597,29598,29600,29602],{},[898,29599,1677],{},[1931,29601,1933],{},[1700,29603,4543],{},[898,29605,1979],{"mathvariant":1791},[2030,29607,29608,29610,29612],{},[898,29609,1677],{},[1931,29611,2343],{},[1700,29613,4543],{},[902,29615,29164],{"encoding":904},", která dá vztah mezi ",[883,29618,29620],{"className":29619},[886],[888,29621,29622],{"xmlns":890},[892,29623,29624,29632],{},[895,29625,29626],{},[2007,29627,29628,29630],{},[898,29629,1662],{},[1931,29631,1933],{},[902,29633,29187],{"encoding":904},[883,29635,29637],{"className":29636},[886],[888,29638,29639],{"xmlns":890},[892,29640,29641,29649],{},[895,29642,29643],{},[2007,29644,29645,29647],{},[898,29646,1662],{},[1931,29648,2343],{},[902,29650,29206],{"encoding":904},[123,29652,29653,29656,29657,29687,29688,29705,29706,2196],{},[38,29654,29655],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,29658,29660],{"className":29659},[886],[888,29661,29662],{"xmlns":890},[892,29663,29664,29684],{},[895,29665,29666,29674,29676],{},[2030,29667,29668,29670,29672],{},[898,29669,1662],{},[1931,29671,1933],{},[1700,29673,4543],{},[1700,29675,1732],{"separator":1731},[2030,29677,29678,29680,29682],{},[898,29679,1662],{},[1931,29681,2343],{},[1700,29683,4543],{},[902,29685,29686],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,29689,29691],{"className":29690},[886],[888,29692,29693],{"xmlns":890},[892,29694,29695,29703],{},[895,29696,29697],{},[1785,29698,29699,29701],{},[898,29700,16628],{},[1700,29702,4543],{},[902,29704,29326],{"encoding":904}," a maximální užitečnost ",[883,29707,29709],{"className":29708},[886],[888,29710,29711],{"xmlns":890},[892,29712,29713,29747],{},[895,29714,29715,29721,29723,29725,29727,29735,29737,29745],{},[1785,29716,29717,29719],{},[898,29718,900],{},[1700,29720,4543],{},[1700,29722,1765],{},[898,29724,900],{},[1700,29726,1703],{"stretchy":1702},[2030,29728,29729,29731,29733],{},[898,29730,1662],{},[1931,29732,1933],{},[1700,29734,4543],{},[1700,29736,1732],{"separator":1731},[2030,29738,29739,29741,29743],{},[898,29740,1662],{},[1931,29742,2343],{},[1700,29744,4543],{},[1700,29746,1709],{"stretchy":1702},[902,29748,29749],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,29751,29753],{"id":29752},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,29755,29756],{},[2756,29757],{"alt":29758,"className":29759,"src":29760},"imek-uzitecnost-optimum",[210,2760],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,29762,29763],{},[614,29764,29765,29766,29815,29816,2114,29844,29872,29873,29907,29908,29947,29948,29966,29967,29985,29986,30004],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,29767,29769],{"className":29768},[886],[888,29770,29771],{"xmlns":890},[892,29772,29773,29813],{},[895,29774,29775,29781,29783,29791,29797,29799,29807],{},[1785,29776,29777,29779],{},[898,29778,9316],{},[1700,29780,4543],{},[1700,29782,1765],{},[2030,29784,29785,29787,29789],{},[898,29786,1677],{},[1931,29788,1933],{},[1700,29790,4543],{},[2007,29792,29793,29795],{},[898,29794,1662],{},[1931,29796,1933],{},[1700,29798,1897],{},[2030,29800,29801,29803,29805],{},[898,29802,1677],{},[1931,29804,2343],{},[1700,29806,4543],{},[2007,29808,29809,29811],{},[898,29810,1662],{},[1931,29812,2343],{},[902,29814,17483],{"encoding":904}," protíná osy v ",[883,29817,29819],{"className":29818},[886],[888,29820,29821],{"xmlns":890},[892,29822,29823,29841],{},[895,29824,29825,29831,29833],{},[1785,29826,29827,29829],{},[898,29828,9316],{},[1700,29830,4543],{},[898,29832,1979],{"mathvariant":1791},[2030,29834,29835,29837,29839],{},[898,29836,1677],{},[1931,29838,1933],{},[1700,29840,4543],{},[902,29842,29843],{"encoding":904},"Y^*\u002FP_1^*",[883,29845,29847],{"className":29846},[886],[888,29848,29849],{"xmlns":890},[892,29850,29851,29869],{},[895,29852,29853,29859,29861],{},[1785,29854,29855,29857],{},[898,29856,9316],{},[1700,29858,4543],{},[898,29860,1979],{"mathvariant":1791},[2030,29862,29863,29865,29867],{},[898,29864,1677],{},[1931,29866,2343],{},[1700,29868,4543],{},[902,29870,29871],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,29874,29876],{"className":29875},[886],[888,29877,29878],{"xmlns":890},[892,29879,29880,29904],{},[895,29881,29882,29888,29890,29896,29898],{},[2007,29883,29884,29886],{},[898,29885,2354],{},[1931,29887,1933],{},[1700,29889,3640],{},[1785,29891,29892,29894],{},[898,29893,2354],{},[1700,29895,4543],{},[1700,29897,3640],{},[2007,29899,29900,29902],{},[898,29901,2354],{},[1931,29903,2343],{},[902,29905,29906],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,29909,29911],{"className":29910},[886],[888,29912,29913],{"xmlns":890},[892,29914,29915,29945],{},[895,29916,29917,29923,29925,29933,29935,29943],{},[1785,29918,29919,29921],{},[898,29920,1662],{},[1700,29922,4543],{},[1700,29924,1927],{"stretchy":1702},[2030,29926,29927,29929,29931],{},[898,29928,1662],{},[1931,29930,1933],{},[1700,29932,4543],{},[1700,29934,1732],{"separator":1731},[2030,29936,29937,29939,29941],{},[898,29938,1662],{},[1931,29940,2343],{},[1700,29942,4543],{},[1700,29944,1970],{"stretchy":1702},[902,29946,28512],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,29949,29951],{"className":29950},[886],[888,29952,29953],{"xmlns":890},[892,29954,29955,29963],{},[895,29956,29957],{},[1785,29958,29959,29961],{},[898,29960,2354],{},[1700,29962,4543],{},[902,29964,29965],{"encoding":904},"c^*",". Křivka ",[883,29968,29970],{"className":29969},[886],[888,29971,29972],{"xmlns":890},[892,29973,29974,29982],{},[895,29975,29976],{},[2007,29977,29978,29980],{},[898,29979,2354],{},[1931,29981,1933],{},[902,29983,29984],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,29987,29989],{"className":29988},[886],[888,29990,29991],{"xmlns":890},[892,29992,29993,30001],{},[895,29994,29995],{},[2007,29996,29997,29999],{},[898,29998,2354],{},[1931,30000,2343],{},[902,30002,30003],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,30006,30007,30008,30011,30012,30030,30031,30060],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,30009,30010],{},"dotýkají",", tj. mají v bodě ",[883,30013,30015],{"className":30014},[886],[888,30016,30017],{"xmlns":890},[892,30018,30019,30027],{},[895,30020,30021],{},[1785,30022,30023,30025],{},[898,30024,1662],{},[1700,30026,4543],{},[902,30028,30029],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,30032,30034],{"className":30033},[886],[888,30035,30036],{"xmlns":890},[892,30037,30038,30058],{},[895,30039,30040,30042,30044,30050,30052],{},[1781,30041,10786],{},[1700,30043,1765],{},[2007,30045,30046,30048],{},[898,30047,1677],{},[1931,30049,1933],{},[898,30051,1979],{"mathvariant":1791},[2007,30053,30054,30056],{},[898,30055,1677],{},[1931,30057,2343],{},[902,30059,28183],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,30062,30064],{"id":30063},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,30066,9850,30067,30129],{},[883,30068,30070],{"className":30069},[886],[888,30071,30072],{"xmlns":890},[892,30073,30074,30126],{},[895,30075,30076,30078,30080,30086,30088,30094,30096,30098,30112],{},[898,30077,900],{},[1700,30079,1703],{"stretchy":1702},[2007,30081,30082,30084],{},[898,30083,1662],{},[1931,30085,1933],{},[1700,30087,1732],{"separator":1731},[2007,30089,30090,30092],{},[898,30091,1662],{},[1931,30093,2343],{},[1700,30095,1709],{"stretchy":1702},[1700,30097,1765],{},[2030,30099,30100,30102,30104],{},[898,30101,1662],{},[1931,30103,1933],{},[895,30105,30106,30108,30110],{},[1931,30107,1933],{},[898,30109,1979],{"mathvariant":1791},[1931,30111,2343],{},[2030,30113,30114,30116,30118],{},[898,30115,1662],{},[1931,30117,2343],{},[895,30119,30120,30122,30124],{},[1931,30121,1933],{},[898,30123,1979],{"mathvariant":1791},[1931,30125,2343],{},[902,30127,30128],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,30131,30132],{},[883,30133,30135],{"className":30134},[886],[888,30136,30137],{"xmlns":890},[892,30138,30139,30245],{},[895,30140,30141,30143,30145,30227,30229,30243],{},[1781,30142,10786],{},[1700,30144,1765],{},[1774,30146,30147,30187],{},[895,30148,30149,30157,30173],{},[1770,30150,30151],{"scriptlevel":1772,"displaystyle":1702},[1774,30152,30153,30155],{},[1931,30154,1933],{},[1931,30156,2343],{},[2030,30158,30159,30161,30163],{},[898,30160,1662],{},[1931,30162,1933],{},[895,30164,30165,30167,30169,30171],{},[1700,30166,1768],{},[1931,30168,1933],{},[898,30170,1979],{"mathvariant":1791},[1931,30172,2343],{},[2030,30174,30175,30177,30179],{},[898,30176,1662],{},[1931,30178,2343],{},[895,30180,30181,30183,30185],{},[1931,30182,1933],{},[898,30184,1979],{"mathvariant":1791},[1931,30186,2343],{},[895,30188,30189,30197,30211],{},[1770,30190,30191],{"scriptlevel":1772,"displaystyle":1702},[1774,30192,30193,30195],{},[1931,30194,1933],{},[1931,30196,2343],{},[2030,30198,30199,30201,30203],{},[898,30200,1662],{},[1931,30202,1933],{},[895,30204,30205,30207,30209],{},[1931,30206,1933],{},[898,30208,1979],{"mathvariant":1791},[1931,30210,2343],{},[2030,30212,30213,30215,30217],{},[898,30214,1662],{},[1931,30216,2343],{},[895,30218,30219,30221,30223,30225],{},[1700,30220,1768],{},[1931,30222,1933],{},[898,30224,1979],{"mathvariant":1791},[1931,30226,2343],{},[1700,30228,1765],{},[1774,30230,30231,30237],{},[2007,30232,30233,30235],{},[898,30234,1662],{},[1931,30236,2343],{},[2007,30238,30239,30241],{},[898,30240,1662],{},[1931,30242,1933],{},[898,30244,2196],{"mathvariant":1791},[902,30246,30247],{"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}.",[724,30249,30250,30251,3122,30296,30298,30299,30319,30320,30350,30351,2196],{},"Tedy ",[883,30252,30254],{"className":30253},[886],[888,30255,30256],{"xmlns":890},[892,30257,30258,30293],{},[895,30259,30260,30262,30264,30267,30269,30271,30273,30275,30283,30285],{},[1781,30261,10786],{},[1700,30263,1703],{"stretchy":1702},[1931,30265,30266],{},"300",[1700,30268,1732],{"separator":1731},[1931,30270,15295],{},[1700,30272,1709],{"stretchy":1702},[1700,30274,1765],{},[1770,30276,30277],{"scriptlevel":1772,"displaystyle":1702},[1774,30278,30279,30281],{},[1931,30280,15295],{},[1931,30282,30266],{},[1700,30284,1765],{},[1770,30286,30287],{"scriptlevel":1772,"displaystyle":1702},[1774,30288,30289,30291],{},[1931,30290,2438],{},[1931,30292,2385],{},[902,30294,30295],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,30297,9403],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,30300,30302],{"className":30301},[886],[888,30303,30304],{"xmlns":890},[892,30305,30306,30316],{},[895,30307,30308],{},[1770,30309,30310],{"scriptlevel":1772,"displaystyle":1702},[1774,30311,30312,30314],{},[1931,30313,2438],{},[1931,30315,2385],{},[902,30317,30318],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,30321,30323],{"className":30322},[886],[888,30324,30325],{"xmlns":890},[892,30326,30327,30347],{},[895,30328,30329,30331,30333,30339,30341],{},[1781,30330,10786],{},[1700,30332,1765],{},[2007,30334,30335,30337],{},[898,30336,1662],{},[1931,30338,2343],{},[898,30340,1979],{"mathvariant":1791},[2007,30342,30343,30345],{},[898,30344,1662],{},[1931,30346,1933],{},[902,30348,30349],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,30352,30354],{"className":30353},[886],[888,30355,30356],{"xmlns":890},[892,30357,30358,30378],{},[895,30359,30360,30362,30364,30370,30372],{},[1781,30361,10786],{},[1700,30363,1765],{},[2007,30365,30366,30368],{},[898,30367,1677],{},[1931,30369,1933],{},[898,30371,1979],{"mathvariant":1791},[2007,30373,30374,30376],{},[898,30375,1677],{},[1931,30377,2343],{},[902,30379,28183],{"encoding":904},[115,30381,30383,30384],{"id":30382},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,30385,30387],{"className":30386},[886],[888,30388,30389],{"xmlns":890},[892,30390,30391,30409],{},[895,30392,30393,30395,30397,30403],{},[898,30394,900],{},[1700,30396,1765],{},[2007,30398,30399,30401],{},[898,30400,1662],{},[1931,30402,1933],{},[2007,30404,30405,30407],{},[898,30406,1662],{},[1931,30408,2343],{},[902,30410,30411],{"encoding":904},"U = Q_1 Q_2",[724,30413,30414,30415,1343,30461,1343,30485,1343,30509,30531],{},"Je dána ",[883,30416,30418],{"className":30417},[886],[888,30419,30420],{"xmlns":890},[892,30421,30422,30458],{},[895,30423,30424,30426,30428,30434,30436,30442,30444,30446,30452],{},[898,30425,900],{},[1700,30427,1703],{"stretchy":1702},[2007,30429,30430,30432],{},[898,30431,1662],{},[1931,30433,1933],{},[1700,30435,1732],{"separator":1731},[2007,30437,30438,30440],{},[898,30439,1662],{},[1931,30441,2343],{},[1700,30443,1709],{"stretchy":1702},[1700,30445,1765],{},[2007,30447,30448,30450],{},[898,30449,1662],{},[1931,30451,1933],{},[2007,30453,30454,30456],{},[898,30455,1662],{},[1931,30457,2343],{},[902,30459,30460],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,30462,30464],{"className":30463},[886],[888,30465,30466],{"xmlns":890},[892,30467,30468,30482],{},[895,30469,30470,30478,30480],{},[2030,30471,30472,30474,30476],{},[898,30473,1677],{},[1931,30475,1933],{},[1700,30477,4543],{},[1700,30479,1765],{},[1931,30481,2343],{},[902,30483,30484],{"encoding":904},"P_1^* = 2",[883,30486,30488],{"className":30487},[886],[888,30489,30490],{"xmlns":890},[892,30491,30492,30506],{},[895,30493,30494,30502,30504],{},[2030,30495,30496,30498,30500],{},[898,30497,1677],{},[1931,30499,2343],{},[1700,30501,4543],{},[1700,30503,1765],{},[1931,30505,2438],{},[902,30507,30508],{"encoding":904},"P_2^* = 5",[883,30510,30512],{"className":30511},[886],[888,30513,30514],{"xmlns":890},[892,30515,30516,30528],{},[895,30517,30518,30524,30526],{},[1785,30519,30520,30522],{},[898,30521,9316],{},[1700,30523,4543],{},[1700,30525,1765],{},[1931,30527,3284],{},[902,30529,30530],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,30533,30535],{"className":30534},[886],[888,30536,30537],{"xmlns":890,"display":28251},[892,30538,30539,30611],{},[895,30540,30541,30543,30545,30551,30553,30559,30561,30563,30565,30567,30573,30579,30581,30583,30585,30587,30589,30591,30597,30599,30601,30607,30609],{},[898,30542,1706],{"mathvariant":28733},[1700,30544,1703],{"stretchy":1702},[2007,30546,30547,30549],{},[898,30548,1662],{},[1931,30550,1933],{},[1700,30552,1732],{"separator":1731},[2007,30554,30555,30557],{},[898,30556,1662],{},[1931,30558,2343],{},[1700,30560,1732],{"separator":1731},[898,30562,16628],{},[1700,30564,1709],{"stretchy":1702},[1700,30566,1765],{},[2007,30568,30569,30571],{},[898,30570,1662],{},[1931,30572,1933],{},[2007,30574,30575,30577],{},[898,30576,1662],{},[1931,30578,2343],{},[1700,30580,1897],{},[898,30582,16628],{},[1700,30584,1703],{"stretchy":1702},[1931,30586,3284],{},[1700,30588,1768],{},[1931,30590,2343],{},[2007,30592,30593,30595],{},[898,30594,1662],{},[1931,30596,1933],{},[1700,30598,1768],{},[1931,30600,2438],{},[2007,30602,30603,30605],{},[898,30604,1662],{},[1931,30606,2343],{},[1700,30608,1709],{"stretchy":1702},[898,30610,2196],{"mathvariant":1791},[902,30612,30613],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,30615,30616],{},"Soustava:",[883,30618,30620],{"className":30619},[886],[888,30621,30622],{"xmlns":890,"display":28251},[892,30623,30624,30736],{},[20939,30625,30626,30660,30694],{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},[20944,30627,30628,30646],{},[20947,30629,30630],{},[1770,30631,30632],{"scriptlevel":1772,"displaystyle":1731},[895,30633,30634,30640,30642,30644],{},[2007,30635,30636,30638],{},[898,30637,1662],{},[1931,30639,2343],{},[1700,30641,1768],{},[1931,30643,2343],{},[898,30645,16628],{},[20947,30647,30648],{},[1770,30649,30650],{"scriptlevel":1772,"displaystyle":1731},[895,30651,30652,30654,30656,30658],{},[895,30653],{},[1700,30655,1765],{},[1931,30657,1772],{},[1700,30659,1732],{"separator":1731},[20944,30661,30662,30680],{},[20947,30663,30664],{},[1770,30665,30666],{"scriptlevel":1772,"displaystyle":1731},[895,30667,30668,30674,30676,30678],{},[2007,30669,30670,30672],{},[898,30671,1662],{},[1931,30673,1933],{},[1700,30675,1768],{},[1931,30677,2438],{},[898,30679,16628],{},[20947,30681,30682],{},[1770,30683,30684],{"scriptlevel":1772,"displaystyle":1731},[895,30685,30686,30688,30690,30692],{},[895,30687],{},[1700,30689,1765],{},[1931,30691,1772],{},[1700,30693,1732],{"separator":1731},[20944,30695,30696,30724],{},[20947,30697,30698],{},[1770,30699,30700],{"scriptlevel":1772,"displaystyle":1731},[895,30701,30702,30704,30706,30708,30714,30716,30718],{},[1931,30703,3284],{},[1700,30705,1768],{},[1931,30707,2343],{},[2007,30709,30710,30712],{},[898,30711,1662],{},[1931,30713,1933],{},[1700,30715,1768],{},[1931,30717,2438],{},[2007,30719,30720,30722],{},[898,30721,1662],{},[1931,30723,2343],{},[20947,30725,30726],{},[1770,30727,30728],{"scriptlevel":1772,"displaystyle":1731},[895,30729,30730,30732,30734],{},[895,30731],{},[1700,30733,1765],{},[1931,30735,12645],{},[902,30737,30738],{"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}",[724,30740,30741,30742,1343,30766,30790,30791,5777,30831,30849,30850,30900,30901,2196],{},"Z prvních dvou rovnic ",[883,30743,30745],{"className":30744},[886],[888,30746,30747],{"xmlns":890},[892,30748,30749,30763],{},[895,30750,30751,30757,30759,30761],{},[2007,30752,30753,30755],{},[898,30754,1662],{},[1931,30756,2343],{},[1700,30758,1765],{},[1931,30760,2343],{},[898,30762,16628],{},[902,30764,30765],{"encoding":904},"Q_2 = 2\\lambda",[883,30767,30769],{"className":30768},[886],[888,30770,30771],{"xmlns":890},[892,30772,30773,30787],{},[895,30774,30775,30781,30783,30785],{},[2007,30776,30777,30779],{},[898,30778,1662],{},[1931,30780,1933],{},[1700,30782,1765],{},[1931,30784,2438],{},[898,30786,16628],{},[902,30788,30789],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,30792,30794],{"className":30793},[886],[888,30795,30796],{"xmlns":890},[892,30797,30798,30828],{},[895,30799,30800,30802,30804,30806,30808,30810,30812,30814,30816,30818,30820,30822,30824,30826],{},[1931,30801,3284],{},[1700,30803,1765],{},[1931,30805,2343],{},[1700,30807,2065],{},[1931,30809,2438],{},[898,30811,16628],{},[1700,30813,1897],{},[1931,30815,2438],{},[1700,30817,2065],{},[1931,30819,2343],{},[898,30821,16628],{},[1700,30823,1765],{},[1931,30825,9223],{},[898,30827,16628],{},[902,30829,30830],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,30832,30834],{"className":30833},[886],[888,30835,30836],{"xmlns":890},[892,30837,30838,30846],{},[895,30839,30840,30842,30844],{},[898,30841,16628],{},[1700,30843,1765],{},[1931,30845,2438],{},[902,30847,30848],{"encoding":904},"\\lambda = 5",". Odtud ",[38,30851,30852,1343,30876],{},[883,30853,30855],{"className":30854},[886],[888,30856,30857],{"xmlns":890},[892,30858,30859,30873],{},[895,30860,30861,30869,30871],{},[2030,30862,30863,30865,30867],{},[898,30864,1662],{},[1931,30866,1933],{},[1700,30868,4543],{},[1700,30870,1765],{},[1931,30872,5192],{},[902,30874,30875],{"encoding":904},"Q_1^* = 25",[883,30877,30879],{"className":30878},[886],[888,30880,30881],{"xmlns":890},[892,30882,30883,30897],{},[895,30884,30885,30893,30895],{},[2030,30886,30887,30889,30891],{},[898,30888,1662],{},[1931,30890,2343],{},[1700,30892,4543],{},[1700,30894,1765],{},[1931,30896,3058],{},[902,30898,30899],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,30902,30904],{"className":30903},[886],[888,30905,30906],{"xmlns":890},[892,30907,30908,30929],{},[895,30909,30910,30916,30918,30920,30922,30924,30926],{},[1785,30911,30912,30914],{},[898,30913,900],{},[1700,30915,4543],{},[1700,30917,1765],{},[1931,30919,5192],{},[1700,30921,2065],{},[1931,30923,3058],{},[1700,30925,1765],{},[1931,30927,30928],{},"250",[902,30930,30931],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,30933,30934],{},[614,30935,30936,30937,28322,30975,2114,30999,31023,31024,31054,31055,31079,31080,31102,31103,2196],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,30938,30940],{"className":30939},[886],[888,30941,30942],{"xmlns":890},[892,30943,30944,30972],{},[895,30945,30946,30948,30950,30952,30958,30960,30962,30968,30970],{},[1931,30947,3284],{},[1700,30949,1768],{},[1931,30951,2343],{},[2007,30953,30954,30956],{},[898,30955,1662],{},[1931,30957,1933],{},[1700,30959,1768],{},[1931,30961,2438],{},[2007,30963,30964,30966],{},[898,30965,1662],{},[1931,30967,2343],{},[1700,30969,1765],{},[1931,30971,1772],{},[902,30973,30974],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,30976,30978],{"className":30977},[886],[888,30979,30980],{"xmlns":890},[892,30981,30982,30996],{},[895,30983,30984,30986,30988,30990,30992,30994],{},[898,30985,1862],{},[1700,30987,1927],{"stretchy":1702},[1931,30989,1772],{},[1700,30991,1732],{"separator":1731},[1931,30993,9223],{},[1700,30995,1970],{"stretchy":1702},[902,30997,30998],{"encoding":904},"A[0, 20]",[883,31000,31002],{"className":31001},[886],[888,31003,31004],{"xmlns":890},[892,31005,31006,31020],{},[895,31007,31008,31010,31012,31014,31016,31018],{},[898,31009,23438],{},[1700,31011,1927],{"stretchy":1702},[1931,31013,3314],{},[1700,31015,1732],{"separator":1731},[1931,31017,1772],{},[1700,31019,1970],{"stretchy":1702},[902,31021,31022],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,31025,31027],{"className":31026},[886],[888,31028,31029],{"xmlns":890},[892,31030,31031,31051],{},[895,31032,31033,31039,31041,31043,31045],{},[2007,31034,31035,31037],{},[898,31036,1662],{},[1931,31038,2343],{},[1700,31040,1765],{},[1931,31042,30928],{},[898,31044,1979],{"mathvariant":1791},[2007,31046,31047,31049],{},[898,31048,1662],{},[1931,31050,1933],{},[902,31052,31053],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,31056,31058],{"className":31057},[886],[888,31059,31060],{"xmlns":890},[892,31061,31062,31076],{},[895,31063,31064,31066,31068,31070,31072,31074],{},[898,31065,1762],{},[1700,31067,1927],{"stretchy":1702},[1931,31069,5192],{},[1700,31071,1732],{"separator":1731},[1931,31073,3058],{},[1700,31075,1970],{"stretchy":1702},[902,31077,31078],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,31081,31083],{"className":31082},[886],[888,31084,31085],{"xmlns":890},[892,31086,31087,31099],{},[895,31088,31089,31091],{},[1700,31090,1768],{},[1770,31092,31093],{"scriptlevel":1772,"displaystyle":1702},[1774,31094,31095,31097],{},[1931,31096,2343],{},[1931,31098,2438],{},[902,31100,31101],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,31104,31106],{"className":31105},[886],[888,31107,31108],{"xmlns":890},[892,31109,31110,31150],{},[895,31111,31112,31114,31116,31118,31120,31122,31124,31126,31128,31130,31138,31140,31142],{},[1700,31113,1768],{},[1781,31115,10786],{},[1700,31117,1703],{"stretchy":1702},[1931,31119,5192],{},[1700,31121,1732],{"separator":1731},[1931,31123,3058],{},[1700,31125,1709],{"stretchy":1702},[1700,31127,1765],{},[1700,31129,1768],{},[1770,31131,31132],{"scriptlevel":1772,"displaystyle":1702},[1774,31133,31134,31136],{},[1931,31135,3058],{},[1931,31137,5192],{},[1700,31139,1765],{},[1700,31141,1768],{},[1770,31143,31144],{"scriptlevel":1772,"displaystyle":1702},[1774,31145,31146,31148],{},[1931,31147,2343],{},[1931,31149,2438],{},[902,31151,31152],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,31154,31156],{"id":31155},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,31158,31159,31160,29188,31190,31193,31194,2901],{},"Považujeme-li v úloze ",[883,31161,31163],{"className":31162},[886],[888,31164,31165],{"xmlns":890},[892,31166,31167,31187],{},[895,31168,31169,31175,31177,31183,31185],{},[2007,31170,31171,31173],{},[898,31172,1677],{},[1931,31174,1933],{},[1700,31176,1732],{"separator":1731},[2007,31178,31179,31181],{},[898,31180,1677],{},[1931,31182,2343],{},[1700,31184,1732],{"separator":1731},[898,31186,9316],{},[902,31188,31189],{"encoding":904},"P_1, P_2, Y",[38,31191,31192],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,31195,31196],{},"Marshallovy poptávkové funkce",[883,31198,31200],{"className":31199},[886],[888,31201,31202],{"xmlns":890,"display":28251},[892,31203,31204,31299],{},[20939,31205,31206],{"width":28256},[20944,31207,31208,31210,31292,31294],{},[20947,31209],{"width":28261},[20947,31211,31212],{},[895,31213,31214,31220,31222,31228,31230,31236,31238,31244,31246,31248,31250,31252,31254,31260,31262,31268,31270,31276,31278,31284,31286,31288,31290],{},[2007,31215,31216,31218],{},[898,31217,1662],{},[1931,31219,1933],{},[1700,31221,1765],{},[2007,31223,31224,31226],{},[898,31225,4374],{},[1931,31227,1933],{},[1700,31229,1703],{"stretchy":1702},[2007,31231,31232,31234],{},[898,31233,1677],{},[1931,31235,1933],{},[1700,31237,1732],{"separator":1731},[2007,31239,31240,31242],{},[898,31241,1677],{},[1931,31243,2343],{},[1700,31245,1732],{"separator":1731},[898,31247,9316],{},[1700,31249,1709],{"stretchy":1702},[1700,31251,1732],{"separator":1731},[6066,31253],{"width":15469},[2007,31255,31256,31258],{},[898,31257,1662],{},[1931,31259,2343],{},[1700,31261,1765],{},[2007,31263,31264,31266],{},[898,31265,4374],{},[1931,31267,2343],{},[1700,31269,1703],{"stretchy":1702},[2007,31271,31272,31274],{},[898,31273,1677],{},[1931,31275,1933],{},[1700,31277,1732],{"separator":1731},[2007,31279,31280,31282],{},[898,31281,1677],{},[1931,31283,2343],{},[1700,31285,1732],{"separator":1731},[898,31287,9316],{},[1700,31289,1709],{"stretchy":1702},[1700,31291,1732],{"separator":1731},[20947,31293],{"width":28261},[20947,31295,31296],{},[1781,31297,31298],{},"(6.15)",[902,31300,31301],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,31303,31305],{"className":31304},[886],[888,31306,31307],{"xmlns":890,"display":28251},[892,31308,31309,31356],{},[20939,31310,31311],{"width":28256},[20944,31312,31313,31315,31349,31351],{},[20947,31314],{"width":28261},[20947,31316,31317],{},[895,31318,31319,31321,31323,31325,31327,31333,31335,31341,31343,31345,31347],{},[898,31320,16628],{},[1700,31322,1765],{},[898,31324,16628],{},[1700,31326,1703],{"stretchy":1702},[2007,31328,31329,31331],{},[898,31330,1677],{},[1931,31332,1933],{},[1700,31334,1732],{"separator":1731},[2007,31336,31337,31339],{},[898,31338,1677],{},[1931,31340,2343],{},[1700,31342,1732],{"separator":1731},[898,31344,9316],{},[1700,31346,1709],{"stretchy":1702},[898,31348,2196],{"mathvariant":1791},[20947,31350],{"width":28261},[20947,31352,31353],{},[1781,31354,31355],{},"(6.16)",[902,31357,31358],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,31360,31361,31391,31392,31458],{},[38,31362,31363,31364,2196],{},"Odvození pro ",[883,31365,31367],{"className":31366},[886],[888,31368,31369],{"xmlns":890},[892,31370,31371,31389],{},[895,31372,31373,31375,31377,31383],{},[898,31374,900],{},[1700,31376,1765],{},[2007,31378,31379,31381],{},[898,31380,1662],{},[1931,31382,1933],{},[2007,31384,31385,31387],{},[898,31386,1662],{},[1931,31388,2343],{},[902,31390,30411],{"encoding":904}," Lagrangeova funkce ",[883,31393,31395],{"className":31394},[886],[888,31396,31397],{"xmlns":890},[892,31398,31399,31455],{},[895,31400,31401,31403,31405,31411,31417,31419,31421,31423,31425,31427,31433,31439,31441,31447,31453],{},[898,31402,1706],{"mathvariant":28733},[1700,31404,1765],{},[2007,31406,31407,31409],{},[898,31408,1662],{},[1931,31410,1933],{},[2007,31412,31413,31415],{},[898,31414,1662],{},[1931,31416,2343],{},[1700,31418,1897],{},[898,31420,16628],{},[1700,31422,1703],{"stretchy":1702},[898,31424,9316],{},[1700,31426,1768],{},[2007,31428,31429,31431],{},[898,31430,1677],{},[1931,31432,1933],{},[2007,31434,31435,31437],{},[898,31436,1662],{},[1931,31438,1933],{},[1700,31440,1768],{},[2007,31442,31443,31445],{},[898,31444,1677],{},[1931,31446,2343],{},[2007,31448,31449,31451],{},[898,31450,1662],{},[1931,31452,2343],{},[1700,31454,1709],{"stretchy":1702},[902,31456,31457],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,31460,31462],{"className":31461},[886],[888,31463,31464],{"xmlns":890,"display":28251},[892,31465,31466,31633],{},[20939,31467,31468],{"width":28256},[20944,31469,31470,31472,31626,31628],{},[20947,31471],{"width":28261},[20947,31473,31474],{},[20939,31475,31476,31522,31568],{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},[20944,31477,31478,31490],{},[20947,31479,31480],{},[1770,31481,31482],{"scriptlevel":1772,"displaystyle":1731},[2030,31483,31484,31486,31488],{},[898,31485,1706],{"mathvariant":28733},[1931,31487,1933],{},[1700,31489,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,31491,31492],{},[1770,31493,31494],{"scriptlevel":1772,"displaystyle":1731},[895,31495,31496,31498,31500,31506,31508,31510,31516,31518,31520],{},[895,31497],{},[1700,31499,1765],{},[2007,31501,31502,31504],{},[898,31503,1662],{},[1931,31505,2343],{},[1700,31507,1768],{},[898,31509,16628],{},[2007,31511,31512,31514],{},[898,31513,1677],{},[1931,31515,1933],{},[1700,31517,1765],{},[1931,31519,1772],{},[1700,31521,1732],{"separator":1731},[20944,31523,31524,31536],{},[20947,31525,31526],{},[1770,31527,31528],{"scriptlevel":1772,"displaystyle":1731},[2030,31529,31530,31532,31534],{},[898,31531,1706],{"mathvariant":28733},[1931,31533,2343],{},[1700,31535,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,31537,31538],{},[1770,31539,31540],{"scriptlevel":1772,"displaystyle":1731},[895,31541,31542,31544,31546,31552,31554,31556,31562,31564,31566],{},[895,31543],{},[1700,31545,1765],{},[2007,31547,31548,31550],{},[898,31549,1662],{},[1931,31551,1933],{},[1700,31553,1768],{},[898,31555,16628],{},[2007,31557,31558,31560],{},[898,31559,1677],{},[1931,31561,2343],{},[1700,31563,1765],{},[1931,31565,1772],{},[1700,31567,1732],{"separator":1731},[20944,31569,31570,31582],{},[20947,31571,31572],{},[1770,31573,31574],{"scriptlevel":1772,"displaystyle":1731},[2030,31575,31576,31578,31580],{},[898,31577,1706],{"mathvariant":28733},[898,31579,16628],{},[1700,31581,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,31583,31584],{},[1770,31585,31586],{"scriptlevel":1772,"displaystyle":1731},[895,31587,31588,31590,31592,31594,31596,31602,31608,31610,31616,31622,31624],{},[895,31589],{},[1700,31591,1765],{},[898,31593,9316],{},[1700,31595,1768],{},[2007,31597,31598,31600],{},[898,31599,1677],{},[1931,31601,1933],{},[2007,31603,31604,31606],{},[898,31605,1662],{},[1931,31607,1933],{},[1700,31609,1768],{},[2007,31611,31612,31614],{},[898,31613,1677],{},[1931,31615,2343],{},[2007,31617,31618,31620],{},[898,31619,1662],{},[1931,31621,2343],{},[1700,31623,1765],{},[1931,31625,12645],{},[20947,31627],{"width":28261},[20947,31629,31630],{},[1781,31631,31632],{},"(6.17)",[902,31634,31635],{"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}",[724,31637,31638,31639,31667,31668,31696,31697,31765],{},"Z prvních dvou: ",[883,31640,31642],{"className":31641},[886],[888,31643,31644],{"xmlns":890},[892,31645,31646,31664],{},[895,31647,31648,31654,31656,31662],{},[2007,31649,31650,31652],{},[898,31651,1662],{},[1931,31653,2343],{},[1700,31655,1765],{},[2007,31657,31658,31660],{},[898,31659,1677],{},[1931,31661,1933],{},[898,31663,16628],{},[902,31665,31666],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,31669,31671],{"className":31670},[886],[888,31672,31673],{"xmlns":890},[892,31674,31675,31693],{},[895,31676,31677,31683,31685,31691],{},[2007,31678,31679,31681],{},[898,31680,1662],{},[1931,31682,1933],{},[1700,31684,1765],{},[2007,31686,31687,31689],{},[898,31688,1677],{},[1931,31690,2343],{},[898,31692,16628],{},[902,31694,31695],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,31698,31700],{"className":31699},[886],[888,31701,31702],{"xmlns":890},[892,31703,31704,31762],{},[895,31705,31706,31708,31710,31716,31718,31724,31726,31728,31734,31736,31742,31744,31746,31748,31754,31760],{},[898,31707,9316],{},[1700,31709,1765],{},[2007,31711,31712,31714],{},[898,31713,1677],{},[1931,31715,1933],{},[1700,31717,2065],{},[2007,31719,31720,31722],{},[898,31721,1677],{},[1931,31723,2343],{},[898,31725,16628],{},[1700,31727,1897],{},[2007,31729,31730,31732],{},[898,31731,1677],{},[1931,31733,2343],{},[1700,31735,2065],{},[2007,31737,31738,31740],{},[898,31739,1677],{},[1931,31741,1933],{},[898,31743,16628],{},[1700,31745,1765],{},[1931,31747,2343],{},[2007,31749,31750,31752],{},[898,31751,1677],{},[1931,31753,1933],{},[2007,31755,31756,31758],{},[898,31757,1677],{},[1931,31759,2343],{},[898,31761,16628],{},[902,31763,31764],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,31767,31769],{"className":31768},[886],[888,31770,31771],{"xmlns":890,"display":28251},[892,31772,31773,31816],{},[20939,31774,31775],{"width":28256},[20944,31776,31777,31779,31809,31811],{},[20947,31778],{"width":28261},[20947,31780,31781],{},[895,31782,31783,31785,31787,31807],{},[898,31784,16628],{},[1700,31786,1765],{},[1774,31788,31789,31791],{},[898,31790,9316],{},[895,31792,31793,31795,31801],{},[1931,31794,2343],{},[2007,31796,31797,31799],{},[898,31798,1677],{},[1931,31800,1933],{},[2007,31802,31803,31805],{},[898,31804,1677],{},[1931,31806,2343],{},[898,31808,2196],{"mathvariant":1791},[20947,31810],{"width":28261},[20947,31812,31813],{},[1781,31814,31815],{},"(6.20)",[902,31817,31818],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,31820,31821],{},"Zpětně:",[883,31823,31825],{"className":31824},[886],[888,31826,31827],{"xmlns":890,"display":28251},[892,31828,31829,31906],{},[20939,31830,31831],{"width":28256},[20944,31832,31833,31835,31899,31901],{},[20947,31834],{"width":28261},[20947,31836,31837],{},[13017,31838,31839],{"notation":13019},[1770,31840,31841],{"scriptlevel":1772,"displaystyle":1702},[1770,31842,31843],{"scriptlevel":1772,"displaystyle":1702},[1770,31844,31845],{"scriptlevel":1772,"displaystyle":1731},[895,31846,31847,31849,31855,31857,31871,31873,31875,31881,31883,31897],{},[1781,31848,4175],{},[2007,31850,31851,31853],{},[898,31852,1662],{},[1931,31854,1933],{},[1700,31856,1765],{},[1774,31858,31859,31861],{},[898,31860,9316],{},[895,31862,31863,31865],{},[1931,31864,2343],{},[2007,31866,31867,31869],{},[898,31868,1677],{},[1931,31870,1933],{},[1700,31872,1732],{"separator":1731},[6066,31874],{"width":15469},[2007,31876,31877,31879],{},[898,31878,1662],{},[1931,31880,2343],{},[1700,31882,1765],{},[1774,31884,31885,31887],{},[898,31886,9316],{},[895,31888,31889,31891],{},[1931,31890,2343],{},[2007,31892,31893,31895],{},[898,31894,1677],{},[1931,31896,2343],{},[1781,31898,4175],{},[20947,31900],{"width":28261},[20947,31902,31903],{},[1781,31904,31905],{},"(6.21)",[902,31907,31908],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,31910,31912],{"id":31911},"engelova-funkce","Engelova funkce",[724,31914,9850,31915,31918,31919,31922,31923,20052,31940,1343,31970,32000,32001,32035,32036,1343,32062,32088],{},[38,31916,31917],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,31920,31921],{},"Engelovou funkcí",": pro ",[883,31924,31926],{"className":31925},[886],[888,31927,31928],{"xmlns":890},[892,31929,31930,31938],{},[895,31931,31932,31934,31936],{},[898,31933,9316],{},[1700,31935,1765],{},[1931,31937,3284],{},[902,31939,20504],{"encoding":904},[883,31941,31943],{"className":31942},[886],[888,31944,31945],{"xmlns":890},[892,31946,31947,31967],{},[895,31948,31949,31955,31957,31959,31961],{},[2007,31950,31951,31953],{},[898,31952,1662],{},[1931,31954,1933],{},[1700,31956,1765],{},[1931,31958,3314],{},[898,31960,1979],{"mathvariant":1791},[2007,31962,31963,31965],{},[898,31964,1677],{},[1931,31966,1933],{},[902,31968,31969],{"encoding":904},"Q_1 = 50\u002FP_1",[883,31971,31973],{"className":31972},[886],[888,31974,31975],{"xmlns":890},[892,31976,31977,31997],{},[895,31978,31979,31985,31987,31989,31991],{},[2007,31980,31981,31983],{},[898,31982,1662],{},[1931,31984,2343],{},[1700,31986,1765],{},[1931,31988,3314],{},[898,31990,1979],{"mathvariant":1791},[2007,31992,31993,31995],{},[898,31994,1677],{},[1931,31996,2343],{},[902,31998,31999],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,32002,32004],{"className":32003},[886],[888,32005,32006],{"xmlns":890},[892,32007,32008,32032],{},[895,32009,32010,32016,32018,32020,32022,32028,32030],{},[2007,32011,32012,32014],{},[898,32013,1677],{},[1931,32015,1933],{},[1700,32017,1765],{},[1931,32019,3058],{},[1700,32021,1732],{"separator":1731},[2007,32023,32024,32026],{},[898,32025,1677],{},[1931,32027,2343],{},[1700,32029,1765],{},[1931,32031,9223],{},[902,32033,32034],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,32037,32039],{"className":32038},[886],[888,32040,32041],{"xmlns":890},[892,32042,32043,32059],{},[895,32044,32045,32051,32053,32055,32057],{},[2007,32046,32047,32049],{},[898,32048,1662],{},[1931,32050,1933],{},[1700,32052,1765],{},[898,32054,9316],{},[898,32056,1979],{"mathvariant":1791},[1931,32058,9223],{},[902,32060,32061],{"encoding":904},"Q_1 = Y\u002F20",[883,32063,32065],{"className":32064},[886],[888,32066,32067],{"xmlns":890},[892,32068,32069,32085],{},[895,32070,32071,32077,32079,32081,32083],{},[2007,32072,32073,32075],{},[898,32074,1662],{},[1931,32076,2343],{},[1700,32078,1765],{},[898,32080,9316],{},[898,32082,1979],{"mathvariant":1791},[1931,32084,5399],{},[902,32086,32087],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,32090,32092],{"id":32091},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,32094,32095],{},"Výdaje spotřebitele jsou",[883,32097,32099],{"className":32098},[886],[888,32100,32101],{"xmlns":890,"display":28251},[892,32102,32103,32178],{},[20939,32104,32105],{"width":28256},[20944,32106,32107,32109,32171,32173],{},[20947,32108],{"width":28261},[20947,32110,32111],{},[895,32112,32113,32115,32117,32119,32121,32127,32129,32135,32137,32139,32147,32153,32155,32163,32169],{},[898,32114,1762],{},[1700,32116,1765],{},[898,32118,1762],{},[1700,32120,1703],{"stretchy":1702},[2007,32122,32123,32125],{},[898,32124,1662],{},[1931,32126,1933],{},[1700,32128,1732],{"separator":1731},[2007,32130,32131,32133],{},[898,32132,1662],{},[1931,32134,2343],{},[1700,32136,1709],{"stretchy":1702},[1700,32138,1765],{},[2030,32140,32141,32143,32145],{},[898,32142,1677],{},[1931,32144,1933],{},[1700,32146,4543],{},[2007,32148,32149,32151],{},[898,32150,1662],{},[1931,32152,1933],{},[1700,32154,1897],{},[2030,32156,32157,32159,32161],{},[898,32158,1677],{},[1931,32160,2343],{},[1700,32162,4543],{},[2007,32164,32165,32167],{},[898,32166,1662],{},[1931,32168,2343],{},[1700,32170,1732],{"separator":1731},[20947,32172],{"width":28261},[20947,32174,32175],{},[1781,32176,32177],{},"(6.22)",[902,32179,32180],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,32182,32183],{},"a je pevně zadána hladina užitečnosti",[883,32185,32187],{"className":32186},[886],[888,32188,32189],{"xmlns":890,"display":28251},[892,32190,32191,32238],{},[20939,32192,32193],{"width":28256},[20944,32194,32195,32197,32231,32233],{},[20947,32196],{"width":28261},[20947,32198,32199],{},[895,32200,32201,32207,32209,32211,32213,32219,32221,32227,32229],{},[1785,32202,32203,32205],{},[898,32204,900],{},[1700,32206,4543],{},[1700,32208,1765],{},[898,32210,900],{},[1700,32212,1703],{"stretchy":1702},[2007,32214,32215,32217],{},[898,32216,1662],{},[1931,32218,1933],{},[1700,32220,1732],{"separator":1731},[2007,32222,32223,32225],{},[898,32224,1662],{},[1931,32226,2343],{},[1700,32228,1709],{"stretchy":1702},[898,32230,2196],{"mathvariant":1791},[20947,32232],{"width":28261},[20947,32234,32235],{},[1781,32236,32237],{},"(6.23)",[902,32239,32240],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,32242,32243,32246,32247,32279,32280,2196],{},[38,32244,32245],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,32248,32250],{"className":32249},[886],[888,32251,32252],{"xmlns":890},[892,32253,32254,32276],{},[895,32255,32256,32258,32260,32266,32268,32274],{},[898,32257,1762],{},[1700,32259,1703],{"stretchy":1702},[2007,32261,32262,32264],{},[898,32263,1662],{},[1931,32265,1933],{},[1700,32267,1732],{"separator":1731},[2007,32269,32270,32272],{},[898,32271,1662],{},[1931,32273,2343],{},[1700,32275,1709],{"stretchy":1702},[902,32277,32278],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,32281,32283],{"className":32282},[886],[888,32284,32285],{"xmlns":890},[892,32286,32287,32343],{},[895,32288,32289,32291,32293,32299,32301,32307,32309,32311,32317,32319,32321,32323,32329,32331,32337,32339,32341],{},[898,32290,11224],{},[1700,32292,1703],{"stretchy":1702},[2007,32294,32295,32297],{},[898,32296,1662],{},[1931,32298,1933],{},[1700,32300,1732],{"separator":1731},[2007,32302,32303,32305],{},[898,32304,1662],{},[1931,32306,2343],{},[1700,32308,1709],{"stretchy":1702},[1700,32310,1765],{},[1785,32312,32313,32315],{},[898,32314,900],{},[1700,32316,4543],{},[1700,32318,1768],{},[898,32320,900],{},[1700,32322,1703],{"stretchy":1702},[2007,32324,32325,32327],{},[898,32326,1662],{},[1931,32328,1933],{},[1700,32330,1732],{"separator":1731},[2007,32332,32333,32335],{},[898,32334,1662],{},[1931,32336,2343],{},[1700,32338,1709],{"stretchy":1702},[1700,32340,1765],{},[1931,32342,1772],{},[902,32344,32345],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,32347,32349],{"id":32348},"lagrangeova-funkce","Lagrangeova funkce",[883,32351,32353],{"className":32352},[886],[888,32354,32355],{"xmlns":890,"display":28251},[892,32356,32357,32468],{},[20939,32358,32359],{"width":28256},[20944,32360,32361,32363,32461,32463],{},[20947,32362],{"width":28261},[20947,32364,32365],{},[895,32366,32367,32369,32371,32377,32379,32385,32387,32389,32391,32393,32401,32407,32409,32417,32423,32425,32427,32429,32435,32437,32439,32441,32447,32449,32455,32457,32459],{},[898,32368,1706],{"mathvariant":28733},[1700,32370,1703],{"stretchy":1702},[2007,32372,32373,32375],{},[898,32374,1662],{},[1931,32376,1933],{},[1700,32378,1732],{"separator":1731},[2007,32380,32381,32383],{},[898,32382,1662],{},[1931,32384,2343],{},[1700,32386,1732],{"separator":1731},[898,32388,16628],{},[1700,32390,1709],{"stretchy":1702},[1700,32392,1765],{},[2030,32394,32395,32397,32399],{},[898,32396,1677],{},[1931,32398,1933],{},[1700,32400,4543],{},[2007,32402,32403,32405],{},[898,32404,1662],{},[1931,32406,1933],{},[1700,32408,1897],{},[2030,32410,32411,32413,32415],{},[898,32412,1677],{},[1931,32414,2343],{},[1700,32416,4543],{},[2007,32418,32419,32421],{},[898,32420,1662],{},[1931,32422,2343],{},[1700,32424,1897],{},[898,32426,16628],{},[1700,32428,1703],{"stretchy":1702},[1785,32430,32431,32433],{},[898,32432,900],{},[1700,32434,4543],{},[1700,32436,1768],{},[898,32438,900],{},[1700,32440,1703],{"stretchy":1702},[2007,32442,32443,32445],{},[898,32444,1662],{},[1931,32446,1933],{},[1700,32448,1732],{"separator":1731},[2007,32450,32451,32453],{},[898,32452,1662],{},[1931,32454,2343],{},[1700,32456,1709],{"stretchy":1702},[1700,32458,1709],{"stretchy":1702},[898,32460,2196],{"mathvariant":1791},[20947,32462],{"width":28261},[20947,32464,32465],{},[1781,32466,32467],{},"(6.24)",[902,32469,32470],{"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}",[724,32472,32473],{},"Soustava podmínek prvního řádu:",[883,32475,32477],{"className":32476},[886],[888,32478,32479],{"xmlns":890,"display":28251},[892,32480,32481,32654],{},[20939,32482,32483],{"width":28256},[20944,32484,32485,32487,32647,32649],{},[20947,32486],{"width":28261},[20947,32488,32489],{},[20939,32490,32491,32541,32591],{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},[20944,32492,32493,32505],{},[20947,32494,32495],{},[1770,32496,32497],{"scriptlevel":1772,"displaystyle":1731},[2030,32498,32499,32501,32503],{},[898,32500,1706],{"mathvariant":28733},[1931,32502,1933],{},[1700,32504,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,32506,32507],{},[1770,32508,32509],{"scriptlevel":1772,"displaystyle":1731},[895,32510,32511,32513,32515,32523,32525,32527,32535,32537,32539],{},[895,32512],{},[1700,32514,1765],{},[2030,32516,32517,32519,32521],{},[898,32518,1677],{},[1931,32520,1933],{},[1700,32522,4543],{},[1700,32524,1768],{},[898,32526,16628],{},[2030,32528,32529,32531,32533],{},[898,32530,900],{},[1931,32532,1933],{},[1700,32534,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,32536,1765],{},[1931,32538,1772],{},[1700,32540,1732],{"separator":1731},[20944,32542,32543,32555],{},[20947,32544,32545],{},[1770,32546,32547],{"scriptlevel":1772,"displaystyle":1731},[2030,32548,32549,32551,32553],{},[898,32550,1706],{"mathvariant":28733},[1931,32552,2343],{},[1700,32554,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,32556,32557],{},[1770,32558,32559],{"scriptlevel":1772,"displaystyle":1731},[895,32560,32561,32563,32565,32573,32575,32577,32585,32587,32589],{},[895,32562],{},[1700,32564,1765],{},[2030,32566,32567,32569,32571],{},[898,32568,1677],{},[1931,32570,2343],{},[1700,32572,4543],{},[1700,32574,1768],{},[898,32576,16628],{},[2030,32578,32579,32581,32583],{},[898,32580,900],{},[1931,32582,2343],{},[1700,32584,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,32586,1765],{},[1931,32588,1772],{},[1700,32590,1732],{"separator":1731},[20944,32592,32593,32605],{},[20947,32594,32595],{},[1770,32596,32597],{"scriptlevel":1772,"displaystyle":1731},[2030,32598,32599,32601,32603],{},[898,32600,1706],{"mathvariant":28733},[898,32602,16628],{},[1700,32604,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,32606,32607],{},[1770,32608,32609],{"scriptlevel":1772,"displaystyle":1731},[895,32610,32611,32613,32615,32621,32623,32625,32627,32633,32635,32641,32643,32645],{},[895,32612],{},[1700,32614,1765],{},[1785,32616,32617,32619],{},[898,32618,900],{},[1700,32620,4543],{},[1700,32622,1768],{},[898,32624,900],{},[1700,32626,1703],{"stretchy":1702},[2007,32628,32629,32631],{},[898,32630,1662],{},[1931,32632,1933],{},[1700,32634,1732],{"separator":1731},[2007,32636,32637,32639],{},[898,32638,1662],{},[1931,32640,2343],{},[1700,32642,1709],{"stretchy":1702},[1700,32644,1765],{},[1931,32646,12645],{},[20947,32648],{"width":28261},[20947,32650,32651],{},[1781,32652,32653],{},"(6.25)",[902,32655,32656],{"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}",[724,32658,32659],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,32661,32663],{"className":32662},[886],[888,32664,32665],{"xmlns":890,"display":28251},[892,32666,32667,32765],{},[20939,32668,32669],{"width":28256},[20944,32670,32671,32673,32758,32760],{},[20947,32672],{"width":28261},[20947,32674,32675],{},[895,32676,32677,32679,32681,32687,32689,32695,32697,32699,32701,32703,32705,32707,32756],{},[898,32678,4374],{},[1700,32680,1703],{"stretchy":1702},[2007,32682,32683,32685],{},[898,32684,1662],{},[1931,32686,1933],{},[1700,32688,1732],{"separator":1731},[2007,32690,32691,32693],{},[898,32692,1662],{},[1931,32694,2343],{},[1700,32696,1732],{"separator":1731},[898,32698,16628],{},[1700,32700,1709],{"stretchy":1702},[1700,32702,1765],{},[1700,32704,1768],{},[898,32706,16628],{},[895,32708,32709,32711,32723,32725,32738,32740,32742,32754],{},[1700,32710,1703],{"fence":1731},[2030,32712,32713,32715,32717],{},[898,32714,900],{},[1931,32716,3099],{},[895,32718,32719,32721],{},[1700,32720,1793],{"mathvariant":1791},[1700,32722,1793],{"mathvariant":1791},[1700,32724,1897],{},[2030,32726,32727,32729,32732],{},[898,32728,900],{},[1931,32730,32731],{},"22",[895,32733,32734,32736],{},[1700,32735,1793],{"mathvariant":1791},[1700,32737,1793],{"mathvariant":1791},[1700,32739,1897],{},[1931,32741,2343],{},[2030,32743,32744,32746,32748],{},[898,32745,900],{},[1931,32747,3702],{},[895,32749,32750,32752],{},[1700,32751,1793],{"mathvariant":1791},[1700,32753,1793],{"mathvariant":1791},[1700,32755,1709],{"fence":1731},[898,32757,2196],{"mathvariant":1791},[20947,32759],{"width":28261},[20947,32761,32762],{},[1781,32763,32764],{},"(6.26)",[902,32766,32767],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,32769,32770,32773,32774,32813,32814,32853,32854,32904,32905,32931,32932,32949,32950,32976],{},[38,32771,32772],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,32775,32777],{"className":32776},[886],[888,32778,32779],{"xmlns":890},[892,32780,32781,32811],{},[895,32782,32783,32789,32791,32799,32801,32809],{},[1785,32784,32785,32787],{},[898,32786,1662],{},[1700,32788,4543],{},[1700,32790,1927],{"stretchy":1702},[2030,32792,32793,32795,32797],{},[898,32794,1662],{},[1931,32796,1933],{},[1700,32798,4543],{},[1700,32800,1732],{"separator":1731},[2030,32802,32803,32805,32807],{},[898,32804,1662],{},[1931,32806,2343],{},[1700,32808,4543],{},[1700,32810,1970],{"stretchy":1702},[902,32812,28512],{"encoding":904}," dotyku křivky užitečnosti ",[883,32815,32817],{"className":32816},[886],[888,32818,32819],{"xmlns":890},[892,32820,32821,32851],{},[895,32822,32823,32829,32831,32833,32835,32841,32843,32849],{},[1785,32824,32825,32827],{},[898,32826,900],{},[1700,32828,4543],{},[1700,32830,1765],{},[898,32832,900],{},[1700,32834,1703],{"stretchy":1702},[2007,32836,32837,32839],{},[898,32838,1662],{},[1931,32840,1933],{},[1700,32842,1732],{"separator":1731},[2007,32844,32845,32847],{},[898,32846,1662],{},[1931,32848,2343],{},[1700,32850,1709],{"stretchy":1702},[902,32852,17850],{"encoding":904}," s přímkou výdajů ",[883,32855,32857],{"className":32856},[886],[888,32858,32859],{"xmlns":890},[892,32860,32861,32901],{},[895,32862,32863,32869,32871,32879,32885,32887,32895],{},[1785,32864,32865,32867],{},[898,32866,1762],{},[1700,32868,4543],{},[1700,32870,1765],{},[2030,32872,32873,32875,32877],{},[898,32874,1677],{},[1931,32876,1933],{},[1700,32878,4543],{},[2007,32880,32881,32883],{},[898,32882,1662],{},[1931,32884,1933],{},[1700,32886,1897],{},[2030,32888,32889,32891,32893],{},[898,32890,1677],{},[1931,32892,2343],{},[1700,32894,4543],{},[2007,32896,32897,32899],{},[898,32898,1662],{},[1931,32900,2343],{},[902,32902,32903],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,32906,32908],{"className":32907},[886],[888,32909,32910],{"xmlns":890},[892,32911,32912,32928],{},[895,32913,32914,32920,32922],{},[2007,32915,32916,32918],{},[898,32917,1762],{},[1931,32919,1772],{},[1700,32921,3640],{},[1785,32923,32924,32926],{},[898,32925,1762],{},[1700,32927,4543],{},[902,32929,32930],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,32933,32935],{"className":32934},[886],[888,32936,32937],{"xmlns":890},[892,32938,32939,32947],{},[895,32940,32941],{},[1785,32942,32943,32945],{},[898,32944,900],{},[1700,32946,4543],{},[902,32948,28147],{"encoding":904},", hladina ",[883,32951,32953],{"className":32952},[886],[888,32954,32955],{"xmlns":890},[892,32956,32957,32973],{},[895,32958,32959,32965,32967],{},[2007,32960,32961,32963],{},[898,32962,1762],{},[1931,32964,1933],{},[1700,32966,3601],{},[1785,32968,32969,32971],{},[898,32970,1762],{},[1700,32972,4543],{},[902,32974,32975],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[4060,32978,32979,32984],{},[724,32980,32981,32983],{},[883,32982,4761],{}," Postup — duální úloha (minimalizace výdajů)",[152,32985,32986,33036,33122,33162,33237],{},[123,32987,32988,2106,32991,33035],{},[38,32989,32990],{},"Zapiš vazbu",[883,32992,32994],{"className":32993},[886],[888,32995,32996],{"xmlns":890},[892,32997,32998,33032],{},[895,32999,33000,33006,33008,33010,33012,33018,33020,33026,33028,33030],{},[1785,33001,33002,33004],{},[898,33003,900],{},[1700,33005,4543],{},[1700,33007,1768],{},[898,33009,900],{},[1700,33011,1703],{"stretchy":1702},[2007,33013,33014,33016],{},[898,33015,1662],{},[1931,33017,1933],{},[1700,33019,1732],{"separator":1731},[2007,33021,33022,33024],{},[898,33023,1662],{},[1931,33025,2343],{},[1700,33027,1709],{"stretchy":1702},[1700,33029,1765],{},[1931,33031,1772],{},[902,33033,33034],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,33037,33038,2106,33040,2196],{},[38,33039,29445],{},[883,33041,33043],{"className":33042},[886],[888,33044,33045],{"xmlns":890},[892,33046,33047,33119],{},[895,33048,33049,33051,33053,33061,33067,33069,33077,33083,33085,33087,33089,33095,33097,33099,33101,33107,33109,33115,33117],{},[898,33050,1706],{"mathvariant":28733},[1700,33052,1765],{},[2030,33054,33055,33057,33059],{},[898,33056,1677],{},[1931,33058,1933],{},[1700,33060,4543],{},[2007,33062,33063,33065],{},[898,33064,1662],{},[1931,33066,1933],{},[1700,33068,1897],{},[2030,33070,33071,33073,33075],{},[898,33072,1677],{},[1931,33074,2343],{},[1700,33076,4543],{},[2007,33078,33079,33081],{},[898,33080,1662],{},[1931,33082,2343],{},[1700,33084,1897],{},[898,33086,16628],{},[1700,33088,1703],{"stretchy":1702},[1785,33090,33091,33093],{},[898,33092,900],{},[1700,33094,4543],{},[1700,33096,1768],{},[898,33098,900],{},[1700,33100,1703],{"stretchy":1702},[2007,33102,33103,33105],{},[898,33104,1662],{},[1931,33106,1933],{},[1700,33108,1732],{"separator":1731},[2007,33110,33111,33113],{},[898,33112,1662],{},[1931,33114,2343],{},[1700,33116,1709],{"stretchy":1702},[1700,33118,1709],{"stretchy":1702},[902,33120,33121],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,33123,33124,33127,33128,33161],{},[38,33125,33126],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,33129,33131],{"className":33130},[886],[888,33132,33133],{"xmlns":890},[892,33134,33135,33159],{},[895,33136,33137,33139,33141,33149,33151],{},[1781,33138,10786],{},[1700,33140,1765],{},[2030,33142,33143,33145,33147],{},[898,33144,1677],{},[1931,33146,1933],{},[1700,33148,4543],{},[898,33150,1979],{"mathvariant":1791},[2030,33152,33153,33155,33157],{},[898,33154,1677],{},[1931,33156,2343],{},[1700,33158,4543],{},[902,33160,29164],{"encoding":904}," (stejná jako u maximalizace!).",[123,33163,33164,2106,33167,33207,33208,2196],{},[38,33165,33166],{},"Dosaď do vazby",[883,33168,33170],{"className":33169},[886],[888,33171,33172],{"xmlns":890},[892,33173,33174,33204],{},[895,33175,33176,33178,33180,33186,33188,33194,33196,33198],{},[898,33177,900],{},[1700,33179,1703],{"stretchy":1702},[2007,33181,33182,33184],{},[898,33183,1662],{},[1931,33185,1933],{},[1700,33187,1732],{"separator":1731},[2007,33189,33190,33192],{},[898,33191,1662],{},[1931,33193,2343],{},[1700,33195,1709],{"stretchy":1702},[1700,33197,1765],{},[1785,33199,33200,33202],{},[898,33201,900],{},[1700,33203,4543],{},[902,33205,33206],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,33209,33211],{"className":33210},[886],[888,33212,33213],{"xmlns":890},[892,33214,33215,33235],{},[895,33216,33217,33225,33227],{},[2030,33218,33219,33221,33223],{},[898,33220,1662],{},[1931,33222,1933],{},[1700,33224,4543],{},[1700,33226,1732],{"separator":1731},[2030,33228,33229,33231,33233],{},[898,33230,1662],{},[1931,33232,2343],{},[1700,33234,4543],{},[902,33236,29686],{"encoding":904},[123,33238,33239,2106,33242,33296],{},[38,33240,33241],{},"Vypočítej minimální výdaje",[883,33243,33245],{"className":33244},[886],[888,33246,33247],{"xmlns":890},[892,33248,33249,33293],{},[895,33250,33251,33257,33259,33267,33275,33277,33285],{},[1785,33252,33253,33255],{},[898,33254,1762],{},[1700,33256,4543],{},[1700,33258,1765],{},[2030,33260,33261,33263,33265],{},[898,33262,1677],{},[1931,33264,1933],{},[1700,33266,4543],{},[2030,33268,33269,33271,33273],{},[898,33270,1662],{},[1931,33272,1933],{},[1700,33274,4543],{},[1700,33276,1897],{},[2030,33278,33279,33281,33283],{},[898,33280,1677],{},[1931,33282,2343],{},[1700,33284,4543],{},[2030,33286,33287,33289,33291],{},[898,33288,1662],{},[1931,33290,2343],{},[1700,33292,4543],{},[902,33294,33295],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,33298,33300,33301],{"id":33299},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,33302,33304],{"className":33303},[886],[888,33305,33306],{"xmlns":890},[892,33307,33308,33342],{},[895,33309,33310,33312,33314,33328],{},[898,33311,900],{},[1700,33313,1765],{},[2030,33315,33316,33318,33320],{},[898,33317,1662],{},[1931,33319,1933],{},[895,33321,33322,33324,33326],{},[1931,33323,1933],{},[898,33325,1979],{"mathvariant":1791},[1931,33327,2343],{},[2030,33329,33330,33332,33334],{},[898,33331,1662],{},[1931,33333,2343],{},[895,33335,33336,33338,33340],{},[1931,33337,1933],{},[898,33339,1979],{"mathvariant":1791},[1931,33341,2343],{},[902,33343,33344],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,33346,33347,33348,1343,33370,1343,33394,30531],{},"Dáno ",[883,33349,33351],{"className":33350},[886],[888,33352,33353],{"xmlns":890},[892,33354,33355,33367],{},[895,33356,33357,33363,33365],{},[1785,33358,33359,33361],{},[898,33360,900],{},[1700,33362,4543],{},[1700,33364,1765],{},[1931,33366,2343],{},[902,33368,33369],{"encoding":904},"U^* = 2",[883,33371,33373],{"className":33372},[886],[888,33374,33375],{"xmlns":890},[892,33376,33377,33391],{},[895,33378,33379,33387,33389],{},[2030,33380,33381,33383,33385],{},[898,33382,1677],{},[1931,33384,1933],{},[1700,33386,4543],{},[1700,33388,1765],{},[1931,33390,23974],{},[902,33392,33393],{"encoding":904},"P_1^* = 0{,}25",[883,33395,33397],{"className":33396},[886],[888,33398,33399],{"xmlns":890},[892,33400,33401,33415],{},[895,33402,33403,33411,33413],{},[2030,33404,33405,33407,33409],{},[898,33406,1677],{},[1931,33408,2343],{},[1700,33410,4543],{},[1700,33412,1765],{},[1931,33414,1933],{},[902,33416,33417],{"encoding":904},"P_2^* = 1",[883,33419,33421],{"className":33420},[886],[888,33422,33423],{"xmlns":890,"display":28251},[892,33424,33425,33489],{},[895,33426,33427,33429,33431,33433,33439,33441,33447,33449,33451,33453,33455,33457,33471,33485,33487],{},[898,33428,1706],{"mathvariant":28733},[1700,33430,1765],{},[1931,33432,23974],{},[2007,33434,33435,33437],{},[898,33436,1662],{},[1931,33438,1933],{},[1700,33440,1897],{},[2007,33442,33443,33445],{},[898,33444,1662],{},[1931,33446,2343],{},[1700,33448,1897],{},[898,33450,16628],{},[1700,33452,1703],{"stretchy":1702},[1931,33454,2343],{},[1700,33456,1768],{},[2030,33458,33459,33461,33463],{},[898,33460,1662],{},[1931,33462,1933],{},[895,33464,33465,33467,33469],{},[1931,33466,1933],{},[898,33468,1979],{"mathvariant":1791},[1931,33470,2343],{},[2030,33472,33473,33475,33477],{},[898,33474,1662],{},[1931,33476,2343],{},[895,33478,33479,33481,33483],{},[1931,33480,1933],{},[898,33482,1979],{"mathvariant":1791},[1931,33484,2343],{},[1700,33486,1709],{"stretchy":1702},[898,33488,2196],{"mathvariant":1791},[902,33490,33491],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,33493,30616],{},[883,33495,33497],{"className":33496},[886],[888,33498,33499],{"xmlns":890,"display":28251},[892,33500,33501,33715],{},[20939,33502,33503,33579,33655],{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},[20944,33504,33505,33517],{},[20947,33506,33507],{},[1770,33508,33509],{"scriptlevel":1772,"displaystyle":1731},[2030,33510,33511,33513,33515],{},[898,33512,1706],{"mathvariant":28733},[1931,33514,1933],{},[1700,33516,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,33518,33519],{},[1770,33520,33521],{"scriptlevel":1772,"displaystyle":1731},[895,33522,33523,33525,33527,33529,33531,33533,33535,33543,33559,33573,33575,33577],{},[895,33524],{},[1700,33526,1765],{},[1931,33528,23974],{},[1700,33530,1768],{},[898,33532,16628],{},[1700,33534,2065],{},[1770,33536,33537],{"scriptlevel":1772,"displaystyle":1702},[1774,33538,33539,33541],{},[1931,33540,1933],{},[1931,33542,2343],{},[2030,33544,33545,33547,33549],{},[898,33546,1662],{},[1931,33548,1933],{},[895,33550,33551,33553,33555,33557],{},[1700,33552,1768],{},[1931,33554,1933],{},[898,33556,1979],{"mathvariant":1791},[1931,33558,2343],{},[2030,33560,33561,33563,33565],{},[898,33562,1662],{},[1931,33564,2343],{},[895,33566,33567,33569,33571],{},[1931,33568,1933],{},[898,33570,1979],{"mathvariant":1791},[1931,33572,2343],{},[1700,33574,1765],{},[1931,33576,1772],{},[1700,33578,1732],{"separator":1731},[20944,33580,33581,33593],{},[20947,33582,33583],{},[1770,33584,33585],{"scriptlevel":1772,"displaystyle":1731},[2030,33586,33587,33589,33591],{},[898,33588,1706],{"mathvariant":28733},[1931,33590,2343],{},[1700,33592,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,33594,33595],{},[1770,33596,33597],{"scriptlevel":1772,"displaystyle":1731},[895,33598,33599,33601,33603,33605,33607,33609,33611,33619,33633,33649,33651,33653],{},[895,33600],{},[1700,33602,1765],{},[1931,33604,1933],{},[1700,33606,1768],{},[898,33608,16628],{},[1700,33610,2065],{},[1770,33612,33613],{"scriptlevel":1772,"displaystyle":1702},[1774,33614,33615,33617],{},[1931,33616,1933],{},[1931,33618,2343],{},[2030,33620,33621,33623,33625],{},[898,33622,1662],{},[1931,33624,1933],{},[895,33626,33627,33629,33631],{},[1931,33628,1933],{},[898,33630,1979],{"mathvariant":1791},[1931,33632,2343],{},[2030,33634,33635,33637,33639],{},[898,33636,1662],{},[1931,33638,2343],{},[895,33640,33641,33643,33645,33647],{},[1700,33642,1768],{},[1931,33644,1933],{},[898,33646,1979],{"mathvariant":1791},[1931,33648,2343],{},[1700,33650,1765],{},[1931,33652,1772],{},[1700,33654,1732],{"separator":1731},[20944,33656,33657,33669],{},[20947,33658,33659],{},[1770,33660,33661],{"scriptlevel":1772,"displaystyle":1731},[2030,33662,33663,33665,33667],{},[898,33664,1706],{"mathvariant":28733},[898,33666,16628],{},[1700,33668,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,33670,33671],{},[1770,33672,33673],{"scriptlevel":1772,"displaystyle":1731},[895,33674,33675,33677,33679,33681,33683,33697,33711,33713],{},[895,33676],{},[1700,33678,1765],{},[1931,33680,2343],{},[1700,33682,1768],{},[2030,33684,33685,33687,33689],{},[898,33686,1662],{},[1931,33688,1933],{},[895,33690,33691,33693,33695],{},[1931,33692,1933],{},[898,33694,1979],{"mathvariant":1791},[1931,33696,2343],{},[2030,33698,33699,33701,33703],{},[898,33700,1662],{},[1931,33702,2343],{},[895,33704,33705,33707,33709],{},[1931,33706,1933],{},[898,33708,1979],{"mathvariant":1791},[1931,33710,2343],{},[1700,33712,1765],{},[1931,33714,12645],{},[902,33716,33717],{"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}",[724,33719,33720,33721,17761,33751,33779,33780,5777,33842,1343,33892,33914,33915,2196],{},"Podílem prvních dvou rovnic: ",[883,33722,33724],{"className":33723},[886],[888,33725,33726],{"xmlns":890},[892,33727,33728,33748],{},[895,33729,33730,33732,33734,33740,33742],{},[1931,33731,23974],{},[1700,33733,1765],{},[2007,33735,33736,33738],{},[898,33737,1662],{},[1931,33739,2343],{},[898,33741,1979],{"mathvariant":1791},[2007,33743,33744,33746],{},[898,33745,1662],{},[1931,33747,1933],{},[902,33749,33750],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,33752,33754],{"className":33753},[886],[888,33755,33756],{"xmlns":890},[892,33757,33758,33776],{},[895,33759,33760,33766,33768,33770],{},[2007,33761,33762,33764],{},[898,33763,1662],{},[1931,33765,2343],{},[1700,33767,1765],{},[1931,33769,23974],{},[2007,33771,33772,33774],{},[898,33773,1662],{},[1931,33775,1933],{},[902,33777,33778],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,33781,33783],{"className":33782},[886],[888,33784,33785],{"xmlns":890},[892,33786,33787,33839],{},[895,33788,33789,33803,33805,33807,33813,33825,33827,33829,33835,33837],{},[2030,33790,33791,33793,33795],{},[898,33792,1662],{},[1931,33794,1933],{},[895,33796,33797,33799,33801],{},[1931,33798,1933],{},[898,33800,1979],{"mathvariant":1791},[1931,33802,2343],{},[1700,33804,1703],{"stretchy":1702},[1931,33806,23974],{},[2007,33808,33809,33811],{},[898,33810,1662],{},[1931,33812,1933],{},[1785,33814,33815,33817],{},[1700,33816,1709],{"stretchy":1702},[895,33818,33819,33821,33823],{},[1931,33820,1933],{},[898,33822,1979],{"mathvariant":1791},[1931,33824,2343],{},[1700,33826,1765],{},[1931,33828,5197],{},[2007,33830,33831,33833],{},[898,33832,1662],{},[1931,33834,1933],{},[1700,33836,1765],{},[1931,33838,2343],{},[902,33840,33841],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,33843,33844,1343,33868],{},[883,33845,33847],{"className":33846},[886],[888,33848,33849],{"xmlns":890},[892,33850,33851,33865],{},[895,33852,33853,33861,33863],{},[2030,33854,33855,33857,33859],{},[898,33856,1662],{},[1931,33858,1933],{},[1700,33860,4543],{},[1700,33862,1765],{},[1931,33864,2553],{},[902,33866,33867],{"encoding":904},"Q_1^* = 4",[883,33869,33871],{"className":33870},[886],[888,33872,33873],{"xmlns":890},[892,33874,33875,33889],{},[895,33876,33877,33885,33887],{},[2030,33878,33879,33881,33883],{},[898,33880,1662],{},[1931,33882,2343],{},[1700,33884,4543],{},[1700,33886,1765],{},[1931,33888,1933],{},[902,33890,33891],{"encoding":904},"Q_2^* = 1",[883,33893,33895],{"className":33894},[886],[888,33896,33897],{"xmlns":890},[892,33898,33899,33911],{},[895,33900,33901,33907,33909],{},[1785,33902,33903,33905],{},[898,33904,16628],{},[1700,33906,4543],{},[1700,33908,1765],{},[1931,33910,1933],{},[902,33912,33913],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,33916,33918],{"className":33917},[886],[888,33919,33920],{"xmlns":890},[892,33921,33922,33950],{},[895,33923,33924,33930,33932,33934,33936,33938,33940,33942,33944,33946,33948],{},[1785,33925,33926,33928],{},[898,33927,1762],{},[1700,33929,4543],{},[1700,33931,1765],{},[1931,33933,23974],{},[1700,33935,2065],{},[1931,33937,2553],{},[1700,33939,1897],{},[1931,33941,1933],{},[1700,33943,2065],{},[1931,33945,1933],{},[1700,33947,1765],{},[1931,33949,2343],{},[902,33951,33952],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,33954,33955,33958,33959,1343,34025,1343,34091,34157,34158,34195,34196,34218,34219,2196],{},[614,33956,33957],{},"Ověření postačující podmínky"," (6.26): ",[883,33960,33962],{"className":33961},[886],[888,33963,33964],{"xmlns":890},[892,33965,33966,34022],{},[895,33967,33968,33980,33982,33984,33992,34008],{},[2030,33969,33970,33972,33974],{},[898,33971,900],{},[1931,33973,3099],{},[895,33975,33976,33978],{},[1700,33977,1793],{"mathvariant":1791},[1700,33979,1793],{"mathvariant":1791},[1700,33981,1765],{},[1700,33983,1768],{},[1770,33985,33986],{"scriptlevel":1772,"displaystyle":1702},[1774,33987,33988,33990],{},[1931,33989,1933],{},[1931,33991,2553],{},[2030,33993,33994,33996,33998],{},[898,33995,1662],{},[1931,33997,1933],{},[895,33999,34000,34002,34004,34006],{},[1700,34001,1768],{},[1931,34003,2385],{},[898,34005,1979],{"mathvariant":1791},[1931,34007,2343],{},[2030,34009,34010,34012,34014],{},[898,34011,1662],{},[1931,34013,2343],{},[895,34015,34016,34018,34020],{},[1931,34017,1933],{},[898,34019,1979],{"mathvariant":1791},[1931,34021,2343],{},[902,34023,34024],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,34026,34028],{"className":34027},[886],[888,34029,34030],{"xmlns":890},[892,34031,34032,34088],{},[895,34033,34034,34046,34048,34050,34058,34072],{},[2030,34035,34036,34038,34040],{},[898,34037,900],{},[1931,34039,32731],{},[895,34041,34042,34044],{},[1700,34043,1793],{"mathvariant":1791},[1700,34045,1793],{"mathvariant":1791},[1700,34047,1765],{},[1700,34049,1768],{},[1770,34051,34052],{"scriptlevel":1772,"displaystyle":1702},[1774,34053,34054,34056],{},[1931,34055,1933],{},[1931,34057,2553],{},[2030,34059,34060,34062,34064],{},[898,34061,1662],{},[1931,34063,1933],{},[895,34065,34066,34068,34070],{},[1931,34067,1933],{},[898,34069,1979],{"mathvariant":1791},[1931,34071,2343],{},[2030,34073,34074,34076,34078],{},[898,34075,1662],{},[1931,34077,2343],{},[895,34079,34080,34082,34084,34086],{},[1700,34081,1768],{},[1931,34083,2385],{},[898,34085,1979],{"mathvariant":1791},[1931,34087,2343],{},[902,34089,34090],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,34092,34094],{"className":34093},[886],[888,34095,34096],{"xmlns":890},[892,34097,34098,34154],{},[895,34099,34100,34112,34114,34122,34138],{},[2030,34101,34102,34104,34106],{},[898,34103,900],{},[1931,34105,3702],{},[895,34107,34108,34110],{},[1700,34109,1793],{"mathvariant":1791},[1700,34111,1793],{"mathvariant":1791},[1700,34113,1765],{},[1770,34115,34116],{"scriptlevel":1772,"displaystyle":1702},[1774,34117,34118,34120],{},[1931,34119,1933],{},[1931,34121,2553],{},[2030,34123,34124,34126,34128],{},[898,34125,1662],{},[1931,34127,1933],{},[895,34129,34130,34132,34134,34136],{},[1700,34131,1768],{},[1931,34133,1933],{},[898,34135,1979],{"mathvariant":1791},[1931,34137,2343],{},[2030,34139,34140,34142,34144],{},[898,34141,1662],{},[1931,34143,2343],{},[895,34145,34146,34148,34150,34152],{},[1700,34147,1768],{},[1931,34149,1933],{},[898,34151,1979],{"mathvariant":1791},[1931,34153,2343],{},[902,34155,34156],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,34159,34161],{"className":34160},[886],[888,34162,34163],{"xmlns":890},[892,34164,34165,34192],{},[895,34166,34167,34169,34171,34173,34175,34177,34179,34181,34183,34185,34188,34190],{},[898,34168,4374],{},[1700,34170,1703],{"stretchy":1702},[1931,34172,2553],{},[1700,34174,1732],{"separator":1731},[1931,34176,1933],{},[1700,34178,1732],{"separator":1731},[1931,34180,1933],{},[1700,34182,1709],{"stretchy":1702},[1700,34184,1765],{},[1931,34186,34187],{},"0,28125",[1700,34189,3601],{},[1931,34191,1772],{},[902,34193,34194],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,34197,34199],{"className":34198},[886],[888,34200,34201],{"xmlns":890},[892,34202,34203,34215],{},[895,34204,34205,34207,34209,34211,34213],{},[1700,34206,1927],{"stretchy":1702},[1931,34208,2553],{},[1700,34210,1732],{"separator":1731},[1931,34212,1933],{},[1700,34214,1970],{"stretchy":1702},[902,34216,34217],{"encoding":904},"[4, 1]"," je vázané ",[38,34220,3968],{},[115,34222,34224],{"id":34223},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,34226,34227],{},"Obecně:",[883,34229,34231],{"className":34230},[886],[888,34232,34233],{"xmlns":890,"display":28251},[892,34234,34235,34330],{},[20939,34236,34237],{"width":28256},[20944,34238,34239,34241,34323,34325],{},[20947,34240],{"width":28261},[20947,34242,34243],{},[895,34244,34245,34251,34253,34259,34261,34267,34269,34275,34277,34279,34281,34283,34285,34291,34293,34299,34301,34307,34309,34315,34317,34319,34321],{},[2007,34246,34247,34249],{},[898,34248,1662],{},[1931,34250,1933],{},[1700,34252,1765],{},[2007,34254,34255,34257],{},[898,34256,4374],{},[1931,34258,1933],{},[1700,34260,1703],{"stretchy":1702},[2007,34262,34263,34265],{},[898,34264,1677],{},[1931,34266,1933],{},[1700,34268,1732],{"separator":1731},[2007,34270,34271,34273],{},[898,34272,1677],{},[1931,34274,2343],{},[1700,34276,1732],{"separator":1731},[898,34278,900],{},[1700,34280,1709],{"stretchy":1702},[1700,34282,1732],{"separator":1731},[6066,34284],{"width":15469},[2007,34286,34287,34289],{},[898,34288,1662],{},[1931,34290,2343],{},[1700,34292,1765],{},[2007,34294,34295,34297],{},[898,34296,4374],{},[1931,34298,2343],{},[1700,34300,1703],{"stretchy":1702},[2007,34302,34303,34305],{},[898,34304,1677],{},[1931,34306,1933],{},[1700,34308,1732],{"separator":1731},[2007,34310,34311,34313],{},[898,34312,1677],{},[1931,34314,2343],{},[1700,34316,1732],{"separator":1731},[898,34318,900],{},[1700,34320,1709],{"stretchy":1702},[1700,34322,1732],{"separator":1731},[20947,34324],{"width":28261},[20947,34326,34327],{},[1781,34328,34329],{},"(6.27)",[902,34331,34332],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,34334,34336],{"className":34335},[886],[888,34337,34338],{"xmlns":890,"display":28251},[892,34339,34340,34387],{},[20939,34341,34342],{"width":28256},[20944,34343,34344,34346,34380,34382],{},[20947,34345],{"width":28261},[20947,34347,34348],{},[895,34349,34350,34352,34354,34356,34358,34364,34366,34372,34374,34376,34378],{},[898,34351,16628],{},[1700,34353,1765],{},[898,34355,16628],{},[1700,34357,1703],{"stretchy":1702},[2007,34359,34360,34362],{},[898,34361,1677],{},[1931,34363,1933],{},[1700,34365,1732],{"separator":1731},[2007,34367,34368,34370],{},[898,34369,1677],{},[1931,34371,2343],{},[1700,34373,1732],{"separator":1731},[898,34375,900],{},[1700,34377,1709],{"stretchy":1702},[898,34379,2196],{"mathvariant":1791},[20947,34381],{"width":28261},[20947,34383,34384],{},[1781,34385,34386],{},"(6.28)",[902,34388,34389],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,34391,34392,34393,2106,34396,34409,34410,34423],{},"Hicksova poptávka závisí na ",[38,34394,34395],{},"hladině užitečnosti",[883,34397,34399],{"className":34398},[886],[888,34400,34401],{"xmlns":890},[892,34402,34403,34407],{},[895,34404,34405],{},[898,34406,900],{},[902,34408,900],{"encoding":904}," (nikoli na důchodu ",[883,34411,34413],{"className":34412},[886],[888,34414,34415],{"xmlns":890},[892,34416,34417,34421],{},[895,34418,34419],{},[898,34420,9316],{},[902,34422,9316],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,34425,34427,34428],{"id":34426},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,34429,34431],{"className":34430},[886],[888,34432,34433],{"xmlns":890},[892,34434,34435,34469],{},[895,34436,34437,34439,34441,34455],{},[898,34438,900],{},[1700,34440,1765],{},[2030,34442,34443,34445,34447],{},[898,34444,1662],{},[1931,34446,1933],{},[895,34448,34449,34451,34453],{},[1931,34450,1933],{},[898,34452,1979],{"mathvariant":1791},[1931,34454,2343],{},[2030,34456,34457,34459,34461],{},[898,34458,1662],{},[1931,34460,2343],{},[895,34462,34463,34465,34467],{},[1931,34464,1933],{},[898,34466,1979],{"mathvariant":1791},[1931,34468,2343],{},[902,34470,33344],{"encoding":904},[724,34472,34473,34503],{},[883,34474,34476],{"className":34475},[886],[888,34477,34478],{"xmlns":890},[892,34479,34480,34500],{},[895,34481,34482,34488,34490,34496,34498],{},[2007,34483,34484,34486],{},[898,34485,1677],{},[1931,34487,1933],{},[1700,34489,1732],{"separator":1731},[2007,34491,34492,34494],{},[898,34493,1677],{},[1931,34495,2343],{},[1700,34497,1732],{"separator":1731},[898,34499,900],{},[902,34501,34502],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,34505,34507],{"className":34506},[886],[888,34508,34509],{"xmlns":890,"display":28251},[892,34510,34511,34585],{},[895,34512,34513,34515,34517,34523,34529,34531,34537,34543,34545,34547,34549,34551,34553,34567,34581,34583],{},[898,34514,1706],{"mathvariant":28733},[1700,34516,1765],{},[2007,34518,34519,34521],{},[898,34520,1677],{},[1931,34522,1933],{},[2007,34524,34525,34527],{},[898,34526,1662],{},[1931,34528,1933],{},[1700,34530,1897],{},[2007,34532,34533,34535],{},[898,34534,1677],{},[1931,34536,2343],{},[2007,34538,34539,34541],{},[898,34540,1662],{},[1931,34542,2343],{},[1700,34544,1897],{},[898,34546,16628],{},[1700,34548,1703],{"stretchy":1702},[898,34550,900],{},[1700,34552,1768],{},[2030,34554,34555,34557,34559],{},[898,34556,1662],{},[1931,34558,1933],{},[895,34560,34561,34563,34565],{},[1931,34562,1933],{},[898,34564,1979],{"mathvariant":1791},[1931,34566,2343],{},[2030,34568,34569,34571,34573],{},[898,34570,1662],{},[1931,34572,2343],{},[895,34574,34575,34577,34579],{},[1931,34576,1933],{},[898,34578,1979],{"mathvariant":1791},[1931,34580,2343],{},[1700,34582,1709],{"stretchy":1702},[898,34584,2196],{"mathvariant":1791},[902,34586,34587],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,34589,30616],{},[883,34591,34593],{"className":34592},[886],[888,34594,34595],{"xmlns":890,"display":28251},[892,34596,34597,34819],{},[20939,34598,34599,34679,34759],{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},[20944,34600,34601,34613],{},[20947,34602,34603],{},[1770,34604,34605],{"scriptlevel":1772,"displaystyle":1731},[2030,34606,34607,34609,34611],{},[898,34608,1706],{"mathvariant":28733},[1931,34610,1933],{},[1700,34612,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,34614,34615],{},[1770,34616,34617],{"scriptlevel":1772,"displaystyle":1731},[895,34618,34619,34621,34623,34629,34631,34633,34635,34643,34659,34673,34675,34677],{},[895,34620],{},[1700,34622,1765],{},[2007,34624,34625,34627],{},[898,34626,1677],{},[1931,34628,1933],{},[1700,34630,1768],{},[898,34632,16628],{},[1700,34634,2065],{},[1770,34636,34637],{"scriptlevel":1772,"displaystyle":1702},[1774,34638,34639,34641],{},[1931,34640,1933],{},[1931,34642,2343],{},[2030,34644,34645,34647,34649],{},[898,34646,1662],{},[1931,34648,1933],{},[895,34650,34651,34653,34655,34657],{},[1700,34652,1768],{},[1931,34654,1933],{},[898,34656,1979],{"mathvariant":1791},[1931,34658,2343],{},[2030,34660,34661,34663,34665],{},[898,34662,1662],{},[1931,34664,2343],{},[895,34666,34667,34669,34671],{},[1931,34668,1933],{},[898,34670,1979],{"mathvariant":1791},[1931,34672,2343],{},[1700,34674,1765],{},[1931,34676,1772],{},[1700,34678,1732],{"separator":1731},[20944,34680,34681,34693],{},[20947,34682,34683],{},[1770,34684,34685],{"scriptlevel":1772,"displaystyle":1731},[2030,34686,34687,34689,34691],{},[898,34688,1706],{"mathvariant":28733},[1931,34690,2343],{},[1700,34692,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,34694,34695],{},[1770,34696,34697],{"scriptlevel":1772,"displaystyle":1731},[895,34698,34699,34701,34703,34709,34711,34713,34715,34723,34737,34753,34755,34757],{},[895,34700],{},[1700,34702,1765],{},[2007,34704,34705,34707],{},[898,34706,1677],{},[1931,34708,2343],{},[1700,34710,1768],{},[898,34712,16628],{},[1700,34714,2065],{},[1770,34716,34717],{"scriptlevel":1772,"displaystyle":1702},[1774,34718,34719,34721],{},[1931,34720,1933],{},[1931,34722,2343],{},[2030,34724,34725,34727,34729],{},[898,34726,1662],{},[1931,34728,1933],{},[895,34730,34731,34733,34735],{},[1931,34732,1933],{},[898,34734,1979],{"mathvariant":1791},[1931,34736,2343],{},[2030,34738,34739,34741,34743],{},[898,34740,1662],{},[1931,34742,2343],{},[895,34744,34745,34747,34749,34751],{},[1700,34746,1768],{},[1931,34748,1933],{},[898,34750,1979],{"mathvariant":1791},[1931,34752,2343],{},[1700,34754,1765],{},[1931,34756,1772],{},[1700,34758,1732],{"separator":1731},[20944,34760,34761,34773],{},[20947,34762,34763],{},[1770,34764,34765],{"scriptlevel":1772,"displaystyle":1731},[2030,34766,34767,34769,34771],{},[898,34768,1706],{"mathvariant":28733},[898,34770,16628],{},[1700,34772,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[20947,34774,34775],{},[1770,34776,34777],{"scriptlevel":1772,"displaystyle":1731},[895,34778,34779,34781,34783,34785,34787,34801,34815,34817],{},[895,34780],{},[1700,34782,1765],{},[898,34784,900],{},[1700,34786,1768],{},[2030,34788,34789,34791,34793],{},[898,34790,1662],{},[1931,34792,1933],{},[895,34794,34795,34797,34799],{},[1931,34796,1933],{},[898,34798,1979],{"mathvariant":1791},[1931,34800,2343],{},[2030,34802,34803,34805,34807],{},[898,34804,1662],{},[1931,34806,2343],{},[895,34808,34809,34811,34813],{},[1931,34810,1933],{},[898,34812,1979],{"mathvariant":1791},[1931,34814,2343],{},[1700,34816,1765],{},[1931,34818,12645],{},[902,34820,34821],{"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}",[724,34823,34824,34825,34895,34896,34954],{},"Podílem rovnic: ",[883,34826,34828],{"className":34827},[886],[888,34829,34830],{"xmlns":890},[892,34831,34832,34892],{},[895,34833,34834,34840,34842,34848,34850,34856,34858,34864,34866,34872,34878,34880,34886],{},[2007,34835,34836,34838],{},[898,34837,1677],{},[1931,34839,1933],{},[898,34841,1979],{"mathvariant":1791},[2007,34843,34844,34846],{},[898,34845,1677],{},[1931,34847,2343],{},[1700,34849,1765],{},[2007,34851,34852,34854],{},[898,34853,1662],{},[1931,34855,2343],{},[898,34857,1979],{"mathvariant":1791},[2007,34859,34860,34862],{},[898,34861,1662],{},[1931,34863,1933],{},[1700,34865,4178],{},[2007,34867,34868,34870],{},[898,34869,1677],{},[1931,34871,1933],{},[2007,34873,34874,34876],{},[898,34875,1662],{},[1931,34877,1933],{},[1700,34879,1765],{},[2007,34881,34882,34884],{},[898,34883,1677],{},[1931,34885,2343],{},[2007,34887,34888,34890],{},[898,34889,1662],{},[1931,34891,2343],{},[902,34893,34894],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,34897,34899],{"className":34898},[886],[888,34900,34901],{"xmlns":890},[892,34902,34903,34951],{},[895,34904,34905,34907,34909,34915,34921,34923,34929,34935,34937,34939,34945],{},[898,34906,1762],{},[1700,34908,1765],{},[2007,34910,34911,34913],{},[898,34912,1677],{},[1931,34914,1933],{},[2007,34916,34917,34919],{},[898,34918,1662],{},[1931,34920,1933],{},[1700,34922,1897],{},[2007,34924,34925,34927],{},[898,34926,1677],{},[1931,34928,2343],{},[2007,34930,34931,34933],{},[898,34932,1662],{},[1931,34934,2343],{},[1700,34936,1765],{},[1931,34938,2343],{},[2007,34940,34941,34943],{},[898,34942,1677],{},[1931,34944,1933],{},[2007,34946,34947,34949],{},[898,34948,1662],{},[1931,34950,1933],{},[902,34952,34953],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,34956,34958],{"className":34957},[886],[888,34959,34960],{"xmlns":890,"display":28251},[892,34961,34962,35029],{},[20939,34963,34964],{"width":28256},[20944,34965,34966,34968,35022,35024],{},[20947,34967],{"width":28261},[20947,34969,34970],{},[895,34971,34972,34978,34980,34994,34996,34998,35004,35006,35020],{},[2007,34973,34974,34976],{},[898,34975,1662],{},[1931,34977,1933],{},[1700,34979,1765],{},[1774,34981,34982,34984],{},[898,34983,1762],{},[895,34985,34986,34988],{},[1931,34987,2343],{},[2007,34989,34990,34992],{},[898,34991,1677],{},[1931,34993,1933],{},[1700,34995,1732],{"separator":1731},[6066,34997],{"width":15469},[2007,34999,35000,35002],{},[898,35001,1662],{},[1931,35003,2343],{},[1700,35005,1765],{},[1774,35007,35008,35010],{},[898,35009,1762],{},[895,35011,35012,35014],{},[1931,35013,2343],{},[2007,35015,35016,35018],{},[898,35017,1677],{},[1931,35019,2343],{},[898,35021,2196],{"mathvariant":1791},[20947,35023],{"width":28261},[20947,35025,35026],{},[1781,35027,35028],{},"(6.29)",[902,35030,35031],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,35033,35034,35035,17761,35117,35153],{},"Ze třetí rovnice ",[883,35036,35038],{"className":35037},[886],[888,35039,35040],{"xmlns":890},[892,35041,35042,35114],{},[895,35043,35044,35046,35048,35086,35088],{},[898,35045,900],{},[1700,35047,1765],{},[8305,35049,35050],{},[895,35051,35052,35068,35070],{},[1770,35053,35054],{"scriptlevel":1772,"displaystyle":1702},[1774,35055,35056,35058],{},[898,35057,1762],{},[895,35059,35060,35062],{},[1931,35061,2343],{},[2007,35063,35064,35066],{},[898,35065,1677],{},[1931,35067,1933],{},[1700,35069,2065],{},[1770,35071,35072],{"scriptlevel":1772,"displaystyle":1702},[1774,35073,35074,35076],{},[898,35075,1762],{},[895,35077,35078,35080],{},[1931,35079,2343],{},[2007,35081,35082,35084],{},[898,35083,1677],{},[1931,35085,2343],{},[1700,35087,1765],{},[1770,35089,35090],{"scriptlevel":1772,"displaystyle":1702},[1774,35091,35092,35094],{},[898,35093,1762],{},[895,35095,35096,35098],{},[1931,35097,2343],{},[8305,35099,35100],{},[895,35101,35102,35108],{},[2007,35103,35104,35106],{},[898,35105,1677],{},[1931,35107,1933],{},[2007,35109,35110,35112],{},[898,35111,1677],{},[1931,35113,2343],{},[902,35115,35116],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,35118,35120],{"className":35119},[886],[888,35121,35122],{"xmlns":890},[892,35123,35124,35150],{},[895,35125,35126,35128,35130,35132,35134],{},[898,35127,1762],{},[1700,35129,1765],{},[1931,35131,2343],{},[898,35133,900],{},[8305,35135,35136],{},[895,35137,35138,35144],{},[2007,35139,35140,35142],{},[898,35141,1677],{},[1931,35143,1933],{},[2007,35145,35146,35148],{},[898,35147,1677],{},[1931,35149,2343],{},[902,35151,35152],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,35155,35157],{"className":35156},[886],[888,35158,35159],{"xmlns":890,"display":28251},[892,35160,35161,35306],{},[20939,35162,35163],{"width":28256},[20944,35164,35165,35167,35299,35301],{},[20947,35166],{"width":28261},[20947,35168,35169],{},[13017,35170,35171],{"notation":13019},[1770,35172,35173],{"scriptlevel":1772,"displaystyle":1702},[1770,35174,35175],{"scriptlevel":1772,"displaystyle":1702},[1770,35176,35177],{"scriptlevel":1772,"displaystyle":1731},[895,35178,35179,35181,35187,35189,35191,35207,35209,35215,35217,35223,35225,35231,35233,35235,35237,35239,35241,35247,35249,35251,35267,35269,35275,35277,35283,35285,35291,35293,35295,35297],{},[1781,35180,4175],{},[2007,35182,35183,35185],{},[898,35184,1662],{},[1931,35186,1933],{},[1700,35188,1765],{},[898,35190,900],{},[8305,35192,35193],{},[1774,35194,35195,35201],{},[2007,35196,35197,35199],{},[898,35198,1677],{},[1931,35200,2343],{},[2007,35202,35203,35205],{},[898,35204,1677],{},[1931,35206,1933],{},[1700,35208,1765],{},[2007,35210,35211,35213],{},[898,35212,4374],{},[1931,35214,1933],{},[1700,35216,1703],{"stretchy":1702},[2007,35218,35219,35221],{},[898,35220,1677],{},[1931,35222,1933],{},[1700,35224,1732],{"separator":1731},[2007,35226,35227,35229],{},[898,35228,1677],{},[1931,35230,2343],{},[1700,35232,1732],{"separator":1731},[898,35234,900],{},[1700,35236,1709],{"stretchy":1702},[1700,35238,1732],{"separator":1731},[6066,35240],{"width":15469},[2007,35242,35243,35245],{},[898,35244,1662],{},[1931,35246,2343],{},[1700,35248,1765],{},[898,35250,900],{},[8305,35252,35253],{},[1774,35254,35255,35261],{},[2007,35256,35257,35259],{},[898,35258,1677],{},[1931,35260,1933],{},[2007,35262,35263,35265],{},[898,35264,1677],{},[1931,35266,2343],{},[1700,35268,1765],{},[2007,35270,35271,35273],{},[898,35272,4374],{},[1931,35274,2343],{},[1700,35276,1703],{"stretchy":1702},[2007,35278,35279,35281],{},[898,35280,1677],{},[1931,35282,1933],{},[1700,35284,1732],{"separator":1731},[2007,35286,35287,35289],{},[898,35288,1677],{},[1931,35290,2343],{},[1700,35292,1732],{"separator":1731},[898,35294,900],{},[1700,35296,1709],{"stretchy":1702},[1781,35298,4175],{},[20947,35300],{"width":28261},[20947,35302,35303],{},[1781,35304,35305],{},"(6.30)",[902,35307,35308],{"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}",[115,35310,35312],{"id":35311},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,35314,35315,35316,35329,35330,35347,35348,35361,35362,35379,35380,35383,35384,35423,35424,35453],{},"Primární (max ",[883,35317,35319],{"className":35318},[886],[888,35320,35321],{"xmlns":890},[892,35322,35323,35327],{},[895,35324,35325],{},[898,35326,900],{},[902,35328,900],{"encoding":904}," při rozpočtu ",[883,35331,35333],{"className":35332},[886],[888,35334,35335],{"xmlns":890},[892,35336,35337,35345],{},[895,35338,35339],{},[1785,35340,35341,35343],{},[898,35342,9316],{},[1700,35344,4543],{},[902,35346,28213],{"encoding":904},") a duální (min ",[883,35349,35351],{"className":35350},[886],[888,35352,35353],{"xmlns":890},[892,35354,35355,35359],{},[895,35356,35357],{},[898,35358,1762],{},[902,35360,1762],{"encoding":904}," při užitečnosti ",[883,35363,35365],{"className":35364},[886],[888,35366,35367],{"xmlns":890},[892,35368,35369,35377],{},[895,35370,35371],{},[1785,35372,35373,35375],{},[898,35374,900],{},[1700,35376,4543],{},[902,35378,28147],{"encoding":904},") úloha jsou ",[38,35381,35382],{},"ekvivalentní",": mají tentýž bod optima ",[883,35385,35387],{"className":35386},[886],[888,35388,35389],{"xmlns":890},[892,35390,35391,35421],{},[895,35392,35393,35399,35401,35409,35411,35419],{},[1785,35394,35395,35397],{},[898,35396,1662],{},[1700,35398,4543],{},[1700,35400,1927],{"stretchy":1702},[2030,35402,35403,35405,35407],{},[898,35404,1662],{},[1931,35406,1933],{},[1700,35408,4543],{},[1700,35410,1732],{"separator":1731},[2030,35412,35413,35415,35417],{},[898,35414,1662],{},[1931,35416,2343],{},[1700,35418,4543],{},[1700,35420,1970],{"stretchy":1702},[902,35422,28512],{"encoding":904}," a v obou platí ",[883,35425,35427],{"className":35426},[886],[888,35428,35429],{"xmlns":890},[892,35430,35431,35451],{},[895,35432,35433,35435,35437,35443,35445],{},[1781,35434,10786],{},[1700,35436,1765],{},[2007,35438,35439,35441],{},[898,35440,1677],{},[1931,35442,1933],{},[898,35444,1979],{"mathvariant":1791},[2007,35446,35447,35449],{},[898,35448,1677],{},[1931,35450,2343],{},[902,35452,28183],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,35455,35456],{},[2756,35457],{"alt":35458,"className":35459,"src":35460},"imek-primarni-vs-dualni",[210,2760],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,35462,35463,35574],{},[123,35464,35465,35468,35469,35482,35483,35523,35524,2196],{},[38,35466,35467],{},"Primární"," (Marshall): zadáno ",[883,35470,35472],{"className":35471},[886],[888,35473,35474],{"xmlns":890},[892,35475,35476,35480],{},[895,35477,35478],{},[898,35479,9316],{},[902,35481,9316],{"encoding":904},", hledáme maximální ",[883,35484,35486],{"className":35485},[886],[888,35487,35488],{"xmlns":890},[892,35489,35490,35520],{},[895,35491,35492,35498,35500,35506,35508,35514,35516,35518],{},[1785,35493,35494,35496],{},[898,35495,900],{},[1700,35497,4543],{},[1700,35499,1703],{"stretchy":1702},[2007,35501,35502,35504],{},[898,35503,1677],{},[1931,35505,1933],{},[1700,35507,1732],{"separator":1731},[2007,35509,35510,35512],{},[898,35511,1677],{},[1931,35513,2343],{},[1700,35515,1732],{"separator":1731},[898,35517,9316],{},[1700,35519,1709],{"stretchy":1702},[902,35521,35522],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,35525,35527],{"className":35526},[886],[888,35528,35529],{"xmlns":890},[892,35530,35531,35571],{},[895,35532,35533,35539,35541,35549,35551,35557,35559,35565,35567,35569],{},[2007,35534,35535,35537],{},[898,35536,1662],{},[898,35538,17975],{},[1700,35540,1765],{},[2030,35542,35543,35545,35547],{},[898,35544,4374],{},[898,35546,17975],{},[898,35548,2005],{},[1700,35550,1703],{"stretchy":1702},[2007,35552,35553,35555],{},[898,35554,1677],{},[1931,35556,1933],{},[1700,35558,1732],{"separator":1731},[2007,35560,35561,35563],{},[898,35562,1677],{},[1931,35564,2343],{},[1700,35566,1732],{"separator":1731},[898,35568,9316],{},[1700,35570,1709],{"stretchy":1702},[902,35572,35573],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,35575,35576,35579,35580,35593,35594,35523,35634,2196],{},[38,35577,35578],{},"Duální"," (Hicks): zadáno ",[883,35581,35583],{"className":35582},[886],[888,35584,35585],{"xmlns":890},[892,35586,35587,35591],{},[895,35588,35589],{},[898,35590,900],{},[902,35592,900],{"encoding":904},", hledáme minimální ",[883,35595,35597],{"className":35596},[886],[888,35598,35599],{"xmlns":890},[892,35600,35601,35631],{},[895,35602,35603,35609,35611,35617,35619,35625,35627,35629],{},[1785,35604,35605,35607],{},[898,35606,1762],{},[1700,35608,4543],{},[1700,35610,1703],{"stretchy":1702},[2007,35612,35613,35615],{},[898,35614,1677],{},[1931,35616,1933],{},[1700,35618,1732],{"separator":1731},[2007,35620,35621,35623],{},[898,35622,1677],{},[1931,35624,2343],{},[1700,35626,1732],{"separator":1731},[898,35628,900],{},[1700,35630,1709],{"stretchy":1702},[902,35632,35633],{"encoding":904},"E^*(P_1, P_2, U)",[883,35635,35637],{"className":35636},[886],[888,35638,35639],{"xmlns":890},[892,35640,35641,35682],{},[895,35642,35643,35649,35651,35660,35662,35668,35670,35676,35678,35680],{},[2007,35644,35645,35647],{},[898,35646,1662],{},[898,35648,17975],{},[1700,35650,1765],{},[2030,35652,35653,35655,35657],{},[898,35654,4374],{},[898,35656,17975],{},[898,35658,35659],{},"H",[1700,35661,1703],{"stretchy":1702},[2007,35663,35664,35666],{},[898,35665,1677],{},[1931,35667,1933],{},[1700,35669,1732],{"separator":1731},[2007,35671,35672,35674],{},[898,35673,1677],{},[1931,35675,2343],{},[1700,35677,1732],{"separator":1731},[898,35679,900],{},[1700,35681,1709],{"stretchy":1702},[902,35683,35684],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,35686,35687,35688,35691,35692,35695],{},"Proč se studují obě? Marshallova poptávka je ",[38,35689,35690],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,35693,35694],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,35697,35699],{"id":35698},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,35701,35703],{"id":35702},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,35705,35706,35709,35710,35742,35743,35781,35782,35808],{},[38,35707,35708],{},"6.8"," Jsou dány užitečnost ",[883,35711,35713],{"className":35712},[886],[888,35714,35715],{"xmlns":890},[892,35716,35717,35739],{},[895,35718,35719,35721,35723,35731],{},[898,35720,900],{},[1700,35722,1765],{},[2030,35724,35725,35727,35729],{},[898,35726,1662],{},[1931,35728,1933],{},[1931,35730,5197],{},[2030,35732,35733,35735,35737],{},[898,35734,1662],{},[1931,35736,2343],{},[1931,35738,5197],{},[902,35740,35741],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,35744,35746],{"className":35745},[886],[888,35747,35748],{"xmlns":890},[892,35749,35750,35778],{},[895,35751,35752,35760,35762,35764,35766,35774,35776],{},[2030,35753,35754,35756,35758],{},[898,35755,1677],{},[1931,35757,1933],{},[1700,35759,4543],{},[1700,35761,1765],{},[1931,35763,2553],{},[1700,35765,1732],{"separator":1731},[2030,35767,35768,35770,35772],{},[898,35769,1677],{},[1931,35771,2343],{},[1700,35773,4543],{},[1700,35775,1765],{},[1931,35777,3058],{},[902,35779,35780],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,35783,35785],{"className":35784},[886],[888,35786,35787],{"xmlns":890},[892,35788,35789,35805],{},[895,35790,35791,35797,35799],{},[2007,35792,35793,35795],{},[898,35794,1662],{},[1931,35796,1933],{},[1700,35798,1732],{"separator":1731},[2007,35800,35801,35803],{},[898,35802,1662],{},[1931,35804,2343],{},[902,35806,35807],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,35810,35811,35814,35815,35857,35858,35889,35890,35912,35913,2196],{},[38,35812,35813],{},"6.9"," Jsou dány rozpočtové omezení ",[883,35816,35818],{"className":35817},[886],[888,35819,35820],{"xmlns":890},[892,35821,35822,35854],{},[895,35823,35824,35826,35828,35834,35840,35842,35848],{},[898,35825,9316],{},[1700,35827,1765],{},[2007,35829,35830,35832],{},[898,35831,1677],{},[1931,35833,1933],{},[2007,35835,35836,35838],{},[898,35837,1662],{},[1931,35839,1933],{},[1700,35841,1897],{},[2007,35843,35844,35846],{},[898,35845,1677],{},[1931,35847,2343],{},[2007,35849,35850,35852],{},[898,35851,1662],{},[1931,35853,2343],{},[902,35855,35856],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,35859,35861],{"className":35860},[886],[888,35862,35863],{"xmlns":890},[892,35864,35865,35887],{},[895,35866,35867,35869,35871,35879],{},[898,35868,900],{},[1700,35870,1765],{},[2030,35872,35873,35875,35877],{},[898,35874,1662],{},[1931,35876,1933],{},[1931,35878,5197],{},[2030,35880,35881,35883,35885],{},[898,35882,1662],{},[1931,35884,2343],{},[1931,35886,5197],{},[902,35888,35741],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,35891,35893],{"className":35892},[886],[888,35894,35895],{"xmlns":890},[892,35896,35897,35909],{},[895,35898,35899,35905,35907],{},[1785,35900,35901,35903],{},[898,35902,9316],{},[1700,35904,4543],{},[1700,35906,1765],{},[1931,35908,15295],{},[902,35910,35911],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,35914,35916],{"className":35915},[886],[888,35917,35918],{"xmlns":890},[892,35919,35920,35948],{},[895,35921,35922,35930,35932,35934,35936,35944,35946],{},[2030,35923,35924,35926,35928],{},[898,35925,1677],{},[1931,35927,1933],{},[1700,35929,4543],{},[1700,35931,1765],{},[1931,35933,2438],{},[1700,35935,1732],{"separator":1731},[2030,35937,35938,35940,35942],{},[898,35939,1677],{},[1931,35941,2343],{},[1700,35943,4543],{},[1700,35945,1765],{},[1931,35947,3058],{},[902,35949,35950],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,35952,35953,35956,35957,21779,35989,36019,36020,2196],{},[38,35954,35955],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,35958,35960],{"className":35959},[886],[888,35961,35962],{"xmlns":890},[892,35963,35964,35986],{},[895,35965,35966,35968,35970,35978],{},[898,35967,900],{},[1700,35969,1765],{},[2030,35971,35972,35974,35976],{},[898,35973,1662],{},[1931,35975,1933],{},[898,35977,207],{},[2030,35979,35980,35982,35984],{},[898,35981,1662],{},[1931,35983,2343],{},[898,35985,1879],{},[902,35987,35988],{"encoding":904},"U = Q_1^a Q_2^b",[883,35990,35992],{"className":35991},[886],[888,35993,35994],{"xmlns":890},[892,35995,35996,36016],{},[895,35997,35998,36000,36002,36004,36006,36008,36010,36012,36014],{},[898,35999,207],{},[1700,36001,1732],{"separator":1731},[898,36003,1879],{},[1700,36005,6694],{},[1700,36007,5512],{"stretchy":1702},[1931,36009,1772],{},[1700,36011,1732],{"separator":1731},[1931,36013,1933],{},[1700,36015,5529],{"stretchy":1702},[902,36017,36018],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,36021,36023],{"className":36022},[886],[888,36024,36025],{"xmlns":890},[892,36026,36027,36059],{},[895,36028,36029,36031,36033,36039,36045,36047,36053],{},[898,36030,9316],{},[1700,36032,1765],{},[2007,36034,36035,36037],{},[898,36036,1677],{},[1931,36038,1933],{},[2007,36040,36041,36043],{},[898,36042,1662],{},[1931,36044,1933],{},[1700,36046,1897],{},[2007,36048,36049,36051],{},[898,36050,1677],{},[1931,36052,2343],{},[2007,36054,36055,36057],{},[898,36056,1662],{},[1931,36058,2343],{},[902,36060,35856],{"encoding":904},[724,36062,36063,36066,36067,21779,36101,36019,36119,2196],{},[38,36064,36065],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,36068,36070],{"className":36069},[886],[888,36071,36072],{"xmlns":890},[892,36073,36074,36098],{},[895,36075,36076,36078,36080,36088,36090],{},[898,36077,900],{},[1700,36079,1765],{},[2030,36081,36082,36084,36086],{},[898,36083,1662],{},[1931,36085,1933],{},[898,36087,207],{},[1700,36089,1897],{},[2030,36091,36092,36094,36096],{},[898,36093,1662],{},[1931,36095,2343],{},[898,36097,207],{},[902,36099,36100],{"encoding":904},"U = Q_1^a + Q_2^a",[883,36102,36104],{"className":36103},[886],[888,36105,36106],{"xmlns":890},[892,36107,36108,36116],{},[895,36109,36110,36112,36114],{},[898,36111,207],{},[1700,36113,3564],{"mathvariant":1791},[1931,36115,1772],{},[902,36117,36118],{"encoding":904},"a \\neq 0",[883,36120,36122],{"className":36121},[886],[888,36123,36124],{"xmlns":890},[892,36125,36126,36158],{},[895,36127,36128,36130,36132,36138,36144,36146,36152],{},[898,36129,9316],{},[1700,36131,1765],{},[2007,36133,36134,36136],{},[898,36135,1677],{},[1931,36137,1933],{},[2007,36139,36140,36142],{},[898,36141,1662],{},[1931,36143,1933],{},[1700,36145,1897],{},[2007,36147,36148,36150],{},[898,36149,1677],{},[1931,36151,2343],{},[2007,36153,36154,36156],{},[898,36155,1662],{},[1931,36157,2343],{},[902,36159,35856],{"encoding":904},[198,36161,36163],{"id":36162},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,36165,36166,35709,36169,1343,36196,36218,36219,1343,36242,36266,36267,36292,36293,2196],{},[38,36167,36168],{},"6.12",[883,36170,36172],{"className":36171},[886],[888,36173,36174],{"xmlns":890},[892,36175,36176,36194],{},[895,36177,36178,36180,36182,36188],{},[898,36179,900],{},[1700,36181,1765],{},[2007,36183,36184,36186],{},[898,36185,1662],{},[1931,36187,1933],{},[2007,36189,36190,36192],{},[898,36191,1662],{},[1931,36193,2343],{},[902,36195,30411],{"encoding":904},[883,36197,36199],{"className":36198},[886],[888,36200,36201],{"xmlns":890},[892,36202,36203,36215],{},[895,36204,36205,36211,36213],{},[1785,36206,36207,36209],{},[898,36208,900],{},[1700,36210,4543],{},[1700,36212,1765],{},[1931,36214,3058],{},[902,36216,36217],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,36220,36222],{"className":36221},[886],[888,36223,36224],{"xmlns":890},[892,36225,36226,36240],{},[895,36227,36228,36236,36238],{},[2030,36229,36230,36232,36234],{},[898,36231,1677],{},[1931,36233,1933],{},[1700,36235,4543],{},[1700,36237,1765],{},[1931,36239,2343],{},[902,36241,30484],{"encoding":904},[883,36243,36245],{"className":36244},[886],[888,36246,36247],{"xmlns":890},[892,36248,36249,36263],{},[895,36250,36251,36259,36261],{},[2030,36252,36253,36255,36257],{},[898,36254,1677],{},[1931,36256,2343],{},[1700,36258,4543],{},[1700,36260,1765],{},[1931,36262,2553],{},[902,36264,36265],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,36268,36270],{"className":36269},[886],[888,36271,36272],{"xmlns":890},[892,36273,36274,36290],{},[895,36275,36276,36282,36284],{},[2007,36277,36278,36280],{},[898,36279,1662],{},[1931,36281,1933],{},[1700,36283,1732],{"separator":1731},[2007,36285,36286,36288],{},[898,36287,1662],{},[1931,36289,2343],{},[902,36291,35807],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,36294,36296],{"className":36295},[886],[888,36297,36298],{"xmlns":890},[892,36299,36300,36320],{},[895,36301,36302,36304,36306,36312,36314],{},[898,36303,900],{},[1700,36305,1765],{},[2007,36307,36308,36310],{},[898,36309,1662],{},[1931,36311,1933],{},[1700,36313,2065],{},[2007,36315,36316,36318],{},[898,36317,1662],{},[1931,36319,2343],{},[902,36321,36322],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,36324,36325,36328,36329,36370,36371,36393,36394,2196],{},[38,36326,36327],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,36330,36332],{"className":36331},[886],[888,36333,36334],{"xmlns":890},[892,36335,36336,36368],{},[895,36337,36338,36340,36342,36348,36354,36356,36362],{},[898,36339,1762],{},[1700,36341,1765],{},[2007,36343,36344,36346],{},[898,36345,1677],{},[1931,36347,1933],{},[2007,36349,36350,36352],{},[898,36351,1662],{},[1931,36353,1933],{},[1700,36355,1897],{},[2007,36357,36358,36360],{},[898,36359,1677],{},[1931,36361,2343],{},[2007,36363,36364,36366],{},[898,36365,1662],{},[1931,36367,2343],{},[902,36369,28128],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,36372,36374],{"className":36373},[886],[888,36375,36376],{"xmlns":890},[892,36377,36378,36390],{},[895,36379,36380,36386,36388],{},[1785,36381,36382,36384],{},[898,36383,900],{},[1700,36385,4543],{},[1700,36387,1765],{},[1931,36389,5192],{},[902,36391,36392],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,36395,36397],{"className":36396},[886],[888,36398,36399],{"xmlns":890},[892,36400,36401,36430],{},[895,36402,36403,36411,36413,36415,36417,36425,36427],{},[2030,36404,36405,36407,36409],{},[898,36406,1677],{},[1931,36408,1933],{},[1700,36410,4543],{},[1700,36412,1765],{},[1931,36414,9223],{},[1700,36416,1732],{"separator":1731},[2030,36418,36419,36421,36423],{},[898,36420,1677],{},[1931,36422,2343],{},[1700,36424,4543],{},[1700,36426,1765],{},[1931,36428,36429],{},"15",[902,36431,36432],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,36434,15905],{"id":15904},[120,36436,36437,36494,36533,36553,36588,36642,36647,36653,36749,36794],{},[123,36438,36439,2106,36442,36491,36492,2196],{},[38,36440,36441],{},"Rozpočtové omezení (budget constraint)",[883,36443,36445],{"className":36444},[886],[888,36446,36447],{"xmlns":890},[892,36448,36449,36489],{},[895,36450,36451,36457,36459,36467,36473,36475,36483],{},[1785,36452,36453,36455],{},[898,36454,9316],{},[1700,36456,4543],{},[1700,36458,1765],{},[2030,36460,36461,36463,36465],{},[898,36462,1677],{},[1931,36464,1933],{},[1700,36466,4543],{},[2007,36468,36469,36471],{},[898,36470,1662],{},[1931,36472,1933],{},[1700,36474,1897],{},[2030,36476,36477,36479,36481],{},[898,36478,1677],{},[1931,36480,2343],{},[1700,36482,4543],{},[2007,36484,36485,36487],{},[898,36486,1662],{},[1931,36488,2343],{},[902,36490,17483],{"encoding":904}," — (6.12); ",[38,36493,28321],{},[123,36495,36496,36499,36500,2196],{},[38,36497,36498],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,36501,36503],{"className":36502},[886],[888,36504,36505],{"xmlns":890},[892,36506,36507,36531],{},[895,36508,36509,36511,36513,36521,36523],{},[1781,36510,10786],{},[1700,36512,1765],{},[2030,36514,36515,36517,36519],{},[898,36516,1677],{},[1931,36518,1933],{},[1700,36520,4543],{},[898,36522,1979],{"mathvariant":1791},[2030,36524,36525,36527,36529],{},[898,36526,1677],{},[1931,36528,2343],{},[1700,36530,4543],{},[902,36532,29164],{"encoding":904},[123,36534,36535,36550,36551,2196],{},[38,36536,29308,36537],{},[883,36538,36540],{"className":36539},[886],[888,36541,36542],{"xmlns":890},[892,36543,36544,36548],{},[895,36545,36546],{},[898,36547,16628],{},[902,36549,16681],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,36552,29330],{},[123,36554,36555,36558,36559,2196],{},[38,36556,36557],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,36560,36562],{"className":36561},[886],[888,36563,36564],{"xmlns":890},[892,36565,36566,36586],{},[895,36567,36568,36570,36572,36578,36580],{},[1781,36569,10786],{},[1700,36571,1765],{},[2007,36573,36574,36576],{},[898,36575,1677],{},[1931,36577,1933],{},[898,36579,1979],{"mathvariant":1791},[2007,36581,36582,36584],{},[898,36583,1677],{},[1931,36585,2343],{},[902,36587,28183],{"encoding":904},[123,36589,36590,7203,36593,36641],{},[38,36591,36592],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,36594,36596],{"className":36595},[886],[888,36597,36598],{"xmlns":890},[892,36599,36600,36638],{},[895,36601,36602,36608,36610,36616,36618,36624,36626,36632,36634,36636],{},[2007,36603,36604,36606],{},[898,36605,1662],{},[898,36607,17975],{},[1700,36609,1765],{},[2007,36611,36612,36614],{},[898,36613,4374],{},[898,36615,17975],{},[1700,36617,1703],{"stretchy":1702},[2007,36619,36620,36622],{},[898,36621,1677],{},[1931,36623,1933],{},[1700,36625,1732],{"separator":1731},[2007,36627,36628,36630],{},[898,36629,1677],{},[1931,36631,2343],{},[1700,36633,1732],{"separator":1731},[898,36635,9316],{},[1700,36637,1709],{"stretchy":1702},[902,36639,36640],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,36643,36644,36646],{},[38,36645,31912],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,36648,36649,36652],{},[38,36650,36651],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,36654,36655,7203,36657,36704,36705,36748],{},[38,36656,34224],{},[883,36658,36660],{"className":36659},[886],[888,36661,36662],{"xmlns":890},[892,36663,36664,36702],{},[895,36665,36666,36672,36674,36680,36682,36688,36690,36696,36698,36700],{},[2007,36667,36668,36670],{},[898,36669,1662],{},[898,36671,17975],{},[1700,36673,1765],{},[2007,36675,36676,36678],{},[898,36677,4374],{},[898,36679,17975],{},[1700,36681,1703],{"stretchy":1702},[2007,36683,36684,36686],{},[898,36685,1677],{},[1931,36687,1933],{},[1700,36689,1732],{"separator":1731},[2007,36691,36692,36694],{},[898,36693,1677],{},[1931,36695,2343],{},[1700,36697,1732],{"separator":1731},[898,36699,900],{},[1700,36701,1709],{"stretchy":1702},[902,36703,18008],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,36706,36708],{"className":36707},[886],[888,36709,36710],{"xmlns":890},[892,36711,36712,36746],{},[895,36713,36714,36716,36718,36732],{},[898,36715,900],{},[1700,36717,1765],{},[2030,36719,36720,36722,36724],{},[898,36721,1662],{},[1931,36723,1933],{},[895,36725,36726,36728,36730],{},[1931,36727,1933],{},[898,36729,1979],{"mathvariant":1791},[1931,36731,2343],{},[2030,36733,36734,36736,36738],{},[898,36735,1662],{},[1931,36737,2343],{},[895,36739,36740,36742,36744],{},[1931,36741,1933],{},[898,36743,1979],{"mathvariant":1791},[1931,36745,2343],{},[902,36747,33344],{"encoding":904},": (6.30).",[123,36750,36751,36793],{},[38,36752,36753,36754],{},"Bod dotyku ",[883,36755,36757],{"className":36756},[886],[888,36758,36759],{"xmlns":890},[892,36760,36761,36791],{},[895,36762,36763,36769,36771,36779,36781,36789],{},[1785,36764,36765,36767],{},[898,36766,1662],{},[1700,36768,4543],{},[1700,36770,1927],{"stretchy":1702},[2030,36772,36773,36775,36777],{},[898,36774,1662],{},[1931,36776,1933],{},[1700,36778,4543],{},[1700,36780,1732],{"separator":1731},[2030,36782,36783,36785,36787],{},[898,36784,1662],{},[1931,36786,2343],{},[1700,36788,4543],{},[1700,36790,1970],{"stretchy":1702},[902,36792,28512],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,36795,36796,36799,36800,36813,36814,36827],{},[38,36797,36798],{},"Dualita"," — ekvivalence max ",[883,36801,36803],{"className":36802},[886],[888,36804,36805],{"xmlns":890},[892,36806,36807,36811],{},[895,36808,36809],{},[898,36810,900],{},[902,36812,900],{"encoding":904}," a min ",[883,36815,36817],{"className":36816},[886],[888,36818,36819],{"xmlns":890},[892,36820,36821,36825],{},[895,36822,36823],{},[898,36824,1762],{},[902,36826,1762],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,36829,3985],{"id":3984},[120,36831,36832,36855,36871,36884,36895],{},[123,36833,36834,2106,36837,36840,36841,36854],{},[38,36835,36836],{},"Teorie před optimalizací:",[207,36838,880],{"className":36839,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,36842,36844],{"className":36843},[886],[888,36845,36846],{"xmlns":890},[892,36847,36848,36852],{},[895,36849,36850],{},[898,36851,900],{},[902,36853,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,36856,36857,2106,36860,36863,36864,36867,36868,2196],{},[38,36858,36859],{},"Matematický aparát:",[207,36861,793],{"className":36862,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,36865,784],{"className":36866,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,36869,2559],{"className":36870,"dataFsResolvedFilePath":764,"href":765},[210],[123,36872,36873,2106,36876,36879,36880,36883],{},[38,36874,36875],{},"Paralely:",[207,36877,11271],{"className":36878,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,36881,12125],{"className":36882,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,36885,36886,2106,36889,1343,36892],{},[38,36887,36888],{},"Přednášky:",[207,36890,1094],{"className":36891,"dataFsResolvedFilePath":838,"href":839},[210],[207,36893,1101],{"className":36894,"dataFsResolvedFilePath":868,"href":869},[210],[123,36896,36897,2106,36899],{},[38,36898,16389],{},[207,36900,16393],{"className":36901,"dataFsResolvedFilePath":2140,"href":2141},[210],{"title":641,"searchDepth":642,"depth":642,"links":36903},[36904,36905,36906,36911,36912,36913,36915,36918,36921,36923,36924,36926,36927,36931,36932],{"id":12190,"depth":642,"text":12191},{"id":28191,"depth":642,"text":28192},{"id":28589,"depth":642,"text":28590,"children":36907},[36908,36909],{"id":28709,"depth":649,"text":28710},{"id":29290,"depth":649,"text":36910},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":29752,"depth":642,"text":29753},{"id":30063,"depth":642,"text":30064},{"id":30382,"depth":642,"text":36914},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":31155,"depth":642,"text":31156,"children":36916},[36917],{"id":31911,"depth":649,"text":31912},{"id":32091,"depth":642,"text":32092,"children":36919},[36920],{"id":32348,"depth":649,"text":32349},{"id":33299,"depth":642,"text":36922},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":34223,"depth":642,"text":34224},{"id":34426,"depth":642,"text":36925},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":35311,"depth":642,"text":35312},{"id":35698,"depth":642,"text":35699,"children":36928},[36929,36930],{"id":35702,"depth":649,"text":35703},{"id":36162,"depth":649,"text":36163},{"id":15904,"depth":642,"text":15905},{"id":3984,"depth":642,"text":3985},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":27952,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,36939,1144,9960,36940,36941,36942],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":36945,"title":802,"body":36946,"course":1128,"courses":659,"created":9743,"description":641,"extension":661,"meta":50999,"navigation":664,"path":51000,"seo":51001,"sources":51002,"stem":51003,"tags":51004,"type":4049,"updated":677,"__hash__":51010},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":36947,"toc":50955},[36948,36951,36977,36981,36988,37140,37154,37157,37159,37246,37250,37286,37359,37380,37505,37515,37528,37532,37537,37567,37629,37638,37642,37704,37711,37732,37850,37928,37932,37935,37994,38109,38114,38146,38208,38256,38311,38315,38336,38360,38408,38412,38424,38428,38538,38542,38558,38599,38610,38769,38779,38784,38788,38910,38920,38927,38931,39009,39020,39100,39106,39113,39252,39259,39262,39319,39323,39401,39447,39491,39497,39610,39614,39617,39812,39816,40053,40056,40210,40363,40365,40367,40447,40450,40555,40624,40633,40637,40640,40701,40710,40714,40747,40825,40864,40868,40917,40971,40975,41004,41033,41085,41092,41146,41224,41228,41271,41338,41382,41486,41505,41507,41511,41619,41623,41691,41740,41747,41832,41836,41908,41913,41961,42150,42154,42159,42335,42340,42399,42504,42508,42535,42539,42546,42710,42797,42802,42804,42807,42907,43057,43129,43203,43205,43209,43223,43227,43360,43415,43527,43604,43608,43665,43768,43827,43988,43992,44067,44139,44237,44295,44389,44442,44463,44517,44522,44600,44648,44735,44773,44861,45014,45050,45104,45107,45109,45111,45160,45167,45175,45262,45271,45358,45365,45367,45371,45596,45598,45602,45606,45675,45726,45929,45935,45946,46014,46020,46442,46446,46510,46534,46730,46736,46750,46818,46821,46861,47085,47153,47455,47864,47941,48107,48113,48116,48191,48644,48695,49101,49206,49869,49872,49949,49957,50031,50062,50064,50068,50112,50114,50116,50120,50350,50354,50445,50450,50544,50549,50722,50726,50844,50849,50898,50900,50902],[12,36949,802],{"id":36950},"poptávka-nabídka-a-tržní-rovnováha",[4060,36952,36953],{},[724,36954,36955,36957,36958,36961,36962,36965,36966,36969,36970,36972,36973,36976],{},[883,36956,4346],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,36959,36960],{},"poptávka",") a výrobce (",[38,36963,36964],{},"nabídka","), jejich interakci v ",[38,36967,36968],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,36971,18162],{},"). Uzavírá ji pojem ",[38,36974,36975],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,36978,36980],{"id":36979},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,36982,36983,36984,36987],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,36985,36986],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,36989,36990,37007,37049,37065],{},[123,36991,36992,36993,37006],{},"cena ",[883,36994,36996],{"className":36995},[886],[888,36997,36998],{"xmlns":890},[892,36999,37000,37004],{},[895,37001,37002],{},[898,37003,1677],{},[902,37005,1677],{"encoding":904}," zkoumaného zboží,",[123,37008,37009,37010,1732],{},"ceny alternativních zboží ",[883,37011,37013],{"className":37012},[886],[888,37014,37015],{"xmlns":890},[892,37016,37017,37046],{},[895,37018,37019,37025,37027,37033,37035,37037,37039],{},[2007,37020,37021,37023],{},[898,37022,1677],{},[1931,37024,1933],{},[1700,37026,1732],{"separator":1731},[2007,37028,37029,37031],{},[898,37030,1677],{},[1931,37032,2343],{},[1700,37034,1732],{"separator":1731},[1700,37036,9833],{},[1700,37038,1732],{"separator":1731},[2007,37040,37041,37043],{},[898,37042,1677],{},[898,37044,37045],{},"n",[902,37047,37048],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,37050,37051,37052,1732],{},"důchod ",[883,37053,37055],{"className":37054},[886],[888,37056,37057],{"xmlns":890},[892,37058,37059,37063],{},[895,37060,37061],{},[898,37062,9316],{},[902,37064,9316],{"encoding":904},[123,37066,37067,37068,37081,37082,37095,37096,37109,37110,37124,37125,37139],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,37069,37071],{"className":37070},[886],[888,37072,37073],{"xmlns":890},[892,37074,37075,37079],{},[895,37076,37077],{},[898,37078,1706],{},[902,37080,1706],{"encoding":904},", kapitál ",[883,37083,37085],{"className":37084},[886],[888,37086,37087],{"xmlns":890},[892,37088,37089,37093],{},[895,37090,37091],{},[898,37092,1735],{},[902,37094,1735],{"encoding":904},", půda ",[883,37097,37099],{"className":37098},[886],[888,37100,37101],{"xmlns":890},[892,37102,37103,37107],{},[895,37104,37105],{},[898,37106,1762],{},[902,37108,1762],{"encoding":904},"), technologie, počet výrobců ",[883,37111,37113],{"className":37112},[886],[888,37114,37115],{"xmlns":890},[892,37116,37117,37122],{},[895,37118,37119],{},[898,37120,37121],{},"O",[902,37123,37121],{"encoding":904},", počasí ",[883,37126,37128],{"className":37127},[886],[888,37129,37130],{"xmlns":890},[892,37131,37132,37137],{},[895,37133,37134],{},[898,37135,37136],{},"W",[902,37138,37136],{"encoding":904}," atd.",[724,37141,37142,37143,37146,37147,37150,37151,2196],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,37144,37145],{},"ceteris paribus","), hovoříme o ",[38,37148,37149],{},"jednofaktorovém modelu","; jinak jde o model ",[38,37152,37153],{},"vícefaktorový",[37155,37156],"hr",{},[115,37158,13346],{"id":36960},[4060,37160,37161],{},[724,37162,37163,37165,37166,37179,37180,37193,37194,37197,37198,37221,37222,2196],{},[883,37164,4346],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,37167,37169],{"className":37168},[886],[888,37170,37171],{"xmlns":890},[892,37172,37173,37177],{},[895,37174,37175],{},[898,37176,1662],{},[902,37178,1662],{"encoding":904}," na ceně ",[883,37181,37183],{"className":37182},[886],[888,37184,37185],{"xmlns":890},[892,37186,37187,37191],{},[895,37188,37189],{},[898,37190,1677],{},[902,37192,1677],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,37195,37196],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,37199,37201],{"className":37200},[886],[888,37202,37203],{"xmlns":890},[892,37204,37205,37219],{},[895,37206,37207,37209,37211,37213,37215,37217],{},[898,37208,1662],{},[1700,37210,1765],{},[898,37212,4374],{},[1700,37214,1703],{"stretchy":1702},[898,37216,1677],{},[1700,37218,1709],{"stretchy":1702},[902,37220,4383],{"encoding":904}," a jeho lineární verzí ",[883,37223,37225],{"className":37224},[886],[888,37226,37227],{"xmlns":890},[892,37228,37229,37243],{},[895,37230,37231,37233,37235,37237,37239,37241],{},[898,37232,1677],{},[1700,37234,1765],{},[898,37236,207],{},[898,37238,1662],{},[1700,37240,1897],{},[898,37242,1879],{},[902,37244,37245],{"encoding":904},"P = aQ + b",[198,37247,37249],{"id":37248},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,37251,37252,37253,37266,37267,37280,37281,10208,37283,3345],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,37254,37256],{"className":37255},[886],[888,37257,37258],{"xmlns":890},[892,37259,37260,37264],{},[895,37261,37262],{},[898,37263,1662],{},[902,37265,1662],{"encoding":904}," závisí na ceně ",[883,37268,37270],{"className":37269},[886],[888,37271,37272],{"xmlns":890},[892,37273,37274,37278],{},[895,37275,37276],{},[898,37277,1677],{},[902,37279,1677],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,37282,28187],{},[614,37284,37285],{},"demand function",[883,37287,37289],{"className":37288},[886],[888,37290,37291],{"xmlns":890,"display":28251},[892,37292,37293,37356],{},[20939,37294,37295],{"width":28256},[20944,37296,37297,37299,37349,37351],{},[20947,37298],{"width":28261},[20947,37300,37301],{},[895,37302,37303,37305,37307,37309,37311,37313,37315,37321,37323,37329,37331,37333,37335,37341,37343,37345,37347],{},[898,37304,1662],{},[1700,37306,1765],{},[898,37308,4374],{},[1700,37310,1703],{"stretchy":1702},[898,37312,1677],{},[1700,37314,1732],{"separator":1731},[2007,37316,37317,37319],{},[898,37318,1677],{},[1931,37320,1933],{},[1700,37322,1732],{"separator":1731},[2007,37324,37325,37327],{},[898,37326,1677],{},[1931,37328,2343],{},[1700,37330,1732],{"separator":1731},[1700,37332,9833],{},[1700,37334,1732],{"separator":1731},[2007,37336,37337,37339],{},[898,37338,1677],{},[898,37340,37045],{},[1700,37342,1732],{"separator":1731},[898,37344,9316],{},[1700,37346,1709],{"stretchy":1702},[898,37348,2196],{"mathvariant":1791},[20947,37350],{"width":28261},[20947,37352,37353],{},[1781,37354,37355],{},"(2.1)",[902,37357,37358],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,37360,37361,37362,37365,37366,37379],{},"Důležitou vlastností je ",[38,37363,37364],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,37367,37369],{"className":37368},[886],[888,37370,37371],{"xmlns":890},[892,37372,37373,37377],{},[895,37374,37375],{},[898,37376,12226],{},[902,37378,12226],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,37381,37383],{"className":37382},[886],[888,37384,37385],{"xmlns":890,"display":28251},[892,37386,37387,37502],{},[20939,37388,37389],{"width":28256},[20944,37390,37391,37393,37495,37497],{},[20947,37392],{"width":28261},[20947,37394,37395],{},[895,37396,37397,37399,37401,37403,37405,37407,37409,37411,37413,37419,37421,37423,37429,37431,37433,37435,37437,37443,37445,37447,37449,37451,37453,37455,37457,37459,37461,37467,37469,37475,37477,37479,37481,37487,37489,37491,37493],{},[898,37398,1662],{},[1700,37400,1765],{},[898,37402,4374],{},[1700,37404,1703],{"stretchy":1702},[898,37406,12226],{},[898,37408,1677],{},[1700,37410,1732],{"separator":1731},[898,37412,12226],{},[2007,37414,37415,37417],{},[898,37416,1677],{},[1931,37418,1933],{},[1700,37420,1732],{"separator":1731},[898,37422,12226],{},[2007,37424,37425,37427],{},[898,37426,1677],{},[1931,37428,2343],{},[1700,37430,1732],{"separator":1731},[1700,37432,9833],{},[1700,37434,1732],{"separator":1731},[898,37436,12226],{},[2007,37438,37439,37441],{},[898,37440,1677],{},[898,37442,37045],{},[1700,37444,1732],{"separator":1731},[898,37446,12226],{},[898,37448,9316],{},[1700,37450,1709],{"stretchy":1702},[1700,37452,1765],{},[898,37454,4374],{},[1700,37456,1703],{"stretchy":1702},[898,37458,1677],{},[1700,37460,1732],{"separator":1731},[2007,37462,37463,37465],{},[898,37464,1677],{},[1931,37466,1933],{},[1700,37468,1732],{"separator":1731},[2007,37470,37471,37473],{},[898,37472,1677],{},[1931,37474,2343],{},[1700,37476,1732],{"separator":1731},[1700,37478,9833],{},[1700,37480,1732],{"separator":1731},[2007,37482,37483,37485],{},[898,37484,1677],{},[898,37486,37045],{},[1700,37488,1732],{"separator":1731},[898,37490,9316],{},[1700,37492,1709],{"stretchy":1702},[898,37494,2196],{"mathvariant":1791},[20947,37496],{"width":28261},[20947,37498,37499],{},[1781,37500,37501],{},"(2.2)",[902,37503,37504],{"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}",[4060,37506,37507],{},[724,37508,37509,37511,37512,2196],{},[883,37510,4601],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,37513,37514],{},"v jednofaktorových modelech neplatí",[724,37516,37517,37518,1343,37521,2114,37524,37527],{},"Rozlišuje se poptávka ",[38,37519,37520],{},"individuální",[38,37522,37523],{},"tržní",[38,37525,37526],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,37529,37531],{"id":37530},"jednofaktorové-modely","Jednofaktorové modely",[37533,37534,37536],"h4",{"id":37535},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,37538,37539,37540,37553,37554,2901],{},"Poptávané množství ",[883,37541,37543],{"className":37542},[886],[888,37544,37545],{"xmlns":890},[892,37546,37547,37551],{},[895,37548,37549],{},[898,37550,1662],{},[902,37552,1662],{"encoding":904}," závisí pouze na ceně ",[883,37555,37557],{"className":37556},[886],[888,37558,37559],{"xmlns":890},[892,37560,37561,37565],{},[895,37562,37563],{},[898,37564,1677],{},[902,37566,1677],{"encoding":904},[883,37568,37570],{"className":37569},[886],[888,37571,37572],{"xmlns":890,"display":28251},[892,37573,37574,37626],{},[20939,37575,37576],{"width":28256},[20944,37577,37578,37580,37619,37621],{},[20947,37579],{"width":28261},[20947,37581,37582],{},[895,37583,37584,37586,37588,37590,37592,37594,37596,37598,37600,37603,37605,37607,37609,37611,37613,37615,37617],{},[898,37585,1662],{},[1700,37587,1765],{},[898,37589,4374],{},[1700,37591,1703],{"stretchy":1702},[898,37593,1677],{},[1700,37595,1709],{"stretchy":1702},[1700,37597,1732],{"separator":1731},[6066,37599],{"width":6068},[1781,37601,37602],{},"resp.",[6066,37604],{"width":6068},[898,37606,1677],{},[1700,37608,1765],{},[898,37610,4374],{},[1700,37612,1703],{"stretchy":1702},[898,37614,1662],{},[1700,37616,1709],{"stretchy":1702},[898,37618,2196],{"mathvariant":1791},[20947,37620],{"width":28261},[20947,37622,37623],{},[1781,37624,37625],{},"(2.3)",[902,37627,37628],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,37630,37631,37632,10208,37635,4110],{},"Graf této funkce se nazývá ",[38,37633,37634],{},"křivka poptávky",[614,37636,37637],{},"demand curve",[37533,37639,37641],{"id":37640},"zákon-klesající-poptávky","Zákon klesající poptávky",[4060,37643,37644],{},[724,37645,37646],{},[38,37647,37648,37649,37662,37663,37676,37677,37662,37690,37703],{},"Roste-li cena ",[883,37650,37652],{"className":37651},[886],[888,37653,37654],{"xmlns":890},[892,37655,37656,37660],{},[895,37657,37658],{},[898,37659,1677],{},[902,37661,1677],{"encoding":904},", pak množství ",[883,37664,37666],{"className":37665},[886],[888,37667,37668],{"xmlns":890},[892,37669,37670,37674],{},[895,37671,37672],{},[898,37673,1662],{},[902,37675,1662],{"encoding":904}," klesá; klesá-li cena ",[883,37678,37680],{"className":37679},[886],[888,37681,37682],{"xmlns":890},[892,37683,37684,37688],{},[895,37685,37686],{},[898,37687,1677],{},[902,37689,1677],{"encoding":904},[883,37691,37693],{"className":37692},[886],[888,37694,37695],{"xmlns":890},[892,37696,37697,37701],{},[895,37698,37699],{},[898,37700,1662],{},[902,37702,1662],{"encoding":904}," roste.",[724,37705,37706,37707,37710],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,37708,37709],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[4060,37712,37713,37718],{},[724,37714,37715,37717],{},[883,37716,4346],{}," Intuice — proč zákon platí",[120,37719,37720,37726],{},[123,37721,37722,37725],{},[38,37723,37724],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,37727,37728,37731],{},[38,37729,37730],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,37733,37734,37735,37748,37749,37762,37763,37789,37790,37816,37817,8290,37843,37846,37847,2196],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,37736,37738],{"className":37737},[886],[888,37739,37740],{"xmlns":890},[892,37741,37742,37746],{},[895,37743,37744],{},[898,37745,1677],{},[902,37747,1677],{"encoding":904}," se vynáší na svislou osu, množství ",[883,37750,37752],{"className":37751},[886],[888,37753,37754],{"xmlns":890},[892,37755,37756,37760],{},[895,37757,37758],{},[898,37759,1662],{},[902,37761,1662],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,37764,37766],{"className":37765},[886],[888,37767,37768],{"xmlns":890},[892,37769,37770,37786],{},[895,37771,37772,37774,37776,37778,37784],{},[1700,37773,1927],{"stretchy":1702},[1931,37775,1772],{},[1700,37777,1732],{"separator":1731},[2007,37779,37780,37782],{},[898,37781,1677],{},[1931,37783,1772],{},[1700,37785,1970],{"stretchy":1702},[902,37787,37788],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,37791,37793],{"className":37792},[886],[888,37794,37795],{"xmlns":890},[892,37796,37797,37813],{},[895,37798,37799,37801,37807,37809,37811],{},[1700,37800,1927],{"stretchy":1702},[2007,37802,37803,37805],{},[898,37804,1662],{},[1931,37806,1772],{},[1700,37808,1732],{"separator":1731},[1931,37810,1772],{},[1700,37812,1970],{"stretchy":1702},[902,37814,37815],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,37818,37820],{"className":37819},[886],[888,37821,37822],{"xmlns":890},[892,37823,37824,37840],{},[895,37825,37826,37828,37830,37832,37838],{},[1700,37827,1703],{"stretchy":1702},[1931,37829,1772],{},[1700,37831,1732],{"separator":1731},[2007,37833,37834,37836],{},[898,37835,1677],{},[1931,37837,1772],{},[1700,37839,1709],{"stretchy":1702},[902,37841,37842],{"encoding":904},"(0, P_0)",[38,37844,37845],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,37848,37849],{},"konvexní",[724,37851,37852],{},[614,37853,37854,37855,37877,37878,2114,37903,2196],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,37856,37858],{"className":37857},[886],[888,37859,37860],{"xmlns":890},[892,37861,37862,37874],{},[895,37863,37864,37866,37868,37870,37872],{},[1700,37865,1703],{"stretchy":1702},[898,37867,1662],{},[1700,37869,1732],{"separator":1731},[898,37871,1677],{},[1700,37873,1709],{"stretchy":1702},[902,37875,37876],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,37879,37881],{"className":37880},[886],[888,37882,37883],{"xmlns":890},[892,37884,37885,37901],{},[895,37886,37887,37889,37891,37893,37899],{},[1700,37888,1927],{"stretchy":1702},[1931,37890,1772],{},[1700,37892,1732],{"separator":1731},[2007,37894,37895,37897],{},[898,37896,1677],{},[1931,37898,1772],{},[1700,37900,1970],{"stretchy":1702},[902,37902,37788],{"encoding":904},[883,37904,37906],{"className":37905},[886],[888,37907,37908],{"xmlns":890},[892,37909,37910,37926],{},[895,37911,37912,37914,37920,37922,37924],{},[1700,37913,1927],{"stretchy":1702},[2007,37915,37916,37918],{},[898,37917,1662],{},[1931,37919,1772],{},[1700,37921,1732],{"separator":1731},[1931,37923,1772],{},[1700,37925,1970],{"stretchy":1702},[902,37927,37815],{"encoding":904},[37533,37929,37931],{"id":37930},"lineární-model-poptávky","Lineární model poptávky",[724,37933,37934],{},"Nejjednodušší závislostí je",[883,37936,37938],{"className":37937},[886],[888,37939,37940],{"xmlns":890,"display":28251},[892,37941,37942,37991],{},[20939,37943,37944],{"width":28256},[20944,37945,37946,37948,37984,37986],{},[20947,37947],{"width":28261},[20947,37949,37950],{},[895,37951,37952,37954,37956,37958,37960,37962,37964,37966,37968,37970,37972,37974,37976,37978,37980,37982],{},[898,37953,1677],{},[1700,37955,1765],{},[898,37957,207],{},[898,37959,1662],{},[1700,37961,1897],{},[898,37963,1879],{},[1700,37965,1732],{"separator":1731},[6066,37967],{"width":6068},[898,37969,207],{},[1700,37971,3640],{},[1931,37973,1772],{},[1700,37975,1732],{"separator":1731},[1781,37977,2495],{},[898,37979,1879],{},[1700,37981,3601],{},[1931,37983,12645],{},[20947,37985],{"width":28261},[20947,37987,37988],{},[1781,37989,37990],{},"(2.4)",[902,37992,37993],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,37995,37996,37997,21779,38033,2114,38057,8225,38083,38105,38106,2196],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,37998,38000],{"className":37999},[886],[888,38001,38002],{"xmlns":890},[892,38003,38004,38030],{},[895,38005,38006,38008,38010,38018,38020,38022],{},[898,38007,1662],{},[1700,38009,1765],{},[1770,38011,38012],{"scriptlevel":1772,"displaystyle":1702},[1774,38013,38014,38016],{},[1931,38015,1933],{},[898,38017,207],{},[898,38019,1677],{},[1700,38021,1768],{},[1770,38023,38024],{"scriptlevel":1772,"displaystyle":1702},[1774,38025,38026,38028],{},[898,38027,1879],{},[898,38029,207],{},[902,38031,38032],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,38034,38036],{"className":38035},[886],[888,38037,38038],{"xmlns":890},[892,38039,38040,38054],{},[895,38041,38042,38050,38052],{},[1770,38043,38044],{"scriptlevel":1772,"displaystyle":1702},[1774,38045,38046,38048],{},[1931,38047,1933],{},[898,38049,207],{},[1700,38051,3640],{},[1931,38053,1772],{},[902,38055,38056],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,38058,38060],{"className":38059},[886],[888,38061,38062],{"xmlns":890},[892,38063,38064,38080],{},[895,38065,38066,38068,38076,38078],{},[1700,38067,1768],{},[1770,38069,38070],{"scriptlevel":1772,"displaystyle":1702},[1774,38071,38072,38074],{},[898,38073,1879],{},[898,38075,207],{},[1700,38077,3601],{},[1931,38079,1772],{},[902,38081,38082],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,38084,38086],{"className":38085},[886],[888,38087,38088],{"xmlns":890},[892,38089,38090,38102],{},[895,38091,38092,38094,38096,38098,38100],{},[1700,38093,1703],{"stretchy":1702},[1931,38095,1772],{},[1700,38097,1732],{"separator":1731},[898,38099,1879],{},[1700,38101,1709],{"stretchy":1702},[902,38103,38104],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,38107,38108],{},"nedokonalé konkurenci",[38110,38111,38113],"h5",{"id":38112},"příklad-21","Příklad 2.1",[724,38115,38116,38119,38120,2196],{},[38,38117,38118],{},"Zadání:"," Lineární poptávka ",[883,38121,38123],{"className":38122},[886],[888,38124,38125],{"xmlns":890},[892,38126,38127,38143],{},[895,38128,38129,38131,38133,38135,38137,38139,38141],{},[898,38130,1677],{},[1700,38132,1765],{},[1700,38134,1768],{},[1931,38136,2343],{},[898,38138,1662],{},[1700,38140,1897],{},[1931,38142,3320],{},[902,38144,38145],{"encoding":904},"P = -2Q + 60",[724,38147,38148,38151,38152,38174,38175,2196],{},[38,38149,38150],{},"Řešení:"," Reálné cenové rozpětí je ",[883,38153,38155],{"className":38154},[886],[888,38156,38157],{"xmlns":890},[892,38158,38159,38171],{},[895,38160,38161,38163,38165,38167,38169],{},[1700,38162,1703],{"stretchy":1702},[1931,38164,1772],{},[1700,38166,1732],{"separator":1731},[1931,38168,3320],{},[1700,38170,1709],{"stretchy":1702},[902,38172,38173],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,38176,38178],{"className":38177},[886],[888,38179,38180],{"xmlns":890},[892,38181,38182,38205],{},[895,38183,38184,38186,38188,38190,38198,38200,38202],{},[898,38185,1662],{},[1700,38187,1765],{},[1700,38189,1768],{},[1770,38191,38192],{"scriptlevel":1772,"displaystyle":1702},[1774,38193,38194,38196],{},[1931,38195,1933],{},[1931,38197,2343],{},[898,38199,1677],{},[1700,38201,1897],{},[1931,38203,38204],{},"30",[902,38206,38207],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,38209,38210,38233],{},[19,38211,38212],{},[22,38213,38214,38229,38231],{},[25,38215,38216],{},[883,38217,38219],{"className":38218},[886],[888,38220,38221],{"xmlns":890},[892,38222,38223,38227],{},[895,38224,38225],{},[898,38226,1677],{},[902,38228,1677],{"encoding":904},[25,38230,5399],{},[25,38232,9223],{},[30,38234,38235],{},[22,38236,38237,38252,38254],{},[35,38238,38239],{},[883,38240,38242],{"className":38241},[886],[888,38243,38244],{"xmlns":890},[892,38245,38246,38250],{},[895,38247,38248],{},[898,38249,1662],{},[902,38251,1662],{"encoding":904},[35,38253,3058],{},[35,38255,9223],{},[724,38257,38258],{},[614,38259,38260,38261,2114,38283,2196],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,38262,38264],{"className":38263},[886],[888,38265,38266],{"xmlns":890},[892,38267,38268,38280],{},[895,38269,38270,38272,38274,38276,38278],{},[1700,38271,1927],{"stretchy":1702},[1931,38273,1772],{},[1700,38275,1732],{"separator":1731},[898,38277,1879],{},[1700,38279,1970],{"stretchy":1702},[902,38281,38282],{"encoding":904},"[0, b]",[883,38284,38286],{"className":38285},[886],[888,38287,38288],{"xmlns":890},[892,38289,38290,38308],{},[895,38291,38292,38294,38296,38298,38300,38302,38304,38306],{},[1700,38293,1927],{"stretchy":1702},[1700,38295,1768],{},[898,38297,1879],{},[898,38299,1979],{"mathvariant":1791},[898,38301,207],{},[1700,38303,1732],{"separator":1731},[1931,38305,1772],{},[1700,38307,1970],{"stretchy":1702},[902,38309,38310],{"encoding":904},"[-b\u002Fa, 0]",[37533,38312,38314],{"id":38313},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,38316,38317,38318,38335],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,38319,38321],{"className":38320},[886],[888,38322,38323],{"xmlns":890},[892,38324,38325,38333],{},[895,38326,38327],{},[1785,38328,38329,38331],{},[898,38330,1677],{},[1700,38332,4543],{},[902,38334,4593],{"encoding":904},", je funkce poptávky konstantní:",[883,38337,38339],{"className":38338},[886],[888,38340,38341],{"xmlns":890,"display":28251},[892,38342,38343,38357],{},[895,38344,38345,38347,38349,38355],{},[898,38346,1677],{},[1700,38348,1765],{},[1785,38350,38351,38353],{},[898,38352,1677],{},[1700,38354,4543],{},[898,38356,2196],{"mathvariant":1791},[902,38358,38359],{"encoding":904},"P = P^*.",[724,38361,38362],{},[614,38363,38364,38365,38386,38387,2196],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,38366,38368],{"className":38367},[886],[888,38369,38370],{"xmlns":890},[892,38371,38372,38384],{},[895,38373,38374,38376,38378,38380,38382],{},[1700,38375,1703],{"stretchy":1702},[898,38377,1662],{},[1700,38379,1732],{"separator":1731},[898,38381,1677],{},[1700,38383,1709],{"stretchy":1702},[902,38385,37876],{"encoding":904}," na úrovni ",[883,38388,38390],{"className":38389},[886],[888,38391,38392],{"xmlns":890},[892,38393,38394,38406],{},[895,38395,38396,38398,38400],{},[898,38397,1677],{},[1700,38399,1765],{},[1785,38401,38402,38404],{},[898,38403,1677],{},[1700,38405,4543],{},[902,38407,4546],{"encoding":904},[37533,38409,38411],{"id":38410},"giffenův-statek","Giffenův statek",[724,38413,38414,38415,38417,38418,38420,38421,2196],{},"Existují zboží, u nichž je křivka poptávky ",[38,38416,13842],{}," — tzv. ",[38,38419,38411],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,38422,38423],{},"podřadnému zboží",[38110,38425,38427],{"id":38426},"příklad-22","Příklad 2.2",[724,38429,38430,38433,38434,38452,38453,38475,38476,38494,38495,38513,38514,38537],{},[38,38431,38432],{},"Zadání a popis:"," Křivka ",[883,38435,38437],{"className":38436},[886],[888,38438,38439],{"xmlns":890},[892,38440,38441,38449],{},[895,38442,38443],{},[2007,38444,38445,38447],{},[898,38446,4374],{},[1931,38448,1933],{},[902,38450,38451],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,38454,38456],{"className":38455},[886],[888,38457,38458],{"xmlns":890},[892,38459,38460,38472],{},[895,38461,38462,38464,38466,38468,38470],{},[1700,38463,1703],{"stretchy":1702},[1931,38465,1772],{},[1700,38467,1732],{"separator":1731},[1931,38469,36429],{},[1700,38471,1709],{"stretchy":1702},[902,38473,38474],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,38477,38479],{"className":38478},[886],[888,38480,38481],{"xmlns":890},[892,38482,38483,38491],{},[895,38484,38485],{},[2007,38486,38487,38489],{},[898,38488,1662],{},[1931,38490,1772],{},[902,38492,38493],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,38496,38498],{"className":38497},[886],[888,38499,38500],{"xmlns":890},[892,38501,38502,38510],{},[895,38503,38504],{},[2007,38505,38506,38508],{},[898,38507,4374],{},[1931,38509,2343],{},[902,38511,38512],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,38515,38517],{"className":38516},[886],[888,38518,38519],{"xmlns":890},[892,38520,38521,38534],{},[895,38522,38523,38525,38527,38529,38532],{},[1700,38524,1927],{"stretchy":1702},[1931,38526,1772],{},[1700,38528,1732],{"separator":1731},[1931,38530,38531],{},"21",[1700,38533,1970],{"stretchy":1702},[902,38535,38536],{"encoding":904},"[0, 21]"," centů.",[198,38539,38541],{"id":38540},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,38543,38544,38545,2901],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,38546,38548],{"className":38547},[886],[888,38549,38550],{"xmlns":890},[892,38551,38552,38556],{},[895,38553,38554],{},[898,38555,9316],{},[902,38557,9316],{"encoding":904},[883,38559,38561],{"className":38560},[886],[888,38562,38563],{"xmlns":890,"display":28251},[892,38564,38565,38596],{},[20939,38566,38567],{"width":28256},[20944,38568,38569,38571,38589,38591],{},[20947,38570],{"width":28261},[20947,38572,38573],{},[895,38574,38575,38577,38579,38581,38583,38585,38587],{},[898,38576,1662],{},[1700,38578,1765],{},[898,38580,1762],{},[1700,38582,1703],{"stretchy":1702},[898,38584,9316],{},[1700,38586,1709],{"stretchy":1702},[898,38588,2196],{"mathvariant":1791},[20947,38590],{"width":28261},[20947,38592,38593],{},[1781,38594,38595],{},"(2.5)",[902,38597,38598],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,38600,38601,38602,38605,38606,38609],{},"Funkce se nazývá ",[38,38603,38604],{},"Engelova",", její graf ",[38,38607,38608],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,38611,38612,38744],{},[123,38613,38614,7203,38617,38630,38631,38644,38645,38662,38663],{},[38,38615,38616],{},"Normální (superior) zboží",[883,38618,38620],{"className":38619},[886],[888,38621,38622],{"xmlns":890},[892,38623,38624,38628],{},[895,38625,38626],{},[898,38627,1662],{},[902,38629,1662],{"encoding":904}," roste s ",[883,38632,38634],{"className":38633},[886],[888,38635,38636],{"xmlns":890},[892,38637,38638,38642],{},[895,38639,38640],{},[898,38641,9316],{},[902,38643,9316],{"encoding":904},", nepřesáhne hodnotu ",[883,38646,38648],{"className":38647},[886],[888,38649,38650],{"xmlns":890},[892,38651,38652,38660],{},[895,38653,38654],{},[2007,38655,38656,38658],{},[898,38657,1662],{},[1931,38659,1772],{},[902,38661,38493],{"encoding":904},":\n",[120,38664,38665,38697],{},[123,38666,38667,38670,38671,38674,38675,2196],{},[38,38668,38669],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,38672,38673],{},"konkávní"," křivka, autonomní spotřeba ",[883,38676,38678],{"className":38677},[886],[888,38679,38680],{"xmlns":890},[892,38681,38682,38694],{},[895,38683,38684,38690,38692],{},[2007,38685,38686,38688],{},[898,38687,1662],{},[1931,38689,1933],{},[1700,38691,3601],{},[1931,38693,1772],{},[902,38695,38696],{"encoding":904},"Q_1 > 0",[123,38698,38699,38702,38703,38721,38722,38724,38725,2106,38742,2196],{},[38,38700,38701],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,38704,38706],{"className":38705},[886],[888,38707,38708],{"xmlns":890},[892,38709,38710,38718],{},[895,38711,38712],{},[2007,38713,38714,38716],{},[898,38715,9316],{},[1931,38717,1933],{},[902,38719,38720],{"encoding":904},"Y_1",", křivka je nejprve ",[38,38723,37849],{}," a od ",[883,38726,38728],{"className":38727},[886],[888,38729,38730],{"xmlns":890},[892,38731,38732,38740],{},[895,38733,38734],{},[2007,38735,38736,38738],{},[898,38737,9316],{},[1931,38739,1933],{},[902,38741,38720],{"encoding":904},[38,38743,38673],{},[123,38745,38746,38749,38750,38768],{},[38,38747,38748],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,38751,38753],{"className":38752},[886],[888,38754,38755],{"xmlns":890},[892,38756,38757,38765],{},[895,38758,38759],{},[2007,38760,38761,38763],{},[898,38762,9316],{},[1931,38764,1772],{},[902,38766,38767],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,38770,38771,38772,38775,38776,4110],{},"Mírou citlivosti je ",[614,38773,38774],{},"důchodová elasticita"," (viz ",[207,38777,2155],{"className":38778,"dataFsResolvedFilePath":848,"href":849},[210],[724,38780,38781],{},[614,38782,38783],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[37533,38785,38787],{"id":38786},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[4060,38789,38790,38861,38904],{},[724,38791,38792,38794,38795,2106,38798,2106,38811,5857,38813,38826,38827,38830,38831,2196],{},[883,38793,4601],{}," Pozor — nezbytné ≠ podřadné\n",[38,38796,38797],{},"Nezbytné zboží:",[883,38799,38801],{"className":38800},[886],[888,38802,38803],{"xmlns":890},[892,38804,38805,38809],{},[895,38806,38807],{},[898,38808,1662],{},[902,38810,1662],{"encoding":904},[38,38812,7510],{},[883,38814,38816],{"className":38815},[886],[888,38817,38818],{"xmlns":890},[892,38819,38820,38824],{},[895,38821,38822],{},[898,38823,9316],{},[902,38825,9316],{"encoding":904},", ale ",[38,38828,38829],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,38832,38834],{"className":38833},[886],[888,38835,38836],{"xmlns":890},[892,38837,38838,38858],{},[895,38839,38840,38846,38848,38850,38852,38854,38856],{},[2007,38841,38842,38844],{},[898,38843,1762],{},[898,38845,9316],{},[1700,38847,6694],{},[1700,38849,1703],{"stretchy":1702},[1931,38851,1772],{},[1700,38853,1732],{"separator":1731},[1931,38855,1933],{},[1700,38857,1709],{"stretchy":1702},[902,38859,38860],{"encoding":904},"E_Y \\in (0, 1)",[724,38862,38863,2106,38866,2106,38879,38881,38882,2196],{},[38,38864,38865],{},"Podřadné zboží:",[883,38867,38869],{"className":38868},[886],[888,38870,38871],{"xmlns":890},[892,38872,38873,38877],{},[895,38874,38875],{},[898,38876,1662],{},[902,38878,1662],{"encoding":904},[38,38880,7530],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,38883,38885],{"className":38884},[886],[888,38886,38887],{"xmlns":890},[892,38888,38889,38901],{},[895,38890,38891,38897,38899],{},[2007,38892,38893,38895],{},[898,38894,1762],{},[898,38896,9316],{},[1700,38898,3640],{},[1931,38900,1772],{},[902,38902,38903],{"encoding":904},"E_Y \u003C 0",[724,38905,38906,38907,2196],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,38908,38909],{},"méně kusů, ne jen proporčně méně",[724,38911,38912,38915,38916,38919],{},[38,38913,38914],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,38917,38918],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,38921,38922],{},[2756,38923],{"alt":38924,"className":38925,"src":38926},"imek-engelovy-krivky-3typy",[210,2760],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[38110,38928,38930],{"id":38929},"české-příklady","České příklady",[16,38932,38933,38943],{},[19,38934,38935],{},[22,38936,38937,38940],{},[25,38938,38939],{},"Podřadné",[25,38941,38942],{},"Nahradí se za",[30,38944,38945,38953,38961,38969,38977,38985,38993,39001],{},[22,38946,38947,38950],{},[35,38948,38949],{},"Instantní polévky, ramen",[35,38951,38952],{},"Čerstvé jídlo, restaurace",[22,38954,38955,38958],{},[35,38956,38957],{},"MHD (autobus, tramvaj)",[35,38959,38960],{},"Vlastní auto, Uber, taxi",[22,38962,38963,38966],{},[35,38964,38965],{},"Mražené polotovary, pizza z mrazáku",[35,38967,38968],{},"Čerstvé suroviny, hotovky",[22,38970,38971,38974],{},[35,38972,38973],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,38975,38976],{},"Značkové produkty",[22,38978,38979,38982],{},[35,38980,38981],{},"Paštika Májka, obyčejný měkký salám",[35,38983,38984],{},"Kvalitní uzeniny, šunka od kosti",[22,38986,38987,38990],{},[35,38988,38989],{},"Second hand oblečení",[35,38991,38992],{},"Nové oblečení, značky",[22,38994,38995,38998],{},[35,38996,38997],{},"Krabicové víno, nejlevnější pivo",[35,38999,39000],{},"Lahvové víno, řemeslná piva",[22,39002,39003,39006],{},[35,39004,39005],{},"Ojetá auta nižších tříd",[35,39007,39008],{},"Nová auta, prémiové značky",[4060,39010,39011],{},[724,39012,39013,39015,39016,39019],{},[883,39014,4761],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,39017,39018],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,39021,39022,39025,39026,10208,39029,39051,39052,10208,39055,39076,39077,39095,39096,39099],{},[38,39023,39024],{},"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 ",[38,39027,39028],{},"luxus",[883,39030,39032],{"className":39031},[886],[888,39033,39034],{"xmlns":890},[892,39035,39036,39048],{},[895,39037,39038,39044,39046],{},[2007,39039,39040,39042],{},[898,39041,1762],{},[898,39043,9316],{},[1700,39045,3601],{},[1931,39047,1933],{},[902,39049,39050],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,39053,39054],{},"podřadné",[883,39056,39058],{"className":39057},[886],[888,39059,39060],{"xmlns":890},[892,39061,39062,39074],{},[895,39063,39064,39070,39072],{},[2007,39065,39066,39068],{},[898,39067,1762],{},[898,39069,9316],{},[1700,39071,3640],{},[1931,39073,1772],{},[902,39075,38903],{"encoding":904},"). Proto je ",[883,39078,39080],{"className":39079},[886],[888,39081,39082],{"xmlns":890},[892,39083,39084,39092],{},[895,39085,39086],{},[2007,39087,39088,39090],{},[898,39089,1762],{},[898,39091,9316],{},[902,39093,39094],{"encoding":904},"E_Y"," vždy ",[38,39097,39098],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,39101,39102,39103,39105],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,39104,38411],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,39107,39109,39110,1709],{"id":39108},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,39111,39112],{},"shift of demand",[724,39114,39115,39116,39134,39135,39152,39153,39166,39167,2882,39180,39202,39203,39220,39221,39247,39248,39251],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,39117,39119],{"className":39118},[886],[888,39120,39121],{"xmlns":890},[892,39122,39123,39131],{},[895,39124,39125],{},[2007,39126,39127,39129],{},[898,39128,1677],{},[1931,39130,1772],{},[902,39132,39133],{"encoding":904},"P_0"," odpovídá množství ",[883,39136,39138],{"className":39137},[886],[888,39139,39140],{"xmlns":890},[892,39141,39142,39150],{},[895,39143,39144],{},[2007,39145,39146,39148],{},[898,39147,1662],{},[1931,39149,1772],{},[902,39151,38493],{"encoding":904}," na křivce ",[883,39154,39156],{"className":39155},[886],[888,39157,39158],{"xmlns":890},[892,39159,39160,39164],{},[895,39161,39162],{},[898,39163,4374],{},[902,39165,4374],{"encoding":904},"; vzroste-li důchod z ",[883,39168,39170],{"className":39169},[886],[888,39171,39172],{"xmlns":890},[892,39173,39174,39178],{},[895,39175,39176],{},[898,39177,9316],{},[902,39179,9316],{"encoding":904},[883,39181,39183],{"className":39182},[886],[888,39184,39185],{"xmlns":890},[892,39186,39187,39199],{},[895,39188,39189,39195,39197],{},[2007,39190,39191,39193],{},[898,39192,9316],{},[1931,39194,1933],{},[1700,39196,3601],{},[898,39198,9316],{},[902,39200,39201],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,39204,39206],{"className":39205},[886],[888,39207,39208],{"xmlns":890},[892,39209,39210,39218],{},[895,39211,39212],{},[2007,39213,39214,39216],{},[898,39215,1677],{},[1931,39217,1772],{},[902,39219,39133],{"encoding":904}," odpovídá vyšší ",[883,39222,39224],{"className":39223},[886],[888,39225,39226],{"xmlns":890},[892,39227,39228,39244],{},[895,39229,39230,39236,39238],{},[2007,39231,39232,39234],{},[898,39233,1662],{},[1931,39235,1933],{},[1700,39237,3601],{},[2007,39239,39240,39242],{},[898,39241,1662],{},[1931,39243,1772],{},[902,39245,39246],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,39249,39250],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,39253,39254],{},[2756,39255],{"alt":39256,"className":39257,"src":39258},"imek-posun-vs-pohyb-po-krivce",[210,2760],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,39260,39261],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,39263,39264],{},[614,39265,39266,39267,14196,39297,39318],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,39268,39270],{"className":39269},[886],[888,39271,39272],{"xmlns":890},[892,39273,39274,39294],{},[895,39275,39276,39282,39284,39286,39288],{},[2007,39277,39278,39280],{},[898,39279,4374],{},[1931,39281,2343],{},[1700,39283,1732],{"separator":1731},[898,39285,4374],{},[1700,39287,1732],{"separator":1731},[2007,39289,39290,39292],{},[898,39291,4374],{},[1931,39293,1933],{},[902,39295,39296],{"encoding":904},"D_2, D, D_1",[883,39298,39300],{"className":39299},[886],[888,39301,39302],{"xmlns":890},[892,39303,39304,39316],{},[895,39305,39306,39308,39310,39312,39314],{},[1700,39307,1703],{"stretchy":1702},[898,39309,1662],{},[1700,39311,1732],{"separator":1731},[898,39313,1677],{},[1700,39315,1709],{"stretchy":1702},[902,39317,37876],{"encoding":904},", šipky naznačují posuny.",[38110,39320,39322],{"id":39321},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,39324,39325,39327,39328,39351,39352,39369,39370,39387,39388,2196],{},[38,39326,38118],{}," Poptávce ",[883,39329,39331],{"className":39330},[886],[888,39332,39333],{"xmlns":890},[892,39334,39335,39349],{},[895,39336,39337,39339,39341,39343,39345,39347],{},[898,39338,1677],{},[1700,39340,1765],{},[898,39342,4374],{},[1700,39344,1703],{"stretchy":1702},[898,39346,1662],{},[1700,39348,1709],{"stretchy":1702},[902,39350,4829],{"encoding":904}," odpovídá ceně ",[883,39353,39355],{"className":39354},[886],[888,39356,39357],{"xmlns":890},[892,39358,39359,39367],{},[895,39360,39361],{},[2007,39362,39363,39365],{},[898,39364,1677],{},[1931,39366,1772],{},[902,39368,39133],{"encoding":904}," množství ",[883,39371,39373],{"className":39372},[886],[888,39374,39375],{"xmlns":890},[892,39376,39377,39385],{},[895,39378,39379],{},[2007,39380,39381,39383],{},[898,39382,1662],{},[1931,39384,1772],{},[902,39386,38493],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,39389,39391],{"className":39390},[886],[888,39392,39393],{"xmlns":890},[892,39394,39395,39399],{},[895,39396,39397],{},[898,39398,2971],{},[902,39400,2971],{"encoding":904},[724,39402,39403,39405,39406,39423,39424,39446],{},[38,39404,38150],{}," Kupující nakupuje množství ",[883,39407,39409],{"className":39408},[886],[888,39410,39411],{"xmlns":890},[892,39412,39413,39421],{},[895,39414,39415],{},[2007,39416,39417,39419],{},[898,39418,1662],{},[1931,39420,1933],{},[902,39422,29187],{"encoding":904},", které odpovídá ceně ",[883,39425,39427],{"className":39426},[886],[888,39428,39429],{"xmlns":890},[892,39430,39431,39443],{},[895,39432,39433,39439,39441],{},[2007,39434,39435,39437],{},[898,39436,1677],{},[1931,39438,1772],{},[1700,39440,1897],{},[898,39442,2971],{},[902,39444,39445],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,39448,39450],{"className":39449},[886],[888,39451,39452],{"xmlns":890,"display":28251},[892,39453,39454,39488],{},[895,39455,39456,39458,39460,39466,39468,39470,39472,39474,39476,39478,39480,39482,39484,39486],{},[898,39457,1677],{},[1700,39459,1765],{},[2007,39461,39462,39464],{},[898,39463,4374],{},[1931,39465,1933],{},[1700,39467,1703],{"stretchy":1702},[898,39469,1662],{},[1700,39471,1709],{"stretchy":1702},[1700,39473,1765],{},[898,39475,4374],{},[1700,39477,1703],{"stretchy":1702},[898,39479,1662],{},[1700,39481,1709],{"stretchy":1702},[1700,39483,1768],{},[898,39485,2971],{},[1700,39487,1732],{"separator":1731},[902,39489,39490],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,39492,39493,39494,2196],{},"tj. dojde k ",[38,39495,39496],{},"posunu poptávky doleva",[724,39498,39499],{},[614,39500,39501,39502,39523,39524,1343,39541,1343,39554,39575,39576,2114,39593,2196],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,39503,39505],{"className":39504},[886],[888,39506,39507],{"xmlns":890},[892,39508,39509,39521],{},[895,39510,39511,39513,39515,39517,39519],{},[1700,39512,1703],{"stretchy":1702},[898,39514,1662],{},[1700,39516,1732],{"separator":1731},[898,39518,1677],{},[1700,39520,1709],{"stretchy":1702},[902,39522,37876],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,39525,39527],{"className":39526},[886],[888,39528,39529],{"xmlns":890},[892,39530,39531,39539],{},[895,39532,39533],{},[2007,39534,39535,39537],{},[898,39536,1677],{},[1931,39538,1772],{},[902,39540,39133],{"encoding":904},[883,39542,39544],{"className":39543},[886],[888,39545,39546],{"xmlns":890},[892,39547,39548,39552],{},[895,39549,39550],{},[898,39551,2971],{},[902,39553,2971],{"encoding":904},[883,39555,39557],{"className":39556},[886],[888,39558,39559],{"xmlns":890},[892,39560,39561,39573],{},[895,39562,39563,39569,39571],{},[2007,39564,39565,39567],{},[898,39566,1677],{},[1931,39568,1772],{},[1700,39570,1897],{},[898,39572,2971],{},[902,39574,39445],{"encoding":904},"; na vodorovné ",[883,39577,39579],{"className":39578},[886],[888,39580,39581],{"xmlns":890},[892,39582,39583,39591],{},[895,39584,39585],{},[2007,39586,39587,39589],{},[898,39588,1662],{},[1931,39590,1933],{},[902,39592,29187],{"encoding":904},[883,39594,39596],{"className":39595},[886],[888,39597,39598],{"xmlns":890},[892,39599,39600,39608],{},[895,39601,39602],{},[2007,39603,39604,39606],{},[898,39605,1662],{},[1931,39607,1772],{},[902,39609,38493],{"encoding":904},[198,39611,39613],{"id":39612},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,39615,39616],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,39618,39620],{"className":39619},[886],[888,39621,39622],{"xmlns":890,"display":28251},[892,39623,39624,39809],{},[20939,39625,39626],{"width":28256},[20944,39627,39628,39630,39802,39804],{},[20947,39629],{"width":28261},[20947,39631,39632],{},[20939,39633,39634,39718],{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},[20944,39635,39636,39646],{},[20947,39637,39638],{},[1770,39639,39640],{"scriptlevel":1772,"displaystyle":1731},[2007,39641,39642,39644],{},[898,39643,1662],{},[1931,39645,1933],{},[20947,39647,39648],{},[1770,39649,39650],{"scriptlevel":1772,"displaystyle":1731},[895,39651,39652,39654,39656,39662,39664,39670,39672,39678,39680,39682,39688,39690,39696,39702,39704,39710,39716],{},[895,39653],{},[1700,39655,1765],{},[2007,39657,39658,39660],{},[898,39659,4374],{},[1931,39661,1933],{},[1700,39663,1703],{"stretchy":1702},[2007,39665,39666,39668],{},[898,39667,1677],{},[1931,39669,1933],{},[1700,39671,1732],{"separator":1731},[2007,39673,39674,39676],{},[898,39675,1677],{},[1931,39677,2343],{},[1700,39679,1709],{"stretchy":1702},[1700,39681,1765],{},[2007,39683,39684,39686],{},[898,39685,207],{},[1931,39687,1933],{},[1700,39689,1897],{},[2007,39691,39692,39694],{},[898,39693,1879],{},[1931,39695,1933],{},[2007,39697,39698,39700],{},[898,39699,1677],{},[1931,39701,1933],{},[1700,39703,1897],{},[2007,39705,39706,39708],{},[898,39707,2354],{},[1931,39709,1933],{},[2007,39711,39712,39714],{},[898,39713,1677],{},[1931,39715,2343],{},[1700,39717,1732],{"separator":1731},[20944,39719,39720,39730],{},[20947,39721,39722],{},[1770,39723,39724],{"scriptlevel":1772,"displaystyle":1731},[2007,39725,39726,39728],{},[898,39727,1662],{},[1931,39729,2343],{},[20947,39731,39732],{},[1770,39733,39734],{"scriptlevel":1772,"displaystyle":1731},[895,39735,39736,39738,39740,39746,39748,39754,39756,39762,39764,39766,39772,39774,39780,39786,39788,39794,39800],{},[895,39737],{},[1700,39739,1765],{},[2007,39741,39742,39744],{},[898,39743,4374],{},[1931,39745,2343],{},[1700,39747,1703],{"stretchy":1702},[2007,39749,39750,39752],{},[898,39751,1677],{},[1931,39753,1933],{},[1700,39755,1732],{"separator":1731},[2007,39757,39758,39760],{},[898,39759,1677],{},[1931,39761,2343],{},[1700,39763,1709],{"stretchy":1702},[1700,39765,1765],{},[2007,39767,39768,39770],{},[898,39769,207],{},[1931,39771,2343],{},[1700,39773,1897],{},[2007,39775,39776,39778],{},[898,39777,1879],{},[1931,39779,2343],{},[2007,39781,39782,39784],{},[898,39783,1677],{},[1931,39785,1933],{},[1700,39787,1897],{},[2007,39789,39790,39792],{},[898,39791,2354],{},[1931,39793,2343],{},[2007,39795,39796,39798],{},[898,39797,1677],{},[1931,39799,2343],{},[898,39801,2196],{"mathvariant":1791},[20947,39803],{"width":28261},[20947,39805,39806],{},[1781,39807,39808],{},"(2.6)",[902,39810,39811],{"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}",[37533,39813,39815],{"id":39814},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,39817,39818,39865,39912],{},[123,39819,39820,1343,39842,39864],{},[883,39821,39823],{"className":39822},[886],[888,39824,39825],{"xmlns":890},[892,39826,39827,39839],{},[895,39828,39829,39835,39837],{},[2007,39830,39831,39833],{},[898,39832,207],{},[1931,39834,1933],{},[1700,39836,3601],{},[1931,39838,1772],{},[902,39840,39841],{"encoding":904},"a_1 > 0",[883,39843,39845],{"className":39844},[886],[888,39846,39847],{"xmlns":890},[892,39848,39849,39861],{},[895,39850,39851,39857,39859],{},[2007,39852,39853,39855],{},[898,39854,207],{},[1931,39856,2343],{},[1700,39858,3601],{},[1931,39860,1772],{},[902,39862,39863],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,39866,39867,1343,39889,39911],{},[883,39868,39870],{"className":39869},[886],[888,39871,39872],{"xmlns":890},[892,39873,39874,39886],{},[895,39875,39876,39882,39884],{},[2007,39877,39878,39880],{},[898,39879,1879],{},[1931,39881,1933],{},[1700,39883,3640],{},[1931,39885,1772],{},[902,39887,39888],{"encoding":904},"b_1 \u003C 0",[883,39890,39892],{"className":39891},[886],[888,39893,39894],{"xmlns":890},[892,39895,39896,39908],{},[895,39897,39898,39904,39906],{},[2007,39899,39900,39902],{},[898,39901,2354],{},[1931,39903,2343],{},[1700,39905,3640],{},[1931,39907,1772],{},[902,39909,39910],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,39913,39914,39915,1343,39932,39950,39951],{},"zkřížené koeficienty ",[883,39916,39918],{"className":39917},[886],[888,39919,39920],{"xmlns":890},[892,39921,39922,39930],{},[895,39923,39924],{},[2007,39925,39926,39928],{},[898,39927,2354],{},[1931,39929,1933],{},[902,39931,29984],{"encoding":904},[883,39933,39935],{"className":39934},[886],[888,39936,39937],{"xmlns":890},[892,39938,39939,39947],{},[895,39940,39941],{},[2007,39942,39943,39945],{},[898,39944,1879],{},[1931,39946,2343],{},[902,39948,39949],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,39952,39953,40003],{},[123,39954,39955,39958,39959,1343,39981,1732],{},[38,39956,39957],{},"substituty"," (máslo vs. margarín): ",[883,39960,39962],{"className":39961},[886],[888,39963,39964],{"xmlns":890},[892,39965,39966,39978],{},[895,39967,39968,39974,39976],{},[2007,39969,39970,39972],{},[898,39971,2354],{},[1931,39973,1933],{},[1700,39975,3601],{},[1931,39977,1772],{},[902,39979,39980],{"encoding":904},"c_1 > 0",[883,39982,39984],{"className":39983},[886],[888,39985,39986],{"xmlns":890},[892,39987,39988,40000],{},[895,39989,39990,39996,39998],{},[2007,39991,39992,39994],{},[898,39993,1879],{},[1931,39995,2343],{},[1700,39997,3601],{},[1931,39999,1772],{},[902,40001,40002],{"encoding":904},"b_2 > 0",[123,40004,40005,40008,40009,1343,40031,2196],{},[38,40006,40007],{},"komplementy"," (auto vs. benzín): ",[883,40010,40012],{"className":40011},[886],[888,40013,40014],{"xmlns":890},[892,40015,40016,40028],{},[895,40017,40018,40024,40026],{},[2007,40019,40020,40022],{},[898,40021,2354],{},[1931,40023,1933],{},[1700,40025,3640],{},[1931,40027,1772],{},[902,40029,40030],{"encoding":904},"c_1 \u003C 0",[883,40032,40034],{"className":40033},[886],[888,40035,40036],{"xmlns":890},[892,40037,40038,40050],{},[895,40039,40040,40046,40048],{},[2007,40041,40042,40044],{},[898,40043,1879],{},[1931,40045,2343],{},[1700,40047,3640],{},[1931,40049,1772],{},[902,40051,40052],{"encoding":904},"b_2 \u003C 0",[724,40054,40055],{},"Schematicky:",[724,40057,40058,40061],{},[38,40059,40060],{},"Substituty",[883,40062,40064],{"className":40063},[886],[888,40065,40066],{"xmlns":890},[892,40067,40068,40207],{},[895,40069,40070,40076,40078,40093,40095,40115,40117,40137,40139,40141,40147,40149,40163,40165,40185,40187],{},[2007,40071,40072,40074],{},[898,40073,1662],{},[1931,40075,1933],{},[1700,40077,1765],{},[898,40079,40080],{},[40081,40082,40083,40091],"munder",{},[1700,40084,40085],{},[2007,40086,40087,40089],{},[898,40088,207],{},[1931,40090,1933],{},[1700,40092,1897],{"lspace":1792,"rspace":1792},[1700,40094,1897],{},[898,40096,40097],{},[40081,40098,40099,40113],{},[1700,40100,40101,40107],{},[2007,40102,40103,40105],{},[898,40104,1879],{},[1931,40106,1933],{},[2007,40108,40109,40111],{},[898,40110,1677],{},[1931,40112,1933],{},[1700,40114,1768],{"lspace":1792,"rspace":1792},[1700,40116,1897],{},[898,40118,40119],{},[40081,40120,40121,40135],{},[1700,40122,40123,40129],{},[2007,40124,40125,40127],{},[898,40126,2354],{},[1931,40128,1933],{},[2007,40130,40131,40133],{},[898,40132,1677],{},[1931,40134,2343],{},[1700,40136,1897],{"lspace":1792,"rspace":1792},[1700,40138,1732],{"separator":1731},[6066,40140],{"width":6068},[2007,40142,40143,40145],{},[898,40144,1662],{},[1931,40146,2343],{},[1700,40148,1765],{},[898,40150,40151],{},[40081,40152,40153,40161],{},[1700,40154,40155],{},[2007,40156,40157,40159],{},[898,40158,207],{},[1931,40160,2343],{},[1700,40162,1897],{"lspace":1792,"rspace":1792},[1700,40164,1897],{},[898,40166,40167],{},[40081,40168,40169,40183],{},[1700,40170,40171,40177],{},[2007,40172,40173,40175],{},[898,40174,1879],{},[1931,40176,2343],{},[2007,40178,40179,40181],{},[898,40180,1677],{},[1931,40182,1933],{},[1700,40184,1897],{"lspace":1792,"rspace":1792},[1700,40186,1897],{},[898,40188,40189],{},[40081,40190,40191,40205],{},[1700,40192,40193,40199],{},[2007,40194,40195,40197],{},[898,40196,2354],{},[1931,40198,2343],{},[2007,40200,40201,40203],{},[898,40202,1677],{},[1931,40204,2343],{},[1700,40206,1768],{"lspace":1792,"rspace":1792},[902,40208,40209],{"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}",[724,40211,40212,40215],{},[38,40213,40214],{},"Komplementy",[883,40216,40218],{"className":40217},[886],[888,40219,40220],{"xmlns":890},[892,40221,40222,40360],{},[895,40223,40224,40230,40232,40246,40248,40268,40270,40290,40292,40294,40300,40302,40316,40318,40338,40340],{},[2007,40225,40226,40228],{},[898,40227,1662],{},[1931,40229,1933],{},[1700,40231,1765],{},[898,40233,40234],{},[40081,40235,40236,40244],{},[1700,40237,40238],{},[2007,40239,40240,40242],{},[898,40241,207],{},[1931,40243,1933],{},[1700,40245,1897],{"lspace":1792,"rspace":1792},[1700,40247,1897],{},[898,40249,40250],{},[40081,40251,40252,40266],{},[1700,40253,40254,40260],{},[2007,40255,40256,40258],{},[898,40257,1879],{},[1931,40259,1933],{},[2007,40261,40262,40264],{},[898,40263,1677],{},[1931,40265,1933],{},[1700,40267,1768],{"lspace":1792,"rspace":1792},[1700,40269,1897],{},[898,40271,40272],{},[40081,40273,40274,40288],{},[1700,40275,40276,40282],{},[2007,40277,40278,40280],{},[898,40279,2354],{},[1931,40281,1933],{},[2007,40283,40284,40286],{},[898,40285,1677],{},[1931,40287,2343],{},[1700,40289,1768],{"lspace":1792,"rspace":1792},[1700,40291,1732],{"separator":1731},[6066,40293],{"width":6068},[2007,40295,40296,40298],{},[898,40297,1662],{},[1931,40299,2343],{},[1700,40301,1765],{},[898,40303,40304],{},[40081,40305,40306,40314],{},[1700,40307,40308],{},[2007,40309,40310,40312],{},[898,40311,207],{},[1931,40313,2343],{},[1700,40315,1897],{"lspace":1792,"rspace":1792},[1700,40317,1897],{},[898,40319,40320],{},[40081,40321,40322,40336],{},[1700,40323,40324,40330],{},[2007,40325,40326,40328],{},[898,40327,1879],{},[1931,40329,2343],{},[2007,40331,40332,40334],{},[898,40333,1677],{},[1931,40335,1933],{},[1700,40337,1768],{"lspace":1792,"rspace":1792},[1700,40339,1897],{},[898,40341,40342],{},[40081,40343,40344,40358],{},[1700,40345,40346,40352],{},[2007,40347,40348,40350],{},[898,40349,2354],{},[1931,40351,2343],{},[2007,40353,40354,40356],{},[898,40355,1677],{},[1931,40357,2343],{},[1700,40359,1768],{"lspace":1792,"rspace":1792},[902,40361,40362],{"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}",[37155,40364],{},[115,40366,13310],{"id":36964},[4060,40368,40369],{},[724,40370,40371,40373,40374,37179,40387,37193,40400,40403,40404,5857,40428,40446],{},[883,40372,4346],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,40375,40377],{"className":40376},[886],[888,40378,40379],{"xmlns":890},[892,40380,40381,40385],{},[895,40382,40383],{},[898,40384,1662],{},[902,40386,1662],{"encoding":904},[883,40388,40390],{"className":40389},[886],[888,40391,40392],{"xmlns":890},[892,40393,40394,40398],{},[895,40395,40396],{},[898,40397,1677],{},[902,40399,1677],{"encoding":904},[38,40401,40402],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,40405,40407],{"className":40406},[886],[888,40408,40409],{"xmlns":890},[892,40410,40411,40425],{},[895,40412,40413,40415,40417,40419,40421,40423],{},[898,40414,1677],{},[1700,40416,1765],{},[898,40418,2354],{},[898,40420,1662],{},[1700,40422,1897],{},[898,40424,2406],{},[902,40426,40427],{"encoding":904},"P = cQ + d",[883,40429,40431],{"className":40430},[886],[888,40432,40433],{"xmlns":890},[892,40434,40435,40443],{},[895,40436,40437,40439,40441],{},[898,40438,2354],{},[1700,40440,3601],{},[1931,40442,1772],{},[902,40444,40445],{"encoding":904},"c > 0"," je standardní aproximací.",[198,40448,37249],{"id":40449},"obecný-vícefaktorový-model-1",[724,40451,40452,10208,40455,40458,40459,40472,40473,37081,40486,37095,40499,40512,40513,40527,40528,37124,40541,40554],{},[38,40453,40454],{},"Nabízené množství",[614,40456,40457],{},"quantity supplied",") závisí na ceně ",[883,40460,40462],{"className":40461},[886],[888,40463,40464],{"xmlns":890},[892,40465,40466,40470],{},[895,40467,40468],{},[898,40469,1677],{},[902,40471,1677],{"encoding":904},", cenách výrobních faktorů (práce ",[883,40474,40476],{"className":40475},[886],[888,40477,40478],{"xmlns":890},[892,40479,40480,40484],{},[895,40481,40482],{},[898,40483,1706],{},[902,40485,1706],{"encoding":904},[883,40487,40489],{"className":40488},[886],[888,40490,40491],{"xmlns":890},[892,40492,40493,40497],{},[895,40494,40495],{},[898,40496,1735],{},[902,40498,1735],{"encoding":904},[883,40500,40502],{"className":40501},[886],[888,40503,40504],{"xmlns":890},[892,40505,40506,40510],{},[895,40507,40508],{},[898,40509,1762],{},[902,40511,1762],{"encoding":904},"), očekávání ",[883,40514,40516],{"className":40515},[886],[888,40517,40518],{"xmlns":890},[892,40519,40520,40525],{},[895,40521,40522],{},[898,40523,40524],{},"V",[902,40526,40524],{"encoding":904},", počtu výrobců ",[883,40529,40531],{"className":40530},[886],[888,40532,40533],{"xmlns":890},[892,40534,40535,40539],{},[895,40536,40537],{},[898,40538,37121],{},[902,40540,37121],{"encoding":904},[883,40542,40544],{"className":40543},[886],[888,40545,40546],{"xmlns":890},[892,40547,40548,40552],{},[895,40549,40550],{},[898,40551,37136],{},[902,40553,37136],{"encoding":904}," a dalších:",[883,40556,40558],{"className":40557},[886],[888,40559,40560],{"xmlns":890,"display":28251},[892,40561,40562,40621],{},[20939,40563,40564],{"width":28256},[20944,40565,40566,40568,40614,40616],{},[20947,40567],{"width":28261},[20947,40569,40570],{},[895,40571,40572,40574,40576,40578,40580,40582,40584,40586,40588,40590,40592,40594,40596,40598,40600,40602,40604,40606,40608,40610,40612],{},[898,40573,1662],{},[1700,40575,1765],{},[898,40577,8861],{},[1700,40579,1703],{"stretchy":1702},[898,40581,1677],{},[1700,40583,1732],{"separator":1731},[898,40585,1706],{},[1700,40587,1732],{"separator":1731},[898,40589,1735],{},[1700,40591,1732],{"separator":1731},[898,40593,1762],{},[1700,40595,1732],{"separator":1731},[898,40597,40524],{},[1700,40599,1732],{"separator":1731},[898,40601,37121],{},[1700,40603,1732],{"separator":1731},[898,40605,37136],{},[1700,40607,1732],{"separator":1731},[1700,40609,9833],{},[1700,40611,1709],{"stretchy":1702},[898,40613,2196],{"mathvariant":1791},[20947,40615],{"width":28261},[20947,40617,40618],{},[1781,40619,40620],{},"(2.7)",[902,40622,40623],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,40625,38601,40626,10208,40629,40632],{},[38,40627,40628],{},"funkce nabídky",[614,40630,40631],{},"supply function",") v širším slova smyslu.",[198,40634,40636],{"id":40635},"jednofaktorový-model","Jednofaktorový model",[724,40638,40639],{},"V nejpřirozenějším jednofaktorovém modelu",[883,40641,40643],{"className":40642},[886],[888,40644,40645],{"xmlns":890,"display":28251},[892,40646,40647,40698],{},[20939,40648,40649],{"width":28256},[20944,40650,40651,40653,40691,40693],{},[20947,40652],{"width":28261},[20947,40654,40655],{},[895,40656,40657,40659,40661,40663,40665,40667,40669,40671,40673,40675,40677,40679,40681,40683,40685,40687,40689],{},[898,40658,1662],{},[1700,40660,1765],{},[898,40662,8861],{},[1700,40664,1703],{"stretchy":1702},[898,40666,1677],{},[1700,40668,1709],{"stretchy":1702},[1700,40670,1732],{"separator":1731},[6066,40672],{"width":6068},[1781,40674,37602],{},[6066,40676],{"width":6068},[898,40678,1677],{},[1700,40680,1765],{},[898,40682,8861],{},[1700,40684,1703],{"stretchy":1702},[898,40686,1662],{},[1700,40688,1709],{"stretchy":1702},[898,40690,2196],{"mathvariant":1791},[20947,40692],{"width":28261},[20947,40694,40695],{},[1781,40696,40697],{},"(2.8)",[902,40699,40700],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,40702,40703,40704,10208,40707,4110],{},"Graf je ",[38,40705,40706],{},"křivka nabídky",[614,40708,40709],{},"supply curve",[37533,40711,40713],{"id":40712},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[4060,40715,40716],{},[724,40717,40718],{},[38,40719,37648,40720,40733,40734,37703],{},[883,40721,40723],{"className":40722},[886],[888,40724,40725],{"xmlns":890},[892,40726,40727,40731],{},[895,40728,40729],{},[898,40730,1677],{},[902,40732,1677],{"encoding":904},", pak nabízené množství ",[883,40735,40737],{"className":40736},[886],[888,40738,40739],{"xmlns":890},[892,40740,40741,40745],{},[895,40742,40743],{},[898,40744,1662],{},[902,40746,1662],{"encoding":904},[724,40748,40749,40750,40775,40776,40806,40807,40824],{},"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 ",[883,40751,40753],{"className":40752},[886],[888,40754,40755],{"xmlns":890},[892,40756,40757,40773],{},[895,40758,40759,40761,40763,40765,40771],{},[1700,40760,1927],{"stretchy":1702},[1931,40762,1772],{},[1700,40764,1732],{"separator":1731},[2007,40766,40767,40769],{},[898,40768,1677],{},[1931,40770,1772],{},[1700,40772,1970],{"stretchy":1702},[902,40774,37788],{"encoding":904}," na svislé ose (případně z ",[883,40777,40779],{"className":40778},[886],[888,40780,40781],{"xmlns":890},[892,40782,40783,40803],{},[895,40784,40785,40787,40793,40795,40801],{},[1700,40786,1927],{"stretchy":1702},[2007,40788,40789,40791],{},[898,40790,1662],{},[1931,40792,1933],{},[1700,40794,1732],{"separator":1731},[2007,40796,40797,40799],{},[898,40798,1677],{},[1931,40800,1933],{},[1700,40802,1970],{"stretchy":1702},[902,40804,40805],{"encoding":904},"[Q_1, P_1]","), kde ",[883,40808,40810],{"className":40809},[886],[888,40811,40812],{"xmlns":890},[892,40813,40814,40822],{},[895,40815,40816],{},[2007,40817,40818,40820],{},[898,40819,1677],{},[1931,40821,1772],{},[902,40823,39133],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,40826,40827],{},[614,40828,40829,40830,3911,40843,2196],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,40831,40833],{"className":40832},[886],[888,40834,40835],{"xmlns":890},[892,40836,40837,40841],{},[895,40838,40839],{},[898,40840,8861],{},[902,40842,8861],{"encoding":904},[883,40844,40846],{"className":40845},[886],[888,40847,40848],{"xmlns":890},[892,40849,40850,40862],{},[895,40851,40852,40854,40856,40858,40860],{},[1700,40853,1703],{"stretchy":1702},[898,40855,1662],{},[1700,40857,1732],{"separator":1731},[898,40859,1677],{},[1700,40861,1709],{"stretchy":1702},[902,40863,37876],{"encoding":904},[37533,40865,40867],{"id":40866},"lineární-model-nabídky","Lineární model nabídky",[883,40869,40871],{"className":40870},[886],[888,40872,40873],{"xmlns":890,"display":28251},[892,40874,40875,40914],{},[20939,40876,40877],{"width":28256},[20944,40878,40879,40881,40907,40909],{},[20947,40880],{"width":28261},[20947,40882,40883],{},[895,40884,40885,40887,40889,40891,40893,40895,40897,40899,40901,40903,40905],{},[898,40886,1677],{},[1700,40888,1765],{},[898,40890,2354],{},[898,40892,1662],{},[1700,40894,1897],{},[898,40896,2406],{},[1700,40898,1732],{"separator":1731},[6066,40900],{"width":6068},[898,40902,2354],{},[1700,40904,3601],{},[1931,40906,12645],{},[20947,40908],{"width":28261},[20947,40910,40911],{},[1781,40912,40913],{},"(2.9)",[902,40915,40916],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,40918,40919,40920,40956,40957,40970],{},"Alternativně ",[883,40921,40923],{"className":40922},[886],[888,40924,40925],{"xmlns":890},[892,40926,40927,40953],{},[895,40928,40929,40931,40933,40941,40943,40945],{},[898,40930,1662],{},[1700,40932,1765],{},[1770,40934,40935],{"scriptlevel":1772,"displaystyle":1702},[1774,40936,40937,40939],{},[1931,40938,1933],{},[898,40940,2354],{},[898,40942,1677],{},[1700,40944,1768],{},[1770,40946,40947],{"scriptlevel":1772,"displaystyle":1702},[1774,40948,40949,40951],{},[898,40950,2406],{},[898,40952,2354],{},[902,40954,40955],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,40958,40960],{"className":40959},[886],[888,40961,40962],{"xmlns":890},[892,40963,40964,40968],{},[895,40965,40966],{},[898,40967,1677],{},[902,40969,1677],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[38110,40972,40974],{"id":40973},"příklad-25","Příklad 2.5",[724,40976,40977,40979,40980,2196],{},[38,40978,38118],{}," Lineární nabídka ",[883,40981,40983],{"className":40982},[886],[888,40984,40985],{"xmlns":890},[892,40986,40987,41001],{},[895,40988,40989,40991,40993,40995,40997,40999],{},[898,40990,1677],{},[1700,40992,1765],{},[1931,40994,5197],{},[898,40996,1662],{},[1700,40998,1897],{},[1931,41000,5192],{},[902,41002,41003],{"encoding":904},"P = 0{,}5Q + 25",[724,41005,41006,41008,41009,2196],{},[38,41007,38150],{}," Alternativní tvar ",[883,41010,41012],{"className":41011},[886],[888,41013,41014],{"xmlns":890},[892,41015,41016,41030],{},[895,41017,41018,41020,41022,41024,41026,41028],{},[898,41019,1662],{},[1700,41021,1765],{},[1931,41023,2343],{},[898,41025,1677],{},[1700,41027,1768],{},[1931,41029,3314],{},[902,41031,41032],{"encoding":904},"Q = 2P - 50",[16,41034,41035,41060],{},[19,41036,41037],{},[22,41038,41039,41054,41056,41058],{},[25,41040,41041],{},[883,41042,41044],{"className":41043},[886],[888,41045,41046],{"xmlns":890},[892,41047,41048,41052],{},[895,41049,41050],{},[898,41051,1677],{},[902,41053,1677],{"encoding":904},[25,41055,38204],{},[25,41057,15223],{},[25,41059,5399],{},[30,41061,41062],{},[22,41063,41064,41079,41081,41083],{},[35,41065,41066],{},[883,41067,41069],{"className":41068},[886],[888,41070,41071],{"xmlns":890},[892,41072,41073,41077],{},[895,41074,41075],{},[898,41076,1662],{},[902,41078,1662],{"encoding":904},[35,41080,3058],{},[35,41082,9223],{},[35,41084,38204],{},[198,41086,41088,41089,1709],{"id":41087},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,41090,41091],{},"shift of supply",[724,41093,41094,41095,41098,41099,41116,41117,41142,41143,2196],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,41096,41097],{},"doprava",": při stejné ceně ",[883,41100,41102],{"className":41101},[886],[888,41103,41104],{"xmlns":890},[892,41105,41106,41114],{},[895,41107,41108],{},[2007,41109,41110,41112],{},[898,41111,1677],{},[1931,41113,1772],{},[902,41115,39133],{"encoding":904}," vyrobí výrobce větší ",[883,41118,41120],{"className":41119},[886],[888,41121,41122],{"xmlns":890},[892,41123,41124,41140],{},[895,41125,41126,41132,41134],{},[2007,41127,41128,41130],{},[898,41129,1662],{},[1931,41131,1933],{},[1700,41133,3601],{},[2007,41135,41136,41138],{},[898,41137,1662],{},[1931,41139,1772],{},[902,41141,39246],{"encoding":904},"); zdražení vstupů posune křivku ",[38,41144,41145],{},"doleva",[724,41147,41148],{},[614,41149,41150,41151,41164,41165,41183,41184,41202,41203,2196],{},"Obrázek 2.11: Původní ",[883,41152,41154],{"className":41153},[886],[888,41155,41156],{"xmlns":890},[892,41157,41158,41162],{},[895,41159,41160],{},[898,41161,8861],{},[902,41163,8861],{"encoding":904},", posunuté ",[883,41166,41168],{"className":41167},[886],[888,41169,41170],{"xmlns":890},[892,41171,41172,41180],{},[895,41173,41174],{},[2007,41175,41176,41178],{},[898,41177,8861],{},[1931,41179,1933],{},[902,41181,41182],{"encoding":904},"S_1"," (doprava) a ",[883,41185,41187],{"className":41186},[886],[888,41188,41189],{"xmlns":890},[892,41190,41191,41199],{},[895,41192,41193],{},[2007,41194,41195,41197],{},[898,41196,8861],{},[1931,41198,2343],{},[902,41200,41201],{"encoding":904},"S_2"," (doleva) v ",[883,41204,41206],{"className":41205},[886],[888,41207,41208],{"xmlns":890},[892,41209,41210,41222],{},[895,41211,41212,41214,41216,41218,41220],{},[1700,41213,1703],{"stretchy":1702},[898,41215,1662],{},[1700,41217,1732],{"separator":1731},[898,41219,1677],{},[1700,41221,1709],{"stretchy":1702},[902,41223,37876],{"encoding":904},[38110,41225,41227],{"id":41226},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,41229,41230,41232,41233,41257,41258,2196],{},[38,41231,38118],{}," Nabídka ",[883,41234,41236],{"className":41235},[886],[888,41237,41238],{"xmlns":890},[892,41239,41240,41254],{},[895,41241,41242,41244,41246,41248,41250,41252],{},[898,41243,1677],{},[1700,41245,1765],{},[898,41247,8861],{},[1700,41249,1703],{"stretchy":1702},[898,41251,1662],{},[1700,41253,1709],{"stretchy":1702},[902,41255,41256],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,41259,41261],{"className":41260},[886],[888,41262,41263],{"xmlns":890},[892,41264,41265,41269],{},[895,41266,41267],{},[898,41268,2971],{},[902,41270,2971],{"encoding":904},[724,41272,41273,41275,41276,41289,41290,41308,41309,41337],{},[38,41274,38150],{}," Spotřebitel zaplatí ",[883,41277,41279],{"className":41278},[886],[888,41280,41281],{"xmlns":890},[892,41282,41283,41287],{},[895,41284,41285],{},[898,41286,1677],{},[902,41288,1677],{"encoding":904},", výrobce obdrží ",[883,41291,41293],{"className":41292},[886],[888,41294,41295],{"xmlns":890},[892,41296,41297,41305],{},[895,41298,41299,41301,41303],{},[898,41300,1677],{},[1700,41302,1768],{},[898,41304,2971],{},[902,41306,41307],{"encoding":904},"P - T",". Z podmínky ",[883,41310,41312],{"className":41311},[886],[888,41313,41314],{"xmlns":890},[892,41315,41316,41334],{},[895,41317,41318,41320,41322,41324,41326,41328,41330,41332],{},[898,41319,1677],{},[1700,41321,1768],{},[898,41323,2971],{},[1700,41325,1765],{},[898,41327,8861],{},[1700,41329,1703],{"stretchy":1702},[898,41331,1662],{},[1700,41333,1709],{"stretchy":1702},[902,41335,41336],{"encoding":904},"P - T = S(Q)"," plyne",[883,41339,41341],{"className":41340},[886],[888,41342,41343],{"xmlns":890,"display":28251},[892,41344,41345,41379],{},[895,41346,41347,41349,41351,41357,41359,41361,41363,41365,41367,41369,41371,41373,41375,41377],{},[898,41348,1677],{},[1700,41350,1765],{},[2007,41352,41353,41355],{},[898,41354,8861],{},[1931,41356,1933],{},[1700,41358,1703],{"stretchy":1702},[898,41360,1662],{},[1700,41362,1709],{"stretchy":1702},[1700,41364,1765],{},[898,41366,8861],{},[1700,41368,1703],{"stretchy":1702},[898,41370,1662],{},[1700,41372,1709],{"stretchy":1702},[1700,41374,1897],{},[898,41376,2971],{},[898,41378,2196],{"mathvariant":1791},[902,41380,41381],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,41383,41384,41385,41398,41399,2106,41412,41415,41416,2114,41436,8290,41454,2196],{},"Křivka ",[883,41386,41388],{"className":41387},[886],[888,41389,41390],{"xmlns":890},[892,41391,41392,41396],{},[895,41393,41394],{},[898,41395,8861],{},[902,41397,8861],{"encoding":904}," se tedy posune o ",[883,41400,41402],{"className":41401},[886],[888,41403,41404],{"xmlns":890},[892,41405,41406,41410],{},[895,41407,41408],{},[898,41409,2971],{},[902,41411,2971],{"encoding":904},[38,41413,41414],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,41417,41419],{"className":41418},[886],[888,41420,41421],{"xmlns":890},[892,41422,41423,41433],{},[895,41424,41425,41427,41429,41431],{},[898,41426,1677],{},[1700,41428,1765],{},[1931,41430,2343],{},[898,41432,1662],{},[902,41434,41435],{"encoding":904},"P = 2Q",[883,41437,41439],{"className":41438},[886],[888,41440,41441],{"xmlns":890},[892,41442,41443,41451],{},[895,41444,41445,41447,41449],{},[898,41446,2971],{},[1700,41448,1765],{},[1931,41450,2445],{},[902,41452,41453],{"encoding":904},"T = 6",[883,41455,41457],{"className":41456},[886],[888,41458,41459],{"xmlns":890},[892,41460,41461,41483],{},[895,41462,41463,41469,41471,41473,41475,41477,41479,41481],{},[2007,41464,41465,41467],{},[898,41466,8861],{},[1931,41468,1933],{},[1700,41470,2901],{},[898,41472,1677],{},[1700,41474,1765],{},[1931,41476,2343],{},[898,41478,1662],{},[1700,41480,1897],{},[1931,41482,2445],{},[902,41484,41485],{"encoding":904},"S_1: P = 2Q + 6",[724,41487,41488],{},[614,41489,41490,41491,41504],{},"Obrázek 2.12: Posun nabídky o ",[883,41492,41494],{"className":41493},[886],[888,41495,41496],{"xmlns":890},[892,41497,41498,41502],{},[895,41499,41500],{},[898,41501,2971],{},[902,41503,2971],{"encoding":904}," svisle nahoru.",[37155,41506],{},[115,41508,41510],{"id":41509},"tržní-rovnováha","Tržní rovnováha",[4060,41512,41513],{},[724,41514,41515,41517,41518,2106,41521,41553,41554,1343,41577,41600,41601,41604,41605,41618],{},[883,41516,4346],{}," TL;DR\nV ",[38,41519,41520],{},"rovnovážném bodě",[883,41522,41524],{"className":41523},[886],[888,41525,41526],{"xmlns":890},[892,41527,41528,41550],{},[895,41529,41530,41532,41534,41540,41542,41548],{},[898,41531,1762],{},[1700,41533,1927],{"stretchy":1702},[1785,41535,41536,41538],{},[898,41537,1662],{},[898,41539,1762],{},[1700,41541,1732],{"separator":1731},[1785,41543,41544,41546],{},[898,41545,1677],{},[898,41547,1762],{},[1700,41549,1970],{"stretchy":1702},[902,41551,41552],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,41555,41557],{"className":41556},[886],[888,41558,41559],{"xmlns":890},[892,41560,41561,41575],{},[895,41562,41563,41565,41567,41569,41571,41573],{},[898,41564,1677],{},[1700,41566,1765],{},[898,41568,4374],{},[1700,41570,1703],{"stretchy":1702},[898,41572,1662],{},[1700,41574,1709],{"stretchy":1702},[902,41576,4829],{"encoding":904},[883,41578,41580],{"className":41579},[886],[888,41581,41582],{"xmlns":890},[892,41583,41584,41598],{},[895,41585,41586,41588,41590,41592,41594,41596],{},[898,41587,1677],{},[1700,41589,1765],{},[898,41591,8861],{},[1700,41593,1703],{"stretchy":1702},[898,41595,1662],{},[1700,41597,1709],{"stretchy":1702},[902,41599,41256],{"encoding":904},". Čtyři ",[38,41602,41603],{},"pravidla komparativní statiky"," popisují, jak se ",[883,41606,41608],{"className":41607},[886],[888,41609,41610],{"xmlns":890},[892,41611,41612,41616],{},[895,41613,41614],{},[898,41615,1762],{},[902,41617,1762],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,41620,41622],{"id":41621},"definice","Definice",[724,41624,41625,10208,41627,41630,41631,2106,41634,41652,41653,41684,41685,10208,41688,4110],{},[38,41626,41510],{},[614,41628,41629],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,41632,41633],{},"rovnovážné ceně",[883,41635,41637],{"className":41636},[886],[888,41638,41639],{"xmlns":890},[892,41640,41641,41649],{},[895,41642,41643],{},[1785,41644,41645,41647],{},[898,41646,1677],{},[898,41648,1762],{},[902,41650,41651],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,41654,41656],{"className":41655},[886],[888,41657,41658],{"xmlns":890},[892,41659,41660,41682],{},[895,41661,41662,41664,41666,41672,41674,41680],{},[898,41663,1762],{},[1700,41665,1927],{"stretchy":1702},[1785,41667,41668,41670],{},[898,41669,1662],{},[898,41671,1762],{},[1700,41673,1732],{"separator":1731},[1785,41675,41676,41678],{},[898,41677,1677],{},[898,41679,1762],{},[1700,41681,1970],{"stretchy":1702},[902,41683,41552],{"encoding":904}," se nazývá ",[38,41686,41687],{},"rovnovážný bod",[614,41689,41690],{},"equilibrium point",[724,41692,41693,41694,1343,41717,2196],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,41695,41697],{"className":41696},[886],[888,41698,41699],{"xmlns":890},[892,41700,41701,41715],{},[895,41702,41703,41705,41707,41709,41711,41713],{},[898,41704,1677],{},[1700,41706,1765],{},[898,41708,4374],{},[1700,41710,1703],{"stretchy":1702},[898,41712,1662],{},[1700,41714,1709],{"stretchy":1702},[902,41716,4829],{"encoding":904},[883,41718,41720],{"className":41719},[886],[888,41721,41722],{"xmlns":890},[892,41723,41724,41738],{},[895,41725,41726,41728,41730,41732,41734,41736],{},[898,41727,1677],{},[1700,41729,1765],{},[898,41731,8861],{},[1700,41733,1703],{"stretchy":1702},[898,41735,1662],{},[1700,41737,1709],{"stretchy":1702},[902,41739,41256],{"encoding":904},[724,41741,41742],{},[2756,41743],{"alt":41744,"className":41745,"src":41746},"imek-poptavka-nabidka-rovnovaha",[210,2760],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,41748,41749],{},[614,41750,41751,41752,41765,41766,14196,41779,41800,41801,2196],{},"Obrázek 2.13: Klesající ",[883,41753,41755],{"className":41754},[886],[888,41756,41757],{"xmlns":890},[892,41758,41759,41763],{},[895,41760,41761],{},[898,41762,4374],{},[902,41764,4374],{"encoding":904}," a rostoucí ",[883,41767,41769],{"className":41768},[886],[888,41770,41771],{"xmlns":890},[892,41772,41773,41777],{},[895,41774,41775],{},[898,41776,8861],{},[902,41778,8861],{"encoding":904},[883,41780,41782],{"className":41781},[886],[888,41783,41784],{"xmlns":890},[892,41785,41786,41798],{},[895,41787,41788,41790,41792,41794,41796],{},[1700,41789,1703],{"stretchy":1702},[898,41791,1662],{},[1700,41793,1732],{"separator":1731},[898,41795,1677],{},[1700,41797,1709],{"stretchy":1702},[902,41799,37876],{"encoding":904}," protínající se v ",[883,41802,41804],{"className":41803},[886],[888,41805,41806],{"xmlns":890},[892,41807,41808,41830],{},[895,41809,41810,41812,41814,41820,41822,41828],{},[898,41811,1762],{},[1700,41813,1927],{"stretchy":1702},[1785,41815,41816,41818],{},[898,41817,1662],{},[898,41819,1762],{},[1700,41821,1732],{"separator":1731},[1785,41823,41824,41826],{},[898,41825,1677],{},[898,41827,1762],{},[1700,41829,1970],{"stretchy":1702},[902,41831,41552],{"encoding":904},[198,41833,41835],{"id":41834},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,41837,41838,41840,41841,41875,41876,2196],{},[38,41839,38118],{}," Poptávka ",[883,41842,41844],{"className":41843},[886],[888,41845,41846],{"xmlns":890},[892,41847,41848,41872],{},[895,41849,41850,41852,41854,41856,41862,41864,41866,41868,41870],{},[898,41851,1677],{},[1700,41853,1765],{},[1700,41855,1768],{},[1785,41857,41858,41860],{},[898,41859,1662],{},[1931,41861,2343],{},[1700,41863,1768],{},[1931,41865,3058],{},[898,41867,1662],{},[1700,41869,1897],{},[1931,41871,8991],{},[902,41873,41874],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,41877,41879],{"className":41878},[886],[888,41880,41881],{"xmlns":890},[892,41882,41883,41905],{},[895,41884,41885,41887,41889,41895,41897,41899,41901,41903],{},[898,41886,1677],{},[1700,41888,1765],{},[1785,41890,41891,41893],{},[898,41892,1662],{},[1931,41894,2343],{},[1700,41896,1897],{},[1931,41898,23131],{},[898,41900,1662],{},[1700,41902,1897],{},[1931,41904,32731],{},[902,41906,41907],{"encoding":904},"P = Q^2 + 14Q + 22",[724,41909,41910,41912],{},[38,41911,38150],{}," Z rovnosti",[883,41914,41916],{"className":41915},[886],[888,41917,41918],{"xmlns":890,"display":28251},[892,41919,41920,41958],{},[895,41921,41922,41924,41930,41932,41934,41936,41938,41940,41942,41948,41950,41952,41954,41956],{},[1700,41923,1768],{},[1785,41925,41926,41928],{},[898,41927,1662],{},[1931,41929,2343],{},[1700,41931,1768],{},[1931,41933,3058],{},[898,41935,1662],{},[1700,41937,1897],{},[1931,41939,8991],{},[1700,41941,1765],{},[1785,41943,41944,41946],{},[898,41945,1662],{},[1931,41947,2343],{},[1700,41949,1897],{},[1931,41951,23131],{},[898,41953,1662],{},[1700,41955,1897],{},[1931,41957,32731],{},[902,41959,41960],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,41962,41963,41964,41999,42000,42033,42034,42051,42052,42065,42066,1343,42088,42125,42126,2196],{},"dostaneme ",[883,41965,41967],{"className":41966},[886],[888,41968,41969],{"xmlns":890},[892,41970,41971,41996],{},[895,41972,41973,41975,41981,41983,41986,41988,41990,41992,41994],{},[1931,41974,2343],{},[1785,41976,41977,41979],{},[898,41978,1662],{},[1931,41980,2343],{},[1700,41982,1897],{},[1931,41984,41985],{},"24",[898,41987,1662],{},[1700,41989,1768],{},[1931,41991,5805],{},[1700,41993,1765],{},[1931,41995,1772],{},[902,41997,41998],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,42001,42003],{"className":42002},[886],[888,42004,42005],{"xmlns":890},[892,42006,42007,42030],{},[895,42008,42009,42015,42017,42019,42021,42023,42026,42028],{},[1785,42010,42011,42013],{},[898,42012,1662],{},[1931,42014,2343],{},[1700,42016,1897],{},[1931,42018,3702],{},[898,42020,1662],{},[1700,42022,1768],{},[1931,42024,42025],{},"64",[1700,42027,1765],{},[1931,42029,1772],{},[902,42031,42032],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,42035,42037],{"className":42036},[886],[888,42038,42039],{"xmlns":890},[892,42040,42041,42048],{},[895,42042,42043,42045],{},[1700,42044,1768],{},[1931,42046,42047],{},"16",[902,42049,42050],{"encoding":904},"-16"," (nevyhovuje) a ",[883,42053,42055],{"className":42054},[886],[888,42056,42057],{"xmlns":890},[892,42058,42059,42063],{},[895,42060,42061],{},[1931,42062,2553],{},[902,42064,2553],{"encoding":904},". Tedy ",[883,42067,42069],{"className":42068},[886],[888,42070,42071],{"xmlns":890},[892,42072,42073,42085],{},[895,42074,42075,42081,42083],{},[1785,42076,42077,42079],{},[898,42078,1662],{},[898,42080,1762],{},[1700,42082,1765],{},[1931,42084,2553],{},[902,42086,42087],{"encoding":904},"Q^E = 4",[883,42089,42091],{"className":42090},[886],[888,42092,42093],{"xmlns":890},[892,42094,42095,42122],{},[895,42096,42097,42103,42105,42107,42109,42111,42113,42115,42117,42119],{},[1785,42098,42099,42101],{},[898,42100,1677],{},[898,42102,1762],{},[1700,42104,1765],{},[1700,42106,1768],{},[1931,42108,42047],{},[1700,42110,1768],{},[1931,42112,5399],{},[1700,42114,1897],{},[1931,42116,8991],{},[1700,42118,1765],{},[1931,42120,42121],{},"94",[902,42123,42124],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,42127,42129],{"className":42128},[886],[888,42130,42131],{"xmlns":890},[892,42132,42133,42147],{},[895,42134,42135,42137,42139,42141,42143,42145],{},[898,42136,1762],{},[1700,42138,1927],{"stretchy":1702},[1931,42140,2553],{},[1700,42142,1732],{"separator":1731},[1931,42144,42121],{},[1700,42146,1970],{"stretchy":1702},[902,42148,42149],{"encoding":904},"E[4, 94]",[198,42151,42153],{"id":42152},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,42155,42156,42158],{},[38,42157,38118],{}," Poptávky a nabídky dvou zboží",[883,42160,42162],{"className":42161},[886],[888,42163,42164],{"xmlns":890,"display":28251},[892,42165,42166,42332],{},[20939,42167,42170,42258],{"rowspacing":20941,"columnalign":42168,"columnspacing":42169},"right left right left","0em 1em 0em",[20944,42171,42172,42182,42214,42224],{},[20947,42173,42174],{},[1770,42175,42176],{"scriptlevel":1772,"displaystyle":1731},[2007,42177,42178,42180],{},[898,42179,1662],{},[1931,42181,1933],{},[20947,42183,42184],{},[1770,42185,42186],{"scriptlevel":1772,"displaystyle":1731},[895,42187,42188,42190,42192,42194,42196,42198,42204,42206,42212],{},[895,42189],{},[1700,42191,1765],{},[1931,42193,5399],{},[1700,42195,1768],{},[1931,42197,2438],{},[2007,42199,42200,42202],{},[898,42201,1677],{},[1931,42203,1933],{},[1700,42205,1768],{},[2007,42207,42208,42210],{},[898,42209,1677],{},[1931,42211,2343],{},[1700,42213,1732],{"separator":1731},[20947,42215,42216],{},[1770,42217,42218],{"scriptlevel":1772,"displaystyle":1731},[2007,42219,42220,42222],{},[898,42221,1662],{},[1931,42223,2343],{},[20947,42225,42226],{},[1770,42227,42228],{"scriptlevel":1772,"displaystyle":1731},[895,42229,42230,42232,42234,42236,42238,42240,42246,42248,42250,42256],{},[895,42231],{},[1700,42233,1765],{},[1931,42235,3314],{},[1700,42237,1768],{},[1931,42239,2343],{},[2007,42241,42242,42244],{},[898,42243,1677],{},[1931,42245,1933],{},[1700,42247,1768],{},[1931,42249,2553],{},[2007,42251,42252,42254],{},[898,42253,1677],{},[1931,42255,2343],{},[1700,42257,1732],{"separator":1731},[20944,42259,42260,42270,42296,42306],{},[20947,42261,42262],{},[1770,42263,42264],{"scriptlevel":1772,"displaystyle":1731},[2007,42265,42266,42268],{},[898,42267,1662],{},[1931,42269,1933],{},[20947,42271,42272],{},[1770,42273,42274],{"scriptlevel":1772,"displaystyle":1731},[895,42275,42276,42278,42280,42282,42284,42286,42288,42294],{},[895,42277],{},[1700,42279,1765],{},[1700,42281,1768],{},[1931,42283,2385],{},[1700,42285,1897],{},[1931,42287,2553],{},[2007,42289,42290,42292],{},[898,42291,1677],{},[1931,42293,1933],{},[1700,42295,1732],{"separator":1731},[20947,42297,42298],{},[1770,42299,42300],{"scriptlevel":1772,"displaystyle":1731},[2007,42301,42302,42304],{},[898,42303,1662],{},[1931,42305,2343],{},[20947,42307,42308],{},[1770,42309,42310],{"scriptlevel":1772,"displaystyle":1731},[895,42311,42312,42314,42316,42318,42320,42322,42324,42330],{},[895,42313],{},[1700,42315,1765],{},[1700,42317,1768],{},[1931,42319,24386],{},[1700,42321,1897],{},[1931,42323,2385],{},[2007,42325,42326,42328],{},[898,42327,1677],{},[1931,42329,2343],{},[898,42331,2196],{"mathvariant":1791},[902,42333,42334],{"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}",[724,42336,42337,42339],{},[38,42338,38150],{}," Z rovností poptávek a nabídek dostaneme",[883,42341,42343],{"className":42342},[886],[888,42344,42345],{"xmlns":890,"display":28251},[892,42346,42347,42396],{},[895,42348,42349,42351,42357,42359,42365,42367,42369,42371,42373,42375,42381,42383,42385,42391,42393],{},[1931,42350,4190],{},[2007,42352,42353,42355],{},[898,42354,1677],{},[1931,42356,1933],{},[1700,42358,1897],{},[2007,42360,42361,42363],{},[898,42362,1677],{},[1931,42364,2343],{},[1700,42366,1765],{},[1931,42368,21388],{},[1700,42370,1732],{"separator":1731},[6066,42372],{"width":6068},[1931,42374,2343],{},[2007,42376,42377,42379],{},[898,42378,1677],{},[1931,42380,1933],{},[1700,42382,1897],{},[1931,42384,24386],{},[2007,42386,42387,42389],{},[898,42388,1677],{},[1931,42390,2343],{},[1700,42392,1765],{},[1931,42394,42395],{},"57.",[902,42397,42398],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,42400,42401,42402,1343,42426,42450,42451,1343,42476,42500,42501,42503],{},"Řešením je ",[883,42403,42405],{"className":42404},[886],[888,42406,42407],{"xmlns":890},[892,42408,42409,42423],{},[895,42410,42411,42419,42421],{},[2030,42412,42413,42415,42417],{},[898,42414,1677],{},[1931,42416,1933],{},[898,42418,1762],{},[1700,42420,1765],{},[1931,42422,2553],{},[902,42424,42425],{"encoding":904},"P_1^E = 4",[883,42427,42429],{"className":42428},[886],[888,42430,42431],{"xmlns":890},[892,42432,42433,42447],{},[895,42434,42435,42443,42445],{},[2030,42436,42437,42439,42441],{},[898,42438,1677],{},[1931,42440,2343],{},[898,42442,1762],{},[1700,42444,1765],{},[1931,42446,24386],{},[902,42448,42449],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,42452,42454],{"className":42453},[886],[888,42455,42456],{"xmlns":890},[892,42457,42458,42473],{},[895,42459,42460,42468,42470],{},[2030,42461,42462,42464,42466],{},[898,42463,1662],{},[1931,42465,1933],{},[898,42467,1762],{},[1700,42469,1765],{},[1931,42471,42472],{},"13",[902,42474,42475],{"encoding":904},"Q_1^E = 13",[883,42477,42479],{"className":42478},[886],[888,42480,42481],{"xmlns":890},[892,42482,42483,42497],{},[895,42484,42485,42493,42495],{},[2030,42486,42487,42489,42491],{},[898,42488,1662],{},[1931,42490,2343],{},[898,42492,1762],{},[1700,42494,1765],{},[1931,42496,23131],{},[902,42498,42499],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,42502,40007],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,42505,42507],{"id":42506},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,42509,42510,42511,42528,42529,10208,42532,4110],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,42512,42514],{"className":42513},[886],[888,42515,42516],{"xmlns":890},[892,42517,42518,42526],{},[895,42519,42520],{},[1785,42521,42522,42524],{},[898,42523,1677],{},[898,42525,1762],{},[902,42527,41651],{"encoding":904},"; mechanismus popisuje ",[38,42530,42531],{},"teorém pavučiny",[614,42533,42534],{},"cobweb model",[198,42536,42538],{"id":42537},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,42540,42541],{},[2756,42542],{"alt":42543,"className":42544,"src":42545},"imek-komparativni-statika-4pripady",[210,2760],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[4060,42547,42548,42589,42629,42669],{},[724,42549,42550,42553,42554,6378,42571,2196],{},[38,42551,42552],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,42555,42557],{"className":42556},[886],[888,42558,42559],{"xmlns":890},[892,42560,42561,42569],{},[895,42562,42563],{},[1785,42564,42565,42567],{},[898,42566,1677],{},[898,42568,1762],{},[902,42570,41651],{"encoding":904},[883,42572,42574],{"className":42573},[886],[888,42575,42576],{"xmlns":890},[892,42577,42578,42586],{},[895,42579,42580],{},[1785,42581,42582,42584],{},[898,42583,1662],{},[898,42585,1762],{},[902,42587,42588],{"encoding":904},"Q^E",[724,42590,42591,42594,42595,6378,42612,2196],{},[38,42592,42593],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,42596,42598],{"className":42597},[886],[888,42599,42600],{"xmlns":890},[892,42601,42602,42610],{},[895,42603,42604],{},[1785,42605,42606,42608],{},[898,42607,1677],{},[898,42609,1762],{},[902,42611,41651],{"encoding":904},[883,42613,42615],{"className":42614},[886],[888,42616,42617],{"xmlns":890},[892,42618,42619,42627],{},[895,42620,42621],{},[1785,42622,42623,42625],{},[898,42624,1662],{},[898,42626,1762],{},[902,42628,42588],{"encoding":904},[724,42630,42631,42634,42635,9542,42652,2196],{},[38,42632,42633],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,42636,42638],{"className":42637},[886],[888,42639,42640],{"xmlns":890},[892,42641,42642,42650],{},[895,42643,42644],{},[1785,42645,42646,42648],{},[898,42647,1677],{},[898,42649,1762],{},[902,42651,41651],{"encoding":904},[883,42653,42655],{"className":42654},[886],[888,42656,42657],{"xmlns":890},[892,42658,42659,42667],{},[895,42660,42661],{},[1785,42662,42663,42665],{},[898,42664,1662],{},[898,42666,1762],{},[902,42668,42588],{"encoding":904},[724,42670,42671,42674,42675,42692,42693,2196],{},[38,42672,42673],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,42676,42678],{"className":42677},[886],[888,42679,42680],{"xmlns":890},[892,42681,42682,42690],{},[895,42683,42684],{},[1785,42685,42686,42688],{},[898,42687,1677],{},[898,42689,1762],{},[902,42691,41651],{"encoding":904},", pokles ",[883,42694,42696],{"className":42695},[886],[888,42697,42698],{"xmlns":890},[892,42699,42700,42708],{},[895,42701,42702],{},[1785,42703,42704,42706],{},[898,42705,1662],{},[898,42707,1762],{},[902,42709,42588],{"encoding":904},[16,42711,42712,42757],{},[19,42713,42714],{},[22,42715,42716,42719,42738],{},[25,42717,42718],{},"Změna",[25,42720,42721],{},[883,42722,42724],{"className":42723},[886],[888,42725,42726],{"xmlns":890},[892,42727,42728,42736],{},[895,42729,42730],{},[1785,42731,42732,42734],{},[898,42733,1677],{},[898,42735,1762],{},[902,42737,41651],{"encoding":904},[25,42739,42740],{},[883,42741,42743],{"className":42742},[886],[888,42744,42745],{"xmlns":890},[892,42746,42747,42755],{},[895,42748,42749],{},[1785,42750,42751,42753],{},[898,42752,1662],{},[898,42754,1762],{},[902,42756,42588],{"encoding":904},[30,42758,42759,42769,42779,42788],{},[22,42760,42761,42764,42767],{},[35,42762,42763],{},"Růst poptávky",[35,42765,42766],{},"↑",[35,42768,42766],{},[22,42770,42771,42774,42777],{},[35,42772,42773],{},"Pokles poptávky",[35,42775,42776],{},"↓",[35,42778,42776],{},[22,42780,42781,42784,42786],{},[35,42782,42783],{},"Růst nabídky",[35,42785,42776],{},[35,42787,42766],{},[22,42789,42790,42793,42795],{},[35,42791,42792],{},"Pokles nabídky",[35,42794,42766],{},[35,42796,42776],{},[724,42798,42799],{},[614,42800,42801],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[37155,42803],{},[115,42805,811],{"id":42806},"zdanění-trhu",[4060,42808,42809,42898],{},[724,42810,42811,42813,42814,42827,42828,3122,42841,42844,42845,36961,42868,42893,42894,42897],{},[883,42812,4346],{}," TL;DR\nJednotková daň ",[883,42815,42817],{"className":42816},[886],[888,42818,42819],{"xmlns":890},[892,42820,42821,42825],{},[895,42822,42823],{},[898,42824,2971],{},[902,42826,2971],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,42829,42831],{"className":42830},[886],[888,42832,42833],{"xmlns":890},[892,42834,42835,42839],{},[895,42836,42837],{},[898,42838,2971],{},[902,42840,2971],{"encoding":904},[38,42842,42843],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,42846,42848],{"className":42847},[886],[888,42849,42850],{"xmlns":890},[892,42851,42852,42865],{},[895,42853,42854],{},[2007,42855,42856,42858],{},[898,42857,2971],{},[895,42859,42860,42863],{},[898,42861,42862],{},"s",[898,42864,724],{},[902,42866,42867],{"encoding":904},"T_{sp}",[883,42869,42871],{"className":42870},[886],[888,42872,42873],{"xmlns":890},[892,42874,42875,42890],{},[895,42876,42877],{},[2007,42878,42879,42881],{},[898,42880,2971],{},[895,42882,42883,42886,42888],{},[898,42884,42885],{},"v",[898,42887,2215],{},[898,42889,12226],{},[902,42891,42892],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,42895,42896],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,42899,42900],{},[614,42901,42902,42903,2196],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,42904,42906],{"className":42905,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,42908,42909,42910,42913,42914,42940,42941,42944,42945,42971,42972,42989,42990,43030,43031,2114,43044,2196],{},"Existují dvě formy zdanění — daň uložená ",[38,42911,42912],{},"výrobci"," (posun nabídky ",[883,42915,42917],{"className":42916},[886],[888,42918,42919],{"xmlns":890},[892,42920,42921,42937],{},[895,42922,42923,42929,42931,42933,42935],{},[2007,42924,42925,42927],{},[898,42926,8861],{},[1931,42928,1933],{},[1700,42930,1765],{},[898,42932,8861],{},[1700,42934,1897],{},[898,42936,2971],{},[902,42938,42939],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,42942,42943],{},"spotřebiteli"," (posun poptávky ",[883,42946,42948],{"className":42947},[886],[888,42949,42950],{"xmlns":890},[892,42951,42952,42968],{},[895,42953,42954,42960,42962,42964,42966],{},[2007,42955,42956,42958],{},[898,42957,4374],{},[1931,42959,2343],{},[1700,42961,1765],{},[898,42963,4374],{},[1700,42965,1768],{},[898,42967,2971],{},[902,42969,42970],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,42973,42975],{"className":42974},[886],[888,42976,42977],{"xmlns":890},[892,42978,42979,42987],{},[895,42980,42981],{},[1785,42982,42983,42985],{},[898,42984,1662],{},[898,42986,1762],{},[902,42988,42588],{"encoding":904}," klesá a vzniká rozklad daně ",[883,42991,42993],{"className":42992},[886],[888,42994,42995],{"xmlns":890},[892,42996,42997,43027],{},[895,42998,42999,43001,43003,43013,43015],{},[898,43000,2971],{},[1700,43002,1765],{},[2007,43004,43005,43007],{},[898,43006,2971],{},[895,43008,43009,43011],{},[898,43010,42862],{},[898,43012,724],{},[1700,43014,1897],{},[2007,43016,43017,43019],{},[898,43018,2971],{},[895,43020,43021,43023,43025],{},[898,43022,42885],{},[898,43024,2215],{},[898,43026,12226],{},[902,43028,43029],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,43032,43034],{"className":43033},[886],[888,43035,43036],{"xmlns":890},[892,43037,43038,43042],{},[895,43039,43040],{},[898,43041,4374],{},[902,43043,4374],{"encoding":904},[883,43045,43047],{"className":43046},[886],[888,43048,43049],{"xmlns":890},[892,43050,43051,43055],{},[895,43052,43053],{},[898,43054,8861],{},[902,43056,8861],{"encoding":904},[724,43058,43059,43060,43063,43064,2114,43094,43128],{},"Zásadním výsledkem kapitoly je ",[38,43061,43062],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,43065,43067],{"className":43066},[886],[888,43068,43069],{"xmlns":890},[892,43070,43071,43091],{},[895,43072,43073,43081,43083],{},[2030,43074,43075,43077,43079],{},[898,43076,1662],{},[1931,43078,1933],{},[898,43080,1762],{},[1700,43082,1765],{},[2030,43084,43085,43087,43089],{},[898,43086,1662],{},[1931,43088,2343],{},[898,43090,1762],{},[902,43092,43093],{"encoding":904},"Q_1^E = Q_2^E",[883,43095,43097],{"className":43096},[886],[888,43098,43099],{"xmlns":890},[892,43100,43101,43125],{},[895,43102,43103,43111,43113,43115,43117],{},[2030,43104,43105,43107,43109],{},[898,43106,1677],{},[1931,43108,1933],{},[898,43110,1762],{},[1700,43112,1768],{},[898,43114,2971],{},[1700,43116,1765],{},[2030,43118,43119,43121,43123],{},[898,43120,1677],{},[1931,43122,2343],{},[898,43124,1762],{},[902,43126,43127],{"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.",[724,43130,43131,43132,43135,43136,43162,43163,43191,43192,43195,43196,43199,43200,2196],{},"Podrobný výklad, Příklady ",[38,43133,43134],{},"2.9"," (daň výrobci, ",[883,43137,43139],{"className":43138},[886],[888,43140,43141],{"xmlns":890},[892,43142,43143,43159],{},[895,43144,43145,43155,43157],{},[2007,43146,43147,43149],{},[898,43148,2971],{},[895,43150,43151,43153],{},[898,43152,42862],{},[898,43154,724],{},[1700,43156,1765],{},[1931,43158,2343],{},[902,43160,43161],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,43164,43166],{"className":43165},[886],[888,43167,43168],{"xmlns":890},[892,43169,43170,43188],{},[895,43171,43172,43184,43186],{},[2007,43173,43174,43176],{},[898,43175,2971],{},[895,43177,43178,43180,43182],{},[898,43179,42885],{},[898,43181,2215],{},[898,43183,12226],{},[1700,43185,1765],{},[1931,43187,2553],{},[902,43189,43190],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,43193,43194],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,43197,43198],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,43201,42906],{"className":43202,"dataFsResolvedFilePath":809,"href":810},[210],[37155,43204],{},[115,43206,43208],{"id":43207},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[4060,43210,43211],{},[724,43212,43213,43215,43216,43219,43220,43222],{},[883,43214,4346],{}," TL;DR\nMultiplikátory jsou ",[38,43217,43218],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,43221,37145],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,43224,43226],{"id":43225},"redukovaný-tvar","Redukovaný tvar",[724,43228,43229,43230,10208,43253,1343,43271,12313,43288,10208,43311,43328,43329,43359],{},"Pro lineární model ",[883,43231,43233],{"className":43232},[886],[888,43234,43235],{"xmlns":890},[892,43236,43237,43251],{},[895,43238,43239,43241,43243,43245,43247,43249],{},[898,43240,1677],{},[1700,43242,1765],{},[898,43244,207],{},[898,43246,1662],{},[1700,43248,1897],{},[898,43250,1879],{},[902,43252,37245],{"encoding":904},[883,43254,43256],{"className":43255},[886],[888,43257,43258],{"xmlns":890},[892,43259,43260,43268],{},[895,43261,43262,43264,43266],{},[898,43263,207],{},[1700,43265,3640],{},[1931,43267,1772],{},[902,43269,43270],{"encoding":904},"a \u003C 0",[883,43272,43274],{"className":43273},[886],[888,43275,43276],{"xmlns":890},[892,43277,43278,43286],{},[895,43279,43280,43282,43284],{},[898,43281,1879],{},[1700,43283,3601],{},[1931,43285,1772],{},[902,43287,18999],{"encoding":904},[883,43289,43291],{"className":43290},[886],[888,43292,43293],{"xmlns":890},[892,43294,43295,43309],{},[895,43296,43297,43299,43301,43303,43305,43307],{},[898,43298,1677],{},[1700,43300,1765],{},[898,43302,2354],{},[898,43304,1662],{},[1700,43306,1897],{},[898,43308,2406],{},[902,43310,40427],{"encoding":904},[883,43312,43314],{"className":43313},[886],[888,43315,43316],{"xmlns":890},[892,43317,43318,43326],{},[895,43319,43320,43322,43324],{},[898,43321,2354],{},[1700,43323,3601],{},[1931,43325,1772],{},[902,43327,40445],{"encoding":904},") dává podmínka rovnováhy ",[883,43330,43332],{"className":43331},[886],[888,43333,43334],{"xmlns":890},[892,43335,43336,43356],{},[895,43337,43338,43340,43342,43344,43346,43348,43350,43352,43354],{},[898,43339,207],{},[898,43341,1662],{},[1700,43343,1897],{},[898,43345,1879],{},[1700,43347,1765],{},[898,43349,2354],{},[898,43351,1662],{},[1700,43353,1897],{},[898,43355,2406],{},[902,43357,43358],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,43361,43363],{"className":43362},[886],[888,43364,43365],{"xmlns":890,"display":28251},[892,43366,43367,43412],{},[20939,43368,43369],{"width":28256},[20944,43370,43371,43373,43405,43407],{},[20947,43372],{"width":28261},[20947,43374,43375],{},[895,43376,43377,43383,43385,43403],{},[1785,43378,43379,43381],{},[898,43380,1662],{},[898,43382,1762],{},[1700,43384,1765],{},[1774,43386,43387,43395],{},[895,43388,43389,43391,43393],{},[898,43390,1879],{},[1700,43392,1768],{},[898,43394,2406],{},[895,43396,43397,43399,43401],{},[898,43398,2354],{},[1700,43400,1768],{},[898,43402,207],{},[898,43404,2196],{"mathvariant":1791},[20947,43406],{"width":28261},[20947,43408,43409],{},[1781,43410,43411],{},"(2.10)",[902,43413,43414],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,43416,43417,43418,10208,43420,43423,43424,43441,43442,2106,43445,43471,43472,43485,43486,43504,43505,4110],{},"Vztah (2.10) je ",[38,43419,21139],{},[614,43421,43422],{},"reduced form",") pro ",[883,43425,43427],{"className":43426},[886],[888,43428,43429],{"xmlns":890},[892,43430,43431,43439],{},[895,43432,43433],{},[1785,43434,43435,43437],{},[898,43436,1662],{},[898,43438,1762],{},[902,43440,42588],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,43443,43444],{},"parametrů",[883,43446,43448],{"className":43447},[886],[888,43449,43450],{"xmlns":890},[892,43451,43452,43468],{},[895,43453,43454,43456,43458,43460,43462,43464,43466],{},[898,43455,207],{},[1700,43457,1732],{"separator":1731},[898,43459,1879],{},[1700,43461,1732],{"separator":1731},[898,43463,2354],{},[1700,43465,1732],{"separator":1731},[898,43467,2406],{},[902,43469,43470],{"encoding":904},"a, b, c, d",". Aby ",[883,43473,43475],{"className":43474},[886],[888,43476,43477],{"xmlns":890},[892,43478,43479,43483],{},[895,43480,43481],{},[898,43482,1762],{},[902,43484,1762],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,43487,43489],{"className":43488},[886],[888,43490,43491],{"xmlns":890},[892,43492,43493,43501],{},[895,43494,43495,43497,43499],{},[898,43496,1879],{},[1700,43498,3601],{},[898,43500,2406],{},[902,43502,43503],{"encoding":904},"b > d"," (neboť ",[883,43506,43508],{"className":43507},[886],[888,43509,43510],{"xmlns":890},[892,43511,43512,43524],{},[895,43513,43514,43516,43518,43520,43522],{},[898,43515,2354],{},[1700,43517,1768],{},[898,43519,207],{},[1700,43521,3601],{},[1931,43523,1772],{},[902,43525,43526],{"encoding":904},"c - a > 0",[724,43528,43529],{},[614,43530,43531,43532,43545,43546,43559,43560,18833,43573,42125,43590,43603],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,43533,43535],{"className":43534},[886],[888,43536,43537],{"xmlns":890},[892,43538,43539,43543],{},[895,43540,43541],{},[898,43542,1879],{},[902,43544,1879],{"encoding":904}," na ose ",[883,43547,43549],{"className":43548},[886],[888,43550,43551],{"xmlns":890},[892,43552,43553,43557],{},[895,43554,43555],{},[898,43556,1677],{},[902,43558,1677],{"encoding":904},") a nabídka (úsek ",[883,43561,43563],{"className":43562},[886],[888,43564,43565],{"xmlns":890},[892,43566,43567,43571],{},[895,43568,43569],{},[898,43570,2406],{},[902,43572,2406],{"encoding":904},[883,43574,43576],{"className":43575},[886],[888,43577,43578],{"xmlns":890},[892,43579,43580,43588],{},[895,43581,43582,43584,43586],{},[898,43583,1879],{},[1700,43585,3601],{},[898,43587,2406],{},[902,43589,43503],{"encoding":904},[883,43591,43593],{"className":43592},[886],[888,43594,43595],{"xmlns":890},[892,43596,43597,43601],{},[895,43598,43599],{},[898,43600,1762],{},[902,43602,1762],{"encoding":904}," v 1. kvadrantu.",[198,43605,43607],{"id":43606},"definice-multiplikátorů","Definice multiplikátorů",[724,43609,43610,43611,43636,43637,43650,43651,43664],{},"V komparativní statice jsou ",[883,43612,43614],{"className":43613},[886],[888,43615,43616],{"xmlns":890},[892,43617,43618,43634],{},[895,43619,43620,43622,43624,43626,43628,43630,43632],{},[898,43621,207],{},[1700,43623,1732],{"separator":1731},[898,43625,1879],{},[1700,43627,1732],{"separator":1731},[898,43629,2354],{},[1700,43631,1732],{"separator":1731},[898,43633,2406],{},[902,43635,43470],{"encoding":904}," exogenní proměnné a ",[883,43638,43640],{"className":43639},[886],[888,43641,43642],{"xmlns":890},[892,43643,43644,43648],{},[895,43645,43646],{},[898,43647,1662],{},[902,43649,1662],{"encoding":904}," endogenní. Přibližná změna ",[883,43652,43654],{"className":43653},[886],[888,43655,43656],{"xmlns":890},[892,43657,43658,43662],{},[895,43659,43660],{},[898,43661,1662],{},[902,43663,1662],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,43666,43668],{"className":43667},[886],[888,43669,43670],{"xmlns":890,"display":28251},[892,43671,43672,43765],{},[20939,43673,43674],{"width":28256},[20944,43675,43676,43678,43758,43760],{},[20947,43677],{"width":28261},[20947,43679,43680],{},[895,43681,43682,43684,43686,43688,43690,43692,43694,43702,43704,43706,43708,43710,43718,43720,43722,43724,43726,43734,43736,43738,43740,43742,43750,43752,43754,43756],{},[898,43683,3084],{"mathvariant":1791},[898,43685,1662],{},[1700,43687,2927],{},[898,43689,2406],{},[898,43691,1662],{},[1700,43693,1765],{},[2030,43695,43696,43698,43700],{},[898,43697,1662],{},[898,43699,207],{},[1700,43701,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1781,43703,1783],{},[898,43705,2406],{},[898,43707,207],{},[1700,43709,1897],{},[2030,43711,43712,43714,43716],{},[898,43713,1662],{},[898,43715,1879],{},[1700,43717,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1781,43719,1783],{},[898,43721,2406],{},[898,43723,1879],{},[1700,43725,1897],{},[2030,43727,43728,43730,43732],{},[898,43729,1662],{},[898,43731,2354],{},[1700,43733,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1781,43735,1783],{},[898,43737,2406],{},[898,43739,2354],{},[1700,43741,1897],{},[2030,43743,43744,43746,43748],{},[898,43745,1662],{},[898,43747,2406],{},[1700,43749,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1781,43751,1783],{},[898,43753,2406],{},[898,43755,2406],{},[898,43757,2196],{"mathvariant":1791},[20947,43759],{"width":28261},[20947,43761,43762],{},[1781,43763,43764],{},"(2.11)",[902,43766,43767],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,43769,43770,43771,43821,43822,10208,43824,3345],{},"Parciální derivace ",[883,43772,43774],{"className":43773},[886],[888,43775,43776],{"xmlns":890},[892,43777,43778,43818],{},[895,43779,43780,43788,43790,43798,43800,43808,43810],{},[2030,43781,43782,43784,43786],{},[898,43783,1662],{},[898,43785,207],{},[1700,43787,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,43789,1732],{"separator":1731},[2030,43791,43792,43794,43796],{},[898,43793,1662],{},[898,43795,1879],{},[1700,43797,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,43799,1732],{"separator":1731},[2030,43801,43802,43804,43806],{},[898,43803,1662],{},[898,43805,2354],{},[1700,43807,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,43809,1732],{"separator":1731},[2030,43811,43812,43814,43816],{},[898,43813,1662],{},[898,43815,2406],{},[1700,43817,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,43819,43820],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,43823,18162],{},[614,43825,43826],{},"multipliers",[883,43828,43830],{"className":43829},[886],[888,43831,43832],{"xmlns":890,"display":28251},[892,43833,43834,43985],{},[20939,43835,43836],{"width":28256},[20944,43837,43838,43840,43978,43980],{},[20947,43839],{"width":28261},[20947,43841,43842],{},[895,43843,43844,43852,43854,43880,43882,43884,43892,43894,43906,43908,43910,43918,43920,43922,43948,43950,43952,43960,43962,43964,43976],{},[2030,43845,43846,43848,43850],{},[898,43847,1662],{},[898,43849,207],{},[1700,43851,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,43853,1765],{},[1774,43855,43856,43864],{},[895,43857,43858,43860,43862],{},[898,43859,1879],{},[1700,43861,1768],{},[898,43863,2406],{},[895,43865,43866,43868,43870,43872,43874],{},[1700,43867,1703],{"stretchy":1702},[898,43869,2354],{},[1700,43871,1768],{},[898,43873,207],{},[1785,43875,43876,43878],{},[1700,43877,1709],{"stretchy":1702},[1931,43879,2343],{},[1700,43881,1732],{"separator":1731},[6066,43883],{"width":15469},[2030,43885,43886,43888,43890],{},[898,43887,1662],{},[898,43889,1879],{},[1700,43891,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,43893,1765],{},[1774,43895,43896,43898],{},[1931,43897,1933],{},[895,43899,43900,43902,43904],{},[898,43901,2354],{},[1700,43903,1768],{},[898,43905,207],{},[1700,43907,1732],{"separator":1731},[6066,43909],{"width":15469},[2030,43911,43912,43914,43916],{},[898,43913,1662],{},[898,43915,2354],{},[1700,43917,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,43919,1765],{},[1700,43921,1768],{},[1774,43923,43924,43932],{},[895,43925,43926,43928,43930],{},[898,43927,1879],{},[1700,43929,1768],{},[898,43931,2406],{},[895,43933,43934,43936,43938,43940,43942],{},[1700,43935,1703],{"stretchy":1702},[898,43937,2354],{},[1700,43939,1768],{},[898,43941,207],{},[1785,43943,43944,43946],{},[1700,43945,1709],{"stretchy":1702},[1931,43947,2343],{},[1700,43949,1732],{"separator":1731},[6066,43951],{"width":15469},[2030,43953,43954,43956,43958],{},[898,43955,1662],{},[898,43957,2406],{},[1700,43959,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,43961,1765],{},[1700,43963,1768],{},[1774,43965,43966,43968],{},[1931,43967,1933],{},[895,43969,43970,43972,43974],{},[898,43971,2354],{},[1700,43973,1768],{},[898,43975,207],{},[898,43977,2196],{"mathvariant":1791},[20947,43979],{"width":28261},[20947,43981,43982],{},[1781,43983,43984],{},"(2.12)",[902,43986,43987],{"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}",[198,43989,43991],{"id":43990},"znaménka-a-interpretace","Znaménka a interpretace",[724,43993,43994,43995,1343,44012,1343,44029,1343,44046,44063,44064,3345],{},"Za podmínek ",[883,43996,43998],{"className":43997},[886],[888,43999,44000],{"xmlns":890},[892,44001,44002,44010],{},[895,44003,44004,44006,44008],{},[898,44005,207],{},[1700,44007,3640],{},[1931,44009,1772],{},[902,44011,43270],{"encoding":904},[883,44013,44015],{"className":44014},[886],[888,44016,44017],{"xmlns":890},[892,44018,44019,44027],{},[895,44020,44021,44023,44025],{},[898,44022,1879],{},[1700,44024,3601],{},[1931,44026,1772],{},[902,44028,18999],{"encoding":904},[883,44030,44032],{"className":44031},[886],[888,44033,44034],{"xmlns":890},[892,44035,44036,44044],{},[895,44037,44038,44040,44042],{},[898,44039,2354],{},[1700,44041,3601],{},[1931,44043,1772],{},[902,44045,40445],{"encoding":904},[883,44047,44049],{"className":44048},[886],[888,44050,44051],{"xmlns":890},[892,44052,44053,44061],{},[895,44054,44055,44057,44059],{},[898,44056,1879],{},[1700,44058,3601],{},[898,44060,2406],{},[902,44062,43503],{"encoding":904}," platí (znaménka se ",[38,44065,44066],{},"nemění",[883,44068,44070],{"className":44069},[886],[888,44071,44072],{"xmlns":890,"display":28251},[892,44073,44074,44136],{},[895,44075,44076,44084,44086,44088,44090,44092,44100,44102,44104,44106,44108,44116,44118,44120,44122,44124,44132,44134],{},[2030,44077,44078,44080,44082],{},[898,44079,1662],{},[898,44081,207],{},[1700,44083,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,44085,3601],{},[1931,44087,1772],{},[1700,44089,1732],{"separator":1731},[6066,44091],{"width":6068},[2030,44093,44094,44096,44098],{},[898,44095,1662],{},[898,44097,1879],{},[1700,44099,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,44101,3601],{},[1931,44103,1772],{},[1700,44105,1732],{"separator":1731},[6066,44107],{"width":6068},[2030,44109,44110,44112,44114],{},[898,44111,1662],{},[898,44113,2354],{},[1700,44115,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,44117,3640],{},[1931,44119,1772],{},[1700,44121,1732],{"separator":1731},[6066,44123],{"width":6068},[2030,44125,44126,44128,44130],{},[898,44127,1662],{},[898,44129,2406],{},[1700,44131,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,44133,3640],{},[1931,44135,12645],{},[902,44137,44138],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,44140,44141,44200],{},[123,44142,44143,2106,44146,44166,44167,44184,44185,1343,44198,2196],{},[38,44144,44145],{},"Kvantitativní smysl:",[883,44147,44149],{"className":44148},[886],[888,44150,44151],{"xmlns":890},[892,44152,44153,44163],{},[895,44154,44155],{},[2030,44156,44157,44159,44161],{},[898,44158,1662],{},[898,44160,2225],{},[1700,44162,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,44164,44165],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,44168,44170],{"className":44169},[886],[888,44171,44172],{"xmlns":890},[892,44173,44174,44182],{},[895,44175,44176],{},[1785,44177,44178,44180],{},[898,44179,1662],{},[898,44181,1762],{},[902,44183,42588],{"encoding":904}," při jednotkové změně parametru ",[883,44186,44188],{"className":44187},[886],[888,44189,44190],{"xmlns":890},[892,44191,44192,44196],{},[895,44193,44194],{},[898,44195,2225],{},[902,44197,2225],{"encoding":904},[614,44199,37145],{},[123,44201,44202,44205,44206,44223,44224,2196],{},[38,44203,44204],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,44207,44209],{"className":44208},[886],[888,44210,44211],{"xmlns":890},[892,44212,44213,44221],{},[895,44214,44215],{},[1785,44216,44217,44219],{},[898,44218,1662],{},[898,44220,1762],{},[902,44222,42588],{"encoding":904}," na růst ",[883,44225,44227],{"className":44226},[886],[888,44228,44229],{"xmlns":890},[892,44230,44231,44235],{},[895,44232,44233],{},[898,44234,2225],{},[902,44236,2225],{"encoding":904},[724,44238,44239,44240,44253,44254,43504,44271,4110],{},"Např. růst ",[883,44241,44243],{"className":44242},[886],[888,44244,44245],{"xmlns":890},[892,44246,44247,44251],{},[895,44248,44249],{},[898,44250,2354],{},[902,44252,2354],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,44255,44257],{"className":44256},[886],[888,44258,44259],{"xmlns":890},[892,44260,44261,44269],{},[895,44262,44263],{},[1785,44264,44265,44267],{},[898,44266,1662],{},[898,44268,1762],{},[902,44270,42588],{"encoding":904},[883,44272,44274],{"className":44273},[886],[888,44275,44276],{"xmlns":890},[892,44277,44278,44292],{},[895,44279,44280,44288,44290],{},[2030,44281,44282,44284,44286],{},[898,44283,1662],{},[898,44285,2354],{},[1700,44287,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,44289,3640],{},[1931,44291,1772],{},[902,44293,44294],{"encoding":904},"Q'_c \u003C 0",[724,44296,44297],{},[614,44298,44299,44300,44320,44321,44345,44346,44368,44369,2196],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,44301,44303],{"className":44302},[886],[888,44304,44305],{"xmlns":890},[892,44306,44307,44317],{},[895,44308,44309,44311,44313,44315],{},[898,44310,2354],{},[898,44312,1662],{},[1700,44314,1897],{},[898,44316,2406],{},[902,44318,44319],{"encoding":904},"cQ + d"," na strmější ",[883,44322,44324],{"className":44323},[886],[888,44325,44326],{"xmlns":890},[892,44327,44328,44342],{},[895,44329,44330,44336,44338,44340],{},[2007,44331,44332,44334],{},[898,44333,2354],{},[1931,44335,1933],{},[898,44337,1662],{},[1700,44339,1897],{},[898,44341,2406],{},[902,44343,44344],{"encoding":904},"c_1 Q + d"," (při ",[883,44347,44349],{"className":44348},[886],[888,44350,44351],{"xmlns":890},[892,44352,44353,44365],{},[895,44354,44355,44361,44363],{},[2007,44356,44357,44359],{},[898,44358,2354],{},[1931,44360,1933],{},[1700,44362,3601],{},[898,44364,2354],{},[902,44366,44367],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,44370,44372],{"className":44371},[886],[888,44373,44374],{"xmlns":890},[892,44375,44376,44386],{},[895,44377,44378,44384],{},[1785,44379,44380,44382],{},[898,44381,1662],{},[898,44383,1762],{},[1700,44385,42776],{},[902,44387,44388],{"encoding":904},"Q^E \\downarrow",[724,44390,44391,44392,44424,44425,2196],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,44393,44395],{"className":44394},[886],[888,44396,44397],{"xmlns":890},[892,44398,44399,44421],{},[895,44400,44401,44403,44405,44407,44415,44417,44419],{},[898,44402,3084],{"mathvariant":1791},[898,44404,1662],{},[1700,44406,2927],{},[2030,44408,44409,44411,44413],{},[898,44410,1662],{},[898,44412,1879],{},[1700,44414,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1781,44416,1783],{},[898,44418,2406],{},[898,44420,1879],{},[902,44422,44423],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,44426,44428],{"className":44427},[886],[888,44429,44430],{"xmlns":890},[892,44431,44432,44440],{},[895,44433,44434],{},[1785,44435,44436,44438],{},[898,44437,1677],{},[898,44439,1762],{},[902,44441,41651],{"encoding":904},[198,44443,44445,44446],{"id":44444},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,44447,44449],{"className":44448},[886],[888,44450,44451],{"xmlns":890},[892,44452,44453,44461],{},[895,44454,44455],{},[1785,44456,44457,44459],{},[898,44458,1662],{},[898,44460,1762],{},[902,44462,42588],{"encoding":904},[724,44464,44465,41840,44467,41875,44493,2196],{},[38,44466,38118],{},[883,44468,44470],{"className":44469},[886],[888,44471,44472],{"xmlns":890},[892,44473,44474,44490],{},[895,44475,44476,44478,44480,44482,44484,44486,44488],{},[898,44477,1677],{},[1700,44479,1765],{},[1700,44481,1768],{},[1931,44483,2385],{},[898,44485,1662],{},[1700,44487,1897],{},[1931,44489,5399],{},[902,44491,44492],{"encoding":904},"P = -3Q + 40",[883,44494,44496],{"className":44495},[886],[888,44497,44498],{"xmlns":890},[892,44499,44500,44514],{},[895,44501,44502,44504,44506,44508,44510,44512],{},[898,44503,1677],{},[1700,44505,1765],{},[1931,44507,5197],{},[898,44509,1662],{},[1700,44511,1897],{},[1931,44513,3058],{},[902,44515,44516],{"encoding":904},"P = 0{,}5Q + 10",[724,44518,44519,44521],{},[38,44520,38150],{}," Rovnovážné množství",[883,44523,44525],{"className":44524},[886],[888,44526,44527],{"xmlns":890,"display":28251},[892,44528,44529,44597],{},[895,44530,44531,44537,44539,44557,44559,44583,44585,44592,44594],{},[1785,44532,44533,44535],{},[898,44534,1662],{},[898,44536,1762],{},[1700,44538,1765],{},[1774,44540,44541,44549],{},[895,44542,44543,44545,44547],{},[898,44544,1879],{},[1700,44546,1768],{},[898,44548,2406],{},[895,44550,44551,44553,44555],{},[898,44552,2354],{},[1700,44554,1768],{},[898,44556,207],{},[1700,44558,1765],{},[1774,44560,44561,44569],{},[895,44562,44563,44565,44567],{},[1931,44564,5399],{},[1700,44566,1768],{},[1931,44568,3058],{},[895,44570,44571,44573,44575,44577,44579,44581],{},[1931,44572,5197],{},[1700,44574,1768],{},[1700,44576,1703],{"stretchy":1702},[1700,44578,1768],{},[1931,44580,2385],{},[1700,44582,1709],{"stretchy":1702},[1700,44584,1765],{},[1774,44586,44587,44589],{},[1931,44588,38204],{},[1931,44590,44591],{},"3,5",[1700,44593,2927],{},[1931,44595,44596],{},"8,571.",[902,44598,44599],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,44601,44602,44647],{},[38,44603,44604,44605,2868,44618,2882,44632,44646],{},"(a) Změna ",[883,44606,44608],{"className":44607},[886],[888,44609,44610],{"xmlns":890},[892,44611,44612,44616],{},[895,44613,44614],{},[898,44615,2354],{},[902,44617,2354],{"encoding":904},[883,44619,44621],{"className":44620},[886],[888,44622,44623],{"xmlns":890},[892,44624,44625,44629],{},[895,44626,44627],{},[1931,44628,5197],{},[902,44630,44631],{"encoding":904},"0{,}5",[883,44633,44635],{"className":44634},[886],[888,44636,44637],{"xmlns":890},[892,44638,44639,44643],{},[895,44640,44641],{},[1931,44642,19506],{},[902,44644,44645],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,44649,44651],{"className":44650},[886],[888,44652,44653],{"xmlns":890,"display":28251},[892,44654,44655,44732],{},[895,44656,44657,44665,44667,44669,44671,44673,44675,44701,44703,44705,44707,44709,44711,44721,44723,44725,44727,44729],{},[2030,44658,44659,44661,44663],{},[898,44660,1662],{},[898,44662,2354],{},[1700,44664,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1781,44666,1783],{},[898,44668,2406],{},[898,44670,2354],{},[1700,44672,1765],{},[1700,44674,1768],{},[1774,44676,44677,44685],{},[895,44678,44679,44681,44683],{},[898,44680,1879],{},[1700,44682,1768],{},[898,44684,2406],{},[895,44686,44687,44689,44691,44693,44695],{},[1700,44688,1703],{"stretchy":1702},[898,44690,2354],{},[1700,44692,1768],{},[898,44694,207],{},[1785,44696,44697,44699],{},[1700,44698,1709],{"stretchy":1702},[1931,44700,2343],{},[1781,44702,1783],{},[898,44704,2406],{},[898,44706,2354],{},[1700,44708,1765],{},[1700,44710,1768],{},[1774,44712,44713,44715],{},[1931,44714,38204],{},[1785,44716,44717,44719],{},[1931,44718,44591],{},[1931,44720,2343],{},[1700,44722,2065],{},[1931,44724,2990],{},[1700,44726,2927],{},[1700,44728,1768],{},[1931,44730,44731],{},"0,245.",[902,44733,44734],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,44736,44737,44738,2196],{},"Nové rovnovážné množství ",[883,44739,44741],{"className":44740},[886],[888,44742,44743],{"xmlns":890},[892,44744,44745,44770],{},[895,44746,44747,44755,44757,44760,44762,44765,44767],{},[2030,44748,44749,44751,44753],{},[898,44750,1662],{},[1931,44752,1933],{},[898,44754,1762],{},[1700,44756,2927],{},[1931,44758,44759],{},"8,571",[1700,44761,1768],{},[1931,44763,44764],{},"0,245",[1700,44766,1765],{},[1931,44768,44769],{},"8,326",[902,44771,44772],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,44774,44775,44860],{},[38,44776,44777,44778,1343,44798,1343,44820,1343,44840,2196],{},"(b) Současné změny ",[883,44779,44781],{"className":44780},[886],[888,44782,44783],{"xmlns":890},[892,44784,44785,44795],{},[895,44786,44787,44789,44791,44793],{},[898,44788,2406],{},[898,44790,207],{},[1700,44792,1765],{},[1931,44794,5197],{},[902,44796,44797],{"encoding":904},"da = 0{,}5",[883,44799,44801],{"className":44800},[886],[888,44802,44803],{"xmlns":890},[892,44804,44805,44817],{},[895,44806,44807,44809,44811,44813,44815],{},[898,44808,2406],{},[898,44810,1879],{},[1700,44812,1765],{},[1700,44814,1768],{},[1931,44816,2438],{},[902,44818,44819],{"encoding":904},"db = -5",[883,44821,44823],{"className":44822},[886],[888,44824,44825],{"xmlns":890},[892,44826,44827,44837],{},[895,44828,44829,44831,44833,44835],{},[898,44830,2406],{},[898,44832,2354],{},[1700,44834,1765],{},[1931,44836,2990],{},[902,44838,44839],{"encoding":904},"dc = 0{,}1",[883,44841,44843],{"className":44842},[886],[888,44844,44845],{"xmlns":890},[892,44846,44847,44857],{},[895,44848,44849,44851,44853,44855],{},[898,44850,2406],{},[898,44852,2406],{},[1700,44854,1765],{},[1931,44856,1933],{},[902,44858,44859],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,44862,44864],{"className":44863},[886],[888,44865,44866],{"xmlns":890,"display":28251},[892,44867,44868,45011],{},[20939,44869,44870,44952,44988],{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},[20944,44871,44872,44882],{},[20947,44873,44874],{},[1770,44875,44876],{"scriptlevel":1772,"displaystyle":1731},[895,44877,44878,44880],{},[898,44879,3084],{"mathvariant":1791},[898,44881,1662],{},[20947,44883,44884],{},[1770,44885,44886],{"scriptlevel":1772,"displaystyle":1731},[895,44887,44888,44890,44892,44902,44904,44906,44908,44914,44916,44918,44920,44922,44924,44926,44936,44938,44940,44942,44948,44950],{},[895,44889],{},[1700,44891,2927],{},[1774,44893,44894,44896],{},[1931,44895,38204],{},[1785,44897,44898,44900],{},[1931,44899,44591],{},[1931,44901,2343],{},[1700,44903,2065],{},[1931,44905,5197],{},[1700,44907,1897],{},[1774,44909,44910,44912],{},[1931,44911,1933],{},[1931,44913,44591],{},[1700,44915,2065],{},[1700,44917,1703],{"stretchy":1702},[1700,44919,1768],{},[1931,44921,2438],{},[1700,44923,1709],{"stretchy":1702},[1700,44925,1768],{},[1774,44927,44928,44930],{},[1931,44929,38204],{},[1785,44931,44932,44934],{},[1931,44933,44591],{},[1931,44935,2343],{},[1700,44937,2065],{},[1931,44939,2990],{},[1700,44941,1768],{},[1774,44943,44944,44946],{},[1931,44945,1933],{},[1931,44947,44591],{},[1700,44949,2065],{},[1931,44951,1933],{},[20944,44953,44954,44960],{},[20947,44955,44956],{},[1770,44957,44958],{"scriptlevel":1772,"displaystyle":1731},[895,44959],{},[20947,44961,44962],{},[1770,44963,44964],{"scriptlevel":1772,"displaystyle":1731},[895,44965,44966,44968,44970,44973,44975,44978,44980,44983,44985],{},[895,44967],{},[1700,44969,1765],{},[1931,44971,44972],{},"1,2245",[1700,44974,1768],{},[1931,44976,44977],{},"1,4286",[1700,44979,1768],{},[1931,44981,44982],{},"0,2449",[1700,44984,1768],{},[1931,44986,44987],{},"0,2857",[20944,44989,44990,44996],{},[20947,44991,44992],{},[1770,44993,44994],{"scriptlevel":1772,"displaystyle":1731},[895,44995],{},[20947,44997,44998],{},[1770,44999,45000],{"scriptlevel":1772,"displaystyle":1731},[895,45001,45002,45004,45006,45008],{},[895,45003],{},[1700,45005,2927],{},[1700,45007,1768],{},[1931,45009,45010],{},"0,735.",[902,45012,45013],{"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}",[724,45015,30250,45016,2196],{},[883,45017,45019],{"className":45018},[886],[888,45020,45021],{"xmlns":890},[892,45022,45023,45047],{},[895,45024,45025,45033,45035,45037,45039,45042,45044],{},[2030,45026,45027,45029,45031],{},[898,45028,1662],{},[1931,45030,1933],{},[898,45032,1762],{},[1700,45034,2927],{},[1931,45036,44759],{},[1700,45038,1768],{},[1931,45040,45041],{},"0,735",[1700,45043,1765],{},[1931,45045,45046],{},"7,836",[902,45048,45049],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[4060,45051,45052],{},[724,45053,45054,45056,45057,45080,45081,45103],{},[883,45055,4601],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,45058,45060],{"className":45059},[886],[888,45061,45062],{"xmlns":890},[892,45063,45064,45077],{},[895,45065,45066,45068,45070,45072,45074],{},[898,45067,3084],{"mathvariant":1791},[898,45069,1662],{},[1700,45071,2927],{},[1700,45073,1768],{},[1931,45075,45076],{},"2,69",[902,45078,45079],{"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 ",[883,45082,45084],{"className":45083},[886],[888,45085,45086],{"xmlns":890},[892,45087,45088,45100],{},[895,45089,45090,45092,45094,45096,45098],{},[898,45091,3084],{"mathvariant":1791},[898,45093,1662],{},[1700,45095,2927],{},[1700,45097,1768],{},[1931,45099,45041],{},[902,45101,45102],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,45105,45106],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[37155,45108],{},[115,45110,820],{"id":11968},[4060,45112,45113],{},[724,45114,45115,4067,45117,10208,45120,12313,45136,10208,45139,45155,45156,2196],{},[883,45116,4346],{},[38,45118,45119],{},"Přebytek spotřebitele",[883,45121,45123],{"className":45122},[886],[888,45124,45125],{"xmlns":890},[892,45126,45127,45133],{},[895,45128,45129,45131],{},[898,45130,2974],{},[898,45132,8861],{},[902,45134,45135],{"encoding":904},"CS",[38,45137,45138],{},"přebytek výrobce",[883,45140,45142],{"className":45141},[886],[888,45143,45144],{"xmlns":890},[892,45145,45146,45152],{},[895,45147,45148,45150],{},[898,45149,1677],{},[898,45151,8861],{},[902,45153,45154],{"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 ",[207,45157,45159],{"className":45158,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,45161,45162],{},[2756,45163],{"alt":45164,"className":45165,"src":45166},"imek-prebytky-cs-ps",[210,2760],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,45168,45169,10208,45171,45174],{},[38,45170,45119],{},[614,45172,45173],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,45176,45178],{"className":45177},[886],[888,45179,45180],{"xmlns":890,"display":28251},[892,45181,45182,45259],{},[20939,45183,45184],{"width":28256},[20944,45185,45186,45188,45252,45254],{},[20947,45187],{"width":28261},[20947,45189,45190],{},[895,45191,45192,45194,45196,45198,45204,45206,45208,45220,45222,45224,45226,45228,45230,45232,45234,45236,45242,45244,45250],{},[898,45193,2974],{},[898,45195,8861],{},[1700,45197,1703],{"stretchy":1702},[2007,45199,45200,45202],{},[898,45201,1662],{},[1931,45203,1772],{},[1700,45205,1709],{"stretchy":1702},[1700,45207,1765],{},[2030,45209,45210,45212,45214],{},[1700,45211,11353],{},[1931,45213,1772],{},[2007,45215,45216,45218],{},[898,45217,1662],{},[1931,45219,1772],{},[898,45221,4374],{},[1700,45223,1703],{"stretchy":1702},[898,45225,1662],{},[1700,45227,1709],{"stretchy":1702},[1781,45229,1783],{},[898,45231,2406],{},[898,45233,1662],{},[1700,45235,1768],{},[2007,45237,45238,45240],{},[898,45239,1677],{},[1931,45241,1772],{},[1781,45243,1783],{},[2007,45245,45246,45248],{},[898,45247,1662],{},[1931,45249,1772],{},[898,45251,2196],{"mathvariant":1791},[20947,45253],{"width":28261},[20947,45255,45256],{},[1781,45257,45258],{},"(2.14)",[902,45260,45261],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,45263,45264,10208,45267,45270],{},[38,45265,45266],{},"Přebytek výrobce",[614,45268,45269],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,45272,45274],{"className":45273},[886],[888,45275,45276],{"xmlns":890,"display":28251},[892,45277,45278,45355],{},[20939,45279,45280],{"width":28256},[20944,45281,45282,45284,45348,45350],{},[20947,45283],{"width":28261},[20947,45285,45286],{},[895,45287,45288,45290,45292,45294,45300,45302,45304,45310,45312,45318,45320,45332,45334,45336,45338,45340,45342,45344,45346],{},[898,45289,1677],{},[898,45291,8861],{},[1700,45293,1703],{"stretchy":1702},[2007,45295,45296,45298],{},[898,45297,1662],{},[1931,45299,1772],{},[1700,45301,1709],{"stretchy":1702},[1700,45303,1765],{},[2007,45305,45306,45308],{},[898,45307,1677],{},[1931,45309,1772],{},[1781,45311,1783],{},[2007,45313,45314,45316],{},[898,45315,1662],{},[1931,45317,1772],{},[1700,45319,1768],{},[2030,45321,45322,45324,45326],{},[1700,45323,11353],{},[1931,45325,1772],{},[2007,45327,45328,45330],{},[898,45329,1662],{},[1931,45331,1772],{},[898,45333,8861],{},[1700,45335,1703],{"stretchy":1702},[898,45337,1662],{},[1700,45339,1709],{"stretchy":1702},[1781,45341,1783],{},[898,45343,2406],{},[898,45345,1662],{},[898,45347,2196],{"mathvariant":1791},[20947,45349],{"width":28261},[20947,45351,45352],{},[1781,45353,45354],{},"(2.15)",[902,45356,45357],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,45359,45360,45361,2196],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,45362,45364],{"className":45363,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[37155,45366],{},[115,45368,45370],{"id":45369},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,45372,45373,45404,45409,45415,45443,45449,45478,45484,45564,45590],{},[123,45374,45375,45377,45378,45403],{},[38,45376,38113],{}," — lineární poptávka ",[883,45379,45381],{"className":45380},[886],[888,45382,45383],{"xmlns":890},[892,45384,45385,45401],{},[895,45386,45387,45389,45391,45393,45395,45397,45399],{},[898,45388,1677],{},[1700,45390,1765],{},[1700,45392,1768],{},[1931,45394,2343],{},[898,45396,1662],{},[1700,45398,1897],{},[1931,45400,3320],{},[902,45402,38145],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,45405,45406,45408],{},[38,45407,38427],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,45410,45411,45414],{},[38,45412,45413],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,45416,45417,45419,45420,2196],{},[38,45418,40974],{}," — lineární nabídka ",[883,45421,45423],{"className":45422},[886],[888,45424,45425],{"xmlns":890},[892,45426,45427,45441],{},[895,45428,45429,45431,45433,45435,45437,45439],{},[898,45430,1677],{},[1700,45432,1765],{},[1931,45434,5197],{},[898,45436,1662],{},[1700,45438,1897],{},[1931,45440,5192],{},[902,45442,41003],{"encoding":904},[123,45444,45445,45448],{},[38,45446,45447],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,45450,45451,45454,45455,2196],{},[38,45452,45453],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,45456,45458],{"className":45457},[886],[888,45459,45460],{"xmlns":890},[892,45461,45462,45476],{},[895,45463,45464,45466,45468,45470,45472,45474],{},[898,45465,1762],{},[1700,45467,1927],{"stretchy":1702},[1931,45469,2553],{},[1700,45471,1732],{"separator":1731},[1931,45473,42121],{},[1700,45475,1970],{"stretchy":1702},[902,45477,42149],{"encoding":904},[123,45479,45480,45483],{},[38,45481,45482],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,45485,45486,45489,45490,45507,45508,1343,45533,45560,45561,3146],{},[38,45487,45488],{},"Příklad 2.9"," — daň ",[883,45491,45493],{"className":45492},[886],[888,45494,45495],{"xmlns":890},[892,45496,45497,45505],{},[895,45498,45499,45501,45503],{},[898,45500,2971],{},[1700,45502,1765],{},[1931,45504,2445],{},[902,45506,41453],{"encoding":904}," na výrobce; rozklad ",[883,45509,45511],{"className":45510},[886],[888,45512,45513],{"xmlns":890},[892,45514,45515,45531],{},[895,45516,45517,45527,45529],{},[2007,45518,45519,45521],{},[898,45520,2971],{},[895,45522,45523,45525],{},[898,45524,42862],{},[898,45526,724],{},[1700,45528,1765],{},[1931,45530,2343],{},[902,45532,43161],{"encoding":904},[883,45534,45536],{"className":45535},[886],[888,45537,45538],{"xmlns":890},[892,45539,45540,45558],{},[895,45541,45542,45554,45556],{},[2007,45543,45544,45546],{},[898,45545,2971],{},[895,45547,45548,45550,45552],{},[898,45549,42885],{},[898,45551,2215],{},[898,45553,12226],{},[1700,45555,1765],{},[1931,45557,2553],{},[902,45559,43190],{"encoding":904},". (Viz ",[207,45562,42906],{"className":45563,"dataFsResolvedFilePath":809,"href":810},[210],[123,45565,45566,45489,45569,45586,45587,3146],{},[38,45567,45568],{},"Příklad 2.10",[883,45570,45572],{"className":45571},[886],[888,45573,45574],{"xmlns":890},[892,45575,45576,45584],{},[895,45577,45578,45580,45582],{},[898,45579,2971],{},[1700,45581,1765],{},[1931,45583,2445],{},[902,45585,41453],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,45588,42906],{"className":45589,"dataFsResolvedFilePath":809,"href":810},[210],[123,45591,45592,45595],{},[38,45593,45594],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[37155,45597],{},[115,45599,45601],{"id":45600},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,45603,45605],{"id":45604},"základní-analýza-poptávky","Základní analýza poptávky",[724,45607,45608,45611,45612,45647,45648,45674],{},[38,45609,45610],{},"2.1"," Je dána poptávka ",[883,45613,45615],{"className":45614},[886],[888,45616,45617],{"xmlns":890},[892,45618,45619,45644],{},[895,45620,45621,45623,45625,45627,45629,45631,45633,45635,45638,45640,45642],{},[898,45622,1662],{},[1700,45624,1765],{},[898,45626,4374],{},[1700,45628,1703],{"stretchy":1702},[898,45630,1677],{},[1700,45632,1709],{"stretchy":1702},[1700,45634,1765],{},[1931,45636,45637],{},"75",[1700,45639,1768],{},[1931,45641,2438],{},[898,45643,1677],{},[902,45645,45646],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,45649,45651],{"className":45650},[886],[888,45652,45653],{"xmlns":890},[892,45654,45655,45671],{},[895,45656,45657,45659,45661,45663,45665,45667,45669],{},[1931,45658,1772],{},[1700,45660,1732],{"separator":1731},[1931,45662,2438],{},[1700,45664,1732],{"separator":1731},[1931,45666,3058],{},[1700,45668,1732],{"separator":1731},[1931,45670,36429],{},[902,45672,45673],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,45676,45677,45680,45681,45699,45700,3345],{},[38,45678,45679],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,45682,45684],{"className":45683},[886],[888,45685,45686],{"xmlns":890},[892,45687,45688,45696],{},[895,45689,45690,45692,45694],{},[898,45691,1677],{},[1700,45693,1732],{"separator":1731},[898,45695,1662],{},[902,45697,45698],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,45701,45703],{"className":45702},[886],[888,45704,45705],{"xmlns":890},[892,45706,45707,45723],{},[895,45708,45709,45711,45713,45715,45717,45719,45721],{},[898,45710,207],{},[1700,45712,1732],{"separator":1731},[898,45714,1879],{},[1700,45716,1732],{"separator":1731},[898,45718,2354],{},[1700,45720,3601],{},[1931,45722,1772],{},[902,45724,45725],{"encoding":904},"a, b, c > 0",[120,45727,45728,45761,45792,45827,45858,45893],{},[123,45729,45730,45731],{},"(a) ",[883,45732,45734],{"className":45733},[886],[888,45735,45736],{"xmlns":890},[892,45737,45738,45758],{},[895,45739,45740,45742,45744],{},[898,45741,1662],{},[1700,45743,1765],{},[1770,45745,45746],{"scriptlevel":1772,"displaystyle":1731},[1774,45747,45748,45750],{},[898,45749,207],{},[895,45751,45752,45754,45756],{},[898,45753,1677],{},[1700,45755,1897],{},[898,45757,2354],{},[902,45759,45760],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,45762,45763,45764],{},"(b) ",[883,45765,45767],{"className":45766},[886],[888,45768,45769],{"xmlns":890},[892,45770,45771,45789],{},[895,45772,45773,45775,45777],{},[898,45774,1662],{},[1700,45776,1765],{},[8305,45778,45779],{},[895,45780,45781,45783,45785,45787],{},[898,45782,207],{},[1700,45784,1768],{},[898,45786,1879],{},[898,45788,1662],{},[902,45790,45791],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,45793,45794,45795],{},"(c) ",[883,45796,45798],{"className":45797},[886],[888,45799,45800],{"xmlns":890},[892,45801,45802,45824],{},[895,45803,45804,45806,45808],{},[898,45805,1662],{},[1700,45807,1765],{},[1770,45809,45810],{"scriptlevel":1772,"displaystyle":1731},[1774,45811,45812,45822],{},[895,45813,45814,45816,45818],{},[898,45815,207],{},[1700,45817,1768],{},[8305,45819,45820],{},[898,45821,1677],{},[898,45823,1879],{},[902,45825,45826],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,45828,45829,45830],{},"(d) ",[883,45831,45833],{"className":45832},[886],[888,45834,45835],{"xmlns":890},[892,45836,45837,45855],{},[895,45838,45839,45841,45843,45845,45847,45849],{},[898,45840,1677],{},[1700,45842,1765],{},[898,45844,207],{},[1700,45846,1768],{},[898,45848,1879],{},[1785,45850,45851,45853],{},[898,45852,1662],{},[1931,45854,2343],{},[902,45856,45857],{"encoding":904},"P = a - bQ^2",[123,45859,45860,45861],{},"(e) ",[883,45862,45864],{"className":45863},[886],[888,45865,45866],{"xmlns":890},[892,45867,45868,45890],{},[895,45869,45870,45872,45874,45876,45886,45888],{},[898,45871,1662],{},[1700,45873,1765],{},[898,45875,1879],{},[1785,45877,45878,45880],{},[898,45879,1677],{},[895,45881,45882,45884],{},[1700,45883,1768],{},[898,45885,207],{},[1700,45887,1897],{},[898,45889,2354],{},[902,45891,45892],{"encoding":904},"Q = bP^{-a} + c",[123,45894,45895,45896],{},"(f) ",[883,45897,45899],{"className":45898},[886],[888,45900,45901],{"xmlns":890},[892,45902,45903,45926],{},[895,45904,45905,45907,45909,45911,45913],{},[898,45906,1662],{},[1700,45908,1765],{},[898,45910,207],{},[1700,45912,2065],{},[1785,45914,45915,45918],{},[898,45916,45917],{},"e",[895,45919,45920,45922,45924],{},[1700,45921,1768],{},[898,45923,1879],{},[898,45925,1677],{},[902,45927,45928],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,45930,45931,45934],{},[38,45932,45933],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,45936,45937,45940,45943],{},[123,45938,45939],{},"(a) Cena substitutu.",[123,45941,45942],{},"(b) Cena komplementu.",[123,45944,45945],{},"(c) Výdaje na reklamu.",[724,45947,45948,45611,45950,45984,45985,46013],{},[38,45949,24827],{},[883,45951,45953],{"className":45952},[886],[888,45954,45955],{"xmlns":890},[892,45956,45957,45981],{},[895,45958,45959,45961,45963,45965,45967,45969,45971,45973,45975,45977,45979],{},[898,45960,1677],{},[1700,45962,1765],{},[898,45964,4374],{},[1700,45966,1703],{"stretchy":1702},[898,45968,1662],{},[1700,45970,1709],{"stretchy":1702},[1700,45972,1765],{},[1931,45974,3702],{},[1700,45976,1768],{},[1931,45978,2343],{},[898,45980,1662],{},[902,45982,45983],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,45986,45988],{"className":45987},[886],[888,45989,45990],{"xmlns":890},[892,45991,45992,46010],{},[895,45993,45994,45996,45998,46004,46006,46008],{},[898,45995,1677],{},[1700,45997,1765],{},[1785,45999,46000,46002],{},[898,46001,4374],{},[1700,46003,4543],{},[1700,46005,1703],{"stretchy":1702},[898,46007,1662],{},[1700,46009,1709],{"stretchy":1702},[902,46011,46012],{"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.",[724,46015,46016,46019],{},[38,46017,46018],{},"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:",[120,46021,46022,46106,46182,46268,46356],{},[123,46023,45730,46024,1343,46064,2196],{},[883,46025,46027],{"className":46026},[886],[888,46028,46029],{"xmlns":890},[892,46030,46031,46061],{},[895,46032,46033,46039,46041,46043,46045,46047,46053,46055],{},[2007,46034,46035,46037],{},[898,46036,23438],{},[1931,46038,1933],{},[1700,46040,1765],{},[1931,46042,9223],{},[1700,46044,1768],{},[1931,46046,2553],{},[2007,46048,46049,46051],{},[898,46050,1862],{},[1931,46052,1933],{},[1700,46054,1897],{},[2007,46056,46057,46059],{},[898,46058,1862],{},[1931,46060,2343],{},[902,46062,46063],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,46065,46067],{"className":46066},[886],[888,46068,46069],{"xmlns":890},[892,46070,46071,46103],{},[895,46072,46073,46079,46081,46083,46085,46087,46093,46095,46097],{},[2007,46074,46075,46077],{},[898,46076,23438],{},[1931,46078,2343],{},[1700,46080,1765],{},[1931,46082,3058],{},[1700,46084,1897],{},[1931,46086,2343],{},[2007,46088,46089,46091],{},[898,46090,1862],{},[1931,46092,1933],{},[1700,46094,1768],{},[1931,46096,2553],{},[2007,46098,46099,46101],{},[898,46100,1862],{},[1931,46102,2343],{},[902,46104,46105],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,46107,45763,46108,1343,46150,2196],{},[883,46109,46111],{"className":46110},[886],[888,46112,46113],{"xmlns":890},[892,46114,46115,46147],{},[895,46116,46117,46123,46125,46127,46129,46131,46137,46139,46141],{},[2007,46118,46119,46121],{},[898,46120,23438],{},[1931,46122,1933],{},[1700,46124,1765],{},[1931,46126,3314],{},[1700,46128,1768],{},[1931,46130,3058],{},[2007,46132,46133,46135],{},[898,46134,1862],{},[1931,46136,1933],{},[1700,46138,1768],{},[1931,46140,2445],{},[2007,46142,46143,46145],{},[898,46144,1862],{},[1931,46146,2343],{},[902,46148,46149],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,46151,46153],{"className":46152},[886],[888,46154,46155],{"xmlns":890},[892,46156,46157,46179],{},[895,46158,46159,46165,46167,46169,46171,46173],{},[2007,46160,46161,46163],{},[898,46162,23438],{},[1931,46164,2343],{},[1700,46166,1765],{},[1931,46168,36429],{},[1700,46170,1768],{},[1931,46172,3058],{},[2007,46174,46175,46177],{},[898,46176,1862],{},[1931,46178,2343],{},[902,46180,46181],{"encoding":904},"B_2 = 15 - 10A_2",[123,46183,45794,46184,1343,46226,2196],{},[883,46185,46187],{"className":46186},[886],[888,46188,46189],{"xmlns":890},[892,46190,46191,46223],{},[895,46192,46193,46199,46201,46203,46205,46207,46213,46215,46217],{},[2007,46194,46195,46197],{},[898,46196,23438],{},[1931,46198,1933],{},[1700,46200,1765],{},[1931,46202,38204],{},[1700,46204,1768],{},[1931,46206,2343],{},[2007,46208,46209,46211],{},[898,46210,1862],{},[1931,46212,1933],{},[1700,46214,1768],{},[1931,46216,2553],{},[2007,46218,46219,46221],{},[898,46220,1862],{},[1931,46222,2343],{},[902,46224,46225],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,46227,46229],{"className":46228},[886],[888,46230,46231],{"xmlns":890},[892,46232,46233,46265],{},[895,46234,46235,46241,46243,46245,46247,46249,46255,46257,46259],{},[2007,46236,46237,46239],{},[898,46238,23438],{},[1931,46240,2343],{},[1700,46242,1765],{},[1931,46244,36429],{},[1700,46246,1897],{},[1931,46248,2343],{},[2007,46250,46251,46253],{},[898,46252,1862],{},[1931,46254,1933],{},[1700,46256,1768],{},[1931,46258,2343],{},[2007,46260,46261,46263],{},[898,46262,1862],{},[1931,46264,2343],{},[902,46266,46267],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,46269,45829,46270,1343,46314,2196],{},[883,46271,46273],{"className":46272},[886],[888,46274,46275],{"xmlns":890},[892,46276,46277,46311],{},[895,46278,46279,46285,46287,46289,46291,46293,46295,46301,46303,46305],{},[2007,46280,46281,46283],{},[898,46282,23438],{},[1931,46284,1933],{},[1700,46286,1765],{},[1700,46288,1768],{},[1931,46290,9223],{},[1700,46292,1768],{},[1931,46294,2343],{},[2007,46296,46297,46299],{},[898,46298,1862],{},[1931,46300,1933],{},[1700,46302,1897],{},[1931,46304,2385],{},[2007,46306,46307,46309],{},[898,46308,1862],{},[1931,46310,2343],{},[902,46312,46313],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,46315,46317],{"className":46316},[886],[888,46318,46319],{"xmlns":890},[892,46320,46321,46353],{},[895,46322,46323,46329,46331,46333,46335,46337,46343,46345,46347],{},[2007,46324,46325,46327],{},[898,46326,23438],{},[1931,46328,2343],{},[1700,46330,1765],{},[1931,46332,3058],{},[1700,46334,1897],{},[1931,46336,2343],{},[2007,46338,46339,46341],{},[898,46340,1862],{},[1931,46342,1933],{},[1700,46344,1768],{},[1931,46346,2343],{},[2007,46348,46349,46351],{},[898,46350,1862],{},[1931,46352,2343],{},[902,46354,46355],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,46357,45860,46358,1343,46400,2196],{},[883,46359,46361],{"className":46360},[886],[888,46362,46363],{"xmlns":890},[892,46364,46365,46397],{},[895,46366,46367,46373,46375,46377,46379,46381,46387,46389,46391],{},[2007,46368,46369,46371],{},[898,46370,23438],{},[1931,46372,1933],{},[1700,46374,1765],{},[1931,46376,9223],{},[1700,46378,1897],{},[1931,46380,2343],{},[2007,46382,46383,46385],{},[898,46384,1862],{},[1931,46386,1933],{},[1700,46388,1897],{},[1931,46390,2553],{},[2007,46392,46393,46395],{},[898,46394,1862],{},[1931,46396,2343],{},[902,46398,46399],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,46401,46403],{"className":46402},[886],[888,46404,46405],{"xmlns":890},[892,46406,46407,46439],{},[895,46408,46409,46415,46417,46419,46421,46423,46429,46431,46433],{},[2007,46410,46411,46413],{},[898,46412,23438],{},[1931,46414,2343],{},[1700,46416,1765],{},[1931,46418,5399],{},[1700,46420,1768],{},[1931,46422,2385],{},[2007,46424,46425,46427],{},[898,46426,1862],{},[1931,46428,1933],{},[1700,46430,1897],{},[1931,46432,2438],{},[2007,46434,46435,46437],{},[898,46436,1862],{},[1931,46438,2343],{},[902,46440,46441],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,46443,46445],{"id":46444},"základní-analýza-nabídky","Základní analýza nabídky",[724,46447,46448,46451,46452,46486,46487,46509],{},[38,46449,46450],{},"2.6"," Je dána nabídka ",[883,46453,46455],{"className":46454},[886],[888,46456,46457],{"xmlns":890},[892,46458,46459,46483],{},[895,46460,46461,46463,46465,46467,46469,46471,46473,46475,46477,46479,46481],{},[898,46462,1677],{},[1700,46464,1765],{},[898,46466,8861],{},[1700,46468,1703],{"stretchy":1702},[898,46470,1662],{},[1700,46472,1709],{"stretchy":1702},[1700,46474,1765],{},[1931,46476,9223],{},[1700,46478,1897],{},[1931,46480,3034],{},[898,46482,1662],{},[902,46484,46485],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,46488,46490],{"className":46489},[886],[888,46491,46492],{"xmlns":890},[892,46493,46494,46506],{},[895,46495,46496,46498,46500,46502,46504],{},[1931,46497,5192],{},[1700,46499,1732],{"separator":1731},[1931,46501,38204],{},[1700,46503,1732],{"separator":1731},[1931,46505,15223],{},[902,46507,46508],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,46511,46512,46515,46516,46533],{},[38,46513,46514],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,46517,46519],{"className":46518},[886],[888,46520,46521],{"xmlns":890},[892,46522,46523,46531],{},[895,46524,46525,46527,46529],{},[898,46526,1677],{},[1700,46528,1732],{"separator":1731},[898,46530,1662],{},[902,46532,45698],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,46535,46536,46562,46590,46623,46657,46693],{},[123,46537,45730,46538],{},[883,46539,46541],{"className":46540},[886],[888,46542,46543],{"xmlns":890},[892,46544,46545,46559],{},[895,46546,46547,46549,46551,46553,46555,46557],{},[898,46548,1677],{},[1700,46550,1765],{},[1931,46552,38204],{},[1700,46554,1897],{},[1931,46556,2343],{},[898,46558,1662],{},[902,46560,46561],{"encoding":904},"P = 30 + 2Q",[123,46563,45763,46564],{},[883,46565,46567],{"className":46566},[886],[888,46568,46569],{"xmlns":890},[892,46570,46571,46587],{},[895,46572,46573,46575,46577,46579,46581,46583,46585],{},[898,46574,1662],{},[1700,46576,1765],{},[1700,46578,1768],{},[1931,46580,2385],{},[1700,46582,1897],{},[1931,46584,3702],{},[898,46586,1677],{},[902,46588,46589],{"encoding":904},"Q = -3 + 12P",[123,46591,45794,46592],{},[883,46593,46595],{"className":46594},[886],[888,46596,46597],{"xmlns":890},[892,46598,46599,46621],{},[895,46600,46601,46603,46605,46611,46613,46615,46617,46619],{},[898,46602,1677],{},[1700,46604,1765],{},[1785,46606,46607,46609],{},[898,46608,1662],{},[1931,46610,2343],{},[1700,46612,1897],{},[1931,46614,23131],{},[898,46616,1662],{},[1700,46618,1897],{},[1931,46620,32731],{},[902,46622,41907],{"encoding":904},[123,46624,45829,46625],{},[883,46626,46628],{"className":46627},[886],[888,46629,46630],{"xmlns":890},[892,46631,46632,46654],{},[895,46633,46634,46636,46638,46644,46646,46648,46650,46652],{},[898,46635,1677],{},[1700,46637,1765],{},[1785,46639,46640,46642],{},[898,46641,1662],{},[1931,46643,2343],{},[1700,46645,1897],{},[1931,46647,2343],{},[898,46649,1662],{},[1700,46651,1897],{},[1931,46653,3702],{},[902,46655,46656],{"encoding":904},"P = Q^2 + 2Q + 12",[123,46658,45860,46659],{},[883,46660,46662],{"className":46661},[886],[888,46663,46664],{"xmlns":890},[892,46665,46666,46690],{},[895,46667,46668,46670,46672,46674,46676,46678,46680,46682,46684],{},[898,46669,1662],{},[1700,46671,1765],{},[1931,46673,8991],{},[1700,46675,1897],{},[1931,46677,2438],{},[898,46679,1677],{},[1700,46681,1897],{},[1931,46683,2990],{},[1785,46685,46686,46688],{},[898,46687,1677],{},[1931,46689,2343],{},[902,46691,46692],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,46694,45895,46695],{},[883,46696,46698],{"className":46697},[886],[888,46699,46700],{"xmlns":890},[892,46701,46702,46727],{},[895,46703,46704,46706,46708,46710,46712,46714,46716,46718,46721],{},[898,46705,1662],{},[1700,46707,1765],{},[1931,46709,24386],{},[1700,46711,1897],{},[1931,46713,2990],{},[898,46715,1677],{},[1700,46717,1897],{},[1931,46719,46720],{},"0,004",[1785,46722,46723,46725],{},[898,46724,1677],{},[1931,46726,2343],{},[902,46728,46729],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,46731,46732,46735],{},[38,46733,46734],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,46737,46738,46741,46744,46747],{},[123,46739,46740],{},"(a) Sníží ceny surovin — vstupů.",[123,46742,46743],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,46745,46746],{},"(c) Zvýší ceny všech energií.",[123,46748,46749],{},"(d) Sníží daňové odvody státu.",[724,46751,46752,46451,46754,46788,46789,46817],{},[38,46753,43134],{},[883,46755,46757],{"className":46756},[886],[888,46758,46759],{"xmlns":890},[892,46760,46761,46785],{},[895,46762,46763,46765,46767,46769,46771,46773,46775,46777,46779,46781,46783],{},[898,46764,1677],{},[1700,46766,1765],{},[898,46768,8861],{},[1700,46770,1703],{"stretchy":1702},[898,46772,1662],{},[1700,46774,1709],{"stretchy":1702},[1700,46776,1765],{},[1931,46778,5197],{},[898,46780,1662],{},[1700,46782,1897],{},[1931,46784,36429],{},[902,46786,46787],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,46790,46792],{"className":46791},[886],[888,46793,46794],{"xmlns":890},[892,46795,46796,46814],{},[895,46797,46798,46800,46802,46808,46810,46812],{},[898,46799,1677],{},[1700,46801,1765],{},[1785,46803,46804,46806],{},[898,46805,8861],{},[1700,46807,4543],{},[1700,46809,1703],{"stretchy":1702},[898,46811,1662],{},[1700,46813,1709],{"stretchy":1702},[902,46815,46816],{"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.",[198,46819,41510],{"id":46820},"tržní-rovnováha-1",[724,46822,46823,46825,46826,46843,46844,2901],{},[38,46824,43194],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,46827,46829],{"className":46828},[886],[888,46830,46831],{"xmlns":890},[892,46832,46833,46841],{},[895,46834,46835],{},[1785,46836,46837,46839],{},[898,46838,1662],{},[898,46840,1762],{},[902,46842,42588],{"encoding":904}," a rovnovážnou cenu ",[883,46845,46847],{"className":46846},[886],[888,46848,46849],{"xmlns":890},[892,46850,46851,46859],{},[895,46852,46853],{},[1785,46854,46855,46857],{},[898,46856,1677],{},[898,46858,1762],{},[902,46860,41651],{"encoding":904},[120,46862,46863,46916,46967,47026],{},[123,46864,45730,46865,1343,46892,2196],{},[883,46866,46868],{"className":46867},[886],[888,46869,46870],{"xmlns":890},[892,46871,46872,46889],{},[895,46873,46874,46876,46878,46880,46882,46884,46886],{},[898,46875,1677],{},[1700,46877,1765],{},[1700,46879,1768],{},[1931,46881,2438],{},[898,46883,1662],{},[1700,46885,1897],{},[1931,46887,46888],{},"80",[902,46890,46891],{"encoding":904},"P = -5Q + 80",[883,46893,46895],{"className":46894},[886],[888,46896,46897],{"xmlns":890},[892,46898,46899,46913],{},[895,46900,46901,46903,46905,46907,46909,46911],{},[898,46902,1677],{},[1700,46904,1765],{},[1931,46906,2343],{},[898,46908,1662],{},[1700,46910,1897],{},[1931,46912,3058],{},[902,46914,46915],{"encoding":904},"P = 2Q + 10",[123,46917,45763,46918,1343,46944,2196],{},[883,46919,46921],{"className":46920},[886],[888,46922,46923],{"xmlns":890},[892,46924,46925,46941],{},[895,46926,46927,46929,46931,46933,46935,46937,46939],{},[898,46928,1662],{},[1700,46930,1765],{},[1700,46932,1768],{},[1931,46934,5197],{},[898,46936,1677],{},[1700,46938,1897],{},[1931,46940,5192],{},[902,46942,46943],{"encoding":904},"Q = -0{,}5P + 25",[883,46945,46947],{"className":46946},[886],[888,46948,46949],{"xmlns":890},[892,46950,46951,46965],{},[895,46952,46953,46955,46957,46959,46961,46963],{},[898,46954,1662],{},[1700,46956,1765],{},[1931,46958,2343],{},[898,46960,1677],{},[1700,46962,1768],{},[1931,46964,3314],{},[902,46966,41032],{"encoding":904},[123,46968,45794,46969,1343,46995,2196],{},[883,46970,46972],{"className":46971},[886],[888,46973,46974],{"xmlns":890},[892,46975,46976,46992],{},[895,46977,46978,46980,46982,46984,46986,46988,46990],{},[898,46979,1677],{},[1700,46981,1765],{},[1700,46983,1768],{},[1931,46985,2553],{},[898,46987,1662],{},[1700,46989,1897],{},[1931,46991,4237],{},[902,46993,46994],{"encoding":904},"P = -4Q + 120",[883,46996,46998],{"className":46997},[886],[888,46999,47000],{"xmlns":890},[892,47001,47002,47023],{},[895,47003,47004,47006,47008,47016,47018,47020],{},[898,47005,1677],{},[1700,47007,1765],{},[1770,47009,47010],{"scriptlevel":1772,"displaystyle":1702},[1774,47011,47012,47014],{},[1931,47013,1933],{},[1931,47015,2385],{},[898,47017,1662],{},[1700,47019,1897],{},[1931,47021,47022],{},"29",[902,47024,47025],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,47027,45829,47028,1343,47057,2196],{},[883,47029,47031],{"className":47030},[886],[888,47032,47033],{"xmlns":890},[892,47034,47035,47054],{},[895,47036,47037,47039,47041,47043,47049,47051],{},[898,47038,1677],{},[1700,47040,1765],{},[1700,47042,1768],{},[1785,47044,47045,47047],{},[898,47046,1662],{},[1931,47048,2343],{},[1700,47050,1897],{},[1931,47052,47053],{},"52",[902,47055,47056],{"encoding":904},"P = -Q^2 + 52",[883,47058,47060],{"className":47059},[886],[888,47061,47062],{"xmlns":890},[892,47063,47064,47082],{},[895,47065,47066,47068,47070,47072,47078,47080],{},[898,47067,1677],{},[1700,47069,1765],{},[1931,47071,2343],{},[1785,47073,47074,47076],{},[898,47075,1662],{},[1931,47077,2343],{},[1700,47079,1897],{},[1931,47081,3058],{},[902,47083,47084],{"encoding":904},"P = 2Q^2 + 10",[724,47086,47087,47090,47091,47121,47122,47152],{},[38,47088,47089],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,47092,47094],{"className":47093},[886],[888,47095,47096],{"xmlns":890},[892,47097,47098,47118],{},[895,47099,47100,47108,47110],{},[2030,47101,47102,47104,47106],{},[898,47103,1662],{},[1931,47105,1933],{},[898,47107,1762],{},[1700,47109,1732],{"separator":1731},[2030,47111,47112,47114,47116],{},[898,47113,1662],{},[1931,47115,2343],{},[898,47117,1762],{},[902,47119,47120],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,47123,47125],{"className":47124},[886],[888,47126,47127],{"xmlns":890},[892,47128,47129,47149],{},[895,47130,47131,47139,47141],{},[2030,47132,47133,47135,47137],{},[898,47134,1677],{},[1931,47136,1933],{},[898,47138,1762],{},[1700,47140,1732],{"separator":1731},[2030,47142,47143,47145,47147],{},[898,47144,1677],{},[1931,47146,2343],{},[898,47148,1762],{},[902,47150,47151],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,47154,47155,47307],{},[123,47156,45730,47157,1343,47197,1343,47239,1343,47273,2196],{},[883,47158,47160],{"className":47159},[886],[888,47161,47162],{"xmlns":890},[892,47163,47164,47194],{},[895,47165,47166,47172,47174,47176,47178,47180,47186,47188],{},[2007,47167,47168,47170],{},[898,47169,1662],{},[1931,47171,1933],{},[1700,47173,1765],{},[1931,47175,3058],{},[1700,47177,1768],{},[1931,47179,2343],{},[2007,47181,47182,47184],{},[898,47183,1677],{},[1931,47185,1933],{},[1700,47187,1897],{},[2007,47189,47190,47192],{},[898,47191,1677],{},[1931,47193,2343],{},[902,47195,47196],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,47198,47200],{"className":47199},[886],[888,47201,47202],{"xmlns":890},[892,47203,47204,47236],{},[895,47205,47206,47212,47214,47216,47218,47220,47226,47228,47230],{},[2007,47207,47208,47210],{},[898,47209,1662],{},[1931,47211,2343],{},[1700,47213,1765],{},[1931,47215,2438],{},[1700,47217,1897],{},[1931,47219,2343],{},[2007,47221,47222,47224],{},[898,47223,1677],{},[1931,47225,1933],{},[1700,47227,1768],{},[1931,47229,2343],{},[2007,47231,47232,47234],{},[898,47233,1677],{},[1931,47235,2343],{},[902,47237,47238],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,47240,47242],{"className":47241},[886],[888,47243,47244],{"xmlns":890},[892,47245,47246,47270],{},[895,47247,47248,47254,47256,47258,47260,47262,47264],{},[2007,47249,47250,47252],{},[898,47251,1662],{},[1931,47253,1933],{},[1700,47255,1765],{},[1700,47257,1768],{},[1931,47259,2385],{},[1700,47261,1897],{},[1931,47263,2343],{},[2007,47265,47266,47268],{},[898,47267,1677],{},[1931,47269,1933],{},[902,47271,47272],{"encoding":904},"Q_1 = -3 + 2P_1",[883,47274,47276],{"className":47275},[886],[888,47277,47278],{"xmlns":890},[892,47279,47280,47304],{},[895,47281,47282,47288,47290,47292,47294,47296,47298],{},[2007,47283,47284,47286],{},[898,47285,1662],{},[1931,47287,2343],{},[1700,47289,1765],{},[1700,47291,1768],{},[1931,47293,2343],{},[1700,47295,1897],{},[1931,47297,2385],{},[2007,47299,47300,47302],{},[898,47301,1677],{},[1931,47303,2343],{},[902,47305,47306],{"encoding":904},"Q_2 = -2 + 3P_2",[123,47308,45763,47309,1343,47349,1343,47391,1343,47423,2196],{},[883,47310,47312],{"className":47311},[886],[888,47313,47314],{"xmlns":890},[892,47315,47316,47346],{},[895,47317,47318,47324,47326,47328,47330,47332,47338,47340],{},[2007,47319,47320,47322],{},[898,47321,1662],{},[1931,47323,1933],{},[1700,47325,1765],{},[1931,47327,3284],{},[1700,47329,1768],{},[1931,47331,2343],{},[2007,47333,47334,47336],{},[898,47335,1677],{},[1931,47337,1933],{},[1700,47339,1897],{},[2007,47341,47342,47344],{},[898,47343,1677],{},[1931,47345,2343],{},[902,47347,47348],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,47350,47352],{"className":47351},[886],[888,47353,47354],{"xmlns":890},[892,47355,47356,47388],{},[895,47357,47358,47364,47366,47368,47370,47372,47378,47380,47382],{},[2007,47359,47360,47362],{},[898,47361,1662],{},[1931,47363,2343],{},[1700,47365,1765],{},[1931,47367,2438],{},[1700,47369,1897],{},[1931,47371,2343],{},[2007,47373,47374,47376],{},[898,47375,1677],{},[1931,47377,1933],{},[1700,47379,1768],{},[1931,47381,2385],{},[2007,47383,47384,47386],{},[898,47385,1677],{},[1931,47387,2343],{},[902,47389,47390],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,47392,47394],{"className":47393},[886],[888,47395,47396],{"xmlns":890},[892,47397,47398,47420],{},[895,47399,47400,47406,47408,47410,47412,47414],{},[2007,47401,47402,47404],{},[898,47403,1662],{},[1931,47405,1933],{},[1700,47407,1765],{},[1700,47409,1768],{},[1931,47411,3058],{},[1700,47413,1897],{},[2007,47415,47416,47418],{},[898,47417,1677],{},[1931,47419,1933],{},[902,47421,47422],{"encoding":904},"Q_1 = -10 + P_1",[883,47424,47426],{"className":47425},[886],[888,47427,47428],{"xmlns":890},[892,47429,47430,47452],{},[895,47431,47432,47438,47440,47442,47444,47446],{},[2007,47433,47434,47436],{},[898,47435,1662],{},[1931,47437,2343],{},[1700,47439,1765],{},[1931,47441,2438],{},[1700,47443,1897],{},[1931,47445,2445],{},[2007,47447,47448,47450],{},[898,47449,1677],{},[1931,47451,2343],{},[902,47453,47454],{"encoding":904},"Q_2 = 5 + 6P_2",[724,47456,47457,47460,47461,1343,47509,1343,47555,47605,47606,1343,47638,1343,47672,21779,47706,2114,47724,47742,47743,47756,47757,47783,47784,47121,47824,2196],{},[38,47458,47459],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,47462,47464],{"className":47463},[886],[888,47465,47466],{"xmlns":890},[892,47467,47468,47506],{},[895,47469,47470,47476,47478,47480,47482,47488,47490,47492,47498,47500],{},[2007,47471,47472,47474],{},[898,47473,1662],{},[1931,47475,1933],{},[1700,47477,1765],{},[1931,47479,36429],{},[1700,47481,1768],{},[2007,47483,47484,47486],{},[898,47485,1677],{},[1931,47487,1933],{},[1700,47489,1897],{},[1931,47491,2343],{},[2007,47493,47494,47496],{},[898,47495,1677],{},[1931,47497,2343],{},[1700,47499,1897],{},[2007,47501,47502,47504],{},[898,47503,1677],{},[1931,47505,2385],{},[902,47507,47508],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,47510,47512],{"className":47511},[886],[888,47513,47514],{"xmlns":890},[892,47515,47516,47552],{},[895,47517,47518,47524,47526,47528,47530,47536,47538,47544,47546],{},[2007,47519,47520,47522],{},[898,47521,1662],{},[1931,47523,2343],{},[1700,47525,1765],{},[1931,47527,4190],{},[1700,47529,1897],{},[2007,47531,47532,47534],{},[898,47533,1677],{},[1931,47535,1933],{},[1700,47537,1768],{},[2007,47539,47540,47542],{},[898,47541,1677],{},[1931,47543,2343],{},[1700,47545,1768],{},[2007,47547,47548,47550],{},[898,47549,1677],{},[1931,47551,2385],{},[902,47553,47554],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,47556,47558],{"className":47557},[886],[888,47559,47560],{"xmlns":890},[892,47561,47562,47602],{},[895,47563,47564,47570,47572,47574,47576,47578,47584,47586,47592,47594,47596],{},[2007,47565,47566,47568],{},[898,47567,1662],{},[1931,47569,2385],{},[1700,47571,1765],{},[1931,47573,5773],{},[1700,47575,1897],{},[1931,47577,2343],{},[2007,47579,47580,47582],{},[898,47581,1677],{},[1931,47583,1933],{},[1700,47585,1768],{},[2007,47587,47588,47590],{},[898,47589,1677],{},[1931,47591,2343],{},[1700,47593,1768],{},[1931,47595,2553],{},[2007,47597,47598,47600],{},[898,47599,1677],{},[1931,47601,2385],{},[902,47603,47604],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,47607,47609],{"className":47608},[886],[888,47610,47611],{"xmlns":890},[892,47612,47613,47635],{},[895,47614,47615,47621,47623,47625,47627,47629],{},[2007,47616,47617,47619],{},[898,47618,1662],{},[1931,47620,1933],{},[1700,47622,1765],{},[1700,47624,1768],{},[1931,47626,24386],{},[1700,47628,1897],{},[2007,47630,47631,47633],{},[898,47632,1677],{},[1931,47634,1933],{},[902,47636,47637],{"encoding":904},"Q_1 = -7 + P_1",[883,47639,47641],{"className":47640},[886],[888,47642,47643],{"xmlns":890},[892,47644,47645,47669],{},[895,47646,47647,47653,47655,47657,47659,47661,47663],{},[2007,47648,47649,47651],{},[898,47650,1662],{},[1931,47652,2343],{},[1700,47654,1765],{},[1700,47656,1768],{},[1931,47658,2553],{},[1700,47660,1897],{},[1931,47662,2553],{},[2007,47664,47665,47667],{},[898,47666,1677],{},[1931,47668,2343],{},[902,47670,47671],{"encoding":904},"Q_2 = -4 + 4P_2",[883,47673,47675],{"className":47674},[886],[888,47676,47677],{"xmlns":890},[892,47678,47679,47703],{},[895,47680,47681,47687,47689,47691,47693,47695,47697],{},[2007,47682,47683,47685],{},[898,47684,1662],{},[1931,47686,2385],{},[1700,47688,1765],{},[1700,47690,1768],{},[1931,47692,2438],{},[1700,47694,1897],{},[1931,47696,2343],{},[2007,47698,47699,47701],{},[898,47700,1677],{},[1931,47702,2385],{},[902,47704,47705],{"encoding":904},"Q_3 = -5 + 2P_3",[883,47707,47709],{"className":47708},[886],[888,47710,47711],{"xmlns":890},[892,47712,47713,47721],{},[895,47714,47715],{},[2007,47716,47717,47719],{},[898,47718,1662],{},[898,47720,17975],{},[902,47722,47723],{"encoding":904},"Q_i",[883,47725,47727],{"className":47726},[886],[888,47728,47729],{"xmlns":890},[892,47730,47731,47739],{},[895,47732,47733],{},[2007,47734,47735,47737],{},[898,47736,1677],{},[898,47738,17975],{},[902,47740,47741],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,47744,47746],{"className":47745},[886],[888,47747,47748],{"xmlns":890},[892,47749,47750,47754],{},[895,47751,47752],{},[898,47753,17975],{},[902,47755,17975],{"encoding":904},"-tého zboží, ",[883,47758,47760],{"className":47759},[886],[888,47761,47762],{"xmlns":890},[892,47763,47764,47780],{},[895,47765,47766,47768,47770,47772,47774,47776,47778],{},[898,47767,17975],{},[1700,47769,1765],{},[1931,47771,1933],{},[1700,47773,1732],{"separator":1731},[1931,47775,2343],{},[1700,47777,1732],{"separator":1731},[1931,47779,2385],{},[902,47781,47782],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,47785,47787],{"className":47786},[886],[888,47788,47789],{"xmlns":890},[892,47790,47791,47821],{},[895,47792,47793,47801,47803,47811,47813],{},[2030,47794,47795,47797,47799],{},[898,47796,1662],{},[1931,47798,1933],{},[898,47800,1762],{},[1700,47802,1732],{"separator":1731},[2030,47804,47805,47807,47809],{},[898,47806,1662],{},[1931,47808,2343],{},[898,47810,1762],{},[1700,47812,1732],{"separator":1731},[2030,47814,47815,47817,47819],{},[898,47816,1662],{},[1931,47818,2385],{},[898,47820,1762],{},[902,47822,47823],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,47825,47827],{"className":47826},[886],[888,47828,47829],{"xmlns":890},[892,47830,47831,47861],{},[895,47832,47833,47841,47843,47851,47853],{},[2030,47834,47835,47837,47839],{},[898,47836,1677],{},[1931,47838,1933],{},[898,47840,1762],{},[1700,47842,1732],{"separator":1731},[2030,47844,47845,47847,47849],{},[898,47846,1677],{},[1931,47848,2343],{},[898,47850,1762],{},[1700,47852,1732],{"separator":1731},[2030,47854,47855,47857,47859],{},[898,47856,1677],{},[1931,47858,2385],{},[898,47860,1762],{},[902,47862,47863],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,47865,47866,47869,47870,47906,47907,2196],{},[38,47867,47868],{},"2.13"," Jsou dány poptávka ",[883,47871,47873],{"className":47872},[886],[888,47874,47875],{"xmlns":890},[892,47876,47877,47903],{},[895,47878,47879,47881,47883,47885,47887,47889,47891,47893,47895,47897,47899,47901],{},[898,47880,1677],{},[1700,47882,1765],{},[898,47884,4374],{},[1700,47886,1703],{"stretchy":1702},[898,47888,1662],{},[1700,47890,1709],{"stretchy":1702},[1700,47892,1765],{},[1700,47894,1768],{},[1931,47896,2553],{},[898,47898,1662],{},[1700,47900,1897],{},[1931,47902,46888],{},[902,47904,47905],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,47908,47910],{"className":47909},[886],[888,47911,47912],{"xmlns":890},[892,47913,47914,47938],{},[895,47915,47916,47918,47920,47922,47924,47926,47928,47930,47932,47934,47936],{},[898,47917,1677],{},[1700,47919,1765],{},[898,47921,8861],{},[1700,47923,1703],{"stretchy":1702},[898,47925,1662],{},[1700,47927,1709],{"stretchy":1702},[1700,47929,1765],{},[1931,47931,2385],{},[898,47933,1662],{},[1700,47935,1897],{},[1931,47937,3058],{},[902,47939,47940],{"encoding":904},"P = S(Q) = 3Q + 10",[120,47942,47943,47980,48044,48104],{},[123,47944,47945,47946,46843,47963,2196],{},"(a) Určete rovnovážné množství ",[883,47947,47949],{"className":47948},[886],[888,47950,47951],{"xmlns":890},[892,47952,47953,47961],{},[895,47954,47955],{},[1785,47956,47957,47959],{},[898,47958,1662],{},[898,47960,1762],{},[902,47962,42588],{"encoding":904},[883,47964,47966],{"className":47965},[886],[888,47967,47968],{"xmlns":890},[892,47969,47970,47978],{},[895,47971,47972],{},[1785,47973,47974,47976],{},[898,47975,1677],{},[898,47977,1762],{},[902,47979,41651],{"encoding":904},[123,47981,47982,47983,48001,48002,48022,48023,48043],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,47984,47986],{"className":47985},[886],[888,47987,47988],{"xmlns":890},[892,47989,47990,47998],{},[895,47991,47992,47994,47996],{},[898,47993,2971],{},[1700,47995,1765],{},[1931,47997,24386],{},[902,47999,48000],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,48003,48005],{"className":48004},[886],[888,48006,48007],{"xmlns":890},[892,48008,48009,48019],{},[895,48010,48011],{},[2030,48012,48013,48015,48017],{},[898,48014,1662],{},[1931,48016,1933],{},[898,48018,1762],{},[902,48020,48021],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,48024,48026],{"className":48025},[886],[888,48027,48028],{"xmlns":890},[892,48029,48030,48040],{},[895,48031,48032],{},[2030,48033,48034,48036,48038],{},[898,48035,1677],{},[1931,48037,1933],{},[898,48039,1762],{},[902,48041,48042],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,48045,48046,48047,48001,48064,48022,48084,48043],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,48048,48050],{"className":48049},[886],[888,48051,48052],{"xmlns":890},[892,48053,48054,48062],{},[895,48055,48056,48058,48060],{},[898,48057,2971],{},[1700,48059,1765],{},[1931,48061,24386],{},[902,48063,48000],{"encoding":904},[883,48065,48067],{"className":48066},[886],[888,48068,48069],{"xmlns":890},[892,48070,48071,48081],{},[895,48072,48073],{},[2030,48074,48075,48077,48079],{},[898,48076,1662],{},[1931,48078,2343],{},[898,48080,1762],{},[902,48082,48083],{"encoding":904},"Q_2^E",[883,48085,48087],{"className":48086},[886],[888,48088,48089],{"xmlns":890},[892,48090,48091,48101],{},[895,48092,48093],{},[2030,48094,48095,48097,48099],{},[898,48096,1677],{},[1931,48098,2343],{},[898,48100,1762],{},[902,48102,48103],{"encoding":904},"P_2^E",[123,48105,48106],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,48108,48109,48110,2196],{},"Viz též ",[207,48111,42906],{"className":48112,"dataFsResolvedFilePath":809,"href":810},[210],[198,48114,43208],{"id":48115},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,48117,48118,47869,48121,47906,48157,2196],{},[38,48119,48120],{},"2.14",[883,48122,48124],{"className":48123},[886],[888,48125,48126],{"xmlns":890},[892,48127,48128,48154],{},[895,48129,48130,48132,48134,48136,48138,48140,48142,48144,48146,48148,48150,48152],{},[898,48131,1677],{},[1700,48133,1765],{},[898,48135,207],{},[898,48137,1662],{},[1700,48139,1897],{},[898,48141,1879],{},[1700,48143,1765],{},[1700,48145,1768],{},[1931,48147,2343],{},[898,48149,1662],{},[1700,48151,1897],{},[1931,48153,3314],{},[902,48155,48156],{"encoding":904},"P = aQ + b = -2Q + 50",[883,48158,48160],{"className":48159},[886],[888,48161,48162],{"xmlns":890},[892,48163,48164,48188],{},[895,48165,48166,48168,48170,48172,48174,48176,48178,48180,48182,48184,48186],{},[898,48167,1677],{},[1700,48169,1765],{},[898,48171,2354],{},[898,48173,1662],{},[1700,48175,1897],{},[898,48177,2406],{},[1700,48179,1765],{},[1931,48181,19506],{},[898,48183,1662],{},[1700,48185,1897],{},[1931,48187,9223],{},[902,48189,48190],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,48192,48193,48229,48232,48318,48371,48451,48505],{},[123,48194,47945,48195,46843,48212,2196],{},[883,48196,48198],{"className":48197},[886],[888,48199,48200],{"xmlns":890},[892,48201,48202,48210],{},[895,48203,48204],{},[1785,48205,48206,48208],{},[898,48207,1662],{},[898,48209,1762],{},[902,48211,42588],{"encoding":904},[883,48213,48215],{"className":48214},[886],[888,48216,48217],{"xmlns":890},[892,48218,48219,48227],{},[895,48220,48221],{},[1785,48222,48223,48225],{},[898,48224,1677],{},[898,48226,1762],{},[902,48228,41651],{"encoding":904},[123,48230,48231],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,48233,48234,48235,48252,48253,2868,48266,2882,48282,48298,48299,2196],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,48236,48238],{"className":48237},[886],[888,48239,48240],{"xmlns":890},[892,48241,48242,48250],{},[895,48243,48244],{},[1785,48245,48246,48248],{},[898,48247,1662],{},[898,48249,1762],{},[902,48251,42588],{"encoding":904}," odpovídající změně ",[883,48254,48256],{"className":48255},[886],[888,48257,48258],{"xmlns":890},[892,48259,48260,48264],{},[895,48261,48262],{},[898,48263,207],{},[902,48265,207],{"encoding":904},[883,48267,48269],{"className":48268},[886],[888,48270,48271],{"xmlns":890},[892,48272,48273,48279],{},[895,48274,48275,48277],{},[1700,48276,1768],{},[1931,48278,2343],{},[902,48280,48281],{"encoding":904},"-2",[883,48283,48285],{"className":48284},[886],[888,48286,48287],{"xmlns":890},[892,48288,48289,48295],{},[895,48290,48291,48293],{},[1700,48292,1768],{},[1931,48294,2385],{},[902,48296,48297],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48300,48302],{"className":48301},[886],[888,48303,48304],{"xmlns":890},[892,48305,48306,48316],{},[895,48307,48308],{},[2030,48309,48310,48312,48314],{},[898,48311,1662],{},[1931,48313,1933],{},[898,48315,1762],{},[902,48317,48021],{"encoding":904},[123,48319,48320,48321,48252,48338,48351,48352,2196],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,48322,48324],{"className":48323},[886],[888,48325,48326],{"xmlns":890},[892,48327,48328,48336],{},[895,48329,48330],{},[1785,48331,48332,48334],{},[898,48333,1662],{},[898,48335,1762],{},[902,48337,42588],{"encoding":904},[883,48339,48341],{"className":48340},[886],[888,48342,48343],{"xmlns":890},[892,48344,48345,48349],{},[895,48346,48347],{},[898,48348,1879],{},[902,48350,1879],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48353,48355],{"className":48354},[886],[888,48356,48357],{"xmlns":890},[892,48358,48359,48369],{},[895,48360,48361],{},[2030,48362,48363,48365,48367],{},[898,48364,1662],{},[1931,48366,2343],{},[898,48368,1762],{},[902,48370,48083],{"encoding":904},[123,48372,48373,48374,48252,48391,2868,48404,2882,48417,48298,48431,2196],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,48375,48377],{"className":48376},[886],[888,48378,48379],{"xmlns":890},[892,48380,48381,48389],{},[895,48382,48383],{},[1785,48384,48385,48387],{},[898,48386,1662],{},[898,48388,1762],{},[902,48390,42588],{"encoding":904},[883,48392,48394],{"className":48393},[886],[888,48395,48396],{"xmlns":890},[892,48397,48398,48402],{},[895,48399,48400],{},[898,48401,2354],{},[902,48403,2354],{"encoding":904},[883,48405,48407],{"className":48406},[886],[888,48408,48409],{"xmlns":890},[892,48410,48411,48415],{},[895,48412,48413],{},[1931,48414,19506],{},[902,48416,44645],{"encoding":904},[883,48418,48420],{"className":48419},[886],[888,48421,48422],{"xmlns":890},[892,48423,48424,48428],{},[895,48425,48426],{},[1931,48427,14774],{},[902,48429,48430],{"encoding":904},"0{,}8",[883,48432,48434],{"className":48433},[886],[888,48435,48436],{"xmlns":890},[892,48437,48438,48448],{},[895,48439,48440],{},[2030,48441,48442,48444,48446],{},[898,48443,1662],{},[1931,48445,2385],{},[898,48447,1762],{},[902,48449,48450],{"encoding":904},"Q_3^E",[123,48452,48453,48454,48252,48471,48484,48485,2196],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,48455,48457],{"className":48456},[886],[888,48458,48459],{"xmlns":890},[892,48460,48461,48469],{},[895,48462,48463],{},[1785,48464,48465,48467],{},[898,48466,1662],{},[898,48468,1762],{},[902,48470,42588],{"encoding":904},[883,48472,48474],{"className":48473},[886],[888,48475,48476],{"xmlns":890},[892,48477,48478,48482],{},[895,48479,48480],{},[898,48481,2406],{},[902,48483,2406],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48486,48488],{"className":48487},[886],[888,48489,48490],{"xmlns":890},[892,48491,48492,48502],{},[895,48493,48494],{},[2030,48495,48496,48498,48500],{},[898,48497,1662],{},[1931,48499,2553],{},[898,48501,1762],{},[902,48503,48504],{"encoding":904},"Q_4^E",[123,48506,48507,48508,48525,48526,48539,48540,21605,48553,1343,48568,21605,48581,2114,48595,21605,48608,48623,48624,2196],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,48509,48511],{"className":48510},[886],[888,48512,48513],{"xmlns":890},[892,48514,48515,48523],{},[895,48516,48517],{},[1785,48518,48519,48521],{},[898,48520,1662],{},[898,48522,1762],{},[902,48524,42588],{"encoding":904}," odpovídající změnám ",[883,48527,48529],{"className":48528},[886],[888,48530,48531],{"xmlns":890},[892,48532,48533,48537],{},[895,48534,48535],{},[898,48536,207],{},[902,48538,207],{"encoding":904}," o 1, ",[883,48541,48543],{"className":48542},[886],[888,48544,48545],{"xmlns":890},[892,48546,48547,48551],{},[895,48548,48549],{},[898,48550,1879],{},[902,48552,1879],{"encoding":904},[883,48554,48556],{"className":48555},[886],[888,48557,48558],{"xmlns":890},[892,48559,48560,48566],{},[895,48561,48562,48564],{},[1700,48563,1768],{},[1931,48565,3058],{},[902,48567,19640],{"encoding":904},[883,48569,48571],{"className":48570},[886],[888,48572,48573],{"xmlns":890},[892,48574,48575,48579],{},[895,48576,48577],{},[898,48578,2354],{},[902,48580,2354],{"encoding":904},[883,48582,48584],{"className":48583},[886],[888,48585,48586],{"xmlns":890},[892,48587,48588,48592],{},[895,48589,48590],{},[1931,48591,2990],{},[902,48593,48594],{"encoding":904},"0{,}1",[883,48596,48598],{"className":48597},[886],[888,48599,48600],{"xmlns":890},[892,48601,48602,48606],{},[895,48603,48604],{},[898,48605,2406],{},[902,48607,2406],{"encoding":904},[883,48609,48611],{"className":48610},[886],[888,48612,48613],{"xmlns":890},[892,48614,48615,48621],{},[895,48616,48617,48619],{},[1700,48618,1768],{},[1931,48620,3058],{},[902,48622,19640],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,48625,48627],{"className":48626},[886],[888,48628,48629],{"xmlns":890},[892,48630,48631,48641],{},[895,48632,48633],{},[2030,48634,48635,48637,48639],{},[898,48636,1662],{},[1931,48638,2438],{},[898,48640,1762],{},[902,48642,48643],{"encoding":904},"Q_5^E",[724,48645,48646,47869,48649,47906,48672,2196],{},[38,48647,48648],{},"2.15",[883,48650,48652],{"className":48651},[886],[888,48653,48654],{"xmlns":890},[892,48655,48656,48670],{},[895,48657,48658,48660,48662,48664,48666,48668],{},[898,48659,1677],{},[1700,48661,1765],{},[898,48663,207],{},[898,48665,1662],{},[1700,48667,1897],{},[898,48669,1879],{},[902,48671,37245],{"encoding":904},[883,48673,48675],{"className":48674},[886],[888,48676,48677],{"xmlns":890},[892,48678,48679,48693],{},[895,48680,48681,48683,48685,48687,48689,48691],{},[898,48682,1677],{},[1700,48684,1765],{},[898,48686,2354],{},[898,48688,1662],{},[1700,48690,1897],{},[898,48692,2406],{},[902,48694,40427],{"encoding":904},[120,48696,48697,48772,48789,48898,48951,49005],{},[123,48698,48699,48700,48713,48714,48739,48740,48771],{},"(a) Odvoďte redukovaný tvar pro ",[883,48701,48703],{"className":48702},[886],[888,48704,48705],{"xmlns":890},[892,48706,48707,48711],{},[895,48708,48709],{},[898,48710,1677],{},[902,48712,1677],{"encoding":904},". Stanovte podmínky pro ",[883,48715,48717],{"className":48716},[886],[888,48718,48719],{"xmlns":890},[892,48720,48721,48737],{},[895,48722,48723,48725,48727,48729,48731,48733,48735],{},[898,48724,207],{},[1700,48726,1732],{"separator":1731},[898,48728,1879],{},[1700,48730,1732],{"separator":1731},[898,48732,2354],{},[1700,48734,1732],{"separator":1731},[898,48736,2406],{},[902,48738,43470],{"encoding":904}," tak, aby rovnovážný bod ",[883,48741,48743],{"className":48742},[886],[888,48744,48745],{"xmlns":890},[892,48746,48747,48769],{},[895,48748,48749,48751,48753,48759,48761,48767],{},[898,48750,1762],{},[1700,48752,1927],{"stretchy":1702},[1785,48754,48755,48757],{},[898,48756,1662],{},[898,48758,1762],{},[1700,48760,1732],{"separator":1731},[1785,48762,48763,48765],{},[898,48764,1677],{},[898,48766,1762],{},[1700,48768,1970],{"stretchy":1702},[902,48770,41552],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,48773,48774,48775,48788],{},"(b) Vypočtěte multiplikátory pro ",[883,48776,48778],{"className":48777},[886],[888,48779,48780],{"xmlns":890},[892,48781,48782,48786],{},[895,48783,48784],{},[898,48785,1677],{},[902,48787,1677],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,48790,48791,48792,1343,48812,1343,48830,1343,48848,48866,48867,48884,48885,2196],{},"(c) Pro hodnoty parametrů ",[883,48793,48795],{"className":48794},[886],[888,48796,48797],{"xmlns":890},[892,48798,48799,48809],{},[895,48800,48801,48803,48805,48807],{},[898,48802,207],{},[1700,48804,1765],{},[1700,48806,1768],{},[1931,48808,2343],{},[902,48810,48811],{"encoding":904},"a = -2",[883,48813,48815],{"className":48814},[886],[888,48816,48817],{"xmlns":890},[892,48818,48819,48827],{},[895,48820,48821,48823,48825],{},[898,48822,1879],{},[1700,48824,1765],{},[1931,48826,5399],{},[902,48828,48829],{"encoding":904},"b = 40",[883,48831,48833],{"className":48832},[886],[888,48834,48835],{"xmlns":890},[892,48836,48837,48845],{},[895,48838,48839,48841,48843],{},[898,48840,2354],{},[1700,48842,1765],{},[1931,48844,5197],{},[902,48846,48847],{"encoding":904},"c = 0{,}5",[883,48849,48851],{"className":48850},[886],[888,48852,48853],{"xmlns":890},[892,48854,48855,48863],{},[895,48856,48857,48859,48861],{},[898,48858,2406],{},[1700,48860,1765],{},[1931,48862,3058],{},[902,48864,48865],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,48868,48870],{"className":48869},[886],[888,48871,48872],{"xmlns":890},[892,48873,48874,48882],{},[895,48875,48876],{},[1785,48877,48878,48880],{},[898,48879,1677],{},[898,48881,1762],{},[902,48883,41651],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,48886,48888],{"className":48887},[886],[888,48889,48890],{"xmlns":890},[892,48891,48892,48896],{},[895,48893,48894],{},[898,48895,1677],{},[902,48897,1677],{"encoding":904},[123,48899,48900,48901,48252,48918,48931,48932,2196],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,48902,48904],{"className":48903},[886],[888,48905,48906],{"xmlns":890},[892,48907,48908,48916],{},[895,48909,48910],{},[1785,48911,48912,48914],{},[898,48913,1677],{},[898,48915,1762],{},[902,48917,41651],{"encoding":904},[883,48919,48921],{"className":48920},[886],[888,48922,48923],{"xmlns":890},[892,48924,48925,48929],{},[895,48926,48927],{},[898,48928,207],{},[902,48930,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,48933,48935],{"className":48934},[886],[888,48936,48937],{"xmlns":890},[892,48938,48939,48949],{},[895,48940,48941],{},[2030,48942,48943,48945,48947],{},[898,48944,1677],{},[1931,48946,1933],{},[898,48948,1762],{},[902,48950,48042],{"encoding":904},[123,48952,48953,48954,48971,48972,48985,48986,2196],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,48955,48957],{"className":48956},[886],[888,48958,48959],{"xmlns":890},[892,48960,48961,48969],{},[895,48962,48963],{},[1785,48964,48965,48967],{},[898,48966,1677],{},[898,48968,1762],{},[902,48970,41651],{"encoding":904}," odpovídající poklesu ",[883,48973,48975],{"className":48974},[886],[888,48976,48977],{"xmlns":890},[892,48978,48979,48983],{},[895,48980,48981],{},[898,48982,207],{},[902,48984,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,48987,48989],{"className":48988},[886],[888,48990,48991],{"xmlns":890},[892,48992,48993,49003],{},[895,48994,48995],{},[2030,48996,48997,48999,49001],{},[898,48998,1677],{},[1931,49000,2343],{},[898,49002,1762],{},[902,49004,48103],{"encoding":904},[123,49006,49007,49008,48525,49025,49038,49039,2882,49052,2114,49067,49080,49081,2196],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,49009,49011],{"className":49010},[886],[888,49012,49013],{"xmlns":890},[892,49014,49015,49023],{},[895,49016,49017],{},[1785,49018,49019,49021],{},[898,49020,1677],{},[898,49022,1762],{},[902,49024,41651],{"encoding":904},[883,49026,49028],{"className":49027},[886],[888,49029,49030],{"xmlns":890},[892,49031,49032,49036],{},[895,49033,49034],{},[898,49035,207],{},[902,49037,207],{"encoding":904}," na 35, ",[883,49040,49042],{"className":49041},[886],[888,49043,49044],{"xmlns":890},[892,49045,49046,49050],{},[895,49047,49048],{},[898,49049,2354],{},[902,49051,2354],{"encoding":904},[883,49053,49055],{"className":49054},[886],[888,49056,49057],{"xmlns":890},[892,49058,49059,49064],{},[895,49060,49061],{},[1931,49062,49063],{},"0,7",[902,49065,49066],{"encoding":904},"0{,}7",[883,49068,49070],{"className":49069},[886],[888,49071,49072],{"xmlns":890},[892,49073,49074,49078],{},[895,49075,49076],{},[898,49077,2406],{},[902,49079,2406],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,49082,49084],{"className":49083},[886],[888,49085,49086],{"xmlns":890},[892,49087,49088,49098],{},[895,49089,49090],{},[2030,49091,49092,49094,49096],{},[898,49093,1677],{},[1931,49095,2385],{},[898,49097,1762],{},[902,49099,49100],{"encoding":904},"P_3^E",[724,49102,49103,47869,49106,47906,49134,21779,49162,2114,49188,2196],{},[38,49104,49105],{},"2.16",[883,49107,49109],{"className":49108},[886],[888,49110,49111],{"xmlns":890},[892,49112,49113,49131],{},[895,49114,49115,49117,49119,49121,49123,49125],{},[898,49116,1677],{},[1700,49118,1765],{},[898,49120,207],{},[1700,49122,1897],{},[898,49124,1879],{},[1785,49126,49127,49129],{},[898,49128,1662],{},[1931,49130,2343],{},[902,49132,49133],{"encoding":904},"P = a + bQ^2",[883,49135,49137],{"className":49136},[886],[888,49138,49139],{"xmlns":890},[892,49140,49141,49159],{},[895,49142,49143,49145,49147,49149,49151,49153],{},[898,49144,1677],{},[1700,49146,1765],{},[898,49148,2354],{},[1700,49150,1897],{},[898,49152,2406],{},[1785,49154,49155,49157],{},[898,49156,1662],{},[1931,49158,2343],{},[902,49160,49161],{"encoding":904},"P = c + dQ^2",[883,49163,49165],{"className":49164},[886],[888,49166,49167],{"xmlns":890},[892,49168,49169,49185],{},[895,49170,49171,49173,49175,49177,49179,49181,49183],{},[898,49172,207],{},[1700,49174,1732],{"separator":1731},[898,49176,2354],{},[1700,49178,1732],{"separator":1731},[898,49180,2406],{},[1700,49182,3601],{},[1931,49184,1772],{},[902,49186,49187],{"encoding":904},"a, c, d > 0",[883,49189,49191],{"className":49190},[886],[888,49192,49193],{"xmlns":890},[892,49194,49195,49203],{},[895,49196,49197,49199,49201],{},[898,49198,1879],{},[1700,49200,3640],{},[1931,49202,1772],{},[902,49204,49205],{"encoding":904},"b \u003C 0",[120,49207,49208,49256,49272,49379,49431,49483,49592,49608,49707,49760],{},[123,49209,48699,49210,49223,49224,49255],{},[883,49211,49213],{"className":49212},[886],[888,49214,49215],{"xmlns":890},[892,49216,49217,49221],{},[895,49218,49219],{},[898,49220,1662],{},[902,49222,1662],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,49225,49227],{"className":49226},[886],[888,49228,49229],{"xmlns":890},[892,49230,49231,49253],{},[895,49232,49233,49235,49237,49243,49245,49251],{},[898,49234,1762],{},[1700,49236,1927],{"stretchy":1702},[1785,49238,49239,49241],{},[898,49240,1662],{},[898,49242,1762],{},[1700,49244,1732],{"separator":1731},[1785,49246,49247,49249],{},[898,49248,1677],{},[898,49250,1762],{},[1700,49252,1970],{"stretchy":1702},[902,49254,41552],{"encoding":904}," patřil do 1. kvadrantu.",[123,49257,48774,49258,49271],{},[883,49259,49261],{"className":49260},[886],[888,49262,49263],{"xmlns":890},[892,49264,49265,49269],{},[895,49266,49267],{},[898,49268,1662],{},[902,49270,1662],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,49273,48791,49274,1343,49292,1343,49312,1343,49330,49348,49349,48884,49366,2196],{},[883,49275,49277],{"className":49276},[886],[888,49278,49279],{"xmlns":890},[892,49280,49281,49289],{},[895,49282,49283,49285,49287],{},[898,49284,207],{},[1700,49286,1765],{},[1931,49288,3284],{},[902,49290,49291],{"encoding":904},"a = 100",[883,49293,49295],{"className":49294},[886],[888,49296,49297],{"xmlns":890},[892,49298,49299,49309],{},[895,49300,49301,49303,49305,49307],{},[898,49302,1879],{},[1700,49304,1765],{},[1700,49306,1768],{},[1931,49308,1933],{},[902,49310,49311],{"encoding":904},"b = -1",[883,49313,49315],{"className":49314},[886],[888,49316,49317],{"xmlns":890},[892,49318,49319,49327],{},[895,49320,49321,49323,49325],{},[898,49322,2354],{},[1700,49324,1765],{},[1931,49326,9223],{},[902,49328,49329],{"encoding":904},"c = 20",[883,49331,49333],{"className":49332},[886],[888,49334,49335],{"xmlns":890},[892,49336,49337,49345],{},[895,49338,49339,49341,49343],{},[898,49340,2406],{},[1700,49342,1765],{},[1931,49344,1933],{},[902,49346,49347],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,49350,49352],{"className":49351},[886],[888,49353,49354],{"xmlns":890},[892,49355,49356,49364],{},[895,49357,49358],{},[1785,49359,49360,49362],{},[898,49361,1662],{},[898,49363,1762],{},[902,49365,42588],{"encoding":904},[883,49367,49369],{"className":49368},[886],[888,49370,49371],{"xmlns":890},[892,49372,49373,49377],{},[895,49374,49375],{},[898,49376,1662],{},[902,49378,1662],{"encoding":904},[123,49380,48320,49381,48252,49398,49411,49412,2196],{},[883,49382,49384],{"className":49383},[886],[888,49385,49386],{"xmlns":890},[892,49387,49388,49396],{},[895,49389,49390],{},[1785,49391,49392,49394],{},[898,49393,1662],{},[898,49395,1762],{},[902,49397,42588],{"encoding":904},[883,49399,49401],{"className":49400},[886],[888,49402,49403],{"xmlns":890},[892,49404,49405,49409],{},[895,49406,49407],{},[898,49408,207],{},[902,49410,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49413,49415],{"className":49414},[886],[888,49416,49417],{"xmlns":890},[892,49418,49419,49429],{},[895,49420,49421],{},[2030,49422,49423,49425,49427],{},[898,49424,1662],{},[1931,49426,1933],{},[898,49428,1762],{},[902,49430,48021],{"encoding":904},[123,49432,48373,49433,48252,49450,49463,49464,2196],{},[883,49434,49436],{"className":49435},[886],[888,49437,49438],{"xmlns":890},[892,49439,49440,49448],{},[895,49441,49442],{},[1785,49443,49444,49446],{},[898,49445,1662],{},[898,49447,1762],{},[902,49449,42588],{"encoding":904},[883,49451,49453],{"className":49452},[886],[888,49454,49455],{"xmlns":890},[892,49456,49457,49461],{},[895,49458,49459],{},[898,49460,2354],{},[902,49462,2354],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49465,49467],{"className":49466},[886],[888,49468,49469],{"xmlns":890},[892,49470,49471,49481],{},[895,49472,49473],{},[2030,49474,49475,49477,49479],{},[898,49476,1662],{},[1931,49478,2343],{},[898,49480,1762],{},[902,49482,48083],{"encoding":904},[123,49484,48453,49485,48525,49502,49515,49516,2882,49529,49544,49545,49558,49559,49572,49573,2196],{},[883,49486,49488],{"className":49487},[886],[888,49489,49490],{"xmlns":890},[892,49491,49492,49500],{},[895,49493,49494],{},[1785,49495,49496,49498],{},[898,49497,1662],{},[898,49499,1762],{},[902,49501,42588],{"encoding":904},[883,49503,49505],{"className":49504},[886],[888,49506,49507],{"xmlns":890},[892,49508,49509,49513],{},[895,49510,49511],{},[898,49512,207],{},[902,49514,207],{"encoding":904}," na 110, poklesu ",[883,49517,49519],{"className":49518},[886],[888,49520,49521],{"xmlns":890},[892,49522,49523,49527],{},[895,49524,49525],{},[898,49526,1879],{},[902,49528,1879],{"encoding":904},[883,49530,49532],{"className":49531},[886],[888,49533,49534],{"xmlns":890},[892,49535,49536,49542],{},[895,49537,49538,49540],{},[1700,49539,1768],{},[1931,49541,2343],{},[902,49543,48281],{"encoding":904},", růstu ",[883,49546,49548],{"className":49547},[886],[888,49549,49550],{"xmlns":890},[892,49551,49552,49556],{},[895,49553,49554],{},[898,49555,2354],{},[902,49557,2354],{"encoding":904}," na 25 a růstu ",[883,49560,49562],{"className":49561},[886],[888,49563,49564],{"xmlns":890},[892,49565,49566,49570],{},[895,49567,49568],{},[898,49569,2406],{},[902,49571,2406],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,49574,49576],{"className":49575},[886],[888,49577,49578],{"xmlns":890},[892,49579,49580,49590],{},[895,49581,49582],{},[2030,49583,49584,49586,49588],{},[898,49585,1662],{},[1931,49587,2385],{},[898,49589,1762],{},[902,49591,48450],{"encoding":904},[123,49593,49594,49595,49271],{},"(i) Vypočtěte multiplikátory pro ",[883,49596,49598],{"className":49597},[886],[888,49599,49600],{"xmlns":890},[892,49601,49602,49606],{},[895,49603,49604],{},[898,49605,1677],{},[902,49607,1677],{"encoding":904},[123,49609,49610,49611,48884,49628,49641,49642,48252,49659,2882,49672,49687,49688,2196],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,49612,49614],{"className":49613},[886],[888,49615,49616],{"xmlns":890},[892,49617,49618,49626],{},[895,49619,49620],{},[1785,49621,49622,49624],{},[898,49623,1677],{},[898,49625,1762],{},[902,49627,41651],{"encoding":904},[883,49629,49631],{"className":49630},[886],[888,49632,49633],{"xmlns":890},[892,49634,49635,49639],{},[895,49636,49637],{},[898,49638,1677],{},[902,49640,1677],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,49643,49645],{"className":49644},[886],[888,49646,49647],{"xmlns":890},[892,49648,49649,49657],{},[895,49650,49651],{},[1785,49652,49653,49655],{},[898,49654,1677],{},[898,49656,1762],{},[902,49658,41651],{"encoding":904},[883,49660,49662],{"className":49661},[886],[888,49663,49664],{"xmlns":890},[892,49665,49666,49670],{},[895,49667,49668],{},[898,49669,207],{},[902,49671,207],{"encoding":904},[883,49673,49675],{"className":49674},[886],[888,49676,49677],{"xmlns":890},[892,49678,49679,49685],{},[895,49680,49681,49683],{},[1700,49682,1768],{},[1931,49684,2385],{},[902,49686,48297],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49689,49691],{"className":49690},[886],[888,49692,49693],{"xmlns":890},[892,49694,49695,49705],{},[895,49696,49697],{},[2030,49698,49699,49701,49703],{},[898,49700,1677],{},[1931,49702,1933],{},[898,49704,1762],{},[902,49706,48042],{"encoding":904},[123,49708,49709,49710,48252,49727,49740,49741,2196],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,49711,49713],{"className":49712},[886],[888,49714,49715],{"xmlns":890},[892,49716,49717,49725],{},[895,49718,49719],{},[1785,49720,49721,49723],{},[898,49722,1677],{},[898,49724,1762],{},[902,49726,41651],{"encoding":904},[883,49728,49730],{"className":49729},[886],[888,49731,49732],{"xmlns":890},[892,49733,49734,49738],{},[895,49735,49736],{},[898,49737,207],{},[902,49739,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49742,49744],{"className":49743},[886],[888,49745,49746],{"xmlns":890},[892,49747,49748,49758],{},[895,49749,49750],{},[2030,49751,49752,49754,49756],{},[898,49753,1677],{},[1931,49755,2343],{},[898,49757,1762],{},[902,49759,48103],{"encoding":904},[123,49761,49762,49763,48971,49780,49793,49794,2882,49807,49544,49822,49835,49836,49849,49850,2196],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,49764,49766],{"className":49765},[886],[888,49767,49768],{"xmlns":890},[892,49769,49770,49778],{},[895,49771,49772],{},[1785,49773,49774,49776],{},[898,49775,1677],{},[898,49777,1762],{},[902,49779,41651],{"encoding":904},[883,49781,49783],{"className":49782},[886],[888,49784,49785],{"xmlns":890},[892,49786,49787,49791],{},[895,49788,49789],{},[898,49790,207],{},[902,49792,207],{"encoding":904}," na 90, poklesu ",[883,49795,49797],{"className":49796},[886],[888,49798,49799],{"xmlns":890},[892,49800,49801,49805],{},[895,49802,49803],{},[898,49804,1879],{},[902,49806,1879],{"encoding":904},[883,49808,49810],{"className":49809},[886],[888,49811,49812],{"xmlns":890},[892,49813,49814,49820],{},[895,49815,49816,49818],{},[1700,49817,1768],{},[1931,49819,2385],{},[902,49821,48297],{"encoding":904},[883,49823,49825],{"className":49824},[886],[888,49826,49827],{"xmlns":890},[892,49828,49829,49833],{},[895,49830,49831],{},[898,49832,2354],{},[902,49834,2354],{"encoding":904}," na 30 a růstu ",[883,49837,49839],{"className":49838},[886],[888,49840,49841],{"xmlns":890},[892,49842,49843,49847],{},[895,49844,49845],{},[898,49846,2406],{},[902,49848,2406],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49851,49853],{"className":49852},[886],[888,49854,49855],{"xmlns":890},[892,49856,49857,49867],{},[895,49858,49859],{},[2030,49860,49861,49863,49865],{},[898,49862,1677],{},[1931,49864,2385],{},[898,49866,1762],{},[902,49868,49100],{"encoding":904},[198,49870,820],{"id":49871},"přebytek-spotřebitele-a-výrobce-1",[724,49873,49874,47869,49877,47906,49913,2196],{},[38,49875,49876],{},"2.17",[883,49878,49880],{"className":49879},[886],[888,49881,49882],{"xmlns":890},[892,49883,49884,49910],{},[895,49885,49886,49888,49890,49892,49894,49896,49898,49900,49902,49904],{},[898,49887,1677],{},[1700,49889,1765],{},[898,49891,4374],{},[1700,49893,1703],{"stretchy":1702},[898,49895,1662],{},[1700,49897,1709],{"stretchy":1702},[1700,49899,1765],{},[1931,49901,15223],{},[1700,49903,1768],{},[1785,49905,49906,49908],{},[898,49907,1662],{},[1931,49909,2343],{},[902,49911,49912],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,49914,49916],{"className":49915},[886],[888,49917,49918],{"xmlns":890},[892,49919,49920,49946],{},[895,49921,49922,49924,49926,49928,49930,49932,49934,49936,49938,49940],{},[898,49923,1677],{},[1700,49925,1765],{},[898,49927,8861],{},[1700,49929,1703],{"stretchy":1702},[898,49931,1662],{},[1700,49933,1709],{"stretchy":1702},[1700,49935,1765],{},[1931,49937,2385],{},[1700,49939,1897],{},[1785,49941,49942,49944],{},[898,49943,1662],{},[1931,49945,2343],{},[902,49947,49948],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,49950,49951,49954],{},[123,49952,49953],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,49955,49956],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,49958,49959,47869,49962,47906,49996,2196],{},[38,49960,49961],{},"2.18",[883,49963,49965],{"className":49964},[886],[888,49966,49967],{"xmlns":890},[892,49968,49969,49993],{},[895,49970,49971,49973,49975,49977,49979,49981,49983,49985,49987,49989,49991],{},[898,49972,1677],{},[1700,49974,1765],{},[898,49976,4374],{},[1700,49978,1703],{"stretchy":1702},[898,49980,1662],{},[1700,49982,1709],{"stretchy":1702},[1700,49984,1765],{},[1931,49986,3900],{},[1700,49988,1768],{},[1931,49990,2343],{},[898,49992,1662],{},[902,49994,49995],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,49997,49999],{"className":49998},[886],[888,50000,50001],{"xmlns":890},[892,50002,50003,50029],{},[895,50004,50005,50007,50009,50011,50013,50015,50017,50019,50021,50023],{},[898,50006,1677],{},[1700,50008,1765],{},[898,50010,8861],{},[1700,50012,1703],{"stretchy":1702},[898,50014,1662],{},[1700,50016,1709],{"stretchy":1702},[1700,50018,1765],{},[1931,50020,2385],{},[1700,50022,1897],{},[1785,50024,50025,50027],{},[898,50026,1662],{},[1931,50028,2343],{},[902,50030,49948],{"encoding":904},[120,50032,50033,50053,50056,50059],{},[123,50034,50035,50036,2196],{},"(a) Vypočtěte rovnovážné množství ",[883,50037,50039],{"className":50038},[886],[888,50040,50041],{"xmlns":890},[892,50042,50043,50051],{},[895,50044,50045],{},[1785,50046,50047,50049],{},[898,50048,1662],{},[898,50050,1762],{},[902,50052,42588],{"encoding":904},[123,50054,50055],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,50057,50058],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,50060,50061],{},"(c) Graficky interpretujte.",[37155,50063],{},[115,50065,50067],{"id":50066},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,50069,50070,50073,50076,50079,50082,50085,50088,50091,50094,50097,50100,50103,50106,50109],{},[123,50071,50072],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,50074,50075],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,50077,50078],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,50080,50081],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,50083,50084],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,50086,50087],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,50089,50090],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,50092,50093],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,50095,50096],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,50098,50099],{},"K čemu slouží multiplikátory?",[123,50101,50102],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,50104,50105],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,50107,50108],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,50110,50111],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[37155,50113],{},[115,50115,15905],{"id":15904},[724,50117,50118],{},[38,50119,13346],{},[120,50121,50122,50157,50162,50192,50197,50260,50286,50291,50321,50330,50337,50343],{},[123,50123,50124,10208,50127,18833,50130,2106,50132,1343,50155],{},[38,50125,50126],{},"Poptávané množství",[614,50128,50129],{},"quantity demanded",[38,50131,28187],{},[883,50133,50135],{"className":50134},[886],[888,50136,50137],{"xmlns":890},[892,50138,50139,50153],{},[895,50140,50141,50143,50145,50147,50149,50151],{},[898,50142,1662],{},[1700,50144,1765],{},[898,50146,4374],{},[1700,50148,1703],{"stretchy":1702},[898,50150,1677],{},[1700,50152,1709],{"stretchy":1702},[902,50154,4383],{"encoding":904},[38,50156,37634],{},[123,50158,50159,50161],{},[38,50160,37641],{}," — substituční + důchodový efekt",[123,50163,50164,2106,50167],{},[38,50165,50166],{},"Reálné cenové rozpětí",[883,50168,50170],{"className":50169},[886],[888,50171,50172],{"xmlns":890},[892,50173,50174,50190],{},[895,50175,50176,50178,50180,50182,50188],{},[1700,50177,1703],{"stretchy":1702},[1931,50179,1772],{},[1700,50181,1732],{"separator":1731},[2007,50183,50184,50186],{},[898,50185,1677],{},[1931,50187,1772],{},[1700,50189,1709],{"stretchy":1702},[902,50191,37842],{"encoding":904},[123,50193,50194,11280],{},[38,50195,50196],{},"Homogenita poptávky",[123,50198,50199,2106,50202,1343,50225,1343,50242,50259],{},[38,50200,50201],{},"Lineární poptávka",[883,50203,50205],{"className":50204},[886],[888,50206,50207],{"xmlns":890},[892,50208,50209,50223],{},[895,50210,50211,50213,50215,50217,50219,50221],{},[898,50212,1677],{},[1700,50214,1765],{},[898,50216,207],{},[898,50218,1662],{},[1700,50220,1897],{},[898,50222,1879],{},[902,50224,37245],{"encoding":904},[883,50226,50228],{"className":50227},[886],[888,50229,50230],{"xmlns":890},[892,50231,50232,50240],{},[895,50233,50234,50236,50238],{},[898,50235,207],{},[1700,50237,3640],{},[1931,50239,1772],{},[902,50241,43270],{"encoding":904},[883,50243,50245],{"className":50244},[886],[888,50246,50247],{"xmlns":890},[892,50248,50249,50257],{},[895,50250,50251,50253,50255],{},[898,50252,1879],{},[1700,50254,3601],{},[1931,50256,1772],{},[902,50258,18999],{"encoding":904}," — nedokonalá konkurence",[123,50261,50262,7203,50265],{},[38,50263,50264],{},"Dokonalá konkurence",[883,50266,50268],{"className":50267},[886],[888,50269,50270],{"xmlns":890},[892,50271,50272,50284],{},[895,50273,50274,50276,50278],{},[898,50275,1677],{},[1700,50277,1765],{},[1785,50279,50280,50282],{},[898,50281,1677],{},[1700,50283,4543],{},[902,50285,4546],{"encoding":904},[123,50287,50288,50290],{},[38,50289,38411],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,50292,50293,2106,50295,1343,50319],{},[38,50294,31912],{},[883,50296,50298],{"className":50297},[886],[888,50299,50300],{"xmlns":890},[892,50301,50302,50316],{},[895,50303,50304,50306,50308,50310,50312,50314],{},[898,50305,1662],{},[1700,50307,1765],{},[898,50309,1762],{},[1700,50311,1703],{"stretchy":1702},[898,50313,9316],{},[1700,50315,1709],{"stretchy":1702},[902,50317,50318],{"encoding":904},"Q = E(Y)",[38,50320,38608],{},[123,50322,50323,50326,50327,50329],{},[38,50324,50325],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,50328,39054],{}," zboží",[123,50331,50332,2114,50334,50336],{},[38,50333,40060],{},[38,50335,40007],{}," — znaménka zkřížených koeficientů",[123,50338,50339,50342],{},[38,50340,50341],{},"Dvoukomoditní trh"," (2.6)",[123,50344,50345,10208,50348,1709],{},[38,50346,50347],{},"Posun poptávky",[614,50349,39112],{},[724,50351,50352],{},[38,50353,13310],{},[120,50355,50356,50389,50393,50438],{},[123,50357,50358,10208,50360,18833,50362,2106,50364,1343,50387],{},[38,50359,40454],{},[614,50361,40457],{},[38,50363,40628],{},[883,50365,50367],{"className":50366},[886],[888,50368,50369],{"xmlns":890},[892,50370,50371,50385],{},[895,50372,50373,50375,50377,50379,50381,50383],{},[898,50374,1662],{},[1700,50376,1765],{},[898,50378,8861],{},[1700,50380,1703],{"stretchy":1702},[898,50382,1677],{},[1700,50384,1709],{"stretchy":1702},[902,50386,8870],{"encoding":904},[38,50388,40706],{},[123,50390,50391],{},[38,50392,40713],{},[123,50394,50395,2106,50398,1343,50421],{},[38,50396,50397],{},"Lineární nabídka",[883,50399,50401],{"className":50400},[886],[888,50402,50403],{"xmlns":890},[892,50404,50405,50419],{},[895,50406,50407,50409,50411,50413,50415,50417],{},[898,50408,1677],{},[1700,50410,1765],{},[898,50412,2354],{},[898,50414,1662],{},[1700,50416,1897],{},[898,50418,2406],{},[902,50420,40427],{"encoding":904},[883,50422,50424],{"className":50423},[886],[888,50425,50426],{"xmlns":890},[892,50427,50428,50436],{},[895,50429,50430,50432,50434],{},[898,50431,2354],{},[1700,50433,3601],{},[1931,50435,1772],{},[902,50437,40445],{"encoding":904},[123,50439,50440,10208,50443,1709],{},[38,50441,50442],{},"Posun nabídky",[614,50444,41091],{},[724,50446,50447],{},[38,50448,50449],{},"Rovnováha a komparativní statika",[120,50451,50452,50531,50537],{},[123,50453,50454,10208,50456,18833,50458,2106,50461,1343,50478,2106,50481,1343,50498,2106,50500],{},[38,50455,41510],{},[614,50457,41629],{},[38,50459,50460],{},"rovnovážná cena",[883,50462,50464],{"className":50463},[886],[888,50465,50466],{"xmlns":890},[892,50467,50468,50476],{},[895,50469,50470],{},[1785,50471,50472,50474],{},[898,50473,1677],{},[898,50475,1762],{},[902,50477,41651],{"encoding":904},[38,50479,50480],{},"rovnovážné množství",[883,50482,50484],{"className":50483},[886],[888,50485,50486],{"xmlns":890},[892,50487,50488,50496],{},[895,50489,50490],{},[1785,50491,50492,50494],{},[898,50493,1662],{},[898,50495,1762],{},[902,50497,42588],{"encoding":904},[38,50499,41687],{},[883,50501,50503],{"className":50502},[886],[888,50504,50505],{"xmlns":890},[892,50506,50507,50529],{},[895,50508,50509,50511,50513,50519,50521,50527],{},[898,50510,1762],{},[1700,50512,1927],{"stretchy":1702},[1785,50514,50515,50517],{},[898,50516,1662],{},[898,50518,1762],{},[1700,50520,1732],{"separator":1731},[1785,50522,50523,50525],{},[898,50524,1677],{},[898,50526,1762],{},[1700,50528,1970],{"stretchy":1702},[902,50530,41552],{"encoding":904},[123,50532,50533,50536],{},[38,50534,50535],{},"Pravidla 1–4"," komparativní statiky",[123,50538,50539,10208,50542,1709],{},[38,50540,50541],{},"Teorém pavučiny",[614,50543,42534],{},[724,50545,50546],{},[38,50547,50548],{},"Zdanění",[120,50550,50551,50607,50655],{},[123,50552,50553,50555,50556,50581,50582,1709],{},[38,50554,50548],{}," — daň výrobci (",[883,50557,50559],{"className":50558},[886],[888,50560,50561],{"xmlns":890},[892,50562,50563,50579],{},[895,50564,50565,50571,50573,50575,50577],{},[2007,50566,50567,50569],{},[898,50568,8861],{},[1931,50570,1933],{},[1700,50572,1765],{},[898,50574,8861],{},[1700,50576,1897],{},[898,50578,2971],{},[902,50580,42939],{"encoding":904},") vs. daň spotřebiteli (",[883,50583,50585],{"className":50584},[886],[888,50586,50587],{"xmlns":890},[892,50588,50589,50605],{},[895,50590,50591,50597,50599,50601,50603],{},[2007,50592,50593,50595],{},[898,50594,4374],{},[1931,50596,2343],{},[1700,50598,1765],{},[898,50600,4374],{},[1700,50602,1768],{},[898,50604,2971],{},[902,50606,42970],{"encoding":904},[123,50608,50609,2106,50611,1343,50632],{},[38,50610,42843],{},[883,50612,50614],{"className":50613},[886],[888,50615,50616],{"xmlns":890},[892,50617,50618,50630],{},[895,50619,50620],{},[2007,50621,50622,50624],{},[898,50623,2971],{},[895,50625,50626,50628],{},[898,50627,42862],{},[898,50629,724],{},[902,50631,42867],{"encoding":904},[883,50633,50635],{"className":50634},[886],[888,50636,50637],{"xmlns":890},[892,50638,50639,50653],{},[895,50640,50641],{},[2007,50642,50643,50645],{},[898,50644,2971],{},[895,50646,50647,50649,50651],{},[898,50648,42885],{},[898,50650,2215],{},[898,50652,12226],{},[902,50654,42892],{"encoding":904},[123,50656,50657,2106,50660,1343,50689],{},[38,50658,50659],{},"Ekvivalence zdanění",[883,50661,50663],{"className":50662},[886],[888,50664,50665],{"xmlns":890},[892,50666,50667,50687],{},[895,50668,50669,50677,50679],{},[2030,50670,50671,50673,50675],{},[898,50672,1662],{},[1931,50674,1933],{},[898,50676,1762],{},[1700,50678,1765],{},[2030,50680,50681,50683,50685],{},[898,50682,1662],{},[1931,50684,2343],{},[898,50686,1762],{},[902,50688,43093],{"encoding":904},[883,50690,50692],{"className":50691},[886],[888,50693,50694],{"xmlns":890},[892,50695,50696,50720],{},[895,50697,50698,50706,50708,50710,50712],{},[2030,50699,50700,50702,50704],{},[898,50701,1677],{},[1931,50703,1933],{},[898,50705,1762],{},[1700,50707,1768],{},[898,50709,2971],{},[1700,50711,1765],{},[2030,50713,50714,50716,50718],{},[898,50715,1677],{},[1931,50717,2343],{},[898,50719,1762],{},[902,50721,43127],{"encoding":904},[724,50723,50724],{},[38,50725,26593],{},[120,50727,50728,50774,50805,50810,50816,50823],{},[123,50729,50730,2106,50732],{},[38,50731,43226],{},[883,50733,50735],{"className":50734},[886],[888,50736,50737],{"xmlns":890},[892,50738,50739,50771],{},[895,50740,50741,50747,50749,50751,50753,50755,50757,50759,50761,50763,50765,50767,50769],{},[1785,50742,50743,50745],{},[898,50744,1662],{},[898,50746,1762],{},[1700,50748,1765],{},[1700,50750,1703],{"stretchy":1702},[898,50752,1879],{},[1700,50754,1768],{},[898,50756,2406],{},[1700,50758,1709],{"stretchy":1702},[898,50760,1979],{"mathvariant":1791},[1700,50762,1703],{"stretchy":1702},[898,50764,2354],{},[1700,50766,1768],{},[898,50768,207],{},[1700,50770,1709],{"stretchy":1702},[902,50772,50773],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,50775,50776,2106,50779,50804],{},[38,50777,50778],{},"Parametry",[883,50780,50782],{"className":50781},[886],[888,50783,50784],{"xmlns":890},[892,50785,50786,50802],{},[895,50787,50788,50790,50792,50794,50796,50798,50800],{},[898,50789,207],{},[1700,50791,1732],{"separator":1731},[898,50793,1879],{},[1700,50795,1732],{"separator":1731},[898,50797,2354],{},[1700,50799,1732],{"separator":1731},[898,50801,2406],{},[902,50803,43470],{"encoding":904}," — exogenní proměnné",[123,50806,50807],{},[38,50808,50809],{},"Endogenní \u002F exogenní proměnná",[123,50811,50812,50815],{},[38,50813,50814],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,50817,50818,1343,50821],{},[38,50819,50820],{},"Komparativní statika",[38,50822,37145],{},[123,50824,50825,2106,50827,50843],{},[38,50826,3150],{},[883,50828,50830],{"className":50829},[886],[888,50831,50832],{"xmlns":890},[892,50833,50834,50840],{},[895,50835,50836,50838],{},[898,50837,2406],{},[898,50839,1662],{},[902,50841,50842],{"encoding":904},"dQ"," (2.11)",[724,50845,50846],{},[38,50847,50848],{},"Přebytky a ostatní",[120,50850,50851,50889],{},[123,50852,50853,2106,50855,50870,50871,2106,50873,50888],{},[38,50854,45119],{},[883,50856,50858],{"className":50857},[886],[888,50859,50860],{"xmlns":890},[892,50861,50862,50868],{},[895,50863,50864,50866],{},[898,50865,2974],{},[898,50867,8861],{},[902,50869,45135],{"encoding":904}," (2.14), ",[38,50872,45138],{},[883,50874,50876],{"className":50875},[886],[888,50877,50878],{"xmlns":890},[892,50879,50880,50886],{},[895,50881,50882,50884],{},[898,50883,1677],{},[898,50885,8861],{},[902,50887,45154],{"encoding":904}," (2.15)",[123,50890,50891,1343,50894,50897],{},[38,50892,50893],{},"Homo economicus",[38,50895,50896],{},"Marshallova formulace"," (1890)",[37155,50899],{},[115,50901,3985],{"id":3984},[120,50903,50904,50939,50948],{},[123,50905,50906,2106,50909,50912,50913,1343,50916,50919,50920,50923,50924,50927,50928,50931,50932,50935,50936],{},[38,50907,50908],{},"Související témata:",[207,50910,811],{"className":50911,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,50914,820],{"className":50915,"dataFsResolvedFilePath":818,"href":819},[210],[207,50917,2559],{"className":50918,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,50921,775],{"className":50922,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,50925,784],{"className":50926,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,50929,793],{"className":50930,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,50933,1649],{"className":50934,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,50937,4016],{"className":50938,"dataFsResolvedFilePath":827,"href":828},[210],[123,50940,50941,2106,50944],{},[38,50942,50943],{},"Shrnutí přednášek:",[207,50945,50947],{"className":50946,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,50949,50950,2106,50952],{},[38,50951,16389],{},[207,50953,16393],{"className":50954,"dataFsResolvedFilePath":2140,"href":2141},[210],{"title":641,"searchDepth":642,"depth":642,"links":50956},[50957,50958,50966,50972,50979,50980,50987,50988,50989,50996,50997,50998],{"id":36979,"depth":642,"text":36980},{"id":36960,"depth":642,"text":13346,"children":50959},[50960,50961,50962,50963,50965],{"id":37248,"depth":649,"text":37249},{"id":37530,"depth":649,"text":37531},{"id":38540,"depth":649,"text":38541},{"id":39108,"depth":649,"text":50964},"Posun poptávky (shift of demand)",{"id":39612,"depth":649,"text":39613},{"id":36964,"depth":642,"text":13310,"children":50967},[50968,50969,50970],{"id":40449,"depth":649,"text":37249},{"id":40635,"depth":649,"text":40636},{"id":41087,"depth":649,"text":50971},"Posun nabídky (shift of supply)",{"id":41509,"depth":642,"text":41510,"children":50973},[50974,50975,50976,50977,50978],{"id":41621,"depth":649,"text":41622},{"id":41834,"depth":649,"text":41835},{"id":42152,"depth":649,"text":42153},{"id":42506,"depth":649,"text":42507},{"id":42537,"depth":649,"text":42538},{"id":42806,"depth":642,"text":811},{"id":43207,"depth":642,"text":43208,"children":50981},[50982,50983,50984,50985],{"id":43225,"depth":649,"text":43226},{"id":43606,"depth":649,"text":43607},{"id":43990,"depth":649,"text":43991},{"id":44444,"depth":649,"text":50986},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":11968,"depth":642,"text":820},{"id":45369,"depth":642,"text":45370},{"id":45600,"depth":642,"text":45601,"children":50990},[50991,50992,50993,50994,50995],{"id":45604,"depth":649,"text":45605},{"id":46444,"depth":649,"text":46445},{"id":46820,"depth":649,"text":41510},{"id":48115,"depth":649,"text":43208},{"id":49871,"depth":649,"text":820},{"id":50066,"depth":642,"text":50067},{"id":15904,"depth":642,"text":15905},{"id":3984,"depth":642,"text":3985},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,51005,51006,51007,18068,51008,51009],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":51012,"title":820,"body":51013,"course":1128,"courses":659,"created":9743,"description":641,"extension":661,"meta":55291,"navigation":664,"path":55292,"seo":55293,"sources":55294,"stem":55295,"tags":55296,"type":4049,"updated":677,"__hash__":55301},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":51014,"toc":55269},[51015,51017,51085,51135,51137,51140,51398,51474,51479,51481,51500,51504,51580,51665,51667,51981,52074,52076,52095,52099,52173,52258,52261,52437,52442,52444,52863,52865,52869,52873,53109,53153,53253,53319,53322,53355,53531,53593,53723,53801,53912,53946,54144,54163,54182,54247,54251,54254,54299,54302,54420,54466,54468,54472,54820,54822,54824,55102,55104,55108,55143,55150,55223,55225,55227],[12,51016,820],{"id":11968},[4060,51018,51019],{},[724,51020,51021,4067,51023,10208,51025,51040,51041,10208,51043,51058,51059,51081,51082,2196],{},[883,51022,4066],{},[38,51024,45119],{},[883,51026,51028],{"className":51027},[886],[888,51029,51030],{"xmlns":890},[892,51031,51032,51038],{},[895,51033,51034,51036],{},[898,51035,2974],{},[898,51037,8861],{},[902,51039,45135],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,51042,45266],{},[883,51044,51046],{"className":51045},[886],[888,51047,51048],{"xmlns":890},[892,51049,51050,51056],{},[895,51051,51052,51054],{},[898,51053,1677],{},[898,51055,8861],{},[902,51057,45154],{"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 ",[883,51060,51062],{"className":51061},[886],[888,51063,51064],{"xmlns":890},[892,51065,51066,51078],{},[895,51067,51068,51070,51072,51074,51076],{},[898,51069,2974],{},[898,51071,8861],{},[1700,51073,1897],{},[898,51075,1677],{},[898,51077,8861],{},[902,51079,51080],{"encoding":904},"CS + PS"," měří ",[38,51083,51084],{},"celkový blahobyt trhu",[724,51086,51087,10208,51089,1343,51091,12313,51106,10208,51108,1343,51110,51125,51126,51130,51131,2196],{},[38,51088,45119],{},[614,51090,45173],{},[883,51092,51094],{"className":51093},[886],[888,51095,51096],{"xmlns":890},[892,51097,51098,51104],{},[895,51099,51100,51102],{},[898,51101,2974],{},[898,51103,8861],{},[902,51105,45135],{"encoding":904},[38,51107,45138],{},[614,51109,45269],{},[883,51111,51113],{"className":51112},[886],[888,51114,51115],{"xmlns":890},[892,51116,51117,51123],{},[895,51118,51119,51121],{},[898,51120,1677],{},[898,51122,8861],{},[902,51124,45154],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,51127,51129],{"className":51128,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,51132,51134],{"className":51133,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[37155,51136],{},[115,51138,1241],{"id":51139},"úvod",[724,51141,51142,51143,51166,51167,51190,51191,51208,51209,4102,51241,51273,51274,51300,51301,51304,51305,51308,51309,14196,51343,21779,51364,2196],{},"Je dána funkce poptávky ",[883,51144,51146],{"className":51145},[886],[888,51147,51148],{"xmlns":890},[892,51149,51150,51164],{},[895,51151,51152,51154,51156,51158,51160,51162],{},[898,51153,1677],{},[1700,51155,1765],{},[898,51157,4374],{},[1700,51159,1703],{"stretchy":1702},[898,51161,1662],{},[1700,51163,1709],{"stretchy":1702},[902,51165,4829],{"encoding":904},", resp. funkce nabídky ",[883,51168,51170],{"className":51169},[886],[888,51171,51172],{"xmlns":890},[892,51173,51174,51188],{},[895,51175,51176,51178,51180,51182,51184,51186],{},[898,51177,1677],{},[1700,51179,1765],{},[898,51181,8861],{},[1700,51183,1703],{"stretchy":1702},[898,51185,1662],{},[1700,51187,1709],{"stretchy":1702},[902,51189,41256],{"encoding":904},". Pro pevně zadané množství ",[883,51192,51194],{"className":51193},[886],[888,51195,51196],{"xmlns":890},[892,51197,51198,51206],{},[895,51199,51200],{},[2007,51201,51202,51204],{},[898,51203,1662],{},[1931,51205,1772],{},[902,51207,38493],{"encoding":904}," je odpovídající cena ",[883,51210,51212],{"className":51211},[886],[888,51213,51214],{"xmlns":890},[892,51215,51216,51238],{},[895,51217,51218,51224,51226,51228,51230,51236],{},[2007,51219,51220,51222],{},[898,51221,1677],{},[1931,51223,1772],{},[1700,51225,1765],{},[898,51227,4374],{},[1700,51229,1703],{"stretchy":1702},[2007,51231,51232,51234],{},[898,51233,1662],{},[1931,51235,1772],{},[1700,51237,1709],{"stretchy":1702},[902,51239,51240],{"encoding":904},"P_0 = D(Q_0)",[883,51242,51244],{"className":51243},[886],[888,51245,51246],{"xmlns":890},[892,51247,51248,51270],{},[895,51249,51250,51256,51258,51260,51262,51268],{},[2007,51251,51252,51254],{},[898,51253,1677],{},[1931,51255,1772],{},[1700,51257,1765],{},[898,51259,8861],{},[1700,51261,1703],{"stretchy":1702},[2007,51263,51264,51266],{},[898,51265,1662],{},[1931,51267,1772],{},[1700,51269,1709],{"stretchy":1702},[902,51271,51272],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,51275,51277],{"className":51276},[886],[888,51278,51279],{"xmlns":890},[892,51280,51281,51297],{},[895,51282,51283,51289,51291],{},[2007,51284,51285,51287],{},[898,51286,1677],{},[1931,51288,1772],{},[1781,51290,1783],{},[2007,51292,51293,51295],{},[898,51294,1662],{},[1931,51296,1772],{},[902,51298,51299],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,51302,51303],{},"výdaje spotřebitele",", nebo ",[38,51306,51307],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,51310,51312],{"className":51311},[886],[888,51313,51314],{"xmlns":890},[892,51315,51316,51340],{},[895,51317,51318,51320,51322,51328,51330,51332,51334],{},[1931,51319,1772],{},[1781,51321,1783],{},[2007,51323,51324,51326],{},[898,51325,1662],{},[1931,51327,1772],{},[1781,51329,1783],{},[898,51331,1862],{},[1781,51333,1783],{},[2007,51335,51336,51338],{},[898,51337,1677],{},[1931,51339,1772],{},[902,51341,51342],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,51344,51346],{"className":51345},[886],[888,51347,51348],{"xmlns":890},[892,51349,51350,51362],{},[895,51351,51352,51354,51356,51358,51360],{},[1700,51353,1703],{"stretchy":1702},[898,51355,1662],{},[1700,51357,1732],{"separator":1731},[898,51359,1677],{},[1700,51361,1709],{"stretchy":1702},[902,51363,37876],{"encoding":904},[883,51365,51367],{"className":51366},[886],[888,51368,51369],{"xmlns":890},[892,51370,51371,51395],{},[895,51372,51373,51375,51377,51379,51385,51387,51393],{},[898,51374,1862],{},[1700,51376,1765],{},[1700,51378,1927],{"stretchy":1702},[2007,51380,51381,51383],{},[898,51382,1662],{},[1931,51384,1772],{},[1700,51386,1732],{"separator":1731},[2007,51388,51389,51391],{},[898,51390,1677],{},[1931,51392,1772],{},[1700,51394,1970],{"stretchy":1702},[902,51396,51397],{"encoding":904},"A = [Q_0, P_0]",[4060,51399,51400,51405,51463],{},[724,51401,51402,51404],{},[883,51403,4346],{}," Intuice",[120,51406,51407,51435],{},[123,51408,51409,51410,51413,51414,51416,51417,51434],{},"Za jednotky zboží nakoupené ",[38,51411,51412],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,51415,25455],{}," než ",[883,51418,51420],{"className":51419},[886],[888,51421,51422],{"xmlns":890},[892,51423,51424,51432],{},[895,51425,51426],{},[2007,51427,51428,51430],{},[898,51429,1677],{},[1931,51431,1772],{},[902,51433,39133],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,51436,51437,51438,51440,51441,51444,51445,51462],{},"Za jednotky zboží prodané ",[38,51439,51412],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,51442,51443],{},"nižší"," cenu než ",[883,51446,51448],{"className":51447},[886],[888,51449,51450],{"xmlns":890},[892,51451,51452,51460],{},[895,51453,51454],{},[2007,51455,51456,51458],{},[898,51457,1677],{},[1931,51459,1772],{},[902,51461,39133],{"encoding":904}," — rozdíl je jeho přebytek.",[724,51464,51465,51466,51469,51470,51473],{},"Přebytek je tedy rozdíl mezi ",[614,51467,51468],{},"ochotou"," (platit \u002F prodávat) a ",[614,51471,51472],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,51475,51476],{},[2756,51477],{"alt":45164,"className":51478,"src":45166},[210,2760],[37155,51480],{},[115,51482,51484,51485,1709],{"id":51483},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,51486,51488],{"className":51487},[886],[888,51489,51490],{"xmlns":890},[892,51491,51492,51498],{},[895,51493,51494,51496],{},[898,51495,2974],{},[898,51497,8861],{},[902,51499,45135],{"encoding":904},[198,51501,51503],{"id":51502},"definice-vzorec-214","Definice (vzorec 2.14)",[724,51505,51506,51507,51530,51531,51548,51549,2901],{},"Pro poptávku ",[883,51508,51510],{"className":51509},[886],[888,51511,51512],{"xmlns":890},[892,51513,51514,51528],{},[895,51515,51516,51518,51520,51522,51524,51526],{},[898,51517,1677],{},[1700,51519,1765],{},[898,51521,4374],{},[1700,51523,1703],{"stretchy":1702},[898,51525,1662],{},[1700,51527,1709],{"stretchy":1702},[902,51529,4829],{"encoding":904}," a pevně zadané ",[883,51532,51534],{"className":51533},[886],[888,51535,51536],{"xmlns":890},[892,51537,51538,51546],{},[895,51539,51540],{},[2007,51541,51542,51544],{},[898,51543,1662],{},[1931,51545,1772],{},[902,51547,38493],{"encoding":904}," s cenou ",[883,51550,51552],{"className":51551},[886],[888,51553,51554],{"xmlns":890},[892,51555,51556,51578],{},[895,51557,51558,51564,51566,51568,51570,51576],{},[2007,51559,51560,51562],{},[898,51561,1677],{},[1931,51563,1772],{},[1700,51565,1765],{},[898,51567,4374],{},[1700,51569,1703],{"stretchy":1702},[2007,51571,51572,51574],{},[898,51573,1662],{},[1931,51575,1772],{},[1700,51577,1709],{"stretchy":1702},[902,51579,51240],{"encoding":904},[883,51581,51583],{"className":51582},[886],[888,51584,51585],{"xmlns":890,"display":28251},[892,51586,51587,51663],{},[20939,51588,51589],{"width":28256},[20944,51590,51591,51593,51657,51659],{},[20947,51592],{"width":28261},[20947,51594,51595],{},[895,51596,51597,51599,51601,51603,51609,51611,51613,51625,51627,51629,51631,51633,51635,51637,51639,51641,51647,51649,51655],{},[898,51598,2974],{},[898,51600,8861],{},[1700,51602,1703],{"stretchy":1702},[2007,51604,51605,51607],{},[898,51606,1662],{},[1931,51608,1772],{},[1700,51610,1709],{"stretchy":1702},[1700,51612,1765],{},[2030,51614,51615,51617,51619],{},[1700,51616,11353],{},[1931,51618,1772],{},[2007,51620,51621,51623],{},[898,51622,1662],{},[1931,51624,1772],{},[898,51626,4374],{},[1700,51628,1703],{"stretchy":1702},[898,51630,1662],{},[1700,51632,1709],{"stretchy":1702},[1781,51634,1783],{},[898,51636,2406],{},[898,51638,1662],{},[1700,51640,1768],{},[2007,51642,51643,51645],{},[898,51644,1677],{},[1931,51646,1772],{},[1781,51648,1783],{},[2007,51650,51651,51653],{},[898,51652,1662],{},[1931,51654,1772],{},[898,51656,2196],{"mathvariant":1791},[20947,51658],{"width":28261},[20947,51660,51661],{},[1781,51662,45258],{},[902,51664,45261],{"encoding":904},[198,51666,2643],{"id":2642},[120,51668,51669,51761,51823],{},[123,51670,51671,51711,51712,51738,51739,51742,51743,51760],{},[883,51672,51674],{"className":51673},[886],[888,51675,51676],{"xmlns":890},[892,51677,51678,51708],{},[895,51679,51680],{},[1770,51681,51682,51694,51696,51698,51700,51702,51704,51706],{"scriptlevel":1772,"displaystyle":1731},[2030,51683,51684,51686,51688],{},[1700,51685,11353],{},[1931,51687,1772],{},[2007,51689,51690,51692],{},[898,51691,1662],{},[1931,51693,1772],{},[898,51695,4374],{},[1700,51697,1703],{"stretchy":1702},[898,51699,1662],{},[1700,51701,1709],{"stretchy":1702},[1781,51703,1783],{},[898,51705,2406],{},[898,51707,1662],{},[902,51709,51710],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,51713,51715],{"className":51714},[886],[888,51716,51717],{"xmlns":890},[892,51718,51719,51735],{},[895,51720,51721,51723,51725,51727,51733],{},[1700,51722,1927],{"stretchy":1702},[1931,51724,1772],{},[1700,51726,1732],{"separator":1731},[2007,51728,51729,51731],{},[898,51730,1662],{},[1931,51732,1772],{},[1700,51734,1970],{"stretchy":1702},[902,51736,51737],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,51740,51741],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,51744,51746],{"className":51745},[886],[888,51747,51748],{"xmlns":890},[892,51749,51750,51758],{},[895,51751,51752],{},[2007,51753,51754,51756],{},[898,51755,1662],{},[1931,51757,1772],{},[902,51759,38493],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,51762,51763,51789,51790,4110],{},[883,51764,51766],{"className":51765},[886],[888,51767,51768],{"xmlns":890},[892,51769,51770,51786],{},[895,51771,51772,51778,51780],{},[2007,51773,51774,51776],{},[898,51775,1677],{},[1931,51777,1772],{},[1781,51779,1783],{},[2007,51781,51782,51784],{},[898,51783,1662],{},[1931,51785,1772],{},[902,51787,51788],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,51791,51793],{"className":51792},[886],[888,51794,51795],{"xmlns":890},[892,51796,51797,51821],{},[895,51798,51799,51801,51803,51809,51811,51813,51815],{},[1931,51800,1772],{},[1781,51802,1783],{},[2007,51804,51805,51807],{},[898,51806,1662],{},[1931,51808,1772],{},[1781,51810,1783],{},[898,51812,1862],{},[1781,51814,1783],{},[2007,51816,51817,51819],{},[898,51818,1677],{},[1931,51820,1772],{},[902,51822,51342],{"encoding":904},[123,51824,51825,51840,51841,51863,51864,51889,51890,21779,51916,2114,51948,2196],{},[883,51826,51828],{"className":51827},[886],[888,51829,51830],{"xmlns":890},[892,51831,51832,51838],{},[895,51833,51834,51836],{},[898,51835,2974],{},[898,51837,8861],{},[902,51839,45135],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,51842,51844],{"className":51843},[886],[888,51845,51846],{"xmlns":890},[892,51847,51848,51860],{},[895,51849,51850,51852,51854],{},[898,51851,1677],{},[1700,51853,1765],{},[2007,51855,51856,51858],{},[898,51857,1677],{},[1931,51859,1772],{},[902,51861,51862],{"encoding":904},"P = P_0"," v pásu ",[883,51865,51867],{"className":51866},[886],[888,51868,51869],{"xmlns":890},[892,51870,51871,51887],{},[895,51872,51873,51875,51877,51879,51885],{},[1700,51874,1927],{"stretchy":1702},[1931,51876,1772],{},[1700,51878,1732],{"separator":1731},[2007,51880,51881,51883],{},[898,51882,1662],{},[1931,51884,1772],{},[1700,51886,1970],{"stretchy":1702},[902,51888,51737],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,51891,51893],{"className":51892},[886],[888,51894,51895],{"xmlns":890},[892,51896,51897,51913],{},[895,51898,51899,51905,51907,51909,51911],{},[2007,51900,51901,51903],{},[898,51902,1677],{},[1931,51904,1772],{},[1781,51906,1783],{},[898,51908,23438],{},[1781,51910,1783],{},[898,51912,1862],{},[902,51914,51915],{"encoding":904},"P_0\\,B\\,A",[883,51917,51919],{"className":51918},[886],[888,51920,51921],{"xmlns":890},[892,51922,51923,51945],{},[895,51924,51925,51927,51929,51931,51933,51935,51937,51939,51941,51943],{},[898,51926,23438],{},[1700,51928,1765],{},[1700,51930,1927],{"stretchy":1702},[1931,51932,1772],{},[1700,51934,1732],{"separator":1731},[898,51936,4374],{},[1700,51938,1703],{"stretchy":1702},[1931,51940,1772],{},[1700,51942,1709],{"stretchy":1702},[1700,51944,1970],{"stretchy":1702},[902,51946,51947],{"encoding":904},"B = [0, D(0)]",[883,51949,51951],{"className":51950},[886],[888,51952,51953],{"xmlns":890},[892,51954,51955,51979],{},[895,51956,51957,51959,51961,51963,51969,51971,51977],{},[898,51958,1862],{},[1700,51960,1765],{},[1700,51962,1927],{"stretchy":1702},[2007,51964,51965,51967],{},[898,51966,1662],{},[1931,51968,1772],{},[1700,51970,1732],{"separator":1731},[2007,51972,51973,51975],{},[898,51974,1677],{},[1931,51976,1772],{},[1700,51978,1970],{"stretchy":1702},[902,51980,51397],{"encoding":904},[724,51982,51983],{},[614,51984,51985,51986,51999,52000,52033,52034,29327,52059,2196],{},"Obrázek 2.24: Křivka poptávky ",[883,51987,51989],{"className":51988},[886],[888,51990,51991],{"xmlns":890},[892,51992,51993,51997],{},[895,51994,51995],{},[898,51996,4374],{},[902,51998,4374],{"encoding":904},", bod ",[883,52001,52003],{"className":52002},[886],[888,52004,52005],{"xmlns":890},[892,52006,52007,52031],{},[895,52008,52009,52011,52013,52015,52021,52023,52029],{},[898,52010,1862],{},[1700,52012,1765],{},[1700,52014,1927],{"stretchy":1702},[2007,52016,52017,52019],{},[898,52018,1662],{},[1931,52020,1772],{},[1700,52022,1732],{"separator":1731},[2007,52024,52025,52027],{},[898,52026,1677],{},[1931,52028,1772],{},[1700,52030,1970],{"stretchy":1702},[902,52032,51397],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,52035,52037],{"className":52036},[886],[888,52038,52039],{"xmlns":890},[892,52040,52041,52057],{},[895,52042,52043,52049,52051,52053,52055],{},[2007,52044,52045,52047],{},[898,52046,1677],{},[1931,52048,1772],{},[1781,52050,1783],{},[898,52052,23438],{},[1781,52054,1783],{},[898,52056,1862],{},[902,52058,51915],{"encoding":904},[883,52060,52062],{"className":52061},[886],[888,52063,52064],{"xmlns":890},[892,52065,52066,52072],{},[895,52067,52068,52070],{},[898,52069,2974],{},[898,52071,8861],{},[902,52073,45135],{"encoding":904},[37155,52075],{},[115,52077,52079,52080,1709],{"id":52078},"přebytek-výrobce-psps","Přebytek výrobce (",[883,52081,52083],{"className":52082},[886],[888,52084,52085],{"xmlns":890},[892,52086,52087,52093],{},[895,52088,52089,52091],{},[898,52090,1677],{},[898,52092,8861],{},[902,52094,45154],{"encoding":904},[198,52096,52098],{"id":52097},"definice-vzorec-215","Definice (vzorec 2.15)",[724,52100,52101,52102,51530,52125,51548,52142,2901],{},"Analogicky — pro nabídku ",[883,52103,52105],{"className":52104},[886],[888,52106,52107],{"xmlns":890},[892,52108,52109,52123],{},[895,52110,52111,52113,52115,52117,52119,52121],{},[898,52112,1677],{},[1700,52114,1765],{},[898,52116,8861],{},[1700,52118,1703],{"stretchy":1702},[898,52120,1662],{},[1700,52122,1709],{"stretchy":1702},[902,52124,41256],{"encoding":904},[883,52126,52128],{"className":52127},[886],[888,52129,52130],{"xmlns":890},[892,52131,52132,52140],{},[895,52133,52134],{},[2007,52135,52136,52138],{},[898,52137,1662],{},[1931,52139,1772],{},[902,52141,38493],{"encoding":904},[883,52143,52145],{"className":52144},[886],[888,52146,52147],{"xmlns":890},[892,52148,52149,52171],{},[895,52150,52151,52157,52159,52161,52163,52169],{},[2007,52152,52153,52155],{},[898,52154,1677],{},[1931,52156,1772],{},[1700,52158,1765],{},[898,52160,8861],{},[1700,52162,1703],{"stretchy":1702},[2007,52164,52165,52167],{},[898,52166,1662],{},[1931,52168,1772],{},[1700,52170,1709],{"stretchy":1702},[902,52172,51272],{"encoding":904},[883,52174,52176],{"className":52175},[886],[888,52177,52178],{"xmlns":890,"display":28251},[892,52179,52180,52256],{},[20939,52181,52182],{"width":28256},[20944,52183,52184,52186,52250,52252],{},[20947,52185],{"width":28261},[20947,52187,52188],{},[895,52189,52190,52192,52194,52196,52202,52204,52206,52212,52214,52220,52222,52234,52236,52238,52240,52242,52244,52246,52248],{},[898,52191,1677],{},[898,52193,8861],{},[1700,52195,1703],{"stretchy":1702},[2007,52197,52198,52200],{},[898,52199,1662],{},[1931,52201,1772],{},[1700,52203,1709],{"stretchy":1702},[1700,52205,1765],{},[2007,52207,52208,52210],{},[898,52209,1677],{},[1931,52211,1772],{},[1781,52213,1783],{},[2007,52215,52216,52218],{},[898,52217,1662],{},[1931,52219,1772],{},[1700,52221,1768],{},[2030,52223,52224,52226,52228],{},[1700,52225,11353],{},[1931,52227,1772],{},[2007,52229,52230,52232],{},[898,52231,1662],{},[1931,52233,1772],{},[898,52235,8861],{},[1700,52237,1703],{"stretchy":1702},[898,52239,1662],{},[1700,52241,1709],{"stretchy":1702},[1781,52243,1783],{},[898,52245,2406],{},[898,52247,1662],{},[898,52249,2196],{"mathvariant":1791},[20947,52251],{"width":28261},[20947,52253,52254],{},[1781,52255,45354],{},[902,52257,45357],{"encoding":904},[198,52259,2643],{"id":52260},"geometrická-interpretace-1",[120,52262,52263,52311,52372],{},[123,52264,52265,7203,52290,52293,52294,2196],{},[883,52266,52268],{"className":52267},[886],[888,52269,52270],{"xmlns":890},[892,52271,52272,52288],{},[895,52273,52274,52280,52282],{},[2007,52275,52276,52278],{},[898,52277,1677],{},[1931,52279,1772],{},[1781,52281,1783],{},[2007,52283,52284,52286],{},[898,52285,1662],{},[1931,52287,1772],{},[902,52289,51788],{"encoding":904},[38,52291,52292],{},"tržba"," výrobce za prodané množství ",[883,52295,52297],{"className":52296},[886],[888,52298,52299],{"xmlns":890},[892,52300,52301,52309],{},[895,52302,52303],{},[2007,52304,52305,52307],{},[898,52306,1662],{},[1931,52308,1772],{},[902,52310,38493],{"encoding":904},[123,52312,52313,52353,52354,52371],{},[883,52314,52316],{"className":52315},[886],[888,52317,52318],{"xmlns":890},[892,52319,52320,52350],{},[895,52321,52322],{},[1770,52323,52324,52336,52338,52340,52342,52344,52346,52348],{"scriptlevel":1772,"displaystyle":1731},[2030,52325,52326,52328,52330],{},[1700,52327,11353],{},[1931,52329,1772],{},[2007,52331,52332,52334],{},[898,52333,1662],{},[1931,52335,1772],{},[898,52337,8861],{},[1700,52339,1703],{"stretchy":1702},[898,52341,1662],{},[1700,52343,1709],{"stretchy":1702},[1781,52345,1783],{},[898,52347,2406],{},[898,52349,1662],{},[902,52351,52352],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,52355,52357],{"className":52356},[886],[888,52358,52359],{"xmlns":890},[892,52360,52361,52369],{},[895,52362,52363],{},[2007,52364,52365,52367],{},[898,52366,1662],{},[1931,52368,1772],{},[902,52370,38493],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,52373,52374,52389,52390,52411,52412,2196],{},[883,52375,52377],{"className":52376},[886],[888,52378,52379],{"xmlns":890},[892,52380,52381,52387],{},[895,52382,52383,52385],{},[898,52384,1677],{},[898,52386,8861],{},[902,52388,45154],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,52391,52393],{"className":52392},[886],[888,52394,52395],{"xmlns":890},[892,52396,52397,52409],{},[895,52398,52399,52401,52403],{},[898,52400,1677],{},[1700,52402,1765],{},[2007,52404,52405,52407],{},[898,52406,1677],{},[1931,52408,1772],{},[902,52410,51862],{"encoding":904}," a křivkou nabídky v pásu ",[883,52413,52415],{"className":52414},[886],[888,52416,52417],{"xmlns":890},[892,52418,52419,52435],{},[895,52420,52421,52423,52425,52427,52433],{},[1700,52422,1927],{"stretchy":1702},[1931,52424,1772],{},[1700,52426,1732],{"separator":1731},[2007,52428,52429,52431],{},[898,52430,1662],{},[1931,52432,1772],{},[1700,52434,1970],{"stretchy":1702},[902,52436,51737],{"encoding":904},[724,52438,52439],{},[614,52440,52441],{},"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.",[37155,52443],{},[4060,52445,52446,52451],{},[724,52447,52448,52450],{},[883,52449,4761],{}," Postup výpočtu CS a PS",[152,52452,52453,52583,52693,52722,52856],{},[123,52454,52455,52456,52473,52474,1713,52505,52536,52537,2196],{},"Zjisti (nebo si zvol) množství ",[883,52457,52459],{"className":52458},[886],[888,52460,52461],{"xmlns":890},[892,52462,52463,52471],{},[895,52464,52465],{},[2007,52466,52467,52469],{},[898,52468,1662],{},[1931,52470,1772],{},[902,52472,38493],{"encoding":904}," a odpovídající cenu ",[883,52475,52477],{"className":52476},[886],[888,52478,52479],{"xmlns":890},[892,52480,52481,52503],{},[895,52482,52483,52489,52491,52493,52495,52501],{},[2007,52484,52485,52487],{},[898,52486,1677],{},[1931,52488,1772],{},[1700,52490,1765],{},[898,52492,4374],{},[1700,52494,1703],{"stretchy":1702},[2007,52496,52497,52499],{},[898,52498,1662],{},[1931,52500,1772],{},[1700,52502,1709],{"stretchy":1702},[902,52504,51240],{"encoding":904},[883,52506,52508],{"className":52507},[886],[888,52509,52510],{"xmlns":890},[892,52511,52512,52534],{},[895,52513,52514,52520,52522,52524,52526,52532],{},[2007,52515,52516,52518],{},[898,52517,1677],{},[1931,52519,1772],{},[1700,52521,1765],{},[898,52523,8861],{},[1700,52525,1703],{"stretchy":1702},[2007,52527,52528,52530],{},[898,52529,1662],{},[1931,52531,1772],{},[1700,52533,1709],{"stretchy":1702},[902,52535,51272],{"encoding":904},". V rovnováze platí ",[883,52538,52540],{"className":52539},[886],[888,52541,52542],{"xmlns":890},[892,52543,52544,52580],{},[895,52545,52546,52548,52550,52556,52558,52560,52562,52564,52570,52572,52574],{},[898,52547,4374],{},[1700,52549,1703],{"stretchy":1702},[1785,52551,52552,52554],{},[898,52553,1662],{},[898,52555,1762],{},[1700,52557,1709],{"stretchy":1702},[1700,52559,1765],{},[898,52561,8861],{},[1700,52563,1703],{"stretchy":1702},[1785,52565,52566,52568],{},[898,52567,1662],{},[898,52569,1762],{},[1700,52571,1709],{"stretchy":1702},[1700,52573,1765],{},[1785,52575,52576,52578],{},[898,52577,1677],{},[898,52579,1762],{},[902,52581,52582],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,52584,52585,52586,20311,52624,52639,52640,20311,52678,4110],{},"Spočti určitý integrál ",[883,52587,52589],{"className":52588},[886],[888,52590,52591],{"xmlns":890},[892,52592,52593,52621],{},[895,52594,52595,52607,52609,52611,52613,52615,52617,52619],{},[2030,52596,52597,52599,52601],{},[1700,52598,11353],{},[1931,52600,1772],{},[2007,52602,52603,52605],{},[898,52604,1662],{},[1931,52606,1772],{},[898,52608,4374],{},[1700,52610,1703],{"stretchy":1702},[898,52612,1662],{},[1700,52614,1709],{"stretchy":1702},[1781,52616,1783],{},[898,52618,2406],{},[898,52620,1662],{},[902,52622,52623],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,52625,52627],{"className":52626},[886],[888,52628,52629],{"xmlns":890},[892,52630,52631,52637],{},[895,52632,52633,52635],{},[898,52634,2974],{},[898,52636,8861],{},[902,52638,45135],{"encoding":904},") nebo ",[883,52641,52643],{"className":52642},[886],[888,52644,52645],{"xmlns":890},[892,52646,52647,52675],{},[895,52648,52649,52661,52663,52665,52667,52669,52671,52673],{},[2030,52650,52651,52653,52655],{},[1700,52652,11353],{},[1931,52654,1772],{},[2007,52656,52657,52659],{},[898,52658,1662],{},[1931,52660,1772],{},[898,52662,8861],{},[1700,52664,1703],{"stretchy":1702},[898,52666,1662],{},[1700,52668,1709],{"stretchy":1702},[1781,52670,1783],{},[898,52672,2406],{},[898,52674,1662],{},[902,52676,52677],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,52679,52681],{"className":52680},[886],[888,52682,52683],{"xmlns":890},[892,52684,52685,52691],{},[895,52686,52687,52689],{},[898,52688,1677],{},[898,52690,8861],{},[902,52692,45154],{"encoding":904},[123,52694,52695,52696,2196],{},"Sestav obdélník ",[883,52697,52699],{"className":52698},[886],[888,52700,52701],{"xmlns":890},[892,52702,52703,52719],{},[895,52704,52705,52711,52713],{},[2007,52706,52707,52709],{},[898,52708,1677],{},[1931,52710,1772],{},[1700,52712,2065],{},[2007,52714,52715,52717],{},[898,52716,1662],{},[1931,52718,1772],{},[902,52720,52721],{"encoding":904},"P_0 \\cdot Q_0",[123,52723,52724,52725],{},"Dosaď:\n",[120,52726,52727,52792],{},[123,52728,52729,52787,52788,52791],{},[883,52730,52732],{"className":52731},[886],[888,52733,52734],{"xmlns":890},[892,52735,52736,52784],{},[895,52737,52738,52740,52742,52744,52756,52758,52760,52762,52764,52766,52768,52770,52772,52778],{},[898,52739,2974],{},[898,52741,8861],{},[1700,52743,1765],{},[2030,52745,52746,52748,52750],{},[1700,52747,11353],{},[1931,52749,1772],{},[2007,52751,52752,52754],{},[898,52753,1662],{},[1931,52755,1772],{},[898,52757,4374],{},[1700,52759,1703],{"stretchy":1702},[898,52761,1662],{},[1700,52763,1709],{"stretchy":1702},[1781,52765,1783],{},[898,52767,2406],{},[898,52769,1662],{},[1700,52771,1768],{},[2007,52773,52774,52776],{},[898,52775,1677],{},[1931,52777,1772],{},[2007,52779,52780,52782],{},[898,52781,1662],{},[1931,52783,1772],{},[902,52785,52786],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,52789,52790],{},"mínus"," obdélník)",[123,52793,52794,52852,52853,52855],{},[883,52795,52797],{"className":52796},[886],[888,52798,52799],{"xmlns":890},[892,52800,52801,52849],{},[895,52802,52803,52805,52807,52809,52815,52821,52823,52835,52837,52839,52841,52843,52845,52847],{},[898,52804,1677],{},[898,52806,8861],{},[1700,52808,1765],{},[2007,52810,52811,52813],{},[898,52812,1677],{},[1931,52814,1772],{},[2007,52816,52817,52819],{},[898,52818,1662],{},[1931,52820,1772],{},[1700,52822,1768],{},[2030,52824,52825,52827,52829],{},[1700,52826,11353],{},[1931,52828,1772],{},[2007,52830,52831,52833],{},[898,52832,1662],{},[1931,52834,1772],{},[898,52836,8861],{},[1700,52838,1703],{"stretchy":1702},[898,52840,1662],{},[1700,52842,1709],{"stretchy":1702},[1781,52844,1783],{},[898,52846,2406],{},[898,52848,1662],{},[902,52850,52851],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,52854,52790],{}," integrál)",[123,52857,52858,52859,52862],{},"Kontrola znaménka: obě hodnoty musí být ",[38,52860,52861],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[37155,52864],{},[115,52866,52868],{"id":52867},"příklady","Příklady",[198,52870,52872],{"id":52871},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[4060,52874,52875],{},[724,52876,52877,52880,52881,47906,52904,52927,52928,1343,52948,1343,52965,1343,52982,52999,53000,53076,53077,53094,53095,53108],{},[883,52878,52879],{},"!example"," Zadání\nJsou dány poptávka ",[883,52882,52884],{"className":52883},[886],[888,52885,52886],{"xmlns":890},[892,52887,52888,52902],{},[895,52889,52890,52892,52894,52896,52898,52900],{},[898,52891,1677],{},[1700,52893,1765],{},[898,52895,207],{},[898,52897,1662],{},[1700,52899,1897],{},[898,52901,1879],{},[902,52903,37245],{"encoding":904},[883,52905,52907],{"className":52906},[886],[888,52908,52909],{"xmlns":890},[892,52910,52911,52925],{},[895,52912,52913,52915,52917,52919,52921,52923],{},[898,52914,1677],{},[1700,52916,1765],{},[898,52918,2354],{},[898,52920,1662],{},[1700,52922,1897],{},[898,52924,2406],{},[902,52926,40427],{"encoding":904}," s hodnotami ",[883,52929,52931],{"className":52930},[886],[888,52932,52933],{"xmlns":890},[892,52934,52935,52945],{},[895,52936,52937,52939,52941,52943],{},[898,52938,207],{},[1700,52940,1765],{},[1700,52942,1768],{},[1931,52944,2385],{},[902,52946,52947],{"encoding":904},"a = -3",[883,52949,52951],{"className":52950},[886],[888,52952,52953],{"xmlns":890},[892,52954,52955,52963],{},[895,52956,52957,52959,52961],{},[898,52958,1879],{},[1700,52960,1765],{},[1931,52962,5399],{},[902,52964,48829],{"encoding":904},[883,52966,52968],{"className":52967},[886],[888,52969,52970],{"xmlns":890},[892,52971,52972,52980],{},[895,52973,52974,52976,52978],{},[898,52975,2354],{},[1700,52977,1765],{},[1931,52979,5197],{},[902,52981,48847],{"encoding":904},[883,52983,52985],{"className":52984},[886],[888,52986,52987],{"xmlns":890},[892,52988,52989,52997],{},[895,52990,52991,52993,52995],{},[898,52992,2406],{},[1700,52994,1765],{},[1931,52996,3058],{},[902,52998,48865],{"encoding":904},".\nRovnovážné množství:\n",[883,53001,53003],{"className":53002},[886],[888,53004,53005],{"xmlns":890},[892,53006,53007,53073],{},[895,53008,53009,53015,53017,53035,53037,53061,53063,53069,53071],{},[1785,53010,53011,53013],{},[898,53012,1662],{},[898,53014,1762],{},[1700,53016,1765],{},[1774,53018,53019,53027],{},[895,53020,53021,53023,53025],{},[898,53022,1879],{},[1700,53024,1768],{},[898,53026,2406],{},[895,53028,53029,53031,53033],{},[898,53030,2354],{},[1700,53032,1768],{},[898,53034,207],{},[1700,53036,1765],{},[1774,53038,53039,53047],{},[895,53040,53041,53043,53045],{},[1931,53042,5399],{},[1700,53044,1768],{},[1931,53046,3058],{},[895,53048,53049,53051,53053,53055,53057,53059],{},[1931,53050,5197],{},[1700,53052,1768],{},[1700,53054,1703],{"stretchy":1702},[1700,53056,1768],{},[1931,53058,2385],{},[1700,53060,1709],{"stretchy":1702},[1700,53062,1765],{},[1774,53064,53065,53067],{},[1931,53066,38204],{},[1931,53068,44591],{},[1700,53070,6088],{},[1931,53072,44596],{},[902,53074,53075],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,53078,53080],{"className":53079},[886],[888,53081,53082],{"xmlns":890},[892,53083,53084,53092],{},[895,53085,53086],{},[1785,53087,53088,53090],{},[898,53089,1662],{},[898,53091,1762],{},[902,53093,42588],{"encoding":904}," (a) při změně samotného parametru ",[883,53096,53098],{"className":53097},[886],[888,53099,53100],{"xmlns":890},[892,53101,53102,53106],{},[895,53103,53104],{},[898,53105,2354],{},[902,53107,2354],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,53110,53111],{},[38,53112,53113,53114,2868,53127,2882,53140,9482],{},"Řešení (a) — změna ",[883,53115,53117],{"className":53116},[886],[888,53118,53119],{"xmlns":890},[892,53120,53121,53125],{},[895,53122,53123],{},[898,53124,2354],{},[902,53126,2354],{"encoding":904},[883,53128,53130],{"className":53129},[886],[888,53131,53132],{"xmlns":890},[892,53133,53134,53138],{},[895,53135,53136],{},[1931,53137,5197],{},[902,53139,44631],{"encoding":904},[883,53141,53143],{"className":53142},[886],[888,53144,53145],{"xmlns":890},[892,53146,53147,53151],{},[895,53148,53149],{},[1931,53150,19506],{},[902,53152,44645],{"encoding":904},[724,53154,53155,53156,53220,53221,2901],{},"Pomocí vzorce (2.13) pro ",[883,53157,53159],{"className":53158},[886],[888,53160,53161],{"xmlns":890},[892,53162,53163,53217],{},[895,53164,53165,53185,53187,53189],{},[1770,53166,53167],{"scriptlevel":1772,"displaystyle":1731},[1774,53168,53169,53179],{},[895,53170,53171,53173],{},[898,53172,10056],{"mathvariant":1791},[1785,53174,53175,53177],{},[898,53176,1662],{},[898,53178,1762],{},[895,53180,53181,53183],{},[898,53182,10056],{"mathvariant":1791},[898,53184,2354],{},[1700,53186,1765],{},[1700,53188,1768],{},[1770,53190,53191],{"scriptlevel":1772,"displaystyle":1731},[1774,53192,53193,53201],{},[895,53194,53195,53197,53199],{},[898,53196,1879],{},[1700,53198,1768],{},[898,53200,2406],{},[895,53202,53203,53205,53207,53209,53211],{},[1700,53204,1703],{"stretchy":1702},[898,53206,2354],{},[1700,53208,1768],{},[898,53210,207],{},[1785,53212,53213,53215],{},[1700,53214,1709],{"stretchy":1702},[1931,53216,2343],{},[902,53218,53219],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,53222,53224],{"className":53223},[886],[888,53225,53226],{"xmlns":890},[892,53227,53228,53250],{},[895,53229,53230,53232],{},[1700,53231,1768],{},[1770,53233,53234],{"scriptlevel":1772,"displaystyle":1731},[1774,53235,53236,53242],{},[1785,53237,53238,53240],{},[898,53239,1662],{},[898,53241,1762],{},[895,53243,53244,53246,53248],{},[898,53245,2354],{},[1700,53247,1768],{},[898,53249,207],{},[902,53251,53252],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,53254,53256],{"className":53255},[886],[888,53257,53258],{"xmlns":890,"display":28251},[892,53259,53260,53316],{},[895,53261,53262,53264,53270,53272,53274,53290,53292,53294,53296,53298,53300,53306,53308,53310,53312,53314],{},[898,53263,2406],{},[1785,53265,53266,53268],{},[898,53267,1662],{},[898,53269,1762],{},[1700,53271,1765],{},[1700,53273,1768],{},[1774,53275,53276,53282],{},[1785,53277,53278,53280],{},[898,53279,1662],{},[898,53281,1762],{},[895,53283,53284,53286,53288],{},[898,53285,2354],{},[1700,53287,1768],{},[898,53289,207],{},[1781,53291,1783],{},[898,53293,2406],{},[898,53295,2354],{},[1700,53297,1765],{},[1700,53299,1768],{},[1774,53301,53302,53304],{},[1931,53303,44759],{},[1931,53305,44591],{},[1700,53307,2065],{},[1931,53309,2990],{},[1700,53311,6088],{},[1700,53313,1768],{},[1931,53315,44731],{},[902,53317,53318],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,53320,53321],{},"Nové rovnovážné množství:",[883,53323,53325],{"className":53324},[886],[888,53326,53327],{"xmlns":890,"display":28251},[892,53328,53329,53352],{},[895,53330,53331,53339,53341,53343,53345,53347,53349],{},[2030,53332,53333,53335,53337],{},[898,53334,1662],{},[1931,53336,1933],{},[898,53338,1762],{},[1700,53340,2927],{},[1931,53342,44759],{},[1700,53344,1768],{},[1931,53346,44764],{},[1700,53348,1765],{},[1931,53350,53351],{},"8,326.",[902,53353,53354],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,53356,53357,2106,53360,1343,53387,1343,53409,1343,53431,5777,53453,1343,53472,1343,53493,1343,53512,2196],{},[38,53358,53359],{},"Řešení (b) — současná změna všech parametrů:",[883,53361,53363],{"className":53362},[886],[888,53364,53365],{"xmlns":890},[892,53366,53367,53384],{},[895,53368,53369,53371,53373,53375,53377,53379,53381],{},[898,53370,207],{},[1700,53372,2901],{},[1700,53374,1768],{},[1931,53376,2385],{},[1700,53378,3317],{},[1700,53380,1768],{},[1931,53382,53383],{},"2,5",[902,53385,53386],{"encoding":904},"a: -3 \\to -2{,}5",[883,53388,53390],{"className":53389},[886],[888,53391,53392],{"xmlns":890},[892,53393,53394,53406],{},[895,53395,53396,53398,53400,53402,53404],{},[898,53397,1879],{},[1700,53399,2901],{},[1931,53401,5399],{},[1700,53403,3317],{},[1931,53405,15223],{},[902,53407,53408],{"encoding":904},"b: 40 \\to 35",[883,53410,53412],{"className":53411},[886],[888,53413,53414],{"xmlns":890},[892,53415,53416,53428],{},[895,53417,53418,53420,53422,53424,53426],{},[898,53419,2354],{},[1700,53421,2901],{},[1931,53423,5197],{},[1700,53425,3317],{},[1931,53427,19506],{},[902,53429,53430],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,53432,53434],{"className":53433},[886],[888,53435,53436],{"xmlns":890},[892,53437,53438,53450],{},[895,53439,53440,53442,53444,53446,53448],{},[898,53441,2406],{},[1700,53443,2901],{},[1931,53445,3058],{},[1700,53447,3317],{},[1931,53449,3099],{},[902,53451,53452],{"encoding":904},"d: 10 \\to 11",[883,53454,53456],{"className":53455},[886],[888,53457,53458],{"xmlns":890},[892,53459,53460,53470],{},[895,53461,53462,53464,53466,53468],{},[898,53463,2406],{},[898,53465,207],{},[1700,53467,1765],{},[1931,53469,5197],{},[902,53471,44797],{"encoding":904},[883,53473,53475],{"className":53474},[886],[888,53476,53477],{"xmlns":890},[892,53478,53479,53491],{},[895,53480,53481,53483,53485,53487,53489],{},[898,53482,2406],{},[898,53484,1879],{},[1700,53486,1765],{},[1700,53488,1768],{},[1931,53490,2438],{},[902,53492,44819],{"encoding":904},[883,53494,53496],{"className":53495},[886],[888,53497,53498],{"xmlns":890},[892,53499,53500,53510],{},[895,53501,53502,53504,53506,53508],{},[898,53503,2406],{},[898,53505,2354],{},[1700,53507,1765],{},[1931,53509,2990],{},[902,53511,44839],{"encoding":904},[883,53513,53515],{"className":53514},[886],[888,53516,53517],{"xmlns":890},[892,53518,53519,53529],{},[895,53520,53521,53523,53525,53527],{},[898,53522,2406],{},[898,53524,2406],{},[1700,53526,1765],{},[1931,53528,1933],{},[902,53530,44859],{"encoding":904},[724,53532,53533,53534,53592],{},"Totální diferenciál ",[883,53535,53537],{"className":53536},[886],[888,53538,53539],{"xmlns":890},[892,53540,53541,53589],{},[895,53542,53543,53549,53551,53553,53555,53557,53559,53561,53563,53565,53567,53569],{},[1785,53544,53545,53547],{},[898,53546,1662],{},[898,53548,1762],{},[1700,53550,1703],{"stretchy":1702},[898,53552,207],{},[1700,53554,1732],{"separator":1731},[898,53556,1879],{},[1700,53558,1732],{"separator":1731},[898,53560,2354],{},[1700,53562,1732],{"separator":1731},[898,53564,2406],{},[1700,53566,1709],{"stretchy":1702},[1700,53568,1765],{},[1770,53570,53571],{"scriptlevel":1772,"displaystyle":1731},[1774,53572,53573,53581],{},[895,53574,53575,53577,53579],{},[898,53576,1879],{},[1700,53578,1768],{},[898,53580,2406],{},[895,53582,53583,53585,53587],{},[898,53584,2354],{},[1700,53586,1768],{},[898,53588,207],{},[902,53590,53591],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,53594,53596],{"className":53595},[886],[888,53597,53598],{"xmlns":890,"display":28251},[892,53599,53600,53720],{},[895,53601,53602,53604,53610,53612,53638,53640,53642,53644,53646,53658,53660,53662,53664,53666,53692,53694,53696,53698,53700,53712,53714,53716,53718],{},[898,53603,2406],{},[1785,53605,53606,53608],{},[898,53607,1662],{},[898,53609,1762],{},[1700,53611,1765],{},[1774,53613,53614,53622],{},[895,53615,53616,53618,53620],{},[898,53617,1879],{},[1700,53619,1768],{},[898,53621,2406],{},[895,53623,53624,53626,53628,53630,53632],{},[1700,53625,1703],{"stretchy":1702},[898,53627,2354],{},[1700,53629,1768],{},[898,53631,207],{},[1785,53633,53634,53636],{},[1700,53635,1709],{"stretchy":1702},[1931,53637,2343],{},[1781,53639,1783],{},[898,53641,2406],{},[898,53643,207],{},[1700,53645,1897],{},[1774,53647,53648,53650],{},[1931,53649,1933],{},[895,53651,53652,53654,53656],{},[898,53653,2354],{},[1700,53655,1768],{},[898,53657,207],{},[1781,53659,1783],{},[898,53661,2406],{},[898,53663,1879],{},[1700,53665,1768],{},[1774,53667,53668,53676],{},[895,53669,53670,53672,53674],{},[898,53671,1879],{},[1700,53673,1768],{},[898,53675,2406],{},[895,53677,53678,53680,53682,53684,53686],{},[1700,53679,1703],{"stretchy":1702},[898,53681,2354],{},[1700,53683,1768],{},[898,53685,207],{},[1785,53687,53688,53690],{},[1700,53689,1709],{"stretchy":1702},[1931,53691,2343],{},[1781,53693,1783],{},[898,53695,2406],{},[898,53697,2354],{},[1700,53699,1768],{},[1774,53701,53702,53704],{},[1931,53703,1933],{},[895,53705,53706,53708,53710],{},[898,53707,2354],{},[1700,53709,1768],{},[898,53711,207],{},[1781,53713,1783],{},[898,53715,2406],{},[898,53717,2406],{},[898,53719,2196],{"mathvariant":1791},[902,53721,53722],{"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.",[724,53724,53725,53726,1343,53748,1343,53779,3345],{},"Dosazením číselných hodnot (",[883,53727,53729],{"className":53728},[886],[888,53730,53731],{"xmlns":890},[892,53732,53733,53745],{},[895,53734,53735,53737,53739,53741,53743],{},[898,53736,2354],{},[1700,53738,1768],{},[898,53740,207],{},[1700,53742,1765],{},[1931,53744,44591],{},[902,53746,53747],{"encoding":904},"c - a = 3{,}5",[883,53749,53751],{"className":53750},[886],[888,53752,53753],{"xmlns":890},[892,53754,53755,53776],{},[895,53756,53757,53759,53761,53763,53765,53771,53773],{},[1700,53758,1703],{"stretchy":1702},[898,53760,2354],{},[1700,53762,1768],{},[898,53764,207],{},[1785,53766,53767,53769],{},[1700,53768,1709],{"stretchy":1702},[1931,53770,2343],{},[1700,53772,1765],{},[1931,53774,53775],{},"12,25",[902,53777,53778],{"encoding":904},"(c-a)^2 = 12{,}25",[883,53780,53782],{"className":53781},[886],[888,53783,53784],{"xmlns":890},[892,53785,53786,53798],{},[895,53787,53788,53790,53792,53794,53796],{},[898,53789,1879],{},[1700,53791,1768],{},[898,53793,2406],{},[1700,53795,1765],{},[1931,53797,38204],{},[902,53799,53800],{"encoding":904},"b - d = 30",[883,53802,53804],{"className":53803},[886],[888,53805,53806],{"xmlns":890,"display":28251},[892,53807,53808,53909],{},[895,53809,53810,53812,53818,53820,53828,53830,53832,53834,53836,53844,53846,53848,53850,53852,53854,53862,53864,53866,53868,53870,53878,53880,53882,53884,53886,53889,53891,53894,53896,53898,53900,53903,53905,53907],{},[898,53811,2406],{},[1785,53813,53814,53816],{},[898,53815,1662],{},[898,53817,1762],{},[1700,53819,2927],{},[1770,53821,53822],{"scriptlevel":1772,"displaystyle":1702},[1774,53823,53824,53826],{},[1931,53825,38204],{},[1931,53827,53775],{},[1700,53829,1703],{"stretchy":1702},[1931,53831,5197],{},[1700,53833,1709],{"stretchy":1702},[1700,53835,1897],{},[1770,53837,53838],{"scriptlevel":1772,"displaystyle":1702},[1774,53839,53840,53842],{},[1931,53841,1933],{},[1931,53843,44591],{},[1700,53845,1703],{"stretchy":1702},[1700,53847,1768],{},[1931,53849,2438],{},[1700,53851,1709],{"stretchy":1702},[1700,53853,1768],{},[1770,53855,53856],{"scriptlevel":1772,"displaystyle":1702},[1774,53857,53858,53860],{},[1931,53859,38204],{},[1931,53861,53775],{},[1700,53863,1703],{"stretchy":1702},[1931,53865,2990],{},[1700,53867,1709],{"stretchy":1702},[1700,53869,1768],{},[1770,53871,53872],{"scriptlevel":1772,"displaystyle":1702},[1774,53873,53874,53876],{},[1931,53875,1933],{},[1931,53877,44591],{},[1700,53879,1703],{"stretchy":1702},[1931,53881,1933],{},[1700,53883,1709],{"stretchy":1702},[1700,53885,6088],{},[1931,53887,53888],{},"1,224",[1700,53890,1768],{},[1931,53892,53893],{},"1,429",[1700,53895,1768],{},[1931,53897,44764],{},[1700,53899,1768],{},[1931,53901,53902],{},"0,286",[1700,53904,6088],{},[1700,53906,1768],{},[1931,53908,45010],{},[902,53910,53911],{"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.",[724,53913,30250,53914,2196],{},[883,53915,53917],{"className":53916},[886],[888,53918,53919],{"xmlns":890},[892,53920,53921,53943],{},[895,53922,53923,53931,53933,53935,53937,53939,53941],{},[2030,53924,53925,53927,53929],{},[898,53926,1662],{},[1931,53928,1933],{},[898,53930,1762],{},[1700,53932,2927],{},[1931,53934,44759],{},[1700,53936,1768],{},[1931,53938,45041],{},[1700,53940,6088],{},[1931,53942,45046],{},[902,53944,53945],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[4060,53947,53948],{},[724,53949,53950,53952,53953,53974,53975,54001,54002,54005,54006,54102,54103,54126,54127,54143],{},[883,53951,4601],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,53954,53956],{"className":53955},[886],[888,53957,53958],{"xmlns":890},[892,53959,53960,53972],{},[895,53961,53962,53964,53966,53968,53970],{},[898,53963,3084],{"mathvariant":1791},[898,53965,1662],{},[1700,53967,2927],{},[1700,53969,1768],{},[1931,53971,45076],{},[902,53973,45079],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,53976,53978],{"className":53977},[886],[888,53979,53980],{"xmlns":890},[892,53981,53982,53998],{},[895,53983,53984,53986,53992,53994,53996],{},[898,53985,2406],{},[1785,53987,53988,53990],{},[898,53989,1662],{},[898,53991,1762],{},[1700,53993,6088],{},[1700,53995,1768],{},[1931,53997,45041],{},[902,53999,54000],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,54003,54004],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,54007,54009],{"className":54008},[886],[888,54010,54011],{"xmlns":890},[892,54012,54013,54099],{},[895,54014,54015,54023,54025,54059,54061,54085,54087,54094,54096],{},[2030,54016,54017,54019,54021],{},[898,54018,1662],{},[1931,54020,1933],{},[898,54022,1762],{},[1700,54024,1765],{},[1774,54026,54027,54043],{},[895,54028,54029,54035,54037],{},[1785,54030,54031,54033],{},[898,54032,1879],{},[1700,54034,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,54036,1768],{},[1785,54038,54039,54041],{},[898,54040,2406],{},[1700,54042,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[895,54044,54045,54051,54053],{},[1785,54046,54047,54049],{},[898,54048,2354],{},[1700,54050,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,54052,1768],{},[1785,54054,54055,54057],{},[898,54056,207],{},[1700,54058,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,54060,1765],{},[1774,54062,54063,54071],{},[895,54064,54065,54067,54069],{},[1931,54066,15223],{},[1700,54068,1768],{},[1931,54070,3099],{},[895,54072,54073,54075,54077,54079,54081,54083],{},[1931,54074,19506],{},[1700,54076,1768],{},[1700,54078,1703],{"stretchy":1702},[1700,54080,1768],{},[1931,54082,53383],{},[1700,54084,1709],{"stretchy":1702},[1700,54086,1765],{},[1774,54088,54089,54091],{},[1931,54090,41985],{},[1931,54092,54093],{},"3,1",[1700,54095,6088],{},[1931,54097,54098],{},"7,742",[902,54100,54101],{"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 ",[883,54104,54106],{"className":54105},[886],[888,54107,54108],{"xmlns":890},[892,54109,54110,54123],{},[895,54111,54112,54114,54116,54118,54120],{},[898,54113,3084],{"mathvariant":1791},[898,54115,1662],{},[1700,54117,6088],{},[1700,54119,1768],{},[1931,54121,54122],{},"0,829",[902,54124,54125],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,54128,54130],{"className":54129},[886],[888,54131,54132],{"xmlns":890},[892,54133,54134,54140],{},[895,54135,54136,54138],{},[1700,54137,1768],{},[1931,54139,45076],{},[902,54141,54142],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,54145,54146],{},[614,54147,54148,54149,54162],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,54150,54152],{"className":54151},[886],[888,54153,54154],{"xmlns":890},[892,54155,54156,54160],{},[895,54157,54158],{},[898,54159,1662],{},[902,54161,1662],{"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.",[198,54164,54166,54167],{"id":54165},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,54168,54170],{"className":54169},[886],[888,54171,54172],{"xmlns":890},[892,54173,54174,54180],{},[895,54175,54176,54178],{},[898,54177,1677],{},[898,54179,8861],{},[902,54181,45154],{"encoding":904},[4060,54183,54184],{},[724,54185,54186,54188,54189,54223,54224,54246],{},[883,54187,52879],{}," Zadání\nPro nabídku ",[883,54190,54192],{"className":54191},[886],[888,54193,54194],{"xmlns":890},[892,54195,54196,54220],{},[895,54197,54198,54200,54202,54204,54206,54208,54210,54212,54214,54216,54218],{},[898,54199,1677],{},[1700,54201,1765],{},[898,54203,8861],{},[1700,54205,1703],{"stretchy":1702},[898,54207,1662],{},[1700,54209,1709],{"stretchy":1702},[1700,54211,1765],{},[1931,54213,3058],{},[1700,54215,1897],{},[1931,54217,2343],{},[898,54219,1662],{},[902,54221,54222],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,54225,54227],{"className":54226},[886],[888,54228,54229],{"xmlns":890},[892,54230,54231,54243],{},[895,54232,54233,54239,54241],{},[2007,54234,54235,54237],{},[898,54236,1662],{},[1931,54238,1772],{},[1700,54240,1765],{},[1931,54242,3058],{},[902,54244,54245],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,54248,54249],{},[38,54250,22955],{},[724,54252,54253],{},"Odpovídající cena:",[883,54255,54257],{"className":54256},[886],[888,54258,54259],{"xmlns":890,"display":28251},[892,54260,54261,54296],{},[895,54262,54263,54269,54271,54273,54275,54277,54279,54281,54283,54285,54287,54289,54291,54293],{},[2007,54264,54265,54267],{},[898,54266,1677],{},[1931,54268,1772],{},[1700,54270,1765],{},[898,54272,8861],{},[1700,54274,1703],{"stretchy":1702},[1931,54276,3058],{},[1700,54278,1709],{"stretchy":1702},[1700,54280,1765],{},[1931,54282,3058],{},[1700,54284,1897],{},[1931,54286,2343],{},[1700,54288,2065],{},[1931,54290,3058],{},[1700,54292,1765],{},[1931,54294,54295],{},"30.",[902,54297,54298],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,54300,54301],{},"Dle vzorce (2.15):",[883,54303,54305],{"className":54304},[886],[888,54306,54307],{"xmlns":890,"display":28251},[892,54308,54309,54417],{},[895,54310,54311,54313,54315,54317,54319,54321,54323,54329,54335,54337,54345,54347,54349,54351,54353,54355,54357,54359,54361,54363,54365,54367,54369,54371,54373,54376,54378,54380,54382,54388,54396,54398,54400,54402,54404,54406,54408,54410,54412,54414],{},[898,54312,1677],{},[898,54314,8861],{},[1700,54316,1703],{"stretchy":1702},[1931,54318,3058],{},[1700,54320,1709],{"stretchy":1702},[1700,54322,1765],{},[2007,54324,54325,54327],{},[898,54326,1677],{},[1931,54328,1772],{},[2007,54330,54331,54333],{},[898,54332,1662],{},[1931,54334,1772],{},[1700,54336,1768],{},[2030,54338,54339,54341,54343],{},[1700,54340,11353],{},[1931,54342,1772],{},[1931,54344,3058],{},[1700,54346,1703],{"stretchy":1702},[1931,54348,3058],{},[1700,54350,1897],{},[1931,54352,2343],{},[898,54354,1662],{},[1700,54356,1709],{"stretchy":1702},[1781,54358,1783],{},[898,54360,2406],{},[898,54362,1662],{},[1700,54364,1765],{},[1931,54366,3058],{},[1700,54368,2065],{},[1931,54370,38204],{},[1700,54372,1768],{},[1700,54374,1927],{"fence":1702,"stretchy":1731,"minsize":54375,"maxsize":54375},"1.8em",[1931,54377,3058],{},[898,54379,1662],{},[1700,54381,1897],{},[1785,54383,54384,54386],{},[898,54385,1662],{},[1931,54387,2343],{},[2030,54389,54390,54392,54394],{},[1700,54391,1970],{"fence":1702,"stretchy":1731,"minsize":54375,"maxsize":54375},[1931,54393,1772],{},[1931,54395,3058],{},[1700,54397,1765],{},[1931,54399,30266],{},[1700,54401,1768],{},[1700,54403,1703],{"stretchy":1702},[1931,54405,3284],{},[1700,54407,1897],{},[1931,54409,3284],{},[1700,54411,1709],{"stretchy":1702},[1700,54413,1765],{},[1931,54415,54416],{},"100.",[902,54418,54419],{"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.",[724,54421,54422,54423,54444,54445,54465],{},"Přebytek výrobce při množství ",[883,54424,54426],{"className":54425},[886],[888,54427,54428],{"xmlns":890},[892,54429,54430,54442],{},[895,54431,54432,54438,54440],{},[2007,54433,54434,54436],{},[898,54435,1662],{},[1931,54437,1772],{},[1700,54439,1765],{},[1931,54441,3058],{},[902,54443,54245],{"encoding":904}," je tedy ",[883,54446,54448],{"className":54447},[886],[888,54449,54450],{"xmlns":890},[892,54451,54452,54462],{},[895,54453,54454,54456,54458,54460],{},[898,54455,1677],{},[898,54457,8861],{},[1700,54459,1765],{},[1931,54461,3284],{},[902,54463,54464],{"encoding":904},"PS = 100"," (peněžních jednotek).",[37155,54467],{},[115,54469,54471],{"id":54470},"cheat-sheet","Cheat sheet",[16,54473,54474,54487],{},[19,54475,54476],{},[22,54477,54478,54481,54484],{},[25,54479,54480],{},"Veličina",[25,54482,54483],{},"Vzorec",[25,54485,54486],{},"Geometrie",[30,54488,54489,54607,54721,54789],{},[22,54490,54491,54519,54575],{},[35,54492,54493],{},[883,54494,54496],{"className":54495},[886],[888,54497,54498],{"xmlns":890},[892,54499,54500,54516],{},[895,54501,54502,54504,54506,54508,54514],{},[898,54503,2974],{},[898,54505,8861],{},[1700,54507,1703],{"stretchy":1702},[2007,54509,54510,54512],{},[898,54511,1662],{},[1931,54513,1772],{},[1700,54515,1709],{"stretchy":1702},[902,54517,54518],{"encoding":904},"CS(Q_0)",[35,54520,54521],{},[883,54522,54524],{"className":54523},[886],[888,54525,54526],{"xmlns":890},[892,54527,54528,54572],{},[895,54529,54530],{},[1770,54531,54532,54544,54546,54548,54550,54552,54554,54556,54558,54560,54566],{"scriptlevel":1772,"displaystyle":1731},[2030,54533,54534,54536,54538],{},[1700,54535,11353],{},[1931,54537,1772],{},[2007,54539,54540,54542],{},[898,54541,1662],{},[1931,54543,1772],{},[898,54545,4374],{},[1700,54547,1703],{"stretchy":1702},[898,54549,1662],{},[1700,54551,1709],{"stretchy":1702},[1781,54553,1783],{},[898,54555,2406],{},[898,54557,1662],{},[1700,54559,1768],{},[2007,54561,54562,54564],{},[898,54563,1677],{},[1931,54565,1772],{},[2007,54567,54568,54570],{},[898,54569,1662],{},[1931,54571,1772],{},[902,54573,54574],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,54576,54577,54578,54581,54582,54585,54586],{},"plocha ",[38,54579,54580],{},"pod"," křivkou poptávky, ",[38,54583,54584],{},"nad"," čárou ",[883,54587,54589],{"className":54588},[886],[888,54590,54591],{"xmlns":890},[892,54592,54593,54605],{},[895,54594,54595,54597,54599],{},[898,54596,1677],{},[1700,54598,1765],{},[2007,54600,54601,54603],{},[898,54602,1677],{},[1931,54604,1772],{},[902,54606,51862],{"encoding":904},[22,54608,54609,54637,54693],{},[35,54610,54611],{},[883,54612,54614],{"className":54613},[886],[888,54615,54616],{"xmlns":890},[892,54617,54618,54634],{},[895,54619,54620,54622,54624,54626,54632],{},[898,54621,1677],{},[898,54623,8861],{},[1700,54625,1703],{"stretchy":1702},[2007,54627,54628,54630],{},[898,54629,1662],{},[1931,54631,1772],{},[1700,54633,1709],{"stretchy":1702},[902,54635,54636],{"encoding":904},"PS(Q_0)",[35,54638,54639],{},[883,54640,54642],{"className":54641},[886],[888,54643,54644],{"xmlns":890},[892,54645,54646,54690],{},[895,54647,54648],{},[1770,54649,54650,54656,54662,54664,54676,54678,54680,54682,54684,54686,54688],{"scriptlevel":1772,"displaystyle":1731},[2007,54651,54652,54654],{},[898,54653,1677],{},[1931,54655,1772],{},[2007,54657,54658,54660],{},[898,54659,1662],{},[1931,54661,1772],{},[1700,54663,1768],{},[2030,54665,54666,54668,54670],{},[1700,54667,11353],{},[1931,54669,1772],{},[2007,54671,54672,54674],{},[898,54673,1662],{},[1931,54675,1772],{},[898,54677,8861],{},[1700,54679,1703],{"stretchy":1702},[898,54681,1662],{},[1700,54683,1709],{"stretchy":1702},[1781,54685,1783],{},[898,54687,2406],{},[898,54689,1662],{},[902,54691,54692],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,54694,54577,54695,54697,54698,54585,54700],{},[38,54696,54584],{}," křivkou nabídky, ",[38,54699,54580],{},[883,54701,54703],{"className":54702},[886],[888,54704,54705],{"xmlns":890},[892,54706,54707,54719],{},[895,54708,54709,54711,54713],{},[898,54710,1677],{},[1700,54712,1765],{},[2007,54714,54715,54717],{},[898,54716,1677],{},[1931,54718,1772],{},[902,54720,51862],{"encoding":904},[22,54722,54723,54726,54753],{},[35,54724,54725],{},"Výdaje \u002F tržby",[35,54727,54728],{},[883,54729,54731],{"className":54730},[886],[888,54732,54733],{"xmlns":890},[892,54734,54735,54751],{},[895,54736,54737,54743,54745],{},[2007,54738,54739,54741],{},[898,54740,1677],{},[1931,54742,1772],{},[1700,54744,2065],{},[2007,54746,54747,54749],{},[898,54748,1662],{},[1931,54750,1772],{},[902,54752,52721],{"encoding":904},[35,54754,54755,54756],{},"obdélník ",[883,54757,54759],{"className":54758},[886],[888,54760,54761],{"xmlns":890},[892,54762,54763,54787],{},[895,54764,54765,54767,54769,54775,54777,54779,54781],{},[1931,54766,1772],{},[1781,54768,1783],{},[2007,54770,54771,54773],{},[898,54772,1662],{},[1931,54774,1772],{},[1781,54776,1783],{},[898,54778,1862],{},[1781,54780,1783],{},[2007,54782,54783,54785],{},[898,54784,1677],{},[1931,54786,1772],{},[902,54788,51342],{"encoding":904},[22,54790,54791,54794,54817],{},[35,54792,54793],{},"Celkový přebytek",[35,54795,54796],{},[883,54797,54799],{"className":54798},[886],[888,54800,54801],{"xmlns":890},[892,54802,54803,54815],{},[895,54804,54805,54807,54809,54811,54813],{},[898,54806,2974],{},[898,54808,8861],{},[1700,54810,1897],{},[898,54812,1677],{},[898,54814,8861],{},[902,54816,51080],{"encoding":904},[35,54818,54819],{},"součet obou ploch v rovnováze",[37155,54821],{},[115,54823,15905],{"id":15904},[120,54825,54826,54848,54870,54914,54958,55021,55049],{},[123,54827,54828,10208,54830,1343,54845,54847],{},[38,54829,45119],{},[883,54831,54833],{"className":54832},[886],[888,54834,54835],{"xmlns":890},[892,54836,54837,54843],{},[895,54838,54839,54841],{},[898,54840,2974],{},[898,54842,8861],{},[902,54844,45135],{"encoding":904},[614,54846,45173],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,54849,54850,10208,54852,1343,54867,54869],{},[38,54851,45266],{},[883,54853,54855],{"className":54854},[886],[888,54856,54857],{"xmlns":890},[892,54858,54859,54865],{},[895,54860,54861,54863],{},[898,54862,1677],{},[898,54864,8861],{},[902,54866,45154],{"encoding":904},[614,54868,45269],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,54871,54872,7203,54875,2196],{},[38,54873,54874],{},"Ochota platit",[883,54876,54878],{"className":54877},[886],[888,54879,54880],{"xmlns":890},[892,54881,54882,54912],{},[895,54883,54884],{},[1770,54885,54886,54898,54900,54902,54904,54906,54908,54910],{"scriptlevel":1772,"displaystyle":1731},[2030,54887,54888,54890,54892],{},[1700,54889,11353],{},[1931,54891,1772],{},[2007,54893,54894,54896],{},[898,54895,1662],{},[1931,54897,1772],{},[898,54899,4374],{},[1700,54901,1703],{"stretchy":1702},[898,54903,1662],{},[1700,54905,1709],{"stretchy":1702},[1781,54907,1783],{},[898,54909,2406],{},[898,54911,1662],{},[902,54913,51710],{"encoding":904},[123,54915,54916,7203,54919,2196],{},[38,54917,54918],{},"Minimální cena výrobce",[883,54920,54922],{"className":54921},[886],[888,54923,54924],{"xmlns":890},[892,54925,54926,54956],{},[895,54927,54928],{},[1770,54929,54930,54942,54944,54946,54948,54950,54952,54954],{"scriptlevel":1772,"displaystyle":1731},[2030,54931,54932,54934,54936],{},[1700,54933,11353],{},[1931,54935,1772],{},[2007,54937,54938,54940],{},[898,54939,1662],{},[1931,54941,1772],{},[898,54943,8861],{},[1700,54945,1703],{"stretchy":1702},[898,54947,1662],{},[1700,54949,1709],{"stretchy":1702},[1781,54951,1783],{},[898,54953,2406],{},[898,54955,1662],{},[902,54957,52352],{"encoding":904},[123,54959,54960,7203,54963,52852,54988,4110],{},[38,54961,54962],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,54964,54966],{"className":54965},[886],[888,54967,54968],{"xmlns":890},[892,54969,54970,54986],{},[895,54971,54972,54978,54980],{},[2007,54973,54974,54976],{},[898,54975,1677],{},[1931,54977,1772],{},[1781,54979,1783],{},[2007,54981,54982,54984],{},[898,54983,1662],{},[1931,54985,1772],{},[902,54987,51788],{"encoding":904},[883,54989,54991],{"className":54990},[886],[888,54992,54993],{"xmlns":890},[892,54994,54995,55019],{},[895,54996,54997,54999,55001,55007,55009,55011,55013],{},[1931,54998,1772],{},[1781,55000,1783],{},[2007,55002,55003,55005],{},[898,55004,1662],{},[1931,55006,1772],{},[1781,55008,1783],{},[898,55010,1862],{},[1781,55012,1783],{},[2007,55014,55015,55017],{},[898,55016,1677],{},[1931,55018,1772],{},[902,55020,51342],{"encoding":904},[123,55022,55023,55026,55027,55048],{},[38,55024,55025],{},"Celkový přebytek trhu"," — součet ",[883,55028,55030],{"className":55029},[886],[888,55031,55032],{"xmlns":890},[892,55033,55034,55046],{},[895,55035,55036,55038,55040,55042,55044],{},[898,55037,2974],{},[898,55039,8861],{},[1700,55041,1897],{},[898,55043,1677],{},[898,55045,8861],{},[902,55047,51080],{"encoding":904}," v rovnovážném bodě.",[123,55050,55051,55053,55054,1343,55067,55080,55081,2196],{},[38,55052,2643],{}," — plochy ohraničené křivkami ",[883,55055,55057],{"className":55056},[886],[888,55058,55059],{"xmlns":890},[892,55060,55061,55065],{},[895,55062,55063],{},[898,55064,4374],{},[902,55066,4374],{"encoding":904},[883,55068,55070],{"className":55069},[886],[888,55071,55072],{"xmlns":890},[892,55073,55074,55078],{},[895,55075,55076],{},[898,55077,8861],{},[902,55079,8861],{"encoding":904}," a přímkou ",[883,55082,55084],{"className":55083},[886],[888,55085,55086],{"xmlns":890},[892,55087,55088,55100],{},[895,55089,55090,55092,55094],{},[898,55091,1677],{},[1700,55093,1765],{},[2007,55095,55096,55098],{},[898,55097,1677],{},[1931,55099,1772],{},[902,55101,51862],{"encoding":904},[37155,55103],{},[115,55105,55107],{"id":55106},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,55109,55110,55111,55124,55125,55142],{},"Uvalení jednotkové daně ",[883,55112,55114],{"className":55113},[886],[888,55115,55116],{"xmlns":890},[892,55117,55118,55122],{},[895,55119,55120],{},[898,55121,2971],{},[902,55123,2971],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,55126,55128],{"className":55127},[886],[888,55129,55130],{"xmlns":890},[892,55131,55132,55140],{},[895,55133,55134],{},[1785,55135,55136,55138],{},[898,55137,1662],{},[898,55139,1762],{},[902,55141,42588],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,55144,55145],{},[2756,55146],{"alt":55147,"className":55148,"src":55149},"imek-prebytky-s-dani-deadweight",[210,2760],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,55151,55152,55153,55168,55169,55184,55185,52852,55188,55212,55213,10208,55216,55219,55220,2196],{},"Přebytek spotřebitele ",[883,55154,55156],{"className":55155},[886],[888,55157,55158],{"xmlns":890},[892,55159,55160,55166],{},[895,55161,55162,55164],{},[898,55163,2974],{},[898,55165,8861],{},[902,55167,45135],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,55170,55172],{"className":55171},[886],[888,55173,55174],{"xmlns":890},[892,55175,55176,55182],{},[895,55177,55178,55180],{},[898,55179,1677],{},[898,55181,8861],{},[902,55183,45154],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,55186,55187],{},"daňový příjem",[883,55189,55191],{"className":55190},[886],[888,55192,55193],{"xmlns":890},[892,55194,55195,55209],{},[895,55196,55197,55199,55201],{},[898,55198,2971],{},[1700,55200,2065],{},[2030,55202,55203,55205,55207],{},[898,55204,1662],{},[1931,55206,1933],{},[898,55208,1762],{},[902,55210,55211],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,55214,55215],{},"mrtvá ztráta",[614,55217,55218],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,55221,811],{"className":55222,"dataFsResolvedFilePath":809,"href":810},[210],[37155,55224],{},[115,55226,3985],{"id":3984},[120,55228,55229,55236,55248,55255,55262],{},[123,55230,55231,2106,55233],{},[38,55232,16407],{},[207,55234,802],{"className":55235,"dataFsResolvedFilePath":800,"href":801},[210],[123,55237,55238,2106,55240,55243,55244,55247],{},[38,55239,36859],{},[207,55241,775],{"className":55242,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,55245,2559],{"className":55246,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,55249,55250,2106,55252],{},[38,55251,16417],{},[207,55253,4016],{"className":55254,"dataFsResolvedFilePath":827,"href":828},[210],[123,55256,55257,2106,55259],{},[38,55258,50943],{},[207,55260,50947],{"className":55261,"dataFsResolvedFilePath":745,"href":746},[210],[123,55263,55264,2106,55266],{},[38,55265,16389],{},[207,55267,16393],{"className":55268,"dataFsResolvedFilePath":2140,"href":2141},[210],{"title":641,"searchDepth":642,"depth":642,"links":55270},[55271,55272,55277,55282,55287,55288,55289,55290],{"id":51139,"depth":642,"text":1241},{"id":51483,"depth":642,"text":55273,"children":55274},"Přebytek spotřebitele (CSCS)",[55275,55276],{"id":51502,"depth":649,"text":51503},{"id":2642,"depth":649,"text":2643},{"id":52078,"depth":642,"text":55278,"children":55279},"Přebytek výrobce (PSPS)",[55280,55281],{"id":52097,"depth":649,"text":52098},{"id":52260,"depth":649,"text":2643},{"id":52867,"depth":642,"text":52868,"children":55283},[55284,55285],{"id":52871,"depth":649,"text":52872},{"id":54165,"depth":649,"text":55286},"Příklad 2.13 — numerický výpočet PSPS",{"id":54470,"depth":642,"text":54471},{"id":15904,"depth":642,"text":15905},{"id":55106,"depth":642,"text":55107},{"id":3984,"depth":642,"text":3985},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,51009,55297,55298,12173,16425,55299,55300],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":55303,"title":55304,"body":55305,"course":1128,"courses":659,"created":9743,"description":641,"extension":661,"meta":74634,"navigation":664,"path":74635,"seo":74636,"sources":74637,"stem":74638,"tags":74639,"type":4049,"updated":677,"__hash__":74645},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":55306,"toc":74598},[55307,55310,55496,55498,55589,55594,55920,55924,55931,55935,55980,56047,56078,56128,56163,56167,56226,56231,56297,56415,56517,56521,56544,56622,56665,56669,56698,56765,56771,56885,56889,56969,57006,57058,57256,57320,57407,57411,57414,57493,57496,57614,57633,57698,57702,57794,57862,57903,57957,58025,58062,58066,58124,58154,58365,58437,58489,58655,58748,58783,58787,58791,58828,58893,58948,58952,58975,59064,59168,59237,59241,59338,59451,59507,59561,59619,59680,59683,59719,59784,59814,60043,60101,60135,60139,60166,60245,60359,60380,60459,60461,60569,60573,60711,61033,61037,61040,61044,61093,61097,61351,61503,61510,61583,61767,61772,62115,62119,62142,62144,62165,62224,62234,62283,62425,62499,62594,62709,62807,62925,62929,62998,63003,63115,63260,63311,63423,63465,63469,63489,63550,63577,63639,63643,63665,63734,64014,64021,64051,64058,64251,64255,64333,64338,64414,64417,64505,64581,64648,64697,64800,64873,64994,65345,65458,65560,65564,65567,65574,65577,65613,65672,65681,65830,66054,66058,66121,66300,66392,66447,66451,66507,66577,66629,66650,66731,66734,66809,66853,66857,66898,66941,66967,66971,67042,67138,67200,67252,67355,67433,67456,67485,67489,67655,67772,67844,68159,68319,68323,68374,68436,68471,68501,68601,68643,68812,68817,68913,68951,68955,69074,69375,69377,69412,69416,69420,69548,69680,70002,70190,70268,70272,70577,70690,70836,71021,71127,71359,71474,71556,71675,71773,71814,71818,71873,72017,72171,72331,72424,72618,72930,73061,73190,73194,73266,73308,73359,73361,74556,74558],[12,55308,55304],{"id":55309},"příjem-náklady-zisk-a-nabídka-firmy",[4060,55311,55312],{},[724,55313,55314,4067,55316,2106,55319,55334,55335,2106,55338,55353,55354,2106,55357,55385,55386,55408,55409,55433,55434,55456,55457,55460,55461,55477,55478,2196],{},[883,55315,4066],{},[38,55317,55318],{},"Příjem",[883,55320,55322],{"className":55321},[886],[888,55323,55324],{"xmlns":890},[892,55325,55326,55332],{},[895,55327,55328,55330],{},[898,55329,2971],{},[898,55331,4185],{},[902,55333,4285],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,55336,55337],{},"náklady",[883,55339,55341],{"className":55340},[886],[888,55342,55343],{"xmlns":890},[892,55344,55345,55351],{},[895,55346,55347,55349],{},[898,55348,2971],{},[898,55350,2974],{},[902,55352,3436],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,55355,55356],{},"zisk",[883,55358,55360],{"className":55359},[886],[888,55361,55362],{"xmlns":890},[892,55363,55364,55382],{},[895,55365,55366,55368,55370,55372,55374,55376,55378,55380],{},[898,55367,1677],{},[898,55369,4185],{},[1700,55371,1765],{},[898,55373,2971],{},[898,55375,4185],{},[1700,55377,1768],{},[898,55379,2971],{},[898,55381,2974],{},[902,55383,55384],{"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: ",[883,55387,55389],{"className":55388},[886],[888,55390,55391],{"xmlns":890},[892,55392,55393,55405],{},[895,55394,55395,55397,55399,55401,55403],{},[898,55396,1862],{},[898,55398,2974],{},[1700,55400,1765],{},[898,55402,2005],{},[898,55404,2974],{},[902,55406,55407],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,55410,55412],{"className":55411},[886],[888,55413,55414],{"xmlns":890},[892,55415,55416,55430],{},[895,55417,55418,55420,55422,55424,55426,55428],{},[898,55419,1862],{},[898,55421,40524],{},[898,55423,2974],{},[1700,55425,1765],{},[898,55427,2005],{},[898,55429,2974],{},[902,55431,55432],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,55435,55437],{"className":55436},[886],[888,55438,55439],{"xmlns":890},[892,55440,55441,55453],{},[895,55442,55443,55445,55447,55449,55451],{},[898,55444,2005],{},[898,55446,4185],{},[1700,55448,1765],{},[898,55450,2005],{},[898,55452,2974],{},[902,55454,55455],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,55458,55459],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,55462,55464],{"className":55463},[886],[888,55465,55466],{"xmlns":890},[892,55467,55468,55474],{},[895,55469,55470,55472],{},[898,55471,2005],{},[898,55473,2974],{},[902,55475,55476],{"encoding":904},"MC"," nad bodem minima ",[883,55479,55481],{"className":55480},[886],[888,55482,55483],{"xmlns":890},[892,55484,55485,55493],{},[895,55486,55487,55489,55491],{},[898,55488,1862],{},[898,55490,40524],{},[898,55492,2974],{},[902,55494,55495],{"encoding":904},"AVC",[115,55497,1241],{"id":51139},[724,55499,55500,55501,55504,55505,55507,55508,1343,55511,1343,55514,55516,55517,55520,55521,55524,55525,55528,55529,2868,55544,1348,55559,2868,55574,4110],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,55502,55503],{},"příjmem"," (revenue) a ",[38,55506,55337],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,55509,55510],{},"zisku",[38,55512,55513],{},"bodů zvratu",[38,55515,2191],{}," a konstrukcí ",[38,55518,55519],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,55522,1145],{"className":55523,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,55526,11314],{"className":55527,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,55530,55532],{"className":55531},[886],[888,55533,55534],{"xmlns":890},[892,55535,55536,55542],{},[895,55537,55538,55540],{},[898,55539,2971],{},[898,55541,4185],{},[902,55543,4285],{"encoding":904},[883,55545,55547],{"className":55546},[886],[888,55548,55549],{"xmlns":890},[892,55550,55551,55557],{},[895,55552,55553,55555],{},[898,55554,2005],{},[898,55556,4185],{},[902,55558,6822],{"encoding":904},[883,55560,55562],{"className":55561},[886],[888,55563,55564],{"xmlns":890},[892,55565,55566,55572],{},[895,55567,55568,55570],{},[898,55569,2971],{},[898,55571,2974],{},[902,55573,3436],{"encoding":904},[883,55575,55577],{"className":55576},[886],[888,55578,55579],{"xmlns":890},[892,55580,55581,55587],{},[895,55582,55583,55585],{},[898,55584,2005],{},[898,55586,2974],{},[902,55588,55476],{"encoding":904},[724,55590,55591],{},[38,55592,55593],{},"Cílové znalosti:",[120,55595,55596,55760,55763,55766,55859,55906,55913],{},[123,55597,55598,55599,1343,55614,1343,55630,2114,55645,1343,55660,1343,55676,1343,55694,1343,55712,1343,55729,1343,55745,8613],{},"odvodit a interpretovat funkce ",[883,55600,55602],{"className":55601},[886],[888,55603,55604],{"xmlns":890},[892,55605,55606,55612],{},[895,55607,55608,55610],{},[898,55609,2971],{},[898,55611,4185],{},[902,55613,4285],{"encoding":904},[883,55615,55617],{"className":55616},[886],[888,55618,55619],{"xmlns":890},[892,55620,55621,55627],{},[895,55622,55623,55625],{},[898,55624,1862],{},[898,55626,4185],{},[902,55628,55629],{"encoding":904},"AR",[883,55631,55633],{"className":55632},[886],[888,55634,55635],{"xmlns":890},[892,55636,55637,55643],{},[895,55638,55639,55641],{},[898,55640,2005],{},[898,55642,4185],{},[902,55644,6822],{"encoding":904},[883,55646,55648],{"className":55647},[886],[888,55649,55650],{"xmlns":890},[892,55651,55652,55658],{},[895,55653,55654,55656],{},[898,55655,2971],{},[898,55657,2974],{},[902,55659,3436],{"encoding":904},[883,55661,55663],{"className":55662},[886],[888,55664,55665],{"xmlns":890},[892,55666,55667,55673],{},[895,55668,55669,55671],{},[898,55670,10619],{},[898,55672,2974],{},[902,55674,55675],{"encoding":904},"FC",[883,55677,55679],{"className":55678},[886],[888,55680,55681],{"xmlns":890},[892,55682,55683,55691],{},[895,55684,55685,55687,55689],{},[898,55686,2971],{},[898,55688,40524],{},[898,55690,2974],{},[902,55692,55693],{"encoding":904},"TVC",[883,55695,55697],{"className":55696},[886],[888,55698,55699],{"xmlns":890},[892,55700,55701,55709],{},[895,55702,55703,55705,55707],{},[898,55704,1862],{},[898,55706,10619],{},[898,55708,2974],{},[902,55710,55711],{"encoding":904},"AFC",[883,55713,55715],{"className":55714},[886],[888,55716,55717],{"xmlns":890},[892,55718,55719,55727],{},[895,55720,55721,55723,55725],{},[898,55722,1862],{},[898,55724,40524],{},[898,55726,2974],{},[902,55728,55495],{"encoding":904},[883,55730,55732],{"className":55731},[886],[888,55733,55734],{"xmlns":890},[892,55735,55736,55742],{},[895,55737,55738,55740],{},[898,55739,1862],{},[898,55741,2974],{},[902,55743,55744],{"encoding":904},"AC",[883,55746,55748],{"className":55747},[886],[888,55749,55750],{"xmlns":890},[892,55751,55752,55758],{},[895,55753,55754,55756],{},[898,55755,2005],{},[898,55757,2974],{},[902,55759,55476],{"encoding":904},[123,55761,55762],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,55764,55765],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,55767,55768,55769,55772,55773,41999,55815,8613],{},"osvojit si ",[38,55770,55771],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,55774,55776],{"className":55775},[886],[888,55777,55778],{"xmlns":890},[892,55779,55780,55812],{},[895,55781,55782,55784,55786,55788,55794,55796,55798,55800,55802,55804,55810],{},[898,55783,1862],{},[898,55785,2974],{},[1700,55787,1703],{"stretchy":1702},[2007,55789,55790,55792],{},[898,55791,1662],{},[1931,55793,1772],{},[1700,55795,1709],{"stretchy":1702},[1700,55797,1765],{},[898,55799,2005],{},[898,55801,2974],{},[1700,55803,1703],{"stretchy":1702},[2007,55805,55806,55808],{},[898,55807,1662],{},[1931,55809,1772],{},[1700,55811,1709],{"stretchy":1702},[902,55813,55814],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,55816,55818],{"className":55817},[886],[888,55819,55820],{"xmlns":890},[892,55821,55822,55856],{},[895,55823,55824,55826,55828,55830,55832,55838,55840,55842,55844,55846,55848,55854],{},[898,55825,1862],{},[898,55827,40524],{},[898,55829,2974],{},[1700,55831,1703],{"stretchy":1702},[2007,55833,55834,55836],{},[898,55835,1662],{},[1931,55837,1772],{},[1700,55839,1709],{"stretchy":1702},[1700,55841,1765],{},[898,55843,2005],{},[898,55845,2974],{},[1700,55847,1703],{"stretchy":1702},[2007,55849,55850,55852],{},[898,55851,1662],{},[1931,55853,1772],{},[1700,55855,1709],{"stretchy":1702},[902,55857,55858],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,55860,55768,55861,55772,55864,8613],{},[38,55862,55863],{},"princip maximalizace zisku",[883,55865,55867],{"className":55866},[886],[888,55868,55869],{"xmlns":890},[892,55870,55871,55903],{},[895,55872,55873,55875,55877,55879,55885,55887,55889,55891,55893,55895,55901],{},[898,55874,2005],{},[898,55876,4185],{},[1700,55878,1703],{"stretchy":1702},[2007,55880,55881,55883],{},[898,55882,1662],{},[1931,55884,1772],{},[1700,55886,1709],{"stretchy":1702},[1700,55888,1765],{},[898,55890,2005],{},[898,55892,2974],{},[1700,55894,1703],{"stretchy":1702},[2007,55896,55897,55899],{},[898,55898,1662],{},[1931,55900,1772],{},[1700,55902,1709],{"stretchy":1702},[902,55904,55905],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,55907,55908,55909,55912],{},"stanovit ",[38,55910,55911],{},"body zvratu"," a interval zisku;",[123,55914,55915,55916,55919],{},"zkonstruovat ",[38,55917,55918],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,55921,55923],{"id":55922},"příjem-firmy","Příjem firmy",[724,55925,55926],{},[2756,55927],{"alt":55928,"className":55929,"src":55930},"imek-ar-mr-dvojnasobny-sklon",[210,2760],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,55932,55934],{"id":55933},"celkový-příjem","Celkový příjem",[724,55936,55937,55938,10208,55953,55956,55957,30129],{},"Celkový příjem ",[883,55939,55941],{"className":55940},[886],[888,55942,55943],{"xmlns":890},[892,55944,55945,55951],{},[895,55946,55947,55949],{},[898,55948,2971],{},[898,55950,4185],{},[902,55952,4285],{"encoding":904},[38,55954,55955],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,55958,55960],{"className":55959},[886],[888,55961,55962],{"xmlns":890},[892,55963,55964,55978],{},[895,55965,55966,55968,55970,55972,55974,55976],{},[898,55967,1677],{},[1700,55969,1765],{},[898,55971,4374],{},[1700,55973,1703],{"stretchy":1702},[898,55975,1662],{},[1700,55977,1709],{"stretchy":1702},[902,55979,4829],{"encoding":904},[883,55981,55983],{"className":55982},[886],[888,55984,55985],{"xmlns":890,"display":28251},[892,55986,55987,56044],{},[20939,55988,55989],{"width":28256},[20944,55990,55991,55993,56037,56039],{},[20947,55992],{"width":28261},[20947,55994,55995],{},[895,55996,55997,55999,56001,56003,56005,56007,56009,56011,56013,56015,56017,56019,56021,56023,56025,56027,56029,56031,56033,56035],{},[898,55998,2971],{},[898,56000,4185],{},[1700,56002,1765],{},[898,56004,2971],{},[898,56006,4185],{},[1700,56008,1703],{"stretchy":1702},[898,56010,1662],{},[1700,56012,1709],{"stretchy":1702},[1700,56014,1765],{},[898,56016,1677],{},[1700,56018,2065],{},[898,56020,1662],{},[1700,56022,1765],{},[898,56024,4374],{},[1700,56026,1703],{"stretchy":1702},[898,56028,1662],{},[1700,56030,1709],{"stretchy":1702},[1700,56032,2065],{},[898,56034,1662],{},[898,56036,2196],{"mathvariant":1791},[20947,56038],{"width":28261},[20947,56040,56041],{},[1781,56042,56043],{},"(3.1)",[902,56045,56046],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,56048,56049,56050,56053,56054,56077],{},"Graf funkce se nazývá ",[38,56051,56052],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,56055,56057],{"className":56056},[886],[888,56058,56059],{"xmlns":890},[892,56060,56061,56075],{},[895,56062,56063,56065,56067,56069,56071,56073],{},[898,56064,1677],{},[1700,56066,1765],{},[898,56068,207],{},[898,56070,1662],{},[1700,56072,1897],{},[898,56074,1879],{},[902,56076,37245],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,56079,56081],{"className":56080},[886],[888,56082,56083],{"xmlns":890,"display":28251},[892,56084,56085,56125],{},[895,56086,56087,56089,56091,56093,56095,56097,56099,56101,56103,56105,56107,56109,56111,56117,56119,56121,56123],{},[898,56088,2971],{},[898,56090,4185],{},[1700,56092,1765],{},[898,56094,1662],{},[1700,56096,1703],{"stretchy":1702},[898,56098,207],{},[898,56100,1662],{},[1700,56102,1897],{},[898,56104,1879],{},[1700,56106,1709],{"stretchy":1702},[1700,56108,1765],{},[898,56110,207],{},[1785,56112,56113,56115],{},[898,56114,1662],{},[1931,56116,2343],{},[1700,56118,1897],{},[898,56120,1879],{},[898,56122,1662],{},[1700,56124,1732],{"separator":1731},[902,56126,56127],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,56129,56130,56131,56144,56145,56162],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,56132,56134],{"className":56133},[886],[888,56135,56136],{"xmlns":890},[892,56137,56138,56142],{},[895,56139,56140],{},[898,56141,900],{},[902,56143,900],{"encoding":904}," (jelikož ",[883,56146,56148],{"className":56147},[886],[888,56149,56150],{"xmlns":890},[892,56151,56152,56160],{},[895,56153,56154,56156,56158],{},[898,56155,207],{},[1700,56157,3640],{},[1931,56159,1772],{},[902,56161,43270],{"encoding":904},") procházející počátkem.",[37533,56164,56166],{"id":56165},"příklad-31","Příklad 3.1",[724,56168,56169,56172,56173,56209,56210,56225],{},[38,56170,56171],{},"Zadání."," Pro poptávku ",[883,56174,56176],{"className":56175},[886],[888,56177,56178],{"xmlns":890},[892,56179,56180,56206],{},[895,56181,56182,56184,56186,56188,56190,56192,56194,56196,56198,56200,56202,56204],{},[898,56183,1677],{},[1700,56185,1765],{},[898,56187,4374],{},[1700,56189,1703],{"stretchy":1702},[898,56191,1662],{},[1700,56193,1709],{"stretchy":1702},[1700,56195,1765],{},[1700,56197,1768],{},[1931,56199,2343],{},[898,56201,1662],{},[1700,56203,1897],{},[1931,56205,3284],{},[902,56207,56208],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,56211,56213],{"className":56212},[886],[888,56214,56215],{"xmlns":890},[892,56216,56217,56223],{},[895,56218,56219,56221],{},[898,56220,2971],{},[898,56222,4185],{},[902,56224,4285],{"encoding":904}," a charakterizujte jeho křivku.",[724,56227,56228,56230],{},[38,56229,22955],{}," Celkový příjem je",[883,56232,56234],{"className":56233},[886],[888,56235,56236],{"xmlns":890,"display":28251},[892,56237,56238,56294],{},[895,56239,56240,56242,56244,56246,56248,56250,56252,56254,56256,56258,56260,56262,56264,56266,56268,56270,56272,56274,56276,56278,56280,56286,56288,56290,56292],{},[898,56241,2971],{},[898,56243,4185],{},[1700,56245,1765],{},[898,56247,2971],{},[898,56249,4185],{},[1700,56251,1703],{"stretchy":1702},[898,56253,1662],{},[1700,56255,1709],{"stretchy":1702},[1700,56257,1765],{},[898,56259,1662],{},[1700,56261,1703],{"stretchy":1702},[1700,56263,1768],{},[1931,56265,2343],{},[898,56267,1662],{},[1700,56269,1897],{},[1931,56271,3284],{},[1700,56273,1709],{"stretchy":1702},[1700,56275,1765],{},[1700,56277,1768],{},[1931,56279,2343],{},[1785,56281,56282,56284],{},[898,56283,1662],{},[1931,56285,2343],{},[1700,56287,1897],{},[1931,56289,3284],{},[898,56291,1662],{},[898,56293,2196],{"mathvariant":1791},[902,56295,56296],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,56298,56299,56300,2114,56322,56344,56345,56363,56364,2196],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,56301,56303],{"className":56302},[886],[888,56304,56305],{"xmlns":890},[892,56306,56307,56319],{},[895,56308,56309,56315,56317],{},[2007,56310,56311,56313],{},[898,56312,1662],{},[1931,56314,1933],{},[1700,56316,1765],{},[1931,56318,1772],{},[902,56320,56321],{"encoding":904},"Q_1 = 0",[883,56323,56325],{"className":56324},[886],[888,56326,56327],{"xmlns":890},[892,56328,56329,56341],{},[895,56330,56331,56337,56339],{},[2007,56332,56333,56335],{},[898,56334,1662],{},[1931,56336,2343],{},[1700,56338,1765],{},[1931,56340,3314],{},[902,56342,56343],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,56346,56348],{"className":56347},[886],[888,56349,56350],{"xmlns":890},[892,56351,56352,56360],{},[895,56353,56354,56356,56358],{},[898,56355,1662],{},[1700,56357,1765],{},[1931,56359,5192],{},[902,56361,56362],{"encoding":904},"Q = 25"," ve výši ",[883,56365,56367],{"className":56366},[886],[888,56368,56369],{"xmlns":890},[892,56370,56371,56412],{},[895,56372,56373,56375,56385,56387,56389,56391,56393,56396,56398,56400,56402,56404,56406,56408,56410],{},[898,56374,2971],{},[2007,56376,56377,56379,56382],{},[898,56378,4185],{},[898,56380,56381],{},"max",[1700,56383,56384],{},"⁡",[1700,56386,1765],{},[1700,56388,1768],{},[1931,56390,2343],{},[1700,56392,2065],{},[1931,56394,56395],{},"625",[1700,56397,1897],{},[1931,56399,3284],{},[1700,56401,2065],{},[1931,56403,5192],{},[1700,56405,1765],{},[1931,56407,1933],{},[1781,56409,1783],{},[1931,56411,30928],{},[902,56413,56414],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,56416,56417],{},[614,56418,56419,56420,56454,56455,2114,56468,56481,56482,2821,56500,2196],{},"Obrázek 3.1: Parabola ",[883,56421,56423],{"className":56422},[886],[888,56424,56425],{"xmlns":890},[892,56426,56427,56451],{},[895,56428,56429,56431,56433,56435,56437,56439,56445,56447,56449],{},[898,56430,2971],{},[898,56432,4185],{},[1700,56434,1765],{},[1700,56436,1768],{},[1931,56438,2343],{},[1785,56440,56441,56443],{},[898,56442,1662],{},[1931,56444,2343],{},[1700,56446,1897],{},[1931,56448,3284],{},[898,56450,1662],{},[902,56452,56453],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,56456,56458],{"className":56457},[886],[888,56459,56460],{"xmlns":890},[892,56461,56462,56466],{},[895,56463,56464],{},[1931,56465,1772],{},[902,56467,1772],{"encoding":904},[883,56469,56471],{"className":56470},[886],[888,56472,56473],{"xmlns":890},[892,56474,56475,56479],{},[895,56476,56477],{},[1931,56478,3314],{},[902,56480,3314],{"encoding":904}," a maximem ",[883,56483,56485],{"className":56484},[886],[888,56486,56487],{"xmlns":890},[892,56488,56489,56497],{},[895,56490,56491,56493,56495],{},[1931,56492,1933],{},[1781,56494,1783],{},[1931,56496,30928],{},[902,56498,56499],{"encoding":904},"1\\,250",[883,56501,56503],{"className":56502},[886],[888,56504,56505],{"xmlns":890},[892,56506,56507,56515],{},[895,56508,56509,56511,56513],{},[898,56510,1662],{},[1700,56512,1765],{},[1931,56514,5192],{},[902,56516,56362],{"encoding":904},[198,56518,56520],{"id":56519},"průměrný-příjem","Průměrný příjem",[724,56522,56523,2106,56525,10208,56540,56543],{},[38,56524,56520],{},[883,56526,56528],{"className":56527},[886],[888,56529,56530],{"xmlns":890},[892,56531,56532,56538],{},[895,56533,56534,56536],{},[898,56535,1862],{},[898,56537,4185],{},[902,56539,55629],{"encoding":904},[38,56541,56542],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,56545,56547],{"className":56546},[886],[888,56548,56549],{"xmlns":890,"display":28251},[892,56550,56551,56619],{},[895,56552,56553,56555,56557,56559,56561,56563,56565,56567,56569,56571,56587,56589,56607,56609,56611,56613,56615,56617],{},[898,56554,1862],{},[898,56556,4185],{},[1700,56558,1765],{},[898,56560,1862],{},[898,56562,4185],{},[1700,56564,1703],{"stretchy":1702},[898,56566,1662],{},[1700,56568,1709],{"stretchy":1702},[1700,56570,1765],{},[1774,56572,56573,56585],{},[895,56574,56575,56577,56579,56581,56583],{},[898,56576,2971],{},[898,56578,4185],{},[1700,56580,1703],{"stretchy":1702},[898,56582,1662],{},[1700,56584,1709],{"stretchy":1702},[898,56586,1662],{},[1700,56588,1765],{},[1774,56590,56591,56605],{},[895,56592,56593,56595,56597,56599,56601,56603],{},[898,56594,1662],{},[1781,56596,1783],{},[898,56598,4374],{},[1700,56600,1703],{"stretchy":1702},[898,56602,1662],{},[1700,56604,1709],{"stretchy":1702},[898,56606,1662],{},[1700,56608,1765],{},[898,56610,4374],{},[1700,56612,1703],{"stretchy":1702},[898,56614,1662],{},[1700,56616,1709],{"stretchy":1702},[898,56618,2196],{"mathvariant":1791},[902,56620,56621],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[4060,56623,56624],{},[724,56625,56626,56629,56630,1343,56633,2196],{},[883,56627,56628],{},"!note"," Klíčové pozorování\n",[38,56631,56632],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,56634,56636],{"className":56635},[886],[888,56637,56638],{"xmlns":890},[892,56639,56640,56662],{},[895,56641,56642,56644,56646,56648,56650,56652,56654,56656,56658,56660],{},[898,56643,1862],{},[898,56645,4185],{},[1700,56647,1703],{"stretchy":1702},[898,56649,1662],{},[1700,56651,1709],{"stretchy":1702},[1700,56653,1765],{},[898,56655,4374],{},[1700,56657,1703],{"stretchy":1702},[898,56659,1662],{},[1700,56661,1709],{"stretchy":1702},[902,56663,56664],{"encoding":904},"AR(Q) = D(Q)",[198,56666,56668],{"id":56667},"mezní-příjem","Mezní příjem",[724,56670,56671,56672,2106,56675,10208,56690,56693,56694,56697],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,56673,56674],{},"mezní příjem",[883,56676,56678],{"className":56677},[886],[888,56679,56680],{"xmlns":890},[892,56681,56682,56688],{},[895,56683,56684,56686],{},[898,56685,2005],{},[898,56687,4185],{},[902,56689,6822],{"encoding":904},[38,56691,56692],{},"marginal revenue","), definovaný jako ",[207,56695,1145],{"className":56696,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,56699,56701],{"className":56700},[886],[888,56702,56703],{"xmlns":890,"display":28251},[892,56704,56705,56762],{},[20939,56706,56707],{"width":28256},[20944,56708,56709,56711,56755,56757],{},[20947,56710],{"width":28261},[20947,56712,56713],{},[895,56714,56715,56717,56719,56721,56737,56739,56741,56747,56749,56751,56753],{},[898,56716,2005],{},[898,56718,4185],{},[1700,56720,1765],{},[1774,56722,56723,56731],{},[895,56724,56725,56727,56729],{},[898,56726,2406],{"mathvariant":1791},[898,56728,2971],{},[898,56730,4185],{},[895,56732,56733,56735],{},[898,56734,2406],{"mathvariant":1791},[898,56736,1662],{},[1700,56738,1765],{},[898,56740,2971],{},[1785,56742,56743,56745],{},[898,56744,4185],{},[1700,56746,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,56748,1703],{"stretchy":1702},[898,56750,1662],{},[1700,56752,1709],{"stretchy":1702},[898,56754,2196],{"mathvariant":1791},[20947,56756],{"width":28261},[20947,56758,56759],{},[1781,56760,56761],{},"(3.2)",[902,56763,56764],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,56766,56767,56768,56770],{},"Mezní příjem udává ",[38,56769,2793],{}," celkového příjmu vzhledem k množství.",[4060,56772,56773],{},[724,56774,56775,56777,56778,56804,56805,56822,56823,2196],{},[883,56776,4346],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,56779,56781],{"className":56780},[886],[888,56782,56783],{"xmlns":890},[892,56784,56785,56801],{},[895,56786,56787,56789,56791,56793,56799],{},[898,56788,2005],{},[898,56790,4185],{},[1700,56792,1703],{"stretchy":1702},[1785,56794,56795,56797],{},[898,56796,1662],{},[1700,56798,4543],{},[1700,56800,1709],{"stretchy":1702},[902,56802,56803],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,56806,56808],{"className":56807},[886],[888,56809,56810],{"xmlns":890},[892,56811,56812,56820],{},[895,56813,56814],{},[1785,56815,56816,56818],{},[898,56817,1662],{},[1700,56819,4543],{},[902,56821,30029],{"encoding":904},". Jinak řečeno: ",[883,56824,56826],{"className":56825},[886],[888,56827,56828],{"xmlns":890},[892,56829,56830,56882],{},[895,56831,56832,56834,56836,56838,56844,56846,56848,56850,56852,56854,56860,56862,56864,56866,56868,56870,56872,56874,56880],{},[898,56833,2005],{},[898,56835,4185],{},[1700,56837,1703],{"stretchy":1702},[1785,56839,56840,56842],{},[898,56841,1662],{},[1700,56843,4543],{},[1700,56845,1709],{"stretchy":1702},[1700,56847,2927],{},[898,56849,2971],{},[898,56851,4185],{},[1700,56853,1703],{"stretchy":1702},[1785,56855,56856,56858],{},[898,56857,1662],{},[1700,56859,4543],{},[1700,56861,1897],{},[1931,56863,1933],{},[1700,56865,1709],{"stretchy":1702},[1700,56867,1768],{},[898,56869,2971],{},[898,56871,4185],{},[1700,56873,1703],{"stretchy":1702},[1785,56875,56876,56878],{},[898,56877,1662],{},[1700,56879,4543],{},[1700,56881,1709],{"stretchy":1702},[902,56883,56884],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[37533,56886,56888],{"id":56887},"příklad-32","Příklad 3.2",[724,56890,56891,56172,56893,56209,56927,56942,56943,2196],{},[38,56892,56171],{},[883,56894,56896],{"className":56895},[886],[888,56897,56898],{"xmlns":890},[892,56899,56900,56924],{},[895,56901,56902,56904,56906,56908,56910,56912,56914,56916,56918,56920,56922],{},[898,56903,1677],{},[1700,56905,1765],{},[898,56907,4374],{},[1700,56909,1703],{"stretchy":1702},[898,56911,1662],{},[1700,56913,1709],{"stretchy":1702},[1700,56915,1765],{},[1931,56917,3284],{},[1700,56919,1768],{},[1931,56921,2343],{},[898,56923,1662],{},[902,56925,56926],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,56928,56930],{"className":56929},[886],[888,56931,56932],{"xmlns":890},[892,56933,56934,56940],{},[895,56935,56936,56938],{},[898,56937,2005],{},[898,56939,4185],{},[902,56941,6822],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,56944,56946],{"className":56945},[886],[888,56947,56948],{"xmlns":890},[892,56949,56950,56966],{},[895,56951,56952,56954,56956,56958,56960,56962,56964],{},[898,56953,1662],{},[1700,56955,1765],{},[1931,56957,36429],{},[1700,56959,1732],{"separator":1731},[1931,56961,42047],{},[1700,56963,1732],{"separator":1731},[1931,56965,9223],{},[902,56967,56968],{"encoding":904},"Q = 15, 16, 20",[724,56970,56971,2106,56973,57005],{},[38,56972,22955],{},[883,56974,56976],{"className":56975},[886],[888,56977,56978],{"xmlns":890},[892,56979,56980,57002],{},[895,56981,56982,56984,56986,56988,56990,56992,56994,56996],{},[898,56983,2971],{},[898,56985,4185],{},[1700,56987,1765],{},[1931,56989,3284],{},[898,56991,1662],{},[1700,56993,1768],{},[1931,56995,2343],{},[1785,56997,56998,57000],{},[898,56999,1662],{},[1931,57001,2343],{},[902,57003,57004],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,57007,57009],{"className":57008},[886],[888,57010,57011],{"xmlns":890,"display":28251},[892,57012,57013,57055],{},[895,57014,57015,57017,57019,57021,57023,57025,57027,57029,57031,57037,57043,57045,57047,57049,57051,57053],{},[898,57016,2005],{},[898,57018,4185],{},[1700,57020,1765],{},[1700,57022,1703],{"stretchy":1702},[1931,57024,3284],{},[898,57026,1662],{},[1700,57028,1768],{},[1931,57030,2343],{},[1785,57032,57033,57035],{},[898,57034,1662],{},[1931,57036,2343],{},[1785,57038,57039,57041],{},[1700,57040,1709],{"stretchy":1702},[1700,57042,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,57044,1765],{},[1931,57046,3284],{},[1700,57048,1768],{},[1931,57050,2553],{},[898,57052,1662],{},[898,57054,2196],{"mathvariant":1791},[902,57056,57057],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,57059,9850,57060,8290,57078,57104,57105,4547,57118,57133,57134,57147,57148,21605,57161,4547,57174,57189,57190,57203,57204,57235,57236,57255],{},[883,57061,57063],{"className":57062},[886],[888,57064,57065],{"xmlns":890},[892,57066,57067,57075],{},[895,57068,57069,57071,57073],{},[898,57070,1662],{},[1700,57072,1765],{},[1931,57074,36429],{},[902,57076,57077],{"encoding":904},"Q = 15",[883,57079,57081],{"className":57080},[886],[888,57082,57083],{"xmlns":890},[892,57084,57085,57101],{},[895,57086,57087,57089,57091,57093,57095,57097,57099],{},[898,57088,2005],{},[898,57090,4185],{},[1700,57092,1703],{"stretchy":1702},[1931,57094,36429],{},[1700,57096,1709],{"stretchy":1702},[1700,57098,1765],{},[1931,57100,5399],{},[902,57102,57103],{"encoding":904},"MR(15) = 40",": při množství ",[883,57106,57108],{"className":57107},[886],[888,57109,57110],{"xmlns":890},[892,57111,57112,57116],{},[895,57113,57114],{},[1931,57115,36429],{},[902,57117,36429],{"encoding":904},[883,57119,57121],{"className":57120},[886],[888,57122,57123],{"xmlns":890},[892,57124,57125,57131],{},[895,57126,57127,57129],{},[898,57128,2971],{},[898,57130,4185],{},[902,57132,4285],{"encoding":904}," mění asi ",[883,57135,57137],{"className":57136},[886],[888,57138,57139],{"xmlns":890},[892,57140,57141,57145],{},[895,57142,57143],{},[1931,57144,5399],{},[902,57146,5399],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,57149,57151],{"className":57150},[886],[888,57152,57153],{"xmlns":890},[892,57154,57155,57159],{},[895,57156,57157],{},[898,57158,1662],{},[902,57160,1662],{"encoding":904},[883,57162,57164],{"className":57163},[886],[888,57165,57166],{"xmlns":890},[892,57167,57168,57172],{},[895,57169,57170],{},[1931,57171,1933],{},[902,57173,1933],{"encoding":904},[883,57175,57177],{"className":57176},[886],[888,57178,57179],{"xmlns":890},[892,57180,57181,57187],{},[895,57182,57183,57185],{},[898,57184,2971],{},[898,57186,4185],{},[902,57188,4285],{"encoding":904}," zvýší přibližně o ",[883,57191,57193],{"className":57192},[886],[888,57194,57195],{"xmlns":890},[892,57196,57197,57201],{},[895,57198,57199],{},[1931,57200,5399],{},[902,57202,5399],{"encoding":904},", tj. ze skutečné hodnoty ",[883,57205,57207],{"className":57206},[886],[888,57208,57209],{"xmlns":890},[892,57210,57211,57232],{},[895,57212,57213,57215,57217,57219,57221,57223,57225,57227,57229],{},[898,57214,2971],{},[898,57216,4185],{},[1700,57218,1703],{"stretchy":1702},[1931,57220,36429],{},[1700,57222,1709],{"stretchy":1702},[1700,57224,1765],{},[1931,57226,1933],{},[1781,57228,1783],{},[1931,57230,57231],{},"050",[902,57233,57234],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,57237,57239],{"className":57238},[886],[888,57240,57241],{"xmlns":890},[892,57242,57243,57252],{},[895,57244,57245,57247,57249],{},[1931,57246,1933],{},[1781,57248,1783],{},[1931,57250,57251],{},"090",[902,57253,57254],{"encoding":904},"1\\,090",". Skutečná změna je",[883,57257,57259],{"className":57258},[886],[888,57260,57261],{"xmlns":890,"display":28251},[892,57262,57263,57317],{},[895,57264,57265,57267,57269,57271,57273,57275,57277,57279,57281,57283,57285,57287,57289,57291,57293,57295,57297,57299,57301,57304,57306,57308,57310,57312,57314],{},[898,57266,3084],{"mathvariant":1791},[898,57268,2971],{},[898,57270,4185],{},[1700,57272,1765],{},[898,57274,2971],{},[898,57276,4185],{},[1700,57278,1703],{"stretchy":1702},[1931,57280,42047],{},[1700,57282,1709],{"stretchy":1702},[1700,57284,1768],{},[898,57286,2971],{},[898,57288,4185],{},[1700,57290,1703],{"stretchy":1702},[1931,57292,36429],{},[1700,57294,1709],{"stretchy":1702},[1700,57296,1765],{},[1931,57298,1933],{},[1781,57300,1783],{},[1931,57302,57303],{},"088",[1700,57305,1768],{},[1931,57307,1933],{},[1781,57309,1783],{},[1931,57311,57231],{},[1700,57313,1765],{},[1931,57315,57316],{},"38.",[902,57318,57319],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,57321,57322,57323,1343,57349,3122,57375,57390,57391,57406],{},"Podobně ",[883,57324,57326],{"className":57325},[886],[888,57327,57328],{"xmlns":890},[892,57329,57330,57346],{},[895,57331,57332,57334,57336,57338,57340,57342,57344],{},[898,57333,2005],{},[898,57335,4185],{},[1700,57337,1703],{"stretchy":1702},[1931,57339,42047],{},[1700,57341,1709],{"stretchy":1702},[1700,57343,1765],{},[1931,57345,5753],{},[902,57347,57348],{"encoding":904},"MR(16) = 36",[883,57350,57352],{"className":57351},[886],[888,57353,57354],{"xmlns":890},[892,57355,57356,57372],{},[895,57357,57358,57360,57362,57364,57366,57368,57370],{},[898,57359,2005],{},[898,57361,4185],{},[1700,57363,1703],{"stretchy":1702},[1931,57365,9223],{},[1700,57367,1709],{"stretchy":1702},[1700,57369,1765],{},[1931,57371,9223],{},[902,57373,57374],{"encoding":904},"MR(20) = 20",[883,57376,57378],{"className":57377},[886],[888,57379,57380],{"xmlns":890},[892,57381,57382,57388],{},[895,57383,57384,57386],{},[898,57385,2005],{},[898,57387,4185],{},[902,57389,6822],{"encoding":904}," je klesající funkce — rychlost změny ",[883,57392,57394],{"className":57393},[886],[888,57395,57396],{"xmlns":890},[892,57397,57398,57404],{},[895,57399,57400,57402],{},[898,57401,2971],{},[898,57403,4185],{},[902,57405,4285],{"encoding":904}," s růstem množství klesá.",[198,57408,57410],{"id":57409},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,57412,57413],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,57415,57417],{"className":57416},[886],[888,57418,57419],{"xmlns":890,"display":28251},[892,57420,57421,57490],{},[20939,57422,57423],{"width":28256},[20944,57424,57425,57427,57483,57485],{},[20947,57426],{"width":28261},[20947,57428,57429],{},[895,57430,57431,57433,57435,57437,57439,57441,57443,57445,57447,57449,57451,57453,57455,57457,57463,57465,57467,57469,57471,57473,57475,57477,57479,57481],{},[898,57432,3084],{"mathvariant":1791},[898,57434,2971],{},[898,57436,4185],{},[1781,57438,4175],{},[1700,57440,2927],{},[1781,57442,4175],{},[898,57444,2406],{"mathvariant":1791},[898,57446,2971],{},[898,57448,4185],{},[1700,57450,1765],{},[1700,57452,1703],{"stretchy":1702},[898,57454,2971],{},[898,57456,4185],{},[1785,57458,57459,57461],{},[1700,57460,1709],{"stretchy":1702},[1700,57462,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1781,57464,1783],{},[898,57466,2406],{"mathvariant":1791},[898,57468,1662],{},[1700,57470,1765],{},[898,57472,2005],{},[898,57474,4185],{},[1781,57476,1783],{},[898,57478,2406],{"mathvariant":1791},[898,57480,1662],{},[1700,57482,1732],{"separator":1731},[20947,57484],{"width":28261},[20947,57486,57487],{},[1781,57488,57489],{},"(3.3)",[902,57491,57492],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,57494,57495],{},"schematicky:",[883,57497,57499],{"className":57498},[886],[888,57500,57501],{"xmlns":890,"display":28251},[892,57502,57503,57611],{},[895,57504,57505,57543,57545,57547,57549,57578,57581,57609],{},[895,57506,57507,57510,57516,57519,57525,57528,57534,57540],{},[1781,57508,57509],{},"zm",[8574,57511,57512,57514],{"accent":1731},[1781,57513,45917],{},[1700,57515,25243],{},[1781,57517,57518],{},"na celkov",[8574,57520,57521,57523],{"accent":1731},[1781,57522,45917],{},[1700,57524,25162],{},[1781,57526,57527],{},"ho p",[8574,57529,57530,57532],{"accent":1731},[1781,57531,12226],{},[1700,57533,25243],{},[8574,57535,57536,57538],{"accent":1731},[1781,57537,25231],{},[1700,57539,25162],{},[1781,57541,57542],{},"jmu",[1781,57544,4175],{},[1700,57546,2927],{},[1781,57548,4175],{},[895,57550,57551,57554,57560,57563,57569,57575],{},[1781,57552,57553],{},"mezn",[8574,57555,57556,57558],{"accent":1731},[1781,57557,25231],{},[1700,57559,25162],{},[1781,57561,57562],{}," p",[8574,57564,57565,57567],{"accent":1731},[1781,57566,12226],{},[1700,57568,25243],{},[8574,57570,57571,57573],{"accent":1731},[1781,57572,25231],{},[1700,57574,25162],{},[1781,57576,57577],{},"jem",[1700,57579,57580],{},"×",[895,57582,57583,57585,57591,57594,57600,57603],{},[1781,57584,57509],{},[8574,57586,57587,57589],{"accent":1731},[1781,57588,45917],{},[1700,57590,25243],{},[1781,57592,57593],{},"na mno",[8574,57595,57596,57598],{"accent":1731},[1781,57597,9781],{},[1700,57599,25243],{},[1781,57601,57602],{},"stv",[8574,57604,57605,57607],{"accent":1731},[1781,57606,25231],{},[1700,57608,25162],{},[898,57610,2196],{"mathvariant":1791},[902,57612,57613],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,57615,57616,57617,57632],{},"Pro porovnání skutečná změna ",[883,57618,57620],{"className":57619},[886],[888,57621,57622],{"xmlns":890},[892,57623,57624,57630],{},[895,57625,57626,57628],{},[898,57627,2971],{},[898,57629,4185],{},[902,57631,4285],{"encoding":904}," je",[883,57634,57636],{"className":57635},[886],[888,57637,57638],{"xmlns":890,"display":28251},[892,57639,57640,57695],{},[20939,57641,57642],{"width":28256},[20944,57643,57644,57646,57688,57690],{},[20947,57645],{"width":28261},[20947,57647,57648],{},[895,57649,57650,57652,57654,57656,57658,57660,57662,57664,57666,57668,57670,57672,57674,57676,57678,57680,57682,57684,57686],{},[898,57651,3084],{"mathvariant":1791},[898,57653,2971],{},[898,57655,4185],{},[1700,57657,1765],{},[898,57659,2971],{},[898,57661,4185],{},[1700,57663,1703],{"stretchy":1702},[898,57665,1662],{},[1700,57667,1897],{},[898,57669,2406],{"mathvariant":1791},[898,57671,1662],{},[1700,57673,1709],{"stretchy":1702},[1700,57675,1768],{},[898,57677,2971],{},[898,57679,4185],{},[1700,57681,1703],{"stretchy":1702},[898,57683,1662],{},[1700,57685,1709],{"stretchy":1702},[898,57687,2196],{"mathvariant":1791},[20947,57689],{"width":28261},[20947,57691,57692],{},[1781,57693,57694],{},"(3.4)",[902,57696,57697],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[37533,57699,57701],{"id":57700},"příklad-33","Příklad 3.3",[724,57703,57704,57706,57707,57737,57738,2854,57753,2868,57766,2882,57779,57793],{},[38,57705,56171],{}," Pro ",[883,57708,57710],{"className":57709},[886],[888,57711,57712],{"xmlns":890},[892,57713,57714,57734],{},[895,57715,57716,57718,57720,57722,57724,57726,57728],{},[898,57717,2971],{},[898,57719,4185],{},[1700,57721,1765],{},[1931,57723,3284],{},[898,57725,1662],{},[1700,57727,1768],{},[1785,57729,57730,57732],{},[898,57731,1662],{},[1931,57733,2343],{},[902,57735,57736],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,57739,57741],{"className":57740},[886],[888,57742,57743],{"xmlns":890},[892,57744,57745,57751],{},[895,57746,57747,57749],{},[898,57748,2971],{},[898,57750,4185],{},[902,57752,4285],{"encoding":904},[883,57754,57756],{"className":57755},[886],[888,57757,57758],{"xmlns":890},[892,57759,57760,57764],{},[895,57761,57762],{},[898,57763,1662],{},[902,57765,1662],{"encoding":904},[883,57767,57769],{"className":57768},[886],[888,57770,57771],{"xmlns":890},[892,57772,57773,57777],{},[895,57774,57775],{},[1931,57776,3320],{},[902,57778,3320],{"encoding":904},[883,57780,57782],{"className":57781},[886],[888,57783,57784],{"xmlns":890},[892,57785,57786,57791],{},[895,57787,57788],{},[1931,57789,57790],{},"63",[902,57792,57790],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,57795,57796,2106,57798,57823,57824,1343,57842,2901],{},[38,57797,22955],{},[883,57799,57801],{"className":57800},[886],[888,57802,57803],{"xmlns":890},[892,57804,57805,57821],{},[895,57806,57807,57809,57811,57813,57815,57817,57819],{},[898,57808,2005],{},[898,57810,4185],{},[1700,57812,1765],{},[1931,57814,3284],{},[1700,57816,1768],{},[1931,57818,2343],{},[898,57820,1662],{},[902,57822,11620],{"encoding":904},", tedy při ",[883,57825,57827],{"className":57826},[886],[888,57828,57829],{"xmlns":890},[892,57830,57831,57839],{},[895,57832,57833,57835,57837],{},[898,57834,1662],{},[1700,57836,1765],{},[1931,57838,3320],{},[902,57840,57841],{"encoding":904},"Q = 60",[883,57843,57845],{"className":57844},[886],[888,57846,57847],{"xmlns":890},[892,57848,57849,57859],{},[895,57850,57851,57853,57855,57857],{},[898,57852,2406],{"mathvariant":1791},[898,57854,1662],{},[1700,57856,1765],{},[1931,57858,2385],{},[902,57860,57861],{"encoding":904},"\\mathrm{d}Q = 3",[883,57863,57865],{"className":57864},[886],[888,57866,57867],{"xmlns":890,"display":28251},[892,57868,57869,57900],{},[895,57870,57871,57873,57875,57877,57879,57881,57883,57885,57887,57889,57891,57893,57895,57897],{},[898,57872,2406],{"mathvariant":1791},[898,57874,2971],{},[898,57876,4185],{},[1700,57878,1765],{},[1700,57880,1703],{"stretchy":1702},[1931,57882,3284],{},[1700,57884,1768],{},[1931,57886,4237],{},[1700,57888,1709],{"stretchy":1702},[1700,57890,2065],{},[1931,57892,2385],{},[1700,57894,1765],{},[1700,57896,1768],{},[1931,57898,57899],{},"60.",[902,57901,57902],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,57904,57905,57906,57936,57937,57956],{},"Celkový příjem klesne z ",[883,57907,57909],{"className":57908},[886],[888,57910,57911],{"xmlns":890},[892,57912,57913,57933],{},[895,57914,57915,57917,57919,57921,57923,57925,57927,57929,57931],{},[898,57916,2971],{},[898,57918,4185],{},[1700,57920,1703],{"stretchy":1702},[1931,57922,3320],{},[1700,57924,1709],{"stretchy":1702},[1700,57926,1765],{},[1931,57928,2343],{},[1781,57930,1783],{},[1931,57932,20327],{},[902,57934,57935],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,57938,57940],{"className":57939},[886],[888,57941,57942],{"xmlns":890},[892,57943,57944,57953],{},[895,57945,57946,57948,57950],{},[1931,57947,2343],{},[1781,57949,1783],{},[1931,57951,57952],{},"340",[902,57954,57955],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,57958,57960],{"className":57959},[886],[888,57961,57962],{"xmlns":890,"display":28251},[892,57963,57964,58022],{},[895,57965,57966,57968,57970,57972,57974,57976,57978,57980,57982,57984,57986,57988,57990,57992,57994,57996,57998,58000,58002,58005,58007,58009,58011,58013,58015,58017,58020],{},[898,57967,3084],{"mathvariant":1791},[898,57969,2971],{},[898,57971,4185],{},[1700,57973,1765],{},[898,57975,2971],{},[898,57977,4185],{},[1700,57979,1703],{"stretchy":1702},[1931,57981,57790],{},[1700,57983,1709],{"stretchy":1702},[1700,57985,1768],{},[898,57987,2971],{},[898,57989,4185],{},[1700,57991,1703],{"stretchy":1702},[1931,57993,3320],{},[1700,57995,1709],{"stretchy":1702},[1700,57997,1765],{},[1931,57999,2343],{},[1781,58001,1783],{},[1931,58003,58004],{},"331",[1700,58006,1768],{},[1931,58008,2343],{},[1781,58010,1783],{},[1931,58012,20327],{},[1700,58014,1765],{},[1700,58016,1768],{},[1931,58018,58019],{},"69",[1700,58021,1732],{"separator":1731},[902,58023,58024],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,58026,58027,58028,58043,58044,2196],{},"tj. ",[883,58029,58031],{"className":58030},[886],[888,58032,58033],{"xmlns":890},[892,58034,58035,58041],{},[895,58036,58037,58039],{},[898,58038,2971],{},[898,58040,4185],{},[902,58042,4285],{"encoding":904}," klesne na ",[883,58045,58047],{"className":58046},[886],[888,58048,58049],{"xmlns":890},[892,58050,58051,58059],{},[895,58052,58053,58055,58057],{},[1931,58054,2343],{},[1781,58056,1783],{},[1931,58058,58004],{},[902,58060,58061],{"encoding":904},"2\\,331",[198,58063,58065],{"id":58064},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,58067,58068,58069,10577,58092,31765],{},"Obecně pro lineární poptávku ",[883,58070,58072],{"className":58071},[886],[888,58073,58074],{"xmlns":890},[892,58075,58076,58090],{},[895,58077,58078,58080,58082,58084,58086,58088],{},[898,58079,1677],{},[1700,58081,1765],{},[898,58083,207],{},[898,58085,1662],{},[1700,58087,1897],{},[898,58089,1879],{},[902,58091,37245],{"encoding":904},[883,58093,58095],{"className":58094},[886],[888,58096,58097],{"xmlns":890},[892,58098,58099,58121],{},[895,58100,58101,58103,58105,58107,58109,58115,58117,58119],{},[898,58102,2971],{},[898,58104,4185],{},[1700,58106,1765],{},[898,58108,207],{},[1785,58110,58111,58113],{},[898,58112,1662],{},[1931,58114,2343],{},[1700,58116,1897],{},[898,58118,1879],{},[898,58120,1662],{},[902,58122,58123],{"encoding":904},"TR = aQ^2 + bQ",[883,58125,58127],{"className":58126},[886],[888,58128,58129],{"xmlns":890,"display":28251},[892,58130,58131,58151],{},[895,58132,58133,58135,58137,58139,58141,58143,58145,58147,58149],{},[898,58134,2005],{},[898,58136,4185],{},[1700,58138,1765],{},[1931,58140,2343],{},[898,58142,207],{},[898,58144,1662],{},[1700,58146,1897],{},[898,58148,1879],{},[898,58150,2196],{"mathvariant":1791},[902,58152,58153],{"encoding":904},"MR = 2aQ + b.",[724,58155,58156,58157,58172,58173,58188,58189,58202,58203,10208,58206,58222,58223,58236,58237,58252,58253,58268,58269,58284,58285,2821,58298,58328,58329,58348,58349,58364],{},"Křivky ",[883,58158,58160],{"className":58159},[886],[888,58161,58162],{"xmlns":890},[892,58163,58164,58170],{},[895,58165,58166,58168],{},[898,58167,2005],{},[898,58169,4185],{},[902,58171,6822],{"encoding":904}," a poptávky (resp. ",[883,58174,58176],{"className":58175},[886],[888,58177,58178],{"xmlns":890},[892,58179,58180,58186],{},[895,58181,58182,58184],{},[898,58183,1862],{},[898,58185,4185],{},[902,58187,55629],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,58190,58192],{"className":58191},[886],[888,58193,58194],{"xmlns":890},[892,58195,58196,58200],{},[895,58197,58198],{},[898,58199,1879],{},[902,58201,1879],{"encoding":904},", přičemž ",[38,58204,58205],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,58207,58209],{"className":58208},[886],[888,58210,58211],{"xmlns":890},[892,58212,58213,58219],{},[895,58214,58215,58217],{},[1931,58216,2343],{},[898,58218,207],{},[902,58220,58221],{"encoding":904},"2a"," vs. ",[883,58224,58226],{"className":58225},[886],[888,58227,58228],{"xmlns":890},[892,58229,58230,58234],{},[895,58231,58232],{},[898,58233,207],{},[902,58235,207],{"encoding":904},", obrázek 3.2). ",[883,58238,58240],{"className":58239},[886],[888,58241,58242],{"xmlns":890},[892,58243,58244,58250],{},[895,58245,58246,58248],{},[898,58247,2005],{},[898,58249,4185],{},[902,58251,6822],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,58254,58256],{"className":58255},[886],[888,58257,58258],{"xmlns":890},[892,58259,58260,58266],{},[895,58261,58262,58264],{},[898,58263,2971],{},[898,58265,4185],{},[902,58267,4285],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,58270,58272],{"className":58271},[886],[888,58273,58274],{"xmlns":890},[892,58275,58276,58282],{},[895,58277,58278,58280],{},[898,58279,2005],{},[898,58281,4185],{},[902,58283,6822],{"encoding":904}," osu ",[883,58286,58288],{"className":58287},[886],[888,58289,58290],{"xmlns":890},[892,58291,58292,58296],{},[895,58293,58294],{},[898,58295,1662],{},[902,58297,1662],{"encoding":904},[883,58299,58301],{"className":58300},[886],[888,58302,58303],{"xmlns":890},[892,58304,58305,58325],{},[895,58306,58307,58309,58311,58313],{},[898,58308,1662],{},[1700,58310,1765],{},[1700,58312,1768],{},[1770,58314,58315],{"scriptlevel":1772,"displaystyle":1702},[1774,58316,58317,58319],{},[898,58318,1879],{},[895,58320,58321,58323],{},[1931,58322,2343],{},[898,58324,207],{},[902,58326,58327],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,58330,58332],{"className":58331},[886],[888,58333,58334],{"xmlns":890},[892,58335,58336,58346],{},[895,58337,58338,58340,58342,58344],{},[898,58339,2005],{},[898,58341,4185],{},[1700,58343,1765],{},[1931,58345,1772],{},[902,58347,7272],{"encoding":904},", a dále ",[883,58350,58352],{"className":58351},[886],[888,58353,58354],{"xmlns":890},[892,58355,58356,58362],{},[895,58357,58358,58360],{},[898,58359,2971],{},[898,58361,4185],{},[902,58363,4285],{"encoding":904}," klesá.",[724,58366,58367,58368,58374,58375,58407,58408,58436],{},"V případě ",[38,58369,58370],{},[207,58371,58373],{"className":58372,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,58376,58378],{"className":58377},[886],[888,58379,58380],{"xmlns":890},[892,58381,58382,58404],{},[895,58383,58384,58386,58388,58390,58392,58394,58396,58398],{},[898,58385,1677],{},[1700,58387,1765],{},[898,58389,4374],{},[1700,58391,1703],{"stretchy":1702},[898,58393,1662],{},[1700,58395,1709],{"stretchy":1702},[1700,58397,1765],{},[1785,58399,58400,58402],{},[898,58401,1677],{},[1700,58403,4543],{},[902,58405,58406],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,58409,58411],{"className":58410},[886],[888,58412,58413],{"xmlns":890},[892,58414,58415,58433],{},[895,58416,58417,58419,58421,58423,58425,58427],{},[898,58418,2971],{},[898,58420,4185],{},[1700,58422,1765],{},[898,58424,1662],{},[1700,58426,2065],{},[1785,58428,58429,58431],{},[898,58430,1677],{},[1700,58432,4543],{},[902,58434,58435],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,58438,58440],{"className":58439},[886],[888,58441,58442],{"xmlns":890,"display":28251},[892,58443,58444,58486],{},[895,58445,58446,58448,58450,58452,58454,58456,58458,58464,58466,58468,58482,58484],{},[898,58447,2005],{},[898,58449,4185],{},[1700,58451,1765],{},[898,58453,1862],{},[898,58455,4185],{},[1700,58457,1765],{},[1785,58459,58460,58462],{},[898,58461,1677],{},[1700,58463,4543],{},[6066,58465],{"width":15469},[1700,58467,1703],{"stretchy":1702},[895,58469,58470,58473,58479],{},[1781,58471,58472],{},"obr",[8574,58474,58475,58477],{"accent":1731},[1781,58476,207],{},[1700,58478,25162],{},[1781,58480,58481],{},"zek 3.4",[1700,58483,1709],{"stretchy":1702},[898,58485,2196],{"mathvariant":1791},[902,58487,58488],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,58490,58491],{},[614,58492,58493,58494,2114,58520,58548,58549,58562,58563,58578,58579,3911,58592,1343,58618,3911,58633,2196],{},"Obrázek 3.2: Přímky ",[883,58495,58497],{"className":58496},[886],[888,58498,58499],{"xmlns":890},[892,58500,58501,58517],{},[895,58502,58503,58505,58507,58509,58511,58513,58515],{},[898,58504,1862],{},[898,58506,4185],{},[1700,58508,1765],{},[898,58510,207],{},[898,58512,1662],{},[1700,58514,1897],{},[898,58516,1879],{},[902,58518,58519],{"encoding":904},"AR = aQ + b",[883,58521,58523],{"className":58522},[886],[888,58524,58525],{"xmlns":890},[892,58526,58527,58545],{},[895,58528,58529,58531,58533,58535,58537,58539,58541,58543],{},[898,58530,2005],{},[898,58532,4185],{},[1700,58534,1765],{},[1931,58536,2343],{},[898,58538,207],{},[898,58540,1662],{},[1700,58542,1897],{},[898,58544,1879],{},[902,58546,58547],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,58550,58552],{"className":58551},[886],[888,58553,58554],{"xmlns":890},[892,58555,58556,58560],{},[895,58557,58558],{},[898,58559,1879],{},[902,58561,1879],{"encoding":904}," se svislou osou, ",[883,58564,58566],{"className":58565},[886],[888,58567,58568],{"xmlns":890},[892,58569,58570,58576],{},[895,58571,58572,58574],{},[898,58573,2005],{},[898,58575,4185],{},[902,58577,6822],{"encoding":904}," protíná osu ",[883,58580,58582],{"className":58581},[886],[888,58583,58584],{"xmlns":890},[892,58585,58586,58590],{},[895,58587,58588],{},[898,58589,1662],{},[902,58591,1662],{"encoding":904},[883,58593,58595],{"className":58594},[886],[888,58596,58597],{"xmlns":890},[892,58598,58599,58615],{},[895,58600,58601,58603],{},[1700,58602,1768],{},[1770,58604,58605],{"scriptlevel":1772,"displaystyle":1702},[1774,58606,58607,58609],{},[898,58608,1879],{},[895,58610,58611,58613],{},[1931,58612,2343],{},[898,58614,207],{},[902,58616,58617],{"encoding":904},"-\\tfrac{b}{2a}",[883,58619,58621],{"className":58620},[886],[888,58622,58623],{"xmlns":890},[892,58624,58625,58631],{},[895,58626,58627,58629],{},[898,58628,1862],{},[898,58630,4185],{},[902,58632,55629],{"encoding":904},[883,58634,58636],{"className":58635},[886],[888,58637,58638],{"xmlns":890},[892,58639,58640,58652],{},[895,58641,58642,58644],{},[1700,58643,1768],{},[1770,58645,58646],{"scriptlevel":1772,"displaystyle":1702},[1774,58647,58648,58650],{},[898,58649,1879],{},[898,58651,207],{},[902,58653,58654],{"encoding":904},"-\\tfrac{b}{a}",[724,58656,58657],{},[614,58658,58659,58660,58691,58692,58721,58722,2196],{},"Obrázek 3.3: Parabola ",[883,58661,58663],{"className":58662},[886],[888,58664,58665],{"xmlns":890},[892,58666,58667,58689],{},[895,58668,58669,58671,58673,58675,58677,58683,58685,58687],{},[898,58670,2971],{},[898,58672,4185],{},[1700,58674,1765],{},[898,58676,207],{},[1785,58678,58679,58681],{},[898,58680,1662],{},[1931,58682,2343],{},[1700,58684,1897],{},[898,58686,1879],{},[898,58688,1662],{},[902,58690,58123],{"encoding":904}," s maximem v ",[883,58693,58695],{"className":58694},[886],[888,58696,58697],{"xmlns":890},[892,58698,58699,58719],{},[895,58700,58701,58703,58705,58707],{},[898,58702,1662],{},[1700,58704,1765],{},[1700,58706,1768],{},[1770,58708,58709],{"scriptlevel":1772,"displaystyle":1702},[1774,58710,58711,58713],{},[898,58712,1879],{},[895,58714,58715,58717],{},[1931,58716,2343],{},[898,58718,207],{},[902,58720,58327],{"encoding":904}," a nulou v ",[883,58723,58725],{"className":58724},[886],[888,58726,58727],{"xmlns":890},[892,58728,58729,58745],{},[895,58730,58731,58733,58735,58737],{},[898,58732,1662],{},[1700,58734,1765],{},[1700,58736,1768],{},[1770,58738,58739],{"scriptlevel":1772,"displaystyle":1702},[1774,58740,58741,58743],{},[898,58742,1879],{},[898,58744,207],{},[902,58746,58747],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,58749,58750],{},[614,58751,58752,58753,2196],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,58754,58756],{"className":58755},[886],[888,58757,58758],{"xmlns":890},[892,58759,58760,58780],{},[895,58761,58762,58764,58766,58768,58770,58772,58774],{},[898,58763,1862],{},[898,58765,4185],{},[1700,58767,1765],{},[898,58769,2005],{},[898,58771,4185],{},[1700,58773,1765],{},[1785,58775,58776,58778],{},[898,58777,1677],{},[1700,58779,4543],{},[902,58781,58782],{"encoding":904},"AR = MR = P^*",[115,58784,58786],{"id":58785},"náklady-firmy","Náklady firmy",[198,58788,58790],{"id":58789},"celkové-náklady","Celkové náklady",[724,58792,58793,2106,58795,10208,58810,58813,58814,58827],{},[38,58794,58790],{},[883,58796,58798],{"className":58797},[886],[888,58799,58800],{"xmlns":890},[892,58801,58802,58808],{},[895,58803,58804,58806],{},[898,58805,2971],{},[898,58807,2974],{},[902,58809,3436],{"encoding":904},[38,58811,58812],{},"total cost",") jsou veškeré náklady na realizaci ",[883,58815,58817],{"className":58816},[886],[888,58818,58819],{"xmlns":890},[892,58820,58821,58825],{},[895,58822,58823],{},[898,58824,1662],{},[902,58826,1662],{"encoding":904}," jednotek produkce:",[883,58829,58831],{"className":58830},[886],[888,58832,58833],{"xmlns":890,"display":28251},[892,58834,58835,58890],{},[20939,58836,58837],{"width":28256},[20944,58838,58839,58841,58883,58885],{},[20947,58840],{"width":28261},[20947,58842,58843],{},[895,58844,58845,58847,58849,58851,58853,58855,58857,58859,58861,58863,58865,58867,58869,58871,58873,58875,58877,58879,58881],{},[898,58846,2971],{},[898,58848,2974],{},[1700,58850,1765],{},[898,58852,2971],{},[898,58854,2974],{},[1700,58856,1703],{"stretchy":1702},[898,58858,1662],{},[1700,58860,1709],{"stretchy":1702},[1700,58862,1765],{},[898,58864,10619],{},[898,58866,2974],{},[1700,58868,1897],{},[898,58870,2971],{},[898,58872,40524],{},[898,58874,2974],{},[1700,58876,1703],{"stretchy":1702},[898,58878,1662],{},[1700,58880,1709],{"stretchy":1702},[1700,58882,1732],{"separator":1731},[20947,58884],{"width":28261},[20947,58886,58887],{},[1781,58888,58889],{},"(3.5)",[902,58891,58892],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,58894,4499,58895,58910,58911,10208,58914,12313,58917,58910,58941,10208,58944,58947],{},[883,58896,58898],{"className":58897},[886],[888,58899,58900],{"xmlns":890},[892,58901,58902,58908],{},[895,58903,58904,58906],{},[898,58905,10619],{},[898,58907,2974],{},[902,58909,55675],{"encoding":904}," jsou ",[38,58912,58913],{},"fixní náklady",[38,58915,58916],{},"fixed cost",[883,58918,58920],{"className":58919},[886],[888,58921,58922],{"xmlns":890},[892,58923,58924,58938],{},[895,58925,58926,58928,58930,58932,58934,58936],{},[898,58927,2971],{},[898,58929,40524],{},[898,58931,2974],{},[1700,58933,1703],{"stretchy":1702},[898,58935,1662],{},[1700,58937,1709],{"stretchy":1702},[902,58939,58940],{"encoding":904},"TVC(Q)",[38,58942,58943],{},"celkové variabilní náklady",[38,58945,58946],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,58949,58951],{"id":58950},"průměrné-náklady","Průměrné náklady",[724,58953,58954,2106,58956,10208,58971,58974],{},[38,58955,58951],{},[883,58957,58959],{"className":58958},[886],[888,58960,58961],{"xmlns":890},[892,58962,58963,58969],{},[895,58964,58965,58967],{},[898,58966,1862],{},[898,58968,2974],{},[902,58970,55744],{"encoding":904},[38,58972,58973],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,58976,58978],{"className":58977},[886],[888,58979,58980],{"xmlns":890,"display":28251},[892,58981,58982,59061],{},[20939,58983,58984],{"width":28256},[20944,58985,58986,58988,59054,59056],{},[20947,58987],{"width":28261},[20947,58989,58990],{},[895,58991,58992,58994,58996,58998,59000,59002,59004,59006,59008,59010,59020,59022,59032,59034,59052],{},[898,58993,1862],{},[898,58995,2974],{},[1700,58997,1765],{},[898,58999,1862],{},[898,59001,2974],{},[1700,59003,1703],{"stretchy":1702},[898,59005,1662],{},[1700,59007,1709],{"stretchy":1702},[1700,59009,1765],{},[1774,59011,59012,59018],{},[895,59013,59014,59016],{},[898,59015,2971],{},[898,59017,2974],{},[898,59019,1662],{},[1700,59021,1765],{},[1774,59023,59024,59030],{},[895,59025,59026,59028],{},[898,59027,10619],{},[898,59029,2974],{},[898,59031,1662],{},[1700,59033,1897],{},[1774,59035,59036,59050],{},[895,59037,59038,59040,59042,59044,59046,59048],{},[898,59039,2971],{},[898,59041,40524],{},[898,59043,2974],{},[1700,59045,1703],{"stretchy":1702},[898,59047,1662],{},[1700,59049,1709],{"stretchy":1702},[898,59051,1662],{},[1700,59053,1732],{"separator":1731},[20947,59055],{"width":28261},[20947,59057,59058],{},[1781,59059,59060],{},"(3.6)",[902,59062,59063],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,59065,4499,59066,58910,59090,2106,59093,10208,59110,12313,59113,58910,59145,2106,59148,10208,59165,3345],{},[883,59067,59069],{"className":59068},[886],[888,59070,59071],{"xmlns":890},[892,59072,59073,59087],{},[895,59074,59075],{},[1770,59076,59077],{"scriptlevel":1772,"displaystyle":1702},[1774,59078,59079,59085],{},[895,59080,59081,59083],{},[898,59082,10619],{},[898,59084,2974],{},[898,59086,1662],{},[902,59088,59089],{"encoding":904},"\\tfrac{FC}{Q}",[38,59091,59092],{},"průměrné fixní náklady",[883,59094,59096],{"className":59095},[886],[888,59097,59098],{"xmlns":890},[892,59099,59100,59108],{},[895,59101,59102,59104,59106],{},[898,59103,1862],{},[898,59105,10619],{},[898,59107,2974],{},[902,59109,55711],{"encoding":904},[38,59111,59112],{},"average fixed cost",[883,59114,59116],{"className":59115},[886],[888,59117,59118],{"xmlns":890},[892,59119,59120,59142],{},[895,59121,59122],{},[1770,59123,59124],{"scriptlevel":1772,"displaystyle":1702},[1774,59125,59126,59140],{},[895,59127,59128,59130,59132,59134,59136,59138],{},[898,59129,2971],{},[898,59131,40524],{},[898,59133,2974],{},[1700,59135,1703],{"stretchy":1702},[898,59137,1662],{},[1700,59139,1709],{"stretchy":1702},[898,59141,1662],{},[902,59143,59144],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,59146,59147],{},"průměrné variabilní náklady",[883,59149,59151],{"className":59150},[886],[888,59152,59153],{"xmlns":890},[892,59154,59155,59163],{},[895,59156,59157,59159,59161],{},[898,59158,1862],{},[898,59160,40524],{},[898,59162,2974],{},[902,59164,55495],{"encoding":904},[38,59166,59167],{},"average variable cost",[883,59169,59171],{"className":59170},[886],[888,59172,59173],{"xmlns":890,"display":28251},[892,59174,59175,59234],{},[20939,59176,59177],{"width":28256},[20944,59178,59179,59181,59227,59229],{},[20947,59180],{"width":28261},[20947,59182,59183],{},[895,59184,59185,59187,59189,59191,59193,59195,59197,59199,59201,59203,59205,59207,59225],{},[898,59186,1862],{},[898,59188,40524],{},[898,59190,2974],{},[1700,59192,1765],{},[898,59194,1862],{},[898,59196,40524],{},[898,59198,2974],{},[1700,59200,1703],{"stretchy":1702},[898,59202,1662],{},[1700,59204,1709],{"stretchy":1702},[1700,59206,1765],{},[1774,59208,59209,59223],{},[895,59210,59211,59213,59215,59217,59219,59221],{},[898,59212,2971],{},[898,59214,40524],{},[898,59216,2974],{},[1700,59218,1703],{"stretchy":1702},[898,59220,1662],{},[1700,59222,1709],{"stretchy":1702},[898,59224,1662],{},[898,59226,2196],{"mathvariant":1791},[20947,59228],{"width":28261},[20947,59230,59231],{},[1781,59232,59233],{},"(3.7)",[902,59235,59236],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[37533,59238,59240],{"id":59239},"příklad-34","Příklad 3.4",[724,59242,59243,57706,59245,2114,59270,56209,59294,2114,59309,59324,59325,2196],{},[38,59244,56171],{},[883,59246,59248],{"className":59247},[886],[888,59249,59250],{"xmlns":890},[892,59251,59252,59267],{},[895,59253,59254,59256,59258,59260,59262,59264],{},[898,59255,10619],{},[898,59257,2974],{},[1700,59259,1765],{},[1931,59261,1933],{},[1781,59263,1783],{},[1931,59265,59266],{},"000",[902,59268,59269],{"encoding":904},"FC = 1\\,000",[883,59271,59273],{"className":59272},[886],[888,59274,59275],{"xmlns":890},[892,59276,59277,59291],{},[895,59278,59279,59281,59283,59285,59287,59289],{},[898,59280,2971],{},[898,59282,40524],{},[898,59284,2974],{},[1700,59286,1765],{},[1931,59288,2553],{},[898,59290,1662],{},[902,59292,59293],{"encoding":904},"TVC = 4Q",[883,59295,59297],{"className":59296},[886],[888,59298,59299],{"xmlns":890},[892,59300,59301,59307],{},[895,59302,59303,59305],{},[898,59304,2971],{},[898,59306,2974],{},[902,59308,3436],{"encoding":904},[883,59310,59312],{"className":59311},[886],[888,59313,59314],{"xmlns":890},[892,59315,59316,59322],{},[895,59317,59318,59320],{},[898,59319,1862],{},[898,59321,2974],{},[902,59323,55744],{"encoding":904}," a jejich chování s rostoucím ",[883,59326,59328],{"className":59327},[886],[888,59329,59330],{"xmlns":890},[892,59331,59332,59336],{},[895,59333,59334],{},[898,59335,1662],{},[902,59337,1662],{"encoding":904},[724,59339,59340,2106,59342,2114,59372,59408,59409,4547,59422,59437,59438,2901],{},[38,59341,22955],{},[883,59343,59345],{"className":59344},[886],[888,59346,59347],{"xmlns":890},[892,59348,59349,59369],{},[895,59350,59351,59353,59355,59357,59359,59361,59363,59365,59367],{},[898,59352,2971],{},[898,59354,2974],{},[1700,59356,1765],{},[1931,59358,1933],{},[1781,59360,1783],{},[1931,59362,59266],{},[1700,59364,1897],{},[1931,59366,2553],{},[898,59368,1662],{},[902,59370,59371],{"encoding":904},"TC = 1\\,000 + 4Q",[883,59373,59375],{"className":59374},[886],[888,59376,59377],{"xmlns":890},[892,59378,59379,59405],{},[895,59380,59381,59383,59385,59387,59401,59403],{},[898,59382,1862],{},[898,59384,2974],{},[1700,59386,1765],{},[1770,59388,59389],{"scriptlevel":1772,"displaystyle":1702},[1774,59390,59391,59399],{},[895,59392,59393,59395,59397],{},[1931,59394,1933],{},[1781,59396,1783],{},[1931,59398,59266],{},[898,59400,1662],{},[1700,59402,1897],{},[1931,59404,2553],{},[902,59406,59407],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,59410,59412],{"className":59411},[886],[888,59413,59414],{"xmlns":890},[892,59415,59416,59420],{},[895,59417,59418],{},[898,59419,1662],{},[902,59421,1662],{"encoding":904},[883,59423,59425],{"className":59424},[886],[888,59426,59427],{"xmlns":890},[892,59428,59429,59435],{},[895,59430,59431,59433],{},[898,59432,1862],{},[898,59434,2974],{},[902,59436,55744],{"encoding":904}," blíží ",[883,59439,59441],{"className":59440},[886],[888,59442,59443],{"xmlns":890},[892,59444,59445,59449],{},[895,59446,59447],{},[1931,59448,2553],{},[902,59450,2553],{"encoding":904},[883,59452,59454],{"className":59453},[886],[888,59455,59456],{"xmlns":890,"display":28251},[892,59457,59458,59504],{},[895,59459,59460,59477,59499,59501],{},[40081,59461,59462,59469],{},[895,59463,59464,59467],{},[898,59465,59466],{},"lim",[1700,59468,56384],{},[895,59470,59471,59473,59475],{},[898,59472,1662],{},[1700,59474,3317],{},[898,59476,6485],{"mathvariant":1791},[895,59478,59479,59481,59493,59495,59497],{},[1700,59480,1703],{"fence":1731},[1774,59482,59483,59491],{},[895,59484,59485,59487,59489],{},[1931,59486,1933],{},[1781,59488,1783],{},[1931,59490,59266],{},[898,59492,1662],{},[1700,59494,1897],{},[1931,59496,2553],{},[1700,59498,1709],{"fence":1731},[1700,59500,1765],{},[1931,59502,59503],{},"4.",[902,59505,59506],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,59508,59509,59547,59548,2196],{},[883,59510,59512],{"className":59511},[886],[888,59513,59514],{"xmlns":890},[892,59515,59516,59544],{},[895,59517,59518,59520,59522,59524,59526,59540,59542],{},[898,59519,1862],{},[898,59521,10619],{},[898,59523,2974],{},[1700,59525,1765],{},[1770,59527,59528],{"scriptlevel":1772,"displaystyle":1702},[1774,59529,59530,59538],{},[895,59531,59532,59534,59536],{},[1931,59533,1933],{},[1781,59535,1783],{},[1931,59537,59266],{},[898,59539,1662],{},[1700,59541,3317],{},[1931,59543,1772],{},[902,59545,59546],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,59549,59551],{"className":59550},[886],[888,59552,59553],{"xmlns":890},[892,59554,59555,59559],{},[895,59556,59557],{},[898,59558,1662],{},[902,59560,1662],{"encoding":904},[724,59562,59563],{},[614,59564,59565,59566,59595,59596,2196],{},"Obrázek 3.5: Přímka ",[883,59567,59569],{"className":59568},[886],[888,59570,59571],{"xmlns":890},[892,59572,59573,59593],{},[895,59574,59575,59577,59579,59581,59583,59585,59587,59589,59591],{},[898,59576,2971],{},[898,59578,2974],{},[1700,59580,1765],{},[1931,59582,1933],{},[1781,59584,1783],{},[1931,59586,59266],{},[1700,59588,1897],{},[1931,59590,2553],{},[898,59592,1662],{},[902,59594,59371],{"encoding":904}," protínající svislou osu ve výši ",[883,59597,59599],{"className":59598},[886],[888,59600,59601],{"xmlns":890},[892,59602,59603,59617],{},[895,59604,59605,59607,59609,59611,59613,59615],{},[898,59606,10619],{},[898,59608,2974],{},[1700,59610,1765],{},[1931,59612,1933],{},[1781,59614,1783],{},[1931,59616,59266],{},[902,59618,59269],{"encoding":904},[724,59620,59621],{},[614,59622,59623,59624,59659,59660,2196],{},"Obrázek 3.6: Hyperbola ",[883,59625,59627],{"className":59626},[886],[888,59628,59629],{"xmlns":890},[892,59630,59631,59657],{},[895,59632,59633,59635,59637,59639,59653,59655],{},[898,59634,1862],{},[898,59636,2974],{},[1700,59638,1765],{},[1770,59640,59641],{"scriptlevel":1772,"displaystyle":1702},[1774,59642,59643,59651],{},[895,59644,59645,59647,59649],{},[1931,59646,1933],{},[1781,59648,1783],{},[1931,59650,59266],{},[898,59652,1662],{},[1700,59654,1897],{},[1931,59656,2553],{},[902,59658,59407],{"encoding":904}," s vodorovnou asymptotou ",[883,59661,59663],{"className":59662},[886],[888,59664,59665],{"xmlns":890},[892,59666,59667,59677],{},[895,59668,59669,59671,59673,59675],{},[898,59670,1862],{},[898,59672,2974],{},[1700,59674,1765],{},[1931,59676,2553],{},[902,59678,59679],{"encoding":904},"AC = 4",[724,59681,59682],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,59684,59686],{"className":59685},[886],[888,59687,59688],{"xmlns":890,"display":28251},[892,59689,59690,59716],{},[895,59691,59692,59694,59696,59698,59700,59702,59704,59706,59708,59710,59712,59714],{},[898,59693,2971],{},[898,59695,40524],{},[898,59697,2974],{},[1700,59699,1765],{},[898,59701,1662],{},[1700,59703,2065],{},[898,59705,40524],{},[898,59707,2974],{},[1700,59709,1703],{"stretchy":1702},[898,59711,1662],{},[1700,59713,1709],{"stretchy":1702},[1700,59715,1732],{"separator":1731},[902,59717,59718],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,59720,4499,59721,58910,59749,59752,59753,59783],{},[883,59722,59724],{"className":59723},[886],[888,59725,59726],{"xmlns":890},[892,59727,59728,59746],{},[895,59729,59730,59732,59734,59736,59738,59740,59742,59744],{},[898,59731,40524],{},[898,59733,2974],{},[1700,59735,1765],{},[898,59737,40524],{},[898,59739,2974],{},[1700,59741,1703],{"stretchy":1702},[898,59743,1662],{},[1700,59745,1709],{"stretchy":1702},[902,59747,59748],{"encoding":904},"VC = VC(Q)",[38,59750,59751],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,59754,59756],{"className":59755},[886],[888,59757,59758],{"xmlns":890},[892,59759,59760,59780],{},[895,59761,59762,59764,59766,59768,59770,59772,59774,59776,59778],{},[898,59763,2971],{},[898,59765,40524],{},[898,59767,2974],{},[1700,59769,1703],{"stretchy":1702},[898,59771,1662],{},[1700,59773,1709],{"stretchy":1702},[1700,59775,1765],{},[898,59777,207],{},[898,59779,1662],{},[902,59781,59782],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,59785,59787],{"className":59786},[886],[888,59788,59789],{"xmlns":890,"display":28251},[892,59790,59791,59811],{},[895,59792,59793,59795,59797,59799,59801,59803,59805,59807,59809],{},[898,59794,2971],{},[898,59796,2974],{},[1700,59798,1765],{},[898,59800,10619],{},[898,59802,2974],{},[1700,59804,1897],{},[898,59806,207],{},[898,59808,1662],{},[898,59810,2196],{"mathvariant":1791},[902,59812,59813],{"encoding":904},"TC = FC + aQ.",[724,59815,59816,59817,59832,59833,59848,59849,59872,59873,59907,59908,59659,59921,59934,59935,2114,59983,60027,60028,2196],{},"Křivkou ",[883,59818,59820],{"className":59819},[886],[888,59821,59822],{"xmlns":890},[892,59823,59824,59830],{},[895,59825,59826,59828],{},[898,59827,2971],{},[898,59829,2974],{},[902,59831,3436],{"encoding":904}," je přímka se svislým průsečíkem ",[883,59834,59836],{"className":59835},[886],[888,59837,59838],{"xmlns":890},[892,59839,59840,59846],{},[895,59841,59842,59844],{},[898,59843,10619],{},[898,59845,2974],{},[902,59847,55675],{"encoding":904}," a sklonem ",[883,59850,59852],{"className":59851},[886],[888,59853,59854],{"xmlns":890},[892,59855,59856,59869],{},[895,59857,59858,59861,59863,59865,59867],{},[898,59859,59860],{},"tan",[1700,59862,56384],{},[898,59864,19047],{},[1700,59866,1765],{},[898,59868,207],{},[902,59870,59871],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,59874,59876],{"className":59875},[886],[888,59877,59878],{"xmlns":890},[892,59879,59880,59904],{},[895,59881,59882,59884,59886,59888,59900,59902],{},[898,59883,1862],{},[898,59885,2974],{},[1700,59887,1765],{},[1770,59889,59890],{"scriptlevel":1772,"displaystyle":1702},[1774,59891,59892,59898],{},[895,59893,59894,59896],{},[898,59895,10619],{},[898,59897,2974],{},[898,59899,1662],{},[1700,59901,1897],{},[898,59903,207],{},[902,59905,59906],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,59909,59911],{"className":59910},[886],[888,59912,59913],{"xmlns":890},[892,59914,59915,59919],{},[895,59916,59917],{},[898,59918,1706],{},[902,59920,1706],{"encoding":904},[883,59922,59924],{"className":59923},[886],[888,59925,59926],{"xmlns":890},[892,59927,59928,59932],{},[895,59929,59930],{},[898,59931,207],{},[902,59933,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,59936,59938],{"className":59937},[886],[888,59939,59940],{"xmlns":890},[892,59941,59942,59980],{},[895,59943,59944,59964,59976,59978],{},[2007,59945,59946,59952],{},[895,59947,59948,59950],{},[898,59949,59466],{},[1700,59951,56384],{},[895,59953,59954,59956,59958],{},[898,59955,1662],{},[1700,59957,3317],{},[1785,59959,59960,59962],{},[1931,59961,1772],{},[1700,59963,1897],{},[1770,59965,59966],{"scriptlevel":1772,"displaystyle":1702},[1774,59967,59968,59974],{},[895,59969,59970,59972],{},[898,59971,10619],{},[898,59973,2974],{},[898,59975,1662],{},[1700,59977,1765],{},[898,59979,6485],{"mathvariant":1791},[902,59981,59982],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,59984,59986],{"className":59985},[886],[888,59987,59988],{"xmlns":890},[892,59989,59990,60024],{},[895,59991,59992,60008,60020,60022],{},[2007,59993,59994,60000],{},[895,59995,59996,59998],{},[898,59997,59466],{},[1700,59999,56384],{},[895,60001,60002,60004,60006],{},[898,60003,1662],{},[1700,60005,3317],{},[898,60007,6485],{"mathvariant":1791},[1770,60009,60010],{"scriptlevel":1772,"displaystyle":1702},[1774,60011,60012,60018],{},[895,60013,60014,60016],{},[898,60015,10619],{},[898,60017,2974],{},[898,60019,1662],{},[1700,60021,1765],{},[1931,60023,1772],{},[902,60025,60026],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,60029,60031],{"className":60030},[886],[888,60032,60033],{"xmlns":890},[892,60034,60035,60041],{},[895,60036,60037,60039],{},[898,60038,1862],{},[898,60040,2974],{},[902,60042,55744],{"encoding":904},[724,60044,60045],{},[614,60046,60047,60048,60063,60064,60079,60080,2196],{},"Obrázek 3.7: Přímka ",[883,60049,60051],{"className":60050},[886],[888,60052,60053],{"xmlns":890},[892,60054,60055,60061],{},[895,60056,60057,60059],{},[898,60058,2971],{},[898,60060,2974],{},[902,60062,3436],{"encoding":904}," s osovým průsečíkem ve výši ",[883,60065,60067],{"className":60066},[886],[888,60068,60069],{"xmlns":890},[892,60070,60071,60077],{},[895,60072,60073,60075],{},[898,60074,10619],{},[898,60076,2974],{},[902,60078,55675],{"encoding":904}," a se sklonem ",[883,60081,60083],{"className":60082},[886],[888,60084,60085],{"xmlns":890},[892,60086,60087,60099],{},[895,60088,60089,60091,60093,60095,60097],{},[898,60090,59860],{},[1700,60092,56384],{},[898,60094,19047],{},[1700,60096,1765],{},[898,60098,207],{},[902,60100,59871],{"encoding":904},[724,60102,60103],{},[614,60104,60105,60106,60121,60122,2196],{},"Obrázek 3.8: Klesající hyperbola ",[883,60107,60109],{"className":60108},[886],[888,60110,60111],{"xmlns":890},[892,60112,60113,60119],{},[895,60114,60115,60117],{},[898,60116,1862],{},[898,60118,2974],{},[902,60120,55744],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,60123,60125],{"className":60124},[886],[888,60126,60127],{"xmlns":890},[892,60128,60129,60133],{},[895,60130,60131],{},[898,60132,207],{},[902,60134,207],{"encoding":904},[198,60136,60138],{"id":60137},"mezní-náklady","Mezní náklady",[724,60140,60141,2106,60143,10208,60158,60161,60162,60165],{},[38,60142,60138],{},[883,60144,60146],{"className":60145},[886],[888,60147,60148],{"xmlns":890},[892,60149,60150,60156],{},[895,60151,60152,60154],{},[898,60153,2005],{},[898,60155,2974],{},[902,60157,55476],{"encoding":904},[38,60159,60160],{},"marginal cost",") jsou ",[207,60163,1145],{"className":60164,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,60167,60169],{"className":60168},[886],[888,60170,60171],{"xmlns":890,"display":28251},[892,60172,60173,60242],{},[20939,60174,60175],{"width":28256},[20944,60176,60177,60179,60235,60237],{},[20947,60178],{"width":28261},[20947,60180,60181],{},[895,60182,60183,60185,60187,60189,60191,60193,60195,60197,60199,60201,60217,60219,60221,60227,60229,60231,60233],{},[898,60184,2005],{},[898,60186,2974],{},[1700,60188,1765],{},[898,60190,2005],{},[898,60192,2974],{},[1700,60194,1703],{"stretchy":1702},[898,60196,1662],{},[1700,60198,1709],{"stretchy":1702},[1700,60200,1765],{},[1774,60202,60203,60211],{},[895,60204,60205,60207,60209],{},[898,60206,2406],{"mathvariant":1791},[898,60208,2971],{},[898,60210,2974],{},[895,60212,60213,60215],{},[898,60214,2406],{"mathvariant":1791},[898,60216,1662],{},[1700,60218,1765],{},[898,60220,2971],{},[1785,60222,60223,60225],{},[898,60224,2974],{},[1700,60226,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,60228,1703],{"stretchy":1702},[898,60230,1662],{},[1700,60232,1709],{"stretchy":1702},[898,60234,2196],{"mathvariant":1791},[20947,60236],{"width":28261},[20947,60238,60239],{},[1781,60240,60241],{},"(3.8)",[902,60243,60244],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[4060,60246,60247],{},[724,60248,60249,60251,60252,60278,60279,60296,60297,2196],{},[883,60250,4346],{}," Intuice — „kolik stojí další kus\"\n",[883,60253,60255],{"className":60254},[886],[888,60256,60257],{"xmlns":890},[892,60258,60259,60275],{},[895,60260,60261,60263,60265,60267,60273],{},[898,60262,2005],{},[898,60264,2974],{},[1700,60266,1703],{"stretchy":1702},[1785,60268,60269,60271],{},[898,60270,1662],{},[1700,60272,4543],{},[1700,60274,1709],{"stretchy":1702},[902,60276,60277],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,60280,60282],{"className":60281},[886],[888,60283,60284],{"xmlns":890},[892,60285,60286,60294],{},[895,60287,60288],{},[1785,60289,60290,60292],{},[898,60291,1662],{},[1700,60293,4543],{},[902,60295,30029],{"encoding":904},". Formálně ",[883,60298,60300],{"className":60299},[886],[888,60301,60302],{"xmlns":890},[892,60303,60304,60356],{},[895,60305,60306,60308,60310,60312,60318,60320,60322,60324,60326,60328,60334,60336,60338,60340,60342,60344,60346,60348,60354],{},[898,60307,2005],{},[898,60309,2974],{},[1700,60311,1703],{"stretchy":1702},[1785,60313,60314,60316],{},[898,60315,1662],{},[1700,60317,4543],{},[1700,60319,1709],{"stretchy":1702},[1700,60321,2927],{},[898,60323,2971],{},[898,60325,2974],{},[1700,60327,1703],{"stretchy":1702},[1785,60329,60330,60332],{},[898,60331,1662],{},[1700,60333,4543],{},[1700,60335,1897],{},[1931,60337,1933],{},[1700,60339,1709],{"stretchy":1702},[1700,60341,1768],{},[898,60343,2971],{},[898,60345,2974],{},[1700,60347,1703],{"stretchy":1702},[1785,60349,60350,60352],{},[898,60351,1662],{},[1700,60353,4543],{},[1700,60355,1709],{"stretchy":1702},[902,60357,60358],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,60360,60361,60362,2901],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,60363,60365],{"className":60364},[886],[888,60366,60367],{"xmlns":890},[892,60368,60369,60377],{},[895,60370,60371,60373,60375],{},[898,60372,3084],{"mathvariant":1791},[898,60374,2971],{},[898,60376,2974],{},[902,60378,60379],{"encoding":904},"\\Delta TC",[883,60381,60383],{"className":60382},[886],[888,60384,60385],{"xmlns":890,"display":28251},[892,60386,60387,60456],{},[20939,60388,60389],{"width":28256},[20944,60390,60391,60393,60449,60451],{},[20947,60392],{"width":28261},[20947,60394,60395],{},[895,60396,60397,60399,60401,60403,60405,60407,60409,60411,60413,60415,60417,60419,60421,60423,60429,60431,60433,60435,60437,60439,60441,60443,60445,60447],{},[898,60398,3084],{"mathvariant":1791},[898,60400,2971],{},[898,60402,2974],{},[1781,60404,4175],{},[1700,60406,2927],{},[1781,60408,4175],{},[898,60410,2406],{"mathvariant":1791},[898,60412,2971],{},[898,60414,2974],{},[1700,60416,1765],{},[1700,60418,1703],{"stretchy":1702},[898,60420,2971],{},[898,60422,2974],{},[1785,60424,60425,60427],{},[1700,60426,1709],{"stretchy":1702},[1700,60428,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1781,60430,1783],{},[898,60432,2406],{"mathvariant":1791},[898,60434,1662],{},[1700,60436,1765],{},[898,60438,2005],{},[898,60440,2974],{},[1781,60442,1783],{},[898,60444,2406],{"mathvariant":1791},[898,60446,1662],{},[1700,60448,1732],{"separator":1731},[20947,60450],{"width":28261},[20947,60452,60453],{},[1781,60454,60455],{},"(3.9)",[902,60457,60458],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,60460,57495],{},[883,60462,60464],{"className":60463},[886],[888,60465,60466],{"xmlns":890,"display":28251},[892,60467,60468,60566],{},[895,60469,60470,60508,60510,60512,60514,60536,60538,60564],{},[895,60471,60472,60474,60480,60482,60488,60491,60497,60500],{},[1781,60473,57509],{},[8574,60475,60476,60478],{"accent":1731},[1781,60477,45917],{},[1700,60479,25243],{},[1781,60481,57518],{},[8574,60483,60484,60486],{"accent":1731},[1781,60485,2215],{},[1700,60487,25162],{},[1781,60489,60490],{},"ch n",[8574,60492,60493,60495],{"accent":1731},[1781,60494,207],{},[1700,60496,25162],{},[1781,60498,60499],{},"klad",[8574,60501,60502,60505],{"accent":1731},[1781,60503,60504],{},"u",[1700,60506,60507],{},"˚",[1781,60509,4175],{},[1700,60511,2927],{},[1781,60513,4175],{},[895,60515,60516,60518,60524,60527,60533],{},[1781,60517,57553],{},[8574,60519,60520,60522],{"accent":1731},[1781,60521,25231],{},[1700,60523,25162],{},[1781,60525,60526],{}," n",[8574,60528,60529,60531],{"accent":1731},[1781,60530,207],{},[1700,60532,25162],{},[1781,60534,60535],{},"klady",[1700,60537,57580],{},[895,60539,60540,60542,60548,60550,60556,60558],{},[1781,60541,57509],{},[8574,60543,60544,60546],{"accent":1731},[1781,60545,45917],{},[1700,60547,25243],{},[1781,60549,57593],{},[8574,60551,60552,60554],{"accent":1731},[1781,60553,9781],{},[1700,60555,25243],{},[1781,60557,57602],{},[8574,60559,60560,60562],{"accent":1731},[1781,60561,25231],{},[1700,60563,25162],{},[898,60565,2196],{"mathvariant":1791},[902,60567,60568],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[37533,60570,60572],{"id":60571},"příklad-35","Příklad 3.5",[724,60574,60575,57706,60577,56209,60613,60628,60629,60644,60645,2868,60658,2882,60671,60684,60685,2882,60698,2196],{},[38,60576,56171],{},[883,60578,60580],{"className":60579},[886],[888,60581,60582],{"xmlns":890},[892,60583,60584,60610],{},[895,60585,60586,60588,60590,60592,60594,60596,60598,60600,60602,60604],{},[898,60587,2971],{},[898,60589,2974],{},[1700,60591,1765],{},[1931,60593,8565],{},[1700,60595,1897],{},[1931,60597,2445],{},[898,60599,1662],{},[1700,60601,1897],{},[1931,60603,2343],{},[1785,60605,60606,60608],{},[898,60607,1662],{},[1931,60609,2343],{},[902,60611,60612],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,60614,60616],{"className":60615},[886],[888,60617,60618],{"xmlns":890},[892,60619,60620,60626],{},[895,60621,60622,60624],{},[898,60623,2005],{},[898,60625,2974],{},[902,60627,55476],{"encoding":904}," a odhadněte změny ",[883,60630,60632],{"className":60631},[886],[888,60633,60634],{"xmlns":890},[892,60635,60636,60642],{},[895,60637,60638,60640],{},[898,60639,2971],{},[898,60641,2974],{},[902,60643,3436],{"encoding":904}," při změnách ",[883,60646,60648],{"className":60647},[886],[888,60649,60650],{"xmlns":890},[892,60651,60652,60656],{},[895,60653,60654],{},[898,60655,1662],{},[902,60657,1662],{"encoding":904},[883,60659,60661],{"className":60660},[886],[888,60662,60663],{"xmlns":890},[892,60664,60665,60669],{},[895,60666,60667],{},[1931,60668,36429],{},[902,60670,36429],{"encoding":904},[883,60672,60674],{"className":60673},[886],[888,60675,60676],{"xmlns":890},[892,60677,60678,60682],{},[895,60679,60680],{},[1931,60681,42047],{},[902,60683,42047],{"encoding":904}," a z ",[883,60686,60688],{"className":60687},[886],[888,60689,60690],{"xmlns":890},[892,60691,60692,60696],{},[895,60693,60694],{},[1931,60695,36429],{},[902,60697,36429],{"encoding":904},[883,60699,60701],{"className":60700},[886],[888,60702,60703],{"xmlns":890},[892,60704,60705,60709],{},[895,60706,60707],{},[1931,60708,3702],{},[902,60710,3702],{"encoding":904},[724,60712,60713,2106,60715,3122,60741,1343,60768,60795,60796,60811,60812,60827,60828,60855,60856,60876,60877,20716,60898,60954,60955,2868,60968,2882,60981,8290,60994,2196],{},[38,60714,22955],{},[883,60716,60718],{"className":60717},[886],[888,60719,60720],{"xmlns":890},[892,60721,60722,60738],{},[895,60723,60724,60726,60728,60730,60732,60734,60736],{},[898,60725,2005],{},[898,60727,2974],{},[1700,60729,1765],{},[1931,60731,2445],{},[1700,60733,1897],{},[1931,60735,2553],{},[898,60737,1662],{},[902,60739,60740],{"encoding":904},"MC = 6 + 4Q",[883,60742,60744],{"className":60743},[886],[888,60745,60746],{"xmlns":890},[892,60747,60748,60765],{},[895,60749,60750,60752,60754,60756,60758,60760,60762],{},[898,60751,2005],{},[898,60753,2974],{},[1700,60755,1703],{"stretchy":1702},[1931,60757,36429],{},[1700,60759,1709],{"stretchy":1702},[1700,60761,1765],{},[1931,60763,60764],{},"66",[902,60766,60767],{"encoding":904},"MC(15) = 66",[883,60769,60771],{"className":60770},[886],[888,60772,60773],{"xmlns":890},[892,60774,60775,60792],{},[895,60776,60777,60779,60781,60783,60785,60787,60789],{},[898,60778,2005],{},[898,60780,2974],{},[1700,60782,1703],{"stretchy":1702},[1931,60784,9223],{},[1700,60786,1709],{"stretchy":1702},[1700,60788,1765],{},[1931,60790,60791],{},"86",[902,60793,60794],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,60797,60799],{"className":60798},[886],[888,60800,60801],{"xmlns":890},[892,60802,60803,60809],{},[895,60804,60805,60807],{},[898,60806,2971],{},[898,60808,2974],{},[902,60810,3436],{"encoding":904}," zvyšuje (",[883,60813,60815],{"className":60814},[886],[888,60816,60817],{"xmlns":890},[892,60818,60819,60825],{},[895,60820,60821,60823],{},[898,60822,2005],{},[898,60824,2974],{},[902,60826,55476],{"encoding":904}," je rostoucí). Z ",[883,60829,60831],{"className":60830},[886],[888,60832,60833],{"xmlns":890},[892,60834,60835,60852],{},[895,60836,60837,60839,60841,60843,60845,60847,60849],{},[898,60838,2971],{},[898,60840,2974],{},[1700,60842,1703],{"stretchy":1702},[1931,60844,36429],{},[1700,60846,1709],{"stretchy":1702},[1700,60848,1765],{},[1931,60850,60851],{},"740",[902,60853,60854],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,60857,60859],{"className":60858},[886],[888,60860,60861],{"xmlns":890},[892,60862,60863,60873],{},[895,60864,60865,60867,60869,60871],{},[898,60866,2406],{"mathvariant":1791},[898,60868,1662],{},[1700,60870,1765],{},[1931,60872,1933],{},[902,60874,60875],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,60878,60880],{"className":60879},[886],[888,60881,60882],{"xmlns":890},[892,60883,60884,60895],{},[895,60885,60886,60888,60890,60892],{},[898,60887,2971],{},[898,60889,2974],{},[1700,60891,2927],{},[1931,60893,60894],{},"806",[902,60896,60897],{"encoding":904},"TC \\approx 806",[883,60899,60901],{"className":60900},[886],[888,60902,60903],{"xmlns":890},[892,60904,60905,60951],{},[895,60906,60907,60909,60911,60913,60915,60917,60919,60921,60923,60925,60927,60929,60931,60933,60935,60937,60939,60942,60944,60946,60948],{},[898,60908,3084],{"mathvariant":1791},[898,60910,2971],{},[898,60912,2974],{},[1700,60914,1765],{},[898,60916,2971],{},[898,60918,2974],{},[1700,60920,1703],{"stretchy":1702},[1931,60922,42047],{},[1700,60924,1709],{"stretchy":1702},[1700,60926,1768],{},[898,60928,2971],{},[898,60930,2974],{},[1700,60932,1703],{"stretchy":1702},[1931,60934,36429],{},[1700,60936,1709],{"stretchy":1702},[1700,60938,1765],{},[1931,60940,60941],{},"808",[1700,60943,1768],{},[1931,60945,60851],{},[1700,60947,1765],{},[1931,60949,60950],{},"68",[902,60952,60953],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,60956,60958],{"className":60957},[886],[888,60959,60960],{"xmlns":890},[892,60961,60962,60966],{},[895,60963,60964],{},[898,60965,1662],{},[902,60967,1662],{"encoding":904},[883,60969,60971],{"className":60970},[886],[888,60972,60973],{"xmlns":890},[892,60974,60975,60979],{},[895,60976,60977],{},[1931,60978,36429],{},[902,60980,36429],{"encoding":904},[883,60982,60984],{"className":60983},[886],[888,60985,60986],{"xmlns":890},[892,60987,60988,60992],{},[895,60989,60990],{},[1931,60991,3702],{},[902,60993,3702],{"encoding":904},[883,60995,60997],{"className":60996},[886],[888,60998,60999],{"xmlns":890},[892,61000,61001,61030],{},[895,61002,61003,61005,61007,61009,61011,61013,61015,61017,61019,61021,61023,61025,61027],{},[898,61004,3084],{"mathvariant":1791},[898,61006,2971],{},[898,61008,2974],{},[1700,61010,2927],{},[1931,61012,60764],{},[1700,61014,2065],{},[1700,61016,1703],{"stretchy":1702},[1700,61018,1768],{},[1931,61020,2385],{},[1700,61022,1709],{"stretchy":1702},[1700,61024,1765],{},[1700,61026,1768],{},[1931,61028,61029],{},"198",[902,61031,61032],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,61034,61036],{"id":61035},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,61038,61039],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[37533,61041,61043],{"id":61042},"příklad-36","Příklad 3.6",[724,61045,61046,57706,61048,61092],{},[38,61047,56171],{},[883,61049,61051],{"className":61050},[886],[888,61052,61053],{"xmlns":890},[892,61054,61055,61089],{},[895,61056,61057,61059,61061,61063,61065,61067,61069,61071,61073,61075,61081,61083],{},[898,61058,2971],{},[898,61060,2974],{},[1700,61062,1765],{},[1931,61064,3284],{},[1700,61066,1897],{},[1931,61068,5192],{},[898,61070,1662],{},[1700,61072,1768],{},[1931,61074,2438],{},[1785,61076,61077,61079],{},[898,61078,1662],{},[1931,61080,2343],{},[1700,61082,1897],{},[1785,61084,61085,61087],{},[898,61086,1662],{},[1931,61088,2385],{},[902,61090,61091],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,61094,61095],{},[38,61096,22955],{},[883,61098,61100],{"className":61099},[886],[888,61101,61102],{"xmlns":890,"display":28251},[892,61103,61104,61348],{},[20939,61105,61106,61132,61180,61214,61256,61306],{"rowspacing":20941,"columnalign":20942,"columnspacing":1792},[20944,61107,61108,61118],{},[20947,61109,61110],{},[1770,61111,61112],{"scriptlevel":1772,"displaystyle":1731},[895,61113,61114,61116],{},[898,61115,10619],{},[898,61117,2974],{},[20947,61119,61120],{},[1770,61121,61122],{"scriptlevel":1772,"displaystyle":1731},[895,61123,61124,61126,61128,61130],{},[895,61125],{},[1700,61127,1765],{},[1931,61129,3284],{},[1700,61131,1732],{"separator":1731},[20944,61133,61134,61146],{},[20947,61135,61136],{},[1770,61137,61138],{"scriptlevel":1772,"displaystyle":1731},[895,61139,61140,61142,61144],{},[898,61141,2971],{},[898,61143,40524],{},[898,61145,2974],{},[20947,61147,61148],{},[1770,61149,61150],{"scriptlevel":1772,"displaystyle":1731},[895,61151,61152,61154,61156,61158,61160,61162,61164,61170,61172,61178],{},[895,61153],{},[1700,61155,1765],{},[1931,61157,5192],{},[898,61159,1662],{},[1700,61161,1768],{},[1931,61163,2438],{},[1785,61165,61166,61168],{},[898,61167,1662],{},[1931,61169,2343],{},[1700,61171,1897],{},[1785,61173,61174,61176],{},[898,61175,1662],{},[1931,61177,2385],{},[1700,61179,1732],{"separator":1731},[20944,61181,61182,61194],{},[20947,61183,61184],{},[1770,61185,61186],{"scriptlevel":1772,"displaystyle":1731},[895,61187,61188,61190,61192],{},[898,61189,1862],{},[898,61191,10619],{},[898,61193,2974],{},[20947,61195,61196],{},[1770,61197,61198],{"scriptlevel":1772,"displaystyle":1731},[895,61199,61200,61202,61204,61212],{},[895,61201],{},[1700,61203,1765],{},[1770,61205,61206],{"scriptlevel":1772,"displaystyle":1702},[1774,61207,61208,61210],{},[1931,61209,3284],{},[898,61211,1662],{},[1700,61213,1732],{"separator":1731},[20944,61215,61216,61228],{},[20947,61217,61218],{},[1770,61219,61220],{"scriptlevel":1772,"displaystyle":1731},[895,61221,61222,61224,61226],{},[898,61223,1862],{},[898,61225,40524],{},[898,61227,2974],{},[20947,61229,61230],{},[1770,61231,61232],{"scriptlevel":1772,"displaystyle":1731},[895,61233,61234,61236,61238,61240,61242,61244,61246,61248,61254],{},[895,61235],{},[1700,61237,1765],{},[1931,61239,5192],{},[1700,61241,1768],{},[1931,61243,2438],{},[898,61245,1662],{},[1700,61247,1897],{},[1785,61249,61250,61252],{},[898,61251,1662],{},[1931,61253,2343],{},[1700,61255,1732],{"separator":1731},[20944,61257,61258,61268],{},[20947,61259,61260],{},[1770,61261,61262],{"scriptlevel":1772,"displaystyle":1731},[895,61263,61264,61266],{},[898,61265,1862],{},[898,61267,2974],{},[20947,61269,61270],{},[1770,61271,61272],{"scriptlevel":1772,"displaystyle":1731},[895,61273,61274,61276,61278,61286,61288,61290,61292,61294,61296,61298,61304],{},[895,61275],{},[1700,61277,1765],{},[1770,61279,61280],{"scriptlevel":1772,"displaystyle":1702},[1774,61281,61282,61284],{},[1931,61283,3284],{},[898,61285,1662],{},[1700,61287,1897],{},[1931,61289,5192],{},[1700,61291,1768],{},[1931,61293,2438],{},[898,61295,1662],{},[1700,61297,1897],{},[1785,61299,61300,61302],{},[898,61301,1662],{},[1931,61303,2343],{},[1700,61305,1732],{"separator":1731},[20944,61307,61308,61318],{},[20947,61309,61310],{},[1770,61311,61312],{"scriptlevel":1772,"displaystyle":1731},[895,61313,61314,61316],{},[898,61315,2005],{},[898,61317,2974],{},[20947,61319,61320],{},[1770,61321,61322],{"scriptlevel":1772,"displaystyle":1731},[895,61323,61324,61326,61328,61330,61332,61334,61336,61338,61340,61346],{},[895,61325],{},[1700,61327,1765],{},[1931,61329,5192],{},[1700,61331,1768],{},[1931,61333,3058],{},[898,61335,1662],{},[1700,61337,1897],{},[1931,61339,2385],{},[1785,61341,61342,61344],{},[898,61343,1662],{},[1931,61345,2343],{},[898,61347,2196],{"mathvariant":1791},[902,61349,61350],{"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}",[724,61352,61353,61354,15977,61369,15977,61384,61399,61400,61415,61416,1343,61434,61415,61451,1343,61469,61415,61484,61502],{},"Význačné body ",[883,61355,61357],{"className":61356},[886],[888,61358,61359],{"xmlns":890},[892,61360,61361,61366],{},[895,61362,61363],{},[1931,61364,61365],{},"1,67",[902,61367,61368],{"encoding":904},"1{,}67",[883,61370,61372],{"className":61371},[886],[888,61373,61374],{"xmlns":890},[892,61375,61376,61381],{},[895,61377,61378],{},[1931,61379,61380],{},"2,50",[902,61382,61383],{"encoding":904},"2{,}50",[883,61385,61387],{"className":61386},[886],[888,61388,61389],{"xmlns":890},[892,61390,61391,61396],{},[895,61392,61393],{},[1931,61394,61395],{},"4,73",[902,61397,61398],{"encoding":904},"4{,}73"," odpovídají: ",[883,61401,61403],{"className":61402},[886],[888,61404,61405],{"xmlns":890},[892,61406,61407,61413],{},[895,61408,61409,61411],{},[898,61410,2005],{},[898,61412,2974],{},[902,61414,55476],{"encoding":904}," minimum v ",[883,61417,61419],{"className":61418},[886],[888,61420,61421],{"xmlns":890},[892,61422,61423,61431],{},[895,61424,61425,61427,61429],{},[898,61426,1662],{},[1700,61428,6088],{},[1931,61430,61365],{},[902,61432,61433],{"encoding":904},"Q \\doteq 1{,}67",[883,61435,61437],{"className":61436},[886],[888,61438,61439],{"xmlns":890},[892,61440,61441,61449],{},[895,61442,61443,61445,61447],{},[898,61444,1862],{},[898,61446,40524],{},[898,61448,2974],{},[902,61450,55495],{"encoding":904},[883,61452,61454],{"className":61453},[886],[888,61455,61456],{"xmlns":890},[892,61457,61458,61466],{},[895,61459,61460,61462,61464],{},[898,61461,1662],{},[1700,61463,1765],{},[1931,61465,61380],{},[902,61467,61468],{"encoding":904},"Q = 2{,}50",[883,61470,61472],{"className":61471},[886],[888,61473,61474],{"xmlns":890},[892,61475,61476,61482],{},[895,61477,61478,61480],{},[898,61479,1862],{},[898,61481,2974],{},[902,61483,55744],{"encoding":904},[883,61485,61487],{"className":61486},[886],[888,61488,61489],{"xmlns":890},[892,61490,61491,61499],{},[895,61492,61493,61495,61497],{},[898,61494,1662],{},[1700,61496,6088],{},[1931,61498,61395],{},[902,61500,61501],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,61504,61505],{},[2756,61506],{"alt":61507,"className":61508,"src":61509},"imek-ac-avc-mc",[210,2760],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,61511,61512],{},[614,61513,61514,61515,2114,61530,61547,61548,15977,61567,61582],{},"Obrázek 3.9: Kubické křivky ",[883,61516,61518],{"className":61517},[886],[888,61519,61520],{"xmlns":890},[892,61521,61522,61528],{},[895,61523,61524,61526],{},[898,61525,2971],{},[898,61527,2974],{},[902,61529,3436],{"encoding":904},[883,61531,61533],{"className":61532},[886],[888,61534,61535],{"xmlns":890},[892,61536,61537,61545],{},[895,61538,61539,61541,61543],{},[898,61540,2971],{},[898,61542,40524],{},[898,61544,2974],{},[902,61546,55693],{"encoding":904}," rostoucí od bodu ",[883,61549,61551],{"className":61550},[886],[888,61552,61553],{"xmlns":890},[892,61554,61555,61565],{},[895,61556,61557,61559,61561,61563],{},[898,61558,10619],{},[898,61560,2974],{},[1700,61562,1765],{},[1931,61564,3284],{},[902,61566,11817],{"encoding":904},[883,61568,61570],{"className":61569},[886],[888,61571,61572],{"xmlns":890},[892,61573,61574,61580],{},[895,61575,61576,61578],{},[898,61577,10619],{},[898,61579,2974],{},[902,61581,55675],{"encoding":904}," je vodorovná přímka.",[724,61584,61585],{},[614,61586,61587,61588,1343,61603,1343,61620,29386,61635,61648,61649,3122,61666,61681,61682,6378,61699,61714,61715,26374,61728,1343,61741,1343,61754,2196],{},"Obrázek 3.10: Křivky ",[883,61589,61591],{"className":61590},[886],[888,61592,61593],{"xmlns":890},[892,61594,61595,61601],{},[895,61596,61597,61599],{},[898,61598,1862],{},[898,61600,2974],{},[902,61602,55744],{"encoding":904},[883,61604,61606],{"className":61605},[886],[888,61607,61608],{"xmlns":890},[892,61609,61610,61618],{},[895,61611,61612,61614,61616],{},[898,61613,1862],{},[898,61615,40524],{},[898,61617,2974],{},[902,61619,55495],{"encoding":904},[883,61621,61623],{"className":61622},[886],[888,61624,61625],{"xmlns":890},[892,61626,61627,61633],{},[895,61628,61629,61631],{},[898,61630,2005],{},[898,61632,2974],{},[902,61634,55476],{"encoding":904},[883,61636,61638],{"className":61637},[886],[888,61639,61640],{"xmlns":890},[892,61641,61642,61646],{},[895,61643,61644],{},[898,61645,900],{},[902,61647,900],{"encoding":904}," a klesající hyperbola ",[883,61650,61652],{"className":61651},[886],[888,61653,61654],{"xmlns":890},[892,61655,61656,61664],{},[895,61657,61658,61660,61662],{},[898,61659,1862],{},[898,61661,10619],{},[898,61663,2974],{},[902,61665,55711],{"encoding":904},[883,61667,61669],{"className":61668},[886],[888,61670,61671],{"xmlns":890},[892,61672,61673,61679],{},[895,61674,61675,61677],{},[898,61676,2005],{},[898,61678,2974],{},[902,61680,55476],{"encoding":904}," protíná ",[883,61683,61685],{"className":61684},[886],[888,61686,61687],{"xmlns":890},[892,61688,61689,61697],{},[895,61690,61691,61693,61695],{},[898,61692,1862],{},[898,61694,40524],{},[898,61696,2974],{},[902,61698,55495],{"encoding":904},[883,61700,61702],{"className":61701},[886],[888,61703,61704],{"xmlns":890},[892,61705,61706,61712],{},[895,61707,61708,61710],{},[898,61709,1862],{},[898,61711,2974],{},[902,61713,55744],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,61716,61718],{"className":61717},[886],[888,61719,61720],{"xmlns":890},[892,61721,61722,61726],{},[895,61723,61724],{},[898,61725,1662],{},[902,61727,1662],{"encoding":904},[883,61729,61731],{"className":61730},[886],[888,61732,61733],{"xmlns":890},[892,61734,61735,61739],{},[895,61736,61737],{},[1931,61738,61365],{},[902,61740,61368],{"encoding":904},[883,61742,61744],{"className":61743},[886],[888,61745,61746],{"xmlns":890},[892,61747,61748,61752],{},[895,61749,61750],{},[1931,61751,61380],{},[902,61753,61383],{"encoding":904},[883,61755,61757],{"className":61756},[886],[888,61758,61759],{"xmlns":890},[892,61760,61761,61765],{},[895,61762,61763],{},[1931,61764,61395],{},[902,61766,61398],{"encoding":904},[724,61768,61769],{},[38,61770,61771],{},"Standardní vlastnosti:",[120,61773,61774,61809,61873,61941,61991,62011],{},[123,61775,61776,2114,61791,61808],{},[883,61777,61779],{"className":61778},[886],[888,61780,61781],{"xmlns":890},[892,61782,61783,61789],{},[895,61784,61785,61787],{},[898,61786,2971],{},[898,61788,2974],{},[902,61790,3436],{"encoding":904},[883,61792,61794],{"className":61793},[886],[888,61795,61796],{"xmlns":890},[892,61797,61798,61806],{},[895,61799,61800,61802,61804],{},[898,61801,2971],{},[898,61803,40524],{},[898,61805,2974],{},[902,61807,55693],{"encoding":904}," jsou kubické funkce;",[123,61810,61811,1343,61826,1343,61843,61858,61859,61872],{},[883,61812,61814],{"className":61813},[886],[888,61815,61816],{"xmlns":890},[892,61817,61818,61824],{},[895,61819,61820,61822],{},[898,61821,1862],{},[898,61823,2974],{},[902,61825,55744],{"encoding":904},[883,61827,61829],{"className":61828},[886],[888,61830,61831],{"xmlns":890},[892,61832,61833,61841],{},[895,61834,61835,61837,61839],{},[898,61836,1862],{},[898,61838,40524],{},[898,61840,2974],{},[902,61842,55495],{"encoding":904},[883,61844,61846],{"className":61845},[886],[888,61847,61848],{"xmlns":890},[892,61849,61850,61856],{},[895,61851,61852,61854],{},[898,61853,2005],{},[898,61855,2974],{},[902,61857,55476],{"encoding":904}," jsou křivky tvaru ",[883,61860,61862],{"className":61861},[886],[888,61863,61864],{"xmlns":890},[892,61865,61866,61870],{},[895,61867,61868],{},[898,61869,900],{},[902,61871,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,61874,61875,61890,61891,1343,61908,61925,61926,8613],{},[883,61876,61878],{"className":61877},[886],[888,61879,61880],{"xmlns":890},[892,61881,61882,61888],{},[895,61883,61884,61886],{},[898,61885,2005],{},[898,61887,2974],{},[902,61889,55476],{"encoding":904}," nabývá minima před ",[883,61892,61894],{"className":61893},[886],[888,61895,61896],{"xmlns":890},[892,61897,61898,61906],{},[895,61899,61900,61902,61904],{},[898,61901,1862],{},[898,61903,40524],{},[898,61905,2974],{},[902,61907,55495],{"encoding":904},[883,61909,61911],{"className":61910},[886],[888,61912,61913],{"xmlns":890},[892,61914,61915,61923],{},[895,61916,61917,61919,61921],{},[898,61918,1862],{},[898,61920,40524],{},[898,61922,2974],{},[902,61924,55495],{"encoding":904}," před ",[883,61927,61929],{"className":61928},[886],[888,61930,61931],{"xmlns":890},[892,61932,61933,61939],{},[895,61934,61935,61937],{},[898,61936,1862],{},[898,61938,2974],{},[902,61940,55744],{"encoding":904},[123,61942,61943,61681,61958,2114,61973,61990],{},[883,61944,61946],{"className":61945},[886],[888,61947,61948],{"xmlns":890},[892,61949,61950,61956],{},[895,61951,61952,61954],{},[898,61953,2005],{},[898,61955,2974],{},[902,61957,55476],{"encoding":904},[883,61959,61961],{"className":61960},[886],[888,61962,61963],{"xmlns":890},[892,61964,61965,61971],{},[895,61966,61967,61969],{},[898,61968,1862],{},[898,61970,2974],{},[902,61972,55744],{"encoding":904},[883,61974,61976],{"className":61975},[886],[888,61977,61978],{"xmlns":890},[892,61979,61980,61988],{},[895,61981,61982,61984,61986],{},[898,61983,1862],{},[898,61985,40524],{},[898,61987,2974],{},[902,61989,55495],{"encoding":904}," zdola právě v jejich minimech;",[123,61992,61993,62010],{},[883,61994,61996],{"className":61995},[886],[888,61997,61998],{"xmlns":890},[892,61999,62000,62008],{},[895,62001,62002,62004,62006],{},[898,62003,1862],{},[898,62005,10619],{},[898,62007,2974],{},[902,62009,55711],{"encoding":904}," je hyperbola, stále klesající;",[123,62012,62013,62045,62046,2114,62061,62078,62079,62092,62093,4110],{},[883,62014,62016],{"className":62015},[886],[888,62017,62018],{"xmlns":890},[892,62019,62020,62042],{},[895,62021,62022,62024,62026,62028,62030,62032,62034,62036,62038,62040],{},[898,62023,1862],{},[898,62025,2974],{},[1700,62027,1765],{},[898,62029,1862],{},[898,62031,10619],{},[898,62033,2974],{},[1700,62035,1897],{},[898,62037,1862],{},[898,62039,40524],{},[898,62041,2974],{},[902,62043,62044],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,62047,62049],{"className":62048},[886],[888,62050,62051],{"xmlns":890},[892,62052,62053,62059],{},[895,62054,62055,62057],{},[898,62056,1862],{},[898,62058,2974],{},[902,62060,55744],{"encoding":904},[883,62062,62064],{"className":62063},[886],[888,62065,62066],{"xmlns":890},[892,62067,62068,62076],{},[895,62069,62070,62072,62074],{},[898,62071,1862],{},[898,62073,40524],{},[898,62075,2974],{},[902,62077,55495],{"encoding":904}," klesá s rostoucím ",[883,62080,62082],{"className":62081},[886],[888,62083,62084],{"xmlns":890},[892,62085,62086,62090],{},[895,62087,62088],{},[898,62089,1662],{},[902,62091,1662],{"encoding":904}," (protože ",[883,62094,62096],{"className":62095},[886],[888,62097,62098],{"xmlns":890},[892,62099,62100,62112],{},[895,62101,62102,62104,62106,62108,62110],{},[898,62103,1862],{},[898,62105,10619],{},[898,62107,2974],{},[1700,62109,3317],{},[1931,62111,1772],{},[902,62113,62114],{"encoding":904},"AFC \\to 0",[115,62116,62118],{"id":62117},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,62120,62121,62122,62125,62126,62141],{},"Častou optimalizační úlohou je ",[38,62123,62124],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,62127,62129],{"className":62128},[886],[888,62130,62131],{"xmlns":890},[892,62132,62133,62139],{},[895,62134,62135,62137],{},[898,62136,1862],{},[898,62138,2974],{},[902,62140,55744],{"encoding":904}," minimální.",[198,62143,16597],{"id":16596},[724,62145,62146,62147,62164],{},"Mají-li průměrné náklady minimum v bodě ",[883,62148,62150],{"className":62149},[886],[888,62151,62152],{"xmlns":890},[892,62153,62154,62162],{},[895,62155,62156],{},[2007,62157,62158,62160],{},[898,62159,1662],{},[1931,62161,1772],{},[902,62163,38493],{"encoding":904},", pak platí",[883,62166,62168],{"className":62167},[886],[888,62169,62170],{"xmlns":890,"display":28251},[892,62171,62172,62221],{},[20939,62173,62174],{"width":28256},[20944,62175,62176,62178,62214,62216],{},[20947,62177],{"width":28261},[20947,62179,62180],{},[895,62181,62182,62184,62186,62188,62194,62196,62198,62200,62202,62204,62210,62212],{},[898,62183,1862],{},[898,62185,2974],{},[1700,62187,1703],{"stretchy":1702},[2007,62189,62190,62192],{},[898,62191,1662],{},[1931,62193,1772],{},[1700,62195,1709],{"stretchy":1702},[1700,62197,1765],{},[898,62199,2005],{},[898,62201,2974],{},[1700,62203,1703],{"stretchy":1702},[2007,62205,62206,62208],{},[898,62207,1662],{},[1931,62209,1772],{},[1700,62211,1709],{"stretchy":1702},[898,62213,2196],{"mathvariant":1791},[20947,62215],{"width":28261},[20947,62217,62218],{},[1781,62219,62220],{},"(3.10)",[902,62222,62223],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[4060,62225,62226],{},[724,62227,62228,62230,62231],{},[883,62229,56628],{}," Princip\n",[38,62232,62233],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,62235,62236,62239,62240,62282],{},[38,62237,62238],{},"Odvození."," Z ",[883,62241,62243],{"className":62242},[886],[888,62244,62245],{"xmlns":890},[892,62246,62247,62279],{},[895,62248,62249,62251,62253,62255,62257,62259,62261],{},[898,62250,1862],{},[898,62252,2974],{},[1700,62254,1703],{"stretchy":1702},[898,62256,1662],{},[1700,62258,1709],{"stretchy":1702},[1700,62260,1765],{},[1770,62262,62263],{"scriptlevel":1772,"displaystyle":1702},[1774,62264,62265,62277],{},[895,62266,62267,62269,62271,62273,62275],{},[898,62268,2971],{},[898,62270,2974],{},[1700,62272,1703],{"stretchy":1702},[898,62274,1662],{},[1700,62276,1709],{"stretchy":1702},[898,62278,1662],{},[902,62280,62281],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,62284,62286],{"className":62285},[886],[888,62287,62288],{"xmlns":890,"display":28251},[892,62289,62290,62422],{},[895,62291,62292,62294,62300,62302,62304,62306,62308,62348,62350,62390,62392,62420],{},[898,62293,1862],{},[1785,62295,62296,62298],{},[898,62297,2974],{},[1700,62299,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,62301,1703],{"stretchy":1702},[898,62303,1662],{},[1700,62305,1709],{"stretchy":1702},[1700,62307,1765],{},[1774,62309,62310,62342],{},[895,62311,62312,62314,62320,62322,62324,62326,62328,62330,62332,62334,62336,62338,62340],{},[898,62313,2971],{},[1785,62315,62316,62318],{},[898,62317,2974],{},[1700,62319,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,62321,1703],{"stretchy":1702},[898,62323,1662],{},[1700,62325,1709],{"stretchy":1702},[1700,62327,2065],{},[898,62329,1662],{},[1700,62331,1768],{},[898,62333,2971],{},[898,62335,2974],{},[1700,62337,1703],{"stretchy":1702},[898,62339,1662],{},[1700,62341,1709],{"stretchy":1702},[1785,62343,62344,62346],{},[898,62345,1662],{},[1931,62347,2343],{},[1700,62349,1765],{},[1774,62351,62352,62384],{},[895,62353,62354,62356,62358,62360,62362,62364,62366,62368,62370,62372,62374,62376,62378,62380,62382],{},[898,62355,2005],{},[898,62357,2974],{},[1700,62359,1703],{"stretchy":1702},[898,62361,1662],{},[1700,62363,1709],{"stretchy":1702},[1700,62365,2065],{},[898,62367,1662],{},[1700,62369,1768],{},[898,62371,1862],{},[898,62373,2974],{},[1700,62375,1703],{"stretchy":1702},[898,62377,1662],{},[1700,62379,1709],{"stretchy":1702},[1700,62381,2065],{},[898,62383,1662],{},[1785,62385,62386,62388],{},[898,62387,1662],{},[1931,62389,2343],{},[1700,62391,1765],{},[1774,62393,62394,62418],{},[895,62395,62396,62398,62400,62402,62404,62406,62408,62410,62412,62414,62416],{},[898,62397,2005],{},[898,62399,2974],{},[1700,62401,1703],{"stretchy":1702},[898,62403,1662],{},[1700,62405,1709],{"stretchy":1702},[1700,62407,1768],{},[898,62409,1862],{},[898,62411,2974],{},[1700,62413,1703],{"stretchy":1702},[898,62415,1662],{},[1700,62417,1709],{"stretchy":1702},[898,62419,1662],{},[898,62421,2196],{"mathvariant":1791},[902,62423,62424],{"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}.",[724,62426,62427,62428,2821,62443,8290,62465,57005],{},"Nutnou podmínkou minima ",[883,62429,62431],{"className":62430},[886],[888,62432,62433],{"xmlns":890},[892,62434,62435,62441],{},[895,62436,62437,62439],{},[898,62438,1862],{},[898,62440,2974],{},[902,62442,55744],{"encoding":904},[883,62444,62446],{"className":62445},[886],[888,62447,62448],{"xmlns":890},[892,62449,62450,62462],{},[895,62451,62452,62458,62460],{},[2007,62453,62454,62456],{},[898,62455,1662],{},[1931,62457,1772],{},[1700,62459,3601],{},[1931,62461,1772],{},[902,62463,62464],{"encoding":904},"Q_0 > 0",[883,62466,62468],{"className":62467},[886],[888,62469,62470],{"xmlns":890},[892,62471,62472,62496],{},[895,62473,62474,62476,62482,62484,62490,62492,62494],{},[898,62475,1862],{},[1785,62477,62478,62480],{},[898,62479,2974],{},[1700,62481,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,62483,1703],{"stretchy":1702},[2007,62485,62486,62488],{},[898,62487,1662],{},[1931,62489,1772],{},[1700,62491,1709],{"stretchy":1702},[1700,62493,1765],{},[1931,62495,1772],{},[902,62497,62498],{"encoding":904},"AC'(Q_0) = 0",[883,62500,62502],{"className":62501},[886],[888,62503,62504],{"xmlns":890,"display":28251},[892,62505,62506,62591],{},[895,62507,62508,62548,62550,62552,62554,62557,62559,62561,62563,62565,62571,62573,62575,62577,62579,62581,62587,62589],{},[1774,62509,62510,62542],{},[895,62511,62512,62514,62516,62518,62524,62526,62528,62530,62532,62534,62540],{},[898,62513,2005],{},[898,62515,2974],{},[1700,62517,1703],{"stretchy":1702},[2007,62519,62520,62522],{},[898,62521,1662],{},[1931,62523,1772],{},[1700,62525,1709],{"stretchy":1702},[1700,62527,1768],{},[898,62529,1862],{},[898,62531,2974],{},[1700,62533,1703],{"stretchy":1702},[2007,62535,62536,62538],{},[898,62537,1662],{},[1931,62539,1772],{},[1700,62541,1709],{"stretchy":1702},[2007,62543,62544,62546],{},[898,62545,1662],{},[1931,62547,1772],{},[1700,62549,1765],{},[1931,62551,1772],{},[6066,62553],{"width":15469},[1700,62555,62556],{},"⟺",[6066,62558],{"width":15469},[898,62560,2005],{},[898,62562,2974],{},[1700,62564,1703],{"stretchy":1702},[2007,62566,62567,62569],{},[898,62568,1662],{},[1931,62570,1772],{},[1700,62572,1709],{"stretchy":1702},[1700,62574,1765],{},[898,62576,1862],{},[898,62578,2974],{},[1700,62580,1703],{"stretchy":1702},[2007,62582,62583,62585],{},[898,62584,1662],{},[1931,62586,1772],{},[1700,62588,1709],{"stretchy":1702},[898,62590,2196],{"mathvariant":1791},[902,62592,62593],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,62595,62596,2106,62599,61681,62614,62629,62630,62645,62646,8290,62663,62685,62686,62708],{},[38,62597,62598],{},"Geometrická interpretace.",[883,62600,62602],{"className":62601},[886],[888,62603,62604],{"xmlns":890},[892,62605,62606,62612],{},[895,62607,62608,62610],{},[898,62609,2005],{},[898,62611,2974],{},[902,62613,55476],{"encoding":904},[883,62615,62617],{"className":62616},[886],[888,62618,62619],{"xmlns":890},[892,62620,62621,62627],{},[895,62622,62623,62625],{},[898,62624,1862],{},[898,62626,2974],{},[902,62628,55744],{"encoding":904}," právě v bodě minima ",[883,62631,62633],{"className":62632},[886],[888,62634,62635],{"xmlns":890},[892,62636,62637,62643],{},[895,62638,62639,62641],{},[898,62640,1862],{},[898,62642,2974],{},[902,62644,55744],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,62647,62649],{"className":62648},[886],[888,62650,62651],{"xmlns":890},[892,62652,62653,62661],{},[895,62654,62655],{},[2007,62656,62657,62659],{},[898,62658,1662],{},[1931,62660,1772],{},[902,62662,38493],{"encoding":904},[883,62664,62666],{"className":62665},[886],[888,62667,62668],{"xmlns":890},[892,62669,62670,62682],{},[895,62671,62672,62674,62676,62678,62680],{},[898,62673,2005],{},[898,62675,2974],{},[1700,62677,3640],{},[898,62679,1862],{},[898,62681,2974],{},[902,62683,62684],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,62687,62689],{"className":62688},[886],[888,62690,62691],{"xmlns":890},[892,62692,62693,62705],{},[895,62694,62695,62697,62699,62701,62703],{},[898,62696,2005],{},[898,62698,2974],{},[1700,62700,3601],{},[898,62702,1862],{},[898,62704,2974],{},[902,62706,62707],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,62710,62711,62712,62754,62755,62772,62773,2196],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,62713,62715],{"className":62714},[886],[888,62716,62717],{"xmlns":890},[892,62718,62719,62751],{},[895,62720,62721,62723,62725,62727,62733,62735,62737,62739,62741,62743,62749],{},[898,62722,1862],{},[898,62724,2974],{},[1700,62726,1703],{"stretchy":1702},[2007,62728,62729,62731],{},[898,62730,1662],{},[1931,62732,1772],{},[1700,62734,1709],{"stretchy":1702},[1700,62736,1765],{},[898,62738,2005],{},[898,62740,2974],{},[1700,62742,1703],{"stretchy":1702},[2007,62744,62745,62747],{},[898,62746,1662],{},[1931,62748,1772],{},[1700,62750,1709],{"stretchy":1702},[902,62752,62753],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,62756,62758],{"className":62757},[886],[888,62759,62760],{"xmlns":890},[892,62761,62762,62770],{},[895,62763,62764],{},[2007,62765,62766,62768],{},[898,62767,1662],{},[1931,62769,1772],{},[902,62771,38493],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,62774,62776],{"className":62775},[886],[888,62777,62778],{"xmlns":890},[892,62779,62780,62804],{},[895,62781,62782,62784,62786,62788,62790,62792,62794,62796,62798,62800,62802],{},[898,62783,1862],{},[898,62785,2974],{},[1700,62787,1703],{"stretchy":1702},[898,62789,1662],{},[1700,62791,1709],{"stretchy":1702},[1700,62793,1765],{},[898,62795,2005],{},[898,62797,2974],{},[1700,62799,1703],{"stretchy":1702},[898,62801,1662],{},[1700,62803,1709],{"stretchy":1702},[902,62805,62806],{"encoding":904},"AC(Q) = MC(Q)",[4060,62808,62809],{},[724,62810,62811,62813,62814,10577,62832,62853,62854,10577,62857,62878,62879,62894,62895,58222,62910,4110],{},[883,62812,4601],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,62815,62816,62817],{},"minimum ",[883,62818,62820],{"className":62819},[886],[888,62821,62822],{"xmlns":890},[892,62823,62824,62830],{},[895,62825,62826,62828],{},[898,62827,1862],{},[898,62829,2974],{},[902,62831,55744],{"encoding":904},[883,62833,62835],{"className":62834},[886],[888,62836,62837],{"xmlns":890},[892,62838,62839,62851],{},[895,62840,62841,62843,62845,62847,62849],{},[898,62842,1862],{},[898,62844,2974],{},[1700,62846,1765],{},[898,62848,2005],{},[898,62850,2974],{},[902,62852,55407],{"encoding":904},", pro ",[38,62855,62856],{},"maximum zisku",[883,62858,62860],{"className":62859},[886],[888,62861,62862],{"xmlns":890},[892,62863,62864,62876],{},[895,62865,62866,62868,62870,62872,62874],{},[898,62867,2005],{},[898,62869,4185],{},[1700,62871,1765],{},[898,62873,2005],{},[898,62875,2974],{},[902,62877,55455],{"encoding":904},". Obě podmínky využívají ",[883,62880,62882],{"className":62881},[886],[888,62883,62884],{"xmlns":890},[892,62885,62886,62892],{},[895,62887,62888,62890],{},[898,62889,2005],{},[898,62891,2974],{},[902,62893,55476],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,62896,62898],{"className":62897},[886],[888,62899,62900],{"xmlns":890},[892,62901,62902,62908],{},[895,62903,62904,62906],{},[898,62905,1862],{},[898,62907,2974],{},[902,62909,55744],{"encoding":904},[883,62911,62913],{"className":62912},[886],[888,62914,62915],{"xmlns":890},[892,62916,62917,62923],{},[895,62918,62919,62921],{},[898,62920,2005],{},[898,62922,4185],{},[902,62924,6822],{"encoding":904},[37533,62926,62928],{"id":62927},"příklad-37","Příklad 3.7",[724,62930,62931,57706,62933,62967,62968,62981,62982,62997],{},[38,62932,56171],{},[883,62934,62936],{"className":62935},[886],[888,62937,62938],{"xmlns":890},[892,62939,62940,62964],{},[895,62941,62942,62944,62946,62948,62954,62956,62958,62960,62962],{},[898,62943,2971],{},[898,62945,2974],{},[1700,62947,1765],{},[1785,62949,62950,62952],{},[898,62951,1662],{},[1931,62953,2343],{},[1700,62955,1897],{},[1931,62957,2385],{},[898,62959,1662],{},[1700,62961,1897],{},[1931,62963,5753],{},[902,62965,62966],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,62969,62971],{"className":62970},[886],[888,62972,62973],{"xmlns":890},[892,62974,62975,62979],{},[895,62976,62977],{},[898,62978,1662],{},[902,62980,1662],{"encoding":904}," minimalizující ",[883,62983,62985],{"className":62984},[886],[888,62986,62987],{"xmlns":890},[892,62988,62989,62995],{},[895,62990,62991,62993],{},[898,62992,1862],{},[898,62994,2974],{},[902,62996,55744],{"encoding":904}," a ověřte princip (3.10).",[724,62999,63000,63002],{},[38,63001,22955],{}," Přímý výpočet:",[883,63004,63006],{"className":63005},[886],[888,63007,63008],{"xmlns":890,"display":28251},[892,63009,63010,63112],{},[895,63011,63012,63014,63016,63018,63040,63042,63044,63046,63048,63050,63056,63058,63060,63062,63064,63066,63072,63074,63076,63078,63088,63090,63110],{},[898,63013,1862],{},[898,63015,2974],{},[1700,63017,1765],{},[1774,63019,63020,63038],{},[895,63021,63022,63028,63030,63032,63034,63036],{},[1785,63023,63024,63026],{},[898,63025,1662],{},[1931,63027,2343],{},[1700,63029,1897],{},[1931,63031,2385],{},[898,63033,1662],{},[1700,63035,1897],{},[1931,63037,5753],{},[898,63039,1662],{},[1700,63041,1765],{},[898,63043,1662],{},[1700,63045,1897],{},[1931,63047,2385],{},[1700,63049,1897],{},[1774,63051,63052,63054],{},[1931,63053,5753],{},[898,63055,1662],{},[1700,63057,1732],{"separator":1731},[6066,63059],{"width":6068},[1700,63061,1703],{"stretchy":1702},[898,63063,1862],{},[898,63065,2974],{},[1785,63067,63068,63070],{},[1700,63069,1709],{"stretchy":1702},[1700,63071,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,63073,1765],{},[1931,63075,1933],{},[1700,63077,1768],{},[1774,63079,63080,63082],{},[1931,63081,5753],{},[1785,63083,63084,63086],{},[898,63085,1662],{},[1931,63087,2343],{},[1700,63089,1765],{},[1774,63091,63092,63104],{},[895,63093,63094,63100,63102],{},[1785,63095,63096,63098],{},[898,63097,1662],{},[1931,63099,2343],{},[1700,63101,1768],{},[1931,63103,5753],{},[1785,63105,63106,63108],{},[898,63107,1662],{},[1931,63109,2343],{},[898,63111,2196],{"mathvariant":1791},[902,63113,63114],{"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}.",[724,63116,63117,63157,63158,63182,63183,63233,63234,2196],{},[883,63118,63120],{"className":63119},[886],[888,63121,63122],{"xmlns":890},[892,63123,63124,63154],{},[895,63125,63126,63128,63130,63132,63138,63140,63142,63144,63150,63152],{},[1700,63127,1703],{"stretchy":1702},[898,63129,1862],{},[898,63131,2974],{},[1785,63133,63134,63136],{},[1700,63135,1709],{"stretchy":1702},[1700,63137,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,63139,1765],{},[1931,63141,1772],{},[1700,63143,4178],{},[2007,63145,63146,63148],{},[898,63147,1662],{},[1931,63149,1933],{},[1700,63151,1765],{},[1931,63153,2445],{},[902,63155,63156],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,63159,63161],{"className":63160},[886],[888,63162,63163],{"xmlns":890},[892,63164,63165,63179],{},[895,63166,63167,63173,63175,63177],{},[2007,63168,63169,63171],{},[898,63170,1662],{},[1931,63172,2343],{},[1700,63174,1765],{},[1700,63176,1768],{},[1931,63178,2445],{},[902,63180,63181],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,63184,63186],{"className":63185},[886],[888,63187,63188],{"xmlns":890},[892,63189,63190,63230],{},[895,63191,63192,63194,63196,63198,63208,63210,63212,63214,63216,63224,63226,63228],{},[1700,63193,1703],{"stretchy":1702},[898,63195,1862],{},[898,63197,2974],{},[1785,63199,63200,63202],{},[1700,63201,1709],{"stretchy":1702},[895,63203,63204,63206],{},[1700,63205,1793],{"mathvariant":1791},[1700,63207,1793],{"mathvariant":1791},[1700,63209,1703],{"stretchy":1702},[1931,63211,2445],{},[1700,63213,1709],{"stretchy":1702},[1700,63215,1765],{},[1770,63217,63218],{"scriptlevel":1772,"displaystyle":1702},[1774,63219,63220,63222],{},[1931,63221,1933],{},[1931,63223,2385],{},[1700,63225,3601],{},[1931,63227,1772],{},[1700,63229,4178],{},[902,63231,63232],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,63235,63237],{"className":63236},[886],[888,63238,63239],{"xmlns":890},[892,63240,63241,63257],{},[895,63242,63243,63245,63247,63249,63251,63253,63255],{},[898,63244,1862],{},[898,63246,2974],{},[1700,63248,1703],{"stretchy":1702},[1931,63250,2445],{},[1700,63252,1709],{"stretchy":1702},[1700,63254,1765],{},[1931,63256,36429],{},[902,63258,63259],{"encoding":904},"AC(6) = 15",[724,63261,63262,63263,63289,63290,2901],{},"Pomocí principu: ",[883,63264,63266],{"className":63265},[886],[888,63267,63268],{"xmlns":890},[892,63269,63270,63286],{},[895,63271,63272,63274,63276,63278,63280,63282,63284],{},[898,63273,2005],{},[898,63275,2974],{},[1700,63277,1765],{},[1931,63279,2343],{},[898,63281,1662],{},[1700,63283,1897],{},[1931,63285,2385],{},[902,63287,63288],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,63291,63293],{"className":63292},[886],[888,63294,63295],{"xmlns":890},[892,63296,63297,63309],{},[895,63298,63299,63301,63303,63305,63307],{},[898,63300,1862],{},[898,63302,2974],{},[1700,63304,1765],{},[898,63306,2005],{},[898,63308,2974],{},[902,63310,55407],{"encoding":904},[883,63312,63314],{"className":63313},[886],[888,63315,63316],{"xmlns":890,"display":28251},[892,63317,63318,63420],{},[895,63319,63320,63342,63344,63346,63348,63350,63352,63354,63356,63358,63364,63366,63368,63370,63372,63374,63376,63378,63384,63386,63388,63390,63392,63394,63396,63402,63404,63406,63408,63410,63412,63414,63416,63418],{},[1774,63321,63322,63340],{},[895,63323,63324,63330,63332,63334,63336,63338],{},[1785,63325,63326,63328],{},[898,63327,1662],{},[1931,63329,2343],{},[1700,63331,1897],{},[1931,63333,2385],{},[898,63335,1662],{},[1700,63337,1897],{},[1931,63339,5753],{},[898,63341,1662],{},[1700,63343,1765],{},[1931,63345,2343],{},[898,63347,1662],{},[1700,63349,1897],{},[1931,63351,2385],{},[1781,63353,4175],{},[1700,63355,4178],{},[1781,63357,4175],{},[1785,63359,63360,63362],{},[898,63361,1662],{},[1931,63363,2343],{},[1700,63365,1897],{},[1931,63367,2385],{},[898,63369,1662],{},[1700,63371,1897],{},[1931,63373,5753],{},[1700,63375,1765],{},[1931,63377,2343],{},[1785,63379,63380,63382],{},[898,63381,1662],{},[1931,63383,2343],{},[1700,63385,1897],{},[1931,63387,2385],{},[898,63389,1662],{},[1781,63391,4175],{},[1700,63393,4178],{},[1781,63395,4175],{},[1785,63397,63398,63400],{},[898,63399,1662],{},[1931,63401,2343],{},[1700,63403,1765],{},[1931,63405,5753],{},[1781,63407,4175],{},[1700,63409,4178],{},[1781,63411,4175],{},[898,63413,1662],{},[1700,63415,1765],{},[1931,63417,2445],{},[1700,63419,1732],{"separator":1731},[902,63421,63422],{"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,",[724,63424,63425,63426,63464],{},"a ",[883,63427,63429],{"className":63428},[886],[888,63430,63431],{"xmlns":890},[892,63432,63433,63461],{},[895,63434,63435,63437,63439,63441,63443,63445,63447,63449,63451,63453,63455,63457,63459],{},[898,63436,1862],{},[898,63438,2974],{},[1700,63440,1703],{"stretchy":1702},[1931,63442,2445],{},[1700,63444,1709],{"stretchy":1702},[1700,63446,1765],{},[898,63448,2005],{},[898,63450,2974],{},[1700,63452,1703],{"stretchy":1702},[1931,63454,2445],{},[1700,63456,1709],{"stretchy":1702},[1700,63458,1765],{},[1931,63460,36429],{},[902,63462,63463],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,63466,63468],{"id":63467},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,63470,63471,63472,2901],{},"Analogicky pro ",[883,63473,63475],{"className":63474},[886],[888,63476,63477],{"xmlns":890},[892,63478,63479,63487],{},[895,63480,63481,63483,63485],{},[898,63482,1862],{},[898,63484,40524],{},[898,63486,2974],{},[902,63488,55495],{"encoding":904},[883,63490,63492],{"className":63491},[886],[888,63493,63494],{"xmlns":890,"display":28251},[892,63495,63496,63547],{},[20939,63497,63498],{"width":28256},[20944,63499,63500,63502,63540,63542],{},[20947,63501],{"width":28261},[20947,63503,63504],{},[895,63505,63506,63508,63510,63512,63514,63520,63522,63524,63526,63528,63530,63536,63538],{},[898,63507,1862],{},[898,63509,40524],{},[898,63511,2974],{},[1700,63513,1703],{"stretchy":1702},[2007,63515,63516,63518],{},[898,63517,1662],{},[1931,63519,1772],{},[1700,63521,1709],{"stretchy":1702},[1700,63523,1765],{},[898,63525,2005],{},[898,63527,2974],{},[1700,63529,1703],{"stretchy":1702},[2007,63531,63532,63534],{},[898,63533,1662],{},[1931,63535,1772],{},[1700,63537,1709],{"stretchy":1702},[898,63539,2196],{"mathvariant":1791},[20947,63541],{"width":28261},[20947,63543,63544],{},[1781,63545,63546],{},"(3.11)",[902,63548,63549],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[4060,63551,63552],{},[724,63553,63554,62230,63556],{},[883,63555,56628],{},[38,63557,63558,63559,63576],{},"V bodě minima průměrných variabilních nákladů se ",[883,63560,63562],{"className":63561},[886],[888,63563,63564],{"xmlns":890},[892,63565,63566,63574],{},[895,63567,63568,63570,63572],{},[898,63569,1862],{},[898,63571,40524],{},[898,63573,2974],{},[902,63575,55495],{"encoding":904}," rovnají mezním nákladům.",[724,63578,63579,63580,63602,63603,2196],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,63581,63583],{"className":63582},[886],[888,63584,63585],{"xmlns":890},[892,63586,63587,63599],{},[895,63588,63589,63595,63597],{},[2007,63590,63591,63593],{},[898,63592,1662],{},[1931,63594,1772],{},[1700,63596,1765],{},[1931,63598,53383],{},[902,63600,63601],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,63604,63606],{"className":63605},[886],[888,63607,63608],{"xmlns":890},[892,63609,63610,63636],{},[895,63611,63612,63614,63616,63618,63620,63622,63624,63626,63628,63630,63632,63634],{},[898,63613,1862],{},[898,63615,40524],{},[898,63617,2974],{},[1700,63619,1703],{"stretchy":1702},[898,63621,1662],{},[1700,63623,1709],{"stretchy":1702},[1700,63625,1765],{},[898,63627,2005],{},[898,63629,2974],{},[1700,63631,1703],{"stretchy":1702},[898,63633,1662],{},[1700,63635,1709],{"stretchy":1702},[902,63637,63638],{"encoding":904},"AVC(Q) = MC(Q)",[115,63640,63642],{"id":63641},"zisk-a-body-zvratu","Zisk a body zvratu",[724,63644,63645,2106,63648,63664],{},[38,63646,63647],{},"Zisk",[883,63649,63651],{"className":63650},[886],[888,63652,63653],{"xmlns":890},[892,63654,63655,63661],{},[895,63656,63657,63659],{},[898,63658,1677],{},[898,63660,4185],{},[902,63662,63663],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,63666,63668],{"className":63667},[886],[888,63669,63670],{"xmlns":890,"display":28251},[892,63671,63672,63731],{},[20939,63673,63674],{"width":28256},[20944,63675,63676,63678,63724,63726],{},[20947,63677],{"width":28261},[20947,63679,63680],{},[895,63681,63682,63684,63686,63688,63690,63692,63694,63696,63698,63700,63702,63704,63706,63708,63710,63712,63714,63716,63718,63720,63722],{},[898,63683,1677],{},[898,63685,4185],{},[1700,63687,1765],{},[898,63689,1677],{},[898,63691,4185],{},[1700,63693,1703],{"stretchy":1702},[898,63695,1662],{},[1700,63697,1709],{"stretchy":1702},[1700,63699,1765],{},[898,63701,2971],{},[898,63703,4185],{},[1700,63705,1703],{"stretchy":1702},[898,63707,1662],{},[1700,63709,1709],{"stretchy":1702},[1700,63711,1768],{},[898,63713,2971],{},[898,63715,2974],{},[1700,63717,1703],{"stretchy":1702},[898,63719,1662],{},[1700,63721,1709],{"stretchy":1702},[898,63723,2196],{"mathvariant":1791},[20947,63725],{"width":28261},[20947,63727,63728],{},[1781,63729,63730],{},"(3.12)",[902,63732,63733],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,63735,63736,63737,2114,63752,43821,63767,63769,63770,63773,63774,63790,63791,63806,63807,63822,63823,1343,63836,63849,63850,1343,63868,63886,63887,10208,63890,63893,63894,1348,63916,8290,63938,63960,63961,8290,63991,64013],{},"Body rovnosti ",[883,63738,63740],{"className":63739},[886],[888,63741,63742],{"xmlns":890},[892,63743,63744,63750],{},[895,63745,63746,63748],{},[898,63747,2971],{},[898,63749,4185],{},[902,63751,4285],{"encoding":904},[883,63753,63755],{"className":63754},[886],[888,63756,63757],{"xmlns":890},[892,63758,63759,63765],{},[895,63760,63761,63763],{},[898,63762,2971],{},[898,63764,2974],{},[902,63766,3436],{"encoding":904},[38,63768,55911],{}," (též vyrovnání, ",[614,63771,63772],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,63775,63777],{"className":63776},[886],[888,63778,63779],{"xmlns":890},[892,63780,63781,63787],{},[895,63782,63783,63785],{},[898,63784,40524],{},[898,63786,2974],{},[902,63788,63789],{"encoding":904},"VC",") je ",[883,63792,63794],{"className":63793},[886],[888,63795,63796],{"xmlns":890},[892,63797,63798,63804],{},[895,63799,63800,63802],{},[898,63801,2971],{},[898,63803,4185],{},[902,63805,4285],{"encoding":904}," kvadratická a ",[883,63808,63810],{"className":63809},[886],[888,63811,63812],{"xmlns":890},[892,63813,63814,63820],{},[895,63815,63816,63818],{},[898,63817,2971],{},[898,63819,2974],{},[902,63821,3436],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,63824,63826],{"className":63825},[886],[888,63827,63828],{"xmlns":890},[892,63829,63830,63834],{},[895,63831,63832],{},[898,63833,1862],{},[902,63835,1862],{"encoding":904},[883,63837,63839],{"className":63838},[886],[888,63840,63841],{"xmlns":890},[892,63842,63843,63847],{},[895,63844,63845],{},[898,63846,23438],{},[902,63848,23438],{"encoding":904}," odpovídajících množstvím ",[883,63851,63853],{"className":63852},[886],[888,63854,63855],{"xmlns":890},[892,63856,63857,63865],{},[895,63858,63859],{},[2007,63860,63861,63863],{},[898,63862,1662],{},[898,63864,1862],{},[902,63866,63867],{"encoding":904},"Q_A",[883,63869,63871],{"className":63870},[886],[888,63872,63873],{"xmlns":890},[892,63874,63875,63883],{},[895,63876,63877],{},[2007,63878,63879,63881],{},[898,63880,1662],{},[898,63882,23438],{},[902,63884,63885],{"encoding":904},"Q_B"," — firma je na ",[38,63888,63889],{},"prahu rentability",[614,63891,63892],{},"break even","). Pro ",[883,63895,63897],{"className":63896},[886],[888,63898,63899],{"xmlns":890},[892,63900,63901,63913],{},[895,63902,63903,63905,63907],{},[898,63904,1662],{},[1700,63906,3640],{},[2007,63908,63909,63911],{},[898,63910,1662],{},[898,63912,1862],{},[902,63914,63915],{"encoding":904},"Q \u003C Q_A",[883,63917,63919],{"className":63918},[886],[888,63920,63921],{"xmlns":890},[892,63922,63923,63935],{},[895,63924,63925,63927,63929],{},[898,63926,1662],{},[1700,63928,3601],{},[2007,63930,63931,63933],{},[898,63932,1662],{},[898,63934,23438],{},[902,63936,63937],{"encoding":904},"Q > Q_B",[883,63939,63941],{"className":63940},[886],[888,63942,63943],{"xmlns":890},[892,63944,63945,63957],{},[895,63946,63947,63949,63951,63953,63955],{},[898,63948,2971],{},[898,63950,2974],{},[1700,63952,3601],{},[898,63954,2971],{},[898,63956,4185],{},[902,63958,63959],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,63962,63964],{"className":63963},[886],[888,63965,63966],{"xmlns":890},[892,63967,63968,63988],{},[895,63969,63970,63976,63978,63980,63982],{},[2007,63971,63972,63974],{},[898,63973,1662],{},[898,63975,1862],{},[1700,63977,3640],{},[898,63979,1662],{},[1700,63981,3640],{},[2007,63983,63984,63986],{},[898,63985,1662],{},[898,63987,23438],{},[902,63989,63990],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,63992,63994],{"className":63993},[886],[888,63995,63996],{"xmlns":890},[892,63997,63998,64010],{},[895,63999,64000,64002,64004,64006,64008],{},[898,64001,2971],{},[898,64003,4185],{},[1700,64005,3601],{},[898,64007,2971],{},[898,64009,2974],{},[902,64011,64012],{"encoding":904},"TR > TC"," (zisk).",[4060,64015,64016],{},[724,64017,64018,64020],{},[883,64019,4346],{}," 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.",[724,64022,64023,64024,64050],{},"Body zvratu jsou řešení rovnice ",[883,64025,64027],{"className":64026},[886],[888,64028,64029],{"xmlns":890},[892,64030,64031,64047],{},[895,64032,64033,64035,64037,64039,64041,64043,64045],{},[898,64034,1677],{},[898,64036,4185],{},[1700,64038,1703],{"stretchy":1702},[898,64040,1662],{},[1700,64042,1709],{"stretchy":1702},[1700,64044,1765],{},[1931,64046,1772],{},[902,64048,64049],{"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.",[724,64052,64053],{},[2756,64054],{"alt":64055,"className":64056,"src":64057},"imek-tr-tc-body-zvratu",[210,2760],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,64059,64060],{},[614,64061,64062,64063,64078,64079,64094,64095,2114,64108,43545,64121,64134,64135,2114,64152,64169,64170,64190,64191,2114,64206,6661,64221,64250],{},"Obrázek 3.11: Body zvratu — křivky ",[883,64064,64066],{"className":64065},[886],[888,64067,64068],{"xmlns":890},[892,64069,64070,64076],{},[895,64071,64072,64074],{},[898,64073,2971],{},[898,64075,4185],{},[902,64077,4285],{"encoding":904}," (obrácená parabola) a ",[883,64080,64082],{"className":64081},[886],[888,64083,64084],{"xmlns":890},[892,64085,64086,64092],{},[895,64087,64088,64090],{},[898,64089,2971],{},[898,64091,2974],{},[902,64093,3436],{"encoding":904}," (přímka) se protínají v bodech ",[883,64096,64098],{"className":64097},[886],[888,64099,64100],{"xmlns":890},[892,64101,64102,64106],{},[895,64103,64104],{},[898,64105,1862],{},[902,64107,1862],{"encoding":904},[883,64109,64111],{"className":64110},[886],[888,64112,64113],{"xmlns":890},[892,64114,64115,64119],{},[895,64116,64117],{},[898,64118,23438],{},[902,64120,23438],{"encoding":904},[883,64122,64124],{"className":64123},[886],[888,64125,64126],{"xmlns":890},[892,64127,64128,64132],{},[895,64129,64130],{},[898,64131,1662],{},[902,64133,1662],{"encoding":904}," v hodnotách ",[883,64136,64138],{"className":64137},[886],[888,64139,64140],{"xmlns":890},[892,64141,64142,64150],{},[895,64143,64144],{},[2007,64145,64146,64148],{},[898,64147,1662],{},[898,64149,1862],{},[902,64151,63867],{"encoding":904},[883,64153,64155],{"className":64154},[886],[888,64156,64157],{"xmlns":890},[892,64158,64159,64167],{},[895,64160,64161],{},[2007,64162,64163,64165],{},[898,64164,1662],{},[898,64166,23438],{},[902,64168,63885],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,64171,64173],{"className":64172},[886],[888,64174,64175],{"xmlns":890},[892,64176,64177,64187],{},[895,64178,64179],{},[2007,64180,64181,64183,64185],{},[898,64182,1662],{},[898,64184,56381],{},[1700,64186,56384],{},[902,64188,64189],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,64192,64194],{"className":64193},[886],[888,64195,64196],{"xmlns":890},[892,64197,64198,64204],{},[895,64199,64200,64202],{},[898,64201,2971],{},[898,64203,4185],{},[902,64205,4285],{"encoding":904},[883,64207,64209],{"className":64208},[886],[888,64210,64211],{"xmlns":890},[892,64212,64213,64219],{},[895,64214,64215,64217],{},[898,64216,2971],{},[898,64218,2974],{},[902,64220,3436],{"encoding":904},[883,64222,64224],{"className":64223},[886],[888,64225,64226],{"xmlns":890},[892,64227,64228,64248],{},[895,64229,64230,64236,64238,64240,64242],{},[2007,64231,64232,64234],{},[898,64233,1662],{},[898,64235,1862],{},[1700,64237,3640],{},[898,64239,1662],{},[1700,64241,3640],{},[2007,64243,64244,64246],{},[898,64245,1662],{},[898,64247,23438],{},[902,64249,63990],{"encoding":904}," vyznačuje zisk.",[37533,64252,64254],{"id":64253},"příklad-38","Příklad 3.8",[724,64256,64257,64259,64260,1343,64280,1343,64306,64332],{},[38,64258,56171],{}," Dáno ",[883,64261,64263],{"className":64262},[886],[888,64264,64265],{"xmlns":890},[892,64266,64267,64277],{},[895,64268,64269,64271,64273,64275],{},[898,64270,10619],{},[898,64272,2974],{},[1700,64274,1765],{},[1931,64276,2553],{},[902,64278,64279],{"encoding":904},"FC = 4",[883,64281,64283],{"className":64282},[886],[888,64284,64285],{"xmlns":890},[892,64286,64287,64303],{},[895,64288,64289,64291,64293,64295,64297],{},[898,64290,2971],{},[898,64292,40524],{},[898,64294,2974],{},[1700,64296,1765],{},[1785,64298,64299,64301],{},[898,64300,1662],{},[1931,64302,2343],{},[902,64304,64305],{"encoding":904},"TVC = Q^2",[883,64307,64309],{"className":64308},[886],[888,64310,64311],{"xmlns":890},[892,64312,64313,64329],{},[895,64314,64315,64317,64319,64321,64323,64325,64327],{},[898,64316,1677],{},[1700,64318,1765],{},[1700,64320,1768],{},[1931,64322,2343],{},[898,64324,1662],{},[1700,64326,1897],{},[1931,64328,4190],{},[902,64330,64331],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,64334,64335,64337],{},[38,64336,22955],{}," Celkové náklady a příjem:",[883,64339,64341],{"className":64340},[886],[888,64342,64343],{"xmlns":890,"display":28251},[892,64344,64345,64411],{},[895,64346,64347,64349,64351,64353,64355,64357,64363,64365,64367,64369,64371,64373,64375,64377,64379,64381,64383,64385,64387,64389,64391,64393,64395,64397,64403,64405,64407,64409],{},[898,64348,2971],{},[898,64350,2974],{},[1700,64352,1765],{},[1931,64354,2553],{},[1700,64356,1897],{},[1785,64358,64359,64361],{},[898,64360,1662],{},[1931,64362,2343],{},[1700,64364,1732],{"separator":1731},[6066,64366],{"width":6068},[898,64368,2971],{},[898,64370,4185],{},[1700,64372,1765],{},[898,64374,1662],{},[1700,64376,2065],{},[1700,64378,1703],{"stretchy":1702},[1700,64380,1768],{},[1931,64382,2343],{},[898,64384,1662],{},[1700,64386,1897],{},[1931,64388,4190],{},[1700,64390,1709],{"stretchy":1702},[1700,64392,1765],{},[1700,64394,1768],{},[1931,64396,2343],{},[1785,64398,64399,64401],{},[898,64400,1662],{},[1931,64402,2343],{},[1700,64404,1897],{},[1931,64406,4190],{},[898,64408,1662],{},[898,64410,2196],{"mathvariant":1791},[902,64412,64413],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,64415,64416],{},"Zisk dle (3.12):",[883,64418,64420],{"className":64419},[886],[888,64421,64422],{"xmlns":890,"display":28251},[892,64423,64424,64502],{},[895,64425,64426,64428,64430,64432,64434,64436,64438,64440,64442,64444,64446,64448,64450,64456,64458,64460,64462,64464,64466,64468,64470,64472,64478,64480,64482,64484,64486,64492,64494,64496,64498,64500],{},[898,64427,1677],{},[898,64429,4185],{},[1700,64431,1765],{},[898,64433,2971],{},[898,64435,4185],{},[1700,64437,1768],{},[898,64439,2971],{},[898,64441,2974],{},[1700,64443,1765],{},[1700,64445,1703],{"stretchy":1702},[1700,64447,1768],{},[1931,64449,2343],{},[1785,64451,64452,64454],{},[898,64453,1662],{},[1931,64455,2343],{},[1700,64457,1897],{},[1931,64459,4190],{},[898,64461,1662],{},[1700,64463,1709],{"stretchy":1702},[1700,64465,1768],{},[1700,64467,1703],{"stretchy":1702},[1931,64469,2553],{},[1700,64471,1897],{},[1785,64473,64474,64476],{},[898,64475,1662],{},[1931,64477,2343],{},[1700,64479,1709],{"stretchy":1702},[1700,64481,1765],{},[1700,64483,1768],{},[1931,64485,2385],{},[1785,64487,64488,64490],{},[898,64489,1662],{},[1931,64491,2343],{},[1700,64493,1897],{},[1931,64495,4190],{},[898,64497,1662],{},[1700,64499,1768],{},[1931,64501,59503],{},[902,64503,64504],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,64506,64507,64510,64511,17761,64547,2901],{},[38,64508,64509],{},"Body zvratu"," jsou kořeny rovnice ",[883,64512,64514],{"className":64513},[886],[888,64515,64516],{"xmlns":890},[892,64517,64518,64544],{},[895,64519,64520,64522,64524,64530,64532,64534,64536,64538,64540,64542],{},[1700,64521,1768],{},[1931,64523,2385],{},[1785,64525,64526,64528],{},[898,64527,1662],{},[1931,64529,2343],{},[1700,64531,1897],{},[1931,64533,4190],{},[898,64535,1662],{},[1700,64537,1768],{},[1931,64539,2553],{},[1700,64541,1765],{},[1931,64543,1772],{},[902,64545,64546],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,64548,64550],{"className":64549},[886],[888,64551,64552],{"xmlns":890},[892,64553,64554,64578],{},[895,64555,64556,64558,64564,64566,64568,64570,64572,64574,64576],{},[1931,64557,2385],{},[1785,64559,64560,64562],{},[898,64561,1662],{},[1931,64563,2343],{},[1700,64565,1768],{},[1931,64567,4190],{},[898,64569,1662],{},[1700,64571,1897],{},[1931,64573,2553],{},[1700,64575,1765],{},[1931,64577,1772],{},[902,64579,64580],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,64582,64584],{"className":64583},[886],[888,64585,64586],{"xmlns":890,"display":28251},[892,64587,64588,64645],{},[895,64589,64590,64602,64604,64627,64629,64643],{},[2007,64591,64592,64594],{},[898,64593,1662],{},[895,64595,64596,64598,64600],{},[1931,64597,1933],{},[1700,64599,1732],{"separator":1731},[1931,64601,2343],{},[1700,64603,1765],{},[1774,64605,64606,64625],{},[895,64607,64608,64610,64613],{},[1931,64609,4190],{},[1700,64611,64612],{},"±",[8305,64614,64615],{},[895,64616,64617,64620,64622],{},[1931,64618,64619],{},"81",[1700,64621,1768],{},[1931,64623,64624],{},"48",[1931,64626,2445],{},[1700,64628,1765],{},[1774,64630,64631,64641],{},[895,64632,64633,64635,64637],{},[1931,64634,4190],{},[1700,64636,64612],{},[8305,64638,64639],{},[1931,64640,9139],{},[1931,64642,2445],{},[1700,64644,1732],{"separator":1731},[902,64646,64647],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,64649,64650,64651,2114,64674,2196],{},"numericky ",[883,64652,64654],{"className":64653},[886],[888,64655,64656],{"xmlns":890},[892,64657,64658,64671],{},[895,64659,64660,64666,64668],{},[2007,64661,64662,64664],{},[898,64663,1662],{},[1931,64665,1933],{},[1700,64667,6088],{},[1931,64669,64670],{},"0,543",[902,64672,64673],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,64675,64677],{"className":64676},[886],[888,64678,64679],{"xmlns":890},[892,64680,64681,64694],{},[895,64682,64683,64689,64691],{},[2007,64684,64685,64687],{},[898,64686,1662],{},[1931,64688,2343],{},[1700,64690,6088],{},[1931,64692,64693],{},"2,457",[902,64695,64696],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,64698,64699,2106,64702,7740,64747,17761,64781,64799],{},[38,64700,64701],{},"Maximum zisku.",[883,64703,64705],{"className":64704},[886],[888,64706,64707],{"xmlns":890},[892,64708,64709,64744],{},[895,64710,64711,64713,64719,64721,64723,64725,64727,64729,64731,64733,64735,64737,64739,64741],{},[898,64712,1677],{},[1785,64714,64715,64717],{},[898,64716,4185],{},[1700,64718,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,64720,1765],{},[1700,64722,1768],{},[1931,64724,2445],{},[898,64726,1662],{},[1700,64728,1897],{},[1931,64730,4190],{},[1700,64732,1765],{},[1931,64734,1772],{},[1700,64736,4178],{},[898,64738,1662],{},[1700,64740,1765],{},[1931,64742,64743],{},"1,5",[902,64745,64746],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,64748,64750],{"className":64749},[886],[888,64751,64752],{"xmlns":890},[892,64753,64754,64778],{},[895,64755,64756,64758,64768,64770,64772,64774,64776],{},[898,64757,1677],{},[1785,64759,64760,64762],{},[898,64761,4185],{},[895,64763,64764,64766],{},[1700,64765,1793],{"mathvariant":1791},[1700,64767,1793],{"mathvariant":1791},[1700,64769,1765],{},[1700,64771,1768],{},[1931,64773,2445],{},[1700,64775,3640],{},[1931,64777,1772],{},[902,64779,64780],{"encoding":904},"PR'' = -6 \u003C 0",[883,64782,64784],{"className":64783},[886],[888,64785,64786],{"xmlns":890},[892,64787,64788,64796],{},[895,64789,64790,64792,64794],{},[898,64791,1662],{},[1700,64793,1765],{},[1931,64795,64743],{},[902,64797,64798],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,64801,64803],{"className":64802},[886],[888,64804,64805],{"xmlns":890,"display":28251},[892,64806,64807,64870],{},[895,64808,64809,64811,64813,64815,64817,64819,64821,64823,64825,64827,64829,64831,64837,64839,64841,64843,64845,64847,64849,64851,64853,64856,64858,64861,64863,64865,64867],{},[898,64810,1677],{},[898,64812,4185],{},[1700,64814,1703],{"stretchy":1702},[1931,64816,64743],{},[1700,64818,1709],{"stretchy":1702},[1700,64820,1765],{},[1700,64822,1768],{},[1931,64824,2385],{},[1700,64826,2065],{},[1700,64828,1703],{"stretchy":1702},[1931,64830,64743],{},[1785,64832,64833,64835],{},[1700,64834,1709],{"stretchy":1702},[1931,64836,2343],{},[1700,64838,1897],{},[1931,64840,4190],{},[1700,64842,2065],{},[1931,64844,64743],{},[1700,64846,1768],{},[1931,64848,2553],{},[1700,64850,1765],{},[1700,64852,1768],{},[1931,64854,64855],{},"6,75",[1700,64857,1897],{},[1931,64859,64860],{},"13,5",[1700,64862,1768],{},[1931,64864,2553],{},[1700,64866,1765],{},[1931,64868,64869],{},"2,75.",[902,64871,64872],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,64874,64875,64876,1343,64921,64974,64975,64993],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,64877,64879],{"className":64878},[886],[888,64880,64881],{"xmlns":890},[892,64882,64883,64918],{},[895,64884,64885,64887,64893,64895,64897,64899,64901,64903,64905,64907,64909,64911,64913,64915],{},[898,64886,2971],{},[1785,64888,64889,64891],{},[898,64890,4185],{},[1700,64892,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,64894,1765],{},[1700,64896,1768],{},[1931,64898,2553],{},[898,64900,1662],{},[1700,64902,1897],{},[1931,64904,4190],{},[1700,64906,1765],{},[1931,64908,1772],{},[1700,64910,4178],{},[898,64912,1662],{},[1700,64914,1765],{},[1931,64916,64917],{},"2,25",[902,64919,64920],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,64922,64924],{"className":64923},[886],[888,64925,64926],{"xmlns":890},[892,64927,64928,64971],{},[895,64929,64930,64932,64940,64942,64944,64946,64948,64950,64952,64958,64960,64962,64964,64966,64968],{},[898,64931,2971],{},[2007,64933,64934,64936,64938],{},[898,64935,4185],{},[898,64937,56381],{},[1700,64939,56384],{},[1700,64941,1765],{},[1700,64943,1768],{},[1931,64945,2343],{},[1700,64947,2065],{},[1700,64949,1703],{"stretchy":1702},[1931,64951,64917],{},[1785,64953,64954,64956],{},[1700,64955,1709],{"stretchy":1702},[1931,64957,2343],{},[1700,64959,1897],{},[1931,64961,4190],{},[1700,64963,2065],{},[1931,64965,64917],{},[1700,64967,1765],{},[1931,64969,64970],{},"10,125",[902,64972,64973],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,64976,64978],{"className":64977},[886],[888,64979,64980],{"xmlns":890},[892,64981,64982,64990],{},[895,64983,64984,64986,64988],{},[898,64985,1662],{},[1700,64987,1765],{},[1931,64989,64917],{},[902,64991,64992],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[4060,64995,64996],{},[724,64997,64998,65000,65001,1343,65023,65045,65046,1343,65063,65084,65085,65117,65118,65156,65157,2868,65175,65192,65193,2114,65221,65255,65256,7873,65294,2114,65318,2196],{},[883,64999,4601],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,65002,65004],{"className":65003},[886],[888,65005,65006],{"xmlns":890},[892,65007,65008,65020],{},[895,65009,65010,65016,65018],{},[2007,65011,65012,65014],{},[898,65013,1662],{},[1931,65015,1933],{},[1700,65017,1765],{},[1931,65019,5197],{},[902,65021,65022],{"encoding":904},"Q_1 = 0{,}5",[883,65024,65026],{"className":65025},[886],[888,65027,65028],{"xmlns":890},[892,65029,65030,65042],{},[895,65031,65032,65038,65040],{},[2007,65033,65034,65036],{},[898,65035,1662],{},[1931,65037,2343],{},[1700,65039,1765],{},[1931,65041,2553],{},[902,65043,65044],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,65047,65049],{"className":65048},[886],[888,65050,65051],{"xmlns":890},[892,65052,65053,65061],{},[895,65054,65055,65057,65059],{},[898,65056,1662],{},[1700,65058,1765],{},[1931,65060,64917],{},[902,65062,64992],{"encoding":904},[883,65064,65066],{"className":65065},[886],[888,65067,65068],{"xmlns":890},[892,65069,65070,65081],{},[895,65071,65072,65074,65076,65078],{},[898,65073,1677],{},[898,65075,4185],{},[1700,65077,1765],{},[1931,65079,65080],{},"6,125",[902,65082,65083],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,65086,65088],{"className":65087},[886],[888,65089,65090],{"xmlns":890},[892,65091,65092,65114],{},[895,65093,65094,65096,65102,65104,65106,65108,65110,65112],{},[898,65095,1677],{},[1785,65097,65098,65100],{},[898,65099,4185],{},[1700,65101,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,65103,1765],{},[1700,65105,1768],{},[1931,65107,2553],{},[898,65109,1662],{},[1700,65111,1897],{},[1931,65113,4190],{},[902,65115,65116],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,65119,65121],{"className":65120},[886],[888,65122,65123],{"xmlns":890},[892,65124,65125,65153],{},[895,65126,65127,65129,65131,65133,65135,65137,65143,65145,65147,65149,65151],{},[898,65128,1677],{},[898,65130,4185],{},[1700,65132,1765],{},[1700,65134,1768],{},[1931,65136,2343],{},[1785,65138,65139,65141],{},[898,65140,1662],{},[1931,65142,2343],{},[1700,65144,1897],{},[1931,65146,4190],{},[898,65148,1662],{},[1700,65150,1768],{},[1931,65152,2553],{},[902,65154,65155],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,65158,65160],{"className":65159},[886],[888,65161,65162],{"xmlns":890},[892,65163,65164,65172],{},[895,65165,65166],{},[1785,65167,65168,65170],{},[898,65169,1662],{},[1931,65171,2343],{},[902,65173,65174],{"encoding":904},"Q^2",[883,65176,65178],{"className":65177},[886],[888,65179,65180],{"xmlns":890},[892,65181,65182,65190],{},[895,65183,65184,65186,65188],{},[898,65185,2971],{},[898,65187,40524],{},[898,65189,2974],{},[902,65191,55693],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,65194,65196],{"className":65195},[886],[888,65197,65198],{"xmlns":890},[892,65199,65200,65218],{},[895,65201,65202,65204,65206,65208,65210,65212],{},[898,65203,2971],{},[898,65205,2974],{},[1700,65207,1765],{},[1931,65209,2553],{},[1700,65211,1897],{},[1785,65213,65214,65216],{},[898,65215,1662],{},[1931,65217,2343],{},[902,65219,65220],{"encoding":904},"TC = 4 + Q^2",[883,65222,65224],{"className":65223},[886],[888,65225,65226],{"xmlns":890},[892,65227,65228,65252],{},[895,65229,65230,65232,65234,65236,65238,65240,65246,65248,65250],{},[898,65231,2971],{},[898,65233,4185],{},[1700,65235,1765],{},[1700,65237,1768],{},[1931,65239,2343],{},[1785,65241,65242,65244],{},[898,65243,1662],{},[1931,65245,2343],{},[1700,65247,1897],{},[1931,65249,4190],{},[898,65251,1662],{},[902,65253,65254],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,65257,65259],{"className":65258},[886],[888,65260,65261],{"xmlns":890},[892,65262,65263,65291],{},[895,65264,65265,65267,65269,65271,65273,65275,65281,65283,65285,65287,65289],{},[898,65266,1677],{},[898,65268,4185],{},[1700,65270,1765],{},[1700,65272,1768],{},[1931,65274,2385],{},[1785,65276,65277,65279],{},[898,65278,1662],{},[1931,65280,2343],{},[1700,65282,1897],{},[1931,65284,4190],{},[898,65286,1662],{},[1700,65288,1768],{},[1931,65290,2553],{},[902,65292,65293],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,65295,65297],{"className":65296},[886],[888,65298,65299],{"xmlns":890},[892,65300,65301,65315],{},[895,65302,65303,65311,65313],{},[2007,65304,65305,65307,65309],{},[898,65306,1662],{},[898,65308,56381],{},[1700,65310,56384],{},[1700,65312,1765],{},[1931,65314,64743],{},[902,65316,65317],{"encoding":904},"Q_{\\max} = 1{,}5",[883,65319,65321],{"className":65320},[886],[888,65322,65323],{"xmlns":890},[892,65324,65325,65342],{},[895,65326,65327,65329,65337,65339],{},[898,65328,1677],{},[2007,65330,65331,65333,65335],{},[898,65332,4185],{},[898,65334,56381],{},[1700,65336,56384],{},[1700,65338,1765],{},[1931,65340,65341],{},"2,75",[902,65343,65344],{"encoding":904},"PR_{\\max} = 2{,}75",[724,65346,65347],{},[614,65348,65349,65350,65377,65378,65411,65412,1343,65435,2196],{},"Obrázek 3.12: Graf ",[883,65351,65353],{"className":65352},[886],[888,65354,65355],{"xmlns":890},[892,65356,65357,65375],{},[895,65358,65359,65361,65363,65365,65367,65369],{},[898,65360,2971],{},[898,65362,2974],{},[1700,65364,1765],{},[1931,65366,2553],{},[1700,65368,1897],{},[1785,65370,65371,65373],{},[898,65372,1662],{},[1931,65374,2343],{},[902,65376,65220],{"encoding":904}," (parabola) a ",[883,65379,65381],{"className":65380},[886],[888,65382,65383],{"xmlns":890},[892,65384,65385,65409],{},[895,65386,65387,65389,65391,65393,65395,65397,65403,65405,65407],{},[898,65388,2971],{},[898,65390,4185],{},[1700,65392,1765],{},[1700,65394,1768],{},[1931,65396,2343],{},[1785,65398,65399,65401],{},[898,65400,1662],{},[1931,65402,2343],{},[1700,65404,1897],{},[1931,65406,4190],{},[898,65408,1662],{},[902,65410,65254],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,65413,65415],{"className":65414},[886],[888,65416,65417],{"xmlns":890},[892,65418,65419,65432],{},[895,65420,65421,65427,65429],{},[2007,65422,65423,65425],{},[898,65424,1662],{},[1931,65426,1933],{},[1700,65428,6088],{},[1931,65430,65431],{},"0,54",[902,65433,65434],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,65436,65438],{"className":65437},[886],[888,65439,65440],{"xmlns":890},[892,65441,65442,65455],{},[895,65443,65444,65450,65452],{},[2007,65445,65446,65448],{},[898,65447,1662],{},[1931,65449,2343],{},[1700,65451,6088],{},[1931,65453,65454],{},"2,46",[902,65456,65457],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,65459,65460],{},[614,65461,65462,65463,58691,65500,65517,65518,1343,65539,2196],{},"Obrázek 3.13: Graf zisku ",[883,65464,65466],{"className":65465},[886],[888,65467,65468],{"xmlns":890},[892,65469,65470,65498],{},[895,65471,65472,65474,65476,65478,65480,65482,65488,65490,65492,65494,65496],{},[898,65473,1677],{},[898,65475,4185],{},[1700,65477,1765],{},[1700,65479,1768],{},[1931,65481,2385],{},[1785,65483,65484,65486],{},[898,65485,1662],{},[1931,65487,2343],{},[1700,65489,1897],{},[1931,65491,4190],{},[898,65493,1662],{},[1700,65495,1768],{},[1931,65497,2553],{},[902,65499,65293],{"encoding":904},[883,65501,65503],{"className":65502},[886],[888,65504,65505],{"xmlns":890},[892,65506,65507,65515],{},[895,65508,65509,65511,65513],{},[898,65510,1662],{},[1700,65512,1765],{},[1931,65514,64743],{},[902,65516,64798],{"encoding":904}," a nulami ",[883,65519,65521],{"className":65520},[886],[888,65522,65523],{"xmlns":890},[892,65524,65525,65537],{},[895,65526,65527,65533,65535],{},[2007,65528,65529,65531],{},[898,65530,1662],{},[1931,65532,1933],{},[1700,65534,6088],{},[1931,65536,65431],{},[902,65538,65434],{"encoding":904},[883,65540,65542],{"className":65541},[886],[888,65543,65544],{"xmlns":890},[892,65545,65546,65558],{},[895,65547,65548,65554,65556],{},[2007,65549,65550,65552],{},[898,65551,1662],{},[1931,65553,2343],{},[1700,65555,6088],{},[1931,65557,65454],{},[902,65559,65457],{"encoding":904},[115,65561,65563],{"id":65562},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,65565,65566],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,65568,65569],{},[2756,65570],{"alt":65571,"className":65572,"src":65573},"imek-max-zisku-dva-pohledy",[210,2760],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,65575,16597],{"id":65576},"princip-1",[724,65578,65579,65580,2821,65595,65612],{},"Má-li zisk ",[883,65581,65583],{"className":65582},[886],[888,65584,65585],{"xmlns":890},[892,65586,65587,65593],{},[895,65588,65589,65591],{},[898,65590,1677],{},[898,65592,4185],{},[902,65594,63663],{"encoding":904},[883,65596,65598],{"className":65597},[886],[888,65599,65600],{"xmlns":890},[892,65601,65602,65610],{},[895,65603,65604],{},[2007,65605,65606,65608],{},[898,65607,1662],{},[1931,65609,1772],{},[902,65611,38493],{"encoding":904}," maximum, pak platí",[883,65614,65616],{"className":65615},[886],[888,65617,65618],{"xmlns":890,"display":28251},[892,65619,65620,65669],{},[20939,65621,65622],{"width":28256},[20944,65623,65624,65626,65662,65664],{},[20947,65625],{"width":28261},[20947,65627,65628],{},[895,65629,65630,65632,65634,65636,65642,65644,65646,65648,65650,65652,65658,65660],{},[898,65631,2005],{},[898,65633,4185],{},[1700,65635,1703],{"stretchy":1702},[2007,65637,65638,65640],{},[898,65639,1662],{},[1931,65641,1772],{},[1700,65643,1709],{"stretchy":1702},[1700,65645,1765],{},[898,65647,2005],{},[898,65649,2974],{},[1700,65651,1703],{"stretchy":1702},[2007,65653,65654,65656],{},[898,65655,1662],{},[1931,65657,1772],{},[1700,65659,1709],{"stretchy":1702},[898,65661,2196],{"mathvariant":1791},[20947,65663],{"width":28261},[20947,65665,65666],{},[1781,65667,65668],{},"(3.13)",[902,65670,65671],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[4060,65673,65674],{},[724,65675,65676,62230,65678],{},[883,65677,56628],{},[38,65679,65680],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,65682,65683,65686,65687,8290,65714,17761,65788,2196],{},[38,65684,65685],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[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],{},[898,65697,1677],{},[898,65699,4185],{},[1700,65701,1765],{},[898,65703,2971],{},[898,65705,4185],{},[1700,65707,1768],{},[898,65709,2971],{},[898,65711,2974],{},[902,65713,55384],{"encoding":904},[883,65715,65717],{"className":65716},[886],[888,65718,65719],{"xmlns":890},[892,65720,65721,65785],{},[895,65722,65723,65725,65731,65733,65739,65741,65743,65745,65751,65753,65759,65761,65763,65765,65771,65773,65779,65781,65783],{},[898,65724,1677],{},[1785,65726,65727,65729],{},[898,65728,4185],{},[1700,65730,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,65732,1703],{"stretchy":1702},[2007,65734,65735,65737],{},[898,65736,1662],{},[1931,65738,1772],{},[1700,65740,1709],{"stretchy":1702},[1700,65742,1765],{},[898,65744,2971],{},[1785,65746,65747,65749],{},[898,65748,4185],{},[1700,65750,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,65752,1703],{"stretchy":1702},[2007,65754,65755,65757],{},[898,65756,1662],{},[1931,65758,1772],{},[1700,65760,1709],{"stretchy":1702},[1700,65762,1768],{},[898,65764,2971],{},[1785,65766,65767,65769],{},[898,65768,2974],{},[1700,65770,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,65772,1703],{"stretchy":1702},[2007,65774,65775,65777],{},[898,65776,1662],{},[1931,65778,1772],{},[1700,65780,1709],{"stretchy":1702},[1700,65782,1765],{},[1931,65784,1772],{},[902,65786,65787],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,65789,65791],{"className":65790},[886],[888,65792,65793],{"xmlns":890},[892,65794,65795,65827],{},[895,65796,65797,65799,65801,65803,65809,65811,65813,65815,65817,65819,65825],{},[898,65798,2005],{},[898,65800,4185],{},[1700,65802,1703],{"stretchy":1702},[2007,65804,65805,65807],{},[898,65806,1662],{},[1931,65808,1772],{},[1700,65810,1709],{"stretchy":1702},[1700,65812,1765],{},[898,65814,2005],{},[898,65816,2974],{},[1700,65818,1703],{"stretchy":1702},[2007,65820,65821,65823],{},[898,65822,1662],{},[1931,65824,1772],{},[1700,65826,1709],{"stretchy":1702},[902,65828,65829],{"encoding":904},"MR(Q_0) = MC(Q_0)",[4060,65831,65832,65837],{},[724,65833,65834,65836],{},[883,65835,4761],{}," Postup — jak najít maximum zisku",[152,65838,65839,65903,65958,65995,66023],{},[123,65840,65841,65842,2114,65857,65872,65873,4110],{},"Sestavte ",[883,65843,65845],{"className":65844},[886],[888,65846,65847],{"xmlns":890},[892,65848,65849,65855],{},[895,65850,65851,65853],{},[898,65852,2971],{},[898,65854,4185],{},[902,65856,4285],{"encoding":904},[883,65858,65860],{"className":65859},[886],[888,65861,65862],{"xmlns":890},[892,65863,65864,65870],{},[895,65865,65866,65868],{},[898,65867,2971],{},[898,65869,2974],{},[902,65871,3436],{"encoding":904}," ze zadání (typicky ",[883,65874,65876],{"className":65875},[886],[888,65877,65878],{"xmlns":890},[892,65879,65880,65900],{},[895,65881,65882,65884,65886,65888,65890,65892,65894,65896,65898],{},[898,65883,2971],{},[898,65885,4185],{},[1700,65887,1765],{},[898,65889,1677],{},[1700,65891,1703],{"stretchy":1702},[898,65893,1662],{},[1700,65895,1709],{"stretchy":1702},[1700,65897,2065],{},[898,65899,1662],{},[902,65901,65902],{"encoding":904},"TR = P(Q) \\cdot Q",[123,65904,65905,65906,2114,65932,2196],{},"Vypočtěte ",[883,65907,65909],{"className":65908},[886],[888,65910,65911],{"xmlns":890},[892,65912,65913,65929],{},[895,65914,65915,65917,65919,65921,65923],{},[898,65916,2005],{},[898,65918,4185],{},[1700,65920,1765],{},[898,65922,2971],{},[1785,65924,65925,65927],{},[898,65926,4185],{},[1700,65928,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,65930,65931],{"encoding":904},"MR = TR'",[883,65933,65935],{"className":65934},[886],[888,65936,65937],{"xmlns":890},[892,65938,65939,65955],{},[895,65940,65941,65943,65945,65947,65949],{},[898,65942,2005],{},[898,65944,2974],{},[1700,65946,1765],{},[898,65948,2971],{},[1785,65950,65951,65953],{},[898,65952,2974],{},[1700,65954,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,65956,65957],{"encoding":904},"MC = TC'",[123,65959,65960,65961,2196],{},"Řešte rovnici ",[883,65962,65964],{"className":65963},[886],[888,65965,65966],{"xmlns":890},[892,65967,65968,65992],{},[895,65969,65970,65972,65974,65976,65978,65980,65982,65984,65986,65988,65990],{},[898,65971,2005],{},[898,65973,4185],{},[1700,65975,1703],{"stretchy":1702},[898,65977,1662],{},[1700,65979,1709],{"stretchy":1702},[1700,65981,1765],{},[898,65983,2005],{},[898,65985,2974],{},[1700,65987,1703],{"stretchy":1702},[898,65989,1662],{},[1700,65991,1709],{"stretchy":1702},[902,65993,65994],{"encoding":904},"MR(Q) = MC(Q)",[123,65996,65997,65998,66022],{},"Ověřte druhou derivaci ",[883,65999,66001],{"className":66000},[886],[888,66002,66003],{"xmlns":890},[892,66004,66005,66019],{},[895,66006,66007,66009],{},[898,66008,1677],{},[1785,66010,66011,66013],{},[898,66012,4185],{},[895,66014,66015,66017],{},[1700,66016,1793],{"mathvariant":1791},[1700,66018,1793],{"mathvariant":1791},[902,66020,66021],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,66024,66025,66026,66053],{},"Dosaďte do ",[883,66027,66029],{"className":66028},[886],[888,66030,66031],{"xmlns":890},[892,66032,66033,66051],{},[895,66034,66035,66037,66039,66041,66043,66045,66047,66049],{},[898,66036,1677],{},[898,66038,4185],{},[1700,66040,1765],{},[898,66042,2971],{},[898,66044,4185],{},[1700,66046,1768],{},[898,66048,2971],{},[898,66050,2974],{},[902,66052,55384],{"encoding":904}," pro hodnotu maxima.",[37533,66055,66057],{"id":66056},"příklad-39","Příklad 3.9",[724,66059,66060,56172,66062,2114,66084,66120],{},[38,66061,56171],{},[883,66063,66065],{"className":66064},[886],[888,66066,66067],{"xmlns":890},[892,66068,66069,66081],{},[895,66070,66071,66073,66075,66077,66079],{},[898,66072,1677],{},[1700,66074,1765],{},[1931,66076,38204],{},[1700,66078,1768],{},[898,66080,1662],{},[902,66082,66083],{"encoding":904},"P = 30 - Q",[883,66085,66087],{"className":66086},[886],[888,66088,66089],{"xmlns":890},[892,66090,66091,66117],{},[895,66092,66093,66095,66097,66099,66101,66107,66109,66111,66113,66115],{},[898,66094,2971],{},[898,66096,2974],{},[1700,66098,1765],{},[1931,66100,5197],{},[1785,66102,66103,66105],{},[898,66104,1662],{},[1931,66106,2343],{},[1700,66108,1897],{},[1931,66110,2445],{},[898,66112,1662],{},[1700,66114,1897],{},[1931,66116,24386],{},[902,66118,66119],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,66122,66123,2106,66125,1343,66155,66193,66194,15977,66238,66272,66273,2196],{},[38,66124,22955],{},[883,66126,66128],{"className":66127},[886],[888,66129,66130],{"xmlns":890},[892,66131,66132,66152],{},[895,66133,66134,66136,66138,66140,66142,66144,66146],{},[898,66135,2971],{},[898,66137,4185],{},[1700,66139,1765],{},[1931,66141,38204],{},[898,66143,1662],{},[1700,66145,1768],{},[1785,66147,66148,66150],{},[898,66149,1662],{},[1931,66151,2343],{},[902,66153,66154],{"encoding":904},"TR = 30Q - Q^2",[883,66156,66158],{"className":66157},[886],[888,66159,66160],{"xmlns":890},[892,66161,66162,66190],{},[895,66163,66164,66166,66168,66170,66172,66174,66180,66182,66184,66186,66188],{},[898,66165,1677],{},[898,66167,4185],{},[1700,66169,1765],{},[1700,66171,1768],{},[1931,66173,64743],{},[1785,66175,66176,66178],{},[898,66177,1662],{},[1931,66179,2343],{},[1700,66181,1897],{},[1931,66183,41985],{},[898,66185,1662],{},[1700,66187,1768],{},[1931,66189,24386],{},[902,66191,66192],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,66195,66197],{"className":66196},[886],[888,66198,66199],{"xmlns":890},[892,66200,66201,66235],{},[895,66202,66203,66205,66211,66213,66215,66217,66219,66221,66223,66225,66227,66229,66231,66233],{},[898,66204,1677],{},[1785,66206,66207,66209],{},[898,66208,4185],{},[1700,66210,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,66212,1765],{},[1700,66214,1768],{},[1931,66216,2385],{},[898,66218,1662],{},[1700,66220,1897],{},[1931,66222,41985],{},[1700,66224,1765],{},[1931,66226,1772],{},[1700,66228,4178],{},[898,66230,1662],{},[1700,66232,1765],{},[1931,66234,5773],{},[902,66236,66237],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,66239,66241],{"className":66240},[886],[888,66242,66243],{"xmlns":890},[892,66244,66245,66269],{},[895,66246,66247,66249,66259,66261,66263,66265,66267],{},[898,66248,1677],{},[1785,66250,66251,66253],{},[898,66252,4185],{},[895,66254,66255,66257],{},[1700,66256,1793],{"mathvariant":1791},[1700,66258,1793],{"mathvariant":1791},[1700,66260,1765],{},[1700,66262,1768],{},[1931,66264,2385],{},[1700,66266,3640],{},[1931,66268,1772],{},[902,66270,66271],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,66274,66276],{"className":66275},[886],[888,66277,66278],{"xmlns":890},[892,66279,66280,66297],{},[895,66281,66282,66284,66286,66288,66290,66292,66294],{},[898,66283,1677],{},[898,66285,4185],{},[1700,66287,1703],{"stretchy":1702},[1931,66289,5773],{},[1700,66291,1709],{"stretchy":1702},[1700,66293,1765],{},[1931,66295,66296],{},"89",[902,66298,66299],{"encoding":904},"PR(8) = 89",[724,66301,66302,66303,1343,66329,15977,66353,66391],{},"Ověření principu: ",[883,66304,66306],{"className":66305},[886],[888,66307,66308],{"xmlns":890},[892,66309,66310,66326],{},[895,66311,66312,66314,66316,66318,66320,66322,66324],{},[898,66313,2005],{},[898,66315,4185],{},[1700,66317,1765],{},[1931,66319,38204],{},[1700,66321,1768],{},[1931,66323,2343],{},[898,66325,1662],{},[902,66327,66328],{"encoding":904},"MR = 30 - 2Q",[883,66330,66332],{"className":66331},[886],[888,66333,66334],{"xmlns":890},[892,66335,66336,66350],{},[895,66337,66338,66340,66342,66344,66346,66348],{},[898,66339,2005],{},[898,66341,2974],{},[1700,66343,1765],{},[898,66345,1662],{},[1700,66347,1897],{},[1931,66349,2445],{},[902,66351,66352],{"encoding":904},"MC = Q + 6",[883,66354,66356],{"className":66355},[886],[888,66357,66358],{"xmlns":890},[892,66359,66360,66388],{},[895,66361,66362,66364,66366,66368,66370,66372,66374,66376,66378,66380,66382,66384,66386],{},[898,66363,2005],{},[898,66365,4185],{},[1700,66367,1703],{"stretchy":1702},[1931,66369,5773],{},[1700,66371,1709],{"stretchy":1702},[1700,66373,1765],{},[1931,66375,23131],{},[1700,66377,1765],{},[898,66379,2005],{},[898,66381,2974],{},[1700,66383,1703],{"stretchy":1702},[1931,66385,5773],{},[1700,66387,1709],{"stretchy":1702},[902,66389,66390],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,66393,66394,66395,66428,66429,66446],{},"V řadě případů — má-li rovnice ",[883,66396,66398],{"className":66397},[886],[888,66399,66400],{"xmlns":890},[892,66401,66402,66426],{},[895,66403,66404,66406,66408,66410,66412,66414,66416,66418,66420,66422,66424],{},[898,66405,2005],{},[898,66407,4185],{},[1700,66409,1703],{"stretchy":1702},[898,66411,1662],{},[1700,66413,1709],{"stretchy":1702},[1700,66415,1765],{},[898,66417,2005],{},[898,66419,2974],{},[1700,66421,1703],{"stretchy":1702},[898,66423,1662],{},[1700,66425,1709],{"stretchy":1702},[902,66427,65994],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,66430,66432],{"className":66431},[886],[888,66433,66434],{"xmlns":890},[892,66435,66436,66444],{},[895,66437,66438],{},[2007,66439,66440,66442],{},[898,66441,1662],{},[1931,66443,1772],{},[902,66445,38493],{"encoding":904}," — není třeba provádět test druhé derivace.",[37533,66448,66450],{"id":66449},"příklad-310","Příklad 3.10",[724,66452,66453,66455,66456,66460,66461,66474,66475,66506],{},[38,66454,56171],{}," Firma vyrábí minipočítače v ",[207,66457,66459],{"className":66458,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,66462,66464],{"className":66463},[886],[888,66465,66466],{"xmlns":890},[892,66467,66468,66472],{},[895,66469,66470],{},[1931,66471,15376],{},[902,66473,15376],{"encoding":904}," EUR\u002Fks. ",[883,66476,66478],{"className":66477},[886],[888,66479,66480],{"xmlns":890},[892,66481,66482,66503],{},[895,66483,66484,66486,66488,66490,66492,66494,66497],{},[898,66485,2971],{},[898,66487,2974],{},[1700,66489,1765],{},[1931,66491,3314],{},[1700,66493,1897],{},[1931,66495,66496],{},"28",[1785,66498,66499,66501],{},[898,66500,1662],{},[1931,66502,2343],{},[902,66504,66505],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,66508,66509,2106,66511,1343,66533,1343,66553,66576],{},[38,66510,22955],{},[883,66512,66514],{"className":66513},[886],[888,66515,66516],{"xmlns":890},[892,66517,66518,66530],{},[895,66519,66520,66522,66524,66526,66528],{},[898,66521,2971],{},[898,66523,4185],{},[1700,66525,1765],{},[1931,66527,15376],{},[898,66529,1662],{},[902,66531,66532],{"encoding":904},"TR = 900Q",[883,66534,66536],{"className":66535},[886],[888,66537,66538],{"xmlns":890},[892,66539,66540,66550],{},[895,66541,66542,66544,66546,66548],{},[898,66543,2005],{},[898,66545,4185],{},[1700,66547,1765],{},[1931,66549,15376],{},[902,66551,66552],{"encoding":904},"MR = 900",[883,66554,66556],{"className":66555},[886],[888,66557,66558],{"xmlns":890},[892,66559,66560,66573],{},[895,66561,66562,66564,66566,66568,66571],{},[898,66563,2005],{},[898,66565,2974],{},[1700,66567,1765],{},[1931,66569,66570],{},"56",[898,66572,1662],{},[902,66574,66575],{"encoding":904},"MC = 56Q",". Z principu:",[883,66578,66580],{"className":66579},[886],[888,66581,66582],{"xmlns":890,"display":28251},[892,66583,66584,66626],{},[895,66585,66586,66588,66590,66592,66594,66596,66598,66600,66602,66604,66612,66614,66617,66619,66621,66623],{},[1931,66587,15376],{},[1700,66589,1765],{},[1931,66591,66570],{},[898,66593,1662],{},[1781,66595,4175],{},[1700,66597,4178],{},[1781,66599,4175],{},[898,66601,1662],{},[1700,66603,1765],{},[1770,66605,66606],{"scriptlevel":1772,"displaystyle":1702},[1774,66607,66608,66610],{},[1931,66609,15376],{},[1931,66611,66570],{},[1700,66613,6088],{},[1931,66615,66616],{},"16,07",[1781,66618,4175],{},[1700,66620,2927],{},[1781,66622,4175],{},[1931,66624,66625],{},"16.",[902,66627,66628],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,66630,66631,66632,2901],{},"Zisk při ",[883,66633,66635],{"className":66634},[886],[888,66636,66637],{"xmlns":890},[892,66638,66639,66647],{},[895,66640,66641,66643,66645],{},[898,66642,1662],{},[1700,66644,1765],{},[1931,66646,42047],{},[902,66648,66649],{"encoding":904},"Q = 16",[883,66651,66653],{"className":66652},[886],[888,66654,66655],{"xmlns":890,"display":28251},[892,66656,66657,66728],{},[895,66658,66659,66661,66663,66665,66667,66669,66671,66673,66675,66677,66679,66681,66683,66685,66687,66689,66695,66697,66699,66701,66703,66705,66707,66709,66711,66714,66716,66718,66720,66723,66726],{},[898,66660,1677],{},[898,66662,4185],{},[1700,66664,1703],{"stretchy":1702},[1931,66666,42047],{},[1700,66668,1709],{"stretchy":1702},[1700,66670,1765],{},[1931,66672,15376],{},[1700,66674,2065],{},[1931,66676,42047],{},[1700,66678,1768],{},[1700,66680,1703],{"stretchy":1702},[1931,66682,3314],{},[1700,66684,1897],{},[1931,66686,66496],{},[1700,66688,2065],{},[1785,66690,66691,66693],{},[1931,66692,42047],{},[1931,66694,2343],{},[1700,66696,1709],{"stretchy":1702},[1700,66698,1765],{},[1931,66700,23131],{},[1781,66702,1783],{},[1931,66704,20327],{},[1700,66706,1768],{},[1931,66708,24386],{},[1781,66710,1783],{},[1931,66712,66713],{},"218",[1700,66715,1765],{},[1931,66717,24386],{},[1781,66719,1783],{},[1931,66721,66722],{},"182",[1781,66724,66725],{}," EUR",[898,66727,2196],{"mathvariant":1791},[902,66729,66730],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,66732,66733],{},"Pro srovnání při původních 30 ks:",[883,66735,66737],{"className":66736},[886],[888,66738,66739],{"xmlns":890,"display":28251},[892,66740,66741,66806],{},[895,66742,66743,66745,66747,66749,66751,66753,66755,66757,66759,66761,66763,66765,66767,66769,66771,66773,66775,66777,66779,66782,66784,66786,66788,66790,66792,66794,66796,66798,66800,66802,66804],{},[898,66744,1677],{},[898,66746,4185],{},[1700,66748,1703],{"stretchy":1702},[1931,66750,38204],{},[1700,66752,1709],{"stretchy":1702},[1700,66754,1765],{},[1931,66756,15376],{},[1700,66758,2065],{},[1931,66760,38204],{},[1700,66762,1768],{},[1700,66764,1703],{"stretchy":1702},[1931,66766,3314],{},[1700,66768,1897],{},[1931,66770,66496],{},[1700,66772,2065],{},[1931,66774,15376],{},[1700,66776,1709],{"stretchy":1702},[1700,66778,1765],{},[1931,66780,66781],{},"27",[1781,66783,1783],{},[1931,66785,59266],{},[1700,66787,1768],{},[1931,66789,5192],{},[1781,66791,1783],{},[1931,66793,30928],{},[1700,66795,1765],{},[1931,66797,1933],{},[1781,66799,1783],{},[1931,66801,23928],{},[1781,66803,66725],{},[898,66805,2196],{"mathvariant":1791},[902,66807,66808],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,66810,66811,66814,66815,66833,66834,66852],{},[38,66812,66813],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,66816,66818],{"className":66817},[886],[888,66819,66820],{"xmlns":890},[892,66821,66822,66830],{},[895,66823,66824,66826,66828],{},[1931,66825,24386],{},[1781,66827,1783],{},[1931,66829,66722],{},[902,66831,66832],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,66835,66837],{"className":66836},[886],[888,66838,66839],{"xmlns":890},[892,66840,66841,66849],{},[895,66842,66843,66845,66847],{},[1931,66844,1933],{},[1781,66846,1783],{},[1931,66848,23928],{},[902,66850,66851],{"encoding":904},"1\\,750"," EUR.",[198,66854,66856],{"id":66855},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,66858,66859,66860,62754,66873,66897],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,66861,66863],{"className":66862},[886],[888,66864,66865],{"xmlns":890},[892,66866,66867,66871],{},[895,66868,66869],{},[898,66870,1677],{},[902,66872,1677],{"encoding":904},[883,66874,66876],{"className":66875},[886],[888,66877,66878],{"xmlns":890},[892,66879,66880,66894],{},[895,66881,66882,66884,66886,66888,66890,66892],{},[898,66883,2971],{},[898,66885,4185],{},[1700,66887,1765],{},[898,66889,1677],{},[1700,66891,2065],{},[898,66893,1662],{},[902,66895,66896],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,66899,66901],{"className":66900},[886],[888,66902,66903],{"xmlns":890,"display":28251},[892,66904,66905,66938],{},[20939,66906,66907],{"width":28256},[20944,66908,66909,66911,66931,66933],{},[20947,66910],{"width":28261},[20947,66912,66913],{},[895,66914,66915,66917,66919,66921,66923,66925,66927,66929],{},[898,66916,1677],{},[1700,66918,1765],{},[898,66920,2005],{},[898,66922,2974],{},[1700,66924,1703],{"stretchy":1702},[898,66926,1662],{},[1700,66928,1709],{"stretchy":1702},[898,66930,2196],{"mathvariant":1791},[20947,66932],{"width":28261},[20947,66934,66935],{},[1781,66936,66937],{},"(3.14)",[902,66939,66940],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,66942,66943,66944,2196],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,66945,66947],{"className":66946},[886],[888,66948,66949],{"xmlns":890},[892,66950,66951,66965],{},[895,66952,66953,66955],{},[898,66954,1677],{},[1785,66956,66957,66959],{},[898,66958,4185],{},[895,66960,66961,66963],{},[1700,66962,1793],{"mathvariant":1791},[1700,66964,1793],{"mathvariant":1791},[902,66966,66021],{"encoding":904},[37533,66968,66970],{"id":66969},"příklad-311","Příklad 3.11",[724,66972,66973,57706,66975,67022,67023,67041],{},[38,66974,56171],{},[883,66976,66978],{"className":66977},[886],[888,66979,66980],{"xmlns":890},[892,66981,66982,67019],{},[895,66983,66984,66986,66988,66990,66993,66999,67001,67003,67009,67011,67013,67015,67017],{},[898,66985,2971],{},[898,66987,2974],{},[1700,66989,1765],{},[1931,66991,66992],{},"0,04",[1785,66994,66995,66997],{},[898,66996,1662],{},[1931,66998,2385],{},[1700,67000,1768],{},[1931,67002,22730],{},[1785,67004,67005,67007],{},[898,67006,1662],{},[1931,67008,2343],{},[1700,67010,1897],{},[1931,67012,3058],{},[898,67014,1662],{},[1700,67016,1897],{},[1931,67018,2438],{},[902,67020,67021],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,67024,67026],{"className":67025},[886],[888,67027,67028],{"xmlns":890},[892,67029,67030,67038],{},[895,67031,67032,67034,67036],{},[898,67033,1677],{},[1700,67035,1765],{},[1931,67037,2553],{},[902,67039,67040],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,67043,67044,67046,67047,17761,67089,67123,67124,2901],{},[38,67045,22955],{}," Z (3.14): ",[883,67048,67050],{"className":67049},[886],[888,67051,67052],{"xmlns":890},[892,67053,67054,67086],{},[895,67055,67056,67058,67060,67062,67065,67071,67073,67076,67078,67080,67082,67084],{},[898,67057,2005],{},[898,67059,2974],{},[1700,67061,1765],{},[1931,67063,67064],{},"0,12",[1785,67066,67067,67069],{},[898,67068,1662],{},[1931,67070,2343],{},[1700,67072,1768],{},[1931,67074,67075],{},"1,8",[898,67077,1662],{},[1700,67079,1897],{},[1931,67081,3058],{},[1700,67083,1765],{},[1931,67085,2553],{},[902,67087,67088],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,67090,67092],{"className":67091},[886],[888,67093,67094],{"xmlns":890},[892,67095,67096,67120],{},[895,67097,67098,67100,67106,67108,67110,67112,67114,67116,67118],{},[1931,67099,67064],{},[1785,67101,67102,67104],{},[898,67103,1662],{},[1931,67105,2343],{},[1700,67107,1768],{},[1931,67109,67075],{},[898,67111,1662],{},[1700,67113,1897],{},[1931,67115,2445],{},[1700,67117,1765],{},[1931,67119,1772],{},[902,67121,67122],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,67125,67127],{"className":67126},[886],[888,67128,67129],{"xmlns":890},[892,67130,67131,67135],{},[895,67132,67133],{},[1931,67134,67064],{},[902,67136,67137],{"encoding":904},"0{,}12",[883,67139,67141],{"className":67140},[886],[888,67142,67143],{"xmlns":890,"display":28251},[892,67144,67145,67197],{},[895,67146,67147,67153,67155,67157,67159,67161,67163,67165,67167,67169,67171,67173,67179,67181,67183,67185,67187,67193,67195],{},[1785,67148,67149,67151],{},[898,67150,1662],{},[1931,67152,2343],{},[1700,67154,1768],{},[1931,67156,36429],{},[898,67158,1662],{},[1700,67160,1897],{},[1931,67162,3314],{},[1700,67164,1765],{},[1931,67166,1772],{},[1781,67168,4175],{},[1700,67170,4178],{},[1781,67172,4175],{},[2007,67174,67175,67177],{},[898,67176,1662],{},[1931,67178,1933],{},[1700,67180,1765],{},[1931,67182,2438],{},[1700,67184,1732],{"separator":1731},[1781,67186,4175],{},[2007,67188,67189,67191],{},[898,67190,1662],{},[1931,67192,2343],{},[1700,67194,1765],{},[1931,67196,19513],{},[902,67198,67199],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,67201,67202,67203,2901],{},"Dále ",[883,67204,67206],{"className":67205},[886],[888,67207,67208],{"xmlns":890},[892,67209,67210,67249],{},[895,67211,67212,67214,67224,67226,67228,67230,67236,67238,67240,67243,67245,67247],{},[898,67213,1677],{},[1785,67215,67216,67218],{},[898,67217,4185],{},[895,67219,67220,67222],{},[1700,67221,1793],{"mathvariant":1791},[1700,67223,1793],{"mathvariant":1791},[1700,67225,1765],{},[1700,67227,1768],{},[898,67229,2005],{},[1785,67231,67232,67234],{},[898,67233,2974],{},[1700,67235,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,67237,1765],{},[1700,67239,1768],{},[1931,67241,67242],{},"0,24",[898,67244,1662],{},[1700,67246,1897],{},[1931,67248,67075],{},[902,67250,67251],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,67253,67254,67304],{},[123,67255,67256,67300,67301,67303],{},[883,67257,67259],{"className":67258},[886],[888,67260,67261],{"xmlns":890},[892,67262,67263,67297],{},[895,67264,67265,67267,67277,67279,67281,67283,67285,67287,67289,67291,67293,67295],{},[898,67266,1677],{},[1785,67268,67269,67271],{},[898,67270,4185],{},[895,67272,67273,67275],{},[1700,67274,1793],{"mathvariant":1791},[1700,67276,1793],{"mathvariant":1791},[1700,67278,1703],{"stretchy":1702},[1931,67280,2438],{},[1700,67282,1709],{"stretchy":1702},[1700,67284,1765],{},[1931,67286,19506],{},[1700,67288,3601],{},[1931,67290,1772],{},[1781,67292,4175],{},[1700,67294,4178],{},[1781,67296,4175],{},[902,67298,67299],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,67302,3968],{}," zisku (minimalizace ztráty);",[123,67305,67306,67300,67352,67354],{},[883,67307,67309],{"className":67308},[886],[888,67310,67311],{"xmlns":890},[892,67312,67313,67349],{},[895,67314,67315,67317,67327,67329,67331,67333,67335,67337,67339,67341,67343,67345,67347],{},[898,67316,1677],{},[1785,67318,67319,67321],{},[898,67320,4185],{},[895,67322,67323,67325],{},[1700,67324,1793],{"mathvariant":1791},[1700,67326,1793],{"mathvariant":1791},[1700,67328,1703],{"stretchy":1702},[1931,67330,3058],{},[1700,67332,1709],{"stretchy":1702},[1700,67334,1765],{},[1700,67336,1768],{},[1931,67338,19506],{},[1700,67340,3640],{},[1931,67342,1772],{},[1781,67344,4175],{},[1700,67346,4178],{},[1781,67348,4175],{},[902,67350,67351],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,67353,3910],{}," zisku, avšak",[883,67356,67358],{"className":67357},[886],[888,67359,67360],{"xmlns":890,"display":28251},[892,67361,67362,67430],{},[895,67363,67364,67366,67368,67370,67372,67374,67376,67378,67380,67382,67384,67386,67388,67390,67392,67394,67396,67398,67400,67402,67404,67406,67408,67410,67412,67414,67416,67418,67420,67422,67424,67426,67428],{},[898,67365,1677],{},[898,67367,4185],{},[1700,67369,1703],{"stretchy":1702},[1931,67371,3058],{},[1700,67373,1709],{"stretchy":1702},[1700,67375,1765],{},[1931,67377,2553],{},[1700,67379,2065],{},[1931,67381,3058],{},[1700,67383,1768],{},[1700,67385,1703],{"stretchy":1702},[1931,67387,66992],{},[1700,67389,2065],{},[1931,67391,1933],{},[1781,67393,1783],{},[1931,67395,59266],{},[1700,67397,1768],{},[1931,67399,22730],{},[1700,67401,2065],{},[1931,67403,3284],{},[1700,67405,1897],{},[1931,67407,3284],{},[1700,67409,1897],{},[1931,67411,2438],{},[1700,67413,1709],{"stretchy":1702},[1700,67415,1765],{},[1931,67417,5399],{},[1700,67419,1768],{},[1931,67421,21365],{},[1700,67423,1765],{},[1700,67425,1768],{},[1931,67427,36429],{},[1700,67429,1732],{"separator":1731},[902,67431,67432],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,67434,67435,67436,2196],{},"tj. ztráta větší než ",[883,67437,67439],{"className":67438},[886],[888,67440,67441],{"xmlns":890},[892,67442,67443,67453],{},[895,67444,67445,67447,67449,67451],{},[898,67446,10619],{},[898,67448,2974],{},[1700,67450,1765],{},[1931,67452,2438],{},[902,67454,67455],{"encoding":904},"FC = 5",[724,67457,67458,67461,67462,67465,67466,2196],{},[38,67459,67460],{},"Závěr:"," firma by měla ",[38,67463,67464],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,67467,67469],{"className":67468},[886],[888,67470,67471],{"xmlns":890},[892,67472,67473,67483],{},[895,67474,67475,67477,67479,67481],{},[898,67476,10619],{},[898,67478,2974],{},[1700,67480,1765],{},[1931,67482,2438],{},[902,67484,67455],{"encoding":904},[115,67486,67488],{"id":67487},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,67490,67491,67492,67494,67495,67510,67511,67524,67525,67551,67552,67565,67566,67583,67584,2821,67601,67604,67605,67625,67626,67641,67642,2901],{},"Důležitým završením analýzy je konstrukce ",[38,67493,55459],{},". S nabízeným množstvím rostou mezní náklady ",[883,67496,67498],{"className":67497},[886],[888,67499,67500],{"xmlns":890},[892,67501,67502,67508],{},[895,67503,67504,67506],{},[898,67505,2005],{},[898,67507,2974],{},[902,67509,55476],{"encoding":904}," a tyto určují cenu ",[883,67512,67514],{"className":67513},[886],[888,67515,67516],{"xmlns":890},[892,67517,67518,67522],{},[895,67519,67520],{},[898,67521,1677],{},[902,67523,1677],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,67526,67528],{"className":67527},[886],[888,67529,67530],{"xmlns":890},[892,67531,67532,67548],{},[895,67533,67534,67536,67538,67540,67542,67544,67546],{},[898,67535,1677],{},[1700,67537,1765],{},[898,67539,2005],{},[898,67541,2974],{},[1700,67543,1703],{"stretchy":1702},[898,67545,1662],{},[1700,67547,1709],{"stretchy":1702},[902,67549,67550],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,67553,67555],{"className":67554},[886],[888,67556,67557],{"xmlns":890},[892,67558,67559,67563],{},[895,67560,67561],{},[898,67562,1677],{},[902,67564,1677],{"encoding":904}," však nemůže být nižší než ",[883,67567,67569],{"className":67568},[886],[888,67570,67571],{"xmlns":890},[892,67572,67573,67581],{},[895,67574,67575],{},[1785,67576,67577,67579],{},[898,67578,1677],{},[1700,67580,4543],{},[902,67582,4593],{"encoding":904}," odpovídající množství ",[883,67585,67587],{"className":67586},[886],[888,67588,67589],{"xmlns":890},[892,67590,67591,67599],{},[895,67592,67593],{},[1785,67594,67595,67597],{},[898,67596,1662],{},[1700,67598,4543],{},[902,67600,30029],{"encoding":904},[38,67602,67603],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,67606,67608],{"className":67607},[886],[888,67609,67610],{"xmlns":890},[892,67611,67612,67622],{},[895,67613,67614,67616],{},[1931,67615,1772],{},[1785,67617,67618,67620],{},[898,67619,1662],{},[1700,67621,4543],{},[902,67623,67624],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,67627,67629],{"className":67628},[886],[888,67630,67631],{"xmlns":890},[892,67632,67633,67639],{},[895,67634,67635,67637],{},[898,67636,2005],{},[898,67638,2974],{},[902,67640,55476],{"encoding":904}," nad bodem ",[883,67643,67645],{"className":67644},[886],[888,67646,67647],{"xmlns":890},[892,67648,67649,67653],{},[895,67650,67651],{},[898,67652,1862],{},[902,67654,1862],{"encoding":904},[883,67656,67658],{"className":67657},[886],[888,67659,67660],{"xmlns":890,"display":28251},[892,67661,67662,67769],{},[20939,67663,67664],{"width":28256},[20944,67665,67666,67668,67762,67764],{},[20947,67667],{"width":28261},[20947,67669,67670],{},[895,67671,67672,67674,67676,67678,67680,67682,67684,67686],{},[898,67673,1677],{},[1700,67675,1765],{},[898,67677,8861],{},[1700,67679,1703],{"stretchy":1702},[898,67681,1662],{},[1700,67683,1709],{"stretchy":1702},[1700,67685,1765],{},[895,67687,67688,67691],{},[1700,67689,67690],{"fence":1731},"{",[20939,67692,67695,67734],{"rowspacing":67693,"columnalign":67694,"columnspacing":15469},"0.36em","left left",[20944,67696,67697,67713],{},[20947,67698,67699],{},[1770,67700,67701],{"scriptlevel":1772,"displaystyle":1702},[895,67702,67703,67705,67707,67709,67711],{},[898,67704,2005],{},[898,67706,2974],{},[1700,67708,1703],{"stretchy":1702},[898,67710,1662],{},[1700,67712,1709],{"stretchy":1702},[20947,67714,67715],{},[1770,67716,67717],{"scriptlevel":1772,"displaystyle":1702},[895,67718,67719,67722,67724,67726,67732],{},[1781,67720,67721],{},"pro ",[898,67723,1662],{},[1700,67725,4674],{},[1785,67727,67728,67730],{},[898,67729,1662],{},[1700,67731,4543],{},[1700,67733,1732],{"separator":1731},[20944,67735,67736,67742],{},[20947,67737,67738],{},[1770,67739,67740],{"scriptlevel":1772,"displaystyle":1702},[1931,67741,1772],{},[20947,67743,67744],{},[1770,67745,67746],{"scriptlevel":1772,"displaystyle":1702},[895,67747,67748,67750,67752,67754,67760],{},[1781,67749,67721],{},[898,67751,1662],{},[1700,67753,3640],{},[1785,67755,67756,67758],{},[898,67757,1662],{},[1700,67759,4543],{},[1700,67761,1732],{"separator":1731},[20947,67763],{"width":28261},[20947,67765,67766],{},[1781,67767,67768],{},"(3.15)",[902,67770,67771],{"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}",[724,67773,4499,67774,67791,67792,67809,67810,41684,67840,67843],{},[883,67775,67777],{"className":67776},[886],[888,67778,67779],{"xmlns":890},[892,67780,67781,67789],{},[895,67782,67783],{},[1785,67784,67785,67787],{},[898,67786,1662],{},[1700,67788,4543],{},[902,67790,30029],{"encoding":904}," je bod minima ",[883,67793,67795],{"className":67794},[886],[888,67796,67797],{"xmlns":890},[892,67798,67799,67807],{},[895,67800,67801,67803,67805],{},[898,67802,1862],{},[898,67804,40524],{},[898,67806,2974],{},[902,67808,55495],{"encoding":904},". Bod ",[883,67811,67813],{"className":67812},[886],[888,67814,67815],{"xmlns":890},[892,67816,67817,67837],{},[895,67818,67819,67821,67827,67829,67835],{},[1700,67820,1703],{"stretchy":1702},[1785,67822,67823,67825],{},[898,67824,1662],{},[1700,67826,4543],{},[1700,67828,1732],{"separator":1731},[1785,67830,67831,67833],{},[898,67832,1677],{},[1700,67834,4543],{},[1700,67836,1709],{"stretchy":1702},[902,67838,67839],{"encoding":904},"(Q^*, P^*)",[38,67841,67842],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[4060,67845,67846,67851],{},[724,67847,67848,67850],{},[883,67849,4761],{}," Postup — jak odvodit nabídku firmy",[152,67852,67853,67902,67997,68052,68123],{},[123,67854,67855,67856,2114,67878,2196],{},"Ze zadaných nákladů určete ",[883,67857,67859],{"className":67858},[886],[888,67860,67861],{"xmlns":890},[892,67862,67863,67875],{},[895,67864,67865,67867,67869,67871,67873],{},[898,67866,2005],{},[898,67868,2974],{},[1700,67870,1703],{"stretchy":1702},[898,67872,1662],{},[1700,67874,1709],{"stretchy":1702},[902,67876,67877],{"encoding":904},"MC(Q)",[883,67879,67881],{"className":67880},[886],[888,67882,67883],{"xmlns":890},[892,67884,67885,67899],{},[895,67886,67887,67889,67891,67893,67895,67897],{},[898,67888,1862],{},[898,67890,40524],{},[898,67892,2974],{},[1700,67894,1703],{"stretchy":1702},[898,67896,1662],{},[1700,67898,1709],{"stretchy":1702},[902,67900,67901],{"encoding":904},"AVC(Q)",[123,67903,67904,67905,67922,67923,67940,67941,67973,67974,4110],{},"Najděte ",[883,67906,67908],{"className":67907},[886],[888,67909,67910],{"xmlns":890},[892,67911,67912,67920],{},[895,67913,67914],{},[1785,67915,67916,67918],{},[898,67917,1662],{},[1700,67919,4543],{},[902,67921,30029],{"encoding":904}," jako bod minima ",[883,67924,67926],{"className":67925},[886],[888,67927,67928],{"xmlns":890},[892,67929,67930,67938],{},[895,67931,67932,67934,67936],{},[898,67933,1862],{},[898,67935,40524],{},[898,67937,2974],{},[902,67939,55495],{"encoding":904}," (řešením ",[883,67942,67944],{"className":67943},[886],[888,67945,67946],{"xmlns":890},[892,67947,67948,67970],{},[895,67949,67950,67952,67954,67960,67962,67964,67966,67968],{},[898,67951,1862],{},[898,67953,40524],{},[1785,67955,67956,67958],{},[898,67957,2974],{},[1700,67959,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,67961,1703],{"stretchy":1702},[898,67963,1662],{},[1700,67965,1709],{"stretchy":1702},[1700,67967,1765],{},[1931,67969,1772],{},[902,67971,67972],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,67975,67977],{"className":67976},[886],[888,67978,67979],{"xmlns":890},[892,67980,67981,67995],{},[895,67982,67983,67985,67987,67989,67991,67993],{},[898,67984,1862],{},[898,67986,40524],{},[898,67988,2974],{},[1700,67990,1765],{},[898,67992,2005],{},[898,67994,2974],{},[902,67996,55432],{"encoding":904},[123,67998,65905,67999,68051],{},[883,68000,68002],{"className":68001},[886],[888,68003,68004],{"xmlns":890},[892,68005,68006,68048],{},[895,68007,68008,68014,68016,68018,68020,68022,68028,68030,68032,68034,68036,68038,68040,68046],{},[1785,68009,68010,68012],{},[898,68011,1677],{},[1700,68013,4543],{},[1700,68015,1765],{},[898,68017,2005],{},[898,68019,2974],{},[1700,68021,1703],{"stretchy":1702},[1785,68023,68024,68026],{},[898,68025,1662],{},[1700,68027,4543],{},[1700,68029,1709],{"stretchy":1702},[1700,68031,1765],{},[898,68033,1862],{},[898,68035,40524],{},[898,68037,2974],{},[1700,68039,1703],{"stretchy":1702},[1785,68041,68042,68044],{},[898,68043,1662],{},[1700,68045,4543],{},[1700,68047,1709],{"stretchy":1702},[902,68049,68050],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,68053,68054,68055,6661,68087,68109,68110,2196],{},"Zapište nabídku: ",[883,68056,68058],{"className":68057},[886],[888,68059,68060],{"xmlns":890},[892,68061,68062,68084],{},[895,68063,68064,68066,68068,68070,68072,68074,68076,68078,68080,68082],{},[898,68065,8861],{},[1700,68067,1703],{"stretchy":1702},[898,68069,1662],{},[1700,68071,1709],{"stretchy":1702},[1700,68073,1765],{},[898,68075,2005],{},[898,68077,2974],{},[1700,68079,1703],{"stretchy":1702},[898,68081,1662],{},[1700,68083,1709],{"stretchy":1702},[902,68085,68086],{"encoding":904},"S(Q) = MC(Q)",[883,68088,68090],{"className":68089},[886],[888,68091,68092],{"xmlns":890},[892,68093,68094,68106],{},[895,68095,68096,68098,68100],{},[898,68097,1662],{},[1700,68099,4674],{},[1785,68101,68102,68104],{},[898,68103,1662],{},[1700,68105,4543],{},[902,68107,68108],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,68111,68113],{"className":68112},[886],[888,68114,68115],{"xmlns":890},[892,68116,68117,68121],{},[895,68118,68119],{},[1931,68120,1772],{},[902,68122,1772],{"encoding":904},[123,68124,68125,68126,68158],{},"V případě potřeby vyjádřete inverzi ",[883,68127,68129],{"className":68128},[886],[888,68130,68131],{"xmlns":890},[892,68132,68133,68155],{},[895,68134,68135,68137,68139,68149,68151,68153],{},[898,68136,1662],{},[1700,68138,1765],{},[1785,68140,68141,68143],{},[898,68142,8861],{},[895,68144,68145,68147],{},[1700,68146,1768],{},[1931,68148,1933],{},[1700,68150,1703],{"stretchy":1702},[898,68152,1677],{},[1700,68154,1709],{"stretchy":1702},[902,68156,68157],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,68160,68161],{},[614,68162,68163,68164,1343,68179,2114,68196,29386,68211,68224,68225,68250,68251,68264,68265,68282,68283,68300,68301,68318],{},"Obrázek 3.14: Křivky ",[883,68165,68167],{"className":68166},[886],[888,68168,68169],{"xmlns":890},[892,68170,68171,68177],{},[895,68172,68173,68175],{},[898,68174,1862],{},[898,68176,2974],{},[902,68178,55744],{"encoding":904},[883,68180,68182],{"className":68181},[886],[888,68183,68184],{"xmlns":890},[892,68185,68186,68194],{},[895,68187,68188,68190,68192],{},[898,68189,1862],{},[898,68191,40524],{},[898,68193,2974],{},[902,68195,55495],{"encoding":904},[883,68197,68199],{"className":68198},[886],[888,68200,68201],{"xmlns":890},[892,68202,68203,68209],{},[895,68204,68205,68207],{},[898,68206,2005],{},[898,68208,2974],{},[902,68210,55476],{"encoding":904},[883,68212,68214],{"className":68213},[886],[888,68215,68216],{"xmlns":890},[892,68217,68218,68222],{},[895,68219,68220],{},[898,68221,900],{},[902,68223,900],{"encoding":904},"; křivka nabídky ",[883,68226,68228],{"className":68227},[886],[888,68229,68230],{"xmlns":890},[892,68231,68232,68248],{},[895,68233,68234,68236,68238,68240,68242,68244,68246],{},[898,68235,1677],{},[1700,68237,1765],{},[898,68239,2005],{},[898,68241,2974],{},[1700,68243,1703],{"stretchy":1702},[898,68245,1662],{},[1700,68247,1709],{"stretchy":1702},[902,68249,67550],{"encoding":904}," začíná v bodě ",[883,68252,68254],{"className":68253},[886],[888,68255,68256],{"xmlns":890},[892,68257,68258,68262],{},[895,68259,68260],{},[898,68261,1862],{},[902,68263,1862],{"encoding":904}," odpovídajícím minimu ",[883,68266,68268],{"className":68267},[886],[888,68269,68270],{"xmlns":890},[892,68271,68272,68280],{},[895,68273,68274,68276,68278],{},[898,68275,1862],{},[898,68277,40524],{},[898,68279,2974],{},[902,68281,55495],{"encoding":904}," při ceně ",[883,68284,68286],{"className":68285},[886],[888,68287,68288],{"xmlns":890},[892,68289,68290,68298],{},[895,68291,68292],{},[1785,68293,68294,68296],{},[898,68295,1677],{},[1700,68297,4543],{},[902,68299,4593],{"encoding":904}," (minimální cena nabídky); pod ",[883,68302,68304],{"className":68303},[886],[888,68305,68306],{"xmlns":890},[892,68307,68308,68316],{},[895,68309,68310],{},[1785,68311,68312,68314],{},[898,68313,1662],{},[1700,68315,4543],{},[902,68317,30029],{"encoding":904}," je nabídka nulová.",[37533,68320,68322],{"id":68321},"příklad-312","Příklad 3.12",[724,68324,68325,57706,68327,68373],{},[38,68326,56171],{},[883,68328,68330],{"className":68329},[886],[888,68331,68332],{"xmlns":890},[892,68333,68334,68370],{},[895,68335,68336,68338,68340,68342,68344,68350,68352,68354,68360,68362,68364,68366,68368],{},[898,68337,2971],{},[898,68339,2974],{},[1700,68341,1765],{},[1931,68343,2990],{},[1785,68345,68346,68348],{},[898,68347,1662],{},[1931,68349,2385],{},[1700,68351,1768],{},[1931,68353,2343],{},[1785,68355,68356,68358],{},[898,68357,1662],{},[1931,68359,2343],{},[1700,68361,1897],{},[1931,68363,36429],{},[898,68365,1662],{},[1700,68367,1897],{},[1931,68369,3058],{},[902,68371,68372],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,68375,68376,2106,68378,68415,68416,2901],{},[38,68377,22955],{},[883,68379,68381],{"className":68380},[886],[888,68382,68383],{"xmlns":890},[892,68384,68385,68412],{},[895,68386,68387,68389,68391,68393,68396,68402,68404,68406,68408,68410],{},[898,68388,2005],{},[898,68390,2974],{},[1700,68392,1765],{},[1931,68394,68395],{},"0,3",[1785,68397,68398,68400],{},[898,68399,1662],{},[1931,68401,2343],{},[1700,68403,1768],{},[1931,68405,2553],{},[898,68407,1662],{},[1700,68409,1897],{},[1931,68411,36429],{},[902,68413,68414],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,68417,68419],{"className":68418},[886],[888,68420,68421],{"xmlns":890},[892,68422,68423,68433],{},[895,68424,68425,68427,68429,68431],{},[898,68426,1677],{},[1700,68428,1765],{},[898,68430,2005],{},[898,68432,2974],{},[902,68434,68435],{"encoding":904},"P = MC",[883,68437,68439],{"className":68438},[886],[888,68440,68441],{"xmlns":890,"display":28251},[892,68442,68443,68468],{},[895,68444,68445,68447,68449,68451,68457,68459,68461,68463,68465],{},[898,68446,1677],{},[1700,68448,1765],{},[1931,68450,68395],{},[1785,68452,68453,68455],{},[898,68454,1662],{},[1931,68456,2343],{},[1700,68458,1768],{},[1931,68460,2553],{},[898,68462,1662],{},[1700,68464,1897],{},[1931,68466,68467],{},"15.",[902,68469,68470],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,68472,68473,68474,5570,68487,68500],{},"Vyjádření ",[883,68475,68477],{"className":68476},[886],[888,68478,68479],{"xmlns":890},[892,68480,68481,68485],{},[895,68482,68483],{},[898,68484,1662],{},[902,68486,1662],{"encoding":904},[883,68488,68490],{"className":68489},[886],[888,68491,68492],{"xmlns":890},[892,68493,68494,68498],{},[895,68495,68496],{},[898,68497,1677],{},[902,68499,1677],{"encoding":904}," doplněním na čtverec:",[883,68502,68504],{"className":68503},[886],[888,68505,68506],{"xmlns":890,"display":28251},[892,68507,68508,68598],{},[895,68509,68510,68512,68514,68516,68554,68556,68558,68580,68582,68596],{},[898,68511,1677],{},[1700,68513,1765],{},[1931,68515,68395],{},[895,68517,68518,68520,68542,68544,68552],{},[1700,68519,1703],{"fence":1731},[1785,68521,68522,68540],{},[895,68523,68524,68526,68528,68530,68538],{},[1700,68525,1703],{"fence":1731},[898,68527,1662],{},[1700,68529,1768],{},[1770,68531,68532],{"scriptlevel":1772,"displaystyle":1702},[1774,68533,68534,68536],{},[1931,68535,9223],{},[1931,68537,2385],{},[1700,68539,1709],{"fence":1731},[1931,68541,2343],{},[1700,68543,1897],{},[1770,68545,68546],{"scriptlevel":1772,"displaystyle":1702},[1774,68547,68548,68550],{},[1931,68549,3314],{},[1931,68551,4190],{},[1700,68553,1709],{"fence":1731},[1700,68555,1732],{"separator":1731},[6066,68557],{"width":6068},[1785,68559,68560,68578],{},[895,68561,68562,68564,68566,68568,68576],{},[1700,68563,1703],{"fence":1731},[898,68565,1662],{},[1700,68567,1768],{},[1770,68569,68570],{"scriptlevel":1772,"displaystyle":1702},[1774,68571,68572,68574],{},[1931,68573,9223],{},[1931,68575,2385],{},[1700,68577,1709],{"fence":1731},[1931,68579,2343],{},[1700,68581,1765],{},[1774,68583,68584,68594],{},[895,68585,68586,68588,68590,68592],{},[1931,68587,38204],{},[898,68589,1677],{},[1700,68591,1768],{},[1931,68593,3314],{},[1931,68595,4190],{},[1700,68597,1732],{"separator":1731},[902,68599,68600],{"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},",[883,68602,68604],{"className":68603},[886],[888,68605,68606],{"xmlns":890,"display":28251},[892,68607,68608,68640],{},[895,68609,68610,68612,68614,68620,68622,68638],{},[898,68611,1662],{},[1700,68613,1765],{},[1774,68615,68616,68618],{},[1931,68617,9223],{},[1931,68619,2385],{},[1700,68621,1897],{},[1774,68623,68624,68636],{},[8305,68625,68626],{},[895,68627,68628,68630,68632,68634],{},[1931,68629,38204],{},[898,68631,1677],{},[1700,68633,1768],{},[1931,68635,3314],{},[1931,68637,2385],{},[898,68639,2196],{"mathvariant":1791},[902,68641,68642],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,68644,67202,68645,1343,68683,1343,68731,68765,68766,2196],{},[883,68646,68648],{"className":68647},[886],[888,68649,68650],{"xmlns":890},[892,68651,68652,68680],{},[895,68653,68654,68656,68658,68660,68662,68664,68670,68672,68674,68676,68678],{},[898,68655,1862],{},[898,68657,40524],{},[898,68659,2974],{},[1700,68661,1765],{},[1931,68663,2990],{},[1785,68665,68666,68668],{},[898,68667,1662],{},[1931,68669,2343],{},[1700,68671,1768],{},[1931,68673,2343],{},[898,68675,1662],{},[1700,68677,1897],{},[1931,68679,36429],{},[902,68681,68682],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,68684,68686],{"className":68685},[886],[888,68687,68688],{"xmlns":890},[892,68689,68690,68728],{},[895,68691,68692,68694,68696,68702,68704,68706,68708,68710,68712,68714,68716,68718,68724,68726],{},[898,68693,1862],{},[898,68695,40524],{},[1785,68697,68698,68700],{},[898,68699,2974],{},[1700,68701,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,68703,1765],{},[1931,68705,3034],{},[898,68707,1662],{},[1700,68709,1768],{},[1931,68711,2343],{},[1700,68713,1765],{},[1931,68715,1772],{},[1700,68717,4178],{},[1785,68719,68720,68722],{},[898,68721,1662],{},[1700,68723,4543],{},[1700,68725,1765],{},[1931,68727,3058],{},[902,68729,68730],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,68732,68734],{"className":68733},[886],[888,68735,68736],{"xmlns":890},[892,68737,68738,68762],{},[895,68739,68740,68742,68744,68754,68756,68758,68760],{},[898,68741,1862],{},[898,68743,40524],{},[1785,68745,68746,68748],{},[898,68747,2974],{},[895,68749,68750,68752],{},[1700,68751,1793],{"mathvariant":1791},[1700,68753,1793],{"mathvariant":1791},[1700,68755,1765],{},[1931,68757,3034],{},[1700,68759,3601],{},[1931,68761,1772],{},[902,68763,68764],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,68767,68769],{"className":68768},[886],[888,68770,68771],{"xmlns":890},[892,68772,68773,68809],{},[895,68774,68775,68781,68783,68785,68787,68789,68791,68793,68795,68797,68799,68801,68803,68805,68807],{},[1785,68776,68777,68779],{},[898,68778,1677],{},[1700,68780,4543],{},[1700,68782,1765],{},[898,68784,2005],{},[898,68786,2974],{},[1700,68788,1703],{"stretchy":1702},[1931,68790,3058],{},[1700,68792,1709],{"stretchy":1702},[1700,68794,1765],{},[1931,68796,38204],{},[1700,68798,1768],{},[1931,68800,5399],{},[1700,68802,1897],{},[1931,68804,36429],{},[1700,68806,1765],{},[1931,68808,2438],{},[902,68810,68811],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,68813,68814],{},[38,68815,68816],{},"Závěr.",[883,68818,68820],{"className":68819},[886],[888,68821,68822],{"xmlns":890,"display":28251},[892,68823,68824,68910],{},[895,68825,68826,68828,68830,68832,68834,68836,68838,68840],{},[898,68827,1677],{},[1700,68829,1765],{},[898,68831,8861],{},[1700,68833,1703],{"stretchy":1702},[898,68835,1662],{},[1700,68837,1709],{"stretchy":1702},[1700,68839,1765],{},[895,68841,68842,68844],{},[1700,68843,67690],{"fence":1731},[20939,68845,68846,68888],{"rowspacing":67693,"columnalign":67694,"columnspacing":15469},[20944,68847,68848,68872],{},[20947,68849,68850],{},[1770,68851,68852],{"scriptlevel":1772,"displaystyle":1702},[895,68853,68854,68856,68862,68864,68866,68868,68870],{},[1931,68855,68395],{},[1785,68857,68858,68860],{},[898,68859,1662],{},[1931,68861,2343],{},[1700,68863,1768],{},[1931,68865,2553],{},[898,68867,1662],{},[1700,68869,1897],{},[1931,68871,36429],{},[20947,68873,68874],{},[1770,68875,68876],{"scriptlevel":1772,"displaystyle":1702},[895,68877,68878,68880,68882,68884,68886],{},[1781,68879,67721],{},[898,68881,1662],{},[1700,68883,4674],{},[1931,68885,3058],{},[1700,68887,1732],{"separator":1731},[20944,68889,68890,68896],{},[20947,68891,68892],{},[1770,68893,68894],{"scriptlevel":1772,"displaystyle":1702},[1931,68895,1772],{},[20947,68897,68898],{},[1770,68899,68900],{"scriptlevel":1772,"displaystyle":1702},[895,68901,68902,68904,68906,68908],{},[1781,68903,67721],{},[898,68905,1662],{},[1700,68907,3640],{},[1931,68909,19513],{},[902,68911,68912],{"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}",[724,68914,68915],{},[614,68916,68917,68918,68933,68934,2196],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,68919,68921],{"className":68920},[886],[888,68922,68923],{"xmlns":890},[892,68924,68925,68931],{},[895,68926,68927,68929],{},[898,68928,2005],{},[898,68930,2974],{},[902,68932,55476],{"encoding":904}," ležící nad minimem ",[883,68935,68937],{"className":68936},[886],[888,68938,68939],{"xmlns":890},[892,68940,68941,68949],{},[895,68942,68943,68945,68947],{},[898,68944,1862],{},[898,68946,40524],{},[898,68948,2974],{},[902,68950,55495],{"encoding":904},[115,68952,68954],{"id":68953},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,68956,68957,68958,68962,68963,68978,68979,68999,69000,2114,69003,69006,69007,69009,69010,20130,69032,69034,69035,2114,69037,58910,69040,2106,69043,41999,69058,69073],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,68959,68961],{"className":68960,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,68964,68966],{"className":68965},[886],[888,68967,68968],{"xmlns":890},[892,68969,68970,68976],{},[895,68971,68972,68974],{},[898,68973,2971],{},[898,68975,4185],{},[902,68977,4285],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,68980,68982],{"className":68981},[886],[888,68983,68984],{"xmlns":890},[892,68985,68986,68996],{},[895,68987,68988,68990,68992,68994],{},[898,68989,2971],{},[898,68991,4185],{},[898,68993,1979],{"mathvariant":1791},[898,68995,1662],{},[902,68997,68998],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,69001,69002],{},"fixních",[38,69004,69005],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,69008,64509],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,69011,69013],{"className":69012},[886],[888,69014,69015],{"xmlns":890},[892,69016,69017,69029],{},[895,69018,69019,69021,69023,69025,69027],{},[898,69020,2971],{},[898,69022,4185],{},[1700,69024,1768],{},[898,69026,2971],{},[898,69028,2974],{},[902,69030,69031],{"encoding":904},"TR - TC",[38,69033,55356],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,69036,56668],{},[38,69038,69039],{},"mezní náklady",[207,69041,1145],{"className":69042,"dataFsResolvedFilePath":764,"href":765},[210],[883,69044,69046],{"className":69045},[886],[888,69047,69048],{"xmlns":890},[892,69049,69050,69056],{},[895,69051,69052,69054],{},[898,69053,2971],{},[898,69055,4185],{},[902,69057,4285],{"encoding":904},[883,69059,69061],{"className":69060},[886],[888,69062,69063],{"xmlns":890},[892,69064,69065,69071],{},[895,69066,69067,69069],{},[898,69068,2971],{},[898,69070,2974],{},[902,69072,3436],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,69075,69076,69138,69204,69266],{},[123,69077,69078,69081,69082,10577,69097,2196],{},[38,69079,69080],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,69083,69085],{"className":69084},[886],[888,69086,69087],{"xmlns":890},[892,69088,69089,69095],{},[895,69090,69091,69093],{},[898,69092,1862],{},[898,69094,2974],{},[902,69096,55744],{"encoding":904},[883,69098,69100],{"className":69099},[886],[888,69101,69102],{"xmlns":890},[892,69103,69104,69136],{},[895,69105,69106,69108,69110,69112,69118,69120,69122,69124,69126,69128,69134],{},[898,69107,1862],{},[898,69109,2974],{},[1700,69111,1703],{"stretchy":1702},[2007,69113,69114,69116],{},[898,69115,1662],{},[1931,69117,1772],{},[1700,69119,1709],{"stretchy":1702},[1700,69121,1765],{},[898,69123,2005],{},[898,69125,2974],{},[1700,69127,1703],{"stretchy":1702},[2007,69129,69130,69132],{},[898,69131,1662],{},[1931,69133,1772],{},[1700,69135,1709],{"stretchy":1702},[902,69137,62753],{"encoding":904},[123,69139,69140,69081,69143,10577,69160,2196],{},[38,69141,69142],{},"Princip minimalizace průměrných variabilních nákladů:",[883,69144,69146],{"className":69145},[886],[888,69147,69148],{"xmlns":890},[892,69149,69150,69158],{},[895,69151,69152,69154,69156],{},[898,69153,1862],{},[898,69155,40524],{},[898,69157,2974],{},[902,69159,55495],{"encoding":904},[883,69161,69163],{"className":69162},[886],[888,69164,69165],{"xmlns":890},[892,69166,69167,69201],{},[895,69168,69169,69171,69173,69175,69177,69183,69185,69187,69189,69191,69193,69199],{},[898,69170,1862],{},[898,69172,40524],{},[898,69174,2974],{},[1700,69176,1703],{"stretchy":1702},[2007,69178,69179,69181],{},[898,69180,1662],{},[1931,69182,1772],{},[1700,69184,1709],{"stretchy":1702},[1700,69186,1765],{},[898,69188,2005],{},[898,69190,2974],{},[1700,69192,1703],{"stretchy":1702},[2007,69194,69195,69197],{},[898,69196,1662],{},[1931,69198,1772],{},[1700,69200,1709],{"stretchy":1702},[902,69202,69203],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,69205,69206,69209,69210,10577,69225,2196],{},[38,69207,69208],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,69211,69213],{"className":69212},[886],[888,69214,69215],{"xmlns":890},[892,69216,69217,69223],{},[895,69218,69219,69221],{},[898,69220,1677],{},[898,69222,4185],{},[902,69224,63663],{"encoding":904},[883,69226,69228],{"className":69227},[886],[888,69229,69230],{"xmlns":890},[892,69231,69232,69264],{},[895,69233,69234,69236,69238,69240,69246,69248,69250,69252,69254,69256,69262],{},[898,69235,2005],{},[898,69237,4185],{},[1700,69239,1703],{"stretchy":1702},[2007,69241,69242,69244],{},[898,69243,1662],{},[1931,69245,1772],{},[1700,69247,1709],{"stretchy":1702},[1700,69249,1765],{},[898,69251,2005],{},[898,69253,2974],{},[1700,69255,1703],{"stretchy":1702},[2007,69257,69258,69260],{},[898,69259,1662],{},[1931,69261,1772],{},[1700,69263,1709],{"stretchy":1702},[902,69265,65829],{"encoding":904},[123,69267,69268,2106,69271,6661,69307,68109,69328,21779,69341,67791,69358,2196],{},[38,69269,69270],{},"Funkce nabídky firmy:",[883,69272,69274],{"className":69273},[886],[888,69275,69276],{"xmlns":890},[892,69277,69278,69304],{},[895,69279,69280,69282,69284,69286,69288,69290,69292,69294,69296,69298,69300,69302],{},[898,69281,1677],{},[1700,69283,1765],{},[898,69285,8861],{},[1700,69287,1703],{"stretchy":1702},[898,69289,1662],{},[1700,69291,1709],{"stretchy":1702},[1700,69293,1765],{},[898,69295,2005],{},[898,69297,2974],{},[1700,69299,1703],{"stretchy":1702},[898,69301,1662],{},[1700,69303,1709],{"stretchy":1702},[902,69305,69306],{"encoding":904},"P = S(Q) = MC(Q)",[883,69308,69310],{"className":69309},[886],[888,69311,69312],{"xmlns":890},[892,69313,69314,69326],{},[895,69315,69316,69318,69320],{},[898,69317,1662],{},[1700,69319,4674],{},[1785,69321,69322,69324],{},[898,69323,1662],{},[1700,69325,4543],{},[902,69327,68108],{"encoding":904},[883,69329,69331],{"className":69330},[886],[888,69332,69333],{"xmlns":890},[892,69334,69335,69339],{},[895,69336,69337],{},[1931,69338,1772],{},[902,69340,1772],{"encoding":904},[883,69342,69344],{"className":69343},[886],[888,69345,69346],{"xmlns":890},[892,69347,69348,69356],{},[895,69349,69350],{},[1785,69351,69352,69354],{},[898,69353,1662],{},[1700,69355,4543],{},[902,69357,30029],{"encoding":904},[883,69359,69361],{"className":69360},[886],[888,69362,69363],{"xmlns":890},[892,69364,69365,69373],{},[895,69366,69367,69369,69371],{},[898,69368,1862],{},[898,69370,40524],{},[898,69372,2974],{},[902,69374,55495],{"encoding":904},[115,69376,50067],{"id":50066},[152,69378,69379,69382,69385,69388,69391,69394,69397,69400,69403,69406,69409],{},[123,69380,69381],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,69383,69384],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,69386,69387],{},"Jak se vypočte mezní příjem a co udává?",[123,69389,69390],{},"Z jakých složek se skládají celkové náklady?",[123,69392,69393],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,69395,69396],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,69398,69399],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,69401,69402],{},"Jak se vypočte zisk?",[123,69404,69405],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,69407,69408],{},"Co jsou body zvratu? Jak se najdou?",[123,69410,69411],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,69413,69415],{"id":69414},"úlohy-31328","Úlohy 3.1–3.28",[198,69417,69419],{"id":69418},"příjem-3135","Příjem (3.1–3.5)",[724,69421,69422,45611,69425,69453,69454,69469,69470,69485,69486,69501,69502,1343,69517,1343,69532,69547],{},[38,69423,69424],{},"3.1",[883,69426,69428],{"className":69427},[886],[888,69429,69430],{"xmlns":890},[892,69431,69432,69450],{},[895,69433,69434,69436,69438,69440,69442,69444,69446,69448],{},[898,69435,1677],{},[1700,69437,1765],{},[898,69439,4374],{},[1700,69441,1703],{"stretchy":1702},[898,69443,1662],{},[1700,69445,1709],{"stretchy":1702},[1700,69447,1765],{},[1931,69449,3284],{},[902,69451,69452],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,69455,69457],{"className":69456},[886],[888,69458,69459],{"xmlns":890},[892,69460,69461,69467],{},[895,69462,69463,69465],{},[898,69464,2971],{},[898,69466,4185],{},[902,69468,4285],{"encoding":904},", průměrný příjem ",[883,69471,69473],{"className":69472},[886],[888,69474,69475],{"xmlns":890},[892,69476,69477,69483],{},[895,69478,69479,69481],{},[898,69480,1862],{},[898,69482,4185],{},[902,69484,55629],{"encoding":904}," a mezní příjem ",[883,69487,69489],{"className":69488},[886],[888,69490,69491],{"xmlns":890},[892,69492,69493,69499],{},[895,69494,69495,69497],{},[898,69496,2005],{},[898,69498,4185],{},[902,69500,6822],{"encoding":904},". (c) Vypočtěte ",[883,69503,69505],{"className":69504},[886],[888,69506,69507],{"xmlns":890},[892,69508,69509,69515],{},[895,69510,69511,69513],{},[898,69512,2971],{},[898,69514,4185],{},[902,69516,4285],{"encoding":904},[883,69518,69520],{"className":69519},[886],[888,69521,69522],{"xmlns":890},[892,69523,69524,69530],{},[895,69525,69526,69528],{},[898,69527,1862],{},[898,69529,4185],{},[902,69531,55629],{"encoding":904},[883,69533,69535],{"className":69534},[886],[888,69536,69537],{"xmlns":890},[892,69538,69539,69545],{},[895,69540,69541,69543],{},[898,69542,2005],{},[898,69544,4185],{},[902,69546,6822],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,69549,69550,45611,69553,69453,69589,69469,69604,69485,69619,69501,69634,1343,69649,1343,69664,69679],{},[38,69551,69552],{},"3.2",[883,69554,69556],{"className":69555},[886],[888,69557,69558],{"xmlns":890},[892,69559,69560,69586],{},[895,69561,69562,69564,69566,69568,69570,69572,69574,69576,69578,69580,69582,69584],{},[898,69563,1677],{},[1700,69565,1765],{},[898,69567,4374],{},[1700,69569,1703],{"stretchy":1702},[898,69571,1662],{},[1700,69573,1709],{"stretchy":1702},[1700,69575,1765],{},[1700,69577,1768],{},[1931,69579,5197],{},[898,69581,1662],{},[1700,69583,1897],{},[1931,69585,9223],{},[902,69587,69588],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,69590,69592],{"className":69591},[886],[888,69593,69594],{"xmlns":890},[892,69595,69596,69602],{},[895,69597,69598,69600],{},[898,69599,2971],{},[898,69601,4185],{},[902,69603,4285],{"encoding":904},[883,69605,69607],{"className":69606},[886],[888,69608,69609],{"xmlns":890},[892,69610,69611,69617],{},[895,69612,69613,69615],{},[898,69614,1862],{},[898,69616,4185],{},[902,69618,55629],{"encoding":904},[883,69620,69622],{"className":69621},[886],[888,69623,69624],{"xmlns":890},[892,69625,69626,69632],{},[895,69627,69628,69630],{},[898,69629,2005],{},[898,69631,4185],{},[902,69633,6822],{"encoding":904},[883,69635,69637],{"className":69636},[886],[888,69638,69639],{"xmlns":890},[892,69640,69641,69647],{},[895,69642,69643,69645],{},[898,69644,2971],{},[898,69646,4185],{},[902,69648,4285],{"encoding":904},[883,69650,69652],{"className":69651},[886],[888,69653,69654],{"xmlns":890},[892,69655,69656,69662],{},[895,69657,69658,69660],{},[898,69659,1862],{},[898,69661,4185],{},[902,69663,55629],{"encoding":904},[883,69665,69667],{"className":69666},[886],[888,69668,69669],{"xmlns":890},[892,69670,69671,69677],{},[895,69672,69673,69675],{},[898,69674,2005],{},[898,69676,4185],{},[902,69678,6822],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,69681,69682,45611,69685,69722,69723,69469,69738,69485,69753,69768,69769,6661,69784,69810,69811,69826,69827,1343,69842,6661,69857,69810,69882,69897,69898,69911,69912,69927,69928,69943,69944,1343,69957,1343,69972,1343,69987,2196],{},[38,69683,69684],{},"3.3",[883,69686,69688],{"className":69687},[886],[888,69689,69690],{"xmlns":890},[892,69691,69692,69719],{},[895,69693,69694,69696,69698,69700,69702,69704,69706,69708,69711,69713],{},[898,69695,1677],{},[1700,69697,1765],{},[898,69699,4374],{},[1700,69701,1703],{"stretchy":1702},[898,69703,1662],{},[1700,69705,1709],{"stretchy":1702},[1700,69707,1765],{},[1931,69709,69710],{},"1200",[1700,69712,1768],{},[1785,69714,69715,69717],{},[898,69716,1662],{},[1931,69718,2343],{},[902,69720,69721],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,69724,69726],{"className":69725},[886],[888,69727,69728],{"xmlns":890},[892,69729,69730,69736],{},[895,69731,69732,69734],{},[898,69733,2971],{},[898,69735,4185],{},[902,69737,4285],{"encoding":904},[883,69739,69741],{"className":69740},[886],[888,69742,69743],{"xmlns":890},[892,69744,69745,69751],{},[895,69746,69747,69749],{},[898,69748,1862],{},[898,69750,4185],{},[902,69752,55629],{"encoding":904},[883,69754,69756],{"className":69755},[886],[888,69757,69758],{"xmlns":890},[892,69759,69760,69766],{},[895,69761,69762,69764],{},[898,69763,2005],{},[898,69765,4185],{},[902,69767,6822],{"encoding":904},". (b) Vypočtěte ",[883,69770,69772],{"className":69771},[886],[888,69773,69774],{"xmlns":890},[892,69775,69776,69782],{},[895,69777,69778,69780],{},[898,69779,2971],{},[898,69781,4185],{},[902,69783,4285],{"encoding":904},[883,69785,69787],{"className":69786},[886],[888,69788,69789],{"xmlns":890},[892,69790,69791,69807],{},[895,69792,69793,69795,69797,69799,69801,69803,69805],{},[898,69794,1662],{},[1700,69796,1765],{},[1931,69798,3058],{},[1700,69800,1732],{"separator":1731},[1931,69802,9223],{},[1700,69804,1732],{"separator":1731},[1931,69806,38204],{},[902,69808,69809],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,69812,69814],{"className":69813},[886],[888,69815,69816],{"xmlns":890},[892,69817,69818,69824],{},[895,69819,69820,69822],{},[898,69821,2971],{},[898,69823,4185],{},[902,69825,4285],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,69828,69830],{"className":69829},[886],[888,69831,69832],{"xmlns":890},[892,69833,69834,69840],{},[895,69835,69836,69838],{},[898,69837,1862],{},[898,69839,4185],{},[902,69841,55629],{"encoding":904},[883,69843,69845],{"className":69844},[886],[888,69846,69847],{"xmlns":890},[892,69848,69849,69855],{},[895,69850,69851,69853],{},[898,69852,2005],{},[898,69854,4185],{},[902,69856,6822],{"encoding":904},[883,69858,69860],{"className":69859},[886],[888,69861,69862],{"xmlns":890},[892,69863,69864,69880],{},[895,69865,69866,69868,69870,69872,69874,69876,69878],{},[898,69867,1662],{},[1700,69869,1765],{},[1931,69871,3058],{},[1700,69873,1732],{"separator":1731},[1931,69875,9223],{},[1700,69877,1732],{"separator":1731},[1931,69879,38204],{},[902,69881,69809],{"encoding":904},[883,69883,69885],{"className":69884},[886],[888,69886,69887],{"xmlns":890},[892,69888,69889,69895],{},[895,69890,69891,69893],{},[898,69892,2005],{},[898,69894,4185],{},[902,69896,6822],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,69899,69901],{"className":69900},[886],[888,69902,69903],{"xmlns":890},[892,69904,69905,69909],{},[895,69906,69907],{},[898,69908,1662],{},[902,69910,1662],{"encoding":904},", které maximalizuje ",[883,69913,69915],{"className":69914},[886],[888,69916,69917],{"xmlns":890},[892,69918,69919,69925],{},[895,69920,69921,69923],{},[898,69922,2971],{},[898,69924,4185],{},[902,69926,4285],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,69929,69931],{"className":69930},[886],[888,69932,69933],{"xmlns":890},[892,69934,69935,69941],{},[895,69936,69937,69939],{},[898,69938,2971],{},[898,69940,4185],{},[902,69942,4285],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,69945,69947],{"className":69946},[886],[888,69948,69949],{"xmlns":890},[892,69950,69951,69955],{},[895,69952,69953],{},[898,69954,4374],{},[902,69956,4374],{"encoding":904},[883,69958,69960],{"className":69959},[886],[888,69961,69962],{"xmlns":890},[892,69963,69964,69970],{},[895,69965,69966,69968],{},[898,69967,2971],{},[898,69969,4185],{},[902,69971,4285],{"encoding":904},[883,69973,69975],{"className":69974},[886],[888,69976,69977],{"xmlns":890},[892,69978,69979,69985],{},[895,69980,69981,69983],{},[898,69982,1862],{},[898,69984,4185],{},[902,69986,55629],{"encoding":904},[883,69988,69990],{"className":69989},[886],[888,69991,69992],{"xmlns":890},[892,69993,69994,70000],{},[895,69995,69996,69998],{},[898,69997,2005],{},[898,69999,4185],{},[902,70001,6822],{"encoding":904},[724,70003,70004,70007,70008,70038,70039,70054,70055,10340,70068,1343,70086,1343,70103,70121,70122,70144,70145,70160,70161,70174,70175,2196],{},[38,70005,70006],{},"3.4"," Je dán celkový příjem ",[883,70009,70011],{"className":70010},[886],[888,70012,70013],{"xmlns":890},[892,70014,70015,70035],{},[895,70016,70017,70019,70021,70023,70025,70027,70029],{},[898,70018,2971],{},[898,70020,4185],{},[1700,70022,1765],{},[1931,70024,69710],{},[898,70026,1662],{},[1700,70028,1768],{},[1785,70030,70031,70033],{},[898,70032,1662],{},[1931,70034,2385],{},[902,70036,70037],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,70040,70042],{"className":70041},[886],[888,70043,70044],{"xmlns":890},[892,70045,70046,70052],{},[895,70047,70048,70050],{},[898,70049,2971],{},[898,70051,4185],{},[902,70053,4285],{"encoding":904}," vzhledem ke ",[883,70056,70058],{"className":70057},[886],[888,70059,70060],{"xmlns":890},[892,70061,70062,70066],{},[895,70063,70064],{},[898,70065,1662],{},[902,70067,1662],{"encoding":904},[883,70069,70071],{"className":70070},[886],[888,70072,70073],{"xmlns":890},[892,70074,70075,70083],{},[895,70076,70077,70079,70081],{},[898,70078,1662],{},[1700,70080,1765],{},[1931,70082,2438],{},[902,70084,70085],{"encoding":904},"Q = 5",[883,70087,70089],{"className":70088},[886],[888,70090,70091],{"xmlns":890},[892,70092,70093,70101],{},[895,70094,70095,70097,70099],{},[898,70096,1662],{},[1700,70098,1765],{},[1931,70100,5773],{},[902,70102,5776],{"encoding":904},[883,70104,70106],{"className":70105},[886],[888,70107,70108],{"xmlns":890},[892,70109,70110,70118],{},[895,70111,70112,70114,70116],{},[898,70113,1662],{},[1700,70115,1765],{},[1931,70117,3702],{},[902,70119,70120],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,70123,70125],{"className":70124},[886],[888,70126,70127],{"xmlns":890},[892,70128,70129,70141],{},[895,70130,70131,70133,70135,70137,70139],{},[898,70132,2005],{},[898,70134,4185],{},[1700,70136,1703],{"stretchy":1702},[1931,70138,3058],{},[1700,70140,1709],{"stretchy":1702},[902,70142,70143],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,70146,70148],{"className":70147},[886],[888,70149,70150],{"xmlns":890},[892,70151,70152,70158],{},[895,70153,70154,70156],{},[898,70155,2971],{},[898,70157,4185],{},[902,70159,4285],{"encoding":904},", jestliže se ",[883,70162,70164],{"className":70163},[886],[888,70165,70166],{"xmlns":890},[892,70167,70168,70172],{},[895,70169,70170],{},[898,70171,1662],{},[902,70173,1662],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,70176,70178],{"className":70177},[886],[888,70179,70180],{"xmlns":890},[892,70181,70182,70188],{},[895,70183,70184,70186],{},[898,70185,2971],{},[898,70187,4185],{},[902,70189,4285],{"encoding":904},[724,70191,70192,70195,70196,70222,70223,70238,70239,70160,70254,70267],{},[38,70193,70194],{},"3.5"," Je dán mezní příjem ",[883,70197,70199],{"className":70198},[886],[888,70200,70201],{"xmlns":890},[892,70202,70203,70219],{},[895,70204,70205,70207,70209,70211,70213,70215,70217],{},[898,70206,2005],{},[898,70208,4185],{},[1700,70210,1765],{},[1700,70212,1768],{},[898,70214,1662],{},[1700,70216,1897],{},[1931,70218,9223],{},[902,70220,70221],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,70224,70226],{"className":70225},[886],[888,70227,70228],{"xmlns":890},[892,70229,70230,70236],{},[895,70231,70232,70234],{},[898,70233,2971],{},[898,70235,4185],{},[902,70237,4285],{"encoding":904},". (b) Vypočtěte změnu ",[883,70240,70242],{"className":70241},[886],[888,70243,70244],{"xmlns":890},[892,70245,70246,70252],{},[895,70247,70248,70250],{},[898,70249,2971],{},[898,70251,4185],{},[902,70253,4285],{"encoding":904},[883,70255,70257],{"className":70256},[886],[888,70258,70259],{"xmlns":890},[892,70260,70261,70265],{},[895,70262,70263],{},[898,70264,1662],{},[902,70266,1662],{"encoding":904}," změní z 8 na 12.",[198,70269,70271],{"id":70270},"náklady-36316","Náklady (3.6–3.16)",[724,70273,70274,70277,70278,70318,70319,70334,70335,70352,70353,70370,70371,70386,70387,70402,70403,69768,70418,1343,70433,1343,70450,1343,70467,1343,70482,1343,70497,6661,70512,70530,70531,1343,70546,1343,70561,70576],{},[38,70275,70276],{},"3.6"," Jsou dány celkové náklady ",[883,70279,70281],{"className":70280},[886],[888,70282,70283],{"xmlns":890},[892,70284,70285,70315],{},[895,70286,70287,70289,70291,70293,70295,70297,70299,70301,70303],{},[898,70288,2971],{},[898,70290,2974],{},[1700,70292,1765],{},[1931,70294,3284],{},[1700,70296,1897],{},[1931,70298,2343],{},[898,70300,1662],{},[1700,70302,1897],{},[1770,70304,70305],{"scriptlevel":1772,"displaystyle":1702},[1774,70306,70307,70313],{},[1785,70308,70309,70311],{},[898,70310,1662],{},[1931,70312,2343],{},[1931,70314,3058],{},[902,70316,70317],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,70320,70322],{"className":70321},[886],[888,70323,70324],{"xmlns":890},[892,70325,70326,70332],{},[895,70327,70328,70330],{},[898,70329,10619],{},[898,70331,2974],{},[902,70333,55675],{"encoding":904},", celkové variabilní náklady ",[883,70336,70338],{"className":70337},[886],[888,70339,70340],{"xmlns":890},[892,70341,70342,70350],{},[895,70343,70344,70346,70348],{},[898,70345,2971],{},[898,70347,40524],{},[898,70349,2974],{},[902,70351,55693],{"encoding":904},", průměrné variabilní náklady ",[883,70354,70356],{"className":70355},[886],[888,70357,70358],{"xmlns":890},[892,70359,70360,70368],{},[895,70361,70362,70364,70366],{},[898,70363,1862],{},[898,70365,40524],{},[898,70367,2974],{},[902,70369,55495],{"encoding":904},", variabilní náklady na jednotku ",[883,70372,70374],{"className":70373},[886],[888,70375,70376],{"xmlns":890},[892,70377,70378,70384],{},[895,70379,70380,70382],{},[898,70381,40524],{},[898,70383,2974],{},[902,70385,63789],{"encoding":904},", průměrné náklady ",[883,70388,70390],{"className":70389},[886],[888,70391,70392],{"xmlns":890},[892,70393,70394,70400],{},[895,70395,70396,70398],{},[898,70397,1862],{},[898,70399,2974],{},[902,70401,55744],{"encoding":904}," a mezní náklady ",[883,70404,70406],{"className":70405},[886],[888,70407,70408],{"xmlns":890},[892,70409,70410,70416],{},[895,70411,70412,70414],{},[898,70413,2005],{},[898,70415,2974],{},[902,70417,55476],{"encoding":904},[883,70419,70421],{"className":70420},[886],[888,70422,70423],{"xmlns":890},[892,70424,70425,70431],{},[895,70426,70427,70429],{},[898,70428,2971],{},[898,70430,2974],{},[902,70432,3436],{"encoding":904},[883,70434,70436],{"className":70435},[886],[888,70437,70438],{"xmlns":890},[892,70439,70440,70448],{},[895,70441,70442,70444,70446],{},[898,70443,2971],{},[898,70445,40524],{},[898,70447,2974],{},[902,70449,55693],{"encoding":904},[883,70451,70453],{"className":70452},[886],[888,70454,70455],{"xmlns":890},[892,70456,70457,70465],{},[895,70458,70459,70461,70463],{},[898,70460,1862],{},[898,70462,40524],{},[898,70464,2974],{},[902,70466,55495],{"encoding":904},[883,70468,70470],{"className":70469},[886],[888,70471,70472],{"xmlns":890},[892,70473,70474,70480],{},[895,70475,70476,70478],{},[898,70477,40524],{},[898,70479,2974],{},[902,70481,63789],{"encoding":904},[883,70483,70485],{"className":70484},[886],[888,70486,70487],{"xmlns":890},[892,70488,70489,70495],{},[895,70490,70491,70493],{},[898,70492,1862],{},[898,70494,2974],{},[902,70496,55744],{"encoding":904},[883,70498,70500],{"className":70499},[886],[888,70501,70502],{"xmlns":890},[892,70503,70504,70510],{},[895,70505,70506,70508],{},[898,70507,2005],{},[898,70509,2974],{},[902,70511,55476],{"encoding":904},[883,70513,70515],{"className":70514},[886],[888,70516,70517],{"xmlns":890},[892,70518,70519,70527],{},[895,70520,70521,70523,70525],{},[898,70522,1662],{},[1700,70524,1765],{},[1931,70526,3314],{},[902,70528,70529],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,70532,70534],{"className":70533},[886],[888,70535,70536],{"xmlns":890},[892,70537,70538,70544],{},[895,70539,70540,70542],{},[898,70541,2971],{},[898,70543,2974],{},[902,70545,3436],{"encoding":904},[883,70547,70549],{"className":70548},[886],[888,70550,70551],{"xmlns":890},[892,70552,70553,70559],{},[895,70554,70555,70557],{},[898,70556,1862],{},[898,70558,2974],{},[902,70560,55744],{"encoding":904},[883,70562,70564],{"className":70563},[886],[888,70565,70566],{"xmlns":890},[892,70567,70568,70574],{},[895,70569,70570,70572],{},[898,70571,2005],{},[898,70573,2974],{},[902,70575,55476],{"encoding":904}," rostou, resp. klesají.",[724,70578,70579,70582,70583,70402,70613,70628,70629,70644,70645,1343,70660,1343,70675,2196],{},[38,70580,70581],{},"3.7"," Jsou dány průměrné náklady ",[883,70584,70586],{"className":70585},[886],[888,70587,70588],{"xmlns":890},[892,70589,70590,70610],{},[895,70591,70592,70594,70596,70598,70606,70608],{},[898,70593,1862],{},[898,70595,2974],{},[1700,70597,1765],{},[1770,70599,70600],{"scriptlevel":1772,"displaystyle":1702},[1774,70601,70602,70604],{},[1931,70603,3284],{},[898,70605,1662],{},[1700,70607,1897],{},[1931,70609,9223],{},[902,70611,70612],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,70614,70616],{"className":70615},[886],[888,70617,70618],{"xmlns":890},[892,70619,70620,70626],{},[895,70621,70622,70624],{},[898,70623,2005],{},[898,70625,2974],{},[902,70627,55476],{"encoding":904},". (a) Určete celkové náklady ",[883,70630,70632],{"className":70631},[886],[888,70633,70634],{"xmlns":890},[892,70635,70636,70642],{},[895,70637,70638,70640],{},[898,70639,2971],{},[898,70641,2974],{},[902,70643,3436],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,70646,70648],{"className":70647},[886],[888,70649,70650],{"xmlns":890},[892,70651,70652,70658],{},[895,70653,70654,70656],{},[898,70655,1862],{},[898,70657,2974],{},[902,70659,55744],{"encoding":904},[883,70661,70663],{"className":70662},[886],[888,70664,70665],{"xmlns":890},[892,70666,70667,70673],{},[895,70668,70669,70671],{},[898,70670,2971],{},[898,70672,2974],{},[902,70674,3436],{"encoding":904},[883,70676,70678],{"className":70677},[886],[888,70679,70680],{"xmlns":890},[892,70681,70682,70688],{},[895,70683,70684,70686],{},[898,70685,2005],{},[898,70687,2974],{},[902,70689,55476],{"encoding":904},[724,70691,70692,70277,70695,70739,70740,1343,70757,1343,70772,1343,70789,1343,70804,1343,70821,2196],{},[38,70693,70694],{},"3.8",[883,70696,70698],{"className":70697},[886],[888,70699,70700],{"xmlns":890},[892,70701,70702,70736],{},[895,70703,70704,70706,70708,70710,70712,70714,70716,70718,70720,70722,70728,70730],{},[898,70705,2971],{},[898,70707,2974],{},[1700,70709,1765],{},[1931,70711,46888],{},[1700,70713,1897],{},[1931,70715,38204],{},[898,70717,1662],{},[1700,70719,1768],{},[1931,70721,2445],{},[1785,70723,70724,70726],{},[898,70725,1662],{},[1931,70727,2343],{},[1700,70729,1897],{},[1785,70731,70732,70734],{},[898,70733,1662],{},[1931,70735,2385],{},[902,70737,70738],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,70741,70743],{"className":70742},[886],[888,70744,70745],{"xmlns":890},[892,70746,70747,70755],{},[895,70748,70749,70751,70753],{},[898,70750,2971],{},[898,70752,40524],{},[898,70754,2974],{},[902,70756,55693],{"encoding":904},[883,70758,70760],{"className":70759},[886],[888,70761,70762],{"xmlns":890},[892,70763,70764,70770],{},[895,70765,70766,70768],{},[898,70767,10619],{},[898,70769,2974],{},[902,70771,55675],{"encoding":904},[883,70773,70775],{"className":70774},[886],[888,70776,70777],{"xmlns":890},[892,70778,70779,70787],{},[895,70780,70781,70783,70785],{},[898,70782,1862],{},[898,70784,40524],{},[898,70786,2974],{},[902,70788,55495],{"encoding":904},[883,70790,70792],{"className":70791},[886],[888,70793,70794],{"xmlns":890},[892,70795,70796,70802],{},[895,70797,70798,70800],{},[898,70799,1862],{},[898,70801,2974],{},[902,70803,55744],{"encoding":904},[883,70805,70807],{"className":70806},[886],[888,70808,70809],{"xmlns":890},[892,70810,70811,70819],{},[895,70812,70813,70815,70817],{},[898,70814,1862],{},[898,70816,10619],{},[898,70818,2974],{},[902,70820,55711],{"encoding":904},[883,70822,70824],{"className":70823},[886],[888,70825,70826],{"xmlns":890},[892,70827,70828,70834],{},[895,70829,70830,70832],{},[898,70831,2005],{},[898,70833,2974],{},[902,70835,55476],{"encoding":904},[724,70837,70838,70277,70841,70871,70872,70054,70887,6661,70900,1343,70918,1343,70936,70121,70954,70144,70976,70991,70992,71005,71006,2196],{},[38,70839,70840],{},"3.9",[883,70842,70844],{"className":70843},[886],[888,70845,70846],{"xmlns":890},[892,70847,70848,70868],{},[895,70849,70850,70852,70854,70856,70858,70860,70862],{},[898,70851,2971],{},[898,70853,2974],{},[1700,70855,1765],{},[1931,70857,15295],{},[1700,70859,1897],{},[1931,70861,19506],{},[1785,70863,70864,70866],{},[898,70865,1662],{},[1931,70867,2343],{},[902,70869,70870],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,70873,70875],{"className":70874},[886],[888,70876,70877],{"xmlns":890},[892,70878,70879,70885],{},[895,70880,70881,70883],{},[898,70882,2971],{},[898,70884,2974],{},[902,70886,3436],{"encoding":904},[883,70888,70890],{"className":70889},[886],[888,70891,70892],{"xmlns":890},[892,70893,70894,70898],{},[895,70895,70896],{},[898,70897,1662],{},[902,70899,1662],{"encoding":904},[883,70901,70903],{"className":70902},[886],[888,70904,70905],{"xmlns":890},[892,70906,70907,70915],{},[895,70908,70909,70911,70913],{},[898,70910,1662],{},[1700,70912,1765],{},[1931,70914,3058],{},[902,70916,70917],{"encoding":904},"Q = 10",[883,70919,70921],{"className":70920},[886],[888,70922,70923],{"xmlns":890},[892,70924,70925,70933],{},[895,70926,70927,70929,70931],{},[898,70928,1662],{},[1700,70930,1765],{},[1931,70932,9223],{},[902,70934,70935],{"encoding":904},"Q = 20",[883,70937,70939],{"className":70938},[886],[888,70940,70941],{"xmlns":890},[892,70942,70943,70951],{},[895,70944,70945,70947,70949],{},[898,70946,1662],{},[1700,70948,1765],{},[1931,70950,38204],{},[902,70952,70953],{"encoding":904},"Q = 30",[883,70955,70957],{"className":70956},[886],[888,70958,70959],{"xmlns":890},[892,70960,70961,70973],{},[895,70962,70963,70965,70967,70969,70971],{},[898,70964,2005],{},[898,70966,2974],{},[1700,70968,1703],{"stretchy":1702},[1931,70970,36429],{},[1700,70972,1709],{"stretchy":1702},[902,70974,70975],{"encoding":904},"MC(15)",[883,70977,70979],{"className":70978},[886],[888,70980,70981],{"xmlns":890},[892,70982,70983,70989],{},[895,70984,70985,70987],{},[898,70986,2971],{},[898,70988,2974],{},[902,70990,3436],{"encoding":904}," v důsledku změny ",[883,70993,70995],{"className":70994},[886],[888,70996,70997],{"xmlns":890},[892,70998,70999,71003],{},[895,71000,71001],{},[898,71002,1662],{},[902,71004,1662],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,71007,71009],{"className":71008},[886],[888,71010,71011],{"xmlns":890},[892,71012,71013,71019],{},[895,71014,71015,71017],{},[898,71016,2971],{},[898,71018,2974],{},[902,71020,3436],{"encoding":904},[724,71022,71023,71026,71027,70628,71063,71078,71079,70238,71098,70991,71113,71126],{},[38,71024,71025],{},"3.10"," Jsou dány mezní náklady ",[883,71028,71030],{"className":71029},[886],[888,71031,71032],{"xmlns":890},[892,71033,71034,71060],{},[895,71035,71036,71038,71040,71042,71044,71046,71048,71050,71052,71054],{},[898,71037,2005],{},[898,71039,2974],{},[1700,71041,1765],{},[1931,71043,3320],{},[1700,71045,1768],{},[1931,71047,42047],{},[898,71049,1662],{},[1700,71051,1897],{},[1931,71053,64743],{},[1785,71055,71056,71058],{},[898,71057,1662],{},[1931,71059,2343],{},[902,71061,71062],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,71064,71066],{"className":71065},[886],[888,71067,71068],{"xmlns":890},[892,71069,71070,71076],{},[895,71071,71072,71074],{},[898,71073,2971],{},[898,71075,2974],{},[902,71077,3436],{"encoding":904},", jestliže fixní náklady ",[883,71080,71082],{"className":71081},[886],[888,71083,71084],{"xmlns":890},[892,71085,71086,71096],{},[895,71087,71088,71090,71092,71094],{},[898,71089,10619],{},[898,71091,2974],{},[1700,71093,1765],{},[1931,71095,3284],{},[902,71097,11817],{"encoding":904},[883,71099,71101],{"className":71100},[886],[888,71102,71103],{"xmlns":890},[892,71104,71105,71111],{},[895,71106,71107,71109],{},[898,71108,2971],{},[898,71110,2974],{},[902,71112,3436],{"encoding":904},[883,71114,71116],{"className":71115},[886],[888,71117,71118],{"xmlns":890},[892,71119,71120,71124],{},[895,71121,71122],{},[898,71123,1662],{},[902,71125,1662],{"encoding":904}," z 15 na 20.",[724,71128,71129,70277,71132,71175,71176,71189,71190,71205,71206,71221,71222,71189,71235,71205,71252,71269,71270,71189,71283,71205,71298,71313,71314,71334,71335,71358],{},[38,71130,71131],{},"3.11",[883,71133,71135],{"className":71134},[886],[888,71136,71137],{"xmlns":890},[892,71138,71139,71173],{},[895,71140,71141,71143,71145,71147,71149,71151,71153,71155,71157,71159,71165,71167],{},[898,71142,2971],{},[898,71144,2974],{},[1700,71146,1765],{},[1931,71148,3284],{},[1700,71150,1897],{},[1931,71152,5192],{},[898,71154,1662],{},[1700,71156,1768],{},[1931,71158,2438],{},[1785,71160,71161,71163],{},[898,71162,1662],{},[1931,71164,2343],{},[1700,71166,1897],{},[1785,71168,71169,71171],{},[898,71170,1662],{},[1931,71172,2385],{},[902,71174,61091],{"encoding":904},". (a) Určete ",[883,71177,71179],{"className":71178},[886],[888,71180,71181],{"xmlns":890},[892,71182,71183,71187],{},[895,71184,71185],{},[898,71186,1662],{},[902,71188,1662],{"encoding":904},", které minimalizuje ",[883,71191,71193],{"className":71192},[886],[888,71194,71195],{"xmlns":890},[892,71196,71197,71203],{},[895,71198,71199,71201],{},[898,71200,2005],{},[898,71202,2974],{},[902,71204,55476],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,71207,71209],{"className":71208},[886],[888,71210,71211],{"xmlns":890},[892,71212,71213,71219],{},[895,71214,71215,71217],{},[898,71216,2005],{},[898,71218,2974],{},[902,71220,55476],{"encoding":904},". (b) Určete ",[883,71223,71225],{"className":71224},[886],[888,71226,71227],{"xmlns":890},[892,71228,71229,71233],{},[895,71230,71231],{},[898,71232,1662],{},[902,71234,1662],{"encoding":904},[883,71236,71238],{"className":71237},[886],[888,71239,71240],{"xmlns":890},[892,71241,71242,71250],{},[895,71243,71244,71246,71248],{},[898,71245,1862],{},[898,71247,40524],{},[898,71249,2974],{},[902,71251,55495],{"encoding":904},[883,71253,71255],{"className":71254},[886],[888,71256,71257],{"xmlns":890},[892,71258,71259,71267],{},[895,71260,71261,71263,71265],{},[898,71262,1862],{},[898,71264,40524],{},[898,71266,2974],{},[902,71268,55495],{"encoding":904},". (c) Určete ",[883,71271,71273],{"className":71272},[886],[888,71274,71275],{"xmlns":890},[892,71276,71277,71281],{},[895,71278,71279],{},[898,71280,1662],{},[902,71282,1662],{"encoding":904},[883,71284,71286],{"className":71285},[886],[888,71287,71288],{"xmlns":890},[892,71289,71290,71296],{},[895,71291,71292,71294],{},[898,71293,1862],{},[898,71295,2974],{},[902,71297,55744],{"encoding":904},[883,71299,71301],{"className":71300},[886],[888,71302,71303],{"xmlns":890},[892,71304,71305,71311],{},[895,71306,71307,71309],{},[898,71308,1862],{},[898,71310,2974],{},[902,71312,55744],{"encoding":904}," (rada: hledaný kořen ",[883,71315,71317],{"className":71316},[886],[888,71318,71319],{"xmlns":890},[892,71320,71321,71331],{},[895,71322,71323,71325],{},[898,71324,1862],{},[1785,71326,71327,71329],{},[898,71328,2974],{},[1700,71330,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,71332,71333],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,71336,71338],{"className":71337},[886],[888,71339,71340],{"xmlns":890},[892,71341,71342,71355],{},[895,71343,71344,71346,71349,71351,71353],{},[1700,71345,1703],{"stretchy":1702},[1931,71347,71348],{},"4,7",[1700,71350,8613],{"separator":1731},[1931,71352,5467],{},[1700,71354,1709],{"stretchy":1702},[902,71356,71357],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,71360,71361,71364,71365,2821,71393,71410,71411,21779,71452,71473],{},[38,71362,71363],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,71366,71368],{"className":71367},[886],[888,71369,71370],{"xmlns":890},[892,71371,71372,71390],{},[895,71373,71374,71376,71378,71380,71382,71384,71386,71388],{},[898,71375,1862],{},[898,71377,2974],{},[1700,71379,1765],{},[898,71381,1862],{},[898,71383,2974],{},[1700,71385,1703],{"stretchy":1702},[898,71387,1662],{},[1700,71389,1709],{"stretchy":1702},[902,71391,71392],{"encoding":904},"AC = AC(Q)",[883,71394,71396],{"className":71395},[886],[888,71397,71398],{"xmlns":890},[892,71399,71400,71408],{},[895,71401,71402],{},[2007,71403,71404,71406],{},[898,71405,1662],{},[1931,71407,1772],{},[902,71409,38493],{"encoding":904}," minimum, pak platí ",[883,71412,71414],{"className":71413},[886],[888,71415,71416],{"xmlns":890},[892,71417,71418,71450],{},[895,71419,71420,71422,71424,71426,71432,71434,71436,71438,71440,71442,71448],{},[898,71421,1862],{},[898,71423,2974],{},[1700,71425,1703],{"stretchy":1702},[2007,71427,71428,71430],{},[898,71429,1662],{},[1931,71431,1772],{},[1700,71433,1709],{"stretchy":1702},[1700,71435,1765],{},[898,71437,2005],{},[898,71439,2974],{},[1700,71441,1703],{"stretchy":1702},[2007,71443,71444,71446],{},[898,71445,1662],{},[1931,71447,1772],{},[1700,71449,1709],{"stretchy":1702},[902,71451,62753],{"encoding":904},[883,71453,71455],{"className":71454},[886],[888,71456,71457],{"xmlns":890},[892,71458,71459,71471],{},[895,71460,71461,71463,71465,71467,71469],{},[898,71462,2005],{},[898,71464,2974],{},[1700,71466,1703],{"stretchy":1702},[898,71468,1662],{},[1700,71470,1709],{"stretchy":1702},[902,71472,67877],{"encoding":904}," jsou mezní náklady.",[724,71475,71476,70277,71479,70739,71513,71189,71526,71205,71541,2196],{},[38,71477,71478],{},"3.13",[883,71480,71482],{"className":71481},[886],[888,71483,71484],{"xmlns":890},[892,71485,71486,71510],{},[895,71487,71488,71490,71492,71494,71500,71502,71504,71506,71508],{},[898,71489,2971],{},[898,71491,2974],{},[1700,71493,1765],{},[1785,71495,71496,71498],{},[898,71497,1662],{},[1931,71499,2343],{},[1700,71501,1897],{},[1931,71503,2343],{},[898,71505,1662],{},[1700,71507,1897],{},[1931,71509,5192],{},[902,71511,71512],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,71514,71516],{"className":71515},[886],[888,71517,71518],{"xmlns":890},[892,71519,71520,71524],{},[895,71521,71522],{},[898,71523,1662],{},[902,71525,1662],{"encoding":904},[883,71527,71529],{"className":71528},[886],[888,71530,71531],{"xmlns":890},[892,71532,71533,71539],{},[895,71534,71535,71537],{},[898,71536,1862],{},[898,71538,2974],{},[902,71540,55744],{"encoding":904},[883,71542,71544],{"className":71543},[886],[888,71545,71546],{"xmlns":890},[892,71547,71548,71554],{},[895,71549,71550,71552],{},[898,71551,1862],{},[898,71553,2974],{},[902,71555,55744],{"encoding":904},[724,71557,71558,71561,71562,2821,71594,71410,71611,21779,71654,71473],{},[38,71559,71560],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,71563,71565],{"className":71564},[886],[888,71566,71567],{"xmlns":890},[892,71568,71569,71591],{},[895,71570,71571,71573,71575,71577,71579,71581,71583,71585,71587,71589],{},[898,71572,1862],{},[898,71574,40524],{},[898,71576,2974],{},[1700,71578,1765],{},[898,71580,1862],{},[898,71582,40524],{},[898,71584,2974],{},[1700,71586,1703],{"stretchy":1702},[898,71588,1662],{},[1700,71590,1709],{"stretchy":1702},[902,71592,71593],{"encoding":904},"AVC = AVC(Q)",[883,71595,71597],{"className":71596},[886],[888,71598,71599],{"xmlns":890},[892,71600,71601,71609],{},[895,71602,71603],{},[2007,71604,71605,71607],{},[898,71606,1662],{},[1931,71608,1772],{},[902,71610,38493],{"encoding":904},[883,71612,71614],{"className":71613},[886],[888,71615,71616],{"xmlns":890},[892,71617,71618,71652],{},[895,71619,71620,71622,71624,71626,71628,71634,71636,71638,71640,71642,71644,71650],{},[898,71621,1862],{},[898,71623,40524],{},[898,71625,2974],{},[1700,71627,1703],{"stretchy":1702},[2007,71629,71630,71632],{},[898,71631,1662],{},[1931,71633,1772],{},[1700,71635,1709],{"stretchy":1702},[1700,71637,1765],{},[898,71639,2005],{},[898,71641,2974],{},[1700,71643,1703],{"stretchy":1702},[2007,71645,71646,71648],{},[898,71647,1662],{},[1931,71649,1772],{},[1700,71651,1709],{"stretchy":1702},[902,71653,69203],{"encoding":904},[883,71655,71657],{"className":71656},[886],[888,71658,71659],{"xmlns":890},[892,71660,71661,71673],{},[895,71662,71663,71665,71667,71669,71671],{},[898,71664,2005],{},[898,71666,2974],{},[1700,71668,1703],{"stretchy":1702},[898,71670,1662],{},[1700,71672,1709],{"stretchy":1702},[902,71674,67877],{"encoding":904},[724,71676,71677,70277,71680,70739,71726,71189,71739,71205,71756,2196],{},[38,71678,71679],{},"3.15",[883,71681,71683],{"className":71682},[886],[888,71684,71685],{"xmlns":890},[892,71686,71687,71723],{},[895,71688,71689,71691,71693,71695,71697,71699,71701,71703,71705,71707,71713,71715,71717],{},[898,71690,2971],{},[898,71692,2974],{},[1700,71694,1765],{},[1931,71696,3314],{},[1700,71698,1897],{},[1931,71700,36429],{},[898,71702,1662],{},[1700,71704,1768],{},[1931,71706,2343],{},[1785,71708,71709,71711],{},[898,71710,1662],{},[1931,71712,2343],{},[1700,71714,1897],{},[1931,71716,3034],{},[1785,71718,71719,71721],{},[898,71720,1662],{},[1931,71722,2385],{},[902,71724,71725],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,71727,71729],{"className":71728},[886],[888,71730,71731],{"xmlns":890},[892,71732,71733,71737],{},[895,71734,71735],{},[898,71736,1662],{},[902,71738,1662],{"encoding":904},[883,71740,71742],{"className":71741},[886],[888,71743,71744],{"xmlns":890},[892,71745,71746,71754],{},[895,71747,71748,71750,71752],{},[898,71749,1862],{},[898,71751,40524],{},[898,71753,2974],{},[902,71755,55495],{"encoding":904},[883,71757,71759],{"className":71758},[886],[888,71760,71761],{"xmlns":890},[892,71762,71763,71771],{},[895,71764,71765,71767,71769],{},[898,71766,1862],{},[898,71768,40524],{},[898,71770,2974],{},[902,71772,55495],{"encoding":904},[724,71774,71775,71778,71779,71792,71793,71813],{},[38,71776,71777],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,71780,71782],{"className":71781},[886],[888,71783,71784],{"xmlns":890},[892,71785,71786,71790],{},[895,71787,71788],{},[898,71789,2225],{},[902,71791,2225],{"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 ",[883,71794,71796],{"className":71795},[886],[888,71797,71798],{"xmlns":890},[892,71799,71800,71810],{},[895,71801,71802,71804,71806,71808],{},[1931,71803,3058],{},[1781,71805,1783],{},[1931,71807,59266],{},[898,71809,2225],{},[902,71811,71812],{"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.",[198,71815,71817],{"id":71816},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,71819,71820,71823,71824,2114,71846,71872],{},[38,71821,71822],{},"3.17"," Jsou dány ",[883,71825,71827],{"className":71826},[886],[888,71828,71829],{"xmlns":890},[892,71830,71831,71843],{},[895,71832,71833,71835,71837,71839,71841],{},[898,71834,2971],{},[898,71836,4185],{},[1700,71838,1765],{},[1931,71840,3058],{},[898,71842,1662],{},[902,71844,71845],{"encoding":904},"TR = 10Q",[883,71847,71849],{"className":71848},[886],[888,71850,71851],{"xmlns":890},[892,71852,71853,71869],{},[895,71854,71855,71857,71859,71861,71863,71865,71867],{},[898,71856,2971],{},[898,71858,2974],{},[1700,71860,1765],{},[1931,71862,3284],{},[1700,71864,1897],{},[1931,71866,2438],{},[898,71868,1662],{},[902,71870,71871],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,71874,71875,71878,71879,6378,71894,71909,71910,1343,71932,21779,71959,71981,71982,72016],{},[38,71876,71877],{},"3.18"," Odvoďte, že jestliže ",[883,71880,71882],{"className":71881},[886],[888,71883,71884],{"xmlns":890},[892,71885,71886,71892],{},[895,71887,71888,71890],{},[898,71889,2971],{},[898,71891,4185],{},[902,71893,4285],{"encoding":904},[883,71895,71897],{"className":71896},[886],[888,71898,71899],{"xmlns":890},[892,71900,71901,71907],{},[895,71902,71903,71905],{},[898,71904,2971],{},[898,71906,2974],{},[902,71908,3436],{"encoding":904}," jsou lineární tvaru ",[883,71911,71913],{"className":71912},[886],[888,71914,71915],{"xmlns":890},[892,71916,71917,71929],{},[895,71918,71919,71921,71923,71925,71927],{},[898,71920,2971],{},[898,71922,4185],{},[1700,71924,1765],{},[898,71926,724],{},[898,71928,1662],{},[902,71930,71931],{"encoding":904},"TR = pQ",[883,71933,71935],{"className":71934},[886],[888,71936,71937],{"xmlns":890},[892,71938,71939,71956],{},[895,71940,71941,71943,71945,71947,71950,71952,71954],{},[898,71942,2971],{},[898,71944,2974],{},[1700,71946,1765],{},[898,71948,71949],{},"m",[1700,71951,1897],{},[898,71953,37045],{},[898,71955,1662],{},[902,71957,71958],{"encoding":904},"TC = m + nQ",[883,71960,71962],{"className":71961},[886],[888,71963,71964],{"xmlns":890},[892,71965,71966,71978],{},[895,71967,71968,71970,71972,71974,71976],{},[898,71969,71949],{},[1700,71971,1732],{"separator":1731},[898,71973,37045],{},[1700,71975,1732],{"separator":1731},[898,71977,724],{},[902,71979,71980],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,71983,71985],{"className":71984},[886],[888,71986,71987],{"xmlns":890},[892,71988,71989,72013],{},[895,71990,71991,71997,71999],{},[1785,71992,71993,71995],{},[898,71994,1662],{},[1700,71996,4543],{},[1700,71998,1765],{},[1770,72000,72001],{"scriptlevel":1772,"displaystyle":1702},[1774,72002,72003,72005],{},[898,72004,71949],{},[895,72006,72007,72009,72011],{},[898,72008,724],{},[1700,72010,1768],{},[898,72012,37045],{},[902,72014,72015],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,72018,72019,71823,72022,2114,72056,71175,72082,72095,72096,69927,72111,72126,72127,69911,72140,69927,72155,72170],{},[38,72020,72021],{},"3.19",[883,72023,72025],{"className":72024},[886],[888,72026,72027],{"xmlns":890},[892,72028,72029,72053],{},[895,72030,72031,72033,72035,72037,72039,72041,72047,72049,72051],{},[898,72032,2971],{},[898,72034,4185],{},[1700,72036,1765],{},[1700,72038,1768],{},[1931,72040,2343],{},[1785,72042,72043,72045],{},[898,72044,1662],{},[1931,72046,2343],{},[1700,72048,1897],{},[1931,72050,23131],{},[898,72052,1662],{},[902,72054,72055],{"encoding":904},"TR = -2Q^2 + 14Q",[883,72057,72059],{"className":72058},[886],[888,72060,72061],{"xmlns":890},[892,72062,72063,72079],{},[895,72064,72065,72067,72069,72071,72073,72075,72077],{},[898,72066,2971],{},[898,72068,2974],{},[1700,72070,1765],{},[1931,72072,2343],{},[898,72074,1662],{},[1700,72076,1897],{},[1931,72078,3058],{},[902,72080,72081],{"encoding":904},"TC = 2Q + 10",[883,72083,72085],{"className":72084},[886],[888,72086,72087],{"xmlns":890},[892,72088,72089,72093],{},[895,72090,72091],{},[898,72092,1662],{},[902,72094,1662],{"encoding":904},", které maximalizuje zisk ",[883,72097,72099],{"className":72098},[886],[888,72100,72101],{"xmlns":890},[892,72102,72103,72109],{},[895,72104,72105,72107],{},[898,72106,1677],{},[898,72108,4185],{},[902,72110,63663],{"encoding":904},[883,72112,72114],{"className":72113},[886],[888,72115,72116],{"xmlns":890},[892,72117,72118,72124],{},[895,72119,72120,72122],{},[898,72121,1677],{},[898,72123,4185],{},[902,72125,63663],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,72128,72130],{"className":72129},[886],[888,72131,72132],{"xmlns":890},[892,72133,72134,72138],{},[895,72135,72136],{},[898,72137,1662],{},[902,72139,1662],{"encoding":904},[883,72141,72143],{"className":72142},[886],[888,72144,72145],{"xmlns":890},[892,72146,72147,72153],{},[895,72148,72149,72151],{},[898,72150,2971],{},[898,72152,4185],{},[902,72154,4285],{"encoding":904},[883,72156,72158],{"className":72157},[886],[888,72159,72160],{"xmlns":890},[892,72161,72162,72168],{},[895,72163,72164,72166],{},[898,72165,2971],{},[898,72167,4185],{},[902,72169,4285],{"encoding":904},". (d) Graficky interpretujte.",[724,72172,72173,47869,72176,1343,72202,1343,72221,71175,72241,72095,72254,69927,72269,72284,72285,72307,72308,71358],{},[38,72174,72175],{},"3.20",[883,72177,72179],{"className":72178},[886],[888,72180,72181],{"xmlns":890},[892,72182,72183,72199],{},[895,72184,72185,72187,72189,72191,72193],{},[898,72186,1677],{},[1700,72188,1765],{},[1931,72190,20327],{},[1700,72192,1768],{},[1785,72194,72195,72197],{},[898,72196,1662],{},[1931,72198,2343],{},[902,72200,72201],{"encoding":904},"P = 400 - Q^2",[883,72203,72205],{"className":72204},[886],[888,72206,72207],{"xmlns":890},[892,72208,72209,72219],{},[895,72210,72211,72213,72215,72217],{},[898,72212,10619],{},[898,72214,2974],{},[1700,72216,1765],{},[1931,72218,3284],{},[902,72220,11817],{"encoding":904},[883,72222,72224],{"className":72223},[886],[888,72225,72226],{"xmlns":890},[892,72227,72228,72238],{},[895,72229,72230,72232,72234,72236],{},[898,72231,2005],{},[898,72233,2974],{},[1700,72235,1765],{},[1931,72237,9223],{},[902,72239,72240],{"encoding":904},"MC = 20",[883,72242,72244],{"className":72243},[886],[888,72245,72246],{"xmlns":890},[892,72247,72248,72252],{},[895,72249,72250],{},[898,72251,1662],{},[902,72253,1662],{"encoding":904},[883,72255,72257],{"className":72256},[886],[888,72258,72259],{"xmlns":890},[892,72260,72261,72267],{},[895,72262,72263,72265],{},[898,72264,1677],{},[898,72266,4185],{},[902,72268,63663],{"encoding":904},[883,72270,72272],{"className":72271},[886],[888,72273,72274],{"xmlns":890},[892,72275,72276,72282],{},[895,72277,72278,72280],{},[898,72279,1677],{},[898,72281,4185],{},[902,72283,63663],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,72286,72288],{"className":72287},[886],[888,72289,72290],{"xmlns":890},[892,72291,72292,72304],{},[895,72293,72294,72296,72298,72300,72302],{},[1700,72295,1703],{"stretchy":1702},[1931,72297,1772],{},[1700,72299,1732],{"separator":1731},[1931,72301,1933],{},[1700,72303,1709],{"stretchy":1702},[902,72305,72306],{"encoding":904},"(0, 1)",", druhý do ",[883,72309,72311],{"className":72310},[886],[888,72312,72313],{"xmlns":890},[892,72314,72315,72328],{},[895,72316,72317,72319,72322,72324,72326],{},[1700,72318,1703],{"stretchy":1702},[1931,72320,72321],{},"19",[1700,72323,1732],{"separator":1731},[1931,72325,9223],{},[1700,72327,1709],{"stretchy":1702},[902,72329,72330],{"encoding":904},"(19, 20)",[724,72332,72333,72336,72337,2821,72365,72382,72383,2196],{},[38,72334,72335],{},"3.21"," Dokažte, že má-li zisk ",[883,72338,72340],{"className":72339},[886],[888,72341,72342],{"xmlns":890},[892,72343,72344,72362],{},[895,72345,72346,72348,72350,72352,72354,72356,72358,72360],{},[898,72347,1677],{},[898,72349,4185],{},[1700,72351,1765],{},[898,72353,1677],{},[898,72355,4185],{},[1700,72357,1703],{"stretchy":1702},[898,72359,1662],{},[1700,72361,1709],{"stretchy":1702},[902,72363,72364],{"encoding":904},"PR = PR(Q)",[883,72366,72368],{"className":72367},[886],[888,72369,72370],{"xmlns":890},[892,72371,72372,72380],{},[895,72373,72374],{},[2007,72375,72376,72378],{},[898,72377,1662],{},[1931,72379,1772],{},[902,72381,38493],{"encoding":904}," maximum, pak platí ",[883,72384,72386],{"className":72385},[886],[888,72387,72388],{"xmlns":890},[892,72389,72390,72422],{},[895,72391,72392,72394,72396,72398,72404,72406,72408,72410,72412,72414,72420],{},[898,72393,2005],{},[898,72395,4185],{},[1700,72397,1703],{"stretchy":1702},[2007,72399,72400,72402],{},[898,72401,1662],{},[1931,72403,1772],{},[1700,72405,1709],{"stretchy":1702},[1700,72407,1765],{},[898,72409,2005],{},[898,72411,2974],{},[1700,72413,1703],{"stretchy":1702},[2007,72415,72416,72418],{},[898,72417,1662],{},[1931,72419,1772],{},[1700,72421,1709],{"stretchy":1702},[902,72423,65829],{"encoding":904},[724,72425,72426,72429,72430,2114,72445,56209,72460,72095,72473,72488,72489,1343,72516,72553,72554,1343,72581,2196],{},[38,72427,72428],{},"3.22"," Pro zadané ",[883,72431,72433],{"className":72432},[886],[888,72434,72435],{"xmlns":890},[892,72436,72437,72443],{},[895,72438,72439,72441],{},[898,72440,2005],{},[898,72442,4185],{},[902,72444,6822],{"encoding":904},[883,72446,72448],{"className":72447},[886],[888,72449,72450],{"xmlns":890},[892,72451,72452,72458],{},[895,72453,72454,72456],{},[898,72455,2005],{},[898,72457,2974],{},[902,72459,55476],{"encoding":904},[883,72461,72463],{"className":72462},[886],[888,72464,72465],{"xmlns":890},[892,72466,72467,72471],{},[895,72468,72469],{},[898,72470,1662],{},[902,72472,1662],{"encoding":904},[883,72474,72476],{"className":72475},[886],[888,72477,72478],{"xmlns":890},[892,72479,72480,72486],{},[895,72481,72482,72484],{},[898,72483,1677],{},[898,72485,4185],{},[902,72487,63663],{"encoding":904},". (a) ",[883,72490,72492],{"className":72491},[886],[888,72493,72494],{"xmlns":890},[892,72495,72496,72513],{},[895,72497,72498,72500,72502,72504,72507,72509,72511],{},[898,72499,2005],{},[898,72501,4185],{},[1700,72503,1765],{},[1931,72505,72506],{},"236",[1700,72508,1768],{},[1931,72510,42047],{},[898,72512,1662],{},[902,72514,72515],{"encoding":904},"MR = 236 - 16Q",[883,72517,72519],{"className":72518},[886],[888,72520,72521],{"xmlns":890},[892,72522,72523,72550],{},[895,72524,72525,72527,72529,72531,72533,72539,72541,72544,72546,72548],{},[898,72526,2005],{},[898,72528,2974],{},[1700,72530,1765],{},[1931,72532,2385],{},[1785,72534,72535,72537],{},[898,72536,1662],{},[1931,72538,2343],{},[1700,72540,1768],{},[1931,72542,72543],{},"32",[898,72545,1662],{},[1700,72547,1897],{},[1931,72549,5932],{},[902,72551,72552],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,72555,72557],{"className":72556},[886],[888,72558,72559],{"xmlns":890},[892,72560,72561,72578],{},[895,72562,72563,72565,72567,72569,72572,72574,72576],{},[898,72564,2005],{},[898,72566,4185],{},[1700,72568,1765],{},[1931,72570,72571],{},"280",[1700,72573,1768],{},[1931,72575,9223],{},[898,72577,1662],{},[902,72579,72580],{"encoding":904},"MR = 280 - 20Q",[883,72582,72584],{"className":72583},[886],[888,72585,72586],{"xmlns":890},[892,72587,72588,72615],{},[895,72589,72590,72592,72594,72596,72599,72605,72607,72609,72611,72613],{},[898,72591,2005],{},[898,72593,2974],{},[1700,72595,1765],{},[1931,72597,72598],{},"1,6",[1785,72600,72601,72603],{},[898,72602,1662],{},[1931,72604,2343],{},[1700,72606,1768],{},[1931,72608,36429],{},[898,72610,1662],{},[1700,72612,1897],{},[1931,72614,3320],{},[902,72616,72617],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,72619,72620,72429,72623,2114,72638,56209,72653,69911,72666,69927,72681,72488,72696,1343,72727,72553,72763,1343,72795,72839,72840,1343,72872,2196],{},[38,72621,72622],{},"3.23",[883,72624,72626],{"className":72625},[886],[888,72627,72628],{"xmlns":890},[892,72629,72630,72636],{},[895,72631,72632,72634],{},[898,72633,2971],{},[898,72635,4185],{},[902,72637,4285],{"encoding":904},[883,72639,72641],{"className":72640},[886],[888,72642,72643],{"xmlns":890},[892,72644,72645,72651],{},[895,72646,72647,72649],{},[898,72648,2971],{},[898,72650,2974],{},[902,72652,3436],{"encoding":904},[883,72654,72656],{"className":72655},[886],[888,72657,72658],{"xmlns":890},[892,72659,72660,72664],{},[895,72661,72662],{},[898,72663,1662],{},[902,72665,1662],{"encoding":904},[883,72667,72669],{"className":72668},[886],[888,72670,72671],{"xmlns":890},[892,72672,72673,72679],{},[895,72674,72675,72677],{},[898,72676,1677],{},[898,72678,4185],{},[902,72680,63663],{"encoding":904},[883,72682,72684],{"className":72683},[886],[888,72685,72686],{"xmlns":890},[892,72687,72688,72694],{},[895,72689,72690,72692],{},[898,72691,1677],{},[898,72693,4185],{},[902,72695,63663],{"encoding":904},[883,72697,72699],{"className":72698},[886],[888,72700,72701],{"xmlns":890},[892,72702,72703,72724],{},[895,72704,72705,72707,72709,72711,72714,72716,72718],{},[898,72706,2971],{},[898,72708,4185],{},[1700,72710,1765],{},[1931,72712,72713],{},"125",[898,72715,1662],{},[1700,72717,1768],{},[1785,72719,72720,72722],{},[898,72721,1662],{},[1931,72723,2343],{},[902,72725,72726],{"encoding":904},"TR = 125Q - Q^2",[883,72728,72730],{"className":72729},[886],[888,72731,72732],{"xmlns":890},[892,72733,72734,72760],{},[895,72735,72736,72738,72740,72742,72744,72746,72748,72750,72752,72754],{},[898,72737,2971],{},[898,72739,2974],{},[1700,72741,1765],{},[1931,72743,15295],{},[1700,72745,1897],{},[1931,72747,2438],{},[898,72749,1662],{},[1700,72751,1897],{},[1931,72753,5197],{},[1785,72755,72756,72758],{},[898,72757,1662],{},[1931,72759,2343],{},[902,72761,72762],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,72764,72766],{"className":72765},[886],[888,72767,72768],{"xmlns":890},[892,72769,72770,72792],{},[895,72771,72772,72774,72776,72778,72780,72782,72784,72786],{},[898,72773,2971],{},[898,72775,4185],{},[1700,72777,1765],{},[1931,72779,9223],{},[898,72781,1662],{},[1700,72783,1768],{},[1931,72785,2343],{},[1785,72787,72788,72790],{},[898,72789,1662],{},[1931,72791,2343],{},[902,72793,72794],{"encoding":904},"TR = 20Q - 2Q^2",[883,72796,72798],{"className":72797},[886],[888,72799,72800],{"xmlns":890},[892,72801,72802,72836],{},[895,72803,72804,72806,72808,72810,72812,72814,72816,72818,72820,72822,72828,72830],{},[898,72805,2971],{},[898,72807,2974],{},[1700,72809,1765],{},[1931,72811,2343],{},[1700,72813,1897],{},[1931,72815,9223],{},[898,72817,1662],{},[1700,72819,1768],{},[1931,72821,5773],{},[1785,72823,72824,72826],{},[898,72825,1662],{},[1931,72827,2343],{},[1700,72829,1897],{},[1785,72831,72832,72834],{},[898,72833,1662],{},[1931,72835,2385],{},[902,72837,72838],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,72841,72843],{"className":72842},[886],[888,72844,72845],{"xmlns":890},[892,72846,72847,72869],{},[895,72848,72849,72851,72853,72855,72857,72859,72861,72863],{},[898,72850,2971],{},[898,72852,4185],{},[1700,72854,1765],{},[1931,72856,2553],{},[898,72858,1662],{},[1700,72860,1768],{},[1931,72862,23974],{},[1785,72864,72865,72867],{},[898,72866,1662],{},[1931,72868,2343],{},[902,72870,72871],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,72873,72875],{"className":72874},[886],[888,72876,72877],{"xmlns":890},[892,72878,72879,72927],{},[895,72880,72881,72883,72885,72887,72889,72891,72893,72895,72897,72913,72915],{},[898,72882,2971],{},[898,72884,2974],{},[1700,72886,1765],{},[1931,72888,2553],{},[1700,72890,1897],{},[1931,72892,2343],{},[898,72894,1662],{},[1700,72896,1768],{},[1770,72898,72899],{"scriptlevel":1772,"displaystyle":1702},[1774,72900,72901,72911],{},[895,72902,72903,72905],{},[1931,72904,2385],{},[1785,72906,72907,72909],{},[898,72908,1662],{},[1931,72910,2343],{},[1931,72912,3058],{},[1700,72914,1897],{},[1770,72916,72917],{"scriptlevel":1772,"displaystyle":1702},[1774,72918,72919,72925],{},[1785,72920,72921,72923],{},[898,72922,1662],{},[1931,72924,2385],{},[1931,72926,9223],{},[902,72928,72929],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,72931,72932,72935,72936,72966,72967,72999,73000,21779,73030,73060],{},[38,72933,72934],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,72937,72939],{"className":72938},[886],[888,72940,72941],{"xmlns":890},[892,72942,72943,72963],{},[895,72944,72945,72951,72953,72955,72957],{},[2007,72946,72947,72949],{},[898,72948,1677],{},[1931,72950,1933],{},[1700,72952,1765],{},[1931,72954,15295],{},[1700,72956,1768],{},[2007,72958,72959,72961],{},[898,72960,1662],{},[1931,72962,1933],{},[902,72964,72965],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,72968,72970],{"className":72969},[886],[888,72971,72972],{"xmlns":890},[892,72973,72974,72996],{},[895,72975,72976,72982,72984,72986,72988,72990],{},[2007,72977,72978,72980],{},[898,72979,1677],{},[1931,72981,2343],{},[1700,72983,1765],{},[1931,72985,30266],{},[1700,72987,1768],{},[1931,72989,64743],{},[2007,72991,72992,72994],{},[898,72993,1662],{},[1931,72995,2343],{},[902,72997,72998],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,73001,73003],{"className":73002},[886],[888,73004,73005],{"xmlns":890},[892,73006,73007,73027],{},[895,73008,73009,73011,73013,73015,73017,73019,73021,73023,73025],{},[898,73010,2971],{},[898,73012,2974],{},[1700,73014,1765],{},[1931,73016,3314],{},[1781,73018,1783],{},[1931,73020,59266],{},[1700,73022,1897],{},[1931,73024,9223],{},[898,73026,1662],{},[902,73028,73029],{"encoding":904},"TC = 50\\,000 + 20Q",[883,73031,73033],{"className":73032},[886],[888,73034,73035],{"xmlns":890},[892,73036,73037,73057],{},[895,73038,73039,73041,73043,73049,73051],{},[898,73040,1662],{},[1700,73042,1765],{},[2007,73044,73045,73047],{},[898,73046,1662],{},[1931,73048,1933],{},[1700,73050,1897],{},[2007,73052,73053,73055],{},[898,73054,1662],{},[1931,73056,2343],{},[902,73058,73059],{"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.",[724,73062,73063,73066,73067,73097,73098,72999,73130,21779,73160,73189],{},[38,73064,73065],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,73068,73070],{"className":73069},[886],[888,73071,73072],{"xmlns":890},[892,73073,73074,73094],{},[895,73075,73076,73082,73084,73086,73088],{},[2007,73077,73078,73080],{},[898,73079,1677],{},[1931,73081,1933],{},[1700,73083,1765],{},[1931,73085,30266],{},[1700,73087,1768],{},[2007,73089,73090,73092],{},[898,73091,1662],{},[1931,73093,1933],{},[902,73095,73096],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,73099,73101],{"className":73100},[886],[888,73102,73103],{"xmlns":890},[892,73104,73105,73127],{},[895,73106,73107,73113,73115,73117,73119,73121],{},[2007,73108,73109,73111],{},[898,73110,1677],{},[1931,73112,2343],{},[1700,73114,1765],{},[1931,73116,8565],{},[1700,73118,1768],{},[1931,73120,5197],{},[2007,73122,73123,73125],{},[898,73124,1662],{},[1931,73126,2343],{},[902,73128,73129],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,73131,73133],{"className":73132},[886],[888,73134,73135],{"xmlns":890},[892,73136,73137,73157],{},[895,73138,73139,73141,73143,73145,73147,73149,73151,73153,73155],{},[898,73140,2971],{},[898,73142,2974],{},[1700,73144,1765],{},[1931,73146,2438],{},[1781,73148,1783],{},[1931,73150,59266],{},[1700,73152,1897],{},[1931,73154,3284],{},[898,73156,1662],{},[902,73158,73159],{"encoding":904},"TC = 5\\,000 + 100Q",[883,73161,73163],{"className":73162},[886],[888,73164,73165],{"xmlns":890},[892,73166,73167,73187],{},[895,73168,73169,73171,73173,73179,73181],{},[898,73170,1662],{},[1700,73172,1765],{},[2007,73174,73175,73177],{},[898,73176,1662],{},[1931,73178,1933],{},[1700,73180,1897],{},[2007,73182,73183,73185],{},[898,73184,1662],{},[1931,73186,2343],{},[902,73188,73059],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,73191,73193],{"id":73192},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,73195,73196,73199,73200,73247,73248,73265],{},[38,73197,73198],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,73201,73203],{"className":73202},[886],[888,73204,73205],{"xmlns":890},[892,73206,73207,73244],{},[895,73208,73209,73211,73213,73215,73217,73220,73226,73228,73231,73237,73239,73242],{},[898,73210,2971],{},[898,73212,40524],{},[898,73214,2974],{},[1700,73216,1765],{},[1931,73218,73219],{},"0,85",[1785,73221,73222,73224],{},[898,73223,1662],{},[1931,73225,2385],{},[1700,73227,1768],{},[1931,73229,73230],{},"11,9",[1785,73232,73233,73235],{},[898,73234,1662],{},[1931,73236,2343],{},[1700,73238,1897],{},[1931,73240,73241],{},"102",[898,73243,1662],{},[902,73245,73246],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,73249,73251],{"className":73250},[886],[888,73252,73253],{"xmlns":890},[892,73254,73255,73263],{},[895,73256,73257],{},[1785,73258,73259,73261],{},[898,73260,1677],{},[1700,73262,4543],{},[902,73264,4593],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,73267,73268,71026,73271,73307],{},[38,73269,73270],{},"3.27",[883,73272,73274],{"className":73273},[886],[888,73275,73276],{"xmlns":890},[892,73277,73278,73304],{},[895,73279,73280,73282,73284,73286,73288,73294,73296,73298,73300,73302],{},[898,73281,2005],{},[898,73283,2974],{},[1700,73285,1765],{},[1931,73287,3118],{},[1785,73289,73290,73292],{},[898,73291,1662],{},[1931,73293,2343],{},[1700,73295,1768],{},[1931,73297,64624],{},[898,73299,1662],{},[1700,73301,1897],{},[1931,73303,30928],{},[902,73305,73306],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,73309,73310,70277,73313,73307],{},[38,73311,73312],{},"3.28",[883,73314,73316],{"className":73315},[886],[888,73317,73318],{"xmlns":890},[892,73319,73320,73356],{},[895,73321,73322,73324,73326,73328,73330,73336,73338,73340,73346,73348,73350,73352,73354],{},[898,73323,2971],{},[898,73325,2974],{},[1700,73327,1765],{},[1931,73329,5197],{},[1785,73331,73332,73334],{},[898,73333,1662],{},[1931,73335,2385],{},[1700,73337,1768],{},[1931,73339,24386],{},[1785,73341,73342,73344],{},[898,73343,1662],{},[1931,73345,2343],{},[1700,73347,1897],{},[1931,73349,3320],{},[898,73351,1662],{},[1700,73353,1897],{},[1931,73355,15295],{},[902,73357,73358],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,73360,15905],{"id":15904},[120,73362,73363,73391,73436,73508,73573,73613,73705,73811,73851,73965,74058,74122,74154,74214,74220,74284,74333,74387,74495,74550],{},[123,73364,73365,2106,73367,73390],{},[38,73366,55934],{},[883,73368,73370],{"className":73369},[886],[888,73371,73372],{"xmlns":890},[892,73373,73374,73388],{},[895,73375,73376,73378,73380,73382,73384,73386],{},[898,73377,2971],{},[898,73379,4185],{},[1700,73381,1765],{},[898,73383,1677],{},[1700,73385,2065],{},[898,73387,1662],{},[902,73389,66896],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,73392,73393,2106,73395,73435],{},[38,73394,56520],{},[883,73396,73398],{"className":73397},[886],[888,73399,73400],{"xmlns":890},[892,73401,73402,73432],{},[895,73403,73404,73406,73408,73410,73422,73424,73426,73428,73430],{},[898,73405,1862],{},[898,73407,4185],{},[1700,73409,1765],{},[1770,73411,73412],{"scriptlevel":1772,"displaystyle":1702},[1774,73413,73414,73420],{},[895,73415,73416,73418],{},[898,73417,2971],{},[898,73419,4185],{},[898,73421,1662],{},[1700,73423,1765],{},[898,73425,4374],{},[1700,73427,1703],{"stretchy":1702},[898,73429,1662],{},[1700,73431,1709],{"stretchy":1702},[902,73433,73434],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,73437,73438,2106,73440,73476,73477,73492,73493,2196],{},[38,73439,56668],{},[883,73441,73443],{"className":73442},[886],[888,73444,73445],{"xmlns":890},[892,73446,73447,73473],{},[895,73448,73449,73451,73453,73455],{},[898,73450,2005],{},[898,73452,4185],{},[1700,73454,1765],{},[1770,73456,73457],{"scriptlevel":1772,"displaystyle":1702},[1774,73458,73459,73467],{},[895,73460,73461,73463,73465],{},[898,73462,2406],{"mathvariant":1791},[898,73464,2971],{},[898,73466,4185],{},[895,73468,73469,73471],{},[898,73470,2406],{"mathvariant":1791},[898,73472,1662],{},[902,73474,73475],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,73478,73480],{"className":73479},[886],[888,73481,73482],{"xmlns":890},[892,73483,73484,73490],{},[895,73485,73486,73488],{},[898,73487,2971],{},[898,73489,4185],{},[902,73491,4285],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,73494,73496],{"className":73495},[886],[888,73497,73498],{"xmlns":890},[892,73499,73500,73506],{},[895,73501,73502,73504],{},[898,73503,1862],{},[898,73505,4185],{},[902,73507,55629],{"encoding":904},[123,73509,73510,2106,73513,1343,73543,2196],{},[38,73511,73512],{},"Diferenciál příjmu\u002Fnákladů",[883,73514,73516],{"className":73515},[886],[888,73517,73518],{"xmlns":890},[892,73519,73520,73540],{},[895,73521,73522,73524,73526,73528,73530,73532,73534,73536,73538],{},[898,73523,3084],{"mathvariant":1791},[898,73525,2971],{},[898,73527,4185],{},[1700,73529,2927],{},[898,73531,2005],{},[898,73533,4185],{},[1781,73535,1783],{},[898,73537,2406],{"mathvariant":1791},[898,73539,1662],{},[902,73541,73542],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,73544,73546],{"className":73545},[886],[888,73547,73548],{"xmlns":890},[892,73549,73550,73570],{},[895,73551,73552,73554,73556,73558,73560,73562,73564,73566,73568],{},[898,73553,3084],{"mathvariant":1791},[898,73555,2971],{},[898,73557,2974],{},[1700,73559,2927],{},[898,73561,2005],{},[898,73563,2974],{},[1781,73565,1783],{},[898,73567,2406],{"mathvariant":1791},[898,73569,1662],{},[902,73571,73572],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,73574,73575,2106,73577,2196],{},[38,73576,58790],{},[883,73578,73580],{"className":73579},[886],[888,73581,73582],{"xmlns":890},[892,73583,73584,73610],{},[895,73585,73586,73588,73590,73592,73594,73596,73598,73600,73602,73604,73606,73608],{},[898,73587,2971],{},[898,73589,2974],{},[1700,73591,1765],{},[898,73593,10619],{},[898,73595,2974],{},[1700,73597,1897],{},[898,73599,2971],{},[898,73601,40524],{},[898,73603,2974],{},[1700,73605,1703],{"stretchy":1702},[898,73607,1662],{},[1700,73609,1709],{"stretchy":1702},[902,73611,73612],{"encoding":904},"TC = FC + TVC(Q)",[123,73614,73615,2106,73618,1343,73633,2106,73635,1343,73658,2106,73661,2196],{},[38,73616,73617],{},"Fixní náklady",[883,73619,73621],{"className":73620},[886],[888,73622,73623],{"xmlns":890},[892,73624,73625,73631],{},[895,73626,73627,73629],{},[898,73628,10619],{},[898,73630,2974],{},[902,73632,55675],{"encoding":904},[38,73634,58943],{},[883,73636,73638],{"className":73637},[886],[888,73639,73640],{"xmlns":890},[892,73641,73642,73656],{},[895,73643,73644,73646,73648,73650,73652,73654],{},[898,73645,2971],{},[898,73647,40524],{},[898,73649,2974],{},[1700,73651,1703],{"stretchy":1702},[898,73653,1662],{},[1700,73655,1709],{"stretchy":1702},[902,73657,58940],{"encoding":904},[38,73659,73660],{},"variabilní náklady na jednotku",[883,73662,73664],{"className":73663},[886],[888,73665,73666],{"xmlns":890},[892,73667,73668,73702],{},[895,73669,73670,73672,73674,73676,73678,73680,73682],{},[898,73671,40524],{},[898,73673,2974],{},[1700,73675,1703],{"stretchy":1702},[898,73677,1662],{},[1700,73679,1709],{"stretchy":1702},[1700,73681,1765],{},[1770,73683,73684],{"scriptlevel":1772,"displaystyle":1702},[1774,73685,73686,73700],{},[895,73687,73688,73690,73692,73694,73696,73698],{},[898,73689,2971],{},[898,73691,40524],{},[898,73693,2974],{},[1700,73695,1703],{"stretchy":1702},[898,73697,1662],{},[1700,73699,1709],{"stretchy":1702},[898,73701,1662],{},[902,73703,73704],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,73706,73707,2106,73709,1343,73739,2106,73742,1343,73774,2106,73777,2196],{},[38,73708,58951],{},[883,73710,73712],{"className":73711},[886],[888,73713,73714],{"xmlns":890},[892,73715,73716,73736],{},[895,73717,73718,73720,73722,73724],{},[898,73719,1862],{},[898,73721,2974],{},[1700,73723,1765],{},[1770,73725,73726],{"scriptlevel":1772,"displaystyle":1702},[1774,73727,73728,73734],{},[895,73729,73730,73732],{},[898,73731,2971],{},[898,73733,2974],{},[898,73735,1662],{},[902,73737,73738],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,73740,73741],{},"průměrné fixní",[883,73743,73745],{"className":73744},[886],[888,73746,73747],{"xmlns":890},[892,73748,73749,73771],{},[895,73750,73751,73753,73755,73757,73759],{},[898,73752,1862],{},[898,73754,10619],{},[898,73756,2974],{},[1700,73758,1765],{},[1770,73760,73761],{"scriptlevel":1772,"displaystyle":1702},[1774,73762,73763,73769],{},[895,73764,73765,73767],{},[898,73766,10619],{},[898,73768,2974],{},[898,73770,1662],{},[902,73772,73773],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,73775,73776],{},"průměrné variabilní",[883,73778,73780],{"className":73779},[886],[888,73781,73782],{"xmlns":890},[892,73783,73784,73808],{},[895,73785,73786,73788,73790,73792,73794],{},[898,73787,1862],{},[898,73789,40524],{},[898,73791,2974],{},[1700,73793,1765],{},[1770,73795,73796],{"scriptlevel":1772,"displaystyle":1702},[1774,73797,73798,73806],{},[895,73799,73800,73802,73804],{},[898,73801,2971],{},[898,73803,40524],{},[898,73805,2974],{},[898,73807,1662],{},[902,73809,73810],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,73812,73813,2106,73815,2196],{},[38,73814,60138],{},[883,73816,73818],{"className":73817},[886],[888,73819,73820],{"xmlns":890},[892,73821,73822,73848],{},[895,73823,73824,73826,73828,73830],{},[898,73825,2005],{},[898,73827,2974],{},[1700,73829,1765],{},[1770,73831,73832],{"scriptlevel":1772,"displaystyle":1702},[1774,73833,73834,73842],{},[895,73835,73836,73838,73840],{},[898,73837,2406],{"mathvariant":1791},[898,73839,2971],{},[898,73841,2974],{},[895,73843,73844,73846],{},[898,73845,2406],{"mathvariant":1791},[898,73847,1662],{},[902,73849,73850],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,73852,73853,2106,73855,73903,73904,73917,73918,1343,73933,1343,73950,2196],{},[38,73854,61036],{},[883,73856,73858],{"className":73857},[886],[888,73859,73860],{"xmlns":890},[892,73861,73862,73900],{},[895,73863,73864,73866,73868,73870,73872,73874,73876,73878,73880,73882,73884,73890,73892,73894],{},[898,73865,2971],{},[898,73867,2974],{},[1700,73869,1765],{},[898,73871,10619],{},[898,73873,2974],{},[1700,73875,1897],{},[898,73877,207],{},[898,73879,1662],{},[1700,73881,1897],{},[898,73883,1879],{},[1785,73885,73886,73888],{},[898,73887,1662],{},[1931,73889,2343],{},[1700,73891,1897],{},[898,73893,2354],{},[1785,73895,73896,73898],{},[898,73897,1662],{},[1931,73899,2385],{},[902,73901,73902],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,73905,73907],{"className":73906},[886],[888,73908,73909],{"xmlns":890},[892,73910,73911,73915],{},[895,73912,73913],{},[898,73914,900],{},[902,73916,900],{"encoding":904},"-průběhem ",[883,73919,73921],{"className":73920},[886],[888,73922,73923],{"xmlns":890},[892,73924,73925,73931],{},[895,73926,73927,73929],{},[898,73928,1862],{},[898,73930,2974],{},[902,73932,55744],{"encoding":904},[883,73934,73936],{"className":73935},[886],[888,73937,73938],{"xmlns":890},[892,73939,73940,73948],{},[895,73941,73942,73944,73946],{},[898,73943,1862],{},[898,73945,40524],{},[898,73947,2974],{},[902,73949,55495],{"encoding":904},[883,73951,73953],{"className":73952},[886],[888,73954,73955],{"xmlns":890},[892,73956,73957,73963],{},[895,73958,73959,73961],{},[898,73960,2005],{},[898,73962,2974],{},[902,73964,55476],{"encoding":904},[123,73966,73967,73969,73970,10577,73985,74026,74027,61681,74042,74057],{},[38,73968,62118],{},": v bodě minima ",[883,73971,73973],{"className":73972},[886],[888,73974,73975],{"xmlns":890},[892,73976,73977,73983],{},[895,73978,73979,73981],{},[898,73980,1862],{},[898,73982,2974],{},[902,73984,55744],{"encoding":904},[883,73986,73988],{"className":73987},[886],[888,73989,73990],{"xmlns":890},[892,73991,73992,74024],{},[895,73993,73994,73996,73998,74000,74006,74008,74010,74012,74014,74016,74022],{},[898,73995,1862],{},[898,73997,2974],{},[1700,73999,1703],{"stretchy":1702},[2007,74001,74002,74004],{},[898,74003,1662],{},[1931,74005,1772],{},[1700,74007,1709],{"stretchy":1702},[1700,74009,1765],{},[898,74011,2005],{},[898,74013,2974],{},[1700,74015,1703],{"stretchy":1702},[2007,74017,74018,74020],{},[898,74019,1662],{},[1931,74021,1772],{},[1700,74023,1709],{"stretchy":1702},[902,74025,62753],{"encoding":904},"; geometricky ",[883,74028,74030],{"className":74029},[886],[888,74031,74032],{"xmlns":890},[892,74033,74034,74040],{},[895,74035,74036,74038],{},[898,74037,2005],{},[898,74039,2974],{},[902,74041,55476],{"encoding":904},[883,74043,74045],{"className":74044},[886],[888,74046,74047],{"xmlns":890},[892,74048,74049,74055],{},[895,74050,74051,74053],{},[898,74052,1862],{},[898,74054,2974],{},[902,74056,55744],{"encoding":904}," v jejím minimu.",[123,74059,74060,73969,74062,10577,74079,2196],{},[38,74061,63468],{},[883,74063,74065],{"className":74064},[886],[888,74066,74067],{"xmlns":890},[892,74068,74069,74077],{},[895,74070,74071,74073,74075],{},[898,74072,1862],{},[898,74074,40524],{},[898,74076,2974],{},[902,74078,55495],{"encoding":904},[883,74080,74082],{"className":74081},[886],[888,74083,74084],{"xmlns":890},[892,74085,74086,74120],{},[895,74087,74088,74090,74092,74094,74096,74102,74104,74106,74108,74110,74112,74118],{},[898,74089,1862],{},[898,74091,40524],{},[898,74093,2974],{},[1700,74095,1703],{"stretchy":1702},[2007,74097,74098,74100],{},[898,74099,1662],{},[1931,74101,1772],{},[1700,74103,1709],{"stretchy":1702},[1700,74105,1765],{},[898,74107,2005],{},[898,74109,2974],{},[1700,74111,1703],{"stretchy":1702},[2007,74113,74114,74116],{},[898,74115,1662],{},[1931,74117,1772],{},[1700,74119,1709],{"stretchy":1702},[902,74121,69203],{"encoding":904},[123,74123,74124,2106,74126,74153],{},[38,74125,63647],{},[883,74127,74129],{"className":74128},[886],[888,74130,74131],{"xmlns":890},[892,74132,74133,74151],{},[895,74134,74135,74137,74139,74141,74143,74145,74147,74149],{},[898,74136,1677],{},[898,74138,4185],{},[1700,74140,1765],{},[898,74142,2971],{},[898,74144,4185],{},[1700,74146,1768],{},[898,74148,2971],{},[898,74150,2974],{},[902,74152,55384],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,74155,74156,10208,74158,74160,74161,74187,74188,74213],{},[38,74157,64509],{},[614,74159,63772],{},") — hodnoty ",[883,74162,74164],{"className":74163},[886],[888,74165,74166],{"xmlns":890},[892,74167,74168,74184],{},[895,74169,74170,74176,74178],{},[2007,74171,74172,74174],{},[898,74173,1662],{},[898,74175,1862],{},[1700,74177,1732],{"separator":1731},[2007,74179,74180,74182],{},[898,74181,1662],{},[898,74183,23438],{},[902,74185,74186],{"encoding":904},"Q_A, Q_B"," splňující ",[883,74189,74191],{"className":74190},[886],[888,74192,74193],{"xmlns":890},[892,74194,74195,74211],{},[895,74196,74197,74199,74201,74203,74205,74207,74209],{},[898,74198,1677],{},[898,74200,4185],{},[1700,74202,1703],{"stretchy":1702},[898,74204,1662],{},[1700,74206,1709],{"stretchy":1702},[1700,74208,1765],{},[1931,74210,1772],{},[902,74212,64049],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,74215,74216,74219],{},[38,74217,74218],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,74221,74222,74224,74225,10577,74242,74283],{},[38,74223,65563],{}," — v bodě maxima zisku ",[883,74226,74228],{"className":74227},[886],[888,74229,74230],{"xmlns":890},[892,74231,74232,74240],{},[895,74233,74234],{},[2007,74235,74236,74238],{},[898,74237,1662],{},[1931,74239,1772],{},[902,74241,38493],{"encoding":904},[883,74243,74245],{"className":74244},[886],[888,74246,74247],{"xmlns":890},[892,74248,74249,74281],{},[895,74250,74251,74253,74255,74257,74263,74265,74267,74269,74271,74273,74279],{},[898,74252,2005],{},[898,74254,4185],{},[1700,74256,1703],{"stretchy":1702},[2007,74258,74259,74261],{},[898,74260,1662],{},[1931,74262,1772],{},[1700,74264,1709],{"stretchy":1702},[1700,74266,1765],{},[898,74268,2005],{},[898,74270,2974],{},[1700,74272,1703],{"stretchy":1702},[2007,74274,74275,74277],{},[898,74276,1662],{},[1931,74278,1772],{},[1700,74280,1709],{"stretchy":1702},[902,74282,65829],{"encoding":904}," (3.13).",[123,74285,74286,20486,74288,10577,74307,74332],{},[38,74287,66856],{},[883,74289,74291],{"className":74290},[886],[888,74292,74293],{"xmlns":890},[892,74294,74295,74304],{},[895,74296,74297,74299,74301],{},[898,74298,1677],{},[1700,74300,1765],{},[1781,74302,74303],{},"konst",[902,74305,74306],{"encoding":904},"P = \\text{konst}",[883,74308,74310],{"className":74309},[886],[888,74311,74312],{"xmlns":890},[892,74313,74314,74330],{},[895,74315,74316,74318,74320,74322,74324,74326,74328],{},[898,74317,1677],{},[1700,74319,1765],{},[898,74321,2005],{},[898,74323,2974],{},[1700,74325,1703],{"stretchy":1702},[898,74327,1662],{},[1700,74329,1709],{"stretchy":1702},[902,74331,67550],{"encoding":904}," (3.14).",[123,74334,74335,74338,74339,74368,74369,74386],{},[38,74336,74337],{},"Shutdown point"," — bod ",[883,74340,74342],{"className":74341},[886],[888,74343,74344],{"xmlns":890},[892,74345,74346,74366],{},[895,74347,74348,74350,74356,74358,74364],{},[1700,74349,1703],{"stretchy":1702},[1785,74351,74352,74354],{},[898,74353,1662],{},[1700,74355,4543],{},[1700,74357,1732],{"separator":1731},[1785,74359,74360,74362],{},[898,74361,1677],{},[1700,74363,4543],{},[1700,74365,1709],{"stretchy":1702},[902,74367,67839],{"encoding":904}," v minimu ",[883,74370,74372],{"className":74371},[886],[888,74373,74374],{"xmlns":890},[892,74375,74376,74384],{},[895,74377,74378,74380,74382],{},[898,74379,1862],{},[898,74381,40524],{},[898,74383,2974],{},[902,74385,55495],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,74388,74389,2106,74392,6661,74427,68109,74448,74461,74462,74477,74478,2196],{},[38,74390,74391],{},"Funkce nabídky firmy",[883,74393,74395],{"className":74394},[886],[888,74396,74397],{"xmlns":890},[892,74398,74399,74425],{},[895,74400,74401,74403,74405,74407,74409,74411,74413,74415,74417,74419,74421,74423],{},[898,74402,1677],{},[1700,74404,1765],{},[898,74406,8861],{},[1700,74408,1703],{"stretchy":1702},[898,74410,1662],{},[1700,74412,1709],{"stretchy":1702},[1700,74414,1765],{},[898,74416,2005],{},[898,74418,2974],{},[1700,74420,1703],{"stretchy":1702},[898,74422,1662],{},[1700,74424,1709],{"stretchy":1702},[902,74426,69306],{"encoding":904},[883,74428,74430],{"className":74429},[886],[888,74431,74432],{"xmlns":890},[892,74433,74434,74446],{},[895,74435,74436,74438,74440],{},[898,74437,1662],{},[1700,74439,4674],{},[1785,74441,74442,74444],{},[898,74443,1662],{},[1700,74445,4543],{},[902,74447,68108],{"encoding":904},[883,74449,74451],{"className":74450},[886],[888,74452,74453],{"xmlns":890},[892,74454,74455,74459],{},[895,74456,74457],{},[1931,74458,1772],{},[902,74460,1772],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,74463,74465],{"className":74464},[886],[888,74466,74467],{"xmlns":890},[892,74468,74469,74475],{},[895,74470,74471,74473],{},[898,74472,2005],{},[898,74474,2974],{},[902,74476,55476],{"encoding":904}," nad minimem ",[883,74479,74481],{"className":74480},[886],[888,74482,74483],{"xmlns":890},[892,74484,74485,74493],{},[895,74486,74487,74489,74491],{},[898,74488,1862],{},[898,74490,40524],{},[898,74492,2974],{},[902,74494,55495],{"encoding":904},[123,74496,74497,7203,74499,74520,74521,2196],{},[38,74498,50264],{},[883,74500,74502],{"className":74501},[886],[888,74503,74504],{"xmlns":890},[892,74505,74506,74518],{},[895,74507,74508,74510,74512],{},[898,74509,1677],{},[1700,74511,1765],{},[1785,74513,74514,74516],{},[898,74515,1677],{},[1700,74517,4543],{},[902,74519,4546],{"encoding":904}," konstantní ⇒ ",[883,74522,74524],{"className":74523},[886],[888,74525,74526],{"xmlns":890},[892,74527,74528,74548],{},[895,74529,74530,74532,74534,74536,74538,74540,74542],{},[898,74531,1862],{},[898,74533,4185],{},[1700,74535,1765],{},[898,74537,2005],{},[898,74539,4185],{},[1700,74541,1765],{},[1785,74543,74544,74546],{},[898,74545,1677],{},[1700,74547,4543],{},[902,74549,58782],{"encoding":904},[123,74551,74552,74555],{},[38,74553,74554],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,74557,3985],{"id":3984},[120,74559,74560,74579,74591],{},[123,74561,74562,2106,74564,1343,74567,1343,74570,1343,74573,1343,74576],{},[38,74563,50908],{},[207,74565,12125],{"className":74566,"dataFsResolvedFilePath":800,"href":801},[210],[207,74568,1649],{"className":74569,"dataFsResolvedFilePath":848,"href":849},[210],[207,74571,2559],{"className":74572,"dataFsResolvedFilePath":764,"href":765},[210],[207,74574,775],{"className":74575,"dataFsResolvedFilePath":773,"href":774},[210],[207,74577,859],{"className":74578,"dataFsResolvedFilePath":857,"href":858},[210],[123,74580,74581,2106,74583,1343,74587],{},[38,74582,36888],{},[207,74584,74586],{"className":74585,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,74588,74590],{"className":74589,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,74592,74593,2106,74595],{},[38,74594,16389],{},[207,74596,16393],{"className":74597,"dataFsResolvedFilePath":2140,"href":2141},[210],{"title":641,"searchDepth":642,"depth":642,"links":74599},[74600,74601,74608,74614,74618,74619,74623,74624,74625,74626,74632,74633],{"id":51139,"depth":642,"text":1241},{"id":55922,"depth":642,"text":55923,"children":74602},[74603,74604,74605,74606,74607],{"id":55933,"depth":649,"text":55934},{"id":56519,"depth":649,"text":56520},{"id":56667,"depth":649,"text":56668},{"id":57409,"depth":649,"text":57410},{"id":58064,"depth":649,"text":58065},{"id":58785,"depth":642,"text":58786,"children":74609},[74610,74611,74612,74613],{"id":58789,"depth":649,"text":58790},{"id":58950,"depth":649,"text":58951},{"id":60137,"depth":649,"text":60138},{"id":61035,"depth":649,"text":61036},{"id":62117,"depth":642,"text":62118,"children":74615},[74616,74617],{"id":16596,"depth":649,"text":16597},{"id":63467,"depth":649,"text":63468},{"id":63641,"depth":642,"text":63642},{"id":65562,"depth":642,"text":65563,"children":74620},[74621,74622],{"id":65576,"depth":649,"text":16597},{"id":66855,"depth":649,"text":66856},{"id":67487,"depth":642,"text":67488},{"id":68953,"depth":642,"text":68954},{"id":50066,"depth":642,"text":50067},{"id":69414,"depth":642,"text":69415,"children":74627},[74628,74629,74630,74631],{"id":69418,"depth":649,"text":69419},{"id":70270,"depth":649,"text":70271},{"id":71816,"depth":649,"text":71817},{"id":73192,"depth":649,"text":73193},{"id":15904,"depth":642,"text":15905},{"id":3984,"depth":642,"text":3985},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":55304,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,74640,74641,55356,74642,74643,74644],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":74647,"title":74648,"body":74649,"course":1128,"courses":659,"created":9743,"description":641,"extension":661,"meta":86745,"navigation":664,"path":86746,"seo":86747,"sources":86748,"stem":86749,"tags":86750,"type":4049,"updated":677,"__hash__":86754},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":74650,"toc":86702},[74651,74654,75010,75014,75017,75084,75136,75146,75150,75184,75225,75249,75272,75301,75368,75475,75518,75575,75650,75695,75699,75707,75715,75718,75983,76034,76114,76184,76207,76235,76280,76302,76306,76313,76362,76388,76539,76542,76579,76742,76850,76854,76891,76966,77035,77154,77276,77357,77363,77404,77477,77570,77574,77610,77698,77812,77917,78002,78142,78146,78194,78239,78245,78249,78252,78303,78353,78360,78426,78559,78604,78608,78629,79008,79103,79120,79174,79178,79260,79344,79514,79517,79560,79627,79701,79705,79710,79779,79787,79796,79874,79940,79945,80040,80083,80088,80136,80141,80189,80307,80390,80428,80531,80590,80731,80735,80778,80851,80875,80929,80936,80938,80983,81028,81039,81044,81080,81142,81165,81174,81275,81342,81415,81422,81513,81575,81611,81668,81727,81912,82008,82012,82016,82095,82100,82224,82310,82316,82426,82463,82554,82652,82655,82659,82725,82762,82884,82936,82940,82968,83020,83094,83199,83223,83282,83286,83304,83447,83595,83597,83632,83636,83638,83728,83858,83984,84076,84151,84155,84271,84375,84565,84601,84695,84701,84814,85117,85123,85241,85340,85416,85418,86580,86582],[12,74652,74648],{"id":74653},"produkce-produkční-funkce-cobb-douglas-mrts",[4060,74655,74656],{},[724,74657,74658,4067,74660,74662,74663,37081,74676,74689,74690,16561,74703,10208,74705,74729,74730,2106,74732,2114,74766,2106,74769,74797,74798,10577,74818,74848,74849,10208,74852,74880,74881,74884,74885,74915,74916,74946,74947,2106,74950,74990,74991,75009],{},[883,74659,4066],{},[38,74661,859],{}," popisuje vztah mezi vstupy (práce ",[883,74664,74666],{"className":74665},[886],[888,74667,74668],{"xmlns":890},[892,74669,74670,74674],{},[895,74671,74672],{},[898,74673,1706],{},[902,74675,1706],{"encoding":904},[883,74677,74679],{"className":74678},[886],[888,74680,74681],{"xmlns":890},[892,74682,74683,74687],{},[895,74684,74685],{},[898,74686,1735],{},[902,74688,1735],{"encoding":904},") a výstupem ",[883,74691,74693],{"className":74692},[886],[888,74694,74695],{"xmlns":890},[892,74696,74697,74701],{},[895,74698,74699],{},[898,74700,1662],{},[902,74702,1662],{"encoding":904},[38,74704,37149],{},[883,74706,74708],{"className":74707},[886],[888,74709,74710],{"xmlns":890},[892,74711,74712,74726],{},[895,74713,74714,74716,74718,74720,74722,74724],{},[898,74715,1662],{},[1700,74717,1765],{},[898,74719,1662],{},[1700,74721,1703],{"stretchy":1702},[898,74723,1706],{},[1700,74725,1709],{"stretchy":1702},[902,74727,74728],{"encoding":904},"Q = Q(L)",") studujeme ",[614,74731,10207],{},[883,74733,74735],{"className":74734},[886],[888,74736,74737],{"xmlns":890},[892,74738,74739,74763],{},[895,74740,74741,74743,74749,74751,74757,74759,74761],{},[898,74742,2005],{},[2007,74744,74745,74747],{},[898,74746,1677],{},[898,74748,1706],{},[1700,74750,1765],{},[1785,74752,74753,74755],{},[898,74754,1662],{},[1700,74756,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,74758,1703],{"stretchy":1702},[898,74760,1706],{},[1700,74762,1709],{"stretchy":1702},[902,74764,74765],{"encoding":904},"MP_L = Q'(L)",[614,74767,74768],{},"průměrný produkt",[883,74770,74772],{"className":74771},[886],[888,74773,74774],{"xmlns":890},[892,74775,74776,74794],{},[895,74777,74778,74780,74786,74788,74790,74792],{},[898,74779,1862],{},[2007,74781,74782,74784],{},[898,74783,1677],{},[898,74785,1706],{},[1700,74787,1765],{},[898,74789,1662],{},[898,74791,1979],{"mathvariant":1791},[898,74793,1706],{},[902,74795,74796],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,74799,74801],{"className":74800},[886],[888,74802,74803],{"xmlns":890},[892,74804,74805,74815],{},[895,74806,74807,74809],{},[898,74808,1862],{},[2007,74810,74811,74813],{},[898,74812,1677],{},[898,74814,1706],{},[902,74816,74817],{"encoding":904},"AP_L",[883,74819,74821],{"className":74820},[886],[888,74822,74823],{"xmlns":890},[892,74824,74825,74845],{},[895,74826,74827,74829,74835,74837,74839],{},[898,74828,2005],{},[2007,74830,74831,74833],{},[898,74832,1677],{},[898,74834,1706],{},[1700,74836,1765],{},[898,74838,1862],{},[2007,74840,74841,74843],{},[898,74842,1677],{},[898,74844,1706],{},[902,74846,74847],{"encoding":904},"MP_L = AP_L",". Ve ",[38,74850,74851],{},"dvoufaktorovém modelu",[883,74853,74855],{"className":74854},[886],[888,74856,74857],{"xmlns":890},[892,74858,74859,74877],{},[895,74860,74861,74863,74865,74867,74869,74871,74873,74875],{},[898,74862,1662],{},[1700,74864,1765],{},[898,74866,1662],{},[1700,74868,1703],{"stretchy":1702},[898,74870,1706],{},[1700,74872,1732],{"separator":1731},[898,74874,1735],{},[1700,74876,1709],{"stretchy":1702},[902,74878,74879],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,74882,74883],{},"Cobb-Douglasovy"," funkce ",[883,74886,74888],{"className":74887},[886],[888,74889,74890],{"xmlns":890},[892,74891,74892,74912],{},[895,74893,74894,74896,74898,74900,74906],{},[898,74895,1662],{},[1700,74897,1765],{},[898,74899,1862],{},[1785,74901,74902,74904],{},[898,74903,1706],{},[898,74905,207],{},[1785,74907,74908,74910],{},[898,74909,1735],{},[898,74911,1879],{},[902,74913,74914],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,74917,74919],{"className":74918},[886],[888,74920,74921],{"xmlns":890},[892,74922,74923,74943],{},[895,74924,74925,74927,74933,74935,74937],{},[898,74926,2005],{},[2007,74928,74929,74931],{},[898,74930,1677],{},[898,74932,1706],{},[1700,74934,1732],{"separator":1731},[898,74936,2005],{},[2007,74938,74939,74941],{},[898,74940,1677],{},[898,74942,1735],{},[902,74944,74945],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,74948,74949],{},"mezní míru technické substituce",[883,74951,74953],{"className":74952},[886],[888,74954,74955],{"xmlns":890},[892,74956,74957,74987],{},[895,74958,74959,74961,74963,74965,74967,74969,74971,74977,74979,74981],{},[898,74960,2005],{},[898,74962,4185],{},[898,74964,2971],{},[898,74966,8861],{},[1700,74968,1765],{},[898,74970,2005],{},[2007,74972,74973,74975],{},[898,74974,1677],{},[898,74976,1706],{},[898,74978,1979],{"mathvariant":1791},[898,74980,2005],{},[2007,74982,74983,74985],{},[898,74984,1677],{},[898,74986,1735],{},[902,74988,74989],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,74992,74994],{"className":74993},[886],[888,74995,74996],{"xmlns":890},[892,74997,74998,75006],{},[895,74999,75000,75002,75004],{},[898,75001,207],{},[1700,75003,1897],{},[898,75005,1879],{},[902,75007,75008],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,75011,75013],{"id":75012},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,75015,75016],{},"Po prostudování kapitoly 5 student umí:",[120,75018,75019,75025,75035,75041,75047,75052,75058,75068,75073,75078],{},[123,75020,75021,75022,1732],{},"popsat ",[38,75023,75024],{},"jednofaktorový model produkce",[123,75026,75027,75028,2114,75031,75034],{},"vypočítat ",[38,75029,75030],{},"mezní",[38,75032,75033],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,75036,75037,75038,1732],{},"charakterizovat průběh ",[38,75039,75040],{},"křivky produkce",[123,75042,75043,75044,1732],{},"formulovat ",[38,75045,75046],{},"princip maximalizace průměrného produktu práce",[123,75048,75021,75049,1732],{},[38,75050,75051],{},"dvoufaktorový model produkce",[123,75053,75054,75055,1732],{},"uvést tvar ",[38,75056,75057],{},"Cobb–Douglasových produkčních funkcí",[123,75059,75060,75061,1343,75063,1343,75065,1732],{},"vyložit, co jsou ",[38,75062,24798],{},[38,75064,13842],{},[38,75066,75067],{},"klesající výnosy z rozsahu",[123,75069,75027,75070,75034],{},[38,75071,75072],{},"mezní produkty práce a kapitálu",[123,75074,75075,75076,1732],{},"najít ",[38,75077,2159],{},[123,75079,75027,75080,75083],{},[38,75081,75082],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,75085,75086,75087,75090,75091,75094,75095,2106,75098,1343,75111,2106,75114,2114,75127,75130,75131,75133,75134,2196],{},"Každý proces produkce je určován ",[38,75088,75089],{},"faktory"," (též ",[38,75092,75093],{},"vstupy",") produkce. K hlavním patří ",[38,75096,75097],{},"práce",[883,75099,75101],{"className":75100},[886],[888,75102,75103],{"xmlns":890},[892,75104,75105,75109],{},[895,75106,75107],{},[898,75108,1706],{},[902,75110,1706],{"encoding":904},[38,75112,75113],{},"kapitál",[883,75115,75117],{"className":75116},[886],[888,75118,75119],{"xmlns":890},[892,75120,75121,75125],{},[895,75122,75123],{},[898,75124,1735],{},[902,75126,1735],{"encoding":904},[38,75128,75129],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,75132,37149],{}," (produkce závisí jen na práci); v opačném případě o ",[38,75135,74851],{},[724,75137,75138,75139,1343,75142,75145],{},"Související matematický aparát: ",[207,75140,2559],{"className":75141,"dataFsResolvedFilePath":764,"href":765},[210],[207,75143,784],{"className":75144,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,75147,75149],{"id":75148},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,75151,75152,75153,75166,75167,75180,75181],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,75154,75156],{"className":75155},[886],[888,75157,75158],{"xmlns":890},[892,75159,75160,75164],{},[895,75161,75162],{},[898,75163,1662],{},[902,75165,1662],{"encoding":904}," na práci ",[883,75168,75170],{"className":75169},[886],[888,75171,75172],{"xmlns":890},[892,75173,75174,75178],{},[895,75175,75176],{},[898,75177,1706],{},[902,75179,1706],{"encoding":904}," vyjadřuje ",[38,75182,75183],{},"produkční funkce",[883,75185,75187],{"className":75186},[886],[888,75188,75189],{"xmlns":890,"display":28251},[892,75190,75191,75222],{},[20939,75192,75193],{"width":28256},[20944,75194,75195,75197,75215,75217],{},[20947,75196],{"width":28261},[20947,75198,75199],{},[895,75200,75201,75203,75205,75207,75209,75211,75213],{},[898,75202,1662],{},[1700,75204,1765],{},[898,75206,1662],{},[1700,75208,1703],{"stretchy":1702},[898,75210,1706],{},[1700,75212,1709],{"stretchy":1702},[1700,75214,1732],{"separator":1731},[20947,75216],{"width":28261},[20947,75218,75219],{},[1781,75220,75221],{},"(5.1)",[902,75223,75224],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,75226,75227,75228,10208,75231,75234,75235,75248],{},"jejíž graf se nazývá ",[38,75229,75230],{},"křivka produkce",[614,75232,75233],{},"production curve","). Práce ",[883,75236,75238],{"className":75237},[886],[888,75239,75240],{"xmlns":890},[892,75241,75242,75246],{},[895,75243,75244],{},[898,75245,1706],{},[902,75247,1706],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,75250,75252,75253,1709],{"id":75251},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,75254,75256],{"className":75255},[886],[888,75257,75258],{"xmlns":890},[892,75259,75260,75270],{},[895,75261,75262,75264],{},[898,75263,2005],{},[2007,75265,75266,75268],{},[898,75267,1677],{},[898,75269,1706],{},[902,75271,10228],{"encoding":904},[724,75273,75274,10208,75277,75280,75281,75300],{},[38,75275,75276],{},"Mezní produkt práce",[614,75278,75279],{},"marginal product of labour",") ",[883,75282,75284],{"className":75283},[886],[888,75285,75286],{"xmlns":890},[892,75287,75288,75298],{},[895,75289,75290,75292],{},[898,75291,2005],{},[2007,75293,75294,75296],{},[898,75295,1677],{},[898,75297,1706],{},[902,75299,10228],{"encoding":904}," je derivace produkce podle práce:",[883,75302,75304],{"className":75303},[886],[888,75305,75306],{"xmlns":890,"display":28251},[892,75307,75308,75365],{},[20939,75309,75310],{"width":28256},[20944,75311,75312,75314,75358,75360],{},[20947,75313],{"width":28261},[20947,75315,75316],{},[895,75317,75318,75320,75326,75328,75342,75344,75350,75352,75354,75356],{},[898,75319,2005],{},[2007,75321,75322,75324],{},[898,75323,1677],{},[898,75325,1706],{},[1700,75327,1765],{},[1774,75329,75330,75336],{},[895,75331,75332,75334],{},[898,75333,2406],{},[898,75335,1662],{},[895,75337,75338,75340],{},[898,75339,2406],{},[898,75341,1706],{},[1700,75343,1765],{},[1785,75345,75346,75348],{},[898,75347,1662],{},[1700,75349,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,75351,1703],{"stretchy":1702},[898,75353,1706],{},[1700,75355,1709],{"stretchy":1702},[898,75357,2196],{"mathvariant":1791},[20947,75359],{"width":28261},[20947,75361,75362],{},[1781,75363,75364],{},"(5.2)",[902,75366,75367],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,75369,75370,75371,20130,75389,75417,75418,75435,75436,2882,75453,4110],{},"Pro pevnou hodnotu ",[883,75372,75374],{"className":75373},[886],[888,75375,75376],{"xmlns":890},[892,75377,75378,75386],{},[895,75379,75380],{},[1785,75381,75382,75384],{},[898,75383,1706],{},[1700,75385,4543],{},[902,75387,75388],{"encoding":904},"L^*",[883,75390,75392],{"className":75391},[886],[888,75393,75394],{"xmlns":890},[892,75395,75396,75414],{},[895,75397,75398,75404,75406,75412],{},[1785,75399,75400,75402],{},[898,75401,1662],{},[1700,75403,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,75405,1703],{"stretchy":1702},[1785,75407,75408,75410],{},[898,75409,1706],{},[1700,75411,4543],{},[1700,75413,1709],{"stretchy":1702},[902,75415,75416],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,75419,75421],{"className":75420},[886],[888,75422,75423],{"xmlns":890},[892,75424,75425,75433],{},[895,75426,75427],{},[1785,75428,75429,75431],{},[898,75430,1706],{},[1700,75432,4543],{},[902,75434,75388],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,75437,75439],{"className":75438},[886],[888,75440,75441],{"xmlns":890},[892,75442,75443,75451],{},[895,75444,75445],{},[1785,75446,75447,75449],{},[898,75448,1706],{},[1700,75450,4543],{},[902,75452,75388],{"encoding":904},[883,75454,75456],{"className":75455},[886],[888,75457,75458],{"xmlns":890},[892,75459,75460,75472],{},[895,75461,75462,75468,75470],{},[1785,75463,75464,75466],{},[898,75465,1706],{},[1700,75467,4543],{},[1700,75469,1897],{},[1931,75471,1933],{},[902,75473,75474],{"encoding":904},"L^*+1",[4060,75476,75477],{},[724,75478,75479,18208,75481,75500,75501,75504,75505,2196],{},[883,75480,4346],{},[883,75482,75484],{"className":75483},[886],[888,75485,75486],{"xmlns":890},[892,75487,75488,75498],{},[895,75489,75490,75492],{},[898,75491,2005],{},[2007,75493,75494,75496],{},[898,75495,1677],{},[898,75497,1706],{},[902,75499,10228],{"encoding":904}," odpovídá na otázku „",[38,75502,75503],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,75506,75508],{"className":75507},[886],[888,75509,75510],{"xmlns":890},[892,75511,75512,75516],{},[895,75513,75514],{},[898,75515,1706],{},[902,75517,1706],{"encoding":904},[724,75519,75520,75523,75524,75540,75541,2882,75554,75574],{},[38,75521,75522],{},"Přibližná změna produkce"," pro změnu práce o ",[883,75525,75527],{"className":75526},[886],[888,75528,75529],{"xmlns":890},[892,75530,75531,75537],{},[895,75532,75533,75535],{},[898,75534,2406],{},[898,75536,1706],{},[902,75538,75539],{"encoding":904},"dL"," (z ",[883,75542,75544],{"className":75543},[886],[888,75545,75546],{"xmlns":890},[892,75547,75548,75552],{},[895,75549,75550],{},[898,75551,1706],{},[902,75553,1706],{"encoding":904},[883,75555,75557],{"className":75556},[886],[888,75558,75559],{"xmlns":890},[892,75560,75561,75571],{},[895,75562,75563,75565,75567,75569],{},[898,75564,1706],{},[1700,75566,1897],{},[898,75568,2406],{},[898,75570,1706],{},[902,75572,75573],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,75576,75578],{"className":75577},[886],[888,75579,75580],{"xmlns":890,"display":28251},[892,75581,75582,75647],{},[20939,75583,75584],{"width":28256},[20944,75585,75586,75588,75640,75642],{},[20947,75587],{"width":28261},[20947,75589,75590],{},[895,75591,75592,75594,75596,75598,75600,75602,75604,75610,75612,75614,75616,75618,75620,75622,75624,75626,75632,75634,75636,75638],{},[898,75593,3084],{"mathvariant":1791},[898,75595,1662],{},[1700,75597,2927],{},[898,75599,2406],{},[898,75601,1662],{},[1700,75603,1765],{},[1785,75605,75606,75608],{},[898,75607,1662],{},[1700,75609,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,75611,1703],{"stretchy":1702},[898,75613,1706],{},[1700,75615,1709],{"stretchy":1702},[1781,75617,1783],{},[898,75619,2406],{},[898,75621,1706],{},[1700,75623,1765],{},[898,75625,2005],{},[2007,75627,75628,75630],{},[898,75629,1677],{},[898,75631,1706],{},[1781,75633,1783],{},[898,75635,2406],{},[898,75637,1706],{},[898,75639,2196],{"mathvariant":1791},[20947,75641],{"width":28261},[20947,75643,75644],{},[1781,75645,75646],{},"(5.3)",[902,75648,75649],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,75651,75652,75653,2196],{},"Skutečná změna je ",[883,75654,75656],{"className":75655},[886],[888,75657,75658],{"xmlns":890},[892,75659,75660,75692],{},[895,75661,75662,75664,75666,75668,75670,75672,75674,75676,75678,75680,75682,75684,75686,75688,75690],{},[898,75663,3084],{"mathvariant":1791},[898,75665,1662],{},[1700,75667,1765],{},[898,75669,1662],{},[1700,75671,1703],{"stretchy":1702},[898,75673,1706],{},[1700,75675,1897],{},[898,75677,2406],{},[898,75679,1706],{},[1700,75681,1709],{"stretchy":1702},[1700,75683,1768],{},[898,75685,1662],{},[1700,75687,1703],{"stretchy":1702},[898,75689,1706],{},[1700,75691,1709],{"stretchy":1702},[902,75693,75694],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,75696,75698],{"id":75697},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,75700,75701,10208,75704,3345],{},[38,75702,75703],{},"Zákon klesajících výnosů",[614,75705,75706],{},"law of diminishing marginal productivity",[4060,75708,75709],{},[724,75710,75711,75712,75714],{},"Roste-li postupně některý ze vstupů (",[614,75713,37145],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,75716,75717],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,75719,75720,75721,2106,75742,75761,75762,75812,75813,75815,75816,2106,75836,75855,75856,75812,75888,3122,75890,75909,75910,21779,75927,75961,75962,8290,75979,75982],{},"1° ",[38,75722,75723,75724,2901],{},"Do bodu ",[883,75725,75727],{"className":75726},[886],[888,75728,75729],{"xmlns":890},[892,75730,75731,75739],{},[895,75732,75733],{},[2007,75734,75735,75737],{},[898,75736,1706],{},[1931,75738,1772],{},[902,75740,75741],{"encoding":904},"L_0",[883,75743,75745],{"className":75744},[886],[888,75746,75747],{"xmlns":890},[892,75748,75749,75759],{},[895,75750,75751,75753],{},[898,75752,2005],{},[2007,75754,75755,75757],{},[898,75756,1677],{},[898,75758,1706],{},[902,75760,10228],{"encoding":904}," roste, tj. ",[883,75763,75765],{"className":75764},[886],[888,75766,75767],{"xmlns":890},[892,75768,75769,75809],{},[895,75770,75771,75773,75775,75781,75787,75789,75799,75801,75803,75805,75807],{},[1700,75772,1703],{"stretchy":1702},[898,75774,2005],{},[2007,75776,75777,75779],{},[898,75778,1677],{},[898,75780,1706],{},[1785,75782,75783,75785],{},[1700,75784,1709],{"stretchy":1702},[1700,75786,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,75788,1765],{},[1785,75790,75791,75793],{},[898,75792,1662],{},[895,75794,75795,75797],{},[1700,75796,1793],{"mathvariant":1791},[1700,75798,1793],{"mathvariant":1791},[1700,75800,1703],{"stretchy":1702},[898,75802,1706],{},[1700,75804,1709],{"stretchy":1702},[1700,75806,3601],{},[1931,75808,1772],{},[902,75810,75811],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,75814,37849],{},".\n2° ",[38,75817,75818,75819,2901],{},"Od bodu ",[883,75820,75822],{"className":75821},[886],[888,75823,75824],{"xmlns":890},[892,75825,75826,75834],{},[895,75827,75828],{},[2007,75829,75830,75832],{},[898,75831,1706],{},[1931,75833,1772],{},[902,75835,75741],{"encoding":904},[883,75837,75839],{"className":75838},[886],[888,75840,75841],{"xmlns":890},[892,75842,75843,75853],{},[895,75844,75845,75847],{},[898,75846,2005],{},[2007,75848,75849,75851],{},[898,75850,1677],{},[898,75852,1706],{},[902,75854,10228],{"encoding":904}," klesá, ",[883,75857,75859],{"className":75858},[886],[888,75860,75861],{"xmlns":890},[892,75862,75863,75885],{},[895,75864,75865,75875,75877,75879,75881,75883],{},[1785,75866,75867,75869],{},[898,75868,1662],{},[895,75870,75871,75873],{},[1700,75872,1793],{"mathvariant":1791},[1700,75874,1793],{"mathvariant":1791},[1700,75876,1703],{"stretchy":1702},[898,75878,1706],{},[1700,75880,1709],{"stretchy":1702},[1700,75882,3640],{},[1931,75884,1772],{},[902,75886,75887],{"encoding":904},"Q''(L) \u003C 0",[38,75889,38673],{},[883,75891,75893],{"className":75892},[886],[888,75894,75895],{"xmlns":890},[892,75896,75897,75907],{},[895,75898,75899,75901],{},[898,75900,2005],{},[2007,75902,75903,75905],{},[898,75904,1677],{},[898,75906,1706],{},[902,75908,10228],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,75911,75913],{"className":75912},[886],[888,75914,75915],{"xmlns":890},[892,75916,75917,75925],{},[895,75918,75919],{},[2007,75920,75921,75923],{},[898,75922,1706],{},[1931,75924,1933],{},[902,75926,13397],{"encoding":904},[883,75928,75930],{"className":75929},[886],[888,75931,75932],{"xmlns":890},[892,75933,75934,75958],{},[895,75935,75936,75938,75944,75946,75952,75954,75956],{},[898,75937,2005],{},[2007,75939,75940,75942],{},[898,75941,1677],{},[898,75943,1706],{},[1700,75945,1703],{"stretchy":1702},[2007,75947,75948,75950],{},[898,75949,1706],{},[1931,75951,1933],{},[1700,75953,1709],{"stretchy":1702},[1700,75955,1765],{},[1931,75957,1772],{},[902,75959,75960],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,75963,75965],{"className":75964},[886],[888,75966,75967],{"xmlns":890},[892,75968,75969,75977],{},[895,75970,75971],{},[2007,75972,75973,75975],{},[898,75974,1706],{},[1931,75976,1772],{},[902,75978,75741],{"encoding":904},[38,75980,75981],{},"inflexním bodem"," produkční funkce.",[724,75984,75985,75986,10577,76003,2196],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,75987,75989],{"className":75988},[886],[888,75990,75991],{"xmlns":890},[892,75992,75993,76001],{},[895,75994,75995],{},[2007,75996,75997,75999],{},[898,75998,1706],{},[1931,76000,1772],{},[902,76002,75741],{"encoding":904},[883,76004,76006],{"className":76005},[886],[888,76007,76008],{"xmlns":890},[892,76009,76010,76032],{},[895,76011,76012,76022,76024,76026,76028,76030],{},[1785,76013,76014,76016],{},[898,76015,1662],{},[895,76017,76018,76020],{},[1700,76019,1793],{"mathvariant":1791},[1700,76021,1793],{"mathvariant":1791},[1700,76023,1703],{"stretchy":1702},[898,76025,1706],{},[1700,76027,1709],{"stretchy":1702},[1700,76029,3640],{},[1931,76031,1772],{},[902,76033,75887],{"encoding":904},[724,76035,76036,2106,76039,5857,76079,1343,76096,76113],{},[38,76037,76038],{},"Typický polynom třetího stupně:",[883,76040,76042],{"className":76041},[886],[888,76043,76044],{"xmlns":890},[892,76045,76046,76076],{},[895,76047,76048,76050,76052,76054,76056,76058,76060,76066,76068,76070],{},[898,76049,1662],{},[1700,76051,1703],{"stretchy":1702},[898,76053,1706],{},[1700,76055,1709],{"stretchy":1702},[1700,76057,1765],{},[898,76059,207],{},[1785,76061,76062,76064],{},[898,76063,1706],{},[1931,76065,2385],{},[1700,76067,1897],{},[898,76069,1879],{},[1785,76071,76072,76074],{},[898,76073,1706],{},[1931,76075,2343],{},[902,76077,76078],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,76080,76082],{"className":76081},[886],[888,76083,76084],{"xmlns":890},[892,76085,76086,76094],{},[895,76087,76088,76090,76092],{},[898,76089,207],{},[1700,76091,3640],{},[1931,76093,1772],{},[902,76095,43270],{"encoding":904},[883,76097,76099],{"className":76098},[886],[888,76100,76101],{"xmlns":890},[892,76102,76103,76111],{},[895,76104,76105,76107,76109],{},[898,76106,1879],{},[1700,76108,3601],{},[1931,76110,1772],{},[902,76112,18999],{"encoding":904},". Pak",[883,76115,76117],{"className":76116},[886],[888,76118,76119],{"xmlns":890,"display":28251},[892,76120,76121,76181],{},[895,76122,76123,76129,76131,76133,76141,76149,76151,76153,76159,76161,76163,76171,76179],{},[2007,76124,76125,76127],{},[898,76126,1706],{},[1931,76128,1772],{},[1700,76130,1765],{},[1700,76132,1768],{},[1770,76134,76135],{"scriptlevel":1772,"displaystyle":1702},[1774,76136,76137,76139],{},[1931,76138,1933],{},[1931,76140,2385],{},[1770,76142,76143],{"scriptlevel":1772,"displaystyle":1702},[1774,76144,76145,76147],{},[898,76146,1879],{},[898,76148,207],{},[1700,76150,1732],{"separator":1731},[6066,76152],{"width":6068},[2007,76154,76155,76157],{},[898,76156,1706],{},[1931,76158,1933],{},[1700,76160,1765],{},[1700,76162,1768],{},[1770,76164,76165],{"scriptlevel":1772,"displaystyle":1702},[1774,76166,76167,76169],{},[1931,76168,2343],{},[1931,76170,2385],{},[1770,76172,76173],{"scriptlevel":1772,"displaystyle":1702},[1774,76174,76175,76177],{},[898,76176,1879],{},[898,76178,207],{},[898,76180,2196],{"mathvariant":1791},[902,76182,76183],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,76185,76187,76188,1709],{"id":76186},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,76189,76191],{"className":76190},[886],[888,76192,76193],{"xmlns":890},[892,76194,76195,76205],{},[895,76196,76197,76199],{},[898,76198,1862],{},[2007,76200,76201,76203],{},[898,76202,1677],{},[898,76204,1706],{},[902,76206,74817],{"encoding":904},[724,76208,76209,10208,76212,75280,76215,76234],{},[38,76210,76211],{},"Průměrný produkt práce",[614,76213,76214],{},"average product of labour",[883,76216,76218],{"className":76217},[886],[888,76219,76220],{"xmlns":890},[892,76221,76222,76232],{},[895,76223,76224,76226],{},[898,76225,1862],{},[2007,76227,76228,76230],{},[898,76229,1677],{},[898,76231,1706],{},[902,76233,74817],{"encoding":904}," je podíl produkce a práce:",[883,76236,76238],{"className":76237},[886],[888,76239,76240],{"xmlns":890,"display":28251},[892,76241,76242,76277],{},[20939,76243,76244],{"width":28256},[20944,76245,76246,76248,76270,76272],{},[20947,76247],{"width":28261},[20947,76249,76250],{},[895,76251,76252,76254,76260,76262,76268],{},[898,76253,1862],{},[2007,76255,76256,76258],{},[898,76257,1677],{},[898,76259,1706],{},[1700,76261,1765],{},[1774,76263,76264,76266],{},[898,76265,1662],{},[898,76267,1706],{},[898,76269,2196],{"mathvariant":1791},[20947,76271],{"width":28261},[20947,76273,76274],{},[1781,76275,76276],{},"(5.4)",[902,76278,76279],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,76281,76282,76283,2196],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,76284,76286],{"className":76285},[886],[888,76287,76288],{"xmlns":890},[892,76289,76290,76300],{},[895,76291,76292,76294],{},[898,76293,1862],{},[2007,76295,76296,76298],{},[898,76297,1677],{},[898,76299,1706],{},[902,76301,74817],{"encoding":904},[115,76303,76305],{"id":76304},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,76307,76308],{},[2756,76309],{"alt":76310,"className":76311,"src":76312},"imek-q-mpl-apl-tripanel",[210,2760],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[4060,76314,76315],{},[724,76316,76317,76320,76321,2821,76340,76357,76358],{},[38,76318,76319],{},"Princip:"," Má-li ",[883,76322,76324],{"className":76323},[886],[888,76325,76326],{"xmlns":890},[892,76327,76328,76338],{},[895,76329,76330,76332],{},[898,76331,1862],{},[2007,76333,76334,76336],{},[898,76335,1677],{},[898,76337,1706],{},[902,76339,74817],{"encoding":904},[883,76341,76343],{"className":76342},[886],[888,76344,76345],{"xmlns":890},[892,76346,76347,76355],{},[895,76348,76349],{},[2007,76350,76351,76353],{},[898,76352,1706],{},[1931,76354,1772],{},[902,76356,75741],{"encoding":904}," maximum, pak platí\n",[883,76359,76361],{"className":76360,"title":4391,"style":4392},[4390],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,76363,76364,76365,76368,76369,2106,76373,2196],{},"Slovně: ",[38,76366,76367],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,76370,76372],{"className":76371,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,76374,76376],{"className":76375},[886],[888,76377,76378],{"xmlns":890},[892,76379,76380,76386],{},[895,76381,76382,76384],{},[898,76383,1862],{},[898,76385,2974],{},[902,76387,55744],{"encoding":904},[4060,76389,76390,76414],{},[724,76391,76392,76394,76395],{},[883,76393,4761],{}," Postup — jak najít max ",[883,76396,76398],{"className":76397},[886],[888,76399,76400],{"xmlns":890},[892,76401,76402,76412],{},[895,76403,76404,76406],{},[898,76405,1862],{},[2007,76407,76408,76410],{},[898,76409,1677],{},[898,76411,1706],{},[902,76413,74817],{"encoding":904},[152,76415,76416,76454,76536],{},[123,76417,76418,76419,76453],{},"Napište ",[883,76420,76422],{"className":76421},[886],[888,76423,76424],{"xmlns":890},[892,76425,76426,76450],{},[895,76427,76428,76430,76436,76438,76440,76442,76444,76446,76448],{},[898,76429,1862],{},[2007,76431,76432,76434],{},[898,76433,1677],{},[898,76435,1706],{},[1700,76437,1765],{},[898,76439,1662],{},[1700,76441,1703],{"stretchy":1702},[898,76443,1706],{},[1700,76445,1709],{"stretchy":1702},[898,76447,1979],{"mathvariant":1791},[898,76449,1706],{},[902,76451,76452],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,76455,76456,76457,76489,76490,76493,76494,2196],{},"Položte ",[883,76458,76460],{"className":76459},[886],[888,76461,76462],{"xmlns":890},[892,76463,76464,76486],{},[895,76465,76466,76468,76470,76476,76482,76484],{},[1700,76467,1703],{"stretchy":1702},[898,76469,1862],{},[2007,76471,76472,76474],{},[898,76473,1677],{},[898,76475,1706],{},[1785,76477,76478,76480],{},[1700,76479,1709],{"stretchy":1702},[1700,76481,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,76483,1765],{},[1931,76485,1772],{},[902,76487,76488],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,76491,76492],{},"Zkratka:"," můžete rovnou řešit ",[883,76495,76497],{"className":76496},[886],[888,76498,76499],{"xmlns":890},[892,76500,76501,76533],{},[895,76502,76503,76505,76511,76513,76515,76517,76519,76521,76527,76529,76531],{},[898,76504,2005],{},[2007,76506,76507,76509],{},[898,76508,1677],{},[898,76510,1706],{},[1700,76512,1703],{"stretchy":1702},[898,76514,1706],{},[1700,76516,1709],{"stretchy":1702},[1700,76518,1765],{},[898,76520,1862],{},[2007,76522,76523,76525],{},[898,76524,1677],{},[898,76526,1706],{},[1700,76528,1703],{"stretchy":1702},[898,76530,1706],{},[1700,76532,1709],{"stretchy":1702},[902,76534,76535],{"encoding":904},"MP_L(L) = AP_L(L)",[123,76537,76538],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,76540,65685],{"id":76541},"odvození",[724,76543,76544,76545,76578],{},"Z ",[883,76546,76548],{"className":76547},[886],[888,76549,76550],{"xmlns":890},[892,76551,76552,76576],{},[895,76553,76554,76556,76562,76564,76566,76568,76570,76572,76574],{},[898,76555,1862],{},[2007,76557,76558,76560],{},[898,76559,1677],{},[898,76561,1706],{},[1700,76563,1765],{},[898,76565,1662],{},[1700,76567,1703],{"stretchy":1702},[898,76569,1706],{},[1700,76571,1709],{"stretchy":1702},[898,76573,1979],{"mathvariant":1791},[898,76575,1706],{},[902,76577,76452],{"encoding":904}," a derivace podílu:",[883,76580,76582],{"className":76581},[886],[888,76583,76584],{"xmlns":890,"display":28251},[892,76585,76586,76739],{},[895,76587,76588,76590,76592,76598,76604,76606,76608,76610,76612,76652,76654,76660,76694,76696,76702,76705,76707,76713,76715,76717,76719,76721,76723,76729,76731,76733,76735,76737],{},[1700,76589,1703],{"stretchy":1702},[898,76591,1862],{},[2007,76593,76594,76596],{},[898,76595,1677],{},[898,76597,1706],{},[1785,76599,76600,76602],{},[1700,76601,1709],{"stretchy":1702},[1700,76603,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,76605,1703],{"stretchy":1702},[898,76607,1706],{},[1700,76609,1709],{"stretchy":1702},[1700,76611,1765],{},[1774,76613,76614,76646],{},[895,76615,76616,76622,76624,76626,76628,76630,76632,76634,76636,76638,76640,76642,76644],{},[1785,76617,76618,76620],{},[898,76619,1662],{},[1700,76621,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,76623,1703],{"stretchy":1702},[898,76625,1706],{},[1700,76627,1709],{"stretchy":1702},[1700,76629,2065],{},[898,76631,1706],{},[1700,76633,1768],{},[898,76635,1662],{},[1700,76637,1703],{"stretchy":1702},[898,76639,1706],{},[1700,76641,1709],{"stretchy":1702},[1700,76643,2065],{},[1931,76645,1933],{},[1785,76647,76648,76650],{},[898,76649,1706],{},[1931,76651,2343],{},[1700,76653,1765],{},[1774,76655,76656,76658],{},[1931,76657,1933],{},[898,76659,1706],{},[895,76661,76662,76664,76670,76672,76674,76676,76678,76692],{},[1700,76663,1703],{"fence":1731},[1785,76665,76666,76668],{},[898,76667,1662],{},[1700,76669,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,76671,1703],{"stretchy":1702},[898,76673,1706],{},[1700,76675,1709],{"stretchy":1702},[1700,76677,1768],{},[1774,76679,76680,76690],{},[895,76681,76682,76684,76686,76688],{},[898,76683,1662],{},[1700,76685,1703],{"stretchy":1702},[898,76687,1706],{},[1700,76689,1709],{"stretchy":1702},[898,76691,1706],{},[1700,76693,1709],{"fence":1731},[1700,76695,1765],{},[1774,76697,76698,76700],{},[1931,76699,1933],{},[898,76701,1706],{},[1700,76703,1703],{"fence":1731,"stretchy":1731,"minsize":76704,"maxsize":76704},"1.2em",[898,76706,2005],{},[2007,76708,76709,76711],{},[898,76710,1677],{},[898,76712,1706],{},[1700,76714,1703],{"stretchy":1702},[898,76716,1706],{},[1700,76718,1709],{"stretchy":1702},[1700,76720,1768],{},[898,76722,1862],{},[2007,76724,76725,76727],{},[898,76726,1677],{},[898,76728,1706],{},[1700,76730,1703],{"stretchy":1702},[898,76732,1706],{},[1700,76734,1709],{"stretchy":1702},[1700,76736,1709],{"fence":1731,"stretchy":1731,"minsize":76704,"maxsize":76704},[898,76738,2196],{"mathvariant":1791},[902,76740,76741],{"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).",[724,76743,9850,76744,8290,76766,76849],{},[883,76745,76747],{"className":76746},[886],[888,76748,76749],{"xmlns":890},[892,76750,76751,76763],{},[895,76752,76753,76759,76761],{},[2007,76754,76755,76757],{},[898,76756,1706],{},[1931,76758,1772],{},[1700,76760,3601],{},[1931,76762,1772],{},[902,76764,76765],{"encoding":904},"L_0 > 0",[883,76767,76769],{"className":76768},[886],[888,76770,76771],{"xmlns":890},[892,76772,76773,76846],{},[895,76774,76775,76777,76779,76785,76791,76793,76799,76801,76803,76805,76808,76810,76816,76818,76824,76826,76828,76830,76836,76838,76844],{},[1700,76776,1703],{"stretchy":1702},[898,76778,1862],{},[2007,76780,76781,76783],{},[898,76782,1677],{},[898,76784,1706],{},[1785,76786,76787,76789],{},[1700,76788,1709],{"stretchy":1702},[1700,76790,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,76792,1703],{"stretchy":1702},[2007,76794,76795,76797],{},[898,76796,1706],{},[1931,76798,1772],{},[1700,76800,1709],{"stretchy":1702},[1700,76802,1765],{},[1931,76804,1772],{},[1700,76806,76807],{},"⇔",[898,76809,2005],{},[2007,76811,76812,76814],{},[898,76813,1677],{},[898,76815,1706],{},[1700,76817,1703],{"stretchy":1702},[2007,76819,76820,76822],{},[898,76821,1706],{},[1931,76823,1772],{},[1700,76825,1709],{"stretchy":1702},[1700,76827,1765],{},[898,76829,1862],{},[2007,76831,76832,76834],{},[898,76833,1677],{},[898,76835,1706],{},[1700,76837,1703],{"stretchy":1702},[2007,76839,76840,76842],{},[898,76841,1706],{},[1931,76843,1772],{},[1700,76845,1709],{"stretchy":1702},[902,76847,76848],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,76851,76853],{"id":76852},"příklad-51","Příklad 5.1",[724,76855,76856,76857,2196],{},"Je dána produkce ",[883,76858,76860],{"className":76859},[886],[888,76861,76862],{"xmlns":890},[892,76863,76864,76888],{},[895,76865,76866,76868,76870,76872,76878,76880,76882],{},[898,76867,1662],{},[1700,76869,1765],{},[1931,76871,2445],{},[1785,76873,76874,76876],{},[898,76875,1706],{},[1931,76877,2343],{},[1700,76879,1768],{},[1931,76881,3034],{},[1785,76883,76884,76886],{},[898,76885,1706],{},[1931,76887,2385],{},[902,76889,76890],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,76892,76893,57706,76896,76946,76947,2196],{},[38,76894,76895],{},"(a)",[883,76897,76899],{"className":76898},[886],[888,76900,76901],{"xmlns":890},[892,76902,76903,76943],{},[895,76904,76905,76907,76909,76911,76913,76915,76917,76919,76921,76923,76925,76927,76929,76931,76933,76935,76937,76939,76941],{},[898,76906,1706],{},[1700,76908,1765],{},[1931,76910,2343],{},[1700,76912,1732],{"separator":1731},[1931,76914,2438],{},[1700,76916,1732],{"separator":1731},[1931,76918,5773],{},[1700,76920,1732],{"separator":1731},[1931,76922,3058],{},[1700,76924,1732],{"separator":1731},[1931,76926,23131],{},[1700,76928,1732],{"separator":1731},[1931,76930,3900],{},[1700,76932,1732],{"separator":1731},[1931,76934,9223],{},[1700,76936,1732],{"separator":1731},[1931,76938,38531],{},[1700,76940,1732],{"separator":1731},[1931,76942,5192],{},[902,76944,76945],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,76948,76950],{"className":76949},[886],[888,76951,76952],{"xmlns":890},[892,76953,76954,76964],{},[895,76955,76956,76958],{},[898,76957,2005],{},[2007,76959,76960,76962],{},[898,76961,1677],{},[898,76963,1706],{},[902,76965,10228],{"encoding":904},[724,76967,76968,76969,35153],{},"Podle (5.2): ",[883,76970,76972],{"className":76971},[886],[888,76973,76974],{"xmlns":890},[892,76975,76976,77032],{},[895,76977,76978,76980,76986,76988,76994,76996,76998,77000,77002,77004,77006,77008,77010,77016,77018,77020,77022,77024,77026,77028,77030],{},[898,76979,2005],{},[2007,76981,76982,76984],{},[898,76983,1677],{},[898,76985,1706],{},[1700,76987,1765],{},[1785,76989,76990,76992],{},[898,76991,1662],{},[1700,76993,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,76995,1703],{"stretchy":1702},[898,76997,1706],{},[1700,76999,1709],{"stretchy":1702},[1700,77001,1765],{},[1931,77003,3702],{},[898,77005,1706],{},[1700,77007,1768],{},[1931,77009,19506],{},[1785,77011,77012,77014],{},[898,77013,1706],{},[1931,77015,2343],{},[1700,77017,1765],{},[898,77019,1706],{},[1700,77021,1703],{"stretchy":1702},[1931,77023,3702],{},[1700,77025,1768],{},[1931,77027,19506],{},[898,77029,1706],{},[1700,77031,1709],{"stretchy":1702},[902,77033,77034],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,77036,77037,77074],{},[19,77038,77039],{},[22,77040,77041,77056,77058,77060,77062,77064,77066,77068,77070,77072],{},[25,77042,77043],{},[883,77044,77046],{"className":77045},[886],[888,77047,77048],{"xmlns":890},[892,77049,77050,77054],{},[895,77051,77052],{},[898,77053,1706],{},[902,77055,1706],{"encoding":904},[25,77057,2343],{},[25,77059,2438],{},[25,77061,5773],{},[25,77063,3058],{},[25,77065,23131],{},[25,77067,3900],{},[25,77069,9223],{},[25,77071,38531],{},[25,77073,5192],{},[30,77075,77076],{},[22,77077,77078,77099,77102,77105,77108,77110,77113,77115,77117,77136],{},[35,77079,77080],{},[883,77081,77083],{"className":77082},[886],[888,77084,77085],{"xmlns":890},[892,77086,77087,77097],{},[895,77088,77089,77091],{},[898,77090,2005],{},[2007,77092,77093,77095],{},[898,77094,1677],{},[898,77096,1706],{},[902,77098,10228],{"encoding":904},[35,77100,77101],{},"21,6",[35,77103,77104],{},"45",[35,77106,77107],{},"57,6",[35,77109,3320],{},[35,77111,77112],{},"50,4",[35,77114,77101],{},[35,77116,1772],{},[35,77118,77119],{},[883,77120,77122],{"className":77121},[886],[888,77123,77124],{"xmlns":890},[892,77125,77126,77133],{},[895,77127,77128,77130],{},[1700,77129,1768],{},[1931,77131,77132],{},"12,6",[902,77134,77135],{"encoding":904},"-12{,}6",[35,77137,77138],{},[883,77139,77141],{"className":77140},[886],[888,77142,77143],{"xmlns":890},[892,77144,77145,77151],{},[895,77146,77147,77149],{},[1700,77148,1768],{},[1931,77150,45637],{},[902,77152,77153],{"encoding":904},"-75",[724,77155,77156,77175,77176,77194,77195,77212,77213,77231,77232,77256,77257,77275],{},[883,77157,77159],{"className":77158},[886],[888,77160,77161],{"xmlns":890},[892,77162,77163,77173],{},[895,77164,77165,77167],{},[898,77166,2005],{},[2007,77168,77169,77171],{},[898,77170,1677],{},[898,77172,1706],{},[902,77174,10228],{"encoding":904}," nabývá maxima pro ",[883,77177,77179],{"className":77178},[886],[888,77180,77181],{"xmlns":890},[892,77182,77183,77191],{},[895,77184,77185,77187,77189],{},[898,77186,1706],{},[1700,77188,1765],{},[1931,77190,3058],{},[902,77192,77193],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,77196,77198],{"className":77197},[886],[888,77199,77200],{"xmlns":890},[892,77201,77202,77210],{},[895,77203,77204,77206,77208],{},[898,77205,1706],{},[1700,77207,1765],{},[1931,77209,3058],{},[902,77211,77193],{"encoding":904}," přírůstky klesají, v ",[883,77214,77216],{"className":77215},[886],[888,77217,77218],{"xmlns":890},[892,77219,77220,77228],{},[895,77221,77222,77224,77226],{},[898,77223,1706],{},[1700,77225,1765],{},[1931,77227,9223],{},[902,77229,77230],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,77233,77235],{"className":77234},[886],[888,77236,77237],{"xmlns":890},[892,77238,77239,77253],{},[895,77240,77241,77243,77245,77247,77249,77251],{},[898,77242,1662],{},[1700,77244,1703],{"stretchy":1702},[1931,77246,9223],{},[1700,77248,1709],{"stretchy":1702},[1700,77250,1765],{},[1931,77252,24043],{},[902,77254,77255],{"encoding":904},"Q(20) = 800","), od ",[883,77258,77260],{"className":77259},[886],[888,77261,77262],{"xmlns":890},[892,77263,77264,77272],{},[895,77265,77266,77268,77270],{},[898,77267,1706],{},[1700,77269,3601],{},[1931,77271,9223],{},[902,77273,77274],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,77277,77278],{},[614,77279,77280,77281,77321,77322,2821,77340,2196],{},"Obrázek 5.1 — graf produkce ",[883,77282,77284],{"className":77283},[886],[888,77285,77286],{"xmlns":890},[892,77287,77288,77318],{},[895,77289,77290,77292,77294,77296,77298,77300,77302,77308,77310,77312],{},[898,77291,1662],{},[1700,77293,1703],{"stretchy":1702},[898,77295,1706],{},[1700,77297,1709],{"stretchy":1702},[1700,77299,1765],{},[1931,77301,2445],{},[1785,77303,77304,77306],{},[898,77305,1706],{},[1931,77307,2343],{},[1700,77309,1768],{},[1931,77311,3034],{},[1785,77313,77314,77316],{},[898,77315,1706],{},[1931,77317,2385],{},[902,77319,77320],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,77323,77325],{"className":77324},[886],[888,77326,77327],{"xmlns":890},[892,77328,77329,77337],{},[895,77330,77331,77333,77335],{},[898,77332,1662],{},[1700,77334,1765],{},[1931,77336,24043],{},[902,77338,77339],{"encoding":904},"Q = 800",[883,77341,77343],{"className":77342},[886],[888,77344,77345],{"xmlns":890},[892,77346,77347,77355],{},[895,77348,77349,77351,77353],{},[898,77350,1706],{},[1700,77352,1765],{},[1931,77354,9223],{},[902,77356,77230],{"encoding":904},[724,77358,77359,77362],{},[38,77360,77361],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,77364,77365,77366,1343,77384,2901],{},"Podle (5.3) s ",[883,77367,77369],{"className":77368},[886],[888,77370,77371],{"xmlns":890},[892,77372,77373,77381],{},[895,77374,77375,77377,77379],{},[898,77376,1706],{},[1700,77378,1765],{},[1931,77380,2445],{},[902,77382,77383],{"encoding":904},"L = 6",[883,77385,77387],{"className":77386},[886],[888,77388,77389],{"xmlns":890},[892,77390,77391,77401],{},[895,77392,77393,77395,77397,77399],{},[898,77394,2406],{},[898,77396,1706],{},[1700,77398,1765],{},[1931,77400,2385],{},[902,77402,77403],{"encoding":904},"dL = 3",[883,77405,77407],{"className":77406},[886],[888,77408,77409],{"xmlns":890,"display":28251},[892,77410,77411,77474],{},[895,77412,77413,77415,77417,77419,77421,77427,77429,77431,77433,77435,77437,77439,77441,77443,77445,77447,77449,77451,77453,77455,77457,77459,77461,77463,77465,77467,77469,77471],{},[898,77414,2406],{},[898,77416,1662],{},[1700,77418,1765],{},[898,77420,2005],{},[2007,77422,77423,77425],{},[898,77424,1677],{},[898,77426,1706],{},[1700,77428,1703],{"stretchy":1702},[1931,77430,2445],{},[1700,77432,1709],{"stretchy":1702},[1700,77434,2065],{},[1931,77436,2385],{},[1700,77438,1765],{},[1700,77440,1703],{"stretchy":1702},[1931,77442,3702],{},[1700,77444,2065],{},[1931,77446,2445],{},[1700,77448,1768],{},[1931,77450,19506],{},[1700,77452,2065],{},[1931,77454,5753],{},[1700,77456,1709],{"stretchy":1702},[1700,77458,2065],{},[1931,77460,2385],{},[1700,77462,1765],{},[1931,77464,77112],{},[1700,77466,2065],{},[1931,77468,2385],{},[1700,77470,1765],{},[1931,77472,77473],{},"151,2.",[902,77475,77476],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,77478,77479,77480,57936,77505,77519,77520,2196],{},"Produkce vzroste z ",[883,77481,77483],{"className":77482},[886],[888,77484,77485],{"xmlns":890},[892,77486,77487,77502],{},[895,77488,77489,77491,77493,77495,77497,77499],{},[898,77490,1662],{},[1700,77492,1703],{"stretchy":1702},[1931,77494,2445],{},[1700,77496,1709],{"stretchy":1702},[1700,77498,1765],{},[1931,77500,77501],{},"172,8",[902,77503,77504],{"encoding":904},"Q(6) = 172{,}8",[883,77506,77508],{"className":77507},[886],[888,77509,77510],{"xmlns":890},[892,77511,77512,77517],{},[895,77513,77514],{},[1931,77515,77516],{},"324",[902,77518,77516],{"encoding":904},". Skutečná hodnota: ",[883,77521,77523],{"className":77522},[886],[888,77524,77525],{"xmlns":890},[892,77526,77527,77567],{},[895,77528,77529,77531,77533,77535,77537,77539,77541,77543,77545,77547,77549,77551,77553,77555,77558,77560,77562,77564],{},[898,77530,3084],{"mathvariant":1791},[898,77532,1662],{},[1700,77534,1765],{},[898,77536,1662],{},[1700,77538,1703],{"stretchy":1702},[1931,77540,4190],{},[1700,77542,1709],{"stretchy":1702},[1700,77544,1768],{},[898,77546,1662],{},[1700,77548,1703],{"stretchy":1702},[1931,77550,2445],{},[1700,77552,1709],{"stretchy":1702},[1700,77554,1765],{},[1931,77556,77557],{},"340,2",[1700,77559,1768],{},[1931,77561,77501],{},[1700,77563,1765],{},[1931,77565,77566],{},"167,4",[902,77568,77569],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,77571,77573],{"id":77572},"příklad-52","Příklad 5.2",[724,77575,77576,77577,2196],{},"Ověříme princip (5.5) pro ",[883,77578,77580],{"className":77579},[886],[888,77581,77582],{"xmlns":890},[892,77583,77584,77608],{},[895,77585,77586,77588,77590,77592,77598,77600,77602],{},[898,77587,1662],{},[1700,77589,1765],{},[1931,77591,2445],{},[1785,77593,77594,77596],{},[898,77595,1706],{},[1931,77597,2343],{},[1700,77599,1768],{},[1931,77601,3034],{},[1785,77603,77604,77606],{},[898,77605,1706],{},[1931,77607,2385],{},[902,77609,76890],{"encoding":904},[883,77611,77613],{"className":77612},[886],[888,77614,77615],{"xmlns":890,"display":28251},[892,77616,77617,77695],{},[895,77618,77619,77621,77627,77629,77635,77637,77639,77641,77643,77645,77651,77653,77655,77657,77665,77667,77669,77671,77673,77675,77677,77679,77681,77683,77685,77691,77693],{},[898,77620,1862],{},[2007,77622,77623,77625],{},[898,77624,1677],{},[898,77626,1706],{},[1700,77628,1765],{},[1774,77630,77631,77633],{},[898,77632,1662],{},[898,77634,1706],{},[1700,77636,1765],{},[1931,77638,2445],{},[898,77640,1706],{},[1700,77642,1768],{},[1931,77644,3034],{},[1785,77646,77647,77649],{},[898,77648,1706],{},[1931,77650,2343],{},[1700,77652,1732],{"separator":1731},[6066,77654],{"width":15469},[898,77656,1862],{},[2030,77658,77659,77661,77663],{},[898,77660,1677],{},[898,77662,1706],{},[1700,77664,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,77666,1765],{},[1931,77668,2445],{},[1700,77670,1768],{},[1931,77672,19456],{},[898,77674,1706],{},[1700,77676,1765],{},[1931,77678,1772],{},[1781,77680,4175],{},[1700,77682,4178],{},[1781,77684,4175],{},[2007,77686,77687,77689],{},[898,77688,1706],{},[1931,77690,1772],{},[1700,77692,1765],{},[1931,77694,68467],{},[902,77696,77697],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,77699,77700,77736,77737,77755,77756,2196],{},[883,77701,77703],{"className":77702},[886],[888,77704,77705],{"xmlns":890},[892,77706,77707,77733],{},[895,77708,77709,77711,77723,77725,77727,77729,77731],{},[898,77710,1862],{},[2030,77712,77713,77715,77717],{},[898,77714,1677],{},[898,77716,1706],{},[895,77718,77719,77721],{},[1700,77720,1793],{"mathvariant":1791},[1700,77722,1793],{"mathvariant":1791},[1700,77724,1765],{},[1700,77726,1768],{},[1931,77728,19456],{},[1700,77730,3640],{},[1931,77732,1772],{},[902,77734,77735],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,77738,77740],{"className":77739},[886],[888,77741,77742],{"xmlns":890},[892,77743,77744,77752],{},[895,77745,77746,77748,77750],{},[898,77747,1706],{},[1700,77749,1765],{},[1931,77751,36429],{},[902,77753,77754],{"encoding":904},"L = 15"," je maximum, ",[883,77757,77759],{"className":77758},[886],[888,77760,77761],{"xmlns":890},[892,77762,77763,77809],{},[895,77764,77765,77767,77773,77775,77777,77779,77781,77783,77785,77787,77789,77791,77793,77796,77798,77801,77803,77805,77807],{},[898,77766,1862],{},[2007,77768,77769,77771],{},[898,77770,1677],{},[898,77772,1706],{},[1700,77774,1703],{"stretchy":1702},[1931,77776,36429],{},[1700,77778,1709],{"stretchy":1702},[1700,77780,1765],{},[1931,77782,2445],{},[1700,77784,2065],{},[1931,77786,36429],{},[1700,77788,1768],{},[1931,77790,3034],{},[1700,77792,2065],{},[1931,77794,77795],{},"225",[1700,77797,1765],{},[1931,77799,77800],{},"90",[1700,77802,1768],{},[1931,77804,77104],{},[1700,77806,1765],{},[1931,77808,77104],{},[902,77810,77811],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,77813,77814,42065,77870,77916],{},[883,77815,77817],{"className":77816},[886],[888,77818,77819],{"xmlns":890},[892,77820,77821,77867],{},[895,77822,77823,77825,77831,77833,77835,77837,77839,77841,77843,77845,77847,77849,77851,77853,77855,77858,77860,77863,77865],{},[898,77824,2005],{},[2007,77826,77827,77829],{},[898,77828,1677],{},[898,77830,1706],{},[1700,77832,1703],{"stretchy":1702},[1931,77834,36429],{},[1700,77836,1709],{"stretchy":1702},[1700,77838,1765],{},[1931,77840,3702],{},[1700,77842,2065],{},[1931,77844,36429],{},[1700,77846,1768],{},[1931,77848,19506],{},[1700,77850,2065],{},[1931,77852,77795],{},[1700,77854,1765],{},[1931,77856,77857],{},"180",[1700,77859,1768],{},[1931,77861,77862],{},"135",[1700,77864,1765],{},[1931,77866,77104],{},[902,77868,77869],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,77871,77873],{"className":77872},[886],[888,77874,77875],{"xmlns":890},[892,77876,77877,77913],{},[895,77878,77879,77881,77887,77889,77891,77893,77895,77897,77903,77905,77907,77909,77911],{},[898,77880,2005],{},[2007,77882,77883,77885],{},[898,77884,1677],{},[898,77886,1706],{},[1700,77888,1703],{"stretchy":1702},[1931,77890,36429],{},[1700,77892,1709],{"stretchy":1702},[1700,77894,1765],{},[898,77896,1862],{},[2007,77898,77899,77901],{},[898,77900,1677],{},[898,77902,1706],{},[1700,77904,1703],{"stretchy":1702},[1931,77906,36429],{},[1700,77908,1709],{"stretchy":1702},[1700,77910,1765],{},[1931,77912,77104],{},[902,77914,77915],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,77918,77919,77922,77923,17761,77952,2196],{},[38,77920,77921],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,77924,77926],{"className":77925},[886],[888,77927,77928],{"xmlns":890},[892,77929,77930,77950],{},[895,77931,77932,77934,77940,77942,77944],{},[898,77933,2005],{},[2007,77935,77936,77938],{},[898,77937,1677],{},[898,77939,1706],{},[1700,77941,1765],{},[898,77943,1862],{},[2007,77945,77946,77948],{},[898,77947,1677],{},[898,77949,1706],{},[902,77951,74847],{"encoding":904},[883,77953,77955],{"className":77954},[886],[888,77956,77957],{"xmlns":890},[892,77958,77959,77999],{},[895,77960,77961,77963,77965,77967,77969,77975,77977,77979,77981,77983,77985,77991,77993,77995,77997],{},[1931,77962,3702],{},[898,77964,1706],{},[1700,77966,1768],{},[1931,77968,19506],{},[1785,77970,77971,77973],{},[898,77972,1706],{},[1931,77974,2343],{},[1700,77976,1765],{},[1931,77978,2445],{},[898,77980,1706],{},[1700,77982,1768],{},[1931,77984,3034],{},[1785,77986,77987,77989],{},[898,77988,1706],{},[1931,77990,2343],{},[1700,77992,4178],{},[898,77994,1706],{},[1700,77996,1765],{},[1931,77998,36429],{},[902,78000,78001],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,78003,78004],{},[614,78005,78006,78007,78026,78027,12313,78045,78064,78065,78083,78084,78101,78102,78121,78122,78141],{},"Obrázek 5.3 — křivky ",[883,78008,78010],{"className":78009},[886],[888,78011,78012],{"xmlns":890},[892,78013,78014,78024],{},[895,78015,78016,78018],{},[898,78017,2005],{},[2007,78019,78020,78022],{},[898,78021,1677],{},[898,78023,1706],{},[902,78025,10228],{"encoding":904}," (max 60 při ",[883,78028,78030],{"className":78029},[886],[888,78031,78032],{"xmlns":890},[892,78033,78034,78042],{},[895,78035,78036,78038,78040],{},[898,78037,1706],{},[1700,78039,1765],{},[1931,78041,3058],{},[902,78043,78044],{"encoding":904},"L=10",[883,78046,78048],{"className":78047},[886],[888,78049,78050],{"xmlns":890},[892,78051,78052,78062],{},[895,78053,78054,78056],{},[898,78055,1862],{},[2007,78057,78058,78060],{},[898,78059,1677],{},[898,78061,1706],{},[902,78063,74817],{"encoding":904}," (max 45 při ",[883,78066,78068],{"className":78067},[886],[888,78069,78070],{"xmlns":890},[892,78071,78072,78080],{},[895,78073,78074,78076,78078],{},[898,78075,1706],{},[1700,78077,1765],{},[1931,78079,36429],{},[902,78081,78082],{"encoding":904},"L=15","), průsečík v ",[883,78085,78087],{"className":78086},[886],[888,78088,78089],{"xmlns":890},[892,78090,78091,78099],{},[895,78092,78093,78095,78097],{},[898,78094,1706],{},[1700,78096,1765],{},[1931,78098,36429],{},[902,78100,77754],{"encoding":904},". Nalevo od 15 leží ",[883,78103,78105],{"className":78104},[886],[888,78106,78107],{"xmlns":890},[892,78108,78109,78119],{},[895,78110,78111,78113],{},[898,78112,2005],{},[2007,78114,78115,78117],{},[898,78116,1677],{},[898,78118,1706],{},[902,78120,10228],{"encoding":904}," nad ",[883,78123,78125],{"className":78124},[886],[888,78126,78127],{"xmlns":890},[892,78128,78129,78139],{},[895,78130,78131,78133],{},[898,78132,1862],{},[2007,78134,78135,78137],{},[898,78136,1677],{},[898,78138,1706],{},[902,78140,74817],{"encoding":904},", napravo pod ní.",[115,78143,78145],{"id":78144},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,78147,78148,78149,2882,78162,2106,78165,6378,78178,2106,78181,2901],{},"V dvoufaktorovém modelu závisí produkce ",[883,78150,78152],{"className":78151},[886],[888,78153,78154],{"xmlns":890},[892,78155,78156,78160],{},[895,78157,78158],{},[898,78159,1662],{},[902,78161,1662],{"encoding":904},[38,78163,78164],{},"práci",[883,78166,78168],{"className":78167},[886],[888,78169,78170],{"xmlns":890},[892,78171,78172,78176],{},[895,78173,78174],{},[898,78175,1706],{},[902,78177,1706],{"encoding":904},[38,78179,78180],{},"kapitálu",[883,78182,78184],{"className":78183},[886],[888,78185,78186],{"xmlns":890},[892,78187,78188,78192],{},[895,78189,78190],{},[898,78191,1735],{},[902,78193,1735],{"encoding":904},[883,78195,78197],{"className":78196},[886],[888,78198,78199],{"xmlns":890,"display":28251},[892,78200,78201,78236],{},[20939,78202,78203],{"width":28256},[20944,78204,78205,78207,78229,78231],{},[20947,78206],{"width":28261},[20947,78208,78209],{},[895,78210,78211,78213,78215,78217,78219,78221,78223,78225,78227],{},[898,78212,1662],{},[1700,78214,1765],{},[898,78216,1662],{},[1700,78218,1703],{"stretchy":1702},[898,78220,1706],{},[1700,78222,1732],{"separator":1731},[898,78224,1735],{},[1700,78226,1709],{"stretchy":1702},[898,78228,2196],{"mathvariant":1791},[20947,78230],{"width":28261},[20947,78232,78233],{},[1781,78234,78235],{},"(5.6)",[902,78237,78238],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,78240,78241,78242,78244],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,78243,75183],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,78246,78248],{"id":78247},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,78250,78251],{},"Široce používané produkční funkce mají tvar",[883,78253,78255],{"className":78254},[886],[888,78256,78257],{"xmlns":890,"display":28251},[892,78258,78259,78300],{},[20939,78260,78261],{"width":28256},[20944,78262,78263,78265,78293,78295],{},[20947,78264],{"width":28261},[20947,78266,78267],{},[895,78268,78269,78271,78273,78275,78277,78283,78285,78291],{},[898,78270,1662],{},[1700,78272,1765],{},[898,78274,1862],{},[1781,78276,1783],{},[1785,78278,78279,78281],{},[898,78280,1706],{},[898,78282,207],{},[1781,78284,1783],{},[1785,78286,78287,78289],{},[898,78288,1735],{},[898,78290,1879],{},[1700,78292,1732],{"separator":1731},[20947,78294],{"width":28261},[20947,78296,78297],{},[1781,78298,78299],{},"(5.7)",[902,78301,78302],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,78304,4499,78305,78327,78328,78330,78331,2196],{},[883,78306,78308],{"className":78307},[886],[888,78309,78310],{"xmlns":890},[892,78311,78312,78324],{},[895,78313,78314,78316,78318,78320,78322],{},[898,78315,1862],{},[1700,78317,1732],{"separator":1731},[898,78319,207],{},[1700,78321,1732],{"separator":1731},[898,78323,1879],{},[902,78325,78326],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,78329,74883],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,78332,78334],{"className":78333},[886],[888,78335,78336],{"xmlns":890},[892,78337,78338,78350],{},[895,78339,78340,78342,78344,78346,78348],{},[898,78341,207],{},[1700,78343,1732],{"separator":1731},[898,78345,1879],{},[1700,78347,3640],{},[1931,78349,1933],{},[902,78351,78352],{"encoding":904},"a, b \u003C 1",[724,78354,78355],{},[2756,78356],{"alt":78357,"className":78358,"src":78359},"imek-vynosy-z-rozsahu-3typy",[210,2760],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,78361,78362,78363,78366,78367,2882,78380,78396,78397,2882,78410,2901],{},"Reflektují ekonomickou zákonitost, že ",[38,78364,78365],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,78368,78370],{"className":78369},[886],[888,78371,78372],{"xmlns":890},[892,78373,78374,78378],{},[895,78375,78376],{},[898,78377,1706],{},[902,78379,1706],{"encoding":904},[883,78381,78383],{"className":78382},[886],[888,78384,78385],{"xmlns":890},[892,78386,78387,78393],{},[895,78388,78389,78391],{},[898,78390,12226],{},[898,78392,1706],{},[902,78394,78395],{"encoding":904},"rL"," a kapitál z ",[883,78398,78400],{"className":78399},[886],[888,78401,78402],{"xmlns":890},[892,78403,78404,78408],{},[895,78405,78406],{},[898,78407,1735],{},[902,78409,1735],{"encoding":904},[883,78411,78413],{"className":78412},[886],[888,78414,78415],{"xmlns":890},[892,78416,78417,78423],{},[895,78418,78419,78421],{},[898,78420,12226],{},[898,78422,1735],{},[902,78424,78425],{"encoding":904},"rK",[883,78427,78429],{"className":78428},[886],[888,78430,78431],{"xmlns":890,"display":28251},[892,78432,78433,78556],{},[20939,78434,78435],{"width":28256},[20944,78436,78437,78439,78549,78551],{},[20947,78438],{"width":28261},[20947,78440,78441],{},[895,78442,78443,78445,78447,78449,78451,78453,78455,78457,78459,78461,78463,78465,78467,78469,78475,78477,78479,78481,78487,78489,78491,78493,78505,78507,78513,78519,78521,78533,78535,78537,78539,78541,78543,78545,78547],{},[898,78444,1662],{},[1700,78446,1703],{"stretchy":1702},[898,78448,12226],{},[898,78450,1706],{},[1700,78452,1732],{"separator":1731},[898,78454,12226],{},[898,78456,1735],{},[1700,78458,1709],{"stretchy":1702},[1700,78460,1765],{},[898,78462,1862],{},[1700,78464,1703],{"stretchy":1702},[898,78466,12226],{},[898,78468,1706],{},[1785,78470,78471,78473],{},[1700,78472,1709],{"stretchy":1702},[898,78474,207],{},[1700,78476,1703],{"stretchy":1702},[898,78478,12226],{},[898,78480,1735],{},[1785,78482,78483,78485],{},[1700,78484,1709],{"stretchy":1702},[898,78486,1879],{},[1700,78488,1765],{},[898,78490,1862],{},[1781,78492,1783],{},[1785,78494,78495,78497],{},[898,78496,12226],{},[895,78498,78499,78501,78503],{},[898,78500,207],{},[1700,78502,1897],{},[898,78504,1879],{},[1781,78506,1783],{},[1785,78508,78509,78511],{},[898,78510,1706],{},[898,78512,207],{},[1785,78514,78515,78517],{},[898,78516,1735],{},[898,78518,1879],{},[1700,78520,1765],{},[1785,78522,78523,78525],{},[898,78524,12226],{},[895,78526,78527,78529,78531],{},[898,78528,207],{},[1700,78530,1897],{},[898,78532,1879],{},[1781,78534,1783],{},[898,78536,1662],{},[1700,78538,1703],{"stretchy":1702},[898,78540,1706],{},[1700,78542,1732],{"separator":1731},[898,78544,1735],{},[1700,78546,1709],{"stretchy":1702},[898,78548,2196],{"mathvariant":1791},[20947,78550],{"width":28261},[20947,78552,78553],{},[1781,78554,78555],{},"(5.8)",[902,78557,78558],{"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}",[724,78560,78561,78562],{},"Volně: ",[38,78563,78564,78565,78578,78579,78603],{},"změní-li se vstupy ",[883,78566,78568],{"className":78567},[886],[888,78569,78570],{"xmlns":890},[892,78571,78572,78576],{},[895,78573,78574],{},[898,78575,12226],{},[902,78577,12226],{"encoding":904},"-krát, změní se výstup ",[883,78580,78582],{"className":78581},[886],[888,78583,78584],{"xmlns":890},[892,78585,78586,78600],{},[895,78587,78588],{},[1785,78589,78590,78592],{},[898,78591,12226],{},[895,78593,78594,78596,78598],{},[898,78595,207],{},[1700,78597,1897],{},[898,78599,1879],{},[902,78601,78602],{"encoding":904},"r^{a+b}","-krát.",[198,78605,78607],{"id":78606},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,78609,78610,78611,78628],{},"Součet exponentů ",[883,78612,78614],{"className":78613},[886],[888,78615,78616],{"xmlns":890},[892,78617,78618,78626],{},[895,78619,78620,78622,78624],{},[898,78621,207],{},[1700,78623,1897],{},[898,78625,1879],{},[902,78627,75008],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,78630,78631,78660],{},[19,78632,78633],{},[22,78634,78635,78638,78641,78658],{},[25,78636,78637],{},"Typ",[25,78639,78640],{},"Podmínka",[25,78642,78643,78644,78657],{},"Chování produkce při ",[883,78645,78647],{"className":78646},[886],[888,78648,78649],{"xmlns":890},[892,78650,78651,78655],{},[895,78652,78653],{},[898,78654,12226],{},[902,78656,12226],{"encoding":904},"-násobném zvýšení vstupů",[25,78659,3264],{},[30,78661,78662,78773,78888],{},[22,78663,78664,78672,78696,78729],{},[35,78665,75720,78666,10208,78669,1709],{},[38,78667,78668],{},"Konstantní",[614,78670,78671],{},"constant returns",[35,78673,78674],{},[883,78675,78677],{"className":78676},[886],[888,78678,78679],{"xmlns":890},[892,78680,78681,78693],{},[895,78682,78683,78685,78687,78689,78691],{},[898,78684,207],{},[1700,78686,1897],{},[898,78688,1879],{},[1700,78690,1765],{},[1931,78692,1933],{},[902,78694,78695],{"encoding":904},"a+b = 1",[35,78697,78698,78711,78712,2106,78715,78728],{},[883,78699,78701],{"className":78700},[886],[888,78702,78703],{"xmlns":890},[892,78704,78705,78709],{},[895,78706,78707],{},[898,78708,1662],{},[902,78710,1662],{"encoding":904}," vzroste ",[38,78713,78714],{},"přesně",[883,78716,78718],{"className":78717},[886],[888,78719,78720],{"xmlns":890},[892,78721,78722,78726],{},[895,78723,78724],{},[898,78725,12226],{},[902,78727,12226],{"encoding":904},"-krát",[35,78730,78731],{},[883,78732,78734],{"className":78733},[886],[888,78735,78736],{"xmlns":890},[892,78737,78738,78770],{},[895,78739,78740,78742,78744,78746,78758],{},[898,78741,1662],{},[1700,78743,1765],{},[1931,78745,2343],{},[1785,78747,78748,78750],{},[898,78749,1706],{},[895,78751,78752,78754,78756],{},[1931,78753,1933],{},[898,78755,1979],{"mathvariant":1791},[1931,78757,2553],{},[1785,78759,78760,78762],{},[898,78761,1735],{},[895,78763,78764,78766,78768],{},[1931,78765,2385],{},[898,78767,1979],{"mathvariant":1791},[1931,78769,2553],{},[902,78771,78772],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,78774,78775,78784,78808,78838],{},[35,78776,78777,78778,10208,78781,1709],{},"2° ",[38,78779,78780],{},"Rostoucí",[614,78782,78783],{},"increasing returns",[35,78785,78786],{},[883,78787,78789],{"className":78788},[886],[888,78790,78791],{"xmlns":890},[892,78792,78793,78805],{},[895,78794,78795,78797,78799,78801,78803],{},[898,78796,207],{},[1700,78798,1897],{},[898,78800,1879],{},[1700,78802,3601],{},[1931,78804,1933],{},[902,78806,78807],{"encoding":904},"a+b > 1",[35,78809,78810,78711,78823,51416,78825,78728],{},[883,78811,78813],{"className":78812},[886],[888,78814,78815],{"xmlns":890},[892,78816,78817,78821],{},[895,78818,78819],{},[898,78820,1662],{},[902,78822,1662],{"encoding":904},[38,78824,25455],{},[883,78826,78828],{"className":78827},[886],[888,78829,78830],{"xmlns":890},[892,78831,78832,78836],{},[895,78833,78834],{},[898,78835,12226],{},[902,78837,12226],{"encoding":904},[35,78839,78840,10208,78866,1709],{},[883,78841,78843],{"className":78842},[886],[888,78844,78845],{"xmlns":890},[892,78846,78847,78863],{},[895,78848,78849,78851,78853,78855,78857],{},[898,78850,1662],{},[1700,78852,1765],{},[1931,78854,24386],{},[898,78856,1706],{},[1785,78858,78859,78861],{},[898,78860,1735],{},[1931,78862,2343],{},[902,78864,78865],{"encoding":904},"Q = 7LK^2",[883,78867,78869],{"className":78868},[886],[888,78870,78871],{"xmlns":890},[892,78872,78873,78885],{},[895,78874,78875,78877,78879,78881,78883],{},[898,78876,207],{},[1700,78878,1897],{},[898,78880,1879],{},[1700,78882,1765],{},[1931,78884,2385],{},[902,78886,78887],{"encoding":904},"a+b = 3",[22,78889,78890,78899,78923,78954],{},[35,78891,78892,78893,10208,78896,1709],{},"3° ",[38,78894,78895],{},"Klesající",[614,78897,78898],{},"decreasing returns",[35,78900,78901],{},[883,78902,78904],{"className":78903},[886],[888,78905,78906],{"xmlns":890},[892,78907,78908,78920],{},[895,78909,78910,78912,78914,78916,78918],{},[898,78911,207],{},[1700,78913,1897],{},[898,78915,1879],{},[1700,78917,3640],{},[1931,78919,1933],{},[902,78921,78922],{"encoding":904},"a+b \u003C 1",[35,78924,78925,78711,78938,51416,78941,78728],{},[883,78926,78928],{"className":78927},[886],[888,78929,78930],{"xmlns":890},[892,78931,78932,78936],{},[895,78933,78934],{},[898,78935,1662],{},[902,78937,1662],{"encoding":904},[38,78939,78940],{},"méně",[883,78942,78944],{"className":78943},[886],[888,78945,78946],{"xmlns":890},[892,78947,78948,78952],{},[895,78949,78950],{},[898,78951,12226],{},[902,78953,12226],{"encoding":904},[35,78955,78956,10208,78986,1709],{},[883,78957,78959],{"className":78958},[886],[888,78960,78961],{"xmlns":890},[892,78962,78963,78983],{},[895,78964,78965,78967,78969,78971,78977],{},[898,78966,1662],{},[1700,78968,1765],{},[1931,78970,3058],{},[1785,78972,78973,78975],{},[898,78974,1706],{},[1931,78976,68395],{},[1785,78978,78979,78981],{},[898,78980,1735],{},[1931,78982,5197],{},[902,78984,78985],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,78987,78989],{"className":78988},[886],[888,78990,78991],{"xmlns":890},[892,78992,78993,79005],{},[895,78994,78995,78997,78999,79001,79003],{},[898,78996,207],{},[1700,78998,1897],{},[898,79000,1879],{},[1700,79002,1765],{},[1931,79004,14774],{},[902,79006,79007],{"encoding":904},"a+b = 0{,}8",[4060,79009,79010],{},[724,79011,79012,79014,79015,79032,79033,79036,79037,2106,79040,79076,79077,79099,79100,2196],{},[883,79013,4601],{}," Pozor\nSoučet ",[883,79016,79018],{"className":79017},[886],[888,79019,79020],{"xmlns":890},[892,79021,79022,79030],{},[895,79023,79024,79026,79028],{},[898,79025,207],{},[1700,79027,1897],{},[898,79029,1879],{},[902,79031,75008],{"encoding":904}," neudává velikost produkce, ale ",[38,79034,79035],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,79038,79039],{},"ryzí Cobb-Douglas",[883,79041,79043],{"className":79042},[886],[888,79044,79045],{"xmlns":890},[892,79046,79047,79073],{},[895,79048,79049,79051,79053,79055,79061],{},[898,79050,1662],{},[1700,79052,1765],{},[898,79054,1862],{},[1785,79056,79057,79059],{},[898,79058,1706],{},[898,79060,207],{},[1785,79062,79063,79065],{},[898,79064,1735],{},[895,79066,79067,79069,79071],{},[1931,79068,1933],{},[1700,79070,1768],{},[898,79072,207],{},[902,79074,79075],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,79078,79080],{"className":79079},[886],[888,79081,79082],{"xmlns":890},[892,79083,79084,79096],{},[895,79085,79086,79088,79090,79092,79094],{},[898,79087,1879],{},[1700,79089,1765],{},[1931,79091,1933],{},[1700,79093,1768],{},[898,79095,207],{},[902,79097,79098],{"encoding":904},"b = 1-a",", tedy vždy ",[38,79101,79102],{},"konstantní výnosy z rozsahu",[198,79104,79106,79107],{"id":79105},"parametr-efektivity-aa","Parametr efektivity ",[883,79108,79110],{"className":79109},[886],[888,79111,79112],{"xmlns":890},[892,79113,79114,79118],{},[895,79115,79116],{},[898,79117,1862],{},[902,79119,1862],{"encoding":904},[724,79121,79122,79123,79136,79137,79150,79151,79169,79170,79173],{},"Konstanta ",[883,79124,79126],{"className":79125},[886],[888,79127,79128],{"xmlns":890},[892,79129,79130,79134],{},[895,79131,79132],{},[898,79133,1862],{},[902,79135,1862],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,79138,79140],{"className":79139},[886],[888,79141,79142],{"xmlns":890},[892,79143,79144,79148],{},[895,79145,79146],{},[898,79147,1662],{},[902,79149,1662],{"encoding":904}," při pevně zadaných ",[883,79152,79154],{"className":79153},[886],[888,79155,79156],{"xmlns":890},[892,79157,79158,79166],{},[895,79159,79160,79162,79164],{},[898,79161,1706],{},[1700,79163,1732],{"separator":1731},[898,79165,1735],{},[902,79167,79168],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,79171,79172],{},"parametr efektivity"," — indikátor stavu technologie.",[198,79175,79177],{"id":79176},"příklad-53","Příklad 5.3",[724,79179,79180,79181,79076,79223,79225,79226,2196],{},"Produkční funkce ",[883,79182,79184],{"className":79183},[886],[888,79185,79186],{"xmlns":890},[892,79187,79188,79220],{},[895,79189,79190,79192,79194,79196,79208],{},[898,79191,1662],{},[1700,79193,1765],{},[1931,79195,2343],{},[1785,79197,79198,79200],{},[898,79199,1706],{},[895,79201,79202,79204,79206],{},[1931,79203,1933],{},[898,79205,1979],{"mathvariant":1791},[1931,79207,2553],{},[1785,79209,79210,79212],{},[898,79211,1735],{},[895,79213,79214,79216,79218],{},[1931,79215,2385],{},[898,79217,1979],{"mathvariant":1791},[1931,79219,2553],{},[902,79221,79222],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,79224,24798],{}," výnosy z rozsahu, neboť ",[883,79227,79229],{"className":79228},[886],[888,79230,79231],{"xmlns":890},[892,79232,79233,79257],{},[895,79234,79235,79243,79245,79253,79255],{},[1770,79236,79237],{"scriptlevel":1772,"displaystyle":1702},[1774,79238,79239,79241],{},[1931,79240,1933],{},[1931,79242,2553],{},[1700,79244,1897],{},[1770,79246,79247],{"scriptlevel":1772,"displaystyle":1702},[1774,79248,79249,79251],{},[1931,79250,2385],{},[1931,79252,2553],{},[1700,79254,1765],{},[1931,79256,1933],{},[902,79258,79259],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,79261,79262,79263,6378,79276,79289,79290,2106,79303,79343],{},"Změní-li se ",[883,79264,79266],{"className":79265},[886],[888,79267,79268],{"xmlns":890},[892,79269,79270,79274],{},[895,79271,79272],{},[898,79273,1706],{},[902,79275,1706],{"encoding":904},[883,79277,79279],{"className":79278},[886],[888,79280,79281],{"xmlns":890},[892,79282,79283,79287],{},[895,79284,79285],{},[898,79286,1735],{},[902,79288,1735],{"encoding":904}," čtyřnásobně, změní se ",[883,79291,79293],{"className":79292},[886],[888,79294,79295],{"xmlns":890},[892,79296,79297,79301],{},[895,79298,79299],{},[898,79300,1662],{},[902,79302,1662],{"encoding":904},[883,79304,79306],{"className":79305},[886],[888,79307,79308],{"xmlns":890},[892,79309,79310,79340],{},[895,79311,79312,79332,79334],{},[1785,79313,79314,79316],{},[1931,79315,2553],{},[895,79317,79318,79320,79322,79324,79326,79328,79330],{},[1931,79319,1933],{},[898,79321,1979],{"mathvariant":1791},[1931,79323,2553],{},[1700,79325,1897],{},[1931,79327,2385],{},[898,79329,1979],{"mathvariant":1791},[1931,79331,2553],{},[1700,79333,1765],{},[1785,79335,79336,79338],{},[1931,79337,2553],{},[1931,79339,1933],{},[902,79341,79342],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,79345,79347],{"className":79346},[886],[888,79348,79349],{"xmlns":890,"display":28251},[892,79350,79351,79511],{},[895,79352,79353,79355,79357,79359,79361,79363,79365,79367,79369,79371,79373,79375,79377,79379,79391,79393,79395,79397,79409,79411,79413,79415,79435,79447,79459,79461,79463,79465,79467,79479,79491,79493,79495,79497,79499,79501,79503,79505,79507,79509],{},[898,79354,1662],{},[1700,79356,1703],{"stretchy":1702},[1931,79358,2553],{},[898,79360,1706],{},[1700,79362,1732],{"separator":1731},[1931,79364,2553],{},[898,79366,1735],{},[1700,79368,1709],{"stretchy":1702},[1700,79370,1765],{},[1931,79372,2343],{},[1700,79374,1703],{"stretchy":1702},[1931,79376,2553],{},[898,79378,1706],{},[1785,79380,79381,79383],{},[1700,79382,1709],{"stretchy":1702},[895,79384,79385,79387,79389],{},[1931,79386,1933],{},[898,79388,1979],{"mathvariant":1791},[1931,79390,2553],{},[1700,79392,1703],{"stretchy":1702},[1931,79394,2553],{},[898,79396,1735],{},[1785,79398,79399,79401],{},[1700,79400,1709],{"stretchy":1702},[895,79402,79403,79405,79407],{},[1931,79404,2385],{},[898,79406,1979],{"mathvariant":1791},[1931,79408,2553],{},[1700,79410,1765],{},[1931,79412,2343],{},[1700,79414,2065],{},[1785,79416,79417,79419],{},[1931,79418,2553],{},[895,79420,79421,79423,79425,79427,79429,79431,79433],{},[1931,79422,1933],{},[898,79424,1979],{"mathvariant":1791},[1931,79426,2553],{},[1700,79428,1897],{},[1931,79430,2385],{},[898,79432,1979],{"mathvariant":1791},[1931,79434,2553],{},[1785,79436,79437,79439],{},[898,79438,1706],{},[895,79440,79441,79443,79445],{},[1931,79442,1933],{},[898,79444,1979],{"mathvariant":1791},[1931,79446,2553],{},[1785,79448,79449,79451],{},[898,79450,1735],{},[895,79452,79453,79455,79457],{},[1931,79454,2385],{},[898,79456,1979],{"mathvariant":1791},[1931,79458,2553],{},[1700,79460,1765],{},[1931,79462,2553],{},[1700,79464,2065],{},[1931,79466,2343],{},[1785,79468,79469,79471],{},[898,79470,1706],{},[895,79472,79473,79475,79477],{},[1931,79474,1933],{},[898,79476,1979],{"mathvariant":1791},[1931,79478,2553],{},[1785,79480,79481,79483],{},[898,79482,1735],{},[895,79484,79485,79487,79489],{},[1931,79486,2385],{},[898,79488,1979],{"mathvariant":1791},[1931,79490,2553],{},[1700,79492,1765],{},[1931,79494,2553],{},[1781,79496,1783],{},[898,79498,1662],{},[1700,79500,1703],{"stretchy":1702},[898,79502,1706],{},[1700,79504,1732],{"separator":1731},[898,79506,1735],{},[1700,79508,1709],{"stretchy":1702},[898,79510,2196],{"mathvariant":1791},[902,79512,79513],{"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).",[198,79515,79516],{"id":37364},"Homogenita",[724,79518,79519,79520,8290,79543,79559],{},"Funkce ",[883,79521,79523],{"className":79522},[886],[888,79524,79525],{"xmlns":890},[892,79526,79527,79541],{},[895,79528,79529,79531,79533,79535,79537,79539],{},[898,79530,1662],{},[1700,79532,1703],{"stretchy":1702},[898,79534,1706],{},[1700,79536,1732],{"separator":1731},[898,79538,1735],{},[1700,79540,1709],{"stretchy":1702},[902,79542,1740],{"encoding":904},[38,79544,79545,79546],{},"homogenní stupně ",[883,79547,79549],{"className":79548},[886],[888,79550,79551],{"xmlns":890},[892,79552,79553,79557],{},[895,79554,79555],{},[898,79556,37045],{},[902,79558,37045],{"encoding":904},", jestliže",[883,79561,79563],{"className":79562},[886],[888,79564,79565],{"xmlns":890,"display":28251},[892,79566,79567,79624],{},[20939,79568,79569],{"width":28256},[20944,79570,79571,79573,79617,79619],{},[20947,79572],{"width":28261},[20947,79574,79575],{},[895,79576,79577,79579,79581,79583,79585,79587,79589,79591,79593,79595,79601,79603,79605,79607,79609,79611,79613,79615],{},[898,79578,1662],{},[1700,79580,1703],{"stretchy":1702},[898,79582,12226],{},[898,79584,1706],{},[1700,79586,1732],{"separator":1731},[898,79588,12226],{},[898,79590,1735],{},[1700,79592,1709],{"stretchy":1702},[1700,79594,1765],{},[1785,79596,79597,79599],{},[898,79598,12226],{},[898,79600,37045],{},[1781,79602,1783],{},[898,79604,1662],{},[1700,79606,1703],{"stretchy":1702},[898,79608,1706],{},[1700,79610,1732],{"separator":1731},[898,79612,1735],{},[1700,79614,1709],{"stretchy":1702},[1700,79616,1732],{"separator":1731},[20947,79618],{"width":28261},[20947,79620,79621],{},[1781,79622,79623],{},"(5.10)",[902,79625,79626],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,79628,4499,79629,79647,79648,79666,79667,43821,79680,79683,79684,2196],{},[883,79630,79632],{"className":79631},[886],[888,79633,79634],{"xmlns":890},[892,79635,79636,79644],{},[895,79637,79638,79640,79642],{},[898,79639,37045],{},[1700,79641,4674],{},[1931,79643,1772],{},[902,79645,79646],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,79649,79651],{"className":79650},[886],[888,79652,79653],{"xmlns":890},[892,79654,79655,79663],{},[895,79656,79657,79659,79661],{},[898,79658,12226],{},[1700,79660,3601],{},[1931,79662,1772],{},[902,79664,79665],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,79668,79670],{"className":79669},[886],[888,79671,79672],{"xmlns":890},[892,79673,79674,79678],{},[895,79675,79676],{},[1931,79677,1933],{},[902,79679,1933],{"encoding":904},[38,79681,79682],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,79685,79687],{"className":79686},[886],[888,79688,79689],{"xmlns":890},[892,79690,79691,79699],{},[895,79692,79693,79695,79697],{},[898,79694,207],{},[1700,79696,1897],{},[898,79698,1879],{},[902,79700,75008],{"encoding":904},[115,79702,79704],{"id":79703},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,79706,79707],{},[38,79708,79709],{},"Ryzí Cobb-Douglasovy funkce:",[883,79711,79713],{"className":79712},[886],[888,79714,79715],{"xmlns":890,"display":28251},[892,79716,79717,79776],{},[20939,79718,79719],{"width":28256},[20944,79720,79721,79723,79769,79771],{},[20947,79722],{"width":28261},[20947,79724,79725],{},[895,79726,79727,79729,79731,79733,79735,79741,79743,79755,79757,79759,79761,79763,79765,79767],{},[898,79728,1662],{},[1700,79730,1765],{},[898,79732,1862],{},[1781,79734,1783],{},[1785,79736,79737,79739],{},[898,79738,1706],{},[898,79740,207],{},[1781,79742,1783],{},[1785,79744,79745,79747],{},[898,79746,1735],{},[895,79748,79749,79751,79753],{},[1931,79750,1933],{},[1700,79752,1768],{},[898,79754,207],{},[1700,79756,1732],{"separator":1731},[6066,79758],{"width":15469},[1931,79760,1772],{},[1700,79762,3640],{},[898,79764,207],{},[1700,79766,3640],{},[1931,79768,13445],{},[20947,79770],{"width":28261},[20947,79772,79773],{},[1781,79774,79775],{},"(5.9)",[902,79777,79778],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,79780,79781,79782,79784,79785,2196],{},"Mají vždy ",[38,79783,79102],{}," a jsou ",[38,79786,79682],{},[724,79788,79789,10208,79792,79795],{},[38,79790,79791],{},"CES produkční funkce",[614,79793,79794],{},"Constant Elasticity of Substitution",", 1961):",[883,79797,79799],{"className":79798},[886],[888,79800,79801],{"xmlns":890,"display":28251},[892,79802,79803,79871],{},[895,79804,79805,79807,79809,79811,79869],{},[898,79806,1662],{},[1700,79808,1765],{},[898,79810,1862],{},[1785,79812,79813,79857],{},[895,79814,79815,79817,79819,79821,79823,79825,79827,79829,79839,79841,79843,79845,79855],{},[1700,79816,1927],{"fence":1731},[1700,79818,1703],{"stretchy":1702},[1931,79820,1933],{},[1700,79822,1768],{},[898,79824,207],{},[1700,79826,1709],{"stretchy":1702},[1781,79828,1783],{},[1785,79830,79831,79833],{},[898,79832,1706],{},[895,79834,79835,79837],{},[1700,79836,1768],{},[898,79838,1879],{},[1700,79840,1897],{},[898,79842,207],{},[1781,79844,1783],{},[1785,79846,79847,79849],{},[898,79848,1735],{},[895,79850,79851,79853],{},[1700,79852,1768],{},[898,79854,1879],{},[1700,79856,1970],{"fence":1731},[895,79858,79859,79861],{},[1700,79860,1768],{},[1770,79862,79863],{"scriptlevel":1772,"displaystyle":1702},[1774,79864,79865,79867],{},[1931,79866,1933],{},[898,79868,1879],{},[1700,79870,1732],{"separator":1731},[902,79872,79873],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,79875,4499,79876,1343,79894,1343,79915,79939],{},[883,79877,79879],{"className":79878},[886],[888,79880,79881],{"xmlns":890},[892,79882,79883,79891],{},[895,79884,79885,79887,79889],{},[898,79886,1862],{},[1700,79888,3601],{},[1931,79890,1772],{},[902,79892,79893],{"encoding":904},"A > 0",[883,79895,79897],{"className":79896},[886],[888,79898,79899],{"xmlns":890},[892,79900,79901,79913],{},[895,79902,79903,79905,79907,79909,79911],{},[1931,79904,1772],{},[1700,79906,3640],{},[898,79908,207],{},[1700,79910,3640],{},[1931,79912,1933],{},[902,79914,19021],{"encoding":904},[883,79916,79918],{"className":79917},[886],[888,79919,79920],{"xmlns":890},[892,79921,79922,79936],{},[895,79923,79924,79926,79928,79930,79932,79934],{},[1700,79925,1768],{},[1931,79927,1933],{},[1700,79929,3640],{},[898,79931,1879],{},[1700,79933,3564],{"mathvariant":1791},[1931,79935,1772],{},[902,79937,79938],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,79941,79942],{},[38,79943,79944],{},"Další typy:",[120,79946,79947,79989],{},[123,79948,79949,2106,79952,79988],{},[38,79950,79951],{},"Lineární:",[883,79953,79955],{"className":79954},[886],[888,79956,79957],{"xmlns":890},[892,79958,79959,79985],{},[895,79960,79961,79963,79965,79967,79969,79971,79973,79975,79977,79979,79981,79983],{},[898,79962,1662],{},[1700,79964,1703],{"stretchy":1702},[898,79966,1706],{},[1700,79968,1732],{"separator":1731},[898,79970,1735],{},[1700,79972,1709],{"stretchy":1702},[1700,79974,1765],{},[898,79976,207],{},[898,79978,1706],{},[1700,79980,1897],{},[898,79982,1879],{},[898,79984,1735],{},[902,79986,79987],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,79990,79991,2106,79994,80039],{},[38,79992,79993],{},"Leontiefova:",[883,79995,79997],{"className":79996},[886],[888,79998,79999],{"xmlns":890},[892,80000,80001,80036],{},[895,80002,80003,80005,80007,80009,80011,80013,80015,80017,80020,80022,80024,80026,80028,80030,80032,80034],{},[898,80004,1662],{},[1700,80006,1703],{"stretchy":1702},[898,80008,1706],{},[1700,80010,1732],{"separator":1731},[898,80012,1735],{},[1700,80014,1709],{"stretchy":1702},[1700,80016,1765],{},[898,80018,80019],{},"min",[1700,80021,56384],{},[1700,80023,1703],{"stretchy":1702},[898,80025,207],{},[898,80027,1706],{},[1700,80029,1732],{"separator":1731},[898,80031,1879],{},[898,80033,1735],{},[1700,80035,1709],{"stretchy":1702},[902,80037,80038],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,80041,80043,80044,1343,80063,80082],{"id":80042},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,80045,80047],{"className":80046},[886],[888,80048,80049],{"xmlns":890},[892,80050,80051,80061],{},[895,80052,80053,80055],{},[898,80054,2005],{},[2007,80056,80057,80059],{},[898,80058,1677],{},[898,80060,1706],{},[902,80062,10228],{"encoding":904},[883,80064,80066],{"className":80065},[886],[888,80067,80068],{"xmlns":890},[892,80069,80070,80080],{},[895,80071,80072,80074],{},[898,80073,2005],{},[2007,80075,80076,80078],{},[898,80077,1677],{},[898,80079,1735],{},[902,80081,10273],{"encoding":904}," a totální diferenciál",[724,80084,80085],{},[38,80086,80087],{},"Mezní produkt práce:",[883,80089,80091],{"className":80090},[886],[888,80092,80093],{"xmlns":890,"display":28251},[892,80094,80095,80133],{},[895,80096,80097,80099,80105,80107,80115,80117,80131],{},[898,80098,2005],{},[2007,80100,80101,80103],{},[898,80102,1677],{},[898,80104,1706],{},[1700,80106,1765],{},[2030,80108,80109,80111,80113],{},[898,80110,1662],{},[898,80112,1706],{},[1700,80114,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,80116,1765],{},[1774,80118,80119,80125],{},[895,80120,80121,80123],{},[898,80122,10056],{"mathvariant":1791},[898,80124,1662],{},[895,80126,80127,80129],{},[898,80128,10056],{"mathvariant":1791},[898,80130,1706],{},[898,80132,2196],{"mathvariant":1791},[902,80134,80135],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,80137,80138],{},[38,80139,80140],{},"Mezní produkt kapitálu:",[883,80142,80144],{"className":80143},[886],[888,80145,80146],{"xmlns":890,"display":28251},[892,80147,80148,80186],{},[895,80149,80150,80152,80158,80160,80168,80170,80184],{},[898,80151,2005],{},[2007,80153,80154,80156],{},[898,80155,1677],{},[898,80157,1735],{},[1700,80159,1765],{},[2030,80161,80162,80164,80166],{},[898,80163,1662],{},[898,80165,1735],{},[1700,80167,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,80169,1765],{},[1774,80171,80172,80178],{},[895,80173,80174,80176],{},[898,80175,10056],{"mathvariant":1791},[898,80177,1662],{},[895,80179,80180,80182],{},[898,80181,10056],{"mathvariant":1791},[898,80183,1735],{},[898,80185,2196],{"mathvariant":1791},[902,80187,80188],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,80190,80191,80221,80222,80243,80244,80262,80263,80276,80277,2196],{},[883,80192,80194],{"className":80193},[886],[888,80195,80196],{"xmlns":890},[892,80197,80198,80218],{},[895,80199,80200,80202,80208,80210,80212,80214,80216],{},[898,80201,2005],{},[2007,80203,80204,80206],{},[898,80205,1677],{},[898,80207,1706],{},[1700,80209,1703],{"stretchy":1702},[898,80211,207],{},[1700,80213,1732],{"separator":1731},[898,80215,1879],{},[1700,80217,1709],{"stretchy":1702},[902,80219,80220],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,80223,80225],{"className":80224},[886],[888,80226,80227],{"xmlns":890},[892,80228,80229,80241],{},[895,80230,80231,80233,80235,80237,80239],{},[1700,80232,1927],{"stretchy":1702},[898,80234,207],{},[1700,80236,1732],{"separator":1731},[898,80238,1879],{},[1700,80240,1970],{"stretchy":1702},[902,80242,11007],{"encoding":904}," (na hladině ",[883,80245,80247],{"className":80246},[886],[888,80248,80249],{"xmlns":890},[892,80250,80251,80259],{},[895,80252,80253,80255,80257],{},[898,80254,1735],{},[1700,80256,1765],{},[898,80258,1879],{},[902,80260,80261],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,80264,80266],{"className":80265},[886],[888,80267,80268],{"xmlns":890},[892,80269,80270,80274],{},[895,80271,80272],{},[898,80273,1706],{},[902,80275,1706],{"encoding":904},". Analogicky ",[883,80278,80280],{"className":80279},[886],[888,80281,80282],{"xmlns":890},[892,80283,80284,80304],{},[895,80285,80286,80288,80294,80296,80298,80300,80302],{},[898,80287,2005],{},[2007,80289,80290,80292],{},[898,80291,1677],{},[898,80293,1735],{},[1700,80295,1703],{"stretchy":1702},[898,80297,207],{},[1700,80299,1732],{"separator":1731},[898,80301,1879],{},[1700,80303,1709],{"stretchy":1702},[902,80305,80306],{"encoding":904},"MP_K(a, b)",[4060,80308,80309,80313],{},[724,80310,80311,51404],{},[883,80312,4346],{},[120,80314,80315,80353],{},[123,80316,80317,26374,80336],{},[883,80318,80320],{"className":80319},[886],[888,80321,80322],{"xmlns":890},[892,80323,80324,80334],{},[895,80325,80326,80328],{},[898,80327,2005],{},[2007,80329,80330,80332],{},[898,80331,1677],{},[898,80333,1706],{},[902,80335,10228],{"encoding":904},[614,80337,80338,80339,80352],{},"„o kolik vzroste ",[883,80340,80342],{"className":80341},[886],[888,80343,80344],{"xmlns":890},[892,80345,80346,80350],{},[895,80347,80348],{},[898,80349,1662],{},[902,80351,1662],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,80354,80355,26374,80374],{},[883,80356,80358],{"className":80357},[886],[888,80359,80360],{"xmlns":890},[892,80361,80362,80372],{},[895,80363,80364,80366],{},[898,80365,2005],{},[2007,80367,80368,80370],{},[898,80369,1677],{},[898,80371,1735],{},[902,80373,10273],{"encoding":904},[614,80375,80338,80376,80389],{},[883,80377,80379],{"className":80378},[886],[888,80380,80381],{"xmlns":890},[892,80382,80383,80387],{},[895,80384,80385],{},[898,80386,1662],{},[902,80388,1662],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,80391,80392,80395,80396,80411,80412,2901],{},[38,80393,80394],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,80397,80399],{"className":80398},[886],[888,80400,80401],{"xmlns":890},[892,80402,80403,80409],{},[895,80404,80405,80407],{},[898,80406,2406],{},[898,80408,1706],{},[902,80410,75539],{"encoding":904}," a kapitálu o ",[883,80413,80415],{"className":80414},[886],[888,80416,80417],{"xmlns":890},[892,80418,80419,80425],{},[895,80420,80421,80423],{},[898,80422,2406],{},[898,80424,1735],{},[902,80426,80427],{"encoding":904},"dK",[883,80429,80431],{"className":80430},[886],[888,80432,80433],{"xmlns":890,"display":28251},[892,80434,80435,80528],{},[20939,80436,80437],{"width":28256},[20944,80438,80439,80441,80521,80523],{},[20947,80440],{"width":28261},[20947,80442,80443],{},[895,80444,80445,80447,80449,80451,80453,80455,80457,80465,80467,80469,80471,80473,80481,80483,80485,80487,80489,80491,80497,80499,80501,80503,80505,80507,80513,80515,80517,80519],{},[898,80446,3084],{"mathvariant":1791},[898,80448,1662],{},[1700,80450,2927],{},[898,80452,2406],{},[898,80454,1662],{},[1700,80456,1765],{},[2030,80458,80459,80461,80463],{},[898,80460,1662],{},[898,80462,1706],{},[1700,80464,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1781,80466,1783],{},[898,80468,2406],{},[898,80470,1706],{},[1700,80472,1897],{},[2030,80474,80475,80477,80479],{},[898,80476,1662],{},[898,80478,1735],{},[1700,80480,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1781,80482,1783],{},[898,80484,2406],{},[898,80486,1735],{},[1700,80488,1765],{},[898,80490,2005],{},[2007,80492,80493,80495],{},[898,80494,1677],{},[898,80496,1706],{},[1781,80498,1783],{},[898,80500,2406],{},[898,80502,1706],{},[1700,80504,1897],{},[898,80506,2005],{},[2007,80508,80509,80511],{},[898,80510,1677],{},[898,80512,1735],{},[1781,80514,1783],{},[898,80516,2406],{},[898,80518,1735],{},[898,80520,2196],{"mathvariant":1791},[20947,80522],{"width":28261},[20947,80524,80525],{},[1781,80526,80527],{},"(5.11)",[902,80529,80530],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,80532,80533,80534,2196],{},"Skutečná změna: ",[883,80535,80537],{"className":80536},[886],[888,80538,80539],{"xmlns":890},[892,80540,80541,80587],{},[895,80542,80543,80545,80547,80549,80551,80553,80555,80557,80559,80561,80563,80565,80567,80569,80571,80573,80575,80577,80579,80581,80583,80585],{},[898,80544,3084],{"mathvariant":1791},[898,80546,1662],{},[1700,80548,1765],{},[898,80550,1662],{},[1700,80552,1703],{"stretchy":1702},[898,80554,1706],{},[1700,80556,1897],{},[898,80558,2406],{},[898,80560,1706],{},[1700,80562,1732],{"separator":1731},[898,80564,1735],{},[1700,80566,1897],{},[898,80568,2406],{},[898,80570,1735],{},[1700,80572,1709],{"stretchy":1702},[1700,80574,1768],{},[898,80576,1662],{},[1700,80578,1703],{"stretchy":1702},[898,80580,1706],{},[1700,80582,1732],{"separator":1731},[898,80584,1735],{},[1700,80586,1709],{"stretchy":1702},[902,80588,80589],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,80591,80592,80594,80595,80613,80614,80627,80628,80647,80648,80680,80681,80713,80714,2196],{},[38,80593,75703],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,80596,80598],{"className":80597},[886],[888,80599,80600],{"xmlns":890},[892,80601,80602,80610],{},[895,80603,80604],{},[2007,80605,80606,80608],{},[898,80607,1735],{},[1931,80609,1772],{},[902,80611,80612],{"encoding":904},"K_0"," se od jistého ",[883,80615,80617],{"className":80616},[886],[888,80618,80619],{"xmlns":890},[892,80620,80621,80625],{},[895,80622,80623],{},[898,80624,1706],{},[902,80626,1706],{"encoding":904}," stane ",[883,80629,80631],{"className":80630},[886],[888,80632,80633],{"xmlns":890},[892,80634,80635,80645],{},[895,80636,80637,80639],{},[898,80638,2005],{},[2007,80640,80641,80643],{},[898,80642,1677],{},[898,80644,1706],{},[902,80646,10228],{"encoding":904}," klesající (",[883,80649,80651],{"className":80650},[886],[888,80652,80653],{"xmlns":890},[892,80654,80655,80677],{},[895,80656,80657,80673,80675],{},[2030,80658,80659,80661,80667],{},[898,80660,1662],{},[895,80662,80663,80665],{},[898,80664,1706],{},[898,80666,1706],{},[895,80668,80669,80671],{},[1700,80670,1793],{"mathvariant":1791},[1700,80672,1793],{"mathvariant":1791},[1700,80674,3640],{},[1931,80676,1772],{},[902,80678,80679],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,80682,80684],{"className":80683},[886],[888,80685,80686],{"xmlns":890},[892,80687,80688,80710],{},[895,80689,80690,80706,80708],{},[2030,80691,80692,80694,80700],{},[898,80693,1662],{},[895,80695,80696,80698],{},[898,80697,1735],{},[898,80699,1735],{},[895,80701,80702,80704],{},[1700,80703,1793],{"mathvariant":1791},[1700,80705,1793],{"mathvariant":1791},[1700,80707,3640],{},[1931,80709,1772],{},[902,80711,80712],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,80715,80717],{"className":80716},[886],[888,80718,80719],{"xmlns":890},[892,80720,80721,80729],{},[895,80722,80723],{},[2007,80724,80725,80727],{},[898,80726,1706],{},[1931,80728,1772],{},[902,80730,75741],{"encoding":904},[115,80732,80734],{"id":80733},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,80736,80737,80740,80741,80764,80765,30129],{},[38,80738,80739],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,80742,80744],{"className":80743},[886],[888,80745,80746],{"xmlns":890},[892,80747,80748,80762],{},[895,80749,80750,80752,80754,80756,80758,80760],{},[898,80751,1662],{},[1700,80753,1703],{"stretchy":1702},[898,80755,1706],{},[1700,80757,1732],{"separator":1731},[898,80759,1735],{},[1700,80761,1709],{"stretchy":1702},[902,80763,1740],{"encoding":904}," stupně ",[883,80766,80768],{"className":80767},[886],[888,80769,80770],{"xmlns":890},[892,80771,80772,80776],{},[895,80773,80774],{},[898,80775,37045],{},[902,80777,37045],{"encoding":904},[883,80779,80781],{"className":80780},[886],[888,80782,80783],{"xmlns":890,"display":28251},[892,80784,80785,80848],{},[20939,80786,80787],{"width":28256},[20944,80788,80789,80791,80841,80843],{},[20947,80790],{"width":28261},[20947,80792,80793],{},[895,80794,80795,80797,80799,80807,80809,80811,80813,80821,80823,80825,80827,80829,80831,80833,80835,80837,80839],{},[898,80796,1706],{},[1781,80798,1783],{},[2030,80800,80801,80803,80805],{},[898,80802,1662],{},[898,80804,1706],{},[1700,80806,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,80808,1897],{},[898,80810,1735],{},[1781,80812,1783],{},[2030,80814,80815,80817,80819],{},[898,80816,1662],{},[898,80818,1735],{},[1700,80820,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,80822,1765],{},[898,80824,37045],{},[1781,80826,1783],{},[898,80828,1662],{},[1700,80830,1703],{"stretchy":1702},[898,80832,1706],{},[1700,80834,1732],{"separator":1731},[898,80836,1735],{},[1700,80838,1709],{"stretchy":1702},[898,80840,2196],{"mathvariant":1791},[20947,80842],{"width":28261},[20947,80844,80845],{},[1781,80846,80847],{},"(5.12)",[902,80849,80850],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,80852,80853,80874],{},[38,80854,80855,80856],{},"Speciální případ ",[883,80857,80859],{"className":80858},[886],[888,80860,80861],{"xmlns":890},[892,80862,80863,80871],{},[895,80864,80865,80867,80869],{},[898,80866,37045],{},[1700,80868,1765],{},[1931,80870,1933],{},[902,80872,80873],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,80876,80878],{"className":80877},[886],[888,80879,80880],{"xmlns":890,"display":28251},[892,80881,80882,80926],{},[895,80883,80884,80886,80888,80890,80896,80898,80900,80902,80904,80910,80912,80914,80916,80918,80920,80922,80924],{},[898,80885,1706],{},[1700,80887,2065],{},[898,80889,2005],{},[2007,80891,80892,80894],{},[898,80893,1677],{},[898,80895,1706],{},[1700,80897,1897],{},[898,80899,1735],{},[1700,80901,2065],{},[898,80903,2005],{},[2007,80905,80906,80908],{},[898,80907,1677],{},[898,80909,1735],{},[1700,80911,1765],{},[898,80913,1662],{},[1700,80915,1703],{"stretchy":1702},[898,80917,1706],{},[1700,80919,1732],{"separator":1731},[898,80921,1735],{},[1700,80923,1709],{"stretchy":1702},[898,80925,2196],{"mathvariant":1791},[902,80927,80928],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,80930,80931,80932,80935],{},"Slovně — ",[38,80933,80934],{},"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).",[115,80937,9965],{"id":2159},[724,80939,80940,10208,80942,80945,80946,80968,80969,2901],{},[38,80941,9965],{},[614,80943,80944],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,80947,80949],{"className":80948},[886],[888,80950,80951],{"xmlns":890},[892,80952,80953,80965],{},[895,80954,80955,80957,80959,80961,80963],{},[1700,80956,1927],{"stretchy":1702},[898,80958,1706],{},[1700,80960,1732],{"separator":1731},[898,80962,1735],{},[1700,80964,1970],{"stretchy":1702},[902,80966,80967],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,80970,80972],{"className":80971},[886],[888,80973,80974],{"xmlns":890},[892,80975,80976,80981],{},[895,80977,80978],{},[898,80979,80980],{},"q",[902,80982,80980],{"encoding":904},[883,80984,80986],{"className":80985},[886],[888,80987,80988],{"xmlns":890,"display":28251},[892,80989,80990,81025],{},[20939,80991,80992],{"width":28256},[20944,80993,80994,80996,81018,81020],{},[20947,80995],{"width":28261},[20947,80997,80998],{},[895,80999,81000,81002,81004,81006,81008,81010,81012,81014,81016],{},[898,81001,1662],{},[1700,81003,1703],{"stretchy":1702},[898,81005,1706],{},[1700,81007,1732],{"separator":1731},[898,81009,1735],{},[1700,81011,1709],{"stretchy":1702},[1700,81013,1765],{},[898,81015,80980],{},[898,81017,2196],{"mathvariant":1791},[20947,81019],{"width":28261},[20947,81021,81022],{},[1781,81023,81024],{},"(5.13)",[902,81026,81027],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,81029,81030,81031,81034,81035,4110],{},"Jsou to ",[38,81032,81033],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,81036,81038],{"className":81037,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,81040,81041],{},[38,81042,81043],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,81045,81046,81051,81056,81061],{},[123,81047,81048,81050],{},[38,81049,12704],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,81052,81053,81055],{},[38,81054,37849],{}," (úloha 5.14);",[123,81057,81058,8613],{},[38,81059,81060],{},"neprotínají se",[123,81062,81063,81064,4547,81077,2196],{},"s rostoucím ",[883,81065,81067],{"className":81066},[886],[888,81068,81069],{"xmlns":890},[892,81070,81071,81075],{},[895,81072,81073],{},[898,81074,80980],{},[902,81076,80980],{"encoding":904},[38,81078,81079],{},"vzdalují od počátku",[724,81081,81082],{},[614,81083,81084,81085,81107,81108,2196],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,81086,81088],{"className":81087},[886],[888,81089,81090],{"xmlns":890},[892,81091,81092,81104],{},[895,81093,81094,81096,81098,81100,81102],{},[1700,81095,1703],{"stretchy":1702},[898,81097,1706],{},[1700,81099,1732],{"separator":1731},[898,81101,1735],{},[1700,81103,1709],{"stretchy":1702},[902,81105,81106],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,81109,81111],{"className":81110},[886],[888,81112,81113],{"xmlns":890},[892,81114,81115,81139],{},[895,81116,81117,81123,81125,81131,81133],{},[2007,81118,81119,81121],{},[898,81120,80980],{},[1931,81122,1933],{},[1700,81124,3640],{},[2007,81126,81127,81129],{},[898,81128,80980],{},[1931,81130,1772],{},[1700,81132,3640],{},[2007,81134,81135,81137],{},[898,81136,80980],{},[1931,81138,2343],{},[902,81140,81141],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,81143,81145,81146,1709],{"id":81144},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,81147,81149],{"className":81148},[886],[888,81150,81151],{"xmlns":890},[892,81152,81153,81163],{},[895,81154,81155,81157,81159,81161],{},[898,81156,2005],{},[898,81158,4185],{},[898,81160,2971],{},[898,81162,8861],{},[902,81164,10782],{"encoding":904},[724,81166,81167,10208,81170,81173],{},[38,81168,81169],{},"Mezní míra technické substituce",[614,81171,81172],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,81175,81177],{"className":81176},[886],[888,81178,81179],{"xmlns":890,"display":28251},[892,81180,81181,81272],{},[20939,81182,81183],{"width":28256},[20944,81184,81185,81187,81265,81267],{},[20947,81186],{"width":28261},[20947,81188,81189],{},[895,81190,81191,81193,81195,81197,81199,81201,81203,81205,81207,81209,81211,81213,81215,81217,81219,81221,81243,81245,81263],{},[898,81192,2005],{},[898,81194,4185],{},[898,81196,2971],{},[898,81198,8861],{},[1700,81200,1765],{},[898,81202,2005],{},[898,81204,4185],{},[898,81206,2971],{},[898,81208,8861],{},[1700,81210,1703],{"stretchy":1702},[898,81212,1706],{},[1700,81214,1732],{"separator":1731},[898,81216,1735],{},[1700,81218,1709],{"stretchy":1702},[1700,81220,1765],{},[1774,81222,81223,81233],{},[895,81224,81225,81227],{},[898,81226,2005],{},[2007,81228,81229,81231],{},[898,81230,1677],{},[898,81232,1706],{},[895,81234,81235,81237],{},[898,81236,2005],{},[2007,81238,81239,81241],{},[898,81240,1677],{},[898,81242,1735],{},[1700,81244,1765],{},[1774,81246,81247,81255],{},[2030,81248,81249,81251,81253],{},[898,81250,1662],{},[898,81252,1706],{},[1700,81254,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[2030,81256,81257,81259,81261],{},[898,81258,1662],{},[898,81260,1735],{},[1700,81262,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[898,81264,2196],{"mathvariant":1791},[20947,81266],{"width":28261},[20947,81268,81269],{},[1781,81270,81271],{},"(5.14)",[902,81273,81274],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,81276,81277,2106,81279,81309,81310,81341],{},[38,81278,9403],{},[883,81280,81282],{"className":81281},[886],[888,81283,81284],{"xmlns":890},[892,81285,81286,81306],{},[895,81287,81288,81290,81292,81294,81296,81298,81300,81302,81304],{},[898,81289,2005],{},[898,81291,4185],{},[898,81293,2971],{},[898,81295,8861],{},[1700,81297,1703],{"stretchy":1702},[898,81299,1706],{},[1700,81301,1732],{"separator":1731},[898,81303,1735],{},[1700,81305,1709],{"stretchy":1702},[902,81307,81308],{"encoding":904},"MRTS(L, K)"," udává, ",[38,81311,81312,81313,81326,81327,81340],{},"o kolik se musí přibližně změnit kapitál ",[883,81314,81316],{"className":81315},[886],[888,81317,81318],{"xmlns":890},[892,81319,81320,81324],{},[895,81321,81322],{},[898,81323,1735],{},[902,81325,1735],{"encoding":904},", jestliže se práce ",[883,81328,81330],{"className":81329},[886],[888,81331,81332],{"xmlns":890},[892,81333,81334,81338],{},[895,81335,81336],{},[898,81337,1706],{},[902,81339,1706],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[4060,81343,81344],{},[724,81345,81346,18208,81348,81367,81368,81405,81406,81409,81410,81414],{},[883,81347,4346],{},[883,81349,81351],{"className":81350},[886],[888,81352,81353],{"xmlns":890},[892,81354,81355,81365],{},[895,81356,81357,81359,81361,81363],{},[898,81358,2005],{},[898,81360,4185],{},[898,81362,2971],{},[898,81364,8861],{},[902,81366,10782],{"encoding":904}," říká: ",[614,81369,81370,81371,81390,81391,81404],{},"„jednu jednotku práce musím nahradit přibližně ",[883,81372,81374],{"className":81373},[886],[888,81375,81376],{"xmlns":890},[892,81377,81378,81388],{},[895,81379,81380,81382,81384,81386],{},[898,81381,2005],{},[898,81383,4185],{},[898,81385,2971],{},[898,81387,8861],{},[902,81389,10782],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,81392,81394],{"className":81393},[886],[888,81395,81396],{"xmlns":890},[892,81397,81398,81402],{},[895,81399,81400],{},[898,81401,1662],{},[902,81403,1662],{"encoding":904}," zůstala stejná.\""," Je to ",[38,81407,81408],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,81411,81413],{"className":81412,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,81416,81417],{},[2756,81418],{"alt":81419,"className":81420,"src":81421},"imek-izokvanty-mrts",[210,2760],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,81423,81424,81427,81428,8290,81458,81480,81481,3345],{},[38,81425,81426],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,81429,81431],{"className":81430},[886],[888,81432,81433],{"xmlns":890},[892,81434,81435,81455],{},[895,81436,81437,81439,81445,81447,81453],{},[1700,81438,1927],{"stretchy":1702},[2007,81440,81441,81443],{},[898,81442,1706],{},[1931,81444,1772],{},[1700,81446,1732],{"separator":1731},[2007,81448,81449,81451],{},[898,81450,1735],{},[1931,81452,1772],{},[1700,81454,1970],{"stretchy":1702},[902,81456,81457],{"encoding":904},"[L_0, K_0]",[883,81459,81461],{"className":81460},[886],[888,81462,81463],{"xmlns":890},[892,81464,81465,81477],{},[895,81466,81467,81469,81471,81473,81475],{},[1700,81468,1768],{},[898,81470,2005],{},[898,81472,4185],{},[898,81474,2971],{},[898,81476,8861],{},[902,81478,81479],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,81482,81484],{"className":81483},[886],[888,81485,81486],{"xmlns":890},[892,81487,81488,81510],{},[895,81489,81490,81492,81494,81496,81498,81500,81502,81504],{},[898,81491,1662],{},[1700,81493,1703],{"stretchy":1702},[898,81495,1706],{},[1700,81497,1732],{"separator":1731},[898,81499,1735],{},[1700,81501,1709],{"stretchy":1702},[1700,81503,1765],{},[2007,81505,81506,81508],{},[898,81507,80980],{},[1931,81509,1772],{},[902,81511,81512],{"encoding":904},"Q(L,K) = q_0",[883,81514,81516],{"className":81515},[886],[888,81517,81518],{"xmlns":890,"display":28251},[892,81519,81520,81572],{},[895,81521,81522,81536,81538,81540,81558,81560,81562,81564,81566,81568,81570],{},[1774,81523,81524,81530],{},[895,81525,81526,81528],{},[898,81527,2406],{},[898,81529,1735],{},[895,81531,81532,81534],{},[898,81533,2406],{},[898,81535,1706],{},[1700,81537,1765],{},[1700,81539,1768],{},[1774,81541,81542,81550],{},[2030,81543,81544,81546,81548],{},[898,81545,1662],{},[898,81547,1706],{},[1700,81549,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[2030,81551,81552,81554,81556],{},[898,81553,1662],{},[898,81555,1735],{},[1700,81557,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,81559,1765],{},[1700,81561,1768],{},[898,81563,2005],{},[898,81565,4185],{},[898,81567,2971],{},[898,81569,8861],{},[898,81571,2196],{"mathvariant":1791},[902,81573,81574],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,81576,81577,81578,81593,81594,81610],{},"Změní-li se práce o ",[883,81579,81581],{"className":81580},[886],[888,81582,81583],{"xmlns":890},[892,81584,81585,81591],{},[895,81586,81587,81589],{},[898,81588,2406],{},[898,81590,1706],{},[902,81592,75539],{"encoding":904},", lze pro odhad změny kapitálu ",[883,81595,81597],{"className":81596},[886],[888,81598,81599],{"xmlns":890},[892,81600,81601,81607],{},[895,81602,81603,81605],{},[898,81604,3084],{"mathvariant":1791},[898,81606,1735],{},[902,81608,81609],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,81612,81614],{"className":81613},[886],[888,81615,81616],{"xmlns":890,"display":28251},[892,81617,81618,81665],{},[20939,81619,81620],{"width":28256},[20944,81621,81622,81624,81658,81660],{},[20947,81623],{"width":28261},[20947,81625,81626],{},[895,81627,81628,81630,81632,81634,81636,81638,81640,81642,81644,81646,81648,81650,81652,81654,81656],{},[898,81629,3084],{"mathvariant":1791},[898,81631,1735],{},[1700,81633,2927],{},[898,81635,2406],{},[898,81637,1735],{},[1700,81639,1765],{},[1700,81641,1768],{},[898,81643,2005],{},[898,81645,4185],{},[898,81647,2971],{},[898,81649,8861],{},[1781,81651,1783],{},[898,81653,2406],{},[898,81655,1706],{},[1700,81657,1732],{"separator":1731},[20947,81659],{"width":28261},[20947,81661,81662],{},[1781,81663,81664],{},"(5.15)",[902,81666,81667],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,81669,81671],{"className":81670},[886],[888,81672,81673],{"xmlns":890,"display":28251},[892,81674,81675,81724],{},[20939,81676,81677],{"width":28256},[20944,81678,81679,81681,81717,81719],{},[20947,81680],{"width":28261},[20947,81682,81683],{},[895,81684,81685,81687,81689,81691,81709,81711,81713,81715],{},[898,81686,2406],{},[898,81688,1706],{},[1700,81690,1765],{},[1774,81692,81693,81699],{},[895,81694,81695,81697],{},[1700,81696,1768],{},[1931,81698,1933],{},[895,81700,81701,81703,81705,81707],{},[898,81702,2005],{},[898,81704,4185],{},[898,81706,2971],{},[898,81708,8861],{},[1781,81710,1783],{},[898,81712,2406],{},[898,81714,1735],{},[898,81716,2196],{"mathvariant":1791},[20947,81718],{"width":28261},[20947,81720,81721],{},[1781,81722,81723],{},"(5.16)",[902,81725,81726],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[4060,81728,81729,81753],{},[724,81730,81731,81733,81734],{},[883,81732,4761],{}," Postup — jak spočítat ",[883,81735,81737],{"className":81736},[886],[888,81738,81739],{"xmlns":890},[892,81740,81741,81751],{},[895,81742,81743,81745,81747,81749],{},[898,81744,2005],{},[898,81746,4185],{},[898,81748,2971],{},[898,81750,8861],{},[902,81752,10782],{"encoding":904},[152,81754,81755,81796,81839,81871],{},[123,81756,81757,81758,2114,81777,2196],{},"Vypočtěte parciální derivace ",[883,81759,81761],{"className":81760},[886],[888,81762,81763],{"xmlns":890},[892,81764,81765,81775],{},[895,81766,81767],{},[2030,81768,81769,81771,81773],{},[898,81770,1662],{},[898,81772,1706],{},[1700,81774,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,81776,10204],{"encoding":904},[883,81778,81780],{"className":81779},[886],[888,81781,81782],{"xmlns":890},[892,81783,81784,81794],{},[895,81785,81786],{},[2030,81787,81788,81790,81792],{},[898,81789,1662],{},[898,81791,1735],{},[1700,81793,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,81795,10250],{"encoding":904},[123,81797,66025,81798,81838],{},[883,81799,81801],{"className":81800},[886],[888,81802,81803],{"xmlns":890},[892,81804,81805,81835],{},[895,81806,81807,81809,81811,81813,81815,81817,81825,81827],{},[898,81808,2005],{},[898,81810,4185],{},[898,81812,2971],{},[898,81814,8861],{},[1700,81816,1765],{},[2030,81818,81819,81821,81823],{},[898,81820,1662],{},[898,81822,1706],{},[1700,81824,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[898,81826,1979],{"mathvariant":1791},[2030,81828,81829,81831,81833],{},[898,81830,1662],{},[898,81832,1735],{},[1700,81834,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,81836,81837],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,81840,81841,81842,2196],{},"Případně dosaďte konkrétní ",[883,81843,81845],{"className":81844},[886],[888,81846,81847],{"xmlns":890},[892,81848,81849,81869],{},[895,81850,81851,81853,81859,81861,81867],{},[1700,81852,1927],{"stretchy":1702},[2007,81854,81855,81857],{},[898,81856,1706],{},[1931,81858,1772],{},[1700,81860,1732],{"separator":1731},[2007,81862,81863,81865],{},[898,81864,1735],{},[1931,81866,1772],{},[1700,81868,1970],{"stretchy":1702},[902,81870,81457],{"encoding":904},[123,81872,81873,81874,81908,81909,81911],{},"Pro odhad substituce použijte ",[883,81875,81877],{"className":81876},[886],[888,81878,81879],{"xmlns":890},[892,81880,81881,81905],{},[895,81882,81883,81885,81887,81889,81891,81893,81895,81897,81899,81901,81903],{},[898,81884,3084],{"mathvariant":1791},[898,81886,1735],{},[1700,81888,2927],{},[1700,81890,1768],{},[898,81892,2005],{},[898,81894,4185],{},[898,81896,2971],{},[898,81898,8861],{},[1700,81900,2065],{},[898,81902,3084],{"mathvariant":1791},[898,81904,1706],{},[902,81906,81907],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,81910,52790],{}," — substituce, ne doplnění).",[724,81913,81914],{},[614,81915,81916,81917,81949,81950,2821,81963,15977,81992,82007],{},"Obrázek 5.7 — izokvanta ",[883,81918,81920],{"className":81919},[886],[888,81921,81922],{"xmlns":890},[892,81923,81924,81946],{},[895,81925,81926,81932,81934,81936,81938,81940,81942,81944],{},[2007,81927,81928,81930],{},[898,81929,80980],{},[1931,81931,1772],{},[1700,81933,1765],{},[898,81935,1662],{},[1700,81937,1703],{"stretchy":1702},[898,81939,1706],{},[1700,81941,1732],{"separator":1731},[898,81943,1735],{},[1700,81945,1709],{"stretchy":1702},[902,81947,81948],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,81951,81953],{"className":81952},[886],[888,81954,81955],{"xmlns":890},[892,81956,81957,81961],{},[895,81958,81959],{},[898,81960,19040],{},[902,81962,19040],{"encoding":904},[883,81964,81966],{"className":81965},[886],[888,81967,81968],{"xmlns":890},[892,81969,81970,81990],{},[895,81971,81972,81974,81980,81982,81988],{},[1700,81973,1927],{"stretchy":1702},[2007,81975,81976,81978],{},[898,81977,1706],{},[1931,81979,1772],{},[1700,81981,1732],{"separator":1731},[2007,81983,81984,81986],{},[898,81985,1735],{},[1931,81987,1772],{},[1700,81989,1970],{"stretchy":1702},[902,81991,81457],{"encoding":904},[883,81993,81995],{"className":81994},[886],[888,81996,81997],{"xmlns":890},[892,81998,81999,82005],{},[895,82000,82001,82003],{},[898,82002,3084],{"mathvariant":1791},[898,82004,1735],{},[902,82006,81609],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,82009,82011],{"id":82010},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,82013,82015],{"id":82014},"příklad-54","Příklad 5.4",[724,82017,76856,82018,1343,82060,1343,82077,2196],{},[883,82019,82021],{"className":82020},[886],[888,82022,82023],{"xmlns":890},[892,82024,82025,82057],{},[895,82026,82027,82029,82031,82033,82045],{},[898,82028,1662],{},[1700,82030,1765],{},[1931,82032,36429],{},[1785,82034,82035,82037],{},[898,82036,1706],{},[895,82038,82039,82041,82043],{},[1931,82040,1933],{},[898,82042,1979],{"mathvariant":1791},[1931,82044,2343],{},[1785,82046,82047,82049],{},[898,82048,1735],{},[895,82050,82051,82053,82055],{},[1931,82052,1933],{},[898,82054,1979],{"mathvariant":1791},[1931,82056,2385],{},[902,82058,82059],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,82061,82063],{"className":82062},[886],[888,82064,82065],{"xmlns":890},[892,82066,82067,82075],{},[895,82068,82069,82071,82073],{},[898,82070,1706],{},[1700,82072,1765],{},[1931,82074,9223],{},[902,82076,77230],{"encoding":904},[883,82078,82080],{"className":82079},[886],[888,82081,82082],{"xmlns":890},[892,82083,82084,82092],{},[895,82085,82086,82088,82090],{},[898,82087,1735],{},[1700,82089,1765],{},[1931,82091,3284],{},[902,82093,82094],{"encoding":904},"K = 100",[724,82096,82097],{},[38,82098,82099],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,82101,82103],{"className":82102},[886],[888,82104,82105],{"xmlns":890,"display":28251},[892,82106,82107,82221],{},[895,82108,82109,82111,82117,82119,82127,82129,82137,82151,82163,82165,82167,82169,82175,82177,82179,82181,82183,82185,82187,82195,82197,82207,82209,82216,82218],{},[898,82110,2005],{},[2007,82112,82113,82115],{},[898,82114,1677],{},[898,82116,1706],{},[1700,82118,1765],{},[2030,82120,82121,82123,82125],{},[898,82122,1662],{},[898,82124,1706],{},[1700,82126,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,82128,1765],{},[1770,82130,82131],{"scriptlevel":1772,"displaystyle":1702},[1774,82132,82133,82135],{},[1931,82134,36429],{},[1931,82136,2343],{},[1785,82138,82139,82141],{},[898,82140,1706],{},[895,82142,82143,82145,82147,82149],{},[1700,82144,1768],{},[1931,82146,1933],{},[898,82148,1979],{"mathvariant":1791},[1931,82150,2343],{},[1785,82152,82153,82155],{},[898,82154,1735],{},[895,82156,82157,82159,82161],{},[1931,82158,1933],{},[898,82160,1979],{"mathvariant":1791},[1931,82162,2385],{},[1700,82164,1732],{"separator":1731},[6066,82166],{"width":15469},[898,82168,2005],{},[2007,82170,82171,82173],{},[898,82172,1677],{},[898,82174,1706],{},[1700,82176,1703],{"stretchy":1702},[1931,82178,9223],{},[1700,82180,1732],{"separator":1731},[1931,82182,3284],{},[1700,82184,1709],{"stretchy":1702},[1700,82186,1765],{},[1770,82188,82189],{"scriptlevel":1772,"displaystyle":1702},[1774,82190,82191,82193],{},[1931,82192,36429],{},[1931,82194,2343],{},[1700,82196,2065],{},[1770,82198,82199],{"scriptlevel":1772,"displaystyle":1702},[1774,82200,82201,82203],{},[1931,82202,1933],{},[8305,82204,82205],{},[1931,82206,9223],{},[1700,82208,2065],{},[82210,82211,82212,82214],"mroot",{},[1931,82213,3284],{},[1931,82215,2385],{},[1700,82217,2927],{},[1931,82219,82220],{},"7,153.",[902,82222,82223],{"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.",[724,82225,82226,82227,44345,82249,10416,82266,82287,82288,82309],{},"Přibližná změna při ",[883,82228,82230],{"className":82229},[886],[888,82231,82232],{"xmlns":890},[892,82233,82234,82246],{},[895,82235,82236,82238,82240,82242,82244],{},[898,82237,1706],{},[1700,82239,2901],{},[1931,82241,9223],{},[1700,82243,3317],{},[1931,82245,38531],{},[902,82247,82248],{"encoding":904},"L: 20 \\to 21",[883,82250,82252],{"className":82251},[886],[888,82253,82254],{"xmlns":890},[892,82255,82256,82264],{},[895,82257,82258,82260,82262],{},[898,82259,1735],{},[1700,82261,1765],{},[1931,82263,3284],{},[902,82265,82094],{"encoding":904},[883,82267,82269],{"className":82268},[886],[888,82270,82271],{"xmlns":890},[892,82272,82273,82284],{},[895,82274,82275,82277,82279,82281],{},[898,82276,3084],{"mathvariant":1791},[898,82278,1662],{},[1700,82280,2927],{},[1931,82282,82283],{},"7,153",[902,82285,82286],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,82289,82291],{"className":82290},[886],[888,82292,82293],{"xmlns":890},[892,82294,82295,82306],{},[895,82296,82297,82299,82301,82303],{},[898,82298,3084],{"mathvariant":1791},[898,82300,1662],{},[1700,82302,2927],{},[1931,82304,82305],{},"26,888",[902,82307,82308],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,82311,82312,82315],{},[38,82313,82314],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,82317,82319],{"className":82318},[886],[888,82320,82321],{"xmlns":890,"display":28251},[892,82322,82323,82423],{},[895,82324,82325,82327,82333,82335,82343,82345,82347,82359,82373,82375,82377,82379,82385,82387,82389,82391,82393,82395,82397,82399,82403,82405,82418,82420],{},[898,82326,2005],{},[2007,82328,82329,82331],{},[898,82330,1677],{},[898,82332,1735],{},[1700,82334,1765],{},[2030,82336,82337,82339,82341],{},[898,82338,1662],{},[898,82340,1735],{},[1700,82342,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,82344,1765],{},[1931,82346,2438],{},[1785,82348,82349,82351],{},[898,82350,1706],{},[895,82352,82353,82355,82357],{},[1931,82354,1933],{},[898,82356,1979],{"mathvariant":1791},[1931,82358,2343],{},[1785,82360,82361,82363],{},[898,82362,1735],{},[895,82364,82365,82367,82369,82371],{},[1700,82366,1768],{},[1931,82368,2343],{},[898,82370,1979],{"mathvariant":1791},[1931,82372,2385],{},[1700,82374,1732],{"separator":1731},[6066,82376],{"width":15469},[898,82378,2005],{},[2007,82380,82381,82383],{},[898,82382,1677],{},[898,82384,1735],{},[1700,82386,1703],{"stretchy":1702},[1931,82388,9223],{},[1700,82390,1732],{"separator":1731},[1931,82392,3284],{},[1700,82394,1709],{"stretchy":1702},[1700,82396,1765],{},[1931,82398,2438],{},[8305,82400,82401],{},[1931,82402,9223],{},[1700,82404,2065],{},[1770,82406,82407],{"scriptlevel":1772,"displaystyle":1702},[1774,82408,82409,82411],{},[1931,82410,1933],{},[82210,82412,82413,82416],{},[1931,82414,82415],{},"10000",[1931,82417,2385],{},[1700,82419,2927],{},[1931,82421,82422],{},"4,525.",[902,82424,82425],{"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.",[724,82427,82428,82429,2882,82446,4110],{},"Produkce poklesne přibližně o 4,525 (z ",[883,82430,82432],{"className":82431},[886],[888,82433,82434],{"xmlns":890},[892,82435,82436,82443],{},[895,82437,82438,82440],{},[1700,82439,2927],{},[1931,82441,82442],{},"905,126",[902,82444,82445],{"encoding":904},"\\approx 905{,}126",[883,82447,82449],{"className":82448},[886],[888,82450,82451],{"xmlns":890},[892,82452,82453,82460],{},[895,82454,82455,82457],{},[1700,82456,2927],{},[1931,82458,82459],{},"900,601",[902,82461,82462],{"encoding":904},"\\approx 900{,}601",[724,82464,82465,3324,82512,1343,82534,4110],{},[38,82466,82467,82468,2114,82490],{},"(c) Změna ",[883,82469,82471],{"className":82470},[886],[888,82472,82473],{"xmlns":890},[892,82474,82475,82487],{},[895,82476,82477,82479,82481,82483,82485],{},[898,82478,1706],{},[1700,82480,2901],{},[1931,82482,9223],{},[1700,82484,3317],{},[1931,82486,36429],{},[902,82488,82489],{"encoding":904},"L: 20 \\to 15",[883,82491,82493],{"className":82492},[886],[888,82494,82495],{"xmlns":890},[892,82496,82497,82509],{},[895,82498,82499,82501,82503,82505,82507],{},[898,82500,1735],{},[1700,82502,2901],{},[1931,82504,3284],{},[1700,82506,3317],{},[1931,82508,8991],{},[902,82510,82511],{"encoding":904},"K: 100 \\to 150",[883,82513,82515],{"className":82514},[886],[888,82516,82517],{"xmlns":890},[892,82518,82519,82531],{},[895,82520,82521,82523,82525,82527,82529],{},[898,82522,2406],{},[898,82524,1706],{},[1700,82526,1765],{},[1700,82528,1768],{},[1931,82530,2438],{},[902,82532,82533],{"encoding":904},"dL = -5",[883,82535,82537],{"className":82536},[886],[888,82538,82539],{"xmlns":890},[892,82540,82541,82551],{},[895,82542,82543,82545,82547,82549],{},[898,82544,2406],{},[898,82546,1735],{},[1700,82548,1765],{},[1931,82550,3314],{},[902,82552,82553],{"encoding":904},"dK = 50",[883,82555,82557],{"className":82556},[886],[888,82558,82559],{"xmlns":890,"display":28251},[892,82560,82561,82649],{},[895,82562,82563,82565,82567,82569,82571,82577,82579,82581,82583,82585,82587,82589,82591,82593,82595,82597,82599,82601,82607,82609,82611,82613,82615,82617,82619,82621,82623,82625,82627,82629,82631,82633,82635,82637,82640,82642,82644,82646],{},[898,82564,2406],{},[898,82566,1662],{},[1700,82568,1765],{},[898,82570,2005],{},[2007,82572,82573,82575],{},[898,82574,1677],{},[898,82576,1706],{},[1700,82578,1703],{"stretchy":1702},[1931,82580,9223],{},[1700,82582,1732],{"separator":1731},[1931,82584,3284],{},[1700,82586,1709],{"stretchy":1702},[1700,82588,2065],{},[1700,82590,1703],{"stretchy":1702},[1700,82592,1768],{},[1931,82594,2438],{},[1700,82596,1709],{"stretchy":1702},[1700,82598,1897],{},[898,82600,2005],{},[2007,82602,82603,82605],{},[898,82604,1677],{},[898,82606,1735],{},[1700,82608,1703],{"stretchy":1702},[1931,82610,9223],{},[1700,82612,1732],{"separator":1731},[1931,82614,3284],{},[1700,82616,1709],{"stretchy":1702},[1700,82618,2065],{},[1931,82620,3314],{},[1700,82622,1765],{},[1931,82624,82283],{},[1700,82626,2065],{},[1700,82628,1703],{"stretchy":1702},[1700,82630,1768],{},[1931,82632,2438],{},[1700,82634,1709],{"stretchy":1702},[1700,82636,1897],{},[1931,82638,82639],{},"4,525",[1700,82641,2065],{},[1931,82643,3314],{},[1700,82645,2927],{},[1931,82647,82648],{},"190,485.",[902,82650,82651],{"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.",[724,82653,82654],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,82656,82658],{"id":82657},"příklad-55","Příklad 5.5",[724,82660,82661,82662,82698,82699,2196],{},"Pro produkci ",[883,82663,82665],{"className":82664},[886],[888,82666,82667],{"xmlns":890},[892,82668,82669,82695],{},[895,82670,82671,82673,82675,82677,82679,82681,82683,82685,82691],{},[898,82672,1662],{},[1700,82674,1703],{"stretchy":1702},[898,82676,1706],{},[1700,82678,1732],{"separator":1731},[898,82680,1735],{},[1700,82682,1709],{"stretchy":1702},[1700,82684,1765],{},[82210,82686,82687,82689],{},[898,82688,1706],{},[1931,82690,2385],{},[8305,82692,82693],{},[898,82694,1735],{},[902,82696,82697],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,82700,82702],{"className":82701},[886],[888,82703,82704],{"xmlns":890},[892,82705,82706,82722],{},[895,82707,82708,82714,82718,82720],{},[82210,82709,82710,82712],{},[898,82711,1706],{},[1931,82713,2385],{},[8305,82715,82716],{},[898,82717,1735],{},[1700,82719,1765],{},[898,82721,80980],{},[902,82723,82724],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,82726,82727,82728,2196],{},"Umocněním na druhou: ",[883,82729,82731],{"className":82730},[886],[888,82732,82733],{"xmlns":890},[892,82734,82735,82759],{},[895,82736,82737,82739,82741,82747,82749],{},[898,82738,1735],{},[1700,82740,1765],{},[1785,82742,82743,82745],{},[898,82744,80980],{},[1931,82746,2343],{},[898,82748,1979],{"mathvariant":1791},[82210,82750,82751,82757],{},[1785,82752,82753,82755],{},[898,82754,1706],{},[1931,82756,2343],{},[1931,82758,2385],{},[902,82760,82761],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,82763,82764,82804,82844],{},[123,82765,82766],{},[883,82767,82769],{"className":82768},[886],[888,82770,82771],{"xmlns":890},[892,82772,82773,82801],{},[895,82774,82775,82777,82779,82781,82783,82785,82787,82789,82791],{},[898,82776,80980],{},[1700,82778,1765],{},[1931,82780,1933],{},[1700,82782,4178],{},[898,82784,1735],{},[1700,82786,1765],{},[1931,82788,1933],{},[898,82790,1979],{"mathvariant":1791},[82210,82792,82793,82799],{},[1785,82794,82795,82797],{},[898,82796,1706],{},[1931,82798,2343],{},[1931,82800,2385],{},[902,82802,82803],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,82805,82806],{},[883,82807,82809],{"className":82808},[886],[888,82810,82811],{"xmlns":890},[892,82812,82813,82841],{},[895,82814,82815,82817,82819,82821,82823,82825,82827,82829,82831],{},[898,82816,80980],{},[1700,82818,1765],{},[1931,82820,2343],{},[1700,82822,4178],{},[898,82824,1735],{},[1700,82826,1765],{},[1931,82828,2553],{},[898,82830,1979],{"mathvariant":1791},[82210,82832,82833,82839],{},[1785,82834,82835,82837],{},[898,82836,1706],{},[1931,82838,2343],{},[1931,82840,2385],{},[902,82842,82843],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,82845,82846],{},[883,82847,82849],{"className":82848},[886],[888,82850,82851],{"xmlns":890},[892,82852,82853,82881],{},[895,82854,82855,82857,82859,82861,82863,82865,82867,82869,82871],{},[898,82856,80980],{},[1700,82858,1765],{},[1931,82860,2385],{},[1700,82862,4178],{},[898,82864,1735],{},[1700,82866,1765],{},[1931,82868,4190],{},[898,82870,1979],{"mathvariant":1791},[82210,82872,82873,82879],{},[1785,82874,82875,82877],{},[898,82876,1706],{},[1931,82878,2343],{},[1931,82880,2385],{},[902,82882,82883],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,82885,82886],{},[614,82887,82888,82889,6661,82910,2196],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,82890,82892],{"className":82891},[886],[888,82893,82894],{"xmlns":890},[892,82895,82896,82908],{},[895,82897,82898,82900,82902,82904,82906],{},[1700,82899,1703],{"stretchy":1702},[898,82901,1706],{},[1700,82903,1732],{"separator":1731},[898,82905,1735],{},[1700,82907,1709],{"stretchy":1702},[902,82909,81106],{"encoding":904},[883,82911,82913],{"className":82912},[886],[888,82914,82915],{"xmlns":890},[892,82916,82917,82933],{},[895,82918,82919,82921,82923,82925,82927,82929,82931],{},[898,82920,80980],{},[1700,82922,1765],{},[1931,82924,1933],{},[1700,82926,1732],{"separator":1731},[1931,82928,2343],{},[1700,82930,1732],{"separator":1731},[1931,82932,2385],{},[902,82934,82935],{"encoding":904},"q = 1, 2, 3",[198,82937,82939],{"id":82938},"příklad-56","Příklad 5.6",[724,82941,76856,82942,2196],{},[883,82943,82945],{"className":82944},[886],[888,82946,82947],{"xmlns":890},[892,82948,82949,82965],{},[895,82950,82951,82953,82955,82957,82959,82961],{},[898,82952,1662],{},[1700,82954,1765],{},[1931,82956,2343],{},[898,82958,1706],{},[1700,82960,1897],{},[8305,82962,82963],{},[898,82964,1735],{},[902,82966,82967],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,82969,82971],{"className":82970},[886],[888,82972,82973],{"xmlns":890,"display":28251},[892,82974,82975,83017],{},[895,82976,82977,82979,82985,82987,82989,82991,82993,82995,83001,83003,83015],{},[898,82978,2005],{},[2007,82980,82981,82983],{},[898,82982,1677],{},[898,82984,1706],{},[1700,82986,1765],{},[1931,82988,2343],{},[1700,82990,1732],{"separator":1731},[6066,82992],{"width":6068},[898,82994,2005],{},[2007,82996,82997,82999],{},[898,82998,1677],{},[898,83000,1735],{},[1700,83002,1765],{},[1774,83004,83005,83007],{},[1931,83006,1933],{},[895,83008,83009,83011],{},[1931,83010,2343],{},[8305,83012,83013],{},[898,83014,1735],{},[898,83016,2196],{"mathvariant":1791},[902,83018,83019],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,83021,83023],{"className":83022},[886],[888,83024,83025],{"xmlns":890,"display":28251},[892,83026,83027,83091],{},[895,83028,83029,83031,83033,83035,83037,83039,83061,83063,83081,83083,83085,83089],{},[898,83030,2005],{},[898,83032,4185],{},[898,83034,2971],{},[898,83036,8861],{},[1700,83038,1765],{},[1774,83040,83041,83051],{},[895,83042,83043,83045],{},[898,83044,2005],{},[2007,83046,83047,83049],{},[898,83048,1677],{},[898,83050,1706],{},[895,83052,83053,83055],{},[898,83054,2005],{},[2007,83056,83057,83059],{},[898,83058,1677],{},[898,83060,1735],{},[1700,83062,1765],{},[1774,83064,83065,83067],{},[1931,83066,2343],{},[1770,83068,83069],{"scriptlevel":1772,"displaystyle":1702},[1774,83070,83071,83073],{},[1931,83072,1933],{},[895,83074,83075,83077],{},[1931,83076,2343],{},[8305,83078,83079],{},[898,83080,1735],{},[1700,83082,1765],{},[1931,83084,2553],{},[8305,83086,83087],{},[898,83088,1735],{},[898,83090,2196],{"mathvariant":1791},[902,83092,83093],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,83095,83096,83097,83140,83141,83180,83181,2196],{},"Například ",[883,83098,83100],{"className":83099},[886],[888,83101,83102],{"xmlns":890},[892,83103,83104,83137],{},[895,83105,83106,83108,83110,83112,83114,83116,83118,83120,83122,83124,83126,83128,83132,83134],{},[898,83107,2005],{},[898,83109,4185],{},[898,83111,2971],{},[898,83113,8861],{},[1700,83115,1703],{"stretchy":1702},[1931,83117,2553],{},[1700,83119,1732],{"separator":1731},[1931,83121,24386],{},[1700,83123,1709],{"stretchy":1702},[1700,83125,1765],{},[1931,83127,2553],{},[8305,83129,83130],{},[1931,83131,24386],{},[1700,83133,2927],{},[1931,83135,83136],{},"10,58",[902,83138,83139],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,83142,83144],{"className":83143},[886],[888,83145,83146],{"xmlns":890},[892,83147,83148,83177],{},[895,83149,83150,83152,83154,83156,83158,83160,83162,83164,83166,83168,83172,83174],{},[898,83151,1662],{},[1700,83153,1703],{"stretchy":1702},[1931,83155,2553],{},[1700,83157,1732],{"separator":1731},[1931,83159,24386],{},[1700,83161,1709],{"stretchy":1702},[1700,83163,1765],{},[1931,83165,5773],{},[1700,83167,1897],{},[8305,83169,83170],{},[1931,83171,24386],{},[1700,83173,2927],{},[1931,83175,83176],{},"10,646",[902,83178,83179],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,83182,83184],{"className":83183},[886],[888,83185,83186],{"xmlns":890},[892,83187,83188,83196],{},[895,83189,83190,83192],{},[1931,83191,2553],{},[8305,83193,83194],{},[1931,83195,24386],{},[902,83197,83198],{"encoding":904},"4\\sqrt{7}",[724,83200,83201,83202,83222],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,83203,83205],{"className":83204},[886],[888,83206,83207],{"xmlns":890},[892,83208,83209,83219],{},[895,83210,83211,83213,83215,83217],{},[898,83212,2406],{},[898,83214,1706],{},[1700,83216,1765],{},[1931,83218,2343],{},[902,83220,83221],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,83224,83226],{"className":83225},[886],[888,83227,83228],{"xmlns":890,"display":28251},[892,83229,83230,83279],{},[895,83231,83232,83234,83236,83238,83240,83242,83244,83246,83248,83250,83252,83254,83256,83258,83260,83262,83264,83266,83268,83272,83274,83276],{},[898,83233,2406],{},[898,83235,1735],{},[1700,83237,1765],{},[1700,83239,1768],{},[898,83241,2005],{},[898,83243,4185],{},[898,83245,2971],{},[898,83247,8861],{},[1700,83249,1703],{"stretchy":1702},[1931,83251,2553],{},[1700,83253,1732],{"separator":1731},[1931,83255,24386],{},[1700,83257,1709],{"stretchy":1702},[1700,83259,2065],{},[1931,83261,2343],{},[1700,83263,1765],{},[1700,83265,1768],{},[1931,83267,5773],{},[8305,83269,83270],{},[1931,83271,24386],{},[1700,83273,2927],{},[1700,83275,1768],{},[1931,83277,83278],{},"21,17.",[902,83280,83281],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,83283,83285],{"id":83284},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,83287,83288,83289,1343,83291,2114,83293,83295,83296,83299,83300,83303],{},"Hlavními faktory produkce jsou ",[38,83290,75097],{},[38,83292,75113],{},[38,83294,75129],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,83297,83298],{},"jednofaktorový"," (pouze práce) a ",[38,83301,83302],{},"dvoufaktorový"," (práce + kapitál) model.",[724,83305,83306,83307,83310,83311,83313,83314,83316,83317,26374,83320,83339,83340,83357,83358,83375,83376,83398,83399,4547,83418,2196],{},"V ",[38,83308,83309],{},"1F modelu"," se definuje ",[38,83312,10207],{}," (derivace produkce podle práce) a ",[38,83315,75033],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,83318,83319],{},"zákonu klesajících výnosů",[883,83321,83323],{"className":83322},[886],[888,83324,83325],{"xmlns":890},[892,83326,83327,83337],{},[895,83328,83329,83331],{},[898,83330,2005],{},[2007,83332,83333,83335],{},[898,83334,1677],{},[898,83336,1706],{},[902,83338,10228],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,83341,83343],{"className":83342},[886],[888,83344,83345],{"xmlns":890},[892,83346,83347,83355],{},[895,83348,83349],{},[2007,83350,83351,83353],{},[898,83352,1706],{},[1931,83354,1772],{},[902,83356,75741],{"encoding":904}," klesá a v bodě ",[883,83359,83361],{"className":83360},[886],[888,83362,83363],{"xmlns":890},[892,83364,83365,83373],{},[895,83366,83367],{},[2007,83368,83369,83371],{},[898,83370,1706],{},[1931,83372,1933],{},[902,83374,13397],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,83377,83378,83379],{},"princip maximalizace ",[883,83380,83382],{"className":83381},[886],[888,83383,83384],{"xmlns":890},[892,83385,83386,83396],{},[895,83387,83388,83390],{},[898,83389,1862],{},[2007,83391,83392,83394],{},[898,83393,1677],{},[898,83395,1706],{},[902,83397,74817],{"encoding":904},": v bodě maxima ",[883,83400,83402],{"className":83401},[886],[888,83403,83404],{"xmlns":890},[892,83405,83406,83416],{},[895,83407,83408,83410],{},[898,83409,1862],{},[2007,83411,83412,83414],{},[898,83413,1677],{},[898,83415,1706],{},[902,83417,74817],{"encoding":904},[883,83419,83421],{"className":83420},[886],[888,83422,83423],{"xmlns":890},[892,83424,83425,83445],{},[895,83426,83427,83429,83435,83437,83439],{},[898,83428,2005],{},[2007,83430,83431,83433],{},[898,83432,1677],{},[898,83434,1706],{},[1700,83436,1765],{},[898,83438,1862],{},[2007,83440,83441,83443],{},[898,83442,1677],{},[898,83444,1706],{},[902,83446,74847],{"encoding":904},[724,83448,83449,83450,83453,83454,2106,83457,83486,83487,83504,83505,83508,83509,83538,83539,83541,83542,8290,83572,83594],{},"Ve ",[38,83451,83452],{},"2F modelu"," se obvykle používají ",[38,83455,83456],{},"Cobb-Douglasovy funkce",[883,83458,83460],{"className":83459},[886],[888,83461,83462],{"xmlns":890},[892,83463,83464,83484],{},[895,83465,83466,83468,83470,83472,83478],{},[898,83467,1662],{},[1700,83469,1765],{},[898,83471,1862],{},[1785,83473,83474,83476],{},[898,83475,1706],{},[898,83477,207],{},[1785,83479,83480,83482],{},[898,83481,1735],{},[898,83483,1879],{},[902,83485,74914],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,83488,83490],{"className":83489},[886],[888,83491,83492],{"xmlns":890},[892,83493,83494,83502],{},[895,83495,83496,83498,83500],{},[898,83497,207],{},[1700,83499,1897],{},[898,83501,1879],{},[902,83503,75008],{"encoding":904}," rozlišujeme ",[38,83506,83507],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,83510,83512],{"className":83511},[886],[888,83513,83514],{"xmlns":890},[892,83515,83516,83536],{},[895,83517,83518,83520,83526,83528,83530],{},[898,83519,2005],{},[2007,83521,83522,83524],{},[898,83523,1677],{},[898,83525,1706],{},[1700,83527,1732],{"separator":1731},[898,83529,2005],{},[2007,83531,83532,83534],{},[898,83533,1677],{},[898,83535,1735],{},[902,83537,74945],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,83540,9965],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,83543,83545],{"className":83544},[886],[888,83546,83547],{"xmlns":890},[892,83548,83549,83569],{},[895,83550,83551,83553,83559,83561,83563],{},[898,83552,2005],{},[2007,83554,83555,83557],{},[898,83556,1677],{},[898,83558,1706],{},[898,83560,1979],{"mathvariant":1791},[898,83562,2005],{},[2007,83564,83565,83567],{},[898,83566,1677],{},[898,83568,1735],{},[902,83570,83571],{"encoding":904},"MP_L\u002FMP_K",[38,83573,83574,83575,1709],{},"mezní míra technické substituce (",[883,83576,83578],{"className":83577},[886],[888,83579,83580],{"xmlns":890},[892,83581,83582,83592],{},[895,83583,83584,83586,83588,83590],{},[898,83585,2005],{},[898,83587,4185],{},[898,83589,2971],{},[898,83591,8861],{},[902,83593,10782],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,83596,50067],{"id":50066},[152,83598,83599,83602,83605,83608,83611,83614,83617,83620,83623,83626,83629],{},[123,83600,83601],{},"Jaké jsou faktory produkce?",[123,83603,83604],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,83606,83607],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,83609,83610],{},"Co udává mezní produkt práce?",[123,83612,83613],{},"Co musí respektovat průběh křivky produkce?",[123,83615,83616],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,83618,83619],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,83621,83622],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,83624,83625],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,83627,83628],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,83630,83631],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,83633,83635],{"id":83634},"úlohy-51517","Úlohy 5.1–5.17",[198,83637,40636],{"id":40635},[724,83639,83640,83643,83644,83666,83667,1343,83687,1343,83707,83727],{},[38,83641,83642],{},"5.1"," Je dána produkce ",[883,83645,83647],{"className":83646},[886],[888,83648,83649],{"xmlns":890},[892,83650,83651,83663],{},[895,83652,83653,83655,83657,83659],{},[898,83654,1662],{},[1700,83656,1765],{},[1931,83658,3058],{},[8305,83660,83661],{},[898,83662,1706],{},[902,83664,83665],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,83668,83670],{"className":83669},[886],[888,83671,83672],{"xmlns":890},[892,83673,83674,83684],{},[895,83675,83676,83678,83680,83682],{},[898,83677,1662],{},[1700,83679,1703],{"stretchy":1702},[1931,83681,1933],{},[1700,83683,1709],{"stretchy":1702},[902,83685,83686],{"encoding":904},"Q(1)",[883,83688,83690],{"className":83689},[886],[888,83691,83692],{"xmlns":890},[892,83693,83694,83704],{},[895,83695,83696,83698,83700,83702],{},[898,83697,1662],{},[1700,83699,1703],{"stretchy":1702},[1931,83701,2553],{},[1700,83703,1709],{"stretchy":1702},[902,83705,83706],{"encoding":904},"Q(4)",[883,83708,83710],{"className":83709},[886],[888,83711,83712],{"xmlns":890},[892,83713,83714,83724],{},[895,83715,83716,83718,83720,83722],{},[898,83717,1662],{},[1700,83719,1703],{"stretchy":1702},[1931,83721,4190],{},[1700,83723,1709],{"stretchy":1702},[902,83725,83726],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,83729,83730,83643,83733,83769,83770,83783,83784,83803,83804,83830,83831,2882,83844,83857],{},[38,83731,83732],{},"5.2",[883,83734,83736],{"className":83735},[886],[888,83737,83738],{"xmlns":890},[892,83739,83740,83766],{},[895,83741,83742,83744,83746,83748,83750,83756,83758,83760],{},[898,83743,1662],{},[1700,83745,1765],{},[1700,83747,1768],{},[1931,83749,2990],{},[1785,83751,83752,83754],{},[898,83753,1706],{},[1931,83755,2385],{},[1700,83757,1897],{},[1931,83759,4190],{},[1785,83761,83762,83764],{},[898,83763,1706],{},[1931,83765,2343],{},[902,83767,83768],{"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 ",[883,83771,83773],{"className":83772},[886],[888,83774,83775],{"xmlns":890},[892,83776,83777,83781],{},[895,83778,83779],{},[898,83780,1706],{},[902,83782,1706],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,83785,83787],{"className":83786},[886],[888,83788,83789],{"xmlns":890},[892,83790,83791,83801],{},[895,83792,83793,83795],{},[898,83794,2005],{},[2007,83796,83797,83799],{},[898,83798,1677],{},[898,83800,1706],{},[902,83802,10228],{"encoding":904},". (f) Vypočtěte ",[883,83805,83807],{"className":83806},[886],[888,83808,83809],{"xmlns":890},[892,83810,83811,83827],{},[895,83812,83813,83815,83821,83823,83825],{},[898,83814,2005],{},[2007,83816,83817,83819],{},[898,83818,1677],{},[898,83820,1706],{},[1700,83822,1703],{"stretchy":1702},[1931,83824,3058],{},[1700,83826,1709],{"stretchy":1702},[902,83828,83829],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,83832,83834],{"className":83833},[886],[888,83835,83836],{"xmlns":890},[892,83837,83838,83842],{},[895,83839,83840],{},[1931,83841,3058],{},[902,83843,3058],{"encoding":904},[883,83845,83847],{"className":83846},[886],[888,83848,83849],{"xmlns":890},[892,83850,83851,83855],{},[895,83852,83853],{},[1931,83854,42472],{},[902,83856,42472],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,83859,83860,83863,83864,83886,83887,83915,83916,83947,83948,2196],{},[38,83861,83862],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,83865,83867],{"className":83866},[886],[888,83868,83869],{"xmlns":890},[892,83870,83871,83883],{},[895,83872,83873,83875,83877,83879],{},[898,83874,1662],{},[1700,83876,1765],{},[1931,83878,15295],{},[8305,83880,83881],{},[898,83882,1706],{},[902,83884,83885],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,83888,83890],{"className":83889},[886],[888,83891,83892],{"xmlns":890},[892,83893,83894,83912],{},[895,83895,83896,83898,83900,83902,83906,83908,83910],{},[898,83897,1662],{},[1700,83899,1765],{},[1931,83901,30266],{},[8305,83903,83904],{},[898,83905,1706],{},[1700,83907,1768],{},[1931,83909,2553],{},[898,83911,1706],{},[902,83913,83914],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,83917,83919],{"className":83918},[886],[888,83920,83921],{"xmlns":890},[892,83922,83923,83944],{},[895,83924,83925,83927,83929,83931,83933,83935,83938],{},[898,83926,1662],{},[1700,83928,1765],{},[1931,83930,3314],{},[898,83932,1706],{},[1700,83934,1768],{},[1931,83936,83937],{},"0,01",[1785,83939,83940,83942],{},[898,83941,1706],{},[1931,83943,2343],{},[902,83945,83946],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,83949,83951],{"className":83950},[886],[888,83952,83953],{"xmlns":890},[892,83954,83955,83981],{},[895,83956,83957,83959,83961,83963,83965,83971,83973,83975],{},[898,83958,1662],{},[1700,83960,1765],{},[1700,83962,1768],{},[1931,83964,68395],{},[1785,83966,83967,83969],{},[898,83968,1706],{},[1931,83970,2385],{},[1700,83972,1897],{},[1931,83974,4190],{},[1785,83976,83977,83979],{},[898,83978,1706],{},[1931,83980,2343],{},[902,83982,83983],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,83985,83986,83989,83990,2821,84009,72382,84026,2196],{},[38,83987,83988],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,83991,83993],{"className":83992},[886],[888,83994,83995],{"xmlns":890},[892,83996,83997,84007],{},[895,83998,83999,84001],{},[898,84000,1862],{},[2007,84002,84003,84005],{},[898,84004,1677],{},[898,84006,1706],{},[902,84008,74817],{"encoding":904},[883,84010,84012],{"className":84011},[886],[888,84013,84014],{"xmlns":890},[892,84015,84016,84024],{},[895,84017,84018],{},[2007,84019,84020,84022],{},[898,84021,1706],{},[1931,84023,1772],{},[902,84025,75741],{"encoding":904},[883,84027,84029],{"className":84028},[886],[888,84030,84031],{"xmlns":890},[892,84032,84033,84073],{},[895,84034,84035,84037,84043,84045,84051,84053,84055,84057,84063,84065,84071],{},[898,84036,1862],{},[2007,84038,84039,84041],{},[898,84040,1677],{},[898,84042,1706],{},[1700,84044,1703],{"stretchy":1702},[2007,84046,84047,84049],{},[898,84048,1706],{},[1931,84050,1772],{},[1700,84052,1709],{"stretchy":1702},[1700,84054,1765],{},[898,84056,2005],{},[2007,84058,84059,84061],{},[898,84060,1677],{},[898,84062,1706],{},[1700,84064,1703],{"stretchy":1702},[2007,84066,84067,84069],{},[898,84068,1706],{},[1931,84070,1772],{},[1700,84072,1709],{"stretchy":1702},[902,84074,84075],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,84077,84078,83643,84081,21779,84117,84130,84131,84150],{},[38,84079,84080],{},"5.5",[883,84082,84084],{"className":84083},[886],[888,84085,84086],{"xmlns":890},[892,84087,84088,84114],{},[895,84089,84090,84092,84094,84096,84098,84104,84106,84108],{},[898,84091,1662],{},[1700,84093,1765],{},[1700,84095,1768],{},[1931,84097,3034],{},[1785,84099,84100,84102],{},[898,84101,1706],{},[1931,84103,2385],{},[1700,84105,1897],{},[1931,84107,3702],{},[1785,84109,84110,84112],{},[898,84111,1706],{},[1931,84113,2343],{},[902,84115,84116],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,84118,84120],{"className":84119},[886],[888,84121,84122],{"xmlns":890},[892,84123,84124,84128],{},[895,84125,84126],{},[898,84127,1706],{},[902,84129,1706],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,84132,84134],{"className":84133},[886],[888,84135,84136],{"xmlns":890},[892,84137,84138,84148],{},[895,84139,84140,84142],{},[898,84141,1862],{},[2007,84143,84144,84146],{},[898,84145,1677],{},[898,84147,1706],{},[902,84149,74817],{"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.",[198,84152,84154],{"id":84153},"dvoufaktorový-model","Dvoufaktorový model",[724,84156,84157,84160,84161,83886,84187,83915,84229,2196],{},[38,84158,84159],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,84162,84164],{"className":84163},[886],[888,84165,84166],{"xmlns":890},[892,84167,84168,84184],{},[895,84169,84170,84172,84174,84176,84178],{},[898,84171,1662],{},[1700,84173,1765],{},[1931,84175,24386],{},[898,84177,1706],{},[1785,84179,84180,84182],{},[898,84181,1735],{},[1931,84183,2343],{},[902,84185,84186],{"encoding":904},"Q = 7 L K^{2}",[883,84188,84190],{"className":84189},[886],[888,84191,84192],{"xmlns":890},[892,84193,84194,84226],{},[895,84195,84196,84198,84200,84202,84214],{},[898,84197,1662],{},[1700,84199,1765],{},[1931,84201,3314],{},[1785,84203,84204,84206],{},[898,84205,1706],{},[895,84207,84208,84210,84212],{},[1931,84209,2343],{},[898,84211,1979],{"mathvariant":1791},[1931,84213,2385],{},[1785,84215,84216,84218],{},[898,84217,1735],{},[895,84219,84220,84222,84224],{},[1931,84221,1933],{},[898,84223,1979],{"mathvariant":1791},[1931,84225,2385],{},[902,84227,84228],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,84230,84232],{"className":84231},[886],[888,84233,84234],{"xmlns":890},[892,84235,84236,84268],{},[895,84237,84238,84240,84242,84244,84256],{},[898,84239,1662],{},[1700,84241,1765],{},[1931,84243,3900],{},[1785,84245,84246,84248],{},[898,84247,1706],{},[895,84249,84250,84252,84254],{},[1931,84251,2385],{},[898,84253,1979],{"mathvariant":1791},[1931,84255,2438],{},[1785,84257,84258,84260],{},[898,84259,1735],{},[895,84261,84262,84264,84266],{},[1931,84263,2343],{},[898,84265,1979],{"mathvariant":1791},[1931,84267,2438],{},[902,84269,84270],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,84272,84273,83643,84276,84318,84319,1343,84337,84356,84357,84374],{},[38,84274,84275],{},"5.7",[883,84277,84279],{"className":84278},[886],[888,84280,84281],{"xmlns":890},[892,84282,84283,84315],{},[895,84284,84285,84287,84289,84291,84303],{},[898,84286,1662],{},[1700,84288,1765],{},[1931,84290,3058],{},[1785,84292,84293,84295],{},[898,84294,1706],{},[895,84296,84297,84299,84301],{},[1931,84298,1933],{},[898,84300,1979],{"mathvariant":1791},[1931,84302,2343],{},[1785,84304,84305,84307],{},[898,84306,1735],{},[895,84308,84309,84311,84313],{},[1931,84310,1933],{},[898,84312,1979],{"mathvariant":1791},[1931,84314,2343],{},[902,84316,84317],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,84320,84322],{"className":84321},[886],[888,84323,84324],{"xmlns":890},[892,84325,84326,84334],{},[895,84327,84328,84330,84332],{},[898,84329,1706],{},[1700,84331,1765],{},[1931,84333,20327],{},[902,84335,84336],{"encoding":904},"L = 400",[883,84338,84340],{"className":84339},[886],[888,84341,84342],{"xmlns":890},[892,84343,84344,84353],{},[895,84345,84346,84348,84350],{},[898,84347,1735],{},[1700,84349,1765],{},[1931,84351,84352],{},"17576",[902,84354,84355],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,84358,84360],{"className":84359},[886],[888,84361,84362],{"xmlns":890},[892,84363,84364,84372],{},[895,84365,84366,84368,84370],{},[898,84367,1706],{},[1700,84369,1732],{"separator":1731},[898,84371,1735],{},[902,84373,79168],{"encoding":904}," zdvojnásobí.",[724,84376,84377,84380,84381,84318,84412,1343,84430,69768,84448,84478,84479,84509,84510,2882,84523,84537,84538,2882,84551,84564],{},[38,84378,84379],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,84382,84384],{"className":84383},[886],[888,84385,84386],{"xmlns":890},[892,84387,84388,84409],{},[895,84389,84390,84392,84394,84397,84403],{},[898,84391,1662],{},[1700,84393,1765],{},[1931,84395,84396],{},"1,01",[1785,84398,84399,84401],{},[898,84400,1706],{},[1931,84402,23915],{},[1785,84404,84405,84407],{},[898,84406,1735],{},[1931,84408,23974],{},[902,84410,84411],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,84413,84415],{"className":84414},[886],[888,84416,84417],{"xmlns":890},[892,84418,84419,84427],{},[895,84420,84421,84423,84425],{},[898,84422,1706],{},[1700,84424,1765],{},[1931,84426,30928],{},[902,84428,84429],{"encoding":904},"L = 250",[883,84431,84433],{"className":84432},[886],[888,84434,84435],{"xmlns":890},[892,84436,84437,84445],{},[895,84438,84439,84441,84443],{},[898,84440,1735],{},[1700,84442,1765],{},[1931,84444,2979],{},[902,84446,84447],{"encoding":904},"K = 1000",[883,84449,84451],{"className":84450},[886],[888,84452,84453],{"xmlns":890},[892,84454,84455,84475],{},[895,84456,84457,84459,84465,84467,84469,84471,84473],{},[898,84458,2005],{},[2007,84460,84461,84463],{},[898,84462,1677],{},[898,84464,1706],{},[1700,84466,1703],{"stretchy":1702},[1931,84468,30928],{},[1700,84470,1732],{"separator":1731},[1931,84472,2979],{},[1700,84474,1709],{"stretchy":1702},[902,84476,84477],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,84480,84482],{"className":84481},[886],[888,84483,84484],{"xmlns":890},[892,84485,84486,84506],{},[895,84487,84488,84490,84496,84498,84500,84502,84504],{},[898,84489,2005],{},[2007,84491,84492,84494],{},[898,84493,1677],{},[898,84495,1735],{},[1700,84497,1703],{"stretchy":1702},[1931,84499,30928],{},[1700,84501,1732],{"separator":1731},[1931,84503,2979],{},[1700,84505,1709],{"stretchy":1702},[902,84507,84508],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,84511,84513],{"className":84512},[886],[888,84514,84515],{"xmlns":890},[892,84516,84517,84521],{},[895,84518,84519],{},[898,84520,1706],{},[902,84522,1706],{"encoding":904},[883,84524,84526],{"className":84525},[886],[888,84527,84528],{"xmlns":890},[892,84529,84530,84535],{},[895,84531,84532],{},[1931,84533,84534],{},"260",[902,84536,84534],{"encoding":904}," a současném poklesu ",[883,84539,84541],{"className":84540},[886],[888,84542,84543],{"xmlns":890},[892,84544,84545,84549],{},[895,84546,84547],{},[898,84548,1735],{},[902,84550,1735],{"encoding":904},[883,84552,84554],{"className":84553},[886],[888,84555,84556],{"xmlns":890},[892,84557,84558,84562],{},[895,84559,84560],{},[1931,84561,15376],{},[902,84563,15376],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,84566,84567,84570,84571,2196],{},[38,84568,84569],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,84572,84574],{"className":84573},[886],[888,84575,84576],{"xmlns":890},[892,84577,84578,84598],{},[895,84579,84580,84582,84584,84586,84592],{},[898,84581,1662],{},[1700,84583,1765],{},[1931,84585,3058],{},[1785,84587,84588,84590],{},[898,84589,1706],{},[1931,84591,68395],{},[1785,84593,84594,84596],{},[898,84595,1735],{},[1931,84597,5197],{},[902,84599,84600],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,84602,84603,84606,84607,80764,84630,10577,84643,10208,84693,4110],{},[38,84604,84605],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,84608,84610],{"className":84609},[886],[888,84611,84612],{"xmlns":890},[892,84613,84614,84628],{},[895,84615,84616,84618,84620,84622,84624,84626],{},[898,84617,1662],{},[1700,84619,1703],{"stretchy":1702},[898,84621,1706],{},[1700,84623,1732],{"separator":1731},[898,84625,1735],{},[1700,84627,1709],{"stretchy":1702},[902,84629,1740],{"encoding":904},[883,84631,84633],{"className":84632},[886],[888,84634,84635],{"xmlns":890},[892,84636,84637,84641],{},[895,84638,84639],{},[898,84640,37045],{},[902,84642,37045],{"encoding":904},[883,84644,84646],{"className":84645},[886],[888,84647,84648],{"xmlns":890},[892,84649,84650,84690],{},[895,84651,84652,84654,84662,84664,84666,84674,84676,84678,84680,84682,84684,84686,84688],{},[898,84653,1706],{},[2030,84655,84656,84658,84660],{},[898,84657,1662],{},[898,84659,1706],{},[1700,84661,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,84663,1897],{},[898,84665,1735],{},[2030,84667,84668,84670,84672],{},[898,84669,1662],{},[898,84671,1735],{},[1700,84673,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,84675,1765],{},[898,84677,37045],{},[898,84679,1662],{},[1700,84681,1703],{"stretchy":1702},[898,84683,1706],{},[1700,84685,1732],{"separator":1731},[898,84687,1735],{},[1700,84689,1709],{"stretchy":1702},[902,84691,84692],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,84694,80739],{},[724,84696,84697,84700],{},[38,84698,84699],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,84702,84703,83643,84706,84746,84747,1343,84769,1343,84791,84813],{},[38,84704,84705],{},"5.12",[883,84707,84709],{"className":84708},[886],[888,84710,84711],{"xmlns":890},[892,84712,84713,84743],{},[895,84714,84715,84717,84719,84731],{},[898,84716,1662],{},[1700,84718,1765],{},[1785,84720,84721,84723],{},[898,84722,1706],{},[895,84724,84725,84727,84729],{},[1931,84726,1933],{},[898,84728,1979],{"mathvariant":1791},[1931,84730,2385],{},[1785,84732,84733,84735],{},[898,84734,1735],{},[895,84736,84737,84739,84741],{},[1931,84738,1933],{},[898,84740,1979],{"mathvariant":1791},[1931,84742,2553],{},[902,84744,84745],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,84748,84750],{"className":84749},[886],[888,84751,84752],{"xmlns":890},[892,84753,84754,84766],{},[895,84755,84756,84762,84764],{},[2007,84757,84758,84760],{},[898,84759,80980],{},[1931,84761,1772],{},[1700,84763,1765],{},[1931,84765,1933],{},[902,84767,84768],{"encoding":904},"q_0 = 1",[883,84770,84772],{"className":84771},[886],[888,84773,84774],{"xmlns":890},[892,84775,84776,84788],{},[895,84777,84778,84784,84786],{},[2007,84779,84780,84782],{},[898,84781,80980],{},[1931,84783,1933],{},[1700,84785,1765],{},[1931,84787,2343],{},[902,84789,84790],{"encoding":904},"q_1 = 2",[883,84792,84794],{"className":84793},[886],[888,84795,84796],{"xmlns":890},[892,84797,84798,84810],{},[895,84799,84800,84806,84808],{},[2007,84801,84802,84804],{},[898,84803,80980],{},[1931,84805,2343],{},[1700,84807,1765],{},[1931,84809,2385],{},[902,84811,84812],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,84815,84816,83643,84819,84859,84860,1343,84888,1343,84916,1343,84944,1343,84973,1343,85002,1343,85031,1343,85060,1343,85089,2196],{},[38,84817,84818],{},"5.13",[883,84820,84822],{"className":84821},[886],[888,84823,84824],{"xmlns":890},[892,84825,84826,84856],{},[895,84827,84828,84830,84832,84844],{},[898,84829,1662],{},[1700,84831,1765],{},[1785,84833,84834,84836],{},[898,84835,1706],{},[895,84837,84838,84840,84842],{},[1931,84839,1933],{},[898,84841,1979],{"mathvariant":1791},[1931,84843,2385],{},[1785,84845,84846,84848],{},[898,84847,1735],{},[895,84849,84850,84852,84854],{},[1931,84851,1933],{},[898,84853,1979],{"mathvariant":1791},[1931,84855,2343],{},[902,84857,84858],{"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): ",[883,84861,84863],{"className":84862},[886],[888,84864,84865],{"xmlns":890},[892,84866,84867,84885],{},[895,84868,84869,84875,84877,84879,84881,84883],{},[2007,84870,84871,84873],{},[898,84872,1862],{},[1931,84874,1933],{},[1700,84876,1927],{"stretchy":1702},[1931,84878,1933],{},[1700,84880,8613],{"separator":1731},[1931,84882,1933],{},[1700,84884,1970],{"stretchy":1702},[902,84886,84887],{"encoding":904},"A_1[1; 1]",[883,84889,84891],{"className":84890},[886],[888,84892,84893],{"xmlns":890},[892,84894,84895,84913],{},[895,84896,84897,84903,84905,84907,84909,84911],{},[2007,84898,84899,84901],{},[898,84900,1862],{},[1931,84902,2343],{},[1700,84904,1927],{"stretchy":1702},[1931,84906,1933],{},[1700,84908,8613],{"separator":1731},[1931,84910,5773],{},[1700,84912,1970],{"stretchy":1702},[902,84914,84915],{"encoding":904},"A_2[1; 8]",[883,84917,84919],{"className":84918},[886],[888,84920,84921],{"xmlns":890},[892,84922,84923,84941],{},[895,84924,84925,84931,84933,84935,84937,84939],{},[2007,84926,84927,84929],{},[898,84928,1862],{},[1931,84930,2385],{},[1700,84932,1927],{"stretchy":1702},[1931,84934,1933],{},[1700,84936,8613],{"separator":1731},[1931,84938,66781],{},[1700,84940,1970],{"stretchy":1702},[902,84942,84943],{"encoding":904},"A_3[1; 27]",[883,84945,84947],{"className":84946},[886],[888,84948,84949],{"xmlns":890},[892,84950,84951,84970],{},[895,84952,84953,84959,84961,84963,84965,84968],{},[2007,84954,84955,84957],{},[898,84956,1862],{},[1931,84958,2553],{},[1700,84960,1927],{"stretchy":1702},[1931,84962,2343],{},[1700,84964,8613],{"separator":1731},[1931,84966,84967],{},"0,353",[1700,84969,1970],{"stretchy":1702},[902,84971,84972],{"encoding":904},"A_4[2; 0{,}353]",[883,84974,84976],{"className":84975},[886],[888,84977,84978],{"xmlns":890},[892,84979,84980,84999],{},[895,84981,84982,84988,84990,84992,84994,84997],{},[2007,84983,84984,84986],{},[898,84985,1862],{},[1931,84987,2438],{},[1700,84989,1927],{"stretchy":1702},[1931,84991,2343],{},[1700,84993,8613],{"separator":1731},[1931,84995,84996],{},"2,828",[1700,84998,1970],{"stretchy":1702},[902,85000,85001],{"encoding":904},"A_5[2; 2{,}828]",[883,85003,85005],{"className":85004},[886],[888,85006,85007],{"xmlns":890},[892,85008,85009,85028],{},[895,85010,85011,85017,85019,85021,85023,85026],{},[2007,85012,85013,85015],{},[898,85014,1862],{},[1931,85016,2445],{},[1700,85018,1927],{"stretchy":1702},[1931,85020,2343],{},[1700,85022,8613],{"separator":1731},[1931,85024,85025],{},"9,545",[1700,85027,1970],{"stretchy":1702},[902,85029,85030],{"encoding":904},"A_6[2; 9{,}545]",[883,85032,85034],{"className":85033},[886],[888,85035,85036],{"xmlns":890},[892,85037,85038,85057],{},[895,85039,85040,85046,85048,85050,85052,85055],{},[2007,85041,85042,85044],{},[898,85043,1862],{},[1931,85045,24386],{},[1700,85047,1927],{"stretchy":1702},[1931,85049,64743],{},[1700,85051,8613],{"separator":1731},[1931,85053,85054],{},"0,544",[1700,85056,1970],{"stretchy":1702},[902,85058,85059],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,85061,85063],{"className":85062},[886],[888,85064,85065],{"xmlns":890},[892,85066,85067,85086],{},[895,85068,85069,85075,85077,85079,85081,85084],{},[2007,85070,85071,85073],{},[898,85072,1862],{},[1931,85074,5773],{},[1700,85076,1927],{"stretchy":1702},[1931,85078,64743],{},[1700,85080,8613],{"separator":1731},[1931,85082,85083],{},"14,696",[1700,85085,1970],{"stretchy":1702},[902,85087,85088],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,85090,85092],{"className":85091},[886],[888,85093,85094],{"xmlns":890},[892,85095,85096,85114],{},[895,85097,85098,85104,85106,85108,85110,85112],{},[2007,85099,85100,85102],{},[898,85101,1862],{},[1931,85103,4190],{},[1700,85105,1927],{"stretchy":1702},[1931,85107,2343],{},[1700,85109,8613],{"separator":1731},[1931,85111,2438],{},[1700,85113,1970],{"stretchy":1702},[902,85115,85116],{"encoding":904},"A_9[2; 5]",[724,85118,85119,85122],{},[38,85120,85121],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,85124,85125,85128,85129,85159,85160,85173,85174,85187,85188,69501,85207,85226,85227,2196],{},[38,85126,85127],{},"5.15"," Produkce firmy je dána vztahem ",[883,85130,85132],{"className":85131},[886],[888,85133,85134],{"xmlns":890},[892,85135,85136,85156],{},[895,85137,85138,85140,85142,85144,85150],{},[898,85139,1662],{},[1700,85141,1765],{},[1931,85143,2343],{},[1785,85145,85146,85148],{},[898,85147,1706],{},[1931,85149,5197],{},[1785,85151,85152,85154],{},[898,85153,1735],{},[1931,85155,23974],{},[902,85157,85158],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,85161,85163],{"className":85162},[886],[888,85164,85165],{"xmlns":890},[892,85166,85167,85171],{},[895,85168,85169],{},[1931,85170,3284],{},[902,85172,3284],{"encoding":904}," pracovníků a disponuje-li ",[883,85175,85177],{"className":85176},[886],[888,85178,85179],{"xmlns":890},[892,85180,85181,85185],{},[895,85182,85183],{},[1931,85184,64619],{},[902,85186,64619],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,85189,85191],{"className":85190},[886],[888,85192,85193],{"xmlns":890},[892,85194,85195,85205],{},[895,85196,85197,85199,85201,85203],{},[898,85198,2005],{},[898,85200,4185],{},[898,85202,2971],{},[898,85204,8861],{},[902,85206,10782],{"encoding":904},[883,85208,85210],{"className":85209},[886],[888,85211,85212],{"xmlns":890},[892,85213,85214,85224],{},[895,85215,85216,85218,85220,85222],{},[898,85217,2005],{},[898,85219,4185],{},[898,85221,2971],{},[898,85223,8861],{},[902,85225,10782],{"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 ",[883,85228,85230],{"className":85229},[886],[888,85231,85232],{"xmlns":890},[892,85233,85234,85239],{},[895,85235,85236],{},[1931,85237,85238],{},"95",[902,85240,85238],{"encoding":904},[724,85242,85243,83643,85246,71175,85278,85297,85298,85311,85312,85325,85326,85339],{},[38,85244,85245],{},"5.16",[883,85247,85249],{"className":85248},[886],[888,85250,85251],{"xmlns":890},[892,85252,85253,85275],{},[895,85254,85255,85257,85259,85265,85267,85269],{},[898,85256,1662],{},[1700,85258,1765],{},[1785,85260,85261,85263],{},[898,85262,1735],{},[1931,85264,2343],{},[1700,85266,1897],{},[1931,85268,2343],{},[1785,85270,85271,85273],{},[898,85272,1706],{},[1931,85274,2343],{},[902,85276,85277],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,85279,85281],{"className":85280},[886],[888,85282,85283],{"xmlns":890},[892,85284,85285,85295],{},[895,85286,85287,85289,85291,85293],{},[898,85288,2005],{},[898,85290,4185],{},[898,85292,2971],{},[898,85294,8861],{},[902,85296,10782],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,85299,85301],{"className":85300},[886],[888,85302,85303],{"xmlns":890},[892,85304,85305,85309],{},[895,85306,85307],{},[1931,85308,3314],{},[902,85310,3314],{"encoding":904}," pracovníky a ",[883,85313,85315],{"className":85314},[886],[888,85316,85317],{"xmlns":890},[892,85318,85319,85323],{},[895,85320,85321],{},[1931,85322,77800],{},[902,85324,77800],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,85327,85329],{"className":85328},[886],[888,85330,85331],{"xmlns":890},[892,85332,85333,85337],{},[895,85334,85335],{},[1931,85336,46888],{},[902,85338,46888],{"encoding":904}," jednotek.",[724,85341,85342,85345,85346,10577,85376,2196],{},[38,85343,85344],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,85347,85349],{"className":85348},[886],[888,85350,85351],{"xmlns":890},[892,85352,85353,85373],{},[895,85354,85355,85357,85359,85361,85367],{},[898,85356,1662],{},[1700,85358,1765],{},[898,85360,1862],{},[1785,85362,85363,85365],{},[898,85364,1706],{},[898,85366,207],{},[1785,85368,85369,85371],{},[898,85370,1735],{},[898,85372,1879],{},[902,85374,85375],{"encoding":904},"Q = A L^{a} K^{b}",[883,85377,85379],{"className":85378},[886],[888,85380,85381],{"xmlns":890},[892,85382,85383,85413],{},[895,85384,85385,85387,85389,85391,85393,85395,85403,85405],{},[898,85386,2005],{},[898,85388,4185],{},[898,85390,2971],{},[898,85392,8861],{},[1700,85394,1765],{},[1770,85396,85397],{"scriptlevel":1772,"displaystyle":1702},[1774,85398,85399,85401],{},[898,85400,207],{},[898,85402,1879],{},[1700,85404,2065],{},[1770,85406,85407],{"scriptlevel":1772,"displaystyle":1702},[1774,85408,85409,85411],{},[898,85410,1735],{},[898,85412,1706],{},[902,85414,85415],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,85417,15905],{"id":15904},[120,85419,85420,85453,85480,85489,85539,85570,85623,85646,85701,85774,85852,85895,85927,85960,86001,86073,86134,86200,86217,86290,86356,86408,86464,86498,86541],{},[123,85421,85422,85425,85426,37081,85439,85452],{},[38,85423,85424],{},"Faktory (vstupy) produkce:"," práce ",[883,85427,85429],{"className":85428},[886],[888,85430,85431],{"xmlns":890},[892,85432,85433,85437],{},[895,85434,85435],{},[898,85436,1706],{},[902,85438,1706],{"encoding":904},[883,85440,85442],{"className":85441},[886],[888,85443,85444],{"xmlns":890},[892,85445,85446,85450],{},[895,85447,85448],{},[898,85449,1735],{},[902,85451,1735],{"encoding":904},", půda.",[123,85454,85455,7203,85457,2196],{},[38,85456,40636],{},[883,85458,85460],{"className":85459},[886],[888,85461,85462],{"xmlns":890},[892,85463,85464,85478],{},[895,85465,85466,85468,85470,85472,85474,85476],{},[898,85467,1662],{},[1700,85469,1765],{},[898,85471,1662],{},[1700,85473,1703],{"stretchy":1702},[898,85475,1706],{},[1700,85477,1709],{"stretchy":1702},[902,85479,74728],{"encoding":904},[123,85481,85482,10208,85484,12313,85487,2196],{},[38,85483,859],{},[614,85485,85486],{},"production function",[38,85488,75230],{},[123,85490,85491,2106,85493,2196],{},[38,85492,75276],{},[883,85494,85496],{"className":85495},[886],[888,85497,85498],{"xmlns":890},[892,85499,85500,85536],{},[895,85501,85502,85504,85510,85512,85514,85516,85518,85520,85522,85524,85530,85532,85534],{},[898,85503,2005],{},[2007,85505,85506,85508],{},[898,85507,1677],{},[898,85509,1706],{},[1700,85511,1765],{},[898,85513,2406],{},[898,85515,1662],{},[898,85517,1979],{"mathvariant":1791},[898,85519,2406],{},[898,85521,1706],{},[1700,85523,1765],{},[1785,85525,85526,85528],{},[898,85527,1662],{},[1700,85529,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,85531,1703],{"stretchy":1702},[898,85533,1706],{},[1700,85535,1709],{"stretchy":1702},[902,85537,85538],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,85540,85541,2106,85543,2196],{},[38,85542,76211],{},[883,85544,85546],{"className":85545},[886],[888,85547,85548],{"xmlns":890},[892,85549,85550,85568],{},[895,85551,85552,85554,85560,85562,85564,85566],{},[898,85553,1862],{},[2007,85555,85556,85558],{},[898,85557,1677],{},[898,85559,1706],{},[1700,85561,1765],{},[898,85563,1662],{},[898,85565,1979],{"mathvariant":1791},[898,85567,1706],{},[902,85569,74796],{"encoding":904},[123,85571,85572,85574,85575,10577,85592,2196],{},[38,85573,75698],{}," — od určitého ",[883,85576,85578],{"className":85577},[886],[888,85579,85580],{"xmlns":890},[892,85581,85582,85590],{},[895,85583,85584],{},[2007,85585,85586,85588],{},[898,85587,1706],{},[1931,85589,1772],{},[902,85591,75741],{"encoding":904},[883,85593,85595],{"className":85594},[886],[888,85596,85597],{"xmlns":890},[892,85598,85599,85621],{},[895,85600,85601,85611,85613,85615,85617,85619],{},[1785,85602,85603,85605],{},[898,85604,1662],{},[895,85606,85607,85609],{},[1700,85608,1793],{"mathvariant":1791},[1700,85610,1793],{"mathvariant":1791},[1700,85612,1703],{"stretchy":1702},[898,85614,1706],{},[1700,85616,1709],{"stretchy":1702},[1700,85618,3640],{},[1931,85620,1772],{},[902,85622,75887],{"encoding":904},[123,85624,85625,2106,85628,85645],{},[38,85626,85627],{},"Inflexní bod",[883,85629,85631],{"className":85630},[886],[888,85632,85633],{"xmlns":890},[892,85634,85635,85643],{},[895,85636,85637],{},[2007,85638,85639,85641],{},[898,85640,1706],{},[1931,85642,1772],{},[902,85644,75741],{"encoding":904}," — přechod z konvexity do konkavity.",[123,85647,85648,2106,85651,7203,85668,2196],{},[38,85649,85650],{},"Bod maxima produkce",[883,85652,85654],{"className":85653},[886],[888,85655,85656],{"xmlns":890},[892,85657,85658,85666],{},[895,85659,85660],{},[2007,85661,85662,85664],{},[898,85663,1706],{},[1931,85665,1933],{},[902,85667,13397],{"encoding":904},[883,85669,85671],{"className":85670},[886],[888,85672,85673],{"xmlns":890},[892,85674,85675,85699],{},[895,85676,85677,85679,85685,85687,85693,85695,85697],{},[898,85678,2005],{},[2007,85680,85681,85683],{},[898,85682,1677],{},[898,85684,1706],{},[1700,85686,1703],{"stretchy":1702},[2007,85688,85689,85691],{},[898,85690,1706],{},[1931,85692,1933],{},[1700,85694,1709],{"stretchy":1702},[1700,85696,1765],{},[1931,85698,1772],{},[902,85700,75960],{"encoding":904},[123,85702,85703,85725,85726,10577,85745,2196],{},[38,85704,85705,85706],{},"Princip maximalizace ",[883,85707,85709],{"className":85708},[886],[888,85710,85711],{"xmlns":890},[892,85712,85713,85723],{},[895,85714,85715,85717],{},[898,85716,1862],{},[2007,85718,85719,85721],{},[898,85720,1677],{},[898,85722,1706],{},[902,85724,74817],{"encoding":904}," — v bodě maxima ",[883,85727,85729],{"className":85728},[886],[888,85730,85731],{"xmlns":890},[892,85732,85733,85743],{},[895,85734,85735,85737],{},[898,85736,1862],{},[2007,85738,85739,85741],{},[898,85740,1677],{},[898,85742,1706],{},[902,85744,74817],{"encoding":904},[883,85746,85748],{"className":85747},[886],[888,85749,85750],{"xmlns":890},[892,85751,85752,85772],{},[895,85753,85754,85756,85762,85764,85766],{},[898,85755,2005],{},[2007,85757,85758,85760],{},[898,85759,1677],{},[898,85761,1706],{},[1700,85763,1765],{},[898,85765,1862],{},[2007,85767,85768,85770],{},[898,85769,1677],{},[898,85771,1706],{},[902,85773,74847],{"encoding":904},[123,85775,85776,2106,85779,1343,85818,1343,85835,2196],{},[38,85777,85778],{},"Polynomiální produkční funkce",[883,85780,85782],{"className":85781},[886],[888,85783,85784],{"xmlns":890},[892,85785,85786,85816],{},[895,85787,85788,85790,85792,85794,85796,85798,85800,85806,85808,85810],{},[898,85789,1662],{},[1700,85791,1703],{"stretchy":1702},[898,85793,1706],{},[1700,85795,1709],{"stretchy":1702},[1700,85797,1765],{},[898,85799,207],{},[1785,85801,85802,85804],{},[898,85803,1706],{},[1931,85805,2385],{},[1700,85807,1897],{},[898,85809,1879],{},[1785,85811,85812,85814],{},[898,85813,1706],{},[1931,85815,2343],{},[902,85817,76078],{"encoding":904},[883,85819,85821],{"className":85820},[886],[888,85822,85823],{"xmlns":890},[892,85824,85825,85833],{},[895,85826,85827,85829,85831],{},[898,85828,207],{},[1700,85830,3640],{},[1931,85832,1772],{},[902,85834,43270],{"encoding":904},[883,85836,85838],{"className":85837},[886],[888,85839,85840],{"xmlns":890},[892,85841,85842,85850],{},[895,85843,85844,85846,85848],{},[898,85845,1879],{},[1700,85847,3601],{},[1931,85849,1772],{},[902,85851,18999],{"encoding":904},[123,85853,85854,2106,85857,2196],{},[38,85855,85856],{},"Diferenciál produkce",[883,85858,85860],{"className":85859},[886],[888,85861,85862],{"xmlns":890},[892,85863,85864,85892],{},[895,85865,85866,85868,85870,85872,85874,85876,85878,85880,85886,85888,85890],{},[898,85867,3084],{"mathvariant":1791},[898,85869,1662],{},[1700,85871,2927],{},[898,85873,2406],{},[898,85875,1662],{},[1700,85877,1765],{},[898,85879,2005],{},[2007,85881,85882,85884],{},[898,85883,1677],{},[898,85885,1706],{},[1781,85887,1783],{},[898,85889,2406],{},[898,85891,1706],{},[902,85893,85894],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,85896,85897,7203,85899,2196],{},[38,85898,84154],{},[883,85900,85902],{"className":85901},[886],[888,85903,85904],{"xmlns":890},[892,85905,85906,85924],{},[895,85907,85908,85910,85912,85914,85916,85918,85920,85922],{},[898,85909,1662],{},[1700,85911,1765],{},[898,85913,1662],{},[1700,85915,1703],{"stretchy":1702},[898,85917,1706],{},[1700,85919,1732],{"separator":1731},[898,85921,1735],{},[1700,85923,1709],{"stretchy":1702},[902,85925,85926],{"encoding":904},"Q = Q(L, K)",[123,85928,85929,7203,85931,2196],{},[38,85930,78248],{},[883,85932,85934],{"className":85933},[886],[888,85935,85936],{"xmlns":890},[892,85937,85938,85958],{},[895,85939,85940,85942,85944,85946,85952],{},[898,85941,1662],{},[1700,85943,1765],{},[898,85945,1862],{},[1785,85947,85948,85950],{},[898,85949,1706],{},[898,85951,207],{},[1785,85953,85954,85956],{},[898,85955,1735],{},[898,85957,1879],{},[902,85959,74914],{"encoding":904},[123,85961,85962,7203,85965,86000],{},[38,85963,85964],{},"Ryzí Cobb-Douglas",[883,85966,85968],{"className":85967},[886],[888,85969,85970],{"xmlns":890},[892,85971,85972,85998],{},[895,85973,85974,85976,85978,85980,85986],{},[898,85975,1662],{},[1700,85977,1765],{},[898,85979,1862],{},[1785,85981,85982,85984],{},[898,85983,1706],{},[898,85985,207],{},[1785,85987,85988,85990],{},[898,85989,1735],{},[895,85991,85992,85994,85996],{},[1931,85993,1933],{},[1700,85995,1768],{},[898,85997,207],{},[902,85999,79075],{"encoding":904}," (konstantní výnosy).",[123,86002,86003,7203,86005,2196],{},[38,86004,79791],{},[883,86006,86008],{"className":86007},[886],[888,86009,86010],{"xmlns":890},[892,86011,86012,86070],{},[895,86013,86014,86016,86018,86020,86022,86024,86026,86028,86030,86032,86042,86044,86046,86056],{},[898,86015,1662],{},[1700,86017,1765],{},[898,86019,1862],{},[1700,86021,1927],{"stretchy":1702},[1700,86023,1703],{"stretchy":1702},[1931,86025,1933],{},[1700,86027,1768],{},[898,86029,207],{},[1700,86031,1709],{"stretchy":1702},[1785,86033,86034,86036],{},[898,86035,1706],{},[895,86037,86038,86040],{},[1700,86039,1768],{},[898,86041,1879],{},[1700,86043,1897],{},[898,86045,207],{},[1785,86047,86048,86050],{},[898,86049,1735],{},[895,86051,86052,86054],{},[1700,86053,1768],{},[898,86055,1879],{},[1785,86057,86058,86060],{},[1700,86059,1970],{"stretchy":1702},[895,86061,86062,86064,86066,86068],{},[1700,86063,1768],{},[1931,86065,1933],{},[898,86067,1979],{"mathvariant":1791},[898,86069,1879],{},[902,86071,86072],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,86074,86075,10208,86078,12313,86100,10208,86103,86133],{},[38,86076,86077],{},"Lineární",[883,86079,86081],{"className":86080},[886],[888,86082,86083],{"xmlns":890},[892,86084,86085,86097],{},[895,86086,86087,86089,86091,86093,86095],{},[898,86088,207],{},[898,86090,1706],{},[1700,86092,1897],{},[898,86094,1879],{},[898,86096,1735],{},[902,86098,86099],{"encoding":904},"aL + bK",[38,86101,86102],{},"Leontiefova",[883,86104,86106],{"className":86105},[886],[888,86107,86108],{"xmlns":890},[892,86109,86110,86130],{},[895,86111,86112,86114,86116,86118,86120,86122,86124,86126,86128],{},[898,86113,80019],{},[1700,86115,56384],{},[1700,86117,1703],{"stretchy":1702},[898,86119,207],{},[898,86121,1706],{},[1700,86123,1732],{"separator":1731},[898,86125,1879],{},[898,86127,1735],{},[1700,86129,1709],{"stretchy":1702},[902,86131,86132],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,86135,86136,7203,86152,2196],{},[38,86137,86138,86139],{},"Homogenita stupně ",[883,86140,86142],{"className":86141},[886],[888,86143,86144],{"xmlns":890},[892,86145,86146,86150],{},[895,86147,86148],{},[898,86149,37045],{},[902,86151,37045],{"encoding":904},[883,86153,86155],{"className":86154},[886],[888,86156,86157],{"xmlns":890},[892,86158,86159,86197],{},[895,86160,86161,86163,86165,86167,86169,86171,86173,86175,86177,86179,86185,86187,86189,86191,86193,86195],{},[898,86162,1662],{},[1700,86164,1703],{"stretchy":1702},[898,86166,12226],{},[898,86168,1706],{},[1700,86170,1732],{"separator":1731},[898,86172,12226],{},[898,86174,1735],{},[1700,86176,1709],{"stretchy":1702},[1700,86178,1765],{},[1785,86180,86181,86183],{},[898,86182,12226],{},[898,86184,37045],{},[898,86186,1662],{},[1700,86188,1703],{"stretchy":1702},[898,86190,1706],{},[1700,86192,1732],{"separator":1731},[898,86194,1735],{},[1700,86196,1709],{"stretchy":1702},[902,86198,86199],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,86201,86202,79173],{},[38,86203,79106,86204],{},[883,86205,86207],{"className":86206},[886],[888,86208,86209],{"xmlns":890},[892,86210,86211,86215],{},[895,86212,86213],{},[898,86214,1862],{},[902,86216,1862],{"encoding":904},[123,86218,86219,86221,86222,86244,86245,86267,86268,4110],{},[38,86220,78607],{}," — konstantní (",[883,86223,86225],{"className":86224},[886],[888,86226,86227],{"xmlns":890},[892,86228,86229,86241],{},[895,86230,86231,86233,86235,86237,86239],{},[898,86232,207],{},[1700,86234,1897],{},[898,86236,1879],{},[1700,86238,1765],{},[1931,86240,1933],{},[902,86242,86243],{"encoding":904},"a+b=1","), rostoucí (",[883,86246,86248],{"className":86247},[886],[888,86249,86250],{"xmlns":890},[892,86251,86252,86264],{},[895,86253,86254,86256,86258,86260,86262],{},[898,86255,207],{},[1700,86257,1897],{},[898,86259,1879],{},[1700,86261,3601],{},[1931,86263,1933],{},[902,86265,86266],{"encoding":904},"a+b>1","), klesající (",[883,86269,86271],{"className":86270},[886],[888,86272,86273],{"xmlns":890},[892,86274,86275,86287],{},[895,86276,86277,86279,86281,86283,86285],{},[898,86278,207],{},[1700,86280,1897],{},[898,86282,1879],{},[1700,86284,3640],{},[1931,86286,1933],{},[902,86288,86289],{"encoding":904},"a+b\u003C1",[123,86291,86292,2106,86294,1343,86324,2106,86326,2196],{},[38,86293,75276],{},[883,86295,86297],{"className":86296},[886],[888,86298,86299],{"xmlns":890},[892,86300,86301,86321],{},[895,86302,86303,86305,86311,86313],{},[898,86304,2005],{},[2007,86306,86307,86309],{},[898,86308,1677],{},[898,86310,1706],{},[1700,86312,1765],{},[2030,86314,86315,86317,86319],{},[898,86316,1662],{},[898,86318,1706],{},[1700,86320,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,86322,86323],{"encoding":904},"MP_L = Q'_L",[38,86325,78180],{},[883,86327,86329],{"className":86328},[886],[888,86330,86331],{"xmlns":890},[892,86332,86333,86353],{},[895,86334,86335,86337,86343,86345],{},[898,86336,2005],{},[2007,86338,86339,86341],{},[898,86340,1677],{},[898,86342,1735],{},[1700,86344,1765],{},[2030,86346,86347,86349,86351],{},[898,86348,1662],{},[898,86350,1735],{},[1700,86352,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,86354,86355],{"encoding":904},"MP_K = Q'_K",[123,86357,86358,2106,86360,2196],{},[38,86359,80394],{},[883,86361,86363],{"className":86362},[886],[888,86364,86365],{"xmlns":890},[892,86366,86367,86405],{},[895,86368,86369,86371,86373,86375,86377,86383,86385,86387,86389,86391,86393,86399,86401,86403],{},[898,86370,2406],{},[898,86372,1662],{},[1700,86374,1765],{},[898,86376,2005],{},[2007,86378,86379,86381],{},[898,86380,1677],{},[898,86382,1706],{},[1781,86384,1783],{},[898,86386,2406],{},[898,86388,1706],{},[1700,86390,1897],{},[898,86392,2005],{},[2007,86394,86395,86397],{},[898,86396,1677],{},[898,86398,1735],{},[1781,86400,1783],{},[898,86402,2406],{},[898,86404,1735],{},[902,86406,86407],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,86409,86410,7203,86412,2196],{},[38,86411,80739],{},[883,86413,86415],{"className":86414},[886],[888,86416,86417],{"xmlns":890},[892,86418,86419,86461],{},[895,86420,86421,86423,86431,86433,86435,86443,86445,86447,86449,86451,86453,86455,86457,86459],{},[898,86422,1706],{},[2030,86424,86425,86427,86429],{},[898,86426,1662],{},[898,86428,1706],{},[1700,86430,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,86432,1897],{},[898,86434,1735],{},[2030,86436,86437,86439,86441],{},[898,86438,1662],{},[898,86440,1735],{},[1700,86442,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,86444,1765],{},[898,86446,37045],{},[1781,86448,1783],{},[898,86450,1662],{},[1700,86452,1703],{"stretchy":1702},[898,86454,1706],{},[1700,86456,1732],{"separator":1731},[898,86458,1735],{},[1700,86460,1709],{"stretchy":1702},[902,86462,86463],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,86465,86466,86469,86470,2196],{},[38,86467,86468],{},"Izokvanta"," — křivka ",[883,86471,86473],{"className":86472},[886],[888,86474,86475],{"xmlns":890},[892,86476,86477,86495],{},[895,86478,86479,86481,86483,86485,86487,86489,86491,86493],{},[898,86480,1662],{},[1700,86482,1703],{"stretchy":1702},[898,86484,1706],{},[1700,86486,1732],{"separator":1731},[898,86488,1735],{},[1700,86490,1709],{"stretchy":1702},[1700,86492,1765],{},[898,86494,80980],{},[902,86496,86497],{"encoding":904},"Q(L, K) = q",[123,86499,86500,2106,86502,2196],{},[38,86501,81169],{},[883,86503,86505],{"className":86504},[886],[888,86506,86507],{"xmlns":890},[892,86508,86509,86539],{},[895,86510,86511,86513,86515,86517,86519,86521,86523,86529,86531,86533],{},[898,86512,2005],{},[898,86514,4185],{},[898,86516,2971],{},[898,86518,8861],{},[1700,86520,1765],{},[898,86522,2005],{},[2007,86524,86525,86527],{},[898,86526,1677],{},[898,86528,1706],{},[898,86530,1979],{"mathvariant":1791},[898,86532,2005],{},[2007,86534,86535,86537],{},[898,86536,1677],{},[898,86538,1735],{},[902,86540,74989],{"encoding":904},[123,86542,86543,2106,86546,2196],{},[38,86544,86545],{},"Substituční vztah",[883,86547,86549],{"className":86548},[886],[888,86550,86551],{"xmlns":890},[892,86552,86553,86577],{},[895,86554,86555,86557,86559,86561,86563,86565,86567,86569,86571,86573,86575],{},[898,86556,3084],{"mathvariant":1791},[898,86558,1735],{},[1700,86560,2927],{},[1700,86562,1768],{},[898,86564,2005],{},[898,86566,4185],{},[898,86568,2971],{},[898,86570,8861],{},[1781,86572,1783],{},[898,86574,2406],{},[898,86576,1706],{},[902,86578,86579],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,86581,3985],{"id":3984},[120,86583,86584,86681,86688,86695],{},[123,86585,86586,2106,86588,86591,86592,1343,86595,86598,86599,86602,86603,86622,86623,18833,86642,86645,86646,86665,86666,4110],{},[38,86587,50908],{},[207,86589,784],{"className":86590,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,86593,2559],{"className":86594,"dataFsResolvedFilePath":764,"href":765},[210],[207,86596,793],{"className":86597,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,86600,880],{"className":86601,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,86604,86606],{"className":86605},[886],[888,86607,86608],{"xmlns":890},[892,86609,86610,86620],{},[895,86611,86612,86614,86616,86618],{},[898,86613,2005],{},[898,86615,4185],{},[898,86617,2971],{},[898,86619,8861],{},[902,86621,10782],{"encoding":904}," ↔ ",[883,86624,86626],{"className":86625},[886],[888,86627,86628],{"xmlns":890},[892,86629,86630,86640],{},[895,86631,86632,86634,86636,86638],{},[898,86633,2005],{},[898,86635,4185],{},[898,86637,2974],{},[898,86639,8861],{},[902,86641,10786],{"encoding":904},[207,86643,4016],{"className":86644,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,86647,86649],{"className":86648},[886],[888,86650,86651],{"xmlns":890},[892,86652,86653,86663],{},[895,86654,86655,86657],{},[898,86656,1862],{},[2007,86658,86659,86661],{},[898,86660,1677],{},[898,86662,1706],{},[902,86664,74817],{"encoding":904}," ↔ min ",[883,86667,86669],{"className":86668},[886],[888,86670,86671],{"xmlns":890},[892,86672,86673,86679],{},[895,86674,86675,86677],{},[898,86676,1862],{},[898,86678,2974],{},[902,86680,55744],{"encoding":904},[123,86682,86683,2106,86685,2196],{},[38,86684,3992],{},[207,86686,1649],{"className":86687,"dataFsResolvedFilePath":848,"href":849},[210],[123,86689,86690,2106,86692,2196],{},[38,86691,16398],{},[207,86693,1094],{"className":86694,"dataFsResolvedFilePath":838,"href":839},[210],[123,86696,86697,2106,86699,2196],{},[38,86698,16389],{},[207,86700,16393],{"className":86701,"dataFsResolvedFilePath":2140,"href":2141},[210],{"title":641,"searchDepth":642,"depth":642,"links":86703},[86704,86705,86706,86710,86712,86717,86718,86725,86726,86728,86729,86730,86732,86737,86738,86739,86743,86744],{"id":75012,"depth":642,"text":75013},{"id":75148,"depth":642,"text":75149},{"id":75251,"depth":642,"text":86707,"children":86708},"Mezní produkt práce (MPLMP_L)",[86709],{"id":75697,"depth":649,"text":75698},{"id":76186,"depth":642,"text":86711},"Průměrný produkt práce (APLAP_L)",{"id":76304,"depth":642,"text":76305,"children":86713},[86714,86715,86716],{"id":76541,"depth":649,"text":65685},{"id":76852,"depth":649,"text":76853},{"id":77572,"depth":649,"text":77573},{"id":78144,"depth":642,"text":78145},{"id":78247,"depth":642,"text":78248,"children":86719},[86720,86721,86723,86724],{"id":78606,"depth":649,"text":78607},{"id":79105,"depth":649,"text":86722},"Parametr efektivity AA",{"id":79176,"depth":649,"text":79177},{"id":37364,"depth":649,"text":79516},{"id":79703,"depth":642,"text":79704},{"id":80042,"depth":642,"text":86727},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":80733,"depth":642,"text":80734},{"id":2159,"depth":642,"text":9965},{"id":81144,"depth":642,"text":86731},"Mezní míra technické substituce (MRTSMRTS)",{"id":82010,"depth":642,"text":82011,"children":86733},[86734,86735,86736],{"id":82014,"depth":649,"text":82015},{"id":82657,"depth":649,"text":82658},{"id":82938,"depth":649,"text":82939},{"id":83284,"depth":642,"text":83285},{"id":50066,"depth":642,"text":50067},{"id":83634,"depth":642,"text":83635,"children":86740},[86741,86742],{"id":40635,"depth":649,"text":40636},{"id":84153,"depth":649,"text":84154},{"id":15904,"depth":642,"text":15905},{"id":3984,"depth":642,"text":3985},{},"\u002Ftopics\u002Fprodukce",{"title":74648,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,2156,86751,86752,2157,2159,2160,86753],"produkcni-funkce","mpl-apl","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":86756,"title":86757,"body":86758,"course":1128,"courses":659,"created":9743,"description":641,"extension":661,"meta":95705,"navigation":664,"path":95706,"seo":95707,"sources":95708,"stem":95709,"tags":95710,"type":4049,"updated":677,"__hash__":95713},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":86759,"toc":95679},[86760,86763,86765,86962,86971,86975,86978,87031,87035,87047,87051,87054,87071,87194,87200,87344,87354,87358,87393,87431,87479,87536,87596,87638,88214,88218,88301,88410,88503,88761,88764,88817,88928,89010,89014,89025,89258,89313,89319,89359,89422,89433,89624,89730,89883,89931,89936,90050,90088,90214,90260,90287,90364,90439,90519,90649,90710,90798,90802,90805,90874,90957,90964,91024,91334,91338,91344,91397,91413,91464,91602,91678,91791,92108,92112,92119,92279,92338,92342,92364,92461,92582,92696,92719,92782,92839,93091,93099,93103,93110,93364,93414,93470,93473,93637,93641,93739,93741,93773,93777,93910,94152,94336,94504,94811,94944,95131,95143,95145,95580,95582],[12,86761,86757],{"id":86762},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,86764,12191],{"id":12190},[724,86766,86767,2106,86769,86800,86801,86804,86805,86835,86836,86854,86855,86895,86896,86899,86900,86913,86914,28438,86917,86930,86931,86944,86945,86958,86959,2196],{},[38,86768,880],{},[883,86770,86772],{"className":86771},[886],[888,86773,86774],{"xmlns":890},[892,86775,86776,86798],{},[895,86777,86778,86780,86782,86788,86790,86796],{},[898,86779,900],{},[1700,86781,1703],{"stretchy":1702},[2007,86783,86784,86786],{},[898,86785,1662],{},[1931,86787,1933],{},[1700,86789,1732],{"separator":1731},[2007,86791,86792,86794],{},[898,86793,1662],{},[1931,86795,2343],{},[1700,86797,1709],{"stretchy":1702},[902,86799,16528],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,86802,86803],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,86806,86808],{"className":86807},[886],[888,86809,86810],{"xmlns":890},[892,86811,86812,86832],{},[895,86813,86814,86816,86822,86824],{},[898,86815,2005],{},[2007,86817,86818,86820],{},[898,86819,900],{},[898,86821,17975],{},[1700,86823,1765],{},[2030,86825,86826,86828,86830],{},[898,86827,900],{},[898,86829,17975],{},[1700,86831,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,86833,86834],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,86837,86839],{"className":86838},[886],[888,86840,86841],{"xmlns":890},[892,86842,86843,86851],{},[895,86844,86845,86847,86849],{},[898,86846,900],{},[1700,86848,1765],{},[898,86850,2354],{},[902,86852,86853],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,86856,86858],{"className":86857},[886],[888,86859,86860],{"xmlns":890},[892,86861,86862,86892],{},[895,86863,86864,86866,86868,86870,86872,86874,86876,86882,86884,86886],{},[898,86865,2005],{},[898,86867,4185],{},[898,86869,2974],{},[898,86871,8861],{},[1700,86873,1765],{},[898,86875,2005],{},[2007,86877,86878,86880],{},[898,86879,900],{},[1931,86881,1933],{},[898,86883,1979],{"mathvariant":1791},[898,86885,2005],{},[2007,86887,86888,86890],{},[898,86889,900],{},[1931,86891,2343],{},[902,86893,86894],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,86897,86898],{},"teorii užitečnosti"," — funkce ",[883,86901,86903],{"className":86902},[886],[888,86904,86905],{"xmlns":890},[892,86906,86907,86911],{},[895,86908,86909],{},[898,86910,900],{},[902,86912,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,86915,86916],{},"Optimalizaci spotřebitele",[883,86918,86920],{"className":86919},[886],[888,86921,86922],{"xmlns":890},[892,86923,86924,86928],{},[895,86925,86926],{},[898,86927,900],{},[902,86929,900],{"encoding":904}," při rozpočtu, min ",[883,86932,86934],{"className":86933},[886],[888,86935,86936],{"xmlns":890},[892,86937,86938,86942],{},[895,86939,86940],{},[898,86941,1762],{},[902,86943,1762],{"encoding":904}," při dané ",[883,86946,86948],{"className":86947},[886],[888,86949,86950],{"xmlns":890},[892,86951,86952,86956],{},[895,86953,86954],{},[898,86955,900],{},[902,86957,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,86960,913],{"className":86961,"dataFsResolvedFilePath":911,"href":912},[210],[724,86963,86964,86965,86967,86968,2196],{},"Kapitola 6 knihy ",[614,86966,16393],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,86969,36939],{"className":86970,"dataFsResolvedFilePath":911,"href":912},[210],[115,86972,86974],{"id":86973},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,86976,86977],{},"Po prostudování této kapitoly byste měli umět:",[120,86979,86980,86986,86995,87000,87003,87009,87015,87018,87024],{},[123,86981,86982,86983,1732],{},"vyložit, co se rozumí termínem ",[38,86984,86985],{},"užitečnost",[123,86987,86988,86989,2114,86992,1732],{},"definovat pojmy ",[38,86990,86991],{},"svazek zboží",[38,86993,86994],{},"funkce užitečnosti",[123,86996,75027,86997,75034],{},[38,86998,86999],{},"mezní užitečnosti",[123,87001,87002],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,87004,75054,87005,87008],{},[38,87006,87007],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,87010,75075,87011,87014],{},[38,87012,87013],{},"křivky užitečnosti"," (indiferenční křivky),",[123,87016,87017],{},"vyjmenovat jejich základní vlastnosti,",[123,87019,75027,87020,87023],{},[38,87021,87022],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,87025,87026,87027,87030],{},"řešit ",[38,87028,87029],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,87032,87034],{"id":87033},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,87036,87037,87038,87042,87043,87046],{},"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 ",[207,87039,87041],{"className":87040,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,87044,87045],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,87048,87050],{"id":87049},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,87052,87053],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,87055,87056,87062],{},[123,87057,87058,87061],{},[38,87059,87060],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,87063,87064,87067,87068,87070],{},[38,87065,87066],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,87069,86803],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[4060,87072,87073],{},[724,87074,87075,87077,87078,87081,87082,2106,87095,87098,87099,2114,87112,87131,87132,1343,87158,87185,87186,87189,87190,87193],{},[883,87076,4601],{}," Pozor — ordinalisté užitečnost ",[38,87079,87080],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,87083,87085],{"className":87084},[886],[888,87086,87087],{"xmlns":890},[892,87088,87089,87093],{},[895,87090,87091],{},[898,87092,900],{},[902,87094,900],{"encoding":904},[38,87096,87097],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,87100,87102],{"className":87101},[886],[888,87103,87104],{"xmlns":890},[892,87105,87106,87110],{},[895,87107,87108],{},[898,87109,900],{},[902,87111,900],{"encoding":904},[883,87113,87115],{"className":87114},[886],[888,87116,87117],{"xmlns":890},[892,87118,87119,87128],{},[895,87120,87121],{},[8574,87122,87123,87125],{"accent":1731},[898,87124,900],{},[1700,87126,87127],{},"~",[902,87129,87130],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,87133,87135],{"className":87134},[886],[888,87136,87137],{"xmlns":890},[892,87138,87139,87155],{},[895,87140,87141,87147,87149],{},[8574,87142,87143,87145],{"accent":1731},[898,87144,900],{},[1700,87146,87127],{},[1700,87148,1765],{},[1785,87150,87151,87153],{},[898,87152,900],{},[1931,87154,2343],{},[902,87156,87157],{"encoding":904},"\\tilde U = U^2",[883,87159,87161],{"className":87160},[886],[888,87162,87163],{"xmlns":890},[892,87164,87165,87182],{},[895,87166,87167,87173,87175,87178,87180],{},[8574,87168,87169,87171],{"accent":1731},[898,87170,900],{},[1700,87172,87127],{},[1700,87174,1765],{},[898,87176,87177],{},"ln",[1700,87179,56384],{},[898,87181,900],{},[902,87183,87184],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,87187,87188],{},"porovnání"," mezi svazky a ",[38,87191,87192],{},"poměry"," mezních veličin.",[724,87195,87196,87197,2901],{},"Ordinalistický přístup vychází z ",[38,87198,87199],{},"pěti hlavních předpokladů",[152,87201,87202,87208,87214,87332,87338],{},[123,87203,87204,87207],{},[38,87205,87206],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,87209,87210,87213],{},[38,87211,87212],{},"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.",[123,87215,87216,87219,87220,61925,87233,87246,87247,61925,87260,3122,87273,87276,87277,2114,87296,62754,87314,2196],{},[38,87217,87218],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,87221,87223],{"className":87222},[886],[888,87224,87225],{"xmlns":890},[892,87226,87227,87231],{},[895,87228,87229],{},[898,87230,1862],{},[902,87232,1862],{"encoding":904},[883,87234,87236],{"className":87235},[886],[888,87237,87238],{"xmlns":890},[892,87239,87240,87244],{},[895,87241,87242],{},[898,87243,23438],{},[902,87245,23438],{"encoding":904},", nebude jindy preferovat ",[883,87248,87250],{"className":87249},[886],[888,87251,87252],{"xmlns":890},[892,87253,87254,87258],{},[895,87255,87256],{},[898,87257,23438],{},[902,87259,23438],{"encoding":904},[883,87261,87263],{"className":87262},[886],[888,87264,87265],{"xmlns":890},[892,87266,87267,87271],{},[895,87268,87269],{},[898,87270,1862],{},[902,87272,1862],{"encoding":904},[38,87274,87275],{},"Tranzitivita",": pokud ",[883,87278,87280],{"className":87279},[886],[888,87281,87282],{"xmlns":890},[892,87283,87284,87293],{},[895,87285,87286,87288,87291],{},[898,87287,1862],{},[1700,87289,87290],{},"≻",[898,87292,23438],{},[902,87294,87295],{"encoding":904},"A \\succ B",[883,87297,87299],{"className":87298},[886],[888,87300,87301],{"xmlns":890},[892,87302,87303,87311],{},[895,87304,87305,87307,87309],{},[898,87306,23438],{},[1700,87308,87290],{},[898,87310,2974],{},[902,87312,87313],{"encoding":904},"B \\succ C",[883,87315,87317],{"className":87316},[886],[888,87318,87319],{"xmlns":890},[892,87320,87321,87329],{},[895,87322,87323,87325,87327],{},[898,87324,1862],{},[1700,87326,87290],{},[898,87328,2974],{},[902,87330,87331],{"encoding":904},"A \\succ C",[123,87333,87334,87337],{},[38,87335,87336],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,87339,87340,87343],{},[38,87341,87342],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,87345,87346,87347,87350,87351,2196],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,87348,87349],{},"preference"," a na příbuzné ",[614,87352,87353],{},"funkci užitečnosti",[115,87355,87357],{"id":87356},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,87359,87360,87361,87374,87375,87378,87379,87392],{},"Uvažujme ",[883,87362,87364],{"className":87363},[886],[888,87365,87366],{"xmlns":890},[892,87367,87368,87372],{},[895,87369,87370],{},[898,87371,37045],{},[902,87373,37045],{"encoding":904}," různých zboží. ",[38,87376,87377],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,87380,87382],{"className":87381},[886],[888,87383,87384],{"xmlns":890},[892,87385,87386,87390],{},[895,87387,87388],{},[898,87389,37045],{},[902,87391,37045],{"encoding":904},"-tice",[724,87394,87395],{},[883,87396,87398],{"className":87397},[886],[888,87399,87400],{"xmlns":890},[892,87401,87402,87428],{},[895,87403,87404,87406,87412,87414,87416,87418,87424,87426],{},[1700,87405,1703],{"stretchy":1702},[2007,87407,87408,87410],{},[898,87409,1662],{},[1931,87411,1933],{},[1700,87413,1732],{"separator":1731},[1700,87415,9833],{},[1700,87417,1732],{"separator":1731},[2007,87419,87420,87422],{},[898,87421,1662],{},[898,87423,37045],{},[1700,87425,1709],{"stretchy":1702},[1700,87427,1732],{"separator":1731},[902,87429,87430],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,87432,4499,87433,87450,87451,87464,87465,87468,87469,87472,87473,87476,87477,2901],{},[883,87434,87436],{"className":87435},[886],[888,87437,87438],{"xmlns":890},[892,87439,87440,87448],{},[895,87441,87442],{},[2007,87443,87444,87446],{},[898,87445,1662],{},[898,87447,17975],{},[902,87449,47723],{"encoding":904}," značí množství ",[883,87452,87454],{"className":87453},[886],[888,87455,87456],{"xmlns":890},[892,87457,87458,87462],{},[895,87459,87460],{},[898,87461,17975],{},[902,87463,17975],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,87466,87467],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,87470,87471],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,87474,87475],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,87478,87353],{},[883,87480,87482],{"className":87481},[886],[888,87483,87484],{"xmlns":890,"display":28251},[892,87485,87486,87533],{},[20939,87487,87488],{"width":28256},[20944,87489,87490,87492,87526,87528],{},[20947,87491],{"width":28261},[20947,87493,87494],{},[895,87495,87496,87498,87500,87502,87504,87510,87512,87514,87516,87522,87524],{},[898,87497,900],{},[1700,87499,1765],{},[898,87501,900],{},[1700,87503,1703],{"stretchy":1702},[2007,87505,87506,87508],{},[898,87507,1662],{},[1931,87509,1933],{},[1700,87511,1732],{"separator":1731},[1700,87513,9833],{},[1700,87515,1732],{"separator":1731},[2007,87517,87518,87520],{},[898,87519,1662],{},[898,87521,37045],{},[1700,87523,1709],{"stretchy":1702},[1700,87525,1732],{"separator":1731},[20947,87527],{"width":28261},[20947,87529,87530],{},[1781,87531,87532],{},"(6.1)",[902,87534,87535],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,87537,4499,87538,87568,87569,87591,87592,87595],{},[883,87539,87541],{"className":87540},[886],[888,87542,87543],{"xmlns":890},[892,87544,87545,87565],{},[895,87546,87547,87553,87555,87557,87559],{},[2007,87548,87549,87551],{},[898,87550,1662],{},[1931,87552,1933],{},[1700,87554,1732],{"separator":1731},[1700,87556,9833],{},[1700,87558,1732],{"separator":1731},[2007,87560,87561,87563],{},[898,87562,1662],{},[898,87564,37045],{},[902,87566,87567],{"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 ",[883,87570,87572],{"className":87571},[886],[888,87573,87574],{"xmlns":890},[892,87575,87576,87588],{},[895,87577,87578,87580,87582],{},[898,87579,900],{},[1700,87581,1732],{"separator":1731},[8574,87583,87584,87586],{"accent":1731},[898,87585,900],{},[1700,87587,87127],{},[902,87589,87590],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,87593,87594],{},"monotónní transformace"," zachovávající pořadí.",[724,87597,87598,87599,7203,87602,2196],{},"Dále se omezíme na funkce pro ",[38,87600,87601],{},"dvě zboží",[883,87603,87605],{"className":87604},[886],[888,87606,87607],{"xmlns":890},[892,87608,87609,87635],{},[895,87610,87611,87613,87615,87617,87619,87625,87627,87633],{},[898,87612,900],{},[1700,87614,1765],{},[898,87616,900],{},[1700,87618,1703],{"stretchy":1702},[2007,87620,87621,87623],{},[898,87622,1662],{},[1931,87624,1933],{},[1700,87626,1732],{"separator":1731},[2007,87628,87629,87631],{},[898,87630,1662],{},[1931,87632,2343],{},[1700,87634,1709],{"stretchy":1702},[902,87636,87637],{"encoding":904},"U = U(Q_1, Q_2)",[4060,87639,87640,87715],{},[724,87641,87642,87644,87645,2901],{},[883,87643,52879],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,87646,87648],{"className":87647},[886],[888,87649,87650],{"xmlns":890},[892,87651,87652,87712],{},[895,87653,87654,87656,87658,87660,87662,87668,87670,87676,87678,87684,87686,87688,87690],{},[898,87655,900],{},[1700,87657,1765],{},[898,87659,900],{},[1700,87661,1703],{"stretchy":1702},[2007,87663,87664,87666],{},[898,87665,1662],{},[1931,87667,1933],{},[1700,87669,1732],{"separator":1731},[2007,87671,87672,87674],{},[898,87673,1662],{},[1931,87675,2343],{},[1700,87677,1732],{"separator":1731},[2007,87679,87680,87682],{},[898,87681,1662],{},[1931,87683,2385],{},[1700,87685,1709],{"stretchy":1702},[1700,87687,1765],{},[1931,87689,2343],{},[8305,87691,87692],{},[895,87693,87694,87700,87706],{},[2007,87695,87696,87698],{},[898,87697,1662],{},[1931,87699,1933],{},[2007,87701,87702,87704],{},[898,87703,1662],{},[1931,87705,2343],{},[2007,87707,87708,87710],{},[898,87709,1662],{},[1931,87711,2385],{},[902,87713,87714],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,87716,87717,87910],{},[123,87718,87719,87720,87746,87747,13123,87773,2114,87832,5777,87892,8613],{},"svazek ",[883,87721,87723],{"className":87722},[886],[888,87724,87725],{"xmlns":890},[892,87726,87727,87743],{},[895,87728,87729,87731,87733,87735,87737,87739,87741],{},[1700,87730,1703],{"stretchy":1702},[1931,87732,42047],{},[1700,87734,1732],{"separator":1731},[1931,87736,2553],{},[1700,87738,1732],{"separator":1731},[1931,87740,42025],{},[1700,87742,1709],{"stretchy":1702},[902,87744,87745],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,87748,87750],{"className":87749},[886],[888,87751,87752],{"xmlns":890},[892,87753,87754,87770],{},[895,87755,87756,87758,87760,87762,87764,87766,87768],{},[1700,87757,1703],{"stretchy":1702},[1931,87759,4190],{},[1700,87761,1732],{"separator":1731},[1931,87763,4190],{},[1700,87765,1732],{"separator":1731},[1931,87767,66781],{},[1700,87769,1709],{"stretchy":1702},[902,87771,87772],{"encoding":904},"(9, 9, 27)",[883,87774,87776],{"className":87775},[886],[888,87777,87778],{"xmlns":890},[892,87779,87780,87829],{},[895,87781,87782,87784,87786,87788,87790,87792,87794,87796,87798,87800,87802,87816,87818,87820,87825,87827],{},[898,87783,900],{},[1700,87785,1703],{"stretchy":1702},[1931,87787,42047],{},[1700,87789,1732],{"separator":1731},[1931,87791,2553],{},[1700,87793,1732],{"separator":1731},[1931,87795,42025],{},[1700,87797,1709],{"stretchy":1702},[1700,87799,1765],{},[1931,87801,2343],{},[8305,87803,87804],{},[895,87805,87806,87808,87810,87812,87814],{},[1931,87807,42047],{},[1700,87809,2065],{},[1931,87811,2553],{},[1700,87813,2065],{},[1931,87815,42025],{},[1700,87817,1765],{},[1931,87819,2343],{},[8305,87821,87822],{},[1931,87823,87824],{},"4096",[1700,87826,1765],{},[1931,87828,5805],{},[902,87830,87831],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,87833,87835],{"className":87834},[886],[888,87836,87837],{"xmlns":890},[892,87838,87839,87889],{},[895,87840,87841,87843,87845,87847,87849,87851,87853,87855,87857,87859,87861,87875,87877,87879,87884,87886],{},[898,87842,900],{},[1700,87844,1703],{"stretchy":1702},[1931,87846,4190],{},[1700,87848,1732],{"separator":1731},[1931,87850,4190],{},[1700,87852,1732],{"separator":1731},[1931,87854,66781],{},[1700,87856,1709],{"stretchy":1702},[1700,87858,1765],{},[1931,87860,2343],{},[8305,87862,87863],{},[895,87864,87865,87867,87869,87871,87873],{},[1931,87866,4190],{},[1700,87868,2065],{},[1931,87870,4190],{},[1700,87872,2065],{},[1931,87874,66781],{},[1700,87876,1765],{},[1931,87878,2343],{},[8305,87880,87881],{},[1931,87882,87883],{},"2187",[1700,87885,6088],{},[1931,87887,87888],{},"93,53",[902,87890,87891],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,87893,87895],{"className":87894},[886],[888,87896,87897],{"xmlns":890},[892,87898,87899,87907],{},[895,87900,87901,87903,87905],{},[1931,87902,5805],{},[1700,87904,3601],{},[1931,87906,87888],{},[902,87908,87909],{"encoding":904},"128 > 93{,}53",[123,87911,87912,87913,2114,87939,87965,87966,2114,88006,88047,88048,88094,88095,2114,88121,3040,88147,2114,88165,88183,88184,2196],{},"svazky ",[883,87914,87916],{"className":87915},[886],[888,87917,87918],{"xmlns":890},[892,87919,87920,87936],{},[895,87921,87922,87924,87926,87928,87930,87932,87934],{},[1700,87923,1703],{"stretchy":1702},[1931,87925,2553],{},[1700,87927,1732],{"separator":1731},[1931,87929,5773],{},[1700,87931,1732],{"separator":1731},[1931,87933,2343],{},[1700,87935,1709],{"stretchy":1702},[902,87937,87938],{"encoding":904},"(4, 8, 2)",[883,87940,87942],{"className":87941},[886],[888,87943,87944],{"xmlns":890},[892,87945,87946,87962],{},[895,87947,87948,87950,87952,87954,87956,87958,87960],{},[1700,87949,1703],{"stretchy":1702},[1931,87951,42025],{},[1700,87953,1732],{"separator":1731},[1931,87955,1933],{},[1700,87957,1732],{"separator":1731},[1931,87959,2553],{},[1700,87961,1709],{"stretchy":1702},[902,87963,87964],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,87967,87969],{"className":87968},[886],[888,87970,87971],{"xmlns":890},[892,87972,87973,88003],{},[895,87974,87975,87977,87979,87981,87983,87985,87987,87989,87991,87993,87995,87999,88001],{},[898,87976,900],{},[1700,87978,1703],{"stretchy":1702},[1931,87980,2553],{},[1700,87982,1732],{"separator":1731},[1931,87984,5773],{},[1700,87986,1732],{"separator":1731},[1931,87988,2343],{},[1700,87990,1709],{"stretchy":1702},[1700,87992,1765],{},[1931,87994,2343],{},[8305,87996,87997],{},[1931,87998,42025],{},[1700,88000,1765],{},[1931,88002,42047],{},[902,88004,88005],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,88007,88009],{"className":88008},[886],[888,88010,88011],{"xmlns":890},[892,88012,88013,88044],{},[895,88014,88015,88017,88019,88021,88023,88025,88027,88029,88031,88033,88035,88040,88042],{},[898,88016,900],{},[1700,88018,1703],{"stretchy":1702},[1931,88020,42025],{},[1700,88022,1732],{"separator":1731},[1931,88024,1933],{},[1700,88026,1732],{"separator":1731},[1931,88028,2553],{},[1700,88030,1709],{"stretchy":1702},[1700,88032,1765],{},[1931,88034,2343],{},[8305,88036,88037],{},[1931,88038,88039],{},"256",[1700,88041,1765],{},[1931,88043,72543],{},[902,88045,88046],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,88049,88051],{"className":88050},[886],[888,88052,88053],{"xmlns":890},[892,88054,88055,88091],{},[895,88056,88057,88059,88061,88063,88065,88067,88069,88071,88073,88075,88077,88079,88081,88083,88085,88087,88089],{},[898,88058,900],{},[1700,88060,1703],{"stretchy":1702},[1931,88062,2553],{},[1700,88064,1732],{"separator":1731},[1931,88066,5773],{},[1700,88068,1732],{"separator":1731},[1931,88070,2343],{},[1700,88072,1709],{"stretchy":1702},[1700,88074,1765],{},[898,88076,900],{},[1700,88078,1703],{"stretchy":1702},[1931,88080,42025],{},[1700,88082,1732],{"separator":1731},[1931,88084,1933],{},[1700,88086,1732],{"separator":1731},[1931,88088,2553],{},[1700,88090,1709],{"stretchy":1702},[902,88092,88093],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,88096,88098],{"className":88097},[886],[888,88099,88100],{"xmlns":890},[892,88101,88102,88118],{},[895,88103,88104,88106,88108,88110,88112,88114,88116],{},[1931,88105,2553],{},[1700,88107,2065],{},[1931,88109,5773],{},[1700,88111,2065],{},[1931,88113,2343],{},[1700,88115,1765],{},[1931,88117,42025],{},[902,88119,88120],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,88122,88124],{"className":88123},[886],[888,88125,88126],{"xmlns":890},[892,88127,88128,88144],{},[895,88129,88130,88132,88134,88136,88138,88140,88142],{},[1931,88131,42025],{},[1700,88133,2065],{},[1931,88135,1933],{},[1700,88137,2065],{},[1931,88139,2553],{},[1700,88141,1765],{},[1931,88143,88039],{},[902,88145,88146],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,88148,88150],{"className":88149},[886],[888,88151,88152],{"xmlns":890},[892,88153,88154,88162],{},[895,88155,88156,88158,88160],{},[898,88157,900],{},[1700,88159,1765],{},[1931,88161,42047],{},[902,88163,88164],{"encoding":904},"U = 16",[883,88166,88168],{"className":88167},[886],[888,88169,88170],{"xmlns":890},[892,88171,88172,88180],{},[895,88173,88174,88176,88178],{},[898,88175,900],{},[1700,88177,1765],{},[1931,88179,72543],{},[902,88181,88182],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,88185,88187],{"className":88186},[886],[888,88188,88189],{"xmlns":890},[892,88190,88191,88211],{},[895,88192,88193,88199,88205],{},[2007,88194,88195,88197],{},[898,88196,1662],{},[1931,88198,1933],{},[2007,88200,88201,88203],{},[898,88202,1662],{},[1931,88204,2343],{},[2007,88206,88207,88209],{},[898,88208,1662],{},[1931,88210,2385],{},[902,88212,88213],{"encoding":904},"Q_1 Q_2 Q_3",[115,88215,88217],{"id":88216},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,88219,88220,88221,8290,88256,2106,88259,41999,88276,10208,88293,88296,88297,88300],{},"Pro funkci užitečnosti ",[883,88222,88224],{"className":88223},[886],[888,88225,88226],{"xmlns":890},[892,88227,88228,88254],{},[895,88229,88230,88232,88234,88236,88238,88244,88246,88252],{},[898,88231,900],{},[1700,88233,1765],{},[898,88235,900],{},[1700,88237,1703],{"stretchy":1702},[2007,88239,88240,88242],{},[898,88241,1662],{},[1931,88243,1933],{},[1700,88245,1732],{"separator":1731},[2007,88247,88248,88250],{},[898,88249,1662],{},[1931,88251,2343],{},[1700,88253,1709],{"stretchy":1702},[902,88255,87637],{"encoding":904},[38,88257,88258],{},"mezní užitečnost",[883,88260,88262],{"className":88261},[886],[888,88263,88264],{"xmlns":890},[892,88265,88266,88274],{},[895,88267,88268],{},[2007,88269,88270,88272],{},[898,88271,1662],{},[1931,88273,1933],{},[902,88275,29187],{"encoding":904},[883,88277,88279],{"className":88278},[886],[888,88280,88281],{"xmlns":890},[892,88282,88283,88291],{},[895,88284,88285],{},[2007,88286,88287,88289],{},[898,88288,1662],{},[1931,88290,2343],{},[902,88292,29206],{"encoding":904},[38,88294,88295],{},"marginal utility",") parciální ",[207,88298,1145],{"className":88299,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,88302,88304],{"className":88303},[886],[888,88305,88306],{"xmlns":890,"display":28251},[892,88307,88308,88407],{},[20939,88309,88310],{"width":28256},[20944,88311,88312,88314,88400,88402],{},[20947,88313],{"width":28261},[20947,88315,88316],{},[895,88317,88318,88320,88326,88328,88336,88338,88356,88358,88360,88362,88368,88370,88378,88380,88398],{},[898,88319,2005],{},[2007,88321,88322,88324],{},[898,88323,900],{},[1931,88325,1933],{},[1700,88327,1765],{},[2030,88329,88330,88332,88334],{},[898,88331,900],{},[1931,88333,1933],{},[1700,88335,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,88337,1765],{},[1774,88339,88340,88346],{},[895,88341,88342,88344],{},[898,88343,10056],{"mathvariant":1791},[898,88345,900],{},[895,88347,88348,88350],{},[898,88349,10056],{"mathvariant":1791},[2007,88351,88352,88354],{},[898,88353,1662],{},[1931,88355,1933],{},[1700,88357,1732],{"separator":1731},[6066,88359],{"width":15469},[898,88361,2005],{},[2007,88363,88364,88366],{},[898,88365,900],{},[1931,88367,2343],{},[1700,88369,1765],{},[2030,88371,88372,88374,88376],{},[898,88373,900],{},[1931,88375,2343],{},[1700,88377,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,88379,1765],{},[1774,88381,88382,88388],{},[895,88383,88384,88386],{},[898,88385,10056],{"mathvariant":1791},[898,88387,900],{},[895,88389,88390,88392],{},[898,88391,10056],{"mathvariant":1791},[2007,88393,88394,88396],{},[898,88395,1662],{},[1931,88397,2343],{},[898,88399,2196],{"mathvariant":1791},[20947,88401],{"width":28261},[20947,88403,88404],{},[1781,88405,88406],{},"(6.2)",[902,88408,88409],{"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}",[724,88411,88412,88413,88447,88448,88478,88479,2106,88482,2196],{},"Pro pevné ",[883,88414,88416],{"className":88415},[886],[888,88417,88418],{"xmlns":890},[892,88419,88420,88444],{},[895,88421,88422,88428,88430,88432,88434,88440,88442],{},[2007,88423,88424,88426],{},[898,88425,1662],{},[1931,88427,1933],{},[1700,88429,1765],{},[898,88431,207],{},[1700,88433,1732],{"separator":1731},[2007,88435,88436,88438],{},[898,88437,1662],{},[1931,88439,2343],{},[1700,88441,1765],{},[898,88443,1879],{},[902,88445,88446],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,88449,88451],{"className":88450},[886],[888,88452,88453],{"xmlns":890},[892,88454,88455,88475],{},[895,88456,88457,88459,88465,88467,88469,88471,88473],{},[898,88458,2005],{},[2007,88460,88461,88463],{},[898,88462,900],{},[1931,88464,1933],{},[1700,88466,1703],{"stretchy":1702},[898,88468,207],{},[1700,88470,1732],{"separator":1731},[898,88472,1879],{},[1700,88474,1709],{"stretchy":1702},[902,88476,88477],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,88480,88481],{},"v bodě (na hladině)",[883,88483,88485],{"className":88484},[886],[888,88486,88487],{"xmlns":890},[892,88488,88489,88501],{},[895,88490,88491,88493,88495,88497,88499],{},[1700,88492,1927],{"stretchy":1702},[898,88494,207],{},[1700,88496,1732],{"separator":1731},[898,88498,1879],{},[1700,88500,1970],{"stretchy":1702},[902,88502,11007],{"encoding":904},[4060,88504,88505],{},[724,88506,88507,88509,88510,88540,88569,88570,2807,88583,2821,88600,88621,88622,2868,88639,2882,88652,88669,88670,88692,88693,88722,88723,6661,88743,88760],{},[883,88508,4346],{}," Intuice — co říká ",[883,88511,88513],{"className":88512},[886],[888,88514,88515],{"xmlns":890},[892,88516,88517,88537],{},[895,88518,88519,88521,88527,88529,88531,88533,88535],{},[898,88520,2005],{},[2007,88522,88523,88525],{},[898,88524,900],{},[1931,88526,1933],{},[1700,88528,1703],{"stretchy":1702},[898,88530,207],{},[1700,88532,1732],{"separator":1731},[898,88534,1879],{},[1700,88536,1709],{"stretchy":1702},[902,88538,88539],{"encoding":904},"MU_1(a,b)",[883,88541,88543],{"className":88542},[886],[888,88544,88545],{"xmlns":890},[892,88546,88547,88567],{},[895,88548,88549,88551,88557,88559,88561,88563,88565],{},[898,88550,2005],{},[2007,88552,88553,88555],{},[898,88554,900],{},[1931,88556,1933],{},[1700,88558,1703],{"stretchy":1702},[898,88560,207],{},[1700,88562,1732],{"separator":1731},[898,88564,1879],{},[1700,88566,1709],{"stretchy":1702},[902,88568,88477],{"encoding":904}," je rychlost změny ",[883,88571,88573],{"className":88572},[886],[888,88574,88575],{"xmlns":890},[892,88576,88577,88581],{},[895,88578,88579],{},[898,88580,900],{},[902,88582,900],{"encoding":904},[883,88584,88586],{"className":88585},[886],[888,88587,88588],{"xmlns":890},[892,88589,88590,88598],{},[895,88591,88592],{},[2007,88593,88594,88596],{},[898,88595,1662],{},[1931,88597,1933],{},[902,88599,29187],{"encoding":904},[883,88601,88603],{"className":88602},[886],[888,88604,88605],{"xmlns":890},[892,88606,88607,88619],{},[895,88608,88609,88611,88613,88615,88617],{},[1700,88610,1927],{"stretchy":1702},[898,88612,207],{},[1700,88614,1732],{"separator":1731},[898,88616,1879],{},[1700,88618,1970],{"stretchy":1702},[902,88620,11007],{"encoding":904},". Přibližně: změní-li se ",[883,88623,88625],{"className":88624},[886],[888,88626,88627],{"xmlns":890},[892,88628,88629,88637],{},[895,88630,88631],{},[2007,88632,88633,88635],{},[898,88634,1662],{},[1931,88636,1933],{},[902,88638,29187],{"encoding":904},[883,88640,88642],{"className":88641},[886],[888,88643,88644],{"xmlns":890},[892,88645,88646,88650],{},[895,88647,88648],{},[898,88649,207],{},[902,88651,207],{"encoding":904},[883,88653,88655],{"className":88654},[886],[888,88656,88657],{"xmlns":890},[892,88658,88659,88667],{},[895,88660,88661,88663,88665],{},[898,88662,207],{},[1700,88664,1897],{},[1931,88666,1933],{},[902,88668,2900],{"encoding":904}," při pevném ",[883,88671,88673],{"className":88672},[886],[888,88674,88675],{"xmlns":890},[892,88676,88677,88689],{},[895,88678,88679,88685,88687],{},[2007,88680,88681,88683],{},[898,88682,1662],{},[1931,88684,2343],{},[1700,88686,1765],{},[898,88688,1879],{},[902,88690,88691],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,88694,88696],{"className":88695},[886],[888,88697,88698],{"xmlns":890},[892,88699,88700,88720],{},[895,88701,88702,88704,88710,88712,88714,88716,88718],{},[898,88703,2005],{},[2007,88705,88706,88708],{},[898,88707,900],{},[1931,88709,1933],{},[1700,88711,1703],{"stretchy":1702},[898,88713,207],{},[1700,88715,1732],{"separator":1731},[898,88717,1879],{},[1700,88719,1709],{"stretchy":1702},[902,88721,88477],{"encoding":904},". Stejně tak ",[883,88724,88726],{"className":88725},[886],[888,88727,88728],{"xmlns":890},[892,88729,88730,88740],{},[895,88731,88732,88734],{},[898,88733,2005],{},[2007,88735,88736,88738],{},[898,88737,900],{},[1931,88739,2343],{},[902,88741,88742],{"encoding":904},"MU_2",[883,88744,88746],{"className":88745},[886],[888,88747,88748],{"xmlns":890},[892,88749,88750,88758],{},[895,88751,88752],{},[2007,88753,88754,88756],{},[898,88755,1662],{},[1931,88757,2343],{},[902,88759,29206],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,88762,80394],{"id":88763},"totální-diferenciál",[724,88765,88766,88767,48525,88783,88813,88814,2901],{},"Přibližnou změnu užitečnosti ",[883,88768,88770],{"className":88769},[886],[888,88771,88772],{"xmlns":890},[892,88773,88774,88780],{},[895,88775,88776,88778],{},[898,88777,3084],{"mathvariant":1791},[898,88779,900],{},[902,88781,88782],{"encoding":904},"\\Delta U",[883,88784,88786],{"className":88785},[886],[888,88787,88788],{"xmlns":890},[892,88789,88790,88810],{},[895,88791,88792,88794,88800,88802,88804],{},[898,88793,2406],{"mathvariant":1791},[2007,88795,88796,88798],{},[898,88797,1662],{},[1931,88799,1933],{},[1700,88801,1732],{"separator":1731},[898,88803,2406],{"mathvariant":1791},[2007,88805,88806,88808],{},[898,88807,1662],{},[1931,88809,2343],{},[902,88811,88812],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,88815,88816],{},"totálního diferenciálu",[883,88818,88820],{"className":88819},[886],[888,88821,88822],{"xmlns":890,"display":28251},[892,88823,88824,88925],{},[20939,88825,88826],{"width":28256},[20944,88827,88828,88830,88918,88920],{},[20947,88829],{"width":28261},[20947,88831,88832],{},[895,88833,88834,88836,88838,88840,88842,88844,88846,88854,88856,88862,88864,88872,88874,88880,88882,88884,88890,88892,88898,88900,88902,88908,88910,88916],{},[898,88835,3084],{"mathvariant":1791},[898,88837,900],{},[1700,88839,2927],{},[898,88841,2406],{"mathvariant":1791},[898,88843,900],{},[1700,88845,1765],{},[2030,88847,88848,88850,88852],{},[898,88849,900],{},[1931,88851,1933],{},[1700,88853,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[898,88855,2406],{"mathvariant":1791},[2007,88857,88858,88860],{},[898,88859,1662],{},[1931,88861,1933],{},[1700,88863,1897],{},[2030,88865,88866,88868,88870],{},[898,88867,900],{},[1931,88869,2343],{},[1700,88871,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[898,88873,2406],{"mathvariant":1791},[2007,88875,88876,88878],{},[898,88877,1662],{},[1931,88879,2343],{},[1700,88881,1765],{},[898,88883,2005],{},[2007,88885,88886,88888],{},[898,88887,900],{},[1931,88889,1933],{},[898,88891,2406],{"mathvariant":1791},[2007,88893,88894,88896],{},[898,88895,1662],{},[1931,88897,1933],{},[1700,88899,1897],{},[898,88901,2005],{},[2007,88903,88904,88906],{},[898,88905,900],{},[1931,88907,2343],{},[898,88909,2406],{"mathvariant":1791},[2007,88911,88912,88914],{},[898,88913,1662],{},[1931,88915,2343],{},[898,88917,2196],{"mathvariant":1791},[20947,88919],{"width":28261},[20947,88921,88922],{},[1781,88923,88924],{},"(6.3)",[902,88926,88927],{"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}",[724,88929,75652,88930,2196],{},[883,88931,88933],{"className":88932},[886],[888,88934,88935],{"xmlns":890},[892,88936,88937,89007],{},[895,88938,88939,88941,88943,88945,88947,88949,88955,88957,88959,88965,88967,88973,88975,88977,88983,88985,88987,88989,88991,88997,88999,89005],{},[898,88940,3084],{"mathvariant":1791},[898,88942,900],{},[1700,88944,1765],{},[898,88946,900],{},[1700,88948,1703],{"stretchy":1702},[2007,88950,88951,88953],{},[898,88952,1662],{},[1931,88954,1933],{},[1700,88956,1897],{},[898,88958,2406],{"mathvariant":1791},[2007,88960,88961,88963],{},[898,88962,1662],{},[1931,88964,1933],{},[1700,88966,1732],{"separator":1731},[2007,88968,88969,88971],{},[898,88970,1662],{},[1931,88972,2343],{},[1700,88974,1897],{},[898,88976,2406],{"mathvariant":1791},[2007,88978,88979,88981],{},[898,88980,1662],{},[1931,88982,2343],{},[1700,88984,1709],{"stretchy":1702},[1700,88986,1768],{},[898,88988,900],{},[1700,88990,1703],{"stretchy":1702},[2007,88992,88993,88995],{},[898,88994,1662],{},[1931,88996,1933],{},[1700,88998,1732],{"separator":1731},[2007,89000,89001,89003],{},[898,89002,1662],{},[1931,89004,2343],{},[1700,89006,1709],{"stretchy":1702},[902,89008,89009],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,89011,89013],{"id":89012},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,89015,89016,89017,89020,89021,89024],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,89018,89019],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,89022,89023],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,89026,89027,89030,89031,41999,89057,89083,89084,1343,89116,89148,89149,2114,89203,89257],{},[38,89028,89029],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,89032,89034],{"className":89033},[886],[888,89035,89036],{"xmlns":890},[892,89037,89038,89054],{},[895,89039,89040,89046,89048],{},[2007,89041,89042,89044],{},[898,89043,1662],{},[1931,89045,2343],{},[1700,89047,1765],{},[2007,89049,89050,89052],{},[898,89051,207],{},[1931,89053,1772],{},[902,89055,89056],{"encoding":904},"Q_2 = a_0",[883,89058,89060],{"className":89059},[886],[888,89061,89062],{"xmlns":890},[892,89063,89064,89080],{},[895,89065,89066,89072,89074],{},[2007,89067,89068,89070],{},[898,89069,1662],{},[1931,89071,1933],{},[1700,89073,1765],{},[2007,89075,89076,89078],{},[898,89077,1879],{},[1931,89079,1772],{},[902,89081,89082],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,89085,89087],{"className":89086},[886],[888,89088,89089],{"xmlns":890},[892,89090,89091,89113],{},[895,89092,89093,89095,89097,89103,89105,89111],{},[898,89094,900],{},[1700,89096,1703],{"stretchy":1702},[2007,89098,89099,89101],{},[898,89100,1662],{},[1931,89102,1933],{},[1700,89104,1732],{"separator":1731},[2007,89106,89107,89109],{},[898,89108,207],{},[1931,89110,1772],{},[1700,89112,1709],{"stretchy":1702},[902,89114,89115],{"encoding":904},"U(Q_1, a_0)",[883,89117,89119],{"className":89118},[886],[888,89120,89121],{"xmlns":890},[892,89122,89123,89145],{},[895,89124,89125,89127,89129,89135,89137,89143],{},[898,89126,900],{},[1700,89128,1703],{"stretchy":1702},[2007,89130,89131,89133],{},[898,89132,1879],{},[1931,89134,1772],{},[1700,89136,1732],{"separator":1731},[2007,89138,89139,89141],{},[898,89140,1662],{},[1931,89142,2343],{},[1700,89144,1709],{"stretchy":1702},[902,89146,89147],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,89150,89152],{"className":89151},[886],[888,89153,89154],{"xmlns":890},[892,89155,89156,89200],{},[895,89157,89158,89196,89198],{},[1770,89159,89160],{"scriptlevel":1772,"displaystyle":1731},[1774,89161,89162,89186],{},[895,89163,89164,89166,89168,89170,89176,89178,89184],{},[898,89165,2406],{"mathvariant":1791},[898,89167,900],{},[1700,89169,1703],{"stretchy":1702},[2007,89171,89172,89174],{},[898,89173,1662],{},[1931,89175,1933],{},[1700,89177,1732],{"separator":1731},[2007,89179,89180,89182],{},[898,89181,207],{},[1931,89183,1772],{},[1700,89185,1709],{"stretchy":1702},[895,89187,89188,89190],{},[898,89189,2406],{"mathvariant":1791},[2007,89191,89192,89194],{},[898,89193,1662],{},[1931,89195,1933],{},[1700,89197,3601],{},[1931,89199,1772],{},[902,89201,89202],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,89204,89206],{"className":89205},[886],[888,89207,89208],{"xmlns":890},[892,89209,89210,89254],{},[895,89211,89212,89250,89252],{},[1770,89213,89214],{"scriptlevel":1772,"displaystyle":1731},[1774,89215,89216,89240],{},[895,89217,89218,89220,89222,89224,89230,89232,89238],{},[898,89219,2406],{"mathvariant":1791},[898,89221,900],{},[1700,89223,1703],{"stretchy":1702},[2007,89225,89226,89228],{},[898,89227,1879],{},[1931,89229,1772],{},[1700,89231,1732],{"separator":1731},[2007,89233,89234,89236],{},[898,89235,1662],{},[1931,89237,2343],{},[1700,89239,1709],{"stretchy":1702},[895,89241,89242,89244],{},[898,89243,2406],{"mathvariant":1791},[2007,89245,89246,89248],{},[898,89247,1662],{},[1931,89249,2343],{},[1700,89251,3601],{},[1931,89253,1772],{},[902,89255,89256],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,89259,89261],{"className":89260},[886],[888,89262,89263],{"xmlns":890,"display":28251},[892,89264,89265,89310],{},[20939,89266,89267],{"width":28256},[20944,89268,89269,89271,89303,89305],{},[20947,89270],{"width":28261},[20947,89272,89273],{},[895,89274,89275,89283,89285,89287,89289,89291,89299,89301],{},[2030,89276,89277,89279,89281],{},[898,89278,900],{},[1931,89280,1933],{},[1700,89282,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,89284,3601],{},[1931,89286,1772],{},[1700,89288,1732],{"separator":1731},[6066,89290],{"width":15469},[2030,89292,89293,89295,89297],{},[898,89294,900],{},[1931,89296,2343],{},[1700,89298,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,89300,3601],{},[1931,89302,12645],{},[20947,89304],{"width":28261},[20947,89306,89307],{},[1781,89308,89309],{},"(6.4)",[902,89311,89312],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,89314,89315,89316,89318],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,89317,52861],{}," — užitečnost roste s množstvím každého zboží.",[724,89320,89321,89324,89325,89355,89356,2901],{},[38,89322,89323],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,89326,89328],{"className":89327},[886],[888,89329,89330],{"xmlns":890},[892,89331,89332,89352],{},[895,89333,89334,89342,89344],{},[2030,89335,89336,89338,89340],{},[898,89337,900],{},[1931,89339,1933],{},[1700,89341,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,89343,1732],{"separator":1731},[2030,89345,89346,89348,89350],{},[898,89347,900],{},[1931,89349,2343],{},[1700,89351,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,89353,89354],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,89357,89358],{},"záporné",[883,89360,89362],{"className":89361},[886],[888,89363,89364],{"xmlns":890,"display":28251},[892,89365,89366,89419],{},[20939,89367,89368],{"width":28256},[20944,89369,89370,89372,89412,89414],{},[20947,89371],{"width":28261},[20947,89373,89374],{},[895,89375,89376,89388,89390,89392,89394,89396,89408,89410],{},[2030,89377,89378,89380,89382],{},[898,89379,900],{},[1931,89381,3099],{},[895,89383,89384,89386],{},[1700,89385,1793],{"mathvariant":1791},[1700,89387,1793],{"mathvariant":1791},[1700,89389,3640],{},[1931,89391,1772],{},[1700,89393,1732],{"separator":1731},[6066,89395],{"width":15469},[2030,89397,89398,89400,89402],{},[898,89399,900],{},[1931,89401,32731],{},[895,89403,89404,89406],{},[1700,89405,1793],{"mathvariant":1791},[1700,89407,1793],{"mathvariant":1791},[1700,89409,3640],{},[1931,89411,12645],{},[20947,89413],{"width":28261},[20947,89415,89416],{},[1781,89417,89418],{},"(6.5)",[902,89420,89421],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,89423,89424,89425,89428,89429,2196],{},"Podmínka (6.5) je známa jako ",[38,89426,89427],{},"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 ",[207,89430,89432],{"className":89431,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,89434,89435,89436,2114,89468,89500,89501,2114,89527,89553,89554,89582,89583,2114,89585,89587,89588,89623],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,89437,89439],{"className":89438},[886],[888,89440,89441],{"xmlns":890},[892,89442,89443,89465],{},[895,89444,89445,89447,89449,89455,89457,89463],{},[898,89446,900],{},[1700,89448,1703],{"stretchy":1702},[2007,89450,89451,89453],{},[898,89452,1662],{},[1931,89454,1933],{},[1700,89456,1732],{"separator":1731},[2007,89458,89459,89461],{},[898,89460,1879],{},[1931,89462,1772],{},[1700,89464,1709],{"stretchy":1702},[902,89466,89467],{"encoding":904},"U(Q_1, b_0)",[883,89469,89471],{"className":89470},[886],[888,89472,89473],{"xmlns":890},[892,89474,89475,89497],{},[895,89476,89477,89479,89481,89487,89489,89495],{},[898,89478,900],{},[1700,89480,1703],{"stretchy":1702},[2007,89482,89483,89485],{},[898,89484,207],{},[1931,89486,1772],{},[1700,89488,1732],{"separator":1731},[2007,89490,89491,89493],{},[898,89492,1662],{},[1931,89494,2343],{},[1700,89496,1709],{"stretchy":1702},[902,89498,89499],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,89502,89504],{"className":89503},[886],[888,89505,89506],{"xmlns":890},[892,89507,89508,89524],{},[895,89509,89510,89512,89514,89516,89522],{},[1700,89511,1703],{"stretchy":1702},[898,89513,900],{},[1700,89515,1732],{"separator":1731},[2007,89517,89518,89520],{},[898,89519,1662],{},[1931,89521,1933],{},[1700,89523,1709],{"stretchy":1702},[902,89525,89526],{"encoding":904},"(U, Q_1)",[883,89528,89530],{"className":89529},[886],[888,89531,89532],{"xmlns":890},[892,89533,89534,89550],{},[895,89535,89536,89538,89540,89542,89548],{},[1700,89537,1703],{"stretchy":1702},[898,89539,900],{},[1700,89541,1732],{"separator":1731},[2007,89543,89544,89546],{},[898,89545,1662],{},[1931,89547,2343],{},[1700,89549,1709],{"stretchy":1702},[902,89551,89552],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,89555,89557],{"className":89556},[886],[888,89558,89559],{"xmlns":890},[892,89560,89561,89579],{},[895,89562,89563,89565,89567,89569,89571,89573,89575,89577],{},[898,89564,900],{},[1700,89566,1703],{"stretchy":1702},[1931,89568,1772],{},[1700,89570,1732],{"separator":1731},[1931,89572,1772],{},[1700,89574,1709],{"stretchy":1702},[1700,89576,1765],{},[1931,89578,1772],{},[902,89580,89581],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,89584,13842],{},[38,89586,38673],{},". Typický tvar grafu ",[883,89589,89591],{"className":89590},[886],[888,89592,89593],{"xmlns":890},[892,89594,89595,89621],{},[895,89596,89597,89599,89601,89603,89605,89611,89613,89619],{},[898,89598,900],{},[1700,89600,1765],{},[898,89602,900],{},[1700,89604,1703],{"stretchy":1702},[2007,89606,89607,89609],{},[898,89608,1662],{},[1931,89610,1933],{},[1700,89612,1732],{"separator":1731},[2007,89614,89615,89617],{},[898,89616,1662],{},[1931,89618,2343],{},[1700,89620,1709],{"stretchy":1702},[902,89622,87637],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,89625,89626],{},[614,89627,89628,89629,88669,89657,89678,89679,88669,89707,89729],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,89630,89632],{"className":89631},[886],[888,89633,89634],{"xmlns":890},[892,89635,89636,89654],{},[895,89637,89638,89640,89642,89648,89650,89652],{},[898,89639,900],{},[1700,89641,1703],{"stretchy":1702},[2007,89643,89644,89646],{},[898,89645,1662],{},[1931,89647,1933],{},[1700,89649,1732],{"separator":1731},[898,89651,1879],{},[1700,89653,1709],{"stretchy":1702},[902,89655,89656],{"encoding":904},"U(Q_1, b)",[883,89658,89660],{"className":89659},[886],[888,89661,89662],{"xmlns":890},[892,89663,89664,89676],{},[895,89665,89666,89672,89674],{},[2007,89667,89668,89670],{},[898,89669,1662],{},[1931,89671,2343],{},[1700,89673,1765],{},[898,89675,1879],{},[902,89677,88691],{"encoding":904}," (vlevo) a ",[883,89680,89682],{"className":89681},[886],[888,89683,89684],{"xmlns":890},[892,89685,89686,89704],{},[895,89687,89688,89690,89692,89694,89696,89702],{},[898,89689,900],{},[1700,89691,1703],{"stretchy":1702},[898,89693,207],{},[1700,89695,1732],{"separator":1731},[2007,89697,89698,89700],{},[898,89699,1662],{},[1931,89701,2343],{},[1700,89703,1709],{"stretchy":1702},[902,89705,89706],{"encoding":904},"U(a, Q_2)",[883,89708,89710],{"className":89709},[886],[888,89711,89712],{"xmlns":890},[892,89713,89714,89726],{},[895,89715,89716,89722,89724],{},[2007,89717,89718,89720],{},[898,89719,1662],{},[1931,89721,1933],{},[1700,89723,1765],{},[898,89725,207],{},[902,89727,89728],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,89731,89732],{},[614,89733,89734,89735,89770,89771,89801,89802,2114,89825,89847,89848,2196],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,89736,89738],{"className":89737},[886],[888,89739,89740],{"xmlns":890},[892,89741,89742,89768],{},[895,89743,89744,89746,89748,89750,89752,89758,89760,89766],{},[898,89745,900],{},[1700,89747,1765],{},[898,89749,900],{},[1700,89751,1703],{"stretchy":1702},[2007,89753,89754,89756],{},[898,89755,1662],{},[1931,89757,1933],{},[1700,89759,1732],{"separator":1731},[2007,89761,89762,89764],{},[898,89763,1662],{},[1931,89765,2343],{},[1700,89767,1709],{"stretchy":1702},[902,89769,87637],{"encoding":904}," nad rovinou ",[883,89772,89774],{"className":89773},[886],[888,89775,89776],{"xmlns":890},[892,89777,89778,89798],{},[895,89779,89780,89782,89788,89790,89796],{},[1700,89781,1703],{"stretchy":1702},[2007,89783,89784,89786],{},[898,89785,1662],{},[1931,89787,1933],{},[1700,89789,1732],{"separator":1731},[2007,89791,89792,89794],{},[898,89793,1662],{},[1931,89795,2343],{},[1700,89797,1709],{"stretchy":1702},[902,89799,89800],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,89803,89805],{"className":89804},[886],[888,89806,89807],{"xmlns":890},[892,89808,89809,89822],{},[895,89810,89811,89817,89819],{},[2007,89812,89813,89815],{},[898,89814,1662],{},[1931,89816,1933],{},[1700,89818,1765],{},[1781,89820,89821],{},"const",[902,89823,89824],{"encoding":904},"Q_1 = \\text{const}",[883,89826,89828],{"className":89827},[886],[888,89829,89830],{"xmlns":890},[892,89831,89832,89844],{},[895,89833,89834,89840,89842],{},[2007,89835,89836,89838],{},[898,89837,1662],{},[1931,89839,2343],{},[1700,89841,1765],{},[1781,89843,89821],{},[902,89845,89846],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,89849,89851],{"className":89850},[886],[888,89852,89853],{"xmlns":890},[892,89854,89855,89881],{},[895,89856,89857,89859,89861,89867,89869,89875,89877,89879],{},[898,89858,900],{},[1700,89860,1703],{"stretchy":1702},[2007,89862,89863,89865],{},[898,89864,1662],{},[1931,89866,1933],{},[1700,89868,1732],{"separator":1731},[2007,89870,89871,89873],{},[898,89872,1662],{},[1931,89874,2343],{},[1700,89876,1709],{"stretchy":1702},[1700,89878,1765],{},[898,89880,2354],{},[902,89882,9955],{"encoding":904},[198,89884,89886,89887],{"id":89885},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,89888,89890],{"className":89889},[886],[888,89891,89892],{"xmlns":890},[892,89893,89894,89928],{},[895,89895,89896,89898,89900,89914],{},[898,89897,900],{},[1700,89899,1765],{},[2030,89901,89902,89904,89906],{},[898,89903,1662],{},[1931,89905,1933],{},[895,89907,89908,89910,89912],{},[1931,89909,1933],{},[898,89911,1979],{"mathvariant":1791},[1931,89913,2343],{},[2030,89915,89916,89918,89920],{},[898,89917,1662],{},[1931,89919,2343],{},[895,89921,89922,89924,89926],{},[1931,89923,1933],{},[898,89925,1979],{"mathvariant":1791},[1931,89927,2385],{},[902,89929,89930],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,89932,89933],{},[38,89934,89935],{},"Ověření (6.4) a (6.5).",[883,89937,89939],{"className":89938},[886],[888,89940,89941],{"xmlns":890,"display":28251},[892,89942,89943,90047],{},[895,89944,89945,89953,89955,89963,89979,89993,89995,89997,90005,90007,90015,90029,90045],{},[2030,89946,89947,89949,89951],{},[898,89948,900],{},[1931,89950,1933],{},[1700,89952,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,89954,1765],{},[1770,89956,89957],{"scriptlevel":1772,"displaystyle":1702},[1774,89958,89959,89961],{},[1931,89960,1933],{},[1931,89962,2343],{},[2030,89964,89965,89967,89969],{},[898,89966,1662],{},[1931,89968,1933],{},[895,89970,89971,89973,89975,89977],{},[1700,89972,1768],{},[1931,89974,1933],{},[898,89976,1979],{"mathvariant":1791},[1931,89978,2343],{},[2030,89980,89981,89983,89985],{},[898,89982,1662],{},[1931,89984,2343],{},[895,89986,89987,89989,89991],{},[1931,89988,1933],{},[898,89990,1979],{"mathvariant":1791},[1931,89992,2385],{},[1700,89994,1732],{"separator":1731},[6066,89996],{"width":15469},[2030,89998,89999,90001,90003],{},[898,90000,900],{},[1931,90002,2343],{},[1700,90004,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,90006,1765],{},[1770,90008,90009],{"scriptlevel":1772,"displaystyle":1702},[1774,90010,90011,90013],{},[1931,90012,1933],{},[1931,90014,2385],{},[2030,90016,90017,90019,90021],{},[898,90018,1662],{},[1931,90020,1933],{},[895,90022,90023,90025,90027],{},[1931,90024,1933],{},[898,90026,1979],{"mathvariant":1791},[1931,90028,2343],{},[2030,90030,90031,90033,90035],{},[898,90032,1662],{},[1931,90034,2343],{},[895,90036,90037,90039,90041,90043],{},[1700,90038,1768],{},[1931,90040,2343],{},[898,90042,1979],{"mathvariant":1791},[1931,90044,2385],{},[1700,90046,1732],{"separator":1731},[902,90048,90049],{"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},",[724,90051,90052,90053,90087],{},"zřejmě ",[883,90054,90056],{"className":90055},[886],[888,90057,90058],{"xmlns":890},[892,90059,90060,90084],{},[895,90061,90062,90070,90072,90080,90082],{},[2030,90063,90064,90066,90068],{},[898,90065,900],{},[1931,90067,1933],{},[1700,90069,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,90071,1732],{"separator":1731},[2030,90073,90074,90076,90078],{},[898,90075,900],{},[1931,90077,2343],{},[1700,90079,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,90081,3601],{},[1931,90083,1772],{},[902,90085,90086],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,90089,90091],{"className":90090},[886],[888,90092,90093],{"xmlns":890,"display":28251},[892,90094,90095,90211],{},[895,90096,90097,90109,90111,90113,90121,90137,90151,90153,90155,90167,90169,90171,90179,90193,90209],{},[2030,90098,90099,90101,90103],{},[898,90100,900],{},[1931,90102,3099],{},[895,90104,90105,90107],{},[1700,90106,1793],{"mathvariant":1791},[1700,90108,1793],{"mathvariant":1791},[1700,90110,1765],{},[1700,90112,1768],{},[1770,90114,90115],{"scriptlevel":1772,"displaystyle":1702},[1774,90116,90117,90119],{},[1931,90118,1933],{},[1931,90120,2553],{},[2030,90122,90123,90125,90127],{},[898,90124,1662],{},[1931,90126,1933],{},[895,90128,90129,90131,90133,90135],{},[1700,90130,1768],{},[1931,90132,2385],{},[898,90134,1979],{"mathvariant":1791},[1931,90136,2343],{},[2030,90138,90139,90141,90143],{},[898,90140,1662],{},[1931,90142,2343],{},[895,90144,90145,90147,90149],{},[1931,90146,1933],{},[898,90148,1979],{"mathvariant":1791},[1931,90150,2385],{},[1700,90152,1732],{"separator":1731},[6066,90154],{"width":15469},[2030,90156,90157,90159,90161],{},[898,90158,900],{},[1931,90160,32731],{},[895,90162,90163,90165],{},[1700,90164,1793],{"mathvariant":1791},[1700,90166,1793],{"mathvariant":1791},[1700,90168,1765],{},[1700,90170,1768],{},[1770,90172,90173],{"scriptlevel":1772,"displaystyle":1702},[1774,90174,90175,90177],{},[1931,90176,2343],{},[1931,90178,4190],{},[2030,90180,90181,90183,90185],{},[898,90182,1662],{},[1931,90184,1933],{},[895,90186,90187,90189,90191],{},[1931,90188,1933],{},[898,90190,1979],{"mathvariant":1791},[1931,90192,2343],{},[2030,90194,90195,90197,90199],{},[898,90196,1662],{},[1931,90198,2343],{},[895,90200,90201,90203,90205,90207],{},[1700,90202,1768],{},[1931,90204,2438],{},[898,90206,1979],{"mathvariant":1791},[1931,90208,2385],{},[1700,90210,1732],{"separator":1731},[902,90212,90213],{"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},",[724,90215,90216,90217,90259],{},"opět ",[883,90218,90220],{"className":90219},[886],[888,90221,90222],{"xmlns":890},[892,90223,90224,90256],{},[895,90225,90226,90238,90240,90252,90254],{},[2030,90227,90228,90230,90232],{},[898,90229,900],{},[1931,90231,3099],{},[895,90233,90234,90236],{},[1700,90235,1793],{"mathvariant":1791},[1700,90237,1793],{"mathvariant":1791},[1700,90239,1732],{"separator":1731},[2030,90241,90242,90244,90246],{},[898,90243,900],{},[1931,90245,32731],{},[895,90247,90248,90250],{},[1700,90249,1793],{"mathvariant":1791},[1700,90251,1793],{"mathvariant":1791},[1700,90253,3640],{},[1931,90255,1772],{},[902,90257,90258],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,90261,90262],{},[38,90263,90264,90265,2196],{},"(a) Mezní užitečnosti v bodě ",[883,90266,90268],{"className":90267},[886],[888,90269,90270],{"xmlns":890},[892,90271,90272,90284],{},[895,90273,90274,90276,90278,90280,90282],{},[1700,90275,1927],{"stretchy":1702},[1931,90277,3284],{},[1700,90279,1732],{"separator":1731},[1931,90281,8565],{},[1700,90283,1970],{"stretchy":1702},[902,90285,90286],{"encoding":904},"[100, 200]",[883,90288,90290],{"className":90289},[886],[888,90291,90292],{"xmlns":890,"display":28251},[892,90293,90294,90361],{},[895,90295,90296,90298,90304,90306,90308,90310,90312,90314,90316,90324,90326,90340,90342,90354,90356,90359],{},[898,90297,2005],{},[2007,90299,90300,90302],{},[898,90301,900],{},[1931,90303,1933],{},[1700,90305,1703],{"stretchy":1702},[1931,90307,3284],{},[1700,90309,1732],{"separator":1731},[1931,90311,8565],{},[1700,90313,1709],{"stretchy":1702},[1700,90315,1765],{},[1770,90317,90318],{"scriptlevel":1772,"displaystyle":1702},[1774,90319,90320,90322],{},[1931,90321,1933],{},[1931,90323,2343],{},[1700,90325,2065],{},[1785,90327,90328,90330],{},[1931,90329,3284],{},[895,90331,90332,90334,90336,90338],{},[1700,90333,1768],{},[1931,90335,1933],{},[898,90337,1979],{"mathvariant":1791},[1931,90339,2343],{},[1700,90341,2065],{},[1785,90343,90344,90346],{},[1931,90345,8565],{},[895,90347,90348,90350,90352],{},[1931,90349,1933],{},[898,90351,1979],{"mathvariant":1791},[1931,90353,2385],{},[1700,90355,6088],{},[1931,90357,90358],{},"0,4204",[1700,90360,1732],{"separator":1731},[902,90362,90363],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,90365,90367],{"className":90366},[886],[888,90368,90369],{"xmlns":890,"display":28251},[892,90370,90371,90436],{},[895,90372,90373,90375,90381,90383,90385,90387,90389,90391,90393,90401,90403,90415,90417,90431,90433],{},[898,90374,2005],{},[2007,90376,90377,90379],{},[898,90378,900],{},[1931,90380,2343],{},[1700,90382,1703],{"stretchy":1702},[1931,90384,3284],{},[1700,90386,1732],{"separator":1731},[1931,90388,8565],{},[1700,90390,1709],{"stretchy":1702},[1700,90392,1765],{},[1770,90394,90395],{"scriptlevel":1772,"displaystyle":1702},[1774,90396,90397,90399],{},[1931,90398,1933],{},[1931,90400,2385],{},[1700,90402,2065],{},[1785,90404,90405,90407],{},[1931,90406,3284],{},[895,90408,90409,90411,90413],{},[1931,90410,1933],{},[898,90412,1979],{"mathvariant":1791},[1931,90414,2343],{},[1700,90416,2065],{},[1785,90418,90419,90421],{},[1931,90420,8565],{},[895,90422,90423,90425,90427,90429],{},[1700,90424,1768],{},[1931,90426,2343],{},[898,90428,1979],{"mathvariant":1791},[1931,90430,2385],{},[1700,90432,6088],{},[1931,90434,90435],{},"0,63067.",[902,90437,90438],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,90440,90441,2106,90443,90478,90479,90500,90501,90518],{},[614,90442,9403],{},[883,90444,90446],{"className":90445},[886],[888,90447,90448],{"xmlns":890},[892,90449,90450,90475],{},[895,90451,90452,90454,90460,90462,90464,90466,90468,90470,90472],{},[898,90453,2005],{},[2007,90455,90456,90458],{},[898,90457,900],{},[1931,90459,2343],{},[1700,90461,1703],{"stretchy":1702},[1931,90463,3284],{},[1700,90465,1732],{"separator":1731},[1931,90467,8565],{},[1700,90469,1709],{"stretchy":1702},[1700,90471,6088],{},[1931,90473,90474],{},"0,63067",[902,90476,90477],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,90480,90482],{"className":90481},[886],[888,90483,90484],{"xmlns":890},[892,90485,90486,90498],{},[895,90487,90488,90490,90492,90494,90496],{},[1700,90489,1927],{"stretchy":1702},[1931,90491,3284],{},[1700,90493,1732],{"separator":1731},[1931,90495,8565],{},[1700,90497,1970],{"stretchy":1702},[902,90499,90286],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,90502,90504],{"className":90503},[886],[888,90505,90506],{"xmlns":890},[892,90507,90508,90516],{},[895,90509,90510],{},[2007,90511,90512,90514],{},[898,90513,1662],{},[1931,90515,2343],{},[902,90517,29206],{"encoding":904}," přibližně o 0,63067.",[724,90520,90521,90540,90541,39369,90562,90579,90580,90606,90607,90624,90625,3345],{},[38,90522,90523,90524,90539],{},"(b) Odhad změny ",[883,90525,90527],{"className":90526},[886],[888,90528,90529],{"xmlns":890},[892,90530,90531,90537],{},[895,90532,90533,90535],{},[898,90534,3084],{"mathvariant":1791},[898,90536,900],{},[902,90538,88782],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,90542,90544],{"className":90543},[886],[888,90545,90546],{"xmlns":890},[892,90547,90548,90560],{},[895,90549,90550,90552,90554,90556,90558],{},[1700,90551,1927],{"stretchy":1702},[1931,90553,3284],{},[1700,90555,1732],{"separator":1731},[1931,90557,8565],{},[1700,90559,1970],{"stretchy":1702},[902,90561,90286],{"encoding":904},[883,90563,90565],{"className":90564},[886],[888,90566,90567],{"xmlns":890},[892,90568,90569,90577],{},[895,90570,90571],{},[2007,90572,90573,90575],{},[898,90574,1662],{},[1931,90576,1933],{},[902,90578,29187],{"encoding":904}," na 98 (tj. ",[883,90581,90583],{"className":90582},[886],[888,90584,90585],{"xmlns":890},[892,90586,90587,90603],{},[895,90588,90589,90591,90597,90599,90601],{},[898,90590,2406],{"mathvariant":1791},[2007,90592,90593,90595],{},[898,90594,1662],{},[1931,90596,1933],{},[1700,90598,1765],{},[1700,90600,1768],{},[1931,90602,2343],{},[902,90604,90605],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,90608,90610],{"className":90609},[886],[888,90611,90612],{"xmlns":890},[892,90613,90614,90622],{},[895,90615,90616],{},[2007,90617,90618,90620],{},[898,90619,1662],{},[1931,90621,2343],{},[902,90623,29206],{"encoding":904}," o 3 (tj. ",[883,90626,90628],{"className":90627},[886],[888,90629,90630],{"xmlns":890},[892,90631,90632,90646],{},[895,90633,90634,90636,90642,90644],{},[898,90635,2406],{"mathvariant":1791},[2007,90637,90638,90640],{},[898,90639,1662],{},[1931,90641,2343],{},[1700,90643,1765],{},[1931,90645,2385],{},[902,90647,90648],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,90650,90652],{"className":90651},[886],[888,90653,90654],{"xmlns":890,"display":28251},[892,90655,90656,90707],{},[895,90657,90658,90660,90662,90664,90666,90668,90670,90672,90674,90676,90678,90680,90682,90684,90686,90688,90690,90692,90694,90697,90699,90702,90704],{},[898,90659,3084],{"mathvariant":1791},[898,90661,900],{},[1700,90663,2927],{},[898,90665,2406],{"mathvariant":1791},[898,90667,900],{},[1700,90669,1765],{},[1931,90671,90358],{},[1700,90673,2065],{},[1700,90675,1703],{"stretchy":1702},[1700,90677,1768],{},[1931,90679,2343],{},[1700,90681,1709],{"stretchy":1702},[1700,90683,1897],{},[1931,90685,90474],{},[1700,90687,2065],{},[1931,90689,2385],{},[1700,90691,1765],{},[1700,90693,1768],{},[1931,90695,90696],{},"0,8408",[1700,90698,1897],{},[1931,90700,90701],{},"1,89201",[1700,90703,6088],{},[1931,90705,90706],{},"1,05.",[902,90708,90709],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,90711,90712,90713,90716,90717,90768,90769,2196],{},"Užitečnost se tedy zvýší přibližně o ",[38,90714,90715],{},"1,05",". Skutečná změna je ",[883,90718,90720],{"className":90719},[886],[888,90721,90722],{"xmlns":890},[892,90723,90724,90765],{},[895,90725,90726,90728,90730,90732,90734,90736,90739,90741,90744,90746,90748,90750,90752,90754,90756,90758,90760,90762],{},[898,90727,3084],{"mathvariant":1791},[898,90729,900],{},[1700,90731,1765],{},[898,90733,900],{},[1700,90735,1703],{"stretchy":1702},[1931,90737,90738],{},"98",[1700,90740,1732],{"separator":1731},[1931,90742,90743],{},"203",[1700,90745,1709],{"stretchy":1702},[1700,90747,1768],{},[898,90749,900],{},[1700,90751,1703],{"stretchy":1702},[1931,90753,3284],{},[1700,90755,1732],{"separator":1731},[1931,90757,8565],{},[1700,90759,1709],{"stretchy":1702},[1700,90761,6088],{},[1931,90763,90764],{},"1,031",[902,90766,90767],{"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 ",[883,90770,90772],{"className":90771},[886],[888,90773,90774],{"xmlns":890},[892,90775,90776,90796],{},[895,90777,90778,90780,90786,90788,90790],{},[898,90779,2406],{"mathvariant":1791},[2007,90781,90782,90784],{},[898,90783,1662],{},[1931,90785,1933],{},[1700,90787,1732],{"separator":1731},[898,90789,2406],{"mathvariant":1791},[2007,90791,90792,90794],{},[898,90793,1662],{},[1931,90795,2343],{},[902,90797,88812],{"encoding":904},[115,90799,90801],{"id":90800},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,90803,90804],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,90806,90808],{"className":90807},[886],[888,90809,90810],{"xmlns":890,"display":28251},[892,90811,90812,90871],{},[20939,90813,90814],{"width":28256},[20944,90815,90816,90818,90864,90866],{},[20947,90817],{"width":28261},[20947,90819,90820],{},[895,90821,90822,90824,90826,90832,90834,90840,90842,90844,90852,90854,90862],{},[898,90823,900],{},[1700,90825,1703],{"stretchy":1702},[2007,90827,90828,90830],{},[898,90829,1662],{},[1931,90831,1933],{},[1700,90833,1732],{"separator":1731},[2007,90835,90836,90838],{},[898,90837,1662],{},[1931,90839,2343],{},[1700,90841,1709],{"stretchy":1702},[1700,90843,1765],{},[2030,90845,90846,90848,90850],{},[898,90847,1662],{},[1931,90849,1933],{},[898,90851,207],{},[1700,90853,2065],{},[2030,90855,90856,90858,90860],{},[898,90857,1662],{},[1931,90859,2343],{},[898,90861,1879],{},[1700,90863,1732],{"separator":1731},[20947,90865],{"width":28261},[20947,90867,90868],{},[1781,90869,90870],{},"(6.6)",[902,90872,90873],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,90875,4499,90876,90894,90895,90897,90898,90902,90903,90933,90934,90956],{},[883,90877,90879],{"className":90878},[886],[888,90880,90881],{"xmlns":890},[892,90882,90883,90891],{},[895,90884,90885,90887,90889],{},[898,90886,207],{},[1700,90888,1732],{"separator":1731},[898,90890,1879],{},[902,90892,90893],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,90896,74883],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,90899,90901],{"className":90900,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,90904,90906],{"className":90905},[886],[888,90907,90908],{"xmlns":890},[892,90909,90910,90930],{},[895,90911,90912,90914,90916,90918,90920,90922,90924,90926,90928],{},[898,90913,207],{},[1700,90915,1732],{"separator":1731},[898,90917,1879],{},[1700,90919,6694],{},[1700,90921,1703],{"stretchy":1702},[1931,90923,1772],{},[1700,90925,1732],{"separator":1731},[1931,90927,1933],{},[1700,90929,1709],{"stretchy":1702},[902,90931,90932],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,90935,90937],{"className":90936},[886],[888,90938,90939],{"xmlns":890},[892,90940,90941,90953],{},[895,90942,90943,90945,90947,90949,90951],{},[898,90944,1879],{},[1700,90946,1765],{},[1931,90948,1933],{},[1700,90950,1768],{},[898,90952,207],{},[902,90954,90955],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,90958,90959],{},[2756,90960],{"alt":90961,"className":90962,"src":90963},"imek-cobb-douglas-3d-plus-ic",[210,2760],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,90965,90967],{"className":90966},[886],[888,90968,90969],{"xmlns":890,"display":28251},[892,90970,90971,91021],{},[895,90972,90973,90975,90977,90983,90985,90991,90993,90995,91003,91005,91019],{},[898,90974,900],{},[1700,90976,1703],{"stretchy":1702},[2007,90978,90979,90981],{},[898,90980,1662],{},[1931,90982,1933],{},[1700,90984,1732],{"separator":1731},[2007,90986,90987,90989],{},[898,90988,1662],{},[1931,90990,2343],{},[1700,90992,1709],{"stretchy":1702},[1700,90994,1765],{},[2030,90996,90997,90999,91001],{},[898,90998,1662],{},[1931,91000,1933],{},[898,91002,207],{},[1700,91004,2065],{},[2030,91006,91007,91009,91011],{},[898,91008,1662],{},[1931,91010,2343],{},[895,91012,91013,91015,91017],{},[1931,91014,1933],{},[1700,91016,1768],{},[898,91018,207],{},[898,91020,2196],{"mathvariant":1791},[902,91022,91023],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[4060,91025,91026,91075,91197,91331],{},[724,91027,91028,91030,91031],{},[883,91029,52879],{}," Příklad 6.3 — ověření vlastností pro ",[883,91032,91034],{"className":91033},[886],[888,91035,91036],{"xmlns":890},[892,91037,91038,91072],{},[895,91039,91040,91042,91044,91058],{},[898,91041,900],{},[1700,91043,1765],{},[2030,91045,91046,91048,91050],{},[898,91047,1662],{},[1931,91049,1933],{},[895,91051,91052,91054,91056],{},[1931,91053,1933],{},[898,91055,1979],{"mathvariant":1791},[1931,91057,2553],{},[2030,91059,91060,91062,91064],{},[898,91061,1662],{},[1931,91063,2343],{},[895,91065,91066,91068,91070],{},[1931,91067,2385],{},[898,91069,1979],{"mathvariant":1791},[1931,91071,2553],{},[902,91073,91074],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,91076,91078],{"className":91077},[886],[888,91079,91080],{"xmlns":890,"display":28251},[892,91081,91082,91194],{},[895,91083,91084,91092,91094,91102,91118,91132,91134,91136,91138,91140,91148,91150,91158,91172,91188,91190,91192],{},[2030,91085,91086,91088,91090],{},[898,91087,900],{},[1931,91089,1933],{},[1700,91091,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,91093,1765],{},[1770,91095,91096],{"scriptlevel":1772,"displaystyle":1702},[1774,91097,91098,91100],{},[1931,91099,1933],{},[1931,91101,2553],{},[2030,91103,91104,91106,91108],{},[898,91105,1662],{},[1931,91107,1933],{},[895,91109,91110,91112,91114,91116],{},[1700,91111,1768],{},[1931,91113,2385],{},[898,91115,1979],{"mathvariant":1791},[1931,91117,2553],{},[2030,91119,91120,91122,91124],{},[898,91121,1662],{},[1931,91123,2343],{},[895,91125,91126,91128,91130],{},[1931,91127,2385],{},[898,91129,1979],{"mathvariant":1791},[1931,91131,2553],{},[1700,91133,3601],{},[1931,91135,1772],{},[1700,91137,1732],{"separator":1731},[6066,91139],{"width":15469},[2030,91141,91142,91144,91146],{},[898,91143,900],{},[1931,91145,2343],{},[1700,91147,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,91149,1765],{},[1770,91151,91152],{"scriptlevel":1772,"displaystyle":1702},[1774,91153,91154,91156],{},[1931,91155,2385],{},[1931,91157,2553],{},[2030,91159,91160,91162,91164],{},[898,91161,1662],{},[1931,91163,1933],{},[895,91165,91166,91168,91170],{},[1931,91167,1933],{},[898,91169,1979],{"mathvariant":1791},[1931,91171,2553],{},[2030,91173,91174,91176,91178],{},[898,91175,1662],{},[1931,91177,2343],{},[895,91179,91180,91182,91184,91186],{},[1700,91181,1768],{},[1931,91183,1933],{},[898,91185,1979],{"mathvariant":1791},[1931,91187,2553],{},[1700,91189,3601],{},[1931,91191,1772],{},[1700,91193,1732],{"separator":1731},[902,91195,91196],{"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,",[883,91198,91200],{"className":91199},[886],[888,91201,91202],{"xmlns":890,"display":28251},[892,91203,91204,91328],{},[895,91205,91206,91218,91220,91222,91230,91246,91260,91262,91264,91266,91268,91280,91282,91284,91292,91306,91322,91324,91326],{},[2030,91207,91208,91210,91212],{},[898,91209,900],{},[1931,91211,3099],{},[895,91213,91214,91216],{},[1700,91215,1793],{"mathvariant":1791},[1700,91217,1793],{"mathvariant":1791},[1700,91219,1765],{},[1700,91221,1768],{},[1770,91223,91224],{"scriptlevel":1772,"displaystyle":1702},[1774,91225,91226,91228],{},[1931,91227,2385],{},[1931,91229,42047],{},[2030,91231,91232,91234,91236],{},[898,91233,1662],{},[1931,91235,1933],{},[895,91237,91238,91240,91242,91244],{},[1700,91239,1768],{},[1931,91241,24386],{},[898,91243,1979],{"mathvariant":1791},[1931,91245,2553],{},[2030,91247,91248,91250,91252],{},[898,91249,1662],{},[1931,91251,2343],{},[895,91253,91254,91256,91258],{},[1931,91255,2385],{},[898,91257,1979],{"mathvariant":1791},[1931,91259,2553],{},[1700,91261,3640],{},[1931,91263,1772],{},[1700,91265,1732],{"separator":1731},[6066,91267],{"width":15469},[2030,91269,91270,91272,91274],{},[898,91271,900],{},[1931,91273,32731],{},[895,91275,91276,91278],{},[1700,91277,1793],{"mathvariant":1791},[1700,91279,1793],{"mathvariant":1791},[1700,91281,1765],{},[1700,91283,1768],{},[1770,91285,91286],{"scriptlevel":1772,"displaystyle":1702},[1774,91287,91288,91290],{},[1931,91289,2385],{},[1931,91291,42047],{},[2030,91293,91294,91296,91298],{},[898,91295,1662],{},[1931,91297,1933],{},[895,91299,91300,91302,91304],{},[1931,91301,1933],{},[898,91303,1979],{"mathvariant":1791},[1931,91305,2553],{},[2030,91307,91308,91310,91312],{},[898,91309,1662],{},[1931,91311,2343],{},[895,91313,91314,91316,91318,91320],{},[1700,91315,1768],{},[1931,91317,2438],{},[898,91319,1979],{"mathvariant":1791},[1931,91321,2553],{},[1700,91323,3640],{},[1931,91325,1772],{},[1700,91327,1732],{"separator":1731},[902,91329,91330],{"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,",[724,91332,91333],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,91335,91337],{"id":91336},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,91339,91340,91343],{},[38,91341,91342],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,91345,91347],{"className":91346},[886],[888,91348,91349],{"xmlns":890,"display":28251},[892,91350,91351,91394],{},[20939,91352,91353],{"width":28256},[20944,91354,91355,91357,91387,91389],{},[20947,91356],{"width":28261},[20947,91358,91359],{},[895,91360,91361,91363,91365,91371,91373,91379,91381,91383,91385],{},[898,91362,900],{},[1700,91364,1703],{"stretchy":1702},[2007,91366,91367,91369],{},[898,91368,1662],{},[1931,91370,1933],{},[1700,91372,1732],{"separator":1731},[2007,91374,91375,91377],{},[898,91376,1662],{},[1931,91378,2343],{},[1700,91380,1709],{"stretchy":1702},[1700,91382,1765],{},[898,91384,2354],{},[1700,91386,1732],{"separator":1731},[20947,91388],{"width":28261},[20947,91390,91391],{},[1781,91392,91393],{},"(6.7)",[902,91395,91396],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,91398,4499,91399,91412],{},[883,91400,91402],{"className":91401},[886],[888,91403,91404],{"xmlns":890},[892,91405,91406,91410],{},[895,91407,91408],{},[898,91409,2354],{},[902,91411,2354],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,91414,91416],{"className":91415},[886],[888,91417,91418],{"xmlns":890,"display":28251},[892,91419,91420,91461],{},[20939,91421,91422],{"width":28256},[20944,91423,91424,91426,91454,91456],{},[20947,91425],{"width":28261},[20947,91427,91428],{},[895,91429,91430,91438,91440,91448,91450,91452],{},[2030,91431,91432,91434,91436],{},[898,91433,1662],{},[1931,91435,1933],{},[898,91437,207],{},[1700,91439,2065],{},[2030,91441,91442,91444,91446],{},[898,91443,1662],{},[1931,91445,2343],{},[898,91447,1879],{},[1700,91449,1765],{},[898,91451,2354],{},[898,91453,2196],{"mathvariant":1791},[20947,91455],{"width":28261},[20947,91457,91458],{},[1781,91459,91460],{},"(6.8)",[902,91462,91463],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,91465,91466,91467,4547,91497,2106,91500,91513,91514,91549,91550,91567,91568,91597,91598,91601],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,91468,91470],{"className":91469},[886],[888,91471,91472],{"xmlns":890},[892,91473,91474,91494],{},[895,91475,91476,91478,91484,91486,91492],{},[1700,91477,1927],{"stretchy":1702},[2007,91479,91480,91482],{},[898,91481,1662],{},[1931,91483,1933],{},[1700,91485,1732],{"separator":1731},[2007,91487,91488,91490],{},[898,91489,1662],{},[1931,91491,2343],{},[1700,91493,1970],{"stretchy":1702},[902,91495,91496],{"encoding":904},"[Q_1, Q_2]",[38,91498,91499],{},"stejnou úrovní uspokojení",[883,91501,91503],{"className":91502},[886],[888,91504,91505],{"xmlns":890},[892,91506,91507,91511],{},[895,91508,91509],{},[898,91510,2354],{},[902,91512,2354],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,91515,91517],{"className":91516},[886],[888,91518,91519],{"xmlns":890},[892,91520,91521,91547],{},[895,91522,91523,91525,91527,91529,91531,91537,91539,91545],{},[898,91524,900],{},[1700,91526,1765],{},[898,91528,900],{},[1700,91530,1703],{"stretchy":1702},[2007,91532,91533,91535],{},[898,91534,1662],{},[1931,91536,1933],{},[1700,91538,1732],{"separator":1731},[2007,91540,91541,91543],{},[898,91542,1662],{},[1931,91544,2343],{},[1700,91546,1709],{"stretchy":1702},[902,91548,87637],{"encoding":904}," s rovinami ",[883,91551,91553],{"className":91552},[886],[888,91554,91555],{"xmlns":890},[892,91556,91557,91565],{},[895,91558,91559,91561,91563],{},[898,91560,900],{},[1700,91562,1765],{},[898,91564,2354],{},[902,91566,86853],{"encoding":904}," rovnoběžnými s rovinou ",[883,91569,91571],{"className":91570},[886],[888,91572,91573],{"xmlns":890},[892,91574,91575,91595],{},[895,91576,91577,91579,91585,91587,91593],{},[1700,91578,1703],{"stretchy":1702},[2007,91580,91581,91583],{},[898,91582,1662],{},[1931,91584,1933],{},[1700,91586,1732],{"separator":1731},[2007,91588,91589,91591],{},[898,91590,1662],{},[1931,91592,2343],{},[1700,91594,1709],{"stretchy":1702},[902,91596,89800],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,91599,91600],{},"izokvantami"," produkčních funkcí.",[724,91603,91604],{},[614,91605,91606,91607,89678,91625,91643,91644,2196],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,91608,91610],{"className":91609},[886],[888,91611,91612],{"xmlns":890},[892,91613,91614,91622],{},[895,91615,91616,91618,91620],{},[898,91617,207],{},[1700,91619,3640],{},[898,91621,1879],{},[902,91623,91624],{"encoding":904},"a \u003C b",[883,91626,91628],{"className":91627},[886],[888,91629,91630],{"xmlns":890},[892,91631,91632,91640],{},[895,91633,91634,91636,91638],{},[898,91635,207],{},[1700,91637,3601],{},[898,91639,1879],{},[902,91641,91642],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,91645,91647],{"className":91646},[886],[888,91648,91649],{"xmlns":890},[892,91650,91651,91675],{},[895,91652,91653,91659,91661,91667,91669],{},[2007,91654,91655,91657],{},[898,91656,2354],{},[1931,91658,1772],{},[1700,91660,3640],{},[2007,91662,91663,91665],{},[898,91664,2354],{},[1931,91666,1933],{},[1700,91668,3640],{},[2007,91670,91671,91673],{},[898,91672,2354],{},[1931,91674,2343],{},[902,91676,91677],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,91679,91680],{},[614,91681,91682,91683,91712,91713,91771,91772,91790],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,91684,91686],{"className":91685},[886],[888,91687,91688],{"xmlns":890},[892,91689,91690,91710],{},[895,91691,91692,91694,91700,91702,91708],{},[1700,91693,1703],{"stretchy":1702},[2007,91695,91696,91698],{},[898,91697,1662],{},[1931,91699,1933],{},[1700,91701,1732],{"separator":1731},[2007,91703,91704,91706],{},[898,91705,1662],{},[1931,91707,2343],{},[1700,91709,1709],{"stretchy":1702},[902,91711,89800],{"encoding":904},"; body ",[883,91714,91716],{"className":91715},[886],[888,91717,91718],{"xmlns":890},[892,91719,91720,91768],{},[895,91721,91722,91724,91726,91728,91734,91736,91742,91744,91746,91748,91750,91752,91758,91760,91766],{},[898,91723,1862],{},[1700,91725,1765],{},[1700,91727,1927],{"stretchy":1702},[2007,91729,91730,91732],{},[898,91731,207],{},[1931,91733,1933],{},[1700,91735,1732],{"separator":1731},[2007,91737,91738,91740],{},[898,91739,207],{},[1931,91741,2343],{},[1700,91743,1970],{"stretchy":1702},[1700,91745,1732],{"separator":1731},[898,91747,23438],{},[1700,91749,1765],{},[1700,91751,1927],{"stretchy":1702},[2007,91753,91754,91756],{},[898,91755,1879],{},[1931,91757,1933],{},[1700,91759,1732],{"separator":1731},[2007,91761,91762,91764],{},[898,91763,1879],{},[1931,91765,2343],{},[1700,91767,1970],{"stretchy":1702},[902,91769,91770],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,91773,91775],{"className":91774},[886],[888,91776,91777],{"xmlns":890},[892,91778,91779,91787],{},[895,91780,91781,91783,91785],{},[898,91782,2974],{},[1700,91784,1732],{"separator":1731},[898,91786,4374],{},[902,91788,91789],{"encoding":904},"C, D"," na vyšší hladině.",[4060,91792,91793],{},[724,91794,91795,91797,91798,91860,91861,91905,91906,91940,91941,26374,91959,91940,92013,26374,92031,92107],{},[883,91796,52879],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,91799,91801],{"className":91800},[886],[888,91802,91803],{"xmlns":890},[892,91804,91805,91857],{},[895,91806,91807,91809,91811,91817,91819,91825,91827,91829,91843],{},[898,91808,900],{},[1700,91810,1703],{"stretchy":1702},[2007,91812,91813,91815],{},[898,91814,1662],{},[1931,91816,1933],{},[1700,91818,1732],{"separator":1731},[2007,91820,91821,91823],{},[898,91822,1662],{},[1931,91824,2343],{},[1700,91826,1709],{"stretchy":1702},[1700,91828,1765],{},[2030,91830,91831,91833,91835],{},[898,91832,1662],{},[1931,91834,1933],{},[895,91836,91837,91839,91841],{},[1931,91838,1933],{},[898,91840,1979],{"mathvariant":1791},[1931,91842,2553],{},[2030,91844,91845,91847,91849],{},[898,91846,1662],{},[1931,91848,2343],{},[895,91850,91851,91853,91855],{},[1931,91852,2385],{},[898,91854,1979],{"mathvariant":1791},[1931,91856,2553],{},[902,91858,91859],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,91862,91864],{"className":91863},[886],[888,91865,91866],{"xmlns":890},[892,91867,91868,91902],{},[895,91869,91870,91884,91898,91900],{},[2030,91871,91872,91874,91876],{},[898,91873,1662],{},[1931,91875,1933],{},[895,91877,91878,91880,91882],{},[1931,91879,1933],{},[898,91881,1979],{"mathvariant":1791},[1931,91883,2553],{},[2030,91885,91886,91888,91890],{},[898,91887,1662],{},[1931,91889,2343],{},[895,91891,91892,91894,91896],{},[1931,91893,2385],{},[898,91895,1979],{"mathvariant":1791},[1931,91897,2553],{},[1700,91899,1765],{},[898,91901,2354],{},[902,91903,91904],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,91907,91909],{"className":91908},[886],[888,91910,91911],{"xmlns":890},[892,91912,91913,91937],{},[895,91914,91915,91921,91929,91931],{},[2007,91916,91917,91919],{},[898,91918,1662],{},[1931,91920,1933],{},[2030,91922,91923,91925,91927],{},[898,91924,1662],{},[1931,91926,2343],{},[1931,91928,2385],{},[1700,91930,1765],{},[1785,91932,91933,91935],{},[898,91934,2354],{},[1931,91936,2553],{},[902,91938,91939],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,91942,91944],{"className":91943},[886],[888,91945,91946],{"xmlns":890},[892,91947,91948,91956],{},[895,91949,91950,91952,91954],{},[898,91951,2354],{},[1700,91953,1765],{},[1931,91955,1933],{},[902,91957,91958],{"encoding":904},"c = 1",[883,91960,91962],{"className":91961},[886],[888,91963,91964],{"xmlns":890},[892,91965,91966,92010],{},[895,91967,91968,91974,91976,91992,91994],{},[2007,91969,91970,91972],{},[898,91971,1662],{},[1931,91973,2343],{},[1700,91975,1765],{},[2030,91977,91978,91980,91982],{},[898,91979,1662],{},[1931,91981,1933],{},[895,91983,91984,91986,91988,91990],{},[1700,91985,1768],{},[1931,91987,1933],{},[898,91989,1979],{"mathvariant":1791},[1931,91991,2385],{},[1700,91993,1765],{},[1770,91995,91996],{"scriptlevel":1772,"displaystyle":1731},[1774,91997,91998,92000],{},[1931,91999,1933],{},[82210,92001,92002,92008],{},[2007,92003,92004,92006],{},[898,92005,1662],{},[1931,92007,1933],{},[1931,92009,2385],{},[902,92011,92012],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,92014,92016],{"className":92015},[886],[888,92017,92018],{"xmlns":890},[892,92019,92020,92028],{},[895,92021,92022,92024,92026],{},[898,92023,2354],{},[1700,92025,1765],{},[1931,92027,2343],{},[902,92029,92030],{"encoding":904},"c = 2",[883,92032,92034],{"className":92033},[886],[888,92035,92036],{"xmlns":890},[892,92037,92038,92104],{},[895,92039,92040,92046,92048,92060,92062,92078,92080],{},[2007,92041,92042,92044],{},[898,92043,1662],{},[1931,92045,2343],{},[1700,92047,1765],{},[1785,92049,92050,92052],{},[1931,92051,2343],{},[895,92053,92054,92056,92058],{},[1931,92055,2553],{},[898,92057,1979],{"mathvariant":1791},[1931,92059,2385],{},[1700,92061,2065],{},[2030,92063,92064,92066,92068],{},[898,92065,1662],{},[1931,92067,1933],{},[895,92069,92070,92072,92074,92076],{},[1700,92071,1768],{},[1931,92073,1933],{},[898,92075,1979],{"mathvariant":1791},[1931,92077,2385],{},[1700,92079,1765],{},[1770,92081,92082],{"scriptlevel":1772,"displaystyle":1731},[1774,92083,92084,92094],{},[895,92085,92086,92088],{},[1931,92087,2343],{},[82210,92089,92090,92092],{},[1931,92091,2343],{},[1931,92093,2385],{},[82210,92095,92096,92102],{},[2007,92097,92098,92100],{},[898,92099,1662],{},[1931,92101,1933],{},[1931,92103,2385],{},[902,92105,92106],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,92109,92111],{"id":92110},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,92113,92114],{},[2756,92115],{"alt":92116,"className":92117,"src":92118},"imek-ic-4vlastnosti-anotovane",[210,2760],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[4060,92120,92121,92130,92177,92221,92227,92233],{},[724,92122,92123,92125,92126,92129],{},[883,92124,4601],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,92127,92128],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,92131,92132],{},[883,92133,92135],{"className":92134},[886],[888,92136,92137],{"xmlns":890},[892,92138,92139,92174],{},[895,92140,92141,92144,92146,92148,92150,92152,92170,92172],{},[898,92142,92143],{"mathvariant":1791},"tg",[1700,92145,56384],{},[898,92147,19047],{},[1700,92149,1765],{},[1700,92151,1768],{},[1774,92153,92154,92162],{},[2030,92155,92156,92158,92160],{},[898,92157,900],{},[1931,92159,1933],{},[1700,92161,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[2030,92163,92164,92166,92168],{},[898,92165,900],{},[1931,92167,2343],{},[1700,92169,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,92171,3640],{},[1931,92173,1772],{},[902,92175,92176],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,92178,92179,92180,92220],{},"(derivace implicitně zadané funkce ",[883,92181,92183],{"className":92182},[886],[888,92184,92185],{"xmlns":890},[892,92186,92187,92217],{},[895,92188,92189,92191,92193,92199,92201,92207,92209,92211,92213,92215],{},[898,92190,900],{},[1700,92192,1703],{"stretchy":1702},[2007,92194,92195,92197],{},[898,92196,1662],{},[1931,92198,1933],{},[1700,92200,1732],{"separator":1731},[2007,92202,92203,92205],{},[898,92204,1662],{},[1931,92206,2343],{},[1700,92208,1709],{"stretchy":1702},[1700,92210,1768],{},[898,92212,2354],{},[1700,92214,1765],{},[1931,92216,1772],{},[902,92218,92219],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,92222,92223,92226],{},[38,92224,92225],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,92228,92229,92232],{},[38,92230,92231],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,92234,92235,92238,92239,92257,92258,92274,92275,92278],{},[38,92236,92237],{},"4° Konvexní."," Pro každé dva body ",[883,92240,92242],{"className":92241},[886],[888,92243,92244],{"xmlns":890},[892,92245,92246,92254],{},[895,92247,92248,92250,92252],{},[898,92249,1862],{},[1700,92251,1732],{"separator":1731},[898,92253,23438],{},[902,92255,92256],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,92259,92261],{"className":92260},[886],[888,92262,92263],{"xmlns":890},[892,92264,92265,92271],{},[895,92266,92267,92269],{},[898,92268,1862],{},[898,92270,23438],{},[902,92272,92273],{"encoding":904},"AB"," ve ",[38,92276,92277],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,92280,92281],{},[614,92282,92283,92284,92319,92320,2196],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,92285,92287],{"className":92286},[886],[888,92288,92289],{"xmlns":890},[892,92290,92291,92317],{},[895,92292,92293,92295,92297,92303,92305,92311,92313,92315],{},[898,92294,900],{},[1700,92296,1703],{"stretchy":1702},[2007,92298,92299,92301],{},[898,92300,1662],{},[1931,92302,1933],{},[1700,92304,1732],{"separator":1731},[2007,92306,92307,92309],{},[898,92308,1662],{},[1931,92310,2343],{},[1700,92312,1709],{"stretchy":1702},[1700,92314,1765],{},[898,92316,2354],{},[902,92318,9955],{"encoding":904}," s tečnou se sklonem ",[883,92321,92323],{"className":92322},[886],[888,92324,92325],{"xmlns":890},[892,92326,92327,92335],{},[895,92328,92329,92331,92333],{},[898,92330,92143],{"mathvariant":1791},[1700,92332,56384],{},[898,92334,19047],{},[902,92336,92337],{"encoding":904},"\\operatorname{tg}\\alpha",[115,92339,92341],{"id":92340},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,92343,92344,2106,92347,10208,92360,92363],{},[38,92345,92346],{},"Mezní míra komoditní substituce",[883,92348,92350],{"className":92349},[886],[888,92351,92352],{"xmlns":890},[892,92353,92354,92358],{},[895,92355,92356],{},[1781,92357,10786],{},[902,92359,28423],{"encoding":904},[38,92361,92362],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,92365,92367],{"className":92366},[886],[888,92368,92369],{"xmlns":890,"display":28251},[892,92370,92371,92458],{},[20939,92372,92373],{"width":28256},[20944,92374,92375,92377,92451,92453],{},[20947,92376],{"width":28261},[20947,92378,92379],{},[895,92380,92381,92383,92385,92387,92389,92395,92397,92403,92405,92407,92429,92431,92449],{},[1781,92382,10786],{},[1700,92384,1765],{},[1781,92386,10786],{},[1700,92388,1703],{"stretchy":1702},[2007,92390,92391,92393],{},[898,92392,1662],{},[1931,92394,1933],{},[1700,92396,1732],{"separator":1731},[2007,92398,92399,92401],{},[898,92400,1662],{},[1931,92402,2343],{},[1700,92404,1709],{"stretchy":1702},[1700,92406,1765],{},[1774,92408,92409,92419],{},[895,92410,92411,92413],{},[898,92412,2005],{},[2007,92414,92415,92417],{},[898,92416,900],{},[1931,92418,1933],{},[895,92420,92421,92423],{},[898,92422,2005],{},[2007,92424,92425,92427],{},[898,92426,900],{},[1931,92428,2343],{},[1700,92430,1765],{},[1774,92432,92433,92441],{},[2030,92434,92435,92437,92439],{},[898,92436,900],{},[1931,92438,1933],{},[1700,92440,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[2030,92442,92443,92445,92447],{},[898,92444,900],{},[1931,92446,2343],{},[1700,92448,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[898,92450,2196],{"mathvariant":1791},[20947,92452],{"width":28261},[20947,92454,92455],{},[1781,92456,92457],{},"(6.9)",[902,92459,92460],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,92462,92463,92464,92498,92499,92531,92532,92567,92568,92581],{},"Geometricky: ",[883,92465,92467],{"className":92466},[886],[888,92468,92469],{"xmlns":890},[892,92470,92471,92495],{},[895,92472,92473,92475],{},[1700,92474,1768],{},[1770,92476,92477],{"scriptlevel":1772,"displaystyle":1702},[1774,92478,92479,92487],{},[2030,92480,92481,92483,92485],{},[898,92482,900],{},[1931,92484,1933],{},[1700,92486,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[2030,92488,92489,92491,92493],{},[898,92490,900],{},[1931,92492,2343],{},[1700,92494,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,92496,92497],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,92500,92502],{"className":92501},[886],[888,92503,92504],{"xmlns":890},[892,92505,92506,92528],{},[895,92507,92508,92514,92516,92518,92520,92526],{},[2007,92509,92510,92512],{},[898,92511,1662],{},[1931,92513,2343],{},[1700,92515,1765],{},[898,92517,2220],{},[1700,92519,1703],{"stretchy":1702},[2007,92521,92522,92524],{},[898,92523,1662],{},[1931,92525,1933],{},[1700,92527,1709],{"stretchy":1702},[902,92529,92530],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,92533,92535],{"className":92534},[886],[888,92536,92537],{"xmlns":890},[892,92538,92539,92565],{},[895,92540,92541,92543,92545,92551,92553,92559,92561,92563],{},[898,92542,900],{},[1700,92544,1703],{"stretchy":1702},[2007,92546,92547,92549],{},[898,92548,1662],{},[1931,92550,1933],{},[1700,92552,1732],{"separator":1731},[2007,92554,92555,92557],{},[898,92556,1662],{},[1931,92558,2343],{},[1700,92560,1709],{"stretchy":1702},[1700,92562,1765],{},[898,92564,2354],{},[902,92566,9955],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,92569,92571],{"className":92570},[886],[888,92572,92573],{"xmlns":890},[892,92574,92575,92579],{},[895,92576,92577],{},[1781,92578,10786],{},[902,92580,28423],{"encoding":904}," chápeme jako velikost kompenzace.",[4060,92583,92584],{},[724,92585,92586,92588,92589,8290,92621,92659,92660,92677,92678,92695],{},[883,92587,4346],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,92590,92592],{"className":92591},[886],[888,92593,92594],{"xmlns":890},[892,92595,92596,92618],{},[895,92597,92598,92600,92602,92608,92610,92616],{},[1781,92599,10786],{},[1700,92601,1703],{"stretchy":1702},[2007,92603,92604,92606],{},[898,92605,1662],{},[1931,92607,1933],{},[1700,92609,1732],{"separator":1731},[2007,92611,92612,92614],{},[898,92613,1662],{},[1931,92615,2343],{},[1700,92617,1709],{"stretchy":1702},[902,92619,92620],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,92622,92623,92624,29188,92641,92658],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,92625,92627],{"className":92626},[886],[888,92628,92629],{"xmlns":890},[892,92630,92631,92639],{},[895,92632,92633],{},[2007,92634,92635,92637],{},[898,92636,1662],{},[1931,92638,1933],{},[902,92640,29187],{"encoding":904},[883,92642,92644],{"className":92643},[886],[888,92645,92646],{"xmlns":890},[892,92647,92648,92656],{},[895,92649,92650],{},[2007,92651,92652,92654],{},[898,92653,1662],{},[1931,92655,2343],{},[902,92657,29206],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,92661,92663],{"className":92662},[886],[888,92664,92665],{"xmlns":890},[892,92666,92667,92675],{},[895,92668,92669],{},[2007,92670,92671,92673],{},[898,92672,1662],{},[1931,92674,2343],{},[902,92676,29206],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,92679,92681],{"className":92680},[886],[888,92682,92683],{"xmlns":890},[892,92684,92685,92693],{},[895,92686,92687],{},[2007,92688,92689,92691],{},[898,92690,1662],{},[1931,92692,1933],{},[902,92694,29187],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,92697,92698,92699,30129],{},"Pro obecnou změnu ",[883,92700,92702],{"className":92701},[886],[888,92703,92704],{"xmlns":890},[892,92705,92706,92716],{},[895,92707,92708,92710],{},[898,92709,2406],{"mathvariant":1791},[2007,92711,92712,92714],{},[898,92713,1662],{},[1931,92715,1933],{},[902,92717,92718],{"encoding":904},"\\mathrm{d} Q_1",[883,92720,92722],{"className":92721},[886],[888,92723,92724],{"xmlns":890,"display":28251},[892,92725,92726,92779],{},[20939,92727,92728],{"width":28256},[20944,92729,92730,92732,92772,92774],{},[20947,92731],{"width":28261},[20947,92733,92734],{},[895,92735,92736,92738,92744,92746,92748,92754,92756,92758,92760,92762,92764,92770],{},[898,92737,3084],{"mathvariant":1791},[2007,92739,92740,92742],{},[898,92741,1662],{},[1931,92743,2343],{},[1700,92745,2927],{},[898,92747,2406],{"mathvariant":1791},[2007,92749,92750,92752],{},[898,92751,1662],{},[1931,92753,2343],{},[1700,92755,1765],{},[1700,92757,1768],{},[1781,92759,10786],{},[1700,92761,2065],{},[898,92763,2406],{"mathvariant":1791},[2007,92765,92766,92768],{},[898,92767,1662],{},[1931,92769,1933],{},[1700,92771,1732],{"separator":1731},[20947,92773],{"width":28261},[20947,92775,92776],{},[1781,92777,92778],{},"(6.10)",[902,92780,92781],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,92783,92785],{"className":92784},[886],[888,92786,92787],{"xmlns":890,"display":28251},[892,92788,92789,92836],{},[20939,92790,92791],{"width":28256},[20944,92792,92793,92795,92829,92831],{},[20947,92794],{"width":28261},[20947,92796,92797],{},[895,92798,92799,92801,92807,92809,92811,92817,92819,92821,92827],{},[898,92800,2406],{"mathvariant":1791},[2007,92802,92803,92805],{},[898,92804,1662],{},[1931,92806,1933],{},[1700,92808,1765],{},[1700,92810,1768],{},[1774,92812,92813,92815],{},[1931,92814,1933],{},[1781,92816,10786],{},[1781,92818,1783],{},[898,92820,2406],{"mathvariant":1791},[2007,92822,92823,92825],{},[898,92824,1662],{},[1931,92826,2343],{},[898,92828,2196],{"mathvariant":1791},[20947,92830],{"width":28261},[20947,92832,92833],{},[1781,92834,92835],{},"(6.11)",[902,92837,92838],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[4060,92840,92841,92907,93024],{},[724,92842,92843,92845,92846,30129],{},[883,92844,52879],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,92847,92849],{"className":92848},[886],[888,92850,92851],{"xmlns":890},[892,92852,92853,92905],{},[895,92854,92855,92857,92859,92865,92867,92873,92875,92877,92891],{},[898,92856,900],{},[1700,92858,1703],{"stretchy":1702},[2007,92860,92861,92863],{},[898,92862,1662],{},[1931,92864,1933],{},[1700,92866,1732],{"separator":1731},[2007,92868,92869,92871],{},[898,92870,1662],{},[1931,92872,2343],{},[1700,92874,1709],{"stretchy":1702},[1700,92876,1765],{},[2030,92878,92879,92881,92883],{},[898,92880,1662],{},[1931,92882,1933],{},[895,92884,92885,92887,92889],{},[1931,92886,1933],{},[898,92888,1979],{"mathvariant":1791},[1931,92890,2343],{},[2030,92892,92893,92895,92897],{},[898,92894,1662],{},[1931,92896,2343],{},[895,92898,92899,92901,92903],{},[1931,92900,1933],{},[898,92902,1979],{"mathvariant":1791},[1931,92904,2343],{},[902,92906,30128],{"encoding":904},[724,92908,92909],{},[883,92910,92912],{"className":92911},[886],[888,92913,92914],{"xmlns":890},[892,92915,92916,93022],{},[895,92917,92918,92920,92922,93004,93006,93020],{},[1781,92919,10786],{},[1700,92921,1765],{},[1774,92923,92924,92964],{},[895,92925,92926,92934,92950],{},[1770,92927,92928],{"scriptlevel":1772,"displaystyle":1702},[1774,92929,92930,92932],{},[1931,92931,1933],{},[1931,92933,2343],{},[2030,92935,92936,92938,92940],{},[898,92937,1662],{},[1931,92939,1933],{},[895,92941,92942,92944,92946,92948],{},[1700,92943,1768],{},[1931,92945,1933],{},[898,92947,1979],{"mathvariant":1791},[1931,92949,2343],{},[2030,92951,92952,92954,92956],{},[898,92953,1662],{},[1931,92955,2343],{},[895,92957,92958,92960,92962],{},[1931,92959,1933],{},[898,92961,1979],{"mathvariant":1791},[1931,92963,2343],{},[895,92965,92966,92974,92988],{},[1770,92967,92968],{"scriptlevel":1772,"displaystyle":1702},[1774,92969,92970,92972],{},[1931,92971,1933],{},[1931,92973,2343],{},[2030,92975,92976,92978,92980],{},[898,92977,1662],{},[1931,92979,1933],{},[895,92981,92982,92984,92986],{},[1931,92983,1933],{},[898,92985,1979],{"mathvariant":1791},[1931,92987,2343],{},[2030,92989,92990,92992,92994],{},[898,92991,1662],{},[1931,92993,2343],{},[895,92995,92996,92998,93000,93002],{},[1700,92997,1768],{},[1931,92999,1933],{},[898,93001,1979],{"mathvariant":1791},[1931,93003,2343],{},[1700,93005,1765],{},[1774,93007,93008,93014],{},[2007,93009,93010,93012],{},[898,93011,1662],{},[1931,93013,2343],{},[2007,93015,93016,93018],{},[898,93017,1662],{},[1931,93019,1933],{},[898,93021,2196],{"mathvariant":1791},[902,93023,30247],{"encoding":904},[724,93025,30250,93026,3122,93069,30298,93071,93090],{},[883,93027,93029],{"className":93028},[886],[888,93030,93031],{"xmlns":890},[892,93032,93033,93067],{},[895,93034,93035,93037,93039,93041,93043,93045,93047,93049,93057,93059],{},[1781,93036,10786],{},[1700,93038,1703],{"stretchy":1702},[1931,93040,30266],{},[1700,93042,1732],{"separator":1731},[1931,93044,15295],{},[1700,93046,1709],{"stretchy":1702},[1700,93048,1765],{},[1770,93050,93051],{"scriptlevel":1772,"displaystyle":1702},[1774,93052,93053,93055],{},[1931,93054,15295],{},[1931,93056,30266],{},[1700,93058,1765],{},[1770,93060,93061],{"scriptlevel":1772,"displaystyle":1702},[1774,93062,93063,93065],{},[1931,93064,2438],{},[1931,93066,2385],{},[902,93068,30295],{"encoding":904},[614,93070,9403],{},[883,93072,93074],{"className":93073},[886],[888,93075,93076],{"xmlns":890},[892,93077,93078,93088],{},[895,93079,93080],{},[1770,93081,93082],{"scriptlevel":1772,"displaystyle":1702},[1774,93083,93084,93086],{},[1931,93085,2438],{},[1931,93087,2385],{},[902,93089,30318],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,93092,93093,93094,93098],{},"(Paralelou je ",[207,93095,93097],{"className":93096,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,93100,93102],{"id":93101},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,93104,93105,93106,93109],{},"Rámcově se v kapitole 6 studují ",[38,93107,93108],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,93111,93112,93248],{},[123,93113,93114,93116,93117,10340,93148,2106,93151,93200,93201,2196],{},[38,93115,28437],{}," — maximalizace ",[883,93118,93120],{"className":93119},[886],[888,93121,93122],{"xmlns":890},[892,93123,93124,93146],{},[895,93125,93126,93128,93130,93136,93138,93144],{},[898,93127,900],{},[1700,93129,1703],{"stretchy":1702},[2007,93131,93132,93134],{},[898,93133,1662],{},[1931,93135,1933],{},[1700,93137,1732],{"separator":1731},[2007,93139,93140,93142],{},[898,93141,1662],{},[1931,93143,2343],{},[1700,93145,1709],{"stretchy":1702},[902,93147,16528],{"encoding":904},[38,93149,93150],{},"rozpočtovém omezení",[883,93152,93154],{"className":93153},[886],[888,93155,93156],{"xmlns":890},[892,93157,93158,93198],{},[895,93159,93160,93166,93168,93176,93182,93184,93192],{},[1785,93161,93162,93164],{},[898,93163,9316],{},[1700,93165,4543],{},[1700,93167,1765],{},[2030,93169,93170,93172,93174],{},[898,93171,1677],{},[1931,93173,1933],{},[1700,93175,4543],{},[2007,93177,93178,93180],{},[898,93179,1662],{},[1931,93181,1933],{},[1700,93183,1897],{},[2030,93185,93186,93188,93190],{},[898,93187,1677],{},[1931,93189,2343],{},[1700,93191,4543],{},[2007,93193,93194,93196],{},[898,93195,1662],{},[1931,93197,2343],{},[902,93199,17483],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,93202,93204],{"className":93203},[886],[888,93205,93206],{"xmlns":890},[892,93207,93208,93246],{},[895,93209,93210,93216,93218,93224,93226,93232,93234,93240,93242,93244],{},[2007,93211,93212,93214],{},[898,93213,1662],{},[898,93215,17975],{},[1700,93217,1765],{},[2007,93219,93220,93222],{},[898,93221,4374],{},[898,93223,17975],{},[1700,93225,1703],{"stretchy":1702},[2007,93227,93228,93230],{},[898,93229,1677],{},[1931,93231,1933],{},[1700,93233,1732],{"separator":1731},[2007,93235,93236,93238],{},[898,93237,1677],{},[1931,93239,2343],{},[1700,93241,1732],{"separator":1731},[898,93243,9316],{},[1700,93245,1709],{"stretchy":1702},[902,93247,36640],{"encoding":904},[123,93249,93250,28086,93253,28129,93299,93316,93317,2196],{},[38,93251,93252],{},"Duální úloha",[883,93254,93256],{"className":93255},[886],[888,93257,93258],{"xmlns":890},[892,93259,93260,93296],{},[895,93261,93262,93264,93266,93274,93280,93282,93290],{},[898,93263,1762],{},[1700,93265,1765],{},[2030,93267,93268,93270,93272],{},[898,93269,1677],{},[1931,93271,1933],{},[1700,93273,4543],{},[2007,93275,93276,93278],{},[898,93277,1662],{},[1931,93279,1933],{},[1700,93281,1897],{},[2030,93283,93284,93286,93288],{},[898,93285,1677],{},[1931,93287,2343],{},[1700,93289,4543],{},[2007,93291,93292,93294],{},[898,93293,1662],{},[1931,93295,2343],{},[902,93297,93298],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,93300,93302],{"className":93301},[886],[888,93303,93304],{"xmlns":890},[892,93305,93306,93314],{},[895,93307,93308],{},[1785,93309,93310,93312],{},[898,93311,900],{},[1700,93313,4543],{},[902,93315,28147],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,93318,93320],{"className":93319},[886],[888,93321,93322],{"xmlns":890},[892,93323,93324,93362],{},[895,93325,93326,93332,93334,93340,93342,93348,93350,93356,93358,93360],{},[2007,93327,93328,93330],{},[898,93329,1662],{},[898,93331,17975],{},[1700,93333,1765],{},[2007,93335,93336,93338],{},[898,93337,4374],{},[898,93339,17975],{},[1700,93341,1703],{"stretchy":1702},[2007,93343,93344,93346],{},[898,93345,1677],{},[1931,93347,1933],{},[1700,93349,1732],{"separator":1731},[2007,93351,93352,93354],{},[898,93353,1677],{},[1931,93355,2343],{},[1700,93357,1732],{"separator":1731},[898,93359,900],{},[1700,93361,1709],{"stretchy":1702},[902,93363,18008],{"encoding":904},[724,93365,93366,93367,93370,93371,2106,93374,93413],{},"Obě úlohy se řeší ",[207,93368,28152],{"className":93369,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,93372,93373],{},"tentýž bod dotyku",[883,93375,93377],{"className":93376},[886],[888,93378,93379],{"xmlns":890},[892,93380,93381,93411],{},[895,93382,93383,93389,93391,93399,93401,93409],{},[1785,93384,93385,93387],{},[898,93386,1662],{},[1700,93388,4543],{},[1700,93390,1927],{"stretchy":1702},[2030,93392,93393,93395,93397],{},[898,93394,1662],{},[1931,93396,1933],{},[1700,93398,4543],{},[1700,93400,1732],{"separator":1731},[2030,93402,93403,93405,93407],{},[898,93404,1662],{},[1931,93406,2343],{},[1700,93408,4543],{},[1700,93410,1970],{"stretchy":1702},[902,93412,28512],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,93415,93417],{"className":93416},[886],[888,93418,93419],{"xmlns":890,"display":28251},[892,93420,93421,93467],{},[895,93422,93423,93425,93427,93445,93447,93465],{},[1781,93424,10786],{},[1700,93426,1765],{},[1774,93428,93429,93437],{},[2030,93430,93431,93433,93435],{},[898,93432,900],{},[1931,93434,1933],{},[1700,93436,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[2030,93438,93439,93441,93443],{},[898,93440,900],{},[1931,93442,2343],{},[1700,93444,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,93446,1765],{},[1774,93448,93449,93457],{},[2030,93450,93451,93453,93455],{},[898,93452,1677],{},[1931,93454,1933],{},[1700,93456,4543],{},[2030,93458,93459,93461,93463],{},[898,93460,1677],{},[1931,93462,2343],{},[1700,93464,4543],{},[898,93466,2196],{"mathvariant":1791},[902,93468,93469],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,93471,93472],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[4060,93474,93475],{},[724,93476,93477,93479,93480,93483,93484,93487,93488,93515,93516,93550,93551,93585,93586,93629,93630,93633,93634,2196],{},[883,93478,4346],{}," Pro detailní postup viz ",[207,93481,36939],{"className":93482,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,93485,93486],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,93489,93491],{"className":93490},[886],[888,93492,93493],{"xmlns":890},[892,93494,93495,93513],{},[895,93496,93497,93499,93501,93507],{},[898,93498,900],{},[1700,93500,1765],{},[2007,93502,93503,93505],{},[898,93504,1662],{},[1931,93506,1933],{},[2007,93508,93509,93511],{},[898,93510,1662],{},[1931,93512,2343],{},[902,93514,30411],{"encoding":904}," s výsledkem ",[883,93517,93519],{"className":93518},[886],[888,93520,93521],{"xmlns":890},[892,93522,93523,93547],{},[895,93524,93525,93531,93533,93535,93537,93543,93545],{},[2007,93526,93527,93529],{},[898,93528,1662],{},[1931,93530,1933],{},[1700,93532,1765],{},[1931,93534,5192],{},[1700,93536,1732],{"separator":1731},[2007,93538,93539,93541],{},[898,93540,1662],{},[1931,93542,2343],{},[1700,93544,1765],{},[1931,93546,3058],{},[902,93548,93549],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,93552,93554],{"className":93553},[886],[888,93555,93556],{"xmlns":890},[892,93557,93558,93582],{},[895,93559,93560,93566,93568,93570,93572,93578,93580],{},[2007,93561,93562,93564],{},[898,93563,1662],{},[1931,93565,1933],{},[1700,93567,1765],{},[1931,93569,2553],{},[1700,93571,1732],{"separator":1731},[2007,93573,93574,93576],{},[898,93575,1662],{},[1931,93577,2343],{},[1700,93579,1765],{},[1931,93581,1933],{},[902,93583,93584],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,93587,93589],{"className":93588},[886],[888,93590,93591],{"xmlns":890},[892,93592,93593,93627],{},[895,93594,93595,93597,93599,93613],{},[898,93596,900],{},[1700,93598,1765],{},[2030,93600,93601,93603,93605],{},[898,93602,1662],{},[1931,93604,1933],{},[895,93606,93607,93609,93611],{},[1931,93608,1933],{},[898,93610,1979],{"mathvariant":1791},[1931,93612,2343],{},[2030,93614,93615,93617,93619],{},[898,93616,1662],{},[1931,93618,2343],{},[895,93620,93621,93623,93625],{},[1931,93622,1933],{},[898,93624,1979],{"mathvariant":1791},[1931,93626,2343],{},[902,93628,33344],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,93631,93632],{},"6.8–6.13"," jsou na stránce ",[207,93635,27952],{"className":93636,"dataFsResolvedFilePath":911,"href":912},[210],[115,93638,93640],{"id":93639},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,93642,93643,93644,93657,93658,93660,93661,93663,93664,93666,93667,93669,93670,93672,93673,93675,93676,2106,93678,93713,93714,93727,93728,93731,93732,93735,93736,2196],{},"Každá ",[883,93645,93647],{"className":93646},[886],[888,93648,93649],{"xmlns":890},[892,93650,93651,93655],{},[895,93652,93653],{},[898,93654,37045],{},[902,93656,37045],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,93659,86991],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,93662,87475],{}," a současně ",[38,93665,86994],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,93668,86999],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,93671,52861],{}," (6.4) a druhé parciální derivace ",[38,93674,89358],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,93677,9918],{},[883,93679,93681],{"className":93680},[886],[888,93682,93683],{"xmlns":890},[892,93684,93685,93711],{},[895,93686,93687,93689,93691,93697,93699,93705,93707,93709],{},[898,93688,900],{},[1700,93690,1703],{"stretchy":1702},[2007,93692,93693,93695],{},[898,93694,1662],{},[1931,93696,1933],{},[1700,93698,1732],{"separator":1731},[2007,93700,93701,93703],{},[898,93702,1662],{},[1931,93704,2343],{},[1700,93706,1709],{"stretchy":1702},[1700,93708,1765],{},[898,93710,2354],{},[902,93712,9955],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,93715,93717],{"className":93716},[886],[888,93718,93719],{"xmlns":890},[892,93720,93721,93725],{},[895,93722,93723],{},[1781,93724,10786],{},[902,93726,28423],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,93729,93730],{},"maximalizace užitečnosti"," a duální ",[38,93733,93734],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,93737,36939],{"className":93738,"dataFsResolvedFilePath":911,"href":912},[210],[115,93740,50067],{"id":50066},[152,93742,93743,93746,93749,93752,93755,93758,93761,93764,93767,93770],{},[123,93744,93745],{},"Co se zahrnuje pod termín užitečnost?",[123,93747,93748],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,93750,93751],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,93753,93754],{},"Jak se vypočítá mezní užitečnost?",[123,93756,93757],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,93759,93760],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,93762,93763],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,93765,93766],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,93768,93769],{},"Proč mají křivky užitečnosti záporný sklon?",[123,93771,93772],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,93774,93776],{"id":93775},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,93778,93779,93782,93783,83666,93825,1343,93853,1343,93881,93909],{},[38,93780,93781],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,93784,93786],{"className":93785},[886],[888,93787,93788],{"xmlns":890},[892,93789,93790,93822],{},[895,93791,93792,93794,93796,93802,93804,93806,93812,93814,93816],{},[898,93793,900],{},[1700,93795,1765],{},[2007,93797,93798,93800],{},[898,93799,1662],{},[1931,93801,1933],{},[1700,93803,1897],{},[1931,93805,64743],{},[2007,93807,93808,93810],{},[898,93809,1662],{},[1931,93811,2343],{},[1700,93813,1897],{},[1931,93815,2343],{},[2007,93817,93818,93820],{},[898,93819,1662],{},[1931,93821,2385],{},[902,93823,93824],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,93826,93828],{"className":93827},[886],[888,93829,93830],{"xmlns":890},[892,93831,93832,93850],{},[895,93833,93834,93836,93838,93840,93842,93844,93846,93848],{},[898,93835,900],{},[1700,93837,1703],{"stretchy":1702},[1931,93839,2553],{},[1700,93841,1732],{"separator":1731},[1931,93843,2343],{},[1700,93845,1732],{"separator":1731},[1931,93847,2343],{},[1700,93849,1709],{"stretchy":1702},[902,93851,93852],{"encoding":904},"U(4, 2, 2)",[883,93854,93856],{"className":93855},[886],[888,93857,93858],{"xmlns":890},[892,93859,93860,93878],{},[895,93861,93862,93864,93866,93868,93870,93872,93874,93876],{},[898,93863,900],{},[1700,93865,1703],{"stretchy":1702},[1931,93867,1933],{},[1700,93869,1732],{"separator":1731},[1931,93871,2553],{},[1700,93873,1732],{"separator":1731},[1931,93875,2343],{},[1700,93877,1709],{"stretchy":1702},[902,93879,93880],{"encoding":904},"U(1, 4, 2)",[883,93882,93884],{"className":93883},[886],[888,93885,93886],{"xmlns":890},[892,93887,93888,93906],{},[895,93889,93890,93892,93894,93896,93898,93900,93902,93904],{},[898,93891,900],{},[1700,93893,1703],{"stretchy":1702},[1931,93895,2343],{},[1700,93897,1732],{"separator":1731},[1931,93899,2385],{},[1700,93901,1732],{"separator":1731},[1931,93903,1933],{},[1700,93905,1709],{"stretchy":1702},[902,93907,93908],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,93911,93912,93915,93916,93968,93969,1343,93995,1343,94021,1343,94047,1343,94073,1343,94099,1343,94125,94151],{},[38,93913,93914],{},"6.2"," Je dána užitečnost ",[883,93917,93919],{"className":93918},[886],[888,93920,93921],{"xmlns":890},[892,93922,93923,93965],{},[895,93924,93925,93927,93929,93931,93945,93959],{},[898,93926,900],{},[1700,93928,1765],{},[1931,93930,2343],{},[2030,93932,93933,93935,93937],{},[898,93934,1662],{},[1931,93936,1933],{},[895,93938,93939,93941,93943],{},[1931,93940,1933],{},[898,93942,1979],{"mathvariant":1791},[1931,93944,2385],{},[2030,93946,93947,93949,93951],{},[898,93948,1662],{},[1931,93950,2343],{},[895,93952,93953,93955,93957],{},[1931,93954,1933],{},[898,93956,1979],{"mathvariant":1791},[1931,93958,2343],{},[2007,93960,93961,93963],{},[898,93962,1662],{},[1931,93964,2385],{},[902,93966,93967],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,93970,93972],{"className":93971},[886],[888,93973,93974],{"xmlns":890},[892,93975,93976,93992],{},[895,93977,93978,93980,93982,93984,93986,93988,93990],{},[1700,93979,1703],{"stretchy":1702},[1931,93981,5753],{},[1700,93983,1732],{"separator":1731},[1931,93985,66781],{},[1700,93987,1732],{"separator":1731},[1931,93989,3058],{},[1700,93991,1709],{"stretchy":1702},[902,93993,93994],{"encoding":904},"(36, 27, 10)",[883,93996,93998],{"className":93997},[886],[888,93999,94000],{"xmlns":890},[892,94001,94002,94018],{},[895,94003,94004,94006,94008,94010,94012,94014,94016],{},[1700,94005,1703],{"stretchy":1702},[1931,94007,42025],{},[1700,94009,1732],{"separator":1731},[1931,94011,5773],{},[1700,94013,1732],{"separator":1731},[1931,94015,9223],{},[1700,94017,1709],{"stretchy":1702},[902,94019,94020],{"encoding":904},"(64, 8, 20)",[883,94022,94024],{"className":94023},[886],[888,94025,94026],{"xmlns":890},[892,94027,94028,94044],{},[895,94029,94030,94032,94034,94036,94038,94040,94042],{},[1700,94031,1703],{"stretchy":1702},[1931,94033,5192],{},[1700,94035,1732],{"separator":1731},[1931,94037,42025],{},[1700,94039,1732],{"separator":1731},[1931,94041,5773],{},[1700,94043,1709],{"stretchy":1702},[902,94045,94046],{"encoding":904},"(25, 64, 8)",[883,94048,94050],{"className":94049},[886],[888,94051,94052],{"xmlns":890},[892,94053,94054,94070],{},[895,94055,94056,94058,94060,94062,94064,94066,94068],{},[1700,94057,1703],{"stretchy":1702},[1931,94059,2553],{},[1700,94061,1732],{"separator":1731},[1931,94063,72713],{},[1700,94065,1732],{"separator":1731},[1931,94067,2445],{},[1700,94069,1709],{"stretchy":1702},[902,94071,94072],{"encoding":904},"(4, 125, 6)",[883,94074,94076],{"className":94075},[886],[888,94077,94078],{"xmlns":890},[892,94079,94080,94096],{},[895,94081,94082,94084,94086,94088,94090,94092,94094],{},[1700,94083,1703],{"stretchy":1702},[1931,94085,4190],{},[1700,94087,1732],{"separator":1731},[1931,94089,5399],{},[1700,94091,1732],{"separator":1731},[1931,94093,3702],{},[1700,94095,1709],{"stretchy":1702},[902,94097,94098],{"encoding":904},"(9, 40, 12)",[883,94100,94102],{"className":94101},[886],[888,94103,94104],{"xmlns":890},[892,94105,94106,94122],{},[895,94107,94108,94110,94112,94114,94116,94118,94120],{},[1700,94109,1703],{"stretchy":1702},[1931,94111,4190],{},[1700,94113,1732],{"separator":1731},[1931,94115,42025],{},[1700,94117,1732],{"separator":1731},[1931,94119,2438],{},[1700,94121,1709],{"stretchy":1702},[902,94123,94124],{"encoding":904},"(9, 64, 5)",[883,94126,94128],{"className":94127},[886],[888,94129,94130],{"xmlns":890},[892,94131,94132,94148],{},[895,94133,94134,94136,94138,94140,94142,94144,94146],{},[1700,94135,1703],{"stretchy":1702},[1931,94137,42025],{},[1700,94139,1732],{"separator":1731},[1931,94141,5773],{},[1700,94143,1732],{"separator":1731},[1931,94145,3058],{},[1700,94147,1709],{"stretchy":1702},[902,94149,94150],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,94153,94154,93915,94157,94200,94201,94235,94236,6661,94266,94299,94300,94317,94318,94335],{},[38,94155,94156],{},"6.3",[883,94158,94160],{"className":94159},[886],[888,94161,94162],{"xmlns":890},[892,94163,94164,94198],{},[895,94165,94166,94168,94170,94184],{},[898,94167,900],{},[1700,94169,1765],{},[2030,94171,94172,94174,94176],{},[898,94173,1662],{},[1931,94175,1933],{},[895,94177,94178,94180,94182],{},[1931,94179,1933],{},[898,94181,1979],{"mathvariant":1791},[1931,94183,2343],{},[2030,94185,94186,94188,94190],{},[898,94187,1662],{},[1931,94189,2343],{},[895,94191,94192,94194,94196],{},[1931,94193,1933],{},[898,94195,1979],{"mathvariant":1791},[1931,94197,2343],{},[902,94199,33344],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,94202,94204],{"className":94203},[886],[888,94205,94206],{"xmlns":890},[892,94207,94208,94232],{},[895,94209,94210,94216,94218,94220,94222,94228,94230],{},[2007,94211,94212,94214],{},[898,94213,1662],{},[1931,94215,1933],{},[1700,94217,1765],{},[1931,94219,3314],{},[1700,94221,1732],{"separator":1731},[2007,94223,94224,94226],{},[898,94225,1662],{},[1931,94227,2343],{},[1700,94229,1765],{},[1931,94231,46888],{},[902,94233,94234],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,94237,94239],{"className":94238},[886],[888,94240,94241],{"xmlns":890},[892,94242,94243,94263],{},[895,94244,94245,94247,94253,94255,94257],{},[898,94246,2005],{},[2007,94248,94249,94251],{},[898,94250,900],{},[1931,94252,1933],{},[1700,94254,1732],{"separator":1731},[898,94256,2005],{},[2007,94258,94259,94261],{},[898,94260,900],{},[1931,94262,2343],{},[902,94264,94265],{"encoding":904},"MU_1, MU_2",[883,94267,94269],{"className":94268},[886],[888,94270,94271],{"xmlns":890},[892,94272,94273,94297],{},[895,94274,94275,94281,94283,94285,94287,94293,94295],{},[2007,94276,94277,94279],{},[898,94278,1662],{},[1931,94280,1933],{},[1700,94282,1765],{},[1931,94284,3314],{},[1700,94286,1732],{"separator":1731},[2007,94288,94289,94291],{},[898,94290,1662],{},[1931,94292,2343],{},[1700,94294,1765],{},[1931,94296,46888],{},[902,94298,94234],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,94301,94303],{"className":94302},[886],[888,94304,94305],{"xmlns":890},[892,94306,94307,94315],{},[895,94308,94309],{},[2007,94310,94311,94313],{},[898,94312,1662],{},[1931,94314,1933],{},[902,94316,29187],{"encoding":904}," na 60 a poklesu ",[883,94319,94321],{"className":94320},[886],[888,94322,94323],{"xmlns":890},[892,94324,94325,94333],{},[895,94326,94327],{},[2007,94328,94329,94331],{},[898,94330,1662],{},[1931,94332,2343],{},[902,94334,29206],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,94337,94338,94341,94342,94403,94404,2196],{},[38,94339,94340],{},"6.4"," Je dána funkce ",[883,94343,94345],{"className":94344},[886],[888,94346,94347],{"xmlns":890},[892,94348,94349,94401],{},[895,94350,94351,94353,94355,94361,94363,94369,94371,94373,94387],{},[898,94352,900],{},[1700,94354,1703],{"stretchy":1702},[2007,94356,94357,94359],{},[898,94358,1662],{},[1931,94360,1933],{},[1700,94362,1732],{"separator":1731},[2007,94364,94365,94367],{},[898,94366,1662],{},[1931,94368,2343],{},[1700,94370,1709],{"stretchy":1702},[1700,94372,1765],{},[2030,94374,94375,94377,94379],{},[898,94376,1662],{},[1931,94378,1933],{},[895,94380,94381,94383,94385],{},[1931,94382,1933],{},[898,94384,1979],{"mathvariant":1791},[1931,94386,2343],{},[2030,94388,94389,94391,94393],{},[898,94390,1662],{},[1931,94392,2343],{},[895,94394,94395,94397,94399],{},[1931,94396,1933],{},[898,94398,1979],{"mathvariant":1791},[1931,94400,2343],{},[902,94402,30128],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,94405,94407],{"className":94406},[886],[888,94408,94409],{"xmlns":890},[892,94410,94411,94501],{},[895,94412,94413,94415,94417,94423,94425,94427,94429,94431,94433,94435,94441,94443,94445,94447,94449,94451,94453,94455,94457,94463,94465,94467,94469,94471,94473,94475,94481,94483,94485,94487,94489,94491,94493,94499],{},[898,94414,900],{},[1700,94416,1703],{"stretchy":1702},[2007,94418,94419,94421],{},[898,94420,1662],{},[1931,94422,1933],{},[1700,94424,1732],{"separator":1731},[1931,94426,1933],{},[1700,94428,1709],{"stretchy":1702},[1700,94430,1732],{"separator":1731},[898,94432,900],{},[1700,94434,1703],{"stretchy":1702},[2007,94436,94437,94439],{},[898,94438,1662],{},[1931,94440,1933],{},[1700,94442,1732],{"separator":1731},[1931,94444,2343],{},[1700,94446,1709],{"stretchy":1702},[1700,94448,1732],{"separator":1731},[898,94450,900],{},[1700,94452,1703],{"stretchy":1702},[1931,94454,1933],{},[1700,94456,1732],{"separator":1731},[2007,94458,94459,94461],{},[898,94460,1662],{},[1931,94462,2343],{},[1700,94464,1709],{"stretchy":1702},[1700,94466,1732],{"separator":1731},[898,94468,900],{},[1700,94470,1703],{"stretchy":1702},[1931,94472,2343],{},[1700,94474,1732],{"separator":1731},[2007,94476,94477,94479],{},[898,94478,1662],{},[1931,94480,2343],{},[1700,94482,1709],{"stretchy":1702},[1700,94484,1732],{"separator":1731},[898,94486,900],{},[1700,94488,1703],{"stretchy":1702},[1931,94490,2385],{},[1700,94492,1732],{"separator":1731},[2007,94494,94495,94497],{},[898,94496,1662],{},[1931,94498,2343],{},[1700,94500,1709],{"stretchy":1702},[902,94502,94503],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,94505,94506,93915,94509,94553,94554,94662,94663,1343,94688,1343,94713,94755,94756,1343,94785,94810],{},[38,94507,94508],{},"6.5",[883,94510,94512],{"className":94511},[886],[888,94513,94514],{"xmlns":890},[892,94515,94516,94550],{},[895,94517,94518,94520,94522,94536],{},[898,94519,900],{},[1700,94521,1765],{},[2030,94523,94524,94526,94528],{},[898,94525,1662],{},[1931,94527,1933],{},[895,94529,94530,94532,94534],{},[1931,94531,2343],{},[898,94533,1979],{"mathvariant":1791},[1931,94535,2385],{},[2030,94537,94538,94540,94542],{},[898,94539,1662],{},[1931,94541,2343],{},[895,94543,94544,94546,94548],{},[1931,94545,1933],{},[898,94547,1979],{"mathvariant":1791},[1931,94549,2385],{},[902,94551,94552],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,94555,94557],{"className":94556},[886],[888,94558,94559],{"xmlns":890},[892,94560,94561,94659],{},[895,94562,94563,94565,94567,94573,94575,94581,94583,94585,94587,94589,94591,94593,94599,94601,94603,94605,94607,94609,94611,94617,94619,94621,94623,94625,94627,94629,94631,94633,94639,94641,94643,94645,94647,94649,94651,94657],{},[898,94564,900],{},[1700,94566,1703],{"stretchy":1702},[2007,94568,94569,94571],{},[898,94570,1662],{},[1931,94572,1933],{},[1700,94574,1732],{"separator":1731},[2007,94576,94577,94579],{},[898,94578,1662],{},[1931,94580,2343],{},[1700,94582,1709],{"stretchy":1702},[1700,94584,1765],{},[1931,94586,2343],{},[1700,94588,1732],{"separator":1731},[898,94590,900],{},[1700,94592,1703],{"stretchy":1702},[2007,94594,94595,94597],{},[898,94596,1662],{},[1931,94598,1933],{},[1700,94600,1732],{"separator":1731},[1931,94602,2385],{},[1700,94604,1709],{"stretchy":1702},[1700,94606,1732],{"separator":1731},[898,94608,900],{},[1700,94610,1703],{"stretchy":1702},[2007,94612,94613,94615],{},[898,94614,1662],{},[1931,94616,1933],{},[1700,94618,1732],{"separator":1731},[1931,94620,2343],{},[1700,94622,1709],{"stretchy":1702},[1700,94624,1732],{"separator":1731},[898,94626,900],{},[1700,94628,1703],{"stretchy":1702},[1931,94630,2343],{},[1700,94632,1732],{"separator":1731},[2007,94634,94635,94637],{},[898,94636,1662],{},[1931,94638,2343],{},[1700,94640,1709],{"stretchy":1702},[1700,94642,1732],{"separator":1731},[898,94644,900],{},[1700,94646,1703],{"stretchy":1702},[1931,94648,2385],{},[1700,94650,1732],{"separator":1731},[2007,94652,94653,94655],{},[898,94654,1662],{},[1931,94656,2343],{},[1700,94658,1709],{"stretchy":1702},[902,94660,94661],{"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 ",[883,94664,94666],{"className":94665},[886],[888,94667,94668],{"xmlns":890},[892,94669,94670,94685],{},[895,94671,94672,94674,94676,94678,94680,94683],{},[898,94673,1862],{},[1700,94675,1927],{"stretchy":1702},[1931,94677,64743],{},[1700,94679,8613],{"separator":1731},[1931,94681,94682],{},"3,555",[1700,94684,1970],{"stretchy":1702},[902,94686,94687],{"encoding":904},"A[1{,}5; 3{,}555]",[883,94689,94691],{"className":94690},[886],[888,94692,94693],{"xmlns":890},[892,94694,94695,94710],{},[895,94696,94697,94699,94701,94703,94705,94708],{},[898,94698,23438],{},[1700,94700,1927],{"stretchy":1702},[1931,94702,53383],{},[1700,94704,8613],{"separator":1731},[1931,94706,94707],{},"1,28",[1700,94709,1970],{"stretchy":1702},[902,94711,94712],{"encoding":904},"B[2{,}5; 1{,}28]",[883,94714,94716],{"className":94715},[886],[888,94717,94718],{"xmlns":890},[892,94719,94720,94752],{},[895,94721,94722,94724,94726,94728,94730,94732,94734,94740,94742,94744,94746,94748,94750],{},[898,94723,2974],{},[1700,94725,1927],{"stretchy":1702},[1931,94727,2343],{},[1700,94729,8613],{"separator":1731},[898,94731,900],{},[1700,94733,1703],{"stretchy":1702},[2007,94735,94736,94738],{},[898,94737,1662],{},[1931,94739,1933],{},[1700,94741,1732],{"separator":1731},[1931,94743,2385],{},[1700,94745,1709],{"stretchy":1702},[1700,94747,1765],{},[1931,94749,2385],{},[1700,94751,1970],{"stretchy":1702},[902,94753,94754],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,94757,94759],{"className":94758},[886],[888,94760,94761],{"xmlns":890},[892,94762,94763,94782],{},[895,94764,94765,94767,94769,94771,94773,94775,94777,94780],{},[898,94766,4374],{},[1700,94768,1927],{"stretchy":1702},[1931,94770,2385],{},[1700,94772,8613],{"separator":1731},[1931,94774,1933],{},[1700,94776,8613],{"separator":1731},[1931,94778,94779],{},"0,832",[1700,94781,1970],{"stretchy":1702},[902,94783,94784],{"encoding":904},"D[3; 1; 0{,}832]",[883,94786,94788],{"className":94787},[886],[888,94789,94790],{"xmlns":890},[892,94791,94792,94807],{},[895,94793,94794,94796,94798,94800,94802,94805],{},[898,94795,1762],{},[1700,94797,1927],{"stretchy":1702},[1931,94799,53383],{},[1700,94801,8613],{"separator":1731},[1931,94803,94804],{},"4,32",[1700,94806,1970],{"stretchy":1702},[902,94808,94809],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,94812,94813,93915,94816,94859,94860,6661,94873,94907,94908,94925,94926,94943],{},[38,94814,94815],{},"6.6",[883,94817,94819],{"className":94818},[886],[888,94820,94821],{"xmlns":890},[892,94822,94823,94857],{},[895,94824,94825,94827,94829,94843],{},[898,94826,900],{},[1700,94828,1765],{},[2030,94830,94831,94833,94835],{},[898,94832,1662],{},[1931,94834,1933],{},[895,94836,94837,94839,94841],{},[1931,94838,2343],{},[898,94840,1979],{"mathvariant":1791},[1931,94842,2385],{},[2030,94844,94845,94847,94849],{},[898,94846,1662],{},[1931,94848,2343],{},[895,94850,94851,94853,94855],{},[1931,94852,1933],{},[898,94854,1979],{"mathvariant":1791},[1931,94856,2385],{},[902,94858,94552],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,94861,94863],{"className":94862},[886],[888,94864,94865],{"xmlns":890},[892,94866,94867,94871],{},[895,94868,94869],{},[1781,94870,10786],{},[902,94872,28423],{"encoding":904},[883,94874,94876],{"className":94875},[886],[888,94877,94878],{"xmlns":890},[892,94879,94880,94904],{},[895,94881,94882,94888,94890,94892,94894,94900,94902],{},[2007,94883,94884,94886],{},[898,94885,1662],{},[1931,94887,1933],{},[1700,94889,1765],{},[1931,94891,3284],{},[1700,94893,1732],{"separator":1731},[2007,94895,94896,94898],{},[898,94897,1662],{},[1931,94899,2343],{},[1700,94901,1765],{},[1931,94903,8565],{},[902,94905,94906],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,94909,94911],{"className":94910},[886],[888,94912,94913],{"xmlns":890},[892,94914,94915,94923],{},[895,94916,94917],{},[2007,94918,94919,94921],{},[898,94920,1662],{},[1931,94922,1933],{},[902,94924,29187],{"encoding":904},", poklesne-li ",[883,94927,94929],{"className":94928},[886],[888,94930,94931],{"xmlns":890},[892,94932,94933,94941],{},[895,94934,94935],{},[2007,94936,94937,94939],{},[898,94938,1662],{},[1931,94940,2343],{},[902,94942,29206],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,94945,94946,94949,94950,94967,94968,94985,94986,95018,95019,95044,95045,95058,95059,1343,95083,1343,95107,2196],{},[38,94947,94948],{},"6.7"," Míra uspokojení z nákupu množství ",[883,94951,94953],{"className":94952},[886],[888,94954,94955],{"xmlns":890},[892,94956,94957,94965],{},[895,94958,94959],{},[2007,94960,94961,94963],{},[898,94962,1662],{},[1931,94964,1933],{},[902,94966,29187],{"encoding":904}," nealko nápojů a množství ",[883,94969,94971],{"className":94970},[886],[888,94972,94973],{"xmlns":890},[892,94974,94975,94983],{},[895,94976,94977],{},[2007,94978,94979,94981],{},[898,94980,1662],{},[1931,94982,2343],{},[902,94984,29206],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,94987,94989],{"className":94988},[886],[888,94990,94991],{"xmlns":890},[892,94992,94993,95015],{},[895,94994,94995,94997,94999],{},[898,94996,900],{},[1700,94998,1765],{},[8305,95000,95001],{},[895,95002,95003,95009],{},[2007,95004,95005,95007],{},[898,95006,1662],{},[1931,95008,1933],{},[2007,95010,95011,95013],{},[898,95012,1662],{},[1931,95014,2343],{},[902,95016,95017],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,95020,95022],{"className":95021},[886],[888,95023,95024],{"xmlns":890},[892,95025,95026,95042],{},[895,95027,95028,95034,95036],{},[2007,95029,95030,95032],{},[898,95031,1662],{},[1931,95033,1933],{},[1700,95035,1732],{"separator":1731},[2007,95037,95038,95040],{},[898,95039,1662],{},[1931,95041,2343],{},[902,95043,35807],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,95046,95048],{"className":95047},[886],[888,95049,95050],{"xmlns":890},[892,95051,95052,95056],{},[895,95053,95054],{},[1781,95055,10786],{},[902,95057,28423],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,95060,95062],{"className":95061},[886],[888,95063,95064],{"xmlns":890},[892,95065,95066,95080],{},[895,95067,95068,95070,95072,95074,95076,95078],{},[1781,95069,10786],{},[1700,95071,1703],{"stretchy":1702},[1931,95073,2438],{},[1700,95075,1732],{"separator":1731},[1931,95077,9223],{},[1700,95079,1709],{"stretchy":1702},[902,95081,95082],{"encoding":904},"\\text{MRCS}(5, 20)",[883,95084,95086],{"className":95085},[886],[888,95087,95088],{"xmlns":890},[892,95089,95090,95104],{},[895,95091,95092,95094,95096,95098,95100,95102],{},[1781,95093,10786],{},[1700,95095,1703],{"stretchy":1702},[1931,95097,9223],{},[1700,95099,1732],{"separator":1731},[1931,95101,2438],{},[1700,95103,1709],{"stretchy":1702},[902,95105,95106],{"encoding":904},"\\text{MRCS}(20, 5)",[883,95108,95110],{"className":95109},[886],[888,95111,95112],{"xmlns":890},[892,95113,95114,95128],{},[895,95115,95116,95118,95120,95122,95124,95126],{},[1781,95117,10786],{},[1700,95119,1703],{"stretchy":1702},[1931,95121,2343],{},[1700,95123,1732],{"separator":1731},[1931,95125,3314],{},[1700,95127,1709],{"stretchy":1702},[902,95129,95130],{"encoding":904},"\\text{MRCS}(2, 50)",[4060,95132,95133],{},[724,95134,95135,95137,95138,2196],{},[883,95136,4761],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,95139,95142],{"className":95140,"dataFsResolvedFilePath":911,"href":95141},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,95144,15905],{"id":15904},[120,95146,95147,95153,95158,95164,95217,95227,95273,95328,95391,95448,95503,95542],{},[123,95148,95149,95152],{},[38,95150,95151],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,95154,95155,95157],{},[38,95156,87050],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,95159,95160,95163],{},[38,95161,95162],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,95165,95166,95168,95169,95182,95183,2196],{},[38,95167,87377],{}," — uspořádaná ",[883,95170,95172],{"className":95171},[886],[888,95173,95174],{"xmlns":890},[892,95175,95176,95180],{},[895,95177,95178],{},[898,95179,37045],{},[902,95181,37045],{"encoding":904},"-tice ",[883,95184,95186],{"className":95185},[886],[888,95187,95188],{"xmlns":890},[892,95189,95190,95214],{},[895,95191,95192,95194,95200,95202,95204,95206,95212],{},[1700,95193,1703],{"stretchy":1702},[2007,95195,95196,95198],{},[898,95197,1662],{},[1931,95199,1933],{},[1700,95201,1732],{"separator":1731},[1700,95203,9833],{},[1700,95205,1732],{"separator":1731},[2007,95207,95208,95210],{},[898,95209,1662],{},[898,95211,37045],{},[1700,95213,1709],{"stretchy":1702},[902,95215,95216],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,95218,95219,95222,95223,95226],{},[38,95220,95221],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,95224,95225],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,95228,95229,2106,95232,95272],{},[38,95230,95231],{},"Funkce užitečnosti",[883,95233,95235],{"className":95234},[886],[888,95236,95237],{"xmlns":890},[892,95238,95239,95269],{},[895,95240,95241,95243,95245,95247,95249,95255,95257,95259,95261,95267],{},[898,95242,900],{},[1700,95244,1765],{},[898,95246,900],{},[1700,95248,1703],{"stretchy":1702},[2007,95250,95251,95253],{},[898,95252,1662],{},[1931,95254,1933],{},[1700,95256,1732],{"separator":1731},[1700,95258,9833],{},[1700,95260,1732],{"separator":1731},[2007,95262,95263,95265],{},[898,95264,1662],{},[898,95266,37045],{},[1700,95268,1709],{"stretchy":1702},[902,95270,95271],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,95274,95275,2106,95278,95307,95308,2106,95311,95327],{},[38,95276,95277],{},"Mezní užitečnost",[883,95279,95281],{"className":95280},[886],[888,95282,95283],{"xmlns":890},[892,95284,95285,95305],{},[895,95286,95287,95289,95295,95297],{},[898,95288,2005],{},[2007,95290,95291,95293],{},[898,95292,900],{},[898,95294,17975],{},[1700,95296,1765],{},[2030,95298,95299,95301,95303],{},[898,95300,900],{},[898,95302,17975],{},[1700,95304,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[902,95306,86834],{"encoding":904}," — vzorec (6.2); ",[38,95309,95310],{},"totální diferenciál",[883,95312,95314],{"className":95313},[886],[888,95315,95316],{"xmlns":890},[892,95317,95318,95324],{},[895,95319,95320,95322],{},[898,95321,2406],{"mathvariant":1791},[898,95323,900],{},[902,95325,95326],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,95329,95330,95332,95333,95357,95358,95390],{},[38,95331,89013],{}," — (6.4) ",[883,95334,95336],{"className":95335},[886],[888,95337,95338],{"xmlns":890},[892,95339,95340,95354],{},[895,95341,95342,95350,95352],{},[2030,95343,95344,95346,95348],{},[898,95345,900],{},[898,95347,17975],{},[1700,95349,1793],{"mathvariant":1791,"lspace":1792,"rspace":1792},[1700,95351,3601],{},[1931,95353,1772],{},[902,95355,95356],{"encoding":904},"U'_i > 0",", (6.5) ",[883,95359,95361],{"className":95360},[886],[888,95362,95363],{"xmlns":890},[892,95364,95365,95387],{},[895,95366,95367,95383,95385],{},[2030,95368,95369,95371,95377],{},[898,95370,900],{},[895,95372,95373,95375],{},[898,95374,17975],{},[898,95376,17975],{},[895,95378,95379,95381],{},[1700,95380,1793],{"mathvariant":1791},[1700,95382,1793],{"mathvariant":1791},[1700,95384,3640],{},[1931,95386,1772],{},[902,95388,95389],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,95392,95393,2106,95395,95426,95427,2196],{},[38,95394,90801],{},[883,95396,95398],{"className":95397},[886],[888,95399,95400],{"xmlns":890},[892,95401,95402,95424],{},[895,95403,95404,95406,95408,95416],{},[898,95405,900],{},[1700,95407,1765],{},[2030,95409,95410,95412,95414],{},[898,95411,1662],{},[1931,95413,1933],{},[898,95415,207],{},[2030,95417,95418,95420,95422],{},[898,95419,1662],{},[1931,95421,2343],{},[898,95423,1879],{},[902,95425,35988],{"encoding":904}," — (6.6), speciálně ",[883,95428,95430],{"className":95429},[886],[888,95431,95432],{"xmlns":890},[892,95433,95434,95446],{},[895,95435,95436,95438,95440,95442,95444],{},[898,95437,1879],{},[1700,95439,1765],{},[1931,95441,1933],{},[1700,95443,1768],{},[898,95445,207],{},[902,95447,90955],{"encoding":904},[123,95449,95450,2106,95453,95488,95489,95502],{},[38,95451,95452],{},"Křivky užitečnosti (indiferenční)",[883,95454,95456],{"className":95455},[886],[888,95457,95458],{"xmlns":890},[892,95459,95460,95486],{},[895,95461,95462,95464,95466,95472,95474,95480,95482,95484],{},[898,95463,900],{},[1700,95465,1703],{"stretchy":1702},[2007,95467,95468,95470],{},[898,95469,1662],{},[1931,95471,1933],{},[1700,95473,1732],{"separator":1731},[2007,95475,95476,95478],{},[898,95477,1662],{},[1931,95479,2343],{},[1700,95481,1709],{"stretchy":1702},[1700,95483,1765],{},[898,95485,2354],{},[902,95487,9955],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,95490,95492],{"className":95491},[886],[888,95493,95494],{"xmlns":890},[892,95495,95496,95500],{},[895,95497,95498],{},[898,95499,900],{},[902,95501,900],{"encoding":904},", konvexní.",[123,95504,95505,2106,95507,95541],{},[38,95506,92346],{},[883,95508,95510],{"className":95509},[886],[888,95511,95512],{"xmlns":890},[892,95513,95514,95538],{},[895,95515,95516,95518,95520,95522,95528,95530,95532],{},[1781,95517,10786],{},[1700,95519,1765],{},[898,95521,2005],{},[2007,95523,95524,95526],{},[898,95525,900],{},[1931,95527,1933],{},[898,95529,1979],{"mathvariant":1791},[898,95531,2005],{},[2007,95533,95534,95536],{},[898,95535,900],{},[1931,95537,2343],{},[902,95539,95540],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,95543,95544,2106,95547,9956,95576,95579],{},[38,95545,95546],{},"Podmínka optimality",[883,95548,95550],{"className":95549},[886],[888,95551,95552],{"xmlns":890},[892,95553,95554,95574],{},[895,95555,95556,95558,95560,95566,95568],{},[1781,95557,10786],{},[1700,95559,1765],{},[2007,95561,95562,95564],{},[898,95563,1677],{},[1931,95565,1933],{},[898,95567,1979],{"mathvariant":1791},[2007,95569,95570,95572],{},[898,95571,1677],{},[1931,95573,2343],{},[902,95575,28183],{"encoding":904},[207,95577,36939],{"className":95578,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,95581,3985],{"id":3984},[120,95583,95584,95621,95662,95672],{},[123,95585,95586,2106,95589,95592,95593,95606,95607,95620],{},[38,95587,95588],{},"Navazující téma:",[207,95590,913],{"className":95591,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,95594,95596],{"className":95595},[886],[888,95597,95598],{"xmlns":890},[892,95599,95600,95604],{},[895,95601,95602],{},[898,95603,900],{},[902,95605,900],{"encoding":904},", min ",[883,95608,95610],{"className":95609},[886],[888,95611,95612],{"xmlns":890},[892,95613,95614,95618],{},[895,95615,95616],{},[898,95617,1762],{},[902,95619,1762],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,95622,95623,2106,95626,11276,95629,86591,95632,95635,95636,95639,95640,18833,95658,95661],{},[38,95624,95625],{},"Související pojmy:",[207,95627,784],{"className":95628,"dataFsResolvedFilePath":782,"href":783},[210],[207,95630,2559],{"className":95631,"dataFsResolvedFilePath":764,"href":765},[210],[207,95633,11271],{"className":95634,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,95637,12125],{"className":95638,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,95641,95643],{"className":95642},[886],[888,95644,95645],{"xmlns":890},[892,95646,95647,95655],{},[895,95648,95649],{},[2007,95650,95651,95653],{},[898,95652,4374],{},[898,95654,17975],{},[902,95656,95657],{"encoding":904},"D_i",[207,95659,793],{"className":95660,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,95663,95664,2106,95666,1343,95669],{},[38,95665,36888],{},[207,95667,1094],{"className":95668,"dataFsResolvedFilePath":838,"href":839},[210],[207,95670,1101],{"className":95671,"dataFsResolvedFilePath":868,"href":869},[210],[123,95673,95674,2106,95676],{},[38,95675,16389],{},[207,95677,16393],{"className":95678,"dataFsResolvedFilePath":2140,"href":2141},[210],{"title":641,"searchDepth":642,"depth":642,"links":95680},[95681,95682,95683,95686,95687,95690,95694,95695,95698,95699,95700,95701,95702,95703,95704],{"id":12190,"depth":642,"text":12191},{"id":86973,"depth":642,"text":86974},{"id":87033,"depth":642,"text":87034,"children":95684},[95685],{"id":87049,"depth":649,"text":87050},{"id":87356,"depth":642,"text":87357},{"id":88216,"depth":642,"text":88217,"children":95688},[95689],{"id":88763,"depth":649,"text":80394},{"id":89012,"depth":642,"text":89013,"children":95691},[95692],{"id":89885,"depth":649,"text":95693},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":90800,"depth":642,"text":90801},{"id":91336,"depth":642,"text":91337,"children":95696},[95697],{"id":92110,"depth":649,"text":92111},{"id":92340,"depth":642,"text":92341},{"id":93101,"depth":642,"text":93102},{"id":93639,"depth":642,"text":93640},{"id":50066,"depth":642,"text":50067},{"id":93775,"depth":642,"text":93776},{"id":15904,"depth":642,"text":15905},{"id":3984,"depth":642,"text":3985},{},"\u002Ftopics\u002Fuzitecnost",{"title":86757,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,9960,95711,2157,11306,95712],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":95715,"title":757,"body":95716,"course":1128,"courses":659,"created":1129,"description":95989,"extension":661,"meta":95990,"navigation":664,"path":95991,"seo":95992,"sources":95993,"stem":95994,"tags":95995,"type":4049,"updated":677,"__hash__":96001},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":95717,"toc":95981},[95718,95721,95728,95735,95739,95749,95751,95785,95789,95832,95835,95893,95897,95927,95931,95952,95954],[12,95719,757],{"id":95720},"základy-matematické-ekonomie",[724,95722,95723,95724,95727],{},"Úvodní pojmy a princip modelování v ",[207,95725,16565],{"className":95726,"dataFsResolvedFilePath":2140,"href":2141},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,95729,95730],{},[2756,95731],{"alt":95732,"className":95733,"src":95734},"imek-model-promenne",[210,2760],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,95736,95738],{"id":95737},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,95740,95741,95744,95745,95748],{},[38,95742,95743],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,95746,95747],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,95750,15905],{"id":15904},[120,95752,95753,95759,95765,95771,95780],{},[123,95754,95755,95758],{},[38,95756,95757],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,95760,95761,95764],{},[38,95762,95763],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,95766,95767,95770],{},[38,95768,95769],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,95772,95773,7203,95776,95779],{},[38,95774,95775],{},"Ceteris paribus",[614,95777,95778],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,95781,95782,95784],{},[38,95783,50820],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,95786,95788],{"id":95787},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,95790,95791,95831],{},[883,95792,95794],{"className":95793},[886],[888,95795,95796],{"xmlns":890},[892,95797,95798,95828],{},[895,95799,95800,95802,95804,95806,95808,95810,95812,95814,95816,95818,95820,95822,95824,95826],{},[898,95801,1662],{},[1700,95803,1765],{},[898,95805,4374],{},[1700,95807,1703],{"stretchy":1702},[898,95809,1677],{},[1700,95811,1732],{"separator":1731},[898,95813,9316],{},[1700,95815,1732],{"separator":1731},[898,95817,18479],{},[1700,95819,1732],{"separator":1731},[898,95821,900],{},[1700,95823,1732],{"separator":1731},[1700,95825,9833],{},[1700,95827,1709],{"stretchy":1702},[902,95829,95830],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,95833,95834],{},"Zjednodušení:",[120,95836,95837,95865],{},[123,95838,95839,2106,95842],{},[38,95840,95841],{},"Jednofaktorový model:",[883,95843,95845],{"className":95844},[886],[888,95846,95847],{"xmlns":890},[892,95848,95849,95863],{},[895,95850,95851,95853,95855,95857,95859,95861],{},[898,95852,1662],{},[1700,95854,1765],{},[898,95856,4374],{},[1700,95858,1703],{"stretchy":1702},[898,95860,1677],{},[1700,95862,1709],{"stretchy":1702},[902,95864,4383],{"encoding":904},[123,95866,95867,2106,95870],{},[38,95868,95869],{},"Inverzní zápis:",[883,95871,95873],{"className":95872},[886],[888,95874,95875],{"xmlns":890},[892,95876,95877,95891],{},[895,95878,95879,95881,95883,95885,95887,95889],{},[898,95880,1677],{},[1700,95882,1765],{},[898,95884,4374],{},[1700,95886,1703],{"stretchy":1702},[898,95888,1662],{},[1700,95890,1709],{"stretchy":1702},[902,95892,4829],{"encoding":904},[115,95894,95896],{"id":95895},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,95898,95899,95908],{},[123,95900,95901,95904,95905,4110],{},[38,95902,95903],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,95906,16425],{"className":95907,"dataFsResolvedFilePath":800,"href":801},[210],[123,95909,95910,95913,95914,95917,95918,95921,95922,95926],{},[38,95911,95912],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,95915,1145],{"className":95916,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,95919,2118],{"className":95920,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,95923,95925],{"className":95924,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,95928,95930],{"id":95929},"konvence-z-přednášek","Konvence z přednášek",[120,95932,95933,95940,95946],{},[123,95934,95935,95936,95939],{},"Symbol ",[95937,95938,2927],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,95941,95942,95943,2196],{},"Numerické výsledky ",[38,95944,95945],{},"na 3 desetinná místa",[123,95947,4087,95948,95951],{},[614,95949,95950],{},"jednotková změna"," má standardní význam (změna o 1).",[115,95953,3985],{"id":3984},[120,95955,95956,95961,95969],{},[123,95957,95958,95960],{},[38,95959,3992],{}," —",[123,95962,95963,2106,95965],{},[38,95964,4000],{},[207,95966,95968],{"className":95967,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,95970,95971,2106,95973,1343,95977],{},[38,95972,4008],{},[207,95974,95976],{"className":95975,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,95978,95980],{"className":95979,"dataFsResolvedFilePath":2140,"href":2141},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":95982},[95983,95984,95985,95986,95987,95988],{"id":95737,"depth":642,"text":95738},{"id":15904,"depth":642,"text":15905},{"id":95787,"depth":642,"text":95788},{"id":95895,"depth":642,"text":95896},{"id":95929,"depth":642,"text":95930},{"id":3984,"depth":642,"text":3985},"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":95989},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,95996,95997,95998,95999,96000],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":96003,"title":96004,"body":96005,"course":1128,"courses":659,"created":9743,"description":641,"extension":661,"meta":100277,"navigation":664,"path":100278,"seo":100279,"sources":100280,"stem":100281,"tags":100282,"type":4049,"updated":677,"__hash__":100286},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":96006,"toc":100260},[96007,96010,96104,96108,96130,96144,96196,96198,96202,96265,96308,96327,96490,96589,96592,96659,96663,96792,96831,96861,96973,97018,97084,97137,97213,97269,97271,97275,97339,97383,97403,97564,97567,97651,97748,97751,97817,97821,97870,97896,98001,98065,98070,98166,98213,98215,98218,98240,98282,98289,98322,98324,98395,98449,98558,98562,98651,98727,98991,99029,99031,99035,99038,99045,99356,99359,99417,99597,99626,99628,99632,99638,99776,99785,99787,99789,100214,100216,100218],[12,96008,96004],{"id":96009},"zdanění-trhu-dopady-daně-na-rovnováhu",[4060,96011,96012],{},[724,96013,96014,42813,96016,96029,96030,96033,96034,96036,96037,96040,96041,96062,96063,96086,96087,96090,96091,2196],{},[883,96015,4346],{},[883,96017,96019],{"className":96018},[886],[888,96020,96021],{"xmlns":890},[892,96022,96023,96027],{},[895,96024,96025],{},[898,96026,2971],{},[902,96028,2971],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,96031,96032],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,96035,87041],{}," (je-li uložena spotřebiteli). Výsledné ",[38,96038,96039],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,96042,96044],{"className":96043},[886],[888,96045,96046],{"xmlns":890},[892,96047,96048,96060],{},[895,96049,96050],{},[2007,96051,96052,96054],{},[898,96053,2971],{},[895,96055,96056,96058],{},[898,96057,42862],{},[898,96059,724],{},[902,96061,42867],{"encoding":904}," (spotřebitel) a ",[883,96064,96066],{"className":96065},[886],[888,96067,96068],{"xmlns":890},[892,96069,96070,96084],{},[895,96071,96072],{},[2007,96073,96074,96076],{},[898,96075,2971],{},[895,96077,96078,96080,96082],{},[898,96079,42885],{},[898,96081,2215],{},[898,96083,12226],{},[902,96085,42892],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,96088,96089],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,96092,96094],{"className":96093},[886],[888,96095,96096],{"xmlns":890},[892,96097,96098,96102],{},[895,96099,96100],{},[898,96101,2971],{},[902,96103,2971],{"encoding":904},[115,96105,96107],{"id":96106},"dvě-formy-zdanění","Dvě formy zdanění",[724,96109,96110,96111,96129],{},"Uvažujme jednotkovou daň ",[883,96112,96114],{"className":96113},[886],[888,96115,96116],{"xmlns":890},[892,96117,96118,96126],{},[895,96119,96120,96122,96124],{},[898,96121,2971],{},[1700,96123,3601],{},[1931,96125,1772],{},[902,96127,96128],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,96131,96132,96138],{},[123,96133,96134,96137],{},[38,96135,96136],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,96139,96140,96143],{},[38,96141,96142],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,96145,96146,96147,96160,96161,96164,96165,2196],{},"V obou případech dochází k posunu jedné z křivek o ",[883,96148,96150],{"className":96149},[886],[888,96151,96152],{"xmlns":890},[892,96153,96154,96158],{},[895,96155,96156],{},[898,96157,2971],{},[902,96159,2971],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,96162,96163],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,96166,96168],{"className":96167},[886],[888,96169,96170],{"xmlns":890},[892,96171,96172,96194],{},[895,96173,96174,96176,96178,96184,96186,96192],{},[898,96175,1762],{},[1700,96177,1927],{"stretchy":1702},[1785,96179,96180,96182],{},[898,96181,1662],{},[898,96183,1762],{},[1700,96185,1732],{"separator":1731},[1785,96187,96188,96190],{},[898,96189,1677],{},[898,96191,1762],{},[1700,96193,1970],{"stretchy":1702},[902,96195,41552],{"encoding":904},[37155,96197],{},[115,96199,96201],{"id":96200},"daň-uložená-výrobci","Daň uložená výrobci",[724,96203,96204,96205,96218,96219,96236,96237,96264],{},"Je-li daň ",[883,96206,96208],{"className":96207},[886],[888,96209,96210],{"xmlns":890},[892,96211,96212,96216],{},[895,96213,96214],{},[898,96215,2971],{},[902,96217,2971],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,96220,96222],{"className":96221},[886],[888,96223,96224],{"xmlns":890},[892,96225,96226,96234],{},[895,96227,96228,96230,96232],{},[898,96229,1677],{},[1700,96231,1768],{},[898,96233,2971],{},[902,96235,41307],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,96238,96240],{"className":96239},[886],[888,96241,96242],{"xmlns":890},[892,96243,96244,96262],{},[895,96245,96246,96248,96250,96252,96254,96256,96258,96260],{},[898,96247,1677],{},[1700,96249,1768],{},[898,96251,2971],{},[1700,96253,1765],{},[898,96255,8861],{},[1700,96257,1703],{"stretchy":1702},[898,96259,1662],{},[1700,96261,1709],{"stretchy":1702},[902,96263,41336],{"encoding":904}," nová funkce nabídky:",[883,96266,96268],{"className":96267},[886],[888,96269,96270],{"xmlns":890,"display":28251},[892,96271,96272,96306],{},[895,96273,96274,96276,96278,96284,96286,96288,96290,96292,96294,96296,96298,96300,96302,96304],{},[898,96275,1677],{},[1700,96277,1765],{},[2007,96279,96280,96282],{},[898,96281,8861],{},[1931,96283,1933],{},[1700,96285,1703],{"stretchy":1702},[898,96287,1662],{},[1700,96289,1709],{"stretchy":1702},[1700,96291,1765],{},[898,96293,8861],{},[1700,96295,1703],{"stretchy":1702},[898,96297,1662],{},[1700,96299,1709],{"stretchy":1702},[1700,96301,1897],{},[898,96303,2971],{},[898,96305,2196],{"mathvariant":1791},[902,96307,41381],{"encoding":904},[724,96309,96310,96311,2106,96324,96326],{},"Nabídka se tedy posouvá o ",[883,96312,96314],{"className":96313},[886],[888,96315,96316],{"xmlns":890},[892,96317,96318,96322],{},[895,96319,96320],{},[898,96321,2971],{},[902,96323,2971],{"encoding":904},[38,96325,41414],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,96328,96329,96330,96370,96371,2114,96399,96427,96428,96447,96448,96472,96473,4110],{},"Nový rovnovážný bod ",[883,96331,96333],{"className":96332},[886],[888,96334,96335],{"xmlns":890},[892,96336,96337,96367],{},[895,96338,96339,96345,96347,96355,96357,96365],{},[2007,96340,96341,96343],{},[898,96342,1762],{},[1931,96344,1933],{},[1700,96346,1927],{"stretchy":1702},[2030,96348,96349,96351,96353],{},[898,96350,1662],{},[1931,96352,1933],{},[898,96354,1762],{},[1700,96356,1732],{"separator":1731},[2030,96358,96359,96361,96363],{},[898,96360,1677],{},[1931,96362,1933],{},[898,96364,1762],{},[1700,96366,1970],{"stretchy":1702},[902,96368,96369],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,96372,96374],{"className":96373},[886],[888,96375,96376],{"xmlns":890},[892,96377,96378,96396],{},[895,96379,96380,96388,96390],{},[2030,96381,96382,96384,96386],{},[898,96383,1662],{},[1931,96385,1933],{},[898,96387,1762],{},[1700,96389,3640],{},[1785,96391,96392,96394],{},[898,96393,1662],{},[898,96395,1762],{},[902,96397,96398],{"encoding":904},"Q_1^E \u003C Q^E",[883,96400,96402],{"className":96401},[886],[888,96403,96404],{"xmlns":890},[892,96405,96406,96424],{},[895,96407,96408,96416,96418],{},[2030,96409,96410,96412,96414],{},[898,96411,1677],{},[1931,96413,1933],{},[898,96415,1762],{},[1700,96417,3601],{},[1785,96419,96420,96422],{},[898,96421,1677],{},[898,96423,1762],{},[902,96425,96426],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,96429,96431],{"className":96430},[886],[888,96432,96433],{"xmlns":890},[892,96434,96435,96445],{},[895,96436,96437],{},[2030,96438,96439,96441,96443],{},[898,96440,1677],{},[1931,96442,1933],{},[898,96444,1762],{},[902,96446,48042],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,96449,96451],{"className":96450},[886],[888,96452,96453],{"xmlns":890},[892,96454,96455,96469],{},[895,96456,96457,96465,96467],{},[2030,96458,96459,96461,96463],{},[898,96460,1677],{},[1931,96462,1933],{},[898,96464,1762],{},[1700,96466,1768],{},[898,96468,2971],{},[902,96470,96471],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,96474,96476],{"className":96475},[886],[888,96477,96478],{"xmlns":890},[892,96479,96480,96488],{},[895,96481,96482],{},[1785,96483,96484,96486],{},[898,96485,1677],{},[898,96487,1762],{},[902,96489,41651],{"encoding":904},[724,96491,96492],{},[614,96493,96494,96495,96525,96526,96539,96540,5857,96557,96570,96571,2196],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,96496,96498],{"className":96497},[886],[888,96499,96500],{"xmlns":890},[892,96501,96502,96522],{},[895,96503,96504,96506,96508,96514,96516,96518,96520],{},[898,96505,8861],{},[1700,96507,3317],{},[2007,96509,96510,96512],{},[898,96511,8861],{},[1931,96513,1933],{},[1700,96515,1765],{},[898,96517,8861],{},[1700,96519,1897],{},[898,96521,2971],{},[902,96523,96524],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,96527,96529],{"className":96528},[886],[888,96530,96531],{"xmlns":890},[892,96532,96533,96537],{},[895,96534,96535],{},[898,96536,2971],{},[902,96538,2971],{"encoding":904},". Průsečík ",[883,96541,96543],{"className":96542},[886],[888,96544,96545],{"xmlns":890},[892,96546,96547,96555],{},[895,96548,96549],{},[2007,96550,96551,96553],{},[898,96552,8861],{},[1931,96554,1933],{},[902,96556,41182],{"encoding":904},[883,96558,96560],{"className":96559},[886],[888,96561,96562],{"xmlns":890},[892,96563,96564,96568],{},[895,96565,96566],{},[898,96567,4374],{},[902,96569,4374],{"encoding":904}," je nový rovnovážný bod ",[883,96572,96574],{"className":96573},[886],[888,96575,96576],{"xmlns":890},[892,96577,96578,96586],{},[895,96579,96580],{},[2007,96581,96582,96584],{},[898,96583,1762],{},[1931,96585,1933],{},[902,96587,96588],{"encoding":904},"E_1",[198,96590,45488],{"id":96591},"příklad-29",[724,96593,96594,41840,96596,41875,96620,96640,96641,96658],{},[38,96595,38118],{},[883,96597,96599],{"className":96598},[886],[888,96600,96601],{"xmlns":890},[892,96602,96603,96617],{},[895,96604,96605,96607,96609,96611,96613,96615],{},[898,96606,1677],{},[1700,96608,1765],{},[1931,96610,3702],{},[1700,96612,1768],{},[1931,96614,2343],{},[898,96616,1662],{},[902,96618,96619],{"encoding":904},"P = 12 - 2Q",[883,96621,96623],{"className":96622},[886],[888,96624,96625],{"xmlns":890},[892,96626,96627,96637],{},[895,96628,96629,96631,96633,96635],{},[898,96630,1677],{},[1700,96632,1765],{},[1931,96634,2553],{},[898,96636,1662],{},[902,96638,96639],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,96642,96644],{"className":96643},[886],[888,96645,96646],{"xmlns":890},[892,96647,96648,96656],{},[895,96649,96650,96652,96654],{},[898,96651,2971],{},[1700,96653,1765],{},[1931,96655,2445],{},[902,96657,41453],{"encoding":904}," Kč.",[724,96660,96661],{},[38,96662,38150],{},[724,96664,96665,96668,96669,5757,96695,5777,96715,1343,96737,96767,96768,2196],{},[614,96666,96667],{},"Bez daně."," Z rovnosti ",[883,96670,96672],{"className":96671},[886],[888,96673,96674],{"xmlns":890},[892,96675,96676,96692],{},[895,96677,96678,96680,96682,96684,96686,96688,96690],{},[1931,96679,3702],{},[1700,96681,1768],{},[1931,96683,2343],{},[898,96685,1662],{},[1700,96687,1765],{},[1931,96689,2553],{},[898,96691,1662],{},[902,96693,96694],{"encoding":904},"12 - 2Q = 4Q",[883,96696,96698],{"className":96697},[886],[888,96699,96700],{"xmlns":890},[892,96701,96702,96712],{},[895,96703,96704,96706,96708,96710],{},[1931,96705,2445],{},[898,96707,1662],{},[1700,96709,1765],{},[1931,96711,3702],{},[902,96713,96714],{"encoding":904},"6Q = 12",[883,96716,96718],{"className":96717},[886],[888,96719,96720],{"xmlns":890},[892,96721,96722,96734],{},[895,96723,96724,96730,96732],{},[1785,96725,96726,96728],{},[898,96727,1662],{},[898,96729,1762],{},[1700,96731,1765],{},[1931,96733,2343],{},[902,96735,96736],{"encoding":904},"Q^E = 2",[883,96738,96740],{"className":96739},[886],[888,96741,96742],{"xmlns":890},[892,96743,96744,96764],{},[895,96745,96746,96752,96754,96756,96758,96760,96762],{},[1785,96747,96748,96750],{},[898,96749,1677],{},[898,96751,1762],{},[1700,96753,1765],{},[1931,96755,2553],{},[1700,96757,2065],{},[1931,96759,2343],{},[1700,96761,1765],{},[1931,96763,5773],{},[902,96765,96766],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,96769,96771],{"className":96770},[886],[888,96772,96773],{"xmlns":890},[892,96774,96775,96789],{},[895,96776,96777,96779,96781,96783,96785,96787],{},[898,96778,1762],{},[1700,96780,1927],{"stretchy":1702},[1931,96782,2343],{},[1700,96784,1732],{"separator":1731},[1931,96786,5773],{},[1700,96788,1970],{"stretchy":1702},[902,96790,96791],{"encoding":904},"E[2, 8]",[724,96793,96794,96797,96798,96830],{},[614,96795,96796],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,96799,96801],{"className":96800},[886],[888,96802,96803],{"xmlns":890},[892,96804,96805,96827],{},[895,96806,96807,96813,96815,96817,96819,96821,96823,96825],{},[2007,96808,96809,96811],{},[898,96810,8861],{},[1931,96812,1933],{},[1700,96814,2901],{},[898,96816,1677],{},[1700,96818,1765],{},[1931,96820,2553],{},[898,96822,1662],{},[1700,96824,1897],{},[1931,96826,2445],{},[902,96828,96829],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,96832,96834],{"className":96833},[886],[888,96835,96836],{"xmlns":890,"display":28251},[892,96837,96838,96858],{},[895,96839,96840,96842,96844,96846,96848,96850,96852,96854,96856],{},[1931,96841,3702],{},[1700,96843,1768],{},[1931,96845,2343],{},[898,96847,1662],{},[1700,96849,1765],{},[1931,96851,2553],{},[898,96853,1662],{},[1700,96855,1897],{},[1931,96857,2445],{},[902,96859,96860],{"encoding":904},"12 - 2Q = 4Q + 6",[724,96862,96863,96864,5777,96884,1343,96908,96944,96945,2196],{},"plyne ",[883,96865,96867],{"className":96866},[886],[888,96868,96869],{"xmlns":890},[892,96870,96871,96881],{},[895,96872,96873,96875,96877,96879],{},[1931,96874,2445],{},[898,96876,1662],{},[1700,96878,1765],{},[1931,96880,2445],{},[902,96882,96883],{"encoding":904},"6Q = 6",[883,96885,96887],{"className":96886},[886],[888,96888,96889],{"xmlns":890},[892,96890,96891,96905],{},[895,96892,96893,96901,96903],{},[2030,96894,96895,96897,96899],{},[898,96896,1662],{},[1931,96898,1933],{},[898,96900,1762],{},[1700,96902,1765],{},[1931,96904,1933],{},[902,96906,96907],{"encoding":904},"Q_1^E = 1",[883,96909,96911],{"className":96910},[886],[888,96912,96913],{"xmlns":890},[892,96914,96915,96941],{},[895,96916,96917,96925,96927,96929,96931,96933,96935,96937,96939],{},[2030,96918,96919,96921,96923],{},[898,96920,1677],{},[1931,96922,1933],{},[898,96924,1762],{},[1700,96926,1765],{},[1931,96928,2553],{},[1700,96930,2065],{},[1931,96932,1933],{},[1700,96934,1897],{},[1931,96936,2445],{},[1700,96938,1765],{},[1931,96940,3058],{},[902,96942,96943],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,96946,96948],{"className":96947},[886],[888,96949,96950],{"xmlns":890},[892,96951,96952,96970],{},[895,96953,96954,96960,96962,96964,96966,96968],{},[2007,96955,96956,96958],{},[898,96957,1762],{},[1931,96959,1933],{},[1700,96961,1927],{"stretchy":1702},[1931,96963,1933],{},[1700,96965,1732],{"separator":1731},[1931,96967,3058],{},[1700,96969,1970],{"stretchy":1702},[902,96971,96972],{"encoding":904},"E_1[1, 10]",[724,96974,96975,96978,96979,97003,97004,97017],{},[614,96976,96977],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,96980,96982],{"className":96981},[886],[888,96983,96984],{"xmlns":890},[892,96985,96986,97000],{},[895,96987,96988,96996,96998],{},[2030,96989,96990,96992,96994],{},[898,96991,1677],{},[1931,96993,1933],{},[898,96995,1762],{},[1700,96997,1765],{},[1931,96999,3058],{},[902,97001,97002],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,97005,97007],{"className":97006},[886],[888,97008,97009],{"xmlns":890},[892,97010,97011,97015],{},[895,97012,97013],{},[1931,97014,5773],{},[902,97016,5773],{"encoding":904},", navýšení je",[883,97019,97021],{"className":97020},[886],[888,97022,97023],{"xmlns":890,"display":28251},[892,97024,97025,97081],{},[895,97026,97027,97037,97039,97047,97049,97055,97057,97059,97061,97063,97065,97067,97069,97079],{},[2007,97028,97029,97031],{},[898,97030,2971],{},[895,97032,97033,97035],{},[898,97034,42862],{},[898,97036,724],{},[1700,97038,1765],{},[2030,97040,97041,97043,97045],{},[898,97042,1677],{},[1931,97044,1933],{},[898,97046,1762],{},[1700,97048,1768],{},[1785,97050,97051,97053],{},[898,97052,1677],{},[898,97054,1762],{},[1700,97056,1765],{},[1931,97058,3058],{},[1700,97060,1768],{},[1931,97062,5773],{},[1700,97064,1765],{},[1931,97066,2343],{},[1781,97068,2495],{},[895,97070,97071,97073],{},[1781,97072,1735],{},[8574,97074,97075,97077],{"accent":1731},[1781,97076,2354],{},[1700,97078,25243],{},[898,97080,2196],{"mathvariant":1791},[902,97082,97083],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,97085,97086,97087,97003,97123,97136],{},"Výrobci zůstává čistá cena ",[883,97088,97090],{"className":97089},[886],[888,97091,97092],{"xmlns":890},[892,97093,97094,97120],{},[895,97095,97096,97104,97106,97108,97110,97112,97114,97116,97118],{},[2030,97097,97098,97100,97102],{},[898,97099,1677],{},[1931,97101,1933],{},[898,97103,1762],{},[1700,97105,1768],{},[898,97107,2971],{},[1700,97109,1765],{},[1931,97111,3058],{},[1700,97113,1768],{},[1931,97115,2445],{},[1700,97117,1765],{},[1931,97119,2553],{},[902,97121,97122],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,97124,97126],{"className":97125},[886],[888,97127,97128],{"xmlns":890},[892,97129,97130,97134],{},[895,97131,97132],{},[1931,97133,5773],{},[902,97135,5773],{"encoding":904},", pokles je",[883,97138,97140],{"className":97139},[886],[888,97141,97142],{"xmlns":890,"display":28251},[892,97143,97144,97210],{},[895,97145,97146,97158,97160,97166,97168,97170,97178,97180,97182,97184,97186,97188,97190,97192,97194,97196,97198,97208],{},[2007,97147,97148,97150],{},[898,97149,2971],{},[895,97151,97152,97154,97156],{},[898,97153,42885],{},[898,97155,2215],{},[898,97157,12226],{},[1700,97159,1765],{},[1785,97161,97162,97164],{},[898,97163,1677],{},[898,97165,1762],{},[1700,97167,1768],{},[1700,97169,1703],{"stretchy":1702},[2030,97171,97172,97174,97176],{},[898,97173,1677],{},[1931,97175,1933],{},[898,97177,1762],{},[1700,97179,1768],{},[898,97181,2971],{},[1700,97183,1709],{"stretchy":1702},[1700,97185,1765],{},[1931,97187,5773],{},[1700,97189,1768],{},[1931,97191,2553],{},[1700,97193,1765],{},[1931,97195,2553],{},[1781,97197,2495],{},[895,97199,97200,97202],{},[1781,97201,1735],{},[8574,97203,97204,97206],{"accent":1731},[1781,97205,2354],{},[1700,97207,25243],{},[898,97209,2196],{"mathvariant":1791},[902,97211,97212],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,97214,97215,97216,97268],{},"Kontrola: ",[883,97217,97219],{"className":97218},[886],[888,97220,97221],{"xmlns":890},[892,97222,97223,97265],{},[895,97224,97225,97235,97237,97249,97251,97253,97255,97257,97259,97261,97263],{},[2007,97226,97227,97229],{},[898,97228,2971],{},[895,97230,97231,97233],{},[898,97232,42862],{},[898,97234,724],{},[1700,97236,1897],{},[2007,97238,97239,97241],{},[898,97240,2971],{},[895,97242,97243,97245,97247],{},[898,97244,42885],{},[898,97246,2215],{},[898,97248,12226],{},[1700,97250,1765],{},[1931,97252,2343],{},[1700,97254,1897],{},[1931,97256,2553],{},[1700,97258,1765],{},[1931,97260,2445],{},[1700,97262,1765],{},[898,97264,2971],{},[902,97266,97267],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[37155,97270],{},[115,97272,97274],{"id":97273},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,97276,96204,97277,97290,97291,97309,97310,97338],{},[883,97278,97280],{"className":97279},[886],[888,97281,97282],{"xmlns":890},[892,97283,97284,97288],{},[895,97285,97286],{},[898,97287,2971],{},[902,97289,2971],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,97292,97294],{"className":97293},[886],[888,97295,97296],{"xmlns":890},[892,97297,97298,97306],{},[895,97299,97300,97302,97304],{},[898,97301,1677],{},[1700,97303,1897],{},[898,97305,2971],{},[902,97307,97308],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,97311,97313],{"className":97312},[886],[888,97314,97315],{"xmlns":890},[892,97316,97317,97335],{},[895,97318,97319,97321,97323,97325,97327,97329,97331,97333],{},[898,97320,1677],{},[1700,97322,1897],{},[898,97324,2971],{},[1700,97326,1765],{},[898,97328,4374],{},[1700,97330,1703],{"stretchy":1702},[898,97332,1662],{},[1700,97334,1709],{"stretchy":1702},[902,97336,97337],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,97340,97342],{"className":97341},[886],[888,97343,97344],{"xmlns":890,"display":28251},[892,97345,97346,97380],{},[895,97347,97348,97350,97352,97358,97360,97362,97364,97366,97368,97370,97372,97374,97376,97378],{},[898,97349,1677],{},[1700,97351,1765],{},[2007,97353,97354,97356],{},[898,97355,4374],{},[1931,97357,2343],{},[1700,97359,1703],{"stretchy":1702},[898,97361,1662],{},[1700,97363,1709],{"stretchy":1702},[1700,97365,1765],{},[898,97367,4374],{},[1700,97369,1703],{"stretchy":1702},[898,97371,1662],{},[1700,97373,1709],{"stretchy":1702},[1700,97375,1768],{},[898,97377,2971],{},[898,97379,2196],{"mathvariant":1791},[902,97381,97382],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,97384,97385,97386,2106,97399,97402],{},"Poptávka se tedy posouvá o ",[883,97387,97389],{"className":97388},[886],[888,97390,97391],{"xmlns":890},[892,97392,97393,97397],{},[895,97394,97395],{},[898,97396,2971],{},[902,97398,2971],{"encoding":904},[38,97400,97401],{},"svisle dolů",". Nabídka se nemění.",[724,97404,96329,97405,96370,97445,2114,97473,97501,97502,97521,97522,97546,97547,4110],{},[883,97406,97408],{"className":97407},[886],[888,97409,97410],{"xmlns":890},[892,97411,97412,97442],{},[895,97413,97414,97420,97422,97430,97432,97440],{},[2007,97415,97416,97418],{},[898,97417,1762],{},[1931,97419,2343],{},[1700,97421,1927],{"stretchy":1702},[2030,97423,97424,97426,97428],{},[898,97425,1662],{},[1931,97427,2343],{},[898,97429,1762],{},[1700,97431,1732],{"separator":1731},[2030,97433,97434,97436,97438],{},[898,97435,1677],{},[1931,97437,2343],{},[898,97439,1762],{},[1700,97441,1970],{"stretchy":1702},[902,97443,97444],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,97446,97448],{"className":97447},[886],[888,97449,97450],{"xmlns":890},[892,97451,97452,97470],{},[895,97453,97454,97462,97464],{},[2030,97455,97456,97458,97460],{},[898,97457,1662],{},[1931,97459,2343],{},[898,97461,1762],{},[1700,97463,3640],{},[1785,97465,97466,97468],{},[898,97467,1662],{},[898,97469,1762],{},[902,97471,97472],{"encoding":904},"Q_2^E \u003C Q^E",[883,97474,97476],{"className":97475},[886],[888,97477,97478],{"xmlns":890},[892,97479,97480,97498],{},[895,97481,97482,97490,97492],{},[2030,97483,97484,97486,97488],{},[898,97485,1677],{},[1931,97487,2343],{},[898,97489,1762],{},[1700,97491,3640],{},[1785,97493,97494,97496],{},[898,97495,1677],{},[898,97497,1762],{},[902,97499,97500],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,97503,97505],{"className":97504},[886],[888,97506,97507],{"xmlns":890},[892,97508,97509,97519],{},[895,97510,97511],{},[2030,97512,97513,97515,97517],{},[898,97514,1677],{},[1931,97516,2343],{},[898,97518,1762],{},[902,97520,48103],{"encoding":904},", spotřebitel platí celkem ",[883,97523,97525],{"className":97524},[886],[888,97526,97527],{"xmlns":890},[892,97528,97529,97543],{},[895,97530,97531,97539,97541],{},[2030,97532,97533,97535,97537],{},[898,97534,1677],{},[1931,97536,2343],{},[898,97538,1762],{},[1700,97540,1897],{},[898,97542,2971],{},[902,97544,97545],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,97548,97550],{"className":97549},[886],[888,97551,97552],{"xmlns":890},[892,97553,97554,97562],{},[895,97555,97556],{},[1785,97557,97558,97560],{},[898,97559,1677],{},[898,97561,1762],{},[902,97563,41651],{"encoding":904},[724,97565,97566],{},"Daňové břemeno:",[883,97568,97570],{"className":97569},[886],[888,97571,97572],{"xmlns":890,"display":28251},[892,97573,97574,97648],{},[895,97575,97576,97586,97588,97590,97598,97600,97602,97604,97606,97612,97614,97616,97628,97630,97636,97638,97646],{},[2007,97577,97578,97580],{},[898,97579,2971],{},[895,97581,97582,97584],{},[898,97583,42862],{},[898,97585,724],{},[1700,97587,1765],{},[1700,97589,1703],{"stretchy":1702},[2030,97591,97592,97594,97596],{},[898,97593,1677],{},[1931,97595,2343],{},[898,97597,1762],{},[1700,97599,1897],{},[898,97601,2971],{},[1700,97603,1709],{"stretchy":1702},[1700,97605,1768],{},[1785,97607,97608,97610],{},[898,97609,1677],{},[898,97611,1762],{},[1700,97613,1732],{"separator":1731},[6066,97615],{"width":6068},[2007,97617,97618,97620],{},[898,97619,2971],{},[895,97621,97622,97624,97626],{},[898,97623,42885],{},[898,97625,2215],{},[898,97627,12226],{},[1700,97629,1765],{},[1785,97631,97632,97634],{},[898,97633,1677],{},[898,97635,1762],{},[1700,97637,1768],{},[2030,97639,97640,97642,97644],{},[898,97641,1677],{},[1931,97643,2343],{},[898,97645,1762],{},[898,97647,2196],{"mathvariant":1791},[902,97649,97650],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,97652,97653],{},[614,97654,97655,97656,97686,97687,96539,97700,5857,97717,96570,97730,2196],{},"Obrázek 2.19: Posun ",[883,97657,97659],{"className":97658},[886],[888,97660,97661],{"xmlns":890},[892,97662,97663,97683],{},[895,97664,97665,97667,97669,97675,97677,97679,97681],{},[898,97666,4374],{},[1700,97668,3317],{},[2007,97670,97671,97673],{},[898,97672,4374],{},[1931,97674,2343],{},[1700,97676,1765],{},[898,97678,4374],{},[1700,97680,1768],{},[898,97682,2971],{},[902,97684,97685],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,97688,97690],{"className":97689},[886],[888,97691,97692],{"xmlns":890},[892,97693,97694,97698],{},[895,97695,97696],{},[898,97697,2971],{},[902,97699,2971],{"encoding":904},[883,97701,97703],{"className":97702},[886],[888,97704,97705],{"xmlns":890},[892,97706,97707,97715],{},[895,97708,97709],{},[2007,97710,97711,97713],{},[898,97712,4374],{},[1931,97714,2343],{},[902,97716,38512],{"encoding":904},[883,97718,97720],{"className":97719},[886],[888,97721,97722],{"xmlns":890},[892,97723,97724,97728],{},[895,97725,97726],{},[898,97727,8861],{},[902,97729,8861],{"encoding":904},[883,97731,97733],{"className":97732},[886],[888,97734,97735],{"xmlns":890},[892,97736,97737,97745],{},[895,97738,97739],{},[2007,97740,97741,97743],{},[898,97742,1762],{},[1931,97744,2343],{},[902,97746,97747],{"encoding":904},"E_2",[198,97749,45568],{"id":97750},"příklad-210",[724,97752,97753,97755,97756,41875,97779,97798,97799,97816],{},[38,97754,38118],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,97757,97759],{"className":97758},[886],[888,97760,97761],{"xmlns":890},[892,97762,97763,97777],{},[895,97764,97765,97767,97769,97771,97773,97775],{},[898,97766,1677],{},[1700,97768,1765],{},[1931,97770,3702],{},[1700,97772,1768],{},[1931,97774,2343],{},[898,97776,1662],{},[902,97778,96619],{"encoding":904},[883,97780,97782],{"className":97781},[886],[888,97783,97784],{"xmlns":890},[892,97785,97786,97796],{},[895,97787,97788,97790,97792,97794],{},[898,97789,1677],{},[1700,97791,1765],{},[1931,97793,2553],{},[898,97795,1662],{},[902,97797,96639],{"encoding":904},". Daň ",[883,97800,97802],{"className":97801},[886],[888,97803,97804],{"xmlns":890},[892,97805,97806,97814],{},[895,97807,97808,97810,97812],{},[898,97809,2971],{},[1700,97811,1765],{},[1931,97813,2445],{},[902,97815,41453],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,97818,97819],{},[38,97820,38150],{},[724,97822,97823,97824,96830],{},"Nová poptávka je ",[883,97825,97827],{"className":97826},[886],[888,97828,97829],{"xmlns":890},[892,97830,97831,97867],{},[895,97832,97833,97839,97841,97843,97845,97847,97849,97851,97853,97855,97857,97859,97861,97863,97865],{},[2007,97834,97835,97837],{},[898,97836,4374],{},[1931,97838,2343],{},[1700,97840,2901],{},[898,97842,1677],{},[1700,97844,1765],{},[1931,97846,3702],{},[1700,97848,1768],{},[1931,97850,2343],{},[898,97852,1662],{},[1700,97854,1768],{},[1931,97856,2445],{},[1700,97858,1765],{},[1931,97860,2445],{},[1700,97862,1768],{},[1931,97864,2343],{},[898,97866,1662],{},[902,97868,97869],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,97871,97873],{"className":97872},[886],[888,97874,97875],{"xmlns":890,"display":28251},[892,97876,97877,97893],{},[895,97878,97879,97881,97883,97885,97887,97889,97891],{},[1931,97880,2445],{},[1700,97882,1768],{},[1931,97884,2343],{},[898,97886,1662],{},[1700,97888,1765],{},[1931,97890,2553],{},[898,97892,1662],{},[902,97894,97895],{"encoding":904},"6 - 2Q = 4Q",[724,97897,96863,97898,5777,97917,1343,97941,96944,97973,2196],{},[883,97899,97901],{"className":97900},[886],[888,97902,97903],{"xmlns":890},[892,97904,97905,97915],{},[895,97906,97907,97909,97911,97913],{},[1931,97908,2445],{},[898,97910,1662],{},[1700,97912,1765],{},[1931,97914,2445],{},[902,97916,96883],{"encoding":904},[883,97918,97920],{"className":97919},[886],[888,97921,97922],{"xmlns":890},[892,97923,97924,97938],{},[895,97925,97926,97934,97936],{},[2030,97927,97928,97930,97932],{},[898,97929,1662],{},[1931,97931,2343],{},[898,97933,1762],{},[1700,97935,1765],{},[1931,97937,1933],{},[902,97939,97940],{"encoding":904},"Q_2^E = 1",[883,97942,97944],{"className":97943},[886],[888,97945,97946],{"xmlns":890},[892,97947,97948,97970],{},[895,97949,97950,97958,97960,97962,97964,97966,97968],{},[2030,97951,97952,97954,97956],{},[898,97953,1677],{},[1931,97955,2343],{},[898,97957,1762],{},[1700,97959,1765],{},[1931,97961,2553],{},[1700,97963,2065],{},[1931,97965,1933],{},[1700,97967,1765],{},[1931,97969,2553],{},[902,97971,97972],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,97974,97976],{"className":97975},[886],[888,97977,97978],{"xmlns":890},[892,97979,97980,97998],{},[895,97981,97982,97988,97990,97992,97994,97996],{},[2007,97983,97984,97986],{},[898,97985,1762],{},[1931,97987,2343],{},[1700,97989,1927],{"stretchy":1702},[1931,97991,1933],{},[1700,97993,1732],{"separator":1731},[1931,97995,2553],{},[1700,97997,1970],{"stretchy":1702},[902,97999,98000],{"encoding":904},"E_2[1, 4]",[724,98002,98003,98004,98040,98041,96658],{},"Spotřebitel platí celkem ",[883,98005,98007],{"className":98006},[886],[888,98008,98009],{"xmlns":890},[892,98010,98011,98037],{},[895,98012,98013,98021,98023,98025,98027,98029,98031,98033,98035],{},[2030,98014,98015,98017,98019],{},[898,98016,1677],{},[1931,98018,2343],{},[898,98020,1762],{},[1700,98022,1897],{},[898,98024,2971],{},[1700,98026,1765],{},[1931,98028,2553],{},[1700,98030,1897],{},[1931,98032,2445],{},[1700,98034,1765],{},[1931,98036,3058],{},[902,98038,98039],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,98042,98044],{"className":98043},[886],[888,98045,98046],{"xmlns":890},[892,98047,98048,98062],{},[895,98049,98050,98058,98060],{},[2030,98051,98052,98054,98056],{},[898,98053,1677],{},[1931,98055,2343],{},[898,98057,1762],{},[1700,98059,1765],{},[1931,98061,2553],{},[902,98063,98064],{"encoding":904},"P_2^E = 4",[724,98066,98067],{},[614,98068,98069],{},"Rozklad daňového břemene:",[883,98071,98073],{"className":98072},[886],[888,98074,98075],{"xmlns":890,"display":28251},[892,98076,98077,98163],{},[895,98078,98079,98089,98091,98093,98095,98097,98099,98101,98103,98105,98107,98109,98111,98121,98123,98125,98137,98139,98141,98143,98145,98147,98149,98151,98161],{},[2007,98080,98081,98083],{},[898,98082,2971],{},[895,98084,98085,98087],{},[898,98086,42862],{},[898,98088,724],{},[1700,98090,1765],{},[1700,98092,1703],{"stretchy":1702},[1931,98094,2553],{},[1700,98096,1897],{},[1931,98098,2445],{},[1700,98100,1709],{"stretchy":1702},[1700,98102,1768],{},[1931,98104,5773],{},[1700,98106,1765],{},[1931,98108,2343],{},[1781,98110,2495],{},[895,98112,98113,98115],{},[1781,98114,1735],{},[8574,98116,98117,98119],{"accent":1731},[1781,98118,2354],{},[1700,98120,25243],{},[1700,98122,1732],{"separator":1731},[6066,98124],{"width":6068},[2007,98126,98127,98129],{},[898,98128,2971],{},[895,98130,98131,98133,98135],{},[898,98132,42885],{},[898,98134,2215],{},[898,98136,12226],{},[1700,98138,1765],{},[1931,98140,5773],{},[1700,98142,1768],{},[1931,98144,2553],{},[1700,98146,1765],{},[1931,98148,2553],{},[1781,98150,2495],{},[895,98152,98153,98155],{},[1781,98154,1735],{},[8574,98156,98157,98159],{"accent":1731},[1781,98158,2354],{},[1700,98160,25243],{},[898,98162,2196],{"mathvariant":1791},[902,98164,98165],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,98167,98168,98169,2196],{},"Opět ",[883,98170,98172],{"className":98171},[886],[888,98173,98174],{"xmlns":890},[892,98175,98176,98210],{},[895,98177,98178,98188,98190,98202,98204,98206,98208],{},[2007,98179,98180,98182],{},[898,98181,2971],{},[895,98183,98184,98186],{},[898,98185,42862],{},[898,98187,724],{},[1700,98189,1897],{},[2007,98191,98192,98194],{},[898,98193,2971],{},[895,98195,98196,98198,98200],{},[898,98197,42885],{},[898,98199,2215],{},[898,98201,12226],{},[1700,98203,1765],{},[1931,98205,2445],{},[1700,98207,1765],{},[898,98209,2971],{},[902,98211,98212],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[37155,98214],{},[115,98216,42843],{"id":98217},"daňové-břemeno",[724,98219,98220,10208,98222,98225,98226,98239],{},[38,98221,42843],{},[614,98223,98224],{},"tax burden",") je rozdělení zaplacené daně ",[883,98227,98229],{"className":98228},[886],[888,98230,98231],{"xmlns":890},[892,98232,98233,98237],{},[895,98234,98235],{},[898,98236,2971],{},[902,98238,2971],{"encoding":904}," mezi spotřebitele a výrobce:",[883,98241,98243],{"className":98242},[886],[888,98244,98245],{"xmlns":890,"display":28251},[892,98246,98247,98279],{},[895,98248,98249,98251,98253,98263,98265,98277],{},[898,98250,2971],{},[1700,98252,1765],{},[2007,98254,98255,98257],{},[898,98256,2971],{},[895,98258,98259,98261],{},[898,98260,42862],{},[898,98262,724],{},[1700,98264,1897],{},[2007,98266,98267,98269],{},[898,98268,2971],{},[895,98270,98271,98273,98275],{},[898,98272,42885],{},[898,98274,2215],{},[898,98276,12226],{},[898,98278,2196],{"mathvariant":1791},[902,98280,98281],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,98283,98284],{},[2756,98285],{"alt":98286,"className":98287,"src":98288},"imek-dan-rozklad-bremene-sklony",[210,2760],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[4060,98290,98291],{},[724,98292,98293,98295,98296,2114,98309,2196],{},[883,98294,4346],{}," 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 ",[883,98297,98299],{"className":98298},[886],[888,98300,98301],{"xmlns":890},[892,98302,98303,98307],{},[895,98304,98305],{},[898,98306,4374],{},[902,98308,4374],{"encoding":904},[883,98310,98312],{"className":98311},[886],[888,98313,98314],{"xmlns":890},[892,98315,98316,98320],{},[895,98317,98318],{},[898,98319,8861],{},[902,98321,8861],{"encoding":904},[198,98323,2643],{"id":2642},[724,98325,98326,98327,98348,98349,98362,98363,98380,98381,98394],{},"V grafu ",[883,98328,98330],{"className":98329},[886],[888,98331,98332],{"xmlns":890},[892,98333,98334,98346],{},[895,98335,98336,98338,98340,98342,98344],{},[1700,98337,1703],{"stretchy":1702},[898,98339,1662],{},[1700,98341,1732],{"separator":1731},[898,98343,1677],{},[1700,98345,1709],{"stretchy":1702},[902,98347,37876],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,98350,98352],{"className":98351},[886],[888,98353,98354],{"xmlns":890},[892,98355,98356,98360],{},[895,98357,98358],{},[898,98359,2971],{},[902,98361,2971],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,98364,98366],{"className":98365},[886],[888,98367,98368],{"xmlns":890},[892,98369,98370,98378],{},[895,98371,98372],{},[1785,98373,98374,98376],{},[898,98375,1677],{},[898,98377,1762],{},[902,98379,41651],{"encoding":904},", rozdělí se úsečka ",[883,98382,98384],{"className":98383},[886],[888,98385,98386],{"xmlns":890},[892,98387,98388,98392],{},[895,98389,98390],{},[898,98391,2971],{},[902,98393,2971],{"encoding":904}," na dvě části:",[120,98396,98397,98422],{},[123,98398,98399,98400,98421],{},"horní část odpovídá ",[883,98401,98403],{"className":98402},[886],[888,98404,98405],{"xmlns":890},[892,98406,98407,98419],{},[895,98408,98409],{},[2007,98410,98411,98413],{},[898,98412,2971],{},[895,98414,98415,98417],{},[898,98416,42862],{},[898,98418,724],{},[902,98420,42867],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,98423,98424,98425,98448],{},"dolní část odpovídá ",[883,98426,98428],{"className":98427},[886],[888,98429,98430],{"xmlns":890},[892,98431,98432,98446],{},[895,98433,98434],{},[2007,98435,98436,98438],{},[898,98437,2971],{},[895,98439,98440,98442,98444],{},[898,98441,42885],{},[898,98443,2215],{},[898,98445,12226],{},[902,98447,42892],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,98450,98451],{},[614,98452,98453,98454,2882,98467,98488,98489,98512,98513,2114,98534,98557],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,98455,98457],{"className":98456},[886],[888,98458,98459],{"xmlns":890},[892,98460,98461,98465],{},[895,98462,98463],{},[898,98464,2971],{},[902,98466,2971],{"encoding":904},[883,98468,98470],{"className":98469},[886],[888,98471,98472],{"xmlns":890},[892,98473,98474,98486],{},[895,98475,98476],{},[2007,98477,98478,98480],{},[898,98479,2971],{},[895,98481,98482,98484],{},[898,98483,42862],{},[898,98485,724],{},[902,98487,42867],{"encoding":904}," (nahoře) a ",[883,98490,98492],{"className":98491},[886],[888,98493,98494],{"xmlns":890},[892,98495,98496,98510],{},[895,98497,98498],{},[2007,98499,98500,98502],{},[898,98501,2971],{},[895,98503,98504,98506,98508],{},[898,98505,42885],{},[898,98507,2215],{},[898,98509,12226],{},[902,98511,42892],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,98514,98516],{"className":98515},[886],[888,98517,98518],{"xmlns":890},[892,98519,98520,98532],{},[895,98521,98522],{},[2007,98523,98524,98526],{},[898,98525,2971],{},[895,98527,98528,98530],{},[898,98529,42862],{},[898,98531,724],{},[902,98533,42867],{"encoding":904},[883,98535,98537],{"className":98536},[886],[888,98538,98539],{"xmlns":890},[892,98540,98541,98555],{},[895,98542,98543],{},[2007,98544,98545,98547],{},[898,98546,2971],{},[895,98548,98549,98551,98553],{},[898,98550,42885],{},[898,98552,2215],{},[898,98554,12226],{},[902,98556,42892],{"encoding":904}," je v obou případech stejná.",[198,98559,98561],{"id":98560},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,98563,98564,98565,98568,98569,10208,98592,98609,98610,10208,98633,98650],{},"Platí obecně: ",[38,98566,98567],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,98570,98572],{"className":98571},[886],[888,98573,98574],{"xmlns":890},[892,98575,98576,98590],{},[895,98577,98578,98580,98582,98584,98586,98588],{},[898,98579,1677],{},[1700,98581,1765],{},[898,98583,207],{},[898,98585,1662],{},[1700,98587,1897],{},[898,98589,1879],{},[902,98591,37245],{"encoding":904},[883,98593,98595],{"className":98594},[886],[888,98596,98597],{"xmlns":890},[892,98598,98599,98607],{},[895,98600,98601,98603,98605],{},[898,98602,207],{},[1700,98604,3640],{},[1931,98606,1772],{},[902,98608,43270],{"encoding":904},") a lineární nabídku ",[883,98611,98613],{"className":98612},[886],[888,98614,98615],{"xmlns":890},[892,98616,98617,98631],{},[895,98618,98619,98621,98623,98625,98627,98629],{},[898,98620,1677],{},[1700,98622,1765],{},[898,98624,2354],{},[898,98626,1662],{},[1700,98628,1897],{},[898,98630,2406],{},[902,98632,40427],{"encoding":904},[883,98634,98636],{"className":98635},[886],[888,98637,98638],{"xmlns":890},[892,98639,98640,98648],{},[895,98641,98642,98644,98646],{},[898,98643,2354],{},[1700,98645,3601],{},[1931,98647,1772],{},[902,98649,40445],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,98652,98654],{"className":98653},[886],[888,98655,98656],{"xmlns":890,"display":28251},[892,98657,98658,98724],{},[895,98659,98660,98684,98686,98696,98698,98722],{},[1774,98661,98662,98672],{},[2007,98663,98664,98666],{},[898,98665,2971],{},[895,98667,98668,98670],{},[898,98669,42862],{},[898,98671,724],{},[2007,98673,98674,98676],{},[898,98675,2971],{},[895,98677,98678,98680,98682],{},[898,98679,42885],{},[898,98681,2215],{},[898,98683,12226],{},[1700,98685,1765],{},[1774,98687,98688,98690],{},[898,98689,2354],{},[895,98691,98692,98694],{},[1700,98693,1768],{},[898,98695,207],{},[1700,98697,1765],{},[1774,98699,98700,98712],{},[895,98701,98702,98705,98708,98710],{},[898,98703,98704],{"mathvariant":1791},"∣",[1781,98706,98707],{},"sklon ",[898,98709,8861],{},[898,98711,98704],{"mathvariant":1791},[895,98713,98714,98716,98718,98720],{},[898,98715,98704],{"mathvariant":1791},[1781,98717,98707],{},[898,98719,4374],{},[898,98721,98704],{"mathvariant":1791},[898,98723,2196],{"mathvariant":1791},[902,98725,98726],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[4060,98728,98729,98734],{},[724,98730,98731,98733],{},[883,98732,4761],{}," Postup výpočtu rozkladu",[152,98735,98736,98771,98824,98903],{},[123,98737,98738,98739,98770],{},"Spočti rovnovážný bod ",[883,98740,98742],{"className":98741},[886],[888,98743,98744],{"xmlns":890},[892,98745,98746,98768],{},[895,98747,98748,98750,98752,98758,98760,98766],{},[898,98749,1762],{},[1700,98751,1927],{"stretchy":1702},[1785,98753,98754,98756],{},[898,98755,1662],{},[898,98757,1762],{},[1700,98759,1732],{"separator":1731},[1785,98761,98762,98764],{},[898,98763,1677],{},[898,98765,1762],{},[1700,98767,1970],{"stretchy":1702},[902,98769,41552],{"encoding":904}," bez daně.",[123,98772,98773,98774,1348,98799,4110],{},"Urči posunutou křivku (",[883,98775,98777],{"className":98776},[886],[888,98778,98779],{"xmlns":890},[892,98780,98781,98797],{},[895,98782,98783,98789,98791,98793,98795],{},[2007,98784,98785,98787],{},[898,98786,8861],{},[1931,98788,1933],{},[1700,98790,1765],{},[898,98792,8861],{},[1700,98794,1897],{},[898,98796,2971],{},[902,98798,42939],{"encoding":904},[883,98800,98802],{"className":98801},[886],[888,98803,98804],{"xmlns":890},[892,98805,98806,98822],{},[895,98807,98808,98814,98816,98818,98820],{},[2007,98809,98810,98812],{},[898,98811,4374],{},[1931,98813,2343],{},[1700,98815,1765],{},[898,98817,4374],{},[1700,98819,1768],{},[898,98821,2971],{},[902,98823,42970],{"encoding":904},[123,98825,98826,98827,4102,98846,12313,98865,4102,98884,4110],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,98828,98830],{"className":98829},[886],[888,98831,98832],{"xmlns":890},[892,98833,98834,98844],{},[895,98835,98836],{},[2030,98837,98838,98840,98842],{},[898,98839,1662],{},[1931,98841,1933],{},[898,98843,1762],{},[902,98845,48021],{"encoding":904},[883,98847,98849],{"className":98848},[886],[888,98850,98851],{"xmlns":890},[892,98852,98853,98863],{},[895,98854,98855],{},[2030,98856,98857,98859,98861],{},[898,98858,1662],{},[1931,98860,2343],{},[898,98862,1762],{},[902,98864,48083],{"encoding":904},[883,98866,98868],{"className":98867},[886],[888,98869,98870],{"xmlns":890},[892,98871,98872,98882],{},[895,98873,98874],{},[2030,98875,98876,98878,98880],{},[898,98877,1677],{},[1931,98879,1933],{},[898,98881,1762],{},[902,98883,48042],{"encoding":904},[883,98885,98887],{"className":98886},[886],[888,98888,98889],{"xmlns":890},[892,98890,98891,98901],{},[895,98892,98893],{},[2030,98894,98895,98897,98899],{},[898,98896,1677],{},[1931,98898,2343],{},[898,98900,1762],{},[902,98902,48103],{"encoding":904},[123,98904,98905,98906,2114,98927,98950,98951,2196],{},"Dopočítej ",[883,98907,98909],{"className":98908},[886],[888,98910,98911],{"xmlns":890},[892,98912,98913,98925],{},[895,98914,98915],{},[2007,98916,98917,98919],{},[898,98918,2971],{},[895,98920,98921,98923],{},[898,98922,42862],{},[898,98924,724],{},[902,98926,42867],{"encoding":904},[883,98928,98930],{"className":98929},[886],[888,98931,98932],{"xmlns":890},[892,98933,98934,98948],{},[895,98935,98936],{},[2007,98937,98938,98940],{},[898,98939,2971],{},[895,98941,98942,98944,98946],{},[898,98943,42885],{},[898,98945,2215],{},[898,98947,12226],{},[902,98949,42892],{"encoding":904}," z definice, vždy ověř ",[883,98952,98954],{"className":98953},[886],[888,98955,98956],{"xmlns":890},[892,98957,98958,98988],{},[895,98959,98960,98970,98972,98984,98986],{},[2007,98961,98962,98964],{},[898,98963,2971],{},[895,98965,98966,98968],{},[898,98967,42862],{},[898,98969,724],{},[1700,98971,1897],{},[2007,98973,98974,98976],{},[898,98975,2971],{},[895,98977,98978,98980,98982],{},[898,98979,42885],{},[898,98981,2215],{},[898,98983,12226],{},[1700,98985,1765],{},[898,98987,2971],{},[902,98989,98990],{"encoding":904},"T_{sp} + T_{vyr} = T",[4060,98992,98993],{},[724,98994,98995,98997,98998,99001,99002,2114,99015,99028],{},[883,98996,4601],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,98999,99000],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,99003,99005],{"className":99004},[886],[888,99006,99007],{"xmlns":890},[892,99008,99009,99013],{},[895,99010,99011],{},[898,99012,4374],{},[902,99014,4374],{"encoding":904},[883,99016,99018],{"className":99017},[886],[888,99019,99020],{"xmlns":890},[892,99021,99022,99026],{},[895,99023,99024],{},[898,99025,8861],{},[902,99027,8861],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[37155,99030],{},[115,99032,99034],{"id":99033},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,99036,99037],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,99039,99040],{},[2756,99041],{"alt":99042,"className":99043,"src":99044},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,2760],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,99046,99047,99059],{},[19,99048,99049],{},[22,99050,99051,99053,99056],{},[25,99052,54480],{},[25,99054,99055],{},"(a) daň výrobci",[25,99057,99058],{},"(b) daň spotřebiteli",[30,99060,99061,99116,99183,99243],{},[22,99062,99063,99066,99091],{},[35,99064,99065],{},"Rovnovážné množství",[35,99067,99068],{},[883,99069,99071],{"className":99070},[886],[888,99072,99073],{"xmlns":890},[892,99074,99075,99089],{},[895,99076,99077,99085,99087],{},[2030,99078,99079,99081,99083],{},[898,99080,1662],{},[1931,99082,1933],{},[898,99084,1762],{},[1700,99086,1765],{},[1931,99088,1933],{},[902,99090,96907],{"encoding":904},[35,99092,99093],{},[883,99094,99096],{"className":99095},[886],[888,99097,99098],{"xmlns":890},[892,99099,99100,99114],{},[895,99101,99102,99110,99112],{},[2030,99103,99104,99106,99108],{},[898,99105,1662],{},[1931,99107,2343],{},[898,99109,1762],{},[1700,99111,1765],{},[1931,99113,1933],{},[902,99115,97940],{"encoding":904},[22,99117,99118,99121,99146],{},[35,99119,99120],{},"Cena placená spotřebitelem",[35,99122,99123],{},[883,99124,99126],{"className":99125},[886],[888,99127,99128],{"xmlns":890},[892,99129,99130,99144],{},[895,99131,99132,99140,99142],{},[2030,99133,99134,99136,99138],{},[898,99135,1677],{},[1931,99137,1933],{},[898,99139,1762],{},[1700,99141,1765],{},[1931,99143,3058],{},[902,99145,97002],{"encoding":904},[35,99147,99148],{},[883,99149,99151],{"className":99150},[886],[888,99152,99153],{"xmlns":890},[892,99154,99155,99181],{},[895,99156,99157,99165,99167,99169,99171,99173,99175,99177,99179],{},[2030,99158,99159,99161,99163],{},[898,99160,1677],{},[1931,99162,2343],{},[898,99164,1762],{},[1700,99166,1897],{},[898,99168,2971],{},[1700,99170,1765],{},[1931,99172,2553],{},[1700,99174,1897],{},[1931,99176,2445],{},[1700,99178,1765],{},[1931,99180,3058],{},[902,99182,98039],{"encoding":904},[22,99184,99185,99188,99218],{},[35,99186,99187],{},"Cena přijímaná výrobcem",[35,99189,99190],{},[883,99191,99193],{"className":99192},[886],[888,99194,99195],{"xmlns":890},[892,99196,99197,99215],{},[895,99198,99199,99207,99209,99211,99213],{},[2030,99200,99201,99203,99205],{},[898,99202,1677],{},[1931,99204,1933],{},[898,99206,1762],{},[1700,99208,1768],{},[898,99210,2971],{},[1700,99212,1765],{},[1931,99214,2553],{},[902,99216,99217],{"encoding":904},"P_1^E - T = 4",[35,99219,99220],{},[883,99221,99223],{"className":99222},[886],[888,99224,99225],{"xmlns":890},[892,99226,99227,99241],{},[895,99228,99229,99237,99239],{},[2030,99230,99231,99233,99235],{},[898,99232,1677],{},[1931,99234,2343],{},[898,99236,1762],{},[1700,99238,1765],{},[1931,99240,2553],{},[902,99242,98064],{"encoding":904},[22,99244,99245,99248,99302],{},[35,99246,99247],{},"Rozklad břemene",[35,99249,99250,1343,99275],{},[883,99251,99253],{"className":99252},[886],[888,99254,99255],{"xmlns":890},[892,99256,99257,99273],{},[895,99258,99259,99269,99271],{},[2007,99260,99261,99263],{},[898,99262,2971],{},[895,99264,99265,99267],{},[898,99266,42862],{},[898,99268,724],{},[1700,99270,1765],{},[1931,99272,2343],{},[902,99274,43161],{"encoding":904},[883,99276,99278],{"className":99277},[886],[888,99279,99280],{"xmlns":890},[892,99281,99282,99300],{},[895,99283,99284,99296,99298],{},[2007,99285,99286,99288],{},[898,99287,2971],{},[895,99289,99290,99292,99294],{},[898,99291,42885],{},[898,99293,2215],{},[898,99295,12226],{},[1700,99297,1765],{},[1931,99299,2553],{},[902,99301,43190],{"encoding":904},[35,99303,99304,1343,99329],{},[883,99305,99307],{"className":99306},[886],[888,99308,99309],{"xmlns":890},[892,99310,99311,99327],{},[895,99312,99313,99323,99325],{},[2007,99314,99315,99317],{},[898,99316,2971],{},[895,99318,99319,99321],{},[898,99320,42862],{},[898,99322,724],{},[1700,99324,1765],{},[1931,99326,2343],{},[902,99328,43161],{"encoding":904},[883,99330,99332],{"className":99331},[886],[888,99333,99334],{"xmlns":890},[892,99335,99336,99354],{},[895,99337,99338,99350,99352],{},[2007,99339,99340,99342],{},[898,99341,2971],{},[895,99343,99344,99346,99348],{},[898,99345,42885],{},[898,99347,2215],{},[898,99349,12226],{},[1700,99351,1765],{},[1931,99353,2553],{},[902,99355,43190],{"encoding":904},[724,99357,99358],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,99360,99362],{"className":99361},[886],[888,99363,99364],{"xmlns":890,"display":28251},[892,99365,99366,99414],{},[895,99367,99368,99376,99378,99386,99388,99390,99398,99400,99402,99404,99412],{},[2030,99369,99370,99372,99374],{},[898,99371,1662],{},[1931,99373,1933],{},[898,99375,1762],{},[1700,99377,1765],{},[2030,99379,99380,99382,99384],{},[898,99381,1662],{},[1931,99383,2343],{},[898,99385,1762],{},[1700,99387,1732],{"separator":1731},[6066,99389],{"width":6068},[2030,99391,99392,99394,99396],{},[898,99393,1677],{},[1931,99395,1933],{},[898,99397,1762],{},[1700,99399,1768],{},[898,99401,2971],{},[1700,99403,1765],{},[2030,99405,99406,99408,99410],{},[898,99407,1677],{},[1931,99409,2343],{},[898,99411,1762],{},[898,99413,2196],{"mathvariant":1791},[902,99415,99416],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[4060,99418,99419,99438,99592],{},[724,99420,99421,99423,99424,99437],{},[883,99422,4761],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,99425,99427],{"className":99426},[886],[888,99428,99429],{"xmlns":890},[892,99430,99431,99435],{},[895,99432,99433],{},[898,99434,2971],{},[902,99436,2971],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,99439,99440,99472,99508,99545],{},[123,99441,99442,99443,1732],{},"rovnovážná množství obou režimů, ",[883,99444,99446],{"className":99445},[886],[888,99447,99448],{"xmlns":890},[892,99449,99450,99470],{},[895,99451,99452,99460,99462],{},[2030,99453,99454,99456,99458],{},[898,99455,1662],{},[1931,99457,1933],{},[898,99459,1762],{},[1700,99461,1765],{},[2030,99463,99464,99466,99468],{},[898,99465,1662],{},[1931,99467,2343],{},[898,99469,1762],{},[902,99471,43093],{"encoding":904},[123,99473,99474,99475,1732],{},"čistá cena přijímaná výrobcem, ",[883,99476,99478],{"className":99477},[886],[888,99479,99480],{"xmlns":890},[892,99481,99482,99506],{},[895,99483,99484,99492,99494,99496,99498],{},[2030,99485,99486,99488,99490],{},[898,99487,1677],{},[1931,99489,1933],{},[898,99491,1762],{},[1700,99493,1768],{},[898,99495,2971],{},[1700,99497,1765],{},[2030,99499,99500,99502,99504],{},[898,99501,1677],{},[1931,99503,2343],{},[898,99505,1762],{},[902,99507,43127],{"encoding":904},[123,99509,99510,99511,1732],{},"celková cena placená spotřebitelem, ",[883,99512,99514],{"className":99513},[886],[888,99515,99516],{"xmlns":890},[892,99517,99518,99542],{},[895,99519,99520,99528,99530,99538,99540],{},[2030,99521,99522,99524,99526],{},[898,99523,1677],{},[1931,99525,1933],{},[898,99527,1762],{},[1700,99529,1765],{},[2030,99531,99532,99534,99536],{},[898,99533,1677],{},[1931,99535,2343],{},[898,99537,1762],{},[1700,99539,1897],{},[898,99541,2971],{},[902,99543,99544],{"encoding":904},"P_1^E = P_2^E + T",[123,99546,99547,99548,2114,99569,2196],{},"rozklad daňového břemene ",[883,99549,99551],{"className":99550},[886],[888,99552,99553],{"xmlns":890},[892,99554,99555,99567],{},[895,99556,99557],{},[2007,99558,99559,99561],{},[898,99560,2971],{},[895,99562,99563,99565],{},[898,99564,42862],{},[898,99566,724],{},[902,99568,42867],{"encoding":904},[883,99570,99572],{"className":99571},[886],[888,99573,99574],{"xmlns":890},[892,99575,99576,99590],{},[895,99577,99578],{},[2007,99579,99580,99582],{},[898,99581,2971],{},[895,99583,99584,99586,99588],{},[898,99585,42885],{},[898,99587,2215],{},[898,99589,12226],{},[902,99591,42892],{"encoding":904},[724,99593,99594,99595,2196],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,99596,35382],{},[724,99598,99599,99600,2114,99613,4110],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,99601,99603],{"className":99602},[886],[888,99604,99605],{"xmlns":890},[892,99606,99607,99611],{},[895,99608,99609],{},[898,99610,4374],{},[902,99612,4374],{"encoding":904},[883,99614,99616],{"className":99615},[886],[888,99617,99618],{"xmlns":890},[892,99619,99620,99624],{},[895,99621,99622],{},[898,99623,8861],{},[902,99625,8861],{"encoding":904},[37155,99627],{},[115,99629,99631],{"id":99630},"úlohy","Úlohy",[724,99633,99634,99635,3345],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,99636,16425],{"className":99637,"dataFsResolvedFilePath":800,"href":801},[210],[120,99639,99640,99670,99701],{},[123,99641,99642,99645,99646,99669],{},[38,99643,99644],{},"Úloha 2.4"," — Poptávka ",[883,99647,99649],{"className":99648},[886],[888,99650,99651],{"xmlns":890},[892,99652,99653,99667],{},[895,99654,99655,99657,99659,99661,99663,99665],{},[898,99656,1677],{},[1700,99658,1765],{},[1931,99660,3702],{},[1700,99662,1768],{},[1931,99664,2343],{},[898,99666,1662],{},[902,99668,96619],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,99671,99672,99675,99676,99700],{},[38,99673,99674],{},"Úloha 2.9"," — Nabídka ",[883,99677,99679],{"className":99678},[886],[888,99680,99681],{"xmlns":890},[892,99682,99683,99697],{},[895,99684,99685,99687,99689,99691,99693,99695],{},[898,99686,1677],{},[1700,99688,1765],{},[1931,99690,5197],{},[898,99692,1662],{},[1700,99694,1897],{},[1931,99696,36429],{},[902,99698,99699],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,99702,99703,99706,99707,2114,99733,99757,99758,99775],{},[38,99704,99705],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,99708,99710],{"className":99709},[886],[888,99711,99712],{"xmlns":890},[892,99713,99714,99730],{},[895,99715,99716,99718,99720,99722,99724,99726,99728],{},[898,99717,1677],{},[1700,99719,1765],{},[1700,99721,1768],{},[1931,99723,2553],{},[898,99725,1662],{},[1700,99727,1897],{},[1931,99729,46888],{},[902,99731,99732],{"encoding":904},"P = -4Q + 80",[883,99734,99736],{"className":99735},[886],[888,99737,99738],{"xmlns":890},[892,99739,99740,99754],{},[895,99741,99742,99744,99746,99748,99750,99752],{},[898,99743,1677],{},[1700,99745,1765],{},[1931,99747,2385],{},[898,99749,1662],{},[1700,99751,1897],{},[1931,99753,3058],{},[902,99755,99756],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,99759,99761],{"className":99760},[886],[888,99762,99763],{"xmlns":890},[892,99764,99765,99773],{},[895,99766,99767,99769,99771],{},[898,99768,2971],{},[1700,99770,1765],{},[1931,99772,24386],{},[902,99774,48000],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,99777,99778,99779,99781,99782,99784],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,99780,45413],{}," (posun poptávky při zdanění kupujícího) a ",[38,99783,45447],{}," (posun nabídky při zdanění výrobce).",[37155,99786],{},[115,99788,15905],{"id":15904},[120,99790,99791,99810,99868,99925,100008,100054,100097,100142,100208],{},[123,99792,99793,2106,99796,99809],{},[38,99794,99795],{},"Jednotková daň",[883,99797,99799],{"className":99798},[886],[888,99800,99801],{"xmlns":890},[892,99802,99803,99807],{},[895,99804,99805],{},[898,99806,2971],{},[902,99808,2971],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,99811,99812,99814,99815,99853,99854,99867],{},[38,99813,96201],{}," — posun nabídky ",[883,99816,99818],{"className":99817},[886],[888,99819,99820],{"xmlns":890},[892,99821,99822,99850],{},[895,99823,99824,99830,99832,99834,99836,99838,99840,99842,99844,99846,99848],{},[2007,99825,99826,99828],{},[898,99827,8861],{},[1931,99829,1933],{},[1700,99831,1703],{"stretchy":1702},[898,99833,1662],{},[1700,99835,1709],{"stretchy":1702},[1700,99837,1765],{},[898,99839,8861],{},[1700,99841,1703],{"stretchy":1702},[898,99843,1662],{},[1700,99845,1709],{"stretchy":1702},[1700,99847,1897],{},[898,99849,2971],{},[902,99851,99852],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,99855,99857],{"className":99856},[886],[888,99858,99859],{"xmlns":890},[892,99860,99861,99865],{},[895,99862,99863],{},[898,99864,2971],{},[902,99866,2971],{"encoding":904}," svisle nahoru)",[123,99869,99870,99872,99873,99853,99911,99924],{},[38,99871,97274],{}," — posun poptávky ",[883,99874,99876],{"className":99875},[886],[888,99877,99878],{"xmlns":890},[892,99879,99880,99908],{},[895,99881,99882,99888,99890,99892,99894,99896,99898,99900,99902,99904,99906],{},[2007,99883,99884,99886],{},[898,99885,4374],{},[1931,99887,2343],{},[1700,99889,1703],{"stretchy":1702},[898,99891,1662],{},[1700,99893,1709],{"stretchy":1702},[1700,99895,1765],{},[898,99897,4374],{},[1700,99899,1703],{"stretchy":1702},[898,99901,1662],{},[1700,99903,1709],{"stretchy":1702},[1700,99905,1768],{},[898,99907,2971],{},[902,99909,99910],{"encoding":904},"D_2(Q) = D(Q) - T",[883,99912,99914],{"className":99913},[886],[888,99915,99916],{"xmlns":890},[892,99917,99918,99922],{},[895,99919,99920],{},[898,99921,2971],{},[902,99923,2971],{"encoding":904}," svisle dolů)",[123,99926,99927,7203,99930,41999,99969],{},[38,99928,99929],{},"Rovnovážný bod s daní",[883,99931,99933],{"className":99932},[886],[888,99934,99935],{"xmlns":890},[892,99936,99937,99967],{},[895,99938,99939,99945,99947,99955,99957,99965],{},[2007,99940,99941,99943],{},[898,99942,1762],{},[1931,99944,1933],{},[1700,99946,1927],{"stretchy":1702},[2030,99948,99949,99951,99953],{},[898,99950,1662],{},[1931,99952,1933],{},[898,99954,1762],{},[1700,99956,1732],{"separator":1731},[2030,99958,99959,99961,99963],{},[898,99960,1677],{},[1931,99962,1933],{},[898,99964,1762],{},[1700,99966,1970],{"stretchy":1702},[902,99968,96369],{"encoding":904},[883,99970,99972],{"className":99971},[886],[888,99973,99974],{"xmlns":890},[892,99975,99976,100006],{},[895,99977,99978,99984,99986,99994,99996,100004],{},[2007,99979,99980,99982],{},[898,99981,1762],{},[1931,99983,2343],{},[1700,99985,1927],{"stretchy":1702},[2030,99987,99988,99990,99992],{},[898,99989,1662],{},[1931,99991,2343],{},[898,99993,1762],{},[1700,99995,1732],{"separator":1731},[2030,99997,99998,100000,100002],{},[898,99999,1677],{},[1931,100001,2343],{},[898,100003,1762],{},[1700,100005,1970],{"stretchy":1702},[902,100007,97444],{"encoding":904},[123,100009,100010,10208,100012,100014,100015],{},[38,100011,42843],{},[614,100013,98224],{},") — rozklad ",[883,100016,100018],{"className":100017},[886],[888,100019,100020],{"xmlns":890},[892,100021,100022,100052],{},[895,100023,100024,100026,100028,100038,100040],{},[898,100025,2971],{},[1700,100027,1765],{},[2007,100029,100030,100032],{},[898,100031,2971],{},[895,100033,100034,100036],{},[898,100035,42862],{},[898,100037,724],{},[1700,100039,1897],{},[2007,100041,100042,100044],{},[898,100043,2971],{},[895,100045,100046,100048,100050],{},[898,100047,42885],{},[898,100049,2215],{},[898,100051,12226],{},[902,100053,43029],{"encoding":904},[123,100055,100056,100079,100080,1709],{},[38,100057,100058],{},[883,100059,100061],{"className":100060},[886],[888,100062,100063],{"xmlns":890},[892,100064,100065,100077],{},[895,100066,100067],{},[2007,100068,100069,100071],{},[898,100070,2971],{},[895,100072,100073,100075],{},[898,100074,42862],{},[898,100076,724],{},[902,100078,42867],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,100081,100083],{"className":100082},[886],[888,100084,100085],{"xmlns":890},[892,100086,100087,100095],{},[895,100088,100089],{},[1785,100090,100091,100093],{},[898,100092,1677],{},[898,100094,1762],{},[902,100096,41651],{"encoding":904},[123,100098,100099,100124,100125,1709],{},[38,100100,100101],{},[883,100102,100104],{"className":100103},[886],[888,100105,100106],{"xmlns":890},[892,100107,100108,100122],{},[895,100109,100110],{},[2007,100111,100112,100114],{},[898,100113,2971],{},[895,100115,100116,100118,100120],{},[898,100117,42885],{},[898,100119,2215],{},[898,100121,12226],{},[902,100123,42892],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,100126,100128],{"className":100127},[886],[888,100129,100130],{"xmlns":890},[892,100131,100132,100140],{},[895,100133,100134],{},[1785,100135,100136,100138],{},[898,100137,1677],{},[898,100139,1762],{},[902,100141,41651],{"encoding":904},[123,100143,100144,7203,100146,1343,100175],{},[38,100145,50659],{},[883,100147,100149],{"className":100148},[886],[888,100150,100151],{"xmlns":890},[892,100152,100153,100173],{},[895,100154,100155,100163,100165],{},[2030,100156,100157,100159,100161],{},[898,100158,1662],{},[1931,100160,1933],{},[898,100162,1762],{},[1700,100164,1765],{},[2030,100166,100167,100169,100171],{},[898,100168,1662],{},[1931,100170,2343],{},[898,100172,1762],{},[902,100174,43093],{"encoding":904},[883,100176,100178],{"className":100177},[886],[888,100179,100180],{"xmlns":890},[892,100181,100182,100206],{},[895,100183,100184,100192,100194,100196,100198],{},[2030,100185,100186,100188,100190],{},[898,100187,1677],{},[1931,100189,1933],{},[898,100191,1762],{},[1700,100193,1768],{},[898,100195,2971],{},[1700,100197,1765],{},[2030,100199,100200,100202,100204],{},[898,100201,1677],{},[1931,100203,2343],{},[898,100205,1762],{},[902,100207,43127],{"encoding":904},[123,100209,100210,100213],{},[38,100211,100212],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[37155,100215],{},[115,100217,3985],{"id":3984},[120,100219,100220,100228,100246,100253],{},[123,100221,100222,2106,100225],{},[38,100223,100224],{},"Kontext (hub):",[207,100226,802],{"className":100227,"dataFsResolvedFilePath":800,"href":801},[210],[123,100229,100230,2106,100232,100235,100236,18833,100238,100241,100242,100245],{},[38,100231,50908],{},[207,100233,820],{"className":100234,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,100237,55218],{},[207,100239,2559],{"className":100240,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,100243,1649],{"className":100244,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran 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