[{"data":1,"prerenderedAt":101261},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-funkce-vice-promennych":1626,"course-stats-imek":3255,"course-topics-imek":3259,"backlinks-funkce-vice-promennych":101232,"related-funkce-vice-promennych":101258},{"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":3254},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":1129,"description":3240,"extension":661,"meta":3241,"navigation":664,"path":3242,"seo":3243,"sources":3244,"stem":3245,"tags":3246,"type":3252,"updated":677,"__hash__":3253},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":1631,"toc":3225},[1632,1635,1720,1729,1733,1798,1892,1896,1923,1997,2055,2059,2087,2183,2187,2219,2393,2397,2469,2519,2523,2585,2693,2709,2713,2717,2748,2814,2818,2825,2915,2940,3144,3148,3184,3188],[12,1633,1629],{"id":1634},"kalkul-funkcí-více-proměnných",[724,1636,1637,1638,1641,1642,1343,1681,1719],{},"Většina ekonomických veličin závisí na ",[38,1639,1640],{},"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 ",[883,1643,1645],{"className":1644},[886],[888,1646,1647],{"xmlns":890},[892,1648,1649,1678],{},[895,1650,1651,1654,1658,1661,1665,1668,1672,1675],{},[898,1652,1653],{},"z",[1655,1656,1657],"mo",{},"=",[898,1659,1660],{},"f",[1655,1662,1664],{"stretchy":1663},"false","(",[898,1666,1667],{},"x",[1655,1669,1671],{"separator":1670},"true",",",[898,1673,1674],{},"y",[1655,1676,1677],{"stretchy":1663},")",[902,1679,1680],{"encoding":904},"z = f(x, y)",[883,1682,1684],{"className":1683},[886],[888,1685,1686],{"xmlns":890},[892,1687,1688,1716],{},[895,1689,1690,1693,1695,1697,1699,1701,1703,1705,1707,1709,1711,1713],{},[898,1691,1692],{},"w",[1655,1694,1657],{},[898,1696,1660],{},[1655,1698,1664],{"stretchy":1663},[898,1700,1667],{},[1655,1702,1671],{"separator":1670},[898,1704,1674],{},[1655,1706,1671],{"separator":1670},[898,1708,1653],{},[1655,1710,1677],{"stretchy":1663},[1655,1712,1671],{"separator":1670},[1655,1714,1715],{},"…",[902,1717,1718],{"encoding":904},"w = f(x, y, z), \\ldots",".",[724,1721,1722],{},[1723,1724],"img",{"alt":1725,"className":1726,"src":1728},"imek-funkce-2d-vrstevnice",[210,1727],"wikilink-broken","\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,1730,1732],{"id":1731},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,1734,1735,1736,1763,1764,1793,1794,1797],{},"Pro ",[883,1737,1739],{"className":1738},[886],[888,1740,1741],{"xmlns":890},[892,1742,1743,1761],{},[895,1744,1745,1747,1749,1751,1753,1755,1757,1759],{},[898,1746,1653],{},[1655,1748,1657],{},[898,1750,1660],{},[1655,1752,1664],{"stretchy":1663},[898,1754,1667],{},[1655,1756,1671],{"separator":1670},[898,1758,1674],{},[1655,1760,1677],{"stretchy":1663},[902,1762,1680],{"encoding":904}," se křivkou s předpisem ",[883,1765,1767],{"className":1766},[886],[888,1768,1769],{"xmlns":890},[892,1770,1771,1790],{},[895,1772,1773,1775,1777,1779,1781,1783,1785,1787],{},[898,1774,1660],{},[1655,1776,1664],{"stretchy":1663},[898,1778,1667],{},[1655,1780,1671],{"separator":1670},[898,1782,1674],{},[1655,1784,1677],{"stretchy":1663},[1655,1786,1657],{},[898,1788,1789],{},"c",[902,1791,1792],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,1795,1796],{},"vrstevnice"," funkce. V ekonomii:",[120,1799,1800,1852],{},[123,1801,1802,1805,1806,1847,1848,1719],{},[38,1803,1804],{},"Indiferenční křivky"," užitečnosti ",[883,1807,1809],{"className":1808},[886],[888,1810,1811],{"xmlns":890},[892,1812,1813,1844],{},[895,1814,1815,1817,1819,1829,1831,1838,1840,1842],{},[898,1816,900],{},[1655,1818,1664],{"stretchy":1663},[1820,1821,1822,1825],"msub",{},[898,1823,1824],{},"Q",[1826,1827,1828],"mn",{},"1",[1655,1830,1671],{"separator":1670},[1820,1832,1833,1835],{},[898,1834,1824],{},[1826,1836,1837],{},"2",[1655,1839,1677],{"stretchy":1663},[1655,1841,1657],{},[898,1843,1789],{},[902,1845,1846],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,1849,1851],{"className":1850,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,1853,1854,1857,1858,1847,1888,1719],{},[38,1855,1856],{},"Izokvanty"," produkce ",[883,1859,1861],{"className":1860},[886],[888,1862,1863],{"xmlns":890},[892,1864,1865,1885],{},[895,1866,1867,1869,1871,1874,1876,1879,1881,1883],{},[898,1868,1824],{},[1655,1870,1664],{"stretchy":1663},[898,1872,1873],{},"L",[1655,1875,1671],{"separator":1670},[898,1877,1878],{},"K",[1655,1880,1677],{"stretchy":1663},[1655,1882,1657],{},[898,1884,1789],{},[902,1886,1887],{"encoding":904},"Q(L, K) = c",[207,1889,1891],{"className":1890,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,1893,1895],{"id":1894},"parciální-derivace","Parciální derivace",[724,1897,1735,1898,1922],{},[883,1899,1901],{"className":1900},[886],[888,1902,1903],{"xmlns":890},[892,1904,1905,1919],{},[895,1906,1907,1909,1911,1913,1915,1917],{},[898,1908,1660],{},[1655,1910,1664],{"stretchy":1663},[898,1912,1667],{},[1655,1914,1671],{"separator":1670},[898,1916,1674],{},[1655,1918,1677],{"stretchy":1663},[902,1920,1921],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,1924,1925],{},[883,1926,1928],{"className":1927},[886],[888,1929,1930],{"xmlns":890},[892,1931,1932,1994],{},[895,1933,1934,1946,1948,1964,1966,1970,1978,1980],{},[1935,1936,1937,1939,1941],"msubsup",{},[898,1938,1660],{},[898,1940,1667],{},[1655,1942,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},"normal","0em","′",[1655,1947,1657],{},[1949,1950,1951,1958],"mfrac",{},[895,1952,1953,1956],{},[898,1954,1955],{"mathvariant":1943},"∂",[898,1957,1660],{},[895,1959,1960,1962],{},[898,1961,1955],{"mathvariant":1943},[898,1963,1667],{},[1655,1965,1671],{"separator":1670},[1967,1968],"mspace",{"width":1969},"2em",[1935,1971,1972,1974,1976],{},[898,1973,1660],{},[898,1975,1674],{},[1655,1977,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,1979,1657],{},[1949,1981,1982,1988],{},[895,1983,1984,1986],{},[898,1985,1955],{"mathvariant":1943},[898,1987,1660],{},[895,1989,1990,1992],{},[898,1991,1955],{"mathvariant":1943},[898,1993,1674],{},[902,1995,1996],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,1998,1999,2000,1719],{},"Hodnoty v bodě: ",[883,2001,2003],{"className":2002},[886],[888,2004,2005],{"xmlns":890},[892,2006,2007,2052],{},[895,2008,2009,2017,2019,2021,2023,2026,2028,2030,2034,2042,2044,2046,2048,2050],{},[1935,2010,2011,2013,2015],{},[898,2012,1660],{},[898,2014,1667],{},[1655,2016,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,2018,1664],{"stretchy":1663},[898,2020,207],{},[1655,2022,1671],{"separator":1670},[898,2024,2025],{},"b",[1655,2027,1677],{"stretchy":1663},[1655,2029,1671],{"separator":1670},[2031,2032,2033],"mtext",{}," ",[1935,2035,2036,2038,2040],{},[898,2037,1660],{},[898,2039,1674],{},[1655,2041,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,2043,1664],{"stretchy":1663},[898,2045,207],{},[1655,2047,1671],{"separator":1670},[898,2049,2025],{},[1655,2051,1677],{"stretchy":1663},[902,2053,2054],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,2056,2058],{"id":2057},"ekonomické-značení","Ekonomické značení",[724,2060,2061,2062,2086],{},"Pro produkční funkci ",[883,2063,2065],{"className":2064},[886],[888,2066,2067],{"xmlns":890},[892,2068,2069,2083],{},[895,2070,2071,2073,2075,2077,2079,2081],{},[898,2072,1824],{},[1655,2074,1664],{"stretchy":1663},[898,2076,1873],{},[1655,2078,1671],{"separator":1670},[898,2080,1878],{},[1655,2082,1677],{"stretchy":1663},[902,2084,2085],{"encoding":904},"Q(L, K)",":",[120,2088,2089,2138],{},[123,2090,2091,2111,2112,2115,2116,1677],{},[883,2092,2094],{"className":2093},[886],[888,2095,2096],{"xmlns":890},[892,2097,2098,2108],{},[895,2099,2100],{},[1935,2101,2102,2104,2106],{},[898,2103,1824],{},[898,2105,1873],{},[1655,2107,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,2109,2110],{"encoding":904},"Q'_L"," = ",[38,2113,2114],{},"mezní produkt práce"," (",[883,2117,2119],{"className":2118},[886],[888,2120,2121],{"xmlns":890},[892,2122,2123,2135],{},[895,2124,2125,2128],{},[898,2126,2127],{},"M",[1820,2129,2130,2133],{},[898,2131,2132],{},"P",[898,2134,1873],{},[902,2136,2137],{"encoding":904},"MP_L",[123,2139,2140,2111,2160,2115,2163,1677],{},[883,2141,2143],{"className":2142},[886],[888,2144,2145],{"xmlns":890},[892,2146,2147,2157],{},[895,2148,2149],{},[1935,2150,2151,2153,2155],{},[898,2152,1824],{},[898,2154,1878],{},[1655,2156,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,2158,2159],{"encoding":904},"Q'_K",[38,2161,2162],{},"mezní produkt kapitálu",[883,2164,2166],{"className":2165},[886],[888,2167,2168],{"xmlns":890},[892,2169,2170,2180],{},[895,2171,2172,2174],{},[898,2173,2127],{},[1820,2175,2176,2178],{},[898,2177,2132],{},[898,2179,1878],{},[902,2181,2182],{"encoding":904},"MP_K",[198,2184,2186],{"id":2185},"inženýrská-interpretace","Inženýrská interpretace",[724,2188,2189,2086],{},[883,2190,2192],{"className":2191},[886],[888,2193,2194],{"xmlns":890},[892,2195,2196,2216],{},[895,2197,2198,2206,2208,2210,2212,2214],{},[1935,2199,2200,2202,2204],{},[898,2201,1660],{},[898,2203,1667],{},[1655,2205,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,2207,1664],{"stretchy":1663},[898,2209,207],{},[1655,2211,1671],{"separator":1670},[898,2213,2025],{},[1655,2215,1677],{"stretchy":1663},[902,2217,2218],{"encoding":904},"f'_x(a, b)",[120,2220,2221,2279],{},[123,2222,2223,2224,2237,2238,2251,2252,2278],{},"rychlost změny ",[883,2225,2227],{"className":2226},[886],[888,2228,2229],{"xmlns":890},[892,2230,2231,2235],{},[895,2232,2233],{},[898,2234,1660],{},[902,2236,1660],{"encoding":904}," vůči ",[883,2239,2241],{"className":2240},[886],[888,2242,2243],{"xmlns":890},[892,2244,2245,2249],{},[895,2246,2247],{},[898,2248,1667],{},[902,2250,1667],{"encoding":904}," při ",[883,2253,2255],{"className":2254},[886],[888,2256,2257],{"xmlns":890},[892,2258,2259,2275],{},[895,2260,2261,2263,2265,2267,2269,2271,2273],{},[898,2262,1667],{},[1655,2264,1657],{},[898,2266,207],{},[1655,2268,1671],{"separator":1670},[898,2270,1674],{},[1655,2272,1657],{},[898,2274,2025],{},[902,2276,2277],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,2280,2281,2282,2295,2296,2309,2310,2328,2329,1719],{},"přibližná změna ",[883,2283,2285],{"className":2284},[886],[888,2286,2287],{"xmlns":890},[892,2288,2289,2293],{},[895,2290,2291],{},[898,2292,1660],{},[902,2294,1660],{"encoding":904}," při změně ",[883,2297,2299],{"className":2298},[886],[888,2300,2301],{"xmlns":890},[892,2302,2303,2307],{},[895,2304,2305],{},[898,2306,1667],{},[902,2308,1667],{"encoding":904}," o 1 (a pevném ",[883,2311,2313],{"className":2312},[886],[888,2314,2315],{"xmlns":890},[892,2316,2317,2325],{},[895,2318,2319,2321,2323],{},[898,2320,1674],{},[1655,2322,1657],{},[898,2324,2025],{},[902,2326,2327],{"encoding":904},"y = b","): ",[883,2330,2332],{"className":2331},[886],[888,2333,2334],{"xmlns":890},[892,2335,2336,2390],{},[895,2337,2338,2340,2342,2344,2347,2349,2351,2353,2355,2358,2360,2362,2364,2366,2368,2370,2372,2380,2382,2384,2386,2388],{},[898,2339,1660],{},[1655,2341,1664],{"stretchy":1663},[898,2343,207],{},[1655,2345,2346],{},"+",[1826,2348,1828],{},[1655,2350,1671],{"separator":1670},[898,2352,2025],{},[1655,2354,1677],{"stretchy":1663},[1655,2356,2357],{},"≈",[898,2359,1660],{},[1655,2361,1664],{"stretchy":1663},[898,2363,207],{},[1655,2365,1671],{"separator":1670},[898,2367,2025],{},[1655,2369,1677],{"stretchy":1663},[1655,2371,2346],{},[1935,2373,2374,2376,2378],{},[898,2375,1660],{},[898,2377,1667],{},[1655,2379,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,2381,1664],{"stretchy":1663},[898,2383,207],{},[1655,2385,1671],{"separator":1670},[898,2387,2025],{},[1655,2389,1677],{"stretchy":1663},[902,2391,2392],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,2394,2396],{"id":2395},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,2398,2399],{},[883,2400,2402],{"className":2401},[886],[888,2403,2404],{"xmlns":890},[892,2405,2406,2466],{},[895,2407,2408,2411,2413,2415,2423,2425,2427,2429,2431,2433,2436,2438,2440,2442,2450,2452,2454,2456,2458,2460,2462,2464],{},[898,2409,2410],{},"d",[898,2412,1660],{},[1655,2414,1657],{},[1935,2416,2417,2419,2421],{},[898,2418,1660],{},[898,2420,1667],{},[1655,2422,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,2424,1664],{"stretchy":1663},[898,2426,1667],{},[1655,2428,1671],{"separator":1670},[898,2430,1674],{},[1655,2432,1677],{"stretchy":1663},[2031,2434,2435],{}," ",[898,2437,2410],{},[898,2439,1667],{},[1655,2441,2346],{},[1935,2443,2444,2446,2448],{},[898,2445,1660],{},[898,2447,1674],{},[1655,2449,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,2451,1664],{"stretchy":1663},[898,2453,1667],{},[1655,2455,1671],{"separator":1670},[898,2457,1674],{},[1655,2459,1677],{"stretchy":1663},[2031,2461,2435],{},[898,2463,2410],{},[898,2465,1674],{},[902,2467,2468],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,2470,2471,2472,2494,2495,2518],{},"Pro malá ",[883,2473,2475],{"className":2474},[886],[888,2476,2477],{"xmlns":890},[892,2478,2479,2491],{},[895,2480,2481,2483,2485,2487,2489],{},[898,2482,2410],{},[898,2484,1667],{},[1655,2486,1671],{"separator":1670},[898,2488,2410],{},[898,2490,1674],{},[902,2492,2493],{"encoding":904},"dx, dy"," platí ",[883,2496,2498],{"className":2497},[886],[888,2499,2500],{"xmlns":890},[892,2501,2502,2515],{},[895,2503,2504,2507,2509,2511,2513],{},[898,2505,2506],{"mathvariant":1943},"Δ",[898,2508,1660],{},[1655,2510,2357],{},[898,2512,2410],{},[898,2514,1660],{},[902,2516,2517],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,2520,2522],{"id":2521},"implicitní-funkce","Implicitní funkce",[724,2524,2525,2526,2556,2557,2570,2571,2584],{},"Je-li vztah dán rovnicí ",[883,2527,2529],{"className":2528},[886],[888,2530,2531],{"xmlns":890},[892,2532,2533,2553],{},[895,2534,2535,2538,2540,2542,2544,2546,2548,2550],{},[898,2536,2537],{},"F",[1655,2539,1664],{"stretchy":1663},[898,2541,1667],{},[1655,2543,1671],{"separator":1670},[898,2545,1674],{},[1655,2547,1677],{"stretchy":1663},[1655,2549,1657],{},[1826,2551,2552],{},"0",[902,2554,2555],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,2558,2560],{"className":2559},[886],[888,2561,2562],{"xmlns":890},[892,2563,2564,2568],{},[895,2565,2566],{},[898,2567,1674],{},[902,2569,1674],{"encoding":904}," podle ",[883,2572,2574],{"className":2573},[886],[888,2575,2576],{"xmlns":890},[892,2577,2578,2582],{},[895,2579,2580],{},[898,2581,1667],{},[902,2583,1667],{"encoding":904}," (nebo naopak):",[724,2586,2587],{},[883,2588,2590],{"className":2589},[886],[888,2591,2592],{"xmlns":890},[892,2593,2594,2690],{},[895,2595,2596,2603,2605,2619,2621,2624,2642,2644,2646,2652,2654,2668,2670,2672],{},[2597,2598,2599,2601],"msup",{},[898,2600,1674],{},[1655,2602,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,2604,1657],{},[1949,2606,2607,2613],{},[895,2608,2609,2611],{},[898,2610,2410],{},[898,2612,1674],{},[895,2614,2615,2617],{},[898,2616,2410],{},[898,2618,1667],{},[1655,2620,1657],{},[1655,2622,2623],{},"−",[1949,2625,2626,2634],{},[1935,2627,2628,2630,2632],{},[898,2629,2537],{},[898,2631,1667],{},[1655,2633,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1935,2635,2636,2638,2640],{},[898,2637,2537],{},[898,2639,1674],{},[1655,2641,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,2643,1671],{"separator":1670},[1967,2645],{"width":1969},[2597,2647,2648,2650],{},[898,2649,1667],{},[1655,2651,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,2653,1657],{},[1949,2655,2656,2662],{},[895,2657,2658,2660],{},[898,2659,2410],{},[898,2661,1667],{},[895,2663,2664,2666],{},[898,2665,2410],{},[898,2667,1674],{},[1655,2669,1657],{},[1655,2671,2623],{},[1949,2673,2674,2682],{},[1935,2675,2676,2678,2680],{},[898,2677,2537],{},[898,2679,1674],{},[1655,2681,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1935,2683,2684,2686,2688],{},[898,2685,2537],{},[898,2687,1667],{},[1655,2689,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,2691,2692],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,2694,2695,2696,2699,2700,2704,2705,1719],{},"Tato vzorec dává ",[38,2697,2698],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,2701,2703],{"className":2702,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS"," a ",[207,2706,2708],{"className":2707,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,2710,2712],{"id":2711},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,2714,2716],{"id":2715},"nutná-podmínka","Nutná podmínka",[724,2718,2719,2720,2747],{},"V bodě extrému ",[883,2721,2723],{"className":2722},[886],[888,2724,2725],{"xmlns":890},[892,2726,2727,2744],{},[895,2728,2729,2732,2735,2737,2739,2741],{},[898,2730,2731],{},"A",[1655,2733,2734],{"stretchy":1663},"[",[898,2736,207],{},[1655,2738,1671],{"separator":1670},[898,2740,2025],{},[1655,2742,2743],{"stretchy":1663},"]",[902,2745,2746],{"encoding":904},"A[a, b]"," musí platit současně:",[724,2749,2750],{},[883,2751,2753],{"className":2752},[886],[888,2754,2755],{"xmlns":890},[892,2756,2757,2811],{},[895,2758,2759,2767,2769,2771,2773,2775,2777,2779,2781,2784,2787,2789,2797,2799,2801,2803,2805,2807,2809],{},[1935,2760,2761,2763,2765],{},[898,2762,1660],{},[898,2764,1667],{},[1655,2766,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,2768,1664],{"stretchy":1663},[898,2770,207],{},[1655,2772,1671],{"separator":1670},[898,2774,2025],{},[1655,2776,1677],{"stretchy":1663},[1655,2778,1657],{},[1826,2780,2552],{},[2031,2782,2783],{},"  ",[1655,2785,2786],{},"∧",[2031,2788,2783],{},[1935,2790,2791,2793,2795],{},[898,2792,1660],{},[898,2794,1674],{},[1655,2796,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,2798,1664],{"stretchy":1663},[898,2800,207],{},[1655,2802,1671],{"separator":1670},[898,2804,2025],{},[1655,2806,1677],{"stretchy":1663},[1655,2808,1657],{},[1826,2810,2552],{},[902,2812,2813],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,2815,2817],{"id":2816},"postačující-podmínka","Postačující podmínka",[724,2819,2820,2821,2824],{},"Definujeme ",[38,2822,2823],{},"diskriminant"," (Hessián zjednodušeně):",[724,2826,2827],{},[883,2828,2830],{"className":2829},[886],[888,2831,2832],{"xmlns":890},[892,2833,2834,2912],{},[895,2835,2836,2839,2841,2843,2845,2847,2849,2851,2867,2870,2886,2888,2890,2906],{},[898,2837,2838],{},"D",[1655,2840,1664],{"stretchy":1663},[898,2842,1667],{},[1655,2844,1671],{"separator":1670},[898,2846,1674],{},[1655,2848,1677],{"stretchy":1663},[1655,2850,1657],{},[1935,2852,2853,2855,2861],{},[898,2854,1660],{},[895,2856,2857,2859],{},[898,2858,1667],{},[898,2860,1667],{},[895,2862,2863,2865],{},[1655,2864,1945],{"mathvariant":1943},[1655,2866,1945],{"mathvariant":1943},[1655,2868,2869],{},"⋅",[1935,2871,2872,2874,2880],{},[898,2873,1660],{},[895,2875,2876,2878],{},[898,2877,1674],{},[898,2879,1674],{},[895,2881,2882,2884],{},[1655,2883,1945],{"mathvariant":1943},[1655,2885,1945],{"mathvariant":1943},[1655,2887,2623],{},[1655,2889,1664],{"stretchy":1663},[1935,2891,2892,2894,2900],{},[898,2893,1660],{},[895,2895,2896,2898],{},[898,2897,1667],{},[898,2899,1674],{},[895,2901,2902,2904],{},[1655,2903,1945],{"mathvariant":1943},[1655,2905,1945],{"mathvariant":1943},[2597,2907,2908,2910],{},[1655,2909,1677],{"stretchy":1663},[1826,2911,1837],{},[902,2913,2914],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,2916,2917,2918,2086],{},"V podezřelém bodě ",[883,2919,2921],{"className":2920},[886],[888,2922,2923],{"xmlns":890},[892,2924,2925,2937],{},[895,2926,2927,2929,2931,2933,2935],{},[1655,2928,2734],{"stretchy":1663},[898,2930,207],{},[1655,2932,1671],{"separator":1670},[898,2934,2025],{},[1655,2936,2743],{"stretchy":1663},[902,2938,2939],{"encoding":904},"[a, b]",[152,2941,2942,3074,3111],{},[123,2943,2944,2975,2976],{},[38,2945,2946,2086],{},[883,2947,2949],{"className":2948},[886],[888,2950,2951],{"xmlns":890},[892,2952,2953,2972],{},[895,2954,2955,2957,2959,2961,2963,2965,2967,2970],{},[898,2956,2838],{},[1655,2958,1664],{"stretchy":1663},[898,2960,207],{},[1655,2962,1671],{"separator":1670},[898,2964,2025],{},[1655,2966,1677],{"stretchy":1663},[1655,2968,2969],{},">",[1826,2971,2552],{},[902,2973,2974],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,2977,2978,3026],{},[123,2979,2980,3022,3023],{},[883,2981,2983],{"className":2982},[886],[888,2984,2985],{"xmlns":890},[892,2986,2987,3019],{},[895,2988,2989,3005,3007,3009,3011,3013,3015,3017],{},[1935,2990,2991,2993,2999],{},[898,2992,1660],{},[895,2994,2995,2997],{},[898,2996,1667],{},[898,2998,1667],{},[895,3000,3001,3003],{},[1655,3002,1945],{"mathvariant":1943},[1655,3004,1945],{"mathvariant":1943},[1655,3006,1664],{"stretchy":1663},[898,3008,207],{},[1655,3010,1671],{"separator":1670},[898,3012,2025],{},[1655,3014,1677],{"stretchy":1663},[1655,3016,2969],{},[1826,3018,2552],{},[902,3020,3021],{"encoding":904},"f''_{xx}(a, b) > 0"," ⇒ ",[38,3024,3025],{},"minimum",[123,3027,3028,3022,3071],{},[883,3029,3031],{"className":3030},[886],[888,3032,3033],{"xmlns":890},[892,3034,3035,3068],{},[895,3036,3037,3053,3055,3057,3059,3061,3063,3066],{},[1935,3038,3039,3041,3047],{},[898,3040,1660],{},[895,3042,3043,3045],{},[898,3044,1667],{},[898,3046,1667],{},[895,3048,3049,3051],{},[1655,3050,1945],{"mathvariant":1943},[1655,3052,1945],{"mathvariant":1943},[1655,3054,1664],{"stretchy":1663},[898,3056,207],{},[1655,3058,1671],{"separator":1670},[898,3060,2025],{},[1655,3062,1677],{"stretchy":1663},[1655,3064,3065],{},"\u003C",[1826,3067,2552],{},[902,3069,3070],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,3072,3073],{},"maximum",[123,3075,3076,3106,3107,3110],{},[38,3077,3078,2086],{},[883,3079,3081],{"className":3080},[886],[888,3082,3083],{"xmlns":890},[892,3084,3085,3103],{},[895,3086,3087,3089,3091,3093,3095,3097,3099,3101],{},[898,3088,2838],{},[1655,3090,1664],{"stretchy":1663},[898,3092,207],{},[1655,3094,1671],{"separator":1670},[898,3096,2025],{},[1655,3098,1677],{"stretchy":1663},[1655,3100,3065],{},[1826,3102,2552],{},[902,3104,3105],{"encoding":904},"D(a, b) \u003C 0"," ",[38,3108,3109],{},"sedlo"," (v daném bodě extrém není).",[123,3112,3113,3143],{},[38,3114,3115,2086],{},[883,3116,3118],{"className":3117},[886],[888,3119,3120],{"xmlns":890},[892,3121,3122,3140],{},[895,3123,3124,3126,3128,3130,3132,3134,3136,3138],{},[898,3125,2838],{},[1655,3127,1664],{"stretchy":1663},[898,3129,207],{},[1655,3131,1671],{"separator":1670},[898,3133,2025],{},[1655,3135,1677],{"stretchy":1663},[1655,3137,1657],{},[1826,3139,2552],{},[902,3141,3142],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,3145,3147],{"id":3146},"vázané-extrémy","Vázané extrémy",[724,3149,3150,3151,3180,3181,1719],{},"Pro extrémy s omezující podmínkou ",[883,3152,3154],{"className":3153},[886],[888,3155,3156],{"xmlns":890},[892,3157,3158,3177],{},[895,3159,3160,3163,3165,3167,3169,3171,3173,3175],{},[898,3161,3162],{},"g",[1655,3164,1664],{"stretchy":1663},[898,3166,1667],{},[1655,3168,1671],{"separator":1670},[898,3170,1674],{},[1655,3172,1677],{"stretchy":1663},[1655,3174,1657],{},[1826,3176,2552],{},[902,3178,3179],{"encoding":904},"g(x, y) = 0"," se používá ",[207,3182,793],{"className":3183,"dataFsResolvedFilePath":791,"href":792},[210],[115,3185,3187],{"id":3186},"navigace","Navigace",[120,3189,3190,3198,3206],{},[123,3191,3192,3106,3195],{},[38,3193,3194],{},"Předchozí:",[207,3196,775],{"className":3197,"dataFsResolvedFilePath":773,"href":774},[210],[123,3199,3200,3106,3203],{},[38,3201,3202],{},"Navazující:",[207,3204,793],{"className":3205,"dataFsResolvedFilePath":791,"href":792},[210],[123,3207,3208,3106,3211,3215,3216,3219,3220,3224],{},[38,3209,3210],{},"Souvislosti:",[207,3212,3214],{"className":3213,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,3217,880],{"className":3218,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,3221,3223],{"className":3222,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":3226},[3227,3228,3232,3233,3234,3238,3239],{"id":1731,"depth":642,"text":1732},{"id":1894,"depth":642,"text":1895,"children":3229},[3230,3231],{"id":2057,"depth":649,"text":2058},{"id":2185,"depth":649,"text":2186},{"id":2395,"depth":642,"text":2396},{"id":2521,"depth":642,"text":2522},{"id":2711,"depth":642,"text":2712,"children":3235},[3236,3237],{"id":2715,"depth":649,"text":2716},{"id":2816,"depth":649,"text":2817},{"id":3146,"depth":642,"text":3147},{"id":3186,"depth":642,"text":3187},"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":1629,"description":3240},[1135],"topics\u002Ffunkce-vice-promennych",[1128,3247,3248,3249,3250,3251],"parcialni-derivace","diferencial","implicitni-funkce","volne-extremy","indiferencni-krivky","topic","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A","topics",{"zapisku":1625,"topics":3256,"summaries":3257,"outputs":3258},15,5,1,[3260,5111,10814,12248,13120,17404,19011,28891,37885,51952,56244,75588,87700,96659,96947],{"id":3261,"title":3262,"body":3263,"course":1128,"courses":659,"created":1129,"description":5101,"extension":661,"meta":5102,"navigation":664,"path":5103,"seo":5104,"sources":5105,"stem":5106,"tags":5107,"type":3252,"updated":677,"__hash__":5110},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":3264,"toc":5084},[3265,3268,3289,3293,3369,3372,3496,3643,3646,3726,3730,3788,3838,3845,3847,3981,4031,4035,4078,4146,4216,4224,4228,4266,4337,4341,4422,4470,4514,4518,4520,4590,4592,4642,4718,4725,4728,4781,5049,5051],[12,3266,3262],{"id":3267},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,3269,3270,3271,3277,3278,3281,3282,3285,3286,1719],{},"Matematický aparát kurzu ",[207,3272,3276],{"className":3273,"dataFsResolvedFilePath":3274,"href":3275},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","ImeK",". Bez derivace se neobejdou ",[38,3279,3280],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,3283,3284],{},"maximalizace zisku"," ani ",[38,3287,3288],{},"minimalizace nákladů",[115,3290,3292],{"id":3291},"funkce-a-polynomy","Funkce a polynomy",[724,3294,3295,3296,3320,3321,3334,3335,3348,3349,1719],{},"Funkce jedné proměnné ",[883,3297,3299],{"className":3298},[886],[888,3300,3301],{"xmlns":890},[892,3302,3303,3317],{},[895,3304,3305,3307,3309,3311,3313,3315],{},[898,3306,1674],{},[1655,3308,1657],{},[898,3310,1660],{},[1655,3312,1664],{"stretchy":1663},[898,3314,1667],{},[1655,3316,1677],{"stretchy":1663},[902,3318,3319],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,3322,3324],{"className":3323},[886],[888,3325,3326],{"xmlns":890},[892,3327,3328,3332],{},[895,3329,3330],{},[898,3331,1667],{},[902,3333,1667],{"encoding":904}," (nezávislá) → ",[883,3336,3338],{"className":3337},[886],[888,3339,3340],{"xmlns":890},[892,3341,3342,3346],{},[895,3343,3344],{},[898,3345,1674],{},[902,3347,1674],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,3350,3352],{"className":3351},[886],[888,3353,3354],{"xmlns":890},[892,3355,3356,3366],{},[895,3357,3358,3360,3362,3364],{},[898,3359,1660],{},[1655,3361,1664],{"stretchy":1663},[898,3363,207],{},[1655,3365,1677],{"stretchy":1663},[902,3367,3368],{"encoding":904},"f(a)",[724,3370,3371],{},"Polynomy:",[120,3373,3374,3405,3445],{},[123,3375,3376],{},[152,3377,3378],{},[123,3379,3380,3381],{},"stupně: ",[883,3382,3384],{"className":3383},[886],[888,3385,3386],{"xmlns":890},[892,3387,3388,3402],{},[895,3389,3390,3392,3394,3396,3398,3400],{},[898,3391,1674],{},[1655,3393,1657],{},[898,3395,207],{},[898,3397,1667],{},[1655,3399,2346],{},[898,3401,2025],{},[902,3403,3404],{"encoding":904},"y = ax + b",[123,3406,3407],{},[152,3408,3409],{"start":642},[123,3410,3380,3411],{},[883,3412,3414],{"className":3413},[886],[888,3415,3416],{"xmlns":890},[892,3417,3418,3442],{},[895,3419,3420,3422,3424,3426,3432,3434,3436,3438,3440],{},[898,3421,1674],{},[1655,3423,1657],{},[898,3425,207],{},[2597,3427,3428,3430],{},[898,3429,1667],{},[1826,3431,1837],{},[1655,3433,2346],{},[898,3435,2025],{},[898,3437,1667],{},[1655,3439,2346],{},[898,3441,1789],{},[902,3443,3444],{"encoding":904},"y = ax^2 + bx + c",[123,3446,3447],{},[152,3448,3449],{"start":649},[123,3450,3380,3451],{},[883,3452,3454],{"className":3453},[886],[888,3455,3456],{"xmlns":890},[892,3457,3458,3493],{},[895,3459,3460,3462,3464,3466,3473,3475,3477,3483,3485,3487,3489,3491],{},[898,3461,1674],{},[1655,3463,1657],{},[898,3465,207],{},[2597,3467,3468,3470],{},[898,3469,1667],{},[1826,3471,3472],{},"3",[1655,3474,2346],{},[898,3476,2025],{},[2597,3478,3479,3481],{},[898,3480,1667],{},[1826,3482,1837],{},[1655,3484,2346],{},[898,3486,1789],{},[898,3488,1667],{},[1655,3490,2346],{},[898,3492,2410],{},[902,3494,3495],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,3497,3498,3106,3501,3557,3558,3594,3595,1719],{},[38,3499,3500],{},"Příklad rozkladu:",[883,3502,3504],{"className":3503},[886],[888,3505,3506],{"xmlns":890},[892,3507,3508,3554],{},[895,3509,3510,3512,3514,3520,3522,3525,3527,3529,3532,3534,3536,3538,3540,3542,3544,3546,3548,3550,3552],{},[898,3511,1674],{},[1655,3513,1657],{},[2597,3515,3516,3518],{},[898,3517,1667],{},[1826,3519,1837],{},[1655,3521,2623],{},[1826,3523,3524],{},"5",[898,3526,1667],{},[1655,3528,2346],{},[1826,3530,3531],{},"6",[1655,3533,1657],{},[1655,3535,1664],{"stretchy":1663},[898,3537,1667],{},[1655,3539,2623],{},[1826,3541,1837],{},[1655,3543,1677],{"stretchy":1663},[1655,3545,1664],{"stretchy":1663},[898,3547,1667],{},[1655,3549,2623],{},[1826,3551,3472],{},[1655,3553,1677],{"stretchy":1663},[902,3555,3556],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,3559,3561],{"className":3560},[886],[888,3562,3563],{"xmlns":890},[892,3564,3565,3591],{},[895,3566,3567,3573,3575,3577,3579,3581,3587,3589],{},[1820,3568,3569,3571],{},[898,3570,1667],{},[1826,3572,1828],{},[1655,3574,1657],{},[1826,3576,1837],{},[1655,3578,1671],{"separator":1670},[2031,3580,2033],{},[1820,3582,3583,3585],{},[898,3584,1667],{},[1826,3586,1837],{},[1655,3588,1657],{},[1826,3590,3472],{},[902,3592,3593],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,3596,3598],{"className":3597},[886],[888,3599,3600],{"xmlns":890},[892,3601,3602,3640],{},[895,3603,3604,3606,3608,3610,3612,3614,3623,3629,3631],{},[898,3605,1674],{},[1655,3607,1657],{},[1655,3609,1664],{"stretchy":1663},[898,3611,1667],{},[1655,3613,2623],{},[3615,3616,3617],"mstyle",{"scriptlevel":2552,"displaystyle":1663},[1949,3618,3619,3621],{},[1826,3620,3524],{},[1826,3622,1837],{},[2597,3624,3625,3627],{},[1655,3626,1677],{"stretchy":1663},[1826,3628,1837],{},[1655,3630,2623],{},[3615,3632,3633],{"scriptlevel":2552,"displaystyle":1663},[1949,3634,3635,3637],{},[1826,3636,1828],{},[1826,3638,3639],{},"4",[902,3641,3642],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,3644,3645],{"id":1145},"Derivace",[724,3647,3648,3649,1348,3673,3701,3702,1719],{},"Označení ",[883,3650,3652],{"className":3651},[886],[888,3653,3654],{"xmlns":890},[892,3655,3656,3670],{},[895,3657,3658,3664,3666,3668],{},[2597,3659,3660,3662],{},[898,3661,1660],{},[1655,3663,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,3665,1664],{"stretchy":1663},[898,3667,1667],{},[1655,3669,1677],{"stretchy":1663},[902,3671,3672],{"encoding":904},"f'(x)",[883,3674,3676],{"className":3675},[886],[888,3677,3678],{"xmlns":890},[892,3679,3680,3698],{},[895,3681,3682],{},[3615,3683,3684],{"scriptlevel":2552,"displaystyle":1670},[1949,3685,3686,3692],{},[895,3687,3688,3690],{},[898,3689,2410],{},[898,3691,1674],{},[895,3693,3694,3696],{},[898,3695,2410],{},[898,3697,1667],{},[902,3699,3700],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,3703,3705],{"className":3704},[886],[888,3706,3707],{"xmlns":890},[892,3708,3709,3723],{},[895,3710,3711,3717,3719,3721],{},[2597,3712,3713,3715],{},[898,3714,1660],{},[1655,3716,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,3718,1664],{"stretchy":1663},[898,3720,207],{},[1655,3722,1677],{"stretchy":1663},[902,3724,3725],{"encoding":904},"f'(a)",[198,3727,3729],{"id":3728},"geometrická-interpretace","Geometrická interpretace",[724,3731,3732,2111,3755,3758,3759,3787],{},[883,3733,3735],{"className":3734},[886],[888,3736,3737],{"xmlns":890},[892,3738,3739,3753],{},[895,3740,3741,3747,3749,3751],{},[2597,3742,3743,3745],{},[898,3744,1660],{},[1655,3746,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,3748,1664],{"stretchy":1663},[898,3750,207],{},[1655,3752,1677],{"stretchy":1663},[902,3754,3725],{"encoding":904},[38,3756,3757],{},"sklon tečny"," ke grafu funkce v bodě ",[883,3760,3762],{"className":3761},[886],[888,3763,3764],{"xmlns":890},[892,3765,3766,3784],{},[895,3767,3768,3770,3772,3774,3776,3778,3780,3782],{},[1655,3769,2734],{"stretchy":1663},[898,3771,207],{},[1655,3773,1671],{"separator":1670},[898,3775,1660],{},[1655,3777,1664],{"stretchy":1663},[898,3779,207],{},[1655,3781,1677],{"stretchy":1663},[1655,3783,2743],{"stretchy":1663},[902,3785,3786],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,3789,3790],{},[883,3791,3793],{"className":3792},[886],[888,3794,3795],{"xmlns":890},[892,3796,3797,3835],{},[895,3798,3799,3801,3803,3805,3807,3809,3811,3813,3819,3821,3823,3825,3827,3829,3831,3833],{},[898,3800,1674],{},[1655,3802,2623],{},[898,3804,1660],{},[1655,3806,1664],{"stretchy":1663},[898,3808,207],{},[1655,3810,1677],{"stretchy":1663},[1655,3812,1657],{},[2597,3814,3815,3817],{},[898,3816,1660],{},[1655,3818,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,3820,1664],{"stretchy":1663},[898,3822,207],{},[1655,3824,1677],{"stretchy":1663},[1655,3826,1664],{"stretchy":1663},[898,3828,1667],{},[1655,3830,2623],{},[898,3832,207],{},[1655,3834,1677],{"stretchy":1663},[902,3836,3837],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,3839,3840],{},[1723,3841],{"alt":3842,"className":3843,"src":3844},"imek-derivace-tecna",[210,1727],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,3846,2186],{"id":2185},[724,3848,3849,2111,3872,3106,3875,3888,3889,3902,3903,3921,3922,2295,3935,3948,3949,3962,3963,2086],{},[883,3850,3852],{"className":3851},[886],[888,3853,3854],{"xmlns":890},[892,3855,3856,3870],{},[895,3857,3858,3864,3866,3868],{},[2597,3859,3860,3862],{},[898,3861,1660],{},[1655,3863,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,3865,1664],{"stretchy":1663},[898,3867,207],{},[1655,3869,1677],{"stretchy":1663},[902,3871,3725],{"encoding":904},[38,3873,3874],{},"rychlost změny",[883,3876,3878],{"className":3877},[886],[888,3879,3880],{"xmlns":890},[892,3881,3882,3886],{},[895,3883,3884],{},[898,3885,1674],{},[902,3887,1674],{"encoding":904}," vzhledem k ",[883,3890,3892],{"className":3891},[886],[888,3893,3894],{"xmlns":890},[892,3895,3896,3900],{},[895,3897,3898],{},[898,3899,1667],{},[902,3901,1667],{"encoding":904}," v bodě ",[883,3904,3906],{"className":3905},[886],[888,3907,3908],{"xmlns":890},[892,3909,3910,3918],{},[895,3911,3912,3914,3916],{},[898,3913,1667],{},[1655,3915,1657],{},[898,3917,207],{},[902,3919,3920],{"encoding":904},"x = a","; přibližná změna ",[883,3923,3925],{"className":3924},[886],[888,3926,3927],{"xmlns":890},[892,3928,3929,3933],{},[895,3930,3931],{},[898,3932,1674],{},[902,3934,1674],{"encoding":904},[883,3936,3938],{"className":3937},[886],[888,3939,3940],{"xmlns":890},[892,3941,3942,3946],{},[895,3943,3944],{},[898,3945,1667],{},[902,3947,1667],{"encoding":904}," z ",[883,3950,3952],{"className":3951},[886],[888,3953,3954],{"xmlns":890},[892,3955,3956,3960],{},[895,3957,3958],{},[898,3959,207],{},[902,3961,207],{"encoding":904}," na ",[883,3964,3966],{"className":3965},[886],[888,3967,3968],{"xmlns":890},[892,3969,3970,3978],{},[895,3971,3972,3974,3976],{},[898,3973,207],{},[1655,3975,2346],{},[1826,3977,1828],{},[902,3979,3980],{"encoding":904},"a+1",[724,3982,3983],{},[883,3984,3986],{"className":3985},[886],[888,3987,3988],{"xmlns":890},[892,3989,3990,4028],{},[895,3991,3992,3994,3996,3998,4000,4002,4004,4006,4008,4010,4012,4014,4016,4022,4024,4026],{},[898,3993,1660],{},[1655,3995,1664],{"stretchy":1663},[898,3997,207],{},[1655,3999,2346],{},[1826,4001,1828],{},[1655,4003,1677],{"stretchy":1663},[1655,4005,2357],{},[898,4007,1660],{},[1655,4009,1664],{"stretchy":1663},[898,4011,207],{},[1655,4013,1677],{"stretchy":1663},[1655,4015,2346],{},[2597,4017,4018,4020],{},[898,4019,1660],{},[1655,4021,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,4023,1664],{"stretchy":1663},[898,4025,207],{},[1655,4027,1677],{"stretchy":1663},[902,4029,4030],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,4032,4034],{"id":4033},"příklad-mezní-náklady","Příklad — mezní náklady",[724,4036,4037,4038,1719],{},"Celkové náklady ",[883,4039,4041],{"className":4040},[886],[888,4042,4043],{"xmlns":890},[892,4044,4045,4075],{},[895,4046,4047,4050,4053,4055,4058,4060,4062,4064,4066,4069],{},[898,4048,4049],{},"T",[898,4051,4052],{},"C",[1655,4054,1657],{},[1826,4056,4057],{},"1000",[1655,4059,2346],{},[1826,4061,1837],{},[898,4063,1824],{},[1655,4065,2346],{},[1826,4067,4068],{},"0,1",[2597,4070,4071,4073],{},[898,4072,1824],{},[1826,4074,1837],{},[902,4076,4077],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,4079,4080,4081,4118,4119,1719],{},"Mezní náklady: ",[883,4082,4084],{"className":4083},[886],[888,4085,4086],{"xmlns":890},[892,4087,4088,4115],{},[895,4089,4090,4092,4094,4096,4098,4104,4106,4108,4110,4113],{},[898,4091,2127],{},[898,4093,4052],{},[1655,4095,1657],{},[898,4097,4049],{},[2597,4099,4100,4102],{},[898,4101,4052],{},[1655,4103,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,4105,1657],{},[1826,4107,1837],{},[1655,4109,2346],{},[1826,4111,4112],{},"0,2",[898,4114,1824],{},[902,4116,4117],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,4120,4122],{"className":4121},[886],[888,4123,4124],{"xmlns":890},[892,4125,4126,4143],{},[895,4127,4128,4130,4132,4134,4137,4139,4141],{},[898,4129,2127],{},[898,4131,4052],{},[1655,4133,1664],{"stretchy":1663},[1826,4135,4136],{},"10",[1655,4138,1677],{"stretchy":1663},[1655,4140,1657],{},[1826,4142,3639],{},[902,4144,4145],{"encoding":904},"MC(10) = 4",[724,4147,4148,3106,4151,4199,4200,3106,4203,1719],{},[38,4149,4150],{},"Skutečný přírůstek:",[883,4152,4154],{"className":4153},[886],[888,4155,4156],{"xmlns":890},[892,4157,4158,4196],{},[895,4159,4160,4162,4164,4166,4168,4170,4172,4174,4177,4179,4181,4183,4185,4187,4189,4191,4193],{},[898,4161,2506],{"mathvariant":1943},[898,4163,4049],{},[898,4165,4052],{},[1655,4167,1657],{},[898,4169,4049],{},[898,4171,4052],{},[1655,4173,1664],{"stretchy":1663},[1826,4175,4176],{},"11",[1655,4178,1677],{"stretchy":1663},[1655,4180,2623],{},[898,4182,4049],{},[898,4184,4052],{},[1655,4186,1664],{"stretchy":1663},[1826,4188,4136],{},[1655,4190,1677],{"stretchy":1663},[1655,4192,1657],{},[1826,4194,4195],{},"4,2",[902,4197,4198],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[38,4201,4202],{},"Přibližný (lineární):",[883,4204,4206],{"className":4205},[886],[888,4207,4208],{"xmlns":890},[892,4209,4210,4214],{},[895,4211,4212],{},[1826,4213,3639],{},[902,4215,3639],{"encoding":904},[724,4217,4218,4219,4223],{},"(Viz aplikace v ",[207,4220,4222],{"className":4221,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,4225,4227],{"id":4226},"diferenciál","Diferenciál",[724,4229,4230],{},[883,4231,4233],{"className":4232},[886],[888,4234,4235],{"xmlns":890},[892,4236,4237,4263],{},[895,4238,4239,4241,4243,4245,4251,4253,4255,4257,4259,4261],{},[898,4240,2410],{},[898,4242,1660],{},[1655,4244,1657],{},[2597,4246,4247,4249],{},[898,4248,1660],{},[1655,4250,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,4252,1664],{"stretchy":1663},[898,4254,1667],{},[1655,4256,1677],{"stretchy":1663},[2031,4258,2435],{},[898,4260,2410],{},[898,4262,1667],{},[902,4264,4265],{"encoding":904},"df = f'(x)\\, dx",[724,4267,2471,4268,4284,4285,4333,4334,1719],{},[883,4269,4271],{"className":4270},[886],[888,4272,4273],{"xmlns":890},[892,4274,4275,4281],{},[895,4276,4277,4279],{},[898,4278,2410],{},[898,4280,1667],{},[902,4282,4283],{"encoding":904},"dx"," platí: ",[883,4286,4288],{"className":4287},[886],[888,4289,4290],{"xmlns":890},[892,4291,4292,4330],{},[895,4293,4294,4296,4298,4300,4302,4304,4306,4308,4310,4312,4314,4316,4318,4320,4322,4324,4326,4328],{},[898,4295,2506],{"mathvariant":1943},[898,4297,1660],{},[1655,4299,1657],{},[898,4301,1660],{},[1655,4303,1664],{"stretchy":1663},[898,4305,1667],{},[1655,4307,2346],{},[898,4309,2410],{},[898,4311,1667],{},[1655,4313,1677],{"stretchy":1663},[1655,4315,2623],{},[898,4317,1660],{},[1655,4319,1664],{"stretchy":1663},[898,4321,1667],{},[1655,4323,1677],{"stretchy":1663},[1655,4325,2357],{},[898,4327,2410],{},[898,4329,1660],{},[902,4331,4332],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,4335,4336],{},"lineární odhad přírůstku",[198,4338,4340],{"id":4339},"příklad","Příklad",[724,4342,4343,4374,4375,4400,4401,4421],{},[883,4344,4346],{"className":4345},[886],[888,4347,4348],{"xmlns":890},[892,4349,4350,4371],{},[895,4351,4352,4354,4356,4358,4361,4363,4365],{},[898,4353,4049],{},[898,4355,4052],{},[1655,4357,1657],{},[1826,4359,4360],{},"100",[1655,4362,2346],{},[1826,4364,4068],{},[2597,4366,4367,4369],{},[898,4368,1824],{},[1826,4370,1837],{},[902,4372,4373],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,4376,4378],{"className":4377},[886],[888,4379,4380],{"xmlns":890},[892,4381,4382,4397],{},[895,4383,4384,4386,4388,4391,4394],{},[898,4385,1824],{},[1655,4387,2086],{},[1826,4389,4390],{},"50",[1655,4392,4393],{},"→",[1826,4395,4396],{},"60",[902,4398,4399],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,4402,4404],{"className":4403},[886],[888,4405,4406],{"xmlns":890},[892,4407,4408,4418],{},[895,4409,4410,4412,4414,4416],{},[898,4411,2410],{},[898,4413,1824],{},[1655,4415,1657],{},[1826,4417,4136],{},[902,4419,4420],{"encoding":904},"dQ = 10","):",[724,4423,4424],{},[883,4425,4427],{"className":4426},[886],[888,4428,4429],{"xmlns":890},[892,4430,4431,4467],{},[895,4432,4433,4435,4437,4439,4441,4443,4445,4447,4449,4451,4453,4455,4457,4459,4461,4463,4465],{},[898,4434,2410],{},[898,4436,4049],{},[898,4438,4052],{},[1655,4440,1657],{},[1826,4442,4112],{},[898,4444,1824],{},[1655,4446,2869],{},[898,4448,2410],{},[898,4450,1824],{},[1655,4452,1657],{},[1826,4454,4112],{},[1655,4456,2869],{},[1826,4458,4390],{},[1655,4460,2869],{},[1826,4462,4136],{},[1655,4464,1657],{},[1826,4466,4360],{},[902,4468,4469],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,4471,4472,4473,4496,4497,4513],{},"Přesná změna: ",[883,4474,4476],{"className":4475},[886],[888,4477,4478],{"xmlns":890},[892,4479,4480,4493],{},[895,4481,4482,4484,4486,4488,4490],{},[898,4483,2506],{"mathvariant":1943},[898,4485,4049],{},[898,4487,4052],{},[1655,4489,1657],{},[1826,4491,4492],{},"110",[902,4494,4495],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,4498,4500],{"className":4499},[886],[888,4501,4502],{"xmlns":890},[892,4503,4504,4510],{},[895,4505,4506,4508],{},[898,4507,4049],{},[898,4509,4052],{},[902,4511,4512],{"encoding":904},"TC"," je konvexní.",[115,4515,4517],{"id":4516},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,4519,2716],{"id":2715},[724,4521,4522,4523,3902,4543,4556,4557,4585,4586,4589],{},"Má-li ",[883,4524,4526],{"className":4525},[886],[888,4527,4528],{"xmlns":890},[892,4529,4530,4540],{},[895,4531,4532,4534,4536,4538],{},[898,4533,1660],{},[1655,4535,1664],{"stretchy":1663},[898,4537,1667],{},[1655,4539,1677],{"stretchy":1663},[902,4541,4542],{"encoding":904},"f(x)",[883,4544,4546],{"className":4545},[886],[888,4547,4548],{"xmlns":890},[892,4549,4550,4554],{},[895,4551,4552],{},[898,4553,207],{},[902,4555,207],{"encoding":904}," extrém, pak ",[883,4558,4560],{"className":4559},[886],[888,4561,4562],{"xmlns":890},[892,4563,4564,4582],{},[895,4565,4566,4572,4574,4576,4578,4580],{},[2597,4567,4568,4570],{},[898,4569,1660],{},[1655,4571,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,4573,1664],{"stretchy":1663},[898,4575,207],{},[1655,4577,1677],{"stretchy":1663},[1655,4579,1657],{},[1826,4581,2552],{},[902,4583,4584],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,4587,4588],{},"stacionární"," (podezřelé) body.",[198,4591,2817],{"id":2816},[724,4593,4594,4595,4608,4609,2086],{},"Pro stacionární bod ",[883,4596,4598],{"className":4597},[886],[888,4599,4600],{"xmlns":890},[892,4601,4602,4606],{},[895,4603,4604],{},[898,4605,207],{},[902,4607,207],{"encoding":904},", je-li ",[883,4610,4612],{"className":4611},[886],[888,4613,4614],{"xmlns":890},[892,4615,4616,4639],{},[895,4617,4618,4628,4630,4632,4634,4637],{},[2597,4619,4620,4622],{},[898,4621,1660],{},[895,4623,4624,4626],{},[1655,4625,1945],{"mathvariant":1943},[1655,4627,1945],{"mathvariant":1943},[1655,4629,1664],{"stretchy":1663},[898,4631,207],{},[1655,4633,1677],{"stretchy":1663},[1655,4635,4636],{"mathvariant":1943},"≠",[1826,4638,2552],{},[902,4640,4641],{"encoding":904},"f''(a) \\neq 0",[120,4643,4644,4681],{},[123,4645,4646,3022,4678],{},[883,4647,4649],{"className":4648},[886],[888,4650,4651],{"xmlns":890},[892,4652,4653,4675],{},[895,4654,4655,4665,4667,4669,4671,4673],{},[2597,4656,4657,4659],{},[898,4658,1660],{},[895,4660,4661,4663],{},[1655,4662,1945],{"mathvariant":1943},[1655,4664,1945],{"mathvariant":1943},[1655,4666,1664],{"stretchy":1663},[898,4668,207],{},[1655,4670,1677],{"stretchy":1663},[1655,4672,2969],{},[1826,4674,2552],{},[902,4676,4677],{"encoding":904},"f''(a) > 0",[38,4679,4680],{},"lokální minimum",[123,4682,4683,3022,4715],{},[883,4684,4686],{"className":4685},[886],[888,4687,4688],{"xmlns":890},[892,4689,4690,4712],{},[895,4691,4692,4702,4704,4706,4708,4710],{},[2597,4693,4694,4696],{},[898,4695,1660],{},[895,4697,4698,4700],{},[1655,4699,1945],{"mathvariant":1943},[1655,4701,1945],{"mathvariant":1943},[1655,4703,1664],{"stretchy":1663},[898,4705,207],{},[1655,4707,1677],{"stretchy":1663},[1655,4709,3065],{},[1826,4711,2552],{},[902,4713,4714],{"encoding":904},"f''(a) \u003C 0",[38,4716,4717],{},"lokální maximum",[724,4719,4720],{},[1723,4721],{"alt":4722,"className":4723,"src":4724},"imek-extremy-1d",[210,1727],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,4726,4340],{"id":4727},"příklad-1",[724,4729,4730],{},[883,4731,4733],{"className":4732},[886],[888,4734,4735],{"xmlns":890},[892,4736,4737,4778],{},[895,4738,4739,4741,4743,4745,4747,4749,4751,4757,4759,4761,4767,4769,4772,4774,4776],{},[898,4740,1660],{},[1655,4742,1664],{"stretchy":1663},[898,4744,1667],{},[1655,4746,1677],{"stretchy":1663},[1655,4748,1657],{},[1826,4750,1837],{},[2597,4752,4753,4755],{},[898,4754,1667],{},[1826,4756,3472],{},[1655,4758,2623],{},[1826,4760,3472],{},[2597,4762,4763,4765],{},[898,4764,1667],{},[1826,4766,1837],{},[1655,4768,2623],{},[1826,4770,4771],{},"12",[898,4773,1667],{},[1655,4775,2346],{},[1826,4777,3472],{},[902,4779,4780],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,4782,4783,4894,4934,4996],{},[123,4784,4785,4857,4858],{},[883,4786,4788],{"className":4787},[886],[888,4789,4790],{"xmlns":890},[892,4791,4792,4854],{},[895,4793,4794,4800,4802,4804,4806,4808,4810,4816,4818,4820,4822,4824,4826,4828,4830,4832,4834,4836,4838,4840,4842,4844,4846,4848,4850,4852],{},[2597,4795,4796,4798],{},[898,4797,1660],{},[1655,4799,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,4801,1664],{"stretchy":1663},[898,4803,1667],{},[1655,4805,1677],{"stretchy":1663},[1655,4807,1657],{},[1826,4809,3531],{},[2597,4811,4812,4814],{},[898,4813,1667],{},[1826,4815,1837],{},[1655,4817,2623],{},[1826,4819,3531],{},[898,4821,1667],{},[1655,4823,2623],{},[1826,4825,4771],{},[1655,4827,1657],{},[1826,4829,3531],{},[1655,4831,1664],{"stretchy":1663},[898,4833,1667],{},[1655,4835,2346],{},[1826,4837,1828],{},[1655,4839,1677],{"stretchy":1663},[1655,4841,1664],{"stretchy":1663},[898,4843,1667],{},[1655,4845,2623],{},[1826,4847,1837],{},[1655,4849,1677],{"stretchy":1663},[1655,4851,1657],{},[1826,4853,2552],{},[902,4855,4856],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,4859,4861],{"className":4860},[886],[888,4862,4863],{"xmlns":890},[892,4864,4865,4891],{},[895,4866,4867,4873,4875,4877,4879,4881,4887,4889],{},[1820,4868,4869,4871],{},[898,4870,1667],{},[1826,4872,1828],{},[1655,4874,1657],{},[1655,4876,2623],{},[1826,4878,1828],{},[1655,4880,1671],{"separator":1670},[1820,4882,4883,4885],{},[898,4884,1667],{},[1826,4886,1837],{},[1655,4888,1657],{},[1826,4890,1837],{},[902,4892,4893],{"encoding":904},"x_1 = -1, x_2 = 2",[123,4895,4896],{},[883,4897,4899],{"className":4898},[886],[888,4900,4901],{"xmlns":890},[892,4902,4903,4931],{},[895,4904,4905,4915,4917,4919,4921,4923,4925,4927,4929],{},[2597,4906,4907,4909],{},[898,4908,1660],{},[895,4910,4911,4913],{},[1655,4912,1945],{"mathvariant":1943},[1655,4914,1945],{"mathvariant":1943},[1655,4916,1664],{"stretchy":1663},[898,4918,1667],{},[1655,4920,1677],{"stretchy":1663},[1655,4922,1657],{},[1826,4924,4771],{},[898,4926,1667],{},[1655,4928,2623],{},[1826,4930,3531],{},[902,4932,4933],{"encoding":904},"f''(x) = 12x - 6",[123,4935,4936,3022,4977,4979,4980],{},[883,4937,4939],{"className":4938},[886],[888,4940,4941],{"xmlns":890},[892,4942,4943,4974],{},[895,4944,4945,4955,4957,4959,4961,4963,4965,4967,4970,4972],{},[2597,4946,4947,4949],{},[898,4948,1660],{},[895,4950,4951,4953],{},[1655,4952,1945],{"mathvariant":1943},[1655,4954,1945],{"mathvariant":1943},[1655,4956,1664],{"stretchy":1663},[1655,4958,2623],{},[1826,4960,1828],{},[1655,4962,1677],{"stretchy":1663},[1655,4964,1657],{},[1655,4966,2623],{},[1826,4968,4969],{},"18",[1655,4971,3065],{},[1826,4973,2552],{},[902,4975,4976],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,4978,3073],{}," v ",[883,4981,4983],{"className":4982},[886],[888,4984,4985],{"xmlns":890},[892,4986,4987,4993],{},[895,4988,4989,4991],{},[1655,4990,2623],{},[1826,4992,1828],{},[902,4994,4995],{"encoding":904},"-1",[123,4997,4998,3022,5034,4979,5036],{},[883,4999,5001],{"className":5000},[886],[888,5002,5003],{"xmlns":890},[892,5004,5005,5031],{},[895,5006,5007,5017,5019,5021,5023,5025,5027,5029],{},[2597,5008,5009,5011],{},[898,5010,1660],{},[895,5012,5013,5015],{},[1655,5014,1945],{"mathvariant":1943},[1655,5016,1945],{"mathvariant":1943},[1655,5018,1664],{"stretchy":1663},[1826,5020,1837],{},[1655,5022,1677],{"stretchy":1663},[1655,5024,1657],{},[1826,5026,4969],{},[1655,5028,2969],{},[1826,5030,2552],{},[902,5032,5033],{"encoding":904},"f''(2) = 18 > 0",[38,5035,3025],{},[883,5037,5039],{"className":5038},[886],[888,5040,5041],{"xmlns":890},[892,5042,5043,5047],{},[895,5044,5045],{},[1826,5046,1837],{},[902,5048,1837],{"encoding":904},[115,5050,3187],{"id":3186},[120,5052,5053,5060,5067],{},[123,5054,5055,3106,5057],{},[38,5056,3194],{},[207,5058,757],{"className":5059,"dataFsResolvedFilePath":755,"href":756},[210],[123,5061,5062,3106,5064],{},[38,5063,3202],{},[207,5065,775],{"className":5066,"dataFsResolvedFilePath":773,"href":774},[210],[123,5068,5069,3106,5071,5074,5075,5079,5080,5083],{},[38,5070,3210],{},[207,5072,784],{"className":5073,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,5076,5078],{"className":5077,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,5081,3223],{"className":5082,"dataFsResolvedFilePath":848,"href":849},[210]," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":5085},[5086,5087,5092,5095,5100],{"id":3291,"depth":642,"text":3292},{"id":1145,"depth":642,"text":3645,"children":5088},[5089,5090,5091],{"id":3728,"depth":649,"text":3729},{"id":2185,"depth":649,"text":2186},{"id":4033,"depth":649,"text":4034},{"id":4226,"depth":642,"text":4227,"children":5093},[5094],{"id":4339,"depth":649,"text":4340},{"id":4516,"depth":642,"text":4517,"children":5096},[5097,5098,5099],{"id":2715,"depth":649,"text":2716},{"id":2816,"depth":649,"text":2817},{"id":4727,"depth":649,"text":4340},{"id":3186,"depth":642,"text":3187},"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":3262,"description":5101},[1135],"topics\u002Fderivace",[1128,1145,3248,5108,5109],"extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":5112,"title":5113,"body":5114,"course":1128,"courses":659,"created":10802,"description":641,"extension":661,"meta":10803,"navigation":664,"path":10804,"seo":10805,"sources":10806,"stem":10807,"tags":10808,"type":3252,"updated":677,"__hash__":10813},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":5115,"toc":10775},[5116,5119,5141,5145,5172,5176,5217,5307,5351,5355,5379,5386,5390,5400,5412,5416,5444,5453,5509,5515,5518,5524,5551,5557,5655,5815,6106,6110,6190,6196,6200,6298,6364,6532,6536,6614,6645,6672,6678,6710,6788,6875,6879,6942,6948,6951,6957,7071,7154,7198,7202,7248,7255,7572,7577,7601,7630,7697,7794,7798,7805,7812,7883,8003,8087,8090,8096,8423,8427,8590,8598,8734,8742,8980,8988,8991,8996,9252,9256,9430,9564,9601,9645,9648,9778,9868,9886,9890,9897,9903,9964,9967,9991,9994,10000,10003,10009,10012,10016,10054,10112,10301,10305,10378,10384,10391,10395,10401,10542,10546,10552,10588,10593,10770],[12,5117,5113],{"id":5118},"elasticita-poptávky-a-nabídky",[5120,5121,5122],"blockquote",{},[724,5123,5124,5127,5128,5130,5131,5134,5135,2704,5138,1719],{},[883,5125,5126],{},"!abstract"," TL;DR\n",[38,5129,3223],{}," 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: ",[38,5132,5133],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,5136,5137],{},"křížově-cenovou elasticitu",[38,5139,5140],{},"důchodovou elasticitu",[115,5142,5144],{"id":5143},"úvod-motivace","Úvod — motivace",[724,5146,5147,5148,5151,5152,5155,5156,5159,5160,5163,5164,5167,5168,5171],{},"Termín ",[614,5149,5150],{},"elasticita"," (alternativně ",[614,5153,5154],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,5157,5158],{},"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 ",[614,5161,5162],{},"cenové elasticity poptávky"," (resp. ",[614,5165,5166],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,5169,3645],{"className":5170,"dataFsResolvedFilePath":764,"href":765},[210],").",[198,5173,5175],{"id":5174},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,5177,5178,5179,5197,5198,5216],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,5180,5182],{"className":5181},[886],[888,5183,5184],{"xmlns":890},[892,5185,5186,5194],{},[895,5187,5188,5190,5192],{},[898,5189,2132],{},[1655,5191,1657],{},[1826,5193,4136],{},[902,5195,5196],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,5199,5201],{"className":5200},[886],[888,5202,5203],{"xmlns":890},[892,5204,5205,5213],{},[895,5206,5207,5209,5211],{},[898,5208,1824],{},[1655,5210,1657],{},[1826,5212,4360],{},[902,5214,5215],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,5218,5219,5264],{},[123,5220,5221,5224,5225,5263],{},[38,5222,5223],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,5226,5228],{"className":5227},[886],[888,5229,5230],{"xmlns":890},[892,5231,5232,5260],{},[895,5233,5234,5236,5239,5241,5243,5246,5248,5251,5253,5255,5257],{},[2031,5235,2783],{},[1655,5237,5238],{},"⇒",[2031,5240,2783],{},[898,5242,4049],{},[898,5244,5245],{},"R",[1655,5247,1657],{},[1826,5249,5250],{},"9",[1655,5252,2869],{},[1826,5254,4492],{},[1655,5256,1657],{},[1826,5258,5259],{},"990",[902,5261,5262],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,5265,5266,5269,5270,5306],{},[38,5267,5268],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,5271,5273],{"className":5272},[886],[888,5274,5275],{"xmlns":890},[892,5276,5277,5303],{},[895,5278,5279,5281,5283,5285,5287,5289,5291,5293,5295,5298,5300],{},[2031,5280,2783],{},[1655,5282,5238],{},[2031,5284,2783],{},[898,5286,4049],{},[898,5288,5245],{},[1655,5290,1657],{},[1826,5292,5250],{},[1655,5294,2869],{},[1826,5296,5297],{},"120",[1655,5299,1657],{},[1826,5301,5302],{},"1080",[902,5304,5305],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,5308,5309,5310,5313,5314,5317,5318,5321,5322,5325,5326,5329,5330,5346,5347,5350],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,5311,5312],{},"nerozumné",", na Trhu 2 ",[38,5315,5316],{},"rozumné",". Trh 2 je ",[38,5319,5320],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,5323,5324],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,5327,5328],{},"neelastická"," a vyššího ",[883,5331,5333],{"className":5332},[886],[888,5334,5335],{"xmlns":890},[892,5336,5337,5343],{},[895,5338,5339,5341],{},[898,5340,4049],{},[898,5342,5245],{},[902,5344,5345],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,5348,5349],{},"zvýšením"," ceny.",[198,5352,5354],{"id":5353},"hypotéza-41","Hypotéza 4.1",[5120,5356,5357],{},[724,5358,5359,5360],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,5361,5363],{"className":5362},[886],[888,5364,5365],{"xmlns":890},[892,5366,5367,5376],{},[895,5368,5369,5371,5374],{},[1655,5370,1664],{"stretchy":1663},[1826,5372,5373],{},"4.1",[1655,5375,1677],{"stretchy":1663},[902,5377,5378],{"encoding":904},"(4.1)",[724,5380,5381,5382,5385],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,5383,5384],{},"procentní změny"," obou faktorů.",[115,5387,5389],{"id":5388},"pojem-elasticity","Pojem elasticity",[724,5391,5392,5393,5395,5396,5399],{},"Obecně ",[38,5394,5150],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,5397,5398],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[5120,5401,5402],{},[724,5403,5404,5407,5408,5411],{},[883,5405,5406],{},"!info"," Intuice\nElasticitu lze číst jako ",[38,5409,5410],{},"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.",[115,5413,5415],{"id":5414},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,5417,5418,5419,5443],{},"Nechť ",[883,5420,5422],{"className":5421},[886],[888,5423,5424],{"xmlns":890},[892,5425,5426,5440],{},[895,5427,5428,5430,5432,5434,5436,5438],{},[898,5429,1824],{},[1655,5431,1657],{},[898,5433,2838],{},[1655,5435,1664],{"stretchy":1663},[898,5437,2132],{},[1655,5439,1677],{"stretchy":1663},[902,5441,5442],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,5445,5446],{},[883,5447,5452],{"className":5448,"title":5450,"style":5451},[5449],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,5454,5455,5456,2704,5472,5488,5489,5508],{},"Znaménko minus je korekce: změny ",[883,5457,5459],{"className":5458},[886],[888,5460,5461],{"xmlns":890},[892,5462,5463,5469],{},[895,5464,5465,5467],{},[898,5466,2506],{"mathvariant":1943},[898,5468,1824],{},[902,5470,5471],{"encoding":904},"\\Delta Q",[883,5473,5475],{"className":5474},[886],[888,5476,5477],{"xmlns":890},[892,5478,5479,5485],{},[895,5480,5481,5483],{},[898,5482,2506],{"mathvariant":1943},[898,5484,2132],{},[902,5486,5487],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,5490,5492],{"className":5491},[886],[888,5493,5494],{"xmlns":890},[892,5495,5496,5505],{},[895,5497,5498],{},[2597,5499,5500,5503],{},[898,5501,5502],{},"E",[898,5504,2731],{},[902,5506,5507],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,5510,5511],{},[883,5512,5514],{"className":5513,"title":5450,"style":5451},[5449],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,5516,5517],{},"Po dosazení:",[724,5519,5520],{},[883,5521,5523],{"className":5522,"title":5450,"style":5451},[5449],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,5525,5526,5527,5547,5548,5550],{},"Limitním přechodem ",[883,5528,5530],{"className":5529},[886],[888,5531,5532],{"xmlns":890},[892,5533,5534,5544],{},[895,5535,5536,5538,5540,5542],{},[898,5537,2506],{"mathvariant":1943},[898,5539,2132],{},[1655,5541,4393],{},[1826,5543,2552],{},[902,5545,5546],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,5549,5162],{}," (price elasticity of demand):",[724,5552,5553],{},[883,5554,5556],{"className":5555,"title":5450,"style":5451},[5449],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,5558,5559,5560,5583,5584,5607,5608,5632,5633,5654],{},"kde ",[883,5561,5563],{"className":5562},[886],[888,5564,5565],{"xmlns":890},[892,5566,5567,5581],{},[895,5568,5569,5571,5573,5575,5577,5579],{},[898,5570,1824],{},[1655,5572,1657],{},[898,5574,2838],{},[1655,5576,1664],{"stretchy":1663},[898,5578,2132],{},[1655,5580,1677],{"stretchy":1663},[902,5582,5442],{"encoding":904},". Pro pevnou cenu ",[883,5585,5587],{"className":5586},[886],[888,5588,5589],{"xmlns":890},[892,5590,5591,5604],{},[895,5592,5593,5595,5597],{},[898,5594,2132],{},[1655,5596,1657],{},[2597,5598,5599,5601],{},[898,5600,2132],{},[1655,5602,5603],{},"∗",[902,5605,5606],{"encoding":904},"P = P^*"," se ",[883,5609,5611],{"className":5610},[886],[888,5612,5613],{"xmlns":890},[892,5614,5615,5629],{},[895,5616,5617,5619,5621,5627],{},[898,5618,5502],{},[1655,5620,1664],{"stretchy":1663},[2597,5622,5623,5625],{},[898,5624,2132],{},[1655,5626,5603],{},[1655,5628,1677],{"stretchy":1663},[902,5630,5631],{"encoding":904},"E(P^*)"," nazývá ",[614,5634,5635,5636],{},"elasticita poptávky při ceně ",[883,5637,5639],{"className":5638},[886],[888,5640,5641],{"xmlns":890},[892,5642,5643,5651],{},[895,5644,5645],{},[2597,5646,5647,5649],{},[898,5648,2132],{},[1655,5650,5603],{},[902,5652,5653],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[5120,5656,5657],{},[724,5658,5659,5662,5663,5681,5682,5710,5711,5740,5741,1343,5759,1343,5777,5795,5796,5811,5812,1719],{},[883,5660,5661],{},"!warning"," Pozor na znaménko\nV (4.5) je ",[38,5664,5665,5666],{},"explicitní ",[883,5667,5669],{"className":5668},[886],[888,5670,5671],{"xmlns":890},[892,5672,5673,5679],{},[895,5674,5675,5677],{},[1655,5676,2623],{},[1826,5678,1828],{},[902,5680,4995],{"encoding":904}," právě proto, že ",[883,5683,5685],{"className":5684},[886],[888,5686,5687],{"xmlns":890},[892,5688,5689,5707],{},[895,5690,5691,5697,5699,5701,5703,5705],{},[2597,5692,5693,5695],{},[898,5694,1824],{},[1655,5696,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,5698,1664],{"stretchy":1663},[898,5700,2132],{},[1655,5702,1677],{"stretchy":1663},[1655,5704,3065],{},[1826,5706,2552],{},[902,5708,5709],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,5712,5714],{"className":5713},[886],[888,5715,5716],{"xmlns":890},[892,5717,5718,5737],{},[895,5719,5720,5722,5724,5730,5732,5735],{},[898,5721,5502],{},[1655,5723,1664],{"stretchy":1663},[2597,5725,5726,5728],{},[898,5727,2132],{},[1655,5729,5603],{},[1655,5731,1677],{"stretchy":1663},[1655,5733,5734],{},"≥",[1826,5736,2552],{},[902,5738,5739],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,5742,5744],{"className":5743},[886],[888,5745,5746],{"xmlns":890},[892,5747,5748,5756],{},[895,5749,5750,5752,5754],{},[898,5751,5502],{},[1655,5753,2969],{},[1826,5755,1828],{},[902,5757,5758],{"encoding":904},"E > 1",[883,5760,5762],{"className":5761},[886],[888,5763,5764],{"xmlns":890},[892,5765,5766,5774],{},[895,5767,5768,5770,5772],{},[898,5769,5502],{},[1655,5771,3065],{},[1826,5773,1828],{},[902,5775,5776],{"encoding":904},"E \u003C 1",[883,5778,5780],{"className":5779},[886],[888,5781,5782],{"xmlns":890},[892,5783,5784,5792],{},[895,5785,5786,5788,5790],{},[898,5787,5502],{},[1655,5789,1657],{},[1826,5791,1828],{},[902,5793,5794],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,5797,5799],{"className":5798},[886],[888,5800,5801],{"xmlns":890},[892,5802,5803,5809],{},[895,5804,5805,5807],{},[1655,5806,2623],{},[1826,5808,1828],{},[902,5810,4995],{"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 ",[38,5813,5814],{},"absolutní hodnotou",[5120,5816,5817,5837],{},[724,5818,5819,5822,5823,5836],{},[883,5820,5821],{},"!tip"," Postup: jak spočítat ",[883,5824,5826],{"className":5825},[886],[888,5827,5828],{"xmlns":890},[892,5829,5830,5834],{},[895,5831,5832],{},[898,5833,5502],{},[902,5835,5502],{"encoding":904}," v bodě",[152,5838,5839,5891,5931,5984,6049],{},[123,5840,5841,5842,5865,5866,5890],{},"Zapište ",[883,5843,5845],{"className":5844},[886],[888,5846,5847],{"xmlns":890},[892,5848,5849,5863],{},[895,5850,5851,5853,5855,5857,5859,5861],{},[898,5852,1824],{},[1655,5854,1657],{},[898,5856,2838],{},[1655,5858,1664],{"stretchy":1663},[898,5860,2132],{},[1655,5862,1677],{"stretchy":1663},[902,5864,5442],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,5867,5869],{"className":5868},[886],[888,5870,5871],{"xmlns":890},[892,5872,5873,5887],{},[895,5874,5875,5877,5879,5881,5883,5885],{},[898,5876,2132],{},[1655,5878,1657],{},[898,5880,2838],{},[1655,5882,1664],{"stretchy":1663},[898,5884,1824],{},[1655,5886,1677],{"stretchy":1663},[902,5888,5889],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,5892,5893,5894,1719],{},"Spočítejte derivaci ",[883,5895,5897],{"className":5896},[886],[888,5898,5899],{"xmlns":890},[892,5900,5901,5928],{},[895,5902,5903,5909,5911,5913,5915,5917,5919,5921,5924,5926],{},[2597,5904,5905,5907],{},[898,5906,1824],{},[1655,5908,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,5910,1664],{"stretchy":1663},[898,5912,2132],{},[1655,5914,1677],{"stretchy":1663},[1655,5916,1657],{},[898,5918,2410],{"mathvariant":1943},[898,5920,1824],{},[898,5922,5923],{"mathvariant":1943},"\u002F",[898,5925,2410],{"mathvariant":1943},[898,5927,2132],{},[902,5929,5930],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,5932,5933,5934,5951,5952,1719],{},"Dosaďte zadanou cenu ",[883,5935,5937],{"className":5936},[886],[888,5938,5939],{"xmlns":890},[892,5940,5941,5949],{},[895,5942,5943],{},[2597,5944,5945,5947],{},[898,5946,2132],{},[1655,5948,5603],{},[902,5950,5653],{"encoding":904}," a dopočítejte odpovídající ",[883,5953,5955],{"className":5954},[886],[888,5956,5957],{"xmlns":890},[892,5958,5959,5981],{},[895,5960,5961,5967,5969,5971,5973,5979],{},[2597,5962,5963,5965],{},[898,5964,1824],{},[1655,5966,5603],{},[1655,5968,1657],{},[898,5970,2838],{},[1655,5972,1664],{"stretchy":1663},[2597,5974,5975,5977],{},[898,5976,2132],{},[1655,5978,5603],{},[1655,5980,1677],{"stretchy":1663},[902,5982,5983],{"encoding":904},"Q^* = D(P^*)",[123,5985,5986,5987,1719],{},"Dosaďte do (4.5): ",[883,5988,5990],{"className":5989},[886],[888,5991,5992],{"xmlns":890},[892,5993,5994,6046],{},[895,5995,5996,5998,6000,6006,6008,6010,6012,6028,6030,6036,6038,6044],{},[898,5997,5502],{},[1655,5999,1664],{"stretchy":1663},[2597,6001,6002,6004],{},[898,6003,2132],{},[1655,6005,5603],{},[1655,6007,1677],{"stretchy":1663},[1655,6009,1657],{},[1655,6011,2623],{},[3615,6013,6014],{"scriptlevel":2552,"displaystyle":1670},[1949,6015,6016,6022],{},[2597,6017,6018,6020],{},[898,6019,2132],{},[1655,6021,5603],{},[2597,6023,6024,6026],{},[898,6025,1824],{},[1655,6027,5603],{},[2031,6029,2435],{},[2597,6031,6032,6034],{},[898,6033,1824],{},[1655,6035,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,6037,1664],{"stretchy":1663},[2597,6039,6040,6042],{},[898,6041,2132],{},[1655,6043,5603],{},[1655,6045,1677],{"stretchy":1663},[902,6047,6048],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,6050,6051,6052,6069,6070,6087,6088,6105],{},"Klasifikujte: ",[883,6053,6055],{"className":6054},[886],[888,6056,6057],{"xmlns":890},[892,6058,6059,6067],{},[895,6060,6061,6063,6065],{},[898,6062,5502],{},[1655,6064,2969],{},[1826,6066,1828],{},[902,6068,5758],{"encoding":904}," elastická, ",[883,6071,6073],{"className":6072},[886],[888,6074,6075],{"xmlns":890},[892,6076,6077,6085],{},[895,6078,6079,6081,6083],{},[898,6080,5502],{},[1655,6082,1657],{},[1826,6084,1828],{},[902,6086,5794],{"encoding":904}," jednotková, ",[883,6089,6091],{"className":6090},[886],[888,6092,6093],{"xmlns":890},[892,6094,6095,6103],{},[895,6096,6097,6099,6101],{},[898,6098,5502],{},[1655,6100,3065],{},[1826,6102,1828],{},[902,6104,5776],{"encoding":904}," neelastická.",[198,6107,6109],{"id":6108},"interpretace-46","Interpretace (4.6)",[5120,6111,6112],{},[724,6113,6114,6115,6138,6139,6152,6153,6170,6171],{},"Číslo ",[883,6116,6118],{"className":6117},[886],[888,6119,6120],{"xmlns":890},[892,6121,6122,6136],{},[895,6123,6124,6126,6128,6134],{},[898,6125,5502],{},[1655,6127,1664],{"stretchy":1663},[2597,6129,6130,6132],{},[898,6131,2132],{},[1655,6133,5603],{},[1655,6135,1677],{"stretchy":1663},[902,6137,5631],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,6140,6142],{"className":6141},[886],[888,6143,6144],{"xmlns":890},[892,6145,6146,6150],{},[895,6147,6148],{},[898,6149,1824],{},[902,6151,1824],{"encoding":904},", jestliže se cena ",[883,6154,6156],{"className":6155},[886],[888,6157,6158],{"xmlns":890},[892,6159,6160,6168],{},[895,6161,6162],{},[2597,6163,6164,6166],{},[898,6165,2132],{},[1655,6167,5603],{},[902,6169,5653],{"encoding":904}," změní o 1 %. ",[883,6172,6174],{"className":6173},[886],[888,6175,6176],{"xmlns":890},[892,6177,6178,6187],{},[895,6179,6180,6182,6185],{},[1655,6181,1664],{"stretchy":1663},[1826,6183,6184],{},"4.6",[1655,6186,1677],{"stretchy":1663},[902,6188,6189],{"encoding":904},"(4.6)",[724,6191,6192,6195],{},[38,6193,6194],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,6197,6199],{"id":6198},"příklad-41","Příklad 4.1",[724,6201,6202,6203,6237,6238,1343,6264,2086],{},"Poptávka ",[883,6204,6206],{"className":6205},[886],[888,6207,6208],{"xmlns":890},[892,6209,6210,6234],{},[895,6211,6212,6214,6216,6218,6220,6222,6224,6226,6228,6230,6232],{},[898,6213,2132],{},[1655,6215,1657],{},[898,6217,2838],{},[1655,6219,1664],{"stretchy":1663},[898,6221,1824],{},[1655,6223,1677],{"stretchy":1663},[1655,6225,1657],{},[1826,6227,4390],{},[1655,6229,2623],{},[1826,6231,1837],{},[898,6233,1824],{},[902,6235,6236],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,6239,6241],{"className":6240},[886],[888,6242,6243],{"xmlns":890},[892,6244,6245,6261],{},[895,6246,6247,6249,6251,6254,6256,6259],{},[898,6248,1824],{},[1655,6250,1657],{},[1826,6252,6253],{},"25",[1655,6255,2623],{},[1826,6257,6258],{},"0,5",[898,6260,2132],{},[902,6262,6263],{"encoding":904},"Q = 25 - 0{,}5P",[883,6265,6267],{"className":6266},[886],[888,6268,6269],{"xmlns":890},[892,6270,6271,6295],{},[895,6272,6273,6289,6291,6293],{},[3615,6274,6275],{"scriptlevel":2552,"displaystyle":1670},[1949,6276,6277,6283],{},[895,6278,6279,6281],{},[898,6280,2410],{"mathvariant":1943},[898,6282,1824],{},[895,6284,6285,6287],{},[898,6286,2410],{"mathvariant":1943},[898,6288,2132],{},[1655,6290,1657],{},[1655,6292,2623],{},[1826,6294,6258],{},[902,6296,6297],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,6299,6300],{},[883,6301,6303],{"className":6302},[886],[888,6304,6305],{"xmlns":890},[892,6306,6307,6361],{},[895,6308,6309,6311,6313,6315,6329,6331,6333,6335,6337,6339,6341,6359],{},[898,6310,5502],{},[1655,6312,1657],{},[1655,6314,2623],{},[1949,6316,6317,6319],{},[898,6318,2132],{},[895,6320,6321,6323,6325,6327],{},[1826,6322,6253],{},[1655,6324,2623],{},[1826,6326,6258],{},[898,6328,2132],{},[1655,6330,2869],{},[1655,6332,1664],{"stretchy":1663},[1655,6334,2623],{},[1826,6336,6258],{},[1655,6338,1677],{"stretchy":1663},[1655,6340,1657],{},[1949,6342,6343,6349],{},[895,6344,6345,6347],{},[1826,6346,6258],{},[898,6348,2132],{},[895,6350,6351,6353,6355,6357],{},[1826,6352,6253],{},[1655,6354,2623],{},[1826,6356,6258],{},[898,6358,2132],{},[898,6360,1719],{"mathvariant":1943},[902,6362,6363],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,6365,6366,6367,1343,6391,1343,6421,1343,6445,6470,6471,6494,6495,3962,6513,5171],{},"Potom ",[883,6368,6370],{"className":6369},[886],[888,6371,6372],{"xmlns":890},[892,6373,6374,6388],{},[895,6375,6376,6378,6380,6382,6384,6386],{},[898,6377,5502],{},[1655,6379,1664],{"stretchy":1663},[1826,6381,2552],{},[1655,6383,1677],{"stretchy":1663},[1655,6385,1657],{},[1826,6387,2552],{},[902,6389,6390],{"encoding":904},"E(0)=0",[883,6392,6394],{"className":6393},[886],[888,6395,6396],{"xmlns":890},[892,6397,6398,6418],{},[895,6399,6400,6402,6404,6406,6408,6410],{},[898,6401,5502],{},[1655,6403,1664],{"stretchy":1663},[1826,6405,4136],{},[1655,6407,1677],{"stretchy":1663},[1655,6409,1657],{},[3615,6411,6412],{"scriptlevel":2552,"displaystyle":1663},[1949,6413,6414,6416],{},[1826,6415,1828],{},[1826,6417,3639],{},[902,6419,6420],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,6422,6424],{"className":6423},[886],[888,6425,6426],{"xmlns":890},[892,6427,6428,6442],{},[895,6429,6430,6432,6434,6436,6438,6440],{},[898,6431,5502],{},[1655,6433,1664],{"stretchy":1663},[1826,6435,6253],{},[1655,6437,1677],{"stretchy":1663},[1655,6439,1657],{},[1826,6441,1828],{},[902,6443,6444],{"encoding":904},"E(25)=1",[883,6446,6448],{"className":6447},[886],[888,6449,6450],{"xmlns":890},[892,6451,6452,6467],{},[895,6453,6454,6456,6458,6461,6463,6465],{},[898,6455,5502],{},[1655,6457,1664],{"stretchy":1663},[1826,6459,6460],{},"40",[1655,6462,1677],{"stretchy":1663},[1655,6464,1657],{},[1826,6466,3639],{},[902,6468,6469],{"encoding":904},"E(40)=4",". Např. ",[883,6472,6474],{"className":6473},[886],[888,6475,6476],{"xmlns":890},[892,6477,6478,6492],{},[895,6479,6480,6482,6484,6486,6488,6490],{},[898,6481,5502],{},[1655,6483,1664],{"stretchy":1663},[1826,6485,6460],{},[1655,6487,1677],{"stretchy":1663},[1655,6489,1657],{},[1826,6491,3639],{},[902,6493,6469],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,6496,6498],{"className":6497},[886],[888,6499,6500],{"xmlns":890},[892,6501,6502,6510],{},[895,6503,6504,6506,6508],{},[898,6505,1824],{},[1655,6507,1657],{},[1826,6509,3524],{},[902,6511,6512],{"encoding":904},"Q=5",[883,6514,6516],{"className":6515},[886],[888,6517,6518],{"xmlns":890},[892,6519,6520,6529],{},[895,6521,6522,6524,6526],{},[898,6523,1824],{},[1655,6525,1657],{},[1826,6527,6528],{},"4,8",[902,6530,6531],{"encoding":904},"Q=4{,}8",[198,6533,6535],{"id":6534},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,6537,6538,6594],{},[123,6539,6540,6543,6544,6561,6562,1719],{},[38,6541,6542],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,6545,6547],{"className":6546},[886],[888,6548,6549],{"xmlns":890},[892,6550,6551,6559],{},[895,6552,6553],{},[2597,6554,6555,6557],{},[898,6556,5502],{},[898,6558,2731],{},[902,6560,5507],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,6563,6565],{"className":6564},[886],[888,6566,6567],{"xmlns":890},[892,6568,6569,6591],{},[895,6570,6571,6574,6576,6578,6580,6582,6584,6586,6588],{},[1655,6572,6573],{"stretchy":1663},"⟨",[898,6575,2132],{},[1655,6577,1671],{"separator":1670},[2031,6579,2435],{},[898,6581,2132],{},[1655,6583,2346],{},[898,6585,2506],{"mathvariant":1943},[898,6587,2132],{},[1655,6589,6590],{"stretchy":1663},"⟩",[902,6592,6593],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,6595,6596,6599,6600,6613],{},[38,6597,6598],{},"Bodová"," (okamžitá) elasticita: ",[883,6601,6603],{"className":6602},[886],[888,6604,6605],{"xmlns":890},[892,6606,6607,6611],{},[895,6608,6609],{},[898,6610,5502],{},[902,6612,5502],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,6615,6617,6618,6631,6632],{"id":6616},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,6619,6621],{"className":6620},[886],[888,6622,6623],{"xmlns":890},[892,6624,6625,6629],{},[895,6626,6627],{},[898,6628,2132],{},[902,6630,2132],{"encoding":904}," jako funkce ",[883,6633,6635],{"className":6634},[886],[888,6636,6637],{"xmlns":890},[892,6638,6639,6643],{},[895,6640,6641],{},[898,6642,1824],{},[902,6644,1824],{"encoding":904},[724,6646,6647,6648,6671],{},"Pokud je poptávka zadaná ve tvaru ",[883,6649,6651],{"className":6650},[886],[888,6652,6653],{"xmlns":890},[892,6654,6655,6669],{},[895,6656,6657,6659,6661,6663,6665,6667],{},[898,6658,2132],{},[1655,6660,1657],{},[898,6662,2838],{},[1655,6664,1664],{"stretchy":1663},[898,6666,1824],{},[1655,6668,1677],{"stretchy":1663},[902,6670,5889],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,6673,6674],{},[883,6675,6677],{"className":6676,"title":5450,"style":5451},[5449],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,6679,6680,3106,6683,6709],{},[38,6681,6682],{},"Příklad 4.3.",[883,6684,6686],{"className":6685},[886],[888,6687,6688],{"xmlns":890},[892,6689,6690,6706],{},[895,6691,6692,6694,6696,6698,6700],{},[898,6693,2132],{},[1655,6695,1657],{},[1826,6697,4360],{},[1655,6699,2623],{},[2597,6701,6702,6704],{},[898,6703,1824],{},[1826,6705,1837],{},[902,6707,6708],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,6711,6712],{},[883,6713,6715],{"className":6714},[886],[888,6716,6717],{"xmlns":890},[892,6718,6719,6785],{},[895,6720,6721,6723,6725,6727,6743,6745,6757,6759,6783],{},[898,6722,5502],{},[1655,6724,1657],{},[1655,6726,2623],{},[1949,6728,6729,6741],{},[895,6730,6731,6733,6735],{},[1826,6732,4360],{},[1655,6734,2623],{},[2597,6736,6737,6739],{},[898,6738,1824],{},[1826,6740,1837],{},[898,6742,1824],{},[1655,6744,2869],{},[1949,6746,6747,6749],{},[1826,6748,1828],{},[895,6750,6751,6753,6755],{},[1655,6752,2623],{},[1826,6754,1837],{},[898,6756,1824],{},[1655,6758,1657],{},[1949,6760,6761,6773],{},[895,6762,6763,6765,6767],{},[1826,6764,4360],{},[1655,6766,2623],{},[2597,6768,6769,6771],{},[898,6770,1824],{},[1826,6772,1837],{},[895,6774,6775,6777],{},[1826,6776,1837],{},[2597,6778,6779,6781],{},[898,6780,1824],{},[1826,6782,1837],{},[898,6784,1719],{"mathvariant":1943},[902,6786,6787],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,6789,6790,6791,6818,6819,6838,6839,1719],{},"Z rovnice ",[883,6792,6794],{"className":6793},[886],[888,6795,6796],{"xmlns":890},[892,6797,6798,6815],{},[895,6799,6800,6802,6804,6810,6812],{},[1826,6801,4360],{},[1655,6803,2623],{},[2597,6805,6806,6808],{},[898,6807,1824],{},[1826,6809,1837],{},[1655,6811,1657],{},[1826,6813,6814],{},"36",[902,6816,6817],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,6820,6822],{"className":6821},[886],[888,6823,6824],{"xmlns":890},[892,6825,6826,6835],{},[895,6827,6828,6830,6832],{},[898,6829,1824],{},[1655,6831,1657],{},[1826,6833,6834],{},"8",[902,6836,6837],{"encoding":904},"Q = 8",", tedy ",[883,6840,6842],{"className":6841},[886],[888,6843,6844],{"xmlns":890},[892,6845,6846,6872],{},[895,6847,6848,6850,6852,6854,6856,6858,6867,6869],{},[898,6849,5502],{},[1655,6851,1664],{"stretchy":1663},[1826,6853,6834],{},[1655,6855,1677],{"stretchy":1663},[1655,6857,1657],{},[3615,6859,6860],{"scriptlevel":2552,"displaystyle":1663},[1949,6861,6862,6864],{},[1826,6863,6814],{},[1826,6865,6866],{},"128",[1655,6868,1657],{},[1826,6870,6871],{},"0,281",[902,6873,6874],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,6876,6878],{"id":6877},"přibližné-změny","Přibližné změny",[724,6880,6881,6882,6918,6919,6941],{},"Diferenciál ",[883,6883,6885],{"className":6884},[886],[888,6886,6887],{"xmlns":890},[892,6888,6889,6915],{},[895,6890,6891,6893,6895,6897,6903,6905,6907,6909,6911,6913],{},[898,6892,2410],{"mathvariant":1943},[898,6894,1824],{},[1655,6896,1657],{},[2597,6898,6899,6901],{},[898,6900,1824],{},[1655,6902,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,6904,1664],{"stretchy":1663},[898,6906,2132],{},[1655,6908,1677],{"stretchy":1663},[2031,6910,2435],{},[898,6912,2410],{"mathvariant":1943},[898,6914,2132],{},[902,6916,6917],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,6920,6922],{"className":6921},[886],[888,6923,6924],{"xmlns":890},[892,6925,6926,6938],{},[895,6927,6928,6930,6932,6934,6936],{},[898,6929,2410],{"mathvariant":1943},[898,6931,2132],{},[1655,6933,1657],{},[898,6935,2506],{"mathvariant":1943},[898,6937,2132],{},[902,6939,6940],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,6943,6944],{},[883,6945,6947],{"className":6946,"title":5450,"style":5451},[5449],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,6949,6950],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,6952,6953],{},[883,6954,6956],{"className":6955,"title":5450,"style":5451},[5449],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,6958,6959,3106,6962,6997,6998,7017,7018,7052,7053,7070],{},[38,6960,6961],{},"Příklad 4.5.",[883,6963,6965],{"className":6964},[886],[888,6966,6967],{"xmlns":890},[892,6968,6969,6994],{},[895,6970,6971,6973,6975,6977,6983,6985,6987,6989,6991],{},[898,6972,2132],{},[1655,6974,1657],{},[1655,6976,2623],{},[2597,6978,6979,6981],{},[898,6980,1824],{},[1826,6982,1837],{},[1655,6984,2623],{},[1826,6986,3639],{},[898,6988,1824],{},[1655,6990,2346],{},[1826,6992,6993],{},"96",[902,6995,6996],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,6999,7001],{"className":7000},[886],[888,7002,7003],{"xmlns":890},[892,7004,7005,7014],{},[895,7006,7007,7009,7011],{},[898,7008,2132],{},[1655,7010,1657],{},[1826,7012,7013],{},"51",[902,7015,7016],{"encoding":904},"P=51",". Z rovnice ",[883,7019,7021],{"className":7020},[886],[888,7022,7023],{"xmlns":890},[892,7024,7025,7049],{},[895,7026,7027,7029,7031,7033,7039,7041,7043,7045,7047],{},[1826,7028,7013],{},[1655,7030,1657],{},[1655,7032,2623],{},[2597,7034,7035,7037],{},[898,7036,1824],{},[1826,7038,1837],{},[1655,7040,2623],{},[1826,7042,3639],{},[898,7044,1824],{},[1655,7046,2346],{},[1826,7048,6993],{},[902,7050,7051],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,7054,7056],{"className":7055},[886],[888,7057,7058],{"xmlns":890},[892,7059,7060,7068],{},[895,7061,7062,7064,7066],{},[898,7063,1824],{},[1655,7065,1657],{},[1826,7067,3524],{},[902,7069,6512],{"encoding":904},". Elasticita:",[724,7072,7073],{},[883,7074,7076],{"className":7075},[886],[888,7077,7078],{"xmlns":890},[892,7079,7080,7151],{},[895,7081,7082,7084,7086,7124,7126,7128,7130,7132,7134,7136,7138,7145,7148],{},[898,7083,5502],{},[1655,7085,1657],{},[1949,7087,7088,7108],{},[895,7089,7090,7092,7098,7100,7102,7104,7106],{},[1655,7091,2623],{},[2597,7093,7094,7096],{},[898,7095,1824],{},[1826,7097,1837],{},[1655,7099,2623],{},[1826,7101,3639],{},[898,7103,1824],{},[1655,7105,2346],{},[1826,7107,6993],{},[895,7109,7110,7112,7114,7116,7118,7120,7122],{},[898,7111,1824],{},[1655,7113,1664],{"stretchy":1663},[1826,7115,1837],{},[898,7117,1824],{},[1655,7119,2346],{},[1826,7121,3639],{},[1655,7123,1677],{"stretchy":1663},[1655,7125,1671],{"separator":1670},[1967,7127],{"width":1969},[898,7129,5502],{},[1655,7131,1664],{"stretchy":1663},[1826,7133,3524],{},[1655,7135,1677],{"stretchy":1663},[1655,7137,1657],{},[1949,7139,7140,7142],{},[1826,7141,7013],{},[1826,7143,7144],{},"70",[1655,7146,7147],{},"≐",[1826,7149,7150],{},"0,728.",[902,7152,7153],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,7155,7156,7157,1719],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,7158,7160],{"className":7159},[886],[888,7161,7162],{"xmlns":890},[892,7163,7164,7195],{},[895,7165,7166,7168,7170,7173,7175,7177,7180,7182,7184,7186,7188,7191,7193],{},[898,7167,2506],{"mathvariant":1943},[898,7169,1824],{},[898,7171,7172],{"mathvariant":1943},"%",[1655,7174,2357],{},[1655,7176,2623],{},[1826,7178,7179],{},"0,728",[1655,7181,2869],{},[1826,7183,1837],{},[1655,7185,1657],{},[1655,7187,2623],{},[1826,7189,7190],{},"1,456",[2031,7192,2435],{},[898,7194,7172],{"mathvariant":1943},[902,7196,7197],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,7199,7201],{"id":7200},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,7203,7204,7205,7228,7229,2086],{},"V závislosti na hodnotě ",[883,7206,7208],{"className":7207},[886],[888,7209,7210],{"xmlns":890},[892,7211,7212,7226],{},[895,7213,7214,7216,7218,7224],{},[898,7215,5502],{},[1655,7217,1664],{"stretchy":1663},[2597,7219,7220,7222],{},[898,7221,2132],{},[1655,7223,5603],{},[1655,7225,1677],{"stretchy":1663},[902,7227,5631],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,7230,7232],{"className":7231},[886],[888,7233,7234],{"xmlns":890},[892,7235,7236,7245],{},[895,7237,7238,7240,7243],{},[1655,7239,1664],{"stretchy":1663},[1826,7241,7242],{},"4.7",[1655,7244,1677],{"stretchy":1663},[902,7246,7247],{"encoding":904},"(4.7)",[724,7249,7250],{},[1723,7251],{"alt":7252,"className":7253,"src":7254},"imek-typy-elasticity-5panelu",[210,1727],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,7256,7257,7296],{},[19,7258,7259],{},[22,7260,7261,7287,7290,7293],{},[25,7262,7263,7264],{},"Hodnota ",[883,7265,7267],{"className":7266},[886],[888,7268,7269],{"xmlns":890},[892,7270,7271,7285],{},[895,7272,7273,7275,7277,7283],{},[898,7274,5502],{},[1655,7276,1664],{"stretchy":1663},[2597,7278,7279,7281],{},[898,7280,2132],{},[1655,7282,5603],{},[1655,7284,1677],{"stretchy":1663},[902,7286,5631],{"encoding":904},[25,7288,7289],{},"Typ poptávky",[25,7291,7292],{},"Termín",[25,7294,7295],{},"Význam",[30,7297,7298,7331,7393,7468,7525],{},[22,7299,7300,7320,7325,7328],{},[35,7301,7302],{},[883,7303,7305],{"className":7304},[886],[888,7306,7307],{"xmlns":890},[892,7308,7309,7317],{},[895,7310,7311,7313,7315],{},[898,7312,5502],{},[1655,7314,1657],{},[1826,7316,2552],{},[902,7318,7319],{"encoding":904},"E = 0",[35,7321,7322],{},[38,7323,7324],{},"dokonale neelastická",[35,7326,7327],{},"perfectly inelastic",[35,7329,7330],{},"množství se nemění bez ohledu na cenu",[22,7332,7333,7357,7361,7364],{},[35,7334,7335],{},[883,7336,7338],{"className":7337},[886],[888,7339,7340],{"xmlns":890},[892,7341,7342,7354],{},[895,7343,7344,7346,7348,7350,7352],{},[1826,7345,2552],{},[1655,7347,3065],{},[898,7349,5502],{},[1655,7351,3065],{},[1826,7353,1828],{},[902,7355,7356],{"encoding":904},"0 \u003C E \u003C 1",[35,7358,7359],{},[38,7360,5328],{},[35,7362,7363],{},"inelastic",[35,7365,7366,7379,7380],{},[883,7367,7369],{"className":7368},[886],[888,7370,7371],{"xmlns":890},[892,7372,7373,7377],{},[895,7374,7375],{},[898,7376,1824],{},[902,7378,1824],{"encoding":904}," se mění pomaleji než ",[883,7381,7383],{"className":7382},[886],[888,7384,7385],{"xmlns":890},[892,7386,7387,7391],{},[895,7388,7389],{},[898,7390,2132],{},[902,7392,2132],{"encoding":904},[22,7394,7395,7414,7419,7422],{},[35,7396,7397],{},[883,7398,7400],{"className":7399},[886],[888,7401,7402],{"xmlns":890},[892,7403,7404,7412],{},[895,7405,7406,7408,7410],{},[898,7407,5502],{},[1655,7409,1657],{},[1826,7411,1828],{},[902,7413,5794],{"encoding":904},[35,7415,7416],{},[38,7417,7418],{},"jednotkově elastická",[35,7420,7421],{},"unit elastic",[35,7423,7424,7437,7438,7451,7452,7467],{},[883,7425,7427],{"className":7426},[886],[888,7428,7429],{"xmlns":890},[892,7430,7431,7435],{},[895,7432,7433],{},[898,7434,1824],{},[902,7436,1824],{"encoding":904}," i ",[883,7439,7441],{"className":7440},[886],[888,7442,7443],{"xmlns":890},[892,7444,7445,7449],{},[895,7446,7447],{},[898,7448,2132],{},[902,7450,2132],{"encoding":904}," se mění stejně rychle; ",[883,7453,7455],{"className":7454},[886],[888,7456,7457],{"xmlns":890},[892,7458,7459,7465],{},[895,7460,7461,7463],{},[898,7462,4049],{},[898,7464,5245],{},[902,7466,5345],{"encoding":904}," má maximum",[22,7469,7470,7489,7493,7496],{},[35,7471,7472],{},[883,7473,7475],{"className":7474},[886],[888,7476,7477],{"xmlns":890},[892,7478,7479,7487],{},[895,7480,7481,7483,7485],{},[898,7482,5502],{},[1655,7484,2969],{},[1826,7486,1828],{},[902,7488,5758],{"encoding":904},[35,7490,7491],{},[38,7492,5324],{},[35,7494,7495],{},"elastic",[35,7497,7498,7511,7512],{},[883,7499,7501],{"className":7500},[886],[888,7502,7503],{"xmlns":890},[892,7504,7505,7509],{},[895,7506,7507],{},[898,7508,1824],{},[902,7510,1824],{"encoding":904}," se mění rychleji než ",[883,7513,7515],{"className":7514},[886],[888,7516,7517],{"xmlns":890},[892,7518,7519,7523],{},[895,7520,7521],{},[898,7522,2132],{},[902,7524,2132],{"encoding":904},[22,7526,7527,7548,7553,7556],{},[35,7528,7529],{},[883,7530,7532],{"className":7531},[886],[888,7533,7534],{"xmlns":890},[892,7535,7536,7545],{},[895,7537,7538,7540,7542],{},[898,7539,5502],{},[1655,7541,4393],{},[898,7543,7544],{"mathvariant":1943},"∞",[902,7546,7547],{"encoding":904},"E \\to \\infty",[35,7549,7550],{},[38,7551,7552],{},"dokonale elastická",[35,7554,7555],{},"perfectly elastic",[35,7557,7558,7559],{},"sebemenší změna ceny úplně mění ",[883,7560,7562],{"className":7561},[886],[888,7563,7564],{"xmlns":890},[892,7565,7566,7570],{},[895,7567,7568],{},[898,7569,1824],{},[902,7571,1824],{"encoding":904},[724,7573,7574],{},[38,7575,7576],{},"Pravidlo růstu elasticity s cenou:",[5120,7578,7579],{},[724,7580,7581,7582],{},"S rostoucí cenou elasticita poptávky roste. ",[883,7583,7585],{"className":7584},[886],[888,7586,7587],{"xmlns":890},[892,7588,7589,7598],{},[895,7590,7591,7593,7596],{},[1655,7592,1664],{"stretchy":1663},[1826,7594,7595],{},"4.8",[1655,7597,1677],{"stretchy":1663},[902,7599,7600],{"encoding":904},"(4.8)",[724,7602,7603,7604,7607,7608,7611,7612,7629],{},"Z toho plyne, že při ",[614,7605,7606],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,7609,7610],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,7613,7615],{"className":7614},[886],[888,7616,7617],{"xmlns":890},[892,7618,7619,7627],{},[895,7620,7621],{},[2597,7622,7623,7625],{},[898,7624,2132],{},[1655,7626,5603],{},[902,7628,5653],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[5120,7631,7632,7637],{},[724,7633,7634,7636],{},[883,7635,5821],{}," Postup: jak klasifikovat poptávku",[152,7638,7639,7666,7669],{},[123,7640,7641,7642,7665],{},"Spočítejte ",[883,7643,7645],{"className":7644},[886],[888,7646,7647],{"xmlns":890},[892,7648,7649,7663],{},[895,7650,7651,7653,7655,7661],{},[898,7652,5502],{},[1655,7654,1664],{"stretchy":1663},[2597,7656,7657,7659],{},[898,7658,2132],{},[1655,7660,5603],{},[1655,7662,1677],{"stretchy":1663},[902,7664,5631],{"encoding":904}," dle (4.5).",[123,7667,7668],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,7670,7671,7672,7696],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,7673,7675],{"className":7674},[886],[888,7676,7677],{"xmlns":890},[892,7678,7679,7693],{},[895,7680,7681,7683,7685,7687,7689,7691],{},[898,7682,5502],{},[1655,7684,1664],{"stretchy":1663},[898,7686,2132],{},[1655,7688,1677],{"stretchy":1663},[1655,7690,1657],{},[1826,7692,1828],{},[902,7694,7695],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,7698,7699,7702,7703,7720,7721,7739,7740,7767,7768,1719],{},[38,7700,7701],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,7704,7706],{"className":7705},[886],[888,7707,7708],{"xmlns":890},[892,7709,7710,7718],{},[895,7711,7712,7714,7716],{},[898,7713,5502],{},[1655,7715,1657],{},[1826,7717,1828],{},[902,7719,5794],{"encoding":904}," pro ",[883,7722,7724],{"className":7723},[886],[888,7725,7726],{"xmlns":890},[892,7727,7728,7736],{},[895,7729,7730,7732,7734],{},[898,7731,2132],{},[1655,7733,1657],{},[1826,7735,6253],{},[902,7737,7738],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,7741,7743],{"className":7742},[886],[888,7744,7745],{"xmlns":890},[892,7746,7747,7764],{},[895,7748,7749,7751,7754,7756,7758,7760,7762],{},[898,7750,2132],{},[1655,7752,7753],{},"∈",[1655,7755,6573],{"stretchy":1663},[1826,7757,2552],{},[1655,7759,1671],{"separator":1670},[1826,7761,6253],{},[1655,7763,1677],{"stretchy":1663},[902,7765,7766],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,7769,7771],{"className":7770},[886],[888,7772,7773],{"xmlns":890},[892,7774,7775,7791],{},[895,7776,7777,7779,7781,7783,7785,7787,7789],{},[898,7778,2132],{},[1655,7780,7753],{},[1655,7782,1664],{"stretchy":1663},[1826,7784,6253],{},[1655,7786,1671],{"separator":1670},[1826,7788,4390],{},[1655,7790,6590],{"stretchy":1663},[902,7792,7793],{"encoding":904},"P \\in (25, 50\\rangle",[115,7795,7797],{"id":7796},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,7799,7800],{},[1723,7801],{"alt":7802,"className":7803,"src":7804},"imek-elasticita-tr",[210,1727],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,7806,7807],{},[1723,7808],{"alt":7809,"className":7810,"src":7811},"imek-elasticita-podel-linearni-poptavky",[210,1727],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,7813,7814,7815,7865,7866,7882],{},"Pro celkový příjem platí ",[883,7816,7818],{"className":7817},[886],[888,7819,7820],{"xmlns":890},[892,7821,7822,7862],{},[895,7823,7824,7826,7828,7830,7832,7834,7836,7838,7840,7842,7844,7846,7848,7850,7852,7854,7856,7858,7860],{},[898,7825,4049],{},[898,7827,5245],{},[1655,7829,1657],{},[898,7831,4049],{},[898,7833,5245],{},[1655,7835,1664],{"stretchy":1663},[898,7837,1824],{},[1655,7839,1677],{"stretchy":1663},[1655,7841,1657],{},[898,7843,2132],{},[1655,7845,2869],{},[898,7847,1824],{},[1655,7849,1657],{},[898,7851,1824],{},[1655,7853,2869],{},[898,7855,2838],{},[1655,7857,1664],{"stretchy":1663},[898,7859,1824],{},[1655,7861,1677],{"stretchy":1663},[902,7863,7864],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,7867,7869],{"className":7868},[886],[888,7870,7871],{"xmlns":890},[892,7872,7873,7879],{},[895,7874,7875,7877],{},[898,7876,2127],{},[898,7878,5245],{},[902,7880,7881],{"encoding":904},"MR"," odvodíme:",[724,7884,7885],{},[883,7886,7888],{"className":7887},[886],[888,7889,7890],{"xmlns":890},[892,7891,7892,8000],{},[895,7893,7894,7896,7898,7900,7902,7908,7910,7912,7914,7916,7918,7920,7922,7924,7926,7928,7930,7936,7938,7940,7942,7944,7946,7948,7950,7964,7966,7968],{},[898,7895,2127],{},[898,7897,5245],{},[1655,7899,1657],{},[898,7901,4049],{},[2597,7903,7904,7906],{},[898,7905,5245],{},[1655,7907,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,7909,1664],{"stretchy":1663},[898,7911,1824],{},[1655,7913,1677],{"stretchy":1663},[1655,7915,1657],{},[898,7917,2838],{},[1655,7919,1664],{"stretchy":1663},[898,7921,1824],{},[1655,7923,1677],{"stretchy":1663},[1655,7925,2346],{},[898,7927,1824],{},[2031,7929,2435],{},[2597,7931,7932,7934],{},[898,7933,2838],{},[1655,7935,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,7937,1664],{"stretchy":1663},[898,7939,1824],{},[1655,7941,1677],{"stretchy":1663},[1655,7943,1657],{},[898,7945,2132],{},[1655,7947,2346],{},[898,7949,1824],{},[1949,7951,7952,7958],{},[895,7953,7954,7956],{},[898,7955,2410],{"mathvariant":1943},[898,7957,2132],{},[895,7959,7960,7962],{},[898,7961,2410],{"mathvariant":1943},[898,7963,1824],{},[1655,7965,1657],{},[898,7967,2132],{},[895,7969,7970,7972,7974,7976,7982,7984,7998],{},[1655,7971,1664],{"fence":1670},[1826,7973,1828],{},[1655,7975,2346],{},[1949,7977,7978,7980],{},[898,7979,1824],{},[898,7981,2132],{},[1655,7983,2869],{},[1949,7985,7986,7992],{},[895,7987,7988,7990],{},[898,7989,2410],{"mathvariant":1943},[898,7991,2132],{},[895,7993,7994,7996],{},[898,7995,2410],{"mathvariant":1943},[898,7997,1824],{},[1655,7999,1677],{"fence":1670},[902,8001,8002],{"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)",[724,8004,8005],{},[883,8006,8008],{"className":8007},[886],[888,8009,8010],{"xmlns":890},[892,8011,8012,8084],{},[895,8013,8014,8016,8018,8060,8062,8064],{},[1655,8015,1657],{},[898,8017,2132],{},[895,8019,8020,8022,8024,8026,8058],{},[1655,8021,1664],{"fence":1670},[1826,8023,1828],{},[1655,8025,2346],{},[1949,8027,8028,8030],{},[1826,8029,1828],{},[895,8031,8032,8040,8042],{},[3615,8033,8034],{"scriptlevel":2552,"displaystyle":1663},[1949,8035,8036,8038],{},[898,8037,2132],{},[898,8039,1824],{},[1655,8041,2869],{},[3615,8043,8044],{"scriptlevel":2552,"displaystyle":1663},[1949,8045,8046,8052],{},[895,8047,8048,8050],{},[898,8049,2410],{"mathvariant":1943},[898,8051,1824],{},[895,8053,8054,8056],{},[898,8055,2410],{"mathvariant":1943},[898,8057,2132],{},[1655,8059,1677],{"fence":1670},[1655,8061,1657],{},[898,8063,2132],{},[895,8065,8066,8068,8070,8072,8082],{},[1655,8067,1664],{"fence":1670},[1826,8069,1828],{},[1655,8071,2346],{},[1949,8073,8074,8076],{},[1826,8075,1828],{},[895,8077,8078,8080],{},[1655,8079,2623],{},[898,8081,5502],{},[1655,8083,1677],{"fence":1670},[902,8085,8086],{"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)",[724,8088,8089],{},"a tedy",[724,8091,8092],{},[883,8093,8095],{"className":8094,"title":5450,"style":5451},[5449],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[5120,8097,8098,8167,8417],{},[724,8099,8100,8102,8103,8137,8138,8153,8154,2086],{},[883,8101,5406],{}," Intuice: vztah ",[883,8104,8106],{"className":8105},[886],[888,8107,8108],{"xmlns":890},[892,8109,8110,8134],{},[895,8111,8112,8114,8116,8118,8120,8122,8124,8126,8128,8130,8132],{},[898,8113,2127],{},[898,8115,5245],{},[1655,8117,1657],{},[898,8119,2132],{},[1655,8121,1664],{"stretchy":1663},[1826,8123,1828],{},[1655,8125,2623],{},[1826,8127,1828],{},[898,8129,5923],{"mathvariant":1943},[898,8131,5502],{},[1655,8133,1677],{"stretchy":1663},[902,8135,8136],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,8139,8141],{"className":8140},[886],[888,8142,8143],{"xmlns":890},[892,8144,8145,8151],{},[895,8146,8147,8149],{},[898,8148,2127],{},[898,8150,5245],{},[902,8152,7881],{"encoding":904}," jednoznačně určuje hodnota ",[883,8155,8157],{"className":8156},[886],[888,8158,8159],{"xmlns":890},[892,8160,8161,8165],{},[895,8162,8163],{},[898,8164,5502],{},[902,8166,5502],{"encoding":904},[120,8168,8169,8279,8348],{},[123,8170,8171,8188,8189,3106,8203,3106,8229,3106,8242,8262,8263,8278],{},[883,8172,8174],{"className":8173},[886],[888,8175,8176],{"xmlns":890},[892,8177,8178,8186],{},[895,8179,8180,8182,8184],{},[898,8181,5502],{},[1655,8183,2969],{},[1826,8185,1828],{},[902,8187,5758],{"encoding":904}," (elastická) ",[883,8190,8192],{"className":8191},[886],[888,8193,8194],{"xmlns":890},[892,8195,8196,8200],{},[895,8197,8198],{},[1655,8199,5238],{},[902,8201,8202],{"encoding":904},"\\Rightarrow",[883,8204,8206],{"className":8205},[886],[888,8207,8208],{"xmlns":890},[892,8209,8210,8226],{},[895,8211,8212,8214,8216,8218,8220,8222,8224],{},[1826,8213,1828],{},[1655,8215,2623],{},[1826,8217,1828],{},[898,8219,5923],{"mathvariant":1943},[898,8221,5502],{},[1655,8223,2969],{},[1826,8225,2552],{},[902,8227,8228],{"encoding":904},"1 - 1\u002FE > 0",[883,8230,8232],{"className":8231},[886],[888,8233,8234],{"xmlns":890},[892,8235,8236,8240],{},[895,8237,8238],{},[1655,8239,5238],{},[902,8241,8202],{"encoding":904},[883,8243,8245],{"className":8244},[886],[888,8246,8247],{"xmlns":890},[892,8248,8249,8259],{},[895,8250,8251,8253,8255,8257],{},[898,8252,2127],{},[898,8254,5245],{},[1655,8256,2969],{},[1826,8258,2552],{},[902,8260,8261],{"encoding":904},"MR > 0"," — ",[883,8264,8266],{"className":8265},[886],[888,8267,8268],{"xmlns":890},[892,8269,8270,8276],{},[895,8271,8272,8274],{},[898,8273,4049],{},[898,8275,5245],{},[902,8277,5345],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,8280,8281,8298,8299,3106,8312,8262,8332,8347],{},[883,8282,8284],{"className":8283},[886],[888,8285,8286],{"xmlns":890},[892,8287,8288,8296],{},[895,8289,8290,8292,8294],{},[898,8291,5502],{},[1655,8293,1657],{},[1826,8295,1828],{},[902,8297,5794],{"encoding":904}," (jednotková) ",[883,8300,8302],{"className":8301},[886],[888,8303,8304],{"xmlns":890},[892,8305,8306,8310],{},[895,8307,8308],{},[1655,8309,5238],{},[902,8311,8202],{"encoding":904},[883,8313,8315],{"className":8314},[886],[888,8316,8317],{"xmlns":890},[892,8318,8319,8329],{},[895,8320,8321,8323,8325,8327],{},[898,8322,2127],{},[898,8324,5245],{},[1655,8326,1657],{},[1826,8328,2552],{},[902,8330,8331],{"encoding":904},"MR = 0",[883,8333,8335],{"className":8334},[886],[888,8336,8337],{"xmlns":890},[892,8338,8339,8345],{},[895,8340,8341,8343],{},[898,8342,4049],{},[898,8344,5245],{},[902,8346,5345],{"encoding":904}," je extrém (maximum).",[123,8349,8350,8367,8368,3106,8381,8262,8401,8416],{},[883,8351,8353],{"className":8352},[886],[888,8354,8355],{"xmlns":890},[892,8356,8357,8365],{},[895,8358,8359,8361,8363],{},[898,8360,5502],{},[1655,8362,3065],{},[1826,8364,1828],{},[902,8366,5776],{"encoding":904}," (neelastická) ",[883,8369,8371],{"className":8370},[886],[888,8372,8373],{"xmlns":890},[892,8374,8375,8379],{},[895,8376,8377],{},[1655,8378,5238],{},[902,8380,8202],{"encoding":904},[883,8382,8384],{"className":8383},[886],[888,8385,8386],{"xmlns":890},[892,8387,8388,8398],{},[895,8389,8390,8392,8394,8396],{},[898,8391,2127],{},[898,8393,5245],{},[1655,8395,3065],{},[1826,8397,2552],{},[902,8399,8400],{"encoding":904},"MR \u003C 0",[883,8402,8404],{"className":8403},[886],[888,8405,8406],{"xmlns":890},[892,8407,8408,8414],{},[895,8409,8410,8412],{},[898,8411,4049],{},[898,8413,5245],{},[902,8415,5345],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,8418,8419,8420,1719],{},"Viz také ",[207,8421,5078],{"className":8422,"dataFsResolvedFilePath":827,"href":828},[210],[198,8424,8426],{"id":8425},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,8428,8429,8449,8450,8476,8477,8492,8493,8506,8507,8520,8521,8534,8535,8551,8552,3106,8567,8570,8571,8551,8587,1719],{},[38,8430,8431,8432,5171],{},"(a) Poptávka elastická (",[883,8433,8435],{"className":8434},[886],[888,8436,8437],{"xmlns":890},[892,8438,8439,8447],{},[895,8440,8441,8443,8445],{},[898,8442,5502],{},[1655,8444,2969],{},[1826,8446,1828],{},[902,8448,5758],{"encoding":904}," Z (4.12) plyne ",[883,8451,8453],{"className":8452},[886],[888,8454,8455],{"xmlns":890},[892,8456,8457,8473],{},[895,8458,8459,8461,8463,8465,8467,8469,8471],{},[898,8460,2127],{},[898,8462,5245],{},[1655,8464,1664],{"stretchy":1663},[898,8466,1824],{},[1655,8468,1677],{"stretchy":1663},[1655,8470,2969],{},[1826,8472,2552],{},[902,8474,8475],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,8478,8480],{"className":8479},[886],[888,8481,8482],{"xmlns":890},[892,8483,8484,8490],{},[895,8485,8486,8488],{},[898,8487,4049],{},[898,8489,5245],{},[902,8491,5345],{"encoding":904}," je rostoucí funkcí ",[883,8494,8496],{"className":8495},[886],[888,8497,8498],{"xmlns":890},[892,8499,8500,8504],{},[895,8501,8502],{},[898,8503,1824],{},[902,8505,1824],{"encoding":904},". Avšak růst ",[883,8508,8510],{"className":8509},[886],[888,8511,8512],{"xmlns":890},[892,8513,8514,8518],{},[895,8515,8516],{},[898,8517,1824],{},[902,8519,1824],{"encoding":904}," je odezvou na pokles ceny ",[883,8522,8524],{"className":8523},[886],[888,8525,8526],{"xmlns":890},[892,8527,8528,8532],{},[895,8529,8530],{},[898,8531,2132],{},[902,8533,2132],{"encoding":904},". Tudíž s ",[614,8536,8537,8538],{},"poklesem ceny ",[883,8539,8541],{"className":8540},[886],[888,8542,8543],{"xmlns":890},[892,8544,8545,8549],{},[895,8546,8547],{},[898,8548,2132],{},[902,8550,2132],{"encoding":904}," celkový příjem ",[883,8553,8555],{"className":8554},[886],[888,8556,8557],{"xmlns":890},[892,8558,8559,8565],{},[895,8560,8561,8563],{},[898,8562,4049],{},[898,8564,5245],{},[902,8566,5345],{"encoding":904},[614,8568,8569],{},"roste"," a s ",[614,8572,8573,8574],{},"růstem ceny ",[883,8575,8577],{"className":8576},[886],[888,8578,8579],{"xmlns":890},[892,8580,8581,8585],{},[895,8582,8583],{},[898,8584,2132],{},[902,8586,2132],{"encoding":904},[614,8588,8589],{},"klesá",[5120,8591,8592],{},[724,8593,8594,8597],{},[38,8595,8596],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,8599,8600,8449,8620,1343,8646,8661,8662,8675,8676,8689,8690,8703,8704,8551,8717,3106,8732,1719],{},[38,8601,8602,8603,5171],{},"(b) Poptávka neelastická (",[883,8604,8606],{"className":8605},[886],[888,8607,8608],{"xmlns":890},[892,8609,8610,8618],{},[895,8611,8612,8614,8616],{},[898,8613,5502],{},[1655,8615,3065],{},[1826,8617,1828],{},[902,8619,5776],{"encoding":904},[883,8621,8623],{"className":8622},[886],[888,8624,8625],{"xmlns":890},[892,8626,8627,8643],{},[895,8628,8629,8631,8633,8635,8637,8639,8641],{},[898,8630,2127],{},[898,8632,5245],{},[1655,8634,1664],{"stretchy":1663},[898,8636,1824],{},[1655,8638,1677],{"stretchy":1663},[1655,8640,3065],{},[1826,8642,2552],{},[902,8644,8645],{"encoding":904},"MR(Q) \u003C 0",[883,8647,8649],{"className":8648},[886],[888,8650,8651],{"xmlns":890},[892,8652,8653,8659],{},[895,8654,8655,8657],{},[898,8656,4049],{},[898,8658,5245],{},[902,8660,5345],{"encoding":904}," je klesající funkce ",[883,8663,8665],{"className":8664},[886],[888,8666,8667],{"xmlns":890},[892,8668,8669,8673],{},[895,8670,8671],{},[898,8672,1824],{},[902,8674,1824],{"encoding":904},", tj. s růstem ",[883,8677,8679],{"className":8678},[886],[888,8680,8681],{"xmlns":890},[892,8682,8683,8687],{},[895,8684,8685],{},[898,8686,1824],{},[902,8688,1824],{"encoding":904}," (s poklesem ceny ",[883,8691,8693],{"className":8692},[886],[888,8694,8695],{"xmlns":890},[892,8696,8697,8701],{},[895,8698,8699],{},[898,8700,2132],{},[902,8702,2132],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,8705,8707],{"className":8706},[886],[888,8708,8709],{"xmlns":890},[892,8710,8711,8715],{},[895,8712,8713],{},[898,8714,2132],{},[902,8716,2132],{"encoding":904},[883,8718,8720],{"className":8719},[886],[888,8721,8722],{"xmlns":890},[892,8723,8724,8730],{},[895,8725,8726,8728],{},[898,8727,4049],{},[898,8729,5245],{},[902,8731,5345],{"encoding":904},[614,8733,8569],{},[5120,8735,8736],{},[724,8737,8738,8741],{},[38,8739,8740],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,8743,8744,8449,8764,8783,8784,8799,8800,8870,8871,2704,8899,8932,8933,6838,8961,8976,8977,1719],{},[38,8745,8746,8747,5171],{},"(c) Jednotková elasticita (",[883,8748,8750],{"className":8749},[886],[888,8751,8752],{"xmlns":890},[892,8753,8754,8762],{},[895,8755,8756,8758,8760],{},[898,8757,5502],{},[1655,8759,1657],{},[1826,8761,1828],{},[902,8763,5794],{"encoding":904},[883,8765,8767],{"className":8766},[886],[888,8768,8769],{"xmlns":890},[892,8770,8771,8781],{},[895,8772,8773,8775,8777,8779],{},[898,8774,2127],{},[898,8776,5245],{},[1655,8778,1657],{},[1826,8780,2552],{},[902,8782,8331],{"encoding":904}," — nutná podmínka extrému ",[883,8785,8787],{"className":8786},[886],[888,8788,8789],{"xmlns":890},[892,8790,8791,8797],{},[895,8792,8793,8795],{},[898,8794,4049],{},[898,8796,5245],{},[902,8798,5345],{"encoding":904},". Dále ",[883,8801,8803],{"className":8802},[886],[888,8804,8805],{"xmlns":890},[892,8806,8807,8867],{},[895,8808,8809,8811,8821,8823,8825,8831,8833,8839,8841,8843,8845,8847,8849,8851,8861,8863,8865],{},[898,8810,4049],{},[2597,8812,8813,8815],{},[898,8814,5245],{},[895,8816,8817,8819],{},[1655,8818,1945],{"mathvariant":1943},[1655,8820,1945],{"mathvariant":1943},[1655,8822,1657],{},[898,8824,2127],{},[2597,8826,8827,8829],{},[898,8828,5245],{},[1655,8830,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,8832,1657],{},[2597,8834,8835,8837],{},[898,8836,2838],{},[1655,8838,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,8840,1664],{"stretchy":1663},[898,8842,1824],{},[1655,8844,1677],{"stretchy":1663},[1655,8846,2346],{},[898,8848,1824],{},[2031,8850,2435],{},[2597,8852,8853,8855],{},[898,8854,2838],{},[895,8856,8857,8859],{},[1655,8858,1945],{"mathvariant":1943},[1655,8860,1945],{"mathvariant":1943},[1655,8862,1664],{"stretchy":1663},[898,8864,1824],{},[1655,8866,1677],{"stretchy":1663},[902,8868,8869],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,8872,8874],{"className":8873},[886],[888,8875,8876],{"xmlns":890},[892,8877,8878,8896],{},[895,8879,8880,8886,8888,8890,8892,8894],{},[2597,8881,8882,8884],{},[898,8883,2838],{},[1655,8885,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,8887,1664],{"stretchy":1663},[898,8889,1824],{},[1655,8891,1677],{"stretchy":1663},[1655,8893,3065],{},[1826,8895,2552],{},[902,8897,8898],{"encoding":904},"D'(Q) \u003C 0",[883,8900,8902],{"className":8901},[886],[888,8903,8904],{"xmlns":890},[892,8905,8906,8929],{},[895,8907,8908,8918,8920,8922,8924,8927],{},[2597,8909,8910,8912],{},[898,8911,2838],{},[895,8913,8914,8916],{},[1655,8915,1945],{"mathvariant":1943},[1655,8917,1945],{"mathvariant":1943},[1655,8919,1664],{"stretchy":1663},[898,8921,1824],{},[1655,8923,1677],{"stretchy":1663},[1655,8925,8926],{},"≤",[1826,8928,2552],{},[902,8930,8931],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,8934,8936],{"className":8935},[886],[888,8937,8938],{"xmlns":890},[892,8939,8940,8958],{},[895,8941,8942,8944,8954,8956],{},[898,8943,4049],{},[2597,8945,8946,8948],{},[898,8947,5245],{},[895,8949,8950,8952],{},[1655,8951,1945],{"mathvariant":1943},[1655,8953,1945],{"mathvariant":1943},[1655,8955,3065],{},[1826,8957,2552],{},[902,8959,8960],{"encoding":904},"TR'' \u003C 0",[883,8962,8964],{"className":8963},[886],[888,8965,8966],{"xmlns":890},[892,8967,8968,8974],{},[895,8969,8970,8972],{},[898,8971,4049],{},[898,8973,5245],{},[902,8975,5345],{"encoding":904}," nabývá ",[38,8978,8979],{},"maxima",[5120,8981,8982],{},[724,8983,8984,8987],{},[38,8985,8986],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,8989,8990],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,8992,8993],{},[38,8994,8995],{},"Souhrnná tabulka Pravidel 1–3:",[16,8997,8998,9102],{},[19,8999,9000],{},[22,9001,9002,9005,9020,9037,9068,9099],{},[25,9003,9004],{},"Charakter poptávky",[25,9006,9007],{},[883,9008,9010],{"className":9009},[886],[888,9011,9012],{"xmlns":890},[892,9013,9014,9018],{},[895,9015,9016],{},[898,9017,5502],{},[902,9019,5502],{"encoding":904},[25,9021,9022],{},[883,9023,9025],{"className":9024},[886],[888,9026,9027],{"xmlns":890},[892,9028,9029,9035],{},[895,9030,9031,9033],{},[898,9032,2127],{},[898,9034,5245],{},[902,9036,7881],{"encoding":904},[25,9038,9039,9040,3106,9053],{},"Pokles ceny ",[883,9041,9043],{"className":9042},[886],[888,9044,9045],{"xmlns":890},[892,9046,9047,9051],{},[895,9048,9049],{},[1655,9050,5238],{},[902,9052,8202],{"encoding":904},[883,9054,9056],{"className":9055},[886],[888,9057,9058],{"xmlns":890},[892,9059,9060,9066],{},[895,9061,9062,9064],{},[898,9063,4049],{},[898,9065,5245],{},[902,9067,5345],{"encoding":904},[25,9069,9070,9071,3106,9084],{},"Růst ceny ",[883,9072,9074],{"className":9073},[886],[888,9075,9076],{"xmlns":890},[892,9077,9078,9082],{},[895,9079,9080],{},[1655,9081,5238],{},[902,9083,8202],{"encoding":904},[883,9085,9087],{"className":9086},[886],[888,9088,9089],{"xmlns":890},[892,9090,9091,9097],{},[895,9092,9093,9095],{},[898,9094,4049],{},[898,9096,5245],{},[902,9098,5345],{"encoding":904},[25,9100,9101],{},"Doporučení",[30,9103,9104,9153,9203],{},[22,9105,9106,9108,9126,9144,9146,9148],{},[35,9107,5324],{},[35,9109,9110],{},[883,9111,9113],{"className":9112},[886],[888,9114,9115],{"xmlns":890},[892,9116,9117,9123],{},[895,9118,9119,9121],{},[1655,9120,2969],{},[1826,9122,1828],{},[902,9124,9125],{"encoding":904},"> 1",[35,9127,9128],{},[883,9129,9131],{"className":9130},[886],[888,9132,9133],{"xmlns":890},[892,9134,9135,9141],{},[895,9136,9137,9139],{},[1655,9138,2969],{},[1826,9140,2552],{},[902,9142,9143],{"encoding":904},"> 0",[35,9145,8569],{},[35,9147,8589],{},[35,9149,9150],{},[38,9151,9152],{},"snížit cenu",[22,9154,9155,9158,9176,9194,9196,9198],{},[35,9156,9157],{},"jednotková",[35,9159,9160],{},[883,9161,9163],{"className":9162},[886],[888,9164,9165],{"xmlns":890},[892,9166,9167,9173],{},[895,9168,9169,9171],{},[1655,9170,1657],{},[1826,9172,1828],{},[902,9174,9175],{"encoding":904},"= 1",[35,9177,9178],{},[883,9179,9181],{"className":9180},[886],[888,9182,9183],{"xmlns":890},[892,9184,9185,9191],{},[895,9186,9187,9189],{},[1655,9188,1657],{},[1826,9190,2552],{},[902,9192,9193],{"encoding":904},"= 0",[35,9195,3073],{},[35,9197,3073],{},[35,9199,9200],{},[38,9201,9202],{},"držet cenu",[22,9204,9205,9207,9225,9243,9245,9247],{},[35,9206,5328],{},[35,9208,9209],{},[883,9210,9212],{"className":9211},[886],[888,9213,9214],{"xmlns":890},[892,9215,9216,9222],{},[895,9217,9218,9220],{},[1655,9219,3065],{},[1826,9221,1828],{},[902,9223,9224],{"encoding":904},"\u003C 1",[35,9226,9227],{},[883,9228,9230],{"className":9229},[886],[888,9231,9232],{"xmlns":890},[892,9233,9234,9240],{},[895,9235,9236,9238],{},[1655,9237,3065],{},[1826,9239,2552],{},[902,9241,9242],{"encoding":904},"\u003C 0",[35,9244,8589],{},[35,9246,8569],{},[35,9248,9249],{},[38,9250,9251],{},"zvýšit cenu",[198,9253,9255],{"id":9254},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,9257,9258,9259,9284,9285,9307,9308,9321,9322,9335,9336,9349,9350,6838,9377,9429],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,9260,9262],{"className":9261},[886],[888,9263,9264],{"xmlns":890},[892,9265,9266,9282],{},[895,9267,9268,9270,9272,9274,9276],{},[898,9269,2132],{},[1655,9271,1657],{},[1826,9273,4360],{},[1655,9275,2623],{},[2597,9277,9278,9280],{},[898,9279,1824],{},[1826,9281,1837],{},[902,9283,6708],{"encoding":904},". Reálné cenové rozpětí je ",[883,9286,9288],{"className":9287},[886],[888,9289,9290],{"xmlns":890},[892,9291,9292,9304],{},[895,9293,9294,9296,9298,9300,9302],{},[1655,9295,6573],{"stretchy":1663},[1826,9297,1828],{},[1655,9299,1671],{"separator":1670},[1826,9301,4360],{},[1655,9303,6590],{"stretchy":1663},[902,9305,9306],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,9309,9311],{"className":9310},[886],[888,9312,9313],{"xmlns":890},[892,9314,9315,9319],{},[895,9316,9317],{},[898,9318,1824],{},[902,9320,1824],{"encoding":904}," jako funkci ",[883,9323,9325],{"className":9324},[886],[888,9326,9327],{"xmlns":890},[892,9328,9329,9333],{},[895,9330,9331],{},[898,9332,2132],{},[902,9334,2132],{"encoding":904},"; pro nezáporné ",[883,9337,9339],{"className":9338},[886],[888,9340,9341],{"xmlns":890},[892,9342,9343,9347],{},[895,9344,9345],{},[898,9346,1824],{},[902,9348,1824],{"encoding":904}," je ",[883,9351,9353],{"className":9352},[886],[888,9354,9355],{"xmlns":890},[892,9356,9357,9374],{},[895,9358,9359,9361,9363],{},[898,9360,1824],{},[1655,9362,1657],{},[9364,9365,9366],"msqrt",{},[895,9367,9368,9370,9372],{},[1826,9369,4360],{},[1655,9371,2623],{},[898,9373,2132],{},[902,9375,9376],{"encoding":904},"Q = \\sqrt{100 - P}",[883,9378,9380],{"className":9379},[886],[888,9381,9382],{"xmlns":890},[892,9383,9384,9426],{},[895,9385,9386,9402,9404,9406],{},[3615,9387,9388],{"scriptlevel":2552,"displaystyle":1670},[1949,9389,9390,9396],{},[895,9391,9392,9394],{},[898,9393,2410],{"mathvariant":1943},[898,9395,1824],{},[895,9397,9398,9400],{},[898,9399,2410],{"mathvariant":1943},[898,9401,2132],{},[1655,9403,1657],{},[1655,9405,2623],{},[3615,9407,9408],{"scriptlevel":2552,"displaystyle":1670},[1949,9409,9410,9412],{},[1826,9411,1828],{},[895,9413,9414,9416],{},[1826,9415,1837],{},[9364,9417,9418],{},[895,9419,9420,9422,9424],{},[1826,9421,4360],{},[1655,9423,2623],{},[898,9425,2132],{},[902,9427,9428],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,9431,9432],{},[883,9433,9435],{"className":9434},[886],[888,9436,9437],{"xmlns":890},[892,9438,9439,9561],{},[895,9440,9441,9443,9445,9447,9449,9451,9453,9459,9461,9475,9477,9479,9493,9495,9521,9523,9541,9543,9559],{},[898,9442,5502],{},[1655,9444,1664],{"stretchy":1663},[898,9446,2132],{},[1655,9448,1677],{"stretchy":1663},[1655,9450,1657],{},[1655,9452,2623],{},[1949,9454,9455,9457],{},[898,9456,2132],{},[898,9458,1824],{},[1655,9460,2869],{},[1949,9462,9463,9469],{},[895,9464,9465,9467],{},[898,9466,2410],{"mathvariant":1943},[898,9468,1824],{},[895,9470,9471,9473],{},[898,9472,2410],{"mathvariant":1943},[898,9474,2132],{},[1655,9476,1657],{},[1655,9478,2623],{},[1949,9480,9481,9483],{},[898,9482,2132],{},[9364,9484,9485],{},[895,9486,9487,9489,9491],{},[1826,9488,4360],{},[1655,9490,2623],{},[898,9492,2132],{},[1655,9494,2869],{},[895,9496,9497,9499,9501,9519],{},[1655,9498,1664],{"fence":1670},[1655,9500,2623],{},[1949,9502,9503,9505],{},[1826,9504,1828],{},[895,9506,9507,9509],{},[1826,9508,1837],{},[9364,9510,9511],{},[895,9512,9513,9515,9517],{},[1826,9514,4360],{},[1655,9516,2623],{},[898,9518,2132],{},[1655,9520,1677],{"fence":1670},[1655,9522,1657],{},[1949,9524,9525,9527],{},[898,9526,2132],{},[895,9528,9529,9531,9533,9535,9537,9539],{},[1826,9530,1837],{},[1655,9532,1664],{"stretchy":1663},[1826,9534,4360],{},[1655,9536,2623],{},[898,9538,2132],{},[1655,9540,1677],{"stretchy":1663},[1655,9542,1657],{},[1949,9544,9545,9551],{},[895,9546,9547,9549],{},[1826,9548,6258],{},[898,9550,2132],{},[895,9552,9553,9555,9557],{},[1826,9554,4360],{},[1655,9556,2623],{},[898,9558,2132],{},[898,9560,1719],{"mathvariant":1943},[902,9562,9563],{"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}.",[724,9565,9566,9567,2086],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,9568,9570],{"className":9569},[886],[888,9571,9572],{"xmlns":890},[892,9573,9574,9598],{},[895,9575,9576,9594,9596],{},[3615,9577,9578],{"scriptlevel":2552,"displaystyle":1670},[1949,9579,9580,9586],{},[895,9581,9582,9584],{},[1826,9583,6258],{},[898,9585,2132],{},[895,9587,9588,9590,9592],{},[1826,9589,4360],{},[1655,9591,2623],{},[898,9593,2132],{},[1655,9595,1657],{},[1826,9597,1828],{},[902,9599,9600],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,9602,9603],{},[883,9604,9606],{"className":9605},[886],[888,9607,9608],{"xmlns":890},[892,9609,9610,9642],{},[895,9611,9612,9618,9620,9627,9629,9632,9640],{},[2597,9613,9614,9616],{},[898,9615,2132],{},[1655,9617,5603],{},[1655,9619,1657],{},[1949,9621,9622,9625],{},[1826,9623,9624],{},"200",[1826,9626,3472],{},[1655,9628,7147],{},[1826,9630,9631],{},"66,",[9633,9634,9635,9637],"mover",{"accent":1670},[1826,9636,3531],{},[1655,9638,9639],{"stretchy":1670},"‾",[898,9641,1719],{"mathvariant":1943},[902,9643,9644],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,9646,9647],{},"S využitím vlastnosti (4.8):",[120,9649,9650,9696,9738],{},[123,9651,9652,9653,9688,9689,9691,9692,9695],{},"Při cenách ",[883,9654,9656],{"className":9655},[886],[888,9657,9658],{"xmlns":890},[892,9659,9660,9685],{},[895,9661,9662,9664,9666,9668,9670,9673,9675,9677,9683],{},[898,9663,2132],{},[1655,9665,7753],{},[1655,9667,6573],{"stretchy":1663},[1826,9669,1828],{},[1655,9671,9672],{"separator":1670},";",[2031,9674,2435],{},[1826,9676,9631],{},[9633,9678,9679,9681],{"accent":1670},[1826,9680,3531],{},[1655,9682,9639],{"stretchy":1670},[1655,9684,1677],{"stretchy":1663},[902,9686,9687],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,9690,5328],{}," — dle ",[614,9693,9694],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,9697,9652,9698,9688,9732,9691,9734,9737],{},[883,9699,9701],{"className":9700},[886],[888,9702,9703],{"xmlns":890},[892,9704,9705,9729],{},[895,9706,9707,9709,9711,9713,9715,9721,9723,9725,9727],{},[898,9708,2132],{},[1655,9710,7753],{},[1655,9712,1664],{"stretchy":1663},[1826,9714,9631],{},[9633,9716,9717,9719],{"accent":1670},[1826,9718,3531],{},[1655,9720,9639],{"stretchy":1670},[1655,9722,9672],{"separator":1670},[2031,9724,2435],{},[1826,9726,4360],{},[1655,9728,6590],{"stretchy":1663},[902,9730,9731],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,9733,5324],{},[614,9735,9736],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,9739,9740,9741,9744,9745,9773,9774,9777],{},"Dle ",[614,9742,9743],{},"Pravidla 3"," je při ceně ",[883,9746,9748],{"className":9747},[886],[888,9749,9750],{"xmlns":890},[892,9751,9752,9770],{},[895,9753,9754,9760,9762,9764],{},[2597,9755,9756,9758],{},[898,9757,2132],{},[1655,9759,5603],{},[1655,9761,1657],{},[1826,9763,9631],{},[9633,9765,9766,9768],{"accent":1670},[1826,9767,3531],{},[1655,9769,9639],{"stretchy":1670},[902,9771,9772],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,9775,9776],{},"maxima celkového příjmu"," ve výši",[724,9779,9780],{},[883,9781,9783],{"className":9782},[886],[888,9784,9785],{"xmlns":890},[892,9786,9787,9865],{},[895,9788,9789,9791,9793,9795,9801,9803,9805,9811,9813,9827,9829,9835,9837,9845,9847,9860,9862],{},[898,9790,4049],{},[898,9792,5245],{},[1655,9794,1664],{"stretchy":1663},[2597,9796,9797,9799],{},[898,9798,2132],{},[1655,9800,5603],{},[1655,9802,1677],{"stretchy":1663},[1655,9804,1657],{},[2597,9806,9807,9809],{},[898,9808,2132],{},[1655,9810,5603],{},[1655,9812,2869],{},[9364,9814,9815],{},[895,9816,9817,9819,9821],{},[1826,9818,4360],{},[1655,9820,2623],{},[2597,9822,9823,9825],{},[898,9824,2132],{},[1655,9826,5603],{},[1655,9828,1657],{},[1949,9830,9831,9833],{},[1826,9832,9624],{},[1826,9834,3472],{},[1655,9836,2869],{},[9364,9838,9839],{},[1949,9840,9841,9843],{},[1826,9842,4360],{},[1826,9844,3472],{},[1655,9846,1657],{},[1949,9848,9849,9852],{},[1826,9850,9851],{},"2000",[895,9853,9854,9856],{},[1826,9855,3472],{},[9364,9857,9858],{},[1826,9859,3472],{},[1655,9861,7147],{},[1826,9863,9864],{},"384,9.",[902,9866,9867],{"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.",[724,9869,9870,9871,1719],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,9872,9874],{"className":9873},[886],[888,9875,9876],{"xmlns":890},[892,9877,9878,9884],{},[895,9879,9880,9882],{},[898,9881,4049],{},[898,9883,5245],{},[902,9885,5345],{"encoding":904},[115,9887,9889],{"id":9888},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,9891,9892,9893,9896],{},"Analogicky se definuje ",[38,9894,9895],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,9898,9899],{},[883,9900,9902],{"className":9901,"title":5450,"style":5451},[5449],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,9904,5559,9905,9930,9931,9963],{},[883,9906,9908],{"className":9907},[886],[888,9909,9910],{"xmlns":890},[892,9911,9912,9927],{},[895,9913,9914,9916,9918,9921,9923,9925],{},[898,9915,1824],{},[1655,9917,1657],{},[898,9919,9920],{},"S",[1655,9922,1664],{"stretchy":1663},[898,9924,2132],{},[1655,9926,1677],{"stretchy":1663},[902,9928,9929],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,9932,9934],{"className":9933},[886],[888,9935,9936],{"xmlns":890},[892,9937,9938,9960],{},[895,9939,9940,9956,9958],{},[3615,9941,9942],{"scriptlevel":2552,"displaystyle":1670},[1949,9943,9944,9950],{},[895,9945,9946,9948],{},[898,9947,2410],{"mathvariant":1943},[898,9949,1824],{},[895,9951,9952,9954],{},[898,9953,2410],{"mathvariant":1943},[898,9955,2132],{},[1655,9957,2969],{},[1826,9959,2552],{},[902,9961,9962],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,9965,9966],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[5120,9968,9969],{},[724,9970,9971,9972],{},"S rostoucí cenou elasticita nabídky roste. ",[883,9973,9975],{"className":9974},[886],[888,9976,9977],{"xmlns":890},[892,9978,9979,9988],{},[895,9980,9981,9983,9986],{},[1655,9982,1664],{"stretchy":1663},[1826,9984,9985],{},"4.14",[1655,9987,1677],{"stretchy":1663},[902,9989,9990],{"encoding":904},"(4.14)",[724,9992,9993],{},"Pro nominální změny platí",[724,9995,9996],{},[883,9997,9999],{"className":9998,"title":5450,"style":5451},[5449],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,10001,10002],{},"a pro procentní změny",[724,10004,10005],{},[883,10006,10008],{"className":10007,"title":5450,"style":5451},[5449],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,10010,10011],{},"(bez znaménka minus).",[198,10013,10015],{"id":10014},"příklad-47","Příklad 4.7",[724,10017,10018,10019,2086],{},"Nabídka ",[883,10020,10022],{"className":10021},[886],[888,10023,10024],{"xmlns":890},[892,10025,10026,10051],{},[895,10027,10028,10030,10032,10034,10040,10042,10044,10046,10048],{},[898,10029,1824],{},[1655,10031,1657],{},[1826,10033,4068],{},[2597,10035,10036,10038],{},[898,10037,2132],{},[1826,10039,1837],{},[1655,10041,2346],{},[1826,10043,3524],{},[898,10045,2132],{},[1655,10047,2346],{},[1826,10049,10050],{},"150",[902,10052,10053],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,10055,10056],{},[883,10057,10059],{"className":10058},[886],[888,10060,10061],{"xmlns":890},[892,10062,10063,10109],{},[895,10064,10065,10067,10069,10093,10095,10097,10099,10101,10103,10105,10107],{},[898,10066,5502],{},[1655,10068,1657],{},[1949,10070,10071,10073],{},[898,10072,2132],{},[895,10074,10075,10077,10083,10085,10087,10089,10091],{},[1826,10076,4068],{},[2597,10078,10079,10081],{},[898,10080,2132],{},[1826,10082,1837],{},[1655,10084,2346],{},[1826,10086,3524],{},[898,10088,2132],{},[1655,10090,2346],{},[1826,10092,10050],{},[2031,10094,2435],{},[1655,10096,1664],{"stretchy":1663},[1826,10098,4112],{},[898,10100,2132],{},[1655,10102,2346],{},[1826,10104,3524],{},[1655,10106,1677],{"stretchy":1663},[898,10108,1719],{"mathvariant":1943},[902,10110,10111],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,10113,6366,10114,1343,10144,1343,10171,10207,10208,10233,10234,10252,10253,1719],{},[883,10115,10117],{"className":10116},[886],[888,10118,10119],{"xmlns":890},[892,10120,10121,10141],{},[895,10122,10123,10125,10127,10129,10131,10133],{},[898,10124,5502],{},[1655,10126,1664],{"stretchy":1663},[1826,10128,4136],{},[1655,10130,1677],{"stretchy":1663},[1655,10132,1657],{},[3615,10134,10135],{"scriptlevel":2552,"displaystyle":1663},[1949,10136,10137,10139],{},[1826,10138,1828],{},[1826,10140,3472],{},[902,10142,10143],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,10145,10147],{"className":10146},[886],[888,10148,10149],{"xmlns":890},[892,10150,10151,10168],{},[895,10152,10153,10155,10157,10162,10164,10166],{},[898,10154,5502],{},[1655,10156,1664],{"stretchy":1663},[9364,10158,10159],{},[1826,10160,10161],{},"1500",[1655,10163,1677],{"stretchy":1663},[1655,10165,1657],{},[1826,10167,1828],{},[902,10169,10170],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,10172,10174],{"className":10173},[886],[888,10175,10176],{"xmlns":890},[892,10177,10178,10204],{},[895,10179,10180,10182,10184,10186,10188,10190,10199,10201],{},[898,10181,5502],{},[1655,10183,1664],{"stretchy":1663},[1826,10185,4360],{},[1655,10187,1677],{"stretchy":1663},[1655,10189,1657],{},[3615,10191,10192],{"scriptlevel":2552,"displaystyle":1663},[1949,10193,10194,10196],{},[1826,10195,4390],{},[1826,10197,10198],{},"33",[1655,10200,7147],{},[1826,10202,10203],{},"1,515",[902,10205,10206],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,10209,10211],{"className":10210},[886],[888,10212,10213],{"xmlns":890},[892,10214,10215,10230],{},[895,10216,10217,10219,10221,10225,10227],{},[898,10218,2132],{},[1655,10220,2969],{},[9364,10222,10223],{},[1826,10224,10161],{},[1655,10226,2357],{},[1826,10228,10229],{},"38,7",[902,10231,10232],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,10235,10237],{"className":10236},[886],[888,10238,10239],{"xmlns":890},[892,10240,10241,10249],{},[895,10242,10243,10245,10247],{},[898,10244,2132],{},[1655,10246,3065],{},[1826,10248,10229],{},[902,10250,10251],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,10254,10256],{"className":10255},[886],[888,10257,10258],{"xmlns":890},[892,10259,10260,10298],{},[895,10261,10262,10264,10266,10268,10270,10278,10280,10283,10285,10288,10294,10296],{},[898,10263,2506],{"mathvariant":1943},[898,10265,1824],{},[898,10267,7172],{"mathvariant":1943},[1655,10269,2357],{},[3615,10271,10272],{"scriptlevel":2552,"displaystyle":1663},[1949,10273,10274,10276],{},[1826,10275,1828],{},[1826,10277,3472],{},[1655,10279,2869],{},[1826,10281,10282],{},"20",[1655,10284,1657],{},[1826,10286,10287],{},"6,",[9633,10289,10290,10292],{"accent":1670},[1826,10291,3531],{},[1655,10293,9639],{"stretchy":1670},[2031,10295,2435],{},[898,10297,7172],{"mathvariant":1943},[902,10299,10300],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,10302,10304],{"id":10303},"vícefaktorový-model","Vícefaktorový model",[724,10306,10307,10308,10321,10322,3106,10325,10338,10339,3106,10342,10360,10361,3106,10364,2086],{},"Předpokládejme, že poptávané množství ",[883,10309,10311],{"className":10310},[886],[888,10312,10313],{"xmlns":890},[892,10314,10315,10319],{},[895,10316,10317],{},[898,10318,1824],{},[902,10320,1824],{"encoding":904}," závisí na ",[38,10323,10324],{},"ceně základního zboží",[883,10326,10328],{"className":10327},[886],[888,10329,10330],{"xmlns":890},[892,10331,10332,10336],{},[895,10333,10334],{},[898,10335,2132],{},[902,10337,2132],{"encoding":904},", na ",[38,10340,10341],{},"ceně alternativního zboží",[883,10343,10345],{"className":10344},[886],[888,10346,10347],{"xmlns":890},[892,10348,10349,10357],{},[895,10350,10351],{},[1820,10352,10353,10355],{},[898,10354,2132],{},[898,10356,2731],{},[902,10358,10359],{"encoding":904},"P_A"," a na ",[38,10362,10363],{},"důchodu",[883,10365,10367],{"className":10366},[886],[888,10368,10369],{"xmlns":890},[892,10370,10371,10376],{},[895,10372,10373],{},[898,10374,10375],{},"Y",[902,10377,10375],{"encoding":904},[724,10379,10380],{},[883,10381,10383],{"className":10382,"title":5450,"style":5451},[5449],"Q = D(P, P_A, Y). \\tag{4.17}",[724,10385,10386,10387,10390],{},"V analogii jednofaktorového modelu pracujeme s ",[38,10388,10389],{},"parciálními derivacemi"," funkce poptávky.",[198,10392,10394],{"id":10393},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,10396,10397],{},[883,10398,10400],{"className":10399,"title":5450,"style":5451},[5449],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,10402,5559,10403,10423,10424,10437,10438,4199,10460,3106,10463,10509,10510,10523,10524,10541],{},[883,10404,10406],{"className":10405},[886],[888,10407,10408],{"xmlns":890},[892,10409,10410,10420],{},[895,10411,10412],{},[1935,10413,10414,10416,10418],{},[898,10415,1824],{},[898,10417,2132],{},[1655,10419,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,10421,10422],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,10425,10427],{"className":10426},[886],[888,10428,10429],{"xmlns":890},[892,10430,10431,10435],{},[895,10432,10433],{},[898,10434,2132],{},[902,10436,2132],{"encoding":904},". Vždy ",[883,10439,10441],{"className":10440},[886],[888,10442,10443],{"xmlns":890},[892,10444,10445,10457],{},[895,10446,10447,10453,10455],{},[1820,10448,10449,10451],{},[898,10450,5502],{},[898,10452,2132],{},[1655,10454,5734],{},[1826,10456,2552],{},[902,10458,10459],{"encoding":904},"E_P \\ge 0",[614,10461,10462],{},"Interpretace:",[883,10464,10466],{"className":10465},[886],[888,10467,10468],{"xmlns":890},[892,10469,10470,10506],{},[895,10471,10472,10478,10480,10486,10488,10496,10498,10504],{},[1820,10473,10474,10476],{},[898,10475,5502],{},[898,10477,2132],{},[1655,10479,1664],{"stretchy":1663},[2597,10481,10482,10484],{},[898,10483,2132],{},[1655,10485,5603],{},[1655,10487,1671],{"separator":1670},[1935,10489,10490,10492,10494],{},[898,10491,2132],{},[898,10493,2731],{},[1655,10495,5603],{},[1655,10497,1671],{"separator":1670},[2597,10499,10500,10502],{},[898,10501,10375],{},[1655,10503,5603],{},[1655,10505,1677],{"stretchy":1663},[902,10507,10508],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,10511,10513],{"className":10512},[886],[888,10514,10515],{"xmlns":890},[892,10516,10517,10521],{},[895,10518,10519],{},[898,10520,1824],{},[902,10522,1824],{"encoding":904}," při 1% změně ",[883,10525,10527],{"className":10526},[886],[888,10528,10529],{"xmlns":890},[892,10530,10531,10539],{},[895,10532,10533],{},[2597,10534,10535,10537],{},[898,10536,2132],{},[1655,10538,5603],{},[902,10540,5653],{"encoding":904},", ceteris paribus.",[198,10543,10545],{"id":10544},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,10547,10548],{},[883,10549,10551],{"className":10550,"title":5450,"style":5451},[5449],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,10553,10554,10509,10556,10569,10570,10587],{},[614,10555,10462],{},[883,10557,10559],{"className":10558},[886],[888,10560,10561],{"xmlns":890},[892,10562,10563,10567],{},[895,10564,10565],{},[898,10566,1824],{},[902,10568,1824],{"encoding":904}," základního zboží při 1% změně ceny ",[883,10571,10573],{"className":10572},[886],[888,10574,10575],{"xmlns":890},[892,10576,10577,10585],{},[895,10578,10579],{},[1820,10580,10581,10583],{},[898,10582,2132],{},[898,10584,2731],{},[902,10586,10359],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,10589,10590],{},[38,10591,10592],{},"Znaménko závisí na povaze alternativního zboží:",[120,10594,10595,10683],{},[123,10596,10597,10598,10601,10602,10619,10620,3106,10633,1719],{},"Je-li alternativní zboží ",[38,10599,10600],{},"komplement",", růst ",[883,10603,10605],{"className":10604},[886],[888,10606,10607],{"xmlns":890},[892,10608,10609,10617],{},[895,10610,10611],{},[1820,10612,10613,10615],{},[898,10614,2132],{},[898,10616,2731],{},[902,10618,10359],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,10621,10623],{"className":10622},[886],[888,10624,10625],{"xmlns":890},[892,10626,10627,10631],{},[895,10628,10629],{},[898,10630,1824],{},[902,10632,1824],{"encoding":904},[883,10634,10636],{"className":10635},[886],[888,10637,10638],{"xmlns":890},[892,10639,10640,10680],{},[895,10641,10642,10644,10646,10658,10660,10662,10664,10666,10676,10678],{},[1655,10643,5238],{},[2031,10645,2783],{},[1935,10647,10648,10650,10656],{},[898,10649,1824],{},[1820,10651,10652,10654],{},[898,10653,2132],{},[898,10655,2731],{},[1655,10657,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,10659,3065],{},[1826,10661,2552],{},[1655,10663,1671],{"separator":1670},[2031,10665,2783],{},[1820,10667,10668,10670],{},[898,10669,5502],{},[1820,10671,10672,10674],{},[898,10673,2132],{},[898,10675,2731],{},[1655,10677,3065],{},[1826,10679,2552],{},[902,10681,10682],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,10684,10597,10685,10601,10688,10705,10706,10719,10720,1719],{},[38,10686,10687],{},"substitut",[883,10689,10691],{"className":10690},[886],[888,10692,10693],{"xmlns":890},[892,10694,10695,10703],{},[895,10696,10697],{},[1820,10698,10699,10701],{},[898,10700,2132],{},[898,10702,2731],{},[902,10704,10359],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,10707,10709],{"className":10708},[886],[888,10710,10711],{"xmlns":890},[892,10712,10713,10717],{},[895,10714,10715],{},[898,10716,1824],{},[902,10718,1824],{"encoding":904}," roste ",[883,10721,10723],{"className":10722},[886],[888,10724,10725],{"xmlns":890},[892,10726,10727,10767],{},[895,10728,10729,10731,10733,10745,10747,10749,10751,10753,10763,10765],{},[1655,10730,5238],{},[2031,10732,2783],{},[1935,10734,10735,10737,10743],{},[898,10736,1824],{},[1820,10738,10739,10741],{},[898,10740,2132],{},[898,10742,2731],{},[1655,10744,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,10746,2969],{},[1826,10748,2552],{},[1655,10750,1671],{"separator":1670},[2031,10752,2783],{},[1820,10754,10755,10757],{},[898,10756,5502],{},[1820,10758,10759,10761],{},[898,10760,2132],{},[898,10762,2731],{},[1655,10764,2969],{},[1826,10766,2552],{},[902,10768,10769],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,10771,10774],{"className":10772,"title":10773,"style":5451},[5449],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":10776},[10777,10781,10782,10790,10791,10795,10798],{"id":5143,"depth":642,"text":5144,"children":10778},[10779,10780],{"id":5174,"depth":649,"text":5175},{"id":5353,"depth":649,"text":5354},{"id":5388,"depth":642,"text":5389},{"id":5414,"depth":642,"text":5415,"children":10783},[10784,10785,10786,10787,10789],{"id":6108,"depth":649,"text":6109},{"id":6198,"depth":649,"text":6199},{"id":6534,"depth":649,"text":6535},{"id":6616,"depth":649,"text":10788},"Výpočet, je-li dáno PP jako funkce QQ",{"id":6877,"depth":649,"text":6878},{"id":7200,"depth":642,"text":7201},{"id":7796,"depth":642,"text":7797,"children":10792},[10793,10794],{"id":8425,"depth":649,"text":8426},{"id":9254,"depth":649,"text":9255},{"id":9888,"depth":642,"text":9889,"children":10796},[10797],{"id":10014,"depth":649,"text":10015},{"id":10303,"depth":642,"text":10304,"children":10799},[10800,10801],{"id":10393,"depth":649,"text":10394},{"id":10544,"depth":649,"text":10545},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":5113,"description":641},[1138,1136],"topics\u002Felasticita",[1128,5150,10809,10810,10811,10812],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":1628,"title":1629,"body":10815,"course":1128,"courses":659,"created":1129,"description":3240,"extension":661,"meta":12244,"navigation":664,"path":3242,"seo":12245,"sources":12246,"stem":3245,"tags":12247,"type":3252,"updated":677,"__hash__":3253},{"type":9,"value":10816,"toc":12229},[10817,10819,10885,10890,10892,10950,11028,11030,11055,11120,11173,11175,11200,11286,11288,11319,11480,11482,11551,11595,11597,11652,11757,11767,11769,11771,11796,11859,11861,11865,11952,11975,12164,12166,12198,12200],[12,10818,1629],{"id":1634},[724,10820,1637,10821,1641,10823,1343,10850,1719],{},[38,10822,1640],{},[883,10824,10826],{"className":10825},[886],[888,10827,10828],{"xmlns":890},[892,10829,10830,10848],{},[895,10831,10832,10834,10836,10838,10840,10842,10844,10846],{},[898,10833,1653],{},[1655,10835,1657],{},[898,10837,1660],{},[1655,10839,1664],{"stretchy":1663},[898,10841,1667],{},[1655,10843,1671],{"separator":1670},[898,10845,1674],{},[1655,10847,1677],{"stretchy":1663},[902,10849,1680],{"encoding":904},[883,10851,10853],{"className":10852},[886],[888,10854,10855],{"xmlns":890},[892,10856,10857,10883],{},[895,10858,10859,10861,10863,10865,10867,10869,10871,10873,10875,10877,10879,10881],{},[898,10860,1692],{},[1655,10862,1657],{},[898,10864,1660],{},[1655,10866,1664],{"stretchy":1663},[898,10868,1667],{},[1655,10870,1671],{"separator":1670},[898,10872,1674],{},[1655,10874,1671],{"separator":1670},[898,10876,1653],{},[1655,10878,1677],{"stretchy":1663},[1655,10880,1671],{"separator":1670},[1655,10882,1715],{},[902,10884,1718],{"encoding":904},[724,10886,10887],{},[1723,10888],{"alt":1725,"className":10889,"src":1728},[210,1727],[115,10891,1732],{"id":1731},[724,10893,1735,10894,1763,10921,1793,10948,1797],{},[883,10895,10897],{"className":10896},[886],[888,10898,10899],{"xmlns":890},[892,10900,10901,10919],{},[895,10902,10903,10905,10907,10909,10911,10913,10915,10917],{},[898,10904,1653],{},[1655,10906,1657],{},[898,10908,1660],{},[1655,10910,1664],{"stretchy":1663},[898,10912,1667],{},[1655,10914,1671],{"separator":1670},[898,10916,1674],{},[1655,10918,1677],{"stretchy":1663},[902,10920,1680],{"encoding":904},[883,10922,10924],{"className":10923},[886],[888,10925,10926],{"xmlns":890},[892,10927,10928,10946],{},[895,10929,10930,10932,10934,10936,10938,10940,10942,10944],{},[898,10931,1660],{},[1655,10933,1664],{"stretchy":1663},[898,10935,1667],{},[1655,10937,1671],{"separator":1670},[898,10939,1674],{},[1655,10941,1677],{"stretchy":1663},[1655,10943,1657],{},[898,10945,1789],{},[902,10947,1792],{"encoding":904},[38,10949,1796],{},[120,10951,10952,10994],{},[123,10953,10954,1805,10956,1847,10991,1719],{},[38,10955,1804],{},[883,10957,10959],{"className":10958},[886],[888,10960,10961],{"xmlns":890},[892,10962,10963,10989],{},[895,10964,10965,10967,10969,10975,10977,10983,10985,10987],{},[898,10966,900],{},[1655,10968,1664],{"stretchy":1663},[1820,10970,10971,10973],{},[898,10972,1824],{},[1826,10974,1828],{},[1655,10976,1671],{"separator":1670},[1820,10978,10979,10981],{},[898,10980,1824],{},[1826,10982,1837],{},[1655,10984,1677],{"stretchy":1663},[1655,10986,1657],{},[898,10988,1789],{},[902,10990,1846],{"encoding":904},[207,10992,1851],{"className":10993,"dataFsResolvedFilePath":878,"href":879},[210],[123,10995,10996,1857,10998,1847,11025,1719],{},[38,10997,1856],{},[883,10999,11001],{"className":11000},[886],[888,11002,11003],{"xmlns":890},[892,11004,11005,11023],{},[895,11006,11007,11009,11011,11013,11015,11017,11019,11021],{},[898,11008,1824],{},[1655,11010,1664],{"stretchy":1663},[898,11012,1873],{},[1655,11014,1671],{"separator":1670},[898,11016,1878],{},[1655,11018,1677],{"stretchy":1663},[1655,11020,1657],{},[898,11022,1789],{},[902,11024,1887],{"encoding":904},[207,11026,1891],{"className":11027,"dataFsResolvedFilePath":857,"href":858},[210],[115,11029,1895],{"id":1894},[724,11031,1735,11032,1922],{},[883,11033,11035],{"className":11034},[886],[888,11036,11037],{"xmlns":890},[892,11038,11039,11053],{},[895,11040,11041,11043,11045,11047,11049,11051],{},[898,11042,1660],{},[1655,11044,1664],{"stretchy":1663},[898,11046,1667],{},[1655,11048,1671],{"separator":1670},[898,11050,1674],{},[1655,11052,1677],{"stretchy":1663},[902,11054,1921],{"encoding":904},[724,11056,11057],{},[883,11058,11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polovina kalkulu jedné proměnné. Slouží k ",[38,12259,12260],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,12263,12264],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,12267,12269],{"id":12268},"neurčitý-integrál","Neurčitý integrál",[724,12271,12272],{},[883,12273,12275],{"className":12274},[886],[888,12276,12277],{"xmlns":890},[892,12278,12279,12312],{},[895,12280,12281,12283,12285,12287,12289,12291,12294,12296,12298,12300,12302,12304,12306,12308,12310],{},[898,12282,2537],{},[1655,12284,1664],{"stretchy":1663},[898,12286,1667],{},[1655,12288,1677],{"stretchy":1663},[1655,12290,1657],{},[1655,12292,12293],{},"∫",[898,12295,1660],{},[1655,12297,1664],{"stretchy":1663},[898,12299,1667],{},[1655,12301,1677],{"stretchy":1663},[2031,12303,2435],{},[898,12305,2410],{},[898,12307,1667],{},[1655,12309,2346],{},[898,12311,4052],{},[902,12313,12314],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,12316,5559,12317,4199,12351,9349,12364,12367,12368,1343,12381,12394],{},[883,12318,12320],{"className":12319},[886],[888,12321,12322],{"xmlns":890},[892,12323,12324,12348],{},[895,12325,12326,12332,12334,12336,12338,12340,12342,12344,12346],{},[2597,12327,12328,12330],{},[898,12329,2537],{},[1655,12331,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,12333,1664],{"stretchy":1663},[898,12335,1667],{},[1655,12337,1677],{"stretchy":1663},[1655,12339,1657],{},[898,12341,1660],{},[1655,12343,1664],{"stretchy":1663},[898,12345,1667],{},[1655,12347,1677],{"stretchy":1663},[902,12349,12350],{"encoding":904},"F'(x) = f(x)",[883,12352,12354],{"className":12353},[886],[888,12355,12356],{"xmlns":890},[892,12357,12358,12362],{},[895,12359,12360],{},[898,12361,2537],{},[902,12363,2537],{"encoding":904},[38,12365,12366],{},"primitivní funkce"," k ",[883,12369,12371],{"className":12370},[886],[888,12372,12373],{"xmlns":890},[892,12374,12375,12379],{},[895,12376,12377],{},[898,12378,1660],{},[902,12380,1660],{"encoding":904},[883,12382,12384],{"className":12383},[886],[888,12385,12386],{"xmlns":890},[892,12387,12388,12392],{},[895,12389,12390],{},[898,12391,4052],{},[902,12393,4052],{"encoding":904}," konstanta.",[115,12396,12398],{"id":12397},"určitý-integrál","Určitý integrál",[724,12400,12401],{},[883,12402,12404],{"className":12403},[886],[888,12405,12406],{"xmlns":890},[892,12407,12408,12472],{},[895,12409,12410,12418,12420,12422,12424,12426,12428,12430,12432,12434,12436,12438,12440,12442,12444,12452,12454,12456,12458,12460,12462,12464,12466,12468,12470],{},[1935,12411,12412,12414,12416],{},[1655,12413,12293],{},[898,12415,207],{},[898,12417,2025],{},[898,12419,1660],{},[1655,12421,1664],{"stretchy":1663},[898,12423,1667],{},[1655,12425,1677],{"stretchy":1663},[2031,12427,2435],{},[898,12429,2410],{},[898,12431,1667],{},[1655,12433,1657],{},[1655,12435,2734],{"stretchy":1663},[898,12437,2537],{},[1655,12439,1664],{"stretchy":1663},[898,12441,1667],{},[1655,12443,1677],{"stretchy":1663},[1935,12445,12446,12448,12450],{},[1655,12447,2743],{"stretchy":1663},[898,12449,207],{},[898,12451,2025],{},[1655,12453,1657],{},[898,12455,2537],{},[1655,12457,1664],{"stretchy":1663},[898,12459,2025],{},[1655,12461,1677],{"stretchy":1663},[1655,12463,2623],{},[898,12465,2537],{},[1655,12467,1664],{"stretchy":1663},[898,12469,207],{},[1655,12471,1677],{"stretchy":1663},[902,12473,12474],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,12476,12477,12478,3106,12481,12494,12495,12516],{},"Geometricky ",[38,12479,12480],{},"plocha pod grafem",[883,12482,12484],{"className":12483},[886],[888,12485,12486],{"xmlns":890},[892,12487,12488,12492],{},[895,12489,12490],{},[898,12491,1660],{},[902,12493,1660],{"encoding":904}," na intervalu ",[883,12496,12498],{"className":12497},[886],[888,12499,12500],{"xmlns":890},[892,12501,12502,12514],{},[895,12503,12504,12506,12508,12510,12512],{},[1655,12505,2734],{"stretchy":1663},[898,12507,207],{},[1655,12509,1671],{"separator":1670},[898,12511,2025],{},[1655,12513,2743],{"stretchy":1663},[902,12515,2939],{"encoding":904}," (orientovaná).",[724,12518,12519],{},[1723,12520],{"alt":12521,"className":12522,"src":12523},"imek-integral-plocha",[210,1727],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,12525,12527],{"id":12526},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,12529,12531],{"id":12530},"příklad-tr-z-mr","Příklad — TR z MR",[724,12533,12534,12535,1719],{},"Mezní příjem ",[883,12536,12538],{"className":12537},[886],[888,12539,12540],{"xmlns":890},[892,12541,12542,12558],{},[895,12543,12544,12546,12548,12550,12552,12554,12556],{},[898,12545,2127],{},[898,12547,5245],{},[1655,12549,1657],{},[1826,12551,4360],{},[1655,12553,2623],{},[1826,12555,1837],{},[898,12557,1824],{},[902,12559,12560],{"encoding":904},"MR = 100 - 2Q",[724,12562,12563],{},[883,12564,12566],{"className":12565},[886],[888,12567,12568],{"xmlns":890},[892,12569,12570,12616],{},[895,12571,12572,12574,12576,12578,12580,12582,12584,12586,12588,12590,12592,12594,12596,12598,12600,12602,12604,12606,12612,12614],{},[898,12573,4049],{},[898,12575,5245],{},[1655,12577,1657],{},[1655,12579,12293],{},[1655,12581,1664],{"stretchy":1663},[1826,12583,4360],{},[1655,12585,2623],{},[1826,12587,1837],{},[898,12589,1824],{},[1655,12591,1677],{"stretchy":1663},[2031,12593,2435],{},[898,12595,2410],{},[898,12597,1824],{},[1655,12599,1657],{},[1826,12601,4360],{},[898,12603,1824],{},[1655,12605,2623],{},[2597,12607,12608,12610],{},[898,12609,1824],{},[1826,12611,1837],{},[1655,12613,2346],{},[898,12615,1789],{},[902,12617,12618],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,12620,12621,12622,3022,12648,2086],{},"Okrajová podmínka ",[883,12623,12625],{"className":12624},[886],[888,12626,12627],{"xmlns":890},[892,12628,12629,12645],{},[895,12630,12631,12633,12635,12637,12639,12641,12643],{},[898,12632,4049],{},[898,12634,5245],{},[1655,12636,1664],{"stretchy":1663},[1826,12638,2552],{},[1655,12640,1677],{"stretchy":1663},[1655,12642,1657],{},[1826,12644,2552],{},[902,12646,12647],{"encoding":904},"TR(0) = 0",[883,12649,12651],{"className":12650},[886],[888,12652,12653],{"xmlns":890},[892,12654,12655,12663],{},[895,12656,12657,12659,12661],{},[898,12658,1789],{},[1655,12660,1657],{},[1826,12662,2552],{},[902,12664,12665],{"encoding":904},"c = 0",[724,12667,12668],{},[883,12669,12671],{"className":12670},[886],[888,12672,12673],{"xmlns":890},[892,12674,12675,12701],{},[895,12676,12677,12679,12681,12683,12685,12687,12689,12691,12693,12695],{},[898,12678,4049],{},[898,12680,5245],{},[1655,12682,1664],{"stretchy":1663},[898,12684,1824],{},[1655,12686,1677],{"stretchy":1663},[1655,12688,1657],{},[1826,12690,4360],{},[898,12692,1824],{},[1655,12694,2623],{},[2597,12696,12697,12699],{},[898,12698,1824],{},[1826,12700,1837],{},[902,12702,12703],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,12705,12707],{"id":12706},"příklad-tc-z-mc","Příklad — TC z MC",[724,12709,12710,12711,12737,12738,1719],{},"Mezní náklady ",[883,12712,12714],{"className":12713},[886],[888,12715,12716],{"xmlns":890},[892,12717,12718,12734],{},[895,12719,12720,12722,12724,12726,12728,12730,12732],{},[898,12721,2127],{},[898,12723,4052],{},[1655,12725,1657],{},[1826,12727,1837],{},[1655,12729,2346],{},[1826,12731,4112],{},[898,12733,1824],{},[902,12735,12736],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,12739,12741],{"className":12740},[886],[888,12742,12743],{"xmlns":890},[892,12744,12745,12755],{},[895,12746,12747,12749,12751,12753],{},[898,12748,2537],{},[898,12750,4052],{},[1655,12752,1657],{},[1826,12754,4360],{},[902,12756,12757],{"encoding":904},"FC = 100",[724,12759,12760],{},[883,12761,12763],{"className":12762},[886],[888,12764,12765],{"xmlns":890},[892,12766,12767,12807],{},[895,12768,12769,12771,12773,12775,12777,12779,12781,12783,12785,12787,12789,12791,12793,12795,12797,12803,12805],{},[898,12770,4049],{},[898,12772,4052],{},[1655,12774,1657],{},[1655,12776,12293],{},[898,12778,2127],{},[898,12780,4052],{},[2031,12782,2435],{},[898,12784,2410],{},[898,12786,1824],{},[1655,12788,1657],{},[1826,12790,1837],{},[898,12792,1824],{},[1655,12794,2346],{},[1826,12796,4068],{},[2597,12798,12799,12801],{},[898,12800,1824],{},[1826,12802,1837],{},[1655,12804,2346],{},[898,12806,1789],{},[902,12808,12809],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,12811,12621,12812,3022,12844,2086],{},[883,12813,12815],{"className":12814},[886],[888,12816,12817],{"xmlns":890},[892,12818,12819,12841],{},[895,12820,12821,12823,12825,12827,12829,12831,12833,12835,12837,12839],{},[898,12822,4049],{},[898,12824,4052],{},[1655,12826,1664],{"stretchy":1663},[1826,12828,2552],{},[1655,12830,1677],{"stretchy":1663},[1655,12832,1657],{},[898,12834,2537],{},[898,12836,4052],{},[1655,12838,1657],{},[1826,12840,4360],{},[902,12842,12843],{"encoding":904},"TC(0) = FC = 100",[883,12845,12847],{"className":12846},[886],[888,12848,12849],{"xmlns":890},[892,12850,12851,12859],{},[895,12852,12853,12855,12857],{},[898,12854,1789],{},[1655,12856,1657],{},[1826,12858,4360],{},[902,12860,12861],{"encoding":904},"c = 100",[724,12863,12864],{},[883,12865,12867],{"className":12866},[886],[888,12868,12869],{"xmlns":890},[892,12870,12871,12903],{},[895,12872,12873,12875,12877,12879,12881,12883,12885,12887,12889,12891,12893,12895,12897],{},[898,12874,4049],{},[898,12876,4052],{},[1655,12878,1664],{"stretchy":1663},[898,12880,1824],{},[1655,12882,1677],{"stretchy":1663},[1655,12884,1657],{},[1826,12886,4360],{},[1655,12888,2346],{},[1826,12890,1837],{},[898,12892,1824],{},[1655,12894,2346],{},[1826,12896,4068],{},[2597,12898,12899,12901],{},[898,12900,1824],{},[1826,12902,1837],{},[902,12904,12905],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,12907,820],{"id":12908},"přebytek-spotřebitele-a-výrobce",[724,12910,12911],{},"Přebytek spotřebitele:",[724,12913,12914],{},[883,12915,12917],{"className":12916},[886],[888,12918,12919],{"xmlns":890},[892,12920,12921,12981],{},[895,12922,12923,12925,12927,12929,12935,12937,12939,12951,12953,12955,12957,12959,12961,12963,12965,12967,12973,12975],{},[898,12924,4052],{},[898,12926,9920],{},[1655,12928,1664],{"stretchy":1663},[1820,12930,12931,12933],{},[898,12932,1824],{},[1826,12934,2552],{},[1655,12936,1677],{"stretchy":1663},[1655,12938,1657],{},[1935,12940,12941,12943,12945],{},[1655,12942,12293],{},[1826,12944,2552],{},[1820,12946,12947,12949],{},[898,12948,1824],{},[1826,12950,2552],{},[898,12952,2838],{},[1655,12954,1664],{"stretchy":1663},[898,12956,1824],{},[1655,12958,1677],{"stretchy":1663},[2031,12960,2435],{},[898,12962,2410],{},[898,12964,1824],{},[1655,12966,2623],{},[1820,12968,12969,12971],{},[898,12970,2132],{},[1826,12972,2552],{},[2031,12974,2435],{},[1820,12976,12977,12979],{},[898,12978,1824],{},[1826,12980,2552],{},[902,12982,12983],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,12985,12986],{},"Přebytek výrobce:",[724,12988,12989],{},[883,12990,12992],{"className":12991},[886],[888,12993,12994],{"xmlns":890},[892,12995,12996,13056],{},[895,12997,12998,13000,13002,13004,13010,13012,13014,13020,13022,13028,13030,13042,13044,13046,13048,13050,13052,13054],{},[898,12999,2132],{},[898,13001,9920],{},[1655,13003,1664],{"stretchy":1663},[1820,13005,13006,13008],{},[898,13007,1824],{},[1826,13009,2552],{},[1655,13011,1677],{"stretchy":1663},[1655,13013,1657],{},[1820,13015,13016,13018],{},[898,13017,2132],{},[1826,13019,2552],{},[2031,13021,2435],{},[1820,13023,13024,13026],{},[898,13025,1824],{},[1826,13027,2552],{},[1655,13029,2623],{},[1935,13031,13032,13034,13036],{},[1655,13033,12293],{},[1826,13035,2552],{},[1820,13037,13038,13040],{},[898,13039,1824],{},[1826,13041,2552],{},[898,13043,9920],{},[1655,13045,1664],{"stretchy":1663},[898,13047,1824],{},[1655,13049,1677],{"stretchy":1663},[2031,13051,2435],{},[898,13053,2410],{},[898,13055,1824],{},[902,13057,13058],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,13060,13061,13062,1719],{},"Detailně viz ",[207,13063,13065],{"className":13064,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,13067,3187],{"id":3186},[120,13069,13070,13077,13084],{},[123,13071,13072,3106,13074],{},[38,13073,3194],{},[207,13075,766],{"className":13076,"dataFsResolvedFilePath":764,"href":765},[210],[123,13078,13079,3106,13081],{},[38,13080,3202],{},[207,13082,784],{"className":13083,"dataFsResolvedFilePath":782,"href":783},[210],[123,13085,13086,3106,13088,13091,13092,13095],{},[38,13087,3210],{},[207,13089,5078],{"className":13090,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,13093,13065],{"className":13094,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":13097},[13098,13099,13100,13105],{"id":12268,"depth":642,"text":12269},{"id":12397,"depth":642,"text":12398},{"id":12526,"depth":642,"text":12527,"children":13101},[13102,13103,13104],{"id":12530,"depth":649,"text":12531},{"id":12706,"depth":649,"text":12707},{"id":12908,"depth":649,"text":820},{"id":3186,"depth":642,"text":3187},"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":13106},[1135],"topics\u002Fintegral",[1128,13113,13114,13115,13116,13117,13118],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":13121,"title":13122,"body":13123,"course":1128,"courses":659,"created":10802,"description":641,"extension":661,"meta":17392,"navigation":664,"path":17393,"seo":17394,"sources":17395,"stem":17396,"tags":17397,"type":3252,"updated":677,"__hash__":17403},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":13124,"toc":17380},[13125,13128,13132,13276,13283,13287,13357,13395,13498,13502,13532,13598,13645,13648,13717,13720,13755,13791,13795,13843,13850,13896,13942,13945,14024,14121,14204,14208,14252,14282,14288,14317,14339,14389,14442,14508,14511,14577,14606,14665,14681,14768,14866,14997,15001,15158,15307,15687,15691,15694,15753,15756,15842,15870,15908,15911,15948,15988,16022,16024,16061,16093,16191,16196,16320,16372,16454,16593,16597,16717,16724,16835,16842,16846,17321,17323],[12,13126,13122],{"id":13127},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,13129,13131],{"id":13130},"tldr","TL;DR",[724,13133,13134,13137,13138,2115,13141,13154,13155,13169,13170,13173,13174,1343,13177,13180,13181,1343,13184,13187,13188,3106,13191,13221,13222,13225,13226,1343,13240,13253,13254,13257,13258,5171],{},[38,13135,13136],{},"IS-LM"," je makroekonomický model se ",[38,13139,13140],{},"dvěma neznámými",[883,13142,13144],{"className":13143},[886],[888,13145,13146],{"xmlns":890},[892,13147,13148,13152],{},[895,13149,13150],{},[898,13151,10375],{},[902,13153,10375],{"encoding":904}," — národní důchod a ",[883,13156,13158],{"className":13157},[886],[888,13159,13160],{"xmlns":890},[892,13161,13162,13167],{},[895,13163,13164],{},[898,13165,13166],{},"r",[902,13168,13166],{"encoding":904}," — úroková míra) a ",[38,13171,13172],{},"dvěma trhy",": trhem zboží (křivka ",[38,13175,13176],{},"IS",[614,13178,13179],{},"Investment = Savings",") a trhem peněz (křivka ",[38,13182,13183],{},"LM",[614,13185,13186],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,13189,13190],{},"simultánní rovnováhu",[883,13192,13194],{"className":13193},[886],[888,13195,13196],{"xmlns":890},[892,13197,13198,13218],{},[895,13199,13200,13202,13208,13210,13216],{},[1655,13201,1664],{"stretchy":1663},[2597,13203,13204,13206],{},[898,13205,10375],{},[898,13207,5502],{},[1655,13209,1671],{"separator":1670},[2597,13211,13212,13214],{},[898,13213,13166],{},[898,13215,5502],{},[1655,13217,1677],{"stretchy":1663},[902,13219,13220],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,13223,13224],{},"fiskální politiky"," (posun IS změnou ",[883,13227,13229],{"className":13228},[886],[888,13230,13231],{"xmlns":890},[892,13232,13233,13238],{},[895,13234,13235],{},[898,13236,13237],{},"G",[902,13239,13237],{"encoding":904},[883,13241,13243],{"className":13242},[886],[888,13244,13245],{"xmlns":890},[892,13246,13247,13251],{},[895,13248,13249],{},[898,13250,4049],{},[902,13252,4049],{"encoding":904},") a ",[38,13255,13256],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,13259,13261],{"className":13260},[886],[888,13262,13263],{"xmlns":890},[892,13264,13265,13273],{},[895,13266,13267],{},[2597,13268,13269,13271],{},[898,13270,2127],{},[1655,13272,5603],{},[902,13274,13275],{"encoding":904},"M^*",[724,13277,13278],{},[1723,13279],{"alt":13280,"className":13281,"src":13282},"imek-is-lm-model",[210,1727],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,13284,13286],{"id":13285},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,13288,13289,13290,13294,13295,2115,13298,13321,13322,13325,13326,13342,13343,13356],{},"V modelech ",[207,13291,13293],{"className":13292,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,13296,13297],{},"investice pokládány za konstantní",[883,13299,13301],{"className":13300},[886],[888,13302,13303],{"xmlns":890},[892,13304,13305,13318],{},[895,13306,13307,13310,13312],{},[898,13308,13309],{},"I",[1655,13311,1657],{},[2597,13313,13314,13316],{},[898,13315,13309],{},[1655,13317,5603],{},[902,13319,13320],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,13323,13324],{},"ceně peněz",", tedy na ",[38,13327,13328,13329],{},"úrokové míře ",[883,13330,13332],{"className":13331},[886],[888,13333,13334],{"xmlns":890},[892,13335,13336,13340],{},[895,13337,13338],{},[898,13339,13166],{},[902,13341,13166],{"encoding":904},": čím vyšší ",[883,13344,13346],{"className":13345},[886],[888,13347,13348],{"xmlns":890},[892,13349,13350,13354],{},[895,13351,13352],{},[898,13353,13166],{},[902,13355,13166],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,13358,13359,13389],{},[123,13360,13361,3106,13364,13388],{},[38,13362,13363],{},"funkci investic",[883,13365,13367],{"className":13366},[886],[888,13368,13369],{"xmlns":890},[892,13370,13371,13385],{},[895,13372,13373,13375,13377,13379,13381,13383],{},[898,13374,13309],{},[1655,13376,1657],{},[898,13378,13309],{},[1655,13380,1664],{"stretchy":1663},[898,13382,13166],{},[1655,13384,1677],{"stretchy":1663},[902,13386,13387],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,13390,13391,13394],{},[38,13392,13393],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[5120,13396,13397],{},[724,13398,13399,13401,13402,13421,13422,13449,13450,13463,13464,13493,13494,13497],{},[883,13400,5661],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,13403,13405],{"className":13404},[886],[888,13406,13407],{"xmlns":890},[892,13408,13409,13418],{},[895,13410,13411,13413,13416],{},[898,13412,4052],{},[2031,13414,13415],{},"-",[898,13417,13309],{},[902,13419,13420],{"encoding":904},"C\\text{-}I"," až ",[883,13423,13425],{"className":13424},[886],[888,13426,13427],{"xmlns":890},[892,13428,13429,13446],{},[895,13430,13431,13433,13435,13437,13439,13441,13443],{},[898,13432,4052],{},[2031,13434,13415],{},[898,13436,13309],{},[2031,13438,13415],{},[898,13440,13237],{},[2031,13442,13415],{},[898,13444,13445],{},"X",[902,13447,13448],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,13451,13453],{"className":13452},[886],[888,13454,13455],{"xmlns":890},[892,13456,13457,13461],{},[895,13458,13459],{},[898,13460,10375],{},[902,13462,10375],{"encoding":904},". V IS-LM jsou ",[38,13465,13466,13467,2704,13480],{},"dvě neznámé ",[883,13468,13470],{"className":13469},[886],[888,13471,13472],{"xmlns":890},[892,13473,13474,13478],{},[895,13475,13476],{},[898,13477,10375],{},[902,13479,10375],{"encoding":904},[883,13481,13483],{"className":13482},[886],[888,13484,13485],{"xmlns":890},[892,13486,13487,13491],{},[895,13488,13489],{},[898,13490,13166],{},[902,13492,13166],{"encoding":904},", a proto potřebujeme ",[38,13495,13496],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,13499,13501],{"id":13500},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,13503,13504,13505,13518,13519,2086],{},"Lineární závislost investic ",[883,13506,13508],{"className":13507},[886],[888,13509,13510],{"xmlns":890},[892,13511,13512,13516],{},[895,13513,13514],{},[898,13515,13309],{},[902,13517,13309],{"encoding":904}," na úrokové míře ",[883,13520,13522],{"className":13521},[886],[888,13523,13524],{"xmlns":890},[892,13525,13526,13530],{},[895,13527,13528],{},[898,13529,13166],{},[902,13531,13166],{"encoding":904},[724,13533,13534],{},[883,13535,13537],{"className":13536},[886],[888,13538,13539],{"xmlns":890},[892,13540,13541,13595],{},[895,13542,13543,13545,13547,13549,13551,13553,13555,13557,13559,13561,13563,13565,13567,13569,13571,13573,13575,13577,13579,13581,13583,13586,13588,13590,13593],{},[898,13544,13309],{},[1655,13546,1657],{},[898,13548,13309],{},[1655,13550,1664],{"stretchy":1663},[898,13552,13166],{},[1655,13554,1677],{"stretchy":1663},[1655,13556,1657],{},[898,13558,1789],{},[898,13560,13166],{},[1655,13562,2346],{},[898,13564,2410],{},[1655,13566,1671],{"separator":1670},[1967,13568],{"width":1969},[898,13570,1789],{},[1655,13572,3065],{},[1826,13574,2552],{},[1655,13576,1671],{"separator":1670},[2031,13578,2033],{},[898,13580,2410],{},[1655,13582,2969],{},[1826,13584,13585],{},"0.",[1967,13587],{"width":1969},[1655,13589,1664],{"stretchy":1663},[1826,13591,13592],{},"7.11",[1655,13594,1677],{"stretchy":1663},[902,13596,13597],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,13599,13600,13621],{},[123,13601,13602,13620],{},[883,13603,13605],{"className":13604},[886],[888,13606,13607],{"xmlns":890},[892,13608,13609,13617],{},[895,13610,13611,13613,13615],{},[898,13612,2410],{},[1655,13614,2969],{},[1826,13616,2552],{},[902,13618,13619],{"encoding":904},"d > 0"," zřejmé,",[123,13622,13623,13641,13642,1719],{},[883,13624,13626],{"className":13625},[886],[888,13627,13628],{"xmlns":890},[892,13629,13630,13638],{},[895,13631,13632,13634,13636],{},[898,13633,1789],{},[1655,13635,3065],{},[1826,13637,2552],{},[902,13639,13640],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,13643,13644],{},"klesající",[724,13646,13647],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,13649,13650],{},[883,13651,13653],{"className":13652},[886],[888,13654,13655],{"xmlns":890},[892,13656,13657,13714],{},[895,13658,13659,13661,13663,13665,13667,13669,13671,13673,13675,13677,13679,13681,13683,13685,13687,13689,13691,13693,13695,13697,13699,13701,13703,13705,13707,13709,13712],{},[898,13660,4052],{},[1655,13662,1657],{},[898,13664,4052],{},[1655,13666,1664],{"stretchy":1663},[898,13668,10375],{},[1655,13670,1677],{"stretchy":1663},[1655,13672,1657],{},[898,13674,207],{},[898,13676,10375],{},[1655,13678,2346],{},[898,13680,2025],{},[1655,13682,1671],{"separator":1670},[1967,13684],{"width":1969},[1826,13686,2552],{},[1655,13688,3065],{},[898,13690,207],{},[1655,13692,3065],{},[1826,13694,1828],{},[1655,13696,1671],{"separator":1670},[2031,13698,2033],{},[898,13700,2025],{},[1655,13702,2969],{},[1826,13704,13585],{},[1967,13706],{"width":1969},[1655,13708,1664],{"stretchy":1663},[1826,13710,13711],{},"7.12",[1655,13713,1677],{"stretchy":1663},[902,13715,13716],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,13718,13719],{},"Podmínka rovnováhy na trhu zboží:",[724,13721,13722],{},[883,13723,13725],{"className":13724},[886],[888,13726,13727],{"xmlns":890},[892,13728,13729,13752],{},[895,13730,13731,13733,13735,13737,13739,13741,13743,13745,13747,13750],{},[898,13732,10375],{},[1655,13734,1657],{},[898,13736,4052],{},[1655,13738,2346],{},[898,13740,13309],{},[898,13742,1719],{"mathvariant":1943},[1967,13744],{"width":1969},[1655,13746,1664],{"stretchy":1663},[1826,13748,13749],{},"7.13",[1655,13751,1677],{"stretchy":1663},[902,13753,13754],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,13756,13757,13758,3106,13761,13787,13788,1719],{},"To dává ",[38,13759,13760],{},"tři rovnice o čtyřech neznámých",[883,13762,13764],{"className":13763},[886],[888,13765,13766],{"xmlns":890},[892,13767,13768,13784],{},[895,13769,13770,13772,13774,13776,13778,13780,13782],{},[898,13771,10375],{},[1655,13773,1671],{"separator":1670},[898,13775,4052],{},[1655,13777,1671],{"separator":1670},[898,13779,13309],{},[1655,13781,1671],{"separator":1670},[898,13783,13166],{},[902,13785,13786],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,13789,13790],{},"rovnováhy na trhu peněz",[115,13792,13794],{"id":13793},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,13796,13797,13798,6818,13820,13838,13839,13842],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,13799,13801],{"className":13800},[886],[888,13802,13803],{"xmlns":890},[892,13804,13805,13817],{},[895,13806,13807,13809,13811,13813,13815],{},[898,13808,10375],{},[1655,13810,1657],{},[898,13812,4052],{},[1655,13814,2346],{},[898,13816,9920],{},[902,13818,13819],{"encoding":904},"Y = C + S",[883,13821,13823],{"className":13822},[886],[888,13824,13825],{"xmlns":890},[892,13826,13827,13835],{},[895,13828,13829,13831,13833],{},[898,13830,13309],{},[1655,13832,1657],{},[898,13834,9920],{},[902,13836,13837],{"encoding":904},"I = S"," (plánované ",[38,13840,13841],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,13844,13845],{},[1723,13846],{"alt":13847,"className":13848,"src":13849},"imek-odvozeni-is-4panelu",[210,1727],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,13851,13852],{},[883,13853,13855],{"className":13854},[886],[888,13856,13857],{"xmlns":890},[892,13858,13859,13893],{},[895,13860,13861,13863,13865,13867,13869,13871,13873,13875,13877,13879,13881,13883,13885,13887,13889,13891],{},[898,13862,10375],{},[1655,13864,1657],{},[1655,13866,1664],{"stretchy":1663},[898,13868,207],{},[898,13870,10375],{},[1655,13872,2346],{},[898,13874,2025],{},[1655,13876,1677],{"stretchy":1663},[1655,13878,2346],{},[1655,13880,1664],{"stretchy":1663},[898,13882,1789],{},[898,13884,13166],{},[1655,13886,2346],{},[898,13888,2410],{},[1655,13890,1677],{"stretchy":1663},[1655,13892,1671],{"separator":1670},[902,13894,13895],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,13897,13898],{},[883,13899,13901],{"className":13900},[886],[888,13902,13903],{"xmlns":890},[892,13904,13905,13939],{},[895,13906,13907,13909,13911,13913,13915,13917,13919,13921,13923,13925,13927,13929,13931,13933,13935,13937],{},[1655,13908,1664],{"stretchy":1663},[1826,13910,1828],{},[1655,13912,2623],{},[898,13914,207],{},[1655,13916,1677],{"stretchy":1663},[898,13918,10375],{},[1655,13920,2623],{},[898,13922,1789],{},[898,13924,13166],{},[1655,13926,2623],{},[898,13928,2025],{},[1655,13930,2623],{},[898,13932,2410],{},[1655,13934,1657],{},[1826,13936,2552],{},[1655,13938,1671],{"separator":1670},[902,13940,13941],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,13943,13944],{},"odkud",[724,13946,13947],{},[883,13948,13950],{"className":13949},[886],[888,13951,13952],{"xmlns":890},[892,13953,13954,14021],{},[895,13955,13956,14012,14014,14016,14019],{},[13957,13958,13960],"menclose",{"notation":13959},"box",[3615,13961,13962],{"scriptlevel":2552,"displaystyle":1663},[3615,13963,13964],{"scriptlevel":2552,"displaystyle":1663},[3615,13965,13966],{"scriptlevel":2552,"displaystyle":1670},[895,13967,13968,13970,13972,13974,13986,13988,13990,13992,14010],{},[2031,13969,2435],{},[898,13971,10375],{},[1655,13973,1657],{},[1949,13975,13976,13978],{},[898,13977,1789],{},[895,13979,13980,13982,13984],{},[1826,13981,1828],{},[1655,13983,2623],{},[898,13985,207],{},[2031,13987,2435],{},[898,13989,13166],{},[1655,13991,2346],{},[1949,13993,13994,14002],{},[895,13995,13996,13998,14000],{},[898,13997,2025],{},[1655,13999,2346],{},[898,14001,2410],{},[895,14003,14004,14006,14008],{},[1826,14005,1828],{},[1655,14007,2623],{},[898,14009,207],{},[2031,14011,2435],{},[1967,14013],{"width":1969},[1655,14015,1664],{"stretchy":1663},[1826,14017,14018],{},"7.14",[1655,14020,1677],{"stretchy":1663},[902,14022,14023],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,14025,14026,14027,2115,14030,14033,14034,14037,14038,14040,14041,14063,14064,14092,14093,14114,14115,14117,14118,14120],{},"Tento vztah se nazývá ",[38,14028,14029],{},"funkce IS",[614,14031,14032],{},"IS schedule",") a její graf ",[38,14035,14036],{},"křivka IS",". Křivka je ",[38,14039,13644],{}," přímka v rovině ",[883,14042,14044],{"className":14043},[886],[888,14045,14046],{"xmlns":890},[892,14047,14048,14060],{},[895,14049,14050,14052,14054,14056,14058],{},[1655,14051,1664],{"stretchy":1663},[898,14053,13166],{},[1655,14055,1671],{"separator":1670},[898,14057,10375],{},[1655,14059,1677],{"stretchy":1663},[902,14061,14062],{"encoding":904},"(r, Y)",", neboť ",[883,14065,14067],{"className":14066},[886],[888,14068,14069],{"xmlns":890},[892,14070,14071,14089],{},[895,14072,14073,14085,14087],{},[1949,14074,14075,14077],{},[898,14076,1789],{},[895,14078,14079,14081,14083],{},[1826,14080,1828],{},[1655,14082,2623],{},[898,14084,207],{},[1655,14086,3065],{},[1826,14088,2552],{},[902,14090,14091],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,14094,14096],{"className":14095},[886],[888,14097,14098],{"xmlns":890},[892,14099,14100,14112],{},[895,14101,14102,14104,14106,14108,14110],{},[1655,14103,1664],{"stretchy":1663},[898,14105,13166],{},[1655,14107,1671],{"separator":1670},[898,14109,10375],{},[1655,14111,1677],{"stretchy":1663},[902,14113,14062],{"encoding":904},", pro které plánované ",[38,14116,13309],{},"nvestment = ",[38,14119,9920],{},"avings.",[5120,14122,14123],{},[724,14124,14125,14127,14128,14141,14142,3106,14145,14158,14159,14172,14173,2704,14186,14199,14200,14203],{},[883,14126,5406],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,14129,14131],{"className":14130},[886],[888,14132,14133],{"xmlns":890},[892,14134,14135,14139],{},[895,14136,14137],{},[898,14138,13166],{},[902,14140,13166],{"encoding":904}," → levnější úvěr → ",[38,14143,14144],{},"více investic",[883,14146,14148],{"className":14147},[886],[888,14149,14150],{"xmlns":890},[892,14151,14152,14156],{},[895,14153,14154],{},[898,14155,13309],{},[902,14157,13309],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,14160,14162],{"className":14161},[886],[888,14163,14164],{"xmlns":890},[892,14165,14166,14170],{},[895,14167,14168],{},[898,14169,10375],{},[902,14171,10375],{"encoding":904},". Vztah mezi ",[883,14174,14176],{"className":14175},[886],[888,14177,14178],{"xmlns":890},[892,14179,14180,14184],{},[895,14181,14182],{},[898,14183,13166],{},[902,14185,13166],{"encoding":904},[883,14187,14189],{"className":14188},[886],[888,14190,14191],{"xmlns":890},[892,14192,14193,14197],{},[895,14194,14195],{},[898,14196,10375],{},[902,14198,10375],{"encoding":904}," na trhu zboží je proto ",[38,14201,14202],{},"nepřímý"," (klesající křivka).",[115,14205,14207],{"id":14206},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,14209,14210,14211,14229,14230,4199,14248,14251],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,14212,14214],{"className":14213},[886],[888,14215,14216],{"xmlns":890},[892,14217,14218,14226],{},[895,14219,14220],{},[2597,14221,14222,14224],{},[898,14223,2127],{},[898,14225,2838],{},[902,14227,14228],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,14231,14233],{"className":14232},[886],[888,14234,14235],{"xmlns":890},[892,14236,14237,14245],{},[895,14238,14239],{},[2597,14240,14241,14243],{},[898,14242,2127],{},[898,14244,9920],{},[902,14246,14247],{"encoding":904},"M^S",[38,14249,14250],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,14253,14254],{},[883,14255,14257],{"className":14256},[886],[888,14258,14259],{"xmlns":890},[892,14260,14261,14279],{},[895,14262,14263,14269,14271,14277],{},[2597,14264,14265,14267],{},[898,14266,2127],{},[898,14268,9920],{},[1655,14270,1657],{},[2597,14272,14273,14275],{},[898,14274,2127],{},[1655,14276,5603],{},[898,14278,1719],{"mathvariant":1943},[902,14280,14281],{"encoding":904},"M^S = M^*.",[724,14283,14284,14287],{},[38,14285,14286],{},"Poptávka"," po penězích má tři zdroje:",[120,14289,14290,14299,14308],{},[123,14291,14292,2115,14295,14298],{},[38,14293,14294],{},"transakční poptávka",[614,14296,14297],{},"transactions demand",") — peníze pro nákup zboží,",[123,14300,14301,2115,14304,14307],{},[38,14302,14303],{},"opatrnostní poptávka",[614,14305,14306],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,14309,14310,2115,14313,14316],{},[38,14311,14312],{},"spekulační poptávka",[614,14314,14315],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,14318,14319,14320,14338],{},"Součet transakční a opatrnostní poptávky ",[883,14321,14323],{"className":14322},[886],[888,14324,14325],{"xmlns":890},[892,14326,14327,14335],{},[895,14328,14329],{},[1820,14330,14331,14333],{},[898,14332,1873],{},[1826,14334,1828],{},[902,14336,14337],{"encoding":904},"L_1"," je úměrný důchodu:",[724,14340,14341],{},[883,14342,14344],{"className":14343},[886],[888,14345,14346],{"xmlns":890},[892,14347,14348,14386],{},[895,14349,14350,14356,14358,14365,14367,14369,14371,14373,14375,14381,14383],{},[1820,14351,14352,14354],{},[898,14353,1873],{},[1826,14355,1828],{},[1655,14357,1657],{},[1820,14359,14360,14363],{},[898,14361,14362],{},"k",[1826,14364,1828],{},[898,14366,10375],{},[1655,14368,1671],{"separator":1670},[1967,14370],{"width":1969},[1826,14372,2552],{},[1655,14374,3065],{},[1820,14376,14377,14379],{},[898,14378,14362],{},[1826,14380,1828],{},[1655,14382,3065],{},[1826,14384,14385],{},"1.",[902,14387,14388],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,14390,14391,14392,14410,14411,1343,14424,14441],{},"Spekulační poptávka ",[883,14393,14395],{"className":14394},[886],[888,14396,14397],{"xmlns":890},[892,14398,14399,14407],{},[895,14400,14401],{},[1820,14402,14403,14405],{},[898,14404,1873],{},[1826,14406,1837],{},[902,14408,14409],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,14412,14414],{"className":14413},[886],[888,14415,14416],{"xmlns":890},[892,14417,14418,14422],{},[895,14419,14420],{},[898,14421,13166],{},[902,14423,13166],{"encoding":904},[883,14425,14427],{"className":14426},[886],[888,14428,14429],{"xmlns":890},[892,14430,14431,14439],{},[895,14432,14433],{},[1820,14434,14435,14437],{},[898,14436,1873],{},[1826,14438,1837],{},[902,14440,14409],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,14443,14444],{},[883,14445,14447],{"className":14446},[886],[888,14448,14449],{"xmlns":890},[892,14450,14451,14505],{},[895,14452,14453,14459,14461,14467,14469,14471,14477,14479,14481,14487,14489,14491,14493,14495,14501,14503],{},[1820,14454,14455,14457],{},[898,14456,1873],{},[1826,14458,1837],{},[1655,14460,1657],{},[1820,14462,14463,14465],{},[898,14464,14362],{},[1826,14466,1837],{},[898,14468,13166],{},[1655,14470,2346],{},[1820,14472,14473,14475],{},[898,14474,14362],{},[1826,14476,3472],{},[1655,14478,1671],{"separator":1670},[1967,14480],{"width":1969},[1820,14482,14483,14485],{},[898,14484,14362],{},[1826,14486,1837],{},[1655,14488,3065],{},[1826,14490,2552],{},[1655,14492,1671],{"separator":1670},[2031,14494,2033],{},[1820,14496,14497,14499],{},[898,14498,14362],{},[1826,14500,3472],{},[1655,14502,2969],{},[1826,14504,13585],{},[902,14506,14507],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,14509,14510],{},"Celková poptávka po penězích:",[724,14512,14513],{},[883,14514,14516],{"className":14515},[886],[888,14517,14518],{"xmlns":890},[892,14519,14520,14574],{},[895,14521,14522,14528,14530,14536,14538,14544,14546,14552,14554,14556,14562,14564,14566,14572],{},[2597,14523,14524,14526],{},[898,14525,2127],{},[898,14527,2838],{},[1655,14529,1657],{},[1820,14531,14532,14534],{},[898,14533,1873],{},[1826,14535,1828],{},[1655,14537,2346],{},[1820,14539,14540,14542],{},[898,14541,1873],{},[1826,14543,1837],{},[1655,14545,1657],{},[1820,14547,14548,14550],{},[898,14549,14362],{},[1826,14551,1828],{},[898,14553,10375],{},[1655,14555,2346],{},[1820,14557,14558,14560],{},[898,14559,14362],{},[1826,14561,1837],{},[898,14563,13166],{},[1655,14565,2346],{},[1820,14567,14568,14570],{},[898,14569,14362],{},[1826,14571,3472],{},[898,14573,1719],{"mathvariant":1943},[902,14575,14576],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,14578,14579,14580,2086],{},"Podmínka rovnováhy na trhu peněz ",[883,14581,14583],{"className":14582},[886],[888,14584,14585],{"xmlns":890},[892,14586,14587,14603],{},[895,14588,14589,14595,14597],{},[2597,14590,14591,14593],{},[898,14592,2127],{},[898,14594,2838],{},[1655,14596,1657],{},[2597,14598,14599,14601],{},[898,14600,2127],{},[1655,14602,5603],{},[902,14604,14605],{"encoding":904},"M^D = M^*",[724,14607,14608],{},[883,14609,14611],{"className":14610},[886],[888,14612,14613],{"xmlns":890},[892,14614,14615,14662],{},[895,14616,14617,14623,14625,14631,14633,14635,14641,14643,14645,14651,14653,14655,14657,14660],{},[2597,14618,14619,14621],{},[898,14620,2127],{},[1655,14622,5603],{},[1655,14624,1657],{},[1820,14626,14627,14629],{},[898,14628,14362],{},[1826,14630,1828],{},[898,14632,10375],{},[1655,14634,2346],{},[1820,14636,14637,14639],{},[898,14638,14362],{},[1826,14640,1837],{},[898,14642,13166],{},[1655,14644,2346],{},[1820,14646,14647,14649],{},[898,14648,14362],{},[1826,14650,3472],{},[1655,14652,1671],{"separator":1670},[1967,14654],{"width":1969},[1655,14656,1664],{"stretchy":1663},[1826,14658,14659],{},"7.15",[1655,14661,1677],{"stretchy":1663},[902,14663,14664],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,14666,14667,14668,4421],{},"po úpravě (vyjádření ",[883,14669,14671],{"className":14670},[886],[888,14672,14673],{"xmlns":890},[892,14674,14675,14679],{},[895,14676,14677],{},[898,14678,10375],{},[902,14680,10375],{"encoding":904},[724,14682,14683],{},[883,14684,14686],{"className":14685},[886],[888,14687,14688],{"xmlns":890},[892,14689,14690,14765],{},[895,14691,14692,14756,14758,14760,14763],{},[13957,14693,14694],{"notation":13959},[3615,14695,14696],{"scriptlevel":2552,"displaystyle":1663},[3615,14697,14698],{"scriptlevel":2552,"displaystyle":1663},[3615,14699,14700],{"scriptlevel":2552,"displaystyle":1670},[895,14701,14702,14704,14706,14708,14710,14724,14726,14728,14730,14754],{},[2031,14703,2435],{},[898,14705,10375],{},[1655,14707,1657],{},[1655,14709,2623],{},[1949,14711,14712,14718],{},[1820,14713,14714,14716],{},[898,14715,14362],{},[1826,14717,1837],{},[1820,14719,14720,14722],{},[898,14721,14362],{},[1826,14723,1828],{},[2031,14725,2435],{},[898,14727,13166],{},[1655,14729,2346],{},[1949,14731,14732,14748],{},[895,14733,14734,14740,14742],{},[2597,14735,14736,14738],{},[898,14737,2127],{},[1655,14739,5603],{},[1655,14741,2623],{},[1820,14743,14744,14746],{},[898,14745,14362],{},[1826,14747,3472],{},[1820,14749,14750,14752],{},[898,14751,14362],{},[1826,14753,1828],{},[2031,14755,2435],{},[1967,14757],{"width":1969},[1655,14759,1664],{"stretchy":1663},[1826,14761,14762],{},"7.16",[1655,14764,1677],{"stretchy":1663},[902,14766,14767],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,14769,14026,14770,2115,14773,14776,14777,14037,14780,14040,14783,14063,14804,14836,14837,14859,14860,14862,14863,14865],{},[38,14771,14772],{},"funkce LM",[614,14774,14775],{},"LM schedule","), její graf ",[38,14778,14779],{},"křivka LM",[38,14781,14782],{},"rostoucí",[883,14784,14786],{"className":14785},[886],[888,14787,14788],{"xmlns":890},[892,14789,14790,14802],{},[895,14791,14792,14794,14796,14798,14800],{},[1655,14793,1664],{"stretchy":1663},[898,14795,13166],{},[1655,14797,1671],{"separator":1670},[898,14799,10375],{},[1655,14801,1677],{"stretchy":1663},[902,14803,14062],{"encoding":904},[883,14805,14807],{"className":14806},[886],[888,14808,14809],{"xmlns":890},[892,14810,14811,14833],{},[895,14812,14813,14815,14829,14831],{},[1655,14814,2623],{},[1949,14816,14817,14823],{},[1820,14818,14819,14821],{},[898,14820,14362],{},[1826,14822,1837],{},[1820,14824,14825,14827],{},[898,14826,14362],{},[1826,14828,1828],{},[1655,14830,2969],{},[1826,14832,2552],{},[902,14834,14835],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,14838,14840],{"className":14839},[886],[888,14841,14842],{"xmlns":890},[892,14843,14844,14856],{},[895,14845,14846,14852,14854],{},[1820,14847,14848,14850],{},[898,14849,14362],{},[1826,14851,1837],{},[1655,14853,3065],{},[1826,14855,2552],{},[902,14857,14858],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,14861,1873],{},"iquidity of ",[38,14864,2127],{},"oney.",[5120,14867,14868],{},[724,14869,14870,14872,14873,14886,14887,14915,14916,14933,14934,14947,14948,14965,14966,2704,14979,14992,14993,14996],{},[883,14871,5406],{}," Intuice — proč LM roste\nVyšší důchod ",[883,14874,14876],{"className":14875},[886],[888,14877,14878],{"xmlns":890},[892,14879,14880,14884],{},[895,14881,14882],{},[898,14883,10375],{},[902,14885,10375],{"encoding":904}," → větší transakční poptávka po penězích ",[883,14888,14890],{"className":14889},[886],[888,14891,14892],{"xmlns":890},[892,14893,14894,14912],{},[895,14895,14896,14902,14904,14910],{},[1820,14897,14898,14900],{},[898,14899,1873],{},[1826,14901,1828],{},[1655,14903,1657],{},[1820,14905,14906,14908],{},[898,14907,14362],{},[1826,14909,1828],{},[898,14911,10375],{},[902,14913,14914],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,14917,14919],{"className":14918},[886],[888,14920,14921],{"xmlns":890},[892,14922,14923,14931],{},[895,14924,14925],{},[2597,14926,14927,14929],{},[898,14928,2127],{},[1655,14930,5603],{},[902,14932,13275],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,14935,14937],{"className":14936},[886],[888,14938,14939],{"xmlns":890},[892,14940,14941,14945],{},[895,14942,14943],{},[898,14944,13166],{},[902,14946,13166],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,14949,14951],{"className":14950},[886],[888,14952,14953],{"xmlns":890},[892,14954,14955,14963],{},[895,14956,14957],{},[1820,14958,14959,14961],{},[898,14960,1873],{},[1826,14962,1837],{},[902,14964,14409],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,14967,14969],{"className":14968},[886],[888,14970,14971],{"xmlns":890},[892,14972,14973,14977],{},[895,14974,14975],{},[898,14976,10375],{},[902,14978,10375],{"encoding":904},[883,14980,14982],{"className":14981},[886],[888,14983,14984],{"xmlns":890},[892,14985,14986,14990],{},[895,14987,14988],{},[898,14989,13166],{},[902,14991,13166],{"encoding":904}," na trhu peněz je proto ",[38,14994,14995],{},"přímý"," (rostoucí křivka).",[115,14998,15000],{"id":14999},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,15002,15003,15004,15007,15008,3106,15011,2704,15029,3106,15032,15050,15051,15069,15070,15088,15089,15105,15106,2704,15121,15136,15137,1719],{},"Řešením ",[38,15005,15006],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,15009,15010],{},"rovnovážný důchod",[883,15012,15014],{"className":15013},[886],[888,15015,15016],{"xmlns":890},[892,15017,15018,15026],{},[895,15019,15020],{},[2597,15021,15022,15024],{},[898,15023,10375],{},[898,15025,5502],{},[902,15027,15028],{"encoding":904},"Y^E",[38,15030,15031],{},"rovnovážnou úrokovou míru",[883,15033,15035],{"className":15034},[886],[888,15036,15037],{"xmlns":890},[892,15038,15039,15047],{},[895,15040,15041],{},[2597,15042,15043,15045],{},[898,15044,13166],{},[898,15046,5502],{},[902,15048,15049],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,15052,15054],{"className":15053},[886],[888,15055,15056],{"xmlns":890},[892,15057,15058,15066],{},[895,15059,15060],{},[2597,15061,15062,15064],{},[898,15063,13309],{},[898,15065,5502],{},[902,15067,15068],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,15071,15073],{"className":15072},[886],[888,15074,15075],{"xmlns":890},[892,15076,15077,15085],{},[895,15078,15079],{},[2597,15080,15081,15083],{},[898,15082,4052],{},[898,15084,5502],{},[902,15086,15087],{"encoding":904},"C^E",". Graficky jde o ",[38,15090,15091,15092],{},"průsečík ",[883,15093,15095],{"className":15094},[886],[888,15096,15097],{"xmlns":890},[892,15098,15099,15103],{},[895,15100,15101],{},[898,15102,5502],{},[902,15104,5502],{"encoding":904}," křivek ",[883,15107,15109],{"className":15108},[886],[888,15110,15111],{"xmlns":890},[892,15112,15113,15119],{},[895,15114,15115,15117],{},[898,15116,13309],{},[898,15118,9920],{},[902,15120,13176],{"encoding":904},[883,15122,15124],{"className":15123},[886],[888,15125,15126],{"xmlns":890},[892,15127,15128,15134],{},[895,15129,15130,15132],{},[898,15131,1873],{},[898,15133,2127],{},[902,15135,13183],{"encoding":904}," v rovině ",[883,15138,15140],{"className":15139},[886],[888,15141,15142],{"xmlns":890},[892,15143,15144,15156],{},[895,15145,15146,15148,15150,15152,15154],{},[1655,15147,1664],{"stretchy":1663},[898,15149,13166],{},[1655,15151,1671],{"separator":1670},[898,15153,10375],{},[1655,15155,1677],{"stretchy":1663},[902,15157,14062],{"encoding":904},[724,15159,15160],{},[614,15161,15162,15163,15184,15185,15200,15201,15216,15217,15230,15231,15248,15249,13253,15262,15248,15279,15292,15293,15306],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,15164,15166],{"className":15165},[886],[888,15167,15168],{"xmlns":890},[892,15169,15170,15182],{},[895,15171,15172,15174,15176,15178,15180],{},[1655,15173,1664],{"stretchy":1663},[898,15175,13166],{},[1655,15177,1671],{"separator":1670},[898,15179,10375],{},[1655,15181,1677],{"stretchy":1663},[902,15183,14062],{"encoding":904},". Rostoucí přímka ",[883,15186,15188],{"className":15187},[886],[888,15189,15190],{"xmlns":890},[892,15191,15192,15198],{},[895,15193,15194,15196],{},[898,15195,1873],{},[898,15197,2127],{},[902,15199,13183],{"encoding":904}," a klesající přímka ",[883,15202,15204],{"className":15203},[886],[888,15205,15206],{"xmlns":890},[892,15207,15208,15214],{},[895,15209,15210,15212],{},[898,15211,13309],{},[898,15213,9920],{},[902,15215,13176],{"encoding":904}," se protínají v bodě ",[883,15218,15220],{"className":15219},[886],[888,15221,15222],{"xmlns":890},[892,15223,15224,15228],{},[895,15225,15226],{},[898,15227,5502],{},[902,15229,5502],{"encoding":904}," se souřadnicemi ",[883,15232,15234],{"className":15233},[886],[888,15235,15236],{"xmlns":890},[892,15237,15238,15246],{},[895,15239,15240],{},[2597,15241,15242,15244],{},[898,15243,13166],{},[898,15245,5502],{},[902,15247,15049],{"encoding":904}," (na ose ",[883,15250,15252],{"className":15251},[886],[888,15253,15254],{"xmlns":890},[892,15255,15256,15260],{},[895,15257,15258],{},[898,15259,13166],{},[902,15261,13166],{"encoding":904},[883,15263,15265],{"className":15264},[886],[888,15266,15267],{"xmlns":890},[892,15268,15269,15277],{},[895,15270,15271],{},[2597,15272,15273,15275],{},[898,15274,10375],{},[898,15276,5502],{},[902,15278,15028],{"encoding":904},[883,15280,15282],{"className":15281},[886],[888,15283,15284],{"xmlns":890},[892,15285,15286,15290],{},[895,15287,15288],{},[898,15289,10375],{},[902,15291,10375],{"encoding":904},"); tečkované čáry z ",[883,15294,15296],{"className":15295},[886],[888,15297,15298],{"xmlns":890},[892,15299,15300,15304],{},[895,15301,15302],{},[898,15303,5502],{},[902,15305,5502],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[5120,15308,15309,15314],{},[724,15310,15311,15313],{},[883,15312,5821],{}," Postup — jak najít IS-LM rovnováhu",[152,15315,15316,15392,15460,15518,15591],{},[123,15317,15318,15321,15322,2704,15342,15362,15363,2704,15376,15389,15390,1719],{},[38,15319,15320],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,15323,15325],{"className":15324},[886],[888,15326,15327],{"xmlns":890},[892,15328,15329,15339],{},[895,15330,15331,15333,15335,15337],{},[898,15332,4052],{},[1655,15334,1664],{"stretchy":1663},[898,15336,10375],{},[1655,15338,1677],{"stretchy":1663},[902,15340,15341],{"encoding":904},"C(Y)",[883,15343,15345],{"className":15344},[886],[888,15346,15347],{"xmlns":890},[892,15348,15349,15359],{},[895,15350,15351,15353,15355,15357],{},[898,15352,13309],{},[1655,15354,1664],{"stretchy":1663},[898,15356,13166],{},[1655,15358,1677],{"stretchy":1663},[902,15360,15361],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,15364,15366],{"className":15365},[886],[888,15367,15368],{"xmlns":890},[892,15369,15370,15374],{},[895,15371,15372],{},[898,15373,10375],{},[902,15375,10375],{"encoding":904},[883,15377,15379],{"className":15378},[886],[888,15380,15381],{"xmlns":890},[892,15382,15383,15387],{},[895,15384,15385],{},[898,15386,13166],{},[902,15388,13166],{"encoding":904}," — dostaneš rovnici ",[38,15391,13176],{},[123,15393,15394,15397,15398,2704,15415,15432,15433,15389,15458,1719],{},[38,15395,15396],{},"Z trhu peněz (7.15)"," dosaď ",[883,15399,15401],{"className":15400},[886],[888,15402,15403],{"xmlns":890},[892,15404,15405,15413],{},[895,15406,15407],{},[1820,15408,15409,15411],{},[898,15410,1873],{},[1826,15412,1828],{},[902,15414,14337],{"encoding":904},[883,15416,15418],{"className":15417},[886],[888,15419,15420],{"xmlns":890},[892,15421,15422,15430],{},[895,15423,15424],{},[1820,15425,15426,15428],{},[898,15427,1873],{},[1826,15429,1837],{},[902,15431,14409],{"encoding":904}," a vztah ",[883,15434,15436],{"className":15435},[886],[888,15437,15438],{"xmlns":890},[892,15439,15440,15456],{},[895,15441,15442,15448,15450],{},[2597,15443,15444,15446],{},[898,15445,2127],{},[898,15447,2838],{},[1655,15449,1657],{},[2597,15451,15452,15454],{},[898,15453,2127],{},[1655,15455,5603],{},[902,15457,14605],{"encoding":904},[38,15459,13183],{},[123,15461,15462,15465,15466,2704,15479,15492,15493,15517],{},[38,15463,15464],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,15467,15469],{"className":15468},[886],[888,15470,15471],{"xmlns":890},[892,15472,15473,15477],{},[895,15474,15475],{},[898,15476,10375],{},[902,15478,10375],{"encoding":904},[883,15480,15482],{"className":15481},[886],[888,15483,15484],{"xmlns":890},[892,15485,15486,15490],{},[895,15487,15488],{},[898,15489,13166],{},[902,15491,13166],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,15494,15496],{"className":15495},[886],[888,15497,15498],{"xmlns":890},[892,15499,15500,15514],{},[895,15501,15502,15504,15506,15508,15510,15512],{},[898,15503,10375],{},[1655,15505,1657],{},[898,15507,1660],{},[1655,15509,1664],{"stretchy":1663},[898,15511,13166],{},[1655,15513,1677],{"stretchy":1663},[902,15515,15516],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,15519,15520,3106,15523,2704,15557,1719],{},[38,15521,15522],{},"Zpětně dopočítej",[883,15524,15526],{"className":15525},[886],[888,15527,15528],{"xmlns":890},[892,15529,15530,15554],{},[895,15531,15532,15538,15540,15542,15544,15550,15552],{},[2597,15533,15534,15536],{},[898,15535,4052],{},[898,15537,5502],{},[1655,15539,1657],{},[898,15541,207],{},[2031,15543,2435],{},[2597,15545,15546,15548],{},[898,15547,10375],{},[898,15549,5502],{},[1655,15551,2346],{},[898,15553,2025],{},[902,15555,15556],{"encoding":904},"C^E = a\\,Y^E + b",[883,15558,15560],{"className":15559},[886],[888,15561,15562],{"xmlns":890},[892,15563,15564,15588],{},[895,15565,15566,15572,15574,15576,15578,15584,15586],{},[2597,15567,15568,15570],{},[898,15569,13309],{},[898,15571,5502],{},[1655,15573,1657],{},[898,15575,1789],{},[2031,15577,2435],{},[2597,15579,15580,15582],{},[898,15581,13166],{},[898,15583,5502],{},[1655,15585,2346],{},[898,15587,2410],{},[902,15589,15590],{"encoding":904},"I^E = c\\,r^E + d",[123,15592,15593,15596,15597,15631,15632,15686],{},[38,15594,15595],{},"Ověř:"," musí platit ",[883,15598,15600],{"className":15599},[886],[888,15601,15602],{"xmlns":890},[892,15603,15604,15628],{},[895,15605,15606,15612,15614,15620,15622],{},[2597,15607,15608,15610],{},[898,15609,10375],{},[898,15611,5502],{},[1655,15613,1657],{},[2597,15615,15616,15618],{},[898,15617,4052],{},[898,15619,5502],{},[1655,15621,2346],{},[2597,15623,15624,15626],{},[898,15625,13309],{},[898,15627,5502],{},[902,15629,15630],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,15633,15635],{"className":15634},[886],[888,15636,15637],{"xmlns":890},[892,15638,15639,15683],{},[895,15640,15641,15647,15649,15655,15661,15663,15669,15675,15677],{},[2597,15642,15643,15645],{},[898,15644,2127],{},[1655,15646,5603],{},[1655,15648,1657],{},[1820,15650,15651,15653],{},[898,15652,14362],{},[1826,15654,1828],{},[2597,15656,15657,15659],{},[898,15658,10375],{},[898,15660,5502],{},[1655,15662,2346],{},[1820,15664,15665,15667],{},[898,15666,14362],{},[1826,15668,1837],{},[2597,15670,15671,15673],{},[898,15672,13166],{},[898,15674,5502],{},[1655,15676,2346],{},[1820,15678,15679,15681],{},[898,15680,14362],{},[1826,15682,3472],{},[902,15684,15685],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,15688,15690],{"id":15689},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,15692,15693],{},"Pro trh zboží jsou dány:",[120,15695,15696,15724],{},[123,15697,15698,15699,1671],{},"spotřeba ",[883,15700,15702],{"className":15701},[886],[888,15703,15704],{"xmlns":890},[892,15705,15706,15721],{},[895,15707,15708,15710,15712,15715,15717,15719],{},[898,15709,4052],{},[1655,15711,1657],{},[1826,15713,15714],{},"0,8",[898,15716,10375],{},[1655,15718,2346],{},[1826,15720,4360],{},[902,15722,15723],{"encoding":904},"C = 0{,}8Y + 100",[123,15725,15726,15727,1719],{},"investice ",[883,15728,15730],{"className":15729},[886],[888,15731,15732],{"xmlns":890},[892,15733,15734,15750],{},[895,15735,15736,15738,15740,15742,15744,15746,15748],{},[898,15737,13309],{},[1655,15739,1657],{},[1655,15741,2623],{},[1826,15743,10282],{},[898,15745,13166],{},[1655,15747,2346],{},[1826,15749,4057],{},[902,15751,15752],{"encoding":904},"I = -20r + 1000",[724,15754,15755],{},"Pro trh peněz:",[120,15757,15758,15784,15816],{},[123,15759,15760,1671],{},[883,15761,15763],{"className":15762},[886],[888,15764,15765],{"xmlns":890},[892,15766,15767,15781],{},[895,15768,15769,15775,15777,15779],{},[1820,15770,15771,15773],{},[898,15772,1873],{},[1826,15774,1828],{},[1655,15776,1657],{},[1826,15778,4068],{},[898,15780,10375],{},[902,15782,15783],{"encoding":904},"L_1 = 0{,}1Y",[123,15785,15786,1671],{},[883,15787,15789],{"className":15788},[886],[888,15790,15791],{"xmlns":890},[892,15792,15793,15813],{},[895,15794,15795,15801,15803,15805,15807,15809,15811],{},[1820,15796,15797,15799],{},[898,15798,1873],{},[1826,15800,1837],{},[1655,15802,1657],{},[1655,15804,2623],{},[1826,15806,6253],{},[898,15808,13166],{},[1655,15810,2346],{},[1826,15812,9851],{},[902,15814,15815],{"encoding":904},"L_2 = -25r + 2000",[123,15817,15818,15819,1719],{},"nabídka peněz ",[883,15820,15822],{"className":15821},[886],[888,15823,15824],{"xmlns":890},[892,15825,15826,15839],{},[895,15827,15828,15834,15836],{},[2597,15829,15830,15832],{},[898,15831,2127],{},[1655,15833,5603],{},[1655,15835,1657],{},[1826,15837,15838],{},"2375",[902,15840,15841],{"encoding":904},"M^* = 2375",[724,15843,15844,15847,15848,2086],{},[38,15845,15846],{},"Funkce IS"," — dosazením do (7.13) ",[883,15849,15851],{"className":15850},[886],[888,15852,15853],{"xmlns":890},[892,15854,15855,15867],{},[895,15856,15857,15859,15861,15863,15865],{},[898,15858,10375],{},[1655,15860,1657],{},[898,15862,4052],{},[1655,15864,2346],{},[898,15866,13309],{},[902,15868,15869],{"encoding":904},"Y = C + I",[724,15871,15872],{},[883,15873,15875],{"className":15874},[886],[888,15876,15877],{"xmlns":890},[892,15878,15879,15905],{},[895,15880,15881,15883,15885,15887,15889,15891,15893,15895,15897,15899,15901,15903],{},[898,15882,10375],{},[1655,15884,1657],{},[1826,15886,15714],{},[898,15888,10375],{},[1655,15890,2346],{},[1826,15892,4360],{},[1655,15894,2623],{},[1826,15896,10282],{},[898,15898,13166],{},[1655,15900,2346],{},[1826,15902,4057],{},[1655,15904,1671],{"separator":1670},[902,15906,15907],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,15909,15910],{},"tj.",[724,15912,15913],{},[883,15914,15916],{"className":15915},[886],[888,15917,15918],{"xmlns":890},[892,15919,15920,15945],{},[895,15921,15922,15924,15926,15928,15930,15932,15934,15937,15939,15941,15943],{},[1826,15923,4112],{},[898,15925,10375],{},[1655,15927,2346],{},[1826,15929,10282],{},[898,15931,13166],{},[1655,15933,1657],{},[1826,15935,15936],{},"1100.",[1967,15938],{"width":1969},[1655,15940,1664],{"stretchy":1663},[2031,15942,13176],{},[1655,15944,1677],{"stretchy":1663},[902,15946,15947],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,15949,15950,15953,15954,2086],{},[38,15951,15952],{},"Funkce LM"," — dosazením do (7.15) ",[883,15955,15957],{"className":15956},[886],[888,15958,15959],{"xmlns":890},[892,15960,15961,15985],{},[895,15962,15963,15969,15971,15977,15979],{},[2597,15964,15965,15967],{},[898,15966,2127],{},[1655,15968,5603],{},[1655,15970,1657],{},[1820,15972,15973,15975],{},[898,15974,1873],{},[1826,15976,1828],{},[1655,15978,2346],{},[1820,15980,15981,15983],{},[898,15982,1873],{},[1826,15984,1837],{},[902,15986,15987],{"encoding":904},"M^* = L_1 + L_2",[724,15989,15990],{},[883,15991,15993],{"className":15992},[886],[888,15994,15995],{"xmlns":890},[892,15996,15997,16019],{},[895,15998,15999,16001,16003,16005,16007,16009,16011,16013,16015,16017],{},[1826,16000,15838],{},[1655,16002,1657],{},[1826,16004,4068],{},[898,16006,10375],{},[1655,16008,2623],{},[1826,16010,6253],{},[898,16012,13166],{},[1655,16014,2346],{},[1826,16016,9851],{},[1655,16018,1671],{"separator":1670},[902,16020,16021],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,16023,15910],{},[724,16025,16026],{},[883,16027,16029],{"className":16028},[886],[888,16030,16031],{"xmlns":890},[892,16032,16033,16058],{},[895,16034,16035,16037,16039,16041,16043,16045,16047,16050,16052,16054,16056],{},[1826,16036,4068],{},[898,16038,10375],{},[1655,16040,2623],{},[1826,16042,6253],{},[898,16044,13166],{},[1655,16046,1657],{},[1826,16048,16049],{},"375.",[1967,16051],{"width":1969},[1655,16053,1664],{"stretchy":1663},[2031,16055,13183],{},[1655,16057,1677],{"stretchy":1663},[902,16059,16060],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,16062,16063,16066,16067,16092],{},[38,16064,16065],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,16068,16070],{"className":16069},[886],[888,16071,16072],{"xmlns":890},[892,16073,16074,16089],{},[895,16075,16076,16078,16080,16083,16085,16087],{},[898,16077,10375],{},[1655,16079,1657],{},[1826,16081,16082],{},"5500",[1655,16084,2623],{},[1826,16086,4360],{},[898,16088,13166],{},[902,16090,16091],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,16094,16095],{},[883,16096,16098],{"className":16097},[886],[888,16099,16100],{"xmlns":890},[892,16101,16102,16188],{},[895,16103,16104,16106,16108,16110,16112,16114,16116,16118,16120,16122,16124,16126,16129,16131,16134,16136,16139,16141,16143,16145,16147,16149,16151,16153,16155,16157,16159,16161,16164,16166,16168,16171,16173,16175,16177,16183,16185],{},[1826,16105,4068],{},[1655,16107,1664],{"stretchy":1663},[1826,16109,16082],{},[1655,16111,2623],{},[1826,16113,4360],{},[898,16115,13166],{},[1655,16117,1677],{"stretchy":1663},[1655,16119,2623],{},[1826,16121,6253],{},[898,16123,13166],{},[1655,16125,1657],{},[1826,16127,16128],{},"375",[2031,16130,2783],{},[1655,16132,16133],{},"⟹",[2031,16135,2783],{},[1826,16137,16138],{},"550",[1655,16140,2623],{},[1826,16142,4136],{},[898,16144,13166],{},[1655,16146,2623],{},[1826,16148,6253],{},[898,16150,13166],{},[1655,16152,1657],{},[1826,16154,16128],{},[2031,16156,2783],{},[1655,16158,16133],{},[2031,16160,2783],{},[1826,16162,16163],{},"35",[898,16165,13166],{},[1655,16167,1657],{},[1826,16169,16170],{},"175",[2031,16172,2783],{},[1655,16174,16133],{},[2031,16176,2783],{},[2597,16178,16179,16181],{},[898,16180,13166],{},[898,16182,5502],{},[1655,16184,1657],{},[1826,16186,16187],{},"5.",[902,16189,16190],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,16192,16193],{},[38,16194,16195],{},"Zpětné dosazení:",[120,16197,16198,16244,16281],{},[123,16199,16200,1671],{},[883,16201,16203],{"className":16202},[886],[888,16204,16205],{"xmlns":890},[892,16206,16207,16241],{},[895,16208,16209,16215,16217,16219,16221,16223,16225,16227,16229,16231,16233,16236,16238],{},[2597,16210,16211,16213],{},[898,16212,10375],{},[898,16214,5502],{},[1655,16216,1657],{},[1826,16218,16082],{},[1655,16220,2623],{},[1826,16222,4360],{},[1655,16224,2869],{},[1826,16226,3524],{},[1655,16228,1657],{},[1826,16230,16082],{},[1655,16232,2623],{},[1826,16234,16235],{},"500",[1655,16237,1657],{},[1826,16239,16240],{},"5000",[902,16242,16243],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,16245,16246,1671],{},[883,16247,16249],{"className":16248},[886],[888,16250,16251],{"xmlns":890},[892,16252,16253,16278],{},[895,16254,16255,16261,16263,16265,16267,16269,16271,16273,16275],{},[2597,16256,16257,16259],{},[898,16258,4052],{},[898,16260,5502],{},[1655,16262,1657],{},[1826,16264,15714],{},[1655,16266,2869],{},[1826,16268,16240],{},[1655,16270,2346],{},[1826,16272,4360],{},[1655,16274,1657],{},[1826,16276,16277],{},"4100",[902,16279,16280],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,16282,16283,1719],{},[883,16284,16286],{"className":16285},[886],[888,16287,16288],{"xmlns":890},[892,16289,16290,16317],{},[895,16291,16292,16298,16300,16302,16304,16306,16308,16310,16312,16314],{},[2597,16293,16294,16296],{},[898,16295,13309],{},[898,16297,5502],{},[1655,16299,1657],{},[1655,16301,2623],{},[1826,16303,10282],{},[1655,16305,2869],{},[1826,16307,3524],{},[1655,16309,2346],{},[1826,16311,4057],{},[1655,16313,1657],{},[1826,16315,16316],{},"900",[902,16318,16319],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,16321,16322,3106,16325,16371],{},[38,16323,16324],{},"Ověření:",[883,16326,16328],{"className":16327},[886],[888,16329,16330],{"xmlns":890},[892,16331,16332,16368],{},[895,16333,16334,16340,16342,16348,16350,16352,16354,16356,16358,16360,16362],{},[2597,16335,16336,16338],{},[898,16337,4052],{},[898,16339,5502],{},[1655,16341,2346],{},[2597,16343,16344,16346],{},[898,16345,13309],{},[898,16347,5502],{},[1655,16349,1657],{},[1826,16351,16277],{},[1655,16353,2346],{},[1826,16355,16316],{},[1655,16357,1657],{},[1826,16359,16240],{},[1655,16361,1657],{},[2597,16363,16364,16366],{},[898,16365,10375],{},[898,16367,5502],{},[902,16369,16370],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,16373,16374],{},[883,16375,16377],{"className":16376},[886],[888,16378,16379],{"xmlns":890},[892,16380,16381,16451],{},[895,16382,16383],{},[13957,16384,16385],{"notation":13959},[3615,16386,16387],{"scriptlevel":2552,"displaystyle":1663},[3615,16388,16389],{"scriptlevel":2552,"displaystyle":1663},[3615,16390,16391],{"scriptlevel":2552,"displaystyle":1670},[895,16392,16393,16395,16401,16403,16405,16407,16410,16416,16418,16420,16422,16424,16430,16432,16434,16436,16438,16444,16446,16449],{},[2031,16394,2435],{},[2597,16396,16397,16399],{},[898,16398,10375],{},[898,16400,5502],{},[1655,16402,1657],{},[1826,16404,16240],{},[1655,16406,1671],{"separator":1670},[1967,16408],{"width":16409},"1em",[2597,16411,16412,16414],{},[898,16413,13166],{},[898,16415,5502],{},[1655,16417,1657],{},[1826,16419,3524],{},[1655,16421,1671],{"separator":1670},[1967,16423],{"width":16409},[2597,16425,16426,16428],{},[898,16427,4052],{},[898,16429,5502],{},[1655,16431,1657],{},[1826,16433,16277],{},[1655,16435,1671],{"separator":1670},[1967,16437],{"width":16409},[2597,16439,16440,16442],{},[898,16441,13309],{},[898,16443,5502],{},[1655,16445,1657],{},[1826,16447,16448],{},"900.",[2031,16450,2435],{},[902,16452,16453],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,16455,16456],{},[614,16457,16458,16459,16472,16473,16486,16487,16502,16503,16516,16517,16532,16533,16546,16547,16560,16561,1719],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,16460,16462],{"className":16461},[886],[888,16463,16464],{"xmlns":890},[892,16465,16466,16470],{},[895,16467,16468],{},[898,16469,10375],{},[902,16471,10375],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,16474,16476],{"className":16475},[886],[888,16477,16478],{"xmlns":890},[892,16479,16480,16484],{},[895,16481,16482],{},[898,16483,13166],{},[902,16485,13166],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,16488,16490],{"className":16489},[886],[888,16491,16492],{"xmlns":890},[892,16493,16494,16500],{},[895,16495,16496,16498],{},[898,16497,1873],{},[898,16499,2127],{},[902,16501,13183],{"encoding":904}," stoupá z oblasti nízkých ",[883,16504,16506],{"className":16505},[886],[888,16507,16508],{"xmlns":890},[892,16509,16510,16514],{},[895,16511,16512],{},[898,16513,13166],{},[902,16515,13166],{"encoding":904},", přímka ",[883,16518,16520],{"className":16519},[886],[888,16521,16522],{"xmlns":890},[892,16523,16524,16530],{},[895,16525,16526,16528],{},[898,16527,13309],{},[898,16529,9920],{},[902,16531,13176],{"encoding":904}," klesá a protíná osu ",[883,16534,16536],{"className":16535},[886],[888,16537,16538],{"xmlns":890},[892,16539,16540,16544],{},[895,16541,16542],{},[898,16543,13166],{},[902,16545,13166],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,16548,16550],{"className":16549},[886],[888,16551,16552],{"xmlns":890},[892,16553,16554,16558],{},[895,16555,16556],{},[898,16557,5502],{},[902,16559,5502],{"encoding":904}," leží v bodě ",[883,16562,16564],{"className":16563},[886],[888,16565,16566],{"xmlns":890},[892,16567,16568,16590],{},[895,16569,16570,16572,16574,16576,16578,16580,16582,16584,16586,16588],{},[1655,16571,2734],{"stretchy":1663},[898,16573,13166],{},[1655,16575,1657],{},[1826,16577,3524],{},[1655,16579,1671],{"separator":1670},[2031,16581,2033],{},[898,16583,10375],{},[1655,16585,1657],{},[1826,16587,16240],{},[1655,16589,2743],{"stretchy":1663},[902,16591,16592],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,16594,16596],{"id":16595},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,16598,16599,16602,16603,16616,16617,8262,16630,16633,16634,16652,16653,16670,16671,16688,16689,16702,16703,16716],{},[38,16600,16601],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,16604,16606],{"className":16605},[886],[888,16607,16608],{"xmlns":890},[892,16609,16610,16614],{},[895,16611,16612],{},[898,16613,13237],{},[902,16615,13237],{"encoding":904}," nebo snížení daní ",[883,16618,16620],{"className":16619},[886],[888,16621,16622],{"xmlns":890},[892,16623,16624,16628],{},[895,16625,16626],{},[898,16627,4049],{},[902,16629,4049],{"encoding":904},[38,16631,16632],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,16635,16637],{"className":16636},[886],[888,16638,16639],{"xmlns":890},[892,16640,16641,16649],{},[895,16642,16643],{},[2597,16644,16645,16647],{},[898,16646,5502],{},[1655,16648,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,16650,16651],{"encoding":904},"E'"," má vyšší ",[883,16654,16656],{"className":16655},[886],[888,16657,16658],{"xmlns":890},[892,16659,16660,16668],{},[895,16661,16662],{},[2597,16663,16664,16666],{},[898,16665,10375],{},[898,16667,5502],{},[902,16669,15028],{"encoding":904}," i vyšší ",[883,16672,16674],{"className":16673},[886],[888,16675,16676],{"xmlns":890},[892,16677,16678,16686],{},[895,16679,16680],{},[2597,16681,16682,16684],{},[898,16683,13166],{},[898,16685,5502],{},[902,16687,15049],{"encoding":904}," (vyšší ",[883,16690,16692],{"className":16691},[886],[888,16693,16694],{"xmlns":890},[892,16695,16696,16700],{},[895,16697,16698],{},[898,16699,10375],{},[902,16701,10375],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,16704,16706],{"className":16705},[886],[888,16707,16708],{"xmlns":890},[892,16709,16710,16714],{},[895,16711,16712],{},[898,16713,13166],{},[902,16715,13166],{"encoding":904}," nahoru).",[724,16718,16719],{},[1723,16720],{"alt":16721,"className":16722,"src":16723},"imek-posun-is-lm-politiky",[210,1727],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,16725,16726,16729,16730,16747,16748,16751,16752,16769,16770,16787,16788,16801,16802,16821,16822,5171],{},[38,16727,16728],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,16731,16733],{"className":16732},[886],[888,16734,16735],{"xmlns":890},[892,16736,16737,16745],{},[895,16738,16739],{},[2597,16740,16741,16743],{},[898,16742,2127],{},[1655,16744,5603],{},[902,16746,13275],{"encoding":904}," národní bankou — ",[38,16749,16750],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,16753,16755],{"className":16754},[886],[888,16756,16757],{"xmlns":890},[892,16758,16759,16767],{},[895,16760,16761],{},[2597,16762,16763,16765],{},[898,16764,13166],{},[898,16766,5502],{},[902,16768,15049],{"encoding":904}," a vyšší ",[883,16771,16773],{"className":16772},[886],[888,16774,16775],{"xmlns":890},[892,16776,16777,16785],{},[895,16778,16779],{},[2597,16780,16781,16783],{},[898,16782,10375],{},[898,16784,5502],{},[902,16786,15028],{"encoding":904}," (nižší ",[883,16789,16791],{"className":16790},[886],[888,16792,16793],{"xmlns":890},[892,16794,16795,16799],{},[895,16796,16797],{},[898,16798,13166],{},[902,16800,13166],{"encoding":904}," povzbuzuje investice ",[883,16803,16805],{"className":16804},[886],[888,16806,16807],{"xmlns":890},[892,16808,16809,16819],{},[895,16810,16811,16813,16815,16817],{},[898,16812,13309],{},[1655,16814,1664],{"stretchy":1663},[898,16816,13166],{},[1655,16818,1677],{"stretchy":1663},[902,16820,15361],{"encoding":904},", ty zvedají ",[883,16823,16825],{"className":16824},[886],[888,16826,16827],{"xmlns":890},[892,16828,16829,16833],{},[895,16830,16831],{},[898,16832,10375],{},[902,16834,10375],{"encoding":904},[724,16836,16837,16838,16841],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,16839,16840],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,16843,16845],{"id":16844},"klíčové-pojmy","Klíčové pojmy",[120,16847,16848,16921,16967,17049,17099,17166,17223,17264,17297],{},[123,16849,16850,8262,16883,1343,16900,16917,16918,16920],{},[38,16851,16852,16853],{},"Funkce investic ",[883,16854,16856],{"className":16855},[886],[888,16857,16858],{"xmlns":890},[892,16859,16860,16880],{},[895,16861,16862,16864,16866,16868,16870,16872,16874,16876,16878],{},[898,16863,13309],{},[1655,16865,1664],{"stretchy":1663},[898,16867,13166],{},[1655,16869,1677],{"stretchy":1663},[1655,16871,1657],{},[898,16873,1789],{},[898,16875,13166],{},[1655,16877,2346],{},[898,16879,2410],{},[902,16881,16882],{"encoding":904},"I(r) = cr + d",[883,16884,16886],{"className":16885},[886],[888,16887,16888],{"xmlns":890},[892,16889,16890,16898],{},[895,16891,16892,16894,16896],{},[898,16893,1789],{},[1655,16895,3065],{},[1826,16897,2552],{},[902,16899,13640],{"encoding":904},[883,16901,16903],{"className":16902},[886],[888,16904,16905],{"xmlns":890},[892,16906,16907,16915],{},[895,16908,16909,16911,16913],{},[898,16910,2410],{},[1655,16912,2969],{},[1826,16914,2552],{},[902,16916,13619],{"encoding":904},"; ",[38,16919,13644],{}," funkce úrokové míry.",[123,16922,16923,16926,16927,16948,16949,16966],{},[38,16924,16925],{},"Trh zboží"," — rovnováha ",[883,16928,16930],{"className":16929},[886],[888,16931,16932],{"xmlns":890},[892,16933,16934,16946],{},[895,16935,16936,16938,16940,16942,16944],{},[898,16937,10375],{},[1655,16939,1657],{},[898,16941,4052],{},[1655,16943,2346],{},[898,16945,13309],{},[902,16947,15869],{"encoding":904},", ekvivalentně ",[883,16950,16952],{"className":16951},[886],[888,16953,16954],{"xmlns":890},[892,16955,16956,16964],{},[895,16957,16958,16960,16962],{},[898,16959,13309],{},[1655,16961,1657],{},[898,16963,9920],{},[902,16965,13837],{"encoding":904}," (investice = úspory).",[123,16968,16969,2115,16972,16974,16975,17025,17026,14040,17028,1719],{},[38,16970,16971],{},"Křivka IS",[614,16973,13179],{},") — ",[883,16976,16978],{"className":16977},[886],[888,16979,16980],{"xmlns":890},[892,16981,16982,17022],{},[895,16983,16984,16986,16988,17000,17002,17004],{},[898,16985,10375],{},[1655,16987,1657],{},[1949,16989,16990,16992],{},[898,16991,1789],{},[895,16993,16994,16996,16998],{},[1826,16995,1828],{},[1655,16997,2623],{},[898,16999,207],{},[898,17001,13166],{},[1655,17003,2346],{},[1949,17005,17006,17014],{},[895,17007,17008,17010,17012],{},[898,17009,2025],{},[1655,17011,2346],{},[898,17013,2410],{},[895,17015,17016,17018,17020],{},[1826,17017,1828],{},[1655,17019,2623],{},[898,17021,207],{},[902,17023,17024],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,17027,13644],{},[883,17029,17031],{"className":17030},[886],[888,17032,17033],{"xmlns":890},[892,17034,17035,17047],{},[895,17036,17037,17039,17041,17043,17045],{},[1655,17038,1664],{"stretchy":1663},[898,17040,13166],{},[1655,17042,1671],{"separator":1670},[898,17044,10375],{},[1655,17046,1677],{"stretchy":1663},[902,17048,14062],{"encoding":904},[123,17050,17051,16926,17054,17080,17081,1719],{},[38,17052,17053],{},"Trh peněz",[883,17055,17057],{"className":17056},[886],[888,17058,17059],{"xmlns":890},[892,17060,17061,17077],{},[895,17062,17063,17069,17071],{},[2597,17064,17065,17067],{},[898,17066,2127],{},[898,17068,2838],{},[1655,17070,1657],{},[2597,17072,17073,17075],{},[898,17074,2127],{},[898,17076,9920],{},[902,17078,17079],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,17082,17084],{"className":17083},[886],[888,17085,17086],{"xmlns":890},[892,17087,17088,17096],{},[895,17089,17090],{},[2597,17091,17092,17094],{},[898,17093,2127],{},[1655,17095,5603],{},[902,17097,17098],{"encoding":904},"M^* ",[123,17100,17101,8262,17104,1719],{},[38,17102,17103],{},"Transakční, opatrnostní, spekulační poptávka",[883,17105,17107],{"className":17106},[886],[888,17108,17109],{"xmlns":890},[892,17110,17111,17163],{},[895,17112,17113,17119,17121,17127,17129,17135,17137,17143,17145,17147,17153,17155,17157],{},[2597,17114,17115,17117],{},[898,17116,2127],{},[898,17118,2838],{},[1655,17120,1657],{},[1820,17122,17123,17125],{},[898,17124,1873],{},[1826,17126,1828],{},[1655,17128,2346],{},[1820,17130,17131,17133],{},[898,17132,1873],{},[1826,17134,1837],{},[1655,17136,1657],{},[1820,17138,17139,17141],{},[898,17140,14362],{},[1826,17142,1828],{},[898,17144,10375],{},[1655,17146,2346],{},[1820,17148,17149,17151],{},[898,17150,14362],{},[1826,17152,1837],{},[898,17154,13166],{},[1655,17156,2346],{},[1820,17158,17159,17161],{},[898,17160,14362],{},[1826,17162,3472],{},[902,17164,17165],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,17167,17168,2115,17171,16974,17173,17219,17220,17222],{},[38,17169,17170],{},"Křivka LM",[614,17172,13186],{},[883,17174,17176],{"className":17175},[886],[888,17177,17178],{"xmlns":890},[892,17179,17180,17216],{},[895,17181,17182,17188,17190,17196,17198,17200,17206,17208,17210],{},[2597,17183,17184,17186],{},[898,17185,2127],{},[1655,17187,5603],{},[1655,17189,1657],{},[1820,17191,17192,17194],{},[898,17193,14362],{},[1826,17195,1828],{},[898,17197,10375],{},[1655,17199,2346],{},[1820,17201,17202,17204],{},[898,17203,14362],{},[1826,17205,1837],{},[898,17207,13166],{},[1655,17209,2346],{},[1820,17211,17212,17214],{},[898,17213,14362],{},[1826,17215,3472],{},[902,17217,17218],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,17221,14782],{}," přímka.",[123,17224,17225,17228,17229,17263],{},[38,17226,17227],{},"Simultánní rovnováha"," — průsečík ",[883,17230,17232],{"className":17231},[886],[888,17233,17234],{"xmlns":890},[892,17235,17236,17260],{},[895,17237,17238,17240,17242,17244,17250,17252,17258],{},[898,17239,5502],{},[1655,17241,1657],{},[1655,17243,1664],{"stretchy":1663},[2597,17245,17246,17248],{},[898,17247,13166],{},[898,17249,5502],{},[1655,17251,1671],{"separator":1670},[2597,17253,17254,17256],{},[898,17255,10375],{},[898,17257,5502],{},[1655,17259,1677],{"stretchy":1663},[902,17261,17262],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,17265,17266,17269,17270,1343,17283,17296],{},[38,17267,17268],{},"Fiskální politika"," — nástroje ",[883,17271,17273],{"className":17272},[886],[888,17274,17275],{"xmlns":890},[892,17276,17277,17281],{},[895,17278,17279],{},[898,17280,13237],{},[902,17282,13237],{"encoding":904},[883,17284,17286],{"className":17285},[886],[888,17287,17288],{"xmlns":890},[892,17289,17290,17294],{},[895,17291,17292],{},[898,17293,4049],{},[902,17295,4049],{"encoding":904}," posouvající křivku IS.",[123,17298,17299,17302,17303,17320],{},[38,17300,17301],{},"Monetární politika"," — nástroj ",[883,17304,17306],{"className":17305},[886],[888,17307,17308],{"xmlns":890},[892,17309,17310,17318],{},[895,17311,17312],{},[2597,17313,17314,17316],{},[898,17315,2127],{},[1655,17317,5603],{},[902,17319,13275],{"encoding":904}," posouvající křivku LM.",[115,17322,3187],{"id":3186},[120,17324,17325,17334,17343,17353],{},[123,17326,17327,3106,17330],{},[38,17328,17329],{},"Kurz:",[207,17331,17333],{"className":17332,"dataFsResolvedFilePath":3274,"href":3275},[210],"Matematická ekonomie",[123,17335,17336,3106,17339],{},[38,17337,17338],{},"Přednáška:",[207,17340,17342],{"className":17341,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,17344,17345,3106,17348,17352],{},[38,17346,17347],{},"Nadřazené téma:",[207,17349,17351],{"className":17350,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,17354,17355,17358],{},[38,17356,17357],{},"Související:",[120,17359,17360,17367,17373],{},[123,17361,17362,17366],{},[207,17363,17365],{"className":17364,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,17368,17369,17372],{},[207,17370,1145],{"className":17371,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,17374,17375,17379],{},[207,17376,17378],{"className":17377,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":17381},[17382,17383,17384,17385,17386,17387,17388,17389,17390,17391],{"id":13130,"depth":642,"text":13131},{"id":13285,"depth":642,"text":13286},{"id":13500,"depth":642,"text":13501},{"id":13793,"depth":642,"text":13794},{"id":14206,"depth":642,"text":14207},{"id":14999,"depth":642,"text":15000},{"id":15689,"depth":642,"text":15690},{"id":16595,"depth":642,"text":16596},{"id":16844,"depth":642,"text":16845},{"id":3186,"depth":642,"text":3187},{},"\u002Ftopics\u002Fis-lm",{"title":13122,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,17398,1143,17399,17400,17401,17402,17351],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":17405,"title":17406,"body":17407,"course":659,"courses":19000,"created":1129,"description":19001,"extension":661,"meta":19002,"navigation":664,"path":19003,"seo":19004,"sources":19005,"stem":19006,"tags":19007,"type":3252,"updated":677,"__hash__":19010},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":17408,"toc":18988},[17409,17412,17508,17515,17535,17539,17544,17607,17626,17628,17631,17767,17769,17979,18013,18150,18154,18218,18234,18262,18266,18364,18368,18372,18425,18531,18745,18749,18792,18898,18950,18952],[12,17410,17406],{"id":17411},"lagrangeova-metoda-vázané-extrémy",[724,17413,17414,17415,5163,17438,17470,17471,17474,17475,17502,17503,17507],{},"Hledáme extrém funkce ",[883,17416,17418],{"className":17417},[886],[888,17419,17420],{"xmlns":890},[892,17421,17422,17436],{},[895,17423,17424,17426,17428,17430,17432,17434],{},[898,17425,1660],{},[1655,17427,1664],{"stretchy":1663},[898,17429,1667],{},[1655,17431,1671],{"separator":1670},[898,17433,1674],{},[1655,17435,1677],{"stretchy":1663},[902,17437,1921],{"encoding":904},[883,17439,17441],{"className":17440},[886],[888,17442,17443],{"xmlns":890},[892,17444,17445,17467],{},[895,17446,17447,17449,17451,17457,17459,17465],{},[898,17448,900],{},[1655,17450,1664],{"stretchy":1663},[1820,17452,17453,17455],{},[898,17454,1824],{},[1826,17456,1828],{},[1655,17458,1671],{"separator":1670},[1820,17460,17461,17463],{},[898,17462,1824],{},[1826,17464,1837],{},[1655,17466,1677],{"stretchy":1663},[902,17468,17469],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,17472,17473],{},"podmíněný"," rovnicí ",[883,17476,17478],{"className":17477},[886],[888,17479,17480],{"xmlns":890},[892,17481,17482,17500],{},[895,17483,17484,17486,17488,17490,17492,17494,17496,17498],{},[898,17485,3162],{},[1655,17487,1664],{"stretchy":1663},[898,17489,1667],{},[1655,17491,1671],{"separator":1670},[898,17493,1674],{},[1655,17495,1677],{"stretchy":1663},[1655,17497,1657],{},[1826,17499,2552],{},[902,17501,3179],{"encoding":904},". V ",[207,17504,17506],{"className":17505,"dataFsResolvedFilePath":3274,"href":3275},[210],"matematické ekonomii"," se používá pro:",[724,17509,17510],{},[1723,17511],{"alt":17512,"className":17513,"src":17514},"imek-lagrange-tecnost",[210,1727],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,17516,17517,17526,17532],{},[123,17518,17519,17522,17523,1677],{},[38,17520,17521],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,17524,1851],{"className":17525,"dataFsResolvedFilePath":878,"href":879},[210],[123,17527,17528,17531],{},[38,17529,17530],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,17533,17534],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,17536,17538],{"id":17537},"princip","Princip",[724,17540,2820,17541,2086],{},[38,17542,17543],{},"Lagrangeovu funkci",[724,17545,17546],{},[883,17547,17549],{"className":17548},[886],[888,17550,17551],{"xmlns":890},[892,17552,17553,17604],{},[895,17554,17555,17557,17559,17561,17563,17565,17567,17570,17572,17574,17576,17578,17580,17582,17584,17586,17588,17590,17592,17594,17596,17598,17600,17602],{},[898,17556,1873],{},[1655,17558,1664],{"stretchy":1663},[898,17560,1667],{},[1655,17562,1671],{"separator":1670},[898,17564,1674],{},[1655,17566,1671],{"separator":1670},[898,17568,17569],{},"λ",[1655,17571,1677],{"stretchy":1663},[1655,17573,1657],{},[898,17575,1660],{},[1655,17577,1664],{"stretchy":1663},[898,17579,1667],{},[1655,17581,1671],{"separator":1670},[898,17583,1674],{},[1655,17585,1677],{"stretchy":1663},[1655,17587,2346],{},[898,17589,17569],{},[2031,17591,2435],{},[898,17593,3162],{},[1655,17595,1664],{"stretchy":1663},[898,17597,1667],{},[1655,17599,1671],{"separator":1670},[898,17601,1674],{},[1655,17603,1677],{"stretchy":1663},[902,17605,17606],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,17608,5559,17609,9349,17623,1719],{},[883,17610,17612],{"className":17611},[886],[888,17613,17614],{"xmlns":890},[892,17615,17616,17620],{},[895,17617,17618],{},[898,17619,17569],{},[902,17621,17622],{"encoding":904},"\\lambda",[38,17624,17625],{},"Lagrangeův multiplikátor",[115,17627,2716],{"id":2715},[724,17629,17630],{},"Řešíme soustavu:",[724,17632,17633,17681,17729],{},[883,17634,17636],{"className":17635},[886],[888,17637,17638],{"xmlns":890},[892,17639,17640,17678],{},[895,17641,17642,17650,17652,17660,17662,17664,17666,17674,17676],{},[1935,17643,17644,17646,17648],{},[898,17645,1873],{},[898,17647,1667],{},[1655,17649,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,17651,1657],{},[1935,17653,17654,17656,17658],{},[898,17655,1660],{},[898,17657,1667],{},[1655,17659,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,17661,2346],{},[898,17663,17569],{},[2031,17665,2435],{},[1935,17667,17668,17670,17672],{},[898,17669,3162],{},[898,17671,1667],{},[1655,17673,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,17675,1657],{},[1826,17677,2552],{},[902,17679,17680],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,17682,17684],{"className":17683},[886],[888,17685,17686],{"xmlns":890},[892,17687,17688,17726],{},[895,17689,17690,17698,17700,17708,17710,17712,17714,17722,17724],{},[1935,17691,17692,17694,17696],{},[898,17693,1873],{},[898,17695,1674],{},[1655,17697,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,17699,1657],{},[1935,17701,17702,17704,17706],{},[898,17703,1660],{},[898,17705,1674],{},[1655,17707,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,17709,2346],{},[898,17711,17569],{},[2031,17713,2435],{},[1935,17715,17716,17718,17720],{},[898,17717,3162],{},[898,17719,1674],{},[1655,17721,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,17723,1657],{},[1826,17725,2552],{},[902,17727,17728],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,17730,17732],{"className":17731},[886],[888,17733,17734],{"xmlns":890},[892,17735,17736,17764],{},[895,17737,17738,17746,17748,17750,17752,17754,17756,17758,17760,17762],{},[1935,17739,17740,17742,17744],{},[898,17741,1873],{},[898,17743,17569],{},[1655,17745,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,17747,1657],{},[898,17749,3162],{},[1655,17751,1664],{"stretchy":1663},[898,17753,1667],{},[1655,17755,1671],{"separator":1670},[898,17757,1674],{},[1655,17759,1677],{"stretchy":1663},[1655,17761,1657],{},[1826,17763,2552],{},[902,17765,17766],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,17768,2817],{"id":2816},[724,17770,17771],{},[883,17772,17774],{"className":17773},[886],[888,17775,17776],{"xmlns":890},[892,17777,17778,17976],{},[895,17779,17780,17782,17784,17786,17788,17790,17792,17794,17796,17798,17800,17816,17818,17820,17836,17838,17840,17848,17854,17856,17858,17874,17876,17878,17894,17896,17898,17906,17912,17914,17916,17918,17934,17936,17938,17954,17956,17958,17966,17968],{},[898,17781,2838],{},[1655,17783,1664],{"stretchy":1663},[898,17785,1667],{},[1655,17787,1671],{"separator":1670},[898,17789,1674],{},[1655,17791,1671],{"separator":1670},[898,17793,17569],{},[1655,17795,1677],{"stretchy":1663},[1655,17797,1657],{},[1655,17799,1664],{"stretchy":1663},[1935,17801,17802,17804,17810],{},[898,17803,1660],{},[895,17805,17806,17808],{},[898,17807,1667],{},[898,17809,1667],{},[895,17811,17812,17814],{},[1655,17813,1945],{"mathvariant":1943},[1655,17815,1945],{"mathvariant":1943},[1655,17817,2346],{},[898,17819,17569],{},[1935,17821,17822,17824,17830],{},[898,17823,3162],{},[895,17825,17826,17828],{},[898,17827,1667],{},[898,17829,1667],{},[895,17831,17832,17834],{},[1655,17833,1945],{"mathvariant":1943},[1655,17835,1945],{"mathvariant":1943},[1655,17837,1677],{"stretchy":1663},[1655,17839,1664],{"stretchy":1663},[1935,17841,17842,17844,17846],{},[898,17843,3162],{},[898,17845,1674],{},[1655,17847,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[2597,17849,17850,17852],{},[1655,17851,1677],{"stretchy":1663},[1826,17853,1837],{},[1655,17855,2346],{},[1655,17857,1664],{"stretchy":1663},[1935,17859,17860,17862,17868],{},[898,17861,1660],{},[895,17863,17864,17866],{},[898,17865,1674],{},[898,17867,1674],{},[895,17869,17870,17872],{},[1655,17871,1945],{"mathvariant":1943},[1655,17873,1945],{"mathvariant":1943},[1655,17875,2346],{},[898,17877,17569],{},[1935,17879,17880,17882,17888],{},[898,17881,3162],{},[895,17883,17884,17886],{},[898,17885,1674],{},[898,17887,1674],{},[895,17889,17890,17892],{},[1655,17891,1945],{"mathvariant":1943},[1655,17893,1945],{"mathvariant":1943},[1655,17895,1677],{"stretchy":1663},[1655,17897,1664],{"stretchy":1663},[1935,17899,17900,17902,17904],{},[898,17901,3162],{},[898,17903,1667],{},[1655,17905,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[2597,17907,17908,17910],{},[1655,17909,1677],{"stretchy":1663},[1826,17911,1837],{},[1655,17913,2623],{},[1826,17915,1837],{},[1655,17917,1664],{"stretchy":1663},[1935,17919,17920,17922,17928],{},[898,17921,1660],{},[895,17923,17924,17926],{},[898,17925,1667],{},[898,17927,1674],{},[895,17929,17930,17932],{},[1655,17931,1945],{"mathvariant":1943},[1655,17933,1945],{"mathvariant":1943},[1655,17935,2346],{},[898,17937,17569],{},[1935,17939,17940,17942,17948],{},[898,17941,3162],{},[895,17943,17944,17946],{},[898,17945,1667],{},[898,17947,1674],{},[895,17949,17950,17952],{},[1655,17951,1945],{"mathvariant":1943},[1655,17953,1945],{"mathvariant":1943},[1655,17955,1677],{"stretchy":1663},[2031,17957,2435],{},[1935,17959,17960,17962,17964],{},[898,17961,3162],{},[898,17963,1667],{},[1655,17965,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[2031,17967,2435],{},[1935,17969,17970,17972,17974],{},[898,17971,3162],{},[898,17973,1674],{},[1655,17975,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,17977,17978],{"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",[724,17980,17981,17982,18012],{},"Je-li ",[883,17983,17985],{"className":17984},[886],[888,17986,17987],{"xmlns":890},[892,17988,17989,18009],{},[895,17990,17991,17993,17995,17997,17999,18001,18007],{},[1655,17992,2734],{"stretchy":1663},[898,17994,207],{},[1655,17996,1671],{"separator":1670},[898,17998,2025],{},[1655,18000,1671],{"separator":1670},[1820,18002,18003,18005],{},[898,18004,17569],{},[1826,18006,2552],{},[1655,18008,2743],{"stretchy":1663},[902,18010,18011],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,18014,18015,18083],{},[123,18016,18017,3022,18053,18055,18056],{},[883,18018,18020],{"className":18019},[886],[888,18021,18022],{"xmlns":890},[892,18023,18024,18050],{},[895,18025,18026,18028,18030,18032,18034,18036,18038,18044,18046,18048],{},[898,18027,2838],{},[1655,18029,1664],{"stretchy":1663},[898,18031,207],{},[1655,18033,1671],{"separator":1670},[898,18035,2025],{},[1655,18037,1671],{"separator":1670},[1820,18039,18040,18042],{},[898,18041,17569],{},[1826,18043,2552],{},[1655,18045,1677],{"stretchy":1663},[1655,18047,3065],{},[1826,18049,2552],{},[902,18051,18052],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,18054,3073],{}," vázané podmínkou ",[883,18057,18059],{"className":18058},[886],[888,18060,18061],{"xmlns":890},[892,18062,18063,18081],{},[895,18064,18065,18067,18069,18071,18073,18075,18077,18079],{},[898,18066,3162],{},[1655,18068,1664],{"stretchy":1663},[898,18070,1667],{},[1655,18072,1671],{"separator":1670},[898,18074,1674],{},[1655,18076,1677],{"stretchy":1663},[1655,18078,1657],{},[1826,18080,2552],{},[902,18082,3179],{"encoding":904},[123,18084,18085,3022,18121,18055,18123],{},[883,18086,18088],{"className":18087},[886],[888,18089,18090],{"xmlns":890},[892,18091,18092,18118],{},[895,18093,18094,18096,18098,18100,18102,18104,18106,18112,18114,18116],{},[898,18095,2838],{},[1655,18097,1664],{"stretchy":1663},[898,18099,207],{},[1655,18101,1671],{"separator":1670},[898,18103,2025],{},[1655,18105,1671],{"separator":1670},[1820,18107,18108,18110],{},[898,18109,17569],{},[1826,18111,2552],{},[1655,18113,1677],{"stretchy":1663},[1655,18115,2969],{},[1826,18117,2552],{},[902,18119,18120],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,18122,3025],{},[883,18124,18126],{"className":18125},[886],[888,18127,18128],{"xmlns":890},[892,18129,18130,18148],{},[895,18131,18132,18134,18136,18138,18140,18142,18144,18146],{},[898,18133,3162],{},[1655,18135,1664],{"stretchy":1663},[898,18137,1667],{},[1655,18139,1671],{"separator":1670},[898,18141,1674],{},[1655,18143,1677],{"stretchy":1663},[1655,18145,1657],{},[1826,18147,2552],{},[902,18149,3179],{"encoding":904},[115,18151,18153],{"id":18152},"význam-multiplikátoru","Význam multiplikátoru",[724,18155,18156],{},[883,18157,18159],{"className":18158},[886],[888,18160,18161],{"xmlns":890},[892,18162,18163,18215],{},[895,18164,18165,18167,18169,18191,18193],{},[898,18166,17569],{},[1655,18168,1657],{},[1949,18170,18171,18179],{},[1935,18172,18173,18175,18177],{},[898,18174,1660],{},[898,18176,1667],{},[1655,18178,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[895,18180,18181,18183],{},[1655,18182,2623],{},[1935,18184,18185,18187,18189],{},[898,18186,3162],{},[898,18188,1667],{},[1655,18190,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,18192,1657],{},[1949,18194,18195,18203],{},[1935,18196,18197,18199,18201],{},[898,18198,1660],{},[898,18200,1674],{},[1655,18202,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[895,18204,18205,18207],{},[1655,18206,2623],{},[1935,18208,18209,18211,18213],{},[898,18210,3162],{},[898,18212,1674],{},[1655,18214,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,18216,18217],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,18219,18220,18233],{},[883,18221,18223],{"className":18222},[886],[888,18224,18225],{"xmlns":890},[892,18226,18227,18231],{},[895,18228,18229],{},[898,18230,17569],{},[902,18232,17622],{"encoding":904}," udává:",[120,18235,18236,18242],{},[123,18237,18238,18239],{},"konstantní ",[38,18240,18241],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,18243,18244,18247,18248,18261],{},[38,18245,18246],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,18249,18251],{"className":18250},[886],[888,18252,18253],{"xmlns":890},[892,18254,18255,18259],{},[895,18256,18257],{},[898,18258,1660],{},[902,18260,1660],{"encoding":904},", uvolní-li se omezení o jednotku",[115,18263,18265],{"id":18264},"alternativní-postup","Alternativní postup",[724,18267,18268,18269,18296,18297,18321,18322,18346,18347,18360,18361,1719],{},"Lze-li z ",[883,18270,18272],{"className":18271},[886],[888,18273,18274],{"xmlns":890},[892,18275,18276,18294],{},[895,18277,18278,18280,18282,18284,18286,18288,18290,18292],{},[898,18279,3162],{},[1655,18281,1664],{"stretchy":1663},[898,18283,1667],{},[1655,18285,1671],{"separator":1670},[898,18287,1674],{},[1655,18289,1677],{"stretchy":1663},[1655,18291,1657],{},[1826,18293,2552],{},[902,18295,3179],{"encoding":904}," vyjádřit ",[883,18298,18300],{"className":18299},[886],[888,18301,18302],{"xmlns":890},[892,18303,18304,18318],{},[895,18305,18306,18308,18310,18312,18314,18316],{},[898,18307,1674],{},[1655,18309,1657],{},[898,18311,1674],{},[1655,18313,1664],{"stretchy":1663},[898,18315,1667],{},[1655,18317,1677],{"stretchy":1663},[902,18319,18320],{"encoding":904},"y = y(x)"," (nebo ",[883,18323,18325],{"className":18324},[886],[888,18326,18327],{"xmlns":890},[892,18328,18329,18343],{},[895,18330,18331,18333,18335,18337,18339,18341],{},[898,18332,1667],{},[1655,18334,1657],{},[898,18336,1667],{},[1655,18338,1664],{"stretchy":1663},[898,18340,1674],{},[1655,18342,1677],{"stretchy":1663},[902,18344,18345],{"encoding":904},"x = x(y)","), dosadíme do ",[883,18348,18350],{"className":18349},[886],[888,18351,18352],{"xmlns":890},[892,18353,18354,18358],{},[895,18355,18356],{},[898,18357,1660],{},[902,18359,1660],{"encoding":904}," a převedeme na ",[38,18362,18363],{},"extrém funkce jedné proměnné",[115,18365,18367],{"id":18366},"použití-v-imek","Použití v ImeK",[198,18369,18371],{"id":18370},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,18373,18374,18375,1719],{},"Rozpočtové omezení: ",[883,18376,18378],{"className":18377},[886],[888,18379,18380],{"xmlns":890},[892,18381,18382,18422],{},[895,18383,18384,18390,18392,18400,18406,18408,18416],{},[2597,18385,18386,18388],{},[898,18387,10375],{},[1655,18389,5603],{},[1655,18391,1657],{},[1935,18393,18394,18396,18398],{},[898,18395,2132],{},[1826,18397,1828],{},[1655,18399,5603],{},[1820,18401,18402,18404],{},[898,18403,1824],{},[1826,18405,1828],{},[1655,18407,2346],{},[1935,18409,18410,18412,18414],{},[898,18411,2132],{},[1826,18413,1837],{},[1655,18415,5603],{},[1820,18417,18418,18420],{},[898,18419,1824],{},[1826,18421,1837],{},[902,18423,18424],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,18426,18427],{},[883,18428,18430],{"className":18429},[886],[888,18431,18432],{"xmlns":890},[892,18433,18434,18528],{},[895,18435,18436,18438,18440,18446,18448,18454,18456,18458,18460,18462,18464,18466,18472,18474,18480,18482,18484,18486,18488,18494,18496,18504,18510,18512,18520,18526],{},[898,18437,1873],{},[1655,18439,1664],{"stretchy":1663},[1820,18441,18442,18444],{},[898,18443,1824],{},[1826,18445,1828],{},[1655,18447,1671],{"separator":1670},[1820,18449,18450,18452],{},[898,18451,1824],{},[1826,18453,1837],{},[1655,18455,1671],{"separator":1670},[898,18457,17569],{},[1655,18459,1677],{"stretchy":1663},[1655,18461,1657],{},[898,18463,900],{},[1655,18465,1664],{"stretchy":1663},[1820,18467,18468,18470],{},[898,18469,1824],{},[1826,18471,1828],{},[1655,18473,1671],{"separator":1670},[1820,18475,18476,18478],{},[898,18477,1824],{},[1826,18479,1837],{},[1655,18481,1677],{"stretchy":1663},[1655,18483,2346],{},[898,18485,17569],{},[1655,18487,1664],{"stretchy":1663},[2597,18489,18490,18492],{},[898,18491,10375],{},[1655,18493,5603],{},[1655,18495,2623],{},[1935,18497,18498,18500,18502],{},[898,18499,2132],{},[1826,18501,1828],{},[1655,18503,5603],{},[1820,18505,18506,18508],{},[898,18507,1824],{},[1826,18509,1828],{},[1655,18511,2623],{},[1935,18513,18514,18516,18518],{},[898,18515,2132],{},[1826,18517,1837],{},[1655,18519,5603],{},[1820,18521,18522,18524],{},[898,18523,1824],{},[1826,18525,1837],{},[1655,18527,1677],{"stretchy":1663},[902,18529,18530],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,18532,18533,18534,1343,18566,1343,18598,18647,18648,18702,18703,1719],{},"Soustava: ",[883,18535,18537],{"className":18536},[886],[888,18538,18539],{"xmlns":890},[892,18540,18541,18563],{},[895,18542,18543,18551,18553,18555],{},[1935,18544,18545,18547,18549],{},[898,18546,900],{},[1826,18548,1828],{},[1655,18550,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,18552,1657],{},[898,18554,17569],{},[1935,18556,18557,18559,18561],{},[898,18558,2132],{},[1826,18560,1828],{},[1655,18562,5603],{},[902,18564,18565],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,18567,18569],{"className":18568},[886],[888,18570,18571],{"xmlns":890},[892,18572,18573,18595],{},[895,18574,18575,18583,18585,18587],{},[1935,18576,18577,18579,18581],{},[898,18578,900],{},[1826,18580,1837],{},[1655,18582,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,18584,1657],{},[898,18586,17569],{},[1935,18588,18589,18591,18593],{},[898,18590,2132],{},[1826,18592,1837],{},[1655,18594,5603],{},[902,18596,18597],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,18599,18601],{"className":18600},[886],[888,18602,18603],{"xmlns":890},[892,18604,18605,18645],{},[895,18606,18607,18613,18615,18623,18629,18631,18639],{},[2597,18608,18609,18611],{},[898,18610,10375],{},[1655,18612,5603],{},[1655,18614,1657],{},[1935,18616,18617,18619,18621],{},[898,18618,2132],{},[1826,18620,1828],{},[1655,18622,5603],{},[1820,18624,18625,18627],{},[898,18626,1824],{},[1826,18628,1828],{},[1655,18630,2346],{},[1935,18632,18633,18635,18637],{},[898,18634,2132],{},[1826,18636,1837],{},[1655,18638,5603],{},[1820,18640,18641,18643],{},[898,18642,1824],{},[1826,18644,1837],{},[902,18646,18424],{"encoding":904},". Z prvních dvou: ",[883,18649,18651],{"className":18650},[886],[888,18652,18653],{"xmlns":890},[892,18654,18655,18699],{},[895,18656,18657,18677,18679],{},[3615,18658,18659],{"scriptlevel":2552,"displaystyle":1663},[1949,18660,18661,18669],{},[1935,18662,18663,18665,18667],{},[898,18664,900],{},[1826,18666,1828],{},[1655,18668,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1935,18670,18671,18673,18675],{},[898,18672,900],{},[1826,18674,1837],{},[1655,18676,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,18678,1657],{},[3615,18680,18681],{"scriptlevel":2552,"displaystyle":1663},[1949,18682,18683,18691],{},[1935,18684,18685,18687,18689],{},[898,18686,2132],{},[1826,18688,1828],{},[1655,18690,5603],{},[1935,18692,18693,18695,18697],{},[898,18694,2132],{},[1826,18696,1837],{},[1655,18698,5603],{},[902,18700,18701],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,18704,18706],{"className":18705},[886],[888,18707,18708],{"xmlns":890},[892,18709,18710,18742],{},[895,18711,18712,18714,18716,18718,18720,18722],{},[898,18713,2127],{},[898,18715,5245],{},[898,18717,4052],{},[898,18719,9920],{},[1655,18721,1657],{},[3615,18723,18724],{"scriptlevel":2552,"displaystyle":1663},[1949,18725,18726,18734],{},[1935,18727,18728,18730,18732],{},[898,18729,2132],{},[1826,18731,1828],{},[1655,18733,5603],{},[1935,18735,18736,18738,18740],{},[898,18737,2132],{},[1826,18739,1837],{},[1655,18741,5603],{},[902,18743,18744],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,18746,18748],{"id":18747},"minimalizace-výdajů","Minimalizace výdajů",[724,18750,18751,18752,1719],{},"Podmínka dané užitečnosti ",[883,18753,18755],{"className":18754},[886],[888,18756,18757],{"xmlns":890},[892,18758,18759,18789],{},[895,18760,18761,18767,18769,18771,18773,18779,18781,18787],{},[2597,18762,18763,18765],{},[898,18764,900],{},[1655,18766,5603],{},[1655,18768,1657],{},[898,18770,900],{},[1655,18772,1664],{"stretchy":1663},[1820,18774,18775,18777],{},[898,18776,1824],{},[1826,18778,1828],{},[1655,18780,1671],{"separator":1670},[1820,18782,18783,18785],{},[898,18784,1824],{},[1826,18786,1837],{},[1655,18788,1677],{"stretchy":1663},[902,18790,18791],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,18793,18794],{},[883,18795,18797],{"className":18796},[886],[888,18798,18799],{"xmlns":890},[892,18800,18801,18895],{},[895,18802,18803,18805,18807,18813,18815,18821,18823,18825,18827,18829,18837,18843,18845,18853,18859,18861,18863,18865,18871,18873,18875,18877,18883,18885,18891,18893],{},[898,18804,1873],{},[1655,18806,1664],{"stretchy":1663},[1820,18808,18809,18811],{},[898,18810,1824],{},[1826,18812,1828],{},[1655,18814,1671],{"separator":1670},[1820,18816,18817,18819],{},[898,18818,1824],{},[1826,18820,1837],{},[1655,18822,1671],{"separator":1670},[898,18824,17569],{},[1655,18826,1677],{"stretchy":1663},[1655,18828,1657],{},[1935,18830,18831,18833,18835],{},[898,18832,2132],{},[1826,18834,1828],{},[1655,18836,5603],{},[1820,18838,18839,18841],{},[898,18840,1824],{},[1826,18842,1828],{},[1655,18844,2346],{},[1935,18846,18847,18849,18851],{},[898,18848,2132],{},[1826,18850,1837],{},[1655,18852,5603],{},[1820,18854,18855,18857],{},[898,18856,1824],{},[1826,18858,1837],{},[1655,18860,2346],{},[898,18862,17569],{},[1655,18864,1664],{"stretchy":1663},[2597,18866,18867,18869],{},[898,18868,900],{},[1655,18870,5603],{},[1655,18872,2623],{},[898,18874,900],{},[1655,18876,1664],{"stretchy":1663},[1820,18878,18879,18881],{},[898,18880,1824],{},[1826,18882,1828],{},[1655,18884,1671],{"separator":1670},[1820,18886,18887,18889],{},[898,18888,1824],{},[1826,18890,1837],{},[1655,18892,1677],{"stretchy":1663},[1655,18894,1677],{"stretchy":1663},[902,18896,18897],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,18899,18900,18901,1719],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,18902,18904],{"className":18903},[886],[888,18905,18906],{"xmlns":890},[892,18907,18908,18947],{},[895,18909,18910,18917,18919,18925,18927,18933,18935,18941,18943,18945],{},[1820,18911,18912,18914],{},[898,18913,1824],{},[898,18915,18916],{},"i",[1655,18918,1657],{},[1820,18920,18921,18923],{},[898,18922,2838],{},[898,18924,18916],{},[1655,18926,1664],{"stretchy":1663},[1820,18928,18929,18931],{},[898,18930,2132],{},[1826,18932,1828],{},[1655,18934,1671],{"separator":1670},[1820,18936,18937,18939],{},[898,18938,2132],{},[1826,18940,1837],{},[1655,18942,1671],{"separator":1670},[898,18944,900],{},[1655,18946,1677],{"stretchy":1663},[902,18948,18949],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,18951,3187],{"id":3186},[120,18953,18954,18961,18968,18977],{},[123,18955,18956,3106,18958],{},[38,18957,3194],{},[207,18959,784],{"className":18960,"dataFsResolvedFilePath":782,"href":783},[210],[123,18962,18963,3106,18965],{},[38,18964,3202],{},[207,18966,13065],{"className":18967,"dataFsResolvedFilePath":800,"href":801},[210],[123,18969,18970,3106,18973,18976],{},[38,18971,18972],{},"Aplikace v kurzu:",[207,18974,880],{"className":18975,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,18978,18979,3106,18981,1343,18984,18987],{},[38,18980,3210],{},[207,18982,936],{"className":18983,"dataFsResolvedFilePath":934,"href":935},[210],[207,18985,1400],{"className":18986,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":18989},[18990,18991,18992,18993,18994,18995,18999],{"id":17537,"depth":642,"text":17538},{"id":2715,"depth":642,"text":2716},{"id":2816,"depth":642,"text":2817},{"id":18152,"depth":642,"text":18153},{"id":18264,"depth":642,"text":18265},{"id":18366,"depth":642,"text":18367,"children":18996},[18997,18998],{"id":18370,"depth":649,"text":18371},{"id":18747,"depth":649,"text":18748},{"id":3186,"depth":642,"text":3187},[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":17406,"description":19001},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,19008,19009],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":19012,"title":936,"body":19013,"course":1128,"courses":659,"created":10802,"description":641,"extension":661,"meta":28881,"navigation":664,"path":28882,"seo":28883,"sources":28884,"stem":28885,"tags":28886,"type":3252,"updated":677,"__hash__":28890},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":19014,"toc":28843},[19015,19018,19020,19143,19278,19282,19285,19398,19402,19430,19477,19480,19546,19591,19594,19620,19651,19655,19659,19703,19747,19809,19864,19867,19871,19874,19921,20018,20124,20130,20207,20236,20375,20379,20408,20458,20605,20695,20699,20725,20763,20790,20828,20890,20965,21043,21101,21167,21211,21215,21273,21322,21367,21580,21700,21706,21710,21733,21737,21744,21748,21779,21814,21818,21868,21956,21998,22019,22081,22141,22145,22216,22284,22356,22471,22519,22523,22526,22567,22606,22629,22743,22907,22915,22942,22972,22975,23052,23205,23289,23628,23632,23756,23892,24028,24081,24084,24334,24415,24419,24422,24480,24512,24515,24564,24567,24638,24834,24838,24989,25219,25257,25310,25356,25359,25415,25464,25668,25758,25762,25778,25785,25954,25958,26029,26110,26191,26270,26416,26504,26508,26691,26822,26867,26964,26968,27707,27709,28760,28762],[12,19016,936],{"id":19017},"národní-důchod",[115,19019,13131],{"id":13130},[724,19021,19022,19023,3106,19027,19030,19031,3106,19034,19047,19048,19051,19052,19055,19056,19059,19060,19062,19063,3106,19065,19082,19083,19100,19101,19104,19105,5171],{},"Kapitola 7 ",[207,19024,19026],{"className":19025,"dataFsResolvedFilePath":3274,"href":3275},[210],"Matematické ekonomie",[38,19028,19029],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,19032,19033],{},"národním důchodem",[883,19035,19037],{"className":19036},[886],[888,19038,19039],{"xmlns":890},[892,19040,19041,19045],{},[895,19042,19043],{},[898,19044,10375],{},[902,19046,10375],{"encoding":904},". Budují se postupně bohatší modely — ",[38,19049,19050],{},"C-I"," (jen spotřeba a investice) → ",[38,19053,19054],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,19057,19058],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,19061,13136],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,19064,15010],{},[883,19066,19068],{"className":19067},[886],[888,19069,19070],{"xmlns":890},[892,19071,19072,19080],{},[895,19073,19074],{},[2597,19075,19076,19078],{},[898,19077,10375],{},[898,19079,5502],{},[902,19081,15028],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,19084,19086],{"className":19085},[886],[888,19087,19088],{"xmlns":890},[892,19089,19090,19098],{},[895,19091,19092],{},[2597,19093,19094,19096],{},[898,19095,10375],{},[898,19097,5502],{},[902,19099,15028],{"encoding":904}," na exogenní veličiny popisují ",[38,19102,19103],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,19106,19108],{"className":19107},[886],[888,19109,19110],{"xmlns":890},[892,19111,19112,19140],{},[895,19113,19114,19116,19118,19120,19122,19124,19126,19128,19130,19132,19134,19136,19138],{},[1826,19115,1828],{},[898,19117,5923],{"mathvariant":1943},[1655,19119,1664],{"stretchy":1663},[1826,19121,1828],{},[1655,19123,2623],{},[898,19125,207],{},[1655,19127,1677],{"stretchy":1663},[1655,19129,1657],{},[1826,19131,1828],{},[898,19133,5923],{"mathvariant":1943},[898,19135,2127],{},[898,19137,2132],{},[898,19139,9920],{},[902,19141,19142],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[5120,19144,19145],{},[724,19146,19147,19149,19150,19153,19154,19172,19173,19203,19204,19251,19252,19254,19255,19277],{},[883,19148,5406],{}," Intuice\n",[38,19151,19152],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,19155,19157],{"className":19156},[886],[888,19158,19159],{"xmlns":890},[892,19160,19161,19169],{},[895,19162,19163,19165,19167],{},[898,19164,2127],{},[898,19166,2132],{},[898,19168,4052],{},[902,19170,19171],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,19174,19176],{"className":19175},[886],[888,19177,19178],{"xmlns":890},[892,19179,19180,19200],{},[895,19181,19182,19184,19186,19188,19190,19192,19194,19196,19198],{},[898,19183,2127],{},[898,19185,2132],{},[898,19187,9920],{},[1655,19189,1657],{},[1826,19191,1828],{},[1655,19193,2623],{},[898,19195,2127],{},[898,19197,2132],{},[898,19199,4052],{},[902,19201,19202],{"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 ",[883,19205,19207],{"className":19206},[886],[888,19208,19209],{"xmlns":890},[892,19210,19211,19248],{},[895,19212,19213,19215,19217,19219,19221,19227,19229,19232,19234,19236,19238,19240,19242,19244,19246],{},[1826,19214,1828],{},[1655,19216,2346],{},[898,19218,207],{},[1655,19220,2346],{},[2597,19222,19223,19225],{},[898,19224,207],{},[1826,19226,1837],{},[1655,19228,2346],{},[1655,19230,19231],{},"⋯",[1655,19233,1657],{},[1826,19235,1828],{},[898,19237,5923],{"mathvariant":1943},[1655,19239,1664],{"stretchy":1663},[1826,19241,1828],{},[1655,19243,2623],{},[898,19245,207],{},[1655,19247,1677],{"stretchy":1663},[902,19249,19250],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,19253,13136],{}," 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 ",[883,19256,19258],{"className":19257},[886],[888,19259,19260],{"xmlns":890},[892,19261,19262,19274],{},[895,19263,19264,19266,19268,19270,19272],{},[1655,19265,1664],{"stretchy":1663},[898,19267,10375],{},[1655,19269,1671],{"separator":1670},[898,19271,13166],{},[1655,19273,1677],{"stretchy":1663},[902,19275,19276],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,19279,19281],{"id":19280},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,19283,19284],{},"Po prostudování kapitoly by čtenář měl umět:",[120,19286,19287,19290,19293,19296,19299,19302,19305,19395],{},[123,19288,19289],{},"popsat zjednodušený model národní ekonomiky,",[123,19291,19292],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,19294,19295],{},"popsat lineární model spotřeby a úspor,",[123,19297,19298],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,19300,19301],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,19303,19304],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,19306,19307,19308,1343,19325,1343,19347,2704,19372,19394],{},"popsat modely ",[883,19309,19311],{"className":19310},[886],[888,19312,19313],{"xmlns":890},[892,19314,19315,19323],{},[895,19316,19317,19319,19321],{},[898,19318,4052],{},[2031,19320,13415],{},[898,19322,13309],{},[902,19324,13420],{"encoding":904},[883,19326,19328],{"className":19327},[886],[888,19329,19330],{"xmlns":890},[892,19331,19332,19344],{},[895,19333,19334,19336,19338,19340,19342],{},[898,19335,4052],{},[2031,19337,13415],{},[898,19339,13309],{},[2031,19341,13415],{},[898,19343,13237],{},[902,19345,19346],{"encoding":904},"C\\text{-}I\\text{-}G",[883,19348,19350],{"className":19349},[886],[888,19351,19352],{"xmlns":890},[892,19353,19354,19370],{},[895,19355,19356,19358,19360,19362,19364,19366,19368],{},[898,19357,4052],{},[2031,19359,13415],{},[898,19361,13309],{},[2031,19363,13415],{},[898,19365,13237],{},[2031,19367,13415],{},[898,19369,13445],{},[902,19371,13448],{"encoding":904},[883,19373,19375],{"className":19374},[886],[888,19376,19377],{"xmlns":890},[892,19378,19379,19391],{},[895,19380,19381,19383,19385,19387,19389],{},[898,19382,13309],{},[898,19384,9920],{},[2031,19386,13415],{},[898,19388,1873],{},[898,19390,2127],{},[902,19392,19393],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,19396,19397],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,19399,19401],{"id":19400},"gnp-a-národní-důchod","GNP a národní důchod",[724,19403,19404,3106,19407,2115,19426,19429],{},[38,19405,19406],{},"Hrubý národní produkt",[883,19408,19410],{"className":19409},[886],[888,19411,19412],{"xmlns":890},[892,19413,19414,19423],{},[895,19415,19416,19418,19421],{},[898,19417,13237],{},[898,19419,19420],{},"N",[898,19422,2132],{},[902,19424,19425],{"encoding":904},"GNP",[614,19427,19428],{},"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:",[724,19431,19432],{},[883,19433,19435],{"className":19434},[886],[888,19436,19437],{"xmlns":890},[892,19438,19439,19474],{},[895,19440,19441,19443,19445,19447,19449,19451,19453,19455,19457,19459,19461,19463,19465,19467,19469,19472],{},[898,19442,13237],{},[898,19444,19420],{},[898,19446,2132],{},[1655,19448,1657],{},[898,19450,4052],{},[1655,19452,2346],{},[898,19454,13309],{},[1655,19456,2346],{},[898,19458,13237],{},[1655,19460,2346],{},[898,19462,13445],{},[1655,19464,1671],{"separator":1670},[1967,19466],{"width":1969},[1655,19468,1664],{"stretchy":1663},[1826,19470,19471],{},"7.1",[1655,19473,1677],{"stretchy":1663},[902,19475,19476],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,19478,19479],{},"kde",[120,19481,19482,19498,19514,19530],{},[123,19483,19484,19497],{},[883,19485,19487],{"className":19486},[886],[888,19488,19489],{"xmlns":890},[892,19490,19491,19495],{},[895,19492,19493],{},[898,19494,4052],{},[902,19496,4052],{"encoding":904}," — výdaje domácností na spotřebu,",[123,19499,19500,19513],{},[883,19501,19503],{"className":19502},[886],[888,19504,19505],{"xmlns":890},[892,19506,19507,19511],{},[895,19508,19509],{},[898,19510,13309],{},[902,19512,13309],{"encoding":904}," — hrubé domácí investice,",[123,19515,19516,19529],{},[883,19517,19519],{"className":19518},[886],[888,19520,19521],{"xmlns":890},[892,19522,19523,19527],{},[895,19524,19525],{},[898,19526,13237],{},[902,19528,13237],{"encoding":904}," — vládní výdaje,",[123,19531,19532,19545],{},[883,19533,19535],{"className":19534},[886],[888,19536,19537],{"xmlns":890},[892,19538,19539,19543],{},[895,19540,19541],{},[898,19542,13445],{},[902,19544,13445],{"encoding":904}," — čistý export.",[724,19547,19548,19549,19566,19567,19570,19571,3106,19574,2115,19587,19590],{},"K měření ",[883,19550,19552],{"className":19551},[886],[888,19553,19554],{"xmlns":890},[892,19555,19556,19564],{},[895,19557,19558,19560,19562],{},[898,19559,13237],{},[898,19561,19420],{},[898,19563,2132],{},[902,19565,19425],{"encoding":904}," se užívá ",[38,19568,19569],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,19572,19573],{},"národní důchod",[883,19575,19577],{"className":19576},[886],[888,19578,19579],{"xmlns":890},[892,19580,19581,19585],{},[895,19582,19583],{},[898,19584,10375],{},[902,19586,10375],{"encoding":904},[614,19588,19589],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,19592,19593],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,19595,19596],{},[883,19597,19599],{"className":19598},[886],[888,19600,19601],{"xmlns":890},[892,19602,19603,19617],{},[895,19604,19605,19607,19609,19611,19613,19615],{},[898,19606,13237],{},[898,19608,19420],{},[898,19610,2132],{},[1655,19612,2357],{},[898,19614,10375],{},[1655,19616,1671],{"separator":1670},[902,19618,19619],{"encoding":904},"GNP \\approx Y,",[724,19621,19622,19623,2115,19626,19629,19630,19643,19644,19647,19648,1719],{},"a užívá se společného názvu ",[38,19624,19625],{},"důchod",[614,19627,19628],{},"income",") s označením ",[883,19631,19633],{"className":19632},[886],[888,19634,19635],{"xmlns":890},[892,19636,19637,19641],{},[895,19638,19639],{},[898,19640,10375],{},[902,19642,10375],{"encoding":904},". Domácnosti důchod použijí ke ",[38,19645,19646],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,19649,19650],{},"úspor",[115,19652,19654],{"id":19653},"spotřeba-a-úspory","Spotřeba a úspory",[198,19656,19658],{"id":19657},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,19660,19661,19662,19675,19676,19689,19690,2086],{},"Jak spotřeba ",[883,19663,19665],{"className":19664},[886],[888,19666,19667],{"xmlns":890},[892,19668,19669,19673],{},[895,19670,19671],{},[898,19672,4052],{},[902,19674,4052],{"encoding":904},", tak úspory ",[883,19677,19679],{"className":19678},[886],[888,19680,19681],{"xmlns":890},[892,19682,19683,19687],{},[895,19684,19685],{},[898,19686,9920],{},[902,19688,9920],{"encoding":904}," závisejí na důchodu ",[883,19691,19693],{"className":19692},[886],[888,19694,19695],{"xmlns":890},[892,19696,19697,19701],{},[895,19698,19699],{},[898,19700,10375],{},[902,19702,10375],{"encoding":904},[724,19704,19705],{},[883,19706,19708],{"className":19707},[886],[888,19709,19710],{"xmlns":890},[892,19711,19712,19744],{},[895,19713,19714,19716,19718,19720,19722,19724,19726,19728,19730,19732,19734,19736,19738,19740,19742],{},[898,19715,4052],{},[1655,19717,1657],{},[898,19719,4052],{},[1655,19721,1664],{"stretchy":1663},[898,19723,10375],{},[1655,19725,1677],{"stretchy":1663},[1655,19727,1671],{"separator":1670},[1967,19729],{"width":1969},[898,19731,9920],{},[1655,19733,1657],{},[898,19735,9920],{},[1655,19737,1664],{"stretchy":1663},[898,19739,10375],{},[1655,19741,1677],{"stretchy":1663},[898,19743,1719],{"mathvariant":1943},[902,19745,19746],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,19748,19749,9349,19768,2115,19771,19774,19775,9349,19795,2115,19798,19801,19802,2704,19805,19808],{},[883,19750,19752],{"className":19751},[886],[888,19753,19754],{"xmlns":890},[892,19755,19756,19766],{},[895,19757,19758,19760,19762,19764],{},[898,19759,4052],{},[1655,19761,1664],{"stretchy":1663},[898,19763,10375],{},[1655,19765,1677],{"stretchy":1663},[902,19767,15341],{"encoding":904},[38,19769,19770],{},"funkce spotřeby",[614,19772,19773],{},"consumption function","), ",[883,19776,19778],{"className":19777},[886],[888,19779,19780],{"xmlns":890},[892,19781,19782,19792],{},[895,19783,19784,19786,19788,19790],{},[898,19785,9920],{},[1655,19787,1664],{"stretchy":1663},[898,19789,10375],{},[1655,19791,1677],{"stretchy":1663},[902,19793,19794],{"encoding":904},"S(Y)",[38,19796,19797],{},"funkce úspor",[614,19799,19800],{},"savings function","); jejich grafy se nazývají ",[38,19803,19804],{},"křivka spotřeby",[38,19806,19807],{},"křivka úspor",". Platí základní identita",[724,19810,19811],{},[883,19812,19814],{"className":19813},[886],[888,19815,19816],{"xmlns":890},[892,19817,19818,19861],{},[895,19819,19820,19822,19824,19826,19828,19830,19832,19834,19836,19838,19840,19842,19844,19846,19848,19850,19852,19854,19856,19859],{},[898,19821,10375],{},[1655,19823,1657],{},[898,19825,4052],{},[1655,19827,2346],{},[898,19829,9920],{},[1655,19831,1657],{},[898,19833,4052],{},[1655,19835,1664],{"stretchy":1663},[898,19837,10375],{},[1655,19839,1677],{"stretchy":1663},[1655,19841,2346],{},[898,19843,9920],{},[1655,19845,1664],{"stretchy":1663},[898,19847,10375],{},[1655,19849,1677],{"stretchy":1663},[898,19851,1719],{"mathvariant":1943},[1967,19853],{"width":1969},[1655,19855,1664],{"stretchy":1663},[1826,19857,19858],{},"7.2",[1655,19860,1677],{"stretchy":1663},[902,19862,19863],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,19865,19866],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,19868,19870],{"id":19869},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,19872,19873],{},"Nejjednodušší model předpokládá lineární tvar",[724,19875,19876],{},[883,19877,19879],{"className":19878},[886],[888,19880,19881],{"xmlns":890},[892,19882,19883,19918],{},[895,19884,19885,19887,19889,19891,19893,19895,19897,19899,19901,19903,19905,19907,19909,19911,19913,19916],{},[898,19886,4052],{},[1655,19888,1657],{},[898,19890,4052],{},[1655,19892,1664],{"stretchy":1663},[898,19894,10375],{},[1655,19896,1677],{"stretchy":1663},[1655,19898,1657],{},[898,19900,207],{},[898,19902,10375],{},[1655,19904,2346],{},[898,19906,2025],{},[1655,19908,1671],{"separator":1670},[1967,19910],{"width":1969},[1655,19912,1664],{"stretchy":1663},[1826,19914,19915],{},"7.3",[1655,19917,1677],{"stretchy":1663},[902,19919,19920],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,19922,5559,19923,2704,19941,19963,19964,20004,20005,1719],{},[883,19924,19926],{"className":19925},[886],[888,19927,19928],{"xmlns":890},[892,19929,19930,19938],{},[895,19931,19932,19934,19936],{},[898,19933,2025],{},[1655,19935,2969],{},[1826,19937,2552],{},[902,19939,19940],{"encoding":904},"b > 0",[883,19942,19944],{"className":19943},[886],[888,19945,19946],{"xmlns":890},[892,19947,19948,19960],{},[895,19949,19950,19952,19954,19956,19958],{},[1826,19951,2552],{},[1655,19953,3065],{},[898,19955,207],{},[1655,19957,3065],{},[1826,19959,1828],{},[902,19961,19962],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,19965,19967],{"className":19966},[886],[888,19968,19969],{"xmlns":890},[892,19970,19971,20001],{},[895,19972,19973,19975,19977,19984,19986,19989,19991,19993,19995,19997,19999],{},[898,19974,207],{},[1655,19976,1657],{},[895,19978,19979,19982],{},[898,19980,19981],{"mathvariant":1943},"t",[898,19983,3162],{"mathvariant":1943},[2031,19985,2435],{},[898,19987,19988],{},"α",[1655,19990,1657],{},[898,19992,2506],{"mathvariant":1943},[898,19994,4052],{},[898,19996,5923],{"mathvariant":1943},[898,19998,2506],{"mathvariant":1943},[898,20000,10375],{},[902,20002,20003],{"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 ",[883,20006,20008],{"className":20007},[886],[888,20009,20010],{"xmlns":890},[892,20011,20012,20016],{},[895,20013,20014],{},[898,20015,10375],{},[902,20017,10375],{"encoding":904},[724,20019,20020],{},[614,20021,20022,20023,20047,20048,20086,20087,20103,20104,1719],{},"Obrázek 7.1 — Přímka spotřeby ",[883,20024,20026],{"className":20025},[886],[888,20027,20028],{"xmlns":890},[892,20029,20030,20044],{},[895,20031,20032,20034,20036,20038,20040,20042],{},[898,20033,4052],{},[1655,20035,1657],{},[898,20037,207],{},[898,20039,10375],{},[1655,20041,2346],{},[898,20043,2025],{},[902,20045,20046],{"encoding":904},"C = aY + b"," se směrnicí ",[883,20049,20051],{"className":20050},[886],[888,20052,20053],{"xmlns":890},[892,20054,20055,20083],{},[895,20056,20057,20059,20061,20067,20069,20071,20073,20075,20077,20079,20081],{},[898,20058,207],{},[1655,20060,1657],{},[895,20062,20063,20065],{},[898,20064,19981],{"mathvariant":1943},[898,20066,3162],{"mathvariant":1943},[2031,20068,2435],{},[898,20070,19988],{},[1655,20072,1657],{},[898,20074,2506],{"mathvariant":1943},[898,20076,4052],{},[898,20078,5923],{"mathvariant":1943},[898,20080,2506],{"mathvariant":1943},[898,20082,10375],{},[902,20084,20085],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,20088,20090],{"className":20089},[886],[888,20091,20092],{"xmlns":890},[892,20093,20094,20100],{},[895,20095,20096,20098],{},[898,20097,2506],{"mathvariant":1943},[898,20099,4052],{},[902,20101,20102],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,20105,20107],{"className":20106},[886],[888,20108,20109],{"xmlns":890},[892,20110,20111,20121],{},[895,20112,20113,20115,20117,20119],{},[898,20114,2506],{"mathvariant":1943},[898,20116,10375],{},[1655,20118,1657],{},[1826,20120,1828],{},[902,20122,20123],{"encoding":904},"\\Delta Y = 1",[724,20125,20126,20127,2086],{},"Dosazením do (7.2) plyne ",[38,20128,20129],{},"lineární model úspor",[724,20131,20132],{},[883,20133,20135],{"className":20134},[886],[888,20136,20137],{"xmlns":890},[892,20138,20139,20204],{},[895,20140,20141,20143,20145,20147,20149,20151,20153,20155,20157,20159,20161,20163,20165,20167,20169,20171,20173,20175,20177,20179,20181,20183,20185,20187,20189,20191,20193,20195,20197,20199,20202],{},[898,20142,9920],{},[1655,20144,1657],{},[898,20146,10375],{},[1655,20148,2623],{},[898,20150,4052],{},[1655,20152,1664],{"stretchy":1663},[898,20154,10375],{},[1655,20156,1677],{"stretchy":1663},[1655,20158,1657],{},[898,20160,10375],{},[1655,20162,2623],{},[1655,20164,1664],{"stretchy":1663},[898,20166,207],{},[898,20168,10375],{},[1655,20170,2346],{},[898,20172,2025],{},[1655,20174,1677],{"stretchy":1663},[1655,20176,1657],{},[1655,20178,1664],{"stretchy":1663},[1826,20180,1828],{},[1655,20182,2623],{},[898,20184,207],{},[1655,20186,1677],{"stretchy":1663},[898,20188,10375],{},[1655,20190,2623],{},[898,20192,2025],{},[898,20194,1719],{"mathvariant":1943},[1967,20196],{"width":1969},[1655,20198,1664],{"stretchy":1663},[1826,20200,20201],{},"7.4",[1655,20203,1677],{"stretchy":1663},[902,20205,20206],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,20208,20209,20210,5171],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,20211,20213],{"className":20212},[886],[888,20214,20215],{"xmlns":890},[892,20216,20217,20233],{},[895,20218,20219,20221,20223,20225,20227,20229,20231],{},[1826,20220,2552],{},[1655,20222,3065],{},[1826,20224,1828],{},[1655,20226,2623],{},[898,20228,207],{},[1655,20230,3065],{},[1826,20232,1828],{},[902,20234,20235],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,20237,20238],{},[614,20239,20240,20241,2704,20264,20296,20297,3902,20310,20340,20341,3902,20359,1719],{},"Obrázek 7.2 — Přímky ",[883,20242,20244],{"className":20243},[886],[888,20245,20246],{"xmlns":890},[892,20247,20248,20262],{},[895,20249,20250,20252,20254,20256,20258,20260],{},[898,20251,4052],{},[1655,20253,1657],{},[898,20255,207],{},[898,20257,10375],{},[1655,20259,2346],{},[898,20261,2025],{},[902,20263,20046],{"encoding":904},[883,20265,20267],{"className":20266},[886],[888,20268,20269],{"xmlns":890},[892,20270,20271,20293],{},[895,20272,20273,20275,20277,20279,20281,20283,20285,20287,20289,20291],{},[898,20274,9920],{},[1655,20276,1657],{},[1655,20278,1664],{"stretchy":1663},[1826,20280,1828],{},[1655,20282,2623],{},[898,20284,207],{},[1655,20286,1677],{"stretchy":1663},[898,20288,10375],{},[1655,20290,2623],{},[898,20292,2025],{},[902,20294,20295],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,20298,20300],{"className":20299},[886],[888,20301,20302],{"xmlns":890},[892,20303,20304,20308],{},[895,20305,20306],{},[898,20307,10375],{},[902,20309,10375],{"encoding":904},[883,20311,20313],{"className":20312},[886],[888,20314,20315],{"xmlns":890},[892,20316,20317,20337],{},[895,20318,20319,20321,20323,20325,20327,20329,20331,20333,20335],{},[898,20320,10375],{},[1655,20322,1657],{},[898,20324,2025],{},[898,20326,5923],{"mathvariant":1943},[1655,20328,1664],{"stretchy":1663},[1826,20330,1828],{},[1655,20332,2623],{},[898,20334,207],{},[1655,20336,1677],{"stretchy":1663},[902,20338,20339],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,20342,20344],{"className":20343},[886],[888,20345,20346],{"xmlns":890},[892,20347,20348,20356],{},[895,20349,20350,20352,20354],{},[898,20351,4052],{},[1655,20353,1671],{"separator":1670},[898,20355,9920],{},[902,20357,20358],{"encoding":904},"C, S",[883,20360,20362],{"className":20361},[886],[888,20363,20364],{"xmlns":890},[892,20365,20366,20372],{},[895,20367,20368,20370],{},[1655,20369,2623],{},[898,20371,2025],{},[902,20373,20374],{"encoding":904},"-b",[198,20376,20378],{"id":20377},"příklad-71","Příklad 7.1",[724,20380,20381,20382,20407],{},"Pro spotřebu ",[883,20383,20385],{"className":20384},[886],[888,20386,20387],{"xmlns":890},[892,20388,20389,20404],{},[895,20390,20391,20393,20395,20398,20400,20402],{},[898,20392,4052],{},[1655,20394,1657],{},[1826,20396,20397],{},"0,4",[898,20399,10375],{},[1655,20401,2346],{},[1826,20403,4136],{},[902,20405,20406],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,20409,20410],{},[883,20411,20413],{"className":20412},[886],[888,20414,20415],{"xmlns":890},[892,20416,20417,20455],{},[895,20418,20419,20421,20423,20425,20427,20429,20431,20433,20435,20437,20439,20441,20443,20445,20448,20450,20452],{},[898,20420,9920],{},[1655,20422,1657],{},[898,20424,10375],{},[1655,20426,2623],{},[898,20428,4052],{},[1655,20430,1657],{},[898,20432,10375],{},[1655,20434,2623],{},[1826,20436,20397],{},[898,20438,10375],{},[1655,20440,2623],{},[1826,20442,4136],{},[1655,20444,1657],{},[1826,20446,20447],{},"0,6",[898,20449,10375],{},[1655,20451,2623],{},[1826,20453,20454],{},"10.",[902,20456,20457],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,20459,20460],{},[614,20461,20462,20463,2704,20486,20510,20511,9349,20524,20548,20549,9349,20566,20582,20583,1719],{},"Obrázek 7.3 — Přímky ",[883,20464,20466],{"className":20465},[886],[888,20467,20468],{"xmlns":890},[892,20469,20470,20484],{},[895,20471,20472,20474,20476,20478,20480,20482],{},[898,20473,4052],{},[1655,20475,1657],{},[1826,20477,20397],{},[898,20479,10375],{},[1655,20481,2346],{},[1826,20483,4136],{},[902,20485,20406],{"encoding":904},[883,20487,20489],{"className":20488},[886],[888,20490,20491],{"xmlns":890},[892,20492,20493,20507],{},[895,20494,20495,20497,20499,20501,20503,20505],{},[898,20496,9920],{},[1655,20498,1657],{},[1826,20500,20447],{},[898,20502,10375],{},[1655,20504,2623],{},[1826,20506,4136],{},[902,20508,20509],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,20512,20514],{"className":20513},[886],[888,20515,20516],{"xmlns":890},[892,20517,20518,20522],{},[895,20519,20520],{},[898,20521,10375],{},[902,20523,10375],{"encoding":904},[883,20525,20527],{"className":20526},[886],[888,20528,20529],{"xmlns":890},[892,20530,20531,20545],{},[895,20532,20533,20535,20538],{},[1655,20534,2357],{},[1826,20536,20537],{},"16,",[9633,20539,20540,20542],{"accent":1670},[1826,20541,3531],{},[1655,20543,20544],{},"ˉ",[902,20546,20547],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,20550,20552],{"className":20551},[886],[888,20553,20554],{"xmlns":890},[892,20555,20556,20564],{},[895,20557,20558,20560,20562],{},[898,20559,4052],{},[1655,20561,1671],{"separator":1670},[898,20563,9920],{},[902,20565,20358],{"encoding":904},[883,20567,20569],{"className":20568},[886],[888,20570,20571],{"xmlns":890},[892,20572,20573,20579],{},[895,20574,20575,20577],{},[1655,20576,2623],{},[1826,20578,4136],{},[902,20580,20581],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,20584,20586],{"className":20585},[886],[888,20587,20588],{"xmlns":890},[892,20589,20590,20602],{},[895,20591,20592,20594,20596,20598,20600],{},[1655,20593,1664],{"stretchy":1663},[1826,20595,2552],{},[1655,20597,1671],{"separator":1670},[1826,20599,4136],{},[1655,20601,1677],{"stretchy":1663},[902,20603,20604],{"encoding":904},"(0, 10)",[724,20606,20607,20608,9349,20626,20656,20657,2115,20660,20663,20664,9349,20688,2115,20691,20694],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,20609,20611],{"className":20610},[886],[888,20612,20613],{"xmlns":890},[892,20614,20615,20623],{},[895,20616,20617,20619,20621],{},[898,20618,10375],{},[1655,20620,1657],{},[1826,20622,2552],{},[902,20624,20625],{"encoding":904},"Y = 0",[883,20627,20629],{"className":20628},[886],[888,20630,20631],{"xmlns":890},[892,20632,20633,20653],{},[895,20634,20635,20637,20639,20641,20643,20645,20647,20649,20651],{},[898,20636,9920],{},[1655,20638,1664],{"stretchy":1663},[1826,20640,2552],{},[1655,20642,1677],{"stretchy":1663},[1655,20644,1657],{},[1655,20646,2623],{},[898,20648,2025],{},[1655,20650,3065],{},[1826,20652,2552],{},[902,20654,20655],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,20658,20659],{},"autonomních úsporách",[614,20661,20662],{},"autonomous savings","). Analogicky ",[883,20665,20667],{"className":20666},[886],[888,20668,20669],{"xmlns":890},[892,20670,20671,20685],{},[895,20672,20673,20675,20677,20679,20681,20683],{},[898,20674,4052],{},[1655,20676,1664],{"stretchy":1663},[1826,20678,2552],{},[1655,20680,1677],{"stretchy":1663},[1655,20682,1657],{},[898,20684,2025],{},[902,20686,20687],{"encoding":904},"C(0) = b",[38,20689,20690],{},"autonomní spotřeba",[614,20692,20693],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,20696,20698],{"id":20697},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,20700,20701,3106,20704,2115,20721,20724],{},[38,20702,20703],{},"Mezní sklon ke spotřebě",[883,20705,20707],{"className":20706},[886],[888,20708,20709],{"xmlns":890},[892,20710,20711,20719],{},[895,20712,20713,20715,20717],{},[898,20714,2127],{},[898,20716,2132],{},[898,20718,4052],{},[902,20720,19171],{"encoding":904},[614,20722,20723],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,20726,20727],{},[883,20728,20730],{"className":20729},[886],[888,20731,20732],{"xmlns":890},[892,20733,20734,20760],{},[895,20735,20736,20738,20740,20742,20744,20758],{},[898,20737,2127],{},[898,20739,2132],{},[898,20741,4052],{},[1655,20743,1657],{},[1949,20745,20746,20752],{},[895,20747,20748,20750],{},[898,20749,2410],{"mathvariant":1943},[898,20751,4052],{},[895,20753,20754,20756],{},[898,20755,2410],{"mathvariant":1943},[898,20757,10375],{},[898,20759,1719],{"mathvariant":1943},[902,20761,20762],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,20764,20765,3106,20768,2115,20786,20789],{},[38,20766,20767],{},"Mezní sklon k úsporám",[883,20769,20771],{"className":20770},[886],[888,20772,20773],{"xmlns":890},[892,20774,20775,20783],{},[895,20776,20777,20779,20781],{},[898,20778,2127],{},[898,20780,2132],{},[898,20782,9920],{},[902,20784,20785],{"encoding":904},"MPS",[614,20787,20788],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,20791,20792],{},[883,20793,20795],{"className":20794},[886],[888,20796,20797],{"xmlns":890},[892,20798,20799,20825],{},[895,20800,20801,20803,20805,20807,20809,20823],{},[898,20802,2127],{},[898,20804,2132],{},[898,20806,9920],{},[1655,20808,1657],{},[1949,20810,20811,20817],{},[895,20812,20813,20815],{},[898,20814,2410],{"mathvariant":1943},[898,20816,9920],{},[895,20818,20819,20821],{},[898,20820,2410],{"mathvariant":1943},[898,20822,10375],{},[898,20824,1719],{"mathvariant":1943},[902,20826,20827],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,20829,20830,20831,20889],{},"Z (7.2) plyne ",[883,20832,20834],{"className":20833},[886],[888,20835,20836],{"xmlns":890},[892,20837,20838,20886],{},[895,20839,20840,20854,20856,20870,20872],{},[1949,20841,20842,20848],{},[895,20843,20844,20846],{},[898,20845,2410],{"mathvariant":1943},[898,20847,10375],{},[895,20849,20850,20852],{},[898,20851,2410],{"mathvariant":1943},[898,20853,10375],{},[1655,20855,1657],{},[1949,20857,20858,20864],{},[895,20859,20860,20862],{},[898,20861,2410],{"mathvariant":1943},[898,20863,4052],{},[895,20865,20866,20868],{},[898,20867,2410],{"mathvariant":1943},[898,20869,10375],{},[1655,20871,2346],{},[1949,20873,20874,20880],{},[895,20875,20876,20878],{},[898,20877,2410],{"mathvariant":1943},[898,20879,9920],{},[895,20881,20882,20884],{},[898,20883,2410],{"mathvariant":1943},[898,20885,10375],{},[902,20887,20888],{"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",[724,20891,20892],{},[883,20893,20895],{"className":20894},[886],[888,20896,20897],{"xmlns":890},[892,20898,20899,20962],{},[895,20900,20901,20953,20955,20957,20960],{},[13957,20902,20903],{"notation":13959},[3615,20904,20905],{"scriptlevel":2552,"displaystyle":1663},[3615,20906,20907],{"scriptlevel":2552,"displaystyle":1663},[3615,20908,20909],{"scriptlevel":2552,"displaystyle":1670},[895,20910,20911,20913,20915,20917,20919,20921,20923,20925,20927,20929,20931,20933,20935,20937,20939,20941,20943,20945,20947,20949,20951],{},[898,20912,2127],{},[898,20914,2132],{},[898,20916,4052],{},[1655,20918,2346],{},[898,20920,2127],{},[898,20922,2132],{},[898,20924,9920],{},[1655,20926,1657],{},[1826,20928,1828],{},[1655,20930,1671],{"separator":1670},[1967,20932],{"width":1969},[898,20934,2127],{},[898,20936,2132],{},[898,20938,9920],{},[1655,20940,1657],{},[1826,20942,1828],{},[1655,20944,2623],{},[898,20946,2127],{},[898,20948,2132],{},[898,20950,4052],{},[898,20952,1719],{"mathvariant":1943},[1967,20954],{"width":1969},[1655,20956,1664],{"stretchy":1663},[1826,20958,20959],{},"7.5",[1655,20961,1677],{"stretchy":1663},[902,20963,20964],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,20966,20967,3106,20970,20993,20994,2704,21016,21042],{},[38,20968,20969],{},"Pro lineární model",[883,20971,20973],{"className":20972},[886],[888,20974,20975],{"xmlns":890},[892,20976,20977,20991],{},[895,20978,20979,20981,20983,20985,20987,20989],{},[898,20980,4052],{},[1655,20982,1657],{},[898,20984,207],{},[898,20986,10375],{},[1655,20988,2346],{},[898,20990,2025],{},[902,20992,20046],{"encoding":904}," vychází ",[883,20995,20997],{"className":20996},[886],[888,20998,20999],{"xmlns":890},[892,21000,21001,21013],{},[895,21002,21003,21005,21007,21009,21011],{},[898,21004,2127],{},[898,21006,2132],{},[898,21008,4052],{},[1655,21010,1657],{},[898,21012,207],{},[902,21014,21015],{"encoding":904},"MPC = a",[883,21017,21019],{"className":21018},[886],[888,21020,21021],{"xmlns":890},[892,21022,21023,21039],{},[895,21024,21025,21027,21029,21031,21033,21035,21037],{},[898,21026,2127],{},[898,21028,2132],{},[898,21030,9920],{},[1655,21032,1657],{},[1826,21034,1828],{},[1655,21036,2623],{},[898,21038,207],{},[902,21040,21041],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,21044,21045,21048,21049,21071,21072,21100],{},[38,21046,21047],{},"Interpretace diferenciálem."," Pro pevné ",[883,21050,21052],{"className":21051},[886],[888,21053,21054],{"xmlns":890},[892,21055,21056,21068],{},[895,21057,21058,21060,21062],{},[898,21059,10375],{},[1655,21061,1657],{},[2597,21063,21064,21066],{},[898,21065,10375],{},[1655,21067,5603],{},[902,21069,21070],{"encoding":904},"Y = Y^*"," udává ",[883,21073,21075],{"className":21074},[886],[888,21076,21077],{"xmlns":890},[892,21078,21079,21097],{},[895,21080,21081,21083,21085,21087,21089,21095],{},[898,21082,2127],{},[898,21084,2132],{},[898,21086,4052],{},[1655,21088,1664],{"stretchy":1663},[2597,21090,21091,21093],{},[898,21092,10375],{},[1655,21094,5603],{},[1655,21096,1677],{"stretchy":1663},[902,21098,21099],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,21102,21103],{},[883,21104,21106],{"className":21105},[886],[888,21107,21108],{"xmlns":890},[892,21109,21110,21164],{},[895,21111,21112,21114,21116,21118,21120,21122,21124,21130,21132,21134,21136,21138,21140,21142,21144,21146,21148,21150,21152,21154,21156,21158,21160,21162],{},[898,21113,2506],{"mathvariant":1943},[898,21115,4052],{},[1655,21117,2357],{},[898,21119,2410],{"mathvariant":1943},[898,21121,4052],{},[1655,21123,1657],{},[2597,21125,21126,21128],{},[898,21127,4052],{},[1655,21129,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,21131,1664],{"stretchy":1663},[898,21133,10375],{},[1655,21135,1677],{"stretchy":1663},[2031,21137,2435],{},[898,21139,2410],{"mathvariant":1943},[898,21141,10375],{},[1655,21143,1657],{},[898,21145,2127],{},[898,21147,2132],{},[898,21149,4052],{},[1655,21151,1664],{"stretchy":1663},[898,21153,10375],{},[1655,21155,1677],{"stretchy":1663},[2031,21157,2435],{},[898,21159,2410],{"mathvariant":1943},[898,21161,10375],{},[898,21163,1719],{"mathvariant":1943},[902,21165,21166],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,21168,21169,21170,21206,21207,21210],{},"Analogicky ",[883,21171,21173],{"className":21172},[886],[888,21174,21175],{"xmlns":890},[892,21176,21177,21203],{},[895,21178,21179,21181,21183,21185,21187,21189,21191,21193,21195,21197,21199,21201],{},[898,21180,2506],{"mathvariant":1943},[898,21182,9920],{},[1655,21184,2357],{},[898,21186,2127],{},[898,21188,2132],{},[898,21190,9920],{},[1655,21192,1664],{"stretchy":1663},[898,21194,10375],{},[1655,21196,1677],{"stretchy":1663},[2031,21198,2435],{},[898,21200,2410],{"mathvariant":1943},[898,21202,10375],{},[902,21204,21205],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,21208,1145],{"className":21209,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,21212,21214],{"id":21213},"příklad-72","Příklad 7.2",[724,21216,20381,21217,21252,21253,21272],{},[883,21218,21220],{"className":21219},[886],[888,21221,21222],{"xmlns":890},[892,21223,21224,21249],{},[895,21225,21226,21228,21230,21233,21239,21241,21243,21245,21247],{},[898,21227,4052],{},[1655,21229,1657],{},[1826,21231,21232],{},"0,001",[2597,21234,21235,21237],{},[898,21236,10375],{},[1826,21238,1837],{},[1655,21240,2346],{},[1826,21242,4112],{},[898,21244,10375],{},[1655,21246,2346],{},[1826,21248,4390],{},[902,21250,21251],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,21254,21256],{"className":21255},[886],[888,21257,21258],{"xmlns":890},[892,21259,21260,21269],{},[895,21261,21262,21264,21266],{},[898,21263,10375],{},[1655,21265,3065],{},[1826,21267,21268],{},"400",[902,21270,21271],{"encoding":904},"Y \u003C 400",") platí",[724,21274,21275],{},[883,21276,21278],{"className":21277},[886],[888,21279,21280],{"xmlns":890},[892,21281,21282,21319],{},[895,21283,21284,21286,21288,21290,21292,21306,21308,21311,21313,21315,21317],{},[898,21285,2127],{},[898,21287,2132],{},[898,21289,4052],{},[1655,21291,1657],{},[1949,21293,21294,21300],{},[895,21295,21296,21298],{},[898,21297,2410],{"mathvariant":1943},[898,21299,4052],{},[895,21301,21302,21304],{},[898,21303,2410],{"mathvariant":1943},[898,21305,10375],{},[1655,21307,1657],{},[1826,21309,21310],{},"0,002",[898,21312,10375],{},[1655,21314,2346],{},[1826,21316,4112],{},[1655,21318,1671],{"separator":1670},[902,21320,21321],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,21323,21324],{},[883,21325,21327],{"className":21326},[886],[888,21328,21329],{"xmlns":890},[892,21330,21331,21364],{},[895,21332,21333,21335,21337,21339,21341,21343,21345,21347,21349,21351,21353,21355,21357,21359,21361],{},[898,21334,2127],{},[898,21336,2132],{},[898,21338,9920],{},[1655,21340,1657],{},[1826,21342,1828],{},[1655,21344,2623],{},[898,21346,2127],{},[898,21348,2132],{},[898,21350,4052],{},[1655,21352,1657],{},[1655,21354,2623],{},[1826,21356,21310],{},[898,21358,10375],{},[1655,21360,2346],{},[1826,21362,21363],{},"0,8.",[902,21365,21366],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,21368,21369,21449,21528],{},[123,21370,21371,1343,21399,21427,21428,9349,21446,1719],{},[883,21372,21374],{"className":21373},[886],[888,21375,21376],{"xmlns":890},[892,21377,21378,21396],{},[895,21379,21380,21382,21384,21386,21388,21390,21392,21394],{},[898,21381,2127],{},[898,21383,2132],{},[898,21385,4052],{},[1655,21387,1664],{"stretchy":1663},[1826,21389,4360],{},[1655,21391,1677],{"stretchy":1663},[1655,21393,1657],{},[1826,21395,20397],{},[902,21397,21398],{"encoding":904},"MPC(100) = 0{,}4",[883,21400,21402],{"className":21401},[886],[888,21403,21404],{"xmlns":890},[892,21405,21406,21424],{},[895,21407,21408,21410,21412,21414,21416,21418,21420,21422],{},[898,21409,2127],{},[898,21411,2132],{},[898,21413,9920],{},[1655,21415,1664],{"stretchy":1663},[1826,21417,4360],{},[1655,21419,1677],{"stretchy":1663},[1655,21421,1657],{},[1826,21423,20447],{},[902,21425,21426],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,21429,21431],{"className":21430},[886],[888,21432,21433],{"xmlns":890},[892,21434,21435,21443],{},[895,21436,21437,21439,21441],{},[898,21438,10375],{},[1655,21440,1657],{},[1826,21442,4360],{},[902,21444,21445],{"encoding":904},"Y = 100",[38,21447,21448],{},"větší sklon k úsporám",[123,21450,21451,1343,21479,21427,21507,9349,21525,1719],{},[883,21452,21454],{"className":21453},[886],[888,21455,21456],{"xmlns":890},[892,21457,21458,21476],{},[895,21459,21460,21462,21464,21466,21468,21470,21472,21474],{},[898,21461,2127],{},[898,21463,2132],{},[898,21465,4052],{},[1655,21467,1664],{"stretchy":1663},[1826,21469,9624],{},[1655,21471,1677],{"stretchy":1663},[1655,21473,1657],{},[1826,21475,20447],{},[902,21477,21478],{"encoding":904},"MPC(200) = 0{,}6",[883,21480,21482],{"className":21481},[886],[888,21483,21484],{"xmlns":890},[892,21485,21486,21504],{},[895,21487,21488,21490,21492,21494,21496,21498,21500,21502],{},[898,21489,2127],{},[898,21491,2132],{},[898,21493,9920],{},[1655,21495,1664],{"stretchy":1663},[1826,21497,9624],{},[1655,21499,1677],{"stretchy":1663},[1655,21501,1657],{},[1826,21503,20397],{},[902,21505,21506],{"encoding":904},"MPS(200) = 0{,}4",[883,21508,21510],{"className":21509},[886],[888,21511,21512],{"xmlns":890},[892,21513,21514,21522],{},[895,21515,21516,21518,21520],{},[898,21517,10375],{},[1655,21519,1657],{},[1826,21521,9624],{},[902,21523,21524],{"encoding":904},"Y = 200",[38,21526,21527],{},"větší sklon ke spotřebě",[123,21529,21530,21531,21549,21550,5171],{},"Přesně při ",[883,21532,21534],{"className":21533},[886],[888,21535,21536],{"xmlns":890},[892,21537,21538,21546],{},[895,21539,21540,21542,21544],{},[898,21541,10375],{},[1655,21543,1657],{},[1826,21545,10050],{},[902,21547,21548],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,21551,21553],{"className":21552},[886],[888,21554,21555],{"xmlns":890},[892,21556,21557,21577],{},[895,21558,21559,21561,21563,21565,21567,21569,21571,21573,21575],{},[898,21560,2127],{},[898,21562,2132],{},[898,21564,4052],{},[1655,21566,1657],{},[898,21568,2127],{},[898,21570,2132],{},[898,21572,9920],{},[1655,21574,1657],{},[1826,21576,6258],{},[902,21578,21579],{"encoding":904},"MPC = MPS = 0{,}5",[724,21581,21582,21583,21600,21601,21615,21616,3962,21629,21643,21644,21657,21658,21699],{},"Interpretace: při ",[883,21584,21586],{"className":21585},[886],[888,21587,21588],{"xmlns":890},[892,21589,21590,21598],{},[895,21591,21592,21594,21596],{},[898,21593,10375],{},[1655,21595,1657],{},[1826,21597,4360],{},[902,21599,21445],{"encoding":904}," se spotřeba mění ",[883,21602,21604],{"className":21603},[886],[888,21605,21606],{"xmlns":890},[892,21607,21608,21612],{},[895,21609,21610],{},[1826,21611,20397],{},[902,21613,21614],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,21617,21619],{"className":21618},[886],[888,21620,21621],{"xmlns":890},[892,21622,21623,21627],{},[895,21624,21625],{},[1826,21626,4360],{},[902,21628,4360],{"encoding":904},[883,21630,21632],{"className":21631},[886],[888,21633,21634],{"xmlns":890},[892,21635,21636,21641],{},[895,21637,21638],{},[1826,21639,21640],{},"101",[902,21642,21640],{"encoding":904},", změní se spotřeba přibližně o ",[883,21645,21647],{"className":21646},[886],[888,21648,21649],{"xmlns":890},[892,21650,21651,21655],{},[895,21652,21653],{},[1826,21654,20397],{},[902,21656,21614],{"encoding":904},". Skutečná změna ",[883,21659,21661],{"className":21660},[886],[888,21662,21663],{"xmlns":890},[892,21664,21665,21696],{},[895,21666,21667,21669,21671,21673,21675,21677,21679,21681,21683,21685,21687,21689,21691,21693],{},[898,21668,2506],{"mathvariant":1943},[898,21670,4052],{},[1655,21672,1657],{},[898,21674,4052],{},[1655,21676,1664],{"stretchy":1663},[1826,21678,21640],{},[1655,21680,1677],{"stretchy":1663},[1655,21682,2623],{},[898,21684,4052],{},[1655,21686,1664],{"stretchy":1663},[1826,21688,4360],{},[1655,21690,1677],{"stretchy":1663},[1655,21692,1657],{},[1826,21694,21695],{},"0,401",[902,21697,21698],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,21701,21702,21703],{},"Obecný trend: ",[38,21704,21705],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,21707,21709],{"id":21708},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,21711,21712,21713,2115,21716,21719,21720,2115,21723,13253,21726,2115,21729,21732],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,21714,21715],{},"makroekonomická rovnováha",[614,21717,21718],{},"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 ",[38,21721,21722],{},"agregátní poptávky",[614,21724,21725],{},"aggregate demand",[38,21727,21728],{},"agregátní nabídky",[614,21730,21731],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,21734,21736],{"id":21735},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,21738,21739],{},[1723,21740],{"alt":21741,"className":21742,"src":21743},"imek-keynesian-kriz",[210,1727],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,21745,21747],{"id":21746},"zadání-modelu","Zadání modelu",[724,21749,21750,21751,21764,21765,21778],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,21752,21754],{"className":21753},[886],[888,21755,21756],{"xmlns":890},[892,21757,21758,21762],{},[895,21759,21760],{},[898,21761,4052],{},[902,21763,4052],{"encoding":904}," a investice ",[883,21766,21768],{"className":21767},[886],[888,21769,21770],{"xmlns":890},[892,21771,21772,21776],{},[895,21773,21774],{},[898,21775,13309],{},[902,21777,13309],{"encoding":904},". Podmínka rovnováhy:",[724,21780,21781],{},[883,21782,21784],{"className":21783},[886],[888,21785,21786],{"xmlns":890},[892,21787,21788,21811],{},[895,21789,21790,21792,21794,21796,21798,21800,21802,21804,21806,21809],{},[898,21791,10375],{},[1655,21793,1657],{},[898,21795,4052],{},[1655,21797,2346],{},[898,21799,13309],{},[898,21801,1719],{"mathvariant":1943},[1967,21803],{"width":1969},[1655,21805,1664],{"stretchy":1663},[1826,21807,21808],{},"7.6",[1655,21810,1677],{"stretchy":1663},[902,21812,21813],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,21815,21817],{"id":21816},"soustava-rovnic","Soustava rovnic",[724,21819,21820,21821,21842,21843,21867],{},"Pro pevně zadané (plánované) investice ",[883,21822,21824],{"className":21823},[886],[888,21825,21826],{"xmlns":890},[892,21827,21828,21840],{},[895,21829,21830,21832,21834],{},[898,21831,13309],{},[1655,21833,1657],{},[2597,21835,21836,21838],{},[898,21837,13309],{},[1655,21839,5603],{},[902,21841,13320],{"encoding":904}," a funkci spotřeby ",[883,21844,21846],{"className":21845},[886],[888,21847,21848],{"xmlns":890},[892,21849,21850,21864],{},[895,21851,21852,21854,21856,21858,21860,21862],{},[898,21853,4052],{},[1655,21855,1657],{},[898,21857,4052],{},[1655,21859,1664],{"stretchy":1663},[898,21861,10375],{},[1655,21863,1677],{"stretchy":1663},[902,21865,21866],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,21869,21870],{},[883,21871,21873],{"className":21872},[886],[888,21874,21875],{"xmlns":890},[892,21876,21877,21953],{},[895,21878,21879,21944,21946,21948,21951],{},[21880,21881,21884,21916],"mtable",{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},"0.25em","right left",[21885,21886,21887,21894],"mtr",{},[21888,21889,21890],"mtd",{},[3615,21891,21892],{"scriptlevel":2552,"displaystyle":1670},[898,21893,10375],{},[21888,21895,21896],{},[3615,21897,21898],{"scriptlevel":2552,"displaystyle":1670},[895,21899,21900,21902,21904,21906,21908,21914],{},[895,21901],{},[1655,21903,1657],{},[898,21905,4052],{},[1655,21907,2346],{},[2597,21909,21910,21912],{},[898,21911,13309],{},[1655,21913,5603],{},[1655,21915,1671],{"separator":1670},[21885,21917,21918,21924],{},[21888,21919,21920],{},[3615,21921,21922],{"scriptlevel":2552,"displaystyle":1670},[898,21923,4052],{},[21888,21925,21926],{},[3615,21927,21928],{"scriptlevel":2552,"displaystyle":1670},[895,21929,21930,21932,21934,21936,21938,21940,21942],{},[895,21931],{},[1655,21933,1657],{},[898,21935,4052],{},[1655,21937,1664],{"stretchy":1663},[898,21939,10375],{},[1655,21941,1677],{"stretchy":1663},[1655,21943,1671],{"separator":1670},[1967,21945],{"width":1969},[1655,21947,1664],{"stretchy":1663},[1826,21949,21950],{},"7.7",[1655,21952,1677],{"stretchy":1663},[902,21954,21955],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,21957,21958,21959,3106,21961,2704,21978,3106,21981,1719],{},"jejímž řešením jsou ",[38,21960,15010],{},[883,21962,21964],{"className":21963},[886],[888,21965,21966],{"xmlns":890},[892,21967,21968,21976],{},[895,21969,21970],{},[2597,21971,21972,21974],{},[898,21973,10375],{},[898,21975,5502],{},[902,21977,15028],{"encoding":904},[38,21979,21980],{},"rovnovážná spotřeba",[883,21982,21984],{"className":21983},[886],[888,21985,21986],{"xmlns":890},[892,21987,21988,21996],{},[895,21989,21990],{},[2597,21991,21992,21994],{},[898,21993,4052],{},[898,21995,5502],{},[902,21997,15087],{"encoding":904},[198,21999,22001,22002],{"id":22000},"výpočet-yeye","Výpočet ",[883,22003,22005],{"className":22004},[886],[888,22006,22007],{"xmlns":890},[892,22008,22009,22017],{},[895,22010,22011],{},[2597,22012,22013,22015],{},[898,22014,10375],{},[898,22016,5502],{},[902,22018,15028],{"encoding":904},[724,22020,22021,22022,22045,22046,8932,22078],{},"Pro lineární spotřebu ",[883,22023,22025],{"className":22024},[886],[888,22026,22027],{"xmlns":890},[892,22028,22029,22043],{},[895,22030,22031,22033,22035,22037,22039,22041],{},[898,22032,4052],{},[1655,22034,1657],{},[898,22036,207],{},[898,22038,10375],{},[1655,22040,2346],{},[898,22042,2025],{},[902,22044,20046],{"encoding":904}," plyne z (7.7) rovnice ",[883,22047,22049],{"className":22048},[886],[888,22050,22051],{"xmlns":890},[892,22052,22053,22075],{},[895,22054,22055,22057,22059,22061,22063,22065,22067,22069],{},[898,22056,10375],{},[1655,22058,1657],{},[898,22060,207],{},[898,22062,10375],{},[1655,22064,2346],{},[898,22066,2025],{},[1655,22068,2346],{},[2597,22070,22071,22073],{},[898,22072,13309],{},[1655,22074,5603],{},[902,22076,22077],{"encoding":904},"Y = aY + b + I^*",[38,22079,22080],{},"redukovaný tvar",[724,22082,22083],{},[883,22084,22086],{"className":22085},[886],[888,22087,22088],{"xmlns":890},[892,22089,22090,22138],{},[895,22091,22092],{},[13957,22093,22094],{"notation":13959},[3615,22095,22096],{"scriptlevel":2552,"displaystyle":1663},[3615,22097,22098],{"scriptlevel":2552,"displaystyle":1663},[3615,22099,22100],{"scriptlevel":2552,"displaystyle":1670},[895,22101,22102,22104,22110,22112,22134,22136],{},[2031,22103,2435],{},[2597,22105,22106,22108],{},[898,22107,10375],{},[898,22109,5502],{},[1655,22111,1657],{},[1949,22113,22114,22126],{},[895,22115,22116,22118,22120],{},[898,22117,2025],{},[1655,22119,2346],{},[2597,22121,22122,22124],{},[898,22123,13309],{},[1655,22125,5603],{},[895,22127,22128,22130,22132],{},[1826,22129,1828],{},[1655,22131,2623],{},[898,22133,207],{},[898,22135,1719],{"mathvariant":1943},[2031,22137,2435],{},[902,22139,22140],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,22142,22144],{"id":22143},"příklad-73","Příklad 7.3",[724,22146,22147,22148,9349,22165,2704,22189,22215],{},"V modelu ",[883,22149,22151],{"className":22150},[886],[888,22152,22153],{"xmlns":890},[892,22154,22155,22163],{},[895,22156,22157,22159,22161],{},[898,22158,4052],{},[2031,22160,13415],{},[898,22162,13309],{},[902,22164,13420],{"encoding":904},[883,22166,22168],{"className":22167},[886],[888,22169,22170],{"xmlns":890},[892,22171,22172,22186],{},[895,22173,22174,22176,22178,22180,22182,22184],{},[898,22175,4052],{},[1655,22177,1657],{},[1826,22179,20447],{},[898,22181,10375],{},[1655,22183,2346],{},[1826,22185,4136],{},[902,22187,22188],{"encoding":904},"C = 0{,}6Y + 10",[883,22190,22192],{"className":22191},[886],[888,22193,22194],{"xmlns":890},[892,22195,22196,22212],{},[895,22197,22198,22200,22202,22204,22206],{},[898,22199,13309],{},[1655,22201,1657],{},[1826,22203,4771],{},[1655,22205,1657],{},[2597,22207,22208,22210],{},[898,22209,13309],{},[1655,22211,5603],{},[902,22213,22214],{"encoding":904},"I = 12 = I^*",". Soustava",[724,22217,22218],{},[883,22219,22221],{"className":22220},[886],[888,22222,22223],{"xmlns":890},[892,22224,22225,22281],{},[21880,22226,22227,22253],{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},[21885,22228,22229,22235],{},[21888,22230,22231],{},[3615,22232,22233],{"scriptlevel":2552,"displaystyle":1670},[898,22234,10375],{},[21888,22236,22237],{},[3615,22238,22239],{"scriptlevel":2552,"displaystyle":1670},[895,22240,22241,22243,22245,22247,22249,22251],{},[895,22242],{},[1655,22244,1657],{},[898,22246,4052],{},[1655,22248,2346],{},[1826,22250,4771],{},[1655,22252,1671],{"separator":1670},[21885,22254,22255,22261],{},[21888,22256,22257],{},[3615,22258,22259],{"scriptlevel":2552,"displaystyle":1670},[898,22260,4052],{},[21888,22262,22263],{},[3615,22264,22265],{"scriptlevel":2552,"displaystyle":1670},[895,22266,22267,22269,22271,22273,22275,22277,22279],{},[895,22268],{},[1655,22270,1657],{},[1826,22272,20447],{},[898,22274,10375],{},[1655,22276,2346],{},[1826,22278,4136],{},[1655,22280,1671],{"separator":1670},[902,22282,22283],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,22285,22286,22287,1343,22310,22333,22334,5171],{},"má řešení ",[883,22288,22290],{"className":22289},[886],[888,22291,22292],{"xmlns":890},[892,22293,22294,22307],{},[895,22295,22296,22302,22304],{},[2597,22297,22298,22300],{},[898,22299,10375],{},[898,22301,5502],{},[1655,22303,1657],{},[1826,22305,22306],{},"55",[902,22308,22309],{"encoding":904},"Y^E = 55",[883,22311,22313],{"className":22312},[886],[888,22314,22315],{"xmlns":890},[892,22316,22317,22330],{},[895,22318,22319,22325,22327],{},[2597,22320,22321,22323],{},[898,22322,4052],{},[898,22324,5502],{},[1655,22326,1657],{},[1826,22328,22329],{},"43",[902,22331,22332],{"encoding":904},"C^E = 43"," (a ",[883,22335,22337],{"className":22336},[886],[888,22338,22339],{"xmlns":890},[892,22340,22341,22353],{},[895,22342,22343,22349,22351],{},[2597,22344,22345,22347],{},[898,22346,9920],{},[898,22348,5502],{},[1655,22350,1657],{},[1826,22352,4771],{},[902,22354,22355],{"encoding":904},"S^E = 12",[724,22357,22358],{},[614,22359,22360,22361,22383,22384,13253,22405,22428,22429,1719],{},"Obrázek 7.5 — Přímky ",[883,22362,22364],{"className":22363},[886],[888,22365,22366],{"xmlns":890},[892,22367,22368,22380],{},[895,22369,22370,22372,22374,22376,22378],{},[898,22371,4052],{},[1655,22373,1657],{},[898,22375,10375],{},[1655,22377,2623],{},[1826,22379,4771],{},[902,22381,22382],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,22385,22387],{"className":22386},[886],[888,22388,22389],{"xmlns":890},[892,22390,22391,22403],{},[895,22392,22393,22395,22397,22399,22401],{},[898,22394,10375],{},[1655,22396,1657],{},[898,22398,4052],{},[1655,22400,2346],{},[898,22402,13309],{},[902,22404,15869],{"encoding":904},[883,22406,22408],{"className":22407},[886],[888,22409,22410],{"xmlns":890},[892,22411,22412,22426],{},[895,22413,22414,22416,22418,22420,22422,22424],{},[898,22415,4052],{},[1655,22417,1657],{},[1826,22419,20447],{},[898,22421,10375],{},[1655,22423,2346],{},[1826,22425,4136],{},[902,22427,22188],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,22430,22432],{"className":22431},[886],[888,22433,22434],{"xmlns":890},[892,22435,22436,22468],{},[895,22437,22438,22440,22446,22448,22454,22456,22458,22460,22462,22464,22466],{},[1655,22439,2734],{"stretchy":1663},[2597,22441,22442,22444],{},[898,22443,10375],{},[898,22445,5502],{},[1655,22447,1671],{"separator":1670},[2597,22449,22450,22452],{},[898,22451,4052],{},[898,22453,5502],{},[1655,22455,2743],{"stretchy":1663},[1655,22457,1657],{},[1655,22459,2734],{"stretchy":1663},[1826,22461,22306],{},[1655,22463,1671],{"separator":1670},[1826,22465,22329],{},[1655,22467,2743],{"stretchy":1663},[902,22469,22470],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,22472,22473,22476,22477,22494,22495,1719],{},[38,22474,22475],{},"Komentář k přechodu."," Model ",[883,22478,22480],{"className":22479},[886],[888,22481,22482],{"xmlns":890},[892,22483,22484,22492],{},[895,22485,22486,22488,22490],{},[898,22487,4052],{},[2031,22489,13415],{},[898,22491,13309],{},[902,22493,13420],{"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 ",[38,22496,22497,22498],{},"model ",[883,22499,22501],{"className":22500},[886],[888,22502,22503],{"xmlns":890},[892,22504,22505,22517],{},[895,22506,22507,22509,22511,22513,22515],{},[898,22508,4052],{},[2031,22510,13415],{},[898,22512,13309],{},[2031,22514,13415],{},[898,22516,13237],{},[902,22518,19346],{"encoding":904},[115,22520,22522],{"id":22521},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,22524,21747],{"id":22525},"zadání-modelu-1",[724,22527,22528,22529,22546,22547,3106,22550,2115,22563,22566],{},"Rozšíření modelu ",[883,22530,22532],{"className":22531},[886],[888,22533,22534],{"xmlns":890},[892,22535,22536,22544],{},[895,22537,22538,22540,22542],{},[898,22539,4052],{},[2031,22541,13415],{},[898,22543,13309],{},[902,22545,13420],{"encoding":904}," o ",[38,22548,22549],{},"vládní výdaje",[883,22551,22553],{"className":22552},[886],[888,22554,22555],{"xmlns":890},[892,22556,22557,22561],{},[895,22558,22559],{},[898,22560,13237],{},[902,22562,13237],{"encoding":904},[614,22564,22565],{},"government expenditure","). Podmínka rovnováhy:",[724,22568,22569],{},[883,22570,22572],{"className":22571},[886],[888,22573,22574],{"xmlns":890},[892,22575,22576,22603],{},[895,22577,22578,22580,22582,22584,22586,22588,22590,22592,22594,22596,22598,22601],{},[898,22579,10375],{},[1655,22581,1657],{},[898,22583,4052],{},[1655,22585,2346],{},[898,22587,13309],{},[1655,22589,2346],{},[898,22591,13237],{},[898,22593,1719],{"mathvariant":1943},[1967,22595],{"width":1969},[1655,22597,1664],{"stretchy":1663},[1826,22599,22600],{},"7.8",[1655,22602,1677],{"stretchy":1663},[902,22604,22605],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,22607,22608,22609,3106,22612,2115,22625,22628],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,22610,22611],{},"zdaněním domácností",[883,22613,22615],{"className":22614},[886],[888,22616,22617],{"xmlns":890},[892,22618,22619,22623],{},[895,22620,22621],{},[898,22622,4049],{},[902,22624,4049],{"encoding":904},[614,22626,22627],{},"taxation","). Zdanění bývá:",[120,22630,22631,22664,22689],{},[123,22632,22633,22634,1671],{},"úměrné důchodu: ",[883,22635,22637],{"className":22636},[886],[888,22638,22639],{"xmlns":890},[892,22640,22641,22661],{},[895,22642,22643,22645,22647,22649,22651,22653,22655,22657,22659],{},[898,22644,4049],{},[1655,22646,1657],{},[898,22648,4049],{},[1655,22650,1664],{"stretchy":1663},[898,22652,10375],{},[1655,22654,1677],{"stretchy":1663},[1655,22656,1657],{},[898,22658,19981],{},[898,22660,10375],{},[902,22662,22663],{"encoding":904},"T = T(Y) = tY",[123,22665,22666,22667,1671],{},"fixní: ",[883,22668,22670],{"className":22669},[886],[888,22671,22672],{"xmlns":890},[892,22673,22674,22686],{},[895,22675,22676,22678,22680],{},[898,22677,4049],{},[1655,22679,1657],{},[2597,22681,22682,22684],{},[898,22683,4049],{},[1655,22685,5603],{},[902,22687,22688],{"encoding":904},"T = T^*",[123,22690,22691,22692,22720,22721,1719],{},"kombinované: ",[883,22693,22695],{"className":22694},[886],[888,22696,22697],{"xmlns":890},[892,22698,22699,22717],{},[895,22700,22701,22703,22705,22711,22713,22715],{},[898,22702,4049],{},[1655,22704,1657],{},[2597,22706,22707,22709],{},[898,22708,4049],{},[1655,22710,5603],{},[1655,22712,2346],{},[898,22714,19981],{},[898,22716,10375],{},[902,22718,22719],{"encoding":904},"T = T^* + tY",", kde ",[883,22722,22724],{"className":22723},[886],[888,22725,22726],{"xmlns":890},[892,22727,22728,22740],{},[895,22729,22730,22732,22734,22736,22738],{},[1826,22731,2552],{},[1655,22733,8926],{},[898,22735,19981],{},[1655,22737,3065],{},[1826,22739,1828],{},[902,22741,22742],{"encoding":904},"0 \\le t \u003C 1",[5120,22744,22745],{},[724,22746,22747,22749,22750,22771,22772,22775,22776,22789,22790,13253,22816,3106,22819,22845,22846,22874,22875,2704,22888,22906],{},[883,22748,5661],{}," Pozor na disponibilní důchod\nV modelu ",[883,22751,22753],{"className":22752},[886],[888,22754,22755],{"xmlns":890},[892,22756,22757,22769],{},[895,22758,22759,22761,22763,22765,22767],{},[898,22760,4052],{},[2031,22762,13415],{},[898,22764,13309],{},[2031,22766,13415],{},[898,22768,13237],{},[902,22770,19346],{"encoding":904}," je nutné ",[38,22773,22774],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,22777,22779],{"className":22778},[886],[888,22780,22781],{"xmlns":890},[892,22782,22783,22787],{},[895,22784,22785],{},[898,22786,10375],{},[902,22788,10375],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,22791,22793],{"className":22792},[886],[888,22794,22795],{"xmlns":890},[892,22796,22797,22813],{},[895,22798,22799,22801,22803,22805,22807,22809,22811],{},[898,22800,10375],{},[1655,22802,1657],{},[898,22804,4052],{},[1655,22806,2346],{},[898,22808,13309],{},[1655,22810,2346],{},[898,22812,13237],{},[902,22814,22815],{"encoding":904},"Y = C + I + G",[38,22817,22818],{},"disponibilní důchod",[883,22820,22822],{"className":22821},[886],[888,22823,22824],{"xmlns":890},[892,22825,22826,22842],{},[895,22827,22828,22834,22836,22838,22840],{},[1820,22829,22830,22832],{},[898,22831,10375],{},[898,22833,2838],{},[1655,22835,1657],{},[898,22837,10375],{},[1655,22839,2623],{},[898,22841,4049],{},[902,22843,22844],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,22847,22849],{"className":22848},[886],[888,22850,22851],{"xmlns":890},[892,22852,22853,22871],{},[895,22854,22855,22857,22859,22861,22863,22869],{},[898,22856,4052],{},[1655,22858,1657],{},[898,22860,4052],{},[1655,22862,1664],{"stretchy":1663},[1820,22864,22865,22867],{},[898,22866,10375],{},[898,22868,2838],{},[1655,22870,1677],{"stretchy":1663},[902,22872,22873],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,22876,22878],{"className":22877},[886],[888,22879,22880],{"xmlns":890},[892,22881,22882,22886],{},[895,22883,22884],{},[898,22885,10375],{},[902,22887,10375],{"encoding":904},[883,22889,22891],{"className":22890},[886],[888,22892,22893],{"xmlns":890},[892,22894,22895,22903],{},[895,22896,22897],{},[1820,22898,22899,22901],{},[898,22900,10375],{},[898,22902,2838],{},[902,22904,22905],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,22908,22909,2115,22912,1677],{},[38,22910,22911],{},"Disponibilní důchod",[614,22913,22914],{},"disposable income",[724,22916,22917],{},[883,22918,22920],{"className":22919},[886],[888,22921,22922],{"xmlns":890},[892,22923,22924,22940],{},[895,22925,22926,22932,22934,22936,22938],{},[1820,22927,22928,22930],{},[898,22929,10375],{},[898,22931,2838],{},[1655,22933,1657],{},[898,22935,10375],{},[1655,22937,2623],{},[898,22939,4049],{},[902,22941,22844],{"encoding":904},[724,22943,22944,22945,1719],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,22946,22948],{"className":22947},[886],[888,22949,22950],{"xmlns":890},[892,22951,22952,22970],{},[895,22953,22954,22956,22958,22960,22962,22968],{},[898,22955,4052],{},[1655,22957,1657],{},[898,22959,4052],{},[1655,22961,1664],{"stretchy":1663},[1820,22963,22964,22966],{},[898,22965,10375],{},[898,22967,2838],{},[1655,22969,1677],{"stretchy":1663},[902,22971,22873],{"encoding":904},[198,22973,21817],{"id":22974},"soustava-rovnic-1",[724,22976,22977,22978,1343,22999,23021,23022,2086],{},"Pro pevně zadané ",[883,22979,22981],{"className":22980},[886],[888,22982,22983],{"xmlns":890},[892,22984,22985,22997],{},[895,22986,22987,22989,22991],{},[898,22988,13309],{},[1655,22990,1657],{},[2597,22992,22993,22995],{},[898,22994,13309],{},[1655,22996,5603],{},[902,22998,13320],{"encoding":904},[883,23000,23002],{"className":23001},[886],[888,23003,23004],{"xmlns":890},[892,23005,23006,23018],{},[895,23007,23008,23010,23012],{},[898,23009,13237],{},[1655,23011,1657],{},[2597,23013,23014,23016],{},[898,23015,13237],{},[1655,23017,5603],{},[902,23019,23020],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,23023,23025],{"className":23024},[886],[888,23026,23027],{"xmlns":890},[892,23028,23029,23049],{},[895,23030,23031,23033,23035,23037,23039,23045,23047],{},[898,23032,10375],{},[1655,23034,1671],{"separator":1670},[898,23036,4052],{},[1655,23038,1671],{"separator":1670},[1820,23040,23041,23043],{},[898,23042,10375],{},[898,23044,2838],{},[1655,23046,1671],{"separator":1670},[898,23048,4049],{},[902,23050,23051],{"encoding":904},"Y, C, Y_D, T",[724,23053,23054],{},[883,23055,23057],{"className":23056},[886],[888,23058,23059],{"xmlns":890},[892,23060,23061,23202],{},[895,23062,23063,23193,23195,23197,23200],{},[21880,23064,23065,23103,23131,23163],{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},[21885,23066,23067,23073],{},[21888,23068,23069],{},[3615,23070,23071],{"scriptlevel":2552,"displaystyle":1670},[898,23072,10375],{},[21888,23074,23075],{},[3615,23076,23077],{"scriptlevel":2552,"displaystyle":1670},[895,23078,23079,23081,23083,23085,23087,23093,23095,23101],{},[895,23080],{},[1655,23082,1657],{},[898,23084,4052],{},[1655,23086,2346],{},[2597,23088,23089,23091],{},[898,23090,13309],{},[1655,23092,5603],{},[1655,23094,2346],{},[2597,23096,23097,23099],{},[898,23098,13237],{},[1655,23100,5603],{},[1655,23102,1671],{"separator":1670},[21885,23104,23105,23111],{},[21888,23106,23107],{},[3615,23108,23109],{"scriptlevel":2552,"displaystyle":1670},[898,23110,4049],{},[21888,23112,23113],{},[3615,23114,23115],{"scriptlevel":2552,"displaystyle":1670},[895,23116,23117,23119,23121,23123,23125,23127,23129],{},[895,23118],{},[1655,23120,1657],{},[898,23122,4049],{},[1655,23124,1664],{"stretchy":1663},[898,23126,10375],{},[1655,23128,1677],{"stretchy":1663},[1655,23130,1671],{"separator":1670},[21885,23132,23133,23139],{},[21888,23134,23135],{},[3615,23136,23137],{"scriptlevel":2552,"displaystyle":1670},[898,23138,4052],{},[21888,23140,23141],{},[3615,23142,23143],{"scriptlevel":2552,"displaystyle":1670},[895,23144,23145,23147,23149,23151,23153,23159,23161],{},[895,23146],{},[1655,23148,1657],{},[898,23150,4052],{},[1655,23152,1664],{"stretchy":1663},[1820,23154,23155,23157],{},[898,23156,10375],{},[898,23158,2838],{},[1655,23160,1677],{"stretchy":1663},[1655,23162,1671],{"separator":1670},[21885,23164,23165,23175],{},[21888,23166,23167],{},[3615,23168,23169],{"scriptlevel":2552,"displaystyle":1670},[1820,23170,23171,23173],{},[898,23172,10375],{},[898,23174,2838],{},[21888,23176,23177],{},[3615,23178,23179],{"scriptlevel":2552,"displaystyle":1670},[895,23180,23181,23183,23185,23187,23189,23191],{},[895,23182],{},[1655,23184,1657],{},[898,23186,10375],{},[1655,23188,2623],{},[898,23190,4049],{},[1655,23192,1671],{"separator":1670},[1967,23194],{"width":1969},[1655,23196,1664],{"stretchy":1663},[1826,23198,23199],{},"7.9",[1655,23201,1677],{"stretchy":1663},[902,23203,23204],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,23206,23207,23208,23252,23253,1719],{},"s řešeními ",[883,23209,23211],{"className":23210},[886],[888,23212,23213],{"xmlns":890},[892,23214,23215,23249],{},[895,23216,23217,23223,23225,23231,23233,23239,23241],{},[2597,23218,23219,23221],{},[898,23220,10375],{},[898,23222,5502],{},[1655,23224,1671],{"separator":1670},[2597,23226,23227,23229],{},[898,23228,4052],{},[898,23230,5502],{},[1655,23232,1671],{"separator":1670},[2597,23234,23235,23237],{},[898,23236,4049],{},[898,23238,5502],{},[1655,23240,1671],{"separator":1670},[1935,23242,23243,23245,23247],{},[898,23244,10375],{},[898,23246,2838],{},[898,23248,5502],{},[902,23250,23251],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,23254,23256],{"className":23255},[886],[888,23257,23258],{"xmlns":890},[892,23259,23260,23286],{},[895,23261,23262,23268,23270,23278,23280],{},[2597,23263,23264,23266],{},[898,23265,9920],{},[898,23267,5502],{},[1655,23269,1657],{},[1935,23271,23272,23274,23276],{},[898,23273,10375],{},[898,23275,2838],{},[898,23277,5502],{},[1655,23279,2623],{},[2597,23281,23282,23284],{},[898,23283,4052],{},[898,23285,5502],{},[902,23287,23288],{"encoding":904},"S^E = Y_D^E - C^E",[5120,23290,23291,23296],{},[724,23292,23293,23295],{},[883,23294,5821],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,23297,23298,23321,23404,23459,23549],{},[123,23299,23300,23303,23304,1719],{},[38,23301,23302],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,23305,23307],{"className":23306},[886],[888,23308,23309],{"xmlns":890},[892,23310,23311,23319],{},[895,23312,23313],{},[1820,23314,23315,23317],{},[898,23316,10375],{},[898,23318,2838],{},[902,23320,22905],{"encoding":904},[123,23322,23323,23372,23373,23390,23391,1719],{},[38,23324,23325,23326,23346,23347],{},"Dosaď ",[883,23327,23329],{"className":23328},[886],[888,23330,23331],{"xmlns":890},[892,23332,23333,23343],{},[895,23334,23335,23337,23339,23341],{},[898,23336,4049],{},[1655,23338,1664],{"stretchy":1663},[898,23340,10375],{},[1655,23342,1677],{"stretchy":1663},[902,23344,23345],{"encoding":904},"T(Y)"," do ",[883,23348,23350],{"className":23349},[886],[888,23351,23352],{"xmlns":890},[892,23353,23354,23370],{},[895,23355,23356,23362,23364,23366,23368],{},[1820,23357,23358,23360],{},[898,23359,10375],{},[898,23361,2838],{},[1655,23363,1657],{},[898,23365,10375],{},[1655,23367,2623],{},[898,23369,4049],{},[902,23371,22844],{"encoding":904}," — dostaneš ",[883,23374,23376],{"className":23375},[886],[888,23377,23378],{"xmlns":890},[892,23379,23380,23388],{},[895,23381,23382],{},[1820,23383,23384,23386],{},[898,23385,10375],{},[898,23387,2838],{},[902,23389,22905],{"encoding":904}," jako lineární funkci ",[883,23392,23394],{"className":23393},[886],[888,23395,23396],{"xmlns":890},[892,23397,23398,23402],{},[895,23399,23400],{},[898,23401,10375],{},[902,23403,10375],{"encoding":904},[123,23405,23406,23372,23433,23390,23446,1719],{},[38,23407,23325,23408,23432],{},[883,23409,23411],{"className":23410},[886],[888,23412,23413],{"xmlns":890},[892,23414,23415,23429],{},[895,23416,23417,23423,23425,23427],{},[1820,23418,23419,23421],{},[898,23420,10375],{},[898,23422,2838],{},[1655,23424,1664],{"stretchy":1663},[898,23426,10375],{},[1655,23428,1677],{"stretchy":1663},[902,23430,23431],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,23434,23436],{"className":23435},[886],[888,23437,23438],{"xmlns":890},[892,23439,23440,23444],{},[895,23441,23442],{},[898,23443,4052],{},[902,23445,4052],{"encoding":904},[883,23447,23449],{"className":23448},[886],[888,23450,23451],{"xmlns":890},[892,23452,23453,23457],{},[895,23454,23455],{},[898,23456,10375],{},[902,23458,10375],{"encoding":904},[123,23460,23461,3106,23483,23517,23518,23531,23532,1719],{},[38,23462,23325,23463,23482],{},[883,23464,23466],{"className":23465},[886],[888,23467,23468],{"xmlns":890},[892,23469,23470,23480],{},[895,23471,23472,23474,23476,23478],{},[898,23473,4052],{},[1655,23475,1664],{"stretchy":1663},[898,23477,10375],{},[1655,23479,1677],{"stretchy":1663},[902,23481,15341],{"encoding":904}," do podmínky rovnováhy",[883,23484,23486],{"className":23485},[886],[888,23487,23488],{"xmlns":890},[892,23489,23490,23514],{},[895,23491,23492,23494,23496,23498,23500,23506,23508],{},[898,23493,10375],{},[1655,23495,1657],{},[898,23497,4052],{},[1655,23499,2346],{},[2597,23501,23502,23504],{},[898,23503,13309],{},[1655,23505,5603],{},[1655,23507,2346],{},[2597,23509,23510,23512],{},[898,23511,13237],{},[1655,23513,5603],{},[902,23515,23516],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,23519,23521],{"className":23520},[886],[888,23522,23523],{"xmlns":890},[892,23524,23525,23529],{},[895,23526,23527],{},[898,23528,10375],{},[902,23530,10375],{"encoding":904},", odtud ",[883,23533,23535],{"className":23534},[886],[888,23536,23537],{"xmlns":890},[892,23538,23539,23547],{},[895,23540,23541],{},[2597,23542,23543,23545],{},[898,23544,10375],{},[898,23546,5502],{},[902,23548,15028],{"encoding":904},[123,23550,23551,23554,23555,1343,23573,1343,23593,1343,23610,1719],{},[38,23552,23553],{},"Zpětným dosazením"," dopočítej ",[883,23556,23558],{"className":23557},[886],[888,23559,23560],{"xmlns":890},[892,23561,23562,23570],{},[895,23563,23564],{},[2597,23565,23566,23568],{},[898,23567,4049],{},[898,23569,5502],{},[902,23571,23572],{"encoding":904},"T^E",[883,23574,23576],{"className":23575},[886],[888,23577,23578],{"xmlns":890},[892,23579,23580,23590],{},[895,23581,23582],{},[1935,23583,23584,23586,23588],{},[898,23585,10375],{},[898,23587,2838],{},[898,23589,5502],{},[902,23591,23592],{"encoding":904},"Y_D^E",[883,23594,23596],{"className":23595},[886],[888,23597,23598],{"xmlns":890},[892,23599,23600,23608],{},[895,23601,23602],{},[2597,23603,23604,23606],{},[898,23605,4052],{},[898,23607,5502],{},[902,23609,15087],{"encoding":904},[883,23611,23613],{"className":23612},[886],[888,23614,23615],{"xmlns":890},[892,23616,23617,23625],{},[895,23618,23619],{},[2597,23620,23621,23623],{},[898,23622,9920],{},[898,23624,5502],{},[902,23626,23627],{"encoding":904},"S^E",[198,23629,23631],{"id":23630},"příklad-74","Příklad 7.4",[724,23633,22147,23634,23655,23656,1343,23687,1343,23711,1343,23733,23755],{},[883,23635,23637],{"className":23636},[886],[888,23638,23639],{"xmlns":890},[892,23640,23641,23653],{},[895,23642,23643,23645,23647,23649,23651],{},[898,23644,4052],{},[2031,23646,13415],{},[898,23648,13309],{},[2031,23650,13415],{},[898,23652,13237],{},[902,23654,19346],{"encoding":904}," jsou dány ",[883,23657,23659],{"className":23658},[886],[888,23660,23661],{"xmlns":890},[892,23662,23663,23684],{},[895,23664,23665,23667,23669,23672,23674,23680,23682],{},[898,23666,4052],{},[1655,23668,1657],{},[1826,23670,23671],{},"0,9",[2031,23673,2435],{},[1820,23675,23676,23678],{},[898,23677,10375],{},[898,23679,2838],{},[1655,23681,2346],{},[1826,23683,7144],{},[902,23685,23686],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,23688,23690],{"className":23689},[886],[888,23691,23692],{"xmlns":890},[892,23693,23694,23708],{},[895,23695,23696,23698,23700,23702,23704,23706],{},[898,23697,4049],{},[1655,23699,1657],{},[1826,23701,4112],{},[898,23703,10375],{},[1655,23705,2346],{},[1826,23707,6253],{},[902,23709,23710],{"encoding":904},"T = 0{,}2Y + 25",[883,23712,23714],{"className":23713},[886],[888,23715,23716],{"xmlns":890},[892,23717,23718,23730],{},[895,23719,23720,23726,23728],{},[2597,23721,23722,23724],{},[898,23723,13309],{},[1655,23725,5603],{},[1655,23727,1657],{},[1826,23729,16163],{},[902,23731,23732],{"encoding":904},"I^* = 35",[883,23734,23736],{"className":23735},[886],[888,23737,23738],{"xmlns":890},[892,23739,23740,23752],{},[895,23741,23742,23748,23750],{},[2597,23743,23744,23746],{},[898,23745,13237],{},[1655,23747,5603],{},[1655,23749,1657],{},[1826,23751,10282],{},[902,23753,23754],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,23757,23758],{},[883,23759,23761],{"className":23760},[886],[888,23762,23763],{"xmlns":890},[892,23764,23765,23889],{},[21880,23766,23767,23797,23825,23859],{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},[21885,23768,23769,23775],{},[21888,23770,23771],{},[3615,23772,23773],{"scriptlevel":2552,"displaystyle":1670},[898,23774,10375],{},[21888,23776,23777],{},[3615,23778,23779],{"scriptlevel":2552,"displaystyle":1670},[895,23780,23781,23783,23785,23787,23789,23791,23793,23795],{},[895,23782],{},[1655,23784,1657],{},[898,23786,4052],{},[1655,23788,2346],{},[1826,23790,16163],{},[1655,23792,2346],{},[1826,23794,10282],{},[1655,23796,1671],{"separator":1670},[21885,23798,23799,23805],{},[21888,23800,23801],{},[3615,23802,23803],{"scriptlevel":2552,"displaystyle":1670},[898,23804,4049],{},[21888,23806,23807],{},[3615,23808,23809],{"scriptlevel":2552,"displaystyle":1670},[895,23810,23811,23813,23815,23817,23819,23821,23823],{},[895,23812],{},[1655,23814,1657],{},[1826,23816,4112],{},[898,23818,10375],{},[1655,23820,2346],{},[1826,23822,6253],{},[1655,23824,1671],{"separator":1670},[21885,23826,23827,23833],{},[21888,23828,23829],{},[3615,23830,23831],{"scriptlevel":2552,"displaystyle":1670},[898,23832,4052],{},[21888,23834,23835],{},[3615,23836,23837],{"scriptlevel":2552,"displaystyle":1670},[895,23838,23839,23841,23843,23845,23847,23853,23855,23857],{},[895,23840],{},[1655,23842,1657],{},[1826,23844,23671],{},[2031,23846,2435],{},[1820,23848,23849,23851],{},[898,23850,10375],{},[898,23852,2838],{},[1655,23854,2346],{},[1826,23856,7144],{},[1655,23858,1671],{"separator":1670},[21885,23860,23861,23871],{},[21888,23862,23863],{},[3615,23864,23865],{"scriptlevel":2552,"displaystyle":1670},[1820,23866,23867,23869],{},[898,23868,10375],{},[898,23870,2838],{},[21888,23872,23873],{},[3615,23874,23875],{"scriptlevel":2552,"displaystyle":1670},[895,23876,23877,23879,23881,23883,23885,23887],{},[895,23878],{},[1655,23880,1657],{},[898,23882,10375],{},[1655,23884,2623],{},[898,23886,4049],{},[898,23888,1719],{"mathvariant":1943},[902,23890,23891],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,23893,23894,23897,23898,23952,23953,23999,24000,2086],{},[38,23895,23896],{},"Řešení."," Z definice ",[883,23899,23901],{"className":23900},[886],[888,23902,23903],{"xmlns":890},[892,23904,23905,23949],{},[895,23906,23907,23913,23915,23917,23919,23921,23923,23925,23927,23929,23931,23933,23935,23937,23939,23941,23943,23945,23947],{},[1820,23908,23909,23911],{},[898,23910,10375],{},[898,23912,2838],{},[1655,23914,1657],{},[898,23916,10375],{},[1655,23918,2623],{},[898,23920,4049],{},[1655,23922,1657],{},[898,23924,10375],{},[1655,23926,2623],{},[1655,23928,1664],{"stretchy":1663},[1826,23930,4112],{},[898,23932,10375],{},[1655,23934,2346],{},[1826,23936,6253],{},[1655,23938,1677],{"stretchy":1663},[1655,23940,1657],{},[1826,23942,15714],{},[898,23944,10375],{},[1655,23946,2623],{},[1826,23948,6253],{},[902,23950,23951],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,23954,23956],{"className":23955},[886],[888,23957,23958],{"xmlns":890},[892,23959,23960,23996],{},[895,23961,23962,23964,23966,23968,23970,23972,23974,23976,23978,23980,23982,23984,23986,23989,23991,23993],{},[898,23963,4052],{},[1655,23965,1657],{},[1826,23967,23671],{},[1655,23969,1664],{"stretchy":1663},[1826,23971,15714],{},[898,23973,10375],{},[1655,23975,2623],{},[1826,23977,6253],{},[1655,23979,1677],{"stretchy":1663},[1655,23981,2346],{},[1826,23983,7144],{},[1655,23985,1657],{},[1826,23987,23988],{},"0,72",[898,23990,10375],{},[1655,23992,2346],{},[1826,23994,23995],{},"47,5",[902,23997,23998],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,24001,24003],{"className":24002},[886],[888,24004,24005],{"xmlns":890},[892,24006,24007,24025],{},[895,24008,24009,24011,24013,24015,24017,24019,24021,24023],{},[898,24010,10375],{},[1655,24012,1657],{},[1826,24014,23988],{},[898,24016,10375],{},[1655,24018,2346],{},[1826,24020,23995],{},[1655,24022,2346],{},[1826,24024,22306],{},[902,24026,24027],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,24029,24030],{},[883,24031,24033],{"className":24032},[886],[888,24034,24035],{"xmlns":890},[892,24036,24037,24078],{},[895,24038,24039,24042,24044,24046,24049,24051,24053,24055,24061,24063,24073,24075],{},[1826,24040,24041],{},"0,28",[898,24043,10375],{},[1655,24045,1657],{},[1826,24047,24048],{},"102,5",[2031,24050,2783],{},[1655,24052,16133],{},[2031,24054,2783],{},[2597,24056,24057,24059],{},[898,24058,10375],{},[898,24060,5502],{},[1655,24062,1657],{},[3615,24064,24065],{"scriptlevel":2552,"displaystyle":1663},[1949,24066,24067,24070],{},[1826,24068,24069],{},"5125",[1826,24071,24072],{},"14",[1655,24074,7147],{},[1826,24076,24077],{},"366,071.",[902,24079,24080],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,24082,24083],{},"Rovnovážné veličiny:",[120,24085,24086,24121,24173,24227,24275],{},[123,24087,24088,1671],{},[883,24089,24091],{"className":24090},[886],[888,24092,24093],{"xmlns":890},[892,24094,24095,24118],{},[895,24096,24097,24103,24105,24113,24115],{},[2597,24098,24099,24101],{},[898,24100,10375],{},[898,24102,5502],{},[1655,24104,1657],{},[3615,24106,24107],{"scriptlevel":2552,"displaystyle":1663},[1949,24108,24109,24111],{},[1826,24110,24069],{},[1826,24112,24072],{},[1655,24114,7147],{},[1826,24116,24117],{},"366,071",[902,24119,24120],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,24122,24123,1671],{},[883,24124,24126],{"className":24125},[886],[888,24127,24128],{"xmlns":890},[892,24129,24130,24170],{},[895,24131,24132,24138,24140,24142,24144,24150,24152,24154,24156,24165,24167],{},[2597,24133,24134,24136],{},[898,24135,4049],{},[898,24137,5502],{},[1655,24139,1657],{},[1826,24141,4112],{},[2031,24143,2435],{},[2597,24145,24146,24148],{},[898,24147,10375],{},[898,24149,5502],{},[1655,24151,2346],{},[1826,24153,6253],{},[1655,24155,1657],{},[3615,24157,24158],{"scriptlevel":2552,"displaystyle":1663},[1949,24159,24160,24163],{},[1826,24161,24162],{},"1375",[1826,24164,24072],{},[1655,24166,7147],{},[1826,24168,24169],{},"98,214",[902,24171,24172],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,24174,24175,1671],{},[883,24176,24178],{"className":24177},[886],[888,24179,24180],{"xmlns":890},[892,24181,24182,24224],{},[895,24183,24184,24192,24194,24200,24202,24208,24210,24219,24221],{},[1935,24185,24186,24188,24190],{},[898,24187,10375],{},[898,24189,2838],{},[898,24191,5502],{},[1655,24193,1657],{},[2597,24195,24196,24198],{},[898,24197,10375],{},[898,24199,5502],{},[1655,24201,2623],{},[2597,24203,24204,24206],{},[898,24205,4049],{},[898,24207,5502],{},[1655,24209,1657],{},[3615,24211,24212],{"scriptlevel":2552,"displaystyle":1663},[1949,24213,24214,24217],{},[1826,24215,24216],{},"3750",[1826,24218,24072],{},[1655,24220,7147],{},[1826,24222,24223],{},"267,857",[902,24225,24226],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,24228,24229,1671],{},[883,24230,24232],{"className":24231},[886],[888,24233,24234],{"xmlns":890},[892,24235,24236,24272],{},[895,24237,24238,24244,24246,24252,24254,24256,24258,24267,24269],{},[2597,24239,24240,24242],{},[898,24241,4052],{},[898,24243,5502],{},[1655,24245,1657],{},[2597,24247,24248,24250],{},[898,24249,10375],{},[898,24251,5502],{},[1655,24253,2623],{},[1826,24255,22306],{},[1655,24257,1657],{},[3615,24259,24260],{"scriptlevel":2552,"displaystyle":1663},[1949,24261,24262,24265],{},[1826,24263,24264],{},"4355",[1826,24266,24072],{},[1655,24268,7147],{},[1826,24270,24271],{},"311,071",[902,24273,24274],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,24276,24277,24333],{},[883,24278,24280],{"className":24279},[886],[888,24281,24282],{"xmlns":890},[892,24283,24284,24330],{},[895,24285,24286,24292,24294,24302,24304,24310,24312,24314,24323,24325,24327],{},[2597,24287,24288,24290],{},[898,24289,9920],{},[898,24291,5502],{},[1655,24293,1657],{},[1935,24295,24296,24298,24300],{},[898,24297,10375],{},[898,24299,2838],{},[898,24301,5502],{},[1655,24303,2623],{},[2597,24305,24306,24308],{},[898,24307,4052],{},[898,24309,5502],{},[1655,24311,1657],{},[1655,24313,2623],{},[3615,24315,24316],{"scriptlevel":2552,"displaystyle":1663},[1949,24317,24318,24321],{},[1826,24319,24320],{},"605",[1826,24322,24072],{},[1655,24324,7147],{},[1655,24326,2623],{},[1826,24328,24329],{},"43,214",[902,24331,24332],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,24335,24336,22476,24338,24359,24360,24363,24364,24387,24388,1719],{},[38,24337,22475],{},[883,24339,24341],{"className":24340},[886],[888,24342,24343],{"xmlns":890},[892,24344,24345,24357],{},[895,24346,24347,24349,24351,24353,24355],{},[898,24348,4052],{},[2031,24350,13415],{},[898,24352,13309],{},[2031,24354,13415],{},[898,24356,13237],{},[902,24358,19346],{"encoding":904}," stále uvažuje ",[38,24361,24362],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,24365,24367],{"className":24366},[886],[888,24368,24369],{"xmlns":890},[892,24370,24371,24384],{},[895,24372,24373,24375,24377,24380,24382],{},[898,24374,13445],{},[1655,24376,1657],{},[898,24378,24379],{},"B",[1655,24381,2623],{},[898,24383,2127],{},[902,24385,24386],{"encoding":904},"X = B - M"," dává ",[38,24389,22497,24390],{},[883,24391,24393],{"className":24392},[886],[888,24394,24395],{"xmlns":890},[892,24396,24397,24413],{},[895,24398,24399,24401,24403,24405,24407,24409,24411],{},[898,24400,4052],{},[2031,24402,13415],{},[898,24404,13309],{},[2031,24406,13415],{},[898,24408,13237],{},[2031,24410,13415],{},[898,24412,13445],{},[902,24414,13448],{"encoding":904},[115,24416,24418],{"id":24417},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,24420,21747],{"id":24421},"zadání-modelu-2",[724,24423,24424,24425,3106,24428,22720,24449,24462,24463,13253,24466,24479],{},"Rozšíření o ",[38,24426,24427],{},"čistý export",[883,24429,24431],{"className":24430},[886],[888,24432,24433],{"xmlns":890},[892,24434,24435,24447],{},[895,24436,24437,24439,24441,24443,24445],{},[898,24438,13445],{},[1655,24440,1657],{},[898,24442,24379],{},[1655,24444,2623],{},[898,24446,2127],{},[902,24448,24386],{"encoding":904},[883,24450,24452],{"className":24451},[886],[888,24453,24454],{"xmlns":890},[892,24455,24456,24460],{},[895,24457,24458],{},[898,24459,24379],{},[902,24461,24379],{"encoding":904}," je hrubý export (",[614,24464,24465],{},"brutto export",[883,24467,24469],{"className":24468},[886],[888,24470,24471],{"xmlns":890},[892,24472,24473,24477],{},[895,24474,24475],{},[898,24476,2127],{},[902,24478,2127],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,24481,24482],{},[883,24483,24485],{"className":24484},[886],[888,24486,24487],{"xmlns":890},[892,24488,24489,24509],{},[895,24490,24491,24493,24495,24497,24499,24505,24507],{},[898,24492,2127],{},[1655,24494,1657],{},[898,24496,2127],{},[1655,24498,1664],{"stretchy":1663},[1820,24500,24501,24503],{},[898,24502,10375],{},[898,24504,2838],{},[1655,24506,1677],{"stretchy":1663},[898,24508,1719],{"mathvariant":1943},[902,24510,24511],{"encoding":904},"M = M(Y_D).",[724,24513,24514],{},"Podmínka rovnováhy:",[724,24516,24517],{},[883,24518,24520],{"className":24519},[886],[888,24521,24522],{"xmlns":890},[892,24523,24524,24561],{},[895,24525,24526,24528,24530,24532,24534,24536,24538,24540,24542,24544,24546,24548,24550,24552,24554,24557,24559],{},[898,24527,10375],{},[1655,24529,1657],{},[898,24531,4052],{},[1655,24533,2346],{},[898,24535,13309],{},[1655,24537,2346],{},[898,24539,13237],{},[1655,24541,2346],{},[898,24543,24379],{},[1655,24545,2623],{},[898,24547,2127],{},[898,24549,1719],{"mathvariant":1943},[1967,24551],{"width":1969},[1655,24553,1664],{"stretchy":1663},[1826,24555,24556],{},"7.10",[2031,24558,207],{},[1655,24560,1677],{"stretchy":1663},[902,24562,24563],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,24565,21817],{"id":24566},"soustava-rovnic-2",[724,24568,22977,24569,24603,24604,2086],{},[883,24570,24572],{"className":24571},[886],[888,24573,24574],{"xmlns":890},[892,24575,24576,24600],{},[895,24577,24578,24584,24586,24592,24594],{},[2597,24579,24580,24582],{},[898,24581,13309],{},[1655,24583,5603],{},[1655,24585,1671],{"separator":1670},[2597,24587,24588,24590],{},[898,24589,13237],{},[1655,24591,5603],{},[1655,24593,1671],{"separator":1670},[2597,24595,24596,24598],{},[898,24597,24379],{},[1655,24599,5603],{},[902,24601,24602],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,24605,24607],{"className":24606},[886],[888,24608,24609],{"xmlns":890},[892,24610,24611,24635],{},[895,24612,24613,24615,24617,24619,24621,24623,24625,24631,24633],{},[898,24614,10375],{},[1655,24616,1671],{"separator":1670},[898,24618,4052],{},[1655,24620,1671],{"separator":1670},[898,24622,4049],{},[1655,24624,1671],{"separator":1670},[1820,24626,24627,24629],{},[898,24628,10375],{},[898,24630,2838],{},[1655,24632,1671],{"separator":1670},[898,24634,2127],{},[902,24636,24637],{"encoding":904},"Y, C, T, Y_D, M",[724,24639,24640],{},[883,24641,24643],{"className":24642},[886],[888,24644,24645],{"xmlns":890},[892,24646,24647,24831],{},[895,24648,24649,24823,24825,24827,24829],{},[21880,24650,24651,24683,24713,24741,24773],{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},[21885,24652,24653,24659],{},[21888,24654,24655],{},[3615,24656,24657],{"scriptlevel":2552,"displaystyle":1670},[898,24658,4052],{},[21888,24660,24661],{},[3615,24662,24663],{"scriptlevel":2552,"displaystyle":1670},[895,24664,24665,24667,24669,24671,24673,24679,24681],{},[895,24666],{},[1655,24668,1657],{},[898,24670,4052],{},[1655,24672,1664],{"stretchy":1663},[1820,24674,24675,24677],{},[898,24676,10375],{},[898,24678,2838],{},[1655,24680,1677],{"stretchy":1663},[1655,24682,1671],{"separator":1670},[21885,24684,24685,24695],{},[21888,24686,24687],{},[3615,24688,24689],{"scriptlevel":2552,"displaystyle":1670},[1820,24690,24691,24693],{},[898,24692,10375],{},[898,24694,2838],{},[21888,24696,24697],{},[3615,24698,24699],{"scriptlevel":2552,"displaystyle":1670},[895,24700,24701,24703,24705,24707,24709,24711],{},[895,24702],{},[1655,24704,1657],{},[898,24706,10375],{},[1655,24708,2623],{},[898,24710,4049],{},[1655,24712,1671],{"separator":1670},[21885,24714,24715,24721],{},[21888,24716,24717],{},[3615,24718,24719],{"scriptlevel":2552,"displaystyle":1670},[898,24720,4049],{},[21888,24722,24723],{},[3615,24724,24725],{"scriptlevel":2552,"displaystyle":1670},[895,24726,24727,24729,24731,24733,24735,24737,24739],{},[895,24728],{},[1655,24730,1657],{},[898,24732,4049],{},[1655,24734,1664],{"stretchy":1663},[898,24736,10375],{},[1655,24738,1677],{"stretchy":1663},[1655,24740,1671],{"separator":1670},[21885,24742,24743,24749],{},[21888,24744,24745],{},[3615,24746,24747],{"scriptlevel":2552,"displaystyle":1670},[898,24748,2127],{},[21888,24750,24751],{},[3615,24752,24753],{"scriptlevel":2552,"displaystyle":1670},[895,24754,24755,24757,24759,24761,24763,24769,24771],{},[895,24756],{},[1655,24758,1657],{},[898,24760,2127],{},[1655,24762,1664],{"stretchy":1663},[1820,24764,24765,24767],{},[898,24766,10375],{},[898,24768,2838],{},[1655,24770,1677],{"stretchy":1663},[1655,24772,1671],{"separator":1670},[21885,24774,24775,24781],{},[21888,24776,24777],{},[3615,24778,24779],{"scriptlevel":2552,"displaystyle":1670},[898,24780,10375],{},[21888,24782,24783],{},[3615,24784,24785],{"scriptlevel":2552,"displaystyle":1670},[895,24786,24787,24789,24791,24793,24795,24801,24803,24809,24811,24817,24819,24821],{},[895,24788],{},[1655,24790,1657],{},[898,24792,4052],{},[1655,24794,2346],{},[2597,24796,24797,24799],{},[898,24798,13309],{},[1655,24800,5603],{},[1655,24802,2346],{},[2597,24804,24805,24807],{},[898,24806,13237],{},[1655,24808,5603],{},[1655,24810,2346],{},[2597,24812,24813,24815],{},[898,24814,24379],{},[1655,24816,5603],{},[1655,24818,2623],{},[898,24820,2127],{},[898,24822,1719],{"mathvariant":1943},[1967,24824],{"width":1969},[1655,24826,1664],{"stretchy":1663},[1826,24828,24556],{},[1655,24830,1677],{"stretchy":1663},[902,24832,24833],{"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)",[198,24835,24837],{"id":24836},"příklad-75","Příklad 7.5",[724,24839,24840,24841,1343,24873,1343,24900,1343,24921,1343,24943,1343,24965,24988],{},"Dáno: ",[883,24842,24844],{"className":24843},[886],[888,24845,24846],{"xmlns":890},[892,24847,24848,24870],{},[895,24849,24850,24852,24854,24857,24859,24865,24867],{},[898,24851,4052],{},[1655,24853,1657],{},[1826,24855,24856],{},"0,75",[2031,24858,2435],{},[1820,24860,24861,24863],{},[898,24862,10375],{},[898,24864,2838],{},[1655,24866,2346],{},[1826,24868,24869],{},"750",[902,24871,24872],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,24874,24876],{"className":24875},[886],[888,24877,24878],{"xmlns":890},[892,24879,24880,24897],{},[895,24881,24882,24884,24886,24889,24891],{},[898,24883,2127],{},[1655,24885,1657],{},[1826,24887,24888],{},"0,15",[2031,24890,2435],{},[1820,24892,24893,24895],{},[898,24894,10375],{},[898,24896,2838],{},[902,24898,24899],{"encoding":904},"M = 0{,}15\\,Y_D",[883,24901,24903],{"className":24902},[886],[888,24904,24905],{"xmlns":890},[892,24906,24907,24918],{},[895,24908,24909,24911,24913,24916],{},[898,24910,4049],{},[1655,24912,1657],{},[1826,24914,24915],{},"0,25",[898,24917,10375],{},[902,24919,24920],{"encoding":904},"T = 0{,}25Y",[883,24922,24924],{"className":24923},[886],[888,24925,24926],{"xmlns":890},[892,24927,24928,24940],{},[895,24929,24930,24936,24938],{},[2597,24931,24932,24934],{},[898,24933,13309],{},[1655,24935,5603],{},[1655,24937,1657],{},[1826,24939,16235],{},[902,24941,24942],{"encoding":904},"I^* = 500",[883,24944,24946],{"className":24945},[886],[888,24947,24948],{"xmlns":890},[892,24949,24950,24962],{},[895,24951,24952,24958,24960],{},[2597,24953,24954,24956],{},[898,24955,13237],{},[1655,24957,5603],{},[1655,24959,1657],{},[1826,24961,10050],{},[902,24963,24964],{"encoding":904},"G^* = 150",[883,24966,24968],{"className":24967},[886],[888,24969,24970],{"xmlns":890},[892,24971,24972,24985],{},[895,24973,24974,24980,24982],{},[2597,24975,24976,24978],{},[898,24977,24379],{},[1655,24979,5603],{},[1655,24981,1657],{},[1826,24983,24984],{},"800",[902,24986,24987],{"encoding":904},"B^* = 800",". Soustava:",[724,24990,24991],{},[883,24992,24994],{"className":24993},[886],[888,24995,24996],{"xmlns":890},[892,24997,24998,25216],{},[21880,24999,25000,25046,25088,25124,25166],{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},[21885,25001,25002,25018],{},[21888,25003,25004],{},[3615,25005,25006],{"scriptlevel":2552,"displaystyle":1670},[895,25007,25008,25010,25012,25014,25016],{},[1655,25009,1664],{"stretchy":1663},[898,25011,13166],{},[1826,25013,1828],{},[1655,25015,1677],{"stretchy":1663},[2031,25017,2033],{},[21888,25019,25020],{},[3615,25021,25022],{"scriptlevel":2552,"displaystyle":1670},[895,25023,25024,25026,25028,25030,25032,25034,25040,25042,25044],{},[895,25025],{},[898,25027,4052],{},[1655,25029,1657],{},[1826,25031,24856],{},[2031,25033,2435],{},[1820,25035,25036,25038],{},[898,25037,10375],{},[898,25039,2838],{},[1655,25041,2346],{},[1826,25043,24869],{},[1655,25045,1671],{"separator":1670},[21885,25047,25048,25064],{},[21888,25049,25050],{},[3615,25051,25052],{"scriptlevel":2552,"displaystyle":1670},[895,25053,25054,25056,25058,25060,25062],{},[1655,25055,1664],{"stretchy":1663},[898,25057,13166],{},[1826,25059,1837],{},[1655,25061,1677],{"stretchy":1663},[2031,25063,2033],{},[21888,25065,25066],{},[3615,25067,25068],{"scriptlevel":2552,"displaystyle":1670},[895,25069,25070,25072,25078,25080,25082,25084,25086],{},[895,25071],{},[1820,25073,25074,25076],{},[898,25075,10375],{},[898,25077,2838],{},[1655,25079,1657],{},[898,25081,10375],{},[1655,25083,2623],{},[898,25085,4049],{},[1655,25087,1671],{"separator":1670},[21885,25089,25090,25106],{},[21888,25091,25092],{},[3615,25093,25094],{"scriptlevel":2552,"displaystyle":1670},[895,25095,25096,25098,25100,25102,25104],{},[1655,25097,1664],{"stretchy":1663},[898,25099,13166],{},[1826,25101,3472],{},[1655,25103,1677],{"stretchy":1663},[2031,25105,2033],{},[21888,25107,25108],{},[3615,25109,25110],{"scriptlevel":2552,"displaystyle":1670},[895,25111,25112,25114,25116,25118,25120,25122],{},[895,25113],{},[898,25115,4049],{},[1655,25117,1657],{},[1826,25119,24915],{},[898,25121,10375],{},[1655,25123,1671],{"separator":1670},[21885,25125,25126,25142],{},[21888,25127,25128],{},[3615,25129,25130],{"scriptlevel":2552,"displaystyle":1670},[895,25131,25132,25134,25136,25138,25140],{},[1655,25133,1664],{"stretchy":1663},[898,25135,13166],{},[1826,25137,3639],{},[1655,25139,1677],{"stretchy":1663},[2031,25141,2033],{},[21888,25143,25144],{},[3615,25145,25146],{"scriptlevel":2552,"displaystyle":1670},[895,25147,25148,25150,25152,25154,25156,25158,25164],{},[895,25149],{},[898,25151,2127],{},[1655,25153,1657],{},[1826,25155,24888],{},[2031,25157,2435],{},[1820,25159,25160,25162],{},[898,25161,10375],{},[898,25163,2838],{},[1655,25165,1671],{"separator":1670},[21885,25167,25168,25184],{},[21888,25169,25170],{},[3615,25171,25172],{"scriptlevel":2552,"displaystyle":1670},[895,25173,25174,25176,25178,25180,25182],{},[1655,25175,1664],{"stretchy":1663},[898,25177,13166],{},[1826,25179,3524],{},[1655,25181,1677],{"stretchy":1663},[2031,25183,2033],{},[21888,25185,25186],{},[3615,25187,25188],{"scriptlevel":2552,"displaystyle":1670},[895,25189,25190,25192,25194,25196,25198,25200,25202,25204,25206,25208,25210,25212,25214],{},[895,25191],{},[898,25193,10375],{},[1655,25195,1657],{},[898,25197,4052],{},[1655,25199,2346],{},[1826,25201,16235],{},[1655,25203,2346],{},[1826,25205,10050],{},[1655,25207,2346],{},[1826,25209,24984],{},[1655,25211,2623],{},[898,25213,2127],{},[898,25215,1719],{"mathvariant":1943},[902,25217,25218],{"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}",[724,25220,25221,25222,25256],{},"Postupná substituce — z (r3) do (r2): ",[883,25223,25225],{"className":25224},[886],[888,25226,25227],{"xmlns":890},[892,25228,25229,25253],{},[895,25230,25231,25237,25239,25241,25243,25245,25247,25249,25251],{},[1820,25232,25233,25235],{},[898,25234,10375],{},[898,25236,2838],{},[1655,25238,1657],{},[898,25240,10375],{},[1655,25242,2623],{},[1826,25244,24915],{},[898,25246,10375],{},[1655,25248,1657],{},[1826,25250,24856],{},[898,25252,10375],{},[902,25254,25255],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,25258,25259],{},[883,25260,25262],{"className":25261},[886],[888,25263,25264],{"xmlns":890},[892,25265,25266,25307],{},[895,25267,25268,25270,25272,25274,25276,25278,25280,25282,25284,25286,25288,25290,25292,25294,25296,25299,25301,25303,25305],{},[1655,25269,1664],{"stretchy":1663},[898,25271,13166],{},[1826,25273,3531],{},[1655,25275,1677],{"stretchy":1663},[2031,25277,2033],{},[898,25279,4052],{},[1655,25281,1657],{},[1826,25283,24856],{},[1655,25285,2869],{},[1826,25287,24856],{},[898,25289,10375],{},[1655,25291,2346],{},[1826,25293,24869],{},[1655,25295,1657],{},[1826,25297,25298],{},"0,5625",[898,25300,10375],{},[1655,25302,2346],{},[1826,25304,24869],{},[1655,25306,1671],{"separator":1670},[902,25308,25309],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,25311,25312],{},[883,25313,25315],{"className":25314},[886],[888,25316,25317],{"xmlns":890},[892,25318,25319,25353],{},[895,25320,25321,25323,25325,25328,25330,25332,25334,25336,25338,25340,25342,25344,25346,25349,25351],{},[1655,25322,1664],{"stretchy":1663},[898,25324,13166],{},[1826,25326,25327],{},"7",[1655,25329,1677],{"stretchy":1663},[2031,25331,2033],{},[898,25333,2127],{},[1655,25335,1657],{},[1826,25337,24888],{},[1655,25339,2869],{},[1826,25341,24856],{},[898,25343,10375],{},[1655,25345,1657],{},[1826,25347,25348],{},"0,1125",[898,25350,10375],{},[898,25352,1719],{"mathvariant":1943},[902,25354,25355],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,25357,25358],{},"Dosazením do (r5):",[724,25360,25361],{},[883,25362,25364],{"className":25363},[886],[888,25365,25366],{"xmlns":890},[892,25367,25368,25412],{},[895,25369,25370,25372,25374,25376,25378,25380,25382,25384,25386,25388,25390,25392,25394,25396,25398,25400,25402,25405,25407,25409],{},[898,25371,10375],{},[1655,25373,1657],{},[1826,25375,25298],{},[898,25377,10375],{},[1655,25379,2346],{},[1826,25381,24869],{},[1655,25383,2346],{},[1826,25385,16235],{},[1655,25387,2346],{},[1826,25389,10050],{},[1655,25391,2346],{},[1826,25393,24984],{},[1655,25395,2623],{},[1826,25397,25348],{},[898,25399,10375],{},[1655,25401,1657],{},[1826,25403,25404],{},"0,45",[898,25406,10375],{},[1655,25408,2346],{},[1826,25410,25411],{},"2200.",[902,25413,25414],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,25416,25417,25418,6838,25440,25463],{},"Odtud ",[883,25419,25421],{"className":25420},[886],[888,25422,25423],{"xmlns":890},[892,25424,25425,25437],{},[895,25426,25427,25430,25432,25434],{},[1826,25428,25429],{},"0,55",[898,25431,10375],{},[1655,25433,1657],{},[1826,25435,25436],{},"2200",[902,25438,25439],{"encoding":904},"0{,}55Y = 2200",[883,25441,25443],{"className":25442},[886],[888,25444,25445],{"xmlns":890},[892,25446,25447,25460],{},[895,25448,25449,25455,25457],{},[2597,25450,25451,25453],{},[898,25452,10375],{},[898,25454,5502],{},[1655,25456,1657],{},[1826,25458,25459],{},"4000",[902,25461,25462],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,25465,25466,25489,25521,25556,25589,25625],{},[123,25467,25468,1671],{},[883,25469,25471],{"className":25470},[886],[888,25472,25473],{"xmlns":890},[892,25474,25475,25487],{},[895,25476,25477,25483,25485],{},[2597,25478,25479,25481],{},[898,25480,10375],{},[898,25482,5502],{},[1655,25484,1657],{},[1826,25486,25459],{},[902,25488,25462],{"encoding":904},[123,25490,25491,1671],{},[883,25492,25494],{"className":25493},[886],[888,25495,25496],{"xmlns":890},[892,25497,25498,25518],{},[895,25499,25500,25506,25508,25510,25512,25514,25516],{},[2597,25501,25502,25504],{},[898,25503,4049],{},[898,25505,5502],{},[1655,25507,1657],{},[1826,25509,24915],{},[1655,25511,2869],{},[1826,25513,25459],{},[1655,25515,1657],{},[1826,25517,4057],{},[902,25519,25520],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,25522,25523,1671],{},[883,25524,25526],{"className":25525},[886],[888,25527,25528],{"xmlns":890},[892,25529,25530,25553],{},[895,25531,25532,25540,25542,25544,25546,25548,25550],{},[1935,25533,25534,25536,25538],{},[898,25535,10375],{},[898,25537,2838],{},[898,25539,5502],{},[1655,25541,1657],{},[1826,25543,24856],{},[1655,25545,2869],{},[1826,25547,25459],{},[1655,25549,1657],{},[1826,25551,25552],{},"3000",[902,25554,25555],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,25557,25558,1671],{},[883,25559,25561],{"className":25560},[886],[888,25562,25563],{"xmlns":890},[892,25564,25565,25586],{},[895,25566,25567,25573,25575,25577,25579,25581,25583],{},[2597,25568,25569,25571],{},[898,25570,2127],{},[898,25572,5502],{},[1655,25574,1657],{},[1826,25576,24888],{},[1655,25578,2869],{},[1826,25580,25552],{},[1655,25582,1657],{},[1826,25584,25585],{},"450",[902,25587,25588],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,25590,25591,1671],{},[883,25592,25594],{"className":25593},[886],[888,25595,25596],{"xmlns":890},[892,25597,25598,25622],{},[895,25599,25600,25606,25608,25610,25612,25614,25616,25618,25620],{},[2597,25601,25602,25604],{},[898,25603,4052],{},[898,25605,5502],{},[1655,25607,1657],{},[1826,25609,24856],{},[1655,25611,2869],{},[1826,25613,25552],{},[1655,25615,2346],{},[1826,25617,24869],{},[1655,25619,1657],{},[1826,25621,25552],{},[902,25623,25624],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,25626,25627,25667],{},[883,25628,25630],{"className":25629},[886],[888,25631,25632],{"xmlns":890},[892,25633,25634,25664],{},[895,25635,25636,25642,25644,25652,25654,25660,25662],{},[2597,25637,25638,25640],{},[898,25639,9920],{},[898,25641,5502],{},[1655,25643,1657],{},[1935,25645,25646,25648,25650],{},[898,25647,10375],{},[898,25649,2838],{},[898,25651,5502],{},[1655,25653,2623],{},[2597,25655,25656,25658],{},[898,25657,4052],{},[898,25659,5502],{},[1655,25661,1657],{},[1826,25663,2552],{},[902,25665,25666],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,25669,25670,25672,25673,1343,25690,2704,25711,25736,25737,25740,25741,25754,25755,1719],{},[38,25671,22475],{}," Modely ",[883,25674,25676],{"className":25675},[886],[888,25677,25678],{"xmlns":890},[892,25679,25680,25688],{},[895,25681,25682,25684,25686],{},[898,25683,4052],{},[2031,25685,13415],{},[898,25687,13309],{},[902,25689,13420],{"encoding":904},[883,25691,25693],{"className":25692},[886],[888,25694,25695],{"xmlns":890},[892,25696,25697,25709],{},[895,25698,25699,25701,25703,25705,25707],{},[898,25700,4052],{},[2031,25702,13415],{},[898,25704,13309],{},[2031,25706,13415],{},[898,25708,13237],{},[902,25710,19346],{"encoding":904},[883,25712,25714],{"className":25713},[886],[888,25715,25716],{"xmlns":890},[892,25717,25718,25734],{},[895,25719,25720,25722,25724,25726,25728,25730,25732],{},[898,25721,4052],{},[2031,25723,13415],{},[898,25725,13309],{},[2031,25727,13415],{},[898,25729,13237],{},[2031,25731,13415],{},[898,25733,13445],{},[902,25735,13448],{"encoding":904}," pokládají investice za ",[38,25738,25739],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,25742,25744],{"className":25743},[886],[888,25745,25746],{"xmlns":890},[892,25747,25748,25752],{},[895,25749,25750],{},[898,25751,13166],{},[902,25753,13166],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,25756,25757],{},"model IS-LM",[115,25759,25761],{"id":25760},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,25763,25764,25765,25769,25770,25773,25774,25777],{},"V článku ",[207,25766,25768],{"className":25767,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,25771,25772],{},"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 ",[38,25775,25776],{},"výraznější"," než v mikroekonomických modelech.",[724,25779,25780],{},[1723,25781],{"alt":25782,"className":25783,"src":25784},"imek-multiplikatorovy-efekt-chain",[210,1727],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,25786,13289,25787,1343,25804,1343,25825,25850,25851,25854,25855,25873,25874,25892,25893,25911,25912,25915,25916,1343,25933,25950,25951,25953],{},[883,25788,25790],{"className":25789},[886],[888,25791,25792],{"xmlns":890},[892,25793,25794,25802],{},[895,25795,25796,25798,25800],{},[898,25797,4052],{},[2031,25799,13415],{},[898,25801,13309],{},[902,25803,13420],{"encoding":904},[883,25805,25807],{"className":25806},[886],[888,25808,25809],{"xmlns":890},[892,25810,25811,25823],{},[895,25812,25813,25815,25817,25819,25821],{},[898,25814,4052],{},[2031,25816,13415],{},[898,25818,13309],{},[2031,25820,13415],{},[898,25822,13237],{},[902,25824,19346],{"encoding":904},[883,25826,25828],{"className":25827},[886],[888,25829,25830],{"xmlns":890},[892,25831,25832,25848],{},[895,25833,25834,25836,25838,25840,25842,25844,25846],{},[898,25835,4052],{},[2031,25837,13415],{},[898,25839,13309],{},[2031,25841,13415],{},[898,25843,13237],{},[2031,25845,13415],{},[898,25847,13445],{},[902,25849,13448],{"encoding":904}," se vyšetřuje vliv změn ",[38,25852,25853],{},"exogenních"," veličin (plánovaných investic ",[883,25856,25858],{"className":25857},[886],[888,25859,25860],{"xmlns":890},[892,25861,25862,25870],{},[895,25863,25864],{},[2597,25865,25866,25868],{},[898,25867,13309],{},[1655,25869,5603],{},[902,25871,25872],{"encoding":904},"I^*",", vládních výdajů ",[883,25875,25877],{"className":25876},[886],[888,25878,25879],{"xmlns":890},[892,25880,25881,25889],{},[895,25882,25883],{},[2597,25884,25885,25887],{},[898,25886,13237],{},[1655,25888,5603],{},[902,25890,25891],{"encoding":904},"G^*",", exportu ",[883,25894,25896],{"className":25895},[886],[888,25897,25898],{"xmlns":890},[892,25899,25900,25908],{},[895,25901,25902],{},[2597,25903,25904,25906],{},[898,25905,24379],{},[1655,25907,5603],{},[902,25909,25910],{"encoding":904},"B^*",") na změny ",[38,25913,25914],{},"endogenních"," rovnovážných veličin (",[883,25917,25919],{"className":25918},[886],[888,25920,25921],{"xmlns":890},[892,25922,25923,25931],{},[895,25924,25925],{},[2597,25926,25927,25929],{},[898,25928,10375],{},[898,25930,5502],{},[902,25932,15028],{"encoding":904},[883,25934,25936],{"className":25935},[886],[888,25937,25938],{"xmlns":890},[892,25939,25940,25948],{},[895,25941,25942],{},[2597,25943,25944,25946],{},[898,25945,4052],{},[898,25947,5502],{},[902,25949,15087],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,25952,19103],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,25955,25957],{"id":25956},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,25959,22021,25960,25983,25984,26028],{},[883,25961,25963],{"className":25962},[886],[888,25964,25965],{"xmlns":890},[892,25966,25967,25981],{},[895,25968,25969,25971,25973,25975,25977,25979],{},[898,25970,4052],{},[1655,25972,1657],{},[898,25974,207],{},[898,25976,10375],{},[1655,25978,2346],{},[898,25980,2025],{},[902,25982,20046],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,25985,25987],{"className":25986},[886],[888,25988,25989],{"xmlns":890},[892,25990,25991,26025],{},[895,25992,25993,25999,26001],{},[2597,25994,25995,25997],{},[898,25996,10375],{},[898,25998,5502],{},[1655,26000,1657],{},[3615,26002,26003],{"scriptlevel":2552,"displaystyle":1670},[1949,26004,26005,26017],{},[895,26006,26007,26009,26011],{},[898,26008,2025],{},[1655,26010,2346],{},[2597,26012,26013,26015],{},[898,26014,13309],{},[1655,26016,5603],{},[895,26018,26019,26021,26023],{},[1826,26020,1828],{},[1655,26022,2623],{},[898,26024,207],{},[902,26026,26027],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,26030,26031],{},[883,26032,26034],{"className":26033},[886],[888,26035,26036],{"xmlns":890},[892,26037,26038,26107],{},[895,26039,26040,26058,26060,26090,26092],{},[1949,26041,26042,26052],{},[895,26043,26044,26046],{},[898,26045,1955],{"mathvariant":1943},[2597,26047,26048,26050],{},[898,26049,10375],{},[898,26051,5502],{},[895,26053,26054,26056],{},[898,26055,1955],{"mathvariant":1943},[898,26057,207],{},[1655,26059,1657],{},[1949,26061,26062,26074],{},[895,26063,26064,26066,26068],{},[898,26065,2025],{},[1655,26067,2346],{},[2597,26069,26070,26072],{},[898,26071,13309],{},[1655,26073,5603],{},[895,26075,26076,26078,26080,26082,26084],{},[1655,26077,1664],{"stretchy":1663},[1826,26079,1828],{},[1655,26081,2623],{},[898,26083,207],{},[2597,26085,26086,26088],{},[1655,26087,1677],{"stretchy":1663},[1826,26089,1837],{},[1967,26091],{"width":1969},[895,26093,26094,26097,26104],{},[2031,26095,26096],{},"(multiplik",[9633,26098,26099,26101],{"accent":1670},[2031,26100,207],{},[1655,26102,26103],{},"ˊ",[2031,26105,26106],{},"tor MPC)",[902,26108,26109],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,26111,26112],{},[883,26113,26115],{"className":26114},[886],[888,26116,26117],{"xmlns":890},[892,26118,26119,26188],{},[895,26120,26121,26139,26141,26153,26155],{},[1949,26122,26123,26133],{},[895,26124,26125,26127],{},[898,26126,1955],{"mathvariant":1943},[2597,26128,26129,26131],{},[898,26130,10375],{},[898,26132,5502],{},[895,26134,26135,26137],{},[898,26136,1955],{"mathvariant":1943},[898,26138,2025],{},[1655,26140,1657],{},[1949,26142,26143,26145],{},[1826,26144,1828],{},[895,26146,26147,26149,26151],{},[1826,26148,1828],{},[1655,26150,2623],{},[898,26152,207],{},[1967,26154],{"width":1969},[895,26156,26157,26159,26165,26168,26175,26178,26185],{},[2031,26158,26096],{},[9633,26160,26161,26163],{"accent":1670},[2031,26162,207],{},[1655,26164,26103],{},[2031,26166,26167],{},"tor autonomn",[9633,26169,26170,26173],{"accent":1670},[2031,26171,26172],{},"ı",[1655,26174,26103],{},[2031,26176,26177],{}," spot",[9633,26179,26180,26182],{"accent":1670},[2031,26181,13166],{},[1655,26183,26184],{},"ˇ",[2031,26186,26187],{},"eby)",[902,26189,26190],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,26192,26193],{},[883,26194,26196],{"className":26195},[886],[888,26197,26198],{"xmlns":890},[892,26199,26200,26267],{},[895,26201,26202,26224,26226,26238,26240,26252,26254],{},[1949,26203,26204,26214],{},[895,26205,26206,26208],{},[898,26207,1955],{"mathvariant":1943},[2597,26209,26210,26212],{},[898,26211,10375],{},[898,26213,5502],{},[895,26215,26216,26218],{},[898,26217,1955],{"mathvariant":1943},[2597,26219,26220,26222],{},[898,26221,13309],{},[1655,26223,5603],{},[1655,26225,1657],{},[1949,26227,26228,26230],{},[1826,26229,1828],{},[895,26231,26232,26234,26236],{},[1826,26233,1828],{},[1655,26235,2623],{},[898,26237,207],{},[1655,26239,1657],{},[1949,26241,26242,26244],{},[1826,26243,1828],{},[895,26245,26246,26248,26250],{},[898,26247,2127],{},[898,26249,2132],{},[898,26251,9920],{},[1967,26253],{"width":1969},[895,26255,26256,26258,26264],{},[2031,26257,26096],{},[9633,26259,26260,26262],{"accent":1670},[2031,26261,207],{},[1655,26263,26103],{},[2031,26265,26266],{},"tor investic)",[902,26268,26269],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[5120,26271,26272],{},[724,26273,26274,26276,26277,26280,26281,26294,26295,26312,26313,26331,26332,26376,26377,22546,26394,26397,26398,26415],{},[883,26275,5406],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,26278,26279],{},"důchodem","; z něj se utratí ",[883,26282,26284],{"className":26283},[886],[888,26285,26286],{"xmlns":890},[892,26287,26288,26292],{},[895,26289,26290],{},[898,26291,207],{},[902,26293,207],{"encoding":904}," Kč (= ",[883,26296,26298],{"className":26297},[886],[888,26299,26300],{"xmlns":890},[892,26301,26302,26310],{},[895,26303,26304,26306,26308],{},[898,26305,2127],{},[898,26307,2132],{},[898,26309,4052],{},[902,26311,19171],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,26314,26316],{"className":26315},[886],[888,26317,26318],{"xmlns":890},[892,26319,26320,26328],{},[895,26321,26322],{},[2597,26323,26324,26326],{},[898,26325,207],{},[1826,26327,1837],{},[902,26329,26330],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,26333,26335],{"className":26334},[886],[888,26336,26337],{"xmlns":890},[892,26338,26339,26373],{},[895,26340,26341,26343,26345,26347,26349,26355,26357,26359,26361],{},[1826,26342,1828],{},[1655,26344,2346],{},[898,26346,207],{},[1655,26348,2346],{},[2597,26350,26351,26353],{},[898,26352,207],{},[1826,26354,1837],{},[1655,26356,2346],{},[1655,26358,19231],{},[1655,26360,1657],{},[1949,26362,26363,26365],{},[1826,26364,1828],{},[895,26366,26367,26369,26371],{},[1826,26368,1828],{},[1655,26370,2623],{},[898,26372,207],{},[902,26374,26375],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,26378,26380],{"className":26379},[886],[888,26381,26382],{"xmlns":890},[892,26383,26384,26392],{},[895,26385,26386],{},[2597,26387,26388,26390],{},[898,26389,10375],{},[898,26391,5502],{},[902,26393,15028],{"encoding":904},[38,26395,26396],{},"více"," než korunu — čím vyšší ",[883,26399,26401],{"className":26400},[886],[888,26402,26403],{"xmlns":890},[892,26404,26405,26413],{},[895,26406,26407,26409,26411],{},[898,26408,2127],{},[898,26410,2132],{},[898,26412,4052],{},[902,26414,19171],{"encoding":904},", tím silnější multiplikační efekt.",[724,26417,26418,26421,26422,26448,26449,26452,26453,2704,26474,26499,26500,1719],{},[38,26419,26420],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,26423,26425],{"className":26424},[886],[888,26426,26427],{"xmlns":890},[892,26428,26429,26445],{},[895,26430,26431],{},[3615,26432,26433],{"scriptlevel":2552,"displaystyle":1663},[1949,26434,26435,26437],{},[1826,26436,1828],{},[895,26438,26439,26441,26443],{},[1826,26440,1828],{},[1655,26442,2623],{},[898,26444,207],{},[902,26446,26447],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,26450,26451],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,26454,26456],{"className":26455},[886],[888,26457,26458],{"xmlns":890},[892,26459,26460,26472],{},[895,26461,26462,26464,26466,26468,26470],{},[898,26463,4052],{},[2031,26465,13415],{},[898,26467,13309],{},[2031,26469,13415],{},[898,26471,13237],{},[902,26473,19346],{"encoding":904},[883,26475,26477],{"className":26476},[886],[888,26478,26479],{"xmlns":890},[892,26480,26481,26497],{},[895,26482,26483,26485,26487,26489,26491,26493,26495],{},[898,26484,4052],{},[2031,26486,13415],{},[898,26488,13309],{},[2031,26490,13415],{},[898,26492,13237],{},[2031,26494,13415],{},[898,26496,13445],{},[902,26498,13448],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,26501,26503],{"className":26502,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,26505,26507],{"id":26506},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,26509,13289,26510,1343,26527,2704,26548,13294,26573,2115,26576,26597,26598,3106,26601,26614,26615,6918,26644,26661,26662,26665,26666,26668,26669,26690],{},[883,26511,26513],{"className":26512},[886],[888,26514,26515],{"xmlns":890},[892,26516,26517,26525],{},[895,26518,26519,26521,26523],{},[898,26520,4052],{},[2031,26522,13415],{},[898,26524,13309],{},[902,26526,13420],{"encoding":904},[883,26528,26530],{"className":26529},[886],[888,26531,26532],{"xmlns":890},[892,26533,26534,26546],{},[895,26535,26536,26538,26540,26542,26544],{},[898,26537,4052],{},[2031,26539,13415],{},[898,26541,13309],{},[2031,26543,13415],{},[898,26545,13237],{},[902,26547,19346],{"encoding":904},[883,26549,26551],{"className":26550},[886],[888,26552,26553],{"xmlns":890},[892,26554,26555,26571],{},[895,26556,26557,26559,26561,26563,26565,26567,26569],{},[898,26558,4052],{},[2031,26560,13415],{},[898,26562,13309],{},[2031,26564,13415],{},[898,26566,13237],{},[2031,26568,13415],{},[898,26570,13445],{},[902,26572,13448],{"encoding":904},[38,26574,26575],{},"investice konstantní",[883,26577,26579],{"className":26578},[886],[888,26580,26581],{"xmlns":890},[892,26582,26583,26595],{},[895,26584,26585,26587,26589],{},[898,26586,13309],{},[1655,26588,1657],{},[2597,26590,26591,26593],{},[898,26592,13309],{},[1655,26594,5603],{},[902,26596,13320],{"encoding":904},"). Reálnější je předpoklad, že ",[38,26599,26600],{},"investice závisejí na úrokové míře",[883,26602,26604],{"className":26603},[886],[888,26605,26606],{"xmlns":890},[892,26607,26608,26612],{},[895,26609,26610],{},[898,26611,13166],{},[902,26613,13166],{"encoding":904}," — klesající funkce ",[883,26616,26618],{"className":26617},[886],[888,26619,26620],{"xmlns":890},[892,26621,26622,26642],{},[895,26623,26624,26626,26628,26630,26632,26634,26636,26638,26640],{},[898,26625,13309],{},[1655,26627,1664],{"stretchy":1663},[898,26629,13166],{},[1655,26631,1677],{"stretchy":1663},[1655,26633,1657],{},[898,26635,1789],{},[898,26637,13166],{},[1655,26639,2346],{},[898,26641,2410],{},[902,26643,16882],{"encoding":904},[883,26645,26647],{"className":26646},[886],[888,26648,26649],{"xmlns":890},[892,26650,26651,26659],{},[895,26652,26653,26655,26657],{},[898,26654,1789],{},[1655,26656,3065],{},[1826,26658,2552],{},[902,26660,13640],{"encoding":904},". Přidáním ",[38,26663,26664],{},"trhu peněz"," k trhu zboží vzniká model ",[38,26667,13136],{}," se dvěma neznámými ",[883,26670,26672],{"className":26671},[886],[888,26673,26674],{"xmlns":890},[892,26675,26676,26688],{},[895,26677,26678,26680,26682,26684,26686],{},[1655,26679,1664],{"stretchy":1663},[898,26681,10375],{},[1655,26683,1671],{"separator":1670},[898,26685,13166],{},[1655,26687,1677],{"stretchy":1663},[902,26689,19276],{"encoding":904}," a dvěma rovnicemi:",[120,26692,26693,26743],{},[123,26694,26695,2115,26697,26699,26700,26721,26722,1719],{},[38,26696,16971],{},[614,26698,13179],{},") — klesající přímka v rovině ",[883,26701,26703],{"className":26702},[886],[888,26704,26705],{"xmlns":890},[892,26706,26707,26719],{},[895,26708,26709,26711,26713,26715,26717],{},[1655,26710,1664],{"stretchy":1663},[898,26712,13166],{},[1655,26714,1671],{"separator":1670},[898,26716,10375],{},[1655,26718,1677],{"stretchy":1663},[902,26720,14062],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,26723,26725],{"className":26724},[886],[888,26726,26727],{"xmlns":890},[892,26728,26729,26741],{},[895,26730,26731,26733,26735,26737,26739],{},[898,26732,10375],{},[1655,26734,1657],{},[898,26736,4052],{},[1655,26738,2346],{},[898,26740,13309],{},[902,26742,15869],{"encoding":904},[123,26744,26745,2115,26747,26749,26750,22720,26775,26821],{},[38,26746,17170],{},[614,26748,13186],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,26751,26753],{"className":26752},[886],[888,26754,26755],{"xmlns":890},[892,26756,26757,26773],{},[895,26758,26759,26765,26767],{},[2597,26760,26761,26763],{},[898,26762,2127],{},[898,26764,2838],{},[1655,26766,1657],{},[2597,26768,26769,26771],{},[898,26770,2127],{},[1655,26772,5603],{},[902,26774,14605],{"encoding":904},[883,26776,26778],{"className":26777},[886],[888,26779,26780],{"xmlns":890},[892,26781,26782,26818],{},[895,26783,26784,26790,26792,26798,26800,26802,26808,26810,26812],{},[2597,26785,26786,26788],{},[898,26787,2127],{},[898,26789,2838],{},[1655,26791,1657],{},[1820,26793,26794,26796],{},[898,26795,14362],{},[1826,26797,1828],{},[898,26799,10375],{},[1655,26801,2346],{},[1820,26803,26804,26806],{},[898,26805,14362],{},[1826,26807,1837],{},[898,26809,13166],{},[1655,26811,2346],{},[1820,26813,26814,26816],{},[898,26815,14362],{},[1826,26817,3472],{},[902,26819,26820],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,26823,26824,3106,26827,26860,26861,26863,26864,26866],{},[38,26825,26826],{},"Simultánní rovnovážný bod",[883,26828,26830],{"className":26829},[886],[888,26831,26832],{"xmlns":890},[892,26833,26834,26858],{},[895,26835,26836,26838,26840,26842,26848,26850,26856],{},[898,26837,5502],{},[1655,26839,1657],{},[1655,26841,1664],{"stretchy":1663},[2597,26843,26844,26846],{},[898,26845,13166],{},[898,26847,5502],{},[1655,26849,1671],{"separator":1670},[2597,26851,26852,26854],{},[898,26853,10375],{},[898,26855,5502],{},[1655,26857,1677],{"stretchy":1663},[902,26859,17262],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,26862,13224],{}," (posun IS) a ",[38,26865,13256],{}," (posun LM).",[724,26868,26869],{},[38,26870,26871,26872,1343,26894,1343,26916,1343,26938,26960,26961,1719],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,26873,26875],{"className":26874},[886],[888,26876,26877],{"xmlns":890},[892,26878,26879,26891],{},[895,26880,26881,26887,26889],{},[2597,26882,26883,26885],{},[898,26884,10375],{},[898,26886,5502],{},[1655,26888,1657],{},[1826,26890,16240],{},[902,26892,26893],{"encoding":904},"Y^E = 5000",[883,26895,26897],{"className":26896},[886],[888,26898,26899],{"xmlns":890},[892,26900,26901,26913],{},[895,26902,26903,26909,26911],{},[2597,26904,26905,26907],{},[898,26906,13166],{},[898,26908,5502],{},[1655,26910,1657],{},[1826,26912,3524],{},[902,26914,26915],{"encoding":904},"r^E = 5",[883,26917,26919],{"className":26918},[886],[888,26920,26921],{"xmlns":890},[892,26922,26923,26935],{},[895,26924,26925,26931,26933],{},[2597,26926,26927,26929],{},[898,26928,4052],{},[898,26930,5502],{},[1655,26932,1657],{},[1826,26934,16277],{},[902,26936,26937],{"encoding":904},"C^E = 4100",[883,26939,26941],{"className":26940},[886],[888,26942,26943],{"xmlns":890},[892,26944,26945,26957],{},[895,26946,26947,26953,26955],{},[2597,26948,26949,26951],{},[898,26950,13309],{},[898,26952,5502],{},[1655,26954,1657],{},[1826,26956,16316],{},[902,26958,26959],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,26962,945],{"className":26963,"dataFsResolvedFilePath":943,"href":944},[210],[115,26965,26967],{"id":26966},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,26969,26970,27034,27145,27288,27530,27598],{},[123,26971,26972,26975,26976,26998,26999,27033],{},[38,26973,26974],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,26977,26979],{"className":26978},[886],[888,26980,26981],{"xmlns":890},[892,26982,26983,26995],{},[895,26984,26985,26987,26989,26991,26993],{},[898,26986,13237],{},[898,26988,19420],{},[898,26990,2132],{},[1655,26992,2357],{},[898,26994,10375],{},[902,26996,26997],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,27000,27002],{"className":27001},[886],[888,27003,27004],{"xmlns":890},[892,27005,27006,27030],{},[895,27007,27008,27010,27012,27014,27016,27018,27020,27022,27024,27026,27028],{},[898,27009,13237],{},[898,27011,19420],{},[898,27013,2132],{},[1655,27015,1657],{},[898,27017,4052],{},[1655,27019,2346],{},[898,27021,13309],{},[1655,27023,2346],{},[898,27025,13237],{},[1655,27027,2346],{},[898,27029,13445],{},[902,27031,27032],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,27035,27036,27038,27039,27060,27061,1343,27084,27115,27116,27129,27130,1719],{},[38,27037,19654],{}," splňují ",[883,27040,27042],{"className":27041},[886],[888,27043,27044],{"xmlns":890},[892,27045,27046,27058],{},[895,27047,27048,27050,27052,27054,27056],{},[898,27049,10375],{},[1655,27051,1657],{},[898,27053,4052],{},[1655,27055,2346],{},[898,27057,9920],{},[902,27059,13819],{"encoding":904}," (7.2); lineární model ",[883,27062,27064],{"className":27063},[886],[888,27065,27066],{"xmlns":890},[892,27067,27068,27082],{},[895,27069,27070,27072,27074,27076,27078,27080],{},[898,27071,4052],{},[1655,27073,1657],{},[898,27075,207],{},[898,27077,10375],{},[1655,27079,2346],{},[898,27081,2025],{},[902,27083,20046],{"encoding":904},[883,27085,27087],{"className":27086},[886],[888,27088,27089],{"xmlns":890},[892,27090,27091,27113],{},[895,27092,27093,27095,27097,27099,27101,27103,27105,27107,27109,27111],{},[898,27094,9920],{},[1655,27096,1657],{},[1655,27098,1664],{"stretchy":1663},[1826,27100,1828],{},[1655,27102,2623],{},[898,27104,207],{},[1655,27106,1677],{"stretchy":1663},[898,27108,10375],{},[1655,27110,2623],{},[898,27112,2025],{},[902,27114,20295],{"encoding":904}," s autonomní spotřebou ",[883,27117,27119],{"className":27118},[886],[888,27120,27121],{"xmlns":890},[892,27122,27123,27127],{},[895,27124,27125],{},[898,27126,2025],{},[902,27128,2025],{"encoding":904}," a autonomními úsporami ",[883,27131,27133],{"className":27132},[886],[888,27134,27135],{"xmlns":890},[892,27136,27137,27143],{},[895,27138,27139,27141],{},[1655,27140,2623],{},[898,27142,2025],{},[902,27144,20374],{"encoding":904},[123,27146,27147,3106,27150,1343,27180,27210,27211,27241,27242,1343,27263,1719],{},[38,27148,27149],{},"Mezní sklony",[883,27151,27153],{"className":27152},[886],[888,27154,27155],{"xmlns":890},[892,27156,27157,27177],{},[895,27158,27159,27161,27163,27165,27167,27169,27171,27173,27175],{},[898,27160,2127],{},[898,27162,2132],{},[898,27164,4052],{},[1655,27166,1657],{},[898,27168,2410],{"mathvariant":1943},[898,27170,4052],{},[898,27172,5923],{"mathvariant":1943},[898,27174,2410],{"mathvariant":1943},[898,27176,10375],{},[902,27178,27179],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,27181,27183],{"className":27182},[886],[888,27184,27185],{"xmlns":890},[892,27186,27187,27207],{},[895,27188,27189,27191,27193,27195,27197,27199,27201,27203,27205],{},[898,27190,2127],{},[898,27192,2132],{},[898,27194,9920],{},[1655,27196,1657],{},[898,27198,2410],{"mathvariant":1943},[898,27200,9920],{},[898,27202,5923],{"mathvariant":1943},[898,27204,2410],{"mathvariant":1943},[898,27206,10375],{},[902,27208,27209],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,27212,27214],{"className":27213},[886],[888,27215,27216],{"xmlns":890},[892,27217,27218,27238],{},[895,27219,27220,27222,27224,27226,27228,27230,27232,27234,27236],{},[898,27221,2127],{},[898,27223,2132],{},[898,27225,4052],{},[1655,27227,2346],{},[898,27229,2127],{},[898,27231,2132],{},[898,27233,9920],{},[1655,27235,1657],{},[1826,27237,1828],{},[902,27239,27240],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,27243,27245],{"className":27244},[886],[888,27246,27247],{"xmlns":890},[892,27248,27249,27261],{},[895,27250,27251,27253,27255,27257,27259],{},[898,27252,2127],{},[898,27254,2132],{},[898,27256,4052],{},[1655,27258,1657],{},[898,27260,207],{},[902,27262,21015],{"encoding":904},[883,27264,27266],{"className":27265},[886],[888,27267,27268],{"xmlns":890},[892,27269,27270,27286],{},[895,27271,27272,27274,27276,27278,27280,27282,27284],{},[898,27273,2127],{},[898,27275,2132],{},[898,27277,9920],{},[1655,27279,1657],{},[1826,27281,1828],{},[1655,27283,2623],{},[898,27285,207],{},[902,27287,21041],{"encoding":904},[123,27289,27290,27293,27294],{},[38,27291,27292],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,27295,27296,27384,27453],{},[123,27297,27298,27315,27316,27337,27338,1671],{},[883,27299,27301],{"className":27300},[886],[888,27302,27303],{"xmlns":890},[892,27304,27305,27313],{},[895,27306,27307,27309,27311],{},[898,27308,4052],{},[2031,27310,13415],{},[898,27312,13309],{},[902,27314,13420],{"encoding":904},": ",[883,27317,27319],{"className":27318},[886],[888,27320,27321],{"xmlns":890},[892,27322,27323,27335],{},[895,27324,27325,27327,27329,27331,27333],{},[898,27326,10375],{},[1655,27328,1657],{},[898,27330,4052],{},[1655,27332,2346],{},[898,27334,13309],{},[902,27336,15869],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,27339,27341],{"className":27340},[886],[888,27342,27343],{"xmlns":890},[892,27344,27345,27381],{},[895,27346,27347,27353,27355,27357,27359,27361,27367,27369,27371,27373,27375,27377,27379],{},[2597,27348,27349,27351],{},[898,27350,10375],{},[898,27352,5502],{},[1655,27354,1657],{},[1655,27356,1664],{"stretchy":1663},[898,27358,2025],{},[1655,27360,2346],{},[2597,27362,27363,27365],{},[898,27364,13309],{},[1655,27366,5603],{},[1655,27368,1677],{"stretchy":1663},[898,27370,5923],{"mathvariant":1943},[1655,27372,1664],{"stretchy":1663},[1826,27374,1828],{},[1655,27376,2623],{},[898,27378,207],{},[1655,27380,1677],{"stretchy":1663},[902,27382,27383],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,27385,27386,27407,27408,27427,27428,1671],{},[883,27387,27389],{"className":27388},[886],[888,27390,27391],{"xmlns":890},[892,27392,27393,27405],{},[895,27394,27395,27397,27399,27401,27403],{},[898,27396,4052],{},[2031,27398,13415],{},[898,27400,13309],{},[2031,27402,13415],{},[898,27404,13237],{},[902,27406,19346],{"encoding":904},": přidává vládu, zdanění ",[883,27409,27411],{"className":27410},[886],[888,27412,27413],{"xmlns":890},[892,27414,27415,27425],{},[895,27416,27417,27419,27421,27423],{},[898,27418,4049],{},[1655,27420,1664],{"stretchy":1663},[898,27422,10375],{},[1655,27424,1677],{"stretchy":1663},[902,27426,23345],{"encoding":904}," a disponibilní důchod ",[883,27429,27431],{"className":27430},[886],[888,27432,27433],{"xmlns":890},[892,27434,27435,27451],{},[895,27436,27437,27443,27445,27447,27449],{},[1820,27438,27439,27441],{},[898,27440,10375],{},[898,27442,2838],{},[1655,27444,1657],{},[898,27446,10375],{},[1655,27448,2623],{},[898,27450,4049],{},[902,27452,22844],{"encoding":904},[123,27454,27455,27480,27481,22720,27502,1719],{},[883,27456,27458],{"className":27457},[886],[888,27459,27460],{"xmlns":890},[892,27461,27462,27478],{},[895,27463,27464,27466,27468,27470,27472,27474,27476],{},[898,27465,4052],{},[2031,27467,13415],{},[898,27469,13309],{},[2031,27471,13415],{},[898,27473,13237],{},[2031,27475,13415],{},[898,27477,13445],{},[902,27479,13448],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,27482,27484],{"className":27483},[886],[888,27485,27486],{"xmlns":890},[892,27487,27488,27500],{},[895,27489,27490,27492,27494,27496,27498],{},[898,27491,13445],{},[1655,27493,1657],{},[898,27495,24379],{},[1655,27497,2623],{},[898,27499,2127],{},[902,27501,24386],{"encoding":904},[883,27503,27505],{"className":27504},[886],[888,27506,27507],{"xmlns":890},[892,27508,27509,27527],{},[895,27510,27511,27513,27515,27517,27519,27525],{},[898,27512,2127],{},[1655,27514,1657],{},[898,27516,2127],{},[1655,27518,1664],{"stretchy":1663},[1820,27520,27521,27523],{},[898,27522,10375],{},[898,27524,2838],{},[1655,27526,1677],{"stretchy":1663},[902,27528,27529],{"encoding":904},"M = M(Y_D)",[123,27531,27532,27535,27536,3106,27539,27597],{},[38,27533,27534],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,27537,27538],{},"multiplikátor investic",[883,27540,27542],{"className":27541},[886],[888,27543,27544],{"xmlns":890},[892,27545,27546,27594],{},[895,27547,27548,27550,27556,27558,27560,27566,27568,27570,27572,27574,27576,27578,27580,27582,27584,27586,27588,27590,27592],{},[898,27549,1955],{"mathvariant":1943},[2597,27551,27552,27554],{},[898,27553,10375],{},[898,27555,5502],{},[898,27557,5923],{"mathvariant":1943},[898,27559,1955],{"mathvariant":1943},[2597,27561,27562,27564],{},[898,27563,13309],{},[1655,27565,5603],{},[1655,27567,1657],{},[1826,27569,1828],{},[898,27571,5923],{"mathvariant":1943},[1655,27573,1664],{"stretchy":1663},[1826,27575,1828],{},[1655,27577,2623],{},[898,27579,207],{},[1655,27581,1677],{"stretchy":1663},[1655,27583,1657],{},[1826,27585,1828],{},[898,27587,5923],{"mathvariant":1943},[898,27589,2127],{},[898,27591,2132],{},[898,27593,9920],{},[902,27595,27596],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,27599,27600,27602,27603,27618,27619,19774,27636,27651,27652,27677,27678,1719],{},[38,27601,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,27604,27606],{"className":27605},[886],[888,27607,27608],{"xmlns":890},[892,27609,27610,27616],{},[895,27611,27612,27614],{},[898,27613,13309],{},[898,27615,9920],{},[902,27617,13176],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,27620,27622],{"className":27621},[886],[888,27623,27624],{"xmlns":890},[892,27625,27626,27634],{},[895,27627,27628,27630,27632],{},[898,27629,13309],{},[1655,27631,1657],{},[898,27633,9920],{},[902,27635,13837],{"encoding":904},[883,27637,27639],{"className":27638},[886],[888,27640,27641],{"xmlns":890},[892,27642,27643,27649],{},[895,27644,27645,27647],{},[898,27646,1873],{},[898,27648,2127],{},[902,27650,13183],{"encoding":904}," rovnováhu trhu peněz (",[883,27653,27655],{"className":27654},[886],[888,27656,27657],{"xmlns":890},[892,27658,27659,27675],{},[895,27660,27661,27667,27669],{},[2597,27662,27663,27665],{},[898,27664,2127],{},[898,27666,2838],{},[1655,27668,1657],{},[2597,27670,27671,27673],{},[898,27672,2127],{},[1655,27674,5603],{},[902,27676,14605],{"encoding":904},"); průsečík dává ",[883,27679,27681],{"className":27680},[886],[888,27682,27683],{"xmlns":890},[892,27684,27685,27705],{},[895,27686,27687,27689,27695,27697,27703],{},[1655,27688,1664],{"stretchy":1663},[2597,27690,27691,27693],{},[898,27692,10375],{},[898,27694,5502],{},[1655,27696,1671],{"separator":1670},[2597,27698,27699,27701],{},[898,27700,13166],{},[898,27702,5502],{},[1655,27704,1677],{"stretchy":1663},[902,27706,13220],{"encoding":904},[115,27708,16845],{"id":16844},[120,27710,27711,27749,27789,27879,27961,28015,28071,28130,28165,28170,28242,28317,28403,28465,28533,28591,28644,28683],{},[123,27712,27713,8262,27716,27033],{},[38,27714,27715],{},"Hrubý národní produkt (GNP)",[883,27717,27719],{"className":27718},[886],[888,27720,27721],{"xmlns":890},[892,27722,27723,27747],{},[895,27724,27725,27727,27729,27731,27733,27735,27737,27739,27741,27743,27745],{},[898,27726,13237],{},[898,27728,19420],{},[898,27730,2132],{},[1655,27732,1657],{},[898,27734,4052],{},[1655,27736,2346],{},[898,27738,13309],{},[1655,27740,2346],{},[898,27742,13237],{},[1655,27744,2346],{},[898,27746,13445],{},[902,27748,27032],{"encoding":904},[123,27750,27751,27767,27768,1719],{},[38,27752,27753,27754],{},"Národní důchod ",[883,27755,27757],{"className":27756},[886],[888,27758,27759],{"xmlns":890},[892,27760,27761,27765],{},[895,27762,27763],{},[898,27764,10375],{},[902,27766,10375],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,27769,27771],{"className":27770},[886],[888,27772,27773],{"xmlns":890},[892,27774,27775,27787],{},[895,27776,27777,27779,27781,27783,27785],{},[898,27778,13237],{},[898,27780,19420],{},[898,27782,2132],{},[1655,27784,2357],{},[898,27786,10375],{},[902,27788,26997],{"encoding":904},[123,27790,27791,27817,27818,1343,27841,1343,27862,1719],{},[38,27792,27793,27794],{},"Funkce spotřeby ",[883,27795,27797],{"className":27796},[886],[888,27798,27799],{"xmlns":890},[892,27800,27801,27815],{},[895,27802,27803,27805,27807,27809,27811,27813],{},[898,27804,4052],{},[1655,27806,1657],{},[898,27808,4052],{},[1655,27810,1664],{"stretchy":1663},[898,27812,10375],{},[1655,27814,1677],{"stretchy":1663},[902,27816,21866],{"encoding":904}," — lineární model ",[883,27819,27821],{"className":27820},[886],[888,27822,27823],{"xmlns":890},[892,27824,27825,27839],{},[895,27826,27827,27829,27831,27833,27835,27837],{},[898,27828,4052],{},[1655,27830,1657],{},[898,27832,207],{},[898,27834,10375],{},[1655,27836,2346],{},[898,27838,2025],{},[902,27840,20046],{"encoding":904},[883,27842,27844],{"className":27843},[886],[888,27845,27846],{"xmlns":890},[892,27847,27848,27860],{},[895,27849,27850,27852,27854,27856,27858],{},[1826,27851,2552],{},[1655,27853,3065],{},[898,27855,207],{},[1655,27857,3065],{},[1826,27859,1828],{},[902,27861,19962],{"encoding":904},[883,27863,27865],{"className":27864},[886],[888,27866,27867],{"xmlns":890},[892,27868,27869,27877],{},[895,27870,27871,27873,27875],{},[898,27872,2025],{},[1655,27874,2969],{},[1826,27876,2552],{},[902,27878,19940],{"encoding":904},[123,27880,27881,8262,27908,27929,27930,1719],{},[38,27882,27883,27884],{},"Funkce úspor ",[883,27885,27887],{"className":27886},[886],[888,27888,27889],{"xmlns":890},[892,27890,27891,27905],{},[895,27892,27893,27895,27897,27899,27901,27903],{},[898,27894,9920],{},[1655,27896,1657],{},[898,27898,9920],{},[1655,27900,1664],{"stretchy":1663},[898,27902,10375],{},[1655,27904,1677],{"stretchy":1663},[902,27906,27907],{"encoding":904},"S = S(Y)",[883,27909,27911],{"className":27910},[886],[888,27912,27913],{"xmlns":890},[892,27914,27915,27927],{},[895,27916,27917,27919,27921,27923,27925],{},[898,27918,10375],{},[1655,27920,1657],{},[898,27922,4052],{},[1655,27924,2346],{},[898,27926,9920],{},[902,27928,13819],{"encoding":904},"; lineární ",[883,27931,27933],{"className":27932},[886],[888,27934,27935],{"xmlns":890},[892,27936,27937,27959],{},[895,27938,27939,27941,27943,27945,27947,27949,27951,27953,27955,27957],{},[898,27940,9920],{},[1655,27942,1657],{},[1655,27944,1664],{"stretchy":1663},[1826,27946,1828],{},[1655,27948,2623],{},[898,27950,207],{},[1655,27952,1677],{"stretchy":1663},[898,27954,10375],{},[1655,27956,2623],{},[898,27958,2025],{},[902,27960,20295],{"encoding":904},[123,27962,27963,8262,27966,1343,27989,1719],{},[38,27964,27965],{},"Autonomní spotřeba\u002Fúspory",[883,27967,27969],{"className":27968},[886],[888,27970,27971],{"xmlns":890},[892,27972,27973,27987],{},[895,27974,27975,27977,27979,27981,27983,27985],{},[898,27976,4052],{},[1655,27978,1664],{"stretchy":1663},[1826,27980,2552],{},[1655,27982,1677],{"stretchy":1663},[1655,27984,1657],{},[898,27986,2025],{},[902,27988,20687],{"encoding":904},[883,27990,27992],{"className":27991},[886],[888,27993,27994],{"xmlns":890},[892,27995,27996,28012],{},[895,27997,27998,28000,28002,28004,28006,28008,28010],{},[898,27999,9920],{},[1655,28001,1664],{"stretchy":1663},[1826,28003,2552],{},[1655,28005,1677],{"stretchy":1663},[1655,28007,1657],{},[1655,28009,2623],{},[898,28011,2025],{},[902,28013,28014],{"encoding":904},"S(0) = -b",[123,28016,28017,28049,28050,5171],{},[38,28018,28019,28020],{},"Mezní sklon ke spotřebě ",[883,28021,28023],{"className":28022},[886],[888,28024,28025],{"xmlns":890},[892,28026,28027,28047],{},[895,28028,28029,28031,28033,28035,28037,28039,28041,28043,28045],{},[898,28030,2127],{},[898,28032,2132],{},[898,28034,4052],{},[1655,28036,1657],{},[898,28038,2410],{"mathvariant":1943},[898,28040,4052],{},[898,28042,5923],{"mathvariant":1943},[898,28044,2410],{"mathvariant":1943},[898,28046,10375],{},[902,28048,27179],{"encoding":904}," (v lineárním modelu ",[883,28051,28053],{"className":28052},[886],[888,28054,28055],{"xmlns":890},[892,28056,28057,28069],{},[895,28058,28059,28061,28063,28065,28067],{},[898,28060,2127],{},[898,28062,2132],{},[898,28064,4052],{},[1655,28066,1657],{},[898,28068,207],{},[902,28070,21015],{"encoding":904},[123,28072,28073,28049,28105,5171],{},[38,28074,28075,28076],{},"Mezní sklon k úsporám ",[883,28077,28079],{"className":28078},[886],[888,28080,28081],{"xmlns":890},[892,28082,28083,28103],{},[895,28084,28085,28087,28089,28091,28093,28095,28097,28099,28101],{},[898,28086,2127],{},[898,28088,2132],{},[898,28090,9920],{},[1655,28092,1657],{},[898,28094,2410],{"mathvariant":1943},[898,28096,9920],{},[898,28098,5923],{"mathvariant":1943},[898,28100,2410],{"mathvariant":1943},[898,28102,10375],{},[902,28104,27209],{"encoding":904},[883,28106,28108],{"className":28107},[886],[888,28109,28110],{"xmlns":890},[892,28111,28112,28128],{},[895,28113,28114,28116,28118,28120,28122,28124,28126],{},[898,28115,2127],{},[898,28117,2132],{},[898,28119,9920],{},[1655,28121,1657],{},[1826,28123,1828],{},[1655,28125,2623],{},[898,28127,207],{},[902,28129,21041],{"encoding":904},[123,28131,28132,3106,28135,28164],{},[38,28133,28134],{},"Vztah",[883,28136,28138],{"className":28137},[886],[888,28139,28140],{"xmlns":890},[892,28141,28142,28162],{},[895,28143,28144,28146,28148,28150,28152,28154,28156,28158,28160],{},[898,28145,2127],{},[898,28147,2132],{},[898,28149,4052],{},[1655,28151,2346],{},[898,28153,2127],{},[898,28155,2132],{},[898,28157,9920],{},[1655,28159,1657],{},[1826,28161,1828],{},[902,28163,27240],{"encoding":904}," (7.5).",[123,28166,28167,28169],{},[38,28168,21709],{}," — rovnováha agregátní poptávky a nabídky.",[123,28171,28172,28175,28176,16917,28197,1719],{},[38,28173,28174],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,28177,28179],{"className":28178},[886],[888,28180,28181],{"xmlns":890},[892,28182,28183,28195],{},[895,28184,28185,28187,28189,28191,28193],{},[898,28186,10375],{},[1655,28188,1657],{},[898,28190,4052],{},[1655,28192,2346],{},[898,28194,13309],{},[902,28196,15869],{"encoding":904},[883,28198,28200],{"className":28199},[886],[888,28201,28202],{"xmlns":890},[892,28203,28204,28240],{},[895,28205,28206,28212,28214,28216,28218,28220,28226,28228,28230,28232,28234,28236,28238],{},[2597,28207,28208,28210],{},[898,28209,10375],{},[898,28211,5502],{},[1655,28213,1657],{},[1655,28215,1664],{"stretchy":1663},[898,28217,2025],{},[1655,28219,2346],{},[2597,28221,28222,28224],{},[898,28223,13309],{},[1655,28225,5603],{},[1655,28227,1677],{"stretchy":1663},[898,28229,5923],{"mathvariant":1943},[1655,28231,1664],{"stretchy":1663},[1826,28233,1828],{},[1655,28235,2623],{},[898,28237,207],{},[1655,28239,1677],{"stretchy":1663},[902,28241,27383],{"encoding":904},[123,28243,28244,28247,28248,1343,28267,16917,28292,1719],{},[38,28245,28246],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,28249,28251],{"className":28250},[886],[888,28252,28253],{"xmlns":890},[892,28254,28255,28265],{},[895,28256,28257,28259,28261,28263],{},[898,28258,4049],{},[1655,28260,1664],{"stretchy":1663},[898,28262,10375],{},[1655,28264,1677],{"stretchy":1663},[902,28266,23345],{"encoding":904},[883,28268,28270],{"className":28269},[886],[888,28271,28272],{"xmlns":890},[892,28273,28274,28290],{},[895,28275,28276,28282,28284,28286,28288],{},[1820,28277,28278,28280],{},[898,28279,10375],{},[898,28281,2838],{},[1655,28283,1657],{},[898,28285,10375],{},[1655,28287,2623],{},[898,28289,4049],{},[902,28291,22844],{"encoding":904},[883,28293,28295],{"className":28294},[886],[888,28296,28297],{"xmlns":890},[892,28298,28299,28315],{},[895,28300,28301,28303,28305,28307,28309,28311,28313],{},[898,28302,10375],{},[1655,28304,1657],{},[898,28306,4052],{},[1655,28308,2346],{},[898,28310,13309],{},[1655,28312,2346],{},[898,28314,13237],{},[902,28316,22815],{"encoding":904},[123,28318,28319,28322,28323,28344,28345,16917,28369,1719],{},[38,28320,28321],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,28324,28326],{"className":28325},[886],[888,28327,28328],{"xmlns":890},[892,28329,28330,28342],{},[895,28331,28332,28334,28336,28338,28340],{},[898,28333,13445],{},[1655,28335,1657],{},[898,28337,24379],{},[1655,28339,2623],{},[898,28341,2127],{},[902,28343,24386],{"encoding":904},", importem ",[883,28346,28348],{"className":28347},[886],[888,28349,28350],{"xmlns":890},[892,28351,28352,28366],{},[895,28353,28354,28356,28358,28364],{},[898,28355,2127],{},[1655,28357,1664],{"stretchy":1663},[1820,28359,28360,28362],{},[898,28361,10375],{},[898,28363,2838],{},[1655,28365,1677],{"stretchy":1663},[902,28367,28368],{"encoding":904},"M(Y_D)",[883,28370,28372],{"className":28371},[886],[888,28373,28374],{"xmlns":890},[892,28375,28376,28400],{},[895,28377,28378,28380,28382,28384,28386,28388,28390,28392,28394,28396,28398],{},[898,28379,10375],{},[1655,28381,1657],{},[898,28383,4052],{},[1655,28385,2346],{},[898,28387,13309],{},[1655,28389,2346],{},[898,28391,13237],{},[1655,28393,2346],{},[898,28395,24379],{},[1655,28397,2623],{},[898,28399,2127],{},[902,28401,28402],{"encoding":904},"Y = C + I + G + B - M",[123,28404,28405,8262,28408,27597],{},[38,28406,28407],{},"Multiplikátor investic",[883,28409,28411],{"className":28410},[886],[888,28412,28413],{"xmlns":890},[892,28414,28415,28463],{},[895,28416,28417,28419,28425,28427,28429,28435,28437,28439,28441,28443,28445,28447,28449,28451,28453,28455,28457,28459,28461],{},[898,28418,1955],{"mathvariant":1943},[2597,28420,28421,28423],{},[898,28422,10375],{},[898,28424,5502],{},[898,28426,5923],{"mathvariant":1943},[898,28428,1955],{"mathvariant":1943},[2597,28430,28431,28433],{},[898,28432,13309],{},[1655,28434,5603],{},[1655,28436,1657],{},[1826,28438,1828],{},[898,28440,5923],{"mathvariant":1943},[1655,28442,1664],{"stretchy":1663},[1826,28444,1828],{},[1655,28446,2623],{},[898,28448,207],{},[1655,28450,1677],{"stretchy":1663},[1655,28452,1657],{},[1826,28454,1828],{},[898,28456,5923],{"mathvariant":1943},[898,28458,2127],{},[898,28460,2132],{},[898,28462,9920],{},[902,28464,27596],{"encoding":904},[123,28466,28467,8262,28498,1343,28515,28532],{},[38,28468,16852,28469],{},[883,28470,28472],{"className":28471},[886],[888,28473,28474],{"xmlns":890},[892,28475,28476,28496],{},[895,28477,28478,28480,28482,28484,28486,28488,28490,28492,28494],{},[898,28479,13309],{},[1655,28481,1664],{"stretchy":1663},[898,28483,13166],{},[1655,28485,1677],{"stretchy":1663},[1655,28487,1657],{},[898,28489,1789],{},[898,28491,13166],{},[1655,28493,2346],{},[898,28495,2410],{},[902,28497,16882],{"encoding":904},[883,28499,28501],{"className":28500},[886],[888,28502,28503],{"xmlns":890},[892,28504,28505,28513],{},[895,28506,28507,28509,28511],{},[898,28508,1789],{},[1655,28510,3065],{},[1826,28512,2552],{},[902,28514,13640],{"encoding":904},[883,28516,28518],{"className":28517},[886],[888,28519,28520],{"xmlns":890},[892,28521,28522,28530],{},[895,28523,28524,28526,28528],{},[898,28525,2410],{},[1655,28527,2969],{},[1826,28529,2552],{},[902,28531,13619],{"encoding":904},"; klesající.",[123,28534,28535,28537,28538,28540,28541,28590],{},[38,28536,16971],{}," — rovnováha na trhu zboží (",[614,28539,13179],{},"); ",[883,28542,28544],{"className":28543},[886],[888,28545,28546],{"xmlns":890},[892,28547,28548,28588],{},[895,28549,28550,28552,28554,28566,28568,28570],{},[898,28551,10375],{},[1655,28553,1657],{},[1949,28555,28556,28558],{},[898,28557,1789],{},[895,28559,28560,28562,28564],{},[1826,28561,1828],{},[1655,28563,2623],{},[898,28565,207],{},[898,28567,13166],{},[1655,28569,2346],{},[1949,28571,28572,28580],{},[895,28573,28574,28576,28578],{},[898,28575,2025],{},[1655,28577,2346],{},[898,28579,2410],{},[895,28581,28582,28584,28586],{},[1826,28583,1828],{},[1655,28585,2623],{},[898,28587,207],{},[902,28589,17024],{"encoding":904}," (7.14); klesající.",[123,28592,28593,28595,28596,28540,28598,28643],{},[38,28594,17170],{}," — rovnováha na trhu peněz (",[614,28597,13186],{},[883,28599,28601],{"className":28600},[886],[888,28602,28603],{"xmlns":890},[892,28604,28605,28641],{},[895,28606,28607,28613,28615,28621,28623,28625,28631,28633,28635],{},[2597,28608,28609,28611],{},[898,28610,2127],{},[1655,28612,5603],{},[1655,28614,1657],{},[1820,28616,28617,28619],{},[898,28618,14362],{},[1826,28620,1828],{},[898,28622,10375],{},[1655,28624,2346],{},[1820,28626,28627,28629],{},[898,28628,14362],{},[1826,28630,1837],{},[898,28632,13166],{},[1655,28634,2346],{},[1820,28636,28637,28639],{},[898,28638,14362],{},[1826,28640,3472],{},[902,28642,17218],{"encoding":904}," (7.15); rostoucí.",[123,28645,28646,8262,28649,1719],{},[38,28647,28648],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,28650,28652],{"className":28651},[886],[888,28653,28654],{"xmlns":890},[892,28655,28656,28680],{},[895,28657,28658,28664,28666,28672,28674],{},[2597,28659,28660,28662],{},[898,28661,2127],{},[898,28663,2838],{},[1655,28665,1657],{},[1820,28667,28668,28670],{},[898,28669,1873],{},[1826,28671,1828],{},[1655,28673,2346],{},[1820,28675,28676,28678],{},[898,28677,1873],{},[1826,28679,1837],{},[902,28681,28682],{"encoding":904},"M^D = L_1 + L_2",[123,28684,28685,17228,28687,15105,28700,2704,28715,28730,28731,1719],{},[38,28686,945],{},[883,28688,28690],{"className":28689},[886],[888,28691,28692],{"xmlns":890},[892,28693,28694,28698],{},[895,28695,28696],{},[898,28697,5502],{},[902,28699,5502],{"encoding":904},[883,28701,28703],{"className":28702},[886],[888,28704,28705],{"xmlns":890},[892,28706,28707,28713],{},[895,28708,28709,28711],{},[898,28710,13309],{},[898,28712,9920],{},[902,28714,13176],{"encoding":904},[883,28716,28718],{"className":28717},[886],[888,28719,28720],{"xmlns":890},[892,28721,28722,28728],{},[895,28723,28724,28726],{},[898,28725,1873],{},[898,28727,2127],{},[902,28729,13183],{"encoding":904}," určuje ",[883,28732,28734],{"className":28733},[886],[888,28735,28736],{"xmlns":890},[892,28737,28738,28758],{},[895,28739,28740,28742,28748,28750,28756],{},[1655,28741,1664],{"stretchy":1663},[2597,28743,28744,28746],{},[898,28745,10375],{},[898,28747,5502],{},[1655,28749,1671],{"separator":1670},[2597,28751,28752,28754],{},[898,28753,13166],{},[898,28755,5502],{},[1655,28757,1677],{"stretchy":1663},[902,28759,13220],{"encoding":904},[115,28761,3187],{"id":3186},[120,28763,28764,28771,28778],{},[123,28765,28766,3106,28768],{},[38,28767,17329],{},[207,28769,17333],{"className":28770,"dataFsResolvedFilePath":3274,"href":3275},[210],[123,28772,28773,3106,28775],{},[38,28774,17338],{},[207,28776,17342],{"className":28777,"dataFsResolvedFilePath":868,"href":869},[210],[123,28779,28780,28782],{},[38,28781,17357],{},[120,28783,28784,28790,28796,28802],{},[123,28785,28786,28789],{},[207,28787,17398],{"className":28788,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,28791,28792,28795],{},[207,28793,17365],{"className":28794,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,28797,28798,28801],{},[207,28799,4222],{"className":28800,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,28803,28804,28807,28808,1343,28825,28842],{},[207,28805,1145],{"className":28806,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,28809,28811],{"className":28810},[886],[888,28812,28813],{"xmlns":890},[892,28814,28815,28823],{},[895,28816,28817,28819,28821],{},[898,28818,2127],{},[898,28820,2132],{},[898,28822,4052],{},[902,28824,19171],{"encoding":904},[883,28826,28828],{"className":28827},[886],[888,28829,28830],{"xmlns":890},[892,28831,28832,28840],{},[895,28833,28834,28836,28838],{},[898,28835,2127],{},[898,28837,2132],{},[898,28839,9920],{},[902,28841,20785],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":28844},[28845,28846,28847,28848,28853,28856,28857,28864,28869,28874,28877,28878,28879,28880],{"id":13130,"depth":642,"text":13131},{"id":19280,"depth":642,"text":19281},{"id":19400,"depth":642,"text":19401},{"id":19653,"depth":642,"text":19654,"children":28849},[28850,28851,28852],{"id":19657,"depth":649,"text":19658},{"id":19869,"depth":649,"text":19870},{"id":20377,"depth":649,"text":20378},{"id":20697,"depth":642,"text":20698,"children":28854},[28855],{"id":21213,"depth":649,"text":21214},{"id":21708,"depth":642,"text":21709},{"id":21735,"depth":642,"text":21736,"children":28858},[28859,28860,28861,28863],{"id":21746,"depth":649,"text":21747},{"id":21816,"depth":649,"text":21817},{"id":22000,"depth":649,"text":28862},"Výpočet YEY^E",{"id":22143,"depth":649,"text":22144},{"id":22521,"depth":642,"text":22522,"children":28865},[28866,28867,28868],{"id":22525,"depth":649,"text":21747},{"id":22974,"depth":649,"text":21817},{"id":23630,"depth":649,"text":23631},{"id":24417,"depth":642,"text":24418,"children":28870},[28871,28872,28873],{"id":24421,"depth":649,"text":21747},{"id":24566,"depth":649,"text":21817},{"id":24836,"depth":649,"text":24837},{"id":25760,"depth":642,"text":25761,"children":28875},[28876],{"id":25956,"depth":649,"text":25957},{"id":26506,"depth":642,"text":26507},{"id":26966,"depth":642,"text":26967},{"id":16844,"depth":642,"text":16845},{"id":3186,"depth":642,"text":3187},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,17351,1143,28887,28888,28889,17398,19009],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":28892,"title":28893,"body":28894,"course":1128,"courses":659,"created":10802,"description":641,"extension":661,"meta":37874,"navigation":664,"path":37875,"seo":37876,"sources":37877,"stem":37878,"tags":37879,"type":3252,"updated":677,"__hash__":37884},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":28895,"toc":37843},[28896,28899,28901,29130,29134,29187,29257,29369,29528,29532,29648,29652,29655,29777,29780,29973,29997,30065,30229,30247,30313,30691,30695,30702,30946,31002,31006,31071,31189,31321,31353,31473,31555,31558,31680,31873,32094,32098,32138,32243,32300,32400,32577,32707,32760,32763,32850,32854,33030,33034,33037,33122,33125,33182,33287,33291,33412,33415,33598,33601,33709,33918,34238,34286,34359,34433,34435,34659,34894,35162,35166,35169,35274,35331,35365,35412,35445,35529,35531,35763,35896,35973,36095,36250,36254,36395,36402,36626,36637,36641,36645,36750,36892,37002,37101,37105,37264,37374,37376,37769,37771],[12,28897,28893],{"id":28898},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,28900,13131],{"id":13130},[724,28902,28903,28905,28906,28940,28941,28944,28945,28976,28977,29023,29024,29027,29028,29070,29071,29089,29090,29094,29095,29125,29126,29129],{},[38,28904,913],{}," řeší, jaký svazek zboží ",[883,28907,28909],{"className":28908},[886],[888,28910,28911],{"xmlns":890},[892,28912,28913,28937],{},[895,28914,28915,28917,28925,28927,28935],{},[1655,28916,2734],{"stretchy":1663},[1935,28918,28919,28921,28923],{},[898,28920,1824],{},[1826,28922,1828],{},[1655,28924,5603],{},[1655,28926,1671],{"separator":1670},[1935,28928,28929,28931,28933],{},[898,28930,1824],{},[1826,28932,1837],{},[1655,28934,5603],{},[1655,28936,2743],{"stretchy":1663},[902,28938,28939],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,28942,28943],{},"primární úloha"," — maximalizace užitečnosti ",[883,28946,28948],{"className":28947},[886],[888,28949,28950],{"xmlns":890},[892,28951,28952,28974],{},[895,28953,28954,28956,28958,28964,28966,28972],{},[898,28955,900],{},[1655,28957,1664],{"stretchy":1663},[1820,28959,28960,28962],{},[898,28961,1824],{},[1826,28963,1828],{},[1655,28965,1671],{"separator":1670},[1820,28967,28968,28970],{},[898,28969,1824],{},[1826,28971,1837],{},[1655,28973,1677],{"stretchy":1663},[902,28975,17469],{"encoding":904}," při rozpočtovém omezení ",[883,28978,28980],{"className":28979},[886],[888,28981,28982],{"xmlns":890},[892,28983,28984,29020],{},[895,28985,28986,28992,28994,29000,29006,29008,29014],{},[2597,28987,28988,28990],{},[898,28989,10375],{},[1655,28991,5603],{},[1655,28993,1657],{},[1820,28995,28996,28998],{},[898,28997,2132],{},[1826,28999,1828],{},[1820,29001,29002,29004],{},[898,29003,1824],{},[1826,29005,1828],{},[1655,29007,2346],{},[1820,29009,29010,29012],{},[898,29011,2132],{},[1826,29013,1837],{},[1820,29015,29016,29018],{},[898,29017,1824],{},[1826,29019,1837],{},[902,29021,29022],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,29025,29026],{},"duální úloha"," — minimalizace výdajů ",[883,29029,29031],{"className":29030},[886],[888,29032,29033],{"xmlns":890},[892,29034,29035,29067],{},[895,29036,29037,29039,29041,29047,29053,29055,29061],{},[898,29038,5502],{},[1655,29040,1657],{},[1820,29042,29043,29045],{},[898,29044,2132],{},[1826,29046,1828],{},[1820,29048,29049,29051],{},[898,29050,1824],{},[1826,29052,1828],{},[1655,29054,2346],{},[1820,29056,29057,29059],{},[898,29058,2132],{},[1826,29060,1837],{},[1820,29062,29063,29065],{},[898,29064,1824],{},[1826,29066,1837],{},[902,29068,29069],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,29072,29074],{"className":29073},[886],[888,29075,29076],{"xmlns":890},[892,29077,29078,29086],{},[895,29079,29080],{},[2597,29081,29082,29084],{},[898,29083,900],{},[1655,29085,5603],{},[902,29087,29088],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,29091,29093],{"className":29092,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,29096,29098],{"className":29097},[886],[888,29099,29100],{"xmlns":890},[892,29101,29102,29122],{},[895,29103,29104,29106,29108,29114,29116],{},[2031,29105,2708],{},[1655,29107,1657],{},[1820,29109,29110,29112],{},[898,29111,2132],{},[1826,29113,1828],{},[898,29115,5923],{"mathvariant":1943},[1820,29117,29118,29120],{},[898,29119,2132],{},[1826,29121,1837],{},[902,29123,29124],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,29127,29128],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,29131,29133],{"id":29132},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,29135,29136,29137,29155,29156,29186],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,29138,29140],{"className":29139},[886],[888,29141,29142],{"xmlns":890},[892,29143,29144,29152],{},[895,29145,29146],{},[2597,29147,29148,29150],{},[898,29149,10375],{},[1655,29151,5603],{},[902,29153,29154],{"encoding":904},"Y^*"," a ceny ",[883,29157,29159],{"className":29158},[886],[888,29160,29161],{"xmlns":890},[892,29162,29163,29183],{},[895,29164,29165,29173,29175],{},[1935,29166,29167,29169,29171],{},[898,29168,2132],{},[1826,29170,1828],{},[1655,29172,5603],{},[1655,29174,1671],{"separator":1670},[1935,29176,29177,29179,29181],{},[898,29178,2132],{},[1826,29180,1837],{},[1655,29182,5603],{},[902,29184,29185],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,29188,29190],{"className":29189},[886],[888,29191,29193],{"xmlns":890,"display":29192},"block",[892,29194,29195,29254],{},[21880,29196,29198],{"width":29197},"100%",[21885,29199,29200,29203,29247,29249],{},[21888,29201],{"width":29202},"50%",[21888,29204,29205],{},[895,29206,29207,29213,29215,29223,29229,29231,29239,29245],{},[2597,29208,29209,29211],{},[898,29210,10375],{},[1655,29212,5603],{},[1655,29214,1657],{},[1935,29216,29217,29219,29221],{},[898,29218,2132],{},[1826,29220,1828],{},[1655,29222,5603],{},[1820,29224,29225,29227],{},[898,29226,1824],{},[1826,29228,1828],{},[1655,29230,2346],{},[1935,29232,29233,29235,29237],{},[898,29234,2132],{},[1826,29236,1837],{},[1655,29238,5603],{},[1820,29240,29241,29243],{},[898,29242,1824],{},[1826,29244,1837],{},[1655,29246,1671],{"separator":1670},[21888,29248],{"width":29202},[21888,29250,29251],{},[2031,29252,29253],{},"(6.12)",[902,29255,29256],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,29258,29259,29260,29263,29264,2704,29300,29336,29337,29350,29351,29365,29366,1719],{},"geometricky ",[38,29261,29262],{},"rozpočtová přímka (budget line)"," procházející body ",[883,29265,29267],{"className":29266},[886],[888,29268,29269],{"xmlns":890},[892,29270,29271,29297],{},[895,29272,29273,29275,29281,29283,29291,29293,29295],{},[1655,29274,2734],{"stretchy":1663},[2597,29276,29277,29279],{},[898,29278,10375],{},[1655,29280,5603],{},[898,29282,5923],{"mathvariant":1943},[1935,29284,29285,29287,29289],{},[898,29286,2132],{},[1826,29288,1828],{},[1655,29290,5603],{},[1655,29292,1671],{"separator":1670},[1826,29294,2552],{},[1655,29296,2743],{"stretchy":1663},[902,29298,29299],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,29301,29303],{"className":29302},[886],[888,29304,29305],{"xmlns":890},[892,29306,29307,29333],{},[895,29308,29309,29311,29313,29315,29321,29323,29331],{},[1655,29310,2734],{"stretchy":1663},[1826,29312,2552],{},[1655,29314,1671],{"separator":1670},[2597,29316,29317,29319],{},[898,29318,10375],{},[1655,29320,5603],{},[898,29322,5923],{"mathvariant":1943},[1935,29324,29325,29327,29329],{},[898,29326,2132],{},[1826,29328,1837],{},[1655,29330,5603],{},[1655,29332,2743],{"stretchy":1663},[902,29334,29335],{"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 ",[883,29338,29340],{"className":29339},[886],[888,29341,29342],{"xmlns":890},[892,29343,29344,29348],{},[895,29345,29346],{},[898,29347,900],{},[902,29349,900],{"encoding":904},", indiferenční křivky a ",[883,29352,29354],{"className":29353},[886],[888,29355,29356],{"xmlns":890},[892,29357,29358,29362],{},[895,29359,29360],{},[2031,29361,2708],{},[902,29363,29364],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,29367,880],{"className":29368,"dataFsResolvedFilePath":878,"href":879},[210],[5120,29370,29371],{},[724,29372,29373,29375,29376,29379,29380,29393,29394,29396,29397,29410,29411,3106,29414,29454,29455,29472,29473,29490,29491,29508,29509,29527],{},[883,29374,5661],{}," Pozor — dvě úlohy, totéž řešení\n",[38,29377,29378],{},"Primární úloha"," (max ",[883,29381,29383],{"className":29382},[886],[888,29384,29385],{"xmlns":890},[892,29386,29387,29391],{},[895,29388,29389],{},[898,29390,900],{},[902,29392,900],{"encoding":904}," při pevném rozpočtu) a ",[38,29395,29026],{}," (min ",[883,29398,29400],{"className":29399},[886],[888,29401,29402],{"xmlns":890},[892,29403,29404,29408],{},[895,29405,29406],{},[898,29407,5502],{},[902,29409,5502],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,29412,29413],{},"tentýž bod",[883,29415,29417],{"className":29416},[886],[888,29418,29419],{"xmlns":890},[892,29420,29421,29451],{},[895,29422,29423,29429,29431,29439,29441,29449],{},[2597,29424,29425,29427],{},[898,29426,1824],{},[1655,29428,5603],{},[1655,29430,2734],{"stretchy":1663},[1935,29432,29433,29435,29437],{},[898,29434,1824],{},[1826,29436,1828],{},[1655,29438,5603],{},[1655,29440,1671],{"separator":1670},[1935,29442,29443,29445,29447],{},[898,29444,1824],{},[1826,29446,1837],{},[1655,29448,5603],{},[1655,29450,2743],{"stretchy":1663},[902,29452,29453],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,29456,29458],{"className":29457},[886],[888,29459,29460],{"xmlns":890},[892,29461,29462,29470],{},[895,29463,29464],{},[2597,29465,29466,29468],{},[898,29467,10375],{},[1655,29469,5603],{},[902,29471,29154],{"encoding":904}," a hledáme maximální ",[883,29474,29476],{"className":29475},[886],[888,29477,29478],{"xmlns":890},[892,29479,29480,29488],{},[895,29481,29482],{},[2597,29483,29484,29486],{},[898,29485,900],{},[1655,29487,5603],{},[902,29489,29088],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,29492,29494],{"className":29493},[886],[888,29495,29496],{"xmlns":890},[892,29497,29498,29506],{},[895,29499,29500],{},[2597,29501,29502,29504],{},[898,29503,900],{},[1655,29505,5603],{},[902,29507,29088],{"encoding":904}," a hledáme minimální ",[883,29510,29512],{"className":29511},[886],[888,29513,29514],{"xmlns":890},[892,29515,29516,29524],{},[895,29517,29518],{},[2597,29519,29520,29522],{},[898,29521,5502],{},[1655,29523,5603],{},[902,29525,29526],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,29529,29531],{"id":29530},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,29533,29534,29535,29566,29567,29643,29644,1719],{},"Úlohou je najít maximum ",[883,29536,29538],{"className":29537},[886],[888,29539,29540],{"xmlns":890},[892,29541,29542,29564],{},[895,29543,29544,29546,29548,29554,29556,29562],{},[898,29545,900],{},[1655,29547,1664],{"stretchy":1663},[1820,29549,29550,29552],{},[898,29551,1824],{},[1826,29553,1828],{},[1655,29555,1671],{"separator":1670},[1820,29557,29558,29560],{},[898,29559,1824],{},[1826,29561,1837],{},[1655,29563,1677],{"stretchy":1663},[902,29565,17469],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,29568,29570],{"className":29569},[886],[888,29571,29572],{"xmlns":890},[892,29573,29574,29640],{},[895,29575,29576,29578,29580,29586,29588,29594,29596,29598,29604,29606,29614,29620,29622,29630,29636,29638],{},[898,29577,3162],{},[1655,29579,1664],{"stretchy":1663},[1820,29581,29582,29584],{},[898,29583,1824],{},[1826,29585,1828],{},[1655,29587,1671],{"separator":1670},[1820,29589,29590,29592],{},[898,29591,1824],{},[1826,29593,1837],{},[1655,29595,1677],{"stretchy":1663},[1655,29597,1657],{},[2597,29599,29600,29602],{},[898,29601,10375],{},[1655,29603,5603],{},[1655,29605,2623],{},[1935,29607,29608,29610,29612],{},[898,29609,2132],{},[1826,29611,1828],{},[1655,29613,5603],{},[1820,29615,29616,29618],{},[898,29617,1824],{},[1826,29619,1828],{},[1655,29621,2623],{},[1935,29623,29624,29626,29628],{},[898,29625,2132],{},[1826,29627,1837],{},[1655,29629,5603],{},[1820,29631,29632,29634],{},[898,29633,1824],{},[1826,29635,1837],{},[1655,29637,1657],{},[1826,29639,2552],{},[902,29641,29642],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,29645,29647],{"className":29646,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,29649,29651],{"id":29650},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,29653,29654],{},"Sestavíme",[883,29656,29658],{"className":29657},[886],[888,29659,29660],{"xmlns":890,"display":29192},[892,29661,29662,29774],{},[21880,29663,29664],{"width":29197},[21885,29665,29666,29668,29767,29769],{},[21888,29667],{"width":29202},[21888,29669,29670],{},[895,29671,29672,29675,29677,29683,29685,29691,29693,29695,29697,29699,29701,29703,29709,29711,29717,29719,29721,29723,29725,29731,29733,29741,29747,29749,29757,29763,29765],{},[898,29673,1873],{"mathvariant":29674},"script",[1655,29676,1664],{"stretchy":1663},[1820,29678,29679,29681],{},[898,29680,1824],{},[1826,29682,1828],{},[1655,29684,1671],{"separator":1670},[1820,29686,29687,29689],{},[898,29688,1824],{},[1826,29690,1837],{},[1655,29692,1671],{"separator":1670},[898,29694,17569],{},[1655,29696,1677],{"stretchy":1663},[1655,29698,1657],{},[898,29700,900],{},[1655,29702,1664],{"stretchy":1663},[1820,29704,29705,29707],{},[898,29706,1824],{},[1826,29708,1828],{},[1655,29710,1671],{"separator":1670},[1820,29712,29713,29715],{},[898,29714,1824],{},[1826,29716,1837],{},[1655,29718,1677],{"stretchy":1663},[1655,29720,2346],{},[898,29722,17569],{},[1655,29724,1664],{"stretchy":1663},[2597,29726,29727,29729],{},[898,29728,10375],{},[1655,29730,5603],{},[1655,29732,2623],{},[1935,29734,29735,29737,29739],{},[898,29736,2132],{},[1826,29738,1828],{},[1655,29740,5603],{},[1820,29742,29743,29745],{},[898,29744,1824],{},[1826,29746,1828],{},[1655,29748,2623],{},[1935,29750,29751,29753,29755],{},[898,29752,2132],{},[1826,29754,1837],{},[1655,29756,5603],{},[1820,29758,29759,29761],{},[898,29760,1824],{},[1826,29762,1837],{},[1655,29764,1677],{"stretchy":1663},[898,29766,1719],{"mathvariant":1943},[21888,29768],{"width":29202},[21888,29770,29771],{},[2031,29772,29773],{},"(6.13)",[902,29775,29776],{"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}",[724,29778,29779],{},"Soustava prvního řádu:",[883,29781,29783],{"className":29782},[886],[888,29784,29785],{"xmlns":890,"display":29192},[892,29786,29787,29970],{},[21880,29788,29789],{"width":29197},[21885,29790,29791,29793,29963,29965],{},[21888,29792],{"width":29202},[21888,29794,29795],{},[21880,29796,29797,29847,29897],{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},[21885,29798,29799,29811],{},[21888,29800,29801],{},[3615,29802,29803],{"scriptlevel":2552,"displaystyle":1670},[1935,29804,29805,29807,29809],{},[898,29806,1873],{"mathvariant":29674},[1826,29808,1828],{},[1655,29810,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,29812,29813],{},[3615,29814,29815],{"scriptlevel":2552,"displaystyle":1670},[895,29816,29817,29819,29821,29829,29831,29833,29841,29843,29845],{},[895,29818],{},[1655,29820,1657],{},[1935,29822,29823,29825,29827],{},[898,29824,900],{},[1826,29826,1828],{},[1655,29828,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,29830,2623],{},[898,29832,17569],{},[1935,29834,29835,29837,29839],{},[898,29836,2132],{},[1826,29838,1828],{},[1655,29840,5603],{},[1655,29842,1657],{},[1826,29844,2552],{},[1655,29846,1671],{"separator":1670},[21885,29848,29849,29861],{},[21888,29850,29851],{},[3615,29852,29853],{"scriptlevel":2552,"displaystyle":1670},[1935,29854,29855,29857,29859],{},[898,29856,1873],{"mathvariant":29674},[1826,29858,1837],{},[1655,29860,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,29862,29863],{},[3615,29864,29865],{"scriptlevel":2552,"displaystyle":1670},[895,29866,29867,29869,29871,29879,29881,29883,29891,29893,29895],{},[895,29868],{},[1655,29870,1657],{},[1935,29872,29873,29875,29877],{},[898,29874,900],{},[1826,29876,1837],{},[1655,29878,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,29880,2623],{},[898,29882,17569],{},[1935,29884,29885,29887,29889],{},[898,29886,2132],{},[1826,29888,1837],{},[1655,29890,5603],{},[1655,29892,1657],{},[1826,29894,2552],{},[1655,29896,1671],{"separator":1670},[21885,29898,29899,29911],{},[21888,29900,29901],{},[3615,29902,29903],{"scriptlevel":2552,"displaystyle":1670},[1935,29904,29905,29907,29909],{},[898,29906,1873],{"mathvariant":29674},[898,29908,17569],{},[1655,29910,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,29912,29913],{},[3615,29914,29915],{"scriptlevel":2552,"displaystyle":1670},[895,29916,29917,29919,29921,29927,29929,29937,29943,29945,29953,29959,29961],{},[895,29918],{},[1655,29920,1657],{},[2597,29922,29923,29925],{},[898,29924,10375],{},[1655,29926,5603],{},[1655,29928,2623],{},[1935,29930,29931,29933,29935],{},[898,29932,2132],{},[1826,29934,1828],{},[1655,29936,5603],{},[1820,29938,29939,29941],{},[898,29940,1824],{},[1826,29942,1828],{},[1655,29944,2623],{},[1935,29946,29947,29949,29951],{},[898,29948,2132],{},[1826,29950,1837],{},[1655,29952,5603],{},[1820,29954,29955,29957],{},[898,29956,1824],{},[1826,29958,1837],{},[1655,29960,1657],{},[1826,29962,13585],{},[21888,29964],{"width":29202},[21888,29966,29967],{},[2031,29968,29969],{},"(6.14)",[902,29971,29972],{"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}",[724,29974,29975,29976,29979,29980,29993,29994,2086],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,29977,29978],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,29981,29983],{"className":29982},[886],[888,29984,29985],{"xmlns":890},[892,29986,29987,29991],{},[895,29988,29989],{},[898,29990,17569],{},[902,29992,17622],{"encoding":904}," dostáváme ",[38,29995,29996],{},"podmínku optimality",[883,29998,30000],{"className":29999},[886],[888,30001,30002],{"xmlns":890,"display":29192},[892,30003,30004,30062],{},[895,30005,30006],{},[13957,30007,30008],{"notation":13959},[3615,30009,30010],{"scriptlevel":2552,"displaystyle":1663},[3615,30011,30012],{"scriptlevel":2552,"displaystyle":1663},[3615,30013,30014],{"scriptlevel":2552,"displaystyle":1670},[895,30015,30016,30018,30020,30022,30040,30042,30060],{},[2031,30017,2783],{},[2031,30019,2708],{},[1655,30021,1657],{},[1949,30023,30024,30032],{},[1935,30025,30026,30028,30030],{},[898,30027,900],{},[1826,30029,1828],{},[1655,30031,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1935,30033,30034,30036,30038],{},[898,30035,900],{},[1826,30037,1837],{},[1655,30039,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,30041,1657],{},[1949,30043,30044,30052],{},[1935,30045,30046,30048,30050],{},[898,30047,2132],{},[1826,30049,1828],{},[1655,30051,5603],{},[1935,30053,30054,30056,30058],{},[898,30055,2132],{},[1826,30057,1837],{},[1655,30059,5603],{},[2031,30061,2783],{},[902,30063,30064],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[5120,30066,30067],{},[724,30068,30069,30071,30072,30106,30107,30110,30111,30129,30130,30148,30149,30179,30180,30197,30198,30228],{},[883,30070,5406],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,30073,30075],{"className":30074},[886],[888,30076,30077],{"xmlns":890},[892,30078,30079,30103],{},[895,30080,30081,30083,30085,30093,30095],{},[2031,30082,2708],{},[1655,30084,1657],{},[1935,30086,30087,30089,30091],{},[898,30088,2132],{},[1826,30090,1828],{},[1655,30092,5603],{},[898,30094,5923],{"mathvariant":1943},[1935,30096,30097,30099,30101],{},[898,30098,2132],{},[1826,30100,1837],{},[1655,30102,5603],{},[902,30104,30105],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,30108,30109],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,30112,30114],{"className":30113},[886],[888,30115,30116],{"xmlns":890},[892,30117,30118,30126],{},[895,30119,30120],{},[1820,30121,30122,30124],{},[898,30123,1824],{},[1826,30125,1828],{},[902,30127,30128],{"encoding":904},"Q_1"," za ",[883,30131,30133],{"className":30132},[886],[888,30134,30135],{"xmlns":890},[892,30136,30137,30145],{},[895,30138,30139],{},[1820,30140,30141,30143],{},[898,30142,1824],{},[1826,30144,1837],{},[902,30146,30147],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,30150,30152],{"className":30151},[886],[888,30153,30154],{"xmlns":890},[892,30155,30156,30176],{},[895,30157,30158,30160,30162,30168,30170],{},[2031,30159,2708],{},[1655,30161,2969],{},[1820,30163,30164,30166],{},[898,30165,2132],{},[1826,30167,1828],{},[898,30169,5923],{"mathvariant":1943},[1820,30171,30172,30174],{},[898,30173,2132],{},[1826,30175,1837],{},[902,30177,30178],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,30181,30183],{"className":30182},[886],[888,30184,30185],{"xmlns":890},[892,30186,30187,30195],{},[895,30188,30189],{},[1820,30190,30191,30193],{},[898,30192,1824],{},[1826,30194,1828],{},[902,30196,30128],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,30199,30201],{"className":30200},[886],[888,30202,30203],{"xmlns":890},[892,30204,30205,30225],{},[895,30206,30207,30209,30211,30217,30219],{},[2031,30208,2708],{},[1655,30210,3065],{},[1820,30212,30213,30215],{},[898,30214,2132],{},[1826,30216,1828],{},[898,30218,5923],{"mathvariant":1943},[1820,30220,30221,30223],{},[898,30222,2132],{},[1826,30224,1837],{},[902,30226,30227],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,30230,30232,30233,30246],{"id":30231},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,30234,30236],{"className":30235},[886],[888,30237,30238],{"xmlns":890},[892,30239,30240,30244],{},[895,30241,30242],{},[898,30243,17569],{},[902,30245,17622],{"encoding":904}," — mezní užitečnost důchodu",[724,30248,30249,30250,30268,30269,30272,30273,30290,30291,30308,30309,30312],{},"Lagrangeův multiplikátor ",[883,30251,30253],{"className":30252},[886],[888,30254,30255],{"xmlns":890},[892,30256,30257,30265],{},[895,30258,30259],{},[2597,30260,30261,30263],{},[898,30262,17569],{},[1655,30264,5603],{},[902,30266,30267],{"encoding":904},"\\lambda^*"," představuje ",[38,30270,30271],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,30274,30276],{"className":30275},[886],[888,30277,30278],{"xmlns":890},[892,30279,30280,30288],{},[895,30281,30282],{},[2597,30283,30284,30286],{},[898,30285,900],{},[1655,30287,5603],{},[902,30289,29088],{"encoding":904}," při jednotkové změně důchodu ",[883,30292,30294],{"className":30293},[886],[888,30295,30296],{"xmlns":890},[892,30297,30298,30306],{},[895,30299,30300],{},[2597,30301,30302,30304],{},[898,30303,10375],{},[1655,30305,5603],{},[902,30307,29154],{"encoding":904},". Je to ",[38,30310,30311],{},"stínová cena"," rozpočtového omezení.",[5120,30314,30315,30320],{},[724,30316,30317,30319],{},[883,30318,5821],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,30321,30322,30382,30469,30505,30592],{},[123,30323,30324,30327,30328,1719],{},[38,30325,30326],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,30329,30331],{"className":30330},[886],[888,30332,30333],{"xmlns":890},[892,30334,30335,30379],{},[895,30336,30337,30343,30345,30353,30359,30361,30369,30375,30377],{},[2597,30338,30339,30341],{},[898,30340,10375],{},[1655,30342,5603],{},[1655,30344,2623],{},[1935,30346,30347,30349,30351],{},[898,30348,2132],{},[1826,30350,1828],{},[1655,30352,5603],{},[1820,30354,30355,30357],{},[898,30356,1824],{},[1826,30358,1828],{},[1655,30360,2623],{},[1935,30362,30363,30365,30367],{},[898,30364,2132],{},[1826,30366,1837],{},[1655,30368,5603],{},[1820,30370,30371,30373],{},[898,30372,1824],{},[1826,30374,1837],{},[1655,30376,1657],{},[1826,30378,2552],{},[902,30380,30381],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,30383,30384,3106,30387,1719],{},[38,30385,30386],{},"Sestav Lagrangeovu funkci",[883,30388,30390],{"className":30389},[886],[888,30391,30392],{"xmlns":890},[892,30393,30394,30466],{},[895,30395,30396,30398,30400,30402,30404,30410,30412,30418,30420,30422,30424,30426,30432,30434,30442,30448,30450,30458,30464],{},[898,30397,1873],{"mathvariant":29674},[1655,30399,1657],{},[898,30401,900],{},[1655,30403,1664],{"stretchy":1663},[1820,30405,30406,30408],{},[898,30407,1824],{},[1826,30409,1828],{},[1655,30411,1671],{"separator":1670},[1820,30413,30414,30416],{},[898,30415,1824],{},[1826,30417,1837],{},[1655,30419,1677],{"stretchy":1663},[1655,30421,2346],{},[898,30423,17569],{},[1655,30425,1664],{"stretchy":1663},[2597,30427,30428,30430],{},[898,30429,10375],{},[1655,30431,5603],{},[1655,30433,2623],{},[1935,30435,30436,30438,30440],{},[898,30437,2132],{},[1826,30439,1828],{},[1655,30441,5603],{},[1820,30443,30444,30446],{},[898,30445,1824],{},[1826,30447,1828],{},[1655,30449,2623],{},[1935,30451,30452,30454,30456],{},[898,30453,2132],{},[1826,30455,1837],{},[1655,30457,5603],{},[1820,30459,30460,30462],{},[898,30461,1824],{},[1826,30463,1837],{},[1655,30465,1677],{"stretchy":1663},[902,30467,30468],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,30470,30471,2570,30474,30504],{},[38,30472,30473],{},"Spočítej parciální derivace",[883,30475,30477],{"className":30476},[886],[888,30478,30479],{"xmlns":890},[892,30480,30481,30501],{},[895,30482,30483,30489,30491,30497,30499],{},[1820,30484,30485,30487],{},[898,30486,1824],{},[1826,30488,1828],{},[1655,30490,1671],{"separator":1670},[1820,30492,30493,30495],{},[898,30494,1824],{},[1826,30496,1837],{},[1655,30498,1671],{"separator":1670},[898,30500,17569],{},[902,30502,30503],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,30506,30507,30523,30524,30557,30558,2704,30575,1719],{},[38,30508,30509,30510],{},"Vyluč ",[883,30511,30513],{"className":30512},[886],[888,30514,30515],{"xmlns":890},[892,30516,30517,30521],{},[895,30518,30519],{},[898,30520,17569],{},[902,30522,17622],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,30525,30527],{"className":30526},[886],[888,30528,30529],{"xmlns":890},[892,30530,30531,30555],{},[895,30532,30533,30535,30537,30545,30547],{},[2031,30534,2708],{},[1655,30536,1657],{},[1935,30538,30539,30541,30543],{},[898,30540,2132],{},[1826,30542,1828],{},[1655,30544,5603],{},[898,30546,5923],{"mathvariant":1943},[1935,30548,30549,30551,30553],{},[898,30550,2132],{},[1826,30552,1837],{},[1655,30554,5603],{},[902,30556,30105],{"encoding":904},", která dá vztah mezi ",[883,30559,30561],{"className":30560},[886],[888,30562,30563],{"xmlns":890},[892,30564,30565,30573],{},[895,30566,30567],{},[1820,30568,30569,30571],{},[898,30570,1824],{},[1826,30572,1828],{},[902,30574,30128],{"encoding":904},[883,30576,30578],{"className":30577},[886],[888,30579,30580],{"xmlns":890},[892,30581,30582,30590],{},[895,30583,30584],{},[1820,30585,30586,30588],{},[898,30587,1824],{},[1826,30589,1837],{},[902,30591,30147],{"encoding":904},[123,30593,30594,30597,30598,30628,30629,30646,30647,1719],{},[38,30595,30596],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,30599,30601],{"className":30600},[886],[888,30602,30603],{"xmlns":890},[892,30604,30605,30625],{},[895,30606,30607,30615,30617],{},[1935,30608,30609,30611,30613],{},[898,30610,1824],{},[1826,30612,1828],{},[1655,30614,5603],{},[1655,30616,1671],{"separator":1670},[1935,30618,30619,30621,30623],{},[898,30620,1824],{},[1826,30622,1837],{},[1655,30624,5603],{},[902,30626,30627],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,30630,30632],{"className":30631},[886],[888,30633,30634],{"xmlns":890},[892,30635,30636,30644],{},[895,30637,30638],{},[2597,30639,30640,30642],{},[898,30641,17569],{},[1655,30643,5603],{},[902,30645,30267],{"encoding":904}," a maximální užitečnost ",[883,30648,30650],{"className":30649},[886],[888,30651,30652],{"xmlns":890},[892,30653,30654,30688],{},[895,30655,30656,30662,30664,30666,30668,30676,30678,30686],{},[2597,30657,30658,30660],{},[898,30659,900],{},[1655,30661,5603],{},[1655,30663,1657],{},[898,30665,900],{},[1655,30667,1664],{"stretchy":1663},[1935,30669,30670,30672,30674],{},[898,30671,1824],{},[1826,30673,1828],{},[1655,30675,5603],{},[1655,30677,1671],{"separator":1670},[1935,30679,30680,30682,30684],{},[898,30681,1824],{},[1826,30683,1837],{},[1655,30685,5603],{},[1655,30687,1677],{"stretchy":1663},[902,30689,30690],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,30692,30694],{"id":30693},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,30696,30697],{},[1723,30698],{"alt":30699,"className":30700,"src":30701},"imek-uzitecnost-optimum",[210,1727],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,30703,30704],{},[614,30705,30706,30707,30756,30757,2704,30785,30813,30814,30848,30849,30888,30889,30907,30908,30926,30927,30945],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,30708,30710],{"className":30709},[886],[888,30711,30712],{"xmlns":890},[892,30713,30714,30754],{},[895,30715,30716,30722,30724,30732,30738,30740,30748],{},[2597,30717,30718,30720],{},[898,30719,10375],{},[1655,30721,5603],{},[1655,30723,1657],{},[1935,30725,30726,30728,30730],{},[898,30727,2132],{},[1826,30729,1828],{},[1655,30731,5603],{},[1820,30733,30734,30736],{},[898,30735,1824],{},[1826,30737,1828],{},[1655,30739,2346],{},[1935,30741,30742,30744,30746],{},[898,30743,2132],{},[1826,30745,1837],{},[1655,30747,5603],{},[1820,30749,30750,30752],{},[898,30751,1824],{},[1826,30753,1837],{},[902,30755,18424],{"encoding":904}," protíná osy v ",[883,30758,30760],{"className":30759},[886],[888,30761,30762],{"xmlns":890},[892,30763,30764,30782],{},[895,30765,30766,30772,30774],{},[2597,30767,30768,30770],{},[898,30769,10375],{},[1655,30771,5603],{},[898,30773,5923],{"mathvariant":1943},[1935,30775,30776,30778,30780],{},[898,30777,2132],{},[1826,30779,1828],{},[1655,30781,5603],{},[902,30783,30784],{"encoding":904},"Y^*\u002FP_1^*",[883,30786,30788],{"className":30787},[886],[888,30789,30790],{"xmlns":890},[892,30791,30792,30810],{},[895,30793,30794,30800,30802],{},[2597,30795,30796,30798],{},[898,30797,10375],{},[1655,30799,5603],{},[898,30801,5923],{"mathvariant":1943},[1935,30803,30804,30806,30808],{},[898,30805,2132],{},[1826,30807,1837],{},[1655,30809,5603],{},[902,30811,30812],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,30815,30817],{"className":30816},[886],[888,30818,30819],{"xmlns":890},[892,30820,30821,30845],{},[895,30822,30823,30829,30831,30837,30839],{},[1820,30824,30825,30827],{},[898,30826,1789],{},[1826,30828,1828],{},[1655,30830,3065],{},[2597,30832,30833,30835],{},[898,30834,1789],{},[1655,30836,5603],{},[1655,30838,3065],{},[1820,30840,30841,30843],{},[898,30842,1789],{},[1826,30844,1837],{},[902,30846,30847],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,30850,30852],{"className":30851},[886],[888,30853,30854],{"xmlns":890},[892,30855,30856,30886],{},[895,30857,30858,30864,30866,30874,30876,30884],{},[2597,30859,30860,30862],{},[898,30861,1824],{},[1655,30863,5603],{},[1655,30865,2734],{"stretchy":1663},[1935,30867,30868,30870,30872],{},[898,30869,1824],{},[1826,30871,1828],{},[1655,30873,5603],{},[1655,30875,1671],{"separator":1670},[1935,30877,30878,30880,30882],{},[898,30879,1824],{},[1826,30881,1837],{},[1655,30883,5603],{},[1655,30885,2743],{"stretchy":1663},[902,30887,29453],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,30890,30892],{"className":30891},[886],[888,30893,30894],{"xmlns":890},[892,30895,30896,30904],{},[895,30897,30898],{},[2597,30899,30900,30902],{},[898,30901,1789],{},[1655,30903,5603],{},[902,30905,30906],{"encoding":904},"c^*",". Křivka ",[883,30909,30911],{"className":30910},[886],[888,30912,30913],{"xmlns":890},[892,30914,30915,30923],{},[895,30916,30917],{},[1820,30918,30919,30921],{},[898,30920,1789],{},[1826,30922,1828],{},[902,30924,30925],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,30928,30930],{"className":30929},[886],[888,30931,30932],{"xmlns":890},[892,30933,30934,30942],{},[895,30935,30936],{},[1820,30937,30938,30940],{},[898,30939,1789],{},[1826,30941,1837],{},[902,30943,30944],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,30947,30948,30949,30952,30953,30971,30972,31001],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,30950,30951],{},"dotýkají",", tj. mají v bodě ",[883,30954,30956],{"className":30955},[886],[888,30957,30958],{"xmlns":890},[892,30959,30960,30968],{},[895,30961,30962],{},[2597,30963,30964,30966],{},[898,30965,1824],{},[1655,30967,5603],{},[902,30969,30970],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,30973,30975],{"className":30974},[886],[888,30976,30977],{"xmlns":890},[892,30978,30979,30999],{},[895,30980,30981,30983,30985,30991,30993],{},[2031,30982,2708],{},[1655,30984,1657],{},[1820,30986,30987,30989],{},[898,30988,2132],{},[1826,30990,1828],{},[898,30992,5923],{"mathvariant":1943},[1820,30994,30995,30997],{},[898,30996,2132],{},[1826,30998,1837],{},[902,31000,29124],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,31003,31005],{"id":31004},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,31007,1735,31008,31070],{},[883,31009,31011],{"className":31010},[886],[888,31012,31013],{"xmlns":890},[892,31014,31015,31067],{},[895,31016,31017,31019,31021,31027,31029,31035,31037,31039,31053],{},[898,31018,900],{},[1655,31020,1664],{"stretchy":1663},[1820,31022,31023,31025],{},[898,31024,1824],{},[1826,31026,1828],{},[1655,31028,1671],{"separator":1670},[1820,31030,31031,31033],{},[898,31032,1824],{},[1826,31034,1837],{},[1655,31036,1677],{"stretchy":1663},[1655,31038,1657],{},[1935,31040,31041,31043,31045],{},[898,31042,1824],{},[1826,31044,1828],{},[895,31046,31047,31049,31051],{},[1826,31048,1828],{},[898,31050,5923],{"mathvariant":1943},[1826,31052,1837],{},[1935,31054,31055,31057,31059],{},[898,31056,1824],{},[1826,31058,1837],{},[895,31060,31061,31063,31065],{},[1826,31062,1828],{},[898,31064,5923],{"mathvariant":1943},[1826,31066,1837],{},[902,31068,31069],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,31072,31073],{},[883,31074,31076],{"className":31075},[886],[888,31077,31078],{"xmlns":890},[892,31079,31080,31186],{},[895,31081,31082,31084,31086,31168,31170,31184],{},[2031,31083,2708],{},[1655,31085,1657],{},[1949,31087,31088,31128],{},[895,31089,31090,31098,31114],{},[3615,31091,31092],{"scriptlevel":2552,"displaystyle":1663},[1949,31093,31094,31096],{},[1826,31095,1828],{},[1826,31097,1837],{},[1935,31099,31100,31102,31104],{},[898,31101,1824],{},[1826,31103,1828],{},[895,31105,31106,31108,31110,31112],{},[1655,31107,2623],{},[1826,31109,1828],{},[898,31111,5923],{"mathvariant":1943},[1826,31113,1837],{},[1935,31115,31116,31118,31120],{},[898,31117,1824],{},[1826,31119,1837],{},[895,31121,31122,31124,31126],{},[1826,31123,1828],{},[898,31125,5923],{"mathvariant":1943},[1826,31127,1837],{},[895,31129,31130,31138,31152],{},[3615,31131,31132],{"scriptlevel":2552,"displaystyle":1663},[1949,31133,31134,31136],{},[1826,31135,1828],{},[1826,31137,1837],{},[1935,31139,31140,31142,31144],{},[898,31141,1824],{},[1826,31143,1828],{},[895,31145,31146,31148,31150],{},[1826,31147,1828],{},[898,31149,5923],{"mathvariant":1943},[1826,31151,1837],{},[1935,31153,31154,31156,31158],{},[898,31155,1824],{},[1826,31157,1837],{},[895,31159,31160,31162,31164,31166],{},[1655,31161,2623],{},[1826,31163,1828],{},[898,31165,5923],{"mathvariant":1943},[1826,31167,1837],{},[1655,31169,1657],{},[1949,31171,31172,31178],{},[1820,31173,31174,31176],{},[898,31175,1824],{},[1826,31177,1837],{},[1820,31179,31180,31182],{},[898,31181,1824],{},[1826,31183,1828],{},[898,31185,1719],{"mathvariant":1943},[902,31187,31188],{"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}.",[724,31190,31191,31192,4199,31237,31239,31240,31260,31261,31291,31292,1719],{},"Tedy ",[883,31193,31195],{"className":31194},[886],[888,31196,31197],{"xmlns":890},[892,31198,31199,31234],{},[895,31200,31201,31203,31205,31208,31210,31212,31214,31216,31224,31226],{},[2031,31202,2708],{},[1655,31204,1664],{"stretchy":1663},[1826,31206,31207],{},"300",[1655,31209,1671],{"separator":1670},[1826,31211,16235],{},[1655,31213,1677],{"stretchy":1663},[1655,31215,1657],{},[3615,31217,31218],{"scriptlevel":2552,"displaystyle":1663},[1949,31219,31220,31222],{},[1826,31221,16235],{},[1826,31223,31207],{},[1655,31225,1657],{},[3615,31227,31228],{"scriptlevel":2552,"displaystyle":1663},[1949,31229,31230,31232],{},[1826,31231,3524],{},[1826,31233,3472],{},[902,31235,31236],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,31238,10462],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,31241,31243],{"className":31242},[886],[888,31244,31245],{"xmlns":890},[892,31246,31247,31257],{},[895,31248,31249],{},[3615,31250,31251],{"scriptlevel":2552,"displaystyle":1663},[1949,31252,31253,31255],{},[1826,31254,3524],{},[1826,31256,3472],{},[902,31258,31259],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,31262,31264],{"className":31263},[886],[888,31265,31266],{"xmlns":890},[892,31267,31268,31288],{},[895,31269,31270,31272,31274,31280,31282],{},[2031,31271,2708],{},[1655,31273,1657],{},[1820,31275,31276,31278],{},[898,31277,1824],{},[1826,31279,1837],{},[898,31281,5923],{"mathvariant":1943},[1820,31283,31284,31286],{},[898,31285,1824],{},[1826,31287,1828],{},[902,31289,31290],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,31293,31295],{"className":31294},[886],[888,31296,31297],{"xmlns":890},[892,31298,31299,31319],{},[895,31300,31301,31303,31305,31311,31313],{},[2031,31302,2708],{},[1655,31304,1657],{},[1820,31306,31307,31309],{},[898,31308,2132],{},[1826,31310,1828],{},[898,31312,5923],{"mathvariant":1943},[1820,31314,31315,31317],{},[898,31316,2132],{},[1826,31318,1837],{},[902,31320,29124],{"encoding":904},[115,31322,31324,31325],{"id":31323},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,31326,31328],{"className":31327},[886],[888,31329,31330],{"xmlns":890},[892,31331,31332,31350],{},[895,31333,31334,31336,31338,31344],{},[898,31335,900],{},[1655,31337,1657],{},[1820,31339,31340,31342],{},[898,31341,1824],{},[1826,31343,1828],{},[1820,31345,31346,31348],{},[898,31347,1824],{},[1826,31349,1837],{},[902,31351,31352],{"encoding":904},"U = Q_1 Q_2",[724,31354,31355,31356,1343,31402,1343,31426,1343,31450,31472],{},"Je dána ",[883,31357,31359],{"className":31358},[886],[888,31360,31361],{"xmlns":890},[892,31362,31363,31399],{},[895,31364,31365,31367,31369,31375,31377,31383,31385,31387,31393],{},[898,31366,900],{},[1655,31368,1664],{"stretchy":1663},[1820,31370,31371,31373],{},[898,31372,1824],{},[1826,31374,1828],{},[1655,31376,1671],{"separator":1670},[1820,31378,31379,31381],{},[898,31380,1824],{},[1826,31382,1837],{},[1655,31384,1677],{"stretchy":1663},[1655,31386,1657],{},[1820,31388,31389,31391],{},[898,31390,1824],{},[1826,31392,1828],{},[1820,31394,31395,31397],{},[898,31396,1824],{},[1826,31398,1837],{},[902,31400,31401],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,31403,31405],{"className":31404},[886],[888,31406,31407],{"xmlns":890},[892,31408,31409,31423],{},[895,31410,31411,31419,31421],{},[1935,31412,31413,31415,31417],{},[898,31414,2132],{},[1826,31416,1828],{},[1655,31418,5603],{},[1655,31420,1657],{},[1826,31422,1837],{},[902,31424,31425],{"encoding":904},"P_1^* = 2",[883,31427,31429],{"className":31428},[886],[888,31430,31431],{"xmlns":890},[892,31432,31433,31447],{},[895,31434,31435,31443,31445],{},[1935,31436,31437,31439,31441],{},[898,31438,2132],{},[1826,31440,1837],{},[1655,31442,5603],{},[1655,31444,1657],{},[1826,31446,3524],{},[902,31448,31449],{"encoding":904},"P_2^* = 5",[883,31451,31453],{"className":31452},[886],[888,31454,31455],{"xmlns":890},[892,31456,31457,31469],{},[895,31458,31459,31465,31467],{},[2597,31460,31461,31463],{},[898,31462,10375],{},[1655,31464,5603],{},[1655,31466,1657],{},[1826,31468,4360],{},[902,31470,31471],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,31474,31476],{"className":31475},[886],[888,31477,31478],{"xmlns":890,"display":29192},[892,31479,31480,31552],{},[895,31481,31482,31484,31486,31492,31494,31500,31502,31504,31506,31508,31514,31520,31522,31524,31526,31528,31530,31532,31538,31540,31542,31548,31550],{},[898,31483,1873],{"mathvariant":29674},[1655,31485,1664],{"stretchy":1663},[1820,31487,31488,31490],{},[898,31489,1824],{},[1826,31491,1828],{},[1655,31493,1671],{"separator":1670},[1820,31495,31496,31498],{},[898,31497,1824],{},[1826,31499,1837],{},[1655,31501,1671],{"separator":1670},[898,31503,17569],{},[1655,31505,1677],{"stretchy":1663},[1655,31507,1657],{},[1820,31509,31510,31512],{},[898,31511,1824],{},[1826,31513,1828],{},[1820,31515,31516,31518],{},[898,31517,1824],{},[1826,31519,1837],{},[1655,31521,2346],{},[898,31523,17569],{},[1655,31525,1664],{"stretchy":1663},[1826,31527,4360],{},[1655,31529,2623],{},[1826,31531,1837],{},[1820,31533,31534,31536],{},[898,31535,1824],{},[1826,31537,1828],{},[1655,31539,2623],{},[1826,31541,3524],{},[1820,31543,31544,31546],{},[898,31545,1824],{},[1826,31547,1837],{},[1655,31549,1677],{"stretchy":1663},[898,31551,1719],{"mathvariant":1943},[902,31553,31554],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,31556,31557],{},"Soustava:",[883,31559,31561],{"className":31560},[886],[888,31562,31563],{"xmlns":890,"display":29192},[892,31564,31565,31677],{},[21880,31566,31567,31601,31635],{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},[21885,31568,31569,31587],{},[21888,31570,31571],{},[3615,31572,31573],{"scriptlevel":2552,"displaystyle":1670},[895,31574,31575,31581,31583,31585],{},[1820,31576,31577,31579],{},[898,31578,1824],{},[1826,31580,1837],{},[1655,31582,2623],{},[1826,31584,1837],{},[898,31586,17569],{},[21888,31588,31589],{},[3615,31590,31591],{"scriptlevel":2552,"displaystyle":1670},[895,31592,31593,31595,31597,31599],{},[895,31594],{},[1655,31596,1657],{},[1826,31598,2552],{},[1655,31600,1671],{"separator":1670},[21885,31602,31603,31621],{},[21888,31604,31605],{},[3615,31606,31607],{"scriptlevel":2552,"displaystyle":1670},[895,31608,31609,31615,31617,31619],{},[1820,31610,31611,31613],{},[898,31612,1824],{},[1826,31614,1828],{},[1655,31616,2623],{},[1826,31618,3524],{},[898,31620,17569],{},[21888,31622,31623],{},[3615,31624,31625],{"scriptlevel":2552,"displaystyle":1670},[895,31626,31627,31629,31631,31633],{},[895,31628],{},[1655,31630,1657],{},[1826,31632,2552],{},[1655,31634,1671],{"separator":1670},[21885,31636,31637,31665],{},[21888,31638,31639],{},[3615,31640,31641],{"scriptlevel":2552,"displaystyle":1670},[895,31642,31643,31645,31647,31649,31655,31657,31659],{},[1826,31644,4360],{},[1655,31646,2623],{},[1826,31648,1837],{},[1820,31650,31651,31653],{},[898,31652,1824],{},[1826,31654,1828],{},[1655,31656,2623],{},[1826,31658,3524],{},[1820,31660,31661,31663],{},[898,31662,1824],{},[1826,31664,1837],{},[21888,31666,31667],{},[3615,31668,31669],{"scriptlevel":2552,"displaystyle":1670},[895,31670,31671,31673,31675],{},[895,31672],{},[1655,31674,1657],{},[1826,31676,13585],{},[902,31678,31679],{"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}",[724,31681,31682,31683,1343,31707,31731,31732,6838,31772,31790,31791,31841,31842,1719],{},"Z prvních dvou rovnic ",[883,31684,31686],{"className":31685},[886],[888,31687,31688],{"xmlns":890},[892,31689,31690,31704],{},[895,31691,31692,31698,31700,31702],{},[1820,31693,31694,31696],{},[898,31695,1824],{},[1826,31697,1837],{},[1655,31699,1657],{},[1826,31701,1837],{},[898,31703,17569],{},[902,31705,31706],{"encoding":904},"Q_2 = 2\\lambda",[883,31708,31710],{"className":31709},[886],[888,31711,31712],{"xmlns":890},[892,31713,31714,31728],{},[895,31715,31716,31722,31724,31726],{},[1820,31717,31718,31720],{},[898,31719,1824],{},[1826,31721,1828],{},[1655,31723,1657],{},[1826,31725,3524],{},[898,31727,17569],{},[902,31729,31730],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,31733,31735],{"className":31734},[886],[888,31736,31737],{"xmlns":890},[892,31738,31739,31769],{},[895,31740,31741,31743,31745,31747,31749,31751,31753,31755,31757,31759,31761,31763,31765,31767],{},[1826,31742,4360],{},[1655,31744,1657],{},[1826,31746,1837],{},[1655,31748,2869],{},[1826,31750,3524],{},[898,31752,17569],{},[1655,31754,2346],{},[1826,31756,3524],{},[1655,31758,2869],{},[1826,31760,1837],{},[898,31762,17569],{},[1655,31764,1657],{},[1826,31766,10282],{},[898,31768,17569],{},[902,31770,31771],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,31773,31775],{"className":31774},[886],[888,31776,31777],{"xmlns":890},[892,31778,31779,31787],{},[895,31780,31781,31783,31785],{},[898,31782,17569],{},[1655,31784,1657],{},[1826,31786,3524],{},[902,31788,31789],{"encoding":904},"\\lambda = 5",". Odtud ",[38,31792,31793,1343,31817],{},[883,31794,31796],{"className":31795},[886],[888,31797,31798],{"xmlns":890},[892,31799,31800,31814],{},[895,31801,31802,31810,31812],{},[1935,31803,31804,31806,31808],{},[898,31805,1824],{},[1826,31807,1828],{},[1655,31809,5603],{},[1655,31811,1657],{},[1826,31813,6253],{},[902,31815,31816],{"encoding":904},"Q_1^* = 25",[883,31818,31820],{"className":31819},[886],[888,31821,31822],{"xmlns":890},[892,31823,31824,31838],{},[895,31825,31826,31834,31836],{},[1935,31827,31828,31830,31832],{},[898,31829,1824],{},[1826,31831,1837],{},[1655,31833,5603],{},[1655,31835,1657],{},[1826,31837,4136],{},[902,31839,31840],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,31843,31845],{"className":31844},[886],[888,31846,31847],{"xmlns":890},[892,31848,31849,31870],{},[895,31850,31851,31857,31859,31861,31863,31865,31867],{},[2597,31852,31853,31855],{},[898,31854,900],{},[1655,31856,5603],{},[1655,31858,1657],{},[1826,31860,6253],{},[1655,31862,2869],{},[1826,31864,4136],{},[1655,31866,1657],{},[1826,31868,31869],{},"250",[902,31871,31872],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,31874,31875],{},[614,31876,31877,31878,29263,31916,2704,31940,31964,31965,31995,31996,32020,32021,32043,32044,1719],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,31879,31881],{"className":31880},[886],[888,31882,31883],{"xmlns":890},[892,31884,31885,31913],{},[895,31886,31887,31889,31891,31893,31899,31901,31903,31909,31911],{},[1826,31888,4360],{},[1655,31890,2623],{},[1826,31892,1837],{},[1820,31894,31895,31897],{},[898,31896,1824],{},[1826,31898,1828],{},[1655,31900,2623],{},[1826,31902,3524],{},[1820,31904,31905,31907],{},[898,31906,1824],{},[1826,31908,1837],{},[1655,31910,1657],{},[1826,31912,2552],{},[902,31914,31915],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,31917,31919],{"className":31918},[886],[888,31920,31921],{"xmlns":890},[892,31922,31923,31937],{},[895,31924,31925,31927,31929,31931,31933,31935],{},[898,31926,2731],{},[1655,31928,2734],{"stretchy":1663},[1826,31930,2552],{},[1655,31932,1671],{"separator":1670},[1826,31934,10282],{},[1655,31936,2743],{"stretchy":1663},[902,31938,31939],{"encoding":904},"A[0, 20]",[883,31941,31943],{"className":31942},[886],[888,31944,31945],{"xmlns":890},[892,31946,31947,31961],{},[895,31948,31949,31951,31953,31955,31957,31959],{},[898,31950,24379],{},[1655,31952,2734],{"stretchy":1663},[1826,31954,4390],{},[1655,31956,1671],{"separator":1670},[1826,31958,2552],{},[1655,31960,2743],{"stretchy":1663},[902,31962,31963],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,31966,31968],{"className":31967},[886],[888,31969,31970],{"xmlns":890},[892,31971,31972,31992],{},[895,31973,31974,31980,31982,31984,31986],{},[1820,31975,31976,31978],{},[898,31977,1824],{},[1826,31979,1837],{},[1655,31981,1657],{},[1826,31983,31869],{},[898,31985,5923],{"mathvariant":1943},[1820,31987,31988,31990],{},[898,31989,1824],{},[1826,31991,1828],{},[902,31993,31994],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,31997,31999],{"className":31998},[886],[888,32000,32001],{"xmlns":890},[892,32002,32003,32017],{},[895,32004,32005,32007,32009,32011,32013,32015],{},[898,32006,5502],{},[1655,32008,2734],{"stretchy":1663},[1826,32010,6253],{},[1655,32012,1671],{"separator":1670},[1826,32014,4136],{},[1655,32016,2743],{"stretchy":1663},[902,32018,32019],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,32022,32024],{"className":32023},[886],[888,32025,32026],{"xmlns":890},[892,32027,32028,32040],{},[895,32029,32030,32032],{},[1655,32031,2623],{},[3615,32033,32034],{"scriptlevel":2552,"displaystyle":1663},[1949,32035,32036,32038],{},[1826,32037,1837],{},[1826,32039,3524],{},[902,32041,32042],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,32045,32047],{"className":32046},[886],[888,32048,32049],{"xmlns":890},[892,32050,32051,32091],{},[895,32052,32053,32055,32057,32059,32061,32063,32065,32067,32069,32071,32079,32081,32083],{},[1655,32054,2623],{},[2031,32056,2708],{},[1655,32058,1664],{"stretchy":1663},[1826,32060,6253],{},[1655,32062,1671],{"separator":1670},[1826,32064,4136],{},[1655,32066,1677],{"stretchy":1663},[1655,32068,1657],{},[1655,32070,2623],{},[3615,32072,32073],{"scriptlevel":2552,"displaystyle":1663},[1949,32074,32075,32077],{},[1826,32076,4136],{},[1826,32078,6253],{},[1655,32080,1657],{},[1655,32082,2623],{},[3615,32084,32085],{"scriptlevel":2552,"displaystyle":1663},[1949,32086,32087,32089],{},[1826,32088,1837],{},[1826,32090,3524],{},[902,32092,32093],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,32095,32097],{"id":32096},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,32099,32100,32101,30129,32131,32134,32135,2086],{},"Považujeme-li v úloze ",[883,32102,32104],{"className":32103},[886],[888,32105,32106],{"xmlns":890},[892,32107,32108,32128],{},[895,32109,32110,32116,32118,32124,32126],{},[1820,32111,32112,32114],{},[898,32113,2132],{},[1826,32115,1828],{},[1655,32117,1671],{"separator":1670},[1820,32119,32120,32122],{},[898,32121,2132],{},[1826,32123,1837],{},[1655,32125,1671],{"separator":1670},[898,32127,10375],{},[902,32129,32130],{"encoding":904},"P_1, P_2, Y",[38,32132,32133],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,32136,32137],{},"Marshallovy poptávkové funkce",[883,32139,32141],{"className":32140},[886],[888,32142,32143],{"xmlns":890,"display":29192},[892,32144,32145,32240],{},[21880,32146,32147],{"width":29197},[21885,32148,32149,32151,32233,32235],{},[21888,32150],{"width":29202},[21888,32152,32153],{},[895,32154,32155,32161,32163,32169,32171,32177,32179,32185,32187,32189,32191,32193,32195,32201,32203,32209,32211,32217,32219,32225,32227,32229,32231],{},[1820,32156,32157,32159],{},[898,32158,1824],{},[1826,32160,1828],{},[1655,32162,1657],{},[1820,32164,32165,32167],{},[898,32166,2838],{},[1826,32168,1828],{},[1655,32170,1664],{"stretchy":1663},[1820,32172,32173,32175],{},[898,32174,2132],{},[1826,32176,1828],{},[1655,32178,1671],{"separator":1670},[1820,32180,32181,32183],{},[898,32182,2132],{},[1826,32184,1837],{},[1655,32186,1671],{"separator":1670},[898,32188,10375],{},[1655,32190,1677],{"stretchy":1663},[1655,32192,1671],{"separator":1670},[1967,32194],{"width":16409},[1820,32196,32197,32199],{},[898,32198,1824],{},[1826,32200,1837],{},[1655,32202,1657],{},[1820,32204,32205,32207],{},[898,32206,2838],{},[1826,32208,1837],{},[1655,32210,1664],{"stretchy":1663},[1820,32212,32213,32215],{},[898,32214,2132],{},[1826,32216,1828],{},[1655,32218,1671],{"separator":1670},[1820,32220,32221,32223],{},[898,32222,2132],{},[1826,32224,1837],{},[1655,32226,1671],{"separator":1670},[898,32228,10375],{},[1655,32230,1677],{"stretchy":1663},[1655,32232,1671],{"separator":1670},[21888,32234],{"width":29202},[21888,32236,32237],{},[2031,32238,32239],{},"(6.15)",[902,32241,32242],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,32244,32246],{"className":32245},[886],[888,32247,32248],{"xmlns":890,"display":29192},[892,32249,32250,32297],{},[21880,32251,32252],{"width":29197},[21885,32253,32254,32256,32290,32292],{},[21888,32255],{"width":29202},[21888,32257,32258],{},[895,32259,32260,32262,32264,32266,32268,32274,32276,32282,32284,32286,32288],{},[898,32261,17569],{},[1655,32263,1657],{},[898,32265,17569],{},[1655,32267,1664],{"stretchy":1663},[1820,32269,32270,32272],{},[898,32271,2132],{},[1826,32273,1828],{},[1655,32275,1671],{"separator":1670},[1820,32277,32278,32280],{},[898,32279,2132],{},[1826,32281,1837],{},[1655,32283,1671],{"separator":1670},[898,32285,10375],{},[1655,32287,1677],{"stretchy":1663},[898,32289,1719],{"mathvariant":1943},[21888,32291],{"width":29202},[21888,32293,32294],{},[2031,32295,32296],{},"(6.16)",[902,32298,32299],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,32301,32302,32332,32333,32399],{},[38,32303,32304,32305,1719],{},"Odvození pro ",[883,32306,32308],{"className":32307},[886],[888,32309,32310],{"xmlns":890},[892,32311,32312,32330],{},[895,32313,32314,32316,32318,32324],{},[898,32315,900],{},[1655,32317,1657],{},[1820,32319,32320,32322],{},[898,32321,1824],{},[1826,32323,1828],{},[1820,32325,32326,32328],{},[898,32327,1824],{},[1826,32329,1837],{},[902,32331,31352],{"encoding":904}," Lagrangeova funkce ",[883,32334,32336],{"className":32335},[886],[888,32337,32338],{"xmlns":890},[892,32339,32340,32396],{},[895,32341,32342,32344,32346,32352,32358,32360,32362,32364,32366,32368,32374,32380,32382,32388,32394],{},[898,32343,1873],{"mathvariant":29674},[1655,32345,1657],{},[1820,32347,32348,32350],{},[898,32349,1824],{},[1826,32351,1828],{},[1820,32353,32354,32356],{},[898,32355,1824],{},[1826,32357,1837],{},[1655,32359,2346],{},[898,32361,17569],{},[1655,32363,1664],{"stretchy":1663},[898,32365,10375],{},[1655,32367,2623],{},[1820,32369,32370,32372],{},[898,32371,2132],{},[1826,32373,1828],{},[1820,32375,32376,32378],{},[898,32377,1824],{},[1826,32379,1828],{},[1655,32381,2623],{},[1820,32383,32384,32386],{},[898,32385,2132],{},[1826,32387,1837],{},[1820,32389,32390,32392],{},[898,32391,1824],{},[1826,32393,1837],{},[1655,32395,1677],{"stretchy":1663},[902,32397,32398],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,32401,32403],{"className":32402},[886],[888,32404,32405],{"xmlns":890,"display":29192},[892,32406,32407,32574],{},[21880,32408,32409],{"width":29197},[21885,32410,32411,32413,32567,32569],{},[21888,32412],{"width":29202},[21888,32414,32415],{},[21880,32416,32417,32463,32509],{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},[21885,32418,32419,32431],{},[21888,32420,32421],{},[3615,32422,32423],{"scriptlevel":2552,"displaystyle":1670},[1935,32424,32425,32427,32429],{},[898,32426,1873],{"mathvariant":29674},[1826,32428,1828],{},[1655,32430,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,32432,32433],{},[3615,32434,32435],{"scriptlevel":2552,"displaystyle":1670},[895,32436,32437,32439,32441,32447,32449,32451,32457,32459,32461],{},[895,32438],{},[1655,32440,1657],{},[1820,32442,32443,32445],{},[898,32444,1824],{},[1826,32446,1837],{},[1655,32448,2623],{},[898,32450,17569],{},[1820,32452,32453,32455],{},[898,32454,2132],{},[1826,32456,1828],{},[1655,32458,1657],{},[1826,32460,2552],{},[1655,32462,1671],{"separator":1670},[21885,32464,32465,32477],{},[21888,32466,32467],{},[3615,32468,32469],{"scriptlevel":2552,"displaystyle":1670},[1935,32470,32471,32473,32475],{},[898,32472,1873],{"mathvariant":29674},[1826,32474,1837],{},[1655,32476,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,32478,32479],{},[3615,32480,32481],{"scriptlevel":2552,"displaystyle":1670},[895,32482,32483,32485,32487,32493,32495,32497,32503,32505,32507],{},[895,32484],{},[1655,32486,1657],{},[1820,32488,32489,32491],{},[898,32490,1824],{},[1826,32492,1828],{},[1655,32494,2623],{},[898,32496,17569],{},[1820,32498,32499,32501],{},[898,32500,2132],{},[1826,32502,1837],{},[1655,32504,1657],{},[1826,32506,2552],{},[1655,32508,1671],{"separator":1670},[21885,32510,32511,32523],{},[21888,32512,32513],{},[3615,32514,32515],{"scriptlevel":2552,"displaystyle":1670},[1935,32516,32517,32519,32521],{},[898,32518,1873],{"mathvariant":29674},[898,32520,17569],{},[1655,32522,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,32524,32525],{},[3615,32526,32527],{"scriptlevel":2552,"displaystyle":1670},[895,32528,32529,32531,32533,32535,32537,32543,32549,32551,32557,32563,32565],{},[895,32530],{},[1655,32532,1657],{},[898,32534,10375],{},[1655,32536,2623],{},[1820,32538,32539,32541],{},[898,32540,2132],{},[1826,32542,1828],{},[1820,32544,32545,32547],{},[898,32546,1824],{},[1826,32548,1828],{},[1655,32550,2623],{},[1820,32552,32553,32555],{},[898,32554,2132],{},[1826,32556,1837],{},[1820,32558,32559,32561],{},[898,32560,1824],{},[1826,32562,1837],{},[1655,32564,1657],{},[1826,32566,13585],{},[21888,32568],{"width":29202},[21888,32570,32571],{},[2031,32572,32573],{},"(6.17)",[902,32575,32576],{"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}",[724,32578,32579,32580,32608,32609,32637,32638,32706],{},"Z prvních dvou: ",[883,32581,32583],{"className":32582},[886],[888,32584,32585],{"xmlns":890},[892,32586,32587,32605],{},[895,32588,32589,32595,32597,32603],{},[1820,32590,32591,32593],{},[898,32592,1824],{},[1826,32594,1837],{},[1655,32596,1657],{},[1820,32598,32599,32601],{},[898,32600,2132],{},[1826,32602,1828],{},[898,32604,17569],{},[902,32606,32607],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,32610,32612],{"className":32611},[886],[888,32613,32614],{"xmlns":890},[892,32615,32616,32634],{},[895,32617,32618,32624,32626,32632],{},[1820,32619,32620,32622],{},[898,32621,1824],{},[1826,32623,1828],{},[1655,32625,1657],{},[1820,32627,32628,32630],{},[898,32629,2132],{},[1826,32631,1837],{},[898,32633,17569],{},[902,32635,32636],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,32639,32641],{"className":32640},[886],[888,32642,32643],{"xmlns":890},[892,32644,32645,32703],{},[895,32646,32647,32649,32651,32657,32659,32665,32667,32669,32675,32677,32683,32685,32687,32689,32695,32701],{},[898,32648,10375],{},[1655,32650,1657],{},[1820,32652,32653,32655],{},[898,32654,2132],{},[1826,32656,1828],{},[1655,32658,2869],{},[1820,32660,32661,32663],{},[898,32662,2132],{},[1826,32664,1837],{},[898,32666,17569],{},[1655,32668,2346],{},[1820,32670,32671,32673],{},[898,32672,2132],{},[1826,32674,1837],{},[1655,32676,2869],{},[1820,32678,32679,32681],{},[898,32680,2132],{},[1826,32682,1828],{},[898,32684,17569],{},[1655,32686,1657],{},[1826,32688,1837],{},[1820,32690,32691,32693],{},[898,32692,2132],{},[1826,32694,1828],{},[1820,32696,32697,32699],{},[898,32698,2132],{},[1826,32700,1837],{},[898,32702,17569],{},[902,32704,32705],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,32708,32710],{"className":32709},[886],[888,32711,32712],{"xmlns":890,"display":29192},[892,32713,32714,32757],{},[21880,32715,32716],{"width":29197},[21885,32717,32718,32720,32750,32752],{},[21888,32719],{"width":29202},[21888,32721,32722],{},[895,32723,32724,32726,32728,32748],{},[898,32725,17569],{},[1655,32727,1657],{},[1949,32729,32730,32732],{},[898,32731,10375],{},[895,32733,32734,32736,32742],{},[1826,32735,1837],{},[1820,32737,32738,32740],{},[898,32739,2132],{},[1826,32741,1828],{},[1820,32743,32744,32746],{},[898,32745,2132],{},[1826,32747,1837],{},[898,32749,1719],{"mathvariant":1943},[21888,32751],{"width":29202},[21888,32753,32754],{},[2031,32755,32756],{},"(6.20)",[902,32758,32759],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,32761,32762],{},"Zpětně:",[883,32764,32766],{"className":32765},[886],[888,32767,32768],{"xmlns":890,"display":29192},[892,32769,32770,32847],{},[21880,32771,32772],{"width":29197},[21885,32773,32774,32776,32840,32842],{},[21888,32775],{"width":29202},[21888,32777,32778],{},[13957,32779,32780],{"notation":13959},[3615,32781,32782],{"scriptlevel":2552,"displaystyle":1663},[3615,32783,32784],{"scriptlevel":2552,"displaystyle":1663},[3615,32785,32786],{"scriptlevel":2552,"displaystyle":1670},[895,32787,32788,32790,32796,32798,32812,32814,32816,32822,32824,32838],{},[2031,32789,2783],{},[1820,32791,32792,32794],{},[898,32793,1824],{},[1826,32795,1828],{},[1655,32797,1657],{},[1949,32799,32800,32802],{},[898,32801,10375],{},[895,32803,32804,32806],{},[1826,32805,1837],{},[1820,32807,32808,32810],{},[898,32809,2132],{},[1826,32811,1828],{},[1655,32813,1671],{"separator":1670},[1967,32815],{"width":16409},[1820,32817,32818,32820],{},[898,32819,1824],{},[1826,32821,1837],{},[1655,32823,1657],{},[1949,32825,32826,32828],{},[898,32827,10375],{},[895,32829,32830,32832],{},[1826,32831,1837],{},[1820,32833,32834,32836],{},[898,32835,2132],{},[1826,32837,1837],{},[2031,32839,2783],{},[21888,32841],{"width":29202},[21888,32843,32844],{},[2031,32845,32846],{},"(6.21)",[902,32848,32849],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,32851,32853],{"id":32852},"engelova-funkce","Engelova funkce",[724,32855,1735,32856,32859,32860,32863,32864,20993,32881,1343,32911,32941,32942,32976,32977,1343,33003,33029],{},[38,32857,32858],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,32861,32862],{},"Engelovou funkcí",": pro ",[883,32865,32867],{"className":32866},[886],[888,32868,32869],{"xmlns":890},[892,32870,32871,32879],{},[895,32872,32873,32875,32877],{},[898,32874,10375],{},[1655,32876,1657],{},[1826,32878,4360],{},[902,32880,21445],{"encoding":904},[883,32882,32884],{"className":32883},[886],[888,32885,32886],{"xmlns":890},[892,32887,32888,32908],{},[895,32889,32890,32896,32898,32900,32902],{},[1820,32891,32892,32894],{},[898,32893,1824],{},[1826,32895,1828],{},[1655,32897,1657],{},[1826,32899,4390],{},[898,32901,5923],{"mathvariant":1943},[1820,32903,32904,32906],{},[898,32905,2132],{},[1826,32907,1828],{},[902,32909,32910],{"encoding":904},"Q_1 = 50\u002FP_1",[883,32912,32914],{"className":32913},[886],[888,32915,32916],{"xmlns":890},[892,32917,32918,32938],{},[895,32919,32920,32926,32928,32930,32932],{},[1820,32921,32922,32924],{},[898,32923,1824],{},[1826,32925,1837],{},[1655,32927,1657],{},[1826,32929,4390],{},[898,32931,5923],{"mathvariant":1943},[1820,32933,32934,32936],{},[898,32935,2132],{},[1826,32937,1837],{},[902,32939,32940],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,32943,32945],{"className":32944},[886],[888,32946,32947],{"xmlns":890},[892,32948,32949,32973],{},[895,32950,32951,32957,32959,32961,32963,32969,32971],{},[1820,32952,32953,32955],{},[898,32954,2132],{},[1826,32956,1828],{},[1655,32958,1657],{},[1826,32960,4136],{},[1655,32962,1671],{"separator":1670},[1820,32964,32965,32967],{},[898,32966,2132],{},[1826,32968,1837],{},[1655,32970,1657],{},[1826,32972,10282],{},[902,32974,32975],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,32978,32980],{"className":32979},[886],[888,32981,32982],{"xmlns":890},[892,32983,32984,33000],{},[895,32985,32986,32992,32994,32996,32998],{},[1820,32987,32988,32990],{},[898,32989,1824],{},[1826,32991,1828],{},[1655,32993,1657],{},[898,32995,10375],{},[898,32997,5923],{"mathvariant":1943},[1826,32999,10282],{},[902,33001,33002],{"encoding":904},"Q_1 = Y\u002F20",[883,33004,33006],{"className":33005},[886],[888,33007,33008],{"xmlns":890},[892,33009,33010,33026],{},[895,33011,33012,33018,33020,33022,33024],{},[1820,33013,33014,33016],{},[898,33015,1824],{},[1826,33017,1837],{},[1655,33019,1657],{},[898,33021,10375],{},[898,33023,5923],{"mathvariant":1943},[1826,33025,6460],{},[902,33027,33028],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,33031,33033],{"id":33032},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,33035,33036],{},"Výdaje spotřebitele jsou",[883,33038,33040],{"className":33039},[886],[888,33041,33042],{"xmlns":890,"display":29192},[892,33043,33044,33119],{},[21880,33045,33046],{"width":29197},[21885,33047,33048,33050,33112,33114],{},[21888,33049],{"width":29202},[21888,33051,33052],{},[895,33053,33054,33056,33058,33060,33062,33068,33070,33076,33078,33080,33088,33094,33096,33104,33110],{},[898,33055,5502],{},[1655,33057,1657],{},[898,33059,5502],{},[1655,33061,1664],{"stretchy":1663},[1820,33063,33064,33066],{},[898,33065,1824],{},[1826,33067,1828],{},[1655,33069,1671],{"separator":1670},[1820,33071,33072,33074],{},[898,33073,1824],{},[1826,33075,1837],{},[1655,33077,1677],{"stretchy":1663},[1655,33079,1657],{},[1935,33081,33082,33084,33086],{},[898,33083,2132],{},[1826,33085,1828],{},[1655,33087,5603],{},[1820,33089,33090,33092],{},[898,33091,1824],{},[1826,33093,1828],{},[1655,33095,2346],{},[1935,33097,33098,33100,33102],{},[898,33099,2132],{},[1826,33101,1837],{},[1655,33103,5603],{},[1820,33105,33106,33108],{},[898,33107,1824],{},[1826,33109,1837],{},[1655,33111,1671],{"separator":1670},[21888,33113],{"width":29202},[21888,33115,33116],{},[2031,33117,33118],{},"(6.22)",[902,33120,33121],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,33123,33124],{},"a je pevně zadána hladina užitečnosti",[883,33126,33128],{"className":33127},[886],[888,33129,33130],{"xmlns":890,"display":29192},[892,33131,33132,33179],{},[21880,33133,33134],{"width":29197},[21885,33135,33136,33138,33172,33174],{},[21888,33137],{"width":29202},[21888,33139,33140],{},[895,33141,33142,33148,33150,33152,33154,33160,33162,33168,33170],{},[2597,33143,33144,33146],{},[898,33145,900],{},[1655,33147,5603],{},[1655,33149,1657],{},[898,33151,900],{},[1655,33153,1664],{"stretchy":1663},[1820,33155,33156,33158],{},[898,33157,1824],{},[1826,33159,1828],{},[1655,33161,1671],{"separator":1670},[1820,33163,33164,33166],{},[898,33165,1824],{},[1826,33167,1837],{},[1655,33169,1677],{"stretchy":1663},[898,33171,1719],{"mathvariant":1943},[21888,33173],{"width":29202},[21888,33175,33176],{},[2031,33177,33178],{},"(6.23)",[902,33180,33181],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,33183,33184,33187,33188,33220,33221,1719],{},[38,33185,33186],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,33189,33191],{"className":33190},[886],[888,33192,33193],{"xmlns":890},[892,33194,33195,33217],{},[895,33196,33197,33199,33201,33207,33209,33215],{},[898,33198,5502],{},[1655,33200,1664],{"stretchy":1663},[1820,33202,33203,33205],{},[898,33204,1824],{},[1826,33206,1828],{},[1655,33208,1671],{"separator":1670},[1820,33210,33211,33213],{},[898,33212,1824],{},[1826,33214,1837],{},[1655,33216,1677],{"stretchy":1663},[902,33218,33219],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,33222,33224],{"className":33223},[886],[888,33225,33226],{"xmlns":890},[892,33227,33228,33284],{},[895,33229,33230,33232,33234,33240,33242,33248,33250,33252,33258,33260,33262,33264,33270,33272,33278,33280,33282],{},[898,33231,3162],{},[1655,33233,1664],{"stretchy":1663},[1820,33235,33236,33238],{},[898,33237,1824],{},[1826,33239,1828],{},[1655,33241,1671],{"separator":1670},[1820,33243,33244,33246],{},[898,33245,1824],{},[1826,33247,1837],{},[1655,33249,1677],{"stretchy":1663},[1655,33251,1657],{},[2597,33253,33254,33256],{},[898,33255,900],{},[1655,33257,5603],{},[1655,33259,2623],{},[898,33261,900],{},[1655,33263,1664],{"stretchy":1663},[1820,33265,33266,33268],{},[898,33267,1824],{},[1826,33269,1828],{},[1655,33271,1671],{"separator":1670},[1820,33273,33274,33276],{},[898,33275,1824],{},[1826,33277,1837],{},[1655,33279,1677],{"stretchy":1663},[1655,33281,1657],{},[1826,33283,2552],{},[902,33285,33286],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,33288,33290],{"id":33289},"lagrangeova-funkce","Lagrangeova funkce",[883,33292,33294],{"className":33293},[886],[888,33295,33296],{"xmlns":890,"display":29192},[892,33297,33298,33409],{},[21880,33299,33300],{"width":29197},[21885,33301,33302,33304,33402,33404],{},[21888,33303],{"width":29202},[21888,33305,33306],{},[895,33307,33308,33310,33312,33318,33320,33326,33328,33330,33332,33334,33342,33348,33350,33358,33364,33366,33368,33370,33376,33378,33380,33382,33388,33390,33396,33398,33400],{},[898,33309,1873],{"mathvariant":29674},[1655,33311,1664],{"stretchy":1663},[1820,33313,33314,33316],{},[898,33315,1824],{},[1826,33317,1828],{},[1655,33319,1671],{"separator":1670},[1820,33321,33322,33324],{},[898,33323,1824],{},[1826,33325,1837],{},[1655,33327,1671],{"separator":1670},[898,33329,17569],{},[1655,33331,1677],{"stretchy":1663},[1655,33333,1657],{},[1935,33335,33336,33338,33340],{},[898,33337,2132],{},[1826,33339,1828],{},[1655,33341,5603],{},[1820,33343,33344,33346],{},[898,33345,1824],{},[1826,33347,1828],{},[1655,33349,2346],{},[1935,33351,33352,33354,33356],{},[898,33353,2132],{},[1826,33355,1837],{},[1655,33357,5603],{},[1820,33359,33360,33362],{},[898,33361,1824],{},[1826,33363,1837],{},[1655,33365,2346],{},[898,33367,17569],{},[1655,33369,1664],{"stretchy":1663},[2597,33371,33372,33374],{},[898,33373,900],{},[1655,33375,5603],{},[1655,33377,2623],{},[898,33379,900],{},[1655,33381,1664],{"stretchy":1663},[1820,33383,33384,33386],{},[898,33385,1824],{},[1826,33387,1828],{},[1655,33389,1671],{"separator":1670},[1820,33391,33392,33394],{},[898,33393,1824],{},[1826,33395,1837],{},[1655,33397,1677],{"stretchy":1663},[1655,33399,1677],{"stretchy":1663},[898,33401,1719],{"mathvariant":1943},[21888,33403],{"width":29202},[21888,33405,33406],{},[2031,33407,33408],{},"(6.24)",[902,33410,33411],{"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}",[724,33413,33414],{},"Soustava podmínek prvního řádu:",[883,33416,33418],{"className":33417},[886],[888,33419,33420],{"xmlns":890,"display":29192},[892,33421,33422,33595],{},[21880,33423,33424],{"width":29197},[21885,33425,33426,33428,33588,33590],{},[21888,33427],{"width":29202},[21888,33429,33430],{},[21880,33431,33432,33482,33532],{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},[21885,33433,33434,33446],{},[21888,33435,33436],{},[3615,33437,33438],{"scriptlevel":2552,"displaystyle":1670},[1935,33439,33440,33442,33444],{},[898,33441,1873],{"mathvariant":29674},[1826,33443,1828],{},[1655,33445,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,33447,33448],{},[3615,33449,33450],{"scriptlevel":2552,"displaystyle":1670},[895,33451,33452,33454,33456,33464,33466,33468,33476,33478,33480],{},[895,33453],{},[1655,33455,1657],{},[1935,33457,33458,33460,33462],{},[898,33459,2132],{},[1826,33461,1828],{},[1655,33463,5603],{},[1655,33465,2623],{},[898,33467,17569],{},[1935,33469,33470,33472,33474],{},[898,33471,900],{},[1826,33473,1828],{},[1655,33475,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,33477,1657],{},[1826,33479,2552],{},[1655,33481,1671],{"separator":1670},[21885,33483,33484,33496],{},[21888,33485,33486],{},[3615,33487,33488],{"scriptlevel":2552,"displaystyle":1670},[1935,33489,33490,33492,33494],{},[898,33491,1873],{"mathvariant":29674},[1826,33493,1837],{},[1655,33495,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,33497,33498],{},[3615,33499,33500],{"scriptlevel":2552,"displaystyle":1670},[895,33501,33502,33504,33506,33514,33516,33518,33526,33528,33530],{},[895,33503],{},[1655,33505,1657],{},[1935,33507,33508,33510,33512],{},[898,33509,2132],{},[1826,33511,1837],{},[1655,33513,5603],{},[1655,33515,2623],{},[898,33517,17569],{},[1935,33519,33520,33522,33524],{},[898,33521,900],{},[1826,33523,1837],{},[1655,33525,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,33527,1657],{},[1826,33529,2552],{},[1655,33531,1671],{"separator":1670},[21885,33533,33534,33546],{},[21888,33535,33536],{},[3615,33537,33538],{"scriptlevel":2552,"displaystyle":1670},[1935,33539,33540,33542,33544],{},[898,33541,1873],{"mathvariant":29674},[898,33543,17569],{},[1655,33545,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,33547,33548],{},[3615,33549,33550],{"scriptlevel":2552,"displaystyle":1670},[895,33551,33552,33554,33556,33562,33564,33566,33568,33574,33576,33582,33584,33586],{},[895,33553],{},[1655,33555,1657],{},[2597,33557,33558,33560],{},[898,33559,900],{},[1655,33561,5603],{},[1655,33563,2623],{},[898,33565,900],{},[1655,33567,1664],{"stretchy":1663},[1820,33569,33570,33572],{},[898,33571,1824],{},[1826,33573,1828],{},[1655,33575,1671],{"separator":1670},[1820,33577,33578,33580],{},[898,33579,1824],{},[1826,33581,1837],{},[1655,33583,1677],{"stretchy":1663},[1655,33585,1657],{},[1826,33587,13585],{},[21888,33589],{"width":29202},[21888,33591,33592],{},[2031,33593,33594],{},"(6.25)",[902,33596,33597],{"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}",[724,33599,33600],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,33602,33604],{"className":33603},[886],[888,33605,33606],{"xmlns":890,"display":29192},[892,33607,33608,33706],{},[21880,33609,33610],{"width":29197},[21885,33611,33612,33614,33699,33701],{},[21888,33613],{"width":29202},[21888,33615,33616],{},[895,33617,33618,33620,33622,33628,33630,33636,33638,33640,33642,33644,33646,33648,33697],{},[898,33619,2838],{},[1655,33621,1664],{"stretchy":1663},[1820,33623,33624,33626],{},[898,33625,1824],{},[1826,33627,1828],{},[1655,33629,1671],{"separator":1670},[1820,33631,33632,33634],{},[898,33633,1824],{},[1826,33635,1837],{},[1655,33637,1671],{"separator":1670},[898,33639,17569],{},[1655,33641,1677],{"stretchy":1663},[1655,33643,1657],{},[1655,33645,2623],{},[898,33647,17569],{},[895,33649,33650,33652,33664,33666,33679,33681,33683,33695],{},[1655,33651,1664],{"fence":1670},[1935,33653,33654,33656,33658],{},[898,33655,900],{},[1826,33657,4176],{},[895,33659,33660,33662],{},[1655,33661,1945],{"mathvariant":1943},[1655,33663,1945],{"mathvariant":1943},[1655,33665,2346],{},[1935,33667,33668,33670,33673],{},[898,33669,900],{},[1826,33671,33672],{},"22",[895,33674,33675,33677],{},[1655,33676,1945],{"mathvariant":1943},[1655,33678,1945],{"mathvariant":1943},[1655,33680,2346],{},[1826,33682,1837],{},[1935,33684,33685,33687,33689],{},[898,33686,900],{},[1826,33688,4771],{},[895,33690,33691,33693],{},[1655,33692,1945],{"mathvariant":1943},[1655,33694,1945],{"mathvariant":1943},[1655,33696,1677],{"fence":1670},[898,33698,1719],{"mathvariant":1943},[21888,33700],{"width":29202},[21888,33702,33703],{},[2031,33704,33705],{},"(6.26)",[902,33707,33708],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,33710,33711,33714,33715,33754,33755,33794,33795,33845,33846,33872,33873,33890,33891,33917],{},[38,33712,33713],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,33716,33718],{"className":33717},[886],[888,33719,33720],{"xmlns":890},[892,33721,33722,33752],{},[895,33723,33724,33730,33732,33740,33742,33750],{},[2597,33725,33726,33728],{},[898,33727,1824],{},[1655,33729,5603],{},[1655,33731,2734],{"stretchy":1663},[1935,33733,33734,33736,33738],{},[898,33735,1824],{},[1826,33737,1828],{},[1655,33739,5603],{},[1655,33741,1671],{"separator":1670},[1935,33743,33744,33746,33748],{},[898,33745,1824],{},[1826,33747,1837],{},[1655,33749,5603],{},[1655,33751,2743],{"stretchy":1663},[902,33753,29453],{"encoding":904}," dotyku křivky užitečnosti ",[883,33756,33758],{"className":33757},[886],[888,33759,33760],{"xmlns":890},[892,33761,33762,33792],{},[895,33763,33764,33770,33772,33774,33776,33782,33784,33790],{},[2597,33765,33766,33768],{},[898,33767,900],{},[1655,33769,5603],{},[1655,33771,1657],{},[898,33773,900],{},[1655,33775,1664],{"stretchy":1663},[1820,33777,33778,33780],{},[898,33779,1824],{},[1826,33781,1828],{},[1655,33783,1671],{"separator":1670},[1820,33785,33786,33788],{},[898,33787,1824],{},[1826,33789,1837],{},[1655,33791,1677],{"stretchy":1663},[902,33793,18791],{"encoding":904}," s přímkou výdajů ",[883,33796,33798],{"className":33797},[886],[888,33799,33800],{"xmlns":890},[892,33801,33802,33842],{},[895,33803,33804,33810,33812,33820,33826,33828,33836],{},[2597,33805,33806,33808],{},[898,33807,5502],{},[1655,33809,5603],{},[1655,33811,1657],{},[1935,33813,33814,33816,33818],{},[898,33815,2132],{},[1826,33817,1828],{},[1655,33819,5603],{},[1820,33821,33822,33824],{},[898,33823,1824],{},[1826,33825,1828],{},[1655,33827,2346],{},[1935,33829,33830,33832,33834],{},[898,33831,2132],{},[1826,33833,1837],{},[1655,33835,5603],{},[1820,33837,33838,33840],{},[898,33839,1824],{},[1826,33841,1837],{},[902,33843,33844],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,33847,33849],{"className":33848},[886],[888,33850,33851],{"xmlns":890},[892,33852,33853,33869],{},[895,33854,33855,33861,33863],{},[1820,33856,33857,33859],{},[898,33858,5502],{},[1826,33860,2552],{},[1655,33862,3065],{},[2597,33864,33865,33867],{},[898,33866,5502],{},[1655,33868,5603],{},[902,33870,33871],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,33874,33876],{"className":33875},[886],[888,33877,33878],{"xmlns":890},[892,33879,33880,33888],{},[895,33881,33882],{},[2597,33883,33884,33886],{},[898,33885,900],{},[1655,33887,5603],{},[902,33889,29088],{"encoding":904},", hladina ",[883,33892,33894],{"className":33893},[886],[888,33895,33896],{"xmlns":890},[892,33897,33898,33914],{},[895,33899,33900,33906,33908],{},[1820,33901,33902,33904],{},[898,33903,5502],{},[1826,33905,1828],{},[1655,33907,2969],{},[2597,33909,33910,33912],{},[898,33911,5502],{},[1655,33913,5603],{},[902,33915,33916],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[5120,33919,33920,33925],{},[724,33921,33922,33924],{},[883,33923,5821],{}," Postup — duální úloha (minimalizace výdajů)",[152,33926,33927,33977,34063,34103,34178],{},[123,33928,33929,3106,33932,33976],{},[38,33930,33931],{},"Zapiš vazbu",[883,33933,33935],{"className":33934},[886],[888,33936,33937],{"xmlns":890},[892,33938,33939,33973],{},[895,33940,33941,33947,33949,33951,33953,33959,33961,33967,33969,33971],{},[2597,33942,33943,33945],{},[898,33944,900],{},[1655,33946,5603],{},[1655,33948,2623],{},[898,33950,900],{},[1655,33952,1664],{"stretchy":1663},[1820,33954,33955,33957],{},[898,33956,1824],{},[1826,33958,1828],{},[1655,33960,1671],{"separator":1670},[1820,33962,33963,33965],{},[898,33964,1824],{},[1826,33966,1837],{},[1655,33968,1677],{"stretchy":1663},[1655,33970,1657],{},[1826,33972,2552],{},[902,33974,33975],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,33978,33979,3106,33981,1719],{},[38,33980,30386],{},[883,33982,33984],{"className":33983},[886],[888,33985,33986],{"xmlns":890},[892,33987,33988,34060],{},[895,33989,33990,33992,33994,34002,34008,34010,34018,34024,34026,34028,34030,34036,34038,34040,34042,34048,34050,34056,34058],{},[898,33991,1873],{"mathvariant":29674},[1655,33993,1657],{},[1935,33995,33996,33998,34000],{},[898,33997,2132],{},[1826,33999,1828],{},[1655,34001,5603],{},[1820,34003,34004,34006],{},[898,34005,1824],{},[1826,34007,1828],{},[1655,34009,2346],{},[1935,34011,34012,34014,34016],{},[898,34013,2132],{},[1826,34015,1837],{},[1655,34017,5603],{},[1820,34019,34020,34022],{},[898,34021,1824],{},[1826,34023,1837],{},[1655,34025,2346],{},[898,34027,17569],{},[1655,34029,1664],{"stretchy":1663},[2597,34031,34032,34034],{},[898,34033,900],{},[1655,34035,5603],{},[1655,34037,2623],{},[898,34039,900],{},[1655,34041,1664],{"stretchy":1663},[1820,34043,34044,34046],{},[898,34045,1824],{},[1826,34047,1828],{},[1655,34049,1671],{"separator":1670},[1820,34051,34052,34054],{},[898,34053,1824],{},[1826,34055,1837],{},[1655,34057,1677],{"stretchy":1663},[1655,34059,1677],{"stretchy":1663},[902,34061,34062],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,34064,34065,34068,34069,34102],{},[38,34066,34067],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,34070,34072],{"className":34071},[886],[888,34073,34074],{"xmlns":890},[892,34075,34076,34100],{},[895,34077,34078,34080,34082,34090,34092],{},[2031,34079,2708],{},[1655,34081,1657],{},[1935,34083,34084,34086,34088],{},[898,34085,2132],{},[1826,34087,1828],{},[1655,34089,5603],{},[898,34091,5923],{"mathvariant":1943},[1935,34093,34094,34096,34098],{},[898,34095,2132],{},[1826,34097,1837],{},[1655,34099,5603],{},[902,34101,30105],{"encoding":904}," (stejná jako u maximalizace!).",[123,34104,34105,3106,34108,34148,34149,1719],{},[38,34106,34107],{},"Dosaď do vazby",[883,34109,34111],{"className":34110},[886],[888,34112,34113],{"xmlns":890},[892,34114,34115,34145],{},[895,34116,34117,34119,34121,34127,34129,34135,34137,34139],{},[898,34118,900],{},[1655,34120,1664],{"stretchy":1663},[1820,34122,34123,34125],{},[898,34124,1824],{},[1826,34126,1828],{},[1655,34128,1671],{"separator":1670},[1820,34130,34131,34133],{},[898,34132,1824],{},[1826,34134,1837],{},[1655,34136,1677],{"stretchy":1663},[1655,34138,1657],{},[2597,34140,34141,34143],{},[898,34142,900],{},[1655,34144,5603],{},[902,34146,34147],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,34150,34152],{"className":34151},[886],[888,34153,34154],{"xmlns":890},[892,34155,34156,34176],{},[895,34157,34158,34166,34168],{},[1935,34159,34160,34162,34164],{},[898,34161,1824],{},[1826,34163,1828],{},[1655,34165,5603],{},[1655,34167,1671],{"separator":1670},[1935,34169,34170,34172,34174],{},[898,34171,1824],{},[1826,34173,1837],{},[1655,34175,5603],{},[902,34177,30627],{"encoding":904},[123,34179,34180,3106,34183,34237],{},[38,34181,34182],{},"Vypočítej minimální výdaje",[883,34184,34186],{"className":34185},[886],[888,34187,34188],{"xmlns":890},[892,34189,34190,34234],{},[895,34191,34192,34198,34200,34208,34216,34218,34226],{},[2597,34193,34194,34196],{},[898,34195,5502],{},[1655,34197,5603],{},[1655,34199,1657],{},[1935,34201,34202,34204,34206],{},[898,34203,2132],{},[1826,34205,1828],{},[1655,34207,5603],{},[1935,34209,34210,34212,34214],{},[898,34211,1824],{},[1826,34213,1828],{},[1655,34215,5603],{},[1655,34217,2346],{},[1935,34219,34220,34222,34224],{},[898,34221,2132],{},[1826,34223,1837],{},[1655,34225,5603],{},[1935,34227,34228,34230,34232],{},[898,34229,1824],{},[1826,34231,1837],{},[1655,34233,5603],{},[902,34235,34236],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,34239,34241,34242],{"id":34240},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,34243,34245],{"className":34244},[886],[888,34246,34247],{"xmlns":890},[892,34248,34249,34283],{},[895,34250,34251,34253,34255,34269],{},[898,34252,900],{},[1655,34254,1657],{},[1935,34256,34257,34259,34261],{},[898,34258,1824],{},[1826,34260,1828],{},[895,34262,34263,34265,34267],{},[1826,34264,1828],{},[898,34266,5923],{"mathvariant":1943},[1826,34268,1837],{},[1935,34270,34271,34273,34275],{},[898,34272,1824],{},[1826,34274,1837],{},[895,34276,34277,34279,34281],{},[1826,34278,1828],{},[898,34280,5923],{"mathvariant":1943},[1826,34282,1837],{},[902,34284,34285],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,34287,34288,34289,1343,34311,1343,34335,31472],{},"Dáno ",[883,34290,34292],{"className":34291},[886],[888,34293,34294],{"xmlns":890},[892,34295,34296,34308],{},[895,34297,34298,34304,34306],{},[2597,34299,34300,34302],{},[898,34301,900],{},[1655,34303,5603],{},[1655,34305,1657],{},[1826,34307,1837],{},[902,34309,34310],{"encoding":904},"U^* = 2",[883,34312,34314],{"className":34313},[886],[888,34315,34316],{"xmlns":890},[892,34317,34318,34332],{},[895,34319,34320,34328,34330],{},[1935,34321,34322,34324,34326],{},[898,34323,2132],{},[1826,34325,1828],{},[1655,34327,5603],{},[1655,34329,1657],{},[1826,34331,24915],{},[902,34333,34334],{"encoding":904},"P_1^* = 0{,}25",[883,34336,34338],{"className":34337},[886],[888,34339,34340],{"xmlns":890},[892,34341,34342,34356],{},[895,34343,34344,34352,34354],{},[1935,34345,34346,34348,34350],{},[898,34347,2132],{},[1826,34349,1837],{},[1655,34351,5603],{},[1655,34353,1657],{},[1826,34355,1828],{},[902,34357,34358],{"encoding":904},"P_2^* = 1",[883,34360,34362],{"className":34361},[886],[888,34363,34364],{"xmlns":890,"display":29192},[892,34365,34366,34430],{},[895,34367,34368,34370,34372,34374,34380,34382,34388,34390,34392,34394,34396,34398,34412,34426,34428],{},[898,34369,1873],{"mathvariant":29674},[1655,34371,1657],{},[1826,34373,24915],{},[1820,34375,34376,34378],{},[898,34377,1824],{},[1826,34379,1828],{},[1655,34381,2346],{},[1820,34383,34384,34386],{},[898,34385,1824],{},[1826,34387,1837],{},[1655,34389,2346],{},[898,34391,17569],{},[1655,34393,1664],{"stretchy":1663},[1826,34395,1837],{},[1655,34397,2623],{},[1935,34399,34400,34402,34404],{},[898,34401,1824],{},[1826,34403,1828],{},[895,34405,34406,34408,34410],{},[1826,34407,1828],{},[898,34409,5923],{"mathvariant":1943},[1826,34411,1837],{},[1935,34413,34414,34416,34418],{},[898,34415,1824],{},[1826,34417,1837],{},[895,34419,34420,34422,34424],{},[1826,34421,1828],{},[898,34423,5923],{"mathvariant":1943},[1826,34425,1837],{},[1655,34427,1677],{"stretchy":1663},[898,34429,1719],{"mathvariant":1943},[902,34431,34432],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,34434,31557],{},[883,34436,34438],{"className":34437},[886],[888,34439,34440],{"xmlns":890,"display":29192},[892,34441,34442,34656],{},[21880,34443,34444,34520,34596],{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},[21885,34445,34446,34458],{},[21888,34447,34448],{},[3615,34449,34450],{"scriptlevel":2552,"displaystyle":1670},[1935,34451,34452,34454,34456],{},[898,34453,1873],{"mathvariant":29674},[1826,34455,1828],{},[1655,34457,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,34459,34460],{},[3615,34461,34462],{"scriptlevel":2552,"displaystyle":1670},[895,34463,34464,34466,34468,34470,34472,34474,34476,34484,34500,34514,34516,34518],{},[895,34465],{},[1655,34467,1657],{},[1826,34469,24915],{},[1655,34471,2623],{},[898,34473,17569],{},[1655,34475,2869],{},[3615,34477,34478],{"scriptlevel":2552,"displaystyle":1663},[1949,34479,34480,34482],{},[1826,34481,1828],{},[1826,34483,1837],{},[1935,34485,34486,34488,34490],{},[898,34487,1824],{},[1826,34489,1828],{},[895,34491,34492,34494,34496,34498],{},[1655,34493,2623],{},[1826,34495,1828],{},[898,34497,5923],{"mathvariant":1943},[1826,34499,1837],{},[1935,34501,34502,34504,34506],{},[898,34503,1824],{},[1826,34505,1837],{},[895,34507,34508,34510,34512],{},[1826,34509,1828],{},[898,34511,5923],{"mathvariant":1943},[1826,34513,1837],{},[1655,34515,1657],{},[1826,34517,2552],{},[1655,34519,1671],{"separator":1670},[21885,34521,34522,34534],{},[21888,34523,34524],{},[3615,34525,34526],{"scriptlevel":2552,"displaystyle":1670},[1935,34527,34528,34530,34532],{},[898,34529,1873],{"mathvariant":29674},[1826,34531,1837],{},[1655,34533,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,34535,34536],{},[3615,34537,34538],{"scriptlevel":2552,"displaystyle":1670},[895,34539,34540,34542,34544,34546,34548,34550,34552,34560,34574,34590,34592,34594],{},[895,34541],{},[1655,34543,1657],{},[1826,34545,1828],{},[1655,34547,2623],{},[898,34549,17569],{},[1655,34551,2869],{},[3615,34553,34554],{"scriptlevel":2552,"displaystyle":1663},[1949,34555,34556,34558],{},[1826,34557,1828],{},[1826,34559,1837],{},[1935,34561,34562,34564,34566],{},[898,34563,1824],{},[1826,34565,1828],{},[895,34567,34568,34570,34572],{},[1826,34569,1828],{},[898,34571,5923],{"mathvariant":1943},[1826,34573,1837],{},[1935,34575,34576,34578,34580],{},[898,34577,1824],{},[1826,34579,1837],{},[895,34581,34582,34584,34586,34588],{},[1655,34583,2623],{},[1826,34585,1828],{},[898,34587,5923],{"mathvariant":1943},[1826,34589,1837],{},[1655,34591,1657],{},[1826,34593,2552],{},[1655,34595,1671],{"separator":1670},[21885,34597,34598,34610],{},[21888,34599,34600],{},[3615,34601,34602],{"scriptlevel":2552,"displaystyle":1670},[1935,34603,34604,34606,34608],{},[898,34605,1873],{"mathvariant":29674},[898,34607,17569],{},[1655,34609,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,34611,34612],{},[3615,34613,34614],{"scriptlevel":2552,"displaystyle":1670},[895,34615,34616,34618,34620,34622,34624,34638,34652,34654],{},[895,34617],{},[1655,34619,1657],{},[1826,34621,1837],{},[1655,34623,2623],{},[1935,34625,34626,34628,34630],{},[898,34627,1824],{},[1826,34629,1828],{},[895,34631,34632,34634,34636],{},[1826,34633,1828],{},[898,34635,5923],{"mathvariant":1943},[1826,34637,1837],{},[1935,34639,34640,34642,34644],{},[898,34641,1824],{},[1826,34643,1837],{},[895,34645,34646,34648,34650],{},[1826,34647,1828],{},[898,34649,5923],{"mathvariant":1943},[1826,34651,1837],{},[1655,34653,1657],{},[1826,34655,13585],{},[902,34657,34658],{"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}",[724,34660,34661,34662,18702,34692,34720,34721,6838,34783,1343,34833,34855,34856,1719],{},"Podílem prvních dvou rovnic: ",[883,34663,34665],{"className":34664},[886],[888,34666,34667],{"xmlns":890},[892,34668,34669,34689],{},[895,34670,34671,34673,34675,34681,34683],{},[1826,34672,24915],{},[1655,34674,1657],{},[1820,34676,34677,34679],{},[898,34678,1824],{},[1826,34680,1837],{},[898,34682,5923],{"mathvariant":1943},[1820,34684,34685,34687],{},[898,34686,1824],{},[1826,34688,1828],{},[902,34690,34691],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,34693,34695],{"className":34694},[886],[888,34696,34697],{"xmlns":890},[892,34698,34699,34717],{},[895,34700,34701,34707,34709,34711],{},[1820,34702,34703,34705],{},[898,34704,1824],{},[1826,34706,1837],{},[1655,34708,1657],{},[1826,34710,24915],{},[1820,34712,34713,34715],{},[898,34714,1824],{},[1826,34716,1828],{},[902,34718,34719],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,34722,34724],{"className":34723},[886],[888,34725,34726],{"xmlns":890},[892,34727,34728,34780],{},[895,34729,34730,34744,34746,34748,34754,34766,34768,34770,34776,34778],{},[1935,34731,34732,34734,34736],{},[898,34733,1824],{},[1826,34735,1828],{},[895,34737,34738,34740,34742],{},[1826,34739,1828],{},[898,34741,5923],{"mathvariant":1943},[1826,34743,1837],{},[1655,34745,1664],{"stretchy":1663},[1826,34747,24915],{},[1820,34749,34750,34752],{},[898,34751,1824],{},[1826,34753,1828],{},[2597,34755,34756,34758],{},[1655,34757,1677],{"stretchy":1663},[895,34759,34760,34762,34764],{},[1826,34761,1828],{},[898,34763,5923],{"mathvariant":1943},[1826,34765,1837],{},[1655,34767,1657],{},[1826,34769,6258],{},[1820,34771,34772,34774],{},[898,34773,1824],{},[1826,34775,1828],{},[1655,34777,1657],{},[1826,34779,1837],{},[902,34781,34782],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,34784,34785,1343,34809],{},[883,34786,34788],{"className":34787},[886],[888,34789,34790],{"xmlns":890},[892,34791,34792,34806],{},[895,34793,34794,34802,34804],{},[1935,34795,34796,34798,34800],{},[898,34797,1824],{},[1826,34799,1828],{},[1655,34801,5603],{},[1655,34803,1657],{},[1826,34805,3639],{},[902,34807,34808],{"encoding":904},"Q_1^* = 4",[883,34810,34812],{"className":34811},[886],[888,34813,34814],{"xmlns":890},[892,34815,34816,34830],{},[895,34817,34818,34826,34828],{},[1935,34819,34820,34822,34824],{},[898,34821,1824],{},[1826,34823,1837],{},[1655,34825,5603],{},[1655,34827,1657],{},[1826,34829,1828],{},[902,34831,34832],{"encoding":904},"Q_2^* = 1",[883,34834,34836],{"className":34835},[886],[888,34837,34838],{"xmlns":890},[892,34839,34840,34852],{},[895,34841,34842,34848,34850],{},[2597,34843,34844,34846],{},[898,34845,17569],{},[1655,34847,5603],{},[1655,34849,1657],{},[1826,34851,1828],{},[902,34853,34854],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,34857,34859],{"className":34858},[886],[888,34860,34861],{"xmlns":890},[892,34862,34863,34891],{},[895,34864,34865,34871,34873,34875,34877,34879,34881,34883,34885,34887,34889],{},[2597,34866,34867,34869],{},[898,34868,5502],{},[1655,34870,5603],{},[1655,34872,1657],{},[1826,34874,24915],{},[1655,34876,2869],{},[1826,34878,3639],{},[1655,34880,2346],{},[1826,34882,1828],{},[1655,34884,2869],{},[1826,34886,1828],{},[1655,34888,1657],{},[1826,34890,1837],{},[902,34892,34893],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,34895,34896,34899,34900,1343,34966,1343,35032,35098,35099,35136,35137,35159,35160,1719],{},[614,34897,34898],{},"Ověření postačující podmínky"," (6.26): ",[883,34901,34903],{"className":34902},[886],[888,34904,34905],{"xmlns":890},[892,34906,34907,34963],{},[895,34908,34909,34921,34923,34925,34933,34949],{},[1935,34910,34911,34913,34915],{},[898,34912,900],{},[1826,34914,4176],{},[895,34916,34917,34919],{},[1655,34918,1945],{"mathvariant":1943},[1655,34920,1945],{"mathvariant":1943},[1655,34922,1657],{},[1655,34924,2623],{},[3615,34926,34927],{"scriptlevel":2552,"displaystyle":1663},[1949,34928,34929,34931],{},[1826,34930,1828],{},[1826,34932,3639],{},[1935,34934,34935,34937,34939],{},[898,34936,1824],{},[1826,34938,1828],{},[895,34940,34941,34943,34945,34947],{},[1655,34942,2623],{},[1826,34944,3472],{},[898,34946,5923],{"mathvariant":1943},[1826,34948,1837],{},[1935,34950,34951,34953,34955],{},[898,34952,1824],{},[1826,34954,1837],{},[895,34956,34957,34959,34961],{},[1826,34958,1828],{},[898,34960,5923],{"mathvariant":1943},[1826,34962,1837],{},[902,34964,34965],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,34967,34969],{"className":34968},[886],[888,34970,34971],{"xmlns":890},[892,34972,34973,35029],{},[895,34974,34975,34987,34989,34991,34999,35013],{},[1935,34976,34977,34979,34981],{},[898,34978,900],{},[1826,34980,33672],{},[895,34982,34983,34985],{},[1655,34984,1945],{"mathvariant":1943},[1655,34986,1945],{"mathvariant":1943},[1655,34988,1657],{},[1655,34990,2623],{},[3615,34992,34993],{"scriptlevel":2552,"displaystyle":1663},[1949,34994,34995,34997],{},[1826,34996,1828],{},[1826,34998,3639],{},[1935,35000,35001,35003,35005],{},[898,35002,1824],{},[1826,35004,1828],{},[895,35006,35007,35009,35011],{},[1826,35008,1828],{},[898,35010,5923],{"mathvariant":1943},[1826,35012,1837],{},[1935,35014,35015,35017,35019],{},[898,35016,1824],{},[1826,35018,1837],{},[895,35020,35021,35023,35025,35027],{},[1655,35022,2623],{},[1826,35024,3472],{},[898,35026,5923],{"mathvariant":1943},[1826,35028,1837],{},[902,35030,35031],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,35033,35035],{"className":35034},[886],[888,35036,35037],{"xmlns":890},[892,35038,35039,35095],{},[895,35040,35041,35053,35055,35063,35079],{},[1935,35042,35043,35045,35047],{},[898,35044,900],{},[1826,35046,4771],{},[895,35048,35049,35051],{},[1655,35050,1945],{"mathvariant":1943},[1655,35052,1945],{"mathvariant":1943},[1655,35054,1657],{},[3615,35056,35057],{"scriptlevel":2552,"displaystyle":1663},[1949,35058,35059,35061],{},[1826,35060,1828],{},[1826,35062,3639],{},[1935,35064,35065,35067,35069],{},[898,35066,1824],{},[1826,35068,1828],{},[895,35070,35071,35073,35075,35077],{},[1655,35072,2623],{},[1826,35074,1828],{},[898,35076,5923],{"mathvariant":1943},[1826,35078,1837],{},[1935,35080,35081,35083,35085],{},[898,35082,1824],{},[1826,35084,1837],{},[895,35086,35087,35089,35091,35093],{},[1655,35088,2623],{},[1826,35090,1828],{},[898,35092,5923],{"mathvariant":1943},[1826,35094,1837],{},[902,35096,35097],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,35100,35102],{"className":35101},[886],[888,35103,35104],{"xmlns":890},[892,35105,35106,35133],{},[895,35107,35108,35110,35112,35114,35116,35118,35120,35122,35124,35126,35129,35131],{},[898,35109,2838],{},[1655,35111,1664],{"stretchy":1663},[1826,35113,3639],{},[1655,35115,1671],{"separator":1670},[1826,35117,1828],{},[1655,35119,1671],{"separator":1670},[1826,35121,1828],{},[1655,35123,1677],{"stretchy":1663},[1655,35125,1657],{},[1826,35127,35128],{},"0,28125",[1655,35130,2969],{},[1826,35132,2552],{},[902,35134,35135],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,35138,35140],{"className":35139},[886],[888,35141,35142],{"xmlns":890},[892,35143,35144,35156],{},[895,35145,35146,35148,35150,35152,35154],{},[1655,35147,2734],{"stretchy":1663},[1826,35149,3639],{},[1655,35151,1671],{"separator":1670},[1826,35153,1828],{},[1655,35155,2743],{"stretchy":1663},[902,35157,35158],{"encoding":904},"[4, 1]"," je vázané ",[38,35161,3025],{},[115,35163,35165],{"id":35164},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,35167,35168],{},"Obecně:",[883,35170,35172],{"className":35171},[886],[888,35173,35174],{"xmlns":890,"display":29192},[892,35175,35176,35271],{},[21880,35177,35178],{"width":29197},[21885,35179,35180,35182,35264,35266],{},[21888,35181],{"width":29202},[21888,35183,35184],{},[895,35185,35186,35192,35194,35200,35202,35208,35210,35216,35218,35220,35222,35224,35226,35232,35234,35240,35242,35248,35250,35256,35258,35260,35262],{},[1820,35187,35188,35190],{},[898,35189,1824],{},[1826,35191,1828],{},[1655,35193,1657],{},[1820,35195,35196,35198],{},[898,35197,2838],{},[1826,35199,1828],{},[1655,35201,1664],{"stretchy":1663},[1820,35203,35204,35206],{},[898,35205,2132],{},[1826,35207,1828],{},[1655,35209,1671],{"separator":1670},[1820,35211,35212,35214],{},[898,35213,2132],{},[1826,35215,1837],{},[1655,35217,1671],{"separator":1670},[898,35219,900],{},[1655,35221,1677],{"stretchy":1663},[1655,35223,1671],{"separator":1670},[1967,35225],{"width":16409},[1820,35227,35228,35230],{},[898,35229,1824],{},[1826,35231,1837],{},[1655,35233,1657],{},[1820,35235,35236,35238],{},[898,35237,2838],{},[1826,35239,1837],{},[1655,35241,1664],{"stretchy":1663},[1820,35243,35244,35246],{},[898,35245,2132],{},[1826,35247,1828],{},[1655,35249,1671],{"separator":1670},[1820,35251,35252,35254],{},[898,35253,2132],{},[1826,35255,1837],{},[1655,35257,1671],{"separator":1670},[898,35259,900],{},[1655,35261,1677],{"stretchy":1663},[1655,35263,1671],{"separator":1670},[21888,35265],{"width":29202},[21888,35267,35268],{},[2031,35269,35270],{},"(6.27)",[902,35272,35273],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,35275,35277],{"className":35276},[886],[888,35278,35279],{"xmlns":890,"display":29192},[892,35280,35281,35328],{},[21880,35282,35283],{"width":29197},[21885,35284,35285,35287,35321,35323],{},[21888,35286],{"width":29202},[21888,35288,35289],{},[895,35290,35291,35293,35295,35297,35299,35305,35307,35313,35315,35317,35319],{},[898,35292,17569],{},[1655,35294,1657],{},[898,35296,17569],{},[1655,35298,1664],{"stretchy":1663},[1820,35300,35301,35303],{},[898,35302,2132],{},[1826,35304,1828],{},[1655,35306,1671],{"separator":1670},[1820,35308,35309,35311],{},[898,35310,2132],{},[1826,35312,1837],{},[1655,35314,1671],{"separator":1670},[898,35316,900],{},[1655,35318,1677],{"stretchy":1663},[898,35320,1719],{"mathvariant":1943},[21888,35322],{"width":29202},[21888,35324,35325],{},[2031,35326,35327],{},"(6.28)",[902,35329,35330],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,35332,35333,35334,3106,35337,35350,35351,35364],{},"Hicksova poptávka závisí na ",[38,35335,35336],{},"hladině užitečnosti",[883,35338,35340],{"className":35339},[886],[888,35341,35342],{"xmlns":890},[892,35343,35344,35348],{},[895,35345,35346],{},[898,35347,900],{},[902,35349,900],{"encoding":904}," (nikoli na důchodu ",[883,35352,35354],{"className":35353},[886],[888,35355,35356],{"xmlns":890},[892,35357,35358,35362],{},[895,35359,35360],{},[898,35361,10375],{},[902,35363,10375],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,35366,35368,35369],{"id":35367},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,35370,35372],{"className":35371},[886],[888,35373,35374],{"xmlns":890},[892,35375,35376,35410],{},[895,35377,35378,35380,35382,35396],{},[898,35379,900],{},[1655,35381,1657],{},[1935,35383,35384,35386,35388],{},[898,35385,1824],{},[1826,35387,1828],{},[895,35389,35390,35392,35394],{},[1826,35391,1828],{},[898,35393,5923],{"mathvariant":1943},[1826,35395,1837],{},[1935,35397,35398,35400,35402],{},[898,35399,1824],{},[1826,35401,1837],{},[895,35403,35404,35406,35408],{},[1826,35405,1828],{},[898,35407,5923],{"mathvariant":1943},[1826,35409,1837],{},[902,35411,34285],{"encoding":904},[724,35413,35414,35444],{},[883,35415,35417],{"className":35416},[886],[888,35418,35419],{"xmlns":890},[892,35420,35421,35441],{},[895,35422,35423,35429,35431,35437,35439],{},[1820,35424,35425,35427],{},[898,35426,2132],{},[1826,35428,1828],{},[1655,35430,1671],{"separator":1670},[1820,35432,35433,35435],{},[898,35434,2132],{},[1826,35436,1837],{},[1655,35438,1671],{"separator":1670},[898,35440,900],{},[902,35442,35443],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,35446,35448],{"className":35447},[886],[888,35449,35450],{"xmlns":890,"display":29192},[892,35451,35452,35526],{},[895,35453,35454,35456,35458,35464,35470,35472,35478,35484,35486,35488,35490,35492,35494,35508,35522,35524],{},[898,35455,1873],{"mathvariant":29674},[1655,35457,1657],{},[1820,35459,35460,35462],{},[898,35461,2132],{},[1826,35463,1828],{},[1820,35465,35466,35468],{},[898,35467,1824],{},[1826,35469,1828],{},[1655,35471,2346],{},[1820,35473,35474,35476],{},[898,35475,2132],{},[1826,35477,1837],{},[1820,35479,35480,35482],{},[898,35481,1824],{},[1826,35483,1837],{},[1655,35485,2346],{},[898,35487,17569],{},[1655,35489,1664],{"stretchy":1663},[898,35491,900],{},[1655,35493,2623],{},[1935,35495,35496,35498,35500],{},[898,35497,1824],{},[1826,35499,1828],{},[895,35501,35502,35504,35506],{},[1826,35503,1828],{},[898,35505,5923],{"mathvariant":1943},[1826,35507,1837],{},[1935,35509,35510,35512,35514],{},[898,35511,1824],{},[1826,35513,1837],{},[895,35515,35516,35518,35520],{},[1826,35517,1828],{},[898,35519,5923],{"mathvariant":1943},[1826,35521,1837],{},[1655,35523,1677],{"stretchy":1663},[898,35525,1719],{"mathvariant":1943},[902,35527,35528],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,35530,31557],{},[883,35532,35534],{"className":35533},[886],[888,35535,35536],{"xmlns":890,"display":29192},[892,35537,35538,35760],{},[21880,35539,35540,35620,35700],{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},[21885,35541,35542,35554],{},[21888,35543,35544],{},[3615,35545,35546],{"scriptlevel":2552,"displaystyle":1670},[1935,35547,35548,35550,35552],{},[898,35549,1873],{"mathvariant":29674},[1826,35551,1828],{},[1655,35553,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,35555,35556],{},[3615,35557,35558],{"scriptlevel":2552,"displaystyle":1670},[895,35559,35560,35562,35564,35570,35572,35574,35576,35584,35600,35614,35616,35618],{},[895,35561],{},[1655,35563,1657],{},[1820,35565,35566,35568],{},[898,35567,2132],{},[1826,35569,1828],{},[1655,35571,2623],{},[898,35573,17569],{},[1655,35575,2869],{},[3615,35577,35578],{"scriptlevel":2552,"displaystyle":1663},[1949,35579,35580,35582],{},[1826,35581,1828],{},[1826,35583,1837],{},[1935,35585,35586,35588,35590],{},[898,35587,1824],{},[1826,35589,1828],{},[895,35591,35592,35594,35596,35598],{},[1655,35593,2623],{},[1826,35595,1828],{},[898,35597,5923],{"mathvariant":1943},[1826,35599,1837],{},[1935,35601,35602,35604,35606],{},[898,35603,1824],{},[1826,35605,1837],{},[895,35607,35608,35610,35612],{},[1826,35609,1828],{},[898,35611,5923],{"mathvariant":1943},[1826,35613,1837],{},[1655,35615,1657],{},[1826,35617,2552],{},[1655,35619,1671],{"separator":1670},[21885,35621,35622,35634],{},[21888,35623,35624],{},[3615,35625,35626],{"scriptlevel":2552,"displaystyle":1670},[1935,35627,35628,35630,35632],{},[898,35629,1873],{"mathvariant":29674},[1826,35631,1837],{},[1655,35633,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,35635,35636],{},[3615,35637,35638],{"scriptlevel":2552,"displaystyle":1670},[895,35639,35640,35642,35644,35650,35652,35654,35656,35664,35678,35694,35696,35698],{},[895,35641],{},[1655,35643,1657],{},[1820,35645,35646,35648],{},[898,35647,2132],{},[1826,35649,1837],{},[1655,35651,2623],{},[898,35653,17569],{},[1655,35655,2869],{},[3615,35657,35658],{"scriptlevel":2552,"displaystyle":1663},[1949,35659,35660,35662],{},[1826,35661,1828],{},[1826,35663,1837],{},[1935,35665,35666,35668,35670],{},[898,35667,1824],{},[1826,35669,1828],{},[895,35671,35672,35674,35676],{},[1826,35673,1828],{},[898,35675,5923],{"mathvariant":1943},[1826,35677,1837],{},[1935,35679,35680,35682,35684],{},[898,35681,1824],{},[1826,35683,1837],{},[895,35685,35686,35688,35690,35692],{},[1655,35687,2623],{},[1826,35689,1828],{},[898,35691,5923],{"mathvariant":1943},[1826,35693,1837],{},[1655,35695,1657],{},[1826,35697,2552],{},[1655,35699,1671],{"separator":1670},[21885,35701,35702,35714],{},[21888,35703,35704],{},[3615,35705,35706],{"scriptlevel":2552,"displaystyle":1670},[1935,35707,35708,35710,35712],{},[898,35709,1873],{"mathvariant":29674},[898,35711,17569],{},[1655,35713,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[21888,35715,35716],{},[3615,35717,35718],{"scriptlevel":2552,"displaystyle":1670},[895,35719,35720,35722,35724,35726,35728,35742,35756,35758],{},[895,35721],{},[1655,35723,1657],{},[898,35725,900],{},[1655,35727,2623],{},[1935,35729,35730,35732,35734],{},[898,35731,1824],{},[1826,35733,1828],{},[895,35735,35736,35738,35740],{},[1826,35737,1828],{},[898,35739,5923],{"mathvariant":1943},[1826,35741,1837],{},[1935,35743,35744,35746,35748],{},[898,35745,1824],{},[1826,35747,1837],{},[895,35749,35750,35752,35754],{},[1826,35751,1828],{},[898,35753,5923],{"mathvariant":1943},[1826,35755,1837],{},[1655,35757,1657],{},[1826,35759,13585],{},[902,35761,35762],{"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}",[724,35764,35765,35766,35836,35837,35895],{},"Podílem rovnic: ",[883,35767,35769],{"className":35768},[886],[888,35770,35771],{"xmlns":890},[892,35772,35773,35833],{},[895,35774,35775,35781,35783,35789,35791,35797,35799,35805,35807,35813,35819,35821,35827],{},[1820,35776,35777,35779],{},[898,35778,2132],{},[1826,35780,1828],{},[898,35782,5923],{"mathvariant":1943},[1820,35784,35785,35787],{},[898,35786,2132],{},[1826,35788,1837],{},[1655,35790,1657],{},[1820,35792,35793,35795],{},[898,35794,1824],{},[1826,35796,1837],{},[898,35798,5923],{"mathvariant":1943},[1820,35800,35801,35803],{},[898,35802,1824],{},[1826,35804,1828],{},[1655,35806,5238],{},[1820,35808,35809,35811],{},[898,35810,2132],{},[1826,35812,1828],{},[1820,35814,35815,35817],{},[898,35816,1824],{},[1826,35818,1828],{},[1655,35820,1657],{},[1820,35822,35823,35825],{},[898,35824,2132],{},[1826,35826,1837],{},[1820,35828,35829,35831],{},[898,35830,1824],{},[1826,35832,1837],{},[902,35834,35835],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,35838,35840],{"className":35839},[886],[888,35841,35842],{"xmlns":890},[892,35843,35844,35892],{},[895,35845,35846,35848,35850,35856,35862,35864,35870,35876,35878,35880,35886],{},[898,35847,5502],{},[1655,35849,1657],{},[1820,35851,35852,35854],{},[898,35853,2132],{},[1826,35855,1828],{},[1820,35857,35858,35860],{},[898,35859,1824],{},[1826,35861,1828],{},[1655,35863,2346],{},[1820,35865,35866,35868],{},[898,35867,2132],{},[1826,35869,1837],{},[1820,35871,35872,35874],{},[898,35873,1824],{},[1826,35875,1837],{},[1655,35877,1657],{},[1826,35879,1837],{},[1820,35881,35882,35884],{},[898,35883,2132],{},[1826,35885,1828],{},[1820,35887,35888,35890],{},[898,35889,1824],{},[1826,35891,1828],{},[902,35893,35894],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,35897,35899],{"className":35898},[886],[888,35900,35901],{"xmlns":890,"display":29192},[892,35902,35903,35970],{},[21880,35904,35905],{"width":29197},[21885,35906,35907,35909,35963,35965],{},[21888,35908],{"width":29202},[21888,35910,35911],{},[895,35912,35913,35919,35921,35935,35937,35939,35945,35947,35961],{},[1820,35914,35915,35917],{},[898,35916,1824],{},[1826,35918,1828],{},[1655,35920,1657],{},[1949,35922,35923,35925],{},[898,35924,5502],{},[895,35926,35927,35929],{},[1826,35928,1837],{},[1820,35930,35931,35933],{},[898,35932,2132],{},[1826,35934,1828],{},[1655,35936,1671],{"separator":1670},[1967,35938],{"width":16409},[1820,35940,35941,35943],{},[898,35942,1824],{},[1826,35944,1837],{},[1655,35946,1657],{},[1949,35948,35949,35951],{},[898,35950,5502],{},[895,35952,35953,35955],{},[1826,35954,1837],{},[1820,35956,35957,35959],{},[898,35958,2132],{},[1826,35960,1837],{},[898,35962,1719],{"mathvariant":1943},[21888,35964],{"width":29202},[21888,35966,35967],{},[2031,35968,35969],{},"(6.29)",[902,35971,35972],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,35974,35975,35976,18702,36058,36094],{},"Ze třetí rovnice ",[883,35977,35979],{"className":35978},[886],[888,35980,35981],{"xmlns":890},[892,35982,35983,36055],{},[895,35984,35985,35987,35989,36027,36029],{},[898,35986,900],{},[1655,35988,1657],{},[9364,35990,35991],{},[895,35992,35993,36009,36011],{},[3615,35994,35995],{"scriptlevel":2552,"displaystyle":1663},[1949,35996,35997,35999],{},[898,35998,5502],{},[895,36000,36001,36003],{},[1826,36002,1837],{},[1820,36004,36005,36007],{},[898,36006,2132],{},[1826,36008,1828],{},[1655,36010,2869],{},[3615,36012,36013],{"scriptlevel":2552,"displaystyle":1663},[1949,36014,36015,36017],{},[898,36016,5502],{},[895,36018,36019,36021],{},[1826,36020,1837],{},[1820,36022,36023,36025],{},[898,36024,2132],{},[1826,36026,1837],{},[1655,36028,1657],{},[3615,36030,36031],{"scriptlevel":2552,"displaystyle":1663},[1949,36032,36033,36035],{},[898,36034,5502],{},[895,36036,36037,36039],{},[1826,36038,1837],{},[9364,36040,36041],{},[895,36042,36043,36049],{},[1820,36044,36045,36047],{},[898,36046,2132],{},[1826,36048,1828],{},[1820,36050,36051,36053],{},[898,36052,2132],{},[1826,36054,1837],{},[902,36056,36057],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,36059,36061],{"className":36060},[886],[888,36062,36063],{"xmlns":890},[892,36064,36065,36091],{},[895,36066,36067,36069,36071,36073,36075],{},[898,36068,5502],{},[1655,36070,1657],{},[1826,36072,1837],{},[898,36074,900],{},[9364,36076,36077],{},[895,36078,36079,36085],{},[1820,36080,36081,36083],{},[898,36082,2132],{},[1826,36084,1828],{},[1820,36086,36087,36089],{},[898,36088,2132],{},[1826,36090,1837],{},[902,36092,36093],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,36096,36098],{"className":36097},[886],[888,36099,36100],{"xmlns":890,"display":29192},[892,36101,36102,36247],{},[21880,36103,36104],{"width":29197},[21885,36105,36106,36108,36240,36242],{},[21888,36107],{"width":29202},[21888,36109,36110],{},[13957,36111,36112],{"notation":13959},[3615,36113,36114],{"scriptlevel":2552,"displaystyle":1663},[3615,36115,36116],{"scriptlevel":2552,"displaystyle":1663},[3615,36117,36118],{"scriptlevel":2552,"displaystyle":1670},[895,36119,36120,36122,36128,36130,36132,36148,36150,36156,36158,36164,36166,36172,36174,36176,36178,36180,36182,36188,36190,36192,36208,36210,36216,36218,36224,36226,36232,36234,36236,36238],{},[2031,36121,2783],{},[1820,36123,36124,36126],{},[898,36125,1824],{},[1826,36127,1828],{},[1655,36129,1657],{},[898,36131,900],{},[9364,36133,36134],{},[1949,36135,36136,36142],{},[1820,36137,36138,36140],{},[898,36139,2132],{},[1826,36141,1837],{},[1820,36143,36144,36146],{},[898,36145,2132],{},[1826,36147,1828],{},[1655,36149,1657],{},[1820,36151,36152,36154],{},[898,36153,2838],{},[1826,36155,1828],{},[1655,36157,1664],{"stretchy":1663},[1820,36159,36160,36162],{},[898,36161,2132],{},[1826,36163,1828],{},[1655,36165,1671],{"separator":1670},[1820,36167,36168,36170],{},[898,36169,2132],{},[1826,36171,1837],{},[1655,36173,1671],{"separator":1670},[898,36175,900],{},[1655,36177,1677],{"stretchy":1663},[1655,36179,1671],{"separator":1670},[1967,36181],{"width":16409},[1820,36183,36184,36186],{},[898,36185,1824],{},[1826,36187,1837],{},[1655,36189,1657],{},[898,36191,900],{},[9364,36193,36194],{},[1949,36195,36196,36202],{},[1820,36197,36198,36200],{},[898,36199,2132],{},[1826,36201,1828],{},[1820,36203,36204,36206],{},[898,36205,2132],{},[1826,36207,1837],{},[1655,36209,1657],{},[1820,36211,36212,36214],{},[898,36213,2838],{},[1826,36215,1837],{},[1655,36217,1664],{"stretchy":1663},[1820,36219,36220,36222],{},[898,36221,2132],{},[1826,36223,1828],{},[1655,36225,1671],{"separator":1670},[1820,36227,36228,36230],{},[898,36229,2132],{},[1826,36231,1837],{},[1655,36233,1671],{"separator":1670},[898,36235,900],{},[1655,36237,1677],{"stretchy":1663},[2031,36239,2783],{},[21888,36241],{"width":29202},[21888,36243,36244],{},[2031,36245,36246],{},"(6.30)",[902,36248,36249],{"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}",[115,36251,36253],{"id":36252},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,36255,36256,36257,36270,36271,36288,36289,36302,36303,36320,36321,36324,36325,36364,36365,36394],{},"Primární (max ",[883,36258,36260],{"className":36259},[886],[888,36261,36262],{"xmlns":890},[892,36263,36264,36268],{},[895,36265,36266],{},[898,36267,900],{},[902,36269,900],{"encoding":904}," při rozpočtu ",[883,36272,36274],{"className":36273},[886],[888,36275,36276],{"xmlns":890},[892,36277,36278,36286],{},[895,36279,36280],{},[2597,36281,36282,36284],{},[898,36283,10375],{},[1655,36285,5603],{},[902,36287,29154],{"encoding":904},") a duální (min ",[883,36290,36292],{"className":36291},[886],[888,36293,36294],{"xmlns":890},[892,36295,36296,36300],{},[895,36297,36298],{},[898,36299,5502],{},[902,36301,5502],{"encoding":904}," při užitečnosti ",[883,36304,36306],{"className":36305},[886],[888,36307,36308],{"xmlns":890},[892,36309,36310,36318],{},[895,36311,36312],{},[2597,36313,36314,36316],{},[898,36315,900],{},[1655,36317,5603],{},[902,36319,29088],{"encoding":904},") úloha jsou ",[38,36322,36323],{},"ekvivalentní",": mají tentýž bod optima ",[883,36326,36328],{"className":36327},[886],[888,36329,36330],{"xmlns":890},[892,36331,36332,36362],{},[895,36333,36334,36340,36342,36350,36352,36360],{},[2597,36335,36336,36338],{},[898,36337,1824],{},[1655,36339,5603],{},[1655,36341,2734],{"stretchy":1663},[1935,36343,36344,36346,36348],{},[898,36345,1824],{},[1826,36347,1828],{},[1655,36349,5603],{},[1655,36351,1671],{"separator":1670},[1935,36353,36354,36356,36358],{},[898,36355,1824],{},[1826,36357,1837],{},[1655,36359,5603],{},[1655,36361,2743],{"stretchy":1663},[902,36363,29453],{"encoding":904}," a v obou platí ",[883,36366,36368],{"className":36367},[886],[888,36369,36370],{"xmlns":890},[892,36371,36372,36392],{},[895,36373,36374,36376,36378,36384,36386],{},[2031,36375,2708],{},[1655,36377,1657],{},[1820,36379,36380,36382],{},[898,36381,2132],{},[1826,36383,1828],{},[898,36385,5923],{"mathvariant":1943},[1820,36387,36388,36390],{},[898,36389,2132],{},[1826,36391,1837],{},[902,36393,29124],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,36396,36397],{},[1723,36398],{"alt":36399,"className":36400,"src":36401},"imek-primarni-vs-dualni",[210,1727],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,36403,36404,36515],{},[123,36405,36406,36409,36410,36423,36424,36464,36465,1719],{},[38,36407,36408],{},"Primární"," (Marshall): zadáno ",[883,36411,36413],{"className":36412},[886],[888,36414,36415],{"xmlns":890},[892,36416,36417,36421],{},[895,36418,36419],{},[898,36420,10375],{},[902,36422,10375],{"encoding":904},", hledáme maximální ",[883,36425,36427],{"className":36426},[886],[888,36428,36429],{"xmlns":890},[892,36430,36431,36461],{},[895,36432,36433,36439,36441,36447,36449,36455,36457,36459],{},[2597,36434,36435,36437],{},[898,36436,900],{},[1655,36438,5603],{},[1655,36440,1664],{"stretchy":1663},[1820,36442,36443,36445],{},[898,36444,2132],{},[1826,36446,1828],{},[1655,36448,1671],{"separator":1670},[1820,36450,36451,36453],{},[898,36452,2132],{},[1826,36454,1837],{},[1655,36456,1671],{"separator":1670},[898,36458,10375],{},[1655,36460,1677],{"stretchy":1663},[902,36462,36463],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,36466,36468],{"className":36467},[886],[888,36469,36470],{"xmlns":890},[892,36471,36472,36512],{},[895,36473,36474,36480,36482,36490,36492,36498,36500,36506,36508,36510],{},[1820,36475,36476,36478],{},[898,36477,1824],{},[898,36479,18916],{},[1655,36481,1657],{},[1935,36483,36484,36486,36488],{},[898,36485,2838],{},[898,36487,18916],{},[898,36489,2127],{},[1655,36491,1664],{"stretchy":1663},[1820,36493,36494,36496],{},[898,36495,2132],{},[1826,36497,1828],{},[1655,36499,1671],{"separator":1670},[1820,36501,36502,36504],{},[898,36503,2132],{},[1826,36505,1837],{},[1655,36507,1671],{"separator":1670},[898,36509,10375],{},[1655,36511,1677],{"stretchy":1663},[902,36513,36514],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,36516,36517,36520,36521,36534,36535,36464,36575,1719],{},[38,36518,36519],{},"Duální"," (Hicks): zadáno ",[883,36522,36524],{"className":36523},[886],[888,36525,36526],{"xmlns":890},[892,36527,36528,36532],{},[895,36529,36530],{},[898,36531,900],{},[902,36533,900],{"encoding":904},", hledáme minimální ",[883,36536,36538],{"className":36537},[886],[888,36539,36540],{"xmlns":890},[892,36541,36542,36572],{},[895,36543,36544,36550,36552,36558,36560,36566,36568,36570],{},[2597,36545,36546,36548],{},[898,36547,5502],{},[1655,36549,5603],{},[1655,36551,1664],{"stretchy":1663},[1820,36553,36554,36556],{},[898,36555,2132],{},[1826,36557,1828],{},[1655,36559,1671],{"separator":1670},[1820,36561,36562,36564],{},[898,36563,2132],{},[1826,36565,1837],{},[1655,36567,1671],{"separator":1670},[898,36569,900],{},[1655,36571,1677],{"stretchy":1663},[902,36573,36574],{"encoding":904},"E^*(P_1, P_2, U)",[883,36576,36578],{"className":36577},[886],[888,36579,36580],{"xmlns":890},[892,36581,36582,36623],{},[895,36583,36584,36590,36592,36601,36603,36609,36611,36617,36619,36621],{},[1820,36585,36586,36588],{},[898,36587,1824],{},[898,36589,18916],{},[1655,36591,1657],{},[1935,36593,36594,36596,36598],{},[898,36595,2838],{},[898,36597,18916],{},[898,36599,36600],{},"H",[1655,36602,1664],{"stretchy":1663},[1820,36604,36605,36607],{},[898,36606,2132],{},[1826,36608,1828],{},[1655,36610,1671],{"separator":1670},[1820,36612,36613,36615],{},[898,36614,2132],{},[1826,36616,1837],{},[1655,36618,1671],{"separator":1670},[898,36620,900],{},[1655,36622,1677],{"stretchy":1663},[902,36624,36625],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,36627,36628,36629,36632,36633,36636],{},"Proč se studují obě? Marshallova poptávka je ",[38,36630,36631],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,36634,36635],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,36638,36640],{"id":36639},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,36642,36644],{"id":36643},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,36646,36647,36650,36651,36683,36684,36722,36723,36749],{},[38,36648,36649],{},"6.8"," Jsou dány užitečnost ",[883,36652,36654],{"className":36653},[886],[888,36655,36656],{"xmlns":890},[892,36657,36658,36680],{},[895,36659,36660,36662,36664,36672],{},[898,36661,900],{},[1655,36663,1657],{},[1935,36665,36666,36668,36670],{},[898,36667,1824],{},[1826,36669,1828],{},[1826,36671,6258],{},[1935,36673,36674,36676,36678],{},[898,36675,1824],{},[1826,36677,1837],{},[1826,36679,6258],{},[902,36681,36682],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,36685,36687],{"className":36686},[886],[888,36688,36689],{"xmlns":890},[892,36690,36691,36719],{},[895,36692,36693,36701,36703,36705,36707,36715,36717],{},[1935,36694,36695,36697,36699],{},[898,36696,2132],{},[1826,36698,1828],{},[1655,36700,5603],{},[1655,36702,1657],{},[1826,36704,3639],{},[1655,36706,1671],{"separator":1670},[1935,36708,36709,36711,36713],{},[898,36710,2132],{},[1826,36712,1837],{},[1655,36714,5603],{},[1655,36716,1657],{},[1826,36718,4136],{},[902,36720,36721],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,36724,36726],{"className":36725},[886],[888,36727,36728],{"xmlns":890},[892,36729,36730,36746],{},[895,36731,36732,36738,36740],{},[1820,36733,36734,36736],{},[898,36735,1824],{},[1826,36737,1828],{},[1655,36739,1671],{"separator":1670},[1820,36741,36742,36744],{},[898,36743,1824],{},[1826,36745,1837],{},[902,36747,36748],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,36751,36752,36755,36756,36798,36799,36830,36831,36853,36854,1719],{},[38,36753,36754],{},"6.9"," Jsou dány rozpočtové omezení ",[883,36757,36759],{"className":36758},[886],[888,36760,36761],{"xmlns":890},[892,36762,36763,36795],{},[895,36764,36765,36767,36769,36775,36781,36783,36789],{},[898,36766,10375],{},[1655,36768,1657],{},[1820,36770,36771,36773],{},[898,36772,2132],{},[1826,36774,1828],{},[1820,36776,36777,36779],{},[898,36778,1824],{},[1826,36780,1828],{},[1655,36782,2346],{},[1820,36784,36785,36787],{},[898,36786,2132],{},[1826,36788,1837],{},[1820,36790,36791,36793],{},[898,36792,1824],{},[1826,36794,1837],{},[902,36796,36797],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,36800,36802],{"className":36801},[886],[888,36803,36804],{"xmlns":890},[892,36805,36806,36828],{},[895,36807,36808,36810,36812,36820],{},[898,36809,900],{},[1655,36811,1657],{},[1935,36813,36814,36816,36818],{},[898,36815,1824],{},[1826,36817,1828],{},[1826,36819,6258],{},[1935,36821,36822,36824,36826],{},[898,36823,1824],{},[1826,36825,1837],{},[1826,36827,6258],{},[902,36829,36682],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,36832,36834],{"className":36833},[886],[888,36835,36836],{"xmlns":890},[892,36837,36838,36850],{},[895,36839,36840,36846,36848],{},[2597,36841,36842,36844],{},[898,36843,10375],{},[1655,36845,5603],{},[1655,36847,1657],{},[1826,36849,16235],{},[902,36851,36852],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,36855,36857],{"className":36856},[886],[888,36858,36859],{"xmlns":890},[892,36860,36861,36889],{},[895,36862,36863,36871,36873,36875,36877,36885,36887],{},[1935,36864,36865,36867,36869],{},[898,36866,2132],{},[1826,36868,1828],{},[1655,36870,5603],{},[1655,36872,1657],{},[1826,36874,3524],{},[1655,36876,1671],{"separator":1670},[1935,36878,36879,36881,36883],{},[898,36880,2132],{},[1826,36882,1837],{},[1655,36884,5603],{},[1655,36886,1657],{},[1826,36888,4136],{},[902,36890,36891],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,36893,36894,36897,36898,22720,36930,36960,36961,1719],{},[38,36895,36896],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,36899,36901],{"className":36900},[886],[888,36902,36903],{"xmlns":890},[892,36904,36905,36927],{},[895,36906,36907,36909,36911,36919],{},[898,36908,900],{},[1655,36910,1657],{},[1935,36912,36913,36915,36917],{},[898,36914,1824],{},[1826,36916,1828],{},[898,36918,207],{},[1935,36920,36921,36923,36925],{},[898,36922,1824],{},[1826,36924,1837],{},[898,36926,2025],{},[902,36928,36929],{"encoding":904},"U = Q_1^a Q_2^b",[883,36931,36933],{"className":36932},[886],[888,36934,36935],{"xmlns":890},[892,36936,36937,36957],{},[895,36938,36939,36941,36943,36945,36947,36949,36951,36953,36955],{},[898,36940,207],{},[1655,36942,1671],{"separator":1670},[898,36944,2025],{},[1655,36946,7753],{},[1655,36948,6573],{"stretchy":1663},[1826,36950,2552],{},[1655,36952,1671],{"separator":1670},[1826,36954,1828],{},[1655,36956,6590],{"stretchy":1663},[902,36958,36959],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,36962,36964],{"className":36963},[886],[888,36965,36966],{"xmlns":890},[892,36967,36968,37000],{},[895,36969,36970,36972,36974,36980,36986,36988,36994],{},[898,36971,10375],{},[1655,36973,1657],{},[1820,36975,36976,36978],{},[898,36977,2132],{},[1826,36979,1828],{},[1820,36981,36982,36984],{},[898,36983,1824],{},[1826,36985,1828],{},[1655,36987,2346],{},[1820,36989,36990,36992],{},[898,36991,2132],{},[1826,36993,1837],{},[1820,36995,36996,36998],{},[898,36997,1824],{},[1826,36999,1837],{},[902,37001,36797],{"encoding":904},[724,37003,37004,37007,37008,22720,37042,36960,37060,1719],{},[38,37005,37006],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,37009,37011],{"className":37010},[886],[888,37012,37013],{"xmlns":890},[892,37014,37015,37039],{},[895,37016,37017,37019,37021,37029,37031],{},[898,37018,900],{},[1655,37020,1657],{},[1935,37022,37023,37025,37027],{},[898,37024,1824],{},[1826,37026,1828],{},[898,37028,207],{},[1655,37030,2346],{},[1935,37032,37033,37035,37037],{},[898,37034,1824],{},[1826,37036,1837],{},[898,37038,207],{},[902,37040,37041],{"encoding":904},"U = Q_1^a + Q_2^a",[883,37043,37045],{"className":37044},[886],[888,37046,37047],{"xmlns":890},[892,37048,37049,37057],{},[895,37050,37051,37053,37055],{},[898,37052,207],{},[1655,37054,4636],{"mathvariant":1943},[1826,37056,2552],{},[902,37058,37059],{"encoding":904},"a \\neq 0",[883,37061,37063],{"className":37062},[886],[888,37064,37065],{"xmlns":890},[892,37066,37067,37099],{},[895,37068,37069,37071,37073,37079,37085,37087,37093],{},[898,37070,10375],{},[1655,37072,1657],{},[1820,37074,37075,37077],{},[898,37076,2132],{},[1826,37078,1828],{},[1820,37080,37081,37083],{},[898,37082,1824],{},[1826,37084,1828],{},[1655,37086,2346],{},[1820,37088,37089,37091],{},[898,37090,2132],{},[1826,37092,1837],{},[1820,37094,37095,37097],{},[898,37096,1824],{},[1826,37098,1837],{},[902,37100,36797],{"encoding":904},[198,37102,37104],{"id":37103},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,37106,37107,36650,37110,1343,37137,37159,37160,1343,37183,37207,37208,37233,37234,1719],{},[38,37108,37109],{},"6.12",[883,37111,37113],{"className":37112},[886],[888,37114,37115],{"xmlns":890},[892,37116,37117,37135],{},[895,37118,37119,37121,37123,37129],{},[898,37120,900],{},[1655,37122,1657],{},[1820,37124,37125,37127],{},[898,37126,1824],{},[1826,37128,1828],{},[1820,37130,37131,37133],{},[898,37132,1824],{},[1826,37134,1837],{},[902,37136,31352],{"encoding":904},[883,37138,37140],{"className":37139},[886],[888,37141,37142],{"xmlns":890},[892,37143,37144,37156],{},[895,37145,37146,37152,37154],{},[2597,37147,37148,37150],{},[898,37149,900],{},[1655,37151,5603],{},[1655,37153,1657],{},[1826,37155,4136],{},[902,37157,37158],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,37161,37163],{"className":37162},[886],[888,37164,37165],{"xmlns":890},[892,37166,37167,37181],{},[895,37168,37169,37177,37179],{},[1935,37170,37171,37173,37175],{},[898,37172,2132],{},[1826,37174,1828],{},[1655,37176,5603],{},[1655,37178,1657],{},[1826,37180,1837],{},[902,37182,31425],{"encoding":904},[883,37184,37186],{"className":37185},[886],[888,37187,37188],{"xmlns":890},[892,37189,37190,37204],{},[895,37191,37192,37200,37202],{},[1935,37193,37194,37196,37198],{},[898,37195,2132],{},[1826,37197,1837],{},[1655,37199,5603],{},[1655,37201,1657],{},[1826,37203,3639],{},[902,37205,37206],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,37209,37211],{"className":37210},[886],[888,37212,37213],{"xmlns":890},[892,37214,37215,37231],{},[895,37216,37217,37223,37225],{},[1820,37218,37219,37221],{},[898,37220,1824],{},[1826,37222,1828],{},[1655,37224,1671],{"separator":1670},[1820,37226,37227,37229],{},[898,37228,1824],{},[1826,37230,1837],{},[902,37232,36748],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,37235,37237],{"className":37236},[886],[888,37238,37239],{"xmlns":890},[892,37240,37241,37261],{},[895,37242,37243,37245,37247,37253,37255],{},[898,37244,900],{},[1655,37246,1657],{},[1820,37248,37249,37251],{},[898,37250,1824],{},[1826,37252,1828],{},[1655,37254,2869],{},[1820,37256,37257,37259],{},[898,37258,1824],{},[1826,37260,1837],{},[902,37262,37263],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,37265,37266,37269,37270,37311,37312,37334,37335,1719],{},[38,37267,37268],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,37271,37273],{"className":37272},[886],[888,37274,37275],{"xmlns":890},[892,37276,37277,37309],{},[895,37278,37279,37281,37283,37289,37295,37297,37303],{},[898,37280,5502],{},[1655,37282,1657],{},[1820,37284,37285,37287],{},[898,37286,2132],{},[1826,37288,1828],{},[1820,37290,37291,37293],{},[898,37292,1824],{},[1826,37294,1828],{},[1655,37296,2346],{},[1820,37298,37299,37301],{},[898,37300,2132],{},[1826,37302,1837],{},[1820,37304,37305,37307],{},[898,37306,1824],{},[1826,37308,1837],{},[902,37310,29069],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,37313,37315],{"className":37314},[886],[888,37316,37317],{"xmlns":890},[892,37318,37319,37331],{},[895,37320,37321,37327,37329],{},[2597,37322,37323,37325],{},[898,37324,900],{},[1655,37326,5603],{},[1655,37328,1657],{},[1826,37330,6253],{},[902,37332,37333],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,37336,37338],{"className":37337},[886],[888,37339,37340],{"xmlns":890},[892,37341,37342,37371],{},[895,37343,37344,37352,37354,37356,37358,37366,37368],{},[1935,37345,37346,37348,37350],{},[898,37347,2132],{},[1826,37349,1828],{},[1655,37351,5603],{},[1655,37353,1657],{},[1826,37355,10282],{},[1655,37357,1671],{"separator":1670},[1935,37359,37360,37362,37364],{},[898,37361,2132],{},[1826,37363,1837],{},[1655,37365,5603],{},[1655,37367,1657],{},[1826,37369,37370],{},"15",[902,37372,37373],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,37375,16845],{"id":16844},[120,37377,37378,37435,37474,37494,37529,37583,37588,37594,37690,37735],{},[123,37379,37380,3106,37383,37432,37433,1719],{},[38,37381,37382],{},"Rozpočtové omezení (budget constraint)",[883,37384,37386],{"className":37385},[886],[888,37387,37388],{"xmlns":890},[892,37389,37390,37430],{},[895,37391,37392,37398,37400,37408,37414,37416,37424],{},[2597,37393,37394,37396],{},[898,37395,10375],{},[1655,37397,5603],{},[1655,37399,1657],{},[1935,37401,37402,37404,37406],{},[898,37403,2132],{},[1826,37405,1828],{},[1655,37407,5603],{},[1820,37409,37410,37412],{},[898,37411,1824],{},[1826,37413,1828],{},[1655,37415,2346],{},[1935,37417,37418,37420,37422],{},[898,37419,2132],{},[1826,37421,1837],{},[1655,37423,5603],{},[1820,37425,37426,37428],{},[898,37427,1824],{},[1826,37429,1837],{},[902,37431,18424],{"encoding":904}," — (6.12); ",[38,37434,29262],{},[123,37436,37437,37440,37441,1719],{},[38,37438,37439],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,37442,37444],{"className":37443},[886],[888,37445,37446],{"xmlns":890},[892,37447,37448,37472],{},[895,37449,37450,37452,37454,37462,37464],{},[2031,37451,2708],{},[1655,37453,1657],{},[1935,37455,37456,37458,37460],{},[898,37457,2132],{},[1826,37459,1828],{},[1655,37461,5603],{},[898,37463,5923],{"mathvariant":1943},[1935,37465,37466,37468,37470],{},[898,37467,2132],{},[1826,37469,1837],{},[1655,37471,5603],{},[902,37473,30105],{"encoding":904},[123,37475,37476,37491,37492,1719],{},[38,37477,30249,37478],{},[883,37479,37481],{"className":37480},[886],[888,37482,37483],{"xmlns":890},[892,37484,37485,37489],{},[895,37486,37487],{},[898,37488,17569],{},[902,37490,17622],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,37493,30271],{},[123,37495,37496,37499,37500,1719],{},[38,37497,37498],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,37501,37503],{"className":37502},[886],[888,37504,37505],{"xmlns":890},[892,37506,37507,37527],{},[895,37508,37509,37511,37513,37519,37521],{},[2031,37510,2708],{},[1655,37512,1657],{},[1820,37514,37515,37517],{},[898,37516,2132],{},[1826,37518,1828],{},[898,37520,5923],{"mathvariant":1943},[1820,37522,37523,37525],{},[898,37524,2132],{},[1826,37526,1837],{},[902,37528,29124],{"encoding":904},[123,37530,37531,8262,37534,37582],{},[38,37532,37533],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,37535,37537],{"className":37536},[886],[888,37538,37539],{"xmlns":890},[892,37540,37541,37579],{},[895,37542,37543,37549,37551,37557,37559,37565,37567,37573,37575,37577],{},[1820,37544,37545,37547],{},[898,37546,1824],{},[898,37548,18916],{},[1655,37550,1657],{},[1820,37552,37553,37555],{},[898,37554,2838],{},[898,37556,18916],{},[1655,37558,1664],{"stretchy":1663},[1820,37560,37561,37563],{},[898,37562,2132],{},[1826,37564,1828],{},[1655,37566,1671],{"separator":1670},[1820,37568,37569,37571],{},[898,37570,2132],{},[1826,37572,1837],{},[1655,37574,1671],{"separator":1670},[898,37576,10375],{},[1655,37578,1677],{"stretchy":1663},[902,37580,37581],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,37584,37585,37587],{},[38,37586,32853],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,37589,37590,37593],{},[38,37591,37592],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,37595,37596,8262,37598,37645,37646,37689],{},[38,37597,35165],{},[883,37599,37601],{"className":37600},[886],[888,37602,37603],{"xmlns":890},[892,37604,37605,37643],{},[895,37606,37607,37613,37615,37621,37623,37629,37631,37637,37639,37641],{},[1820,37608,37609,37611],{},[898,37610,1824],{},[898,37612,18916],{},[1655,37614,1657],{},[1820,37616,37617,37619],{},[898,37618,2838],{},[898,37620,18916],{},[1655,37622,1664],{"stretchy":1663},[1820,37624,37625,37627],{},[898,37626,2132],{},[1826,37628,1828],{},[1655,37630,1671],{"separator":1670},[1820,37632,37633,37635],{},[898,37634,2132],{},[1826,37636,1837],{},[1655,37638,1671],{"separator":1670},[898,37640,900],{},[1655,37642,1677],{"stretchy":1663},[902,37644,18949],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,37647,37649],{"className":37648},[886],[888,37650,37651],{"xmlns":890},[892,37652,37653,37687],{},[895,37654,37655,37657,37659,37673],{},[898,37656,900],{},[1655,37658,1657],{},[1935,37660,37661,37663,37665],{},[898,37662,1824],{},[1826,37664,1828],{},[895,37666,37667,37669,37671],{},[1826,37668,1828],{},[898,37670,5923],{"mathvariant":1943},[1826,37672,1837],{},[1935,37674,37675,37677,37679],{},[898,37676,1824],{},[1826,37678,1837],{},[895,37680,37681,37683,37685],{},[1826,37682,1828],{},[898,37684,5923],{"mathvariant":1943},[1826,37686,1837],{},[902,37688,34285],{"encoding":904},": (6.30).",[123,37691,37692,37734],{},[38,37693,37694,37695],{},"Bod dotyku ",[883,37696,37698],{"className":37697},[886],[888,37699,37700],{"xmlns":890},[892,37701,37702,37732],{},[895,37703,37704,37710,37712,37720,37722,37730],{},[2597,37705,37706,37708],{},[898,37707,1824],{},[1655,37709,5603],{},[1655,37711,2734],{"stretchy":1663},[1935,37713,37714,37716,37718],{},[898,37715,1824],{},[1826,37717,1828],{},[1655,37719,5603],{},[1655,37721,1671],{"separator":1670},[1935,37723,37724,37726,37728],{},[898,37725,1824],{},[1826,37727,1837],{},[1655,37729,5603],{},[1655,37731,2743],{"stretchy":1663},[902,37733,29453],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,37736,37737,37740,37741,37754,37755,37768],{},[38,37738,37739],{},"Dualita"," — ekvivalence max ",[883,37742,37744],{"className":37743},[886],[888,37745,37746],{"xmlns":890},[892,37747,37748,37752],{},[895,37749,37750],{},[898,37751,900],{},[902,37753,900],{"encoding":904}," a min ",[883,37756,37758],{"className":37757},[886],[888,37759,37760],{"xmlns":890},[892,37761,37762,37766],{},[895,37763,37764],{},[898,37765,5502],{},[902,37767,5502],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,37770,3187],{"id":3186},[120,37772,37773,37796,37812,37825,37836],{},[123,37774,37775,3106,37778,37781,37782,37795],{},[38,37776,37777],{},"Teorie před optimalizací:",[207,37779,880],{"className":37780,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,37783,37785],{"className":37784},[886],[888,37786,37787],{"xmlns":890},[892,37788,37789,37793],{},[895,37790,37791],{},[898,37792,900],{},[902,37794,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,37797,37798,3106,37801,37804,37805,37808,37809,1719],{},[38,37799,37800],{},"Matematický aparát:",[207,37802,793],{"className":37803,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,37806,784],{"className":37807,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,37810,3645],{"className":37811,"dataFsResolvedFilePath":764,"href":765},[210],[123,37813,37814,3106,37817,37820,37821,37824],{},[38,37815,37816],{},"Paralely:",[207,37818,3214],{"className":37819,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,37822,13065],{"className":37823,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,37826,37827,3106,37830,1343,37833],{},[38,37828,37829],{},"Přednášky:",[207,37831,1094],{"className":37832,"dataFsResolvedFilePath":838,"href":839},[210],[207,37834,1101],{"className":37835,"dataFsResolvedFilePath":868,"href":869},[210],[123,37837,37838,3106,37840],{},[38,37839,17329],{},[207,37841,17333],{"className":37842,"dataFsResolvedFilePath":3274,"href":3275},[210],{"title":641,"searchDepth":642,"depth":642,"links":37844},[37845,37846,37847,37852,37853,37854,37856,37859,37862,37864,37865,37867,37868,37872,37873],{"id":13130,"depth":642,"text":13131},{"id":29132,"depth":642,"text":29133},{"id":29530,"depth":642,"text":29531,"children":37848},[37849,37850],{"id":29650,"depth":649,"text":29651},{"id":30231,"depth":649,"text":37851},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":30693,"depth":642,"text":30694},{"id":31004,"depth":642,"text":31005},{"id":31323,"depth":642,"text":37855},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":32096,"depth":642,"text":32097,"children":37857},[37858],{"id":32852,"depth":649,"text":32853},{"id":33032,"depth":642,"text":33033,"children":37860},[37861],{"id":33289,"depth":649,"text":33290},{"id":34240,"depth":642,"text":37863},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":35164,"depth":642,"text":35165},{"id":35367,"depth":642,"text":37866},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":36252,"depth":642,"text":36253},{"id":36639,"depth":642,"text":36640,"children":37869},[37870,37871],{"id":36643,"depth":649,"text":36644},{"id":37103,"depth":649,"text":37104},{"id":16844,"depth":642,"text":16845},{"id":3186,"depth":642,"text":3187},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":28893,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,37880,1144,1851,37881,37882,37883],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":37886,"title":802,"body":37887,"course":1128,"courses":659,"created":10802,"description":641,"extension":661,"meta":51940,"navigation":664,"path":51941,"seo":51942,"sources":51943,"stem":51944,"tags":51945,"type":3252,"updated":677,"__hash__":51951},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":37888,"toc":51896},[37889,37892,37918,37922,37929,38081,38095,38098,38100,38187,38191,38227,38300,38321,38446,38456,38469,38473,38478,38508,38570,38579,38583,38645,38652,38673,38791,38869,38873,38876,38935,39050,39055,39087,39149,39197,39252,39256,39277,39301,39349,39353,39365,39369,39479,39483,39499,39540,39551,39710,39720,39725,39729,39851,39861,39868,39872,39950,39961,40041,40047,40054,40193,40200,40203,40260,40264,40342,40388,40432,40438,40551,40555,40558,40753,40757,40994,40997,41151,41304,41306,41308,41388,41391,41496,41565,41574,41578,41581,41642,41651,41655,41688,41766,41805,41809,41858,41912,41916,41945,41974,42026,42033,42087,42165,42169,42212,42279,42323,42427,42446,42448,42452,42560,42564,42632,42681,42688,42773,42777,42849,42854,42902,43091,43095,43100,43276,43281,43340,43445,43449,43476,43480,43487,43651,43738,43743,43745,43748,43848,43998,44070,44144,44146,44150,44164,44168,44301,44356,44468,44545,44549,44606,44709,44768,44929,44933,45008,45080,45178,45236,45330,45383,45404,45458,45463,45541,45589,45676,45714,45802,45955,45991,46045,46048,46050,46052,46101,46108,46116,46203,46212,46299,46306,46308,46312,46537,46539,46543,46547,46616,46667,46870,46876,46887,46955,46961,47383,47387,47451,47475,47671,47677,47691,47759,47762,47802,48026,48094,48396,48805,48882,49048,49054,49057,49132,49585,49636,50042,50147,50810,50813,50890,50898,50972,51003,51005,51009,51053,51055,51057,51061,51291,51295,51386,51391,51485,51490,51663,51667,51785,51790,51839,51841,51843],[12,37890,802],{"id":37891},"poptávka-nabídka-a-tržní-rovnováha",[5120,37893,37894],{},[724,37895,37896,37898,37899,37902,37903,37906,37907,37910,37911,37913,37914,37917],{},[883,37897,5406],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,37900,37901],{},"poptávka",") a výrobce (",[38,37904,37905],{},"nabídka","), jejich interakci v ",[38,37908,37909],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,37912,19103],{},"). Uzavírá ji pojem ",[38,37915,37916],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,37919,37921],{"id":37920},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,37923,37924,37925,37928],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,37926,37927],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,37930,37931,37948,37990,38006],{},[123,37932,37933,37934,37947],{},"cena ",[883,37935,37937],{"className":37936},[886],[888,37938,37939],{"xmlns":890},[892,37940,37941,37945],{},[895,37942,37943],{},[898,37944,2132],{},[902,37946,2132],{"encoding":904}," zkoumaného zboží,",[123,37949,37950,37951,1671],{},"ceny alternativních zboží ",[883,37952,37954],{"className":37953},[886],[888,37955,37956],{"xmlns":890},[892,37957,37958,37987],{},[895,37959,37960,37966,37968,37974,37976,37978,37980],{},[1820,37961,37962,37964],{},[898,37963,2132],{},[1826,37965,1828],{},[1655,37967,1671],{"separator":1670},[1820,37969,37970,37972],{},[898,37971,2132],{},[1826,37973,1837],{},[1655,37975,1671],{"separator":1670},[1655,37977,1715],{},[1655,37979,1671],{"separator":1670},[1820,37981,37982,37984],{},[898,37983,2132],{},[898,37985,37986],{},"n",[902,37988,37989],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,37991,37992,37993,1671],{},"důchod ",[883,37994,37996],{"className":37995},[886],[888,37997,37998],{"xmlns":890},[892,37999,38000,38004],{},[895,38001,38002],{},[898,38003,10375],{},[902,38005,10375],{"encoding":904},[123,38007,38008,38009,38022,38023,38036,38037,38050,38051,38065,38066,38080],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,38010,38012],{"className":38011},[886],[888,38013,38014],{"xmlns":890},[892,38015,38016,38020],{},[895,38017,38018],{},[898,38019,1873],{},[902,38021,1873],{"encoding":904},", kapitál ",[883,38024,38026],{"className":38025},[886],[888,38027,38028],{"xmlns":890},[892,38029,38030,38034],{},[895,38031,38032],{},[898,38033,1878],{},[902,38035,1878],{"encoding":904},", půda ",[883,38038,38040],{"className":38039},[886],[888,38041,38042],{"xmlns":890},[892,38043,38044,38048],{},[895,38045,38046],{},[898,38047,5502],{},[902,38049,5502],{"encoding":904},"), technologie, počet výrobců ",[883,38052,38054],{"className":38053},[886],[888,38055,38056],{"xmlns":890},[892,38057,38058,38063],{},[895,38059,38060],{},[898,38061,38062],{},"O",[902,38064,38062],{"encoding":904},", počasí ",[883,38067,38069],{"className":38068},[886],[888,38070,38071],{"xmlns":890},[892,38072,38073,38078],{},[895,38074,38075],{},[898,38076,38077],{},"W",[902,38079,38077],{"encoding":904}," atd.",[724,38082,38083,38084,38087,38088,38091,38092,1719],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,38085,38086],{},"ceteris paribus","), hovoříme o ",[38,38089,38090],{},"jednofaktorovém modelu","; jinak jde o model ",[38,38093,38094],{},"vícefaktorový",[38096,38097],"hr",{},[115,38099,14286],{"id":37901},[5120,38101,38102],{},[724,38103,38104,38106,38107,38120,38121,38134,38135,38138,38139,38162,38163,1719],{},[883,38105,5406],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,38108,38110],{"className":38109},[886],[888,38111,38112],{"xmlns":890},[892,38113,38114,38118],{},[895,38115,38116],{},[898,38117,1824],{},[902,38119,1824],{"encoding":904}," na ceně ",[883,38122,38124],{"className":38123},[886],[888,38125,38126],{"xmlns":890},[892,38127,38128,38132],{},[895,38129,38130],{},[898,38131,2132],{},[902,38133,2132],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,38136,38137],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,38140,38142],{"className":38141},[886],[888,38143,38144],{"xmlns":890},[892,38145,38146,38160],{},[895,38147,38148,38150,38152,38154,38156,38158],{},[898,38149,1824],{},[1655,38151,1657],{},[898,38153,2838],{},[1655,38155,1664],{"stretchy":1663},[898,38157,2132],{},[1655,38159,1677],{"stretchy":1663},[902,38161,5442],{"encoding":904}," a jeho lineární verzí ",[883,38164,38166],{"className":38165},[886],[888,38167,38168],{"xmlns":890},[892,38169,38170,38184],{},[895,38171,38172,38174,38176,38178,38180,38182],{},[898,38173,2132],{},[1655,38175,1657],{},[898,38177,207],{},[898,38179,1824],{},[1655,38181,2346],{},[898,38183,2025],{},[902,38185,38186],{"encoding":904},"P = aQ + b",[198,38188,38190],{"id":38189},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,38192,38193,38194,38207,38208,38221,38222,2115,38224,4421],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,38195,38197],{"className":38196},[886],[888,38198,38199],{"xmlns":890},[892,38200,38201,38205],{},[895,38202,38203],{},[898,38204,1824],{},[902,38206,1824],{"encoding":904}," závisí na ceně ",[883,38209,38211],{"className":38210},[886],[888,38212,38213],{"xmlns":890},[892,38214,38215,38219],{},[895,38216,38217],{},[898,38218,2132],{},[902,38220,2132],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,38223,29128],{},[614,38225,38226],{},"demand function",[883,38228,38230],{"className":38229},[886],[888,38231,38232],{"xmlns":890,"display":29192},[892,38233,38234,38297],{},[21880,38235,38236],{"width":29197},[21885,38237,38238,38240,38290,38292],{},[21888,38239],{"width":29202},[21888,38241,38242],{},[895,38243,38244,38246,38248,38250,38252,38254,38256,38262,38264,38270,38272,38274,38276,38282,38284,38286,38288],{},[898,38245,1824],{},[1655,38247,1657],{},[898,38249,2838],{},[1655,38251,1664],{"stretchy":1663},[898,38253,2132],{},[1655,38255,1671],{"separator":1670},[1820,38257,38258,38260],{},[898,38259,2132],{},[1826,38261,1828],{},[1655,38263,1671],{"separator":1670},[1820,38265,38266,38268],{},[898,38267,2132],{},[1826,38269,1837],{},[1655,38271,1671],{"separator":1670},[1655,38273,1715],{},[1655,38275,1671],{"separator":1670},[1820,38277,38278,38280],{},[898,38279,2132],{},[898,38281,37986],{},[1655,38283,1671],{"separator":1670},[898,38285,10375],{},[1655,38287,1677],{"stretchy":1663},[898,38289,1719],{"mathvariant":1943},[21888,38291],{"width":29202},[21888,38293,38294],{},[2031,38295,38296],{},"(2.1)",[902,38298,38299],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,38301,38302,38303,38306,38307,38320],{},"Důležitou vlastností je ",[38,38304,38305],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,38308,38310],{"className":38309},[886],[888,38311,38312],{"xmlns":890},[892,38313,38314,38318],{},[895,38315,38316],{},[898,38317,13166],{},[902,38319,13166],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,38322,38324],{"className":38323},[886],[888,38325,38326],{"xmlns":890,"display":29192},[892,38327,38328,38443],{},[21880,38329,38330],{"width":29197},[21885,38331,38332,38334,38436,38438],{},[21888,38333],{"width":29202},[21888,38335,38336],{},[895,38337,38338,38340,38342,38344,38346,38348,38350,38352,38354,38360,38362,38364,38370,38372,38374,38376,38378,38384,38386,38388,38390,38392,38394,38396,38398,38400,38402,38408,38410,38416,38418,38420,38422,38428,38430,38432,38434],{},[898,38339,1824],{},[1655,38341,1657],{},[898,38343,2838],{},[1655,38345,1664],{"stretchy":1663},[898,38347,13166],{},[898,38349,2132],{},[1655,38351,1671],{"separator":1670},[898,38353,13166],{},[1820,38355,38356,38358],{},[898,38357,2132],{},[1826,38359,1828],{},[1655,38361,1671],{"separator":1670},[898,38363,13166],{},[1820,38365,38366,38368],{},[898,38367,2132],{},[1826,38369,1837],{},[1655,38371,1671],{"separator":1670},[1655,38373,1715],{},[1655,38375,1671],{"separator":1670},[898,38377,13166],{},[1820,38379,38380,38382],{},[898,38381,2132],{},[898,38383,37986],{},[1655,38385,1671],{"separator":1670},[898,38387,13166],{},[898,38389,10375],{},[1655,38391,1677],{"stretchy":1663},[1655,38393,1657],{},[898,38395,2838],{},[1655,38397,1664],{"stretchy":1663},[898,38399,2132],{},[1655,38401,1671],{"separator":1670},[1820,38403,38404,38406],{},[898,38405,2132],{},[1826,38407,1828],{},[1655,38409,1671],{"separator":1670},[1820,38411,38412,38414],{},[898,38413,2132],{},[1826,38415,1837],{},[1655,38417,1671],{"separator":1670},[1655,38419,1715],{},[1655,38421,1671],{"separator":1670},[1820,38423,38424,38426],{},[898,38425,2132],{},[898,38427,37986],{},[1655,38429,1671],{"separator":1670},[898,38431,10375],{},[1655,38433,1677],{"stretchy":1663},[898,38435,1719],{"mathvariant":1943},[21888,38437],{"width":29202},[21888,38439,38440],{},[2031,38441,38442],{},"(2.2)",[902,38444,38445],{"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}",[5120,38447,38448],{},[724,38449,38450,38452,38453,1719],{},[883,38451,5661],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,38454,38455],{},"v jednofaktorových modelech neplatí",[724,38457,38458,38459,1343,38462,2704,38465,38468],{},"Rozlišuje se poptávka ",[38,38460,38461],{},"individuální",[38,38463,38464],{},"tržní",[38,38466,38467],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,38470,38472],{"id":38471},"jednofaktorové-modely","Jednofaktorové modely",[38474,38475,38477],"h4",{"id":38476},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,38479,38480,38481,38494,38495,2086],{},"Poptávané množství ",[883,38482,38484],{"className":38483},[886],[888,38485,38486],{"xmlns":890},[892,38487,38488,38492],{},[895,38489,38490],{},[898,38491,1824],{},[902,38493,1824],{"encoding":904}," závisí pouze na ceně ",[883,38496,38498],{"className":38497},[886],[888,38499,38500],{"xmlns":890},[892,38501,38502,38506],{},[895,38503,38504],{},[898,38505,2132],{},[902,38507,2132],{"encoding":904},[883,38509,38511],{"className":38510},[886],[888,38512,38513],{"xmlns":890,"display":29192},[892,38514,38515,38567],{},[21880,38516,38517],{"width":29197},[21885,38518,38519,38521,38560,38562],{},[21888,38520],{"width":29202},[21888,38522,38523],{},[895,38524,38525,38527,38529,38531,38533,38535,38537,38539,38541,38544,38546,38548,38550,38552,38554,38556,38558],{},[898,38526,1824],{},[1655,38528,1657],{},[898,38530,2838],{},[1655,38532,1664],{"stretchy":1663},[898,38534,2132],{},[1655,38536,1677],{"stretchy":1663},[1655,38538,1671],{"separator":1670},[1967,38540],{"width":1969},[2031,38542,38543],{},"resp.",[1967,38545],{"width":1969},[898,38547,2132],{},[1655,38549,1657],{},[898,38551,2838],{},[1655,38553,1664],{"stretchy":1663},[898,38555,1824],{},[1655,38557,1677],{"stretchy":1663},[898,38559,1719],{"mathvariant":1943},[21888,38561],{"width":29202},[21888,38563,38564],{},[2031,38565,38566],{},"(2.3)",[902,38568,38569],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,38571,38572,38573,2115,38576,5171],{},"Graf této funkce se nazývá ",[38,38574,38575],{},"křivka poptávky",[614,38577,38578],{},"demand curve",[38474,38580,38582],{"id":38581},"zákon-klesající-poptávky","Zákon klesající poptávky",[5120,38584,38585],{},[724,38586,38587],{},[38,38588,38589,38590,38603,38604,38617,38618,38603,38631,38644],{},"Roste-li cena ",[883,38591,38593],{"className":38592},[886],[888,38594,38595],{"xmlns":890},[892,38596,38597,38601],{},[895,38598,38599],{},[898,38600,2132],{},[902,38602,2132],{"encoding":904},", pak množství ",[883,38605,38607],{"className":38606},[886],[888,38608,38609],{"xmlns":890},[892,38610,38611,38615],{},[895,38612,38613],{},[898,38614,1824],{},[902,38616,1824],{"encoding":904}," klesá; klesá-li cena ",[883,38619,38621],{"className":38620},[886],[888,38622,38623],{"xmlns":890},[892,38624,38625,38629],{},[895,38626,38627],{},[898,38628,2132],{},[902,38630,2132],{"encoding":904},[883,38632,38634],{"className":38633},[886],[888,38635,38636],{"xmlns":890},[892,38637,38638,38642],{},[895,38639,38640],{},[898,38641,1824],{},[902,38643,1824],{"encoding":904}," roste.",[724,38646,38647,38648,38651],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,38649,38650],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[5120,38653,38654,38659],{},[724,38655,38656,38658],{},[883,38657,5406],{}," Intuice — proč zákon platí",[120,38660,38661,38667],{},[123,38662,38663,38666],{},[38,38664,38665],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,38668,38669,38672],{},[38,38670,38671],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,38674,38675,38676,38689,38690,38703,38704,38730,38731,38757,38758,9349,38784,38787,38788,1719],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,38677,38679],{"className":38678},[886],[888,38680,38681],{"xmlns":890},[892,38682,38683,38687],{},[895,38684,38685],{},[898,38686,2132],{},[902,38688,2132],{"encoding":904}," se vynáší na svislou osu, množství ",[883,38691,38693],{"className":38692},[886],[888,38694,38695],{"xmlns":890},[892,38696,38697,38701],{},[895,38698,38699],{},[898,38700,1824],{},[902,38702,1824],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,38705,38707],{"className":38706},[886],[888,38708,38709],{"xmlns":890},[892,38710,38711,38727],{},[895,38712,38713,38715,38717,38719,38725],{},[1655,38714,2734],{"stretchy":1663},[1826,38716,2552],{},[1655,38718,1671],{"separator":1670},[1820,38720,38721,38723],{},[898,38722,2132],{},[1826,38724,2552],{},[1655,38726,2743],{"stretchy":1663},[902,38728,38729],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,38732,38734],{"className":38733},[886],[888,38735,38736],{"xmlns":890},[892,38737,38738,38754],{},[895,38739,38740,38742,38748,38750,38752],{},[1655,38741,2734],{"stretchy":1663},[1820,38743,38744,38746],{},[898,38745,1824],{},[1826,38747,2552],{},[1655,38749,1671],{"separator":1670},[1826,38751,2552],{},[1655,38753,2743],{"stretchy":1663},[902,38755,38756],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,38759,38761],{"className":38760},[886],[888,38762,38763],{"xmlns":890},[892,38764,38765,38781],{},[895,38766,38767,38769,38771,38773,38779],{},[1655,38768,1664],{"stretchy":1663},[1826,38770,2552],{},[1655,38772,1671],{"separator":1670},[1820,38774,38775,38777],{},[898,38776,2132],{},[1826,38778,2552],{},[1655,38780,1677],{"stretchy":1663},[902,38782,38783],{"encoding":904},"(0, P_0)",[38,38785,38786],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,38789,38790],{},"konvexní",[724,38792,38793],{},[614,38794,38795,38796,38818,38819,2704,38844,1719],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,38797,38799],{"className":38798},[886],[888,38800,38801],{"xmlns":890},[892,38802,38803,38815],{},[895,38804,38805,38807,38809,38811,38813],{},[1655,38806,1664],{"stretchy":1663},[898,38808,1824],{},[1655,38810,1671],{"separator":1670},[898,38812,2132],{},[1655,38814,1677],{"stretchy":1663},[902,38816,38817],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,38820,38822],{"className":38821},[886],[888,38823,38824],{"xmlns":890},[892,38825,38826,38842],{},[895,38827,38828,38830,38832,38834,38840],{},[1655,38829,2734],{"stretchy":1663},[1826,38831,2552],{},[1655,38833,1671],{"separator":1670},[1820,38835,38836,38838],{},[898,38837,2132],{},[1826,38839,2552],{},[1655,38841,2743],{"stretchy":1663},[902,38843,38729],{"encoding":904},[883,38845,38847],{"className":38846},[886],[888,38848,38849],{"xmlns":890},[892,38850,38851,38867],{},[895,38852,38853,38855,38861,38863,38865],{},[1655,38854,2734],{"stretchy":1663},[1820,38856,38857,38859],{},[898,38858,1824],{},[1826,38860,2552],{},[1655,38862,1671],{"separator":1670},[1826,38864,2552],{},[1655,38866,2743],{"stretchy":1663},[902,38868,38756],{"encoding":904},[38474,38870,38872],{"id":38871},"lineární-model-poptávky","Lineární model poptávky",[724,38874,38875],{},"Nejjednodušší závislostí je",[883,38877,38879],{"className":38878},[886],[888,38880,38881],{"xmlns":890,"display":29192},[892,38882,38883,38932],{},[21880,38884,38885],{"width":29197},[21885,38886,38887,38889,38925,38927],{},[21888,38888],{"width":29202},[21888,38890,38891],{},[895,38892,38893,38895,38897,38899,38901,38903,38905,38907,38909,38911,38913,38915,38917,38919,38921,38923],{},[898,38894,2132],{},[1655,38896,1657],{},[898,38898,207],{},[898,38900,1824],{},[1655,38902,2346],{},[898,38904,2025],{},[1655,38906,1671],{"separator":1670},[1967,38908],{"width":1969},[898,38910,207],{},[1655,38912,3065],{},[1826,38914,2552],{},[1655,38916,1671],{"separator":1670},[2031,38918,2033],{},[898,38920,2025],{},[1655,38922,2969],{},[1826,38924,13585],{},[21888,38926],{"width":29202},[21888,38928,38929],{},[2031,38930,38931],{},"(2.4)",[902,38933,38934],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,38936,38937,38938,22720,38974,2704,38998,9284,39024,39046,39047,1719],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,38939,38941],{"className":38940},[886],[888,38942,38943],{"xmlns":890},[892,38944,38945,38971],{},[895,38946,38947,38949,38951,38959,38961,38963],{},[898,38948,1824],{},[1655,38950,1657],{},[3615,38952,38953],{"scriptlevel":2552,"displaystyle":1663},[1949,38954,38955,38957],{},[1826,38956,1828],{},[898,38958,207],{},[898,38960,2132],{},[1655,38962,2623],{},[3615,38964,38965],{"scriptlevel":2552,"displaystyle":1663},[1949,38966,38967,38969],{},[898,38968,2025],{},[898,38970,207],{},[902,38972,38973],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,38975,38977],{"className":38976},[886],[888,38978,38979],{"xmlns":890},[892,38980,38981,38995],{},[895,38982,38983,38991,38993],{},[3615,38984,38985],{"scriptlevel":2552,"displaystyle":1663},[1949,38986,38987,38989],{},[1826,38988,1828],{},[898,38990,207],{},[1655,38992,3065],{},[1826,38994,2552],{},[902,38996,38997],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,38999,39001],{"className":39000},[886],[888,39002,39003],{"xmlns":890},[892,39004,39005,39021],{},[895,39006,39007,39009,39017,39019],{},[1655,39008,2623],{},[3615,39010,39011],{"scriptlevel":2552,"displaystyle":1663},[1949,39012,39013,39015],{},[898,39014,2025],{},[898,39016,207],{},[1655,39018,2969],{},[1826,39020,2552],{},[902,39022,39023],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,39025,39027],{"className":39026},[886],[888,39028,39029],{"xmlns":890},[892,39030,39031,39043],{},[895,39032,39033,39035,39037,39039,39041],{},[1655,39034,1664],{"stretchy":1663},[1826,39036,2552],{},[1655,39038,1671],{"separator":1670},[898,39040,2025],{},[1655,39042,1677],{"stretchy":1663},[902,39044,39045],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,39048,39049],{},"nedokonalé konkurenci",[39051,39052,39054],"h5",{"id":39053},"příklad-21","Příklad 2.1",[724,39056,39057,39060,39061,1719],{},[38,39058,39059],{},"Zadání:"," Lineární poptávka ",[883,39062,39064],{"className":39063},[886],[888,39065,39066],{"xmlns":890},[892,39067,39068,39084],{},[895,39069,39070,39072,39074,39076,39078,39080,39082],{},[898,39071,2132],{},[1655,39073,1657],{},[1655,39075,2623],{},[1826,39077,1837],{},[898,39079,1824],{},[1655,39081,2346],{},[1826,39083,4396],{},[902,39085,39086],{"encoding":904},"P = -2Q + 60",[724,39088,39089,39092,39093,39115,39116,1719],{},[38,39090,39091],{},"Řešení:"," Reálné cenové rozpětí je ",[883,39094,39096],{"className":39095},[886],[888,39097,39098],{"xmlns":890},[892,39099,39100,39112],{},[895,39101,39102,39104,39106,39108,39110],{},[1655,39103,1664],{"stretchy":1663},[1826,39105,2552],{},[1655,39107,1671],{"separator":1670},[1826,39109,4396],{},[1655,39111,1677],{"stretchy":1663},[902,39113,39114],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,39117,39119],{"className":39118},[886],[888,39120,39121],{"xmlns":890},[892,39122,39123,39146],{},[895,39124,39125,39127,39129,39131,39139,39141,39143],{},[898,39126,1824],{},[1655,39128,1657],{},[1655,39130,2623],{},[3615,39132,39133],{"scriptlevel":2552,"displaystyle":1663},[1949,39134,39135,39137],{},[1826,39136,1828],{},[1826,39138,1837],{},[898,39140,2132],{},[1655,39142,2346],{},[1826,39144,39145],{},"30",[902,39147,39148],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,39150,39151,39174],{},[19,39152,39153],{},[22,39154,39155,39170,39172],{},[25,39156,39157],{},[883,39158,39160],{"className":39159},[886],[888,39161,39162],{"xmlns":890},[892,39163,39164,39168],{},[895,39165,39166],{},[898,39167,2132],{},[902,39169,2132],{"encoding":904},[25,39171,6460],{},[25,39173,10282],{},[30,39175,39176],{},[22,39177,39178,39193,39195],{},[35,39179,39180],{},[883,39181,39183],{"className":39182},[886],[888,39184,39185],{"xmlns":890},[892,39186,39187,39191],{},[895,39188,39189],{},[898,39190,1824],{},[902,39192,1824],{"encoding":904},[35,39194,4136],{},[35,39196,10282],{},[724,39198,39199],{},[614,39200,39201,39202,2704,39224,1719],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,39203,39205],{"className":39204},[886],[888,39206,39207],{"xmlns":890},[892,39208,39209,39221],{},[895,39210,39211,39213,39215,39217,39219],{},[1655,39212,2734],{"stretchy":1663},[1826,39214,2552],{},[1655,39216,1671],{"separator":1670},[898,39218,2025],{},[1655,39220,2743],{"stretchy":1663},[902,39222,39223],{"encoding":904},"[0, b]",[883,39225,39227],{"className":39226},[886],[888,39228,39229],{"xmlns":890},[892,39230,39231,39249],{},[895,39232,39233,39235,39237,39239,39241,39243,39245,39247],{},[1655,39234,2734],{"stretchy":1663},[1655,39236,2623],{},[898,39238,2025],{},[898,39240,5923],{"mathvariant":1943},[898,39242,207],{},[1655,39244,1671],{"separator":1670},[1826,39246,2552],{},[1655,39248,2743],{"stretchy":1663},[902,39250,39251],{"encoding":904},"[-b\u002Fa, 0]",[38474,39253,39255],{"id":39254},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,39257,39258,39259,39276],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,39260,39262],{"className":39261},[886],[888,39263,39264],{"xmlns":890},[892,39265,39266,39274],{},[895,39267,39268],{},[2597,39269,39270,39272],{},[898,39271,2132],{},[1655,39273,5603],{},[902,39275,5653],{"encoding":904},", je funkce poptávky konstantní:",[883,39278,39280],{"className":39279},[886],[888,39281,39282],{"xmlns":890,"display":29192},[892,39283,39284,39298],{},[895,39285,39286,39288,39290,39296],{},[898,39287,2132],{},[1655,39289,1657],{},[2597,39291,39292,39294],{},[898,39293,2132],{},[1655,39295,5603],{},[898,39297,1719],{"mathvariant":1943},[902,39299,39300],{"encoding":904},"P = P^*.",[724,39302,39303],{},[614,39304,39305,39306,39327,39328,1719],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,39307,39309],{"className":39308},[886],[888,39310,39311],{"xmlns":890},[892,39312,39313,39325],{},[895,39314,39315,39317,39319,39321,39323],{},[1655,39316,1664],{"stretchy":1663},[898,39318,1824],{},[1655,39320,1671],{"separator":1670},[898,39322,2132],{},[1655,39324,1677],{"stretchy":1663},[902,39326,38817],{"encoding":904}," na úrovni ",[883,39329,39331],{"className":39330},[886],[888,39332,39333],{"xmlns":890},[892,39334,39335,39347],{},[895,39336,39337,39339,39341],{},[898,39338,2132],{},[1655,39340,1657],{},[2597,39342,39343,39345],{},[898,39344,2132],{},[1655,39346,5603],{},[902,39348,5606],{"encoding":904},[38474,39350,39352],{"id":39351},"giffenův-statek","Giffenův statek",[724,39354,39355,39356,39358,39359,39361,39362,1719],{},"Existují zboží, u nichž je křivka poptávky ",[38,39357,14782],{}," — tzv. ",[38,39360,39352],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,39363,39364],{},"podřadnému zboží",[39051,39366,39368],{"id":39367},"příklad-22","Příklad 2.2",[724,39370,39371,39374,39375,39393,39394,39416,39417,39435,39436,39454,39455,39478],{},[38,39372,39373],{},"Zadání a popis:"," Křivka ",[883,39376,39378],{"className":39377},[886],[888,39379,39380],{"xmlns":890},[892,39381,39382,39390],{},[895,39383,39384],{},[1820,39385,39386,39388],{},[898,39387,2838],{},[1826,39389,1828],{},[902,39391,39392],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,39395,39397],{"className":39396},[886],[888,39398,39399],{"xmlns":890},[892,39400,39401,39413],{},[895,39402,39403,39405,39407,39409,39411],{},[1655,39404,1664],{"stretchy":1663},[1826,39406,2552],{},[1655,39408,1671],{"separator":1670},[1826,39410,37370],{},[1655,39412,1677],{"stretchy":1663},[902,39414,39415],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,39418,39420],{"className":39419},[886],[888,39421,39422],{"xmlns":890},[892,39423,39424,39432],{},[895,39425,39426],{},[1820,39427,39428,39430],{},[898,39429,1824],{},[1826,39431,2552],{},[902,39433,39434],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,39437,39439],{"className":39438},[886],[888,39440,39441],{"xmlns":890},[892,39442,39443,39451],{},[895,39444,39445],{},[1820,39446,39447,39449],{},[898,39448,2838],{},[1826,39450,1837],{},[902,39452,39453],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,39456,39458],{"className":39457},[886],[888,39459,39460],{"xmlns":890},[892,39461,39462,39475],{},[895,39463,39464,39466,39468,39470,39473],{},[1655,39465,2734],{"stretchy":1663},[1826,39467,2552],{},[1655,39469,1671],{"separator":1670},[1826,39471,39472],{},"21",[1655,39474,2743],{"stretchy":1663},[902,39476,39477],{"encoding":904},"[0, 21]"," centů.",[198,39480,39482],{"id":39481},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,39484,39485,39486,2086],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,39487,39489],{"className":39488},[886],[888,39490,39491],{"xmlns":890},[892,39492,39493,39497],{},[895,39494,39495],{},[898,39496,10375],{},[902,39498,10375],{"encoding":904},[883,39500,39502],{"className":39501},[886],[888,39503,39504],{"xmlns":890,"display":29192},[892,39505,39506,39537],{},[21880,39507,39508],{"width":29197},[21885,39509,39510,39512,39530,39532],{},[21888,39511],{"width":29202},[21888,39513,39514],{},[895,39515,39516,39518,39520,39522,39524,39526,39528],{},[898,39517,1824],{},[1655,39519,1657],{},[898,39521,5502],{},[1655,39523,1664],{"stretchy":1663},[898,39525,10375],{},[1655,39527,1677],{"stretchy":1663},[898,39529,1719],{"mathvariant":1943},[21888,39531],{"width":29202},[21888,39533,39534],{},[2031,39535,39536],{},"(2.5)",[902,39538,39539],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,39541,39542,39543,39546,39547,39550],{},"Funkce se nazývá ",[38,39544,39545],{},"Engelova",", její graf ",[38,39548,39549],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,39552,39553,39685],{},[123,39554,39555,8262,39558,39571,39572,39585,39586,39603,39604],{},[38,39556,39557],{},"Normální (superior) zboží",[883,39559,39561],{"className":39560},[886],[888,39562,39563],{"xmlns":890},[892,39564,39565,39569],{},[895,39566,39567],{},[898,39568,1824],{},[902,39570,1824],{"encoding":904}," roste s ",[883,39573,39575],{"className":39574},[886],[888,39576,39577],{"xmlns":890},[892,39578,39579,39583],{},[895,39580,39581],{},[898,39582,10375],{},[902,39584,10375],{"encoding":904},", nepřesáhne hodnotu ",[883,39587,39589],{"className":39588},[886],[888,39590,39591],{"xmlns":890},[892,39592,39593,39601],{},[895,39594,39595],{},[1820,39596,39597,39599],{},[898,39598,1824],{},[1826,39600,2552],{},[902,39602,39434],{"encoding":904},":\n",[120,39605,39606,39638],{},[123,39607,39608,39611,39612,39615,39616,1719],{},[38,39609,39610],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,39613,39614],{},"konkávní"," křivka, autonomní spotřeba ",[883,39617,39619],{"className":39618},[886],[888,39620,39621],{"xmlns":890},[892,39622,39623,39635],{},[895,39624,39625,39631,39633],{},[1820,39626,39627,39629],{},[898,39628,1824],{},[1826,39630,1828],{},[1655,39632,2969],{},[1826,39634,2552],{},[902,39636,39637],{"encoding":904},"Q_1 > 0",[123,39639,39640,39643,39644,39662,39663,39665,39666,3106,39683,1719],{},[38,39641,39642],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,39645,39647],{"className":39646},[886],[888,39648,39649],{"xmlns":890},[892,39650,39651,39659],{},[895,39652,39653],{},[1820,39654,39655,39657],{},[898,39656,10375],{},[1826,39658,1828],{},[902,39660,39661],{"encoding":904},"Y_1",", křivka je nejprve ",[38,39664,38790],{}," a od ",[883,39667,39669],{"className":39668},[886],[888,39670,39671],{"xmlns":890},[892,39672,39673,39681],{},[895,39674,39675],{},[1820,39676,39677,39679],{},[898,39678,10375],{},[1826,39680,1828],{},[902,39682,39661],{"encoding":904},[38,39684,39614],{},[123,39686,39687,39690,39691,39709],{},[38,39688,39689],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,39692,39694],{"className":39693},[886],[888,39695,39696],{"xmlns":890},[892,39697,39698,39706],{},[895,39699,39700],{},[1820,39701,39702,39704],{},[898,39703,10375],{},[1826,39705,2552],{},[902,39707,39708],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,39711,39712,39713,39716,39717,5171],{},"Mírou citlivosti je ",[614,39714,39715],{},"důchodová elasticita"," (viz ",[207,39718,5150],{"className":39719,"dataFsResolvedFilePath":848,"href":849},[210],[724,39721,39722],{},[614,39723,39724],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[38474,39726,39728],{"id":39727},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[5120,39730,39731,39802,39845],{},[724,39732,39733,39735,39736,3106,39739,3106,39752,6918,39754,39767,39768,39771,39772,1719],{},[883,39734,5661],{}," Pozor — nezbytné ≠ podřadné\n",[38,39737,39738],{},"Nezbytné zboží:",[883,39740,39742],{"className":39741},[886],[888,39743,39744],{"xmlns":890},[892,39745,39746,39750],{},[895,39747,39748],{},[898,39749,1824],{},[902,39751,1824],{"encoding":904},[38,39753,8569],{},[883,39755,39757],{"className":39756},[886],[888,39758,39759],{"xmlns":890},[892,39760,39761,39765],{},[895,39762,39763],{},[898,39764,10375],{},[902,39766,10375],{"encoding":904},", ale ",[38,39769,39770],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,39773,39775],{"className":39774},[886],[888,39776,39777],{"xmlns":890},[892,39778,39779,39799],{},[895,39780,39781,39787,39789,39791,39793,39795,39797],{},[1820,39782,39783,39785],{},[898,39784,5502],{},[898,39786,10375],{},[1655,39788,7753],{},[1655,39790,1664],{"stretchy":1663},[1826,39792,2552],{},[1655,39794,1671],{"separator":1670},[1826,39796,1828],{},[1655,39798,1677],{"stretchy":1663},[902,39800,39801],{"encoding":904},"E_Y \\in (0, 1)",[724,39803,39804,3106,39807,3106,39820,39822,39823,1719],{},[38,39805,39806],{},"Podřadné zboží:",[883,39808,39810],{"className":39809},[886],[888,39811,39812],{"xmlns":890},[892,39813,39814,39818],{},[895,39815,39816],{},[898,39817,1824],{},[902,39819,1824],{"encoding":904},[38,39821,8589],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,39824,39826],{"className":39825},[886],[888,39827,39828],{"xmlns":890},[892,39829,39830,39842],{},[895,39831,39832,39838,39840],{},[1820,39833,39834,39836],{},[898,39835,5502],{},[898,39837,10375],{},[1655,39839,3065],{},[1826,39841,2552],{},[902,39843,39844],{"encoding":904},"E_Y \u003C 0",[724,39846,39847,39848,1719],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,39849,39850],{},"méně kusů, ne jen proporčně méně",[724,39852,39853,39856,39857,39860],{},[38,39854,39855],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,39858,39859],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,39862,39863],{},[1723,39864],{"alt":39865,"className":39866,"src":39867},"imek-engelovy-krivky-3typy",[210,1727],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[39051,39869,39871],{"id":39870},"české-příklady","České příklady",[16,39873,39874,39884],{},[19,39875,39876],{},[22,39877,39878,39881],{},[25,39879,39880],{},"Podřadné",[25,39882,39883],{},"Nahradí se za",[30,39885,39886,39894,39902,39910,39918,39926,39934,39942],{},[22,39887,39888,39891],{},[35,39889,39890],{},"Instantní polévky, ramen",[35,39892,39893],{},"Čerstvé jídlo, restaurace",[22,39895,39896,39899],{},[35,39897,39898],{},"MHD (autobus, tramvaj)",[35,39900,39901],{},"Vlastní auto, Uber, taxi",[22,39903,39904,39907],{},[35,39905,39906],{},"Mražené polotovary, pizza z mrazáku",[35,39908,39909],{},"Čerstvé suroviny, hotovky",[22,39911,39912,39915],{},[35,39913,39914],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,39916,39917],{},"Značkové produkty",[22,39919,39920,39923],{},[35,39921,39922],{},"Paštika Májka, obyčejný měkký salám",[35,39924,39925],{},"Kvalitní uzeniny, šunka od kosti",[22,39927,39928,39931],{},[35,39929,39930],{},"Second hand oblečení",[35,39932,39933],{},"Nové oblečení, značky",[22,39935,39936,39939],{},[35,39937,39938],{},"Krabicové víno, nejlevnější pivo",[35,39940,39941],{},"Lahvové víno, řemeslná piva",[22,39943,39944,39947],{},[35,39945,39946],{},"Ojetá auta nižších tříd",[35,39948,39949],{},"Nová auta, prémiové značky",[5120,39951,39952],{},[724,39953,39954,39956,39957,39960],{},[883,39955,5821],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,39958,39959],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,39962,39963,39966,39967,2115,39970,39992,39993,2115,39996,40017,40018,40036,40037,40040],{},[38,39964,39965],{},"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 ",[38,39968,39969],{},"luxus",[883,39971,39973],{"className":39972},[886],[888,39974,39975],{"xmlns":890},[892,39976,39977,39989],{},[895,39978,39979,39985,39987],{},[1820,39980,39981,39983],{},[898,39982,5502],{},[898,39984,10375],{},[1655,39986,2969],{},[1826,39988,1828],{},[902,39990,39991],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,39994,39995],{},"podřadné",[883,39997,39999],{"className":39998},[886],[888,40000,40001],{"xmlns":890},[892,40002,40003,40015],{},[895,40004,40005,40011,40013],{},[1820,40006,40007,40009],{},[898,40008,5502],{},[898,40010,10375],{},[1655,40012,3065],{},[1826,40014,2552],{},[902,40016,39844],{"encoding":904},"). Proto je ",[883,40019,40021],{"className":40020},[886],[888,40022,40023],{"xmlns":890},[892,40024,40025,40033],{},[895,40026,40027],{},[1820,40028,40029,40031],{},[898,40030,5502],{},[898,40032,10375],{},[902,40034,40035],{"encoding":904},"E_Y"," vždy ",[38,40038,40039],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,40042,40043,40044,40046],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,40045,39352],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,40048,40050,40051,1677],{"id":40049},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,40052,40053],{},"shift of demand",[724,40055,40056,40057,40075,40076,40093,40094,40107,40108,3962,40121,40143,40144,40161,40162,40188,40189,40192],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,40058,40060],{"className":40059},[886],[888,40061,40062],{"xmlns":890},[892,40063,40064,40072],{},[895,40065,40066],{},[1820,40067,40068,40070],{},[898,40069,2132],{},[1826,40071,2552],{},[902,40073,40074],{"encoding":904},"P_0"," odpovídá množství ",[883,40077,40079],{"className":40078},[886],[888,40080,40081],{"xmlns":890},[892,40082,40083,40091],{},[895,40084,40085],{},[1820,40086,40087,40089],{},[898,40088,1824],{},[1826,40090,2552],{},[902,40092,39434],{"encoding":904}," na křivce ",[883,40095,40097],{"className":40096},[886],[888,40098,40099],{"xmlns":890},[892,40100,40101,40105],{},[895,40102,40103],{},[898,40104,2838],{},[902,40106,2838],{"encoding":904},"; vzroste-li důchod z ",[883,40109,40111],{"className":40110},[886],[888,40112,40113],{"xmlns":890},[892,40114,40115,40119],{},[895,40116,40117],{},[898,40118,10375],{},[902,40120,10375],{"encoding":904},[883,40122,40124],{"className":40123},[886],[888,40125,40126],{"xmlns":890},[892,40127,40128,40140],{},[895,40129,40130,40136,40138],{},[1820,40131,40132,40134],{},[898,40133,10375],{},[1826,40135,1828],{},[1655,40137,2969],{},[898,40139,10375],{},[902,40141,40142],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,40145,40147],{"className":40146},[886],[888,40148,40149],{"xmlns":890},[892,40150,40151,40159],{},[895,40152,40153],{},[1820,40154,40155,40157],{},[898,40156,2132],{},[1826,40158,2552],{},[902,40160,40074],{"encoding":904}," odpovídá vyšší ",[883,40163,40165],{"className":40164},[886],[888,40166,40167],{"xmlns":890},[892,40168,40169,40185],{},[895,40170,40171,40177,40179],{},[1820,40172,40173,40175],{},[898,40174,1824],{},[1826,40176,1828],{},[1655,40178,2969],{},[1820,40180,40181,40183],{},[898,40182,1824],{},[1826,40184,2552],{},[902,40186,40187],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,40190,40191],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,40194,40195],{},[1723,40196],{"alt":40197,"className":40198,"src":40199},"imek-posun-vs-pohyb-po-krivce",[210,1727],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,40201,40202],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,40204,40205],{},[614,40206,40207,40208,15136,40238,40259],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,40209,40211],{"className":40210},[886],[888,40212,40213],{"xmlns":890},[892,40214,40215,40235],{},[895,40216,40217,40223,40225,40227,40229],{},[1820,40218,40219,40221],{},[898,40220,2838],{},[1826,40222,1837],{},[1655,40224,1671],{"separator":1670},[898,40226,2838],{},[1655,40228,1671],{"separator":1670},[1820,40230,40231,40233],{},[898,40232,2838],{},[1826,40234,1828],{},[902,40236,40237],{"encoding":904},"D_2, D, D_1",[883,40239,40241],{"className":40240},[886],[888,40242,40243],{"xmlns":890},[892,40244,40245,40257],{},[895,40246,40247,40249,40251,40253,40255],{},[1655,40248,1664],{"stretchy":1663},[898,40250,1824],{},[1655,40252,1671],{"separator":1670},[898,40254,2132],{},[1655,40256,1677],{"stretchy":1663},[902,40258,38817],{"encoding":904},", šipky naznačují posuny.",[39051,40261,40263],{"id":40262},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,40265,40266,40268,40269,40292,40293,40310,40311,40328,40329,1719],{},[38,40267,39059],{}," Poptávce ",[883,40270,40272],{"className":40271},[886],[888,40273,40274],{"xmlns":890},[892,40275,40276,40290],{},[895,40277,40278,40280,40282,40284,40286,40288],{},[898,40279,2132],{},[1655,40281,1657],{},[898,40283,2838],{},[1655,40285,1664],{"stretchy":1663},[898,40287,1824],{},[1655,40289,1677],{"stretchy":1663},[902,40291,5889],{"encoding":904}," odpovídá ceně ",[883,40294,40296],{"className":40295},[886],[888,40297,40298],{"xmlns":890},[892,40299,40300,40308],{},[895,40301,40302],{},[1820,40303,40304,40306],{},[898,40305,2132],{},[1826,40307,2552],{},[902,40309,40074],{"encoding":904}," množství ",[883,40312,40314],{"className":40313},[886],[888,40315,40316],{"xmlns":890},[892,40317,40318,40326],{},[895,40319,40320],{},[1820,40321,40322,40324],{},[898,40323,1824],{},[1826,40325,2552],{},[902,40327,39434],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,40330,40332],{"className":40331},[886],[888,40333,40334],{"xmlns":890},[892,40335,40336,40340],{},[895,40337,40338],{},[898,40339,4049],{},[902,40341,4049],{"encoding":904},[724,40343,40344,40346,40347,40364,40365,40387],{},[38,40345,39091],{}," Kupující nakupuje množství ",[883,40348,40350],{"className":40349},[886],[888,40351,40352],{"xmlns":890},[892,40353,40354,40362],{},[895,40355,40356],{},[1820,40357,40358,40360],{},[898,40359,1824],{},[1826,40361,1828],{},[902,40363,30128],{"encoding":904},", které odpovídá ceně ",[883,40366,40368],{"className":40367},[886],[888,40369,40370],{"xmlns":890},[892,40371,40372,40384],{},[895,40373,40374,40380,40382],{},[1820,40375,40376,40378],{},[898,40377,2132],{},[1826,40379,2552],{},[1655,40381,2346],{},[898,40383,4049],{},[902,40385,40386],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,40389,40391],{"className":40390},[886],[888,40392,40393],{"xmlns":890,"display":29192},[892,40394,40395,40429],{},[895,40396,40397,40399,40401,40407,40409,40411,40413,40415,40417,40419,40421,40423,40425,40427],{},[898,40398,2132],{},[1655,40400,1657],{},[1820,40402,40403,40405],{},[898,40404,2838],{},[1826,40406,1828],{},[1655,40408,1664],{"stretchy":1663},[898,40410,1824],{},[1655,40412,1677],{"stretchy":1663},[1655,40414,1657],{},[898,40416,2838],{},[1655,40418,1664],{"stretchy":1663},[898,40420,1824],{},[1655,40422,1677],{"stretchy":1663},[1655,40424,2623],{},[898,40426,4049],{},[1655,40428,1671],{"separator":1670},[902,40430,40431],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,40433,40434,40435,1719],{},"tj. dojde k ",[38,40436,40437],{},"posunu poptávky doleva",[724,40439,40440],{},[614,40441,40442,40443,40464,40465,1343,40482,1343,40495,40516,40517,2704,40534,1719],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,40444,40446],{"className":40445},[886],[888,40447,40448],{"xmlns":890},[892,40449,40450,40462],{},[895,40451,40452,40454,40456,40458,40460],{},[1655,40453,1664],{"stretchy":1663},[898,40455,1824],{},[1655,40457,1671],{"separator":1670},[898,40459,2132],{},[1655,40461,1677],{"stretchy":1663},[902,40463,38817],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,40466,40468],{"className":40467},[886],[888,40469,40470],{"xmlns":890},[892,40471,40472,40480],{},[895,40473,40474],{},[1820,40475,40476,40478],{},[898,40477,2132],{},[1826,40479,2552],{},[902,40481,40074],{"encoding":904},[883,40483,40485],{"className":40484},[886],[888,40486,40487],{"xmlns":890},[892,40488,40489,40493],{},[895,40490,40491],{},[898,40492,4049],{},[902,40494,4049],{"encoding":904},[883,40496,40498],{"className":40497},[886],[888,40499,40500],{"xmlns":890},[892,40501,40502,40514],{},[895,40503,40504,40510,40512],{},[1820,40505,40506,40508],{},[898,40507,2132],{},[1826,40509,2552],{},[1655,40511,2346],{},[898,40513,4049],{},[902,40515,40386],{"encoding":904},"; na vodorovné ",[883,40518,40520],{"className":40519},[886],[888,40521,40522],{"xmlns":890},[892,40523,40524,40532],{},[895,40525,40526],{},[1820,40527,40528,40530],{},[898,40529,1824],{},[1826,40531,1828],{},[902,40533,30128],{"encoding":904},[883,40535,40537],{"className":40536},[886],[888,40538,40539],{"xmlns":890},[892,40540,40541,40549],{},[895,40542,40543],{},[1820,40544,40545,40547],{},[898,40546,1824],{},[1826,40548,2552],{},[902,40550,39434],{"encoding":904},[198,40552,40554],{"id":40553},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,40556,40557],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,40559,40561],{"className":40560},[886],[888,40562,40563],{"xmlns":890,"display":29192},[892,40564,40565,40750],{},[21880,40566,40567],{"width":29197},[21885,40568,40569,40571,40743,40745],{},[21888,40570],{"width":29202},[21888,40572,40573],{},[21880,40574,40575,40659],{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},[21885,40576,40577,40587],{},[21888,40578,40579],{},[3615,40580,40581],{"scriptlevel":2552,"displaystyle":1670},[1820,40582,40583,40585],{},[898,40584,1824],{},[1826,40586,1828],{},[21888,40588,40589],{},[3615,40590,40591],{"scriptlevel":2552,"displaystyle":1670},[895,40592,40593,40595,40597,40603,40605,40611,40613,40619,40621,40623,40629,40631,40637,40643,40645,40651,40657],{},[895,40594],{},[1655,40596,1657],{},[1820,40598,40599,40601],{},[898,40600,2838],{},[1826,40602,1828],{},[1655,40604,1664],{"stretchy":1663},[1820,40606,40607,40609],{},[898,40608,2132],{},[1826,40610,1828],{},[1655,40612,1671],{"separator":1670},[1820,40614,40615,40617],{},[898,40616,2132],{},[1826,40618,1837],{},[1655,40620,1677],{"stretchy":1663},[1655,40622,1657],{},[1820,40624,40625,40627],{},[898,40626,207],{},[1826,40628,1828],{},[1655,40630,2346],{},[1820,40632,40633,40635],{},[898,40634,2025],{},[1826,40636,1828],{},[1820,40638,40639,40641],{},[898,40640,2132],{},[1826,40642,1828],{},[1655,40644,2346],{},[1820,40646,40647,40649],{},[898,40648,1789],{},[1826,40650,1828],{},[1820,40652,40653,40655],{},[898,40654,2132],{},[1826,40656,1837],{},[1655,40658,1671],{"separator":1670},[21885,40660,40661,40671],{},[21888,40662,40663],{},[3615,40664,40665],{"scriptlevel":2552,"displaystyle":1670},[1820,40666,40667,40669],{},[898,40668,1824],{},[1826,40670,1837],{},[21888,40672,40673],{},[3615,40674,40675],{"scriptlevel":2552,"displaystyle":1670},[895,40676,40677,40679,40681,40687,40689,40695,40697,40703,40705,40707,40713,40715,40721,40727,40729,40735,40741],{},[895,40678],{},[1655,40680,1657],{},[1820,40682,40683,40685],{},[898,40684,2838],{},[1826,40686,1837],{},[1655,40688,1664],{"stretchy":1663},[1820,40690,40691,40693],{},[898,40692,2132],{},[1826,40694,1828],{},[1655,40696,1671],{"separator":1670},[1820,40698,40699,40701],{},[898,40700,2132],{},[1826,40702,1837],{},[1655,40704,1677],{"stretchy":1663},[1655,40706,1657],{},[1820,40708,40709,40711],{},[898,40710,207],{},[1826,40712,1837],{},[1655,40714,2346],{},[1820,40716,40717,40719],{},[898,40718,2025],{},[1826,40720,1837],{},[1820,40722,40723,40725],{},[898,40724,2132],{},[1826,40726,1828],{},[1655,40728,2346],{},[1820,40730,40731,40733],{},[898,40732,1789],{},[1826,40734,1837],{},[1820,40736,40737,40739],{},[898,40738,2132],{},[1826,40740,1837],{},[898,40742,1719],{"mathvariant":1943},[21888,40744],{"width":29202},[21888,40746,40747],{},[2031,40748,40749],{},"(2.6)",[902,40751,40752],{"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}",[38474,40754,40756],{"id":40755},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,40758,40759,40806,40853],{},[123,40760,40761,1343,40783,40805],{},[883,40762,40764],{"className":40763},[886],[888,40765,40766],{"xmlns":890},[892,40767,40768,40780],{},[895,40769,40770,40776,40778],{},[1820,40771,40772,40774],{},[898,40773,207],{},[1826,40775,1828],{},[1655,40777,2969],{},[1826,40779,2552],{},[902,40781,40782],{"encoding":904},"a_1 > 0",[883,40784,40786],{"className":40785},[886],[888,40787,40788],{"xmlns":890},[892,40789,40790,40802],{},[895,40791,40792,40798,40800],{},[1820,40793,40794,40796],{},[898,40795,207],{},[1826,40797,1837],{},[1655,40799,2969],{},[1826,40801,2552],{},[902,40803,40804],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,40807,40808,1343,40830,40852],{},[883,40809,40811],{"className":40810},[886],[888,40812,40813],{"xmlns":890},[892,40814,40815,40827],{},[895,40816,40817,40823,40825],{},[1820,40818,40819,40821],{},[898,40820,2025],{},[1826,40822,1828],{},[1655,40824,3065],{},[1826,40826,2552],{},[902,40828,40829],{"encoding":904},"b_1 \u003C 0",[883,40831,40833],{"className":40832},[886],[888,40834,40835],{"xmlns":890},[892,40836,40837,40849],{},[895,40838,40839,40845,40847],{},[1820,40840,40841,40843],{},[898,40842,1789],{},[1826,40844,1837],{},[1655,40846,3065],{},[1826,40848,2552],{},[902,40850,40851],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,40854,40855,40856,1343,40873,40891,40892],{},"zkřížené koeficienty ",[883,40857,40859],{"className":40858},[886],[888,40860,40861],{"xmlns":890},[892,40862,40863,40871],{},[895,40864,40865],{},[1820,40866,40867,40869],{},[898,40868,1789],{},[1826,40870,1828],{},[902,40872,30925],{"encoding":904},[883,40874,40876],{"className":40875},[886],[888,40877,40878],{"xmlns":890},[892,40879,40880,40888],{},[895,40881,40882],{},[1820,40883,40884,40886],{},[898,40885,2025],{},[1826,40887,1837],{},[902,40889,40890],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,40893,40894,40944],{},[123,40895,40896,40899,40900,1343,40922,1671],{},[38,40897,40898],{},"substituty"," (máslo vs. margarín): ",[883,40901,40903],{"className":40902},[886],[888,40904,40905],{"xmlns":890},[892,40906,40907,40919],{},[895,40908,40909,40915,40917],{},[1820,40910,40911,40913],{},[898,40912,1789],{},[1826,40914,1828],{},[1655,40916,2969],{},[1826,40918,2552],{},[902,40920,40921],{"encoding":904},"c_1 > 0",[883,40923,40925],{"className":40924},[886],[888,40926,40927],{"xmlns":890},[892,40928,40929,40941],{},[895,40930,40931,40937,40939],{},[1820,40932,40933,40935],{},[898,40934,2025],{},[1826,40936,1837],{},[1655,40938,2969],{},[1826,40940,2552],{},[902,40942,40943],{"encoding":904},"b_2 > 0",[123,40945,40946,40949,40950,1343,40972,1719],{},[38,40947,40948],{},"komplementy"," (auto vs. benzín): ",[883,40951,40953],{"className":40952},[886],[888,40954,40955],{"xmlns":890},[892,40956,40957,40969],{},[895,40958,40959,40965,40967],{},[1820,40960,40961,40963],{},[898,40962,1789],{},[1826,40964,1828],{},[1655,40966,3065],{},[1826,40968,2552],{},[902,40970,40971],{"encoding":904},"c_1 \u003C 0",[883,40973,40975],{"className":40974},[886],[888,40976,40977],{"xmlns":890},[892,40978,40979,40991],{},[895,40980,40981,40987,40989],{},[1820,40982,40983,40985],{},[898,40984,2025],{},[1826,40986,1837],{},[1655,40988,3065],{},[1826,40990,2552],{},[902,40992,40993],{"encoding":904},"b_2 \u003C 0",[724,40995,40996],{},"Schematicky:",[724,40998,40999,41002],{},[38,41000,41001],{},"Substituty",[883,41003,41005],{"className":41004},[886],[888,41006,41007],{"xmlns":890},[892,41008,41009,41148],{},[895,41010,41011,41017,41019,41034,41036,41056,41058,41078,41080,41082,41088,41090,41104,41106,41126,41128],{},[1820,41012,41013,41015],{},[898,41014,1824],{},[1826,41016,1828],{},[1655,41018,1657],{},[898,41020,41021],{},[41022,41023,41024,41032],"munder",{},[1655,41025,41026],{},[1820,41027,41028,41030],{},[898,41029,207],{},[1826,41031,1828],{},[1655,41033,2346],{"lspace":1944,"rspace":1944},[1655,41035,2346],{},[898,41037,41038],{},[41022,41039,41040,41054],{},[1655,41041,41042,41048],{},[1820,41043,41044,41046],{},[898,41045,2025],{},[1826,41047,1828],{},[1820,41049,41050,41052],{},[898,41051,2132],{},[1826,41053,1828],{},[1655,41055,2623],{"lspace":1944,"rspace":1944},[1655,41057,2346],{},[898,41059,41060],{},[41022,41061,41062,41076],{},[1655,41063,41064,41070],{},[1820,41065,41066,41068],{},[898,41067,1789],{},[1826,41069,1828],{},[1820,41071,41072,41074],{},[898,41073,2132],{},[1826,41075,1837],{},[1655,41077,2346],{"lspace":1944,"rspace":1944},[1655,41079,1671],{"separator":1670},[1967,41081],{"width":1969},[1820,41083,41084,41086],{},[898,41085,1824],{},[1826,41087,1837],{},[1655,41089,1657],{},[898,41091,41092],{},[41022,41093,41094,41102],{},[1655,41095,41096],{},[1820,41097,41098,41100],{},[898,41099,207],{},[1826,41101,1837],{},[1655,41103,2346],{"lspace":1944,"rspace":1944},[1655,41105,2346],{},[898,41107,41108],{},[41022,41109,41110,41124],{},[1655,41111,41112,41118],{},[1820,41113,41114,41116],{},[898,41115,2025],{},[1826,41117,1837],{},[1820,41119,41120,41122],{},[898,41121,2132],{},[1826,41123,1828],{},[1655,41125,2346],{"lspace":1944,"rspace":1944},[1655,41127,2346],{},[898,41129,41130],{},[41022,41131,41132,41146],{},[1655,41133,41134,41140],{},[1820,41135,41136,41138],{},[898,41137,1789],{},[1826,41139,1837],{},[1820,41141,41142,41144],{},[898,41143,2132],{},[1826,41145,1837],{},[1655,41147,2623],{"lspace":1944,"rspace":1944},[902,41149,41150],{"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}",[724,41152,41153,41156],{},[38,41154,41155],{},"Komplementy",[883,41157,41159],{"className":41158},[886],[888,41160,41161],{"xmlns":890},[892,41162,41163,41301],{},[895,41164,41165,41171,41173,41187,41189,41209,41211,41231,41233,41235,41241,41243,41257,41259,41279,41281],{},[1820,41166,41167,41169],{},[898,41168,1824],{},[1826,41170,1828],{},[1655,41172,1657],{},[898,41174,41175],{},[41022,41176,41177,41185],{},[1655,41178,41179],{},[1820,41180,41181,41183],{},[898,41182,207],{},[1826,41184,1828],{},[1655,41186,2346],{"lspace":1944,"rspace":1944},[1655,41188,2346],{},[898,41190,41191],{},[41022,41192,41193,41207],{},[1655,41194,41195,41201],{},[1820,41196,41197,41199],{},[898,41198,2025],{},[1826,41200,1828],{},[1820,41202,41203,41205],{},[898,41204,2132],{},[1826,41206,1828],{},[1655,41208,2623],{"lspace":1944,"rspace":1944},[1655,41210,2346],{},[898,41212,41213],{},[41022,41214,41215,41229],{},[1655,41216,41217,41223],{},[1820,41218,41219,41221],{},[898,41220,1789],{},[1826,41222,1828],{},[1820,41224,41225,41227],{},[898,41226,2132],{},[1826,41228,1837],{},[1655,41230,2623],{"lspace":1944,"rspace":1944},[1655,41232,1671],{"separator":1670},[1967,41234],{"width":1969},[1820,41236,41237,41239],{},[898,41238,1824],{},[1826,41240,1837],{},[1655,41242,1657],{},[898,41244,41245],{},[41022,41246,41247,41255],{},[1655,41248,41249],{},[1820,41250,41251,41253],{},[898,41252,207],{},[1826,41254,1837],{},[1655,41256,2346],{"lspace":1944,"rspace":1944},[1655,41258,2346],{},[898,41260,41261],{},[41022,41262,41263,41277],{},[1655,41264,41265,41271],{},[1820,41266,41267,41269],{},[898,41268,2025],{},[1826,41270,1837],{},[1820,41272,41273,41275],{},[898,41274,2132],{},[1826,41276,1828],{},[1655,41278,2623],{"lspace":1944,"rspace":1944},[1655,41280,2346],{},[898,41282,41283],{},[41022,41284,41285,41299],{},[1655,41286,41287,41293],{},[1820,41288,41289,41291],{},[898,41290,1789],{},[1826,41292,1837],{},[1820,41294,41295,41297],{},[898,41296,2132],{},[1826,41298,1837],{},[1655,41300,2623],{"lspace":1944,"rspace":1944},[902,41302,41303],{"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}",[38096,41305],{},[115,41307,14250],{"id":37905},[5120,41309,41310],{},[724,41311,41312,41314,41315,38120,41328,38134,41341,41344,41345,6918,41369,41387],{},[883,41313,5406],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,41316,41318],{"className":41317},[886],[888,41319,41320],{"xmlns":890},[892,41321,41322,41326],{},[895,41323,41324],{},[898,41325,1824],{},[902,41327,1824],{"encoding":904},[883,41329,41331],{"className":41330},[886],[888,41332,41333],{"xmlns":890},[892,41334,41335,41339],{},[895,41336,41337],{},[898,41338,2132],{},[902,41340,2132],{"encoding":904},[38,41342,41343],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,41346,41348],{"className":41347},[886],[888,41349,41350],{"xmlns":890},[892,41351,41352,41366],{},[895,41353,41354,41356,41358,41360,41362,41364],{},[898,41355,2132],{},[1655,41357,1657],{},[898,41359,1789],{},[898,41361,1824],{},[1655,41363,2346],{},[898,41365,2410],{},[902,41367,41368],{"encoding":904},"P = cQ + d",[883,41370,41372],{"className":41371},[886],[888,41373,41374],{"xmlns":890},[892,41375,41376,41384],{},[895,41377,41378,41380,41382],{},[898,41379,1789],{},[1655,41381,2969],{},[1826,41383,2552],{},[902,41385,41386],{"encoding":904},"c > 0"," je standardní aproximací.",[198,41389,38190],{"id":41390},"obecný-vícefaktorový-model-1",[724,41392,41393,2115,41396,41399,41400,41413,41414,38022,41427,38036,41440,41453,41454,41468,41469,38065,41482,41495],{},[38,41394,41395],{},"Nabízené množství",[614,41397,41398],{},"quantity supplied",") závisí na ceně ",[883,41401,41403],{"className":41402},[886],[888,41404,41405],{"xmlns":890},[892,41406,41407,41411],{},[895,41408,41409],{},[898,41410,2132],{},[902,41412,2132],{"encoding":904},", cenách výrobních faktorů (práce ",[883,41415,41417],{"className":41416},[886],[888,41418,41419],{"xmlns":890},[892,41420,41421,41425],{},[895,41422,41423],{},[898,41424,1873],{},[902,41426,1873],{"encoding":904},[883,41428,41430],{"className":41429},[886],[888,41431,41432],{"xmlns":890},[892,41433,41434,41438],{},[895,41435,41436],{},[898,41437,1878],{},[902,41439,1878],{"encoding":904},[883,41441,41443],{"className":41442},[886],[888,41444,41445],{"xmlns":890},[892,41446,41447,41451],{},[895,41448,41449],{},[898,41450,5502],{},[902,41452,5502],{"encoding":904},"), očekávání ",[883,41455,41457],{"className":41456},[886],[888,41458,41459],{"xmlns":890},[892,41460,41461,41466],{},[895,41462,41463],{},[898,41464,41465],{},"V",[902,41467,41465],{"encoding":904},", počtu výrobců ",[883,41470,41472],{"className":41471},[886],[888,41473,41474],{"xmlns":890},[892,41475,41476,41480],{},[895,41477,41478],{},[898,41479,38062],{},[902,41481,38062],{"encoding":904},[883,41483,41485],{"className":41484},[886],[888,41486,41487],{"xmlns":890},[892,41488,41489,41493],{},[895,41490,41491],{},[898,41492,38077],{},[902,41494,38077],{"encoding":904}," a dalších:",[883,41497,41499],{"className":41498},[886],[888,41500,41501],{"xmlns":890,"display":29192},[892,41502,41503,41562],{},[21880,41504,41505],{"width":29197},[21885,41506,41507,41509,41555,41557],{},[21888,41508],{"width":29202},[21888,41510,41511],{},[895,41512,41513,41515,41517,41519,41521,41523,41525,41527,41529,41531,41533,41535,41537,41539,41541,41543,41545,41547,41549,41551,41553],{},[898,41514,1824],{},[1655,41516,1657],{},[898,41518,9920],{},[1655,41520,1664],{"stretchy":1663},[898,41522,2132],{},[1655,41524,1671],{"separator":1670},[898,41526,1873],{},[1655,41528,1671],{"separator":1670},[898,41530,1878],{},[1655,41532,1671],{"separator":1670},[898,41534,5502],{},[1655,41536,1671],{"separator":1670},[898,41538,41465],{},[1655,41540,1671],{"separator":1670},[898,41542,38062],{},[1655,41544,1671],{"separator":1670},[898,41546,38077],{},[1655,41548,1671],{"separator":1670},[1655,41550,1715],{},[1655,41552,1677],{"stretchy":1663},[898,41554,1719],{"mathvariant":1943},[21888,41556],{"width":29202},[21888,41558,41559],{},[2031,41560,41561],{},"(2.7)",[902,41563,41564],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,41566,39542,41567,2115,41570,41573],{},[38,41568,41569],{},"funkce nabídky",[614,41571,41572],{},"supply function",") v širším slova smyslu.",[198,41575,41577],{"id":41576},"jednofaktorový-model","Jednofaktorový model",[724,41579,41580],{},"V nejpřirozenějším jednofaktorovém modelu",[883,41582,41584],{"className":41583},[886],[888,41585,41586],{"xmlns":890,"display":29192},[892,41587,41588,41639],{},[21880,41589,41590],{"width":29197},[21885,41591,41592,41594,41632,41634],{},[21888,41593],{"width":29202},[21888,41595,41596],{},[895,41597,41598,41600,41602,41604,41606,41608,41610,41612,41614,41616,41618,41620,41622,41624,41626,41628,41630],{},[898,41599,1824],{},[1655,41601,1657],{},[898,41603,9920],{},[1655,41605,1664],{"stretchy":1663},[898,41607,2132],{},[1655,41609,1677],{"stretchy":1663},[1655,41611,1671],{"separator":1670},[1967,41613],{"width":1969},[2031,41615,38543],{},[1967,41617],{"width":1969},[898,41619,2132],{},[1655,41621,1657],{},[898,41623,9920],{},[1655,41625,1664],{"stretchy":1663},[898,41627,1824],{},[1655,41629,1677],{"stretchy":1663},[898,41631,1719],{"mathvariant":1943},[21888,41633],{"width":29202},[21888,41635,41636],{},[2031,41637,41638],{},"(2.8)",[902,41640,41641],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,41643,41644,41645,2115,41648,5171],{},"Graf je ",[38,41646,41647],{},"křivka nabídky",[614,41649,41650],{},"supply curve",[38474,41652,41654],{"id":41653},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[5120,41656,41657],{},[724,41658,41659],{},[38,41660,38589,41661,41674,41675,38644],{},[883,41662,41664],{"className":41663},[886],[888,41665,41666],{"xmlns":890},[892,41667,41668,41672],{},[895,41669,41670],{},[898,41671,2132],{},[902,41673,2132],{"encoding":904},", pak nabízené množství ",[883,41676,41678],{"className":41677},[886],[888,41679,41680],{"xmlns":890},[892,41681,41682,41686],{},[895,41683,41684],{},[898,41685,1824],{},[902,41687,1824],{"encoding":904},[724,41689,41690,41691,41716,41717,41747,41748,41765],{},"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 ",[883,41692,41694],{"className":41693},[886],[888,41695,41696],{"xmlns":890},[892,41697,41698,41714],{},[895,41699,41700,41702,41704,41706,41712],{},[1655,41701,2734],{"stretchy":1663},[1826,41703,2552],{},[1655,41705,1671],{"separator":1670},[1820,41707,41708,41710],{},[898,41709,2132],{},[1826,41711,2552],{},[1655,41713,2743],{"stretchy":1663},[902,41715,38729],{"encoding":904}," na svislé ose (případně z ",[883,41718,41720],{"className":41719},[886],[888,41721,41722],{"xmlns":890},[892,41723,41724,41744],{},[895,41725,41726,41728,41734,41736,41742],{},[1655,41727,2734],{"stretchy":1663},[1820,41729,41730,41732],{},[898,41731,1824],{},[1826,41733,1828],{},[1655,41735,1671],{"separator":1670},[1820,41737,41738,41740],{},[898,41739,2132],{},[1826,41741,1828],{},[1655,41743,2743],{"stretchy":1663},[902,41745,41746],{"encoding":904},"[Q_1, P_1]","), kde ",[883,41749,41751],{"className":41750},[886],[888,41752,41753],{"xmlns":890},[892,41754,41755,41763],{},[895,41756,41757],{},[1820,41758,41759,41761],{},[898,41760,2132],{},[1826,41762,2552],{},[902,41764,40074],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,41767,41768],{},[614,41769,41770,41771,4979,41784,1719],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,41772,41774],{"className":41773},[886],[888,41775,41776],{"xmlns":890},[892,41777,41778,41782],{},[895,41779,41780],{},[898,41781,9920],{},[902,41783,9920],{"encoding":904},[883,41785,41787],{"className":41786},[886],[888,41788,41789],{"xmlns":890},[892,41790,41791,41803],{},[895,41792,41793,41795,41797,41799,41801],{},[1655,41794,1664],{"stretchy":1663},[898,41796,1824],{},[1655,41798,1671],{"separator":1670},[898,41800,2132],{},[1655,41802,1677],{"stretchy":1663},[902,41804,38817],{"encoding":904},[38474,41806,41808],{"id":41807},"lineární-model-nabídky","Lineární model nabídky",[883,41810,41812],{"className":41811},[886],[888,41813,41814],{"xmlns":890,"display":29192},[892,41815,41816,41855],{},[21880,41817,41818],{"width":29197},[21885,41819,41820,41822,41848,41850],{},[21888,41821],{"width":29202},[21888,41823,41824],{},[895,41825,41826,41828,41830,41832,41834,41836,41838,41840,41842,41844,41846],{},[898,41827,2132],{},[1655,41829,1657],{},[898,41831,1789],{},[898,41833,1824],{},[1655,41835,2346],{},[898,41837,2410],{},[1655,41839,1671],{"separator":1670},[1967,41841],{"width":1969},[898,41843,1789],{},[1655,41845,2969],{},[1826,41847,13585],{},[21888,41849],{"width":29202},[21888,41851,41852],{},[2031,41853,41854],{},"(2.9)",[902,41856,41857],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,41859,41860,41861,41897,41898,41911],{},"Alternativně ",[883,41862,41864],{"className":41863},[886],[888,41865,41866],{"xmlns":890},[892,41867,41868,41894],{},[895,41869,41870,41872,41874,41882,41884,41886],{},[898,41871,1824],{},[1655,41873,1657],{},[3615,41875,41876],{"scriptlevel":2552,"displaystyle":1663},[1949,41877,41878,41880],{},[1826,41879,1828],{},[898,41881,1789],{},[898,41883,2132],{},[1655,41885,2623],{},[3615,41887,41888],{"scriptlevel":2552,"displaystyle":1663},[1949,41889,41890,41892],{},[898,41891,2410],{},[898,41893,1789],{},[902,41895,41896],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,41899,41901],{"className":41900},[886],[888,41902,41903],{"xmlns":890},[892,41904,41905,41909],{},[895,41906,41907],{},[898,41908,2132],{},[902,41910,2132],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[39051,41913,41915],{"id":41914},"příklad-25","Příklad 2.5",[724,41917,41918,41920,41921,1719],{},[38,41919,39059],{}," Lineární nabídka ",[883,41922,41924],{"className":41923},[886],[888,41925,41926],{"xmlns":890},[892,41927,41928,41942],{},[895,41929,41930,41932,41934,41936,41938,41940],{},[898,41931,2132],{},[1655,41933,1657],{},[1826,41935,6258],{},[898,41937,1824],{},[1655,41939,2346],{},[1826,41941,6253],{},[902,41943,41944],{"encoding":904},"P = 0{,}5Q + 25",[724,41946,41947,41949,41950,1719],{},[38,41948,39091],{}," Alternativní tvar ",[883,41951,41953],{"className":41952},[886],[888,41954,41955],{"xmlns":890},[892,41956,41957,41971],{},[895,41958,41959,41961,41963,41965,41967,41969],{},[898,41960,1824],{},[1655,41962,1657],{},[1826,41964,1837],{},[898,41966,2132],{},[1655,41968,2623],{},[1826,41970,4390],{},[902,41972,41973],{"encoding":904},"Q = 2P - 50",[16,41975,41976,42001],{},[19,41977,41978],{},[22,41979,41980,41995,41997,41999],{},[25,41981,41982],{},[883,41983,41985],{"className":41984},[886],[888,41986,41987],{"xmlns":890},[892,41988,41989,41993],{},[895,41990,41991],{},[898,41992,2132],{},[902,41994,2132],{"encoding":904},[25,41996,39145],{},[25,41998,16163],{},[25,42000,6460],{},[30,42002,42003],{},[22,42004,42005,42020,42022,42024],{},[35,42006,42007],{},[883,42008,42010],{"className":42009},[886],[888,42011,42012],{"xmlns":890},[892,42013,42014,42018],{},[895,42015,42016],{},[898,42017,1824],{},[902,42019,1824],{"encoding":904},[35,42021,4136],{},[35,42023,10282],{},[35,42025,39145],{},[198,42027,42029,42030,1677],{"id":42028},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,42031,42032],{},"shift of supply",[724,42034,42035,42036,42039,42040,42057,42058,42083,42084,1719],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,42037,42038],{},"doprava",": při stejné ceně ",[883,42041,42043],{"className":42042},[886],[888,42044,42045],{"xmlns":890},[892,42046,42047,42055],{},[895,42048,42049],{},[1820,42050,42051,42053],{},[898,42052,2132],{},[1826,42054,2552],{},[902,42056,40074],{"encoding":904}," vyrobí výrobce větší ",[883,42059,42061],{"className":42060},[886],[888,42062,42063],{"xmlns":890},[892,42064,42065,42081],{},[895,42066,42067,42073,42075],{},[1820,42068,42069,42071],{},[898,42070,1824],{},[1826,42072,1828],{},[1655,42074,2969],{},[1820,42076,42077,42079],{},[898,42078,1824],{},[1826,42080,2552],{},[902,42082,40187],{"encoding":904},"); zdražení vstupů posune křivku ",[38,42085,42086],{},"doleva",[724,42088,42089],{},[614,42090,42091,42092,42105,42106,42124,42125,42143,42144,1719],{},"Obrázek 2.11: Původní ",[883,42093,42095],{"className":42094},[886],[888,42096,42097],{"xmlns":890},[892,42098,42099,42103],{},[895,42100,42101],{},[898,42102,9920],{},[902,42104,9920],{"encoding":904},", posunuté ",[883,42107,42109],{"className":42108},[886],[888,42110,42111],{"xmlns":890},[892,42112,42113,42121],{},[895,42114,42115],{},[1820,42116,42117,42119],{},[898,42118,9920],{},[1826,42120,1828],{},[902,42122,42123],{"encoding":904},"S_1"," (doprava) a ",[883,42126,42128],{"className":42127},[886],[888,42129,42130],{"xmlns":890},[892,42131,42132,42140],{},[895,42133,42134],{},[1820,42135,42136,42138],{},[898,42137,9920],{},[1826,42139,1837],{},[902,42141,42142],{"encoding":904},"S_2"," (doleva) v ",[883,42145,42147],{"className":42146},[886],[888,42148,42149],{"xmlns":890},[892,42150,42151,42163],{},[895,42152,42153,42155,42157,42159,42161],{},[1655,42154,1664],{"stretchy":1663},[898,42156,1824],{},[1655,42158,1671],{"separator":1670},[898,42160,2132],{},[1655,42162,1677],{"stretchy":1663},[902,42164,38817],{"encoding":904},[39051,42166,42168],{"id":42167},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,42170,42171,42173,42174,42198,42199,1719],{},[38,42172,39059],{}," Nabídka ",[883,42175,42177],{"className":42176},[886],[888,42178,42179],{"xmlns":890},[892,42180,42181,42195],{},[895,42182,42183,42185,42187,42189,42191,42193],{},[898,42184,2132],{},[1655,42186,1657],{},[898,42188,9920],{},[1655,42190,1664],{"stretchy":1663},[898,42192,1824],{},[1655,42194,1677],{"stretchy":1663},[902,42196,42197],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,42200,42202],{"className":42201},[886],[888,42203,42204],{"xmlns":890},[892,42205,42206,42210],{},[895,42207,42208],{},[898,42209,4049],{},[902,42211,4049],{"encoding":904},[724,42213,42214,42216,42217,42230,42231,42249,42250,42278],{},[38,42215,39091],{}," Spotřebitel zaplatí ",[883,42218,42220],{"className":42219},[886],[888,42221,42222],{"xmlns":890},[892,42223,42224,42228],{},[895,42225,42226],{},[898,42227,2132],{},[902,42229,2132],{"encoding":904},", výrobce obdrží ",[883,42232,42234],{"className":42233},[886],[888,42235,42236],{"xmlns":890},[892,42237,42238,42246],{},[895,42239,42240,42242,42244],{},[898,42241,2132],{},[1655,42243,2623],{},[898,42245,4049],{},[902,42247,42248],{"encoding":904},"P - T",". Z podmínky ",[883,42251,42253],{"className":42252},[886],[888,42254,42255],{"xmlns":890},[892,42256,42257,42275],{},[895,42258,42259,42261,42263,42265,42267,42269,42271,42273],{},[898,42260,2132],{},[1655,42262,2623],{},[898,42264,4049],{},[1655,42266,1657],{},[898,42268,9920],{},[1655,42270,1664],{"stretchy":1663},[898,42272,1824],{},[1655,42274,1677],{"stretchy":1663},[902,42276,42277],{"encoding":904},"P - T = S(Q)"," plyne",[883,42280,42282],{"className":42281},[886],[888,42283,42284],{"xmlns":890,"display":29192},[892,42285,42286,42320],{},[895,42287,42288,42290,42292,42298,42300,42302,42304,42306,42308,42310,42312,42314,42316,42318],{},[898,42289,2132],{},[1655,42291,1657],{},[1820,42293,42294,42296],{},[898,42295,9920],{},[1826,42297,1828],{},[1655,42299,1664],{"stretchy":1663},[898,42301,1824],{},[1655,42303,1677],{"stretchy":1663},[1655,42305,1657],{},[898,42307,9920],{},[1655,42309,1664],{"stretchy":1663},[898,42311,1824],{},[1655,42313,1677],{"stretchy":1663},[1655,42315,2346],{},[898,42317,4049],{},[898,42319,1719],{"mathvariant":1943},[902,42321,42322],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,42324,42325,42326,42339,42340,3106,42353,42356,42357,2704,42377,9349,42395,1719],{},"Křivka ",[883,42327,42329],{"className":42328},[886],[888,42330,42331],{"xmlns":890},[892,42332,42333,42337],{},[895,42334,42335],{},[898,42336,9920],{},[902,42338,9920],{"encoding":904}," se tedy posune o ",[883,42341,42343],{"className":42342},[886],[888,42344,42345],{"xmlns":890},[892,42346,42347,42351],{},[895,42348,42349],{},[898,42350,4049],{},[902,42352,4049],{"encoding":904},[38,42354,42355],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,42358,42360],{"className":42359},[886],[888,42361,42362],{"xmlns":890},[892,42363,42364,42374],{},[895,42365,42366,42368,42370,42372],{},[898,42367,2132],{},[1655,42369,1657],{},[1826,42371,1837],{},[898,42373,1824],{},[902,42375,42376],{"encoding":904},"P = 2Q",[883,42378,42380],{"className":42379},[886],[888,42381,42382],{"xmlns":890},[892,42383,42384,42392],{},[895,42385,42386,42388,42390],{},[898,42387,4049],{},[1655,42389,1657],{},[1826,42391,3531],{},[902,42393,42394],{"encoding":904},"T = 6",[883,42396,42398],{"className":42397},[886],[888,42399,42400],{"xmlns":890},[892,42401,42402,42424],{},[895,42403,42404,42410,42412,42414,42416,42418,42420,42422],{},[1820,42405,42406,42408],{},[898,42407,9920],{},[1826,42409,1828],{},[1655,42411,2086],{},[898,42413,2132],{},[1655,42415,1657],{},[1826,42417,1837],{},[898,42419,1824],{},[1655,42421,2346],{},[1826,42423,3531],{},[902,42425,42426],{"encoding":904},"S_1: P = 2Q + 6",[724,42428,42429],{},[614,42430,42431,42432,42445],{},"Obrázek 2.12: Posun nabídky o ",[883,42433,42435],{"className":42434},[886],[888,42436,42437],{"xmlns":890},[892,42438,42439,42443],{},[895,42440,42441],{},[898,42442,4049],{},[902,42444,4049],{"encoding":904}," svisle nahoru.",[38096,42447],{},[115,42449,42451],{"id":42450},"tržní-rovnováha","Tržní rovnováha",[5120,42453,42454],{},[724,42455,42456,42458,42459,3106,42462,42494,42495,1343,42518,42541,42542,42545,42546,42559],{},[883,42457,5406],{}," TL;DR\nV ",[38,42460,42461],{},"rovnovážném bodě",[883,42463,42465],{"className":42464},[886],[888,42466,42467],{"xmlns":890},[892,42468,42469,42491],{},[895,42470,42471,42473,42475,42481,42483,42489],{},[898,42472,5502],{},[1655,42474,2734],{"stretchy":1663},[2597,42476,42477,42479],{},[898,42478,1824],{},[898,42480,5502],{},[1655,42482,1671],{"separator":1670},[2597,42484,42485,42487],{},[898,42486,2132],{},[898,42488,5502],{},[1655,42490,2743],{"stretchy":1663},[902,42492,42493],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,42496,42498],{"className":42497},[886],[888,42499,42500],{"xmlns":890},[892,42501,42502,42516],{},[895,42503,42504,42506,42508,42510,42512,42514],{},[898,42505,2132],{},[1655,42507,1657],{},[898,42509,2838],{},[1655,42511,1664],{"stretchy":1663},[898,42513,1824],{},[1655,42515,1677],{"stretchy":1663},[902,42517,5889],{"encoding":904},[883,42519,42521],{"className":42520},[886],[888,42522,42523],{"xmlns":890},[892,42524,42525,42539],{},[895,42526,42527,42529,42531,42533,42535,42537],{},[898,42528,2132],{},[1655,42530,1657],{},[898,42532,9920],{},[1655,42534,1664],{"stretchy":1663},[898,42536,1824],{},[1655,42538,1677],{"stretchy":1663},[902,42540,42197],{"encoding":904},". Čtyři ",[38,42543,42544],{},"pravidla komparativní statiky"," popisují, jak se ",[883,42547,42549],{"className":42548},[886],[888,42550,42551],{"xmlns":890},[892,42552,42553,42557],{},[895,42554,42555],{},[898,42556,5502],{},[902,42558,5502],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,42561,42563],{"id":42562},"definice","Definice",[724,42565,42566,2115,42568,42571,42572,3106,42575,42593,42594,42625,42626,2115,42629,5171],{},[38,42567,42451],{},[614,42569,42570],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,42573,42574],{},"rovnovážné ceně",[883,42576,42578],{"className":42577},[886],[888,42579,42580],{"xmlns":890},[892,42581,42582,42590],{},[895,42583,42584],{},[2597,42585,42586,42588],{},[898,42587,2132],{},[898,42589,5502],{},[902,42591,42592],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,42595,42597],{"className":42596},[886],[888,42598,42599],{"xmlns":890},[892,42600,42601,42623],{},[895,42602,42603,42605,42607,42613,42615,42621],{},[898,42604,5502],{},[1655,42606,2734],{"stretchy":1663},[2597,42608,42609,42611],{},[898,42610,1824],{},[898,42612,5502],{},[1655,42614,1671],{"separator":1670},[2597,42616,42617,42619],{},[898,42618,2132],{},[898,42620,5502],{},[1655,42622,2743],{"stretchy":1663},[902,42624,42493],{"encoding":904}," se nazývá ",[38,42627,42628],{},"rovnovážný bod",[614,42630,42631],{},"equilibrium point",[724,42633,42634,42635,1343,42658,1719],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,42636,42638],{"className":42637},[886],[888,42639,42640],{"xmlns":890},[892,42641,42642,42656],{},[895,42643,42644,42646,42648,42650,42652,42654],{},[898,42645,2132],{},[1655,42647,1657],{},[898,42649,2838],{},[1655,42651,1664],{"stretchy":1663},[898,42653,1824],{},[1655,42655,1677],{"stretchy":1663},[902,42657,5889],{"encoding":904},[883,42659,42661],{"className":42660},[886],[888,42662,42663],{"xmlns":890},[892,42664,42665,42679],{},[895,42666,42667,42669,42671,42673,42675,42677],{},[898,42668,2132],{},[1655,42670,1657],{},[898,42672,9920],{},[1655,42674,1664],{"stretchy":1663},[898,42676,1824],{},[1655,42678,1677],{"stretchy":1663},[902,42680,42197],{"encoding":904},[724,42682,42683],{},[1723,42684],{"alt":42685,"className":42686,"src":42687},"imek-poptavka-nabidka-rovnovaha",[210,1727],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,42689,42690],{},[614,42691,42692,42693,42706,42707,15136,42720,42741,42742,1719],{},"Obrázek 2.13: Klesající ",[883,42694,42696],{"className":42695},[886],[888,42697,42698],{"xmlns":890},[892,42699,42700,42704],{},[895,42701,42702],{},[898,42703,2838],{},[902,42705,2838],{"encoding":904}," a rostoucí ",[883,42708,42710],{"className":42709},[886],[888,42711,42712],{"xmlns":890},[892,42713,42714,42718],{},[895,42715,42716],{},[898,42717,9920],{},[902,42719,9920],{"encoding":904},[883,42721,42723],{"className":42722},[886],[888,42724,42725],{"xmlns":890},[892,42726,42727,42739],{},[895,42728,42729,42731,42733,42735,42737],{},[1655,42730,1664],{"stretchy":1663},[898,42732,1824],{},[1655,42734,1671],{"separator":1670},[898,42736,2132],{},[1655,42738,1677],{"stretchy":1663},[902,42740,38817],{"encoding":904}," protínající se v ",[883,42743,42745],{"className":42744},[886],[888,42746,42747],{"xmlns":890},[892,42748,42749,42771],{},[895,42750,42751,42753,42755,42761,42763,42769],{},[898,42752,5502],{},[1655,42754,2734],{"stretchy":1663},[2597,42756,42757,42759],{},[898,42758,1824],{},[898,42760,5502],{},[1655,42762,1671],{"separator":1670},[2597,42764,42765,42767],{},[898,42766,2132],{},[898,42768,5502],{},[1655,42770,2743],{"stretchy":1663},[902,42772,42493],{"encoding":904},[198,42774,42776],{"id":42775},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,42778,42779,42781,42782,42816,42817,1719],{},[38,42780,39059],{}," Poptávka ",[883,42783,42785],{"className":42784},[886],[888,42786,42787],{"xmlns":890},[892,42788,42789,42813],{},[895,42790,42791,42793,42795,42797,42803,42805,42807,42809,42811],{},[898,42792,2132],{},[1655,42794,1657],{},[1655,42796,2623],{},[2597,42798,42799,42801],{},[898,42800,1824],{},[1826,42802,1837],{},[1655,42804,2623],{},[1826,42806,4136],{},[898,42808,1824],{},[1655,42810,2346],{},[1826,42812,10050],{},[902,42814,42815],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,42818,42820],{"className":42819},[886],[888,42821,42822],{"xmlns":890},[892,42823,42824,42846],{},[895,42825,42826,42828,42830,42836,42838,42840,42842,42844],{},[898,42827,2132],{},[1655,42829,1657],{},[2597,42831,42832,42834],{},[898,42833,1824],{},[1826,42835,1837],{},[1655,42837,2346],{},[1826,42839,24072],{},[898,42841,1824],{},[1655,42843,2346],{},[1826,42845,33672],{},[902,42847,42848],{"encoding":904},"P = Q^2 + 14Q + 22",[724,42850,42851,42853],{},[38,42852,39091],{}," Z rovnosti",[883,42855,42857],{"className":42856},[886],[888,42858,42859],{"xmlns":890,"display":29192},[892,42860,42861,42899],{},[895,42862,42863,42865,42871,42873,42875,42877,42879,42881,42883,42889,42891,42893,42895,42897],{},[1655,42864,2623],{},[2597,42866,42867,42869],{},[898,42868,1824],{},[1826,42870,1837],{},[1655,42872,2623],{},[1826,42874,4136],{},[898,42876,1824],{},[1655,42878,2346],{},[1826,42880,10050],{},[1655,42882,1657],{},[2597,42884,42885,42887],{},[898,42886,1824],{},[1826,42888,1837],{},[1655,42890,2346],{},[1826,42892,24072],{},[898,42894,1824],{},[1655,42896,2346],{},[1826,42898,33672],{},[902,42900,42901],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,42903,42904,42905,42940,42941,42974,42975,42992,42993,43006,43007,1343,43029,43066,43067,1719],{},"dostaneme ",[883,42906,42908],{"className":42907},[886],[888,42909,42910],{"xmlns":890},[892,42911,42912,42937],{},[895,42913,42914,42916,42922,42924,42927,42929,42931,42933,42935],{},[1826,42915,1837],{},[2597,42917,42918,42920],{},[898,42919,1824],{},[1826,42921,1837],{},[1655,42923,2346],{},[1826,42925,42926],{},"24",[898,42928,1824],{},[1655,42930,2623],{},[1826,42932,6866],{},[1655,42934,1657],{},[1826,42936,2552],{},[902,42938,42939],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,42942,42944],{"className":42943},[886],[888,42945,42946],{"xmlns":890},[892,42947,42948,42971],{},[895,42949,42950,42956,42958,42960,42962,42964,42967,42969],{},[2597,42951,42952,42954],{},[898,42953,1824],{},[1826,42955,1837],{},[1655,42957,2346],{},[1826,42959,4771],{},[898,42961,1824],{},[1655,42963,2623],{},[1826,42965,42966],{},"64",[1655,42968,1657],{},[1826,42970,2552],{},[902,42972,42973],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,42976,42978],{"className":42977},[886],[888,42979,42980],{"xmlns":890},[892,42981,42982,42989],{},[895,42983,42984,42986],{},[1655,42985,2623],{},[1826,42987,42988],{},"16",[902,42990,42991],{"encoding":904},"-16"," (nevyhovuje) a ",[883,42994,42996],{"className":42995},[886],[888,42997,42998],{"xmlns":890},[892,42999,43000,43004],{},[895,43001,43002],{},[1826,43003,3639],{},[902,43005,3639],{"encoding":904},". Tedy ",[883,43008,43010],{"className":43009},[886],[888,43011,43012],{"xmlns":890},[892,43013,43014,43026],{},[895,43015,43016,43022,43024],{},[2597,43017,43018,43020],{},[898,43019,1824],{},[898,43021,5502],{},[1655,43023,1657],{},[1826,43025,3639],{},[902,43027,43028],{"encoding":904},"Q^E = 4",[883,43030,43032],{"className":43031},[886],[888,43033,43034],{"xmlns":890},[892,43035,43036,43063],{},[895,43037,43038,43044,43046,43048,43050,43052,43054,43056,43058,43060],{},[2597,43039,43040,43042],{},[898,43041,2132],{},[898,43043,5502],{},[1655,43045,1657],{},[1655,43047,2623],{},[1826,43049,42988],{},[1655,43051,2623],{},[1826,43053,6460],{},[1655,43055,2346],{},[1826,43057,10050],{},[1655,43059,1657],{},[1826,43061,43062],{},"94",[902,43064,43065],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,43068,43070],{"className":43069},[886],[888,43071,43072],{"xmlns":890},[892,43073,43074,43088],{},[895,43075,43076,43078,43080,43082,43084,43086],{},[898,43077,5502],{},[1655,43079,2734],{"stretchy":1663},[1826,43081,3639],{},[1655,43083,1671],{"separator":1670},[1826,43085,43062],{},[1655,43087,2743],{"stretchy":1663},[902,43089,43090],{"encoding":904},"E[4, 94]",[198,43092,43094],{"id":43093},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,43096,43097,43099],{},[38,43098,39059],{}," Poptávky a nabídky dvou zboží",[883,43101,43103],{"className":43102},[886],[888,43104,43105],{"xmlns":890,"display":29192},[892,43106,43107,43273],{},[21880,43108,43111,43199],{"rowspacing":21882,"columnalign":43109,"columnspacing":43110},"right left right left","0em 1em 0em",[21885,43112,43113,43123,43155,43165],{},[21888,43114,43115],{},[3615,43116,43117],{"scriptlevel":2552,"displaystyle":1670},[1820,43118,43119,43121],{},[898,43120,1824],{},[1826,43122,1828],{},[21888,43124,43125],{},[3615,43126,43127],{"scriptlevel":2552,"displaystyle":1670},[895,43128,43129,43131,43133,43135,43137,43139,43145,43147,43153],{},[895,43130],{},[1655,43132,1657],{},[1826,43134,6460],{},[1655,43136,2623],{},[1826,43138,3524],{},[1820,43140,43141,43143],{},[898,43142,2132],{},[1826,43144,1828],{},[1655,43146,2623],{},[1820,43148,43149,43151],{},[898,43150,2132],{},[1826,43152,1837],{},[1655,43154,1671],{"separator":1670},[21888,43156,43157],{},[3615,43158,43159],{"scriptlevel":2552,"displaystyle":1670},[1820,43160,43161,43163],{},[898,43162,1824],{},[1826,43164,1837],{},[21888,43166,43167],{},[3615,43168,43169],{"scriptlevel":2552,"displaystyle":1670},[895,43170,43171,43173,43175,43177,43179,43181,43187,43189,43191,43197],{},[895,43172],{},[1655,43174,1657],{},[1826,43176,4390],{},[1655,43178,2623],{},[1826,43180,1837],{},[1820,43182,43183,43185],{},[898,43184,2132],{},[1826,43186,1828],{},[1655,43188,2623],{},[1826,43190,3639],{},[1820,43192,43193,43195],{},[898,43194,2132],{},[1826,43196,1837],{},[1655,43198,1671],{"separator":1670},[21885,43200,43201,43211,43237,43247],{},[21888,43202,43203],{},[3615,43204,43205],{"scriptlevel":2552,"displaystyle":1670},[1820,43206,43207,43209],{},[898,43208,1824],{},[1826,43210,1828],{},[21888,43212,43213],{},[3615,43214,43215],{"scriptlevel":2552,"displaystyle":1670},[895,43216,43217,43219,43221,43223,43225,43227,43229,43235],{},[895,43218],{},[1655,43220,1657],{},[1655,43222,2623],{},[1826,43224,3472],{},[1655,43226,2346],{},[1826,43228,3639],{},[1820,43230,43231,43233],{},[898,43232,2132],{},[1826,43234,1828],{},[1655,43236,1671],{"separator":1670},[21888,43238,43239],{},[3615,43240,43241],{"scriptlevel":2552,"displaystyle":1670},[1820,43242,43243,43245],{},[898,43244,1824],{},[1826,43246,1837],{},[21888,43248,43249],{},[3615,43250,43251],{"scriptlevel":2552,"displaystyle":1670},[895,43252,43253,43255,43257,43259,43261,43263,43265,43271],{},[895,43254],{},[1655,43256,1657],{},[1655,43258,2623],{},[1826,43260,25327],{},[1655,43262,2346],{},[1826,43264,3472],{},[1820,43266,43267,43269],{},[898,43268,2132],{},[1826,43270,1837],{},[898,43272,1719],{"mathvariant":1943},[902,43274,43275],{"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}",[724,43277,43278,43280],{},[38,43279,39091],{}," Z rovností poptávek a nabídek dostaneme",[883,43282,43284],{"className":43283},[886],[888,43285,43286],{"xmlns":890,"display":29192},[892,43287,43288,43337],{},[895,43289,43290,43292,43298,43300,43306,43308,43310,43312,43314,43316,43322,43324,43326,43332,43334],{},[1826,43291,5250],{},[1820,43293,43294,43296],{},[898,43295,2132],{},[1826,43297,1828],{},[1655,43299,2346],{},[1820,43301,43302,43304],{},[898,43303,2132],{},[1826,43305,1837],{},[1655,43307,1657],{},[1826,43309,22329],{},[1655,43311,1671],{"separator":1670},[1967,43313],{"width":1969},[1826,43315,1837],{},[1820,43317,43318,43320],{},[898,43319,2132],{},[1826,43321,1828],{},[1655,43323,2346],{},[1826,43325,25327],{},[1820,43327,43328,43330],{},[898,43329,2132],{},[1826,43331,1837],{},[1655,43333,1657],{},[1826,43335,43336],{},"57.",[902,43338,43339],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,43341,43342,43343,1343,43367,43391,43392,1343,43417,43441,43442,43444],{},"Řešením je ",[883,43344,43346],{"className":43345},[886],[888,43347,43348],{"xmlns":890},[892,43349,43350,43364],{},[895,43351,43352,43360,43362],{},[1935,43353,43354,43356,43358],{},[898,43355,2132],{},[1826,43357,1828],{},[898,43359,5502],{},[1655,43361,1657],{},[1826,43363,3639],{},[902,43365,43366],{"encoding":904},"P_1^E = 4",[883,43368,43370],{"className":43369},[886],[888,43371,43372],{"xmlns":890},[892,43373,43374,43388],{},[895,43375,43376,43384,43386],{},[1935,43377,43378,43380,43382],{},[898,43379,2132],{},[1826,43381,1837],{},[898,43383,5502],{},[1655,43385,1657],{},[1826,43387,25327],{},[902,43389,43390],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,43393,43395],{"className":43394},[886],[888,43396,43397],{"xmlns":890},[892,43398,43399,43414],{},[895,43400,43401,43409,43411],{},[1935,43402,43403,43405,43407],{},[898,43404,1824],{},[1826,43406,1828],{},[898,43408,5502],{},[1655,43410,1657],{},[1826,43412,43413],{},"13",[902,43415,43416],{"encoding":904},"Q_1^E = 13",[883,43418,43420],{"className":43419},[886],[888,43421,43422],{"xmlns":890},[892,43423,43424,43438],{},[895,43425,43426,43434,43436],{},[1935,43427,43428,43430,43432],{},[898,43429,1824],{},[1826,43431,1837],{},[898,43433,5502],{},[1655,43435,1657],{},[1826,43437,24072],{},[902,43439,43440],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,43443,40948],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,43446,43448],{"id":43447},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,43450,43451,43452,43469,43470,2115,43473,5171],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,43453,43455],{"className":43454},[886],[888,43456,43457],{"xmlns":890},[892,43458,43459,43467],{},[895,43460,43461],{},[2597,43462,43463,43465],{},[898,43464,2132],{},[898,43466,5502],{},[902,43468,42592],{"encoding":904},"; mechanismus popisuje ",[38,43471,43472],{},"teorém pavučiny",[614,43474,43475],{},"cobweb model",[198,43477,43479],{"id":43478},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,43481,43482],{},[1723,43483],{"alt":43484,"className":43485,"src":43486},"imek-komparativni-statika-4pripady",[210,1727],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[5120,43488,43489,43530,43570,43610],{},[724,43490,43491,43494,43495,7437,43512,1719],{},[38,43492,43493],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,43496,43498],{"className":43497},[886],[888,43499,43500],{"xmlns":890},[892,43501,43502,43510],{},[895,43503,43504],{},[2597,43505,43506,43508],{},[898,43507,2132],{},[898,43509,5502],{},[902,43511,42592],{"encoding":904},[883,43513,43515],{"className":43514},[886],[888,43516,43517],{"xmlns":890},[892,43518,43519,43527],{},[895,43520,43521],{},[2597,43522,43523,43525],{},[898,43524,1824],{},[898,43526,5502],{},[902,43528,43529],{"encoding":904},"Q^E",[724,43531,43532,43535,43536,7437,43553,1719],{},[38,43533,43534],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,43537,43539],{"className":43538},[886],[888,43540,43541],{"xmlns":890},[892,43542,43543,43551],{},[895,43544,43545],{},[2597,43546,43547,43549],{},[898,43548,2132],{},[898,43550,5502],{},[902,43552,42592],{"encoding":904},[883,43554,43556],{"className":43555},[886],[888,43557,43558],{"xmlns":890},[892,43559,43560,43568],{},[895,43561,43562],{},[2597,43563,43564,43566],{},[898,43565,1824],{},[898,43567,5502],{},[902,43569,43529],{"encoding":904},[724,43571,43572,43575,43576,10601,43593,1719],{},[38,43573,43574],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,43577,43579],{"className":43578},[886],[888,43580,43581],{"xmlns":890},[892,43582,43583,43591],{},[895,43584,43585],{},[2597,43586,43587,43589],{},[898,43588,2132],{},[898,43590,5502],{},[902,43592,42592],{"encoding":904},[883,43594,43596],{"className":43595},[886],[888,43597,43598],{"xmlns":890},[892,43599,43600,43608],{},[895,43601,43602],{},[2597,43603,43604,43606],{},[898,43605,1824],{},[898,43607,5502],{},[902,43609,43529],{"encoding":904},[724,43611,43612,43615,43616,43633,43634,1719],{},[38,43613,43614],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,43617,43619],{"className":43618},[886],[888,43620,43621],{"xmlns":890},[892,43622,43623,43631],{},[895,43624,43625],{},[2597,43626,43627,43629],{},[898,43628,2132],{},[898,43630,5502],{},[902,43632,42592],{"encoding":904},", pokles ",[883,43635,43637],{"className":43636},[886],[888,43638,43639],{"xmlns":890},[892,43640,43641,43649],{},[895,43642,43643],{},[2597,43644,43645,43647],{},[898,43646,1824],{},[898,43648,5502],{},[902,43650,43529],{"encoding":904},[16,43652,43653,43698],{},[19,43654,43655],{},[22,43656,43657,43660,43679],{},[25,43658,43659],{},"Změna",[25,43661,43662],{},[883,43663,43665],{"className":43664},[886],[888,43666,43667],{"xmlns":890},[892,43668,43669,43677],{},[895,43670,43671],{},[2597,43672,43673,43675],{},[898,43674,2132],{},[898,43676,5502],{},[902,43678,42592],{"encoding":904},[25,43680,43681],{},[883,43682,43684],{"className":43683},[886],[888,43685,43686],{"xmlns":890},[892,43687,43688,43696],{},[895,43689,43690],{},[2597,43691,43692,43694],{},[898,43693,1824],{},[898,43695,5502],{},[902,43697,43529],{"encoding":904},[30,43699,43700,43710,43720,43729],{},[22,43701,43702,43705,43708],{},[35,43703,43704],{},"Růst poptávky",[35,43706,43707],{},"↑",[35,43709,43707],{},[22,43711,43712,43715,43718],{},[35,43713,43714],{},"Pokles poptávky",[35,43716,43717],{},"↓",[35,43719,43717],{},[22,43721,43722,43725,43727],{},[35,43723,43724],{},"Růst nabídky",[35,43726,43717],{},[35,43728,43707],{},[22,43730,43731,43734,43736],{},[35,43732,43733],{},"Pokles nabídky",[35,43735,43707],{},[35,43737,43717],{},[724,43739,43740],{},[614,43741,43742],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[38096,43744],{},[115,43746,811],{"id":43747},"zdanění-trhu",[5120,43749,43750,43839],{},[724,43751,43752,43754,43755,43768,43769,4199,43782,43785,43786,37902,43809,43834,43835,43838],{},[883,43753,5406],{}," TL;DR\nJednotková daň ",[883,43756,43758],{"className":43757},[886],[888,43759,43760],{"xmlns":890},[892,43761,43762,43766],{},[895,43763,43764],{},[898,43765,4049],{},[902,43767,4049],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,43770,43772],{"className":43771},[886],[888,43773,43774],{"xmlns":890},[892,43775,43776,43780],{},[895,43777,43778],{},[898,43779,4049],{},[902,43781,4049],{"encoding":904},[38,43783,43784],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,43787,43789],{"className":43788},[886],[888,43790,43791],{"xmlns":890},[892,43792,43793,43806],{},[895,43794,43795],{},[1820,43796,43797,43799],{},[898,43798,4049],{},[895,43800,43801,43804],{},[898,43802,43803],{},"s",[898,43805,724],{},[902,43807,43808],{"encoding":904},"T_{sp}",[883,43810,43812],{"className":43811},[886],[888,43813,43814],{"xmlns":890},[892,43815,43816,43831],{},[895,43817,43818],{},[1820,43819,43820,43822],{},[898,43821,4049],{},[895,43823,43824,43827,43829],{},[898,43825,43826],{},"v",[898,43828,1674],{},[898,43830,13166],{},[902,43832,43833],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,43836,43837],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,43840,43841],{},[614,43842,43843,43844,1719],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,43845,43847],{"className":43846,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,43849,43850,43851,43854,43855,43881,43882,43885,43886,43912,43913,43930,43931,43971,43972,2704,43985,1719],{},"Existují dvě formy zdanění — daň uložená ",[38,43852,43853],{},"výrobci"," (posun nabídky ",[883,43856,43858],{"className":43857},[886],[888,43859,43860],{"xmlns":890},[892,43861,43862,43878],{},[895,43863,43864,43870,43872,43874,43876],{},[1820,43865,43866,43868],{},[898,43867,9920],{},[1826,43869,1828],{},[1655,43871,1657],{},[898,43873,9920],{},[1655,43875,2346],{},[898,43877,4049],{},[902,43879,43880],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,43883,43884],{},"spotřebiteli"," (posun poptávky ",[883,43887,43889],{"className":43888},[886],[888,43890,43891],{"xmlns":890},[892,43892,43893,43909],{},[895,43894,43895,43901,43903,43905,43907],{},[1820,43896,43897,43899],{},[898,43898,2838],{},[1826,43900,1837],{},[1655,43902,1657],{},[898,43904,2838],{},[1655,43906,2623],{},[898,43908,4049],{},[902,43910,43911],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,43914,43916],{"className":43915},[886],[888,43917,43918],{"xmlns":890},[892,43919,43920,43928],{},[895,43921,43922],{},[2597,43923,43924,43926],{},[898,43925,1824],{},[898,43927,5502],{},[902,43929,43529],{"encoding":904}," klesá a vzniká rozklad daně ",[883,43932,43934],{"className":43933},[886],[888,43935,43936],{"xmlns":890},[892,43937,43938,43968],{},[895,43939,43940,43942,43944,43954,43956],{},[898,43941,4049],{},[1655,43943,1657],{},[1820,43945,43946,43948],{},[898,43947,4049],{},[895,43949,43950,43952],{},[898,43951,43803],{},[898,43953,724],{},[1655,43955,2346],{},[1820,43957,43958,43960],{},[898,43959,4049],{},[895,43961,43962,43964,43966],{},[898,43963,43826],{},[898,43965,1674],{},[898,43967,13166],{},[902,43969,43970],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,43973,43975],{"className":43974},[886],[888,43976,43977],{"xmlns":890},[892,43978,43979,43983],{},[895,43980,43981],{},[898,43982,2838],{},[902,43984,2838],{"encoding":904},[883,43986,43988],{"className":43987},[886],[888,43989,43990],{"xmlns":890},[892,43991,43992,43996],{},[895,43993,43994],{},[898,43995,9920],{},[902,43997,9920],{"encoding":904},[724,43999,44000,44001,44004,44005,2704,44035,44069],{},"Zásadním výsledkem kapitoly je ",[38,44002,44003],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,44006,44008],{"className":44007},[886],[888,44009,44010],{"xmlns":890},[892,44011,44012,44032],{},[895,44013,44014,44022,44024],{},[1935,44015,44016,44018,44020],{},[898,44017,1824],{},[1826,44019,1828],{},[898,44021,5502],{},[1655,44023,1657],{},[1935,44025,44026,44028,44030],{},[898,44027,1824],{},[1826,44029,1837],{},[898,44031,5502],{},[902,44033,44034],{"encoding":904},"Q_1^E = Q_2^E",[883,44036,44038],{"className":44037},[886],[888,44039,44040],{"xmlns":890},[892,44041,44042,44066],{},[895,44043,44044,44052,44054,44056,44058],{},[1935,44045,44046,44048,44050],{},[898,44047,2132],{},[1826,44049,1828],{},[898,44051,5502],{},[1655,44053,2623],{},[898,44055,4049],{},[1655,44057,1657],{},[1935,44059,44060,44062,44064],{},[898,44061,2132],{},[1826,44063,1837],{},[898,44065,5502],{},[902,44067,44068],{"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.",[724,44071,44072,44073,44076,44077,44103,44104,44132,44133,44136,44137,44140,44141,1719],{},"Podrobný výklad, Příklady ",[38,44074,44075],{},"2.9"," (daň výrobci, ",[883,44078,44080],{"className":44079},[886],[888,44081,44082],{"xmlns":890},[892,44083,44084,44100],{},[895,44085,44086,44096,44098],{},[1820,44087,44088,44090],{},[898,44089,4049],{},[895,44091,44092,44094],{},[898,44093,43803],{},[898,44095,724],{},[1655,44097,1657],{},[1826,44099,1837],{},[902,44101,44102],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,44105,44107],{"className":44106},[886],[888,44108,44109],{"xmlns":890},[892,44110,44111,44129],{},[895,44112,44113,44125,44127],{},[1820,44114,44115,44117],{},[898,44116,4049],{},[895,44118,44119,44121,44123],{},[898,44120,43826],{},[898,44122,1674],{},[898,44124,13166],{},[1655,44126,1657],{},[1826,44128,3639],{},[902,44130,44131],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,44134,44135],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,44138,44139],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,44142,43847],{"className":44143,"dataFsResolvedFilePath":809,"href":810},[210],[38096,44145],{},[115,44147,44149],{"id":44148},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[5120,44151,44152],{},[724,44153,44154,44156,44157,44160,44161,44163],{},[883,44155,5406],{}," TL;DR\nMultiplikátory jsou ",[38,44158,44159],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,44162,38086],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,44165,44167],{"id":44166},"redukovaný-tvar","Redukovaný tvar",[724,44169,44170,44171,2115,44194,1343,44212,13253,44229,2115,44252,44269,44270,44300],{},"Pro lineární model ",[883,44172,44174],{"className":44173},[886],[888,44175,44176],{"xmlns":890},[892,44177,44178,44192],{},[895,44179,44180,44182,44184,44186,44188,44190],{},[898,44181,2132],{},[1655,44183,1657],{},[898,44185,207],{},[898,44187,1824],{},[1655,44189,2346],{},[898,44191,2025],{},[902,44193,38186],{"encoding":904},[883,44195,44197],{"className":44196},[886],[888,44198,44199],{"xmlns":890},[892,44200,44201,44209],{},[895,44202,44203,44205,44207],{},[898,44204,207],{},[1655,44206,3065],{},[1826,44208,2552],{},[902,44210,44211],{"encoding":904},"a \u003C 0",[883,44213,44215],{"className":44214},[886],[888,44216,44217],{"xmlns":890},[892,44218,44219,44227],{},[895,44220,44221,44223,44225],{},[898,44222,2025],{},[1655,44224,2969],{},[1826,44226,2552],{},[902,44228,19940],{"encoding":904},[883,44230,44232],{"className":44231},[886],[888,44233,44234],{"xmlns":890},[892,44235,44236,44250],{},[895,44237,44238,44240,44242,44244,44246,44248],{},[898,44239,2132],{},[1655,44241,1657],{},[898,44243,1789],{},[898,44245,1824],{},[1655,44247,2346],{},[898,44249,2410],{},[902,44251,41368],{"encoding":904},[883,44253,44255],{"className":44254},[886],[888,44256,44257],{"xmlns":890},[892,44258,44259,44267],{},[895,44260,44261,44263,44265],{},[898,44262,1789],{},[1655,44264,2969],{},[1826,44266,2552],{},[902,44268,41386],{"encoding":904},") dává podmínka rovnováhy ",[883,44271,44273],{"className":44272},[886],[888,44274,44275],{"xmlns":890},[892,44276,44277,44297],{},[895,44278,44279,44281,44283,44285,44287,44289,44291,44293,44295],{},[898,44280,207],{},[898,44282,1824],{},[1655,44284,2346],{},[898,44286,2025],{},[1655,44288,1657],{},[898,44290,1789],{},[898,44292,1824],{},[1655,44294,2346],{},[898,44296,2410],{},[902,44298,44299],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,44302,44304],{"className":44303},[886],[888,44305,44306],{"xmlns":890,"display":29192},[892,44307,44308,44353],{},[21880,44309,44310],{"width":29197},[21885,44311,44312,44314,44346,44348],{},[21888,44313],{"width":29202},[21888,44315,44316],{},[895,44317,44318,44324,44326,44344],{},[2597,44319,44320,44322],{},[898,44321,1824],{},[898,44323,5502],{},[1655,44325,1657],{},[1949,44327,44328,44336],{},[895,44329,44330,44332,44334],{},[898,44331,2025],{},[1655,44333,2623],{},[898,44335,2410],{},[895,44337,44338,44340,44342],{},[898,44339,1789],{},[1655,44341,2623],{},[898,44343,207],{},[898,44345,1719],{"mathvariant":1943},[21888,44347],{"width":29202},[21888,44349,44350],{},[2031,44351,44352],{},"(2.10)",[902,44354,44355],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,44357,44358,44359,2115,44361,44364,44365,44382,44383,3106,44386,44412,44413,44426,44427,44445,44446,5171],{},"Vztah (2.10) je ",[38,44360,22080],{},[614,44362,44363],{},"reduced form",") pro ",[883,44366,44368],{"className":44367},[886],[888,44369,44370],{"xmlns":890},[892,44371,44372,44380],{},[895,44373,44374],{},[2597,44375,44376,44378],{},[898,44377,1824],{},[898,44379,5502],{},[902,44381,43529],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,44384,44385],{},"parametrů",[883,44387,44389],{"className":44388},[886],[888,44390,44391],{"xmlns":890},[892,44392,44393,44409],{},[895,44394,44395,44397,44399,44401,44403,44405,44407],{},[898,44396,207],{},[1655,44398,1671],{"separator":1670},[898,44400,2025],{},[1655,44402,1671],{"separator":1670},[898,44404,1789],{},[1655,44406,1671],{"separator":1670},[898,44408,2410],{},[902,44410,44411],{"encoding":904},"a, b, c, d",". Aby ",[883,44414,44416],{"className":44415},[886],[888,44417,44418],{"xmlns":890},[892,44419,44420,44424],{},[895,44421,44422],{},[898,44423,5502],{},[902,44425,5502],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,44428,44430],{"className":44429},[886],[888,44431,44432],{"xmlns":890},[892,44433,44434,44442],{},[895,44435,44436,44438,44440],{},[898,44437,2025],{},[1655,44439,2969],{},[898,44441,2410],{},[902,44443,44444],{"encoding":904},"b > d"," (neboť ",[883,44447,44449],{"className":44448},[886],[888,44450,44451],{"xmlns":890},[892,44452,44453,44465],{},[895,44454,44455,44457,44459,44461,44463],{},[898,44456,1789],{},[1655,44458,2623],{},[898,44460,207],{},[1655,44462,2969],{},[1826,44464,2552],{},[902,44466,44467],{"encoding":904},"c - a > 0",[724,44469,44470],{},[614,44471,44472,44473,44486,44487,44500,44501,19774,44514,43066,44531,44544],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,44474,44476],{"className":44475},[886],[888,44477,44478],{"xmlns":890},[892,44479,44480,44484],{},[895,44481,44482],{},[898,44483,2025],{},[902,44485,2025],{"encoding":904}," na ose ",[883,44488,44490],{"className":44489},[886],[888,44491,44492],{"xmlns":890},[892,44493,44494,44498],{},[895,44495,44496],{},[898,44497,2132],{},[902,44499,2132],{"encoding":904},") a nabídka (úsek ",[883,44502,44504],{"className":44503},[886],[888,44505,44506],{"xmlns":890},[892,44507,44508,44512],{},[895,44509,44510],{},[898,44511,2410],{},[902,44513,2410],{"encoding":904},[883,44515,44517],{"className":44516},[886],[888,44518,44519],{"xmlns":890},[892,44520,44521,44529],{},[895,44522,44523,44525,44527],{},[898,44524,2025],{},[1655,44526,2969],{},[898,44528,2410],{},[902,44530,44444],{"encoding":904},[883,44532,44534],{"className":44533},[886],[888,44535,44536],{"xmlns":890},[892,44537,44538,44542],{},[895,44539,44540],{},[898,44541,5502],{},[902,44543,5502],{"encoding":904}," v 1. kvadrantu.",[198,44546,44548],{"id":44547},"definice-multiplikátorů","Definice multiplikátorů",[724,44550,44551,44552,44577,44578,44591,44592,44605],{},"V komparativní statice jsou ",[883,44553,44555],{"className":44554},[886],[888,44556,44557],{"xmlns":890},[892,44558,44559,44575],{},[895,44560,44561,44563,44565,44567,44569,44571,44573],{},[898,44562,207],{},[1655,44564,1671],{"separator":1670},[898,44566,2025],{},[1655,44568,1671],{"separator":1670},[898,44570,1789],{},[1655,44572,1671],{"separator":1670},[898,44574,2410],{},[902,44576,44411],{"encoding":904}," exogenní proměnné a ",[883,44579,44581],{"className":44580},[886],[888,44582,44583],{"xmlns":890},[892,44584,44585,44589],{},[895,44586,44587],{},[898,44588,1824],{},[902,44590,1824],{"encoding":904}," endogenní. Přibližná změna ",[883,44593,44595],{"className":44594},[886],[888,44596,44597],{"xmlns":890},[892,44598,44599,44603],{},[895,44600,44601],{},[898,44602,1824],{},[902,44604,1824],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,44607,44609],{"className":44608},[886],[888,44610,44611],{"xmlns":890,"display":29192},[892,44612,44613,44706],{},[21880,44614,44615],{"width":29197},[21885,44616,44617,44619,44699,44701],{},[21888,44618],{"width":29202},[21888,44620,44621],{},[895,44622,44623,44625,44627,44629,44631,44633,44635,44643,44645,44647,44649,44651,44659,44661,44663,44665,44667,44675,44677,44679,44681,44683,44691,44693,44695,44697],{},[898,44624,2506],{"mathvariant":1943},[898,44626,1824],{},[1655,44628,2357],{},[898,44630,2410],{},[898,44632,1824],{},[1655,44634,1657],{},[1935,44636,44637,44639,44641],{},[898,44638,1824],{},[898,44640,207],{},[1655,44642,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[2031,44644,2435],{},[898,44646,2410],{},[898,44648,207],{},[1655,44650,2346],{},[1935,44652,44653,44655,44657],{},[898,44654,1824],{},[898,44656,2025],{},[1655,44658,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[2031,44660,2435],{},[898,44662,2410],{},[898,44664,2025],{},[1655,44666,2346],{},[1935,44668,44669,44671,44673],{},[898,44670,1824],{},[898,44672,1789],{},[1655,44674,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[2031,44676,2435],{},[898,44678,2410],{},[898,44680,1789],{},[1655,44682,2346],{},[1935,44684,44685,44687,44689],{},[898,44686,1824],{},[898,44688,2410],{},[1655,44690,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[2031,44692,2435],{},[898,44694,2410],{},[898,44696,2410],{},[898,44698,1719],{"mathvariant":1943},[21888,44700],{"width":29202},[21888,44702,44703],{},[2031,44704,44705],{},"(2.11)",[902,44707,44708],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,44710,44711,44712,44762,44763,2115,44765,4421],{},"Parciální derivace ",[883,44713,44715],{"className":44714},[886],[888,44716,44717],{"xmlns":890},[892,44718,44719,44759],{},[895,44720,44721,44729,44731,44739,44741,44749,44751],{},[1935,44722,44723,44725,44727],{},[898,44724,1824],{},[898,44726,207],{},[1655,44728,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,44730,1671],{"separator":1670},[1935,44732,44733,44735,44737],{},[898,44734,1824],{},[898,44736,2025],{},[1655,44738,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,44740,1671],{"separator":1670},[1935,44742,44743,44745,44747],{},[898,44744,1824],{},[898,44746,1789],{},[1655,44748,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,44750,1671],{"separator":1670},[1935,44752,44753,44755,44757],{},[898,44754,1824],{},[898,44756,2410],{},[1655,44758,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,44760,44761],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,44764,19103],{},[614,44766,44767],{},"multipliers",[883,44769,44771],{"className":44770},[886],[888,44772,44773],{"xmlns":890,"display":29192},[892,44774,44775,44926],{},[21880,44776,44777],{"width":29197},[21885,44778,44779,44781,44919,44921],{},[21888,44780],{"width":29202},[21888,44782,44783],{},[895,44784,44785,44793,44795,44821,44823,44825,44833,44835,44847,44849,44851,44859,44861,44863,44889,44891,44893,44901,44903,44905,44917],{},[1935,44786,44787,44789,44791],{},[898,44788,1824],{},[898,44790,207],{},[1655,44792,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,44794,1657],{},[1949,44796,44797,44805],{},[895,44798,44799,44801,44803],{},[898,44800,2025],{},[1655,44802,2623],{},[898,44804,2410],{},[895,44806,44807,44809,44811,44813,44815],{},[1655,44808,1664],{"stretchy":1663},[898,44810,1789],{},[1655,44812,2623],{},[898,44814,207],{},[2597,44816,44817,44819],{},[1655,44818,1677],{"stretchy":1663},[1826,44820,1837],{},[1655,44822,1671],{"separator":1670},[1967,44824],{"width":16409},[1935,44826,44827,44829,44831],{},[898,44828,1824],{},[898,44830,2025],{},[1655,44832,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,44834,1657],{},[1949,44836,44837,44839],{},[1826,44838,1828],{},[895,44840,44841,44843,44845],{},[898,44842,1789],{},[1655,44844,2623],{},[898,44846,207],{},[1655,44848,1671],{"separator":1670},[1967,44850],{"width":16409},[1935,44852,44853,44855,44857],{},[898,44854,1824],{},[898,44856,1789],{},[1655,44858,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,44860,1657],{},[1655,44862,2623],{},[1949,44864,44865,44873],{},[895,44866,44867,44869,44871],{},[898,44868,2025],{},[1655,44870,2623],{},[898,44872,2410],{},[895,44874,44875,44877,44879,44881,44883],{},[1655,44876,1664],{"stretchy":1663},[898,44878,1789],{},[1655,44880,2623],{},[898,44882,207],{},[2597,44884,44885,44887],{},[1655,44886,1677],{"stretchy":1663},[1826,44888,1837],{},[1655,44890,1671],{"separator":1670},[1967,44892],{"width":16409},[1935,44894,44895,44897,44899],{},[898,44896,1824],{},[898,44898,2410],{},[1655,44900,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,44902,1657],{},[1655,44904,2623],{},[1949,44906,44907,44909],{},[1826,44908,1828],{},[895,44910,44911,44913,44915],{},[898,44912,1789],{},[1655,44914,2623],{},[898,44916,207],{},[898,44918,1719],{"mathvariant":1943},[21888,44920],{"width":29202},[21888,44922,44923],{},[2031,44924,44925],{},"(2.12)",[902,44927,44928],{"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}",[198,44930,44932],{"id":44931},"znaménka-a-interpretace","Znaménka a interpretace",[724,44934,44935,44936,1343,44953,1343,44970,1343,44987,45004,45005,4421],{},"Za podmínek ",[883,44937,44939],{"className":44938},[886],[888,44940,44941],{"xmlns":890},[892,44942,44943,44951],{},[895,44944,44945,44947,44949],{},[898,44946,207],{},[1655,44948,3065],{},[1826,44950,2552],{},[902,44952,44211],{"encoding":904},[883,44954,44956],{"className":44955},[886],[888,44957,44958],{"xmlns":890},[892,44959,44960,44968],{},[895,44961,44962,44964,44966],{},[898,44963,2025],{},[1655,44965,2969],{},[1826,44967,2552],{},[902,44969,19940],{"encoding":904},[883,44971,44973],{"className":44972},[886],[888,44974,44975],{"xmlns":890},[892,44976,44977,44985],{},[895,44978,44979,44981,44983],{},[898,44980,1789],{},[1655,44982,2969],{},[1826,44984,2552],{},[902,44986,41386],{"encoding":904},[883,44988,44990],{"className":44989},[886],[888,44991,44992],{"xmlns":890},[892,44993,44994,45002],{},[895,44995,44996,44998,45000],{},[898,44997,2025],{},[1655,44999,2969],{},[898,45001,2410],{},[902,45003,44444],{"encoding":904}," platí (znaménka se ",[38,45006,45007],{},"nemění",[883,45009,45011],{"className":45010},[886],[888,45012,45013],{"xmlns":890,"display":29192},[892,45014,45015,45077],{},[895,45016,45017,45025,45027,45029,45031,45033,45041,45043,45045,45047,45049,45057,45059,45061,45063,45065,45073,45075],{},[1935,45018,45019,45021,45023],{},[898,45020,1824],{},[898,45022,207],{},[1655,45024,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,45026,2969],{},[1826,45028,2552],{},[1655,45030,1671],{"separator":1670},[1967,45032],{"width":1969},[1935,45034,45035,45037,45039],{},[898,45036,1824],{},[898,45038,2025],{},[1655,45040,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,45042,2969],{},[1826,45044,2552],{},[1655,45046,1671],{"separator":1670},[1967,45048],{"width":1969},[1935,45050,45051,45053,45055],{},[898,45052,1824],{},[898,45054,1789],{},[1655,45056,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,45058,3065],{},[1826,45060,2552],{},[1655,45062,1671],{"separator":1670},[1967,45064],{"width":1969},[1935,45066,45067,45069,45071],{},[898,45068,1824],{},[898,45070,2410],{},[1655,45072,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,45074,3065],{},[1826,45076,13585],{},[902,45078,45079],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,45081,45082,45141],{},[123,45083,45084,3106,45087,45107,45108,45125,45126,1343,45139,1719],{},[38,45085,45086],{},"Kvantitativní smysl:",[883,45088,45090],{"className":45089},[886],[888,45091,45092],{"xmlns":890},[892,45093,45094,45104],{},[895,45095,45096],{},[1935,45097,45098,45100,45102],{},[898,45099,1824],{},[898,45101,1667],{},[1655,45103,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,45105,45106],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,45109,45111],{"className":45110},[886],[888,45112,45113],{"xmlns":890},[892,45114,45115,45123],{},[895,45116,45117],{},[2597,45118,45119,45121],{},[898,45120,1824],{},[898,45122,5502],{},[902,45124,43529],{"encoding":904}," při jednotkové změně parametru ",[883,45127,45129],{"className":45128},[886],[888,45130,45131],{"xmlns":890},[892,45132,45133,45137],{},[895,45134,45135],{},[898,45136,1667],{},[902,45138,1667],{"encoding":904},[614,45140,38086],{},[123,45142,45143,45146,45147,45164,45165,1719],{},[38,45144,45145],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,45148,45150],{"className":45149},[886],[888,45151,45152],{"xmlns":890},[892,45153,45154,45162],{},[895,45155,45156],{},[2597,45157,45158,45160],{},[898,45159,1824],{},[898,45161,5502],{},[902,45163,43529],{"encoding":904}," na růst ",[883,45166,45168],{"className":45167},[886],[888,45169,45170],{"xmlns":890},[892,45171,45172,45176],{},[895,45173,45174],{},[898,45175,1667],{},[902,45177,1667],{"encoding":904},[724,45179,45180,45181,45194,45195,44445,45212,5171],{},"Např. růst ",[883,45182,45184],{"className":45183},[886],[888,45185,45186],{"xmlns":890},[892,45187,45188,45192],{},[895,45189,45190],{},[898,45191,1789],{},[902,45193,1789],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,45196,45198],{"className":45197},[886],[888,45199,45200],{"xmlns":890},[892,45201,45202,45210],{},[895,45203,45204],{},[2597,45205,45206,45208],{},[898,45207,1824],{},[898,45209,5502],{},[902,45211,43529],{"encoding":904},[883,45213,45215],{"className":45214},[886],[888,45216,45217],{"xmlns":890},[892,45218,45219,45233],{},[895,45220,45221,45229,45231],{},[1935,45222,45223,45225,45227],{},[898,45224,1824],{},[898,45226,1789],{},[1655,45228,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,45230,3065],{},[1826,45232,2552],{},[902,45234,45235],{"encoding":904},"Q'_c \u003C 0",[724,45237,45238],{},[614,45239,45240,45241,45261,45262,45286,45287,45309,45310,1719],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,45242,45244],{"className":45243},[886],[888,45245,45246],{"xmlns":890},[892,45247,45248,45258],{},[895,45249,45250,45252,45254,45256],{},[898,45251,1789],{},[898,45253,1824],{},[1655,45255,2346],{},[898,45257,2410],{},[902,45259,45260],{"encoding":904},"cQ + d"," na strmější ",[883,45263,45265],{"className":45264},[886],[888,45266,45267],{"xmlns":890},[892,45268,45269,45283],{},[895,45270,45271,45277,45279,45281],{},[1820,45272,45273,45275],{},[898,45274,1789],{},[1826,45276,1828],{},[898,45278,1824],{},[1655,45280,2346],{},[898,45282,2410],{},[902,45284,45285],{"encoding":904},"c_1 Q + d"," (při ",[883,45288,45290],{"className":45289},[886],[888,45291,45292],{"xmlns":890},[892,45293,45294,45306],{},[895,45295,45296,45302,45304],{},[1820,45297,45298,45300],{},[898,45299,1789],{},[1826,45301,1828],{},[1655,45303,2969],{},[898,45305,1789],{},[902,45307,45308],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,45311,45313],{"className":45312},[886],[888,45314,45315],{"xmlns":890},[892,45316,45317,45327],{},[895,45318,45319,45325],{},[2597,45320,45321,45323],{},[898,45322,1824],{},[898,45324,5502],{},[1655,45326,43717],{},[902,45328,45329],{"encoding":904},"Q^E \\downarrow",[724,45331,45332,45333,45365,45366,1719],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,45334,45336],{"className":45335},[886],[888,45337,45338],{"xmlns":890},[892,45339,45340,45362],{},[895,45341,45342,45344,45346,45348,45356,45358,45360],{},[898,45343,2506],{"mathvariant":1943},[898,45345,1824],{},[1655,45347,2357],{},[1935,45349,45350,45352,45354],{},[898,45351,1824],{},[898,45353,2025],{},[1655,45355,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[2031,45357,2435],{},[898,45359,2410],{},[898,45361,2025],{},[902,45363,45364],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,45367,45369],{"className":45368},[886],[888,45370,45371],{"xmlns":890},[892,45372,45373,45381],{},[895,45374,45375],{},[2597,45376,45377,45379],{},[898,45378,2132],{},[898,45380,5502],{},[902,45382,42592],{"encoding":904},[198,45384,45386,45387],{"id":45385},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,45388,45390],{"className":45389},[886],[888,45391,45392],{"xmlns":890},[892,45393,45394,45402],{},[895,45395,45396],{},[2597,45397,45398,45400],{},[898,45399,1824],{},[898,45401,5502],{},[902,45403,43529],{"encoding":904},[724,45405,45406,42781,45408,42816,45434,1719],{},[38,45407,39059],{},[883,45409,45411],{"className":45410},[886],[888,45412,45413],{"xmlns":890},[892,45414,45415,45431],{},[895,45416,45417,45419,45421,45423,45425,45427,45429],{},[898,45418,2132],{},[1655,45420,1657],{},[1655,45422,2623],{},[1826,45424,3472],{},[898,45426,1824],{},[1655,45428,2346],{},[1826,45430,6460],{},[902,45432,45433],{"encoding":904},"P = -3Q + 40",[883,45435,45437],{"className":45436},[886],[888,45438,45439],{"xmlns":890},[892,45440,45441,45455],{},[895,45442,45443,45445,45447,45449,45451,45453],{},[898,45444,2132],{},[1655,45446,1657],{},[1826,45448,6258],{},[898,45450,1824],{},[1655,45452,2346],{},[1826,45454,4136],{},[902,45456,45457],{"encoding":904},"P = 0{,}5Q + 10",[724,45459,45460,45462],{},[38,45461,39091],{}," Rovnovážné množství",[883,45464,45466],{"className":45465},[886],[888,45467,45468],{"xmlns":890,"display":29192},[892,45469,45470,45538],{},[895,45471,45472,45478,45480,45498,45500,45524,45526,45533,45535],{},[2597,45473,45474,45476],{},[898,45475,1824],{},[898,45477,5502],{},[1655,45479,1657],{},[1949,45481,45482,45490],{},[895,45483,45484,45486,45488],{},[898,45485,2025],{},[1655,45487,2623],{},[898,45489,2410],{},[895,45491,45492,45494,45496],{},[898,45493,1789],{},[1655,45495,2623],{},[898,45497,207],{},[1655,45499,1657],{},[1949,45501,45502,45510],{},[895,45503,45504,45506,45508],{},[1826,45505,6460],{},[1655,45507,2623],{},[1826,45509,4136],{},[895,45511,45512,45514,45516,45518,45520,45522],{},[1826,45513,6258],{},[1655,45515,2623],{},[1655,45517,1664],{"stretchy":1663},[1655,45519,2623],{},[1826,45521,3472],{},[1655,45523,1677],{"stretchy":1663},[1655,45525,1657],{},[1949,45527,45528,45530],{},[1826,45529,39145],{},[1826,45531,45532],{},"3,5",[1655,45534,2357],{},[1826,45536,45537],{},"8,571.",[902,45539,45540],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,45542,45543,45588],{},[38,45544,45545,45546,3948,45559,3962,45573,45587],{},"(a) Změna ",[883,45547,45549],{"className":45548},[886],[888,45550,45551],{"xmlns":890},[892,45552,45553,45557],{},[895,45554,45555],{},[898,45556,1789],{},[902,45558,1789],{"encoding":904},[883,45560,45562],{"className":45561},[886],[888,45563,45564],{"xmlns":890},[892,45565,45566,45570],{},[895,45567,45568],{},[1826,45569,6258],{},[902,45571,45572],{"encoding":904},"0{,}5",[883,45574,45576],{"className":45575},[886],[888,45577,45578],{"xmlns":890},[892,45579,45580,45584],{},[895,45581,45582],{},[1826,45583,20447],{},[902,45585,45586],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,45590,45592],{"className":45591},[886],[888,45593,45594],{"xmlns":890,"display":29192},[892,45595,45596,45673],{},[895,45597,45598,45606,45608,45610,45612,45614,45616,45642,45644,45646,45648,45650,45652,45662,45664,45666,45668,45670],{},[1935,45599,45600,45602,45604],{},[898,45601,1824],{},[898,45603,1789],{},[1655,45605,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[2031,45607,2435],{},[898,45609,2410],{},[898,45611,1789],{},[1655,45613,1657],{},[1655,45615,2623],{},[1949,45617,45618,45626],{},[895,45619,45620,45622,45624],{},[898,45621,2025],{},[1655,45623,2623],{},[898,45625,2410],{},[895,45627,45628,45630,45632,45634,45636],{},[1655,45629,1664],{"stretchy":1663},[898,45631,1789],{},[1655,45633,2623],{},[898,45635,207],{},[2597,45637,45638,45640],{},[1655,45639,1677],{"stretchy":1663},[1826,45641,1837],{},[2031,45643,2435],{},[898,45645,2410],{},[898,45647,1789],{},[1655,45649,1657],{},[1655,45651,2623],{},[1949,45653,45654,45656],{},[1826,45655,39145],{},[2597,45657,45658,45660],{},[1826,45659,45532],{},[1826,45661,1837],{},[1655,45663,2869],{},[1826,45665,4068],{},[1655,45667,2357],{},[1655,45669,2623],{},[1826,45671,45672],{},"0,245.",[902,45674,45675],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,45677,45678,45679,1719],{},"Nové rovnovážné množství ",[883,45680,45682],{"className":45681},[886],[888,45683,45684],{"xmlns":890},[892,45685,45686,45711],{},[895,45687,45688,45696,45698,45701,45703,45706,45708],{},[1935,45689,45690,45692,45694],{},[898,45691,1824],{},[1826,45693,1828],{},[898,45695,5502],{},[1655,45697,2357],{},[1826,45699,45700],{},"8,571",[1655,45702,2623],{},[1826,45704,45705],{},"0,245",[1655,45707,1657],{},[1826,45709,45710],{},"8,326",[902,45712,45713],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,45715,45716,45801],{},[38,45717,45718,45719,1343,45739,1343,45761,1343,45781,1719],{},"(b) Současné změny ",[883,45720,45722],{"className":45721},[886],[888,45723,45724],{"xmlns":890},[892,45725,45726,45736],{},[895,45727,45728,45730,45732,45734],{},[898,45729,2410],{},[898,45731,207],{},[1655,45733,1657],{},[1826,45735,6258],{},[902,45737,45738],{"encoding":904},"da = 0{,}5",[883,45740,45742],{"className":45741},[886],[888,45743,45744],{"xmlns":890},[892,45745,45746,45758],{},[895,45747,45748,45750,45752,45754,45756],{},[898,45749,2410],{},[898,45751,2025],{},[1655,45753,1657],{},[1655,45755,2623],{},[1826,45757,3524],{},[902,45759,45760],{"encoding":904},"db = -5",[883,45762,45764],{"className":45763},[886],[888,45765,45766],{"xmlns":890},[892,45767,45768,45778],{},[895,45769,45770,45772,45774,45776],{},[898,45771,2410],{},[898,45773,1789],{},[1655,45775,1657],{},[1826,45777,4068],{},[902,45779,45780],{"encoding":904},"dc = 0{,}1",[883,45782,45784],{"className":45783},[886],[888,45785,45786],{"xmlns":890},[892,45787,45788,45798],{},[895,45789,45790,45792,45794,45796],{},[898,45791,2410],{},[898,45793,2410],{},[1655,45795,1657],{},[1826,45797,1828],{},[902,45799,45800],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,45803,45805],{"className":45804},[886],[888,45806,45807],{"xmlns":890,"display":29192},[892,45808,45809,45952],{},[21880,45810,45811,45893,45929],{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},[21885,45812,45813,45823],{},[21888,45814,45815],{},[3615,45816,45817],{"scriptlevel":2552,"displaystyle":1670},[895,45818,45819,45821],{},[898,45820,2506],{"mathvariant":1943},[898,45822,1824],{},[21888,45824,45825],{},[3615,45826,45827],{"scriptlevel":2552,"displaystyle":1670},[895,45828,45829,45831,45833,45843,45845,45847,45849,45855,45857,45859,45861,45863,45865,45867,45877,45879,45881,45883,45889,45891],{},[895,45830],{},[1655,45832,2357],{},[1949,45834,45835,45837],{},[1826,45836,39145],{},[2597,45838,45839,45841],{},[1826,45840,45532],{},[1826,45842,1837],{},[1655,45844,2869],{},[1826,45846,6258],{},[1655,45848,2346],{},[1949,45850,45851,45853],{},[1826,45852,1828],{},[1826,45854,45532],{},[1655,45856,2869],{},[1655,45858,1664],{"stretchy":1663},[1655,45860,2623],{},[1826,45862,3524],{},[1655,45864,1677],{"stretchy":1663},[1655,45866,2623],{},[1949,45868,45869,45871],{},[1826,45870,39145],{},[2597,45872,45873,45875],{},[1826,45874,45532],{},[1826,45876,1837],{},[1655,45878,2869],{},[1826,45880,4068],{},[1655,45882,2623],{},[1949,45884,45885,45887],{},[1826,45886,1828],{},[1826,45888,45532],{},[1655,45890,2869],{},[1826,45892,1828],{},[21885,45894,45895,45901],{},[21888,45896,45897],{},[3615,45898,45899],{"scriptlevel":2552,"displaystyle":1670},[895,45900],{},[21888,45902,45903],{},[3615,45904,45905],{"scriptlevel":2552,"displaystyle":1670},[895,45906,45907,45909,45911,45914,45916,45919,45921,45924,45926],{},[895,45908],{},[1655,45910,1657],{},[1826,45912,45913],{},"1,2245",[1655,45915,2623],{},[1826,45917,45918],{},"1,4286",[1655,45920,2623],{},[1826,45922,45923],{},"0,2449",[1655,45925,2623],{},[1826,45927,45928],{},"0,2857",[21885,45930,45931,45937],{},[21888,45932,45933],{},[3615,45934,45935],{"scriptlevel":2552,"displaystyle":1670},[895,45936],{},[21888,45938,45939],{},[3615,45940,45941],{"scriptlevel":2552,"displaystyle":1670},[895,45942,45943,45945,45947,45949],{},[895,45944],{},[1655,45946,2357],{},[1655,45948,2623],{},[1826,45950,45951],{},"0,735.",[902,45953,45954],{"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}",[724,45956,31191,45957,1719],{},[883,45958,45960],{"className":45959},[886],[888,45961,45962],{"xmlns":890},[892,45963,45964,45988],{},[895,45965,45966,45974,45976,45978,45980,45983,45985],{},[1935,45967,45968,45970,45972],{},[898,45969,1824],{},[1826,45971,1828],{},[898,45973,5502],{},[1655,45975,2357],{},[1826,45977,45700],{},[1655,45979,2623],{},[1826,45981,45982],{},"0,735",[1655,45984,1657],{},[1826,45986,45987],{},"7,836",[902,45989,45990],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[5120,45992,45993],{},[724,45994,45995,45997,45998,46021,46022,46044],{},[883,45996,5661],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,45999,46001],{"className":46000},[886],[888,46002,46003],{"xmlns":890},[892,46004,46005,46018],{},[895,46006,46007,46009,46011,46013,46015],{},[898,46008,2506],{"mathvariant":1943},[898,46010,1824],{},[1655,46012,2357],{},[1655,46014,2623],{},[1826,46016,46017],{},"2,69",[902,46019,46020],{"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 ",[883,46023,46025],{"className":46024},[886],[888,46026,46027],{"xmlns":890},[892,46028,46029,46041],{},[895,46030,46031,46033,46035,46037,46039],{},[898,46032,2506],{"mathvariant":1943},[898,46034,1824],{},[1655,46036,2357],{},[1655,46038,2623],{},[1826,46040,45982],{},[902,46042,46043],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,46046,46047],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[38096,46049],{},[115,46051,820],{"id":12908},[5120,46053,46054],{},[724,46055,46056,5127,46058,2115,46061,13253,46077,2115,46080,46096,46097,1719],{},[883,46057,5406],{},[38,46059,46060],{},"Přebytek spotřebitele",[883,46062,46064],{"className":46063},[886],[888,46065,46066],{"xmlns":890},[892,46067,46068,46074],{},[895,46069,46070,46072],{},[898,46071,4052],{},[898,46073,9920],{},[902,46075,46076],{"encoding":904},"CS",[38,46078,46079],{},"přebytek výrobce",[883,46081,46083],{"className":46082},[886],[888,46084,46085],{"xmlns":890},[892,46086,46087,46093],{},[895,46088,46089,46091],{},[898,46090,2132],{},[898,46092,9920],{},[902,46094,46095],{"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 ",[207,46098,46100],{"className":46099,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,46102,46103],{},[1723,46104],{"alt":46105,"className":46106,"src":46107},"imek-prebytky-cs-ps",[210,1727],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,46109,46110,2115,46112,46115],{},[38,46111,46060],{},[614,46113,46114],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,46117,46119],{"className":46118},[886],[888,46120,46121],{"xmlns":890,"display":29192},[892,46122,46123,46200],{},[21880,46124,46125],{"width":29197},[21885,46126,46127,46129,46193,46195],{},[21888,46128],{"width":29202},[21888,46130,46131],{},[895,46132,46133,46135,46137,46139,46145,46147,46149,46161,46163,46165,46167,46169,46171,46173,46175,46177,46183,46185,46191],{},[898,46134,4052],{},[898,46136,9920],{},[1655,46138,1664],{"stretchy":1663},[1820,46140,46141,46143],{},[898,46142,1824],{},[1826,46144,2552],{},[1655,46146,1677],{"stretchy":1663},[1655,46148,1657],{},[1935,46150,46151,46153,46155],{},[1655,46152,12293],{},[1826,46154,2552],{},[1820,46156,46157,46159],{},[898,46158,1824],{},[1826,46160,2552],{},[898,46162,2838],{},[1655,46164,1664],{"stretchy":1663},[898,46166,1824],{},[1655,46168,1677],{"stretchy":1663},[2031,46170,2435],{},[898,46172,2410],{},[898,46174,1824],{},[1655,46176,2623],{},[1820,46178,46179,46181],{},[898,46180,2132],{},[1826,46182,2552],{},[2031,46184,2435],{},[1820,46186,46187,46189],{},[898,46188,1824],{},[1826,46190,2552],{},[898,46192,1719],{"mathvariant":1943},[21888,46194],{"width":29202},[21888,46196,46197],{},[2031,46198,46199],{},"(2.14)",[902,46201,46202],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,46204,46205,2115,46208,46211],{},[38,46206,46207],{},"Přebytek výrobce",[614,46209,46210],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,46213,46215],{"className":46214},[886],[888,46216,46217],{"xmlns":890,"display":29192},[892,46218,46219,46296],{},[21880,46220,46221],{"width":29197},[21885,46222,46223,46225,46289,46291],{},[21888,46224],{"width":29202},[21888,46226,46227],{},[895,46228,46229,46231,46233,46235,46241,46243,46245,46251,46253,46259,46261,46273,46275,46277,46279,46281,46283,46285,46287],{},[898,46230,2132],{},[898,46232,9920],{},[1655,46234,1664],{"stretchy":1663},[1820,46236,46237,46239],{},[898,46238,1824],{},[1826,46240,2552],{},[1655,46242,1677],{"stretchy":1663},[1655,46244,1657],{},[1820,46246,46247,46249],{},[898,46248,2132],{},[1826,46250,2552],{},[2031,46252,2435],{},[1820,46254,46255,46257],{},[898,46256,1824],{},[1826,46258,2552],{},[1655,46260,2623],{},[1935,46262,46263,46265,46267],{},[1655,46264,12293],{},[1826,46266,2552],{},[1820,46268,46269,46271],{},[898,46270,1824],{},[1826,46272,2552],{},[898,46274,9920],{},[1655,46276,1664],{"stretchy":1663},[898,46278,1824],{},[1655,46280,1677],{"stretchy":1663},[2031,46282,2435],{},[898,46284,2410],{},[898,46286,1824],{},[898,46288,1719],{"mathvariant":1943},[21888,46290],{"width":29202},[21888,46292,46293],{},[2031,46294,46295],{},"(2.15)",[902,46297,46298],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,46300,46301,46302,1719],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,46303,46305],{"className":46304,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[38096,46307],{},[115,46309,46311],{"id":46310},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,46313,46314,46345,46350,46356,46384,46390,46419,46425,46505,46531],{},[123,46315,46316,46318,46319,46344],{},[38,46317,39054],{}," — lineární poptávka ",[883,46320,46322],{"className":46321},[886],[888,46323,46324],{"xmlns":890},[892,46325,46326,46342],{},[895,46327,46328,46330,46332,46334,46336,46338,46340],{},[898,46329,2132],{},[1655,46331,1657],{},[1655,46333,2623],{},[1826,46335,1837],{},[898,46337,1824],{},[1655,46339,2346],{},[1826,46341,4396],{},[902,46343,39086],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,46346,46347,46349],{},[38,46348,39368],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,46351,46352,46355],{},[38,46353,46354],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,46357,46358,46360,46361,1719],{},[38,46359,41915],{}," — lineární nabídka ",[883,46362,46364],{"className":46363},[886],[888,46365,46366],{"xmlns":890},[892,46367,46368,46382],{},[895,46369,46370,46372,46374,46376,46378,46380],{},[898,46371,2132],{},[1655,46373,1657],{},[1826,46375,6258],{},[898,46377,1824],{},[1655,46379,2346],{},[1826,46381,6253],{},[902,46383,41944],{"encoding":904},[123,46385,46386,46389],{},[38,46387,46388],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,46391,46392,46395,46396,1719],{},[38,46393,46394],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,46397,46399],{"className":46398},[886],[888,46400,46401],{"xmlns":890},[892,46402,46403,46417],{},[895,46404,46405,46407,46409,46411,46413,46415],{},[898,46406,5502],{},[1655,46408,2734],{"stretchy":1663},[1826,46410,3639],{},[1655,46412,1671],{"separator":1670},[1826,46414,43062],{},[1655,46416,2743],{"stretchy":1663},[902,46418,43090],{"encoding":904},[123,46420,46421,46424],{},[38,46422,46423],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,46426,46427,46430,46431,46448,46449,1343,46474,46501,46502,4223],{},[38,46428,46429],{},"Příklad 2.9"," — daň ",[883,46432,46434],{"className":46433},[886],[888,46435,46436],{"xmlns":890},[892,46437,46438,46446],{},[895,46439,46440,46442,46444],{},[898,46441,4049],{},[1655,46443,1657],{},[1826,46445,3531],{},[902,46447,42394],{"encoding":904}," na výrobce; rozklad ",[883,46450,46452],{"className":46451},[886],[888,46453,46454],{"xmlns":890},[892,46455,46456,46472],{},[895,46457,46458,46468,46470],{},[1820,46459,46460,46462],{},[898,46461,4049],{},[895,46463,46464,46466],{},[898,46465,43803],{},[898,46467,724],{},[1655,46469,1657],{},[1826,46471,1837],{},[902,46473,44102],{"encoding":904},[883,46475,46477],{"className":46476},[886],[888,46478,46479],{"xmlns":890},[892,46480,46481,46499],{},[895,46482,46483,46495,46497],{},[1820,46484,46485,46487],{},[898,46486,4049],{},[895,46488,46489,46491,46493],{},[898,46490,43826],{},[898,46492,1674],{},[898,46494,13166],{},[1655,46496,1657],{},[1826,46498,3639],{},[902,46500,44131],{"encoding":904},". (Viz ",[207,46503,43847],{"className":46504,"dataFsResolvedFilePath":809,"href":810},[210],[123,46506,46507,46430,46510,46527,46528,4223],{},[38,46508,46509],{},"Příklad 2.10",[883,46511,46513],{"className":46512},[886],[888,46514,46515],{"xmlns":890},[892,46516,46517,46525],{},[895,46518,46519,46521,46523],{},[898,46520,4049],{},[1655,46522,1657],{},[1826,46524,3531],{},[902,46526,42394],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,46529,43847],{"className":46530,"dataFsResolvedFilePath":809,"href":810},[210],[123,46532,46533,46536],{},[38,46534,46535],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[38096,46538],{},[115,46540,46542],{"id":46541},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,46544,46546],{"id":46545},"základní-analýza-poptávky","Základní analýza poptávky",[724,46548,46549,46552,46553,46588,46589,46615],{},[38,46550,46551],{},"2.1"," Je dána poptávka ",[883,46554,46556],{"className":46555},[886],[888,46557,46558],{"xmlns":890},[892,46559,46560,46585],{},[895,46561,46562,46564,46566,46568,46570,46572,46574,46576,46579,46581,46583],{},[898,46563,1824],{},[1655,46565,1657],{},[898,46567,2838],{},[1655,46569,1664],{"stretchy":1663},[898,46571,2132],{},[1655,46573,1677],{"stretchy":1663},[1655,46575,1657],{},[1826,46577,46578],{},"75",[1655,46580,2623],{},[1826,46582,3524],{},[898,46584,2132],{},[902,46586,46587],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,46590,46592],{"className":46591},[886],[888,46593,46594],{"xmlns":890},[892,46595,46596,46612],{},[895,46597,46598,46600,46602,46604,46606,46608,46610],{},[1826,46599,2552],{},[1655,46601,1671],{"separator":1670},[1826,46603,3524],{},[1655,46605,1671],{"separator":1670},[1826,46607,4136],{},[1655,46609,1671],{"separator":1670},[1826,46611,37370],{},[902,46613,46614],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,46617,46618,46621,46622,46640,46641,4421],{},[38,46619,46620],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,46623,46625],{"className":46624},[886],[888,46626,46627],{"xmlns":890},[892,46628,46629,46637],{},[895,46630,46631,46633,46635],{},[898,46632,2132],{},[1655,46634,1671],{"separator":1670},[898,46636,1824],{},[902,46638,46639],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,46642,46644],{"className":46643},[886],[888,46645,46646],{"xmlns":890},[892,46647,46648,46664],{},[895,46649,46650,46652,46654,46656,46658,46660,46662],{},[898,46651,207],{},[1655,46653,1671],{"separator":1670},[898,46655,2025],{},[1655,46657,1671],{"separator":1670},[898,46659,1789],{},[1655,46661,2969],{},[1826,46663,2552],{},[902,46665,46666],{"encoding":904},"a, b, c > 0",[120,46668,46669,46702,46733,46768,46799,46834],{},[123,46670,46671,46672],{},"(a) ",[883,46673,46675],{"className":46674},[886],[888,46676,46677],{"xmlns":890},[892,46678,46679,46699],{},[895,46680,46681,46683,46685],{},[898,46682,1824],{},[1655,46684,1657],{},[3615,46686,46687],{"scriptlevel":2552,"displaystyle":1670},[1949,46688,46689,46691],{},[898,46690,207],{},[895,46692,46693,46695,46697],{},[898,46694,2132],{},[1655,46696,2346],{},[898,46698,1789],{},[902,46700,46701],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,46703,46704,46705],{},"(b) ",[883,46706,46708],{"className":46707},[886],[888,46709,46710],{"xmlns":890},[892,46711,46712,46730],{},[895,46713,46714,46716,46718],{},[898,46715,1824],{},[1655,46717,1657],{},[9364,46719,46720],{},[895,46721,46722,46724,46726,46728],{},[898,46723,207],{},[1655,46725,2623],{},[898,46727,2025],{},[898,46729,1824],{},[902,46731,46732],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,46734,46735,46736],{},"(c) ",[883,46737,46739],{"className":46738},[886],[888,46740,46741],{"xmlns":890},[892,46742,46743,46765],{},[895,46744,46745,46747,46749],{},[898,46746,1824],{},[1655,46748,1657],{},[3615,46750,46751],{"scriptlevel":2552,"displaystyle":1670},[1949,46752,46753,46763],{},[895,46754,46755,46757,46759],{},[898,46756,207],{},[1655,46758,2623],{},[9364,46760,46761],{},[898,46762,2132],{},[898,46764,2025],{},[902,46766,46767],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,46769,46770,46771],{},"(d) ",[883,46772,46774],{"className":46773},[886],[888,46775,46776],{"xmlns":890},[892,46777,46778,46796],{},[895,46779,46780,46782,46784,46786,46788,46790],{},[898,46781,2132],{},[1655,46783,1657],{},[898,46785,207],{},[1655,46787,2623],{},[898,46789,2025],{},[2597,46791,46792,46794],{},[898,46793,1824],{},[1826,46795,1837],{},[902,46797,46798],{"encoding":904},"P = a - bQ^2",[123,46800,46801,46802],{},"(e) ",[883,46803,46805],{"className":46804},[886],[888,46806,46807],{"xmlns":890},[892,46808,46809,46831],{},[895,46810,46811,46813,46815,46817,46827,46829],{},[898,46812,1824],{},[1655,46814,1657],{},[898,46816,2025],{},[2597,46818,46819,46821],{},[898,46820,2132],{},[895,46822,46823,46825],{},[1655,46824,2623],{},[898,46826,207],{},[1655,46828,2346],{},[898,46830,1789],{},[902,46832,46833],{"encoding":904},"Q = bP^{-a} + c",[123,46835,46836,46837],{},"(f) ",[883,46838,46840],{"className":46839},[886],[888,46841,46842],{"xmlns":890},[892,46843,46844,46867],{},[895,46845,46846,46848,46850,46852,46854],{},[898,46847,1824],{},[1655,46849,1657],{},[898,46851,207],{},[1655,46853,2869],{},[2597,46855,46856,46859],{},[898,46857,46858],{},"e",[895,46860,46861,46863,46865],{},[1655,46862,2623],{},[898,46864,2025],{},[898,46866,2132],{},[902,46868,46869],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,46871,46872,46875],{},[38,46873,46874],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,46877,46878,46881,46884],{},[123,46879,46880],{},"(a) Cena substitutu.",[123,46882,46883],{},"(b) Cena komplementu.",[123,46885,46886],{},"(c) Výdaje na reklamu.",[724,46888,46889,46552,46891,46925,46926,46954],{},[38,46890,25768],{},[883,46892,46894],{"className":46893},[886],[888,46895,46896],{"xmlns":890},[892,46897,46898,46922],{},[895,46899,46900,46902,46904,46906,46908,46910,46912,46914,46916,46918,46920],{},[898,46901,2132],{},[1655,46903,1657],{},[898,46905,2838],{},[1655,46907,1664],{"stretchy":1663},[898,46909,1824],{},[1655,46911,1677],{"stretchy":1663},[1655,46913,1657],{},[1826,46915,4771],{},[1655,46917,2623],{},[1826,46919,1837],{},[898,46921,1824],{},[902,46923,46924],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,46927,46929],{"className":46928},[886],[888,46930,46931],{"xmlns":890},[892,46932,46933,46951],{},[895,46934,46935,46937,46939,46945,46947,46949],{},[898,46936,2132],{},[1655,46938,1657],{},[2597,46940,46941,46943],{},[898,46942,2838],{},[1655,46944,5603],{},[1655,46946,1664],{"stretchy":1663},[898,46948,1824],{},[1655,46950,1677],{"stretchy":1663},[902,46952,46953],{"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.",[724,46956,46957,46960],{},[38,46958,46959],{},"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:",[120,46962,46963,47047,47123,47209,47297],{},[123,46964,46671,46965,1343,47005,1719],{},[883,46966,46968],{"className":46967},[886],[888,46969,46970],{"xmlns":890},[892,46971,46972,47002],{},[895,46973,46974,46980,46982,46984,46986,46988,46994,46996],{},[1820,46975,46976,46978],{},[898,46977,24379],{},[1826,46979,1828],{},[1655,46981,1657],{},[1826,46983,10282],{},[1655,46985,2623],{},[1826,46987,3639],{},[1820,46989,46990,46992],{},[898,46991,2731],{},[1826,46993,1828],{},[1655,46995,2346],{},[1820,46997,46998,47000],{},[898,46999,2731],{},[1826,47001,1837],{},[902,47003,47004],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,47006,47008],{"className":47007},[886],[888,47009,47010],{"xmlns":890},[892,47011,47012,47044],{},[895,47013,47014,47020,47022,47024,47026,47028,47034,47036,47038],{},[1820,47015,47016,47018],{},[898,47017,24379],{},[1826,47019,1837],{},[1655,47021,1657],{},[1826,47023,4136],{},[1655,47025,2346],{},[1826,47027,1837],{},[1820,47029,47030,47032],{},[898,47031,2731],{},[1826,47033,1828],{},[1655,47035,2623],{},[1826,47037,3639],{},[1820,47039,47040,47042],{},[898,47041,2731],{},[1826,47043,1837],{},[902,47045,47046],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,47048,46704,47049,1343,47091,1719],{},[883,47050,47052],{"className":47051},[886],[888,47053,47054],{"xmlns":890},[892,47055,47056,47088],{},[895,47057,47058,47064,47066,47068,47070,47072,47078,47080,47082],{},[1820,47059,47060,47062],{},[898,47061,24379],{},[1826,47063,1828],{},[1655,47065,1657],{},[1826,47067,4390],{},[1655,47069,2623],{},[1826,47071,4136],{},[1820,47073,47074,47076],{},[898,47075,2731],{},[1826,47077,1828],{},[1655,47079,2623],{},[1826,47081,3531],{},[1820,47083,47084,47086],{},[898,47085,2731],{},[1826,47087,1837],{},[902,47089,47090],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,47092,47094],{"className":47093},[886],[888,47095,47096],{"xmlns":890},[892,47097,47098,47120],{},[895,47099,47100,47106,47108,47110,47112,47114],{},[1820,47101,47102,47104],{},[898,47103,24379],{},[1826,47105,1837],{},[1655,47107,1657],{},[1826,47109,37370],{},[1655,47111,2623],{},[1826,47113,4136],{},[1820,47115,47116,47118],{},[898,47117,2731],{},[1826,47119,1837],{},[902,47121,47122],{"encoding":904},"B_2 = 15 - 10A_2",[123,47124,46735,47125,1343,47167,1719],{},[883,47126,47128],{"className":47127},[886],[888,47129,47130],{"xmlns":890},[892,47131,47132,47164],{},[895,47133,47134,47140,47142,47144,47146,47148,47154,47156,47158],{},[1820,47135,47136,47138],{},[898,47137,24379],{},[1826,47139,1828],{},[1655,47141,1657],{},[1826,47143,39145],{},[1655,47145,2623],{},[1826,47147,1837],{},[1820,47149,47150,47152],{},[898,47151,2731],{},[1826,47153,1828],{},[1655,47155,2623],{},[1826,47157,3639],{},[1820,47159,47160,47162],{},[898,47161,2731],{},[1826,47163,1837],{},[902,47165,47166],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,47168,47170],{"className":47169},[886],[888,47171,47172],{"xmlns":890},[892,47173,47174,47206],{},[895,47175,47176,47182,47184,47186,47188,47190,47196,47198,47200],{},[1820,47177,47178,47180],{},[898,47179,24379],{},[1826,47181,1837],{},[1655,47183,1657],{},[1826,47185,37370],{},[1655,47187,2346],{},[1826,47189,1837],{},[1820,47191,47192,47194],{},[898,47193,2731],{},[1826,47195,1828],{},[1655,47197,2623],{},[1826,47199,1837],{},[1820,47201,47202,47204],{},[898,47203,2731],{},[1826,47205,1837],{},[902,47207,47208],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,47210,46770,47211,1343,47255,1719],{},[883,47212,47214],{"className":47213},[886],[888,47215,47216],{"xmlns":890},[892,47217,47218,47252],{},[895,47219,47220,47226,47228,47230,47232,47234,47236,47242,47244,47246],{},[1820,47221,47222,47224],{},[898,47223,24379],{},[1826,47225,1828],{},[1655,47227,1657],{},[1655,47229,2623],{},[1826,47231,10282],{},[1655,47233,2623],{},[1826,47235,1837],{},[1820,47237,47238,47240],{},[898,47239,2731],{},[1826,47241,1828],{},[1655,47243,2346],{},[1826,47245,3472],{},[1820,47247,47248,47250],{},[898,47249,2731],{},[1826,47251,1837],{},[902,47253,47254],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,47256,47258],{"className":47257},[886],[888,47259,47260],{"xmlns":890},[892,47261,47262,47294],{},[895,47263,47264,47270,47272,47274,47276,47278,47284,47286,47288],{},[1820,47265,47266,47268],{},[898,47267,24379],{},[1826,47269,1837],{},[1655,47271,1657],{},[1826,47273,4136],{},[1655,47275,2346],{},[1826,47277,1837],{},[1820,47279,47280,47282],{},[898,47281,2731],{},[1826,47283,1828],{},[1655,47285,2623],{},[1826,47287,1837],{},[1820,47289,47290,47292],{},[898,47291,2731],{},[1826,47293,1837],{},[902,47295,47296],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,47298,46801,47299,1343,47341,1719],{},[883,47300,47302],{"className":47301},[886],[888,47303,47304],{"xmlns":890},[892,47305,47306,47338],{},[895,47307,47308,47314,47316,47318,47320,47322,47328,47330,47332],{},[1820,47309,47310,47312],{},[898,47311,24379],{},[1826,47313,1828],{},[1655,47315,1657],{},[1826,47317,10282],{},[1655,47319,2346],{},[1826,47321,1837],{},[1820,47323,47324,47326],{},[898,47325,2731],{},[1826,47327,1828],{},[1655,47329,2346],{},[1826,47331,3639],{},[1820,47333,47334,47336],{},[898,47335,2731],{},[1826,47337,1837],{},[902,47339,47340],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,47342,47344],{"className":47343},[886],[888,47345,47346],{"xmlns":890},[892,47347,47348,47380],{},[895,47349,47350,47356,47358,47360,47362,47364,47370,47372,47374],{},[1820,47351,47352,47354],{},[898,47353,24379],{},[1826,47355,1837],{},[1655,47357,1657],{},[1826,47359,6460],{},[1655,47361,2623],{},[1826,47363,3472],{},[1820,47365,47366,47368],{},[898,47367,2731],{},[1826,47369,1828],{},[1655,47371,2346],{},[1826,47373,3524],{},[1820,47375,47376,47378],{},[898,47377,2731],{},[1826,47379,1837],{},[902,47381,47382],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,47384,47386],{"id":47385},"základní-analýza-nabídky","Základní analýza nabídky",[724,47388,47389,47392,47393,47427,47428,47450],{},[38,47390,47391],{},"2.6"," Je dána nabídka ",[883,47394,47396],{"className":47395},[886],[888,47397,47398],{"xmlns":890},[892,47399,47400,47424],{},[895,47401,47402,47404,47406,47408,47410,47412,47414,47416,47418,47420,47422],{},[898,47403,2132],{},[1655,47405,1657],{},[898,47407,9920],{},[1655,47409,1664],{"stretchy":1663},[898,47411,1824],{},[1655,47413,1677],{"stretchy":1663},[1655,47415,1657],{},[1826,47417,10282],{},[1655,47419,2346],{},[1826,47421,4112],{},[898,47423,1824],{},[902,47425,47426],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,47429,47431],{"className":47430},[886],[888,47432,47433],{"xmlns":890},[892,47434,47435,47447],{},[895,47436,47437,47439,47441,47443,47445],{},[1826,47438,6253],{},[1655,47440,1671],{"separator":1670},[1826,47442,39145],{},[1655,47444,1671],{"separator":1670},[1826,47446,16163],{},[902,47448,47449],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,47452,47453,47456,47457,47474],{},[38,47454,47455],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,47458,47460],{"className":47459},[886],[888,47461,47462],{"xmlns":890},[892,47463,47464,47472],{},[895,47465,47466,47468,47470],{},[898,47467,2132],{},[1655,47469,1671],{"separator":1670},[898,47471,1824],{},[902,47473,46639],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,47476,47477,47503,47531,47564,47598,47634],{},[123,47478,46671,47479],{},[883,47480,47482],{"className":47481},[886],[888,47483,47484],{"xmlns":890},[892,47485,47486,47500],{},[895,47487,47488,47490,47492,47494,47496,47498],{},[898,47489,2132],{},[1655,47491,1657],{},[1826,47493,39145],{},[1655,47495,2346],{},[1826,47497,1837],{},[898,47499,1824],{},[902,47501,47502],{"encoding":904},"P = 30 + 2Q",[123,47504,46704,47505],{},[883,47506,47508],{"className":47507},[886],[888,47509,47510],{"xmlns":890},[892,47511,47512,47528],{},[895,47513,47514,47516,47518,47520,47522,47524,47526],{},[898,47515,1824],{},[1655,47517,1657],{},[1655,47519,2623],{},[1826,47521,3472],{},[1655,47523,2346],{},[1826,47525,4771],{},[898,47527,2132],{},[902,47529,47530],{"encoding":904},"Q = -3 + 12P",[123,47532,46735,47533],{},[883,47534,47536],{"className":47535},[886],[888,47537,47538],{"xmlns":890},[892,47539,47540,47562],{},[895,47541,47542,47544,47546,47552,47554,47556,47558,47560],{},[898,47543,2132],{},[1655,47545,1657],{},[2597,47547,47548,47550],{},[898,47549,1824],{},[1826,47551,1837],{},[1655,47553,2346],{},[1826,47555,24072],{},[898,47557,1824],{},[1655,47559,2346],{},[1826,47561,33672],{},[902,47563,42848],{"encoding":904},[123,47565,46770,47566],{},[883,47567,47569],{"className":47568},[886],[888,47570,47571],{"xmlns":890},[892,47572,47573,47595],{},[895,47574,47575,47577,47579,47585,47587,47589,47591,47593],{},[898,47576,2132],{},[1655,47578,1657],{},[2597,47580,47581,47583],{},[898,47582,1824],{},[1826,47584,1837],{},[1655,47586,2346],{},[1826,47588,1837],{},[898,47590,1824],{},[1655,47592,2346],{},[1826,47594,4771],{},[902,47596,47597],{"encoding":904},"P = Q^2 + 2Q + 12",[123,47599,46801,47600],{},[883,47601,47603],{"className":47602},[886],[888,47604,47605],{"xmlns":890},[892,47606,47607,47631],{},[895,47608,47609,47611,47613,47615,47617,47619,47621,47623,47625],{},[898,47610,1824],{},[1655,47612,1657],{},[1826,47614,10050],{},[1655,47616,2346],{},[1826,47618,3524],{},[898,47620,2132],{},[1655,47622,2346],{},[1826,47624,4068],{},[2597,47626,47627,47629],{},[898,47628,2132],{},[1826,47630,1837],{},[902,47632,47633],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,47635,46836,47636],{},[883,47637,47639],{"className":47638},[886],[888,47640,47641],{"xmlns":890},[892,47642,47643,47668],{},[895,47644,47645,47647,47649,47651,47653,47655,47657,47659,47662],{},[898,47646,1824],{},[1655,47648,1657],{},[1826,47650,25327],{},[1655,47652,2346],{},[1826,47654,4068],{},[898,47656,2132],{},[1655,47658,2346],{},[1826,47660,47661],{},"0,004",[2597,47663,47664,47666],{},[898,47665,2132],{},[1826,47667,1837],{},[902,47669,47670],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,47672,47673,47676],{},[38,47674,47675],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,47678,47679,47682,47685,47688],{},[123,47680,47681],{},"(a) Sníží ceny surovin — vstupů.",[123,47683,47684],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,47686,47687],{},"(c) Zvýší ceny všech energií.",[123,47689,47690],{},"(d) Sníží daňové odvody státu.",[724,47692,47693,47392,47695,47729,47730,47758],{},[38,47694,44075],{},[883,47696,47698],{"className":47697},[886],[888,47699,47700],{"xmlns":890},[892,47701,47702,47726],{},[895,47703,47704,47706,47708,47710,47712,47714,47716,47718,47720,47722,47724],{},[898,47705,2132],{},[1655,47707,1657],{},[898,47709,9920],{},[1655,47711,1664],{"stretchy":1663},[898,47713,1824],{},[1655,47715,1677],{"stretchy":1663},[1655,47717,1657],{},[1826,47719,6258],{},[898,47721,1824],{},[1655,47723,2346],{},[1826,47725,37370],{},[902,47727,47728],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,47731,47733],{"className":47732},[886],[888,47734,47735],{"xmlns":890},[892,47736,47737,47755],{},[895,47738,47739,47741,47743,47749,47751,47753],{},[898,47740,2132],{},[1655,47742,1657],{},[2597,47744,47745,47747],{},[898,47746,9920],{},[1655,47748,5603],{},[1655,47750,1664],{"stretchy":1663},[898,47752,1824],{},[1655,47754,1677],{"stretchy":1663},[902,47756,47757],{"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.",[198,47760,42451],{"id":47761},"tržní-rovnováha-1",[724,47763,47764,47766,47767,47784,47785,2086],{},[38,47765,44135],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,47768,47770],{"className":47769},[886],[888,47771,47772],{"xmlns":890},[892,47773,47774,47782],{},[895,47775,47776],{},[2597,47777,47778,47780],{},[898,47779,1824],{},[898,47781,5502],{},[902,47783,43529],{"encoding":904}," a rovnovážnou cenu ",[883,47786,47788],{"className":47787},[886],[888,47789,47790],{"xmlns":890},[892,47791,47792,47800],{},[895,47793,47794],{},[2597,47795,47796,47798],{},[898,47797,2132],{},[898,47799,5502],{},[902,47801,42592],{"encoding":904},[120,47803,47804,47857,47908,47967],{},[123,47805,46671,47806,1343,47833,1719],{},[883,47807,47809],{"className":47808},[886],[888,47810,47811],{"xmlns":890},[892,47812,47813,47830],{},[895,47814,47815,47817,47819,47821,47823,47825,47827],{},[898,47816,2132],{},[1655,47818,1657],{},[1655,47820,2623],{},[1826,47822,3524],{},[898,47824,1824],{},[1655,47826,2346],{},[1826,47828,47829],{},"80",[902,47831,47832],{"encoding":904},"P = -5Q + 80",[883,47834,47836],{"className":47835},[886],[888,47837,47838],{"xmlns":890},[892,47839,47840,47854],{},[895,47841,47842,47844,47846,47848,47850,47852],{},[898,47843,2132],{},[1655,47845,1657],{},[1826,47847,1837],{},[898,47849,1824],{},[1655,47851,2346],{},[1826,47853,4136],{},[902,47855,47856],{"encoding":904},"P = 2Q + 10",[123,47858,46704,47859,1343,47885,1719],{},[883,47860,47862],{"className":47861},[886],[888,47863,47864],{"xmlns":890},[892,47865,47866,47882],{},[895,47867,47868,47870,47872,47874,47876,47878,47880],{},[898,47869,1824],{},[1655,47871,1657],{},[1655,47873,2623],{},[1826,47875,6258],{},[898,47877,2132],{},[1655,47879,2346],{},[1826,47881,6253],{},[902,47883,47884],{"encoding":904},"Q = -0{,}5P + 25",[883,47886,47888],{"className":47887},[886],[888,47889,47890],{"xmlns":890},[892,47891,47892,47906],{},[895,47893,47894,47896,47898,47900,47902,47904],{},[898,47895,1824],{},[1655,47897,1657],{},[1826,47899,1837],{},[898,47901,2132],{},[1655,47903,2623],{},[1826,47905,4390],{},[902,47907,41973],{"encoding":904},[123,47909,46735,47910,1343,47936,1719],{},[883,47911,47913],{"className":47912},[886],[888,47914,47915],{"xmlns":890},[892,47916,47917,47933],{},[895,47918,47919,47921,47923,47925,47927,47929,47931],{},[898,47920,2132],{},[1655,47922,1657],{},[1655,47924,2623],{},[1826,47926,3639],{},[898,47928,1824],{},[1655,47930,2346],{},[1826,47932,5297],{},[902,47934,47935],{"encoding":904},"P = -4Q + 120",[883,47937,47939],{"className":47938},[886],[888,47940,47941],{"xmlns":890},[892,47942,47943,47964],{},[895,47944,47945,47947,47949,47957,47959,47961],{},[898,47946,2132],{},[1655,47948,1657],{},[3615,47950,47951],{"scriptlevel":2552,"displaystyle":1663},[1949,47952,47953,47955],{},[1826,47954,1828],{},[1826,47956,3472],{},[898,47958,1824],{},[1655,47960,2346],{},[1826,47962,47963],{},"29",[902,47965,47966],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,47968,46770,47969,1343,47998,1719],{},[883,47970,47972],{"className":47971},[886],[888,47973,47974],{"xmlns":890},[892,47975,47976,47995],{},[895,47977,47978,47980,47982,47984,47990,47992],{},[898,47979,2132],{},[1655,47981,1657],{},[1655,47983,2623],{},[2597,47985,47986,47988],{},[898,47987,1824],{},[1826,47989,1837],{},[1655,47991,2346],{},[1826,47993,47994],{},"52",[902,47996,47997],{"encoding":904},"P = -Q^2 + 52",[883,47999,48001],{"className":48000},[886],[888,48002,48003],{"xmlns":890},[892,48004,48005,48023],{},[895,48006,48007,48009,48011,48013,48019,48021],{},[898,48008,2132],{},[1655,48010,1657],{},[1826,48012,1837],{},[2597,48014,48015,48017],{},[898,48016,1824],{},[1826,48018,1837],{},[1655,48020,2346],{},[1826,48022,4136],{},[902,48024,48025],{"encoding":904},"P = 2Q^2 + 10",[724,48027,48028,48031,48032,48062,48063,48093],{},[38,48029,48030],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,48033,48035],{"className":48034},[886],[888,48036,48037],{"xmlns":890},[892,48038,48039,48059],{},[895,48040,48041,48049,48051],{},[1935,48042,48043,48045,48047],{},[898,48044,1824],{},[1826,48046,1828],{},[898,48048,5502],{},[1655,48050,1671],{"separator":1670},[1935,48052,48053,48055,48057],{},[898,48054,1824],{},[1826,48056,1837],{},[898,48058,5502],{},[902,48060,48061],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,48064,48066],{"className":48065},[886],[888,48067,48068],{"xmlns":890},[892,48069,48070,48090],{},[895,48071,48072,48080,48082],{},[1935,48073,48074,48076,48078],{},[898,48075,2132],{},[1826,48077,1828],{},[898,48079,5502],{},[1655,48081,1671],{"separator":1670},[1935,48083,48084,48086,48088],{},[898,48085,2132],{},[1826,48087,1837],{},[898,48089,5502],{},[902,48091,48092],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,48095,48096,48248],{},[123,48097,46671,48098,1343,48138,1343,48180,1343,48214,1719],{},[883,48099,48101],{"className":48100},[886],[888,48102,48103],{"xmlns":890},[892,48104,48105,48135],{},[895,48106,48107,48113,48115,48117,48119,48121,48127,48129],{},[1820,48108,48109,48111],{},[898,48110,1824],{},[1826,48112,1828],{},[1655,48114,1657],{},[1826,48116,4136],{},[1655,48118,2623],{},[1826,48120,1837],{},[1820,48122,48123,48125],{},[898,48124,2132],{},[1826,48126,1828],{},[1655,48128,2346],{},[1820,48130,48131,48133],{},[898,48132,2132],{},[1826,48134,1837],{},[902,48136,48137],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,48139,48141],{"className":48140},[886],[888,48142,48143],{"xmlns":890},[892,48144,48145,48177],{},[895,48146,48147,48153,48155,48157,48159,48161,48167,48169,48171],{},[1820,48148,48149,48151],{},[898,48150,1824],{},[1826,48152,1837],{},[1655,48154,1657],{},[1826,48156,3524],{},[1655,48158,2346],{},[1826,48160,1837],{},[1820,48162,48163,48165],{},[898,48164,2132],{},[1826,48166,1828],{},[1655,48168,2623],{},[1826,48170,1837],{},[1820,48172,48173,48175],{},[898,48174,2132],{},[1826,48176,1837],{},[902,48178,48179],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,48181,48183],{"className":48182},[886],[888,48184,48185],{"xmlns":890},[892,48186,48187,48211],{},[895,48188,48189,48195,48197,48199,48201,48203,48205],{},[1820,48190,48191,48193],{},[898,48192,1824],{},[1826,48194,1828],{},[1655,48196,1657],{},[1655,48198,2623],{},[1826,48200,3472],{},[1655,48202,2346],{},[1826,48204,1837],{},[1820,48206,48207,48209],{},[898,48208,2132],{},[1826,48210,1828],{},[902,48212,48213],{"encoding":904},"Q_1 = -3 + 2P_1",[883,48215,48217],{"className":48216},[886],[888,48218,48219],{"xmlns":890},[892,48220,48221,48245],{},[895,48222,48223,48229,48231,48233,48235,48237,48239],{},[1820,48224,48225,48227],{},[898,48226,1824],{},[1826,48228,1837],{},[1655,48230,1657],{},[1655,48232,2623],{},[1826,48234,1837],{},[1655,48236,2346],{},[1826,48238,3472],{},[1820,48240,48241,48243],{},[898,48242,2132],{},[1826,48244,1837],{},[902,48246,48247],{"encoding":904},"Q_2 = -2 + 3P_2",[123,48249,46704,48250,1343,48290,1343,48332,1343,48364,1719],{},[883,48251,48253],{"className":48252},[886],[888,48254,48255],{"xmlns":890},[892,48256,48257,48287],{},[895,48258,48259,48265,48267,48269,48271,48273,48279,48281],{},[1820,48260,48261,48263],{},[898,48262,1824],{},[1826,48264,1828],{},[1655,48266,1657],{},[1826,48268,4360],{},[1655,48270,2623],{},[1826,48272,1837],{},[1820,48274,48275,48277],{},[898,48276,2132],{},[1826,48278,1828],{},[1655,48280,2346],{},[1820,48282,48283,48285],{},[898,48284,2132],{},[1826,48286,1837],{},[902,48288,48289],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,48291,48293],{"className":48292},[886],[888,48294,48295],{"xmlns":890},[892,48296,48297,48329],{},[895,48298,48299,48305,48307,48309,48311,48313,48319,48321,48323],{},[1820,48300,48301,48303],{},[898,48302,1824],{},[1826,48304,1837],{},[1655,48306,1657],{},[1826,48308,3524],{},[1655,48310,2346],{},[1826,48312,1837],{},[1820,48314,48315,48317],{},[898,48316,2132],{},[1826,48318,1828],{},[1655,48320,2623],{},[1826,48322,3472],{},[1820,48324,48325,48327],{},[898,48326,2132],{},[1826,48328,1837],{},[902,48330,48331],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,48333,48335],{"className":48334},[886],[888,48336,48337],{"xmlns":890},[892,48338,48339,48361],{},[895,48340,48341,48347,48349,48351,48353,48355],{},[1820,48342,48343,48345],{},[898,48344,1824],{},[1826,48346,1828],{},[1655,48348,1657],{},[1655,48350,2623],{},[1826,48352,4136],{},[1655,48354,2346],{},[1820,48356,48357,48359],{},[898,48358,2132],{},[1826,48360,1828],{},[902,48362,48363],{"encoding":904},"Q_1 = -10 + P_1",[883,48365,48367],{"className":48366},[886],[888,48368,48369],{"xmlns":890},[892,48370,48371,48393],{},[895,48372,48373,48379,48381,48383,48385,48387],{},[1820,48374,48375,48377],{},[898,48376,1824],{},[1826,48378,1837],{},[1655,48380,1657],{},[1826,48382,3524],{},[1655,48384,2346],{},[1826,48386,3531],{},[1820,48388,48389,48391],{},[898,48390,2132],{},[1826,48392,1837],{},[902,48394,48395],{"encoding":904},"Q_2 = 5 + 6P_2",[724,48397,48398,48401,48402,1343,48450,1343,48496,48546,48547,1343,48579,1343,48613,22720,48647,2704,48665,48683,48684,48697,48698,48724,48725,48062,48765,1719],{},[38,48399,48400],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,48403,48405],{"className":48404},[886],[888,48406,48407],{"xmlns":890},[892,48408,48409,48447],{},[895,48410,48411,48417,48419,48421,48423,48429,48431,48433,48439,48441],{},[1820,48412,48413,48415],{},[898,48414,1824],{},[1826,48416,1828],{},[1655,48418,1657],{},[1826,48420,37370],{},[1655,48422,2623],{},[1820,48424,48425,48427],{},[898,48426,2132],{},[1826,48428,1828],{},[1655,48430,2346],{},[1826,48432,1837],{},[1820,48434,48435,48437],{},[898,48436,2132],{},[1826,48438,1837],{},[1655,48440,2346],{},[1820,48442,48443,48445],{},[898,48444,2132],{},[1826,48446,3472],{},[902,48448,48449],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,48451,48453],{"className":48452},[886],[888,48454,48455],{"xmlns":890},[892,48456,48457,48493],{},[895,48458,48459,48465,48467,48469,48471,48477,48479,48485,48487],{},[1820,48460,48461,48463],{},[898,48462,1824],{},[1826,48464,1837],{},[1655,48466,1657],{},[1826,48468,5250],{},[1655,48470,2346],{},[1820,48472,48473,48475],{},[898,48474,2132],{},[1826,48476,1828],{},[1655,48478,2623],{},[1820,48480,48481,48483],{},[898,48482,2132],{},[1826,48484,1837],{},[1655,48486,2623],{},[1820,48488,48489,48491],{},[898,48490,2132],{},[1826,48492,3472],{},[902,48494,48495],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,48497,48499],{"className":48498},[886],[888,48500,48501],{"xmlns":890},[892,48502,48503,48543],{},[895,48504,48505,48511,48513,48515,48517,48519,48525,48527,48533,48535,48537],{},[1820,48506,48507,48509],{},[898,48508,1824],{},[1826,48510,3472],{},[1655,48512,1657],{},[1826,48514,6834],{},[1655,48516,2346],{},[1826,48518,1837],{},[1820,48520,48521,48523],{},[898,48522,2132],{},[1826,48524,1828],{},[1655,48526,2623],{},[1820,48528,48529,48531],{},[898,48530,2132],{},[1826,48532,1837],{},[1655,48534,2623],{},[1826,48536,3639],{},[1820,48538,48539,48541],{},[898,48540,2132],{},[1826,48542,3472],{},[902,48544,48545],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,48548,48550],{"className":48549},[886],[888,48551,48552],{"xmlns":890},[892,48553,48554,48576],{},[895,48555,48556,48562,48564,48566,48568,48570],{},[1820,48557,48558,48560],{},[898,48559,1824],{},[1826,48561,1828],{},[1655,48563,1657],{},[1655,48565,2623],{},[1826,48567,25327],{},[1655,48569,2346],{},[1820,48571,48572,48574],{},[898,48573,2132],{},[1826,48575,1828],{},[902,48577,48578],{"encoding":904},"Q_1 = -7 + P_1",[883,48580,48582],{"className":48581},[886],[888,48583,48584],{"xmlns":890},[892,48585,48586,48610],{},[895,48587,48588,48594,48596,48598,48600,48602,48604],{},[1820,48589,48590,48592],{},[898,48591,1824],{},[1826,48593,1837],{},[1655,48595,1657],{},[1655,48597,2623],{},[1826,48599,3639],{},[1655,48601,2346],{},[1826,48603,3639],{},[1820,48605,48606,48608],{},[898,48607,2132],{},[1826,48609,1837],{},[902,48611,48612],{"encoding":904},"Q_2 = -4 + 4P_2",[883,48614,48616],{"className":48615},[886],[888,48617,48618],{"xmlns":890},[892,48619,48620,48644],{},[895,48621,48622,48628,48630,48632,48634,48636,48638],{},[1820,48623,48624,48626],{},[898,48625,1824],{},[1826,48627,3472],{},[1655,48629,1657],{},[1655,48631,2623],{},[1826,48633,3524],{},[1655,48635,2346],{},[1826,48637,1837],{},[1820,48639,48640,48642],{},[898,48641,2132],{},[1826,48643,3472],{},[902,48645,48646],{"encoding":904},"Q_3 = -5 + 2P_3",[883,48648,48650],{"className":48649},[886],[888,48651,48652],{"xmlns":890},[892,48653,48654,48662],{},[895,48655,48656],{},[1820,48657,48658,48660],{},[898,48659,1824],{},[898,48661,18916],{},[902,48663,48664],{"encoding":904},"Q_i",[883,48666,48668],{"className":48667},[886],[888,48669,48670],{"xmlns":890},[892,48671,48672,48680],{},[895,48673,48674],{},[1820,48675,48676,48678],{},[898,48677,2132],{},[898,48679,18916],{},[902,48681,48682],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,48685,48687],{"className":48686},[886],[888,48688,48689],{"xmlns":890},[892,48690,48691,48695],{},[895,48692,48693],{},[898,48694,18916],{},[902,48696,18916],{"encoding":904},"-tého zboží, ",[883,48699,48701],{"className":48700},[886],[888,48702,48703],{"xmlns":890},[892,48704,48705,48721],{},[895,48706,48707,48709,48711,48713,48715,48717,48719],{},[898,48708,18916],{},[1655,48710,1657],{},[1826,48712,1828],{},[1655,48714,1671],{"separator":1670},[1826,48716,1837],{},[1655,48718,1671],{"separator":1670},[1826,48720,3472],{},[902,48722,48723],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,48726,48728],{"className":48727},[886],[888,48729,48730],{"xmlns":890},[892,48731,48732,48762],{},[895,48733,48734,48742,48744,48752,48754],{},[1935,48735,48736,48738,48740],{},[898,48737,1824],{},[1826,48739,1828],{},[898,48741,5502],{},[1655,48743,1671],{"separator":1670},[1935,48745,48746,48748,48750],{},[898,48747,1824],{},[1826,48749,1837],{},[898,48751,5502],{},[1655,48753,1671],{"separator":1670},[1935,48755,48756,48758,48760],{},[898,48757,1824],{},[1826,48759,3472],{},[898,48761,5502],{},[902,48763,48764],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,48766,48768],{"className":48767},[886],[888,48769,48770],{"xmlns":890},[892,48771,48772,48802],{},[895,48773,48774,48782,48784,48792,48794],{},[1935,48775,48776,48778,48780],{},[898,48777,2132],{},[1826,48779,1828],{},[898,48781,5502],{},[1655,48783,1671],{"separator":1670},[1935,48785,48786,48788,48790],{},[898,48787,2132],{},[1826,48789,1837],{},[898,48791,5502],{},[1655,48793,1671],{"separator":1670},[1935,48795,48796,48798,48800],{},[898,48797,2132],{},[1826,48799,3472],{},[898,48801,5502],{},[902,48803,48804],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,48806,48807,48810,48811,48847,48848,1719],{},[38,48808,48809],{},"2.13"," Jsou dány poptávka ",[883,48812,48814],{"className":48813},[886],[888,48815,48816],{"xmlns":890},[892,48817,48818,48844],{},[895,48819,48820,48822,48824,48826,48828,48830,48832,48834,48836,48838,48840,48842],{},[898,48821,2132],{},[1655,48823,1657],{},[898,48825,2838],{},[1655,48827,1664],{"stretchy":1663},[898,48829,1824],{},[1655,48831,1677],{"stretchy":1663},[1655,48833,1657],{},[1655,48835,2623],{},[1826,48837,3639],{},[898,48839,1824],{},[1655,48841,2346],{},[1826,48843,47829],{},[902,48845,48846],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,48849,48851],{"className":48850},[886],[888,48852,48853],{"xmlns":890},[892,48854,48855,48879],{},[895,48856,48857,48859,48861,48863,48865,48867,48869,48871,48873,48875,48877],{},[898,48858,2132],{},[1655,48860,1657],{},[898,48862,9920],{},[1655,48864,1664],{"stretchy":1663},[898,48866,1824],{},[1655,48868,1677],{"stretchy":1663},[1655,48870,1657],{},[1826,48872,3472],{},[898,48874,1824],{},[1655,48876,2346],{},[1826,48878,4136],{},[902,48880,48881],{"encoding":904},"P = S(Q) = 3Q + 10",[120,48883,48884,48921,48985,49045],{},[123,48885,48886,48887,47784,48904,1719],{},"(a) Určete rovnovážné množství ",[883,48888,48890],{"className":48889},[886],[888,48891,48892],{"xmlns":890},[892,48893,48894,48902],{},[895,48895,48896],{},[2597,48897,48898,48900],{},[898,48899,1824],{},[898,48901,5502],{},[902,48903,43529],{"encoding":904},[883,48905,48907],{"className":48906},[886],[888,48908,48909],{"xmlns":890},[892,48910,48911,48919],{},[895,48912,48913],{},[2597,48914,48915,48917],{},[898,48916,2132],{},[898,48918,5502],{},[902,48920,42592],{"encoding":904},[123,48922,48923,48924,48942,48943,48963,48964,48984],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,48925,48927],{"className":48926},[886],[888,48928,48929],{"xmlns":890},[892,48930,48931,48939],{},[895,48932,48933,48935,48937],{},[898,48934,4049],{},[1655,48936,1657],{},[1826,48938,25327],{},[902,48940,48941],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,48944,48946],{"className":48945},[886],[888,48947,48948],{"xmlns":890},[892,48949,48950,48960],{},[895,48951,48952],{},[1935,48953,48954,48956,48958],{},[898,48955,1824],{},[1826,48957,1828],{},[898,48959,5502],{},[902,48961,48962],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,48965,48967],{"className":48966},[886],[888,48968,48969],{"xmlns":890},[892,48970,48971,48981],{},[895,48972,48973],{},[1935,48974,48975,48977,48979],{},[898,48976,2132],{},[1826,48978,1828],{},[898,48980,5502],{},[902,48982,48983],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,48986,48987,48988,48942,49005,48963,49025,48984],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,48989,48991],{"className":48990},[886],[888,48992,48993],{"xmlns":890},[892,48994,48995,49003],{},[895,48996,48997,48999,49001],{},[898,48998,4049],{},[1655,49000,1657],{},[1826,49002,25327],{},[902,49004,48941],{"encoding":904},[883,49006,49008],{"className":49007},[886],[888,49009,49010],{"xmlns":890},[892,49011,49012,49022],{},[895,49013,49014],{},[1935,49015,49016,49018,49020],{},[898,49017,1824],{},[1826,49019,1837],{},[898,49021,5502],{},[902,49023,49024],{"encoding":904},"Q_2^E",[883,49026,49028],{"className":49027},[886],[888,49029,49030],{"xmlns":890},[892,49031,49032,49042],{},[895,49033,49034],{},[1935,49035,49036,49038,49040],{},[898,49037,2132],{},[1826,49039,1837],{},[898,49041,5502],{},[902,49043,49044],{"encoding":904},"P_2^E",[123,49046,49047],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,49049,49050,49051,1719],{},"Viz též ",[207,49052,43847],{"className":49053,"dataFsResolvedFilePath":809,"href":810},[210],[198,49055,44149],{"id":49056},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,49058,49059,48810,49062,48847,49098,1719],{},[38,49060,49061],{},"2.14",[883,49063,49065],{"className":49064},[886],[888,49066,49067],{"xmlns":890},[892,49068,49069,49095],{},[895,49070,49071,49073,49075,49077,49079,49081,49083,49085,49087,49089,49091,49093],{},[898,49072,2132],{},[1655,49074,1657],{},[898,49076,207],{},[898,49078,1824],{},[1655,49080,2346],{},[898,49082,2025],{},[1655,49084,1657],{},[1655,49086,2623],{},[1826,49088,1837],{},[898,49090,1824],{},[1655,49092,2346],{},[1826,49094,4390],{},[902,49096,49097],{"encoding":904},"P = aQ + b = -2Q + 50",[883,49099,49101],{"className":49100},[886],[888,49102,49103],{"xmlns":890},[892,49104,49105,49129],{},[895,49106,49107,49109,49111,49113,49115,49117,49119,49121,49123,49125,49127],{},[898,49108,2132],{},[1655,49110,1657],{},[898,49112,1789],{},[898,49114,1824],{},[1655,49116,2346],{},[898,49118,2410],{},[1655,49120,1657],{},[1826,49122,20447],{},[898,49124,1824],{},[1655,49126,2346],{},[1826,49128,10282],{},[902,49130,49131],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,49133,49134,49170,49173,49259,49312,49392,49446],{},[123,49135,48886,49136,47784,49153,1719],{},[883,49137,49139],{"className":49138},[886],[888,49140,49141],{"xmlns":890},[892,49142,49143,49151],{},[895,49144,49145],{},[2597,49146,49147,49149],{},[898,49148,1824],{},[898,49150,5502],{},[902,49152,43529],{"encoding":904},[883,49154,49156],{"className":49155},[886],[888,49157,49158],{"xmlns":890},[892,49159,49160,49168],{},[895,49161,49162],{},[2597,49163,49164,49166],{},[898,49165,2132],{},[898,49167,5502],{},[902,49169,42592],{"encoding":904},[123,49171,49172],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,49174,49175,49176,49193,49194,3948,49207,3962,49223,49239,49240,1719],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,49177,49179],{"className":49178},[886],[888,49180,49181],{"xmlns":890},[892,49182,49183,49191],{},[895,49184,49185],{},[2597,49186,49187,49189],{},[898,49188,1824],{},[898,49190,5502],{},[902,49192,43529],{"encoding":904}," odpovídající změně ",[883,49195,49197],{"className":49196},[886],[888,49198,49199],{"xmlns":890},[892,49200,49201,49205],{},[895,49202,49203],{},[898,49204,207],{},[902,49206,207],{"encoding":904},[883,49208,49210],{"className":49209},[886],[888,49211,49212],{"xmlns":890},[892,49213,49214,49220],{},[895,49215,49216,49218],{},[1655,49217,2623],{},[1826,49219,1837],{},[902,49221,49222],{"encoding":904},"-2",[883,49224,49226],{"className":49225},[886],[888,49227,49228],{"xmlns":890},[892,49229,49230,49236],{},[895,49231,49232,49234],{},[1655,49233,2623],{},[1826,49235,3472],{},[902,49237,49238],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49241,49243],{"className":49242},[886],[888,49244,49245],{"xmlns":890},[892,49246,49247,49257],{},[895,49248,49249],{},[1935,49250,49251,49253,49255],{},[898,49252,1824],{},[1826,49254,1828],{},[898,49256,5502],{},[902,49258,48962],{"encoding":904},[123,49260,49261,49262,49193,49279,49292,49293,1719],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,49263,49265],{"className":49264},[886],[888,49266,49267],{"xmlns":890},[892,49268,49269,49277],{},[895,49270,49271],{},[2597,49272,49273,49275],{},[898,49274,1824],{},[898,49276,5502],{},[902,49278,43529],{"encoding":904},[883,49280,49282],{"className":49281},[886],[888,49283,49284],{"xmlns":890},[892,49285,49286,49290],{},[895,49287,49288],{},[898,49289,2025],{},[902,49291,2025],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49294,49296],{"className":49295},[886],[888,49297,49298],{"xmlns":890},[892,49299,49300,49310],{},[895,49301,49302],{},[1935,49303,49304,49306,49308],{},[898,49305,1824],{},[1826,49307,1837],{},[898,49309,5502],{},[902,49311,49024],{"encoding":904},[123,49313,49314,49315,49193,49332,3948,49345,3962,49358,49239,49372,1719],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,49316,49318],{"className":49317},[886],[888,49319,49320],{"xmlns":890},[892,49321,49322,49330],{},[895,49323,49324],{},[2597,49325,49326,49328],{},[898,49327,1824],{},[898,49329,5502],{},[902,49331,43529],{"encoding":904},[883,49333,49335],{"className":49334},[886],[888,49336,49337],{"xmlns":890},[892,49338,49339,49343],{},[895,49340,49341],{},[898,49342,1789],{},[902,49344,1789],{"encoding":904},[883,49346,49348],{"className":49347},[886],[888,49349,49350],{"xmlns":890},[892,49351,49352,49356],{},[895,49353,49354],{},[1826,49355,20447],{},[902,49357,45586],{"encoding":904},[883,49359,49361],{"className":49360},[886],[888,49362,49363],{"xmlns":890},[892,49364,49365,49369],{},[895,49366,49367],{},[1826,49368,15714],{},[902,49370,49371],{"encoding":904},"0{,}8",[883,49373,49375],{"className":49374},[886],[888,49376,49377],{"xmlns":890},[892,49378,49379,49389],{},[895,49380,49381],{},[1935,49382,49383,49385,49387],{},[898,49384,1824],{},[1826,49386,3472],{},[898,49388,5502],{},[902,49390,49391],{"encoding":904},"Q_3^E",[123,49393,49394,49395,49193,49412,49425,49426,1719],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,49396,49398],{"className":49397},[886],[888,49399,49400],{"xmlns":890},[892,49401,49402,49410],{},[895,49403,49404],{},[2597,49405,49406,49408],{},[898,49407,1824],{},[898,49409,5502],{},[902,49411,43529],{"encoding":904},[883,49413,49415],{"className":49414},[886],[888,49416,49417],{"xmlns":890},[892,49418,49419,49423],{},[895,49420,49421],{},[898,49422,2410],{},[902,49424,2410],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49427,49429],{"className":49428},[886],[888,49430,49431],{"xmlns":890},[892,49432,49433,49443],{},[895,49434,49435],{},[1935,49436,49437,49439,49441],{},[898,49438,1824],{},[1826,49440,3639],{},[898,49442,5502],{},[902,49444,49445],{"encoding":904},"Q_4^E",[123,49447,49448,49449,49466,49467,49480,49481,22546,49494,1343,49509,22546,49522,2704,49536,22546,49549,49564,49565,1719],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,49450,49452],{"className":49451},[886],[888,49453,49454],{"xmlns":890},[892,49455,49456,49464],{},[895,49457,49458],{},[2597,49459,49460,49462],{},[898,49461,1824],{},[898,49463,5502],{},[902,49465,43529],{"encoding":904}," odpovídající změnám ",[883,49468,49470],{"className":49469},[886],[888,49471,49472],{"xmlns":890},[892,49473,49474,49478],{},[895,49475,49476],{},[898,49477,207],{},[902,49479,207],{"encoding":904}," o 1, ",[883,49482,49484],{"className":49483},[886],[888,49485,49486],{"xmlns":890},[892,49487,49488,49492],{},[895,49489,49490],{},[898,49491,2025],{},[902,49493,2025],{"encoding":904},[883,49495,49497],{"className":49496},[886],[888,49498,49499],{"xmlns":890},[892,49500,49501,49507],{},[895,49502,49503,49505],{},[1655,49504,2623],{},[1826,49506,4136],{},[902,49508,20581],{"encoding":904},[883,49510,49512],{"className":49511},[886],[888,49513,49514],{"xmlns":890},[892,49515,49516,49520],{},[895,49517,49518],{},[898,49519,1789],{},[902,49521,1789],{"encoding":904},[883,49523,49525],{"className":49524},[886],[888,49526,49527],{"xmlns":890},[892,49528,49529,49533],{},[895,49530,49531],{},[1826,49532,4068],{},[902,49534,49535],{"encoding":904},"0{,}1",[883,49537,49539],{"className":49538},[886],[888,49540,49541],{"xmlns":890},[892,49542,49543,49547],{},[895,49544,49545],{},[898,49546,2410],{},[902,49548,2410],{"encoding":904},[883,49550,49552],{"className":49551},[886],[888,49553,49554],{"xmlns":890},[892,49555,49556,49562],{},[895,49557,49558,49560],{},[1655,49559,2623],{},[1826,49561,4136],{},[902,49563,20581],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,49566,49568],{"className":49567},[886],[888,49569,49570],{"xmlns":890},[892,49571,49572,49582],{},[895,49573,49574],{},[1935,49575,49576,49578,49580],{},[898,49577,1824],{},[1826,49579,3524],{},[898,49581,5502],{},[902,49583,49584],{"encoding":904},"Q_5^E",[724,49586,49587,48810,49590,48847,49613,1719],{},[38,49588,49589],{},"2.15",[883,49591,49593],{"className":49592},[886],[888,49594,49595],{"xmlns":890},[892,49596,49597,49611],{},[895,49598,49599,49601,49603,49605,49607,49609],{},[898,49600,2132],{},[1655,49602,1657],{},[898,49604,207],{},[898,49606,1824],{},[1655,49608,2346],{},[898,49610,2025],{},[902,49612,38186],{"encoding":904},[883,49614,49616],{"className":49615},[886],[888,49617,49618],{"xmlns":890},[892,49619,49620,49634],{},[895,49621,49622,49624,49626,49628,49630,49632],{},[898,49623,2132],{},[1655,49625,1657],{},[898,49627,1789],{},[898,49629,1824],{},[1655,49631,2346],{},[898,49633,2410],{},[902,49635,41368],{"encoding":904},[120,49637,49638,49713,49730,49839,49892,49946],{},[123,49639,49640,49641,49654,49655,49680,49681,49712],{},"(a) Odvoďte redukovaný tvar pro ",[883,49642,49644],{"className":49643},[886],[888,49645,49646],{"xmlns":890},[892,49647,49648,49652],{},[895,49649,49650],{},[898,49651,2132],{},[902,49653,2132],{"encoding":904},". Stanovte podmínky pro ",[883,49656,49658],{"className":49657},[886],[888,49659,49660],{"xmlns":890},[892,49661,49662,49678],{},[895,49663,49664,49666,49668,49670,49672,49674,49676],{},[898,49665,207],{},[1655,49667,1671],{"separator":1670},[898,49669,2025],{},[1655,49671,1671],{"separator":1670},[898,49673,1789],{},[1655,49675,1671],{"separator":1670},[898,49677,2410],{},[902,49679,44411],{"encoding":904}," tak, aby rovnovážný bod ",[883,49682,49684],{"className":49683},[886],[888,49685,49686],{"xmlns":890},[892,49687,49688,49710],{},[895,49689,49690,49692,49694,49700,49702,49708],{},[898,49691,5502],{},[1655,49693,2734],{"stretchy":1663},[2597,49695,49696,49698],{},[898,49697,1824],{},[898,49699,5502],{},[1655,49701,1671],{"separator":1670},[2597,49703,49704,49706],{},[898,49705,2132],{},[898,49707,5502],{},[1655,49709,2743],{"stretchy":1663},[902,49711,42493],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,49714,49715,49716,49729],{},"(b) Vypočtěte multiplikátory pro ",[883,49717,49719],{"className":49718},[886],[888,49720,49721],{"xmlns":890},[892,49722,49723,49727],{},[895,49724,49725],{},[898,49726,2132],{},[902,49728,2132],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,49731,49732,49733,1343,49753,1343,49771,1343,49789,49807,49808,49825,49826,1719],{},"(c) Pro hodnoty parametrů ",[883,49734,49736],{"className":49735},[886],[888,49737,49738],{"xmlns":890},[892,49739,49740,49750],{},[895,49741,49742,49744,49746,49748],{},[898,49743,207],{},[1655,49745,1657],{},[1655,49747,2623],{},[1826,49749,1837],{},[902,49751,49752],{"encoding":904},"a = -2",[883,49754,49756],{"className":49755},[886],[888,49757,49758],{"xmlns":890},[892,49759,49760,49768],{},[895,49761,49762,49764,49766],{},[898,49763,2025],{},[1655,49765,1657],{},[1826,49767,6460],{},[902,49769,49770],{"encoding":904},"b = 40",[883,49772,49774],{"className":49773},[886],[888,49775,49776],{"xmlns":890},[892,49777,49778,49786],{},[895,49779,49780,49782,49784],{},[898,49781,1789],{},[1655,49783,1657],{},[1826,49785,6258],{},[902,49787,49788],{"encoding":904},"c = 0{,}5",[883,49790,49792],{"className":49791},[886],[888,49793,49794],{"xmlns":890},[892,49795,49796,49804],{},[895,49797,49798,49800,49802],{},[898,49799,2410],{},[1655,49801,1657],{},[1826,49803,4136],{},[902,49805,49806],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,49809,49811],{"className":49810},[886],[888,49812,49813],{"xmlns":890},[892,49814,49815,49823],{},[895,49816,49817],{},[2597,49818,49819,49821],{},[898,49820,2132],{},[898,49822,5502],{},[902,49824,42592],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,49827,49829],{"className":49828},[886],[888,49830,49831],{"xmlns":890},[892,49832,49833,49837],{},[895,49834,49835],{},[898,49836,2132],{},[902,49838,2132],{"encoding":904},[123,49840,49841,49842,49193,49859,49872,49873,1719],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,49843,49845],{"className":49844},[886],[888,49846,49847],{"xmlns":890},[892,49848,49849,49857],{},[895,49850,49851],{},[2597,49852,49853,49855],{},[898,49854,2132],{},[898,49856,5502],{},[902,49858,42592],{"encoding":904},[883,49860,49862],{"className":49861},[886],[888,49863,49864],{"xmlns":890},[892,49865,49866,49870],{},[895,49867,49868],{},[898,49869,207],{},[902,49871,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,49874,49876],{"className":49875},[886],[888,49877,49878],{"xmlns":890},[892,49879,49880,49890],{},[895,49881,49882],{},[1935,49883,49884,49886,49888],{},[898,49885,2132],{},[1826,49887,1828],{},[898,49889,5502],{},[902,49891,48983],{"encoding":904},[123,49893,49894,49895,49912,49913,49926,49927,1719],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,49896,49898],{"className":49897},[886],[888,49899,49900],{"xmlns":890},[892,49901,49902,49910],{},[895,49903,49904],{},[2597,49905,49906,49908],{},[898,49907,2132],{},[898,49909,5502],{},[902,49911,42592],{"encoding":904}," odpovídající poklesu ",[883,49914,49916],{"className":49915},[886],[888,49917,49918],{"xmlns":890},[892,49919,49920,49924],{},[895,49921,49922],{},[898,49923,207],{},[902,49925,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,49928,49930],{"className":49929},[886],[888,49931,49932],{"xmlns":890},[892,49933,49934,49944],{},[895,49935,49936],{},[1935,49937,49938,49940,49942],{},[898,49939,2132],{},[1826,49941,1837],{},[898,49943,5502],{},[902,49945,49044],{"encoding":904},[123,49947,49948,49949,49466,49966,49979,49980,3962,49993,2704,50008,50021,50022,1719],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,49950,49952],{"className":49951},[886],[888,49953,49954],{"xmlns":890},[892,49955,49956,49964],{},[895,49957,49958],{},[2597,49959,49960,49962],{},[898,49961,2132],{},[898,49963,5502],{},[902,49965,42592],{"encoding":904},[883,49967,49969],{"className":49968},[886],[888,49970,49971],{"xmlns":890},[892,49972,49973,49977],{},[895,49974,49975],{},[898,49976,207],{},[902,49978,207],{"encoding":904}," na 35, ",[883,49981,49983],{"className":49982},[886],[888,49984,49985],{"xmlns":890},[892,49986,49987,49991],{},[895,49988,49989],{},[898,49990,1789],{},[902,49992,1789],{"encoding":904},[883,49994,49996],{"className":49995},[886],[888,49997,49998],{"xmlns":890},[892,49999,50000,50005],{},[895,50001,50002],{},[1826,50003,50004],{},"0,7",[902,50006,50007],{"encoding":904},"0{,}7",[883,50009,50011],{"className":50010},[886],[888,50012,50013],{"xmlns":890},[892,50014,50015,50019],{},[895,50016,50017],{},[898,50018,2410],{},[902,50020,2410],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,50023,50025],{"className":50024},[886],[888,50026,50027],{"xmlns":890},[892,50028,50029,50039],{},[895,50030,50031],{},[1935,50032,50033,50035,50037],{},[898,50034,2132],{},[1826,50036,3472],{},[898,50038,5502],{},[902,50040,50041],{"encoding":904},"P_3^E",[724,50043,50044,48810,50047,48847,50075,22720,50103,2704,50129,1719],{},[38,50045,50046],{},"2.16",[883,50048,50050],{"className":50049},[886],[888,50051,50052],{"xmlns":890},[892,50053,50054,50072],{},[895,50055,50056,50058,50060,50062,50064,50066],{},[898,50057,2132],{},[1655,50059,1657],{},[898,50061,207],{},[1655,50063,2346],{},[898,50065,2025],{},[2597,50067,50068,50070],{},[898,50069,1824],{},[1826,50071,1837],{},[902,50073,50074],{"encoding":904},"P = a + bQ^2",[883,50076,50078],{"className":50077},[886],[888,50079,50080],{"xmlns":890},[892,50081,50082,50100],{},[895,50083,50084,50086,50088,50090,50092,50094],{},[898,50085,2132],{},[1655,50087,1657],{},[898,50089,1789],{},[1655,50091,2346],{},[898,50093,2410],{},[2597,50095,50096,50098],{},[898,50097,1824],{},[1826,50099,1837],{},[902,50101,50102],{"encoding":904},"P = c + dQ^2",[883,50104,50106],{"className":50105},[886],[888,50107,50108],{"xmlns":890},[892,50109,50110,50126],{},[895,50111,50112,50114,50116,50118,50120,50122,50124],{},[898,50113,207],{},[1655,50115,1671],{"separator":1670},[898,50117,1789],{},[1655,50119,1671],{"separator":1670},[898,50121,2410],{},[1655,50123,2969],{},[1826,50125,2552],{},[902,50127,50128],{"encoding":904},"a, c, d > 0",[883,50130,50132],{"className":50131},[886],[888,50133,50134],{"xmlns":890},[892,50135,50136,50144],{},[895,50137,50138,50140,50142],{},[898,50139,2025],{},[1655,50141,3065],{},[1826,50143,2552],{},[902,50145,50146],{"encoding":904},"b \u003C 0",[120,50148,50149,50197,50213,50320,50372,50424,50533,50549,50648,50701],{},[123,50150,49640,50151,50164,50165,50196],{},[883,50152,50154],{"className":50153},[886],[888,50155,50156],{"xmlns":890},[892,50157,50158,50162],{},[895,50159,50160],{},[898,50161,1824],{},[902,50163,1824],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,50166,50168],{"className":50167},[886],[888,50169,50170],{"xmlns":890},[892,50171,50172,50194],{},[895,50173,50174,50176,50178,50184,50186,50192],{},[898,50175,5502],{},[1655,50177,2734],{"stretchy":1663},[2597,50179,50180,50182],{},[898,50181,1824],{},[898,50183,5502],{},[1655,50185,1671],{"separator":1670},[2597,50187,50188,50190],{},[898,50189,2132],{},[898,50191,5502],{},[1655,50193,2743],{"stretchy":1663},[902,50195,42493],{"encoding":904}," patřil do 1. kvadrantu.",[123,50198,49715,50199,50212],{},[883,50200,50202],{"className":50201},[886],[888,50203,50204],{"xmlns":890},[892,50205,50206,50210],{},[895,50207,50208],{},[898,50209,1824],{},[902,50211,1824],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,50214,49732,50215,1343,50233,1343,50253,1343,50271,50289,50290,49825,50307,1719],{},[883,50216,50218],{"className":50217},[886],[888,50219,50220],{"xmlns":890},[892,50221,50222,50230],{},[895,50223,50224,50226,50228],{},[898,50225,207],{},[1655,50227,1657],{},[1826,50229,4360],{},[902,50231,50232],{"encoding":904},"a = 100",[883,50234,50236],{"className":50235},[886],[888,50237,50238],{"xmlns":890},[892,50239,50240,50250],{},[895,50241,50242,50244,50246,50248],{},[898,50243,2025],{},[1655,50245,1657],{},[1655,50247,2623],{},[1826,50249,1828],{},[902,50251,50252],{"encoding":904},"b = -1",[883,50254,50256],{"className":50255},[886],[888,50257,50258],{"xmlns":890},[892,50259,50260,50268],{},[895,50261,50262,50264,50266],{},[898,50263,1789],{},[1655,50265,1657],{},[1826,50267,10282],{},[902,50269,50270],{"encoding":904},"c = 20",[883,50272,50274],{"className":50273},[886],[888,50275,50276],{"xmlns":890},[892,50277,50278,50286],{},[895,50279,50280,50282,50284],{},[898,50281,2410],{},[1655,50283,1657],{},[1826,50285,1828],{},[902,50287,50288],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,50291,50293],{"className":50292},[886],[888,50294,50295],{"xmlns":890},[892,50296,50297,50305],{},[895,50298,50299],{},[2597,50300,50301,50303],{},[898,50302,1824],{},[898,50304,5502],{},[902,50306,43529],{"encoding":904},[883,50308,50310],{"className":50309},[886],[888,50311,50312],{"xmlns":890},[892,50313,50314,50318],{},[895,50315,50316],{},[898,50317,1824],{},[902,50319,1824],{"encoding":904},[123,50321,49261,50322,49193,50339,50352,50353,1719],{},[883,50323,50325],{"className":50324},[886],[888,50326,50327],{"xmlns":890},[892,50328,50329,50337],{},[895,50330,50331],{},[2597,50332,50333,50335],{},[898,50334,1824],{},[898,50336,5502],{},[902,50338,43529],{"encoding":904},[883,50340,50342],{"className":50341},[886],[888,50343,50344],{"xmlns":890},[892,50345,50346,50350],{},[895,50347,50348],{},[898,50349,207],{},[902,50351,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,50354,50356],{"className":50355},[886],[888,50357,50358],{"xmlns":890},[892,50359,50360,50370],{},[895,50361,50362],{},[1935,50363,50364,50366,50368],{},[898,50365,1824],{},[1826,50367,1828],{},[898,50369,5502],{},[902,50371,48962],{"encoding":904},[123,50373,49314,50374,49193,50391,50404,50405,1719],{},[883,50375,50377],{"className":50376},[886],[888,50378,50379],{"xmlns":890},[892,50380,50381,50389],{},[895,50382,50383],{},[2597,50384,50385,50387],{},[898,50386,1824],{},[898,50388,5502],{},[902,50390,43529],{"encoding":904},[883,50392,50394],{"className":50393},[886],[888,50395,50396],{"xmlns":890},[892,50397,50398,50402],{},[895,50399,50400],{},[898,50401,1789],{},[902,50403,1789],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,50406,50408],{"className":50407},[886],[888,50409,50410],{"xmlns":890},[892,50411,50412,50422],{},[895,50413,50414],{},[1935,50415,50416,50418,50420],{},[898,50417,1824],{},[1826,50419,1837],{},[898,50421,5502],{},[902,50423,49024],{"encoding":904},[123,50425,49394,50426,49466,50443,50456,50457,3962,50470,50485,50486,50499,50500,50513,50514,1719],{},[883,50427,50429],{"className":50428},[886],[888,50430,50431],{"xmlns":890},[892,50432,50433,50441],{},[895,50434,50435],{},[2597,50436,50437,50439],{},[898,50438,1824],{},[898,50440,5502],{},[902,50442,43529],{"encoding":904},[883,50444,50446],{"className":50445},[886],[888,50447,50448],{"xmlns":890},[892,50449,50450,50454],{},[895,50451,50452],{},[898,50453,207],{},[902,50455,207],{"encoding":904}," na 110, poklesu ",[883,50458,50460],{"className":50459},[886],[888,50461,50462],{"xmlns":890},[892,50463,50464,50468],{},[895,50465,50466],{},[898,50467,2025],{},[902,50469,2025],{"encoding":904},[883,50471,50473],{"className":50472},[886],[888,50474,50475],{"xmlns":890},[892,50476,50477,50483],{},[895,50478,50479,50481],{},[1655,50480,2623],{},[1826,50482,1837],{},[902,50484,49222],{"encoding":904},", růstu ",[883,50487,50489],{"className":50488},[886],[888,50490,50491],{"xmlns":890},[892,50492,50493,50497],{},[895,50494,50495],{},[898,50496,1789],{},[902,50498,1789],{"encoding":904}," na 25 a růstu ",[883,50501,50503],{"className":50502},[886],[888,50504,50505],{"xmlns":890},[892,50506,50507,50511],{},[895,50508,50509],{},[898,50510,2410],{},[902,50512,2410],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,50515,50517],{"className":50516},[886],[888,50518,50519],{"xmlns":890},[892,50520,50521,50531],{},[895,50522,50523],{},[1935,50524,50525,50527,50529],{},[898,50526,1824],{},[1826,50528,3472],{},[898,50530,5502],{},[902,50532,49391],{"encoding":904},[123,50534,50535,50536,50212],{},"(i) Vypočtěte multiplikátory pro ",[883,50537,50539],{"className":50538},[886],[888,50540,50541],{"xmlns":890},[892,50542,50543,50547],{},[895,50544,50545],{},[898,50546,2132],{},[902,50548,2132],{"encoding":904},[123,50550,50551,50552,49825,50569,50582,50583,49193,50600,3962,50613,50628,50629,1719],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,50553,50555],{"className":50554},[886],[888,50556,50557],{"xmlns":890},[892,50558,50559,50567],{},[895,50560,50561],{},[2597,50562,50563,50565],{},[898,50564,2132],{},[898,50566,5502],{},[902,50568,42592],{"encoding":904},[883,50570,50572],{"className":50571},[886],[888,50573,50574],{"xmlns":890},[892,50575,50576,50580],{},[895,50577,50578],{},[898,50579,2132],{},[902,50581,2132],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,50584,50586],{"className":50585},[886],[888,50587,50588],{"xmlns":890},[892,50589,50590,50598],{},[895,50591,50592],{},[2597,50593,50594,50596],{},[898,50595,2132],{},[898,50597,5502],{},[902,50599,42592],{"encoding":904},[883,50601,50603],{"className":50602},[886],[888,50604,50605],{"xmlns":890},[892,50606,50607,50611],{},[895,50608,50609],{},[898,50610,207],{},[902,50612,207],{"encoding":904},[883,50614,50616],{"className":50615},[886],[888,50617,50618],{"xmlns":890},[892,50619,50620,50626],{},[895,50621,50622,50624],{},[1655,50623,2623],{},[1826,50625,3472],{},[902,50627,49238],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,50630,50632],{"className":50631},[886],[888,50633,50634],{"xmlns":890},[892,50635,50636,50646],{},[895,50637,50638],{},[1935,50639,50640,50642,50644],{},[898,50641,2132],{},[1826,50643,1828],{},[898,50645,5502],{},[902,50647,48983],{"encoding":904},[123,50649,50650,50651,49193,50668,50681,50682,1719],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,50652,50654],{"className":50653},[886],[888,50655,50656],{"xmlns":890},[892,50657,50658,50666],{},[895,50659,50660],{},[2597,50661,50662,50664],{},[898,50663,2132],{},[898,50665,5502],{},[902,50667,42592],{"encoding":904},[883,50669,50671],{"className":50670},[886],[888,50672,50673],{"xmlns":890},[892,50674,50675,50679],{},[895,50676,50677],{},[898,50678,207],{},[902,50680,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,50683,50685],{"className":50684},[886],[888,50686,50687],{"xmlns":890},[892,50688,50689,50699],{},[895,50690,50691],{},[1935,50692,50693,50695,50697],{},[898,50694,2132],{},[1826,50696,1837],{},[898,50698,5502],{},[902,50700,49044],{"encoding":904},[123,50702,50703,50704,49912,50721,50734,50735,3962,50748,50485,50763,50776,50777,50790,50791,1719],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,50705,50707],{"className":50706},[886],[888,50708,50709],{"xmlns":890},[892,50710,50711,50719],{},[895,50712,50713],{},[2597,50714,50715,50717],{},[898,50716,2132],{},[898,50718,5502],{},[902,50720,42592],{"encoding":904},[883,50722,50724],{"className":50723},[886],[888,50725,50726],{"xmlns":890},[892,50727,50728,50732],{},[895,50729,50730],{},[898,50731,207],{},[902,50733,207],{"encoding":904}," na 90, poklesu ",[883,50736,50738],{"className":50737},[886],[888,50739,50740],{"xmlns":890},[892,50741,50742,50746],{},[895,50743,50744],{},[898,50745,2025],{},[902,50747,2025],{"encoding":904},[883,50749,50751],{"className":50750},[886],[888,50752,50753],{"xmlns":890},[892,50754,50755,50761],{},[895,50756,50757,50759],{},[1655,50758,2623],{},[1826,50760,3472],{},[902,50762,49238],{"encoding":904},[883,50764,50766],{"className":50765},[886],[888,50767,50768],{"xmlns":890},[892,50769,50770,50774],{},[895,50771,50772],{},[898,50773,1789],{},[902,50775,1789],{"encoding":904}," na 30 a růstu ",[883,50778,50780],{"className":50779},[886],[888,50781,50782],{"xmlns":890},[892,50783,50784,50788],{},[895,50785,50786],{},[898,50787,2410],{},[902,50789,2410],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,50792,50794],{"className":50793},[886],[888,50795,50796],{"xmlns":890},[892,50797,50798,50808],{},[895,50799,50800],{},[1935,50801,50802,50804,50806],{},[898,50803,2132],{},[1826,50805,3472],{},[898,50807,5502],{},[902,50809,50041],{"encoding":904},[198,50811,820],{"id":50812},"přebytek-spotřebitele-a-výrobce-1",[724,50814,50815,48810,50818,48847,50854,1719],{},[38,50816,50817],{},"2.17",[883,50819,50821],{"className":50820},[886],[888,50822,50823],{"xmlns":890},[892,50824,50825,50851],{},[895,50826,50827,50829,50831,50833,50835,50837,50839,50841,50843,50845],{},[898,50828,2132],{},[1655,50830,1657],{},[898,50832,2838],{},[1655,50834,1664],{"stretchy":1663},[898,50836,1824],{},[1655,50838,1677],{"stretchy":1663},[1655,50840,1657],{},[1826,50842,16163],{},[1655,50844,2623],{},[2597,50846,50847,50849],{},[898,50848,1824],{},[1826,50850,1837],{},[902,50852,50853],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,50855,50857],{"className":50856},[886],[888,50858,50859],{"xmlns":890},[892,50860,50861,50887],{},[895,50862,50863,50865,50867,50869,50871,50873,50875,50877,50879,50881],{},[898,50864,2132],{},[1655,50866,1657],{},[898,50868,9920],{},[1655,50870,1664],{"stretchy":1663},[898,50872,1824],{},[1655,50874,1677],{"stretchy":1663},[1655,50876,1657],{},[1826,50878,3472],{},[1655,50880,2346],{},[2597,50882,50883,50885],{},[898,50884,1824],{},[1826,50886,1837],{},[902,50888,50889],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,50891,50892,50895],{},[123,50893,50894],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,50896,50897],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,50899,50900,48810,50903,48847,50937,1719],{},[38,50901,50902],{},"2.18",[883,50904,50906],{"className":50905},[886],[888,50907,50908],{"xmlns":890},[892,50909,50910,50934],{},[895,50911,50912,50914,50916,50918,50920,50922,50924,50926,50928,50930,50932],{},[898,50913,2132],{},[1655,50915,1657],{},[898,50917,2838],{},[1655,50919,1664],{"stretchy":1663},[898,50921,1824],{},[1655,50923,1677],{"stretchy":1663},[1655,50925,1657],{},[1826,50927,4969],{},[1655,50929,2623],{},[1826,50931,1837],{},[898,50933,1824],{},[902,50935,50936],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,50938,50940],{"className":50939},[886],[888,50941,50942],{"xmlns":890},[892,50943,50944,50970],{},[895,50945,50946,50948,50950,50952,50954,50956,50958,50960,50962,50964],{},[898,50947,2132],{},[1655,50949,1657],{},[898,50951,9920],{},[1655,50953,1664],{"stretchy":1663},[898,50955,1824],{},[1655,50957,1677],{"stretchy":1663},[1655,50959,1657],{},[1826,50961,3472],{},[1655,50963,2346],{},[2597,50965,50966,50968],{},[898,50967,1824],{},[1826,50969,1837],{},[902,50971,50889],{"encoding":904},[120,50973,50974,50994,50997,51000],{},[123,50975,50976,50977,1719],{},"(a) Vypočtěte rovnovážné množství ",[883,50978,50980],{"className":50979},[886],[888,50981,50982],{"xmlns":890},[892,50983,50984,50992],{},[895,50985,50986],{},[2597,50987,50988,50990],{},[898,50989,1824],{},[898,50991,5502],{},[902,50993,43529],{"encoding":904},[123,50995,50996],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,50998,50999],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,51001,51002],{},"(c) Graficky interpretujte.",[38096,51004],{},[115,51006,51008],{"id":51007},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,51010,51011,51014,51017,51020,51023,51026,51029,51032,51035,51038,51041,51044,51047,51050],{},[123,51012,51013],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,51015,51016],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,51018,51019],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,51021,51022],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,51024,51025],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,51027,51028],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,51030,51031],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,51033,51034],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,51036,51037],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,51039,51040],{},"K čemu slouží multiplikátory?",[123,51042,51043],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,51045,51046],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,51048,51049],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,51051,51052],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[38096,51054],{},[115,51056,16845],{"id":16844},[724,51058,51059],{},[38,51060,14286],{},[120,51062,51063,51098,51103,51133,51138,51201,51227,51232,51262,51271,51278,51284],{},[123,51064,51065,2115,51068,19774,51071,3106,51073,1343,51096],{},[38,51066,51067],{},"Poptávané množství",[614,51069,51070],{},"quantity demanded",[38,51072,29128],{},[883,51074,51076],{"className":51075},[886],[888,51077,51078],{"xmlns":890},[892,51079,51080,51094],{},[895,51081,51082,51084,51086,51088,51090,51092],{},[898,51083,1824],{},[1655,51085,1657],{},[898,51087,2838],{},[1655,51089,1664],{"stretchy":1663},[898,51091,2132],{},[1655,51093,1677],{"stretchy":1663},[902,51095,5442],{"encoding":904},[38,51097,38575],{},[123,51099,51100,51102],{},[38,51101,38582],{}," — substituční + důchodový efekt",[123,51104,51105,3106,51108],{},[38,51106,51107],{},"Reálné cenové rozpětí",[883,51109,51111],{"className":51110},[886],[888,51112,51113],{"xmlns":890},[892,51114,51115,51131],{},[895,51116,51117,51119,51121,51123,51129],{},[1655,51118,1664],{"stretchy":1663},[1826,51120,2552],{},[1655,51122,1671],{"separator":1670},[1820,51124,51125,51127],{},[898,51126,2132],{},[1826,51128,2552],{},[1655,51130,1677],{"stretchy":1663},[902,51132,38783],{"encoding":904},[123,51134,51135,3224],{},[38,51136,51137],{},"Homogenita poptávky",[123,51139,51140,3106,51143,1343,51166,1343,51183,51200],{},[38,51141,51142],{},"Lineární poptávka",[883,51144,51146],{"className":51145},[886],[888,51147,51148],{"xmlns":890},[892,51149,51150,51164],{},[895,51151,51152,51154,51156,51158,51160,51162],{},[898,51153,2132],{},[1655,51155,1657],{},[898,51157,207],{},[898,51159,1824],{},[1655,51161,2346],{},[898,51163,2025],{},[902,51165,38186],{"encoding":904},[883,51167,51169],{"className":51168},[886],[888,51170,51171],{"xmlns":890},[892,51172,51173,51181],{},[895,51174,51175,51177,51179],{},[898,51176,207],{},[1655,51178,3065],{},[1826,51180,2552],{},[902,51182,44211],{"encoding":904},[883,51184,51186],{"className":51185},[886],[888,51187,51188],{"xmlns":890},[892,51189,51190,51198],{},[895,51191,51192,51194,51196],{},[898,51193,2025],{},[1655,51195,2969],{},[1826,51197,2552],{},[902,51199,19940],{"encoding":904}," — nedokonalá konkurence",[123,51202,51203,8262,51206],{},[38,51204,51205],{},"Dokonalá konkurence",[883,51207,51209],{"className":51208},[886],[888,51210,51211],{"xmlns":890},[892,51212,51213,51225],{},[895,51214,51215,51217,51219],{},[898,51216,2132],{},[1655,51218,1657],{},[2597,51220,51221,51223],{},[898,51222,2132],{},[1655,51224,5603],{},[902,51226,5606],{"encoding":904},[123,51228,51229,51231],{},[38,51230,39352],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,51233,51234,3106,51236,1343,51260],{},[38,51235,32853],{},[883,51237,51239],{"className":51238},[886],[888,51240,51241],{"xmlns":890},[892,51242,51243,51257],{},[895,51244,51245,51247,51249,51251,51253,51255],{},[898,51246,1824],{},[1655,51248,1657],{},[898,51250,5502],{},[1655,51252,1664],{"stretchy":1663},[898,51254,10375],{},[1655,51256,1677],{"stretchy":1663},[902,51258,51259],{"encoding":904},"Q = E(Y)",[38,51261,39549],{},[123,51263,51264,51267,51268,51270],{},[38,51265,51266],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,51269,39995],{}," zboží",[123,51272,51273,2704,51275,51277],{},[38,51274,41001],{},[38,51276,40948],{}," — znaménka zkřížených koeficientů",[123,51279,51280,51283],{},[38,51281,51282],{},"Dvoukomoditní trh"," (2.6)",[123,51285,51286,2115,51289,1677],{},[38,51287,51288],{},"Posun poptávky",[614,51290,40053],{},[724,51292,51293],{},[38,51294,14250],{},[120,51296,51297,51330,51334,51379],{},[123,51298,51299,2115,51301,19774,51303,3106,51305,1343,51328],{},[38,51300,41395],{},[614,51302,41398],{},[38,51304,41569],{},[883,51306,51308],{"className":51307},[886],[888,51309,51310],{"xmlns":890},[892,51311,51312,51326],{},[895,51313,51314,51316,51318,51320,51322,51324],{},[898,51315,1824],{},[1655,51317,1657],{},[898,51319,9920],{},[1655,51321,1664],{"stretchy":1663},[898,51323,2132],{},[1655,51325,1677],{"stretchy":1663},[902,51327,9929],{"encoding":904},[38,51329,41647],{},[123,51331,51332],{},[38,51333,41654],{},[123,51335,51336,3106,51339,1343,51362],{},[38,51337,51338],{},"Lineární nabídka",[883,51340,51342],{"className":51341},[886],[888,51343,51344],{"xmlns":890},[892,51345,51346,51360],{},[895,51347,51348,51350,51352,51354,51356,51358],{},[898,51349,2132],{},[1655,51351,1657],{},[898,51353,1789],{},[898,51355,1824],{},[1655,51357,2346],{},[898,51359,2410],{},[902,51361,41368],{"encoding":904},[883,51363,51365],{"className":51364},[886],[888,51366,51367],{"xmlns":890},[892,51368,51369,51377],{},[895,51370,51371,51373,51375],{},[898,51372,1789],{},[1655,51374,2969],{},[1826,51376,2552],{},[902,51378,41386],{"encoding":904},[123,51380,51381,2115,51384,1677],{},[38,51382,51383],{},"Posun nabídky",[614,51385,42032],{},[724,51387,51388],{},[38,51389,51390],{},"Rovnováha a komparativní statika",[120,51392,51393,51472,51478],{},[123,51394,51395,2115,51397,19774,51399,3106,51402,1343,51419,3106,51422,1343,51439,3106,51441],{},[38,51396,42451],{},[614,51398,42570],{},[38,51400,51401],{},"rovnovážná cena",[883,51403,51405],{"className":51404},[886],[888,51406,51407],{"xmlns":890},[892,51408,51409,51417],{},[895,51410,51411],{},[2597,51412,51413,51415],{},[898,51414,2132],{},[898,51416,5502],{},[902,51418,42592],{"encoding":904},[38,51420,51421],{},"rovnovážné množství",[883,51423,51425],{"className":51424},[886],[888,51426,51427],{"xmlns":890},[892,51428,51429,51437],{},[895,51430,51431],{},[2597,51432,51433,51435],{},[898,51434,1824],{},[898,51436,5502],{},[902,51438,43529],{"encoding":904},[38,51440,42628],{},[883,51442,51444],{"className":51443},[886],[888,51445,51446],{"xmlns":890},[892,51447,51448,51470],{},[895,51449,51450,51452,51454,51460,51462,51468],{},[898,51451,5502],{},[1655,51453,2734],{"stretchy":1663},[2597,51455,51456,51458],{},[898,51457,1824],{},[898,51459,5502],{},[1655,51461,1671],{"separator":1670},[2597,51463,51464,51466],{},[898,51465,2132],{},[898,51467,5502],{},[1655,51469,2743],{"stretchy":1663},[902,51471,42493],{"encoding":904},[123,51473,51474,51477],{},[38,51475,51476],{},"Pravidla 1–4"," komparativní statiky",[123,51479,51480,2115,51483,1677],{},[38,51481,51482],{},"Teorém pavučiny",[614,51484,43475],{},[724,51486,51487],{},[38,51488,51489],{},"Zdanění",[120,51491,51492,51548,51596],{},[123,51493,51494,51496,51497,51522,51523,1677],{},[38,51495,51489],{}," — daň výrobci (",[883,51498,51500],{"className":51499},[886],[888,51501,51502],{"xmlns":890},[892,51503,51504,51520],{},[895,51505,51506,51512,51514,51516,51518],{},[1820,51507,51508,51510],{},[898,51509,9920],{},[1826,51511,1828],{},[1655,51513,1657],{},[898,51515,9920],{},[1655,51517,2346],{},[898,51519,4049],{},[902,51521,43880],{"encoding":904},") vs. daň spotřebiteli (",[883,51524,51526],{"className":51525},[886],[888,51527,51528],{"xmlns":890},[892,51529,51530,51546],{},[895,51531,51532,51538,51540,51542,51544],{},[1820,51533,51534,51536],{},[898,51535,2838],{},[1826,51537,1837],{},[1655,51539,1657],{},[898,51541,2838],{},[1655,51543,2623],{},[898,51545,4049],{},[902,51547,43911],{"encoding":904},[123,51549,51550,3106,51552,1343,51573],{},[38,51551,43784],{},[883,51553,51555],{"className":51554},[886],[888,51556,51557],{"xmlns":890},[892,51558,51559,51571],{},[895,51560,51561],{},[1820,51562,51563,51565],{},[898,51564,4049],{},[895,51566,51567,51569],{},[898,51568,43803],{},[898,51570,724],{},[902,51572,43808],{"encoding":904},[883,51574,51576],{"className":51575},[886],[888,51577,51578],{"xmlns":890},[892,51579,51580,51594],{},[895,51581,51582],{},[1820,51583,51584,51586],{},[898,51585,4049],{},[895,51587,51588,51590,51592],{},[898,51589,43826],{},[898,51591,1674],{},[898,51593,13166],{},[902,51595,43833],{"encoding":904},[123,51597,51598,3106,51601,1343,51630],{},[38,51599,51600],{},"Ekvivalence zdanění",[883,51602,51604],{"className":51603},[886],[888,51605,51606],{"xmlns":890},[892,51607,51608,51628],{},[895,51609,51610,51618,51620],{},[1935,51611,51612,51614,51616],{},[898,51613,1824],{},[1826,51615,1828],{},[898,51617,5502],{},[1655,51619,1657],{},[1935,51621,51622,51624,51626],{},[898,51623,1824],{},[1826,51625,1837],{},[898,51627,5502],{},[902,51629,44034],{"encoding":904},[883,51631,51633],{"className":51632},[886],[888,51634,51635],{"xmlns":890},[892,51636,51637,51661],{},[895,51638,51639,51647,51649,51651,51653],{},[1935,51640,51641,51643,51645],{},[898,51642,2132],{},[1826,51644,1828],{},[898,51646,5502],{},[1655,51648,2623],{},[898,51650,4049],{},[1655,51652,1657],{},[1935,51654,51655,51657,51659],{},[898,51656,2132],{},[1826,51658,1837],{},[898,51660,5502],{},[902,51662,44068],{"encoding":904},[724,51664,51665],{},[38,51666,27534],{},[120,51668,51669,51715,51746,51751,51757,51764],{},[123,51670,51671,3106,51673],{},[38,51672,44167],{},[883,51674,51676],{"className":51675},[886],[888,51677,51678],{"xmlns":890},[892,51679,51680,51712],{},[895,51681,51682,51688,51690,51692,51694,51696,51698,51700,51702,51704,51706,51708,51710],{},[2597,51683,51684,51686],{},[898,51685,1824],{},[898,51687,5502],{},[1655,51689,1657],{},[1655,51691,1664],{"stretchy":1663},[898,51693,2025],{},[1655,51695,2623],{},[898,51697,2410],{},[1655,51699,1677],{"stretchy":1663},[898,51701,5923],{"mathvariant":1943},[1655,51703,1664],{"stretchy":1663},[898,51705,1789],{},[1655,51707,2623],{},[898,51709,207],{},[1655,51711,1677],{"stretchy":1663},[902,51713,51714],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,51716,51717,3106,51720,51745],{},[38,51718,51719],{},"Parametry",[883,51721,51723],{"className":51722},[886],[888,51724,51725],{"xmlns":890},[892,51726,51727,51743],{},[895,51728,51729,51731,51733,51735,51737,51739,51741],{},[898,51730,207],{},[1655,51732,1671],{"separator":1670},[898,51734,2025],{},[1655,51736,1671],{"separator":1670},[898,51738,1789],{},[1655,51740,1671],{"separator":1670},[898,51742,2410],{},[902,51744,44411],{"encoding":904}," — exogenní proměnné",[123,51747,51748],{},[38,51749,51750],{},"Endogenní \u002F exogenní proměnná",[123,51752,51753,51756],{},[38,51754,51755],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,51758,51759,1343,51762],{},[38,51760,51761],{},"Komparativní statika",[38,51763,38086],{},[123,51765,51766,3106,51768,51784],{},[38,51767,4227],{},[883,51769,51771],{"className":51770},[886],[888,51772,51773],{"xmlns":890},[892,51774,51775,51781],{},[895,51776,51777,51779],{},[898,51778,2410],{},[898,51780,1824],{},[902,51782,51783],{"encoding":904},"dQ"," (2.11)",[724,51786,51787],{},[38,51788,51789],{},"Přebytky a ostatní",[120,51791,51792,51830],{},[123,51793,51794,3106,51796,51811,51812,3106,51814,51829],{},[38,51795,46060],{},[883,51797,51799],{"className":51798},[886],[888,51800,51801],{"xmlns":890},[892,51802,51803,51809],{},[895,51804,51805,51807],{},[898,51806,4052],{},[898,51808,9920],{},[902,51810,46076],{"encoding":904}," (2.14), ",[38,51813,46079],{},[883,51815,51817],{"className":51816},[886],[888,51818,51819],{"xmlns":890},[892,51820,51821,51827],{},[895,51822,51823,51825],{},[898,51824,2132],{},[898,51826,9920],{},[902,51828,46095],{"encoding":904}," (2.15)",[123,51831,51832,1343,51835,51838],{},[38,51833,51834],{},"Homo economicus",[38,51836,51837],{},"Marshallova formulace"," (1890)",[38096,51840],{},[115,51842,3187],{"id":3186},[120,51844,51845,51880,51889],{},[123,51846,51847,3106,51850,51853,51854,1343,51857,51860,51861,51864,51865,51868,51869,51872,51873,51876,51877],{},[38,51848,51849],{},"Související témata:",[207,51851,811],{"className":51852,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,51855,820],{"className":51856,"dataFsResolvedFilePath":818,"href":819},[210],[207,51858,3645],{"className":51859,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,51862,775],{"className":51863,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,51866,784],{"className":51867,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,51870,793],{"className":51871,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,51874,3223],{"className":51875,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,51878,5078],{"className":51879,"dataFsResolvedFilePath":827,"href":828},[210],[123,51881,51882,3106,51885],{},[38,51883,51884],{},"Shrnutí přednášek:",[207,51886,51888],{"className":51887,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,51890,51891,3106,51893],{},[38,51892,17329],{},[207,51894,17333],{"className":51895,"dataFsResolvedFilePath":3274,"href":3275},[210],{"title":641,"searchDepth":642,"depth":642,"links":51897},[51898,51899,51907,51913,51920,51921,51928,51929,51930,51937,51938,51939],{"id":37920,"depth":642,"text":37921},{"id":37901,"depth":642,"text":14286,"children":51900},[51901,51902,51903,51904,51906],{"id":38189,"depth":649,"text":38190},{"id":38471,"depth":649,"text":38472},{"id":39481,"depth":649,"text":39482},{"id":40049,"depth":649,"text":51905},"Posun poptávky (shift of demand)",{"id":40553,"depth":649,"text":40554},{"id":37905,"depth":642,"text":14250,"children":51908},[51909,51910,51911],{"id":41390,"depth":649,"text":38190},{"id":41576,"depth":649,"text":41577},{"id":42028,"depth":649,"text":51912},"Posun nabídky (shift of supply)",{"id":42450,"depth":642,"text":42451,"children":51914},[51915,51916,51917,51918,51919],{"id":42562,"depth":649,"text":42563},{"id":42775,"depth":649,"text":42776},{"id":43093,"depth":649,"text":43094},{"id":43447,"depth":649,"text":43448},{"id":43478,"depth":649,"text":43479},{"id":43747,"depth":642,"text":811},{"id":44148,"depth":642,"text":44149,"children":51922},[51923,51924,51925,51926],{"id":44166,"depth":649,"text":44167},{"id":44547,"depth":649,"text":44548},{"id":44931,"depth":649,"text":44932},{"id":45385,"depth":649,"text":51927},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":12908,"depth":642,"text":820},{"id":46310,"depth":642,"text":46311},{"id":46541,"depth":642,"text":46542,"children":51931},[51932,51933,51934,51935,51936],{"id":46545,"depth":649,"text":46546},{"id":47385,"depth":649,"text":47386},{"id":47761,"depth":649,"text":42451},{"id":49056,"depth":649,"text":44149},{"id":50812,"depth":649,"text":820},{"id":51007,"depth":642,"text":51008},{"id":16844,"depth":642,"text":16845},{"id":3186,"depth":642,"text":3187},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,51946,51947,51948,19009,51949,51950],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":51953,"title":820,"body":51954,"course":1128,"courses":659,"created":10802,"description":641,"extension":661,"meta":56233,"navigation":664,"path":56234,"seo":56235,"sources":56236,"stem":56237,"tags":56238,"type":3252,"updated":677,"__hash__":56243},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":51955,"toc":56211},[51956,51958,52026,52076,52078,52081,52339,52415,52420,52422,52441,52445,52521,52606,52608,52922,53015,53017,53036,53040,53114,53199,53202,53378,53383,53385,53805,53807,53811,53815,54051,54095,54195,54261,54264,54297,54473,54535,54665,54743,54854,54888,55086,55105,55124,55189,55193,55196,55241,55244,55362,55408,55410,55414,55762,55764,55766,56044,56046,56050,56085,56092,56165,56167,56169],[12,51957,820],{"id":12908},[5120,51959,51960],{},[724,51961,51962,5127,51964,2115,51966,51981,51982,2115,51984,51999,52000,52022,52023,1719],{},[883,51963,5126],{},[38,51965,46060],{},[883,51967,51969],{"className":51968},[886],[888,51970,51971],{"xmlns":890},[892,51972,51973,51979],{},[895,51974,51975,51977],{},[898,51976,4052],{},[898,51978,9920],{},[902,51980,46076],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,51983,46207],{},[883,51985,51987],{"className":51986},[886],[888,51988,51989],{"xmlns":890},[892,51990,51991,51997],{},[895,51992,51993,51995],{},[898,51994,2132],{},[898,51996,9920],{},[902,51998,46095],{"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 ",[883,52001,52003],{"className":52002},[886],[888,52004,52005],{"xmlns":890},[892,52006,52007,52019],{},[895,52008,52009,52011,52013,52015,52017],{},[898,52010,4052],{},[898,52012,9920],{},[1655,52014,2346],{},[898,52016,2132],{},[898,52018,9920],{},[902,52020,52021],{"encoding":904},"CS + PS"," měří ",[38,52024,52025],{},"celkový blahobyt trhu",[724,52027,52028,2115,52030,1343,52032,13253,52047,2115,52049,1343,52051,52066,52067,52071,52072,1719],{},[38,52029,46060],{},[614,52031,46114],{},[883,52033,52035],{"className":52034},[886],[888,52036,52037],{"xmlns":890},[892,52038,52039,52045],{},[895,52040,52041,52043],{},[898,52042,4052],{},[898,52044,9920],{},[902,52046,46076],{"encoding":904},[38,52048,46079],{},[614,52050,46210],{},[883,52052,52054],{"className":52053},[886],[888,52055,52056],{"xmlns":890},[892,52057,52058,52064],{},[895,52059,52060,52062],{},[898,52061,2132],{},[898,52063,9920],{},[902,52065,46095],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,52068,52070],{"className":52069,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,52073,52075],{"className":52074,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[38096,52077],{},[115,52079,1241],{"id":52080},"úvod",[724,52082,52083,52084,52107,52108,52131,52132,52149,52150,5163,52182,52214,52215,52241,52242,52245,52246,52249,52250,15136,52284,22720,52305,1719],{},"Je dána funkce poptávky ",[883,52085,52087],{"className":52086},[886],[888,52088,52089],{"xmlns":890},[892,52090,52091,52105],{},[895,52092,52093,52095,52097,52099,52101,52103],{},[898,52094,2132],{},[1655,52096,1657],{},[898,52098,2838],{},[1655,52100,1664],{"stretchy":1663},[898,52102,1824],{},[1655,52104,1677],{"stretchy":1663},[902,52106,5889],{"encoding":904},", resp. funkce nabídky ",[883,52109,52111],{"className":52110},[886],[888,52112,52113],{"xmlns":890},[892,52114,52115,52129],{},[895,52116,52117,52119,52121,52123,52125,52127],{},[898,52118,2132],{},[1655,52120,1657],{},[898,52122,9920],{},[1655,52124,1664],{"stretchy":1663},[898,52126,1824],{},[1655,52128,1677],{"stretchy":1663},[902,52130,42197],{"encoding":904},". Pro pevně zadané množství ",[883,52133,52135],{"className":52134},[886],[888,52136,52137],{"xmlns":890},[892,52138,52139,52147],{},[895,52140,52141],{},[1820,52142,52143,52145],{},[898,52144,1824],{},[1826,52146,2552],{},[902,52148,39434],{"encoding":904}," je odpovídající cena ",[883,52151,52153],{"className":52152},[886],[888,52154,52155],{"xmlns":890},[892,52156,52157,52179],{},[895,52158,52159,52165,52167,52169,52171,52177],{},[1820,52160,52161,52163],{},[898,52162,2132],{},[1826,52164,2552],{},[1655,52166,1657],{},[898,52168,2838],{},[1655,52170,1664],{"stretchy":1663},[1820,52172,52173,52175],{},[898,52174,1824],{},[1826,52176,2552],{},[1655,52178,1677],{"stretchy":1663},[902,52180,52181],{"encoding":904},"P_0 = D(Q_0)",[883,52183,52185],{"className":52184},[886],[888,52186,52187],{"xmlns":890},[892,52188,52189,52211],{},[895,52190,52191,52197,52199,52201,52203,52209],{},[1820,52192,52193,52195],{},[898,52194,2132],{},[1826,52196,2552],{},[1655,52198,1657],{},[898,52200,9920],{},[1655,52202,1664],{"stretchy":1663},[1820,52204,52205,52207],{},[898,52206,1824],{},[1826,52208,2552],{},[1655,52210,1677],{"stretchy":1663},[902,52212,52213],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,52216,52218],{"className":52217},[886],[888,52219,52220],{"xmlns":890},[892,52221,52222,52238],{},[895,52223,52224,52230,52232],{},[1820,52225,52226,52228],{},[898,52227,2132],{},[1826,52229,2552],{},[2031,52231,2435],{},[1820,52233,52234,52236],{},[898,52235,1824],{},[1826,52237,2552],{},[902,52239,52240],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,52243,52244],{},"výdaje spotřebitele",", nebo ",[38,52247,52248],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,52251,52253],{"className":52252},[886],[888,52254,52255],{"xmlns":890},[892,52256,52257,52281],{},[895,52258,52259,52261,52263,52269,52271,52273,52275],{},[1826,52260,2552],{},[2031,52262,2435],{},[1820,52264,52265,52267],{},[898,52266,1824],{},[1826,52268,2552],{},[2031,52270,2435],{},[898,52272,2731],{},[2031,52274,2435],{},[1820,52276,52277,52279],{},[898,52278,2132],{},[1826,52280,2552],{},[902,52282,52283],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,52285,52287],{"className":52286},[886],[888,52288,52289],{"xmlns":890},[892,52290,52291,52303],{},[895,52292,52293,52295,52297,52299,52301],{},[1655,52294,1664],{"stretchy":1663},[898,52296,1824],{},[1655,52298,1671],{"separator":1670},[898,52300,2132],{},[1655,52302,1677],{"stretchy":1663},[902,52304,38817],{"encoding":904},[883,52306,52308],{"className":52307},[886],[888,52309,52310],{"xmlns":890},[892,52311,52312,52336],{},[895,52313,52314,52316,52318,52320,52326,52328,52334],{},[898,52315,2731],{},[1655,52317,1657],{},[1655,52319,2734],{"stretchy":1663},[1820,52321,52322,52324],{},[898,52323,1824],{},[1826,52325,2552],{},[1655,52327,1671],{"separator":1670},[1820,52329,52330,52332],{},[898,52331,2132],{},[1826,52333,2552],{},[1655,52335,2743],{"stretchy":1663},[902,52337,52338],{"encoding":904},"A = [Q_0, P_0]",[5120,52340,52341,52346,52404],{},[724,52342,52343,52345],{},[883,52344,5406],{}," Intuice",[120,52347,52348,52376],{},[123,52349,52350,52351,52354,52355,52357,52358,52375],{},"Za jednotky zboží nakoupené ",[38,52352,52353],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,52356,26396],{}," než ",[883,52359,52361],{"className":52360},[886],[888,52362,52363],{"xmlns":890},[892,52364,52365,52373],{},[895,52366,52367],{},[1820,52368,52369,52371],{},[898,52370,2132],{},[1826,52372,2552],{},[902,52374,40074],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,52377,52378,52379,52381,52382,52385,52386,52403],{},"Za jednotky zboží prodané ",[38,52380,52353],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,52383,52384],{},"nižší"," cenu než ",[883,52387,52389],{"className":52388},[886],[888,52390,52391],{"xmlns":890},[892,52392,52393,52401],{},[895,52394,52395],{},[1820,52396,52397,52399],{},[898,52398,2132],{},[1826,52400,2552],{},[902,52402,40074],{"encoding":904}," — rozdíl je jeho přebytek.",[724,52405,52406,52407,52410,52411,52414],{},"Přebytek je tedy rozdíl mezi ",[614,52408,52409],{},"ochotou"," (platit \u002F prodávat) a ",[614,52412,52413],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,52416,52417],{},[1723,52418],{"alt":46105,"className":52419,"src":46107},[210,1727],[38096,52421],{},[115,52423,52425,52426,1677],{"id":52424},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,52427,52429],{"className":52428},[886],[888,52430,52431],{"xmlns":890},[892,52432,52433,52439],{},[895,52434,52435,52437],{},[898,52436,4052],{},[898,52438,9920],{},[902,52440,46076],{"encoding":904},[198,52442,52444],{"id":52443},"definice-vzorec-214","Definice (vzorec 2.14)",[724,52446,52447,52448,52471,52472,52489,52490,2086],{},"Pro poptávku ",[883,52449,52451],{"className":52450},[886],[888,52452,52453],{"xmlns":890},[892,52454,52455,52469],{},[895,52456,52457,52459,52461,52463,52465,52467],{},[898,52458,2132],{},[1655,52460,1657],{},[898,52462,2838],{},[1655,52464,1664],{"stretchy":1663},[898,52466,1824],{},[1655,52468,1677],{"stretchy":1663},[902,52470,5889],{"encoding":904}," a pevně zadané ",[883,52473,52475],{"className":52474},[886],[888,52476,52477],{"xmlns":890},[892,52478,52479,52487],{},[895,52480,52481],{},[1820,52482,52483,52485],{},[898,52484,1824],{},[1826,52486,2552],{},[902,52488,39434],{"encoding":904}," s cenou ",[883,52491,52493],{"className":52492},[886],[888,52494,52495],{"xmlns":890},[892,52496,52497,52519],{},[895,52498,52499,52505,52507,52509,52511,52517],{},[1820,52500,52501,52503],{},[898,52502,2132],{},[1826,52504,2552],{},[1655,52506,1657],{},[898,52508,2838],{},[1655,52510,1664],{"stretchy":1663},[1820,52512,52513,52515],{},[898,52514,1824],{},[1826,52516,2552],{},[1655,52518,1677],{"stretchy":1663},[902,52520,52181],{"encoding":904},[883,52522,52524],{"className":52523},[886],[888,52525,52526],{"xmlns":890,"display":29192},[892,52527,52528,52604],{},[21880,52529,52530],{"width":29197},[21885,52531,52532,52534,52598,52600],{},[21888,52533],{"width":29202},[21888,52535,52536],{},[895,52537,52538,52540,52542,52544,52550,52552,52554,52566,52568,52570,52572,52574,52576,52578,52580,52582,52588,52590,52596],{},[898,52539,4052],{},[898,52541,9920],{},[1655,52543,1664],{"stretchy":1663},[1820,52545,52546,52548],{},[898,52547,1824],{},[1826,52549,2552],{},[1655,52551,1677],{"stretchy":1663},[1655,52553,1657],{},[1935,52555,52556,52558,52560],{},[1655,52557,12293],{},[1826,52559,2552],{},[1820,52561,52562,52564],{},[898,52563,1824],{},[1826,52565,2552],{},[898,52567,2838],{},[1655,52569,1664],{"stretchy":1663},[898,52571,1824],{},[1655,52573,1677],{"stretchy":1663},[2031,52575,2435],{},[898,52577,2410],{},[898,52579,1824],{},[1655,52581,2623],{},[1820,52583,52584,52586],{},[898,52585,2132],{},[1826,52587,2552],{},[2031,52589,2435],{},[1820,52591,52592,52594],{},[898,52593,1824],{},[1826,52595,2552],{},[898,52597,1719],{"mathvariant":1943},[21888,52599],{"width":29202},[21888,52601,52602],{},[2031,52603,46199],{},[902,52605,46202],{"encoding":904},[198,52607,3729],{"id":3728},[120,52609,52610,52702,52764],{},[123,52611,52612,52652,52653,52679,52680,52683,52684,52701],{},[883,52613,52615],{"className":52614},[886],[888,52616,52617],{"xmlns":890},[892,52618,52619,52649],{},[895,52620,52621],{},[3615,52622,52623,52635,52637,52639,52641,52643,52645,52647],{"scriptlevel":2552,"displaystyle":1670},[1935,52624,52625,52627,52629],{},[1655,52626,12293],{},[1826,52628,2552],{},[1820,52630,52631,52633],{},[898,52632,1824],{},[1826,52634,2552],{},[898,52636,2838],{},[1655,52638,1664],{"stretchy":1663},[898,52640,1824],{},[1655,52642,1677],{"stretchy":1663},[2031,52644,2435],{},[898,52646,2410],{},[898,52648,1824],{},[902,52650,52651],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,52654,52656],{"className":52655},[886],[888,52657,52658],{"xmlns":890},[892,52659,52660,52676],{},[895,52661,52662,52664,52666,52668,52674],{},[1655,52663,2734],{"stretchy":1663},[1826,52665,2552],{},[1655,52667,1671],{"separator":1670},[1820,52669,52670,52672],{},[898,52671,1824],{},[1826,52673,2552],{},[1655,52675,2743],{"stretchy":1663},[902,52677,52678],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,52681,52682],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,52685,52687],{"className":52686},[886],[888,52688,52689],{"xmlns":890},[892,52690,52691,52699],{},[895,52692,52693],{},[1820,52694,52695,52697],{},[898,52696,1824],{},[1826,52698,2552],{},[902,52700,39434],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,52703,52704,52730,52731,5171],{},[883,52705,52707],{"className":52706},[886],[888,52708,52709],{"xmlns":890},[892,52710,52711,52727],{},[895,52712,52713,52719,52721],{},[1820,52714,52715,52717],{},[898,52716,2132],{},[1826,52718,2552],{},[2031,52720,2435],{},[1820,52722,52723,52725],{},[898,52724,1824],{},[1826,52726,2552],{},[902,52728,52729],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,52732,52734],{"className":52733},[886],[888,52735,52736],{"xmlns":890},[892,52737,52738,52762],{},[895,52739,52740,52742,52744,52750,52752,52754,52756],{},[1826,52741,2552],{},[2031,52743,2435],{},[1820,52745,52746,52748],{},[898,52747,1824],{},[1826,52749,2552],{},[2031,52751,2435],{},[898,52753,2731],{},[2031,52755,2435],{},[1820,52757,52758,52760],{},[898,52759,2132],{},[1826,52761,2552],{},[902,52763,52283],{"encoding":904},[123,52765,52766,52781,52782,52804,52805,52830,52831,22720,52857,2704,52889,1719],{},[883,52767,52769],{"className":52768},[886],[888,52770,52771],{"xmlns":890},[892,52772,52773,52779],{},[895,52774,52775,52777],{},[898,52776,4052],{},[898,52778,9920],{},[902,52780,46076],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,52783,52785],{"className":52784},[886],[888,52786,52787],{"xmlns":890},[892,52788,52789,52801],{},[895,52790,52791,52793,52795],{},[898,52792,2132],{},[1655,52794,1657],{},[1820,52796,52797,52799],{},[898,52798,2132],{},[1826,52800,2552],{},[902,52802,52803],{"encoding":904},"P = P_0"," v pásu ",[883,52806,52808],{"className":52807},[886],[888,52809,52810],{"xmlns":890},[892,52811,52812,52828],{},[895,52813,52814,52816,52818,52820,52826],{},[1655,52815,2734],{"stretchy":1663},[1826,52817,2552],{},[1655,52819,1671],{"separator":1670},[1820,52821,52822,52824],{},[898,52823,1824],{},[1826,52825,2552],{},[1655,52827,2743],{"stretchy":1663},[902,52829,52678],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,52832,52834],{"className":52833},[886],[888,52835,52836],{"xmlns":890},[892,52837,52838,52854],{},[895,52839,52840,52846,52848,52850,52852],{},[1820,52841,52842,52844],{},[898,52843,2132],{},[1826,52845,2552],{},[2031,52847,2435],{},[898,52849,24379],{},[2031,52851,2435],{},[898,52853,2731],{},[902,52855,52856],{"encoding":904},"P_0\\,B\\,A",[883,52858,52860],{"className":52859},[886],[888,52861,52862],{"xmlns":890},[892,52863,52864,52886],{},[895,52865,52866,52868,52870,52872,52874,52876,52878,52880,52882,52884],{},[898,52867,24379],{},[1655,52869,1657],{},[1655,52871,2734],{"stretchy":1663},[1826,52873,2552],{},[1655,52875,1671],{"separator":1670},[898,52877,2838],{},[1655,52879,1664],{"stretchy":1663},[1826,52881,2552],{},[1655,52883,1677],{"stretchy":1663},[1655,52885,2743],{"stretchy":1663},[902,52887,52888],{"encoding":904},"B = [0, D(0)]",[883,52890,52892],{"className":52891},[886],[888,52893,52894],{"xmlns":890},[892,52895,52896,52920],{},[895,52897,52898,52900,52902,52904,52910,52912,52918],{},[898,52899,2731],{},[1655,52901,1657],{},[1655,52903,2734],{"stretchy":1663},[1820,52905,52906,52908],{},[898,52907,1824],{},[1826,52909,2552],{},[1655,52911,1671],{"separator":1670},[1820,52913,52914,52916],{},[898,52915,2132],{},[1826,52917,2552],{},[1655,52919,2743],{"stretchy":1663},[902,52921,52338],{"encoding":904},[724,52923,52924],{},[614,52925,52926,52927,52940,52941,52974,52975,30268,53000,1719],{},"Obrázek 2.24: Křivka poptávky ",[883,52928,52930],{"className":52929},[886],[888,52931,52932],{"xmlns":890},[892,52933,52934,52938],{},[895,52935,52936],{},[898,52937,2838],{},[902,52939,2838],{"encoding":904},", bod ",[883,52942,52944],{"className":52943},[886],[888,52945,52946],{"xmlns":890},[892,52947,52948,52972],{},[895,52949,52950,52952,52954,52956,52962,52964,52970],{},[898,52951,2731],{},[1655,52953,1657],{},[1655,52955,2734],{"stretchy":1663},[1820,52957,52958,52960],{},[898,52959,1824],{},[1826,52961,2552],{},[1655,52963,1671],{"separator":1670},[1820,52965,52966,52968],{},[898,52967,2132],{},[1826,52969,2552],{},[1655,52971,2743],{"stretchy":1663},[902,52973,52338],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,52976,52978],{"className":52977},[886],[888,52979,52980],{"xmlns":890},[892,52981,52982,52998],{},[895,52983,52984,52990,52992,52994,52996],{},[1820,52985,52986,52988],{},[898,52987,2132],{},[1826,52989,2552],{},[2031,52991,2435],{},[898,52993,24379],{},[2031,52995,2435],{},[898,52997,2731],{},[902,52999,52856],{"encoding":904},[883,53001,53003],{"className":53002},[886],[888,53004,53005],{"xmlns":890},[892,53006,53007,53013],{},[895,53008,53009,53011],{},[898,53010,4052],{},[898,53012,9920],{},[902,53014,46076],{"encoding":904},[38096,53016],{},[115,53018,53020,53021,1677],{"id":53019},"přebytek-výrobce-psps","Přebytek výrobce (",[883,53022,53024],{"className":53023},[886],[888,53025,53026],{"xmlns":890},[892,53027,53028,53034],{},[895,53029,53030,53032],{},[898,53031,2132],{},[898,53033,9920],{},[902,53035,46095],{"encoding":904},[198,53037,53039],{"id":53038},"definice-vzorec-215","Definice (vzorec 2.15)",[724,53041,53042,53043,52471,53066,52489,53083,2086],{},"Analogicky — pro nabídku ",[883,53044,53046],{"className":53045},[886],[888,53047,53048],{"xmlns":890},[892,53049,53050,53064],{},[895,53051,53052,53054,53056,53058,53060,53062],{},[898,53053,2132],{},[1655,53055,1657],{},[898,53057,9920],{},[1655,53059,1664],{"stretchy":1663},[898,53061,1824],{},[1655,53063,1677],{"stretchy":1663},[902,53065,42197],{"encoding":904},[883,53067,53069],{"className":53068},[886],[888,53070,53071],{"xmlns":890},[892,53072,53073,53081],{},[895,53074,53075],{},[1820,53076,53077,53079],{},[898,53078,1824],{},[1826,53080,2552],{},[902,53082,39434],{"encoding":904},[883,53084,53086],{"className":53085},[886],[888,53087,53088],{"xmlns":890},[892,53089,53090,53112],{},[895,53091,53092,53098,53100,53102,53104,53110],{},[1820,53093,53094,53096],{},[898,53095,2132],{},[1826,53097,2552],{},[1655,53099,1657],{},[898,53101,9920],{},[1655,53103,1664],{"stretchy":1663},[1820,53105,53106,53108],{},[898,53107,1824],{},[1826,53109,2552],{},[1655,53111,1677],{"stretchy":1663},[902,53113,52213],{"encoding":904},[883,53115,53117],{"className":53116},[886],[888,53118,53119],{"xmlns":890,"display":29192},[892,53120,53121,53197],{},[21880,53122,53123],{"width":29197},[21885,53124,53125,53127,53191,53193],{},[21888,53126],{"width":29202},[21888,53128,53129],{},[895,53130,53131,53133,53135,53137,53143,53145,53147,53153,53155,53161,53163,53175,53177,53179,53181,53183,53185,53187,53189],{},[898,53132,2132],{},[898,53134,9920],{},[1655,53136,1664],{"stretchy":1663},[1820,53138,53139,53141],{},[898,53140,1824],{},[1826,53142,2552],{},[1655,53144,1677],{"stretchy":1663},[1655,53146,1657],{},[1820,53148,53149,53151],{},[898,53150,2132],{},[1826,53152,2552],{},[2031,53154,2435],{},[1820,53156,53157,53159],{},[898,53158,1824],{},[1826,53160,2552],{},[1655,53162,2623],{},[1935,53164,53165,53167,53169],{},[1655,53166,12293],{},[1826,53168,2552],{},[1820,53170,53171,53173],{},[898,53172,1824],{},[1826,53174,2552],{},[898,53176,9920],{},[1655,53178,1664],{"stretchy":1663},[898,53180,1824],{},[1655,53182,1677],{"stretchy":1663},[2031,53184,2435],{},[898,53186,2410],{},[898,53188,1824],{},[898,53190,1719],{"mathvariant":1943},[21888,53192],{"width":29202},[21888,53194,53195],{},[2031,53196,46295],{},[902,53198,46298],{"encoding":904},[198,53200,3729],{"id":53201},"geometrická-interpretace-1",[120,53203,53204,53252,53313],{},[123,53205,53206,8262,53231,53234,53235,1719],{},[883,53207,53209],{"className":53208},[886],[888,53210,53211],{"xmlns":890},[892,53212,53213,53229],{},[895,53214,53215,53221,53223],{},[1820,53216,53217,53219],{},[898,53218,2132],{},[1826,53220,2552],{},[2031,53222,2435],{},[1820,53224,53225,53227],{},[898,53226,1824],{},[1826,53228,2552],{},[902,53230,52729],{"encoding":904},[38,53232,53233],{},"tržba"," výrobce za prodané množství ",[883,53236,53238],{"className":53237},[886],[888,53239,53240],{"xmlns":890},[892,53241,53242,53250],{},[895,53243,53244],{},[1820,53245,53246,53248],{},[898,53247,1824],{},[1826,53249,2552],{},[902,53251,39434],{"encoding":904},[123,53253,53254,53294,53295,53312],{},[883,53255,53257],{"className":53256},[886],[888,53258,53259],{"xmlns":890},[892,53260,53261,53291],{},[895,53262,53263],{},[3615,53264,53265,53277,53279,53281,53283,53285,53287,53289],{"scriptlevel":2552,"displaystyle":1670},[1935,53266,53267,53269,53271],{},[1655,53268,12293],{},[1826,53270,2552],{},[1820,53272,53273,53275],{},[898,53274,1824],{},[1826,53276,2552],{},[898,53278,9920],{},[1655,53280,1664],{"stretchy":1663},[898,53282,1824],{},[1655,53284,1677],{"stretchy":1663},[2031,53286,2435],{},[898,53288,2410],{},[898,53290,1824],{},[902,53292,53293],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,53296,53298],{"className":53297},[886],[888,53299,53300],{"xmlns":890},[892,53301,53302,53310],{},[895,53303,53304],{},[1820,53305,53306,53308],{},[898,53307,1824],{},[1826,53309,2552],{},[902,53311,39434],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,53314,53315,53330,53331,53352,53353,1719],{},[883,53316,53318],{"className":53317},[886],[888,53319,53320],{"xmlns":890},[892,53321,53322,53328],{},[895,53323,53324,53326],{},[898,53325,2132],{},[898,53327,9920],{},[902,53329,46095],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,53332,53334],{"className":53333},[886],[888,53335,53336],{"xmlns":890},[892,53337,53338,53350],{},[895,53339,53340,53342,53344],{},[898,53341,2132],{},[1655,53343,1657],{},[1820,53345,53346,53348],{},[898,53347,2132],{},[1826,53349,2552],{},[902,53351,52803],{"encoding":904}," a křivkou nabídky v pásu ",[883,53354,53356],{"className":53355},[886],[888,53357,53358],{"xmlns":890},[892,53359,53360,53376],{},[895,53361,53362,53364,53366,53368,53374],{},[1655,53363,2734],{"stretchy":1663},[1826,53365,2552],{},[1655,53367,1671],{"separator":1670},[1820,53369,53370,53372],{},[898,53371,1824],{},[1826,53373,2552],{},[1655,53375,2743],{"stretchy":1663},[902,53377,52678],{"encoding":904},[724,53379,53380],{},[614,53381,53382],{},"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.",[38096,53384],{},[5120,53386,53387,53392],{},[724,53388,53389,53391],{},[883,53390,5821],{}," Postup výpočtu CS a PS",[152,53393,53394,53525,53635,53664,53798],{},[123,53395,53396,53397,53414,53415,53446,53447,53478,53479,1719],{},"Zjisti (nebo si zvol) množství ",[883,53398,53400],{"className":53399},[886],[888,53401,53402],{"xmlns":890},[892,53403,53404,53412],{},[895,53405,53406],{},[1820,53407,53408,53410],{},[898,53409,1824],{},[1826,53411,2552],{},[902,53413,39434],{"encoding":904}," a odpovídající cenu ",[883,53416,53418],{"className":53417},[886],[888,53419,53420],{"xmlns":890},[892,53421,53422,53444],{},[895,53423,53424,53430,53432,53434,53436,53442],{},[1820,53425,53426,53428],{},[898,53427,2132],{},[1826,53429,2552],{},[1655,53431,1657],{},[898,53433,2838],{},[1655,53435,1664],{"stretchy":1663},[1820,53437,53438,53440],{},[898,53439,1824],{},[1826,53441,2552],{},[1655,53443,1677],{"stretchy":1663},[902,53445,52181],{"encoding":904}," resp. ",[883,53448,53450],{"className":53449},[886],[888,53451,53452],{"xmlns":890},[892,53453,53454,53476],{},[895,53455,53456,53462,53464,53466,53468,53474],{},[1820,53457,53458,53460],{},[898,53459,2132],{},[1826,53461,2552],{},[1655,53463,1657],{},[898,53465,9920],{},[1655,53467,1664],{"stretchy":1663},[1820,53469,53470,53472],{},[898,53471,1824],{},[1826,53473,2552],{},[1655,53475,1677],{"stretchy":1663},[902,53477,52213],{"encoding":904},". V rovnováze platí ",[883,53480,53482],{"className":53481},[886],[888,53483,53484],{"xmlns":890},[892,53485,53486,53522],{},[895,53487,53488,53490,53492,53498,53500,53502,53504,53506,53512,53514,53516],{},[898,53489,2838],{},[1655,53491,1664],{"stretchy":1663},[2597,53493,53494,53496],{},[898,53495,1824],{},[898,53497,5502],{},[1655,53499,1677],{"stretchy":1663},[1655,53501,1657],{},[898,53503,9920],{},[1655,53505,1664],{"stretchy":1663},[2597,53507,53508,53510],{},[898,53509,1824],{},[898,53511,5502],{},[1655,53513,1677],{"stretchy":1663},[1655,53515,1657],{},[2597,53517,53518,53520],{},[898,53519,2132],{},[898,53521,5502],{},[902,53523,53524],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,53526,53527,53528,21252,53566,53581,53582,21252,53620,5171],{},"Spočti určitý integrál ",[883,53529,53531],{"className":53530},[886],[888,53532,53533],{"xmlns":890},[892,53534,53535,53563],{},[895,53536,53537,53549,53551,53553,53555,53557,53559,53561],{},[1935,53538,53539,53541,53543],{},[1655,53540,12293],{},[1826,53542,2552],{},[1820,53544,53545,53547],{},[898,53546,1824],{},[1826,53548,2552],{},[898,53550,2838],{},[1655,53552,1664],{"stretchy":1663},[898,53554,1824],{},[1655,53556,1677],{"stretchy":1663},[2031,53558,2435],{},[898,53560,2410],{},[898,53562,1824],{},[902,53564,53565],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,53567,53569],{"className":53568},[886],[888,53570,53571],{"xmlns":890},[892,53572,53573,53579],{},[895,53574,53575,53577],{},[898,53576,4052],{},[898,53578,9920],{},[902,53580,46076],{"encoding":904},") nebo ",[883,53583,53585],{"className":53584},[886],[888,53586,53587],{"xmlns":890},[892,53588,53589,53617],{},[895,53590,53591,53603,53605,53607,53609,53611,53613,53615],{},[1935,53592,53593,53595,53597],{},[1655,53594,12293],{},[1826,53596,2552],{},[1820,53598,53599,53601],{},[898,53600,1824],{},[1826,53602,2552],{},[898,53604,9920],{},[1655,53606,1664],{"stretchy":1663},[898,53608,1824],{},[1655,53610,1677],{"stretchy":1663},[2031,53612,2435],{},[898,53614,2410],{},[898,53616,1824],{},[902,53618,53619],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,53621,53623],{"className":53622},[886],[888,53624,53625],{"xmlns":890},[892,53626,53627,53633],{},[895,53628,53629,53631],{},[898,53630,2132],{},[898,53632,9920],{},[902,53634,46095],{"encoding":904},[123,53636,53637,53638,1719],{},"Sestav obdélník ",[883,53639,53641],{"className":53640},[886],[888,53642,53643],{"xmlns":890},[892,53644,53645,53661],{},[895,53646,53647,53653,53655],{},[1820,53648,53649,53651],{},[898,53650,2132],{},[1826,53652,2552],{},[1655,53654,2869],{},[1820,53656,53657,53659],{},[898,53658,1824],{},[1826,53660,2552],{},[902,53662,53663],{"encoding":904},"P_0 \\cdot Q_0",[123,53665,53666,53667],{},"Dosaď:\n",[120,53668,53669,53734],{},[123,53670,53671,53729,53730,53733],{},[883,53672,53674],{"className":53673},[886],[888,53675,53676],{"xmlns":890},[892,53677,53678,53726],{},[895,53679,53680,53682,53684,53686,53698,53700,53702,53704,53706,53708,53710,53712,53714,53720],{},[898,53681,4052],{},[898,53683,9920],{},[1655,53685,1657],{},[1935,53687,53688,53690,53692],{},[1655,53689,12293],{},[1826,53691,2552],{},[1820,53693,53694,53696],{},[898,53695,1824],{},[1826,53697,2552],{},[898,53699,2838],{},[1655,53701,1664],{"stretchy":1663},[898,53703,1824],{},[1655,53705,1677],{"stretchy":1663},[2031,53707,2435],{},[898,53709,2410],{},[898,53711,1824],{},[1655,53713,2623],{},[1820,53715,53716,53718],{},[898,53717,2132],{},[1826,53719,2552],{},[1820,53721,53722,53724],{},[898,53723,1824],{},[1826,53725,2552],{},[902,53727,53728],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,53731,53732],{},"mínus"," obdélník)",[123,53735,53736,53794,53795,53797],{},[883,53737,53739],{"className":53738},[886],[888,53740,53741],{"xmlns":890},[892,53742,53743,53791],{},[895,53744,53745,53747,53749,53751,53757,53763,53765,53777,53779,53781,53783,53785,53787,53789],{},[898,53746,2132],{},[898,53748,9920],{},[1655,53750,1657],{},[1820,53752,53753,53755],{},[898,53754,2132],{},[1826,53756,2552],{},[1820,53758,53759,53761],{},[898,53760,1824],{},[1826,53762,2552],{},[1655,53764,2623],{},[1935,53766,53767,53769,53771],{},[1655,53768,12293],{},[1826,53770,2552],{},[1820,53772,53773,53775],{},[898,53774,1824],{},[1826,53776,2552],{},[898,53778,9920],{},[1655,53780,1664],{"stretchy":1663},[898,53782,1824],{},[1655,53784,1677],{"stretchy":1663},[2031,53786,2435],{},[898,53788,2410],{},[898,53790,1824],{},[902,53792,53793],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,53796,53732],{}," integrál)",[123,53799,53800,53801,53804],{},"Kontrola znaménka: obě hodnoty musí být ",[38,53802,53803],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[38096,53806],{},[115,53808,53810],{"id":53809},"příklady","Příklady",[198,53812,53814],{"id":53813},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[5120,53816,53817],{},[724,53818,53819,53822,53823,48847,53846,53869,53870,1343,53890,1343,53907,1343,53924,53941,53942,54018,54019,54036,54037,54050],{},[883,53820,53821],{},"!example"," Zadání\nJsou dány poptávka ",[883,53824,53826],{"className":53825},[886],[888,53827,53828],{"xmlns":890},[892,53829,53830,53844],{},[895,53831,53832,53834,53836,53838,53840,53842],{},[898,53833,2132],{},[1655,53835,1657],{},[898,53837,207],{},[898,53839,1824],{},[1655,53841,2346],{},[898,53843,2025],{},[902,53845,38186],{"encoding":904},[883,53847,53849],{"className":53848},[886],[888,53850,53851],{"xmlns":890},[892,53852,53853,53867],{},[895,53854,53855,53857,53859,53861,53863,53865],{},[898,53856,2132],{},[1655,53858,1657],{},[898,53860,1789],{},[898,53862,1824],{},[1655,53864,2346],{},[898,53866,2410],{},[902,53868,41368],{"encoding":904}," s hodnotami ",[883,53871,53873],{"className":53872},[886],[888,53874,53875],{"xmlns":890},[892,53876,53877,53887],{},[895,53878,53879,53881,53883,53885],{},[898,53880,207],{},[1655,53882,1657],{},[1655,53884,2623],{},[1826,53886,3472],{},[902,53888,53889],{"encoding":904},"a = -3",[883,53891,53893],{"className":53892},[886],[888,53894,53895],{"xmlns":890},[892,53896,53897,53905],{},[895,53898,53899,53901,53903],{},[898,53900,2025],{},[1655,53902,1657],{},[1826,53904,6460],{},[902,53906,49770],{"encoding":904},[883,53908,53910],{"className":53909},[886],[888,53911,53912],{"xmlns":890},[892,53913,53914,53922],{},[895,53915,53916,53918,53920],{},[898,53917,1789],{},[1655,53919,1657],{},[1826,53921,6258],{},[902,53923,49788],{"encoding":904},[883,53925,53927],{"className":53926},[886],[888,53928,53929],{"xmlns":890},[892,53930,53931,53939],{},[895,53932,53933,53935,53937],{},[898,53934,2410],{},[1655,53936,1657],{},[1826,53938,4136],{},[902,53940,49806],{"encoding":904},".\nRovnovážné množství:\n",[883,53943,53945],{"className":53944},[886],[888,53946,53947],{"xmlns":890},[892,53948,53949,54015],{},[895,53950,53951,53957,53959,53977,53979,54003,54005,54011,54013],{},[2597,53952,53953,53955],{},[898,53954,1824],{},[898,53956,5502],{},[1655,53958,1657],{},[1949,53960,53961,53969],{},[895,53962,53963,53965,53967],{},[898,53964,2025],{},[1655,53966,2623],{},[898,53968,2410],{},[895,53970,53971,53973,53975],{},[898,53972,1789],{},[1655,53974,2623],{},[898,53976,207],{},[1655,53978,1657],{},[1949,53980,53981,53989],{},[895,53982,53983,53985,53987],{},[1826,53984,6460],{},[1655,53986,2623],{},[1826,53988,4136],{},[895,53990,53991,53993,53995,53997,53999,54001],{},[1826,53992,6258],{},[1655,53994,2623],{},[1655,53996,1664],{"stretchy":1663},[1655,53998,2623],{},[1826,54000,3472],{},[1655,54002,1677],{"stretchy":1663},[1655,54004,1657],{},[1949,54006,54007,54009],{},[1826,54008,39145],{},[1826,54010,45532],{},[1655,54012,7147],{},[1826,54014,45537],{},[902,54016,54017],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,54020,54022],{"className":54021},[886],[888,54023,54024],{"xmlns":890},[892,54025,54026,54034],{},[895,54027,54028],{},[2597,54029,54030,54032],{},[898,54031,1824],{},[898,54033,5502],{},[902,54035,43529],{"encoding":904}," (a) při změně samotného parametru ",[883,54038,54040],{"className":54039},[886],[888,54041,54042],{"xmlns":890},[892,54043,54044,54048],{},[895,54045,54046],{},[898,54047,1789],{},[902,54049,1789],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,54052,54053],{},[38,54054,54055,54056,3948,54069,3962,54082,10541],{},"Řešení (a) — změna ",[883,54057,54059],{"className":54058},[886],[888,54060,54061],{"xmlns":890},[892,54062,54063,54067],{},[895,54064,54065],{},[898,54066,1789],{},[902,54068,1789],{"encoding":904},[883,54070,54072],{"className":54071},[886],[888,54073,54074],{"xmlns":890},[892,54075,54076,54080],{},[895,54077,54078],{},[1826,54079,6258],{},[902,54081,45572],{"encoding":904},[883,54083,54085],{"className":54084},[886],[888,54086,54087],{"xmlns":890},[892,54088,54089,54093],{},[895,54090,54091],{},[1826,54092,20447],{},[902,54094,45586],{"encoding":904},[724,54096,54097,54098,54162,54163,2086],{},"Pomocí vzorce (2.13) pro ",[883,54099,54101],{"className":54100},[886],[888,54102,54103],{"xmlns":890},[892,54104,54105,54159],{},[895,54106,54107,54127,54129,54131],{},[3615,54108,54109],{"scriptlevel":2552,"displaystyle":1670},[1949,54110,54111,54121],{},[895,54112,54113,54115],{},[898,54114,1955],{"mathvariant":1943},[2597,54116,54117,54119],{},[898,54118,1824],{},[898,54120,5502],{},[895,54122,54123,54125],{},[898,54124,1955],{"mathvariant":1943},[898,54126,1789],{},[1655,54128,1657],{},[1655,54130,2623],{},[3615,54132,54133],{"scriptlevel":2552,"displaystyle":1670},[1949,54134,54135,54143],{},[895,54136,54137,54139,54141],{},[898,54138,2025],{},[1655,54140,2623],{},[898,54142,2410],{},[895,54144,54145,54147,54149,54151,54153],{},[1655,54146,1664],{"stretchy":1663},[898,54148,1789],{},[1655,54150,2623],{},[898,54152,207],{},[2597,54154,54155,54157],{},[1655,54156,1677],{"stretchy":1663},[1826,54158,1837],{},[902,54160,54161],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,54164,54166],{"className":54165},[886],[888,54167,54168],{"xmlns":890},[892,54169,54170,54192],{},[895,54171,54172,54174],{},[1655,54173,2623],{},[3615,54175,54176],{"scriptlevel":2552,"displaystyle":1670},[1949,54177,54178,54184],{},[2597,54179,54180,54182],{},[898,54181,1824],{},[898,54183,5502],{},[895,54185,54186,54188,54190],{},[898,54187,1789],{},[1655,54189,2623],{},[898,54191,207],{},[902,54193,54194],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,54196,54198],{"className":54197},[886],[888,54199,54200],{"xmlns":890,"display":29192},[892,54201,54202,54258],{},[895,54203,54204,54206,54212,54214,54216,54232,54234,54236,54238,54240,54242,54248,54250,54252,54254,54256],{},[898,54205,2410],{},[2597,54207,54208,54210],{},[898,54209,1824],{},[898,54211,5502],{},[1655,54213,1657],{},[1655,54215,2623],{},[1949,54217,54218,54224],{},[2597,54219,54220,54222],{},[898,54221,1824],{},[898,54223,5502],{},[895,54225,54226,54228,54230],{},[898,54227,1789],{},[1655,54229,2623],{},[898,54231,207],{},[2031,54233,2435],{},[898,54235,2410],{},[898,54237,1789],{},[1655,54239,1657],{},[1655,54241,2623],{},[1949,54243,54244,54246],{},[1826,54245,45700],{},[1826,54247,45532],{},[1655,54249,2869],{},[1826,54251,4068],{},[1655,54253,7147],{},[1655,54255,2623],{},[1826,54257,45672],{},[902,54259,54260],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,54262,54263],{},"Nové rovnovážné množství:",[883,54265,54267],{"className":54266},[886],[888,54268,54269],{"xmlns":890,"display":29192},[892,54270,54271,54294],{},[895,54272,54273,54281,54283,54285,54287,54289,54291],{},[1935,54274,54275,54277,54279],{},[898,54276,1824],{},[1826,54278,1828],{},[898,54280,5502],{},[1655,54282,2357],{},[1826,54284,45700],{},[1655,54286,2623],{},[1826,54288,45705],{},[1655,54290,1657],{},[1826,54292,54293],{},"8,326.",[902,54295,54296],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,54298,54299,3106,54302,1343,54329,1343,54351,1343,54373,6838,54395,1343,54414,1343,54435,1343,54454,1719],{},[38,54300,54301],{},"Řešení (b) — současná změna všech parametrů:",[883,54303,54305],{"className":54304},[886],[888,54306,54307],{"xmlns":890},[892,54308,54309,54326],{},[895,54310,54311,54313,54315,54317,54319,54321,54323],{},[898,54312,207],{},[1655,54314,2086],{},[1655,54316,2623],{},[1826,54318,3472],{},[1655,54320,4393],{},[1655,54322,2623],{},[1826,54324,54325],{},"2,5",[902,54327,54328],{"encoding":904},"a: -3 \\to -2{,}5",[883,54330,54332],{"className":54331},[886],[888,54333,54334],{"xmlns":890},[892,54335,54336,54348],{},[895,54337,54338,54340,54342,54344,54346],{},[898,54339,2025],{},[1655,54341,2086],{},[1826,54343,6460],{},[1655,54345,4393],{},[1826,54347,16163],{},[902,54349,54350],{"encoding":904},"b: 40 \\to 35",[883,54352,54354],{"className":54353},[886],[888,54355,54356],{"xmlns":890},[892,54357,54358,54370],{},[895,54359,54360,54362,54364,54366,54368],{},[898,54361,1789],{},[1655,54363,2086],{},[1826,54365,6258],{},[1655,54367,4393],{},[1826,54369,20447],{},[902,54371,54372],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,54374,54376],{"className":54375},[886],[888,54377,54378],{"xmlns":890},[892,54379,54380,54392],{},[895,54381,54382,54384,54386,54388,54390],{},[898,54383,2410],{},[1655,54385,2086],{},[1826,54387,4136],{},[1655,54389,4393],{},[1826,54391,4176],{},[902,54393,54394],{"encoding":904},"d: 10 \\to 11",[883,54396,54398],{"className":54397},[886],[888,54399,54400],{"xmlns":890},[892,54401,54402,54412],{},[895,54403,54404,54406,54408,54410],{},[898,54405,2410],{},[898,54407,207],{},[1655,54409,1657],{},[1826,54411,6258],{},[902,54413,45738],{"encoding":904},[883,54415,54417],{"className":54416},[886],[888,54418,54419],{"xmlns":890},[892,54420,54421,54433],{},[895,54422,54423,54425,54427,54429,54431],{},[898,54424,2410],{},[898,54426,2025],{},[1655,54428,1657],{},[1655,54430,2623],{},[1826,54432,3524],{},[902,54434,45760],{"encoding":904},[883,54436,54438],{"className":54437},[886],[888,54439,54440],{"xmlns":890},[892,54441,54442,54452],{},[895,54443,54444,54446,54448,54450],{},[898,54445,2410],{},[898,54447,1789],{},[1655,54449,1657],{},[1826,54451,4068],{},[902,54453,45780],{"encoding":904},[883,54455,54457],{"className":54456},[886],[888,54458,54459],{"xmlns":890},[892,54460,54461,54471],{},[895,54462,54463,54465,54467,54469],{},[898,54464,2410],{},[898,54466,2410],{},[1655,54468,1657],{},[1826,54470,1828],{},[902,54472,45800],{"encoding":904},[724,54474,54475,54476,54534],{},"Totální diferenciál ",[883,54477,54479],{"className":54478},[886],[888,54480,54481],{"xmlns":890},[892,54482,54483,54531],{},[895,54484,54485,54491,54493,54495,54497,54499,54501,54503,54505,54507,54509,54511],{},[2597,54486,54487,54489],{},[898,54488,1824],{},[898,54490,5502],{},[1655,54492,1664],{"stretchy":1663},[898,54494,207],{},[1655,54496,1671],{"separator":1670},[898,54498,2025],{},[1655,54500,1671],{"separator":1670},[898,54502,1789],{},[1655,54504,1671],{"separator":1670},[898,54506,2410],{},[1655,54508,1677],{"stretchy":1663},[1655,54510,1657],{},[3615,54512,54513],{"scriptlevel":2552,"displaystyle":1670},[1949,54514,54515,54523],{},[895,54516,54517,54519,54521],{},[898,54518,2025],{},[1655,54520,2623],{},[898,54522,2410],{},[895,54524,54525,54527,54529],{},[898,54526,1789],{},[1655,54528,2623],{},[898,54530,207],{},[902,54532,54533],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,54536,54538],{"className":54537},[886],[888,54539,54540],{"xmlns":890,"display":29192},[892,54541,54542,54662],{},[895,54543,54544,54546,54552,54554,54580,54582,54584,54586,54588,54600,54602,54604,54606,54608,54634,54636,54638,54640,54642,54654,54656,54658,54660],{},[898,54545,2410],{},[2597,54547,54548,54550],{},[898,54549,1824],{},[898,54551,5502],{},[1655,54553,1657],{},[1949,54555,54556,54564],{},[895,54557,54558,54560,54562],{},[898,54559,2025],{},[1655,54561,2623],{},[898,54563,2410],{},[895,54565,54566,54568,54570,54572,54574],{},[1655,54567,1664],{"stretchy":1663},[898,54569,1789],{},[1655,54571,2623],{},[898,54573,207],{},[2597,54575,54576,54578],{},[1655,54577,1677],{"stretchy":1663},[1826,54579,1837],{},[2031,54581,2435],{},[898,54583,2410],{},[898,54585,207],{},[1655,54587,2346],{},[1949,54589,54590,54592],{},[1826,54591,1828],{},[895,54593,54594,54596,54598],{},[898,54595,1789],{},[1655,54597,2623],{},[898,54599,207],{},[2031,54601,2435],{},[898,54603,2410],{},[898,54605,2025],{},[1655,54607,2623],{},[1949,54609,54610,54618],{},[895,54611,54612,54614,54616],{},[898,54613,2025],{},[1655,54615,2623],{},[898,54617,2410],{},[895,54619,54620,54622,54624,54626,54628],{},[1655,54621,1664],{"stretchy":1663},[898,54623,1789],{},[1655,54625,2623],{},[898,54627,207],{},[2597,54629,54630,54632],{},[1655,54631,1677],{"stretchy":1663},[1826,54633,1837],{},[2031,54635,2435],{},[898,54637,2410],{},[898,54639,1789],{},[1655,54641,2623],{},[1949,54643,54644,54646],{},[1826,54645,1828],{},[895,54647,54648,54650,54652],{},[898,54649,1789],{},[1655,54651,2623],{},[898,54653,207],{},[2031,54655,2435],{},[898,54657,2410],{},[898,54659,2410],{},[898,54661,1719],{"mathvariant":1943},[902,54663,54664],{"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.",[724,54666,54667,54668,1343,54690,1343,54721,4421],{},"Dosazením číselných hodnot (",[883,54669,54671],{"className":54670},[886],[888,54672,54673],{"xmlns":890},[892,54674,54675,54687],{},[895,54676,54677,54679,54681,54683,54685],{},[898,54678,1789],{},[1655,54680,2623],{},[898,54682,207],{},[1655,54684,1657],{},[1826,54686,45532],{},[902,54688,54689],{"encoding":904},"c - a = 3{,}5",[883,54691,54693],{"className":54692},[886],[888,54694,54695],{"xmlns":890},[892,54696,54697,54718],{},[895,54698,54699,54701,54703,54705,54707,54713,54715],{},[1655,54700,1664],{"stretchy":1663},[898,54702,1789],{},[1655,54704,2623],{},[898,54706,207],{},[2597,54708,54709,54711],{},[1655,54710,1677],{"stretchy":1663},[1826,54712,1837],{},[1655,54714,1657],{},[1826,54716,54717],{},"12,25",[902,54719,54720],{"encoding":904},"(c-a)^2 = 12{,}25",[883,54722,54724],{"className":54723},[886],[888,54725,54726],{"xmlns":890},[892,54727,54728,54740],{},[895,54729,54730,54732,54734,54736,54738],{},[898,54731,2025],{},[1655,54733,2623],{},[898,54735,2410],{},[1655,54737,1657],{},[1826,54739,39145],{},[902,54741,54742],{"encoding":904},"b - d = 30",[883,54744,54746],{"className":54745},[886],[888,54747,54748],{"xmlns":890,"display":29192},[892,54749,54750,54851],{},[895,54751,54752,54754,54760,54762,54770,54772,54774,54776,54778,54786,54788,54790,54792,54794,54796,54804,54806,54808,54810,54812,54820,54822,54824,54826,54828,54831,54833,54836,54838,54840,54842,54845,54847,54849],{},[898,54753,2410],{},[2597,54755,54756,54758],{},[898,54757,1824],{},[898,54759,5502],{},[1655,54761,2357],{},[3615,54763,54764],{"scriptlevel":2552,"displaystyle":1663},[1949,54765,54766,54768],{},[1826,54767,39145],{},[1826,54769,54717],{},[1655,54771,1664],{"stretchy":1663},[1826,54773,6258],{},[1655,54775,1677],{"stretchy":1663},[1655,54777,2346],{},[3615,54779,54780],{"scriptlevel":2552,"displaystyle":1663},[1949,54781,54782,54784],{},[1826,54783,1828],{},[1826,54785,45532],{},[1655,54787,1664],{"stretchy":1663},[1655,54789,2623],{},[1826,54791,3524],{},[1655,54793,1677],{"stretchy":1663},[1655,54795,2623],{},[3615,54797,54798],{"scriptlevel":2552,"displaystyle":1663},[1949,54799,54800,54802],{},[1826,54801,39145],{},[1826,54803,54717],{},[1655,54805,1664],{"stretchy":1663},[1826,54807,4068],{},[1655,54809,1677],{"stretchy":1663},[1655,54811,2623],{},[3615,54813,54814],{"scriptlevel":2552,"displaystyle":1663},[1949,54815,54816,54818],{},[1826,54817,1828],{},[1826,54819,45532],{},[1655,54821,1664],{"stretchy":1663},[1826,54823,1828],{},[1655,54825,1677],{"stretchy":1663},[1655,54827,7147],{},[1826,54829,54830],{},"1,224",[1655,54832,2623],{},[1826,54834,54835],{},"1,429",[1655,54837,2623],{},[1826,54839,45705],{},[1655,54841,2623],{},[1826,54843,54844],{},"0,286",[1655,54846,7147],{},[1655,54848,2623],{},[1826,54850,45951],{},[902,54852,54853],{"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.",[724,54855,31191,54856,1719],{},[883,54857,54859],{"className":54858},[886],[888,54860,54861],{"xmlns":890},[892,54862,54863,54885],{},[895,54864,54865,54873,54875,54877,54879,54881,54883],{},[1935,54866,54867,54869,54871],{},[898,54868,1824],{},[1826,54870,1828],{},[898,54872,5502],{},[1655,54874,2357],{},[1826,54876,45700],{},[1655,54878,2623],{},[1826,54880,45982],{},[1655,54882,7147],{},[1826,54884,45987],{},[902,54886,54887],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[5120,54889,54890],{},[724,54891,54892,54894,54895,54916,54917,54943,54944,54947,54948,55044,55045,55068,55069,55085],{},[883,54893,5661],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,54896,54898],{"className":54897},[886],[888,54899,54900],{"xmlns":890},[892,54901,54902,54914],{},[895,54903,54904,54906,54908,54910,54912],{},[898,54905,2506],{"mathvariant":1943},[898,54907,1824],{},[1655,54909,2357],{},[1655,54911,2623],{},[1826,54913,46017],{},[902,54915,46020],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,54918,54920],{"className":54919},[886],[888,54921,54922],{"xmlns":890},[892,54923,54924,54940],{},[895,54925,54926,54928,54934,54936,54938],{},[898,54927,2410],{},[2597,54929,54930,54932],{},[898,54931,1824],{},[898,54933,5502],{},[1655,54935,7147],{},[1655,54937,2623],{},[1826,54939,45982],{},[902,54941,54942],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,54945,54946],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,54949,54951],{"className":54950},[886],[888,54952,54953],{"xmlns":890},[892,54954,54955,55041],{},[895,54956,54957,54965,54967,55001,55003,55027,55029,55036,55038],{},[1935,54958,54959,54961,54963],{},[898,54960,1824],{},[1826,54962,1828],{},[898,54964,5502],{},[1655,54966,1657],{},[1949,54968,54969,54985],{},[895,54970,54971,54977,54979],{},[2597,54972,54973,54975],{},[898,54974,2025],{},[1655,54976,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,54978,2623],{},[2597,54980,54981,54983],{},[898,54982,2410],{},[1655,54984,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[895,54986,54987,54993,54995],{},[2597,54988,54989,54991],{},[898,54990,1789],{},[1655,54992,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,54994,2623],{},[2597,54996,54997,54999],{},[898,54998,207],{},[1655,55000,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,55002,1657],{},[1949,55004,55005,55013],{},[895,55006,55007,55009,55011],{},[1826,55008,16163],{},[1655,55010,2623],{},[1826,55012,4176],{},[895,55014,55015,55017,55019,55021,55023,55025],{},[1826,55016,20447],{},[1655,55018,2623],{},[1655,55020,1664],{"stretchy":1663},[1655,55022,2623],{},[1826,55024,54325],{},[1655,55026,1677],{"stretchy":1663},[1655,55028,1657],{},[1949,55030,55031,55033],{},[1826,55032,42926],{},[1826,55034,55035],{},"3,1",[1655,55037,7147],{},[1826,55039,55040],{},"7,742",[902,55042,55043],{"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 ",[883,55046,55048],{"className":55047},[886],[888,55049,55050],{"xmlns":890},[892,55051,55052,55065],{},[895,55053,55054,55056,55058,55060,55062],{},[898,55055,2506],{"mathvariant":1943},[898,55057,1824],{},[1655,55059,7147],{},[1655,55061,2623],{},[1826,55063,55064],{},"0,829",[902,55066,55067],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,55070,55072],{"className":55071},[886],[888,55073,55074],{"xmlns":890},[892,55075,55076,55082],{},[895,55077,55078,55080],{},[1655,55079,2623],{},[1826,55081,46017],{},[902,55083,55084],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,55087,55088],{},[614,55089,55090,55091,55104],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,55092,55094],{"className":55093},[886],[888,55095,55096],{"xmlns":890},[892,55097,55098,55102],{},[895,55099,55100],{},[898,55101,1824],{},[902,55103,1824],{"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.",[198,55106,55108,55109],{"id":55107},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,55110,55112],{"className":55111},[886],[888,55113,55114],{"xmlns":890},[892,55115,55116,55122],{},[895,55117,55118,55120],{},[898,55119,2132],{},[898,55121,9920],{},[902,55123,46095],{"encoding":904},[5120,55125,55126],{},[724,55127,55128,55130,55131,55165,55166,55188],{},[883,55129,53821],{}," Zadání\nPro nabídku ",[883,55132,55134],{"className":55133},[886],[888,55135,55136],{"xmlns":890},[892,55137,55138,55162],{},[895,55139,55140,55142,55144,55146,55148,55150,55152,55154,55156,55158,55160],{},[898,55141,2132],{},[1655,55143,1657],{},[898,55145,9920],{},[1655,55147,1664],{"stretchy":1663},[898,55149,1824],{},[1655,55151,1677],{"stretchy":1663},[1655,55153,1657],{},[1826,55155,4136],{},[1655,55157,2346],{},[1826,55159,1837],{},[898,55161,1824],{},[902,55163,55164],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,55167,55169],{"className":55168},[886],[888,55170,55171],{"xmlns":890},[892,55172,55173,55185],{},[895,55174,55175,55181,55183],{},[1820,55176,55177,55179],{},[898,55178,1824],{},[1826,55180,2552],{},[1655,55182,1657],{},[1826,55184,4136],{},[902,55186,55187],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,55190,55191],{},[38,55192,23896],{},[724,55194,55195],{},"Odpovídající cena:",[883,55197,55199],{"className":55198},[886],[888,55200,55201],{"xmlns":890,"display":29192},[892,55202,55203,55238],{},[895,55204,55205,55211,55213,55215,55217,55219,55221,55223,55225,55227,55229,55231,55233,55235],{},[1820,55206,55207,55209],{},[898,55208,2132],{},[1826,55210,2552],{},[1655,55212,1657],{},[898,55214,9920],{},[1655,55216,1664],{"stretchy":1663},[1826,55218,4136],{},[1655,55220,1677],{"stretchy":1663},[1655,55222,1657],{},[1826,55224,4136],{},[1655,55226,2346],{},[1826,55228,1837],{},[1655,55230,2869],{},[1826,55232,4136],{},[1655,55234,1657],{},[1826,55236,55237],{},"30.",[902,55239,55240],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,55242,55243],{},"Dle vzorce (2.15):",[883,55245,55247],{"className":55246},[886],[888,55248,55249],{"xmlns":890,"display":29192},[892,55250,55251,55359],{},[895,55252,55253,55255,55257,55259,55261,55263,55265,55271,55277,55279,55287,55289,55291,55293,55295,55297,55299,55301,55303,55305,55307,55309,55311,55313,55315,55318,55320,55322,55324,55330,55338,55340,55342,55344,55346,55348,55350,55352,55354,55356],{},[898,55254,2132],{},[898,55256,9920],{},[1655,55258,1664],{"stretchy":1663},[1826,55260,4136],{},[1655,55262,1677],{"stretchy":1663},[1655,55264,1657],{},[1820,55266,55267,55269],{},[898,55268,2132],{},[1826,55270,2552],{},[1820,55272,55273,55275],{},[898,55274,1824],{},[1826,55276,2552],{},[1655,55278,2623],{},[1935,55280,55281,55283,55285],{},[1655,55282,12293],{},[1826,55284,2552],{},[1826,55286,4136],{},[1655,55288,1664],{"stretchy":1663},[1826,55290,4136],{},[1655,55292,2346],{},[1826,55294,1837],{},[898,55296,1824],{},[1655,55298,1677],{"stretchy":1663},[2031,55300,2435],{},[898,55302,2410],{},[898,55304,1824],{},[1655,55306,1657],{},[1826,55308,4136],{},[1655,55310,2869],{},[1826,55312,39145],{},[1655,55314,2623],{},[1655,55316,2734],{"fence":1663,"stretchy":1670,"minsize":55317,"maxsize":55317},"1.8em",[1826,55319,4136],{},[898,55321,1824],{},[1655,55323,2346],{},[2597,55325,55326,55328],{},[898,55327,1824],{},[1826,55329,1837],{},[1935,55331,55332,55334,55336],{},[1655,55333,2743],{"fence":1663,"stretchy":1670,"minsize":55317,"maxsize":55317},[1826,55335,2552],{},[1826,55337,4136],{},[1655,55339,1657],{},[1826,55341,31207],{},[1655,55343,2623],{},[1655,55345,1664],{"stretchy":1663},[1826,55347,4360],{},[1655,55349,2346],{},[1826,55351,4360],{},[1655,55353,1677],{"stretchy":1663},[1655,55355,1657],{},[1826,55357,55358],{},"100.",[902,55360,55361],{"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.",[724,55363,55364,55365,55386,55387,55407],{},"Přebytek výrobce při množství ",[883,55366,55368],{"className":55367},[886],[888,55369,55370],{"xmlns":890},[892,55371,55372,55384],{},[895,55373,55374,55380,55382],{},[1820,55375,55376,55378],{},[898,55377,1824],{},[1826,55379,2552],{},[1655,55381,1657],{},[1826,55383,4136],{},[902,55385,55187],{"encoding":904}," je tedy ",[883,55388,55390],{"className":55389},[886],[888,55391,55392],{"xmlns":890},[892,55393,55394,55404],{},[895,55395,55396,55398,55400,55402],{},[898,55397,2132],{},[898,55399,9920],{},[1655,55401,1657],{},[1826,55403,4360],{},[902,55405,55406],{"encoding":904},"PS = 100"," (peněžních jednotek).",[38096,55409],{},[115,55411,55413],{"id":55412},"cheat-sheet","Cheat sheet",[16,55415,55416,55429],{},[19,55417,55418],{},[22,55419,55420,55423,55426],{},[25,55421,55422],{},"Veličina",[25,55424,55425],{},"Vzorec",[25,55427,55428],{},"Geometrie",[30,55430,55431,55549,55663,55731],{},[22,55432,55433,55461,55517],{},[35,55434,55435],{},[883,55436,55438],{"className":55437},[886],[888,55439,55440],{"xmlns":890},[892,55441,55442,55458],{},[895,55443,55444,55446,55448,55450,55456],{},[898,55445,4052],{},[898,55447,9920],{},[1655,55449,1664],{"stretchy":1663},[1820,55451,55452,55454],{},[898,55453,1824],{},[1826,55455,2552],{},[1655,55457,1677],{"stretchy":1663},[902,55459,55460],{"encoding":904},"CS(Q_0)",[35,55462,55463],{},[883,55464,55466],{"className":55465},[886],[888,55467,55468],{"xmlns":890},[892,55469,55470,55514],{},[895,55471,55472],{},[3615,55473,55474,55486,55488,55490,55492,55494,55496,55498,55500,55502,55508],{"scriptlevel":2552,"displaystyle":1670},[1935,55475,55476,55478,55480],{},[1655,55477,12293],{},[1826,55479,2552],{},[1820,55481,55482,55484],{},[898,55483,1824],{},[1826,55485,2552],{},[898,55487,2838],{},[1655,55489,1664],{"stretchy":1663},[898,55491,1824],{},[1655,55493,1677],{"stretchy":1663},[2031,55495,2435],{},[898,55497,2410],{},[898,55499,1824],{},[1655,55501,2623],{},[1820,55503,55504,55506],{},[898,55505,2132],{},[1826,55507,2552],{},[1820,55509,55510,55512],{},[898,55511,1824],{},[1826,55513,2552],{},[902,55515,55516],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,55518,55519,55520,55523,55524,55527,55528],{},"plocha ",[38,55521,55522],{},"pod"," křivkou poptávky, ",[38,55525,55526],{},"nad"," čárou ",[883,55529,55531],{"className":55530},[886],[888,55532,55533],{"xmlns":890},[892,55534,55535,55547],{},[895,55536,55537,55539,55541],{},[898,55538,2132],{},[1655,55540,1657],{},[1820,55542,55543,55545],{},[898,55544,2132],{},[1826,55546,2552],{},[902,55548,52803],{"encoding":904},[22,55550,55551,55579,55635],{},[35,55552,55553],{},[883,55554,55556],{"className":55555},[886],[888,55557,55558],{"xmlns":890},[892,55559,55560,55576],{},[895,55561,55562,55564,55566,55568,55574],{},[898,55563,2132],{},[898,55565,9920],{},[1655,55567,1664],{"stretchy":1663},[1820,55569,55570,55572],{},[898,55571,1824],{},[1826,55573,2552],{},[1655,55575,1677],{"stretchy":1663},[902,55577,55578],{"encoding":904},"PS(Q_0)",[35,55580,55581],{},[883,55582,55584],{"className":55583},[886],[888,55585,55586],{"xmlns":890},[892,55587,55588,55632],{},[895,55589,55590],{},[3615,55591,55592,55598,55604,55606,55618,55620,55622,55624,55626,55628,55630],{"scriptlevel":2552,"displaystyle":1670},[1820,55593,55594,55596],{},[898,55595,2132],{},[1826,55597,2552],{},[1820,55599,55600,55602],{},[898,55601,1824],{},[1826,55603,2552],{},[1655,55605,2623],{},[1935,55607,55608,55610,55612],{},[1655,55609,12293],{},[1826,55611,2552],{},[1820,55613,55614,55616],{},[898,55615,1824],{},[1826,55617,2552],{},[898,55619,9920],{},[1655,55621,1664],{"stretchy":1663},[898,55623,1824],{},[1655,55625,1677],{"stretchy":1663},[2031,55627,2435],{},[898,55629,2410],{},[898,55631,1824],{},[902,55633,55634],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,55636,55519,55637,55639,55640,55527,55642],{},[38,55638,55526],{}," křivkou nabídky, ",[38,55641,55522],{},[883,55643,55645],{"className":55644},[886],[888,55646,55647],{"xmlns":890},[892,55648,55649,55661],{},[895,55650,55651,55653,55655],{},[898,55652,2132],{},[1655,55654,1657],{},[1820,55656,55657,55659],{},[898,55658,2132],{},[1826,55660,2552],{},[902,55662,52803],{"encoding":904},[22,55664,55665,55668,55695],{},[35,55666,55667],{},"Výdaje \u002F tržby",[35,55669,55670],{},[883,55671,55673],{"className":55672},[886],[888,55674,55675],{"xmlns":890},[892,55676,55677,55693],{},[895,55678,55679,55685,55687],{},[1820,55680,55681,55683],{},[898,55682,2132],{},[1826,55684,2552],{},[1655,55686,2869],{},[1820,55688,55689,55691],{},[898,55690,1824],{},[1826,55692,2552],{},[902,55694,53663],{"encoding":904},[35,55696,55697,55698],{},"obdélník ",[883,55699,55701],{"className":55700},[886],[888,55702,55703],{"xmlns":890},[892,55704,55705,55729],{},[895,55706,55707,55709,55711,55717,55719,55721,55723],{},[1826,55708,2552],{},[2031,55710,2435],{},[1820,55712,55713,55715],{},[898,55714,1824],{},[1826,55716,2552],{},[2031,55718,2435],{},[898,55720,2731],{},[2031,55722,2435],{},[1820,55724,55725,55727],{},[898,55726,2132],{},[1826,55728,2552],{},[902,55730,52283],{"encoding":904},[22,55732,55733,55736,55759],{},[35,55734,55735],{},"Celkový přebytek",[35,55737,55738],{},[883,55739,55741],{"className":55740},[886],[888,55742,55743],{"xmlns":890},[892,55744,55745,55757],{},[895,55746,55747,55749,55751,55753,55755],{},[898,55748,4052],{},[898,55750,9920],{},[1655,55752,2346],{},[898,55754,2132],{},[898,55756,9920],{},[902,55758,52021],{"encoding":904},[35,55760,55761],{},"součet obou ploch v rovnováze",[38096,55763],{},[115,55765,16845],{"id":16844},[120,55767,55768,55790,55812,55856,55900,55963,55991],{},[123,55769,55770,2115,55772,1343,55787,55789],{},[38,55771,46060],{},[883,55773,55775],{"className":55774},[886],[888,55776,55777],{"xmlns":890},[892,55778,55779,55785],{},[895,55780,55781,55783],{},[898,55782,4052],{},[898,55784,9920],{},[902,55786,46076],{"encoding":904},[614,55788,46114],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,55791,55792,2115,55794,1343,55809,55811],{},[38,55793,46207],{},[883,55795,55797],{"className":55796},[886],[888,55798,55799],{"xmlns":890},[892,55800,55801,55807],{},[895,55802,55803,55805],{},[898,55804,2132],{},[898,55806,9920],{},[902,55808,46095],{"encoding":904},[614,55810,46210],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,55813,55814,8262,55817,1719],{},[38,55815,55816],{},"Ochota platit",[883,55818,55820],{"className":55819},[886],[888,55821,55822],{"xmlns":890},[892,55823,55824,55854],{},[895,55825,55826],{},[3615,55827,55828,55840,55842,55844,55846,55848,55850,55852],{"scriptlevel":2552,"displaystyle":1670},[1935,55829,55830,55832,55834],{},[1655,55831,12293],{},[1826,55833,2552],{},[1820,55835,55836,55838],{},[898,55837,1824],{},[1826,55839,2552],{},[898,55841,2838],{},[1655,55843,1664],{"stretchy":1663},[898,55845,1824],{},[1655,55847,1677],{"stretchy":1663},[2031,55849,2435],{},[898,55851,2410],{},[898,55853,1824],{},[902,55855,52651],{"encoding":904},[123,55857,55858,8262,55861,1719],{},[38,55859,55860],{},"Minimální cena výrobce",[883,55862,55864],{"className":55863},[886],[888,55865,55866],{"xmlns":890},[892,55867,55868,55898],{},[895,55869,55870],{},[3615,55871,55872,55884,55886,55888,55890,55892,55894,55896],{"scriptlevel":2552,"displaystyle":1670},[1935,55873,55874,55876,55878],{},[1655,55875,12293],{},[1826,55877,2552],{},[1820,55879,55880,55882],{},[898,55881,1824],{},[1826,55883,2552],{},[898,55885,9920],{},[1655,55887,1664],{"stretchy":1663},[898,55889,1824],{},[1655,55891,1677],{"stretchy":1663},[2031,55893,2435],{},[898,55895,2410],{},[898,55897,1824],{},[902,55899,53293],{"encoding":904},[123,55901,55902,8262,55905,53794,55930,5171],{},[38,55903,55904],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,55906,55908],{"className":55907},[886],[888,55909,55910],{"xmlns":890},[892,55911,55912,55928],{},[895,55913,55914,55920,55922],{},[1820,55915,55916,55918],{},[898,55917,2132],{},[1826,55919,2552],{},[2031,55921,2435],{},[1820,55923,55924,55926],{},[898,55925,1824],{},[1826,55927,2552],{},[902,55929,52729],{"encoding":904},[883,55931,55933],{"className":55932},[886],[888,55934,55935],{"xmlns":890},[892,55936,55937,55961],{},[895,55938,55939,55941,55943,55949,55951,55953,55955],{},[1826,55940,2552],{},[2031,55942,2435],{},[1820,55944,55945,55947],{},[898,55946,1824],{},[1826,55948,2552],{},[2031,55950,2435],{},[898,55952,2731],{},[2031,55954,2435],{},[1820,55956,55957,55959],{},[898,55958,2132],{},[1826,55960,2552],{},[902,55962,52283],{"encoding":904},[123,55964,55965,55968,55969,55990],{},[38,55966,55967],{},"Celkový přebytek trhu"," — součet ",[883,55970,55972],{"className":55971},[886],[888,55973,55974],{"xmlns":890},[892,55975,55976,55988],{},[895,55977,55978,55980,55982,55984,55986],{},[898,55979,4052],{},[898,55981,9920],{},[1655,55983,2346],{},[898,55985,2132],{},[898,55987,9920],{},[902,55989,52021],{"encoding":904}," v rovnovážném bodě.",[123,55992,55993,55995,55996,1343,56009,56022,56023,1719],{},[38,55994,3729],{}," — plochy ohraničené křivkami ",[883,55997,55999],{"className":55998},[886],[888,56000,56001],{"xmlns":890},[892,56002,56003,56007],{},[895,56004,56005],{},[898,56006,2838],{},[902,56008,2838],{"encoding":904},[883,56010,56012],{"className":56011},[886],[888,56013,56014],{"xmlns":890},[892,56015,56016,56020],{},[895,56017,56018],{},[898,56019,9920],{},[902,56021,9920],{"encoding":904}," a přímkou ",[883,56024,56026],{"className":56025},[886],[888,56027,56028],{"xmlns":890},[892,56029,56030,56042],{},[895,56031,56032,56034,56036],{},[898,56033,2132],{},[1655,56035,1657],{},[1820,56037,56038,56040],{},[898,56039,2132],{},[1826,56041,2552],{},[902,56043,52803],{"encoding":904},[38096,56045],{},[115,56047,56049],{"id":56048},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,56051,56052,56053,56066,56067,56084],{},"Uvalení jednotkové daně ",[883,56054,56056],{"className":56055},[886],[888,56057,56058],{"xmlns":890},[892,56059,56060,56064],{},[895,56061,56062],{},[898,56063,4049],{},[902,56065,4049],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,56068,56070],{"className":56069},[886],[888,56071,56072],{"xmlns":890},[892,56073,56074,56082],{},[895,56075,56076],{},[2597,56077,56078,56080],{},[898,56079,1824],{},[898,56081,5502],{},[902,56083,43529],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,56086,56087],{},[1723,56088],{"alt":56089,"className":56090,"src":56091},"imek-prebytky-s-dani-deadweight",[210,1727],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,56093,56094,56095,56110,56111,56126,56127,53794,56130,56154,56155,2115,56158,56161,56162,1719],{},"Přebytek spotřebitele ",[883,56096,56098],{"className":56097},[886],[888,56099,56100],{"xmlns":890},[892,56101,56102,56108],{},[895,56103,56104,56106],{},[898,56105,4052],{},[898,56107,9920],{},[902,56109,46076],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,56112,56114],{"className":56113},[886],[888,56115,56116],{"xmlns":890},[892,56117,56118,56124],{},[895,56119,56120,56122],{},[898,56121,2132],{},[898,56123,9920],{},[902,56125,46095],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,56128,56129],{},"daňový příjem",[883,56131,56133],{"className":56132},[886],[888,56134,56135],{"xmlns":890},[892,56136,56137,56151],{},[895,56138,56139,56141,56143],{},[898,56140,4049],{},[1655,56142,2869],{},[1935,56144,56145,56147,56149],{},[898,56146,1824],{},[1826,56148,1828],{},[898,56150,5502],{},[902,56152,56153],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,56156,56157],{},"mrtvá ztráta",[614,56159,56160],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,56163,811],{"className":56164,"dataFsResolvedFilePath":809,"href":810},[210],[38096,56166],{},[115,56168,3187],{"id":3186},[120,56170,56171,56178,56190,56197,56204],{},[123,56172,56173,3106,56175],{},[38,56174,17347],{},[207,56176,802],{"className":56177,"dataFsResolvedFilePath":800,"href":801},[210],[123,56179,56180,3106,56182,56185,56186,56189],{},[38,56181,37800],{},[207,56183,775],{"className":56184,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,56187,3645],{"className":56188,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,56191,56192,3106,56194],{},[38,56193,17357],{},[207,56195,5078],{"className":56196,"dataFsResolvedFilePath":827,"href":828},[210],[123,56198,56199,3106,56201],{},[38,56200,51884],{},[207,56202,51888],{"className":56203,"dataFsResolvedFilePath":745,"href":746},[210],[123,56205,56206,3106,56208],{},[38,56207,17329],{},[207,56209,17333],{"className":56210,"dataFsResolvedFilePath":3274,"href":3275},[210],{"title":641,"searchDepth":642,"depth":642,"links":56212},[56213,56214,56219,56224,56229,56230,56231,56232],{"id":52080,"depth":642,"text":1241},{"id":52424,"depth":642,"text":56215,"children":56216},"Přebytek spotřebitele (CSCS)",[56217,56218],{"id":52443,"depth":649,"text":52444},{"id":3728,"depth":649,"text":3729},{"id":53019,"depth":642,"text":56220,"children":56221},"Přebytek výrobce (PSPS)",[56222,56223],{"id":53038,"depth":649,"text":53039},{"id":53201,"depth":649,"text":3729},{"id":53809,"depth":642,"text":53810,"children":56225},[56226,56227],{"id":53813,"depth":649,"text":53814},{"id":55107,"depth":649,"text":56228},"Příklad 2.13 — numerický výpočet PSPS",{"id":55412,"depth":642,"text":55413},{"id":16844,"depth":642,"text":16845},{"id":56048,"depth":642,"text":56049},{"id":3186,"depth":642,"text":3187},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,51950,56239,56240,13113,17365,56241,56242],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":56245,"title":56246,"body":56247,"course":1128,"courses":659,"created":10802,"description":641,"extension":661,"meta":75576,"navigation":664,"path":75577,"seo":75578,"sources":75579,"stem":75580,"tags":75581,"type":3252,"updated":677,"__hash__":75587},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":56248,"toc":75540},[56249,56252,56438,56440,56531,56536,56862,56866,56873,56877,56922,56989,57020,57070,57105,57109,57168,57173,57239,57357,57459,57463,57486,57564,57607,57611,57640,57707,57713,57827,57831,57911,57948,58000,58198,58262,58349,58353,58356,58435,58438,58556,58575,58640,58644,58736,58804,58845,58899,58967,59004,59008,59066,59096,59307,59379,59431,59597,59690,59725,59729,59733,59770,59835,59890,59894,59917,60006,60110,60179,60183,60280,60393,60449,60503,60561,60622,60625,60661,60726,60756,60985,61043,61077,61081,61108,61187,61301,61322,61401,61403,61511,61515,61653,61975,61979,61982,61986,62035,62039,62293,62445,62452,62525,62709,62714,63057,63061,63084,63086,63107,63166,63176,63225,63367,63441,63536,63651,63749,63867,63871,63940,63945,64057,64202,64253,64365,64407,64411,64431,64492,64519,64581,64585,64607,64676,64956,64963,64993,65000,65193,65197,65275,65280,65356,65359,65447,65523,65590,65639,65742,65815,65936,66287,66400,66502,66506,66509,66516,66519,66555,66614,66623,66772,66996,67000,67063,67242,67334,67389,67393,67449,67519,67571,67592,67673,67676,67751,67795,67799,67840,67883,67909,67913,67984,68080,68142,68194,68297,68375,68398,68427,68431,68597,68714,68786,69101,69261,69265,69316,69378,69413,69443,69543,69585,69754,69759,69855,69893,69897,70016,70317,70319,70354,70358,70362,70490,70622,70944,71132,71210,71214,71519,71632,71778,71963,72069,72301,72416,72498,72617,72715,72756,72760,72815,72959,73113,73273,73366,73560,73872,74003,74132,74136,74208,74250,74301,74303,75498,75500],[12,56250,56246],{"id":56251},"příjem-náklady-zisk-a-nabídka-firmy",[5120,56253,56254],{},[724,56255,56256,5127,56258,3106,56261,56276,56277,3106,56280,56295,56296,3106,56299,56327,56328,56350,56351,56375,56376,56398,56399,56402,56403,56419,56420,1719],{},[883,56257,5126],{},[38,56259,56260],{},"Příjem",[883,56262,56264],{"className":56263},[886],[888,56265,56266],{"xmlns":890},[892,56267,56268,56274],{},[895,56269,56270,56272],{},[898,56271,4049],{},[898,56273,5245],{},[902,56275,5345],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,56278,56279],{},"náklady",[883,56281,56283],{"className":56282},[886],[888,56284,56285],{"xmlns":890},[892,56286,56287,56293],{},[895,56288,56289,56291],{},[898,56290,4049],{},[898,56292,4052],{},[902,56294,4512],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,56297,56298],{},"zisk",[883,56300,56302],{"className":56301},[886],[888,56303,56304],{"xmlns":890},[892,56305,56306,56324],{},[895,56307,56308,56310,56312,56314,56316,56318,56320,56322],{},[898,56309,2132],{},[898,56311,5245],{},[1655,56313,1657],{},[898,56315,4049],{},[898,56317,5245],{},[1655,56319,2623],{},[898,56321,4049],{},[898,56323,4052],{},[902,56325,56326],{"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: ",[883,56329,56331],{"className":56330},[886],[888,56332,56333],{"xmlns":890},[892,56334,56335,56347],{},[895,56336,56337,56339,56341,56343,56345],{},[898,56338,2731],{},[898,56340,4052],{},[1655,56342,1657],{},[898,56344,2127],{},[898,56346,4052],{},[902,56348,56349],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,56352,56354],{"className":56353},[886],[888,56355,56356],{"xmlns":890},[892,56357,56358,56372],{},[895,56359,56360,56362,56364,56366,56368,56370],{},[898,56361,2731],{},[898,56363,41465],{},[898,56365,4052],{},[1655,56367,1657],{},[898,56369,2127],{},[898,56371,4052],{},[902,56373,56374],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,56377,56379],{"className":56378},[886],[888,56380,56381],{"xmlns":890},[892,56382,56383,56395],{},[895,56384,56385,56387,56389,56391,56393],{},[898,56386,2127],{},[898,56388,5245],{},[1655,56390,1657],{},[898,56392,2127],{},[898,56394,4052],{},[902,56396,56397],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,56400,56401],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,56404,56406],{"className":56405},[886],[888,56407,56408],{"xmlns":890},[892,56409,56410,56416],{},[895,56411,56412,56414],{},[898,56413,2127],{},[898,56415,4052],{},[902,56417,56418],{"encoding":904},"MC"," nad bodem minima ",[883,56421,56423],{"className":56422},[886],[888,56424,56425],{"xmlns":890},[892,56426,56427,56435],{},[895,56428,56429,56431,56433],{},[898,56430,2731],{},[898,56432,41465],{},[898,56434,4052],{},[902,56436,56437],{"encoding":904},"AVC",[115,56439,1241],{"id":52080},[724,56441,56442,56443,56446,56447,56449,56450,1343,56453,1343,56456,56458,56459,56462,56463,56466,56467,56470,56471,3948,56486,1348,56501,3948,56516,5171],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,56444,56445],{},"příjmem"," (revenue) a ",[38,56448,56279],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,56451,56452],{},"zisku",[38,56454,56455],{},"bodů zvratu",[38,56457,3284],{}," a konstrukcí ",[38,56460,56461],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,56464,1145],{"className":56465,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,56468,12254],{"className":56469,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,56472,56474],{"className":56473},[886],[888,56475,56476],{"xmlns":890},[892,56477,56478,56484],{},[895,56479,56480,56482],{},[898,56481,4049],{},[898,56483,5245],{},[902,56485,5345],{"encoding":904},[883,56487,56489],{"className":56488},[886],[888,56490,56491],{"xmlns":890},[892,56492,56493,56499],{},[895,56494,56495,56497],{},[898,56496,2127],{},[898,56498,5245],{},[902,56500,7881],{"encoding":904},[883,56502,56504],{"className":56503},[886],[888,56505,56506],{"xmlns":890},[892,56507,56508,56514],{},[895,56509,56510,56512],{},[898,56511,4049],{},[898,56513,4052],{},[902,56515,4512],{"encoding":904},[883,56517,56519],{"className":56518},[886],[888,56520,56521],{"xmlns":890},[892,56522,56523,56529],{},[895,56524,56525,56527],{},[898,56526,2127],{},[898,56528,4052],{},[902,56530,56418],{"encoding":904},[724,56532,56533],{},[38,56534,56535],{},"Cílové znalosti:",[120,56537,56538,56702,56705,56708,56801,56848,56855],{},[123,56539,56540,56541,1343,56556,1343,56572,2704,56587,1343,56602,1343,56618,1343,56636,1343,56654,1343,56671,1343,56687,9672],{},"odvodit a interpretovat funkce ",[883,56542,56544],{"className":56543},[886],[888,56545,56546],{"xmlns":890},[892,56547,56548,56554],{},[895,56549,56550,56552],{},[898,56551,4049],{},[898,56553,5245],{},[902,56555,5345],{"encoding":904},[883,56557,56559],{"className":56558},[886],[888,56560,56561],{"xmlns":890},[892,56562,56563,56569],{},[895,56564,56565,56567],{},[898,56566,2731],{},[898,56568,5245],{},[902,56570,56571],{"encoding":904},"AR",[883,56573,56575],{"className":56574},[886],[888,56576,56577],{"xmlns":890},[892,56578,56579,56585],{},[895,56580,56581,56583],{},[898,56582,2127],{},[898,56584,5245],{},[902,56586,7881],{"encoding":904},[883,56588,56590],{"className":56589},[886],[888,56591,56592],{"xmlns":890},[892,56593,56594,56600],{},[895,56595,56596,56598],{},[898,56597,4049],{},[898,56599,4052],{},[902,56601,4512],{"encoding":904},[883,56603,56605],{"className":56604},[886],[888,56606,56607],{"xmlns":890},[892,56608,56609,56615],{},[895,56610,56611,56613],{},[898,56612,2537],{},[898,56614,4052],{},[902,56616,56617],{"encoding":904},"FC",[883,56619,56621],{"className":56620},[886],[888,56622,56623],{"xmlns":890},[892,56624,56625,56633],{},[895,56626,56627,56629,56631],{},[898,56628,4049],{},[898,56630,41465],{},[898,56632,4052],{},[902,56634,56635],{"encoding":904},"TVC",[883,56637,56639],{"className":56638},[886],[888,56640,56641],{"xmlns":890},[892,56642,56643,56651],{},[895,56644,56645,56647,56649],{},[898,56646,2731],{},[898,56648,2537],{},[898,56650,4052],{},[902,56652,56653],{"encoding":904},"AFC",[883,56655,56657],{"className":56656},[886],[888,56658,56659],{"xmlns":890},[892,56660,56661,56669],{},[895,56662,56663,56665,56667],{},[898,56664,2731],{},[898,56666,41465],{},[898,56668,4052],{},[902,56670,56437],{"encoding":904},[883,56672,56674],{"className":56673},[886],[888,56675,56676],{"xmlns":890},[892,56677,56678,56684],{},[895,56679,56680,56682],{},[898,56681,2731],{},[898,56683,4052],{},[902,56685,56686],{"encoding":904},"AC",[883,56688,56690],{"className":56689},[886],[888,56691,56692],{"xmlns":890},[892,56693,56694,56700],{},[895,56695,56696,56698],{},[898,56697,2127],{},[898,56699,4052],{},[902,56701,56418],{"encoding":904},[123,56703,56704],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,56706,56707],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,56709,56710,56711,56714,56715,42940,56757,9672],{},"osvojit si ",[38,56712,56713],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,56716,56718],{"className":56717},[886],[888,56719,56720],{"xmlns":890},[892,56721,56722,56754],{},[895,56723,56724,56726,56728,56730,56736,56738,56740,56742,56744,56746,56752],{},[898,56725,2731],{},[898,56727,4052],{},[1655,56729,1664],{"stretchy":1663},[1820,56731,56732,56734],{},[898,56733,1824],{},[1826,56735,2552],{},[1655,56737,1677],{"stretchy":1663},[1655,56739,1657],{},[898,56741,2127],{},[898,56743,4052],{},[1655,56745,1664],{"stretchy":1663},[1820,56747,56748,56750],{},[898,56749,1824],{},[1826,56751,2552],{},[1655,56753,1677],{"stretchy":1663},[902,56755,56756],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,56758,56760],{"className":56759},[886],[888,56761,56762],{"xmlns":890},[892,56763,56764,56798],{},[895,56765,56766,56768,56770,56772,56774,56780,56782,56784,56786,56788,56790,56796],{},[898,56767,2731],{},[898,56769,41465],{},[898,56771,4052],{},[1655,56773,1664],{"stretchy":1663},[1820,56775,56776,56778],{},[898,56777,1824],{},[1826,56779,2552],{},[1655,56781,1677],{"stretchy":1663},[1655,56783,1657],{},[898,56785,2127],{},[898,56787,4052],{},[1655,56789,1664],{"stretchy":1663},[1820,56791,56792,56794],{},[898,56793,1824],{},[1826,56795,2552],{},[1655,56797,1677],{"stretchy":1663},[902,56799,56800],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,56802,56710,56803,56714,56806,9672],{},[38,56804,56805],{},"princip maximalizace zisku",[883,56807,56809],{"className":56808},[886],[888,56810,56811],{"xmlns":890},[892,56812,56813,56845],{},[895,56814,56815,56817,56819,56821,56827,56829,56831,56833,56835,56837,56843],{},[898,56816,2127],{},[898,56818,5245],{},[1655,56820,1664],{"stretchy":1663},[1820,56822,56823,56825],{},[898,56824,1824],{},[1826,56826,2552],{},[1655,56828,1677],{"stretchy":1663},[1655,56830,1657],{},[898,56832,2127],{},[898,56834,4052],{},[1655,56836,1664],{"stretchy":1663},[1820,56838,56839,56841],{},[898,56840,1824],{},[1826,56842,2552],{},[1655,56844,1677],{"stretchy":1663},[902,56846,56847],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,56849,56850,56851,56854],{},"stanovit ",[38,56852,56853],{},"body zvratu"," a interval zisku;",[123,56856,56857,56858,56861],{},"zkonstruovat ",[38,56859,56860],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,56863,56865],{"id":56864},"příjem-firmy","Příjem firmy",[724,56867,56868],{},[1723,56869],{"alt":56870,"className":56871,"src":56872},"imek-ar-mr-dvojnasobny-sklon",[210,1727],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,56874,56876],{"id":56875},"celkový-příjem","Celkový příjem",[724,56878,56879,56880,2115,56895,56898,56899,31070],{},"Celkový příjem ",[883,56881,56883],{"className":56882},[886],[888,56884,56885],{"xmlns":890},[892,56886,56887,56893],{},[895,56888,56889,56891],{},[898,56890,4049],{},[898,56892,5245],{},[902,56894,5345],{"encoding":904},[38,56896,56897],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,56900,56902],{"className":56901},[886],[888,56903,56904],{"xmlns":890},[892,56905,56906,56920],{},[895,56907,56908,56910,56912,56914,56916,56918],{},[898,56909,2132],{},[1655,56911,1657],{},[898,56913,2838],{},[1655,56915,1664],{"stretchy":1663},[898,56917,1824],{},[1655,56919,1677],{"stretchy":1663},[902,56921,5889],{"encoding":904},[883,56923,56925],{"className":56924},[886],[888,56926,56927],{"xmlns":890,"display":29192},[892,56928,56929,56986],{},[21880,56930,56931],{"width":29197},[21885,56932,56933,56935,56979,56981],{},[21888,56934],{"width":29202},[21888,56936,56937],{},[895,56938,56939,56941,56943,56945,56947,56949,56951,56953,56955,56957,56959,56961,56963,56965,56967,56969,56971,56973,56975,56977],{},[898,56940,4049],{},[898,56942,5245],{},[1655,56944,1657],{},[898,56946,4049],{},[898,56948,5245],{},[1655,56950,1664],{"stretchy":1663},[898,56952,1824],{},[1655,56954,1677],{"stretchy":1663},[1655,56956,1657],{},[898,56958,2132],{},[1655,56960,2869],{},[898,56962,1824],{},[1655,56964,1657],{},[898,56966,2838],{},[1655,56968,1664],{"stretchy":1663},[898,56970,1824],{},[1655,56972,1677],{"stretchy":1663},[1655,56974,2869],{},[898,56976,1824],{},[898,56978,1719],{"mathvariant":1943},[21888,56980],{"width":29202},[21888,56982,56983],{},[2031,56984,56985],{},"(3.1)",[902,56987,56988],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,56990,56991,56992,56995,56996,57019],{},"Graf funkce se nazývá ",[38,56993,56994],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,56997,56999],{"className":56998},[886],[888,57000,57001],{"xmlns":890},[892,57002,57003,57017],{},[895,57004,57005,57007,57009,57011,57013,57015],{},[898,57006,2132],{},[1655,57008,1657],{},[898,57010,207],{},[898,57012,1824],{},[1655,57014,2346],{},[898,57016,2025],{},[902,57018,38186],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,57021,57023],{"className":57022},[886],[888,57024,57025],{"xmlns":890,"display":29192},[892,57026,57027,57067],{},[895,57028,57029,57031,57033,57035,57037,57039,57041,57043,57045,57047,57049,57051,57053,57059,57061,57063,57065],{},[898,57030,4049],{},[898,57032,5245],{},[1655,57034,1657],{},[898,57036,1824],{},[1655,57038,1664],{"stretchy":1663},[898,57040,207],{},[898,57042,1824],{},[1655,57044,2346],{},[898,57046,2025],{},[1655,57048,1677],{"stretchy":1663},[1655,57050,1657],{},[898,57052,207],{},[2597,57054,57055,57057],{},[898,57056,1824],{},[1826,57058,1837],{},[1655,57060,2346],{},[898,57062,2025],{},[898,57064,1824],{},[1655,57066,1671],{"separator":1670},[902,57068,57069],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,57071,57072,57073,57086,57087,57104],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,57074,57076],{"className":57075},[886],[888,57077,57078],{"xmlns":890},[892,57079,57080,57084],{},[895,57081,57082],{},[898,57083,900],{},[902,57085,900],{"encoding":904}," (jelikož ",[883,57088,57090],{"className":57089},[886],[888,57091,57092],{"xmlns":890},[892,57093,57094,57102],{},[895,57095,57096,57098,57100],{},[898,57097,207],{},[1655,57099,3065],{},[1826,57101,2552],{},[902,57103,44211],{"encoding":904},") procházející počátkem.",[38474,57106,57108],{"id":57107},"příklad-31","Příklad 3.1",[724,57110,57111,57114,57115,57151,57152,57167],{},[38,57112,57113],{},"Zadání."," Pro poptávku ",[883,57116,57118],{"className":57117},[886],[888,57119,57120],{"xmlns":890},[892,57121,57122,57148],{},[895,57123,57124,57126,57128,57130,57132,57134,57136,57138,57140,57142,57144,57146],{},[898,57125,2132],{},[1655,57127,1657],{},[898,57129,2838],{},[1655,57131,1664],{"stretchy":1663},[898,57133,1824],{},[1655,57135,1677],{"stretchy":1663},[1655,57137,1657],{},[1655,57139,2623],{},[1826,57141,1837],{},[898,57143,1824],{},[1655,57145,2346],{},[1826,57147,4360],{},[902,57149,57150],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,57153,57155],{"className":57154},[886],[888,57156,57157],{"xmlns":890},[892,57158,57159,57165],{},[895,57160,57161,57163],{},[898,57162,4049],{},[898,57164,5245],{},[902,57166,5345],{"encoding":904}," a charakterizujte jeho křivku.",[724,57169,57170,57172],{},[38,57171,23896],{}," Celkový příjem je",[883,57174,57176],{"className":57175},[886],[888,57177,57178],{"xmlns":890,"display":29192},[892,57179,57180,57236],{},[895,57181,57182,57184,57186,57188,57190,57192,57194,57196,57198,57200,57202,57204,57206,57208,57210,57212,57214,57216,57218,57220,57222,57228,57230,57232,57234],{},[898,57183,4049],{},[898,57185,5245],{},[1655,57187,1657],{},[898,57189,4049],{},[898,57191,5245],{},[1655,57193,1664],{"stretchy":1663},[898,57195,1824],{},[1655,57197,1677],{"stretchy":1663},[1655,57199,1657],{},[898,57201,1824],{},[1655,57203,1664],{"stretchy":1663},[1655,57205,2623],{},[1826,57207,1837],{},[898,57209,1824],{},[1655,57211,2346],{},[1826,57213,4360],{},[1655,57215,1677],{"stretchy":1663},[1655,57217,1657],{},[1655,57219,2623],{},[1826,57221,1837],{},[2597,57223,57224,57226],{},[898,57225,1824],{},[1826,57227,1837],{},[1655,57229,2346],{},[1826,57231,4360],{},[898,57233,1824],{},[898,57235,1719],{"mathvariant":1943},[902,57237,57238],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,57240,57241,57242,2704,57264,57286,57287,57305,57306,1719],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,57243,57245],{"className":57244},[886],[888,57246,57247],{"xmlns":890},[892,57248,57249,57261],{},[895,57250,57251,57257,57259],{},[1820,57252,57253,57255],{},[898,57254,1824],{},[1826,57256,1828],{},[1655,57258,1657],{},[1826,57260,2552],{},[902,57262,57263],{"encoding":904},"Q_1 = 0",[883,57265,57267],{"className":57266},[886],[888,57268,57269],{"xmlns":890},[892,57270,57271,57283],{},[895,57272,57273,57279,57281],{},[1820,57274,57275,57277],{},[898,57276,1824],{},[1826,57278,1837],{},[1655,57280,1657],{},[1826,57282,4390],{},[902,57284,57285],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,57288,57290],{"className":57289},[886],[888,57291,57292],{"xmlns":890},[892,57293,57294,57302],{},[895,57295,57296,57298,57300],{},[898,57297,1824],{},[1655,57299,1657],{},[1826,57301,6253],{},[902,57303,57304],{"encoding":904},"Q = 25"," ve výši ",[883,57307,57309],{"className":57308},[886],[888,57310,57311],{"xmlns":890},[892,57312,57313,57354],{},[895,57314,57315,57317,57327,57329,57331,57333,57335,57338,57340,57342,57344,57346,57348,57350,57352],{},[898,57316,4049],{},[1820,57318,57319,57321,57324],{},[898,57320,5245],{},[898,57322,57323],{},"max",[1655,57325,57326],{},"⁡",[1655,57328,1657],{},[1655,57330,2623],{},[1826,57332,1837],{},[1655,57334,2869],{},[1826,57336,57337],{},"625",[1655,57339,2346],{},[1826,57341,4360],{},[1655,57343,2869],{},[1826,57345,6253],{},[1655,57347,1657],{},[1826,57349,1828],{},[2031,57351,2435],{},[1826,57353,31869],{},[902,57355,57356],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,57358,57359],{},[614,57360,57361,57362,57396,57397,2704,57410,57423,57424,3902,57442,1719],{},"Obrázek 3.1: Parabola ",[883,57363,57365],{"className":57364},[886],[888,57366,57367],{"xmlns":890},[892,57368,57369,57393],{},[895,57370,57371,57373,57375,57377,57379,57381,57387,57389,57391],{},[898,57372,4049],{},[898,57374,5245],{},[1655,57376,1657],{},[1655,57378,2623],{},[1826,57380,1837],{},[2597,57382,57383,57385],{},[898,57384,1824],{},[1826,57386,1837],{},[1655,57388,2346],{},[1826,57390,4360],{},[898,57392,1824],{},[902,57394,57395],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,57398,57400],{"className":57399},[886],[888,57401,57402],{"xmlns":890},[892,57403,57404,57408],{},[895,57405,57406],{},[1826,57407,2552],{},[902,57409,2552],{"encoding":904},[883,57411,57413],{"className":57412},[886],[888,57414,57415],{"xmlns":890},[892,57416,57417,57421],{},[895,57418,57419],{},[1826,57420,4390],{},[902,57422,4390],{"encoding":904}," a maximem ",[883,57425,57427],{"className":57426},[886],[888,57428,57429],{"xmlns":890},[892,57430,57431,57439],{},[895,57432,57433,57435,57437],{},[1826,57434,1828],{},[2031,57436,2435],{},[1826,57438,31869],{},[902,57440,57441],{"encoding":904},"1\\,250",[883,57443,57445],{"className":57444},[886],[888,57446,57447],{"xmlns":890},[892,57448,57449,57457],{},[895,57450,57451,57453,57455],{},[898,57452,1824],{},[1655,57454,1657],{},[1826,57456,6253],{},[902,57458,57304],{"encoding":904},[198,57460,57462],{"id":57461},"průměrný-příjem","Průměrný příjem",[724,57464,57465,3106,57467,2115,57482,57485],{},[38,57466,57462],{},[883,57468,57470],{"className":57469},[886],[888,57471,57472],{"xmlns":890},[892,57473,57474,57480],{},[895,57475,57476,57478],{},[898,57477,2731],{},[898,57479,5245],{},[902,57481,56571],{"encoding":904},[38,57483,57484],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,57487,57489],{"className":57488},[886],[888,57490,57491],{"xmlns":890,"display":29192},[892,57492,57493,57561],{},[895,57494,57495,57497,57499,57501,57503,57505,57507,57509,57511,57513,57529,57531,57549,57551,57553,57555,57557,57559],{},[898,57496,2731],{},[898,57498,5245],{},[1655,57500,1657],{},[898,57502,2731],{},[898,57504,5245],{},[1655,57506,1664],{"stretchy":1663},[898,57508,1824],{},[1655,57510,1677],{"stretchy":1663},[1655,57512,1657],{},[1949,57514,57515,57527],{},[895,57516,57517,57519,57521,57523,57525],{},[898,57518,4049],{},[898,57520,5245],{},[1655,57522,1664],{"stretchy":1663},[898,57524,1824],{},[1655,57526,1677],{"stretchy":1663},[898,57528,1824],{},[1655,57530,1657],{},[1949,57532,57533,57547],{},[895,57534,57535,57537,57539,57541,57543,57545],{},[898,57536,1824],{},[2031,57538,2435],{},[898,57540,2838],{},[1655,57542,1664],{"stretchy":1663},[898,57544,1824],{},[1655,57546,1677],{"stretchy":1663},[898,57548,1824],{},[1655,57550,1657],{},[898,57552,2838],{},[1655,57554,1664],{"stretchy":1663},[898,57556,1824],{},[1655,57558,1677],{"stretchy":1663},[898,57560,1719],{"mathvariant":1943},[902,57562,57563],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[5120,57565,57566],{},[724,57567,57568,57571,57572,1343,57575,1719],{},[883,57569,57570],{},"!note"," Klíčové pozorování\n",[38,57573,57574],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,57576,57578],{"className":57577},[886],[888,57579,57580],{"xmlns":890},[892,57581,57582,57604],{},[895,57583,57584,57586,57588,57590,57592,57594,57596,57598,57600,57602],{},[898,57585,2731],{},[898,57587,5245],{},[1655,57589,1664],{"stretchy":1663},[898,57591,1824],{},[1655,57593,1677],{"stretchy":1663},[1655,57595,1657],{},[898,57597,2838],{},[1655,57599,1664],{"stretchy":1663},[898,57601,1824],{},[1655,57603,1677],{"stretchy":1663},[902,57605,57606],{"encoding":904},"AR(Q) = D(Q)",[198,57608,57610],{"id":57609},"mezní-příjem","Mezní příjem",[724,57612,57613,57614,3106,57617,2115,57632,57635,57636,57639],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,57615,57616],{},"mezní příjem",[883,57618,57620],{"className":57619},[886],[888,57621,57622],{"xmlns":890},[892,57623,57624,57630],{},[895,57625,57626,57628],{},[898,57627,2127],{},[898,57629,5245],{},[902,57631,7881],{"encoding":904},[38,57633,57634],{},"marginal revenue","), definovaný jako ",[207,57637,1145],{"className":57638,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,57641,57643],{"className":57642},[886],[888,57644,57645],{"xmlns":890,"display":29192},[892,57646,57647,57704],{},[21880,57648,57649],{"width":29197},[21885,57650,57651,57653,57697,57699],{},[21888,57652],{"width":29202},[21888,57654,57655],{},[895,57656,57657,57659,57661,57663,57679,57681,57683,57689,57691,57693,57695],{},[898,57658,2127],{},[898,57660,5245],{},[1655,57662,1657],{},[1949,57664,57665,57673],{},[895,57666,57667,57669,57671],{},[898,57668,2410],{"mathvariant":1943},[898,57670,4049],{},[898,57672,5245],{},[895,57674,57675,57677],{},[898,57676,2410],{"mathvariant":1943},[898,57678,1824],{},[1655,57680,1657],{},[898,57682,4049],{},[2597,57684,57685,57687],{},[898,57686,5245],{},[1655,57688,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,57690,1664],{"stretchy":1663},[898,57692,1824],{},[1655,57694,1677],{"stretchy":1663},[898,57696,1719],{"mathvariant":1943},[21888,57698],{"width":29202},[21888,57700,57701],{},[2031,57702,57703],{},"(3.2)",[902,57705,57706],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,57708,57709,57710,57712],{},"Mezní příjem udává ",[38,57711,3874],{}," celkového příjmu vzhledem k množství.",[5120,57714,57715],{},[724,57716,57717,57719,57720,57746,57747,57764,57765,1719],{},[883,57718,5406],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,57721,57723],{"className":57722},[886],[888,57724,57725],{"xmlns":890},[892,57726,57727,57743],{},[895,57728,57729,57731,57733,57735,57741],{},[898,57730,2127],{},[898,57732,5245],{},[1655,57734,1664],{"stretchy":1663},[2597,57736,57737,57739],{},[898,57738,1824],{},[1655,57740,5603],{},[1655,57742,1677],{"stretchy":1663},[902,57744,57745],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,57748,57750],{"className":57749},[886],[888,57751,57752],{"xmlns":890},[892,57753,57754,57762],{},[895,57755,57756],{},[2597,57757,57758,57760],{},[898,57759,1824],{},[1655,57761,5603],{},[902,57763,30970],{"encoding":904},". Jinak řečeno: ",[883,57766,57768],{"className":57767},[886],[888,57769,57770],{"xmlns":890},[892,57771,57772,57824],{},[895,57773,57774,57776,57778,57780,57786,57788,57790,57792,57794,57796,57802,57804,57806,57808,57810,57812,57814,57816,57822],{},[898,57775,2127],{},[898,57777,5245],{},[1655,57779,1664],{"stretchy":1663},[2597,57781,57782,57784],{},[898,57783,1824],{},[1655,57785,5603],{},[1655,57787,1677],{"stretchy":1663},[1655,57789,2357],{},[898,57791,4049],{},[898,57793,5245],{},[1655,57795,1664],{"stretchy":1663},[2597,57797,57798,57800],{},[898,57799,1824],{},[1655,57801,5603],{},[1655,57803,2346],{},[1826,57805,1828],{},[1655,57807,1677],{"stretchy":1663},[1655,57809,2623],{},[898,57811,4049],{},[898,57813,5245],{},[1655,57815,1664],{"stretchy":1663},[2597,57817,57818,57820],{},[898,57819,1824],{},[1655,57821,5603],{},[1655,57823,1677],{"stretchy":1663},[902,57825,57826],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[38474,57828,57830],{"id":57829},"příklad-32","Příklad 3.2",[724,57832,57833,57114,57835,57151,57869,57884,57885,1719],{},[38,57834,57113],{},[883,57836,57838],{"className":57837},[886],[888,57839,57840],{"xmlns":890},[892,57841,57842,57866],{},[895,57843,57844,57846,57848,57850,57852,57854,57856,57858,57860,57862,57864],{},[898,57845,2132],{},[1655,57847,1657],{},[898,57849,2838],{},[1655,57851,1664],{"stretchy":1663},[898,57853,1824],{},[1655,57855,1677],{"stretchy":1663},[1655,57857,1657],{},[1826,57859,4360],{},[1655,57861,2623],{},[1826,57863,1837],{},[898,57865,1824],{},[902,57867,57868],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,57870,57872],{"className":57871},[886],[888,57873,57874],{"xmlns":890},[892,57875,57876,57882],{},[895,57877,57878,57880],{},[898,57879,2127],{},[898,57881,5245],{},[902,57883,7881],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,57886,57888],{"className":57887},[886],[888,57889,57890],{"xmlns":890},[892,57891,57892,57908],{},[895,57893,57894,57896,57898,57900,57902,57904,57906],{},[898,57895,1824],{},[1655,57897,1657],{},[1826,57899,37370],{},[1655,57901,1671],{"separator":1670},[1826,57903,42988],{},[1655,57905,1671],{"separator":1670},[1826,57907,10282],{},[902,57909,57910],{"encoding":904},"Q = 15, 16, 20",[724,57912,57913,3106,57915,57947],{},[38,57914,23896],{},[883,57916,57918],{"className":57917},[886],[888,57919,57920],{"xmlns":890},[892,57921,57922,57944],{},[895,57923,57924,57926,57928,57930,57932,57934,57936,57938],{},[898,57925,4049],{},[898,57927,5245],{},[1655,57929,1657],{},[1826,57931,4360],{},[898,57933,1824],{},[1655,57935,2623],{},[1826,57937,1837],{},[2597,57939,57940,57942],{},[898,57941,1824],{},[1826,57943,1837],{},[902,57945,57946],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,57949,57951],{"className":57950},[886],[888,57952,57953],{"xmlns":890,"display":29192},[892,57954,57955,57997],{},[895,57956,57957,57959,57961,57963,57965,57967,57969,57971,57973,57979,57985,57987,57989,57991,57993,57995],{},[898,57958,2127],{},[898,57960,5245],{},[1655,57962,1657],{},[1655,57964,1664],{"stretchy":1663},[1826,57966,4360],{},[898,57968,1824],{},[1655,57970,2623],{},[1826,57972,1837],{},[2597,57974,57975,57977],{},[898,57976,1824],{},[1826,57978,1837],{},[2597,57980,57981,57983],{},[1655,57982,1677],{"stretchy":1663},[1655,57984,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,57986,1657],{},[1826,57988,4360],{},[1655,57990,2623],{},[1826,57992,3639],{},[898,57994,1824],{},[898,57996,1719],{"mathvariant":1943},[902,57998,57999],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,58001,1735,58002,9349,58020,58046,58047,5607,58060,58075,58076,58089,58090,22546,58103,5607,58116,58131,58132,58145,58146,58177,58178,58197],{},[883,58003,58005],{"className":58004},[886],[888,58006,58007],{"xmlns":890},[892,58008,58009,58017],{},[895,58010,58011,58013,58015],{},[898,58012,1824],{},[1655,58014,1657],{},[1826,58016,37370],{},[902,58018,58019],{"encoding":904},"Q = 15",[883,58021,58023],{"className":58022},[886],[888,58024,58025],{"xmlns":890},[892,58026,58027,58043],{},[895,58028,58029,58031,58033,58035,58037,58039,58041],{},[898,58030,2127],{},[898,58032,5245],{},[1655,58034,1664],{"stretchy":1663},[1826,58036,37370],{},[1655,58038,1677],{"stretchy":1663},[1655,58040,1657],{},[1826,58042,6460],{},[902,58044,58045],{"encoding":904},"MR(15) = 40",": při množství ",[883,58048,58050],{"className":58049},[886],[888,58051,58052],{"xmlns":890},[892,58053,58054,58058],{},[895,58055,58056],{},[1826,58057,37370],{},[902,58059,37370],{"encoding":904},[883,58061,58063],{"className":58062},[886],[888,58064,58065],{"xmlns":890},[892,58066,58067,58073],{},[895,58068,58069,58071],{},[898,58070,4049],{},[898,58072,5245],{},[902,58074,5345],{"encoding":904}," mění asi ",[883,58077,58079],{"className":58078},[886],[888,58080,58081],{"xmlns":890},[892,58082,58083,58087],{},[895,58084,58085],{},[1826,58086,6460],{},[902,58088,6460],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,58091,58093],{"className":58092},[886],[888,58094,58095],{"xmlns":890},[892,58096,58097,58101],{},[895,58098,58099],{},[898,58100,1824],{},[902,58102,1824],{"encoding":904},[883,58104,58106],{"className":58105},[886],[888,58107,58108],{"xmlns":890},[892,58109,58110,58114],{},[895,58111,58112],{},[1826,58113,1828],{},[902,58115,1828],{"encoding":904},[883,58117,58119],{"className":58118},[886],[888,58120,58121],{"xmlns":890},[892,58122,58123,58129],{},[895,58124,58125,58127],{},[898,58126,4049],{},[898,58128,5245],{},[902,58130,5345],{"encoding":904}," zvýší přibližně o ",[883,58133,58135],{"className":58134},[886],[888,58136,58137],{"xmlns":890},[892,58138,58139,58143],{},[895,58140,58141],{},[1826,58142,6460],{},[902,58144,6460],{"encoding":904},", tj. ze skutečné hodnoty ",[883,58147,58149],{"className":58148},[886],[888,58150,58151],{"xmlns":890},[892,58152,58153,58174],{},[895,58154,58155,58157,58159,58161,58163,58165,58167,58169,58171],{},[898,58156,4049],{},[898,58158,5245],{},[1655,58160,1664],{"stretchy":1663},[1826,58162,37370],{},[1655,58164,1677],{"stretchy":1663},[1655,58166,1657],{},[1826,58168,1828],{},[2031,58170,2435],{},[1826,58172,58173],{},"050",[902,58175,58176],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,58179,58181],{"className":58180},[886],[888,58182,58183],{"xmlns":890},[892,58184,58185,58194],{},[895,58186,58187,58189,58191],{},[1826,58188,1828],{},[2031,58190,2435],{},[1826,58192,58193],{},"090",[902,58195,58196],{"encoding":904},"1\\,090",". Skutečná změna je",[883,58199,58201],{"className":58200},[886],[888,58202,58203],{"xmlns":890,"display":29192},[892,58204,58205,58259],{},[895,58206,58207,58209,58211,58213,58215,58217,58219,58221,58223,58225,58227,58229,58231,58233,58235,58237,58239,58241,58243,58246,58248,58250,58252,58254,58256],{},[898,58208,2506],{"mathvariant":1943},[898,58210,4049],{},[898,58212,5245],{},[1655,58214,1657],{},[898,58216,4049],{},[898,58218,5245],{},[1655,58220,1664],{"stretchy":1663},[1826,58222,42988],{},[1655,58224,1677],{"stretchy":1663},[1655,58226,2623],{},[898,58228,4049],{},[898,58230,5245],{},[1655,58232,1664],{"stretchy":1663},[1826,58234,37370],{},[1655,58236,1677],{"stretchy":1663},[1655,58238,1657],{},[1826,58240,1828],{},[2031,58242,2435],{},[1826,58244,58245],{},"088",[1655,58247,2623],{},[1826,58249,1828],{},[2031,58251,2435],{},[1826,58253,58173],{},[1655,58255,1657],{},[1826,58257,58258],{},"38.",[902,58260,58261],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,58263,58264,58265,1343,58291,4199,58317,58332,58333,58348],{},"Podobně ",[883,58266,58268],{"className":58267},[886],[888,58269,58270],{"xmlns":890},[892,58271,58272,58288],{},[895,58273,58274,58276,58278,58280,58282,58284,58286],{},[898,58275,2127],{},[898,58277,5245],{},[1655,58279,1664],{"stretchy":1663},[1826,58281,42988],{},[1655,58283,1677],{"stretchy":1663},[1655,58285,1657],{},[1826,58287,6814],{},[902,58289,58290],{"encoding":904},"MR(16) = 36",[883,58292,58294],{"className":58293},[886],[888,58295,58296],{"xmlns":890},[892,58297,58298,58314],{},[895,58299,58300,58302,58304,58306,58308,58310,58312],{},[898,58301,2127],{},[898,58303,5245],{},[1655,58305,1664],{"stretchy":1663},[1826,58307,10282],{},[1655,58309,1677],{"stretchy":1663},[1655,58311,1657],{},[1826,58313,10282],{},[902,58315,58316],{"encoding":904},"MR(20) = 20",[883,58318,58320],{"className":58319},[886],[888,58321,58322],{"xmlns":890},[892,58323,58324,58330],{},[895,58325,58326,58328],{},[898,58327,2127],{},[898,58329,5245],{},[902,58331,7881],{"encoding":904}," je klesající funkce — rychlost změny ",[883,58334,58336],{"className":58335},[886],[888,58337,58338],{"xmlns":890},[892,58339,58340,58346],{},[895,58341,58342,58344],{},[898,58343,4049],{},[898,58345,5245],{},[902,58347,5345],{"encoding":904}," s růstem množství klesá.",[198,58350,58352],{"id":58351},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,58354,58355],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,58357,58359],{"className":58358},[886],[888,58360,58361],{"xmlns":890,"display":29192},[892,58362,58363,58432],{},[21880,58364,58365],{"width":29197},[21885,58366,58367,58369,58425,58427],{},[21888,58368],{"width":29202},[21888,58370,58371],{},[895,58372,58373,58375,58377,58379,58381,58383,58385,58387,58389,58391,58393,58395,58397,58399,58405,58407,58409,58411,58413,58415,58417,58419,58421,58423],{},[898,58374,2506],{"mathvariant":1943},[898,58376,4049],{},[898,58378,5245],{},[2031,58380,2783],{},[1655,58382,2357],{},[2031,58384,2783],{},[898,58386,2410],{"mathvariant":1943},[898,58388,4049],{},[898,58390,5245],{},[1655,58392,1657],{},[1655,58394,1664],{"stretchy":1663},[898,58396,4049],{},[898,58398,5245],{},[2597,58400,58401,58403],{},[1655,58402,1677],{"stretchy":1663},[1655,58404,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[2031,58406,2435],{},[898,58408,2410],{"mathvariant":1943},[898,58410,1824],{},[1655,58412,1657],{},[898,58414,2127],{},[898,58416,5245],{},[2031,58418,2435],{},[898,58420,2410],{"mathvariant":1943},[898,58422,1824],{},[1655,58424,1671],{"separator":1670},[21888,58426],{"width":29202},[21888,58428,58429],{},[2031,58430,58431],{},"(3.3)",[902,58433,58434],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,58436,58437],{},"schematicky:",[883,58439,58441],{"className":58440},[886],[888,58442,58443],{"xmlns":890,"display":29192},[892,58444,58445,58553],{},[895,58446,58447,58485,58487,58489,58491,58520,58523,58551],{},[895,58448,58449,58452,58458,58461,58467,58470,58476,58482],{},[2031,58450,58451],{},"zm",[9633,58453,58454,58456],{"accent":1670},[2031,58455,46858],{},[1655,58457,26184],{},[2031,58459,58460],{},"na celkov",[9633,58462,58463,58465],{"accent":1670},[2031,58464,46858],{},[1655,58466,26103],{},[2031,58468,58469],{},"ho p",[9633,58471,58472,58474],{"accent":1670},[2031,58473,13166],{},[1655,58475,26184],{},[9633,58477,58478,58480],{"accent":1670},[2031,58479,26172],{},[1655,58481,26103],{},[2031,58483,58484],{},"jmu",[2031,58486,2783],{},[1655,58488,2357],{},[2031,58490,2783],{},[895,58492,58493,58496,58502,58505,58511,58517],{},[2031,58494,58495],{},"mezn",[9633,58497,58498,58500],{"accent":1670},[2031,58499,26172],{},[1655,58501,26103],{},[2031,58503,58504],{}," p",[9633,58506,58507,58509],{"accent":1670},[2031,58508,13166],{},[1655,58510,26184],{},[9633,58512,58513,58515],{"accent":1670},[2031,58514,26172],{},[1655,58516,26103],{},[2031,58518,58519],{},"jem",[1655,58521,58522],{},"×",[895,58524,58525,58527,58533,58536,58542,58545],{},[2031,58526,58451],{},[9633,58528,58529,58531],{"accent":1670},[2031,58530,46858],{},[1655,58532,26184],{},[2031,58534,58535],{},"na mno",[9633,58537,58538,58540],{"accent":1670},[2031,58539,1653],{},[1655,58541,26184],{},[2031,58543,58544],{},"stv",[9633,58546,58547,58549],{"accent":1670},[2031,58548,26172],{},[1655,58550,26103],{},[898,58552,1719],{"mathvariant":1943},[902,58554,58555],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,58557,58558,58559,58574],{},"Pro porovnání skutečná změna ",[883,58560,58562],{"className":58561},[886],[888,58563,58564],{"xmlns":890},[892,58565,58566,58572],{},[895,58567,58568,58570],{},[898,58569,4049],{},[898,58571,5245],{},[902,58573,5345],{"encoding":904}," je",[883,58576,58578],{"className":58577},[886],[888,58579,58580],{"xmlns":890,"display":29192},[892,58581,58582,58637],{},[21880,58583,58584],{"width":29197},[21885,58585,58586,58588,58630,58632],{},[21888,58587],{"width":29202},[21888,58589,58590],{},[895,58591,58592,58594,58596,58598,58600,58602,58604,58606,58608,58610,58612,58614,58616,58618,58620,58622,58624,58626,58628],{},[898,58593,2506],{"mathvariant":1943},[898,58595,4049],{},[898,58597,5245],{},[1655,58599,1657],{},[898,58601,4049],{},[898,58603,5245],{},[1655,58605,1664],{"stretchy":1663},[898,58607,1824],{},[1655,58609,2346],{},[898,58611,2410],{"mathvariant":1943},[898,58613,1824],{},[1655,58615,1677],{"stretchy":1663},[1655,58617,2623],{},[898,58619,4049],{},[898,58621,5245],{},[1655,58623,1664],{"stretchy":1663},[898,58625,1824],{},[1655,58627,1677],{"stretchy":1663},[898,58629,1719],{"mathvariant":1943},[21888,58631],{"width":29202},[21888,58633,58634],{},[2031,58635,58636],{},"(3.4)",[902,58638,58639],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[38474,58641,58643],{"id":58642},"příklad-33","Příklad 3.3",[724,58645,58646,58648,58649,58679,58680,2295,58695,3948,58708,3962,58721,58735],{},[38,58647,57113],{}," Pro ",[883,58650,58652],{"className":58651},[886],[888,58653,58654],{"xmlns":890},[892,58655,58656,58676],{},[895,58657,58658,58660,58662,58664,58666,58668,58670],{},[898,58659,4049],{},[898,58661,5245],{},[1655,58663,1657],{},[1826,58665,4360],{},[898,58667,1824],{},[1655,58669,2623],{},[2597,58671,58672,58674],{},[898,58673,1824],{},[1826,58675,1837],{},[902,58677,58678],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,58681,58683],{"className":58682},[886],[888,58684,58685],{"xmlns":890},[892,58686,58687,58693],{},[895,58688,58689,58691],{},[898,58690,4049],{},[898,58692,5245],{},[902,58694,5345],{"encoding":904},[883,58696,58698],{"className":58697},[886],[888,58699,58700],{"xmlns":890},[892,58701,58702,58706],{},[895,58703,58704],{},[898,58705,1824],{},[902,58707,1824],{"encoding":904},[883,58709,58711],{"className":58710},[886],[888,58712,58713],{"xmlns":890},[892,58714,58715,58719],{},[895,58716,58717],{},[1826,58718,4396],{},[902,58720,4396],{"encoding":904},[883,58722,58724],{"className":58723},[886],[888,58725,58726],{"xmlns":890},[892,58727,58728,58733],{},[895,58729,58730],{},[1826,58731,58732],{},"63",[902,58734,58732],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,58737,58738,3106,58740,58765,58766,1343,58784,2086],{},[38,58739,23896],{},[883,58741,58743],{"className":58742},[886],[888,58744,58745],{"xmlns":890},[892,58746,58747,58763],{},[895,58748,58749,58751,58753,58755,58757,58759,58761],{},[898,58750,2127],{},[898,58752,5245],{},[1655,58754,1657],{},[1826,58756,4360],{},[1655,58758,2623],{},[1826,58760,1837],{},[898,58762,1824],{},[902,58764,12560],{"encoding":904},", tedy při ",[883,58767,58769],{"className":58768},[886],[888,58770,58771],{"xmlns":890},[892,58772,58773,58781],{},[895,58774,58775,58777,58779],{},[898,58776,1824],{},[1655,58778,1657],{},[1826,58780,4396],{},[902,58782,58783],{"encoding":904},"Q = 60",[883,58785,58787],{"className":58786},[886],[888,58788,58789],{"xmlns":890},[892,58790,58791,58801],{},[895,58792,58793,58795,58797,58799],{},[898,58794,2410],{"mathvariant":1943},[898,58796,1824],{},[1655,58798,1657],{},[1826,58800,3472],{},[902,58802,58803],{"encoding":904},"\\mathrm{d}Q = 3",[883,58805,58807],{"className":58806},[886],[888,58808,58809],{"xmlns":890,"display":29192},[892,58810,58811,58842],{},[895,58812,58813,58815,58817,58819,58821,58823,58825,58827,58829,58831,58833,58835,58837,58839],{},[898,58814,2410],{"mathvariant":1943},[898,58816,4049],{},[898,58818,5245],{},[1655,58820,1657],{},[1655,58822,1664],{"stretchy":1663},[1826,58824,4360],{},[1655,58826,2623],{},[1826,58828,5297],{},[1655,58830,1677],{"stretchy":1663},[1655,58832,2869],{},[1826,58834,3472],{},[1655,58836,1657],{},[1655,58838,2623],{},[1826,58840,58841],{},"60.",[902,58843,58844],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,58846,58847,58848,58878,58879,58898],{},"Celkový příjem klesne z ",[883,58849,58851],{"className":58850},[886],[888,58852,58853],{"xmlns":890},[892,58854,58855,58875],{},[895,58856,58857,58859,58861,58863,58865,58867,58869,58871,58873],{},[898,58858,4049],{},[898,58860,5245],{},[1655,58862,1664],{"stretchy":1663},[1826,58864,4396],{},[1655,58866,1677],{"stretchy":1663},[1655,58868,1657],{},[1826,58870,1837],{},[2031,58872,2435],{},[1826,58874,21268],{},[902,58876,58877],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,58880,58882],{"className":58881},[886],[888,58883,58884],{"xmlns":890},[892,58885,58886,58895],{},[895,58887,58888,58890,58892],{},[1826,58889,1837],{},[2031,58891,2435],{},[1826,58893,58894],{},"340",[902,58896,58897],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,58900,58902],{"className":58901},[886],[888,58903,58904],{"xmlns":890,"display":29192},[892,58905,58906,58964],{},[895,58907,58908,58910,58912,58914,58916,58918,58920,58922,58924,58926,58928,58930,58932,58934,58936,58938,58940,58942,58944,58947,58949,58951,58953,58955,58957,58959,58962],{},[898,58909,2506],{"mathvariant":1943},[898,58911,4049],{},[898,58913,5245],{},[1655,58915,1657],{},[898,58917,4049],{},[898,58919,5245],{},[1655,58921,1664],{"stretchy":1663},[1826,58923,58732],{},[1655,58925,1677],{"stretchy":1663},[1655,58927,2623],{},[898,58929,4049],{},[898,58931,5245],{},[1655,58933,1664],{"stretchy":1663},[1826,58935,4396],{},[1655,58937,1677],{"stretchy":1663},[1655,58939,1657],{},[1826,58941,1837],{},[2031,58943,2435],{},[1826,58945,58946],{},"331",[1655,58948,2623],{},[1826,58950,1837],{},[2031,58952,2435],{},[1826,58954,21268],{},[1655,58956,1657],{},[1655,58958,2623],{},[1826,58960,58961],{},"69",[1655,58963,1671],{"separator":1670},[902,58965,58966],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,58968,58969,58970,58985,58986,1719],{},"tj. ",[883,58971,58973],{"className":58972},[886],[888,58974,58975],{"xmlns":890},[892,58976,58977,58983],{},[895,58978,58979,58981],{},[898,58980,4049],{},[898,58982,5245],{},[902,58984,5345],{"encoding":904}," klesne na ",[883,58987,58989],{"className":58988},[886],[888,58990,58991],{"xmlns":890},[892,58992,58993,59001],{},[895,58994,58995,58997,58999],{},[1826,58996,1837],{},[2031,58998,2435],{},[1826,59000,58946],{},[902,59002,59003],{"encoding":904},"2\\,331",[198,59005,59007],{"id":59006},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,59009,59010,59011,2494,59034,32706],{},"Obecně pro lineární poptávku ",[883,59012,59014],{"className":59013},[886],[888,59015,59016],{"xmlns":890},[892,59017,59018,59032],{},[895,59019,59020,59022,59024,59026,59028,59030],{},[898,59021,2132],{},[1655,59023,1657],{},[898,59025,207],{},[898,59027,1824],{},[1655,59029,2346],{},[898,59031,2025],{},[902,59033,38186],{"encoding":904},[883,59035,59037],{"className":59036},[886],[888,59038,59039],{"xmlns":890},[892,59040,59041,59063],{},[895,59042,59043,59045,59047,59049,59051,59057,59059,59061],{},[898,59044,4049],{},[898,59046,5245],{},[1655,59048,1657],{},[898,59050,207],{},[2597,59052,59053,59055],{},[898,59054,1824],{},[1826,59056,1837],{},[1655,59058,2346],{},[898,59060,2025],{},[898,59062,1824],{},[902,59064,59065],{"encoding":904},"TR = aQ^2 + bQ",[883,59067,59069],{"className":59068},[886],[888,59070,59071],{"xmlns":890,"display":29192},[892,59072,59073,59093],{},[895,59074,59075,59077,59079,59081,59083,59085,59087,59089,59091],{},[898,59076,2127],{},[898,59078,5245],{},[1655,59080,1657],{},[1826,59082,1837],{},[898,59084,207],{},[898,59086,1824],{},[1655,59088,2346],{},[898,59090,2025],{},[898,59092,1719],{"mathvariant":1943},[902,59094,59095],{"encoding":904},"MR = 2aQ + b.",[724,59097,59098,59099,59114,59115,59130,59131,59144,59145,2115,59148,59164,59165,59178,59179,59194,59195,59210,59211,59226,59227,3902,59240,59270,59271,59290,59291,59306],{},"Křivky ",[883,59100,59102],{"className":59101},[886],[888,59103,59104],{"xmlns":890},[892,59105,59106,59112],{},[895,59107,59108,59110],{},[898,59109,2127],{},[898,59111,5245],{},[902,59113,7881],{"encoding":904}," a poptávky (resp. ",[883,59116,59118],{"className":59117},[886],[888,59119,59120],{"xmlns":890},[892,59121,59122,59128],{},[895,59123,59124,59126],{},[898,59125,2731],{},[898,59127,5245],{},[902,59129,56571],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,59132,59134],{"className":59133},[886],[888,59135,59136],{"xmlns":890},[892,59137,59138,59142],{},[895,59139,59140],{},[898,59141,2025],{},[902,59143,2025],{"encoding":904},", přičemž ",[38,59146,59147],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,59149,59151],{"className":59150},[886],[888,59152,59153],{"xmlns":890},[892,59154,59155,59161],{},[895,59156,59157,59159],{},[1826,59158,1837],{},[898,59160,207],{},[902,59162,59163],{"encoding":904},"2a"," vs. ",[883,59166,59168],{"className":59167},[886],[888,59169,59170],{"xmlns":890},[892,59171,59172,59176],{},[895,59173,59174],{},[898,59175,207],{},[902,59177,207],{"encoding":904},", obrázek 3.2). ",[883,59180,59182],{"className":59181},[886],[888,59183,59184],{"xmlns":890},[892,59185,59186,59192],{},[895,59187,59188,59190],{},[898,59189,2127],{},[898,59191,5245],{},[902,59193,7881],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,59196,59198],{"className":59197},[886],[888,59199,59200],{"xmlns":890},[892,59201,59202,59208],{},[895,59203,59204,59206],{},[898,59205,4049],{},[898,59207,5245],{},[902,59209,5345],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,59212,59214],{"className":59213},[886],[888,59215,59216],{"xmlns":890},[892,59217,59218,59224],{},[895,59219,59220,59222],{},[898,59221,2127],{},[898,59223,5245],{},[902,59225,7881],{"encoding":904}," osu ",[883,59228,59230],{"className":59229},[886],[888,59231,59232],{"xmlns":890},[892,59233,59234,59238],{},[895,59235,59236],{},[898,59237,1824],{},[902,59239,1824],{"encoding":904},[883,59241,59243],{"className":59242},[886],[888,59244,59245],{"xmlns":890},[892,59246,59247,59267],{},[895,59248,59249,59251,59253,59255],{},[898,59250,1824],{},[1655,59252,1657],{},[1655,59254,2623],{},[3615,59256,59257],{"scriptlevel":2552,"displaystyle":1663},[1949,59258,59259,59261],{},[898,59260,2025],{},[895,59262,59263,59265],{},[1826,59264,1837],{},[898,59266,207],{},[902,59268,59269],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,59272,59274],{"className":59273},[886],[888,59275,59276],{"xmlns":890},[892,59277,59278,59288],{},[895,59279,59280,59282,59284,59286],{},[898,59281,2127],{},[898,59283,5245],{},[1655,59285,1657],{},[1826,59287,2552],{},[902,59289,8331],{"encoding":904},", a dále ",[883,59292,59294],{"className":59293},[886],[888,59295,59296],{"xmlns":890},[892,59297,59298,59304],{},[895,59299,59300,59302],{},[898,59301,4049],{},[898,59303,5245],{},[902,59305,5345],{"encoding":904}," klesá.",[724,59308,59309,59310,59316,59317,59349,59350,59378],{},"V případě ",[38,59311,59312],{},[207,59313,59315],{"className":59314,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,59318,59320],{"className":59319},[886],[888,59321,59322],{"xmlns":890},[892,59323,59324,59346],{},[895,59325,59326,59328,59330,59332,59334,59336,59338,59340],{},[898,59327,2132],{},[1655,59329,1657],{},[898,59331,2838],{},[1655,59333,1664],{"stretchy":1663},[898,59335,1824],{},[1655,59337,1677],{"stretchy":1663},[1655,59339,1657],{},[2597,59341,59342,59344],{},[898,59343,2132],{},[1655,59345,5603],{},[902,59347,59348],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,59351,59353],{"className":59352},[886],[888,59354,59355],{"xmlns":890},[892,59356,59357,59375],{},[895,59358,59359,59361,59363,59365,59367,59369],{},[898,59360,4049],{},[898,59362,5245],{},[1655,59364,1657],{},[898,59366,1824],{},[1655,59368,2869],{},[2597,59370,59371,59373],{},[898,59372,2132],{},[1655,59374,5603],{},[902,59376,59377],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,59380,59382],{"className":59381},[886],[888,59383,59384],{"xmlns":890,"display":29192},[892,59385,59386,59428],{},[895,59387,59388,59390,59392,59394,59396,59398,59400,59406,59408,59410,59424,59426],{},[898,59389,2127],{},[898,59391,5245],{},[1655,59393,1657],{},[898,59395,2731],{},[898,59397,5245],{},[1655,59399,1657],{},[2597,59401,59402,59404],{},[898,59403,2132],{},[1655,59405,5603],{},[1967,59407],{"width":16409},[1655,59409,1664],{"stretchy":1663},[895,59411,59412,59415,59421],{},[2031,59413,59414],{},"obr",[9633,59416,59417,59419],{"accent":1670},[2031,59418,207],{},[1655,59420,26103],{},[2031,59422,59423],{},"zek 3.4",[1655,59425,1677],{"stretchy":1663},[898,59427,1719],{"mathvariant":1943},[902,59429,59430],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,59432,59433],{},[614,59434,59435,59436,2704,59462,59490,59491,59504,59505,59520,59521,4979,59534,1343,59560,4979,59575,1719],{},"Obrázek 3.2: Přímky ",[883,59437,59439],{"className":59438},[886],[888,59440,59441],{"xmlns":890},[892,59442,59443,59459],{},[895,59444,59445,59447,59449,59451,59453,59455,59457],{},[898,59446,2731],{},[898,59448,5245],{},[1655,59450,1657],{},[898,59452,207],{},[898,59454,1824],{},[1655,59456,2346],{},[898,59458,2025],{},[902,59460,59461],{"encoding":904},"AR = aQ + b",[883,59463,59465],{"className":59464},[886],[888,59466,59467],{"xmlns":890},[892,59468,59469,59487],{},[895,59470,59471,59473,59475,59477,59479,59481,59483,59485],{},[898,59472,2127],{},[898,59474,5245],{},[1655,59476,1657],{},[1826,59478,1837],{},[898,59480,207],{},[898,59482,1824],{},[1655,59484,2346],{},[898,59486,2025],{},[902,59488,59489],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,59492,59494],{"className":59493},[886],[888,59495,59496],{"xmlns":890},[892,59497,59498,59502],{},[895,59499,59500],{},[898,59501,2025],{},[902,59503,2025],{"encoding":904}," se svislou osou, ",[883,59506,59508],{"className":59507},[886],[888,59509,59510],{"xmlns":890},[892,59511,59512,59518],{},[895,59513,59514,59516],{},[898,59515,2127],{},[898,59517,5245],{},[902,59519,7881],{"encoding":904}," protíná osu ",[883,59522,59524],{"className":59523},[886],[888,59525,59526],{"xmlns":890},[892,59527,59528,59532],{},[895,59529,59530],{},[898,59531,1824],{},[902,59533,1824],{"encoding":904},[883,59535,59537],{"className":59536},[886],[888,59538,59539],{"xmlns":890},[892,59540,59541,59557],{},[895,59542,59543,59545],{},[1655,59544,2623],{},[3615,59546,59547],{"scriptlevel":2552,"displaystyle":1663},[1949,59548,59549,59551],{},[898,59550,2025],{},[895,59552,59553,59555],{},[1826,59554,1837],{},[898,59556,207],{},[902,59558,59559],{"encoding":904},"-\\tfrac{b}{2a}",[883,59561,59563],{"className":59562},[886],[888,59564,59565],{"xmlns":890},[892,59566,59567,59573],{},[895,59568,59569,59571],{},[898,59570,2731],{},[898,59572,5245],{},[902,59574,56571],{"encoding":904},[883,59576,59578],{"className":59577},[886],[888,59579,59580],{"xmlns":890},[892,59581,59582,59594],{},[895,59583,59584,59586],{},[1655,59585,2623],{},[3615,59587,59588],{"scriptlevel":2552,"displaystyle":1663},[1949,59589,59590,59592],{},[898,59591,2025],{},[898,59593,207],{},[902,59595,59596],{"encoding":904},"-\\tfrac{b}{a}",[724,59598,59599],{},[614,59600,59601,59602,59633,59634,59663,59664,1719],{},"Obrázek 3.3: Parabola ",[883,59603,59605],{"className":59604},[886],[888,59606,59607],{"xmlns":890},[892,59608,59609,59631],{},[895,59610,59611,59613,59615,59617,59619,59625,59627,59629],{},[898,59612,4049],{},[898,59614,5245],{},[1655,59616,1657],{},[898,59618,207],{},[2597,59620,59621,59623],{},[898,59622,1824],{},[1826,59624,1837],{},[1655,59626,2346],{},[898,59628,2025],{},[898,59630,1824],{},[902,59632,59065],{"encoding":904}," s maximem v ",[883,59635,59637],{"className":59636},[886],[888,59638,59639],{"xmlns":890},[892,59640,59641,59661],{},[895,59642,59643,59645,59647,59649],{},[898,59644,1824],{},[1655,59646,1657],{},[1655,59648,2623],{},[3615,59650,59651],{"scriptlevel":2552,"displaystyle":1663},[1949,59652,59653,59655],{},[898,59654,2025],{},[895,59656,59657,59659],{},[1826,59658,1837],{},[898,59660,207],{},[902,59662,59269],{"encoding":904}," a nulou v ",[883,59665,59667],{"className":59666},[886],[888,59668,59669],{"xmlns":890},[892,59670,59671,59687],{},[895,59672,59673,59675,59677,59679],{},[898,59674,1824],{},[1655,59676,1657],{},[1655,59678,2623],{},[3615,59680,59681],{"scriptlevel":2552,"displaystyle":1663},[1949,59682,59683,59685],{},[898,59684,2025],{},[898,59686,207],{},[902,59688,59689],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,59691,59692],{},[614,59693,59694,59695,1719],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,59696,59698],{"className":59697},[886],[888,59699,59700],{"xmlns":890},[892,59701,59702,59722],{},[895,59703,59704,59706,59708,59710,59712,59714,59716],{},[898,59705,2731],{},[898,59707,5245],{},[1655,59709,1657],{},[898,59711,2127],{},[898,59713,5245],{},[1655,59715,1657],{},[2597,59717,59718,59720],{},[898,59719,2132],{},[1655,59721,5603],{},[902,59723,59724],{"encoding":904},"AR = MR = P^*",[115,59726,59728],{"id":59727},"náklady-firmy","Náklady firmy",[198,59730,59732],{"id":59731},"celkové-náklady","Celkové náklady",[724,59734,59735,3106,59737,2115,59752,59755,59756,59769],{},[38,59736,59732],{},[883,59738,59740],{"className":59739},[886],[888,59741,59742],{"xmlns":890},[892,59743,59744,59750],{},[895,59745,59746,59748],{},[898,59747,4049],{},[898,59749,4052],{},[902,59751,4512],{"encoding":904},[38,59753,59754],{},"total cost",") jsou veškeré náklady na realizaci ",[883,59757,59759],{"className":59758},[886],[888,59760,59761],{"xmlns":890},[892,59762,59763,59767],{},[895,59764,59765],{},[898,59766,1824],{},[902,59768,1824],{"encoding":904}," jednotek produkce:",[883,59771,59773],{"className":59772},[886],[888,59774,59775],{"xmlns":890,"display":29192},[892,59776,59777,59832],{},[21880,59778,59779],{"width":29197},[21885,59780,59781,59783,59825,59827],{},[21888,59782],{"width":29202},[21888,59784,59785],{},[895,59786,59787,59789,59791,59793,59795,59797,59799,59801,59803,59805,59807,59809,59811,59813,59815,59817,59819,59821,59823],{},[898,59788,4049],{},[898,59790,4052],{},[1655,59792,1657],{},[898,59794,4049],{},[898,59796,4052],{},[1655,59798,1664],{"stretchy":1663},[898,59800,1824],{},[1655,59802,1677],{"stretchy":1663},[1655,59804,1657],{},[898,59806,2537],{},[898,59808,4052],{},[1655,59810,2346],{},[898,59812,4049],{},[898,59814,41465],{},[898,59816,4052],{},[1655,59818,1664],{"stretchy":1663},[898,59820,1824],{},[1655,59822,1677],{"stretchy":1663},[1655,59824,1671],{"separator":1670},[21888,59826],{"width":29202},[21888,59828,59829],{},[2031,59830,59831],{},"(3.5)",[902,59833,59834],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,59836,5559,59837,59852,59853,2115,59856,13253,59859,59852,59883,2115,59886,59889],{},[883,59838,59840],{"className":59839},[886],[888,59841,59842],{"xmlns":890},[892,59843,59844,59850],{},[895,59845,59846,59848],{},[898,59847,2537],{},[898,59849,4052],{},[902,59851,56617],{"encoding":904}," jsou ",[38,59854,59855],{},"fixní náklady",[38,59857,59858],{},"fixed cost",[883,59860,59862],{"className":59861},[886],[888,59863,59864],{"xmlns":890},[892,59865,59866,59880],{},[895,59867,59868,59870,59872,59874,59876,59878],{},[898,59869,4049],{},[898,59871,41465],{},[898,59873,4052],{},[1655,59875,1664],{"stretchy":1663},[898,59877,1824],{},[1655,59879,1677],{"stretchy":1663},[902,59881,59882],{"encoding":904},"TVC(Q)",[38,59884,59885],{},"celkové variabilní náklady",[38,59887,59888],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,59891,59893],{"id":59892},"průměrné-náklady","Průměrné náklady",[724,59895,59896,3106,59898,2115,59913,59916],{},[38,59897,59893],{},[883,59899,59901],{"className":59900},[886],[888,59902,59903],{"xmlns":890},[892,59904,59905,59911],{},[895,59906,59907,59909],{},[898,59908,2731],{},[898,59910,4052],{},[902,59912,56686],{"encoding":904},[38,59914,59915],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,59918,59920],{"className":59919},[886],[888,59921,59922],{"xmlns":890,"display":29192},[892,59923,59924,60003],{},[21880,59925,59926],{"width":29197},[21885,59927,59928,59930,59996,59998],{},[21888,59929],{"width":29202},[21888,59931,59932],{},[895,59933,59934,59936,59938,59940,59942,59944,59946,59948,59950,59952,59962,59964,59974,59976,59994],{},[898,59935,2731],{},[898,59937,4052],{},[1655,59939,1657],{},[898,59941,2731],{},[898,59943,4052],{},[1655,59945,1664],{"stretchy":1663},[898,59947,1824],{},[1655,59949,1677],{"stretchy":1663},[1655,59951,1657],{},[1949,59953,59954,59960],{},[895,59955,59956,59958],{},[898,59957,4049],{},[898,59959,4052],{},[898,59961,1824],{},[1655,59963,1657],{},[1949,59965,59966,59972],{},[895,59967,59968,59970],{},[898,59969,2537],{},[898,59971,4052],{},[898,59973,1824],{},[1655,59975,2346],{},[1949,59977,59978,59992],{},[895,59979,59980,59982,59984,59986,59988,59990],{},[898,59981,4049],{},[898,59983,41465],{},[898,59985,4052],{},[1655,59987,1664],{"stretchy":1663},[898,59989,1824],{},[1655,59991,1677],{"stretchy":1663},[898,59993,1824],{},[1655,59995,1671],{"separator":1670},[21888,59997],{"width":29202},[21888,59999,60000],{},[2031,60001,60002],{},"(3.6)",[902,60004,60005],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,60007,5559,60008,59852,60032,3106,60035,2115,60052,13253,60055,59852,60087,3106,60090,2115,60107,4421],{},[883,60009,60011],{"className":60010},[886],[888,60012,60013],{"xmlns":890},[892,60014,60015,60029],{},[895,60016,60017],{},[3615,60018,60019],{"scriptlevel":2552,"displaystyle":1663},[1949,60020,60021,60027],{},[895,60022,60023,60025],{},[898,60024,2537],{},[898,60026,4052],{},[898,60028,1824],{},[902,60030,60031],{"encoding":904},"\\tfrac{FC}{Q}",[38,60033,60034],{},"průměrné fixní náklady",[883,60036,60038],{"className":60037},[886],[888,60039,60040],{"xmlns":890},[892,60041,60042,60050],{},[895,60043,60044,60046,60048],{},[898,60045,2731],{},[898,60047,2537],{},[898,60049,4052],{},[902,60051,56653],{"encoding":904},[38,60053,60054],{},"average fixed cost",[883,60056,60058],{"className":60057},[886],[888,60059,60060],{"xmlns":890},[892,60061,60062,60084],{},[895,60063,60064],{},[3615,60065,60066],{"scriptlevel":2552,"displaystyle":1663},[1949,60067,60068,60082],{},[895,60069,60070,60072,60074,60076,60078,60080],{},[898,60071,4049],{},[898,60073,41465],{},[898,60075,4052],{},[1655,60077,1664],{"stretchy":1663},[898,60079,1824],{},[1655,60081,1677],{"stretchy":1663},[898,60083,1824],{},[902,60085,60086],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,60088,60089],{},"průměrné variabilní náklady",[883,60091,60093],{"className":60092},[886],[888,60094,60095],{"xmlns":890},[892,60096,60097,60105],{},[895,60098,60099,60101,60103],{},[898,60100,2731],{},[898,60102,41465],{},[898,60104,4052],{},[902,60106,56437],{"encoding":904},[38,60108,60109],{},"average variable cost",[883,60111,60113],{"className":60112},[886],[888,60114,60115],{"xmlns":890,"display":29192},[892,60116,60117,60176],{},[21880,60118,60119],{"width":29197},[21885,60120,60121,60123,60169,60171],{},[21888,60122],{"width":29202},[21888,60124,60125],{},[895,60126,60127,60129,60131,60133,60135,60137,60139,60141,60143,60145,60147,60149,60167],{},[898,60128,2731],{},[898,60130,41465],{},[898,60132,4052],{},[1655,60134,1657],{},[898,60136,2731],{},[898,60138,41465],{},[898,60140,4052],{},[1655,60142,1664],{"stretchy":1663},[898,60144,1824],{},[1655,60146,1677],{"stretchy":1663},[1655,60148,1657],{},[1949,60150,60151,60165],{},[895,60152,60153,60155,60157,60159,60161,60163],{},[898,60154,4049],{},[898,60156,41465],{},[898,60158,4052],{},[1655,60160,1664],{"stretchy":1663},[898,60162,1824],{},[1655,60164,1677],{"stretchy":1663},[898,60166,1824],{},[898,60168,1719],{"mathvariant":1943},[21888,60170],{"width":29202},[21888,60172,60173],{},[2031,60174,60175],{},"(3.7)",[902,60177,60178],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[38474,60180,60182],{"id":60181},"příklad-34","Příklad 3.4",[724,60184,60185,58648,60187,2704,60212,57151,60236,2704,60251,60266,60267,1719],{},[38,60186,57113],{},[883,60188,60190],{"className":60189},[886],[888,60191,60192],{"xmlns":890},[892,60193,60194,60209],{},[895,60195,60196,60198,60200,60202,60204,60206],{},[898,60197,2537],{},[898,60199,4052],{},[1655,60201,1657],{},[1826,60203,1828],{},[2031,60205,2435],{},[1826,60207,60208],{},"000",[902,60210,60211],{"encoding":904},"FC = 1\\,000",[883,60213,60215],{"className":60214},[886],[888,60216,60217],{"xmlns":890},[892,60218,60219,60233],{},[895,60220,60221,60223,60225,60227,60229,60231],{},[898,60222,4049],{},[898,60224,41465],{},[898,60226,4052],{},[1655,60228,1657],{},[1826,60230,3639],{},[898,60232,1824],{},[902,60234,60235],{"encoding":904},"TVC = 4Q",[883,60237,60239],{"className":60238},[886],[888,60240,60241],{"xmlns":890},[892,60242,60243,60249],{},[895,60244,60245,60247],{},[898,60246,4049],{},[898,60248,4052],{},[902,60250,4512],{"encoding":904},[883,60252,60254],{"className":60253},[886],[888,60255,60256],{"xmlns":890},[892,60257,60258,60264],{},[895,60259,60260,60262],{},[898,60261,2731],{},[898,60263,4052],{},[902,60265,56686],{"encoding":904}," a jejich chování s rostoucím ",[883,60268,60270],{"className":60269},[886],[888,60271,60272],{"xmlns":890},[892,60273,60274,60278],{},[895,60275,60276],{},[898,60277,1824],{},[902,60279,1824],{"encoding":904},[724,60281,60282,3106,60284,2704,60314,60350,60351,5607,60364,60379,60380,2086],{},[38,60283,23896],{},[883,60285,60287],{"className":60286},[886],[888,60288,60289],{"xmlns":890},[892,60290,60291,60311],{},[895,60292,60293,60295,60297,60299,60301,60303,60305,60307,60309],{},[898,60294,4049],{},[898,60296,4052],{},[1655,60298,1657],{},[1826,60300,1828],{},[2031,60302,2435],{},[1826,60304,60208],{},[1655,60306,2346],{},[1826,60308,3639],{},[898,60310,1824],{},[902,60312,60313],{"encoding":904},"TC = 1\\,000 + 4Q",[883,60315,60317],{"className":60316},[886],[888,60318,60319],{"xmlns":890},[892,60320,60321,60347],{},[895,60322,60323,60325,60327,60329,60343,60345],{},[898,60324,2731],{},[898,60326,4052],{},[1655,60328,1657],{},[3615,60330,60331],{"scriptlevel":2552,"displaystyle":1663},[1949,60332,60333,60341],{},[895,60334,60335,60337,60339],{},[1826,60336,1828],{},[2031,60338,2435],{},[1826,60340,60208],{},[898,60342,1824],{},[1655,60344,2346],{},[1826,60346,3639],{},[902,60348,60349],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,60352,60354],{"className":60353},[886],[888,60355,60356],{"xmlns":890},[892,60357,60358,60362],{},[895,60359,60360],{},[898,60361,1824],{},[902,60363,1824],{"encoding":904},[883,60365,60367],{"className":60366},[886],[888,60368,60369],{"xmlns":890},[892,60370,60371,60377],{},[895,60372,60373,60375],{},[898,60374,2731],{},[898,60376,4052],{},[902,60378,56686],{"encoding":904}," blíží ",[883,60381,60383],{"className":60382},[886],[888,60384,60385],{"xmlns":890},[892,60386,60387,60391],{},[895,60388,60389],{},[1826,60390,3639],{},[902,60392,3639],{"encoding":904},[883,60394,60396],{"className":60395},[886],[888,60397,60398],{"xmlns":890,"display":29192},[892,60399,60400,60446],{},[895,60401,60402,60419,60441,60443],{},[41022,60403,60404,60411],{},[895,60405,60406,60409],{},[898,60407,60408],{},"lim",[1655,60410,57326],{},[895,60412,60413,60415,60417],{},[898,60414,1824],{},[1655,60416,4393],{},[898,60418,7544],{"mathvariant":1943},[895,60420,60421,60423,60435,60437,60439],{},[1655,60422,1664],{"fence":1670},[1949,60424,60425,60433],{},[895,60426,60427,60429,60431],{},[1826,60428,1828],{},[2031,60430,2435],{},[1826,60432,60208],{},[898,60434,1824],{},[1655,60436,2346],{},[1826,60438,3639],{},[1655,60440,1677],{"fence":1670},[1655,60442,1657],{},[1826,60444,60445],{},"4.",[902,60447,60448],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,60450,60451,60489,60490,1719],{},[883,60452,60454],{"className":60453},[886],[888,60455,60456],{"xmlns":890},[892,60457,60458,60486],{},[895,60459,60460,60462,60464,60466,60468,60482,60484],{},[898,60461,2731],{},[898,60463,2537],{},[898,60465,4052],{},[1655,60467,1657],{},[3615,60469,60470],{"scriptlevel":2552,"displaystyle":1663},[1949,60471,60472,60480],{},[895,60473,60474,60476,60478],{},[1826,60475,1828],{},[2031,60477,2435],{},[1826,60479,60208],{},[898,60481,1824],{},[1655,60483,4393],{},[1826,60485,2552],{},[902,60487,60488],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,60491,60493],{"className":60492},[886],[888,60494,60495],{"xmlns":890},[892,60496,60497,60501],{},[895,60498,60499],{},[898,60500,1824],{},[902,60502,1824],{"encoding":904},[724,60504,60505],{},[614,60506,60507,60508,60537,60538,1719],{},"Obrázek 3.5: Přímka ",[883,60509,60511],{"className":60510},[886],[888,60512,60513],{"xmlns":890},[892,60514,60515,60535],{},[895,60516,60517,60519,60521,60523,60525,60527,60529,60531,60533],{},[898,60518,4049],{},[898,60520,4052],{},[1655,60522,1657],{},[1826,60524,1828],{},[2031,60526,2435],{},[1826,60528,60208],{},[1655,60530,2346],{},[1826,60532,3639],{},[898,60534,1824],{},[902,60536,60313],{"encoding":904}," protínající svislou osu ve výši ",[883,60539,60541],{"className":60540},[886],[888,60542,60543],{"xmlns":890},[892,60544,60545,60559],{},[895,60546,60547,60549,60551,60553,60555,60557],{},[898,60548,2537],{},[898,60550,4052],{},[1655,60552,1657],{},[1826,60554,1828],{},[2031,60556,2435],{},[1826,60558,60208],{},[902,60560,60211],{"encoding":904},[724,60562,60563],{},[614,60564,60565,60566,60601,60602,1719],{},"Obrázek 3.6: Hyperbola ",[883,60567,60569],{"className":60568},[886],[888,60570,60571],{"xmlns":890},[892,60572,60573,60599],{},[895,60574,60575,60577,60579,60581,60595,60597],{},[898,60576,2731],{},[898,60578,4052],{},[1655,60580,1657],{},[3615,60582,60583],{"scriptlevel":2552,"displaystyle":1663},[1949,60584,60585,60593],{},[895,60586,60587,60589,60591],{},[1826,60588,1828],{},[2031,60590,2435],{},[1826,60592,60208],{},[898,60594,1824],{},[1655,60596,2346],{},[1826,60598,3639],{},[902,60600,60349],{"encoding":904}," s vodorovnou asymptotou ",[883,60603,60605],{"className":60604},[886],[888,60606,60607],{"xmlns":890},[892,60608,60609,60619],{},[895,60610,60611,60613,60615,60617],{},[898,60612,2731],{},[898,60614,4052],{},[1655,60616,1657],{},[1826,60618,3639],{},[902,60620,60621],{"encoding":904},"AC = 4",[724,60623,60624],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,60626,60628],{"className":60627},[886],[888,60629,60630],{"xmlns":890,"display":29192},[892,60631,60632,60658],{},[895,60633,60634,60636,60638,60640,60642,60644,60646,60648,60650,60652,60654,60656],{},[898,60635,4049],{},[898,60637,41465],{},[898,60639,4052],{},[1655,60641,1657],{},[898,60643,1824],{},[1655,60645,2869],{},[898,60647,41465],{},[898,60649,4052],{},[1655,60651,1664],{"stretchy":1663},[898,60653,1824],{},[1655,60655,1677],{"stretchy":1663},[1655,60657,1671],{"separator":1670},[902,60659,60660],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,60662,5559,60663,59852,60691,60694,60695,60725],{},[883,60664,60666],{"className":60665},[886],[888,60667,60668],{"xmlns":890},[892,60669,60670,60688],{},[895,60671,60672,60674,60676,60678,60680,60682,60684,60686],{},[898,60673,41465],{},[898,60675,4052],{},[1655,60677,1657],{},[898,60679,41465],{},[898,60681,4052],{},[1655,60683,1664],{"stretchy":1663},[898,60685,1824],{},[1655,60687,1677],{"stretchy":1663},[902,60689,60690],{"encoding":904},"VC = VC(Q)",[38,60692,60693],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,60696,60698],{"className":60697},[886],[888,60699,60700],{"xmlns":890},[892,60701,60702,60722],{},[895,60703,60704,60706,60708,60710,60712,60714,60716,60718,60720],{},[898,60705,4049],{},[898,60707,41465],{},[898,60709,4052],{},[1655,60711,1664],{"stretchy":1663},[898,60713,1824],{},[1655,60715,1677],{"stretchy":1663},[1655,60717,1657],{},[898,60719,207],{},[898,60721,1824],{},[902,60723,60724],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,60727,60729],{"className":60728},[886],[888,60730,60731],{"xmlns":890,"display":29192},[892,60732,60733,60753],{},[895,60734,60735,60737,60739,60741,60743,60745,60747,60749,60751],{},[898,60736,4049],{},[898,60738,4052],{},[1655,60740,1657],{},[898,60742,2537],{},[898,60744,4052],{},[1655,60746,2346],{},[898,60748,207],{},[898,60750,1824],{},[898,60752,1719],{"mathvariant":1943},[902,60754,60755],{"encoding":904},"TC = FC + aQ.",[724,60757,60758,60759,60774,60775,60790,60791,60814,60815,60849,60850,60601,60863,60876,60877,2704,60925,60969,60970,1719],{},"Křivkou ",[883,60760,60762],{"className":60761},[886],[888,60763,60764],{"xmlns":890},[892,60765,60766,60772],{},[895,60767,60768,60770],{},[898,60769,4049],{},[898,60771,4052],{},[902,60773,4512],{"encoding":904}," je přímka se svislým průsečíkem ",[883,60776,60778],{"className":60777},[886],[888,60779,60780],{"xmlns":890},[892,60781,60782,60788],{},[895,60783,60784,60786],{},[898,60785,2537],{},[898,60787,4052],{},[902,60789,56617],{"encoding":904}," a sklonem ",[883,60792,60794],{"className":60793},[886],[888,60795,60796],{"xmlns":890},[892,60797,60798,60811],{},[895,60799,60800,60803,60805,60807,60809],{},[898,60801,60802],{},"tan",[1655,60804,57326],{},[898,60806,19988],{},[1655,60808,1657],{},[898,60810,207],{},[902,60812,60813],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,60816,60818],{"className":60817},[886],[888,60819,60820],{"xmlns":890},[892,60821,60822,60846],{},[895,60823,60824,60826,60828,60830,60842,60844],{},[898,60825,2731],{},[898,60827,4052],{},[1655,60829,1657],{},[3615,60831,60832],{"scriptlevel":2552,"displaystyle":1663},[1949,60833,60834,60840],{},[895,60835,60836,60838],{},[898,60837,2537],{},[898,60839,4052],{},[898,60841,1824],{},[1655,60843,2346],{},[898,60845,207],{},[902,60847,60848],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,60851,60853],{"className":60852},[886],[888,60854,60855],{"xmlns":890},[892,60856,60857,60861],{},[895,60858,60859],{},[898,60860,1873],{},[902,60862,1873],{"encoding":904},[883,60864,60866],{"className":60865},[886],[888,60867,60868],{"xmlns":890},[892,60869,60870,60874],{},[895,60871,60872],{},[898,60873,207],{},[902,60875,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,60878,60880],{"className":60879},[886],[888,60881,60882],{"xmlns":890},[892,60883,60884,60922],{},[895,60885,60886,60906,60918,60920],{},[1820,60887,60888,60894],{},[895,60889,60890,60892],{},[898,60891,60408],{},[1655,60893,57326],{},[895,60895,60896,60898,60900],{},[898,60897,1824],{},[1655,60899,4393],{},[2597,60901,60902,60904],{},[1826,60903,2552],{},[1655,60905,2346],{},[3615,60907,60908],{"scriptlevel":2552,"displaystyle":1663},[1949,60909,60910,60916],{},[895,60911,60912,60914],{},[898,60913,2537],{},[898,60915,4052],{},[898,60917,1824],{},[1655,60919,1657],{},[898,60921,7544],{"mathvariant":1943},[902,60923,60924],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,60926,60928],{"className":60927},[886],[888,60929,60930],{"xmlns":890},[892,60931,60932,60966],{},[895,60933,60934,60950,60962,60964],{},[1820,60935,60936,60942],{},[895,60937,60938,60940],{},[898,60939,60408],{},[1655,60941,57326],{},[895,60943,60944,60946,60948],{},[898,60945,1824],{},[1655,60947,4393],{},[898,60949,7544],{"mathvariant":1943},[3615,60951,60952],{"scriptlevel":2552,"displaystyle":1663},[1949,60953,60954,60960],{},[895,60955,60956,60958],{},[898,60957,2537],{},[898,60959,4052],{},[898,60961,1824],{},[1655,60963,1657],{},[1826,60965,2552],{},[902,60967,60968],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,60971,60973],{"className":60972},[886],[888,60974,60975],{"xmlns":890},[892,60976,60977,60983],{},[895,60978,60979,60981],{},[898,60980,2731],{},[898,60982,4052],{},[902,60984,56686],{"encoding":904},[724,60986,60987],{},[614,60988,60989,60990,61005,61006,61021,61022,1719],{},"Obrázek 3.7: Přímka ",[883,60991,60993],{"className":60992},[886],[888,60994,60995],{"xmlns":890},[892,60996,60997,61003],{},[895,60998,60999,61001],{},[898,61000,4049],{},[898,61002,4052],{},[902,61004,4512],{"encoding":904}," s osovým průsečíkem ve výši ",[883,61007,61009],{"className":61008},[886],[888,61010,61011],{"xmlns":890},[892,61012,61013,61019],{},[895,61014,61015,61017],{},[898,61016,2537],{},[898,61018,4052],{},[902,61020,56617],{"encoding":904}," a se sklonem ",[883,61023,61025],{"className":61024},[886],[888,61026,61027],{"xmlns":890},[892,61028,61029,61041],{},[895,61030,61031,61033,61035,61037,61039],{},[898,61032,60802],{},[1655,61034,57326],{},[898,61036,19988],{},[1655,61038,1657],{},[898,61040,207],{},[902,61042,60813],{"encoding":904},[724,61044,61045],{},[614,61046,61047,61048,61063,61064,1719],{},"Obrázek 3.8: Klesající hyperbola ",[883,61049,61051],{"className":61050},[886],[888,61052,61053],{"xmlns":890},[892,61054,61055,61061],{},[895,61056,61057,61059],{},[898,61058,2731],{},[898,61060,4052],{},[902,61062,56686],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,61065,61067],{"className":61066},[886],[888,61068,61069],{"xmlns":890},[892,61070,61071,61075],{},[895,61072,61073],{},[898,61074,207],{},[902,61076,207],{"encoding":904},[198,61078,61080],{"id":61079},"mezní-náklady","Mezní náklady",[724,61082,61083,3106,61085,2115,61100,61103,61104,61107],{},[38,61084,61080],{},[883,61086,61088],{"className":61087},[886],[888,61089,61090],{"xmlns":890},[892,61091,61092,61098],{},[895,61093,61094,61096],{},[898,61095,2127],{},[898,61097,4052],{},[902,61099,56418],{"encoding":904},[38,61101,61102],{},"marginal cost",") jsou ",[207,61105,1145],{"className":61106,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,61109,61111],{"className":61110},[886],[888,61112,61113],{"xmlns":890,"display":29192},[892,61114,61115,61184],{},[21880,61116,61117],{"width":29197},[21885,61118,61119,61121,61177,61179],{},[21888,61120],{"width":29202},[21888,61122,61123],{},[895,61124,61125,61127,61129,61131,61133,61135,61137,61139,61141,61143,61159,61161,61163,61169,61171,61173,61175],{},[898,61126,2127],{},[898,61128,4052],{},[1655,61130,1657],{},[898,61132,2127],{},[898,61134,4052],{},[1655,61136,1664],{"stretchy":1663},[898,61138,1824],{},[1655,61140,1677],{"stretchy":1663},[1655,61142,1657],{},[1949,61144,61145,61153],{},[895,61146,61147,61149,61151],{},[898,61148,2410],{"mathvariant":1943},[898,61150,4049],{},[898,61152,4052],{},[895,61154,61155,61157],{},[898,61156,2410],{"mathvariant":1943},[898,61158,1824],{},[1655,61160,1657],{},[898,61162,4049],{},[2597,61164,61165,61167],{},[898,61166,4052],{},[1655,61168,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,61170,1664],{"stretchy":1663},[898,61172,1824],{},[1655,61174,1677],{"stretchy":1663},[898,61176,1719],{"mathvariant":1943},[21888,61178],{"width":29202},[21888,61180,61181],{},[2031,61182,61183],{},"(3.8)",[902,61185,61186],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[5120,61188,61189],{},[724,61190,61191,61193,61194,61220,61221,61238,61239,1719],{},[883,61192,5406],{}," Intuice — „kolik stojí další kus\"\n",[883,61195,61197],{"className":61196},[886],[888,61198,61199],{"xmlns":890},[892,61200,61201,61217],{},[895,61202,61203,61205,61207,61209,61215],{},[898,61204,2127],{},[898,61206,4052],{},[1655,61208,1664],{"stretchy":1663},[2597,61210,61211,61213],{},[898,61212,1824],{},[1655,61214,5603],{},[1655,61216,1677],{"stretchy":1663},[902,61218,61219],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,61222,61224],{"className":61223},[886],[888,61225,61226],{"xmlns":890},[892,61227,61228,61236],{},[895,61229,61230],{},[2597,61231,61232,61234],{},[898,61233,1824],{},[1655,61235,5603],{},[902,61237,30970],{"encoding":904},". Formálně ",[883,61240,61242],{"className":61241},[886],[888,61243,61244],{"xmlns":890},[892,61245,61246,61298],{},[895,61247,61248,61250,61252,61254,61260,61262,61264,61266,61268,61270,61276,61278,61280,61282,61284,61286,61288,61290,61296],{},[898,61249,2127],{},[898,61251,4052],{},[1655,61253,1664],{"stretchy":1663},[2597,61255,61256,61258],{},[898,61257,1824],{},[1655,61259,5603],{},[1655,61261,1677],{"stretchy":1663},[1655,61263,2357],{},[898,61265,4049],{},[898,61267,4052],{},[1655,61269,1664],{"stretchy":1663},[2597,61271,61272,61274],{},[898,61273,1824],{},[1655,61275,5603],{},[1655,61277,2346],{},[1826,61279,1828],{},[1655,61281,1677],{"stretchy":1663},[1655,61283,2623],{},[898,61285,4049],{},[898,61287,4052],{},[1655,61289,1664],{"stretchy":1663},[2597,61291,61292,61294],{},[898,61293,1824],{},[1655,61295,5603],{},[1655,61297,1677],{"stretchy":1663},[902,61299,61300],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,61302,61303,61304,2086],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,61305,61307],{"className":61306},[886],[888,61308,61309],{"xmlns":890},[892,61310,61311,61319],{},[895,61312,61313,61315,61317],{},[898,61314,2506],{"mathvariant":1943},[898,61316,4049],{},[898,61318,4052],{},[902,61320,61321],{"encoding":904},"\\Delta TC",[883,61323,61325],{"className":61324},[886],[888,61326,61327],{"xmlns":890,"display":29192},[892,61328,61329,61398],{},[21880,61330,61331],{"width":29197},[21885,61332,61333,61335,61391,61393],{},[21888,61334],{"width":29202},[21888,61336,61337],{},[895,61338,61339,61341,61343,61345,61347,61349,61351,61353,61355,61357,61359,61361,61363,61365,61371,61373,61375,61377,61379,61381,61383,61385,61387,61389],{},[898,61340,2506],{"mathvariant":1943},[898,61342,4049],{},[898,61344,4052],{},[2031,61346,2783],{},[1655,61348,2357],{},[2031,61350,2783],{},[898,61352,2410],{"mathvariant":1943},[898,61354,4049],{},[898,61356,4052],{},[1655,61358,1657],{},[1655,61360,1664],{"stretchy":1663},[898,61362,4049],{},[898,61364,4052],{},[2597,61366,61367,61369],{},[1655,61368,1677],{"stretchy":1663},[1655,61370,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[2031,61372,2435],{},[898,61374,2410],{"mathvariant":1943},[898,61376,1824],{},[1655,61378,1657],{},[898,61380,2127],{},[898,61382,4052],{},[2031,61384,2435],{},[898,61386,2410],{"mathvariant":1943},[898,61388,1824],{},[1655,61390,1671],{"separator":1670},[21888,61392],{"width":29202},[21888,61394,61395],{},[2031,61396,61397],{},"(3.9)",[902,61399,61400],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,61402,58437],{},[883,61404,61406],{"className":61405},[886],[888,61407,61408],{"xmlns":890,"display":29192},[892,61409,61410,61508],{},[895,61411,61412,61450,61452,61454,61456,61478,61480,61506],{},[895,61413,61414,61416,61422,61424,61430,61433,61439,61442],{},[2031,61415,58451],{},[9633,61417,61418,61420],{"accent":1670},[2031,61419,46858],{},[1655,61421,26184],{},[2031,61423,58460],{},[9633,61425,61426,61428],{"accent":1670},[2031,61427,1674],{},[1655,61429,26103],{},[2031,61431,61432],{},"ch n",[9633,61434,61435,61437],{"accent":1670},[2031,61436,207],{},[1655,61438,26103],{},[2031,61440,61441],{},"klad",[9633,61443,61444,61447],{"accent":1670},[2031,61445,61446],{},"u",[1655,61448,61449],{},"˚",[2031,61451,2783],{},[1655,61453,2357],{},[2031,61455,2783],{},[895,61457,61458,61460,61466,61469,61475],{},[2031,61459,58495],{},[9633,61461,61462,61464],{"accent":1670},[2031,61463,26172],{},[1655,61465,26103],{},[2031,61467,61468],{}," n",[9633,61470,61471,61473],{"accent":1670},[2031,61472,207],{},[1655,61474,26103],{},[2031,61476,61477],{},"klady",[1655,61479,58522],{},[895,61481,61482,61484,61490,61492,61498,61500],{},[2031,61483,58451],{},[9633,61485,61486,61488],{"accent":1670},[2031,61487,46858],{},[1655,61489,26184],{},[2031,61491,58535],{},[9633,61493,61494,61496],{"accent":1670},[2031,61495,1653],{},[1655,61497,26184],{},[2031,61499,58544],{},[9633,61501,61502,61504],{"accent":1670},[2031,61503,26172],{},[1655,61505,26103],{},[898,61507,1719],{"mathvariant":1943},[902,61509,61510],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[38474,61512,61514],{"id":61513},"příklad-35","Příklad 3.5",[724,61516,61517,58648,61519,57151,61555,61570,61571,61586,61587,3948,61600,3962,61613,61626,61627,3962,61640,1719],{},[38,61518,57113],{},[883,61520,61522],{"className":61521},[886],[888,61523,61524],{"xmlns":890},[892,61525,61526,61552],{},[895,61527,61528,61530,61532,61534,61536,61538,61540,61542,61544,61546],{},[898,61529,4049],{},[898,61531,4052],{},[1655,61533,1657],{},[1826,61535,9624],{},[1655,61537,2346],{},[1826,61539,3531],{},[898,61541,1824],{},[1655,61543,2346],{},[1826,61545,1837],{},[2597,61547,61548,61550],{},[898,61549,1824],{},[1826,61551,1837],{},[902,61553,61554],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,61556,61558],{"className":61557},[886],[888,61559,61560],{"xmlns":890},[892,61561,61562,61568],{},[895,61563,61564,61566],{},[898,61565,2127],{},[898,61567,4052],{},[902,61569,56418],{"encoding":904}," a odhadněte změny ",[883,61572,61574],{"className":61573},[886],[888,61575,61576],{"xmlns":890},[892,61577,61578,61584],{},[895,61579,61580,61582],{},[898,61581,4049],{},[898,61583,4052],{},[902,61585,4512],{"encoding":904}," při změnách ",[883,61588,61590],{"className":61589},[886],[888,61591,61592],{"xmlns":890},[892,61593,61594,61598],{},[895,61595,61596],{},[898,61597,1824],{},[902,61599,1824],{"encoding":904},[883,61601,61603],{"className":61602},[886],[888,61604,61605],{"xmlns":890},[892,61606,61607,61611],{},[895,61608,61609],{},[1826,61610,37370],{},[902,61612,37370],{"encoding":904},[883,61614,61616],{"className":61615},[886],[888,61617,61618],{"xmlns":890},[892,61619,61620,61624],{},[895,61621,61622],{},[1826,61623,42988],{},[902,61625,42988],{"encoding":904}," a z ",[883,61628,61630],{"className":61629},[886],[888,61631,61632],{"xmlns":890},[892,61633,61634,61638],{},[895,61635,61636],{},[1826,61637,37370],{},[902,61639,37370],{"encoding":904},[883,61641,61643],{"className":61642},[886],[888,61644,61645],{"xmlns":890},[892,61646,61647,61651],{},[895,61648,61649],{},[1826,61650,4771],{},[902,61652,4771],{"encoding":904},[724,61654,61655,3106,61657,4199,61683,1343,61710,61737,61738,61753,61754,61769,61770,61797,61798,61818,61819,21657,61840,61896,61897,3948,61910,3962,61923,9349,61936,1719],{},[38,61656,23896],{},[883,61658,61660],{"className":61659},[886],[888,61661,61662],{"xmlns":890},[892,61663,61664,61680],{},[895,61665,61666,61668,61670,61672,61674,61676,61678],{},[898,61667,2127],{},[898,61669,4052],{},[1655,61671,1657],{},[1826,61673,3531],{},[1655,61675,2346],{},[1826,61677,3639],{},[898,61679,1824],{},[902,61681,61682],{"encoding":904},"MC = 6 + 4Q",[883,61684,61686],{"className":61685},[886],[888,61687,61688],{"xmlns":890},[892,61689,61690,61707],{},[895,61691,61692,61694,61696,61698,61700,61702,61704],{},[898,61693,2127],{},[898,61695,4052],{},[1655,61697,1664],{"stretchy":1663},[1826,61699,37370],{},[1655,61701,1677],{"stretchy":1663},[1655,61703,1657],{},[1826,61705,61706],{},"66",[902,61708,61709],{"encoding":904},"MC(15) = 66",[883,61711,61713],{"className":61712},[886],[888,61714,61715],{"xmlns":890},[892,61716,61717,61734],{},[895,61718,61719,61721,61723,61725,61727,61729,61731],{},[898,61720,2127],{},[898,61722,4052],{},[1655,61724,1664],{"stretchy":1663},[1826,61726,10282],{},[1655,61728,1677],{"stretchy":1663},[1655,61730,1657],{},[1826,61732,61733],{},"86",[902,61735,61736],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,61739,61741],{"className":61740},[886],[888,61742,61743],{"xmlns":890},[892,61744,61745,61751],{},[895,61746,61747,61749],{},[898,61748,4049],{},[898,61750,4052],{},[902,61752,4512],{"encoding":904}," zvyšuje (",[883,61755,61757],{"className":61756},[886],[888,61758,61759],{"xmlns":890},[892,61760,61761,61767],{},[895,61762,61763,61765],{},[898,61764,2127],{},[898,61766,4052],{},[902,61768,56418],{"encoding":904}," je rostoucí). Z ",[883,61771,61773],{"className":61772},[886],[888,61774,61775],{"xmlns":890},[892,61776,61777,61794],{},[895,61778,61779,61781,61783,61785,61787,61789,61791],{},[898,61780,4049],{},[898,61782,4052],{},[1655,61784,1664],{"stretchy":1663},[1826,61786,37370],{},[1655,61788,1677],{"stretchy":1663},[1655,61790,1657],{},[1826,61792,61793],{},"740",[902,61795,61796],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,61799,61801],{"className":61800},[886],[888,61802,61803],{"xmlns":890},[892,61804,61805,61815],{},[895,61806,61807,61809,61811,61813],{},[898,61808,2410],{"mathvariant":1943},[898,61810,1824],{},[1655,61812,1657],{},[1826,61814,1828],{},[902,61816,61817],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,61820,61822],{"className":61821},[886],[888,61823,61824],{"xmlns":890},[892,61825,61826,61837],{},[895,61827,61828,61830,61832,61834],{},[898,61829,4049],{},[898,61831,4052],{},[1655,61833,2357],{},[1826,61835,61836],{},"806",[902,61838,61839],{"encoding":904},"TC \\approx 806",[883,61841,61843],{"className":61842},[886],[888,61844,61845],{"xmlns":890},[892,61846,61847,61893],{},[895,61848,61849,61851,61853,61855,61857,61859,61861,61863,61865,61867,61869,61871,61873,61875,61877,61879,61881,61884,61886,61888,61890],{},[898,61850,2506],{"mathvariant":1943},[898,61852,4049],{},[898,61854,4052],{},[1655,61856,1657],{},[898,61858,4049],{},[898,61860,4052],{},[1655,61862,1664],{"stretchy":1663},[1826,61864,42988],{},[1655,61866,1677],{"stretchy":1663},[1655,61868,2623],{},[898,61870,4049],{},[898,61872,4052],{},[1655,61874,1664],{"stretchy":1663},[1826,61876,37370],{},[1655,61878,1677],{"stretchy":1663},[1655,61880,1657],{},[1826,61882,61883],{},"808",[1655,61885,2623],{},[1826,61887,61793],{},[1655,61889,1657],{},[1826,61891,61892],{},"68",[902,61894,61895],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,61898,61900],{"className":61899},[886],[888,61901,61902],{"xmlns":890},[892,61903,61904,61908],{},[895,61905,61906],{},[898,61907,1824],{},[902,61909,1824],{"encoding":904},[883,61911,61913],{"className":61912},[886],[888,61914,61915],{"xmlns":890},[892,61916,61917,61921],{},[895,61918,61919],{},[1826,61920,37370],{},[902,61922,37370],{"encoding":904},[883,61924,61926],{"className":61925},[886],[888,61927,61928],{"xmlns":890},[892,61929,61930,61934],{},[895,61931,61932],{},[1826,61933,4771],{},[902,61935,4771],{"encoding":904},[883,61937,61939],{"className":61938},[886],[888,61940,61941],{"xmlns":890},[892,61942,61943,61972],{},[895,61944,61945,61947,61949,61951,61953,61955,61957,61959,61961,61963,61965,61967,61969],{},[898,61946,2506],{"mathvariant":1943},[898,61948,4049],{},[898,61950,4052],{},[1655,61952,2357],{},[1826,61954,61706],{},[1655,61956,2869],{},[1655,61958,1664],{"stretchy":1663},[1655,61960,2623],{},[1826,61962,3472],{},[1655,61964,1677],{"stretchy":1663},[1655,61966,1657],{},[1655,61968,2623],{},[1826,61970,61971],{},"198",[902,61973,61974],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,61976,61978],{"id":61977},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,61980,61981],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[38474,61983,61985],{"id":61984},"příklad-36","Příklad 3.6",[724,61987,61988,58648,61990,62034],{},[38,61989,57113],{},[883,61991,61993],{"className":61992},[886],[888,61994,61995],{"xmlns":890},[892,61996,61997,62031],{},[895,61998,61999,62001,62003,62005,62007,62009,62011,62013,62015,62017,62023,62025],{},[898,62000,4049],{},[898,62002,4052],{},[1655,62004,1657],{},[1826,62006,4360],{},[1655,62008,2346],{},[1826,62010,6253],{},[898,62012,1824],{},[1655,62014,2623],{},[1826,62016,3524],{},[2597,62018,62019,62021],{},[898,62020,1824],{},[1826,62022,1837],{},[1655,62024,2346],{},[2597,62026,62027,62029],{},[898,62028,1824],{},[1826,62030,3472],{},[902,62032,62033],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,62036,62037],{},[38,62038,23896],{},[883,62040,62042],{"className":62041},[886],[888,62043,62044],{"xmlns":890,"display":29192},[892,62045,62046,62290],{},[21880,62047,62048,62074,62122,62156,62198,62248],{"rowspacing":21882,"columnalign":21883,"columnspacing":1944},[21885,62049,62050,62060],{},[21888,62051,62052],{},[3615,62053,62054],{"scriptlevel":2552,"displaystyle":1670},[895,62055,62056,62058],{},[898,62057,2537],{},[898,62059,4052],{},[21888,62061,62062],{},[3615,62063,62064],{"scriptlevel":2552,"displaystyle":1670},[895,62065,62066,62068,62070,62072],{},[895,62067],{},[1655,62069,1657],{},[1826,62071,4360],{},[1655,62073,1671],{"separator":1670},[21885,62075,62076,62088],{},[21888,62077,62078],{},[3615,62079,62080],{"scriptlevel":2552,"displaystyle":1670},[895,62081,62082,62084,62086],{},[898,62083,4049],{},[898,62085,41465],{},[898,62087,4052],{},[21888,62089,62090],{},[3615,62091,62092],{"scriptlevel":2552,"displaystyle":1670},[895,62093,62094,62096,62098,62100,62102,62104,62106,62112,62114,62120],{},[895,62095],{},[1655,62097,1657],{},[1826,62099,6253],{},[898,62101,1824],{},[1655,62103,2623],{},[1826,62105,3524],{},[2597,62107,62108,62110],{},[898,62109,1824],{},[1826,62111,1837],{},[1655,62113,2346],{},[2597,62115,62116,62118],{},[898,62117,1824],{},[1826,62119,3472],{},[1655,62121,1671],{"separator":1670},[21885,62123,62124,62136],{},[21888,62125,62126],{},[3615,62127,62128],{"scriptlevel":2552,"displaystyle":1670},[895,62129,62130,62132,62134],{},[898,62131,2731],{},[898,62133,2537],{},[898,62135,4052],{},[21888,62137,62138],{},[3615,62139,62140],{"scriptlevel":2552,"displaystyle":1670},[895,62141,62142,62144,62146,62154],{},[895,62143],{},[1655,62145,1657],{},[3615,62147,62148],{"scriptlevel":2552,"displaystyle":1663},[1949,62149,62150,62152],{},[1826,62151,4360],{},[898,62153,1824],{},[1655,62155,1671],{"separator":1670},[21885,62157,62158,62170],{},[21888,62159,62160],{},[3615,62161,62162],{"scriptlevel":2552,"displaystyle":1670},[895,62163,62164,62166,62168],{},[898,62165,2731],{},[898,62167,41465],{},[898,62169,4052],{},[21888,62171,62172],{},[3615,62173,62174],{"scriptlevel":2552,"displaystyle":1670},[895,62175,62176,62178,62180,62182,62184,62186,62188,62190,62196],{},[895,62177],{},[1655,62179,1657],{},[1826,62181,6253],{},[1655,62183,2623],{},[1826,62185,3524],{},[898,62187,1824],{},[1655,62189,2346],{},[2597,62191,62192,62194],{},[898,62193,1824],{},[1826,62195,1837],{},[1655,62197,1671],{"separator":1670},[21885,62199,62200,62210],{},[21888,62201,62202],{},[3615,62203,62204],{"scriptlevel":2552,"displaystyle":1670},[895,62205,62206,62208],{},[898,62207,2731],{},[898,62209,4052],{},[21888,62211,62212],{},[3615,62213,62214],{"scriptlevel":2552,"displaystyle":1670},[895,62215,62216,62218,62220,62228,62230,62232,62234,62236,62238,62240,62246],{},[895,62217],{},[1655,62219,1657],{},[3615,62221,62222],{"scriptlevel":2552,"displaystyle":1663},[1949,62223,62224,62226],{},[1826,62225,4360],{},[898,62227,1824],{},[1655,62229,2346],{},[1826,62231,6253],{},[1655,62233,2623],{},[1826,62235,3524],{},[898,62237,1824],{},[1655,62239,2346],{},[2597,62241,62242,62244],{},[898,62243,1824],{},[1826,62245,1837],{},[1655,62247,1671],{"separator":1670},[21885,62249,62250,62260],{},[21888,62251,62252],{},[3615,62253,62254],{"scriptlevel":2552,"displaystyle":1670},[895,62255,62256,62258],{},[898,62257,2127],{},[898,62259,4052],{},[21888,62261,62262],{},[3615,62263,62264],{"scriptlevel":2552,"displaystyle":1670},[895,62265,62266,62268,62270,62272,62274,62276,62278,62280,62282,62288],{},[895,62267],{},[1655,62269,1657],{},[1826,62271,6253],{},[1655,62273,2623],{},[1826,62275,4136],{},[898,62277,1824],{},[1655,62279,2346],{},[1826,62281,3472],{},[2597,62283,62284,62286],{},[898,62285,1824],{},[1826,62287,1837],{},[898,62289,1719],{"mathvariant":1943},[902,62291,62292],{"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}",[724,62294,62295,62296,16917,62311,16917,62326,62341,62342,62357,62358,1343,62376,62357,62393,1343,62411,62357,62426,62444],{},"Význačné body ",[883,62297,62299],{"className":62298},[886],[888,62300,62301],{"xmlns":890},[892,62302,62303,62308],{},[895,62304,62305],{},[1826,62306,62307],{},"1,67",[902,62309,62310],{"encoding":904},"1{,}67",[883,62312,62314],{"className":62313},[886],[888,62315,62316],{"xmlns":890},[892,62317,62318,62323],{},[895,62319,62320],{},[1826,62321,62322],{},"2,50",[902,62324,62325],{"encoding":904},"2{,}50",[883,62327,62329],{"className":62328},[886],[888,62330,62331],{"xmlns":890},[892,62332,62333,62338],{},[895,62334,62335],{},[1826,62336,62337],{},"4,73",[902,62339,62340],{"encoding":904},"4{,}73"," odpovídají: ",[883,62343,62345],{"className":62344},[886],[888,62346,62347],{"xmlns":890},[892,62348,62349,62355],{},[895,62350,62351,62353],{},[898,62352,2127],{},[898,62354,4052],{},[902,62356,56418],{"encoding":904}," minimum v ",[883,62359,62361],{"className":62360},[886],[888,62362,62363],{"xmlns":890},[892,62364,62365,62373],{},[895,62366,62367,62369,62371],{},[898,62368,1824],{},[1655,62370,7147],{},[1826,62372,62307],{},[902,62374,62375],{"encoding":904},"Q \\doteq 1{,}67",[883,62377,62379],{"className":62378},[886],[888,62380,62381],{"xmlns":890},[892,62382,62383,62391],{},[895,62384,62385,62387,62389],{},[898,62386,2731],{},[898,62388,41465],{},[898,62390,4052],{},[902,62392,56437],{"encoding":904},[883,62394,62396],{"className":62395},[886],[888,62397,62398],{"xmlns":890},[892,62399,62400,62408],{},[895,62401,62402,62404,62406],{},[898,62403,1824],{},[1655,62405,1657],{},[1826,62407,62322],{},[902,62409,62410],{"encoding":904},"Q = 2{,}50",[883,62412,62414],{"className":62413},[886],[888,62415,62416],{"xmlns":890},[892,62417,62418,62424],{},[895,62419,62420,62422],{},[898,62421,2731],{},[898,62423,4052],{},[902,62425,56686],{"encoding":904},[883,62427,62429],{"className":62428},[886],[888,62430,62431],{"xmlns":890},[892,62432,62433,62441],{},[895,62434,62435,62437,62439],{},[898,62436,1824],{},[1655,62438,7147],{},[1826,62440,62337],{},[902,62442,62443],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,62446,62447],{},[1723,62448],{"alt":62449,"className":62450,"src":62451},"imek-ac-avc-mc",[210,1727],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,62453,62454],{},[614,62455,62456,62457,2704,62472,62489,62490,16917,62509,62524],{},"Obrázek 3.9: Kubické křivky ",[883,62458,62460],{"className":62459},[886],[888,62461,62462],{"xmlns":890},[892,62463,62464,62470],{},[895,62465,62466,62468],{},[898,62467,4049],{},[898,62469,4052],{},[902,62471,4512],{"encoding":904},[883,62473,62475],{"className":62474},[886],[888,62476,62477],{"xmlns":890},[892,62478,62479,62487],{},[895,62480,62481,62483,62485],{},[898,62482,4049],{},[898,62484,41465],{},[898,62486,4052],{},[902,62488,56635],{"encoding":904}," rostoucí od bodu ",[883,62491,62493],{"className":62492},[886],[888,62494,62495],{"xmlns":890},[892,62496,62497,62507],{},[895,62498,62499,62501,62503,62505],{},[898,62500,2537],{},[898,62502,4052],{},[1655,62504,1657],{},[1826,62506,4360],{},[902,62508,12757],{"encoding":904},[883,62510,62512],{"className":62511},[886],[888,62513,62514],{"xmlns":890},[892,62515,62516,62522],{},[895,62517,62518,62520],{},[898,62519,2537],{},[898,62521,4052],{},[902,62523,56617],{"encoding":904}," je vodorovná přímka.",[724,62526,62527],{},[614,62528,62529,62530,1343,62545,1343,62562,30327,62577,62590,62591,4199,62608,62623,62624,7437,62641,62656,62657,27315,62670,1343,62683,1343,62696,1719],{},"Obrázek 3.10: Křivky ",[883,62531,62533],{"className":62532},[886],[888,62534,62535],{"xmlns":890},[892,62536,62537,62543],{},[895,62538,62539,62541],{},[898,62540,2731],{},[898,62542,4052],{},[902,62544,56686],{"encoding":904},[883,62546,62548],{"className":62547},[886],[888,62549,62550],{"xmlns":890},[892,62551,62552,62560],{},[895,62553,62554,62556,62558],{},[898,62555,2731],{},[898,62557,41465],{},[898,62559,4052],{},[902,62561,56437],{"encoding":904},[883,62563,62565],{"className":62564},[886],[888,62566,62567],{"xmlns":890},[892,62568,62569,62575],{},[895,62570,62571,62573],{},[898,62572,2127],{},[898,62574,4052],{},[902,62576,56418],{"encoding":904},[883,62578,62580],{"className":62579},[886],[888,62581,62582],{"xmlns":890},[892,62583,62584,62588],{},[895,62585,62586],{},[898,62587,900],{},[902,62589,900],{"encoding":904}," a klesající hyperbola ",[883,62592,62594],{"className":62593},[886],[888,62595,62596],{"xmlns":890},[892,62597,62598,62606],{},[895,62599,62600,62602,62604],{},[898,62601,2731],{},[898,62603,2537],{},[898,62605,4052],{},[902,62607,56653],{"encoding":904},[883,62609,62611],{"className":62610},[886],[888,62612,62613],{"xmlns":890},[892,62614,62615,62621],{},[895,62616,62617,62619],{},[898,62618,2127],{},[898,62620,4052],{},[902,62622,56418],{"encoding":904}," protíná ",[883,62625,62627],{"className":62626},[886],[888,62628,62629],{"xmlns":890},[892,62630,62631,62639],{},[895,62632,62633,62635,62637],{},[898,62634,2731],{},[898,62636,41465],{},[898,62638,4052],{},[902,62640,56437],{"encoding":904},[883,62642,62644],{"className":62643},[886],[888,62645,62646],{"xmlns":890},[892,62647,62648,62654],{},[895,62649,62650,62652],{},[898,62651,2731],{},[898,62653,4052],{},[902,62655,56686],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,62658,62660],{"className":62659},[886],[888,62661,62662],{"xmlns":890},[892,62663,62664,62668],{},[895,62665,62666],{},[898,62667,1824],{},[902,62669,1824],{"encoding":904},[883,62671,62673],{"className":62672},[886],[888,62674,62675],{"xmlns":890},[892,62676,62677,62681],{},[895,62678,62679],{},[1826,62680,62307],{},[902,62682,62310],{"encoding":904},[883,62684,62686],{"className":62685},[886],[888,62687,62688],{"xmlns":890},[892,62689,62690,62694],{},[895,62691,62692],{},[1826,62693,62322],{},[902,62695,62325],{"encoding":904},[883,62697,62699],{"className":62698},[886],[888,62700,62701],{"xmlns":890},[892,62702,62703,62707],{},[895,62704,62705],{},[1826,62706,62337],{},[902,62708,62340],{"encoding":904},[724,62710,62711],{},[38,62712,62713],{},"Standardní vlastnosti:",[120,62715,62716,62751,62815,62883,62933,62953],{},[123,62717,62718,2704,62733,62750],{},[883,62719,62721],{"className":62720},[886],[888,62722,62723],{"xmlns":890},[892,62724,62725,62731],{},[895,62726,62727,62729],{},[898,62728,4049],{},[898,62730,4052],{},[902,62732,4512],{"encoding":904},[883,62734,62736],{"className":62735},[886],[888,62737,62738],{"xmlns":890},[892,62739,62740,62748],{},[895,62741,62742,62744,62746],{},[898,62743,4049],{},[898,62745,41465],{},[898,62747,4052],{},[902,62749,56635],{"encoding":904}," jsou kubické funkce;",[123,62752,62753,1343,62768,1343,62785,62800,62801,62814],{},[883,62754,62756],{"className":62755},[886],[888,62757,62758],{"xmlns":890},[892,62759,62760,62766],{},[895,62761,62762,62764],{},[898,62763,2731],{},[898,62765,4052],{},[902,62767,56686],{"encoding":904},[883,62769,62771],{"className":62770},[886],[888,62772,62773],{"xmlns":890},[892,62774,62775,62783],{},[895,62776,62777,62779,62781],{},[898,62778,2731],{},[898,62780,41465],{},[898,62782,4052],{},[902,62784,56437],{"encoding":904},[883,62786,62788],{"className":62787},[886],[888,62789,62790],{"xmlns":890},[892,62791,62792,62798],{},[895,62793,62794,62796],{},[898,62795,2127],{},[898,62797,4052],{},[902,62799,56418],{"encoding":904}," jsou křivky tvaru ",[883,62802,62804],{"className":62803},[886],[888,62805,62806],{"xmlns":890},[892,62807,62808,62812],{},[895,62809,62810],{},[898,62811,900],{},[902,62813,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,62816,62817,62832,62833,1343,62850,62867,62868,9672],{},[883,62818,62820],{"className":62819},[886],[888,62821,62822],{"xmlns":890},[892,62823,62824,62830],{},[895,62825,62826,62828],{},[898,62827,2127],{},[898,62829,4052],{},[902,62831,56418],{"encoding":904}," nabývá minima před ",[883,62834,62836],{"className":62835},[886],[888,62837,62838],{"xmlns":890},[892,62839,62840,62848],{},[895,62841,62842,62844,62846],{},[898,62843,2731],{},[898,62845,41465],{},[898,62847,4052],{},[902,62849,56437],{"encoding":904},[883,62851,62853],{"className":62852},[886],[888,62854,62855],{"xmlns":890},[892,62856,62857,62865],{},[895,62858,62859,62861,62863],{},[898,62860,2731],{},[898,62862,41465],{},[898,62864,4052],{},[902,62866,56437],{"encoding":904}," před ",[883,62869,62871],{"className":62870},[886],[888,62872,62873],{"xmlns":890},[892,62874,62875,62881],{},[895,62876,62877,62879],{},[898,62878,2731],{},[898,62880,4052],{},[902,62882,56686],{"encoding":904},[123,62884,62885,62623,62900,2704,62915,62932],{},[883,62886,62888],{"className":62887},[886],[888,62889,62890],{"xmlns":890},[892,62891,62892,62898],{},[895,62893,62894,62896],{},[898,62895,2127],{},[898,62897,4052],{},[902,62899,56418],{"encoding":904},[883,62901,62903],{"className":62902},[886],[888,62904,62905],{"xmlns":890},[892,62906,62907,62913],{},[895,62908,62909,62911],{},[898,62910,2731],{},[898,62912,4052],{},[902,62914,56686],{"encoding":904},[883,62916,62918],{"className":62917},[886],[888,62919,62920],{"xmlns":890},[892,62921,62922,62930],{},[895,62923,62924,62926,62928],{},[898,62925,2731],{},[898,62927,41465],{},[898,62929,4052],{},[902,62931,56437],{"encoding":904}," zdola právě v jejich minimech;",[123,62934,62935,62952],{},[883,62936,62938],{"className":62937},[886],[888,62939,62940],{"xmlns":890},[892,62941,62942,62950],{},[895,62943,62944,62946,62948],{},[898,62945,2731],{},[898,62947,2537],{},[898,62949,4052],{},[902,62951,56653],{"encoding":904}," je hyperbola, stále klesající;",[123,62954,62955,62987,62988,2704,63003,63020,63021,63034,63035,5171],{},[883,62956,62958],{"className":62957},[886],[888,62959,62960],{"xmlns":890},[892,62961,62962,62984],{},[895,62963,62964,62966,62968,62970,62972,62974,62976,62978,62980,62982],{},[898,62965,2731],{},[898,62967,4052],{},[1655,62969,1657],{},[898,62971,2731],{},[898,62973,2537],{},[898,62975,4052],{},[1655,62977,2346],{},[898,62979,2731],{},[898,62981,41465],{},[898,62983,4052],{},[902,62985,62986],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,62989,62991],{"className":62990},[886],[888,62992,62993],{"xmlns":890},[892,62994,62995,63001],{},[895,62996,62997,62999],{},[898,62998,2731],{},[898,63000,4052],{},[902,63002,56686],{"encoding":904},[883,63004,63006],{"className":63005},[886],[888,63007,63008],{"xmlns":890},[892,63009,63010,63018],{},[895,63011,63012,63014,63016],{},[898,63013,2731],{},[898,63015,41465],{},[898,63017,4052],{},[902,63019,56437],{"encoding":904}," klesá s rostoucím ",[883,63022,63024],{"className":63023},[886],[888,63025,63026],{"xmlns":890},[892,63027,63028,63032],{},[895,63029,63030],{},[898,63031,1824],{},[902,63033,1824],{"encoding":904}," (protože ",[883,63036,63038],{"className":63037},[886],[888,63039,63040],{"xmlns":890},[892,63041,63042,63054],{},[895,63043,63044,63046,63048,63050,63052],{},[898,63045,2731],{},[898,63047,2537],{},[898,63049,4052],{},[1655,63051,4393],{},[1826,63053,2552],{},[902,63055,63056],{"encoding":904},"AFC \\to 0",[115,63058,63060],{"id":63059},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,63062,63063,63064,63067,63068,63083],{},"Častou optimalizační úlohou je ",[38,63065,63066],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,63069,63071],{"className":63070},[886],[888,63072,63073],{"xmlns":890},[892,63074,63075,63081],{},[895,63076,63077,63079],{},[898,63078,2731],{},[898,63080,4052],{},[902,63082,56686],{"encoding":904}," minimální.",[198,63085,17538],{"id":17537},[724,63087,63088,63089,63106],{},"Mají-li průměrné náklady minimum v bodě ",[883,63090,63092],{"className":63091},[886],[888,63093,63094],{"xmlns":890},[892,63095,63096,63104],{},[895,63097,63098],{},[1820,63099,63100,63102],{},[898,63101,1824],{},[1826,63103,2552],{},[902,63105,39434],{"encoding":904},", pak platí",[883,63108,63110],{"className":63109},[886],[888,63111,63112],{"xmlns":890,"display":29192},[892,63113,63114,63163],{},[21880,63115,63116],{"width":29197},[21885,63117,63118,63120,63156,63158],{},[21888,63119],{"width":29202},[21888,63121,63122],{},[895,63123,63124,63126,63128,63130,63136,63138,63140,63142,63144,63146,63152,63154],{},[898,63125,2731],{},[898,63127,4052],{},[1655,63129,1664],{"stretchy":1663},[1820,63131,63132,63134],{},[898,63133,1824],{},[1826,63135,2552],{},[1655,63137,1677],{"stretchy":1663},[1655,63139,1657],{},[898,63141,2127],{},[898,63143,4052],{},[1655,63145,1664],{"stretchy":1663},[1820,63147,63148,63150],{},[898,63149,1824],{},[1826,63151,2552],{},[1655,63153,1677],{"stretchy":1663},[898,63155,1719],{"mathvariant":1943},[21888,63157],{"width":29202},[21888,63159,63160],{},[2031,63161,63162],{},"(3.10)",[902,63164,63165],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[5120,63167,63168],{},[724,63169,63170,63172,63173],{},[883,63171,57570],{}," Princip\n",[38,63174,63175],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,63177,63178,63181,63182,63224],{},[38,63179,63180],{},"Odvození."," Z ",[883,63183,63185],{"className":63184},[886],[888,63186,63187],{"xmlns":890},[892,63188,63189,63221],{},[895,63190,63191,63193,63195,63197,63199,63201,63203],{},[898,63192,2731],{},[898,63194,4052],{},[1655,63196,1664],{"stretchy":1663},[898,63198,1824],{},[1655,63200,1677],{"stretchy":1663},[1655,63202,1657],{},[3615,63204,63205],{"scriptlevel":2552,"displaystyle":1663},[1949,63206,63207,63219],{},[895,63208,63209,63211,63213,63215,63217],{},[898,63210,4049],{},[898,63212,4052],{},[1655,63214,1664],{"stretchy":1663},[898,63216,1824],{},[1655,63218,1677],{"stretchy":1663},[898,63220,1824],{},[902,63222,63223],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,63226,63228],{"className":63227},[886],[888,63229,63230],{"xmlns":890,"display":29192},[892,63231,63232,63364],{},[895,63233,63234,63236,63242,63244,63246,63248,63250,63290,63292,63332,63334,63362],{},[898,63235,2731],{},[2597,63237,63238,63240],{},[898,63239,4052],{},[1655,63241,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,63243,1664],{"stretchy":1663},[898,63245,1824],{},[1655,63247,1677],{"stretchy":1663},[1655,63249,1657],{},[1949,63251,63252,63284],{},[895,63253,63254,63256,63262,63264,63266,63268,63270,63272,63274,63276,63278,63280,63282],{},[898,63255,4049],{},[2597,63257,63258,63260],{},[898,63259,4052],{},[1655,63261,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,63263,1664],{"stretchy":1663},[898,63265,1824],{},[1655,63267,1677],{"stretchy":1663},[1655,63269,2869],{},[898,63271,1824],{},[1655,63273,2623],{},[898,63275,4049],{},[898,63277,4052],{},[1655,63279,1664],{"stretchy":1663},[898,63281,1824],{},[1655,63283,1677],{"stretchy":1663},[2597,63285,63286,63288],{},[898,63287,1824],{},[1826,63289,1837],{},[1655,63291,1657],{},[1949,63293,63294,63326],{},[895,63295,63296,63298,63300,63302,63304,63306,63308,63310,63312,63314,63316,63318,63320,63322,63324],{},[898,63297,2127],{},[898,63299,4052],{},[1655,63301,1664],{"stretchy":1663},[898,63303,1824],{},[1655,63305,1677],{"stretchy":1663},[1655,63307,2869],{},[898,63309,1824],{},[1655,63311,2623],{},[898,63313,2731],{},[898,63315,4052],{},[1655,63317,1664],{"stretchy":1663},[898,63319,1824],{},[1655,63321,1677],{"stretchy":1663},[1655,63323,2869],{},[898,63325,1824],{},[2597,63327,63328,63330],{},[898,63329,1824],{},[1826,63331,1837],{},[1655,63333,1657],{},[1949,63335,63336,63360],{},[895,63337,63338,63340,63342,63344,63346,63348,63350,63352,63354,63356,63358],{},[898,63339,2127],{},[898,63341,4052],{},[1655,63343,1664],{"stretchy":1663},[898,63345,1824],{},[1655,63347,1677],{"stretchy":1663},[1655,63349,2623],{},[898,63351,2731],{},[898,63353,4052],{},[1655,63355,1664],{"stretchy":1663},[898,63357,1824],{},[1655,63359,1677],{"stretchy":1663},[898,63361,1824],{},[898,63363,1719],{"mathvariant":1943},[902,63365,63366],{"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}.",[724,63368,63369,63370,3902,63385,9349,63407,57947],{},"Nutnou podmínkou minima ",[883,63371,63373],{"className":63372},[886],[888,63374,63375],{"xmlns":890},[892,63376,63377,63383],{},[895,63378,63379,63381],{},[898,63380,2731],{},[898,63382,4052],{},[902,63384,56686],{"encoding":904},[883,63386,63388],{"className":63387},[886],[888,63389,63390],{"xmlns":890},[892,63391,63392,63404],{},[895,63393,63394,63400,63402],{},[1820,63395,63396,63398],{},[898,63397,1824],{},[1826,63399,2552],{},[1655,63401,2969],{},[1826,63403,2552],{},[902,63405,63406],{"encoding":904},"Q_0 > 0",[883,63408,63410],{"className":63409},[886],[888,63411,63412],{"xmlns":890},[892,63413,63414,63438],{},[895,63415,63416,63418,63424,63426,63432,63434,63436],{},[898,63417,2731],{},[2597,63419,63420,63422],{},[898,63421,4052],{},[1655,63423,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,63425,1664],{"stretchy":1663},[1820,63427,63428,63430],{},[898,63429,1824],{},[1826,63431,2552],{},[1655,63433,1677],{"stretchy":1663},[1655,63435,1657],{},[1826,63437,2552],{},[902,63439,63440],{"encoding":904},"AC'(Q_0) = 0",[883,63442,63444],{"className":63443},[886],[888,63445,63446],{"xmlns":890,"display":29192},[892,63447,63448,63533],{},[895,63449,63450,63490,63492,63494,63496,63499,63501,63503,63505,63507,63513,63515,63517,63519,63521,63523,63529,63531],{},[1949,63451,63452,63484],{},[895,63453,63454,63456,63458,63460,63466,63468,63470,63472,63474,63476,63482],{},[898,63455,2127],{},[898,63457,4052],{},[1655,63459,1664],{"stretchy":1663},[1820,63461,63462,63464],{},[898,63463,1824],{},[1826,63465,2552],{},[1655,63467,1677],{"stretchy":1663},[1655,63469,2623],{},[898,63471,2731],{},[898,63473,4052],{},[1655,63475,1664],{"stretchy":1663},[1820,63477,63478,63480],{},[898,63479,1824],{},[1826,63481,2552],{},[1655,63483,1677],{"stretchy":1663},[1820,63485,63486,63488],{},[898,63487,1824],{},[1826,63489,2552],{},[1655,63491,1657],{},[1826,63493,2552],{},[1967,63495],{"width":16409},[1655,63497,63498],{},"⟺",[1967,63500],{"width":16409},[898,63502,2127],{},[898,63504,4052],{},[1655,63506,1664],{"stretchy":1663},[1820,63508,63509,63511],{},[898,63510,1824],{},[1826,63512,2552],{},[1655,63514,1677],{"stretchy":1663},[1655,63516,1657],{},[898,63518,2731],{},[898,63520,4052],{},[1655,63522,1664],{"stretchy":1663},[1820,63524,63525,63527],{},[898,63526,1824],{},[1826,63528,2552],{},[1655,63530,1677],{"stretchy":1663},[898,63532,1719],{"mathvariant":1943},[902,63534,63535],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,63537,63538,3106,63541,62623,63556,63571,63572,63587,63588,9349,63605,63627,63628,63650],{},[38,63539,63540],{},"Geometrická interpretace.",[883,63542,63544],{"className":63543},[886],[888,63545,63546],{"xmlns":890},[892,63547,63548,63554],{},[895,63549,63550,63552],{},[898,63551,2127],{},[898,63553,4052],{},[902,63555,56418],{"encoding":904},[883,63557,63559],{"className":63558},[886],[888,63560,63561],{"xmlns":890},[892,63562,63563,63569],{},[895,63564,63565,63567],{},[898,63566,2731],{},[898,63568,4052],{},[902,63570,56686],{"encoding":904}," právě v bodě minima ",[883,63573,63575],{"className":63574},[886],[888,63576,63577],{"xmlns":890},[892,63578,63579,63585],{},[895,63580,63581,63583],{},[898,63582,2731],{},[898,63584,4052],{},[902,63586,56686],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,63589,63591],{"className":63590},[886],[888,63592,63593],{"xmlns":890},[892,63594,63595,63603],{},[895,63596,63597],{},[1820,63598,63599,63601],{},[898,63600,1824],{},[1826,63602,2552],{},[902,63604,39434],{"encoding":904},[883,63606,63608],{"className":63607},[886],[888,63609,63610],{"xmlns":890},[892,63611,63612,63624],{},[895,63613,63614,63616,63618,63620,63622],{},[898,63615,2127],{},[898,63617,4052],{},[1655,63619,3065],{},[898,63621,2731],{},[898,63623,4052],{},[902,63625,63626],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,63629,63631],{"className":63630},[886],[888,63632,63633],{"xmlns":890},[892,63634,63635,63647],{},[895,63636,63637,63639,63641,63643,63645],{},[898,63638,2127],{},[898,63640,4052],{},[1655,63642,2969],{},[898,63644,2731],{},[898,63646,4052],{},[902,63648,63649],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,63652,63653,63654,63696,63697,63714,63715,1719],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,63655,63657],{"className":63656},[886],[888,63658,63659],{"xmlns":890},[892,63660,63661,63693],{},[895,63662,63663,63665,63667,63669,63675,63677,63679,63681,63683,63685,63691],{},[898,63664,2731],{},[898,63666,4052],{},[1655,63668,1664],{"stretchy":1663},[1820,63670,63671,63673],{},[898,63672,1824],{},[1826,63674,2552],{},[1655,63676,1677],{"stretchy":1663},[1655,63678,1657],{},[898,63680,2127],{},[898,63682,4052],{},[1655,63684,1664],{"stretchy":1663},[1820,63686,63687,63689],{},[898,63688,1824],{},[1826,63690,2552],{},[1655,63692,1677],{"stretchy":1663},[902,63694,63695],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,63698,63700],{"className":63699},[886],[888,63701,63702],{"xmlns":890},[892,63703,63704,63712],{},[895,63705,63706],{},[1820,63707,63708,63710],{},[898,63709,1824],{},[1826,63711,2552],{},[902,63713,39434],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,63716,63718],{"className":63717},[886],[888,63719,63720],{"xmlns":890},[892,63721,63722,63746],{},[895,63723,63724,63726,63728,63730,63732,63734,63736,63738,63740,63742,63744],{},[898,63725,2731],{},[898,63727,4052],{},[1655,63729,1664],{"stretchy":1663},[898,63731,1824],{},[1655,63733,1677],{"stretchy":1663},[1655,63735,1657],{},[898,63737,2127],{},[898,63739,4052],{},[1655,63741,1664],{"stretchy":1663},[898,63743,1824],{},[1655,63745,1677],{"stretchy":1663},[902,63747,63748],{"encoding":904},"AC(Q) = MC(Q)",[5120,63750,63751],{},[724,63752,63753,63755,63756,2494,63774,63795,63796,2494,63799,63820,63821,63836,63837,59164,63852,5171],{},[883,63754,5661],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,63757,63758,63759],{},"minimum ",[883,63760,63762],{"className":63761},[886],[888,63763,63764],{"xmlns":890},[892,63765,63766,63772],{},[895,63767,63768,63770],{},[898,63769,2731],{},[898,63771,4052],{},[902,63773,56686],{"encoding":904},[883,63775,63777],{"className":63776},[886],[888,63778,63779],{"xmlns":890},[892,63780,63781,63793],{},[895,63782,63783,63785,63787,63789,63791],{},[898,63784,2731],{},[898,63786,4052],{},[1655,63788,1657],{},[898,63790,2127],{},[898,63792,4052],{},[902,63794,56349],{"encoding":904},", pro ",[38,63797,63798],{},"maximum zisku",[883,63800,63802],{"className":63801},[886],[888,63803,63804],{"xmlns":890},[892,63805,63806,63818],{},[895,63807,63808,63810,63812,63814,63816],{},[898,63809,2127],{},[898,63811,5245],{},[1655,63813,1657],{},[898,63815,2127],{},[898,63817,4052],{},[902,63819,56397],{"encoding":904},". Obě podmínky využívají ",[883,63822,63824],{"className":63823},[886],[888,63825,63826],{"xmlns":890},[892,63827,63828,63834],{},[895,63829,63830,63832],{},[898,63831,2127],{},[898,63833,4052],{},[902,63835,56418],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,63838,63840],{"className":63839},[886],[888,63841,63842],{"xmlns":890},[892,63843,63844,63850],{},[895,63845,63846,63848],{},[898,63847,2731],{},[898,63849,4052],{},[902,63851,56686],{"encoding":904},[883,63853,63855],{"className":63854},[886],[888,63856,63857],{"xmlns":890},[892,63858,63859,63865],{},[895,63860,63861,63863],{},[898,63862,2127],{},[898,63864,5245],{},[902,63866,7881],{"encoding":904},[38474,63868,63870],{"id":63869},"příklad-37","Příklad 3.7",[724,63872,63873,58648,63875,63909,63910,63923,63924,63939],{},[38,63874,57113],{},[883,63876,63878],{"className":63877},[886],[888,63879,63880],{"xmlns":890},[892,63881,63882,63906],{},[895,63883,63884,63886,63888,63890,63896,63898,63900,63902,63904],{},[898,63885,4049],{},[898,63887,4052],{},[1655,63889,1657],{},[2597,63891,63892,63894],{},[898,63893,1824],{},[1826,63895,1837],{},[1655,63897,2346],{},[1826,63899,3472],{},[898,63901,1824],{},[1655,63903,2346],{},[1826,63905,6814],{},[902,63907,63908],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,63911,63913],{"className":63912},[886],[888,63914,63915],{"xmlns":890},[892,63916,63917,63921],{},[895,63918,63919],{},[898,63920,1824],{},[902,63922,1824],{"encoding":904}," minimalizující ",[883,63925,63927],{"className":63926},[886],[888,63928,63929],{"xmlns":890},[892,63930,63931,63937],{},[895,63932,63933,63935],{},[898,63934,2731],{},[898,63936,4052],{},[902,63938,56686],{"encoding":904}," a ověřte princip (3.10).",[724,63941,63942,63944],{},[38,63943,23896],{}," Přímý výpočet:",[883,63946,63948],{"className":63947},[886],[888,63949,63950],{"xmlns":890,"display":29192},[892,63951,63952,64054],{},[895,63953,63954,63956,63958,63960,63982,63984,63986,63988,63990,63992,63998,64000,64002,64004,64006,64008,64014,64016,64018,64020,64030,64032,64052],{},[898,63955,2731],{},[898,63957,4052],{},[1655,63959,1657],{},[1949,63961,63962,63980],{},[895,63963,63964,63970,63972,63974,63976,63978],{},[2597,63965,63966,63968],{},[898,63967,1824],{},[1826,63969,1837],{},[1655,63971,2346],{},[1826,63973,3472],{},[898,63975,1824],{},[1655,63977,2346],{},[1826,63979,6814],{},[898,63981,1824],{},[1655,63983,1657],{},[898,63985,1824],{},[1655,63987,2346],{},[1826,63989,3472],{},[1655,63991,2346],{},[1949,63993,63994,63996],{},[1826,63995,6814],{},[898,63997,1824],{},[1655,63999,1671],{"separator":1670},[1967,64001],{"width":1969},[1655,64003,1664],{"stretchy":1663},[898,64005,2731],{},[898,64007,4052],{},[2597,64009,64010,64012],{},[1655,64011,1677],{"stretchy":1663},[1655,64013,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,64015,1657],{},[1826,64017,1828],{},[1655,64019,2623],{},[1949,64021,64022,64024],{},[1826,64023,6814],{},[2597,64025,64026,64028],{},[898,64027,1824],{},[1826,64029,1837],{},[1655,64031,1657],{},[1949,64033,64034,64046],{},[895,64035,64036,64042,64044],{},[2597,64037,64038,64040],{},[898,64039,1824],{},[1826,64041,1837],{},[1655,64043,2623],{},[1826,64045,6814],{},[2597,64047,64048,64050],{},[898,64049,1824],{},[1826,64051,1837],{},[898,64053,1719],{"mathvariant":1943},[902,64055,64056],{"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}.",[724,64058,64059,64099,64100,64124,64125,64175,64176,1719],{},[883,64060,64062],{"className":64061},[886],[888,64063,64064],{"xmlns":890},[892,64065,64066,64096],{},[895,64067,64068,64070,64072,64074,64080,64082,64084,64086,64092,64094],{},[1655,64069,1664],{"stretchy":1663},[898,64071,2731],{},[898,64073,4052],{},[2597,64075,64076,64078],{},[1655,64077,1677],{"stretchy":1663},[1655,64079,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,64081,1657],{},[1826,64083,2552],{},[1655,64085,5238],{},[1820,64087,64088,64090],{},[898,64089,1824],{},[1826,64091,1828],{},[1655,64093,1657],{},[1826,64095,3531],{},[902,64097,64098],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,64101,64103],{"className":64102},[886],[888,64104,64105],{"xmlns":890},[892,64106,64107,64121],{},[895,64108,64109,64115,64117,64119],{},[1820,64110,64111,64113],{},[898,64112,1824],{},[1826,64114,1837],{},[1655,64116,1657],{},[1655,64118,2623],{},[1826,64120,3531],{},[902,64122,64123],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,64126,64128],{"className":64127},[886],[888,64129,64130],{"xmlns":890},[892,64131,64132,64172],{},[895,64133,64134,64136,64138,64140,64150,64152,64154,64156,64158,64166,64168,64170],{},[1655,64135,1664],{"stretchy":1663},[898,64137,2731],{},[898,64139,4052],{},[2597,64141,64142,64144],{},[1655,64143,1677],{"stretchy":1663},[895,64145,64146,64148],{},[1655,64147,1945],{"mathvariant":1943},[1655,64149,1945],{"mathvariant":1943},[1655,64151,1664],{"stretchy":1663},[1826,64153,3531],{},[1655,64155,1677],{"stretchy":1663},[1655,64157,1657],{},[3615,64159,64160],{"scriptlevel":2552,"displaystyle":1663},[1949,64161,64162,64164],{},[1826,64163,1828],{},[1826,64165,3472],{},[1655,64167,2969],{},[1826,64169,2552],{},[1655,64171,5238],{},[902,64173,64174],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,64177,64179],{"className":64178},[886],[888,64180,64181],{"xmlns":890},[892,64182,64183,64199],{},[895,64184,64185,64187,64189,64191,64193,64195,64197],{},[898,64186,2731],{},[898,64188,4052],{},[1655,64190,1664],{"stretchy":1663},[1826,64192,3531],{},[1655,64194,1677],{"stretchy":1663},[1655,64196,1657],{},[1826,64198,37370],{},[902,64200,64201],{"encoding":904},"AC(6) = 15",[724,64203,64204,64205,64231,64232,2086],{},"Pomocí principu: ",[883,64206,64208],{"className":64207},[886],[888,64209,64210],{"xmlns":890},[892,64211,64212,64228],{},[895,64213,64214,64216,64218,64220,64222,64224,64226],{},[898,64215,2127],{},[898,64217,4052],{},[1655,64219,1657],{},[1826,64221,1837],{},[898,64223,1824],{},[1655,64225,2346],{},[1826,64227,3472],{},[902,64229,64230],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,64233,64235],{"className":64234},[886],[888,64236,64237],{"xmlns":890},[892,64238,64239,64251],{},[895,64240,64241,64243,64245,64247,64249],{},[898,64242,2731],{},[898,64244,4052],{},[1655,64246,1657],{},[898,64248,2127],{},[898,64250,4052],{},[902,64252,56349],{"encoding":904},[883,64254,64256],{"className":64255},[886],[888,64257,64258],{"xmlns":890,"display":29192},[892,64259,64260,64362],{},[895,64261,64262,64284,64286,64288,64290,64292,64294,64296,64298,64300,64306,64308,64310,64312,64314,64316,64318,64320,64326,64328,64330,64332,64334,64336,64338,64344,64346,64348,64350,64352,64354,64356,64358,64360],{},[1949,64263,64264,64282],{},[895,64265,64266,64272,64274,64276,64278,64280],{},[2597,64267,64268,64270],{},[898,64269,1824],{},[1826,64271,1837],{},[1655,64273,2346],{},[1826,64275,3472],{},[898,64277,1824],{},[1655,64279,2346],{},[1826,64281,6814],{},[898,64283,1824],{},[1655,64285,1657],{},[1826,64287,1837],{},[898,64289,1824],{},[1655,64291,2346],{},[1826,64293,3472],{},[2031,64295,2783],{},[1655,64297,5238],{},[2031,64299,2783],{},[2597,64301,64302,64304],{},[898,64303,1824],{},[1826,64305,1837],{},[1655,64307,2346],{},[1826,64309,3472],{},[898,64311,1824],{},[1655,64313,2346],{},[1826,64315,6814],{},[1655,64317,1657],{},[1826,64319,1837],{},[2597,64321,64322,64324],{},[898,64323,1824],{},[1826,64325,1837],{},[1655,64327,2346],{},[1826,64329,3472],{},[898,64331,1824],{},[2031,64333,2783],{},[1655,64335,5238],{},[2031,64337,2783],{},[2597,64339,64340,64342],{},[898,64341,1824],{},[1826,64343,1837],{},[1655,64345,1657],{},[1826,64347,6814],{},[2031,64349,2783],{},[1655,64351,5238],{},[2031,64353,2783],{},[898,64355,1824],{},[1655,64357,1657],{},[1826,64359,3531],{},[1655,64361,1671],{"separator":1670},[902,64363,64364],{"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,",[724,64366,64367,64368,64406],{},"a ",[883,64369,64371],{"className":64370},[886],[888,64372,64373],{"xmlns":890},[892,64374,64375,64403],{},[895,64376,64377,64379,64381,64383,64385,64387,64389,64391,64393,64395,64397,64399,64401],{},[898,64378,2731],{},[898,64380,4052],{},[1655,64382,1664],{"stretchy":1663},[1826,64384,3531],{},[1655,64386,1677],{"stretchy":1663},[1655,64388,1657],{},[898,64390,2127],{},[898,64392,4052],{},[1655,64394,1664],{"stretchy":1663},[1826,64396,3531],{},[1655,64398,1677],{"stretchy":1663},[1655,64400,1657],{},[1826,64402,37370],{},[902,64404,64405],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,64408,64410],{"id":64409},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,64412,64413,64414,2086],{},"Analogicky pro ",[883,64415,64417],{"className":64416},[886],[888,64418,64419],{"xmlns":890},[892,64420,64421,64429],{},[895,64422,64423,64425,64427],{},[898,64424,2731],{},[898,64426,41465],{},[898,64428,4052],{},[902,64430,56437],{"encoding":904},[883,64432,64434],{"className":64433},[886],[888,64435,64436],{"xmlns":890,"display":29192},[892,64437,64438,64489],{},[21880,64439,64440],{"width":29197},[21885,64441,64442,64444,64482,64484],{},[21888,64443],{"width":29202},[21888,64445,64446],{},[895,64447,64448,64450,64452,64454,64456,64462,64464,64466,64468,64470,64472,64478,64480],{},[898,64449,2731],{},[898,64451,41465],{},[898,64453,4052],{},[1655,64455,1664],{"stretchy":1663},[1820,64457,64458,64460],{},[898,64459,1824],{},[1826,64461,2552],{},[1655,64463,1677],{"stretchy":1663},[1655,64465,1657],{},[898,64467,2127],{},[898,64469,4052],{},[1655,64471,1664],{"stretchy":1663},[1820,64473,64474,64476],{},[898,64475,1824],{},[1826,64477,2552],{},[1655,64479,1677],{"stretchy":1663},[898,64481,1719],{"mathvariant":1943},[21888,64483],{"width":29202},[21888,64485,64486],{},[2031,64487,64488],{},"(3.11)",[902,64490,64491],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[5120,64493,64494],{},[724,64495,64496,63172,64498],{},[883,64497,57570],{},[38,64499,64500,64501,64518],{},"V bodě minima průměrných variabilních nákladů se ",[883,64502,64504],{"className":64503},[886],[888,64505,64506],{"xmlns":890},[892,64507,64508,64516],{},[895,64509,64510,64512,64514],{},[898,64511,2731],{},[898,64513,41465],{},[898,64515,4052],{},[902,64517,56437],{"encoding":904}," rovnají mezním nákladům.",[724,64520,64521,64522,64544,64545,1719],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,64523,64525],{"className":64524},[886],[888,64526,64527],{"xmlns":890},[892,64528,64529,64541],{},[895,64530,64531,64537,64539],{},[1820,64532,64533,64535],{},[898,64534,1824],{},[1826,64536,2552],{},[1655,64538,1657],{},[1826,64540,54325],{},[902,64542,64543],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,64546,64548],{"className":64547},[886],[888,64549,64550],{"xmlns":890},[892,64551,64552,64578],{},[895,64553,64554,64556,64558,64560,64562,64564,64566,64568,64570,64572,64574,64576],{},[898,64555,2731],{},[898,64557,41465],{},[898,64559,4052],{},[1655,64561,1664],{"stretchy":1663},[898,64563,1824],{},[1655,64565,1677],{"stretchy":1663},[1655,64567,1657],{},[898,64569,2127],{},[898,64571,4052],{},[1655,64573,1664],{"stretchy":1663},[898,64575,1824],{},[1655,64577,1677],{"stretchy":1663},[902,64579,64580],{"encoding":904},"AVC(Q) = MC(Q)",[115,64582,64584],{"id":64583},"zisk-a-body-zvratu","Zisk a body zvratu",[724,64586,64587,3106,64590,64606],{},[38,64588,64589],{},"Zisk",[883,64591,64593],{"className":64592},[886],[888,64594,64595],{"xmlns":890},[892,64596,64597,64603],{},[895,64598,64599,64601],{},[898,64600,2132],{},[898,64602,5245],{},[902,64604,64605],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,64608,64610],{"className":64609},[886],[888,64611,64612],{"xmlns":890,"display":29192},[892,64613,64614,64673],{},[21880,64615,64616],{"width":29197},[21885,64617,64618,64620,64666,64668],{},[21888,64619],{"width":29202},[21888,64621,64622],{},[895,64623,64624,64626,64628,64630,64632,64634,64636,64638,64640,64642,64644,64646,64648,64650,64652,64654,64656,64658,64660,64662,64664],{},[898,64625,2132],{},[898,64627,5245],{},[1655,64629,1657],{},[898,64631,2132],{},[898,64633,5245],{},[1655,64635,1664],{"stretchy":1663},[898,64637,1824],{},[1655,64639,1677],{"stretchy":1663},[1655,64641,1657],{},[898,64643,4049],{},[898,64645,5245],{},[1655,64647,1664],{"stretchy":1663},[898,64649,1824],{},[1655,64651,1677],{"stretchy":1663},[1655,64653,2623],{},[898,64655,4049],{},[898,64657,4052],{},[1655,64659,1664],{"stretchy":1663},[898,64661,1824],{},[1655,64663,1677],{"stretchy":1663},[898,64665,1719],{"mathvariant":1943},[21888,64667],{"width":29202},[21888,64669,64670],{},[2031,64671,64672],{},"(3.12)",[902,64674,64675],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,64677,64678,64679,2704,64694,44762,64709,64711,64712,64715,64716,64732,64733,64748,64749,64764,64765,1343,64778,64791,64792,1343,64810,64828,64829,2115,64832,64835,64836,1348,64858,9349,64880,64902,64903,9349,64933,64955],{},"Body rovnosti ",[883,64680,64682],{"className":64681},[886],[888,64683,64684],{"xmlns":890},[892,64685,64686,64692],{},[895,64687,64688,64690],{},[898,64689,4049],{},[898,64691,5245],{},[902,64693,5345],{"encoding":904},[883,64695,64697],{"className":64696},[886],[888,64698,64699],{"xmlns":890},[892,64700,64701,64707],{},[895,64702,64703,64705],{},[898,64704,4049],{},[898,64706,4052],{},[902,64708,4512],{"encoding":904},[38,64710,56853],{}," (též vyrovnání, ",[614,64713,64714],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,64717,64719],{"className":64718},[886],[888,64720,64721],{"xmlns":890},[892,64722,64723,64729],{},[895,64724,64725,64727],{},[898,64726,41465],{},[898,64728,4052],{},[902,64730,64731],{"encoding":904},"VC",") je ",[883,64734,64736],{"className":64735},[886],[888,64737,64738],{"xmlns":890},[892,64739,64740,64746],{},[895,64741,64742,64744],{},[898,64743,4049],{},[898,64745,5245],{},[902,64747,5345],{"encoding":904}," kvadratická a ",[883,64750,64752],{"className":64751},[886],[888,64753,64754],{"xmlns":890},[892,64755,64756,64762],{},[895,64757,64758,64760],{},[898,64759,4049],{},[898,64761,4052],{},[902,64763,4512],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,64766,64768],{"className":64767},[886],[888,64769,64770],{"xmlns":890},[892,64771,64772,64776],{},[895,64773,64774],{},[898,64775,2731],{},[902,64777,2731],{"encoding":904},[883,64779,64781],{"className":64780},[886],[888,64782,64783],{"xmlns":890},[892,64784,64785,64789],{},[895,64786,64787],{},[898,64788,24379],{},[902,64790,24379],{"encoding":904}," odpovídajících množstvím ",[883,64793,64795],{"className":64794},[886],[888,64796,64797],{"xmlns":890},[892,64798,64799,64807],{},[895,64800,64801],{},[1820,64802,64803,64805],{},[898,64804,1824],{},[898,64806,2731],{},[902,64808,64809],{"encoding":904},"Q_A",[883,64811,64813],{"className":64812},[886],[888,64814,64815],{"xmlns":890},[892,64816,64817,64825],{},[895,64818,64819],{},[1820,64820,64821,64823],{},[898,64822,1824],{},[898,64824,24379],{},[902,64826,64827],{"encoding":904},"Q_B"," — firma je na ",[38,64830,64831],{},"prahu rentability",[614,64833,64834],{},"break even","). Pro ",[883,64837,64839],{"className":64838},[886],[888,64840,64841],{"xmlns":890},[892,64842,64843,64855],{},[895,64844,64845,64847,64849],{},[898,64846,1824],{},[1655,64848,3065],{},[1820,64850,64851,64853],{},[898,64852,1824],{},[898,64854,2731],{},[902,64856,64857],{"encoding":904},"Q \u003C Q_A",[883,64859,64861],{"className":64860},[886],[888,64862,64863],{"xmlns":890},[892,64864,64865,64877],{},[895,64866,64867,64869,64871],{},[898,64868,1824],{},[1655,64870,2969],{},[1820,64872,64873,64875],{},[898,64874,1824],{},[898,64876,24379],{},[902,64878,64879],{"encoding":904},"Q > Q_B",[883,64881,64883],{"className":64882},[886],[888,64884,64885],{"xmlns":890},[892,64886,64887,64899],{},[895,64888,64889,64891,64893,64895,64897],{},[898,64890,4049],{},[898,64892,4052],{},[1655,64894,2969],{},[898,64896,4049],{},[898,64898,5245],{},[902,64900,64901],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,64904,64906],{"className":64905},[886],[888,64907,64908],{"xmlns":890},[892,64909,64910,64930],{},[895,64911,64912,64918,64920,64922,64924],{},[1820,64913,64914,64916],{},[898,64915,1824],{},[898,64917,2731],{},[1655,64919,3065],{},[898,64921,1824],{},[1655,64923,3065],{},[1820,64925,64926,64928],{},[898,64927,1824],{},[898,64929,24379],{},[902,64931,64932],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,64934,64936],{"className":64935},[886],[888,64937,64938],{"xmlns":890},[892,64939,64940,64952],{},[895,64941,64942,64944,64946,64948,64950],{},[898,64943,4049],{},[898,64945,5245],{},[1655,64947,2969],{},[898,64949,4049],{},[898,64951,4052],{},[902,64953,64954],{"encoding":904},"TR > TC"," (zisk).",[5120,64957,64958],{},[724,64959,64960,64962],{},[883,64961,5406],{}," 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.",[724,64964,64965,64966,64992],{},"Body zvratu jsou řešení rovnice ",[883,64967,64969],{"className":64968},[886],[888,64970,64971],{"xmlns":890},[892,64972,64973,64989],{},[895,64974,64975,64977,64979,64981,64983,64985,64987],{},[898,64976,2132],{},[898,64978,5245],{},[1655,64980,1664],{"stretchy":1663},[898,64982,1824],{},[1655,64984,1677],{"stretchy":1663},[1655,64986,1657],{},[1826,64988,2552],{},[902,64990,64991],{"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.",[724,64994,64995],{},[1723,64996],{"alt":64997,"className":64998,"src":64999},"imek-tr-tc-body-zvratu",[210,1727],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,65001,65002],{},[614,65003,65004,65005,65020,65021,65036,65037,2704,65050,44486,65063,65076,65077,2704,65094,65111,65112,65132,65133,2704,65148,7720,65163,65192],{},"Obrázek 3.11: Body zvratu — křivky ",[883,65006,65008],{"className":65007},[886],[888,65009,65010],{"xmlns":890},[892,65011,65012,65018],{},[895,65013,65014,65016],{},[898,65015,4049],{},[898,65017,5245],{},[902,65019,5345],{"encoding":904}," (obrácená parabola) a ",[883,65022,65024],{"className":65023},[886],[888,65025,65026],{"xmlns":890},[892,65027,65028,65034],{},[895,65029,65030,65032],{},[898,65031,4049],{},[898,65033,4052],{},[902,65035,4512],{"encoding":904}," (přímka) se protínají v bodech ",[883,65038,65040],{"className":65039},[886],[888,65041,65042],{"xmlns":890},[892,65043,65044,65048],{},[895,65045,65046],{},[898,65047,2731],{},[902,65049,2731],{"encoding":904},[883,65051,65053],{"className":65052},[886],[888,65054,65055],{"xmlns":890},[892,65056,65057,65061],{},[895,65058,65059],{},[898,65060,24379],{},[902,65062,24379],{"encoding":904},[883,65064,65066],{"className":65065},[886],[888,65067,65068],{"xmlns":890},[892,65069,65070,65074],{},[895,65071,65072],{},[898,65073,1824],{},[902,65075,1824],{"encoding":904}," v hodnotách ",[883,65078,65080],{"className":65079},[886],[888,65081,65082],{"xmlns":890},[892,65083,65084,65092],{},[895,65085,65086],{},[1820,65087,65088,65090],{},[898,65089,1824],{},[898,65091,2731],{},[902,65093,64809],{"encoding":904},[883,65095,65097],{"className":65096},[886],[888,65098,65099],{"xmlns":890},[892,65100,65101,65109],{},[895,65102,65103],{},[1820,65104,65105,65107],{},[898,65106,1824],{},[898,65108,24379],{},[902,65110,64827],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,65113,65115],{"className":65114},[886],[888,65116,65117],{"xmlns":890},[892,65118,65119,65129],{},[895,65120,65121],{},[1820,65122,65123,65125,65127],{},[898,65124,1824],{},[898,65126,57323],{},[1655,65128,57326],{},[902,65130,65131],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,65134,65136],{"className":65135},[886],[888,65137,65138],{"xmlns":890},[892,65139,65140,65146],{},[895,65141,65142,65144],{},[898,65143,4049],{},[898,65145,5245],{},[902,65147,5345],{"encoding":904},[883,65149,65151],{"className":65150},[886],[888,65152,65153],{"xmlns":890},[892,65154,65155,65161],{},[895,65156,65157,65159],{},[898,65158,4049],{},[898,65160,4052],{},[902,65162,4512],{"encoding":904},[883,65164,65166],{"className":65165},[886],[888,65167,65168],{"xmlns":890},[892,65169,65170,65190],{},[895,65171,65172,65178,65180,65182,65184],{},[1820,65173,65174,65176],{},[898,65175,1824],{},[898,65177,2731],{},[1655,65179,3065],{},[898,65181,1824],{},[1655,65183,3065],{},[1820,65185,65186,65188],{},[898,65187,1824],{},[898,65189,24379],{},[902,65191,64932],{"encoding":904}," vyznačuje zisk.",[38474,65194,65196],{"id":65195},"příklad-38","Příklad 3.8",[724,65198,65199,65201,65202,1343,65222,1343,65248,65274],{},[38,65200,57113],{}," Dáno ",[883,65203,65205],{"className":65204},[886],[888,65206,65207],{"xmlns":890},[892,65208,65209,65219],{},[895,65210,65211,65213,65215,65217],{},[898,65212,2537],{},[898,65214,4052],{},[1655,65216,1657],{},[1826,65218,3639],{},[902,65220,65221],{"encoding":904},"FC = 4",[883,65223,65225],{"className":65224},[886],[888,65226,65227],{"xmlns":890},[892,65228,65229,65245],{},[895,65230,65231,65233,65235,65237,65239],{},[898,65232,4049],{},[898,65234,41465],{},[898,65236,4052],{},[1655,65238,1657],{},[2597,65240,65241,65243],{},[898,65242,1824],{},[1826,65244,1837],{},[902,65246,65247],{"encoding":904},"TVC = Q^2",[883,65249,65251],{"className":65250},[886],[888,65252,65253],{"xmlns":890},[892,65254,65255,65271],{},[895,65256,65257,65259,65261,65263,65265,65267,65269],{},[898,65258,2132],{},[1655,65260,1657],{},[1655,65262,2623],{},[1826,65264,1837],{},[898,65266,1824],{},[1655,65268,2346],{},[1826,65270,5250],{},[902,65272,65273],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,65276,65277,65279],{},[38,65278,23896],{}," Celkové náklady a příjem:",[883,65281,65283],{"className":65282},[886],[888,65284,65285],{"xmlns":890,"display":29192},[892,65286,65287,65353],{},[895,65288,65289,65291,65293,65295,65297,65299,65305,65307,65309,65311,65313,65315,65317,65319,65321,65323,65325,65327,65329,65331,65333,65335,65337,65339,65345,65347,65349,65351],{},[898,65290,4049],{},[898,65292,4052],{},[1655,65294,1657],{},[1826,65296,3639],{},[1655,65298,2346],{},[2597,65300,65301,65303],{},[898,65302,1824],{},[1826,65304,1837],{},[1655,65306,1671],{"separator":1670},[1967,65308],{"width":1969},[898,65310,4049],{},[898,65312,5245],{},[1655,65314,1657],{},[898,65316,1824],{},[1655,65318,2869],{},[1655,65320,1664],{"stretchy":1663},[1655,65322,2623],{},[1826,65324,1837],{},[898,65326,1824],{},[1655,65328,2346],{},[1826,65330,5250],{},[1655,65332,1677],{"stretchy":1663},[1655,65334,1657],{},[1655,65336,2623],{},[1826,65338,1837],{},[2597,65340,65341,65343],{},[898,65342,1824],{},[1826,65344,1837],{},[1655,65346,2346],{},[1826,65348,5250],{},[898,65350,1824],{},[898,65352,1719],{"mathvariant":1943},[902,65354,65355],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,65357,65358],{},"Zisk dle (3.12):",[883,65360,65362],{"className":65361},[886],[888,65363,65364],{"xmlns":890,"display":29192},[892,65365,65366,65444],{},[895,65367,65368,65370,65372,65374,65376,65378,65380,65382,65384,65386,65388,65390,65392,65398,65400,65402,65404,65406,65408,65410,65412,65414,65420,65422,65424,65426,65428,65434,65436,65438,65440,65442],{},[898,65369,2132],{},[898,65371,5245],{},[1655,65373,1657],{},[898,65375,4049],{},[898,65377,5245],{},[1655,65379,2623],{},[898,65381,4049],{},[898,65383,4052],{},[1655,65385,1657],{},[1655,65387,1664],{"stretchy":1663},[1655,65389,2623],{},[1826,65391,1837],{},[2597,65393,65394,65396],{},[898,65395,1824],{},[1826,65397,1837],{},[1655,65399,2346],{},[1826,65401,5250],{},[898,65403,1824],{},[1655,65405,1677],{"stretchy":1663},[1655,65407,2623],{},[1655,65409,1664],{"stretchy":1663},[1826,65411,3639],{},[1655,65413,2346],{},[2597,65415,65416,65418],{},[898,65417,1824],{},[1826,65419,1837],{},[1655,65421,1677],{"stretchy":1663},[1655,65423,1657],{},[1655,65425,2623],{},[1826,65427,3472],{},[2597,65429,65430,65432],{},[898,65431,1824],{},[1826,65433,1837],{},[1655,65435,2346],{},[1826,65437,5250],{},[898,65439,1824],{},[1655,65441,2623],{},[1826,65443,60445],{},[902,65445,65446],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,65448,65449,65452,65453,18702,65489,2086],{},[38,65450,65451],{},"Body zvratu"," jsou kořeny rovnice ",[883,65454,65456],{"className":65455},[886],[888,65457,65458],{"xmlns":890},[892,65459,65460,65486],{},[895,65461,65462,65464,65466,65472,65474,65476,65478,65480,65482,65484],{},[1655,65463,2623],{},[1826,65465,3472],{},[2597,65467,65468,65470],{},[898,65469,1824],{},[1826,65471,1837],{},[1655,65473,2346],{},[1826,65475,5250],{},[898,65477,1824],{},[1655,65479,2623],{},[1826,65481,3639],{},[1655,65483,1657],{},[1826,65485,2552],{},[902,65487,65488],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,65490,65492],{"className":65491},[886],[888,65493,65494],{"xmlns":890},[892,65495,65496,65520],{},[895,65497,65498,65500,65506,65508,65510,65512,65514,65516,65518],{},[1826,65499,3472],{},[2597,65501,65502,65504],{},[898,65503,1824],{},[1826,65505,1837],{},[1655,65507,2623],{},[1826,65509,5250],{},[898,65511,1824],{},[1655,65513,2346],{},[1826,65515,3639],{},[1655,65517,1657],{},[1826,65519,2552],{},[902,65521,65522],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,65524,65526],{"className":65525},[886],[888,65527,65528],{"xmlns":890,"display":29192},[892,65529,65530,65587],{},[895,65531,65532,65544,65546,65569,65571,65585],{},[1820,65533,65534,65536],{},[898,65535,1824],{},[895,65537,65538,65540,65542],{},[1826,65539,1828],{},[1655,65541,1671],{"separator":1670},[1826,65543,1837],{},[1655,65545,1657],{},[1949,65547,65548,65567],{},[895,65549,65550,65552,65555],{},[1826,65551,5250],{},[1655,65553,65554],{},"±",[9364,65556,65557],{},[895,65558,65559,65562,65564],{},[1826,65560,65561],{},"81",[1655,65563,2623],{},[1826,65565,65566],{},"48",[1826,65568,3531],{},[1655,65570,1657],{},[1949,65572,65573,65583],{},[895,65574,65575,65577,65579],{},[1826,65576,5250],{},[1655,65578,65554],{},[9364,65580,65581],{},[1826,65582,10198],{},[1826,65584,3531],{},[1655,65586,1671],{"separator":1670},[902,65588,65589],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,65591,65592,65593,2704,65616,1719],{},"numericky ",[883,65594,65596],{"className":65595},[886],[888,65597,65598],{"xmlns":890},[892,65599,65600,65613],{},[895,65601,65602,65608,65610],{},[1820,65603,65604,65606],{},[898,65605,1824],{},[1826,65607,1828],{},[1655,65609,7147],{},[1826,65611,65612],{},"0,543",[902,65614,65615],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,65617,65619],{"className":65618},[886],[888,65620,65621],{"xmlns":890},[892,65622,65623,65636],{},[895,65624,65625,65631,65633],{},[1820,65626,65627,65629],{},[898,65628,1824],{},[1826,65630,1837],{},[1655,65632,7147],{},[1826,65634,65635],{},"2,457",[902,65637,65638],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,65640,65641,3106,65644,8799,65689,18702,65723,65741],{},[38,65642,65643],{},"Maximum zisku.",[883,65645,65647],{"className":65646},[886],[888,65648,65649],{"xmlns":890},[892,65650,65651,65686],{},[895,65652,65653,65655,65661,65663,65665,65667,65669,65671,65673,65675,65677,65679,65681,65683],{},[898,65654,2132],{},[2597,65656,65657,65659],{},[898,65658,5245],{},[1655,65660,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,65662,1657],{},[1655,65664,2623],{},[1826,65666,3531],{},[898,65668,1824],{},[1655,65670,2346],{},[1826,65672,5250],{},[1655,65674,1657],{},[1826,65676,2552],{},[1655,65678,5238],{},[898,65680,1824],{},[1655,65682,1657],{},[1826,65684,65685],{},"1,5",[902,65687,65688],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,65690,65692],{"className":65691},[886],[888,65693,65694],{"xmlns":890},[892,65695,65696,65720],{},[895,65697,65698,65700,65710,65712,65714,65716,65718],{},[898,65699,2132],{},[2597,65701,65702,65704],{},[898,65703,5245],{},[895,65705,65706,65708],{},[1655,65707,1945],{"mathvariant":1943},[1655,65709,1945],{"mathvariant":1943},[1655,65711,1657],{},[1655,65713,2623],{},[1826,65715,3531],{},[1655,65717,3065],{},[1826,65719,2552],{},[902,65721,65722],{"encoding":904},"PR'' = -6 \u003C 0",[883,65724,65726],{"className":65725},[886],[888,65727,65728],{"xmlns":890},[892,65729,65730,65738],{},[895,65731,65732,65734,65736],{},[898,65733,1824],{},[1655,65735,1657],{},[1826,65737,65685],{},[902,65739,65740],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,65743,65745],{"className":65744},[886],[888,65746,65747],{"xmlns":890,"display":29192},[892,65748,65749,65812],{},[895,65750,65751,65753,65755,65757,65759,65761,65763,65765,65767,65769,65771,65773,65779,65781,65783,65785,65787,65789,65791,65793,65795,65798,65800,65803,65805,65807,65809],{},[898,65752,2132],{},[898,65754,5245],{},[1655,65756,1664],{"stretchy":1663},[1826,65758,65685],{},[1655,65760,1677],{"stretchy":1663},[1655,65762,1657],{},[1655,65764,2623],{},[1826,65766,3472],{},[1655,65768,2869],{},[1655,65770,1664],{"stretchy":1663},[1826,65772,65685],{},[2597,65774,65775,65777],{},[1655,65776,1677],{"stretchy":1663},[1826,65778,1837],{},[1655,65780,2346],{},[1826,65782,5250],{},[1655,65784,2869],{},[1826,65786,65685],{},[1655,65788,2623],{},[1826,65790,3639],{},[1655,65792,1657],{},[1655,65794,2623],{},[1826,65796,65797],{},"6,75",[1655,65799,2346],{},[1826,65801,65802],{},"13,5",[1655,65804,2623],{},[1826,65806,3639],{},[1655,65808,1657],{},[1826,65810,65811],{},"2,75.",[902,65813,65814],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,65816,65817,65818,1343,65863,65916,65917,65935],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,65819,65821],{"className":65820},[886],[888,65822,65823],{"xmlns":890},[892,65824,65825,65860],{},[895,65826,65827,65829,65835,65837,65839,65841,65843,65845,65847,65849,65851,65853,65855,65857],{},[898,65828,4049],{},[2597,65830,65831,65833],{},[898,65832,5245],{},[1655,65834,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,65836,1657],{},[1655,65838,2623],{},[1826,65840,3639],{},[898,65842,1824],{},[1655,65844,2346],{},[1826,65846,5250],{},[1655,65848,1657],{},[1826,65850,2552],{},[1655,65852,5238],{},[898,65854,1824],{},[1655,65856,1657],{},[1826,65858,65859],{},"2,25",[902,65861,65862],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,65864,65866],{"className":65865},[886],[888,65867,65868],{"xmlns":890},[892,65869,65870,65913],{},[895,65871,65872,65874,65882,65884,65886,65888,65890,65892,65894,65900,65902,65904,65906,65908,65910],{},[898,65873,4049],{},[1820,65875,65876,65878,65880],{},[898,65877,5245],{},[898,65879,57323],{},[1655,65881,57326],{},[1655,65883,1657],{},[1655,65885,2623],{},[1826,65887,1837],{},[1655,65889,2869],{},[1655,65891,1664],{"stretchy":1663},[1826,65893,65859],{},[2597,65895,65896,65898],{},[1655,65897,1677],{"stretchy":1663},[1826,65899,1837],{},[1655,65901,2346],{},[1826,65903,5250],{},[1655,65905,2869],{},[1826,65907,65859],{},[1655,65909,1657],{},[1826,65911,65912],{},"10,125",[902,65914,65915],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,65918,65920],{"className":65919},[886],[888,65921,65922],{"xmlns":890},[892,65923,65924,65932],{},[895,65925,65926,65928,65930],{},[898,65927,1824],{},[1655,65929,1657],{},[1826,65931,65859],{},[902,65933,65934],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[5120,65937,65938],{},[724,65939,65940,65942,65943,1343,65965,65987,65988,1343,66005,66026,66027,66059,66060,66098,66099,3948,66117,66134,66135,2704,66163,66197,66198,8932,66236,2704,66260,1719],{},[883,65941,5661],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,65944,65946],{"className":65945},[886],[888,65947,65948],{"xmlns":890},[892,65949,65950,65962],{},[895,65951,65952,65958,65960],{},[1820,65953,65954,65956],{},[898,65955,1824],{},[1826,65957,1828],{},[1655,65959,1657],{},[1826,65961,6258],{},[902,65963,65964],{"encoding":904},"Q_1 = 0{,}5",[883,65966,65968],{"className":65967},[886],[888,65969,65970],{"xmlns":890},[892,65971,65972,65984],{},[895,65973,65974,65980,65982],{},[1820,65975,65976,65978],{},[898,65977,1824],{},[1826,65979,1837],{},[1655,65981,1657],{},[1826,65983,3639],{},[902,65985,65986],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,65989,65991],{"className":65990},[886],[888,65992,65993],{"xmlns":890},[892,65994,65995,66003],{},[895,65996,65997,65999,66001],{},[898,65998,1824],{},[1655,66000,1657],{},[1826,66002,65859],{},[902,66004,65934],{"encoding":904},[883,66006,66008],{"className":66007},[886],[888,66009,66010],{"xmlns":890},[892,66011,66012,66023],{},[895,66013,66014,66016,66018,66020],{},[898,66015,2132],{},[898,66017,5245],{},[1655,66019,1657],{},[1826,66021,66022],{},"6,125",[902,66024,66025],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,66028,66030],{"className":66029},[886],[888,66031,66032],{"xmlns":890},[892,66033,66034,66056],{},[895,66035,66036,66038,66044,66046,66048,66050,66052,66054],{},[898,66037,2132],{},[2597,66039,66040,66042],{},[898,66041,5245],{},[1655,66043,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,66045,1657],{},[1655,66047,2623],{},[1826,66049,3639],{},[898,66051,1824],{},[1655,66053,2346],{},[1826,66055,5250],{},[902,66057,66058],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,66061,66063],{"className":66062},[886],[888,66064,66065],{"xmlns":890},[892,66066,66067,66095],{},[895,66068,66069,66071,66073,66075,66077,66079,66085,66087,66089,66091,66093],{},[898,66070,2132],{},[898,66072,5245],{},[1655,66074,1657],{},[1655,66076,2623],{},[1826,66078,1837],{},[2597,66080,66081,66083],{},[898,66082,1824],{},[1826,66084,1837],{},[1655,66086,2346],{},[1826,66088,5250],{},[898,66090,1824],{},[1655,66092,2623],{},[1826,66094,3639],{},[902,66096,66097],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,66100,66102],{"className":66101},[886],[888,66103,66104],{"xmlns":890},[892,66105,66106,66114],{},[895,66107,66108],{},[2597,66109,66110,66112],{},[898,66111,1824],{},[1826,66113,1837],{},[902,66115,66116],{"encoding":904},"Q^2",[883,66118,66120],{"className":66119},[886],[888,66121,66122],{"xmlns":890},[892,66123,66124,66132],{},[895,66125,66126,66128,66130],{},[898,66127,4049],{},[898,66129,41465],{},[898,66131,4052],{},[902,66133,56635],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,66136,66138],{"className":66137},[886],[888,66139,66140],{"xmlns":890},[892,66141,66142,66160],{},[895,66143,66144,66146,66148,66150,66152,66154],{},[898,66145,4049],{},[898,66147,4052],{},[1655,66149,1657],{},[1826,66151,3639],{},[1655,66153,2346],{},[2597,66155,66156,66158],{},[898,66157,1824],{},[1826,66159,1837],{},[902,66161,66162],{"encoding":904},"TC = 4 + Q^2",[883,66164,66166],{"className":66165},[886],[888,66167,66168],{"xmlns":890},[892,66169,66170,66194],{},[895,66171,66172,66174,66176,66178,66180,66182,66188,66190,66192],{},[898,66173,4049],{},[898,66175,5245],{},[1655,66177,1657],{},[1655,66179,2623],{},[1826,66181,1837],{},[2597,66183,66184,66186],{},[898,66185,1824],{},[1826,66187,1837],{},[1655,66189,2346],{},[1826,66191,5250],{},[898,66193,1824],{},[902,66195,66196],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,66199,66201],{"className":66200},[886],[888,66202,66203],{"xmlns":890},[892,66204,66205,66233],{},[895,66206,66207,66209,66211,66213,66215,66217,66223,66225,66227,66229,66231],{},[898,66208,2132],{},[898,66210,5245],{},[1655,66212,1657],{},[1655,66214,2623],{},[1826,66216,3472],{},[2597,66218,66219,66221],{},[898,66220,1824],{},[1826,66222,1837],{},[1655,66224,2346],{},[1826,66226,5250],{},[898,66228,1824],{},[1655,66230,2623],{},[1826,66232,3639],{},[902,66234,66235],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,66237,66239],{"className":66238},[886],[888,66240,66241],{"xmlns":890},[892,66242,66243,66257],{},[895,66244,66245,66253,66255],{},[1820,66246,66247,66249,66251],{},[898,66248,1824],{},[898,66250,57323],{},[1655,66252,57326],{},[1655,66254,1657],{},[1826,66256,65685],{},[902,66258,66259],{"encoding":904},"Q_{\\max} = 1{,}5",[883,66261,66263],{"className":66262},[886],[888,66264,66265],{"xmlns":890},[892,66266,66267,66284],{},[895,66268,66269,66271,66279,66281],{},[898,66270,2132],{},[1820,66272,66273,66275,66277],{},[898,66274,5245],{},[898,66276,57323],{},[1655,66278,57326],{},[1655,66280,1657],{},[1826,66282,66283],{},"2,75",[902,66285,66286],{"encoding":904},"PR_{\\max} = 2{,}75",[724,66288,66289],{},[614,66290,66291,66292,66319,66320,66353,66354,1343,66377,1719],{},"Obrázek 3.12: Graf ",[883,66293,66295],{"className":66294},[886],[888,66296,66297],{"xmlns":890},[892,66298,66299,66317],{},[895,66300,66301,66303,66305,66307,66309,66311],{},[898,66302,4049],{},[898,66304,4052],{},[1655,66306,1657],{},[1826,66308,3639],{},[1655,66310,2346],{},[2597,66312,66313,66315],{},[898,66314,1824],{},[1826,66316,1837],{},[902,66318,66162],{"encoding":904}," (parabola) a ",[883,66321,66323],{"className":66322},[886],[888,66324,66325],{"xmlns":890},[892,66326,66327,66351],{},[895,66328,66329,66331,66333,66335,66337,66339,66345,66347,66349],{},[898,66330,4049],{},[898,66332,5245],{},[1655,66334,1657],{},[1655,66336,2623],{},[1826,66338,1837],{},[2597,66340,66341,66343],{},[898,66342,1824],{},[1826,66344,1837],{},[1655,66346,2346],{},[1826,66348,5250],{},[898,66350,1824],{},[902,66352,66196],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,66355,66357],{"className":66356},[886],[888,66358,66359],{"xmlns":890},[892,66360,66361,66374],{},[895,66362,66363,66369,66371],{},[1820,66364,66365,66367],{},[898,66366,1824],{},[1826,66368,1828],{},[1655,66370,7147],{},[1826,66372,66373],{},"0,54",[902,66375,66376],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,66378,66380],{"className":66379},[886],[888,66381,66382],{"xmlns":890},[892,66383,66384,66397],{},[895,66385,66386,66392,66394],{},[1820,66387,66388,66390],{},[898,66389,1824],{},[1826,66391,1837],{},[1655,66393,7147],{},[1826,66395,66396],{},"2,46",[902,66398,66399],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,66401,66402],{},[614,66403,66404,66405,59633,66442,66459,66460,1343,66481,1719],{},"Obrázek 3.13: Graf zisku ",[883,66406,66408],{"className":66407},[886],[888,66409,66410],{"xmlns":890},[892,66411,66412,66440],{},[895,66413,66414,66416,66418,66420,66422,66424,66430,66432,66434,66436,66438],{},[898,66415,2132],{},[898,66417,5245],{},[1655,66419,1657],{},[1655,66421,2623],{},[1826,66423,3472],{},[2597,66425,66426,66428],{},[898,66427,1824],{},[1826,66429,1837],{},[1655,66431,2346],{},[1826,66433,5250],{},[898,66435,1824],{},[1655,66437,2623],{},[1826,66439,3639],{},[902,66441,66235],{"encoding":904},[883,66443,66445],{"className":66444},[886],[888,66446,66447],{"xmlns":890},[892,66448,66449,66457],{},[895,66450,66451,66453,66455],{},[898,66452,1824],{},[1655,66454,1657],{},[1826,66456,65685],{},[902,66458,65740],{"encoding":904}," a nulami ",[883,66461,66463],{"className":66462},[886],[888,66464,66465],{"xmlns":890},[892,66466,66467,66479],{},[895,66468,66469,66475,66477],{},[1820,66470,66471,66473],{},[898,66472,1824],{},[1826,66474,1828],{},[1655,66476,7147],{},[1826,66478,66373],{},[902,66480,66376],{"encoding":904},[883,66482,66484],{"className":66483},[886],[888,66485,66486],{"xmlns":890},[892,66487,66488,66500],{},[895,66489,66490,66496,66498],{},[1820,66491,66492,66494],{},[898,66493,1824],{},[1826,66495,1837],{},[1655,66497,7147],{},[1826,66499,66396],{},[902,66501,66399],{"encoding":904},[115,66503,66505],{"id":66504},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,66507,66508],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,66510,66511],{},[1723,66512],{"alt":66513,"className":66514,"src":66515},"imek-max-zisku-dva-pohledy",[210,1727],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,66517,17538],{"id":66518},"princip-1",[724,66520,66521,66522,3902,66537,66554],{},"Má-li zisk ",[883,66523,66525],{"className":66524},[886],[888,66526,66527],{"xmlns":890},[892,66528,66529,66535],{},[895,66530,66531,66533],{},[898,66532,2132],{},[898,66534,5245],{},[902,66536,64605],{"encoding":904},[883,66538,66540],{"className":66539},[886],[888,66541,66542],{"xmlns":890},[892,66543,66544,66552],{},[895,66545,66546],{},[1820,66547,66548,66550],{},[898,66549,1824],{},[1826,66551,2552],{},[902,66553,39434],{"encoding":904}," maximum, pak platí",[883,66556,66558],{"className":66557},[886],[888,66559,66560],{"xmlns":890,"display":29192},[892,66561,66562,66611],{},[21880,66563,66564],{"width":29197},[21885,66565,66566,66568,66604,66606],{},[21888,66567],{"width":29202},[21888,66569,66570],{},[895,66571,66572,66574,66576,66578,66584,66586,66588,66590,66592,66594,66600,66602],{},[898,66573,2127],{},[898,66575,5245],{},[1655,66577,1664],{"stretchy":1663},[1820,66579,66580,66582],{},[898,66581,1824],{},[1826,66583,2552],{},[1655,66585,1677],{"stretchy":1663},[1655,66587,1657],{},[898,66589,2127],{},[898,66591,4052],{},[1655,66593,1664],{"stretchy":1663},[1820,66595,66596,66598],{},[898,66597,1824],{},[1826,66599,2552],{},[1655,66601,1677],{"stretchy":1663},[898,66603,1719],{"mathvariant":1943},[21888,66605],{"width":29202},[21888,66607,66608],{},[2031,66609,66610],{},"(3.13)",[902,66612,66613],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[5120,66615,66616],{},[724,66617,66618,63172,66620],{},[883,66619,57570],{},[38,66621,66622],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,66624,66625,66628,66629,9349,66656,18702,66730,1719],{},[38,66626,66627],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,66630,66632],{"className":66631},[886],[888,66633,66634],{"xmlns":890},[892,66635,66636,66654],{},[895,66637,66638,66640,66642,66644,66646,66648,66650,66652],{},[898,66639,2132],{},[898,66641,5245],{},[1655,66643,1657],{},[898,66645,4049],{},[898,66647,5245],{},[1655,66649,2623],{},[898,66651,4049],{},[898,66653,4052],{},[902,66655,56326],{"encoding":904},[883,66657,66659],{"className":66658},[886],[888,66660,66661],{"xmlns":890},[892,66662,66663,66727],{},[895,66664,66665,66667,66673,66675,66681,66683,66685,66687,66693,66695,66701,66703,66705,66707,66713,66715,66721,66723,66725],{},[898,66666,2132],{},[2597,66668,66669,66671],{},[898,66670,5245],{},[1655,66672,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,66674,1664],{"stretchy":1663},[1820,66676,66677,66679],{},[898,66678,1824],{},[1826,66680,2552],{},[1655,66682,1677],{"stretchy":1663},[1655,66684,1657],{},[898,66686,4049],{},[2597,66688,66689,66691],{},[898,66690,5245],{},[1655,66692,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,66694,1664],{"stretchy":1663},[1820,66696,66697,66699],{},[898,66698,1824],{},[1826,66700,2552],{},[1655,66702,1677],{"stretchy":1663},[1655,66704,2623],{},[898,66706,4049],{},[2597,66708,66709,66711],{},[898,66710,4052],{},[1655,66712,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,66714,1664],{"stretchy":1663},[1820,66716,66717,66719],{},[898,66718,1824],{},[1826,66720,2552],{},[1655,66722,1677],{"stretchy":1663},[1655,66724,1657],{},[1826,66726,2552],{},[902,66728,66729],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,66731,66733],{"className":66732},[886],[888,66734,66735],{"xmlns":890},[892,66736,66737,66769],{},[895,66738,66739,66741,66743,66745,66751,66753,66755,66757,66759,66761,66767],{},[898,66740,2127],{},[898,66742,5245],{},[1655,66744,1664],{"stretchy":1663},[1820,66746,66747,66749],{},[898,66748,1824],{},[1826,66750,2552],{},[1655,66752,1677],{"stretchy":1663},[1655,66754,1657],{},[898,66756,2127],{},[898,66758,4052],{},[1655,66760,1664],{"stretchy":1663},[1820,66762,66763,66765],{},[898,66764,1824],{},[1826,66766,2552],{},[1655,66768,1677],{"stretchy":1663},[902,66770,66771],{"encoding":904},"MR(Q_0) = MC(Q_0)",[5120,66773,66774,66779],{},[724,66775,66776,66778],{},[883,66777,5821],{}," Postup — jak najít maximum zisku",[152,66780,66781,66845,66900,66937,66965],{},[123,66782,66783,66784,2704,66799,66814,66815,5171],{},"Sestavte ",[883,66785,66787],{"className":66786},[886],[888,66788,66789],{"xmlns":890},[892,66790,66791,66797],{},[895,66792,66793,66795],{},[898,66794,4049],{},[898,66796,5245],{},[902,66798,5345],{"encoding":904},[883,66800,66802],{"className":66801},[886],[888,66803,66804],{"xmlns":890},[892,66805,66806,66812],{},[895,66807,66808,66810],{},[898,66809,4049],{},[898,66811,4052],{},[902,66813,4512],{"encoding":904}," ze zadání (typicky ",[883,66816,66818],{"className":66817},[886],[888,66819,66820],{"xmlns":890},[892,66821,66822,66842],{},[895,66823,66824,66826,66828,66830,66832,66834,66836,66838,66840],{},[898,66825,4049],{},[898,66827,5245],{},[1655,66829,1657],{},[898,66831,2132],{},[1655,66833,1664],{"stretchy":1663},[898,66835,1824],{},[1655,66837,1677],{"stretchy":1663},[1655,66839,2869],{},[898,66841,1824],{},[902,66843,66844],{"encoding":904},"TR = P(Q) \\cdot Q",[123,66846,66847,66848,2704,66874,1719],{},"Vypočtěte ",[883,66849,66851],{"className":66850},[886],[888,66852,66853],{"xmlns":890},[892,66854,66855,66871],{},[895,66856,66857,66859,66861,66863,66865],{},[898,66858,2127],{},[898,66860,5245],{},[1655,66862,1657],{},[898,66864,4049],{},[2597,66866,66867,66869],{},[898,66868,5245],{},[1655,66870,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,66872,66873],{"encoding":904},"MR = TR'",[883,66875,66877],{"className":66876},[886],[888,66878,66879],{"xmlns":890},[892,66880,66881,66897],{},[895,66882,66883,66885,66887,66889,66891],{},[898,66884,2127],{},[898,66886,4052],{},[1655,66888,1657],{},[898,66890,4049],{},[2597,66892,66893,66895],{},[898,66894,4052],{},[1655,66896,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,66898,66899],{"encoding":904},"MC = TC'",[123,66901,66902,66903,1719],{},"Řešte rovnici ",[883,66904,66906],{"className":66905},[886],[888,66907,66908],{"xmlns":890},[892,66909,66910,66934],{},[895,66911,66912,66914,66916,66918,66920,66922,66924,66926,66928,66930,66932],{},[898,66913,2127],{},[898,66915,5245],{},[1655,66917,1664],{"stretchy":1663},[898,66919,1824],{},[1655,66921,1677],{"stretchy":1663},[1655,66923,1657],{},[898,66925,2127],{},[898,66927,4052],{},[1655,66929,1664],{"stretchy":1663},[898,66931,1824],{},[1655,66933,1677],{"stretchy":1663},[902,66935,66936],{"encoding":904},"MR(Q) = MC(Q)",[123,66938,66939,66940,66964],{},"Ověřte druhou derivaci ",[883,66941,66943],{"className":66942},[886],[888,66944,66945],{"xmlns":890},[892,66946,66947,66961],{},[895,66948,66949,66951],{},[898,66950,2132],{},[2597,66952,66953,66955],{},[898,66954,5245],{},[895,66956,66957,66959],{},[1655,66958,1945],{"mathvariant":1943},[1655,66960,1945],{"mathvariant":1943},[902,66962,66963],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,66966,66967,66968,66995],{},"Dosaďte do ",[883,66969,66971],{"className":66970},[886],[888,66972,66973],{"xmlns":890},[892,66974,66975,66993],{},[895,66976,66977,66979,66981,66983,66985,66987,66989,66991],{},[898,66978,2132],{},[898,66980,5245],{},[1655,66982,1657],{},[898,66984,4049],{},[898,66986,5245],{},[1655,66988,2623],{},[898,66990,4049],{},[898,66992,4052],{},[902,66994,56326],{"encoding":904}," pro hodnotu maxima.",[38474,66997,66999],{"id":66998},"příklad-39","Příklad 3.9",[724,67001,67002,57114,67004,2704,67026,67062],{},[38,67003,57113],{},[883,67005,67007],{"className":67006},[886],[888,67008,67009],{"xmlns":890},[892,67010,67011,67023],{},[895,67012,67013,67015,67017,67019,67021],{},[898,67014,2132],{},[1655,67016,1657],{},[1826,67018,39145],{},[1655,67020,2623],{},[898,67022,1824],{},[902,67024,67025],{"encoding":904},"P = 30 - Q",[883,67027,67029],{"className":67028},[886],[888,67030,67031],{"xmlns":890},[892,67032,67033,67059],{},[895,67034,67035,67037,67039,67041,67043,67049,67051,67053,67055,67057],{},[898,67036,4049],{},[898,67038,4052],{},[1655,67040,1657],{},[1826,67042,6258],{},[2597,67044,67045,67047],{},[898,67046,1824],{},[1826,67048,1837],{},[1655,67050,2346],{},[1826,67052,3531],{},[898,67054,1824],{},[1655,67056,2346],{},[1826,67058,25327],{},[902,67060,67061],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,67064,67065,3106,67067,1343,67097,67135,67136,16917,67180,67214,67215,1719],{},[38,67066,23896],{},[883,67068,67070],{"className":67069},[886],[888,67071,67072],{"xmlns":890},[892,67073,67074,67094],{},[895,67075,67076,67078,67080,67082,67084,67086,67088],{},[898,67077,4049],{},[898,67079,5245],{},[1655,67081,1657],{},[1826,67083,39145],{},[898,67085,1824],{},[1655,67087,2623],{},[2597,67089,67090,67092],{},[898,67091,1824],{},[1826,67093,1837],{},[902,67095,67096],{"encoding":904},"TR = 30Q - Q^2",[883,67098,67100],{"className":67099},[886],[888,67101,67102],{"xmlns":890},[892,67103,67104,67132],{},[895,67105,67106,67108,67110,67112,67114,67116,67122,67124,67126,67128,67130],{},[898,67107,2132],{},[898,67109,5245],{},[1655,67111,1657],{},[1655,67113,2623],{},[1826,67115,65685],{},[2597,67117,67118,67120],{},[898,67119,1824],{},[1826,67121,1837],{},[1655,67123,2346],{},[1826,67125,42926],{},[898,67127,1824],{},[1655,67129,2623],{},[1826,67131,25327],{},[902,67133,67134],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,67137,67139],{"className":67138},[886],[888,67140,67141],{"xmlns":890},[892,67142,67143,67177],{},[895,67144,67145,67147,67153,67155,67157,67159,67161,67163,67165,67167,67169,67171,67173,67175],{},[898,67146,2132],{},[2597,67148,67149,67151],{},[898,67150,5245],{},[1655,67152,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,67154,1657],{},[1655,67156,2623],{},[1826,67158,3472],{},[898,67160,1824],{},[1655,67162,2346],{},[1826,67164,42926],{},[1655,67166,1657],{},[1826,67168,2552],{},[1655,67170,5238],{},[898,67172,1824],{},[1655,67174,1657],{},[1826,67176,6834],{},[902,67178,67179],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,67181,67183],{"className":67182},[886],[888,67184,67185],{"xmlns":890},[892,67186,67187,67211],{},[895,67188,67189,67191,67201,67203,67205,67207,67209],{},[898,67190,2132],{},[2597,67192,67193,67195],{},[898,67194,5245],{},[895,67196,67197,67199],{},[1655,67198,1945],{"mathvariant":1943},[1655,67200,1945],{"mathvariant":1943},[1655,67202,1657],{},[1655,67204,2623],{},[1826,67206,3472],{},[1655,67208,3065],{},[1826,67210,2552],{},[902,67212,67213],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,67216,67218],{"className":67217},[886],[888,67219,67220],{"xmlns":890},[892,67221,67222,67239],{},[895,67223,67224,67226,67228,67230,67232,67234,67236],{},[898,67225,2132],{},[898,67227,5245],{},[1655,67229,1664],{"stretchy":1663},[1826,67231,6834],{},[1655,67233,1677],{"stretchy":1663},[1655,67235,1657],{},[1826,67237,67238],{},"89",[902,67240,67241],{"encoding":904},"PR(8) = 89",[724,67243,67244,67245,1343,67271,16917,67295,67333],{},"Ověření principu: ",[883,67246,67248],{"className":67247},[886],[888,67249,67250],{"xmlns":890},[892,67251,67252,67268],{},[895,67253,67254,67256,67258,67260,67262,67264,67266],{},[898,67255,2127],{},[898,67257,5245],{},[1655,67259,1657],{},[1826,67261,39145],{},[1655,67263,2623],{},[1826,67265,1837],{},[898,67267,1824],{},[902,67269,67270],{"encoding":904},"MR = 30 - 2Q",[883,67272,67274],{"className":67273},[886],[888,67275,67276],{"xmlns":890},[892,67277,67278,67292],{},[895,67279,67280,67282,67284,67286,67288,67290],{},[898,67281,2127],{},[898,67283,4052],{},[1655,67285,1657],{},[898,67287,1824],{},[1655,67289,2346],{},[1826,67291,3531],{},[902,67293,67294],{"encoding":904},"MC = Q + 6",[883,67296,67298],{"className":67297},[886],[888,67299,67300],{"xmlns":890},[892,67301,67302,67330],{},[895,67303,67304,67306,67308,67310,67312,67314,67316,67318,67320,67322,67324,67326,67328],{},[898,67305,2127],{},[898,67307,5245],{},[1655,67309,1664],{"stretchy":1663},[1826,67311,6834],{},[1655,67313,1677],{"stretchy":1663},[1655,67315,1657],{},[1826,67317,24072],{},[1655,67319,1657],{},[898,67321,2127],{},[898,67323,4052],{},[1655,67325,1664],{"stretchy":1663},[1826,67327,6834],{},[1655,67329,1677],{"stretchy":1663},[902,67331,67332],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,67335,67336,67337,67370,67371,67388],{},"V řadě případů — má-li rovnice ",[883,67338,67340],{"className":67339},[886],[888,67341,67342],{"xmlns":890},[892,67343,67344,67368],{},[895,67345,67346,67348,67350,67352,67354,67356,67358,67360,67362,67364,67366],{},[898,67347,2127],{},[898,67349,5245],{},[1655,67351,1664],{"stretchy":1663},[898,67353,1824],{},[1655,67355,1677],{"stretchy":1663},[1655,67357,1657],{},[898,67359,2127],{},[898,67361,4052],{},[1655,67363,1664],{"stretchy":1663},[898,67365,1824],{},[1655,67367,1677],{"stretchy":1663},[902,67369,66936],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,67372,67374],{"className":67373},[886],[888,67375,67376],{"xmlns":890},[892,67377,67378,67386],{},[895,67379,67380],{},[1820,67381,67382,67384],{},[898,67383,1824],{},[1826,67385,2552],{},[902,67387,39434],{"encoding":904}," — není třeba provádět test druhé derivace.",[38474,67390,67392],{"id":67391},"příklad-310","Příklad 3.10",[724,67394,67395,67397,67398,67402,67403,67416,67417,67448],{},[38,67396,57113],{}," Firma vyrábí minipočítače v ",[207,67399,67401],{"className":67400,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,67404,67406],{"className":67405},[886],[888,67407,67408],{"xmlns":890},[892,67409,67410,67414],{},[895,67411,67412],{},[1826,67413,16316],{},[902,67415,16316],{"encoding":904}," EUR\u002Fks. ",[883,67418,67420],{"className":67419},[886],[888,67421,67422],{"xmlns":890},[892,67423,67424,67445],{},[895,67425,67426,67428,67430,67432,67434,67436,67439],{},[898,67427,4049],{},[898,67429,4052],{},[1655,67431,1657],{},[1826,67433,4390],{},[1655,67435,2346],{},[1826,67437,67438],{},"28",[2597,67440,67441,67443],{},[898,67442,1824],{},[1826,67444,1837],{},[902,67446,67447],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,67450,67451,3106,67453,1343,67475,1343,67495,67518],{},[38,67452,23896],{},[883,67454,67456],{"className":67455},[886],[888,67457,67458],{"xmlns":890},[892,67459,67460,67472],{},[895,67461,67462,67464,67466,67468,67470],{},[898,67463,4049],{},[898,67465,5245],{},[1655,67467,1657],{},[1826,67469,16316],{},[898,67471,1824],{},[902,67473,67474],{"encoding":904},"TR = 900Q",[883,67476,67478],{"className":67477},[886],[888,67479,67480],{"xmlns":890},[892,67481,67482,67492],{},[895,67483,67484,67486,67488,67490],{},[898,67485,2127],{},[898,67487,5245],{},[1655,67489,1657],{},[1826,67491,16316],{},[902,67493,67494],{"encoding":904},"MR = 900",[883,67496,67498],{"className":67497},[886],[888,67499,67500],{"xmlns":890},[892,67501,67502,67515],{},[895,67503,67504,67506,67508,67510,67513],{},[898,67505,2127],{},[898,67507,4052],{},[1655,67509,1657],{},[1826,67511,67512],{},"56",[898,67514,1824],{},[902,67516,67517],{"encoding":904},"MC = 56Q",". Z principu:",[883,67520,67522],{"className":67521},[886],[888,67523,67524],{"xmlns":890,"display":29192},[892,67525,67526,67568],{},[895,67527,67528,67530,67532,67534,67536,67538,67540,67542,67544,67546,67554,67556,67559,67561,67563,67565],{},[1826,67529,16316],{},[1655,67531,1657],{},[1826,67533,67512],{},[898,67535,1824],{},[2031,67537,2783],{},[1655,67539,5238],{},[2031,67541,2783],{},[898,67543,1824],{},[1655,67545,1657],{},[3615,67547,67548],{"scriptlevel":2552,"displaystyle":1663},[1949,67549,67550,67552],{},[1826,67551,16316],{},[1826,67553,67512],{},[1655,67555,7147],{},[1826,67557,67558],{},"16,07",[2031,67560,2783],{},[1655,67562,2357],{},[2031,67564,2783],{},[1826,67566,67567],{},"16.",[902,67569,67570],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,67572,67573,67574,2086],{},"Zisk při ",[883,67575,67577],{"className":67576},[886],[888,67578,67579],{"xmlns":890},[892,67580,67581,67589],{},[895,67582,67583,67585,67587],{},[898,67584,1824],{},[1655,67586,1657],{},[1826,67588,42988],{},[902,67590,67591],{"encoding":904},"Q = 16",[883,67593,67595],{"className":67594},[886],[888,67596,67597],{"xmlns":890,"display":29192},[892,67598,67599,67670],{},[895,67600,67601,67603,67605,67607,67609,67611,67613,67615,67617,67619,67621,67623,67625,67627,67629,67631,67637,67639,67641,67643,67645,67647,67649,67651,67653,67656,67658,67660,67662,67665,67668],{},[898,67602,2132],{},[898,67604,5245],{},[1655,67606,1664],{"stretchy":1663},[1826,67608,42988],{},[1655,67610,1677],{"stretchy":1663},[1655,67612,1657],{},[1826,67614,16316],{},[1655,67616,2869],{},[1826,67618,42988],{},[1655,67620,2623],{},[1655,67622,1664],{"stretchy":1663},[1826,67624,4390],{},[1655,67626,2346],{},[1826,67628,67438],{},[1655,67630,2869],{},[2597,67632,67633,67635],{},[1826,67634,42988],{},[1826,67636,1837],{},[1655,67638,1677],{"stretchy":1663},[1655,67640,1657],{},[1826,67642,24072],{},[2031,67644,2435],{},[1826,67646,21268],{},[1655,67648,2623],{},[1826,67650,25327],{},[2031,67652,2435],{},[1826,67654,67655],{},"218",[1655,67657,1657],{},[1826,67659,25327],{},[2031,67661,2435],{},[1826,67663,67664],{},"182",[2031,67666,67667],{}," EUR",[898,67669,1719],{"mathvariant":1943},[902,67671,67672],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,67674,67675],{},"Pro srovnání při původních 30 ks:",[883,67677,67679],{"className":67678},[886],[888,67680,67681],{"xmlns":890,"display":29192},[892,67682,67683,67748],{},[895,67684,67685,67687,67689,67691,67693,67695,67697,67699,67701,67703,67705,67707,67709,67711,67713,67715,67717,67719,67721,67724,67726,67728,67730,67732,67734,67736,67738,67740,67742,67744,67746],{},[898,67686,2132],{},[898,67688,5245],{},[1655,67690,1664],{"stretchy":1663},[1826,67692,39145],{},[1655,67694,1677],{"stretchy":1663},[1655,67696,1657],{},[1826,67698,16316],{},[1655,67700,2869],{},[1826,67702,39145],{},[1655,67704,2623],{},[1655,67706,1664],{"stretchy":1663},[1826,67708,4390],{},[1655,67710,2346],{},[1826,67712,67438],{},[1655,67714,2869],{},[1826,67716,16316],{},[1655,67718,1677],{"stretchy":1663},[1655,67720,1657],{},[1826,67722,67723],{},"27",[2031,67725,2435],{},[1826,67727,60208],{},[1655,67729,2623],{},[1826,67731,6253],{},[2031,67733,2435],{},[1826,67735,31869],{},[1655,67737,1657],{},[1826,67739,1828],{},[2031,67741,2435],{},[1826,67743,24869],{},[2031,67745,67667],{},[898,67747,1719],{"mathvariant":1943},[902,67749,67750],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,67752,67753,67756,67757,67775,67776,67794],{},[38,67754,67755],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,67758,67760],{"className":67759},[886],[888,67761,67762],{"xmlns":890},[892,67763,67764,67772],{},[895,67765,67766,67768,67770],{},[1826,67767,25327],{},[2031,67769,2435],{},[1826,67771,67664],{},[902,67773,67774],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,67777,67779],{"className":67778},[886],[888,67780,67781],{"xmlns":890},[892,67782,67783,67791],{},[895,67784,67785,67787,67789],{},[1826,67786,1828],{},[2031,67788,2435],{},[1826,67790,24869],{},[902,67792,67793],{"encoding":904},"1\\,750"," EUR.",[198,67796,67798],{"id":67797},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,67800,67801,67802,63696,67815,67839],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,67803,67805],{"className":67804},[886],[888,67806,67807],{"xmlns":890},[892,67808,67809,67813],{},[895,67810,67811],{},[898,67812,2132],{},[902,67814,2132],{"encoding":904},[883,67816,67818],{"className":67817},[886],[888,67819,67820],{"xmlns":890},[892,67821,67822,67836],{},[895,67823,67824,67826,67828,67830,67832,67834],{},[898,67825,4049],{},[898,67827,5245],{},[1655,67829,1657],{},[898,67831,2132],{},[1655,67833,2869],{},[898,67835,1824],{},[902,67837,67838],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,67841,67843],{"className":67842},[886],[888,67844,67845],{"xmlns":890,"display":29192},[892,67846,67847,67880],{},[21880,67848,67849],{"width":29197},[21885,67850,67851,67853,67873,67875],{},[21888,67852],{"width":29202},[21888,67854,67855],{},[895,67856,67857,67859,67861,67863,67865,67867,67869,67871],{},[898,67858,2132],{},[1655,67860,1657],{},[898,67862,2127],{},[898,67864,4052],{},[1655,67866,1664],{"stretchy":1663},[898,67868,1824],{},[1655,67870,1677],{"stretchy":1663},[898,67872,1719],{"mathvariant":1943},[21888,67874],{"width":29202},[21888,67876,67877],{},[2031,67878,67879],{},"(3.14)",[902,67881,67882],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,67884,67885,67886,1719],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,67887,67889],{"className":67888},[886],[888,67890,67891],{"xmlns":890},[892,67892,67893,67907],{},[895,67894,67895,67897],{},[898,67896,2132],{},[2597,67898,67899,67901],{},[898,67900,5245],{},[895,67902,67903,67905],{},[1655,67904,1945],{"mathvariant":1943},[1655,67906,1945],{"mathvariant":1943},[902,67908,66963],{"encoding":904},[38474,67910,67912],{"id":67911},"příklad-311","Příklad 3.11",[724,67914,67915,58648,67917,67964,67965,67983],{},[38,67916,57113],{},[883,67918,67920],{"className":67919},[886],[888,67921,67922],{"xmlns":890},[892,67923,67924,67961],{},[895,67925,67926,67928,67930,67932,67935,67941,67943,67945,67951,67953,67955,67957,67959],{},[898,67927,4049],{},[898,67929,4052],{},[1655,67931,1657],{},[1826,67933,67934],{},"0,04",[2597,67936,67937,67939],{},[898,67938,1824],{},[1826,67940,3472],{},[1655,67942,2623],{},[1826,67944,23671],{},[2597,67946,67947,67949],{},[898,67948,1824],{},[1826,67950,1837],{},[1655,67952,2346],{},[1826,67954,4136],{},[898,67956,1824],{},[1655,67958,2346],{},[1826,67960,3524],{},[902,67962,67963],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,67966,67968],{"className":67967},[886],[888,67969,67970],{"xmlns":890},[892,67971,67972,67980],{},[895,67973,67974,67976,67978],{},[898,67975,2132],{},[1655,67977,1657],{},[1826,67979,3639],{},[902,67981,67982],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,67985,67986,67988,67989,18702,68031,68065,68066,2086],{},[38,67987,23896],{}," Z (3.14): ",[883,67990,67992],{"className":67991},[886],[888,67993,67994],{"xmlns":890},[892,67995,67996,68028],{},[895,67997,67998,68000,68002,68004,68007,68013,68015,68018,68020,68022,68024,68026],{},[898,67999,2127],{},[898,68001,4052],{},[1655,68003,1657],{},[1826,68005,68006],{},"0,12",[2597,68008,68009,68011],{},[898,68010,1824],{},[1826,68012,1837],{},[1655,68014,2623],{},[1826,68016,68017],{},"1,8",[898,68019,1824],{},[1655,68021,2346],{},[1826,68023,4136],{},[1655,68025,1657],{},[1826,68027,3639],{},[902,68029,68030],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,68032,68034],{"className":68033},[886],[888,68035,68036],{"xmlns":890},[892,68037,68038,68062],{},[895,68039,68040,68042,68048,68050,68052,68054,68056,68058,68060],{},[1826,68041,68006],{},[2597,68043,68044,68046],{},[898,68045,1824],{},[1826,68047,1837],{},[1655,68049,2623],{},[1826,68051,68017],{},[898,68053,1824],{},[1655,68055,2346],{},[1826,68057,3531],{},[1655,68059,1657],{},[1826,68061,2552],{},[902,68063,68064],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,68067,68069],{"className":68068},[886],[888,68070,68071],{"xmlns":890},[892,68072,68073,68077],{},[895,68074,68075],{},[1826,68076,68006],{},[902,68078,68079],{"encoding":904},"0{,}12",[883,68081,68083],{"className":68082},[886],[888,68084,68085],{"xmlns":890,"display":29192},[892,68086,68087,68139],{},[895,68088,68089,68095,68097,68099,68101,68103,68105,68107,68109,68111,68113,68115,68121,68123,68125,68127,68129,68135,68137],{},[2597,68090,68091,68093],{},[898,68092,1824],{},[1826,68094,1837],{},[1655,68096,2623],{},[1826,68098,37370],{},[898,68100,1824],{},[1655,68102,2346],{},[1826,68104,4390],{},[1655,68106,1657],{},[1826,68108,2552],{},[2031,68110,2783],{},[1655,68112,5238],{},[2031,68114,2783],{},[1820,68116,68117,68119],{},[898,68118,1824],{},[1826,68120,1828],{},[1655,68122,1657],{},[1826,68124,3524],{},[1655,68126,1671],{"separator":1670},[2031,68128,2783],{},[1820,68130,68131,68133],{},[898,68132,1824],{},[1826,68134,1837],{},[1655,68136,1657],{},[1826,68138,20454],{},[902,68140,68141],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,68143,68144,68145,2086],{},"Dále ",[883,68146,68148],{"className":68147},[886],[888,68149,68150],{"xmlns":890},[892,68151,68152,68191],{},[895,68153,68154,68156,68166,68168,68170,68172,68178,68180,68182,68185,68187,68189],{},[898,68155,2132],{},[2597,68157,68158,68160],{},[898,68159,5245],{},[895,68161,68162,68164],{},[1655,68163,1945],{"mathvariant":1943},[1655,68165,1945],{"mathvariant":1943},[1655,68167,1657],{},[1655,68169,2623],{},[898,68171,2127],{},[2597,68173,68174,68176],{},[898,68175,4052],{},[1655,68177,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,68179,1657],{},[1655,68181,2623],{},[1826,68183,68184],{},"0,24",[898,68186,1824],{},[1655,68188,2346],{},[1826,68190,68017],{},[902,68192,68193],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,68195,68196,68246],{},[123,68197,68198,68242,68243,68245],{},[883,68199,68201],{"className":68200},[886],[888,68202,68203],{"xmlns":890},[892,68204,68205,68239],{},[895,68206,68207,68209,68219,68221,68223,68225,68227,68229,68231,68233,68235,68237],{},[898,68208,2132],{},[2597,68210,68211,68213],{},[898,68212,5245],{},[895,68214,68215,68217],{},[1655,68216,1945],{"mathvariant":1943},[1655,68218,1945],{"mathvariant":1943},[1655,68220,1664],{"stretchy":1663},[1826,68222,3524],{},[1655,68224,1677],{"stretchy":1663},[1655,68226,1657],{},[1826,68228,20447],{},[1655,68230,2969],{},[1826,68232,2552],{},[2031,68234,2783],{},[1655,68236,5238],{},[2031,68238,2783],{},[902,68240,68241],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,68244,3025],{}," zisku (minimalizace ztráty);",[123,68247,68248,68242,68294,68296],{},[883,68249,68251],{"className":68250},[886],[888,68252,68253],{"xmlns":890},[892,68254,68255,68291],{},[895,68256,68257,68259,68269,68271,68273,68275,68277,68279,68281,68283,68285,68287,68289],{},[898,68258,2132],{},[2597,68260,68261,68263],{},[898,68262,5245],{},[895,68264,68265,68267],{},[1655,68266,1945],{"mathvariant":1943},[1655,68268,1945],{"mathvariant":1943},[1655,68270,1664],{"stretchy":1663},[1826,68272,4136],{},[1655,68274,1677],{"stretchy":1663},[1655,68276,1657],{},[1655,68278,2623],{},[1826,68280,20447],{},[1655,68282,3065],{},[1826,68284,2552],{},[2031,68286,2783],{},[1655,68288,5238],{},[2031,68290,2783],{},[902,68292,68293],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,68295,3073],{}," zisku, avšak",[883,68298,68300],{"className":68299},[886],[888,68301,68302],{"xmlns":890,"display":29192},[892,68303,68304,68372],{},[895,68305,68306,68308,68310,68312,68314,68316,68318,68320,68322,68324,68326,68328,68330,68332,68334,68336,68338,68340,68342,68344,68346,68348,68350,68352,68354,68356,68358,68360,68362,68364,68366,68368,68370],{},[898,68307,2132],{},[898,68309,5245],{},[1655,68311,1664],{"stretchy":1663},[1826,68313,4136],{},[1655,68315,1677],{"stretchy":1663},[1655,68317,1657],{},[1826,68319,3639],{},[1655,68321,2869],{},[1826,68323,4136],{},[1655,68325,2623],{},[1655,68327,1664],{"stretchy":1663},[1826,68329,67934],{},[1655,68331,2869],{},[1826,68333,1828],{},[2031,68335,2435],{},[1826,68337,60208],{},[1655,68339,2623],{},[1826,68341,23671],{},[1655,68343,2869],{},[1826,68345,4360],{},[1655,68347,2346],{},[1826,68349,4360],{},[1655,68351,2346],{},[1826,68353,3524],{},[1655,68355,1677],{"stretchy":1663},[1655,68357,1657],{},[1826,68359,6460],{},[1655,68361,2623],{},[1826,68363,22306],{},[1655,68365,1657],{},[1655,68367,2623],{},[1826,68369,37370],{},[1655,68371,1671],{"separator":1670},[902,68373,68374],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,68376,68377,68378,1719],{},"tj. ztráta větší než ",[883,68379,68381],{"className":68380},[886],[888,68382,68383],{"xmlns":890},[892,68384,68385,68395],{},[895,68386,68387,68389,68391,68393],{},[898,68388,2537],{},[898,68390,4052],{},[1655,68392,1657],{},[1826,68394,3524],{},[902,68396,68397],{"encoding":904},"FC = 5",[724,68399,68400,68403,68404,68407,68408,1719],{},[38,68401,68402],{},"Závěr:"," firma by měla ",[38,68405,68406],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,68409,68411],{"className":68410},[886],[888,68412,68413],{"xmlns":890},[892,68414,68415,68425],{},[895,68416,68417,68419,68421,68423],{},[898,68418,2537],{},[898,68420,4052],{},[1655,68422,1657],{},[1826,68424,3524],{},[902,68426,68397],{"encoding":904},[115,68428,68430],{"id":68429},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,68432,68433,68434,68436,68437,68452,68453,68466,68467,68493,68494,68507,68508,68525,68526,3902,68543,68546,68547,68567,68568,68583,68584,2086],{},"Důležitým završením analýzy je konstrukce ",[38,68435,56401],{},". S nabízeným množstvím rostou mezní náklady ",[883,68438,68440],{"className":68439},[886],[888,68441,68442],{"xmlns":890},[892,68443,68444,68450],{},[895,68445,68446,68448],{},[898,68447,2127],{},[898,68449,4052],{},[902,68451,56418],{"encoding":904}," a tyto určují cenu ",[883,68454,68456],{"className":68455},[886],[888,68457,68458],{"xmlns":890},[892,68459,68460,68464],{},[895,68461,68462],{},[898,68463,2132],{},[902,68465,2132],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,68468,68470],{"className":68469},[886],[888,68471,68472],{"xmlns":890},[892,68473,68474,68490],{},[895,68475,68476,68478,68480,68482,68484,68486,68488],{},[898,68477,2132],{},[1655,68479,1657],{},[898,68481,2127],{},[898,68483,4052],{},[1655,68485,1664],{"stretchy":1663},[898,68487,1824],{},[1655,68489,1677],{"stretchy":1663},[902,68491,68492],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,68495,68497],{"className":68496},[886],[888,68498,68499],{"xmlns":890},[892,68500,68501,68505],{},[895,68502,68503],{},[898,68504,2132],{},[902,68506,2132],{"encoding":904}," však nemůže být nižší než ",[883,68509,68511],{"className":68510},[886],[888,68512,68513],{"xmlns":890},[892,68514,68515,68523],{},[895,68516,68517],{},[2597,68518,68519,68521],{},[898,68520,2132],{},[1655,68522,5603],{},[902,68524,5653],{"encoding":904}," odpovídající množství ",[883,68527,68529],{"className":68528},[886],[888,68530,68531],{"xmlns":890},[892,68532,68533,68541],{},[895,68534,68535],{},[2597,68536,68537,68539],{},[898,68538,1824],{},[1655,68540,5603],{},[902,68542,30970],{"encoding":904},[38,68544,68545],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,68548,68550],{"className":68549},[886],[888,68551,68552],{"xmlns":890},[892,68553,68554,68564],{},[895,68555,68556,68558],{},[1826,68557,2552],{},[2597,68559,68560,68562],{},[898,68561,1824],{},[1655,68563,5603],{},[902,68565,68566],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,68569,68571],{"className":68570},[886],[888,68572,68573],{"xmlns":890},[892,68574,68575,68581],{},[895,68576,68577,68579],{},[898,68578,2127],{},[898,68580,4052],{},[902,68582,56418],{"encoding":904}," nad bodem ",[883,68585,68587],{"className":68586},[886],[888,68588,68589],{"xmlns":890},[892,68590,68591,68595],{},[895,68592,68593],{},[898,68594,2731],{},[902,68596,2731],{"encoding":904},[883,68598,68600],{"className":68599},[886],[888,68601,68602],{"xmlns":890,"display":29192},[892,68603,68604,68711],{},[21880,68605,68606],{"width":29197},[21885,68607,68608,68610,68704,68706],{},[21888,68609],{"width":29202},[21888,68611,68612],{},[895,68613,68614,68616,68618,68620,68622,68624,68626,68628],{},[898,68615,2132],{},[1655,68617,1657],{},[898,68619,9920],{},[1655,68621,1664],{"stretchy":1663},[898,68623,1824],{},[1655,68625,1677],{"stretchy":1663},[1655,68627,1657],{},[895,68629,68630,68633],{},[1655,68631,68632],{"fence":1670},"{",[21880,68634,68637,68676],{"rowspacing":68635,"columnalign":68636,"columnspacing":16409},"0.36em","left left",[21885,68638,68639,68655],{},[21888,68640,68641],{},[3615,68642,68643],{"scriptlevel":2552,"displaystyle":1663},[895,68644,68645,68647,68649,68651,68653],{},[898,68646,2127],{},[898,68648,4052],{},[1655,68650,1664],{"stretchy":1663},[898,68652,1824],{},[1655,68654,1677],{"stretchy":1663},[21888,68656,68657],{},[3615,68658,68659],{"scriptlevel":2552,"displaystyle":1663},[895,68660,68661,68664,68666,68668,68674],{},[2031,68662,68663],{},"pro ",[898,68665,1824],{},[1655,68667,5734],{},[2597,68669,68670,68672],{},[898,68671,1824],{},[1655,68673,5603],{},[1655,68675,1671],{"separator":1670},[21885,68677,68678,68684],{},[21888,68679,68680],{},[3615,68681,68682],{"scriptlevel":2552,"displaystyle":1663},[1826,68683,2552],{},[21888,68685,68686],{},[3615,68687,68688],{"scriptlevel":2552,"displaystyle":1663},[895,68689,68690,68692,68694,68696,68702],{},[2031,68691,68663],{},[898,68693,1824],{},[1655,68695,3065],{},[2597,68697,68698,68700],{},[898,68699,1824],{},[1655,68701,5603],{},[1655,68703,1671],{"separator":1670},[21888,68705],{"width":29202},[21888,68707,68708],{},[2031,68709,68710],{},"(3.15)",[902,68712,68713],{"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}",[724,68715,5559,68716,68733,68734,68751,68752,42625,68782,68785],{},[883,68717,68719],{"className":68718},[886],[888,68720,68721],{"xmlns":890},[892,68722,68723,68731],{},[895,68724,68725],{},[2597,68726,68727,68729],{},[898,68728,1824],{},[1655,68730,5603],{},[902,68732,30970],{"encoding":904}," je bod minima ",[883,68735,68737],{"className":68736},[886],[888,68738,68739],{"xmlns":890},[892,68740,68741,68749],{},[895,68742,68743,68745,68747],{},[898,68744,2731],{},[898,68746,41465],{},[898,68748,4052],{},[902,68750,56437],{"encoding":904},". Bod ",[883,68753,68755],{"className":68754},[886],[888,68756,68757],{"xmlns":890},[892,68758,68759,68779],{},[895,68760,68761,68763,68769,68771,68777],{},[1655,68762,1664],{"stretchy":1663},[2597,68764,68765,68767],{},[898,68766,1824],{},[1655,68768,5603],{},[1655,68770,1671],{"separator":1670},[2597,68772,68773,68775],{},[898,68774,2132],{},[1655,68776,5603],{},[1655,68778,1677],{"stretchy":1663},[902,68780,68781],{"encoding":904},"(Q^*, P^*)",[38,68783,68784],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[5120,68787,68788,68793],{},[724,68789,68790,68792],{},[883,68791,5821],{}," Postup — jak odvodit nabídku firmy",[152,68794,68795,68844,68939,68994,69065],{},[123,68796,68797,68798,2704,68820,1719],{},"Ze zadaných nákladů určete ",[883,68799,68801],{"className":68800},[886],[888,68802,68803],{"xmlns":890},[892,68804,68805,68817],{},[895,68806,68807,68809,68811,68813,68815],{},[898,68808,2127],{},[898,68810,4052],{},[1655,68812,1664],{"stretchy":1663},[898,68814,1824],{},[1655,68816,1677],{"stretchy":1663},[902,68818,68819],{"encoding":904},"MC(Q)",[883,68821,68823],{"className":68822},[886],[888,68824,68825],{"xmlns":890},[892,68826,68827,68841],{},[895,68828,68829,68831,68833,68835,68837,68839],{},[898,68830,2731],{},[898,68832,41465],{},[898,68834,4052],{},[1655,68836,1664],{"stretchy":1663},[898,68838,1824],{},[1655,68840,1677],{"stretchy":1663},[902,68842,68843],{"encoding":904},"AVC(Q)",[123,68845,68846,68847,68864,68865,68882,68883,68915,68916,5171],{},"Najděte ",[883,68848,68850],{"className":68849},[886],[888,68851,68852],{"xmlns":890},[892,68853,68854,68862],{},[895,68855,68856],{},[2597,68857,68858,68860],{},[898,68859,1824],{},[1655,68861,5603],{},[902,68863,30970],{"encoding":904}," jako bod minima ",[883,68866,68868],{"className":68867},[886],[888,68869,68870],{"xmlns":890},[892,68871,68872,68880],{},[895,68873,68874,68876,68878],{},[898,68875,2731],{},[898,68877,41465],{},[898,68879,4052],{},[902,68881,56437],{"encoding":904}," (řešením ",[883,68884,68886],{"className":68885},[886],[888,68887,68888],{"xmlns":890},[892,68889,68890,68912],{},[895,68891,68892,68894,68896,68902,68904,68906,68908,68910],{},[898,68893,2731],{},[898,68895,41465],{},[2597,68897,68898,68900],{},[898,68899,4052],{},[1655,68901,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,68903,1664],{"stretchy":1663},[898,68905,1824],{},[1655,68907,1677],{"stretchy":1663},[1655,68909,1657],{},[1826,68911,2552],{},[902,68913,68914],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,68917,68919],{"className":68918},[886],[888,68920,68921],{"xmlns":890},[892,68922,68923,68937],{},[895,68924,68925,68927,68929,68931,68933,68935],{},[898,68926,2731],{},[898,68928,41465],{},[898,68930,4052],{},[1655,68932,1657],{},[898,68934,2127],{},[898,68936,4052],{},[902,68938,56374],{"encoding":904},[123,68940,66847,68941,68993],{},[883,68942,68944],{"className":68943},[886],[888,68945,68946],{"xmlns":890},[892,68947,68948,68990],{},[895,68949,68950,68956,68958,68960,68962,68964,68970,68972,68974,68976,68978,68980,68982,68988],{},[2597,68951,68952,68954],{},[898,68953,2132],{},[1655,68955,5603],{},[1655,68957,1657],{},[898,68959,2127],{},[898,68961,4052],{},[1655,68963,1664],{"stretchy":1663},[2597,68965,68966,68968],{},[898,68967,1824],{},[1655,68969,5603],{},[1655,68971,1677],{"stretchy":1663},[1655,68973,1657],{},[898,68975,2731],{},[898,68977,41465],{},[898,68979,4052],{},[1655,68981,1664],{"stretchy":1663},[2597,68983,68984,68986],{},[898,68985,1824],{},[1655,68987,5603],{},[1655,68989,1677],{"stretchy":1663},[902,68991,68992],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,68995,68996,68997,7720,69029,69051,69052,1719],{},"Zapište nabídku: ",[883,68998,69000],{"className":68999},[886],[888,69001,69002],{"xmlns":890},[892,69003,69004,69026],{},[895,69005,69006,69008,69010,69012,69014,69016,69018,69020,69022,69024],{},[898,69007,9920],{},[1655,69009,1664],{"stretchy":1663},[898,69011,1824],{},[1655,69013,1677],{"stretchy":1663},[1655,69015,1657],{},[898,69017,2127],{},[898,69019,4052],{},[1655,69021,1664],{"stretchy":1663},[898,69023,1824],{},[1655,69025,1677],{"stretchy":1663},[902,69027,69028],{"encoding":904},"S(Q) = MC(Q)",[883,69030,69032],{"className":69031},[886],[888,69033,69034],{"xmlns":890},[892,69035,69036,69048],{},[895,69037,69038,69040,69042],{},[898,69039,1824],{},[1655,69041,5734],{},[2597,69043,69044,69046],{},[898,69045,1824],{},[1655,69047,5603],{},[902,69049,69050],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,69053,69055],{"className":69054},[886],[888,69056,69057],{"xmlns":890},[892,69058,69059,69063],{},[895,69060,69061],{},[1826,69062,2552],{},[902,69064,2552],{"encoding":904},[123,69066,69067,69068,69100],{},"V případě potřeby vyjádřete inverzi ",[883,69069,69071],{"className":69070},[886],[888,69072,69073],{"xmlns":890},[892,69074,69075,69097],{},[895,69076,69077,69079,69081,69091,69093,69095],{},[898,69078,1824],{},[1655,69080,1657],{},[2597,69082,69083,69085],{},[898,69084,9920],{},[895,69086,69087,69089],{},[1655,69088,2623],{},[1826,69090,1828],{},[1655,69092,1664],{"stretchy":1663},[898,69094,2132],{},[1655,69096,1677],{"stretchy":1663},[902,69098,69099],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,69102,69103],{},[614,69104,69105,69106,1343,69121,2704,69138,30327,69153,69166,69167,69192,69193,69206,69207,69224,69225,69242,69243,69260],{},"Obrázek 3.14: Křivky ",[883,69107,69109],{"className":69108},[886],[888,69110,69111],{"xmlns":890},[892,69112,69113,69119],{},[895,69114,69115,69117],{},[898,69116,2731],{},[898,69118,4052],{},[902,69120,56686],{"encoding":904},[883,69122,69124],{"className":69123},[886],[888,69125,69126],{"xmlns":890},[892,69127,69128,69136],{},[895,69129,69130,69132,69134],{},[898,69131,2731],{},[898,69133,41465],{},[898,69135,4052],{},[902,69137,56437],{"encoding":904},[883,69139,69141],{"className":69140},[886],[888,69142,69143],{"xmlns":890},[892,69144,69145,69151],{},[895,69146,69147,69149],{},[898,69148,2127],{},[898,69150,4052],{},[902,69152,56418],{"encoding":904},[883,69154,69156],{"className":69155},[886],[888,69157,69158],{"xmlns":890},[892,69159,69160,69164],{},[895,69161,69162],{},[898,69163,900],{},[902,69165,900],{"encoding":904},"; křivka nabídky ",[883,69168,69170],{"className":69169},[886],[888,69171,69172],{"xmlns":890},[892,69173,69174,69190],{},[895,69175,69176,69178,69180,69182,69184,69186,69188],{},[898,69177,2132],{},[1655,69179,1657],{},[898,69181,2127],{},[898,69183,4052],{},[1655,69185,1664],{"stretchy":1663},[898,69187,1824],{},[1655,69189,1677],{"stretchy":1663},[902,69191,68492],{"encoding":904}," začíná v bodě ",[883,69194,69196],{"className":69195},[886],[888,69197,69198],{"xmlns":890},[892,69199,69200,69204],{},[895,69201,69202],{},[898,69203,2731],{},[902,69205,2731],{"encoding":904}," odpovídajícím minimu ",[883,69208,69210],{"className":69209},[886],[888,69211,69212],{"xmlns":890},[892,69213,69214,69222],{},[895,69215,69216,69218,69220],{},[898,69217,2731],{},[898,69219,41465],{},[898,69221,4052],{},[902,69223,56437],{"encoding":904}," při ceně ",[883,69226,69228],{"className":69227},[886],[888,69229,69230],{"xmlns":890},[892,69231,69232,69240],{},[895,69233,69234],{},[2597,69235,69236,69238],{},[898,69237,2132],{},[1655,69239,5603],{},[902,69241,5653],{"encoding":904}," (minimální cena nabídky); pod ",[883,69244,69246],{"className":69245},[886],[888,69247,69248],{"xmlns":890},[892,69249,69250,69258],{},[895,69251,69252],{},[2597,69253,69254,69256],{},[898,69255,1824],{},[1655,69257,5603],{},[902,69259,30970],{"encoding":904}," je nabídka nulová.",[38474,69262,69264],{"id":69263},"příklad-312","Příklad 3.12",[724,69266,69267,58648,69269,69315],{},[38,69268,57113],{},[883,69270,69272],{"className":69271},[886],[888,69273,69274],{"xmlns":890},[892,69275,69276,69312],{},[895,69277,69278,69280,69282,69284,69286,69292,69294,69296,69302,69304,69306,69308,69310],{},[898,69279,4049],{},[898,69281,4052],{},[1655,69283,1657],{},[1826,69285,4068],{},[2597,69287,69288,69290],{},[898,69289,1824],{},[1826,69291,3472],{},[1655,69293,2623],{},[1826,69295,1837],{},[2597,69297,69298,69300],{},[898,69299,1824],{},[1826,69301,1837],{},[1655,69303,2346],{},[1826,69305,37370],{},[898,69307,1824],{},[1655,69309,2346],{},[1826,69311,4136],{},[902,69313,69314],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,69317,69318,3106,69320,69357,69358,2086],{},[38,69319,23896],{},[883,69321,69323],{"className":69322},[886],[888,69324,69325],{"xmlns":890},[892,69326,69327,69354],{},[895,69328,69329,69331,69333,69335,69338,69344,69346,69348,69350,69352],{},[898,69330,2127],{},[898,69332,4052],{},[1655,69334,1657],{},[1826,69336,69337],{},"0,3",[2597,69339,69340,69342],{},[898,69341,1824],{},[1826,69343,1837],{},[1655,69345,2623],{},[1826,69347,3639],{},[898,69349,1824],{},[1655,69351,2346],{},[1826,69353,37370],{},[902,69355,69356],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,69359,69361],{"className":69360},[886],[888,69362,69363],{"xmlns":890},[892,69364,69365,69375],{},[895,69366,69367,69369,69371,69373],{},[898,69368,2132],{},[1655,69370,1657],{},[898,69372,2127],{},[898,69374,4052],{},[902,69376,69377],{"encoding":904},"P = MC",[883,69379,69381],{"className":69380},[886],[888,69382,69383],{"xmlns":890,"display":29192},[892,69384,69385,69410],{},[895,69386,69387,69389,69391,69393,69399,69401,69403,69405,69407],{},[898,69388,2132],{},[1655,69390,1657],{},[1826,69392,69337],{},[2597,69394,69395,69397],{},[898,69396,1824],{},[1826,69398,1837],{},[1655,69400,2623],{},[1826,69402,3639],{},[898,69404,1824],{},[1655,69406,2346],{},[1826,69408,69409],{},"15.",[902,69411,69412],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,69414,69415,69416,6631,69429,69442],{},"Vyjádření ",[883,69417,69419],{"className":69418},[886],[888,69420,69421],{"xmlns":890},[892,69422,69423,69427],{},[895,69424,69425],{},[898,69426,1824],{},[902,69428,1824],{"encoding":904},[883,69430,69432],{"className":69431},[886],[888,69433,69434],{"xmlns":890},[892,69435,69436,69440],{},[895,69437,69438],{},[898,69439,2132],{},[902,69441,2132],{"encoding":904}," doplněním na čtverec:",[883,69444,69446],{"className":69445},[886],[888,69447,69448],{"xmlns":890,"display":29192},[892,69449,69450,69540],{},[895,69451,69452,69454,69456,69458,69496,69498,69500,69522,69524,69538],{},[898,69453,2132],{},[1655,69455,1657],{},[1826,69457,69337],{},[895,69459,69460,69462,69484,69486,69494],{},[1655,69461,1664],{"fence":1670},[2597,69463,69464,69482],{},[895,69465,69466,69468,69470,69472,69480],{},[1655,69467,1664],{"fence":1670},[898,69469,1824],{},[1655,69471,2623],{},[3615,69473,69474],{"scriptlevel":2552,"displaystyle":1663},[1949,69475,69476,69478],{},[1826,69477,10282],{},[1826,69479,3472],{},[1655,69481,1677],{"fence":1670},[1826,69483,1837],{},[1655,69485,2346],{},[3615,69487,69488],{"scriptlevel":2552,"displaystyle":1663},[1949,69489,69490,69492],{},[1826,69491,4390],{},[1826,69493,5250],{},[1655,69495,1677],{"fence":1670},[1655,69497,1671],{"separator":1670},[1967,69499],{"width":1969},[2597,69501,69502,69520],{},[895,69503,69504,69506,69508,69510,69518],{},[1655,69505,1664],{"fence":1670},[898,69507,1824],{},[1655,69509,2623],{},[3615,69511,69512],{"scriptlevel":2552,"displaystyle":1663},[1949,69513,69514,69516],{},[1826,69515,10282],{},[1826,69517,3472],{},[1655,69519,1677],{"fence":1670},[1826,69521,1837],{},[1655,69523,1657],{},[1949,69525,69526,69536],{},[895,69527,69528,69530,69532,69534],{},[1826,69529,39145],{},[898,69531,2132],{},[1655,69533,2623],{},[1826,69535,4390],{},[1826,69537,5250],{},[1655,69539,1671],{"separator":1670},[902,69541,69542],{"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},",[883,69544,69546],{"className":69545},[886],[888,69547,69548],{"xmlns":890,"display":29192},[892,69549,69550,69582],{},[895,69551,69552,69554,69556,69562,69564,69580],{},[898,69553,1824],{},[1655,69555,1657],{},[1949,69557,69558,69560],{},[1826,69559,10282],{},[1826,69561,3472],{},[1655,69563,2346],{},[1949,69565,69566,69578],{},[9364,69567,69568],{},[895,69569,69570,69572,69574,69576],{},[1826,69571,39145],{},[898,69573,2132],{},[1655,69575,2623],{},[1826,69577,4390],{},[1826,69579,3472],{},[898,69581,1719],{"mathvariant":1943},[902,69583,69584],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,69586,68144,69587,1343,69625,1343,69673,69707,69708,1719],{},[883,69588,69590],{"className":69589},[886],[888,69591,69592],{"xmlns":890},[892,69593,69594,69622],{},[895,69595,69596,69598,69600,69602,69604,69606,69612,69614,69616,69618,69620],{},[898,69597,2731],{},[898,69599,41465],{},[898,69601,4052],{},[1655,69603,1657],{},[1826,69605,4068],{},[2597,69607,69608,69610],{},[898,69609,1824],{},[1826,69611,1837],{},[1655,69613,2623],{},[1826,69615,1837],{},[898,69617,1824],{},[1655,69619,2346],{},[1826,69621,37370],{},[902,69623,69624],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,69626,69628],{"className":69627},[886],[888,69629,69630],{"xmlns":890},[892,69631,69632,69670],{},[895,69633,69634,69636,69638,69644,69646,69648,69650,69652,69654,69656,69658,69660,69666,69668],{},[898,69635,2731],{},[898,69637,41465],{},[2597,69639,69640,69642],{},[898,69641,4052],{},[1655,69643,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,69645,1657],{},[1826,69647,4112],{},[898,69649,1824],{},[1655,69651,2623],{},[1826,69653,1837],{},[1655,69655,1657],{},[1826,69657,2552],{},[1655,69659,5238],{},[2597,69661,69662,69664],{},[898,69663,1824],{},[1655,69665,5603],{},[1655,69667,1657],{},[1826,69669,4136],{},[902,69671,69672],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,69674,69676],{"className":69675},[886],[888,69677,69678],{"xmlns":890},[892,69679,69680,69704],{},[895,69681,69682,69684,69686,69696,69698,69700,69702],{},[898,69683,2731],{},[898,69685,41465],{},[2597,69687,69688,69690],{},[898,69689,4052],{},[895,69691,69692,69694],{},[1655,69693,1945],{"mathvariant":1943},[1655,69695,1945],{"mathvariant":1943},[1655,69697,1657],{},[1826,69699,4112],{},[1655,69701,2969],{},[1826,69703,2552],{},[902,69705,69706],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,69709,69711],{"className":69710},[886],[888,69712,69713],{"xmlns":890},[892,69714,69715,69751],{},[895,69716,69717,69723,69725,69727,69729,69731,69733,69735,69737,69739,69741,69743,69745,69747,69749],{},[2597,69718,69719,69721],{},[898,69720,2132],{},[1655,69722,5603],{},[1655,69724,1657],{},[898,69726,2127],{},[898,69728,4052],{},[1655,69730,1664],{"stretchy":1663},[1826,69732,4136],{},[1655,69734,1677],{"stretchy":1663},[1655,69736,1657],{},[1826,69738,39145],{},[1655,69740,2623],{},[1826,69742,6460],{},[1655,69744,2346],{},[1826,69746,37370],{},[1655,69748,1657],{},[1826,69750,3524],{},[902,69752,69753],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,69755,69756],{},[38,69757,69758],{},"Závěr.",[883,69760,69762],{"className":69761},[886],[888,69763,69764],{"xmlns":890,"display":29192},[892,69765,69766,69852],{},[895,69767,69768,69770,69772,69774,69776,69778,69780,69782],{},[898,69769,2132],{},[1655,69771,1657],{},[898,69773,9920],{},[1655,69775,1664],{"stretchy":1663},[898,69777,1824],{},[1655,69779,1677],{"stretchy":1663},[1655,69781,1657],{},[895,69783,69784,69786],{},[1655,69785,68632],{"fence":1670},[21880,69787,69788,69830],{"rowspacing":68635,"columnalign":68636,"columnspacing":16409},[21885,69789,69790,69814],{},[21888,69791,69792],{},[3615,69793,69794],{"scriptlevel":2552,"displaystyle":1663},[895,69795,69796,69798,69804,69806,69808,69810,69812],{},[1826,69797,69337],{},[2597,69799,69800,69802],{},[898,69801,1824],{},[1826,69803,1837],{},[1655,69805,2623],{},[1826,69807,3639],{},[898,69809,1824],{},[1655,69811,2346],{},[1826,69813,37370],{},[21888,69815,69816],{},[3615,69817,69818],{"scriptlevel":2552,"displaystyle":1663},[895,69819,69820,69822,69824,69826,69828],{},[2031,69821,68663],{},[898,69823,1824],{},[1655,69825,5734],{},[1826,69827,4136],{},[1655,69829,1671],{"separator":1670},[21885,69831,69832,69838],{},[21888,69833,69834],{},[3615,69835,69836],{"scriptlevel":2552,"displaystyle":1663},[1826,69837,2552],{},[21888,69839,69840],{},[3615,69841,69842],{"scriptlevel":2552,"displaystyle":1663},[895,69843,69844,69846,69848,69850],{},[2031,69845,68663],{},[898,69847,1824],{},[1655,69849,3065],{},[1826,69851,20454],{},[902,69853,69854],{"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}",[724,69856,69857],{},[614,69858,69859,69860,69875,69876,1719],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,69861,69863],{"className":69862},[886],[888,69864,69865],{"xmlns":890},[892,69866,69867,69873],{},[895,69868,69869,69871],{},[898,69870,2127],{},[898,69872,4052],{},[902,69874,56418],{"encoding":904}," ležící nad minimem ",[883,69877,69879],{"className":69878},[886],[888,69880,69881],{"xmlns":890},[892,69882,69883,69891],{},[895,69884,69885,69887,69889],{},[898,69886,2731],{},[898,69888,41465],{},[898,69890,4052],{},[902,69892,56437],{"encoding":904},[115,69894,69896],{"id":69895},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,69898,69899,69900,69904,69905,69920,69921,69941,69942,2704,69945,69948,69949,69951,69952,21071,69974,69976,69977,2704,69979,59852,69982,3106,69985,42940,70000,70015],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,69901,69903],{"className":69902,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,69906,69908],{"className":69907},[886],[888,69909,69910],{"xmlns":890},[892,69911,69912,69918],{},[895,69913,69914,69916],{},[898,69915,4049],{},[898,69917,5245],{},[902,69919,5345],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,69922,69924],{"className":69923},[886],[888,69925,69926],{"xmlns":890},[892,69927,69928,69938],{},[895,69929,69930,69932,69934,69936],{},[898,69931,4049],{},[898,69933,5245],{},[898,69935,5923],{"mathvariant":1943},[898,69937,1824],{},[902,69939,69940],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,69943,69944],{},"fixních",[38,69946,69947],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,69950,65451],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,69953,69955],{"className":69954},[886],[888,69956,69957],{"xmlns":890},[892,69958,69959,69971],{},[895,69960,69961,69963,69965,69967,69969],{},[898,69962,4049],{},[898,69964,5245],{},[1655,69966,2623],{},[898,69968,4049],{},[898,69970,4052],{},[902,69972,69973],{"encoding":904},"TR - TC",[38,69975,56298],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,69978,57610],{},[38,69980,69981],{},"mezní náklady",[207,69983,1145],{"className":69984,"dataFsResolvedFilePath":764,"href":765},[210],[883,69986,69988],{"className":69987},[886],[888,69989,69990],{"xmlns":890},[892,69991,69992,69998],{},[895,69993,69994,69996],{},[898,69995,4049],{},[898,69997,5245],{},[902,69999,5345],{"encoding":904},[883,70001,70003],{"className":70002},[886],[888,70004,70005],{"xmlns":890},[892,70006,70007,70013],{},[895,70008,70009,70011],{},[898,70010,4049],{},[898,70012,4052],{},[902,70014,4512],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,70017,70018,70080,70146,70208],{},[123,70019,70020,70023,70024,2494,70039,1719],{},[38,70021,70022],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,70025,70027],{"className":70026},[886],[888,70028,70029],{"xmlns":890},[892,70030,70031,70037],{},[895,70032,70033,70035],{},[898,70034,2731],{},[898,70036,4052],{},[902,70038,56686],{"encoding":904},[883,70040,70042],{"className":70041},[886],[888,70043,70044],{"xmlns":890},[892,70045,70046,70078],{},[895,70047,70048,70050,70052,70054,70060,70062,70064,70066,70068,70070,70076],{},[898,70049,2731],{},[898,70051,4052],{},[1655,70053,1664],{"stretchy":1663},[1820,70055,70056,70058],{},[898,70057,1824],{},[1826,70059,2552],{},[1655,70061,1677],{"stretchy":1663},[1655,70063,1657],{},[898,70065,2127],{},[898,70067,4052],{},[1655,70069,1664],{"stretchy":1663},[1820,70071,70072,70074],{},[898,70073,1824],{},[1826,70075,2552],{},[1655,70077,1677],{"stretchy":1663},[902,70079,63695],{"encoding":904},[123,70081,70082,70023,70085,2494,70102,1719],{},[38,70083,70084],{},"Princip minimalizace průměrných variabilních nákladů:",[883,70086,70088],{"className":70087},[886],[888,70089,70090],{"xmlns":890},[892,70091,70092,70100],{},[895,70093,70094,70096,70098],{},[898,70095,2731],{},[898,70097,41465],{},[898,70099,4052],{},[902,70101,56437],{"encoding":904},[883,70103,70105],{"className":70104},[886],[888,70106,70107],{"xmlns":890},[892,70108,70109,70143],{},[895,70110,70111,70113,70115,70117,70119,70125,70127,70129,70131,70133,70135,70141],{},[898,70112,2731],{},[898,70114,41465],{},[898,70116,4052],{},[1655,70118,1664],{"stretchy":1663},[1820,70120,70121,70123],{},[898,70122,1824],{},[1826,70124,2552],{},[1655,70126,1677],{"stretchy":1663},[1655,70128,1657],{},[898,70130,2127],{},[898,70132,4052],{},[1655,70134,1664],{"stretchy":1663},[1820,70136,70137,70139],{},[898,70138,1824],{},[1826,70140,2552],{},[1655,70142,1677],{"stretchy":1663},[902,70144,70145],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,70147,70148,70151,70152,2494,70167,1719],{},[38,70149,70150],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,70153,70155],{"className":70154},[886],[888,70156,70157],{"xmlns":890},[892,70158,70159,70165],{},[895,70160,70161,70163],{},[898,70162,2132],{},[898,70164,5245],{},[902,70166,64605],{"encoding":904},[883,70168,70170],{"className":70169},[886],[888,70171,70172],{"xmlns":890},[892,70173,70174,70206],{},[895,70175,70176,70178,70180,70182,70188,70190,70192,70194,70196,70198,70204],{},[898,70177,2127],{},[898,70179,5245],{},[1655,70181,1664],{"stretchy":1663},[1820,70183,70184,70186],{},[898,70185,1824],{},[1826,70187,2552],{},[1655,70189,1677],{"stretchy":1663},[1655,70191,1657],{},[898,70193,2127],{},[898,70195,4052],{},[1655,70197,1664],{"stretchy":1663},[1820,70199,70200,70202],{},[898,70201,1824],{},[1826,70203,2552],{},[1655,70205,1677],{"stretchy":1663},[902,70207,66771],{"encoding":904},[123,70209,70210,3106,70213,7720,70249,69051,70270,22720,70283,68733,70300,1719],{},[38,70211,70212],{},"Funkce nabídky firmy:",[883,70214,70216],{"className":70215},[886],[888,70217,70218],{"xmlns":890},[892,70219,70220,70246],{},[895,70221,70222,70224,70226,70228,70230,70232,70234,70236,70238,70240,70242,70244],{},[898,70223,2132],{},[1655,70225,1657],{},[898,70227,9920],{},[1655,70229,1664],{"stretchy":1663},[898,70231,1824],{},[1655,70233,1677],{"stretchy":1663},[1655,70235,1657],{},[898,70237,2127],{},[898,70239,4052],{},[1655,70241,1664],{"stretchy":1663},[898,70243,1824],{},[1655,70245,1677],{"stretchy":1663},[902,70247,70248],{"encoding":904},"P = S(Q) = MC(Q)",[883,70250,70252],{"className":70251},[886],[888,70253,70254],{"xmlns":890},[892,70255,70256,70268],{},[895,70257,70258,70260,70262],{},[898,70259,1824],{},[1655,70261,5734],{},[2597,70263,70264,70266],{},[898,70265,1824],{},[1655,70267,5603],{},[902,70269,69050],{"encoding":904},[883,70271,70273],{"className":70272},[886],[888,70274,70275],{"xmlns":890},[892,70276,70277,70281],{},[895,70278,70279],{},[1826,70280,2552],{},[902,70282,2552],{"encoding":904},[883,70284,70286],{"className":70285},[886],[888,70287,70288],{"xmlns":890},[892,70289,70290,70298],{},[895,70291,70292],{},[2597,70293,70294,70296],{},[898,70295,1824],{},[1655,70297,5603],{},[902,70299,30970],{"encoding":904},[883,70301,70303],{"className":70302},[886],[888,70304,70305],{"xmlns":890},[892,70306,70307,70315],{},[895,70308,70309,70311,70313],{},[898,70310,2731],{},[898,70312,41465],{},[898,70314,4052],{},[902,70316,56437],{"encoding":904},[115,70318,51008],{"id":51007},[152,70320,70321,70324,70327,70330,70333,70336,70339,70342,70345,70348,70351],{},[123,70322,70323],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,70325,70326],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,70328,70329],{},"Jak se vypočte mezní příjem a co udává?",[123,70331,70332],{},"Z jakých složek se skládají celkové náklady?",[123,70334,70335],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,70337,70338],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,70340,70341],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,70343,70344],{},"Jak se vypočte zisk?",[123,70346,70347],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,70349,70350],{},"Co jsou body zvratu? Jak se najdou?",[123,70352,70353],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,70355,70357],{"id":70356},"úlohy-31328","Úlohy 3.1–3.28",[198,70359,70361],{"id":70360},"příjem-3135","Příjem (3.1–3.5)",[724,70363,70364,46552,70367,70395,70396,70411,70412,70427,70428,70443,70444,1343,70459,1343,70474,70489],{},[38,70365,70366],{},"3.1",[883,70368,70370],{"className":70369},[886],[888,70371,70372],{"xmlns":890},[892,70373,70374,70392],{},[895,70375,70376,70378,70380,70382,70384,70386,70388,70390],{},[898,70377,2132],{},[1655,70379,1657],{},[898,70381,2838],{},[1655,70383,1664],{"stretchy":1663},[898,70385,1824],{},[1655,70387,1677],{"stretchy":1663},[1655,70389,1657],{},[1826,70391,4360],{},[902,70393,70394],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,70397,70399],{"className":70398},[886],[888,70400,70401],{"xmlns":890},[892,70402,70403,70409],{},[895,70404,70405,70407],{},[898,70406,4049],{},[898,70408,5245],{},[902,70410,5345],{"encoding":904},", průměrný příjem ",[883,70413,70415],{"className":70414},[886],[888,70416,70417],{"xmlns":890},[892,70418,70419,70425],{},[895,70420,70421,70423],{},[898,70422,2731],{},[898,70424,5245],{},[902,70426,56571],{"encoding":904}," a mezní příjem ",[883,70429,70431],{"className":70430},[886],[888,70432,70433],{"xmlns":890},[892,70434,70435,70441],{},[895,70436,70437,70439],{},[898,70438,2127],{},[898,70440,5245],{},[902,70442,7881],{"encoding":904},". (c) Vypočtěte ",[883,70445,70447],{"className":70446},[886],[888,70448,70449],{"xmlns":890},[892,70450,70451,70457],{},[895,70452,70453,70455],{},[898,70454,4049],{},[898,70456,5245],{},[902,70458,5345],{"encoding":904},[883,70460,70462],{"className":70461},[886],[888,70463,70464],{"xmlns":890},[892,70465,70466,70472],{},[895,70467,70468,70470],{},[898,70469,2731],{},[898,70471,5245],{},[902,70473,56571],{"encoding":904},[883,70475,70477],{"className":70476},[886],[888,70478,70479],{"xmlns":890},[892,70480,70481,70487],{},[895,70482,70483,70485],{},[898,70484,2127],{},[898,70486,5245],{},[902,70488,7881],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,70491,70492,46552,70495,70395,70531,70411,70546,70427,70561,70443,70576,1343,70591,1343,70606,70621],{},[38,70493,70494],{},"3.2",[883,70496,70498],{"className":70497},[886],[888,70499,70500],{"xmlns":890},[892,70501,70502,70528],{},[895,70503,70504,70506,70508,70510,70512,70514,70516,70518,70520,70522,70524,70526],{},[898,70505,2132],{},[1655,70507,1657],{},[898,70509,2838],{},[1655,70511,1664],{"stretchy":1663},[898,70513,1824],{},[1655,70515,1677],{"stretchy":1663},[1655,70517,1657],{},[1655,70519,2623],{},[1826,70521,6258],{},[898,70523,1824],{},[1655,70525,2346],{},[1826,70527,10282],{},[902,70529,70530],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,70532,70534],{"className":70533},[886],[888,70535,70536],{"xmlns":890},[892,70537,70538,70544],{},[895,70539,70540,70542],{},[898,70541,4049],{},[898,70543,5245],{},[902,70545,5345],{"encoding":904},[883,70547,70549],{"className":70548},[886],[888,70550,70551],{"xmlns":890},[892,70552,70553,70559],{},[895,70554,70555,70557],{},[898,70556,2731],{},[898,70558,5245],{},[902,70560,56571],{"encoding":904},[883,70562,70564],{"className":70563},[886],[888,70565,70566],{"xmlns":890},[892,70567,70568,70574],{},[895,70569,70570,70572],{},[898,70571,2127],{},[898,70573,5245],{},[902,70575,7881],{"encoding":904},[883,70577,70579],{"className":70578},[886],[888,70580,70581],{"xmlns":890},[892,70582,70583,70589],{},[895,70584,70585,70587],{},[898,70586,4049],{},[898,70588,5245],{},[902,70590,5345],{"encoding":904},[883,70592,70594],{"className":70593},[886],[888,70595,70596],{"xmlns":890},[892,70597,70598,70604],{},[895,70599,70600,70602],{},[898,70601,2731],{},[898,70603,5245],{},[902,70605,56571],{"encoding":904},[883,70607,70609],{"className":70608},[886],[888,70610,70611],{"xmlns":890},[892,70612,70613,70619],{},[895,70614,70615,70617],{},[898,70616,2127],{},[898,70618,5245],{},[902,70620,7881],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,70623,70624,46552,70627,70664,70665,70411,70680,70427,70695,70710,70711,7720,70726,70752,70753,70768,70769,1343,70784,7720,70799,70752,70824,70839,70840,70853,70854,70869,70870,70885,70886,1343,70899,1343,70914,1343,70929,1719],{},[38,70625,70626],{},"3.3",[883,70628,70630],{"className":70629},[886],[888,70631,70632],{"xmlns":890},[892,70633,70634,70661],{},[895,70635,70636,70638,70640,70642,70644,70646,70648,70650,70653,70655],{},[898,70637,2132],{},[1655,70639,1657],{},[898,70641,2838],{},[1655,70643,1664],{"stretchy":1663},[898,70645,1824],{},[1655,70647,1677],{"stretchy":1663},[1655,70649,1657],{},[1826,70651,70652],{},"1200",[1655,70654,2623],{},[2597,70656,70657,70659],{},[898,70658,1824],{},[1826,70660,1837],{},[902,70662,70663],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,70666,70668],{"className":70667},[886],[888,70669,70670],{"xmlns":890},[892,70671,70672,70678],{},[895,70673,70674,70676],{},[898,70675,4049],{},[898,70677,5245],{},[902,70679,5345],{"encoding":904},[883,70681,70683],{"className":70682},[886],[888,70684,70685],{"xmlns":890},[892,70686,70687,70693],{},[895,70688,70689,70691],{},[898,70690,2731],{},[898,70692,5245],{},[902,70694,56571],{"encoding":904},[883,70696,70698],{"className":70697},[886],[888,70699,70700],{"xmlns":890},[892,70701,70702,70708],{},[895,70703,70704,70706],{},[898,70705,2127],{},[898,70707,5245],{},[902,70709,7881],{"encoding":904},". (b) Vypočtěte ",[883,70712,70714],{"className":70713},[886],[888,70715,70716],{"xmlns":890},[892,70717,70718,70724],{},[895,70719,70720,70722],{},[898,70721,4049],{},[898,70723,5245],{},[902,70725,5345],{"encoding":904},[883,70727,70729],{"className":70728},[886],[888,70730,70731],{"xmlns":890},[892,70732,70733,70749],{},[895,70734,70735,70737,70739,70741,70743,70745,70747],{},[898,70736,1824],{},[1655,70738,1657],{},[1826,70740,4136],{},[1655,70742,1671],{"separator":1670},[1826,70744,10282],{},[1655,70746,1671],{"separator":1670},[1826,70748,39145],{},[902,70750,70751],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,70754,70756],{"className":70755},[886],[888,70757,70758],{"xmlns":890},[892,70759,70760,70766],{},[895,70761,70762,70764],{},[898,70763,4049],{},[898,70765,5245],{},[902,70767,5345],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,70770,70772],{"className":70771},[886],[888,70773,70774],{"xmlns":890},[892,70775,70776,70782],{},[895,70777,70778,70780],{},[898,70779,2731],{},[898,70781,5245],{},[902,70783,56571],{"encoding":904},[883,70785,70787],{"className":70786},[886],[888,70788,70789],{"xmlns":890},[892,70790,70791,70797],{},[895,70792,70793,70795],{},[898,70794,2127],{},[898,70796,5245],{},[902,70798,7881],{"encoding":904},[883,70800,70802],{"className":70801},[886],[888,70803,70804],{"xmlns":890},[892,70805,70806,70822],{},[895,70807,70808,70810,70812,70814,70816,70818,70820],{},[898,70809,1824],{},[1655,70811,1657],{},[1826,70813,4136],{},[1655,70815,1671],{"separator":1670},[1826,70817,10282],{},[1655,70819,1671],{"separator":1670},[1826,70821,39145],{},[902,70823,70751],{"encoding":904},[883,70825,70827],{"className":70826},[886],[888,70828,70829],{"xmlns":890},[892,70830,70831,70837],{},[895,70832,70833,70835],{},[898,70834,2127],{},[898,70836,5245],{},[902,70838,7881],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,70841,70843],{"className":70842},[886],[888,70844,70845],{"xmlns":890},[892,70846,70847,70851],{},[895,70848,70849],{},[898,70850,1824],{},[902,70852,1824],{"encoding":904},", které maximalizuje ",[883,70855,70857],{"className":70856},[886],[888,70858,70859],{"xmlns":890},[892,70860,70861,70867],{},[895,70862,70863,70865],{},[898,70864,4049],{},[898,70866,5245],{},[902,70868,5345],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,70871,70873],{"className":70872},[886],[888,70874,70875],{"xmlns":890},[892,70876,70877,70883],{},[895,70878,70879,70881],{},[898,70880,4049],{},[898,70882,5245],{},[902,70884,5345],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,70887,70889],{"className":70888},[886],[888,70890,70891],{"xmlns":890},[892,70892,70893,70897],{},[895,70894,70895],{},[898,70896,2838],{},[902,70898,2838],{"encoding":904},[883,70900,70902],{"className":70901},[886],[888,70903,70904],{"xmlns":890},[892,70905,70906,70912],{},[895,70907,70908,70910],{},[898,70909,4049],{},[898,70911,5245],{},[902,70913,5345],{"encoding":904},[883,70915,70917],{"className":70916},[886],[888,70918,70919],{"xmlns":890},[892,70920,70921,70927],{},[895,70922,70923,70925],{},[898,70924,2731],{},[898,70926,5245],{},[902,70928,56571],{"encoding":904},[883,70930,70932],{"className":70931},[886],[888,70933,70934],{"xmlns":890},[892,70935,70936,70942],{},[895,70937,70938,70940],{},[898,70939,2127],{},[898,70941,5245],{},[902,70943,7881],{"encoding":904},[724,70945,70946,70949,70950,70980,70981,70996,70997,2251,71010,1343,71028,1343,71045,71063,71064,71086,71087,71102,71103,71116,71117,1719],{},[38,70947,70948],{},"3.4"," Je dán celkový příjem ",[883,70951,70953],{"className":70952},[886],[888,70954,70955],{"xmlns":890},[892,70956,70957,70977],{},[895,70958,70959,70961,70963,70965,70967,70969,70971],{},[898,70960,4049],{},[898,70962,5245],{},[1655,70964,1657],{},[1826,70966,70652],{},[898,70968,1824],{},[1655,70970,2623],{},[2597,70972,70973,70975],{},[898,70974,1824],{},[1826,70976,3472],{},[902,70978,70979],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,70982,70984],{"className":70983},[886],[888,70985,70986],{"xmlns":890},[892,70987,70988,70994],{},[895,70989,70990,70992],{},[898,70991,4049],{},[898,70993,5245],{},[902,70995,5345],{"encoding":904}," vzhledem ke ",[883,70998,71000],{"className":70999},[886],[888,71001,71002],{"xmlns":890},[892,71003,71004,71008],{},[895,71005,71006],{},[898,71007,1824],{},[902,71009,1824],{"encoding":904},[883,71011,71013],{"className":71012},[886],[888,71014,71015],{"xmlns":890},[892,71016,71017,71025],{},[895,71018,71019,71021,71023],{},[898,71020,1824],{},[1655,71022,1657],{},[1826,71024,3524],{},[902,71026,71027],{"encoding":904},"Q = 5",[883,71029,71031],{"className":71030},[886],[888,71032,71033],{"xmlns":890},[892,71034,71035,71043],{},[895,71036,71037,71039,71041],{},[898,71038,1824],{},[1655,71040,1657],{},[1826,71042,6834],{},[902,71044,6837],{"encoding":904},[883,71046,71048],{"className":71047},[886],[888,71049,71050],{"xmlns":890},[892,71051,71052,71060],{},[895,71053,71054,71056,71058],{},[898,71055,1824],{},[1655,71057,1657],{},[1826,71059,4771],{},[902,71061,71062],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,71065,71067],{"className":71066},[886],[888,71068,71069],{"xmlns":890},[892,71070,71071,71083],{},[895,71072,71073,71075,71077,71079,71081],{},[898,71074,2127],{},[898,71076,5245],{},[1655,71078,1664],{"stretchy":1663},[1826,71080,4136],{},[1655,71082,1677],{"stretchy":1663},[902,71084,71085],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,71088,71090],{"className":71089},[886],[888,71091,71092],{"xmlns":890},[892,71093,71094,71100],{},[895,71095,71096,71098],{},[898,71097,4049],{},[898,71099,5245],{},[902,71101,5345],{"encoding":904},", jestliže se ",[883,71104,71106],{"className":71105},[886],[888,71107,71108],{"xmlns":890},[892,71109,71110,71114],{},[895,71111,71112],{},[898,71113,1824],{},[902,71115,1824],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,71118,71120],{"className":71119},[886],[888,71121,71122],{"xmlns":890},[892,71123,71124,71130],{},[895,71125,71126,71128],{},[898,71127,4049],{},[898,71129,5245],{},[902,71131,5345],{"encoding":904},[724,71133,71134,71137,71138,71164,71165,71180,71181,71102,71196,71209],{},[38,71135,71136],{},"3.5"," Je dán mezní příjem ",[883,71139,71141],{"className":71140},[886],[888,71142,71143],{"xmlns":890},[892,71144,71145,71161],{},[895,71146,71147,71149,71151,71153,71155,71157,71159],{},[898,71148,2127],{},[898,71150,5245],{},[1655,71152,1657],{},[1655,71154,2623],{},[898,71156,1824],{},[1655,71158,2346],{},[1826,71160,10282],{},[902,71162,71163],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,71166,71168],{"className":71167},[886],[888,71169,71170],{"xmlns":890},[892,71171,71172,71178],{},[895,71173,71174,71176],{},[898,71175,4049],{},[898,71177,5245],{},[902,71179,5345],{"encoding":904},". (b) Vypočtěte změnu ",[883,71182,71184],{"className":71183},[886],[888,71185,71186],{"xmlns":890},[892,71187,71188,71194],{},[895,71189,71190,71192],{},[898,71191,4049],{},[898,71193,5245],{},[902,71195,5345],{"encoding":904},[883,71197,71199],{"className":71198},[886],[888,71200,71201],{"xmlns":890},[892,71202,71203,71207],{},[895,71204,71205],{},[898,71206,1824],{},[902,71208,1824],{"encoding":904}," změní z 8 na 12.",[198,71211,71213],{"id":71212},"náklady-36316","Náklady (3.6–3.16)",[724,71215,71216,71219,71220,71260,71261,71276,71277,71294,71295,71312,71313,71328,71329,71344,71345,70710,71360,1343,71375,1343,71392,1343,71409,1343,71424,1343,71439,7720,71454,71472,71473,1343,71488,1343,71503,71518],{},[38,71217,71218],{},"3.6"," Jsou dány celkové náklady ",[883,71221,71223],{"className":71222},[886],[888,71224,71225],{"xmlns":890},[892,71226,71227,71257],{},[895,71228,71229,71231,71233,71235,71237,71239,71241,71243,71245],{},[898,71230,4049],{},[898,71232,4052],{},[1655,71234,1657],{},[1826,71236,4360],{},[1655,71238,2346],{},[1826,71240,1837],{},[898,71242,1824],{},[1655,71244,2346],{},[3615,71246,71247],{"scriptlevel":2552,"displaystyle":1663},[1949,71248,71249,71255],{},[2597,71250,71251,71253],{},[898,71252,1824],{},[1826,71254,1837],{},[1826,71256,4136],{},[902,71258,71259],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,71262,71264],{"className":71263},[886],[888,71265,71266],{"xmlns":890},[892,71267,71268,71274],{},[895,71269,71270,71272],{},[898,71271,2537],{},[898,71273,4052],{},[902,71275,56617],{"encoding":904},", celkové variabilní náklady ",[883,71278,71280],{"className":71279},[886],[888,71281,71282],{"xmlns":890},[892,71283,71284,71292],{},[895,71285,71286,71288,71290],{},[898,71287,4049],{},[898,71289,41465],{},[898,71291,4052],{},[902,71293,56635],{"encoding":904},", průměrné variabilní náklady ",[883,71296,71298],{"className":71297},[886],[888,71299,71300],{"xmlns":890},[892,71301,71302,71310],{},[895,71303,71304,71306,71308],{},[898,71305,2731],{},[898,71307,41465],{},[898,71309,4052],{},[902,71311,56437],{"encoding":904},", variabilní náklady na jednotku ",[883,71314,71316],{"className":71315},[886],[888,71317,71318],{"xmlns":890},[892,71319,71320,71326],{},[895,71321,71322,71324],{},[898,71323,41465],{},[898,71325,4052],{},[902,71327,64731],{"encoding":904},", průměrné náklady ",[883,71330,71332],{"className":71331},[886],[888,71333,71334],{"xmlns":890},[892,71335,71336,71342],{},[895,71337,71338,71340],{},[898,71339,2731],{},[898,71341,4052],{},[902,71343,56686],{"encoding":904}," a mezní náklady ",[883,71346,71348],{"className":71347},[886],[888,71349,71350],{"xmlns":890},[892,71351,71352,71358],{},[895,71353,71354,71356],{},[898,71355,2127],{},[898,71357,4052],{},[902,71359,56418],{"encoding":904},[883,71361,71363],{"className":71362},[886],[888,71364,71365],{"xmlns":890},[892,71366,71367,71373],{},[895,71368,71369,71371],{},[898,71370,4049],{},[898,71372,4052],{},[902,71374,4512],{"encoding":904},[883,71376,71378],{"className":71377},[886],[888,71379,71380],{"xmlns":890},[892,71381,71382,71390],{},[895,71383,71384,71386,71388],{},[898,71385,4049],{},[898,71387,41465],{},[898,71389,4052],{},[902,71391,56635],{"encoding":904},[883,71393,71395],{"className":71394},[886],[888,71396,71397],{"xmlns":890},[892,71398,71399,71407],{},[895,71400,71401,71403,71405],{},[898,71402,2731],{},[898,71404,41465],{},[898,71406,4052],{},[902,71408,56437],{"encoding":904},[883,71410,71412],{"className":71411},[886],[888,71413,71414],{"xmlns":890},[892,71415,71416,71422],{},[895,71417,71418,71420],{},[898,71419,41465],{},[898,71421,4052],{},[902,71423,64731],{"encoding":904},[883,71425,71427],{"className":71426},[886],[888,71428,71429],{"xmlns":890},[892,71430,71431,71437],{},[895,71432,71433,71435],{},[898,71434,2731],{},[898,71436,4052],{},[902,71438,56686],{"encoding":904},[883,71440,71442],{"className":71441},[886],[888,71443,71444],{"xmlns":890},[892,71445,71446,71452],{},[895,71447,71448,71450],{},[898,71449,2127],{},[898,71451,4052],{},[902,71453,56418],{"encoding":904},[883,71455,71457],{"className":71456},[886],[888,71458,71459],{"xmlns":890},[892,71460,71461,71469],{},[895,71462,71463,71465,71467],{},[898,71464,1824],{},[1655,71466,1657],{},[1826,71468,4390],{},[902,71470,71471],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,71474,71476],{"className":71475},[886],[888,71477,71478],{"xmlns":890},[892,71479,71480,71486],{},[895,71481,71482,71484],{},[898,71483,4049],{},[898,71485,4052],{},[902,71487,4512],{"encoding":904},[883,71489,71491],{"className":71490},[886],[888,71492,71493],{"xmlns":890},[892,71494,71495,71501],{},[895,71496,71497,71499],{},[898,71498,2731],{},[898,71500,4052],{},[902,71502,56686],{"encoding":904},[883,71504,71506],{"className":71505},[886],[888,71507,71508],{"xmlns":890},[892,71509,71510,71516],{},[895,71511,71512,71514],{},[898,71513,2127],{},[898,71515,4052],{},[902,71517,56418],{"encoding":904}," rostou, resp. klesají.",[724,71520,71521,71524,71525,71344,71555,71570,71571,71586,71587,1343,71602,1343,71617,1719],{},[38,71522,71523],{},"3.7"," Jsou dány průměrné náklady ",[883,71526,71528],{"className":71527},[886],[888,71529,71530],{"xmlns":890},[892,71531,71532,71552],{},[895,71533,71534,71536,71538,71540,71548,71550],{},[898,71535,2731],{},[898,71537,4052],{},[1655,71539,1657],{},[3615,71541,71542],{"scriptlevel":2552,"displaystyle":1663},[1949,71543,71544,71546],{},[1826,71545,4360],{},[898,71547,1824],{},[1655,71549,2346],{},[1826,71551,10282],{},[902,71553,71554],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,71556,71558],{"className":71557},[886],[888,71559,71560],{"xmlns":890},[892,71561,71562,71568],{},[895,71563,71564,71566],{},[898,71565,2127],{},[898,71567,4052],{},[902,71569,56418],{"encoding":904},". (a) Určete celkové náklady ",[883,71572,71574],{"className":71573},[886],[888,71575,71576],{"xmlns":890},[892,71577,71578,71584],{},[895,71579,71580,71582],{},[898,71581,4049],{},[898,71583,4052],{},[902,71585,4512],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,71588,71590],{"className":71589},[886],[888,71591,71592],{"xmlns":890},[892,71593,71594,71600],{},[895,71595,71596,71598],{},[898,71597,2731],{},[898,71599,4052],{},[902,71601,56686],{"encoding":904},[883,71603,71605],{"className":71604},[886],[888,71606,71607],{"xmlns":890},[892,71608,71609,71615],{},[895,71610,71611,71613],{},[898,71612,4049],{},[898,71614,4052],{},[902,71616,4512],{"encoding":904},[883,71618,71620],{"className":71619},[886],[888,71621,71622],{"xmlns":890},[892,71623,71624,71630],{},[895,71625,71626,71628],{},[898,71627,2127],{},[898,71629,4052],{},[902,71631,56418],{"encoding":904},[724,71633,71634,71219,71637,71681,71682,1343,71699,1343,71714,1343,71731,1343,71746,1343,71763,1719],{},[38,71635,71636],{},"3.8",[883,71638,71640],{"className":71639},[886],[888,71641,71642],{"xmlns":890},[892,71643,71644,71678],{},[895,71645,71646,71648,71650,71652,71654,71656,71658,71660,71662,71664,71670,71672],{},[898,71647,4049],{},[898,71649,4052],{},[1655,71651,1657],{},[1826,71653,47829],{},[1655,71655,2346],{},[1826,71657,39145],{},[898,71659,1824],{},[1655,71661,2623],{},[1826,71663,3531],{},[2597,71665,71666,71668],{},[898,71667,1824],{},[1826,71669,1837],{},[1655,71671,2346],{},[2597,71673,71674,71676],{},[898,71675,1824],{},[1826,71677,3472],{},[902,71679,71680],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,71683,71685],{"className":71684},[886],[888,71686,71687],{"xmlns":890},[892,71688,71689,71697],{},[895,71690,71691,71693,71695],{},[898,71692,4049],{},[898,71694,41465],{},[898,71696,4052],{},[902,71698,56635],{"encoding":904},[883,71700,71702],{"className":71701},[886],[888,71703,71704],{"xmlns":890},[892,71705,71706,71712],{},[895,71707,71708,71710],{},[898,71709,2537],{},[898,71711,4052],{},[902,71713,56617],{"encoding":904},[883,71715,71717],{"className":71716},[886],[888,71718,71719],{"xmlns":890},[892,71720,71721,71729],{},[895,71722,71723,71725,71727],{},[898,71724,2731],{},[898,71726,41465],{},[898,71728,4052],{},[902,71730,56437],{"encoding":904},[883,71732,71734],{"className":71733},[886],[888,71735,71736],{"xmlns":890},[892,71737,71738,71744],{},[895,71739,71740,71742],{},[898,71741,2731],{},[898,71743,4052],{},[902,71745,56686],{"encoding":904},[883,71747,71749],{"className":71748},[886],[888,71750,71751],{"xmlns":890},[892,71752,71753,71761],{},[895,71754,71755,71757,71759],{},[898,71756,2731],{},[898,71758,2537],{},[898,71760,4052],{},[902,71762,56653],{"encoding":904},[883,71764,71766],{"className":71765},[886],[888,71767,71768],{"xmlns":890},[892,71769,71770,71776],{},[895,71771,71772,71774],{},[898,71773,2127],{},[898,71775,4052],{},[902,71777,56418],{"encoding":904},[724,71779,71780,71219,71783,71813,71814,70996,71829,7720,71842,1343,71860,1343,71878,71063,71896,71086,71918,71933,71934,71947,71948,1719],{},[38,71781,71782],{},"3.9",[883,71784,71786],{"className":71785},[886],[888,71787,71788],{"xmlns":890},[892,71789,71790,71810],{},[895,71791,71792,71794,71796,71798,71800,71802,71804],{},[898,71793,4049],{},[898,71795,4052],{},[1655,71797,1657],{},[1826,71799,16235],{},[1655,71801,2346],{},[1826,71803,20447],{},[2597,71805,71806,71808],{},[898,71807,1824],{},[1826,71809,1837],{},[902,71811,71812],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,71815,71817],{"className":71816},[886],[888,71818,71819],{"xmlns":890},[892,71820,71821,71827],{},[895,71822,71823,71825],{},[898,71824,4049],{},[898,71826,4052],{},[902,71828,4512],{"encoding":904},[883,71830,71832],{"className":71831},[886],[888,71833,71834],{"xmlns":890},[892,71835,71836,71840],{},[895,71837,71838],{},[898,71839,1824],{},[902,71841,1824],{"encoding":904},[883,71843,71845],{"className":71844},[886],[888,71846,71847],{"xmlns":890},[892,71848,71849,71857],{},[895,71850,71851,71853,71855],{},[898,71852,1824],{},[1655,71854,1657],{},[1826,71856,4136],{},[902,71858,71859],{"encoding":904},"Q = 10",[883,71861,71863],{"className":71862},[886],[888,71864,71865],{"xmlns":890},[892,71866,71867,71875],{},[895,71868,71869,71871,71873],{},[898,71870,1824],{},[1655,71872,1657],{},[1826,71874,10282],{},[902,71876,71877],{"encoding":904},"Q = 20",[883,71879,71881],{"className":71880},[886],[888,71882,71883],{"xmlns":890},[892,71884,71885,71893],{},[895,71886,71887,71889,71891],{},[898,71888,1824],{},[1655,71890,1657],{},[1826,71892,39145],{},[902,71894,71895],{"encoding":904},"Q = 30",[883,71897,71899],{"className":71898},[886],[888,71900,71901],{"xmlns":890},[892,71902,71903,71915],{},[895,71904,71905,71907,71909,71911,71913],{},[898,71906,2127],{},[898,71908,4052],{},[1655,71910,1664],{"stretchy":1663},[1826,71912,37370],{},[1655,71914,1677],{"stretchy":1663},[902,71916,71917],{"encoding":904},"MC(15)",[883,71919,71921],{"className":71920},[886],[888,71922,71923],{"xmlns":890},[892,71924,71925,71931],{},[895,71926,71927,71929],{},[898,71928,4049],{},[898,71930,4052],{},[902,71932,4512],{"encoding":904}," v důsledku změny ",[883,71935,71937],{"className":71936},[886],[888,71938,71939],{"xmlns":890},[892,71940,71941,71945],{},[895,71942,71943],{},[898,71944,1824],{},[902,71946,1824],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,71949,71951],{"className":71950},[886],[888,71952,71953],{"xmlns":890},[892,71954,71955,71961],{},[895,71956,71957,71959],{},[898,71958,4049],{},[898,71960,4052],{},[902,71962,4512],{"encoding":904},[724,71964,71965,71968,71969,71570,72005,72020,72021,71180,72040,71933,72055,72068],{},[38,71966,71967],{},"3.10"," Jsou dány mezní náklady ",[883,71970,71972],{"className":71971},[886],[888,71973,71974],{"xmlns":890},[892,71975,71976,72002],{},[895,71977,71978,71980,71982,71984,71986,71988,71990,71992,71994,71996],{},[898,71979,2127],{},[898,71981,4052],{},[1655,71983,1657],{},[1826,71985,4396],{},[1655,71987,2623],{},[1826,71989,42988],{},[898,71991,1824],{},[1655,71993,2346],{},[1826,71995,65685],{},[2597,71997,71998,72000],{},[898,71999,1824],{},[1826,72001,1837],{},[902,72003,72004],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,72006,72008],{"className":72007},[886],[888,72009,72010],{"xmlns":890},[892,72011,72012,72018],{},[895,72013,72014,72016],{},[898,72015,4049],{},[898,72017,4052],{},[902,72019,4512],{"encoding":904},", jestliže fixní náklady ",[883,72022,72024],{"className":72023},[886],[888,72025,72026],{"xmlns":890},[892,72027,72028,72038],{},[895,72029,72030,72032,72034,72036],{},[898,72031,2537],{},[898,72033,4052],{},[1655,72035,1657],{},[1826,72037,4360],{},[902,72039,12757],{"encoding":904},[883,72041,72043],{"className":72042},[886],[888,72044,72045],{"xmlns":890},[892,72046,72047,72053],{},[895,72048,72049,72051],{},[898,72050,4049],{},[898,72052,4052],{},[902,72054,4512],{"encoding":904},[883,72056,72058],{"className":72057},[886],[888,72059,72060],{"xmlns":890},[892,72061,72062,72066],{},[895,72063,72064],{},[898,72065,1824],{},[902,72067,1824],{"encoding":904}," z 15 na 20.",[724,72070,72071,71219,72074,72117,72118,72131,72132,72147,72148,72163,72164,72131,72177,72147,72194,72211,72212,72131,72225,72147,72240,72255,72256,72276,72277,72300],{},[38,72072,72073],{},"3.11",[883,72075,72077],{"className":72076},[886],[888,72078,72079],{"xmlns":890},[892,72080,72081,72115],{},[895,72082,72083,72085,72087,72089,72091,72093,72095,72097,72099,72101,72107,72109],{},[898,72084,4049],{},[898,72086,4052],{},[1655,72088,1657],{},[1826,72090,4360],{},[1655,72092,2346],{},[1826,72094,6253],{},[898,72096,1824],{},[1655,72098,2623],{},[1826,72100,3524],{},[2597,72102,72103,72105],{},[898,72104,1824],{},[1826,72106,1837],{},[1655,72108,2346],{},[2597,72110,72111,72113],{},[898,72112,1824],{},[1826,72114,3472],{},[902,72116,62033],{"encoding":904},". (a) Určete ",[883,72119,72121],{"className":72120},[886],[888,72122,72123],{"xmlns":890},[892,72124,72125,72129],{},[895,72126,72127],{},[898,72128,1824],{},[902,72130,1824],{"encoding":904},", které minimalizuje ",[883,72133,72135],{"className":72134},[886],[888,72136,72137],{"xmlns":890},[892,72138,72139,72145],{},[895,72140,72141,72143],{},[898,72142,2127],{},[898,72144,4052],{},[902,72146,56418],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,72149,72151],{"className":72150},[886],[888,72152,72153],{"xmlns":890},[892,72154,72155,72161],{},[895,72156,72157,72159],{},[898,72158,2127],{},[898,72160,4052],{},[902,72162,56418],{"encoding":904},". (b) Určete ",[883,72165,72167],{"className":72166},[886],[888,72168,72169],{"xmlns":890},[892,72170,72171,72175],{},[895,72172,72173],{},[898,72174,1824],{},[902,72176,1824],{"encoding":904},[883,72178,72180],{"className":72179},[886],[888,72181,72182],{"xmlns":890},[892,72183,72184,72192],{},[895,72185,72186,72188,72190],{},[898,72187,2731],{},[898,72189,41465],{},[898,72191,4052],{},[902,72193,56437],{"encoding":904},[883,72195,72197],{"className":72196},[886],[888,72198,72199],{"xmlns":890},[892,72200,72201,72209],{},[895,72202,72203,72205,72207],{},[898,72204,2731],{},[898,72206,41465],{},[898,72208,4052],{},[902,72210,56437],{"encoding":904},". (c) Určete ",[883,72213,72215],{"className":72214},[886],[888,72216,72217],{"xmlns":890},[892,72218,72219,72223],{},[895,72220,72221],{},[898,72222,1824],{},[902,72224,1824],{"encoding":904},[883,72226,72228],{"className":72227},[886],[888,72229,72230],{"xmlns":890},[892,72231,72232,72238],{},[895,72233,72234,72236],{},[898,72235,2731],{},[898,72237,4052],{},[902,72239,56686],{"encoding":904},[883,72241,72243],{"className":72242},[886],[888,72244,72245],{"xmlns":890},[892,72246,72247,72253],{},[895,72248,72249,72251],{},[898,72250,2731],{},[898,72252,4052],{},[902,72254,56686],{"encoding":904}," (rada: hledaný kořen ",[883,72257,72259],{"className":72258},[886],[888,72260,72261],{"xmlns":890},[892,72262,72263,72273],{},[895,72264,72265,72267],{},[898,72266,2731],{},[2597,72268,72269,72271],{},[898,72270,4052],{},[1655,72272,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,72274,72275],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,72278,72280],{"className":72279},[886],[888,72281,72282],{"xmlns":890},[892,72283,72284,72297],{},[895,72285,72286,72288,72291,72293,72295],{},[1655,72287,1664],{"stretchy":1663},[1826,72289,72290],{},"4,7",[1655,72292,9672],{"separator":1670},[1826,72294,6528],{},[1655,72296,1677],{"stretchy":1663},[902,72298,72299],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,72302,72303,72306,72307,3902,72335,72352,72353,22720,72394,72415],{},[38,72304,72305],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,72308,72310],{"className":72309},[886],[888,72311,72312],{"xmlns":890},[892,72313,72314,72332],{},[895,72315,72316,72318,72320,72322,72324,72326,72328,72330],{},[898,72317,2731],{},[898,72319,4052],{},[1655,72321,1657],{},[898,72323,2731],{},[898,72325,4052],{},[1655,72327,1664],{"stretchy":1663},[898,72329,1824],{},[1655,72331,1677],{"stretchy":1663},[902,72333,72334],{"encoding":904},"AC = AC(Q)",[883,72336,72338],{"className":72337},[886],[888,72339,72340],{"xmlns":890},[892,72341,72342,72350],{},[895,72343,72344],{},[1820,72345,72346,72348],{},[898,72347,1824],{},[1826,72349,2552],{},[902,72351,39434],{"encoding":904}," minimum, pak platí ",[883,72354,72356],{"className":72355},[886],[888,72357,72358],{"xmlns":890},[892,72359,72360,72392],{},[895,72361,72362,72364,72366,72368,72374,72376,72378,72380,72382,72384,72390],{},[898,72363,2731],{},[898,72365,4052],{},[1655,72367,1664],{"stretchy":1663},[1820,72369,72370,72372],{},[898,72371,1824],{},[1826,72373,2552],{},[1655,72375,1677],{"stretchy":1663},[1655,72377,1657],{},[898,72379,2127],{},[898,72381,4052],{},[1655,72383,1664],{"stretchy":1663},[1820,72385,72386,72388],{},[898,72387,1824],{},[1826,72389,2552],{},[1655,72391,1677],{"stretchy":1663},[902,72393,63695],{"encoding":904},[883,72395,72397],{"className":72396},[886],[888,72398,72399],{"xmlns":890},[892,72400,72401,72413],{},[895,72402,72403,72405,72407,72409,72411],{},[898,72404,2127],{},[898,72406,4052],{},[1655,72408,1664],{"stretchy":1663},[898,72410,1824],{},[1655,72412,1677],{"stretchy":1663},[902,72414,68819],{"encoding":904}," jsou mezní náklady.",[724,72417,72418,71219,72421,71681,72455,72131,72468,72147,72483,1719],{},[38,72419,72420],{},"3.13",[883,72422,72424],{"className":72423},[886],[888,72425,72426],{"xmlns":890},[892,72427,72428,72452],{},[895,72429,72430,72432,72434,72436,72442,72444,72446,72448,72450],{},[898,72431,4049],{},[898,72433,4052],{},[1655,72435,1657],{},[2597,72437,72438,72440],{},[898,72439,1824],{},[1826,72441,1837],{},[1655,72443,2346],{},[1826,72445,1837],{},[898,72447,1824],{},[1655,72449,2346],{},[1826,72451,6253],{},[902,72453,72454],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,72456,72458],{"className":72457},[886],[888,72459,72460],{"xmlns":890},[892,72461,72462,72466],{},[895,72463,72464],{},[898,72465,1824],{},[902,72467,1824],{"encoding":904},[883,72469,72471],{"className":72470},[886],[888,72472,72473],{"xmlns":890},[892,72474,72475,72481],{},[895,72476,72477,72479],{},[898,72478,2731],{},[898,72480,4052],{},[902,72482,56686],{"encoding":904},[883,72484,72486],{"className":72485},[886],[888,72487,72488],{"xmlns":890},[892,72489,72490,72496],{},[895,72491,72492,72494],{},[898,72493,2731],{},[898,72495,4052],{},[902,72497,56686],{"encoding":904},[724,72499,72500,72503,72504,3902,72536,72352,72553,22720,72596,72415],{},[38,72501,72502],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,72505,72507],{"className":72506},[886],[888,72508,72509],{"xmlns":890},[892,72510,72511,72533],{},[895,72512,72513,72515,72517,72519,72521,72523,72525,72527,72529,72531],{},[898,72514,2731],{},[898,72516,41465],{},[898,72518,4052],{},[1655,72520,1657],{},[898,72522,2731],{},[898,72524,41465],{},[898,72526,4052],{},[1655,72528,1664],{"stretchy":1663},[898,72530,1824],{},[1655,72532,1677],{"stretchy":1663},[902,72534,72535],{"encoding":904},"AVC = AVC(Q)",[883,72537,72539],{"className":72538},[886],[888,72540,72541],{"xmlns":890},[892,72542,72543,72551],{},[895,72544,72545],{},[1820,72546,72547,72549],{},[898,72548,1824],{},[1826,72550,2552],{},[902,72552,39434],{"encoding":904},[883,72554,72556],{"className":72555},[886],[888,72557,72558],{"xmlns":890},[892,72559,72560,72594],{},[895,72561,72562,72564,72566,72568,72570,72576,72578,72580,72582,72584,72586,72592],{},[898,72563,2731],{},[898,72565,41465],{},[898,72567,4052],{},[1655,72569,1664],{"stretchy":1663},[1820,72571,72572,72574],{},[898,72573,1824],{},[1826,72575,2552],{},[1655,72577,1677],{"stretchy":1663},[1655,72579,1657],{},[898,72581,2127],{},[898,72583,4052],{},[1655,72585,1664],{"stretchy":1663},[1820,72587,72588,72590],{},[898,72589,1824],{},[1826,72591,2552],{},[1655,72593,1677],{"stretchy":1663},[902,72595,70145],{"encoding":904},[883,72597,72599],{"className":72598},[886],[888,72600,72601],{"xmlns":890},[892,72602,72603,72615],{},[895,72604,72605,72607,72609,72611,72613],{},[898,72606,2127],{},[898,72608,4052],{},[1655,72610,1664],{"stretchy":1663},[898,72612,1824],{},[1655,72614,1677],{"stretchy":1663},[902,72616,68819],{"encoding":904},[724,72618,72619,71219,72622,71681,72668,72131,72681,72147,72698,1719],{},[38,72620,72621],{},"3.15",[883,72623,72625],{"className":72624},[886],[888,72626,72627],{"xmlns":890},[892,72628,72629,72665],{},[895,72630,72631,72633,72635,72637,72639,72641,72643,72645,72647,72649,72655,72657,72659],{},[898,72632,4049],{},[898,72634,4052],{},[1655,72636,1657],{},[1826,72638,4390],{},[1655,72640,2346],{},[1826,72642,37370],{},[898,72644,1824],{},[1655,72646,2623],{},[1826,72648,1837],{},[2597,72650,72651,72653],{},[898,72652,1824],{},[1826,72654,1837],{},[1655,72656,2346],{},[1826,72658,4112],{},[2597,72660,72661,72663],{},[898,72662,1824],{},[1826,72664,3472],{},[902,72666,72667],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,72669,72671],{"className":72670},[886],[888,72672,72673],{"xmlns":890},[892,72674,72675,72679],{},[895,72676,72677],{},[898,72678,1824],{},[902,72680,1824],{"encoding":904},[883,72682,72684],{"className":72683},[886],[888,72685,72686],{"xmlns":890},[892,72687,72688,72696],{},[895,72689,72690,72692,72694],{},[898,72691,2731],{},[898,72693,41465],{},[898,72695,4052],{},[902,72697,56437],{"encoding":904},[883,72699,72701],{"className":72700},[886],[888,72702,72703],{"xmlns":890},[892,72704,72705,72713],{},[895,72706,72707,72709,72711],{},[898,72708,2731],{},[898,72710,41465],{},[898,72712,4052],{},[902,72714,56437],{"encoding":904},[724,72716,72717,72720,72721,72734,72735,72755],{},[38,72718,72719],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,72722,72724],{"className":72723},[886],[888,72725,72726],{"xmlns":890},[892,72727,72728,72732],{},[895,72729,72730],{},[898,72731,1667],{},[902,72733,1667],{"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 ",[883,72736,72738],{"className":72737},[886],[888,72739,72740],{"xmlns":890},[892,72741,72742,72752],{},[895,72743,72744,72746,72748,72750],{},[1826,72745,4136],{},[2031,72747,2435],{},[1826,72749,60208],{},[898,72751,1667],{},[902,72753,72754],{"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.",[198,72757,72759],{"id":72758},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,72761,72762,72765,72766,2704,72788,72814],{},[38,72763,72764],{},"3.17"," Jsou dány ",[883,72767,72769],{"className":72768},[886],[888,72770,72771],{"xmlns":890},[892,72772,72773,72785],{},[895,72774,72775,72777,72779,72781,72783],{},[898,72776,4049],{},[898,72778,5245],{},[1655,72780,1657],{},[1826,72782,4136],{},[898,72784,1824],{},[902,72786,72787],{"encoding":904},"TR = 10Q",[883,72789,72791],{"className":72790},[886],[888,72792,72793],{"xmlns":890},[892,72794,72795,72811],{},[895,72796,72797,72799,72801,72803,72805,72807,72809],{},[898,72798,4049],{},[898,72800,4052],{},[1655,72802,1657],{},[1826,72804,4360],{},[1655,72806,2346],{},[1826,72808,3524],{},[898,72810,1824],{},[902,72812,72813],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,72816,72817,72820,72821,7437,72836,72851,72852,1343,72874,22720,72901,72923,72924,72958],{},[38,72818,72819],{},"3.18"," Odvoďte, že jestliže ",[883,72822,72824],{"className":72823},[886],[888,72825,72826],{"xmlns":890},[892,72827,72828,72834],{},[895,72829,72830,72832],{},[898,72831,4049],{},[898,72833,5245],{},[902,72835,5345],{"encoding":904},[883,72837,72839],{"className":72838},[886],[888,72840,72841],{"xmlns":890},[892,72842,72843,72849],{},[895,72844,72845,72847],{},[898,72846,4049],{},[898,72848,4052],{},[902,72850,4512],{"encoding":904}," jsou lineární tvaru ",[883,72853,72855],{"className":72854},[886],[888,72856,72857],{"xmlns":890},[892,72858,72859,72871],{},[895,72860,72861,72863,72865,72867,72869],{},[898,72862,4049],{},[898,72864,5245],{},[1655,72866,1657],{},[898,72868,724],{},[898,72870,1824],{},[902,72872,72873],{"encoding":904},"TR = pQ",[883,72875,72877],{"className":72876},[886],[888,72878,72879],{"xmlns":890},[892,72880,72881,72898],{},[895,72882,72883,72885,72887,72889,72892,72894,72896],{},[898,72884,4049],{},[898,72886,4052],{},[1655,72888,1657],{},[898,72890,72891],{},"m",[1655,72893,2346],{},[898,72895,37986],{},[898,72897,1824],{},[902,72899,72900],{"encoding":904},"TC = m + nQ",[883,72902,72904],{"className":72903},[886],[888,72905,72906],{"xmlns":890},[892,72907,72908,72920],{},[895,72909,72910,72912,72914,72916,72918],{},[898,72911,72891],{},[1655,72913,1671],{"separator":1670},[898,72915,37986],{},[1655,72917,1671],{"separator":1670},[898,72919,724],{},[902,72921,72922],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,72925,72927],{"className":72926},[886],[888,72928,72929],{"xmlns":890},[892,72930,72931,72955],{},[895,72932,72933,72939,72941],{},[2597,72934,72935,72937],{},[898,72936,1824],{},[1655,72938,5603],{},[1655,72940,1657],{},[3615,72942,72943],{"scriptlevel":2552,"displaystyle":1663},[1949,72944,72945,72947],{},[898,72946,72891],{},[895,72948,72949,72951,72953],{},[898,72950,724],{},[1655,72952,2623],{},[898,72954,37986],{},[902,72956,72957],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,72960,72961,72765,72964,2704,72998,72117,73024,73037,73038,70869,73053,73068,73069,70853,73082,70869,73097,73112],{},[38,72962,72963],{},"3.19",[883,72965,72967],{"className":72966},[886],[888,72968,72969],{"xmlns":890},[892,72970,72971,72995],{},[895,72972,72973,72975,72977,72979,72981,72983,72989,72991,72993],{},[898,72974,4049],{},[898,72976,5245],{},[1655,72978,1657],{},[1655,72980,2623],{},[1826,72982,1837],{},[2597,72984,72985,72987],{},[898,72986,1824],{},[1826,72988,1837],{},[1655,72990,2346],{},[1826,72992,24072],{},[898,72994,1824],{},[902,72996,72997],{"encoding":904},"TR = -2Q^2 + 14Q",[883,72999,73001],{"className":73000},[886],[888,73002,73003],{"xmlns":890},[892,73004,73005,73021],{},[895,73006,73007,73009,73011,73013,73015,73017,73019],{},[898,73008,4049],{},[898,73010,4052],{},[1655,73012,1657],{},[1826,73014,1837],{},[898,73016,1824],{},[1655,73018,2346],{},[1826,73020,4136],{},[902,73022,73023],{"encoding":904},"TC = 2Q + 10",[883,73025,73027],{"className":73026},[886],[888,73028,73029],{"xmlns":890},[892,73030,73031,73035],{},[895,73032,73033],{},[898,73034,1824],{},[902,73036,1824],{"encoding":904},", které maximalizuje zisk ",[883,73039,73041],{"className":73040},[886],[888,73042,73043],{"xmlns":890},[892,73044,73045,73051],{},[895,73046,73047,73049],{},[898,73048,2132],{},[898,73050,5245],{},[902,73052,64605],{"encoding":904},[883,73054,73056],{"className":73055},[886],[888,73057,73058],{"xmlns":890},[892,73059,73060,73066],{},[895,73061,73062,73064],{},[898,73063,2132],{},[898,73065,5245],{},[902,73067,64605],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,73070,73072],{"className":73071},[886],[888,73073,73074],{"xmlns":890},[892,73075,73076,73080],{},[895,73077,73078],{},[898,73079,1824],{},[902,73081,1824],{"encoding":904},[883,73083,73085],{"className":73084},[886],[888,73086,73087],{"xmlns":890},[892,73088,73089,73095],{},[895,73090,73091,73093],{},[898,73092,4049],{},[898,73094,5245],{},[902,73096,5345],{"encoding":904},[883,73098,73100],{"className":73099},[886],[888,73101,73102],{"xmlns":890},[892,73103,73104,73110],{},[895,73105,73106,73108],{},[898,73107,4049],{},[898,73109,5245],{},[902,73111,5345],{"encoding":904},". (d) Graficky interpretujte.",[724,73114,73115,48810,73118,1343,73144,1343,73163,72117,73183,73037,73196,70869,73211,73226,73227,73249,73250,72300],{},[38,73116,73117],{},"3.20",[883,73119,73121],{"className":73120},[886],[888,73122,73123],{"xmlns":890},[892,73124,73125,73141],{},[895,73126,73127,73129,73131,73133,73135],{},[898,73128,2132],{},[1655,73130,1657],{},[1826,73132,21268],{},[1655,73134,2623],{},[2597,73136,73137,73139],{},[898,73138,1824],{},[1826,73140,1837],{},[902,73142,73143],{"encoding":904},"P = 400 - Q^2",[883,73145,73147],{"className":73146},[886],[888,73148,73149],{"xmlns":890},[892,73150,73151,73161],{},[895,73152,73153,73155,73157,73159],{},[898,73154,2537],{},[898,73156,4052],{},[1655,73158,1657],{},[1826,73160,4360],{},[902,73162,12757],{"encoding":904},[883,73164,73166],{"className":73165},[886],[888,73167,73168],{"xmlns":890},[892,73169,73170,73180],{},[895,73171,73172,73174,73176,73178],{},[898,73173,2127],{},[898,73175,4052],{},[1655,73177,1657],{},[1826,73179,10282],{},[902,73181,73182],{"encoding":904},"MC = 20",[883,73184,73186],{"className":73185},[886],[888,73187,73188],{"xmlns":890},[892,73189,73190,73194],{},[895,73191,73192],{},[898,73193,1824],{},[902,73195,1824],{"encoding":904},[883,73197,73199],{"className":73198},[886],[888,73200,73201],{"xmlns":890},[892,73202,73203,73209],{},[895,73204,73205,73207],{},[898,73206,2132],{},[898,73208,5245],{},[902,73210,64605],{"encoding":904},[883,73212,73214],{"className":73213},[886],[888,73215,73216],{"xmlns":890},[892,73217,73218,73224],{},[895,73219,73220,73222],{},[898,73221,2132],{},[898,73223,5245],{},[902,73225,64605],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,73228,73230],{"className":73229},[886],[888,73231,73232],{"xmlns":890},[892,73233,73234,73246],{},[895,73235,73236,73238,73240,73242,73244],{},[1655,73237,1664],{"stretchy":1663},[1826,73239,2552],{},[1655,73241,1671],{"separator":1670},[1826,73243,1828],{},[1655,73245,1677],{"stretchy":1663},[902,73247,73248],{"encoding":904},"(0, 1)",", druhý do ",[883,73251,73253],{"className":73252},[886],[888,73254,73255],{"xmlns":890},[892,73256,73257,73270],{},[895,73258,73259,73261,73264,73266,73268],{},[1655,73260,1664],{"stretchy":1663},[1826,73262,73263],{},"19",[1655,73265,1671],{"separator":1670},[1826,73267,10282],{},[1655,73269,1677],{"stretchy":1663},[902,73271,73272],{"encoding":904},"(19, 20)",[724,73274,73275,73278,73279,3902,73307,73324,73325,1719],{},[38,73276,73277],{},"3.21"," Dokažte, že má-li zisk ",[883,73280,73282],{"className":73281},[886],[888,73283,73284],{"xmlns":890},[892,73285,73286,73304],{},[895,73287,73288,73290,73292,73294,73296,73298,73300,73302],{},[898,73289,2132],{},[898,73291,5245],{},[1655,73293,1657],{},[898,73295,2132],{},[898,73297,5245],{},[1655,73299,1664],{"stretchy":1663},[898,73301,1824],{},[1655,73303,1677],{"stretchy":1663},[902,73305,73306],{"encoding":904},"PR = PR(Q)",[883,73308,73310],{"className":73309},[886],[888,73311,73312],{"xmlns":890},[892,73313,73314,73322],{},[895,73315,73316],{},[1820,73317,73318,73320],{},[898,73319,1824],{},[1826,73321,2552],{},[902,73323,39434],{"encoding":904}," maximum, pak platí ",[883,73326,73328],{"className":73327},[886],[888,73329,73330],{"xmlns":890},[892,73331,73332,73364],{},[895,73333,73334,73336,73338,73340,73346,73348,73350,73352,73354,73356,73362],{},[898,73335,2127],{},[898,73337,5245],{},[1655,73339,1664],{"stretchy":1663},[1820,73341,73342,73344],{},[898,73343,1824],{},[1826,73345,2552],{},[1655,73347,1677],{"stretchy":1663},[1655,73349,1657],{},[898,73351,2127],{},[898,73353,4052],{},[1655,73355,1664],{"stretchy":1663},[1820,73357,73358,73360],{},[898,73359,1824],{},[1826,73361,2552],{},[1655,73363,1677],{"stretchy":1663},[902,73365,66771],{"encoding":904},[724,73367,73368,73371,73372,2704,73387,57151,73402,73037,73415,73430,73431,1343,73458,73495,73496,1343,73523,1719],{},[38,73369,73370],{},"3.22"," Pro zadané ",[883,73373,73375],{"className":73374},[886],[888,73376,73377],{"xmlns":890},[892,73378,73379,73385],{},[895,73380,73381,73383],{},[898,73382,2127],{},[898,73384,5245],{},[902,73386,7881],{"encoding":904},[883,73388,73390],{"className":73389},[886],[888,73391,73392],{"xmlns":890},[892,73393,73394,73400],{},[895,73395,73396,73398],{},[898,73397,2127],{},[898,73399,4052],{},[902,73401,56418],{"encoding":904},[883,73403,73405],{"className":73404},[886],[888,73406,73407],{"xmlns":890},[892,73408,73409,73413],{},[895,73410,73411],{},[898,73412,1824],{},[902,73414,1824],{"encoding":904},[883,73416,73418],{"className":73417},[886],[888,73419,73420],{"xmlns":890},[892,73421,73422,73428],{},[895,73423,73424,73426],{},[898,73425,2132],{},[898,73427,5245],{},[902,73429,64605],{"encoding":904},". (a) ",[883,73432,73434],{"className":73433},[886],[888,73435,73436],{"xmlns":890},[892,73437,73438,73455],{},[895,73439,73440,73442,73444,73446,73449,73451,73453],{},[898,73441,2127],{},[898,73443,5245],{},[1655,73445,1657],{},[1826,73447,73448],{},"236",[1655,73450,2623],{},[1826,73452,42988],{},[898,73454,1824],{},[902,73456,73457],{"encoding":904},"MR = 236 - 16Q",[883,73459,73461],{"className":73460},[886],[888,73462,73463],{"xmlns":890},[892,73464,73465,73492],{},[895,73466,73467,73469,73471,73473,73475,73481,73483,73486,73488,73490],{},[898,73468,2127],{},[898,73470,4052],{},[1655,73472,1657],{},[1826,73474,3472],{},[2597,73476,73477,73479],{},[898,73478,1824],{},[1826,73480,1837],{},[1655,73482,2623],{},[1826,73484,73485],{},"32",[898,73487,1824],{},[1655,73489,2346],{},[1826,73491,6993],{},[902,73493,73494],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,73497,73499],{"className":73498},[886],[888,73500,73501],{"xmlns":890},[892,73502,73503,73520],{},[895,73504,73505,73507,73509,73511,73514,73516,73518],{},[898,73506,2127],{},[898,73508,5245],{},[1655,73510,1657],{},[1826,73512,73513],{},"280",[1655,73515,2623],{},[1826,73517,10282],{},[898,73519,1824],{},[902,73521,73522],{"encoding":904},"MR = 280 - 20Q",[883,73524,73526],{"className":73525},[886],[888,73527,73528],{"xmlns":890},[892,73529,73530,73557],{},[895,73531,73532,73534,73536,73538,73541,73547,73549,73551,73553,73555],{},[898,73533,2127],{},[898,73535,4052],{},[1655,73537,1657],{},[1826,73539,73540],{},"1,6",[2597,73542,73543,73545],{},[898,73544,1824],{},[1826,73546,1837],{},[1655,73548,2623],{},[1826,73550,37370],{},[898,73552,1824],{},[1655,73554,2346],{},[1826,73556,4396],{},[902,73558,73559],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,73561,73562,73371,73565,2704,73580,57151,73595,70853,73608,70869,73623,73430,73638,1343,73669,73495,73705,1343,73737,73781,73782,1343,73814,1719],{},[38,73563,73564],{},"3.23",[883,73566,73568],{"className":73567},[886],[888,73569,73570],{"xmlns":890},[892,73571,73572,73578],{},[895,73573,73574,73576],{},[898,73575,4049],{},[898,73577,5245],{},[902,73579,5345],{"encoding":904},[883,73581,73583],{"className":73582},[886],[888,73584,73585],{"xmlns":890},[892,73586,73587,73593],{},[895,73588,73589,73591],{},[898,73590,4049],{},[898,73592,4052],{},[902,73594,4512],{"encoding":904},[883,73596,73598],{"className":73597},[886],[888,73599,73600],{"xmlns":890},[892,73601,73602,73606],{},[895,73603,73604],{},[898,73605,1824],{},[902,73607,1824],{"encoding":904},[883,73609,73611],{"className":73610},[886],[888,73612,73613],{"xmlns":890},[892,73614,73615,73621],{},[895,73616,73617,73619],{},[898,73618,2132],{},[898,73620,5245],{},[902,73622,64605],{"encoding":904},[883,73624,73626],{"className":73625},[886],[888,73627,73628],{"xmlns":890},[892,73629,73630,73636],{},[895,73631,73632,73634],{},[898,73633,2132],{},[898,73635,5245],{},[902,73637,64605],{"encoding":904},[883,73639,73641],{"className":73640},[886],[888,73642,73643],{"xmlns":890},[892,73644,73645,73666],{},[895,73646,73647,73649,73651,73653,73656,73658,73660],{},[898,73648,4049],{},[898,73650,5245],{},[1655,73652,1657],{},[1826,73654,73655],{},"125",[898,73657,1824],{},[1655,73659,2623],{},[2597,73661,73662,73664],{},[898,73663,1824],{},[1826,73665,1837],{},[902,73667,73668],{"encoding":904},"TR = 125Q - Q^2",[883,73670,73672],{"className":73671},[886],[888,73673,73674],{"xmlns":890},[892,73675,73676,73702],{},[895,73677,73678,73680,73682,73684,73686,73688,73690,73692,73694,73696],{},[898,73679,4049],{},[898,73681,4052],{},[1655,73683,1657],{},[1826,73685,16235],{},[1655,73687,2346],{},[1826,73689,3524],{},[898,73691,1824],{},[1655,73693,2346],{},[1826,73695,6258],{},[2597,73697,73698,73700],{},[898,73699,1824],{},[1826,73701,1837],{},[902,73703,73704],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,73706,73708],{"className":73707},[886],[888,73709,73710],{"xmlns":890},[892,73711,73712,73734],{},[895,73713,73714,73716,73718,73720,73722,73724,73726,73728],{},[898,73715,4049],{},[898,73717,5245],{},[1655,73719,1657],{},[1826,73721,10282],{},[898,73723,1824],{},[1655,73725,2623],{},[1826,73727,1837],{},[2597,73729,73730,73732],{},[898,73731,1824],{},[1826,73733,1837],{},[902,73735,73736],{"encoding":904},"TR = 20Q - 2Q^2",[883,73738,73740],{"className":73739},[886],[888,73741,73742],{"xmlns":890},[892,73743,73744,73778],{},[895,73745,73746,73748,73750,73752,73754,73756,73758,73760,73762,73764,73770,73772],{},[898,73747,4049],{},[898,73749,4052],{},[1655,73751,1657],{},[1826,73753,1837],{},[1655,73755,2346],{},[1826,73757,10282],{},[898,73759,1824],{},[1655,73761,2623],{},[1826,73763,6834],{},[2597,73765,73766,73768],{},[898,73767,1824],{},[1826,73769,1837],{},[1655,73771,2346],{},[2597,73773,73774,73776],{},[898,73775,1824],{},[1826,73777,3472],{},[902,73779,73780],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,73783,73785],{"className":73784},[886],[888,73786,73787],{"xmlns":890},[892,73788,73789,73811],{},[895,73790,73791,73793,73795,73797,73799,73801,73803,73805],{},[898,73792,4049],{},[898,73794,5245],{},[1655,73796,1657],{},[1826,73798,3639],{},[898,73800,1824],{},[1655,73802,2623],{},[1826,73804,24915],{},[2597,73806,73807,73809],{},[898,73808,1824],{},[1826,73810,1837],{},[902,73812,73813],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,73815,73817],{"className":73816},[886],[888,73818,73819],{"xmlns":890},[892,73820,73821,73869],{},[895,73822,73823,73825,73827,73829,73831,73833,73835,73837,73839,73855,73857],{},[898,73824,4049],{},[898,73826,4052],{},[1655,73828,1657],{},[1826,73830,3639],{},[1655,73832,2346],{},[1826,73834,1837],{},[898,73836,1824],{},[1655,73838,2623],{},[3615,73840,73841],{"scriptlevel":2552,"displaystyle":1663},[1949,73842,73843,73853],{},[895,73844,73845,73847],{},[1826,73846,3472],{},[2597,73848,73849,73851],{},[898,73850,1824],{},[1826,73852,1837],{},[1826,73854,4136],{},[1655,73856,2346],{},[3615,73858,73859],{"scriptlevel":2552,"displaystyle":1663},[1949,73860,73861,73867],{},[2597,73862,73863,73865],{},[898,73864,1824],{},[1826,73866,3472],{},[1826,73868,10282],{},[902,73870,73871],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,73873,73874,73877,73878,73908,73909,73941,73942,22720,73972,74002],{},[38,73875,73876],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,73879,73881],{"className":73880},[886],[888,73882,73883],{"xmlns":890},[892,73884,73885,73905],{},[895,73886,73887,73893,73895,73897,73899],{},[1820,73888,73889,73891],{},[898,73890,2132],{},[1826,73892,1828],{},[1655,73894,1657],{},[1826,73896,16235],{},[1655,73898,2623],{},[1820,73900,73901,73903],{},[898,73902,1824],{},[1826,73904,1828],{},[902,73906,73907],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,73910,73912],{"className":73911},[886],[888,73913,73914],{"xmlns":890},[892,73915,73916,73938],{},[895,73917,73918,73924,73926,73928,73930,73932],{},[1820,73919,73920,73922],{},[898,73921,2132],{},[1826,73923,1837],{},[1655,73925,1657],{},[1826,73927,31207],{},[1655,73929,2623],{},[1826,73931,65685],{},[1820,73933,73934,73936],{},[898,73935,1824],{},[1826,73937,1837],{},[902,73939,73940],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,73943,73945],{"className":73944},[886],[888,73946,73947],{"xmlns":890},[892,73948,73949,73969],{},[895,73950,73951,73953,73955,73957,73959,73961,73963,73965,73967],{},[898,73952,4049],{},[898,73954,4052],{},[1655,73956,1657],{},[1826,73958,4390],{},[2031,73960,2435],{},[1826,73962,60208],{},[1655,73964,2346],{},[1826,73966,10282],{},[898,73968,1824],{},[902,73970,73971],{"encoding":904},"TC = 50\\,000 + 20Q",[883,73973,73975],{"className":73974},[886],[888,73976,73977],{"xmlns":890},[892,73978,73979,73999],{},[895,73980,73981,73983,73985,73991,73993],{},[898,73982,1824],{},[1655,73984,1657],{},[1820,73986,73987,73989],{},[898,73988,1824],{},[1826,73990,1828],{},[1655,73992,2346],{},[1820,73994,73995,73997],{},[898,73996,1824],{},[1826,73998,1837],{},[902,74000,74001],{"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.",[724,74004,74005,74008,74009,74039,74040,73941,74072,22720,74102,74131],{},[38,74006,74007],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,74010,74012],{"className":74011},[886],[888,74013,74014],{"xmlns":890},[892,74015,74016,74036],{},[895,74017,74018,74024,74026,74028,74030],{},[1820,74019,74020,74022],{},[898,74021,2132],{},[1826,74023,1828],{},[1655,74025,1657],{},[1826,74027,31207],{},[1655,74029,2623],{},[1820,74031,74032,74034],{},[898,74033,1824],{},[1826,74035,1828],{},[902,74037,74038],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,74041,74043],{"className":74042},[886],[888,74044,74045],{"xmlns":890},[892,74046,74047,74069],{},[895,74048,74049,74055,74057,74059,74061,74063],{},[1820,74050,74051,74053],{},[898,74052,2132],{},[1826,74054,1837],{},[1655,74056,1657],{},[1826,74058,9624],{},[1655,74060,2623],{},[1826,74062,6258],{},[1820,74064,74065,74067],{},[898,74066,1824],{},[1826,74068,1837],{},[902,74070,74071],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,74073,74075],{"className":74074},[886],[888,74076,74077],{"xmlns":890},[892,74078,74079,74099],{},[895,74080,74081,74083,74085,74087,74089,74091,74093,74095,74097],{},[898,74082,4049],{},[898,74084,4052],{},[1655,74086,1657],{},[1826,74088,3524],{},[2031,74090,2435],{},[1826,74092,60208],{},[1655,74094,2346],{},[1826,74096,4360],{},[898,74098,1824],{},[902,74100,74101],{"encoding":904},"TC = 5\\,000 + 100Q",[883,74103,74105],{"className":74104},[886],[888,74106,74107],{"xmlns":890},[892,74108,74109,74129],{},[895,74110,74111,74113,74115,74121,74123],{},[898,74112,1824],{},[1655,74114,1657],{},[1820,74116,74117,74119],{},[898,74118,1824],{},[1826,74120,1828],{},[1655,74122,2346],{},[1820,74124,74125,74127],{},[898,74126,1824],{},[1826,74128,1837],{},[902,74130,74001],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,74133,74135],{"id":74134},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,74137,74138,74141,74142,74189,74190,74207],{},[38,74139,74140],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,74143,74145],{"className":74144},[886],[888,74146,74147],{"xmlns":890},[892,74148,74149,74186],{},[895,74150,74151,74153,74155,74157,74159,74162,74168,74170,74173,74179,74181,74184],{},[898,74152,4049],{},[898,74154,41465],{},[898,74156,4052],{},[1655,74158,1657],{},[1826,74160,74161],{},"0,85",[2597,74163,74164,74166],{},[898,74165,1824],{},[1826,74167,3472],{},[1655,74169,2623],{},[1826,74171,74172],{},"11,9",[2597,74174,74175,74177],{},[898,74176,1824],{},[1826,74178,1837],{},[1655,74180,2346],{},[1826,74182,74183],{},"102",[898,74185,1824],{},[902,74187,74188],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,74191,74193],{"className":74192},[886],[888,74194,74195],{"xmlns":890},[892,74196,74197,74205],{},[895,74198,74199],{},[2597,74200,74201,74203],{},[898,74202,2132],{},[1655,74204,5603],{},[902,74206,5653],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,74209,74210,71968,74213,74249],{},[38,74211,74212],{},"3.27",[883,74214,74216],{"className":74215},[886],[888,74217,74218],{"xmlns":890},[892,74219,74220,74246],{},[895,74221,74222,74224,74226,74228,74230,74236,74238,74240,74242,74244],{},[898,74223,2127],{},[898,74225,4052],{},[1655,74227,1657],{},[1826,74229,4195],{},[2597,74231,74232,74234],{},[898,74233,1824],{},[1826,74235,1837],{},[1655,74237,2623],{},[1826,74239,65566],{},[898,74241,1824],{},[1655,74243,2346],{},[1826,74245,31869],{},[902,74247,74248],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,74251,74252,71219,74255,74249],{},[38,74253,74254],{},"3.28",[883,74256,74258],{"className":74257},[886],[888,74259,74260],{"xmlns":890},[892,74261,74262,74298],{},[895,74263,74264,74266,74268,74270,74272,74278,74280,74282,74288,74290,74292,74294,74296],{},[898,74265,4049],{},[898,74267,4052],{},[1655,74269,1657],{},[1826,74271,6258],{},[2597,74273,74274,74276],{},[898,74275,1824],{},[1826,74277,3472],{},[1655,74279,2623],{},[1826,74281,25327],{},[2597,74283,74284,74286],{},[898,74285,1824],{},[1826,74287,1837],{},[1655,74289,2346],{},[1826,74291,4396],{},[898,74293,1824],{},[1655,74295,2346],{},[1826,74297,16235],{},[902,74299,74300],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,74302,16845],{"id":16844},[120,74304,74305,74333,74378,74450,74515,74555,74647,74753,74793,74907,75000,75064,75096,75156,75162,75226,75275,75329,75437,75492],{},[123,74306,74307,3106,74309,74332],{},[38,74308,56876],{},[883,74310,74312],{"className":74311},[886],[888,74313,74314],{"xmlns":890},[892,74315,74316,74330],{},[895,74317,74318,74320,74322,74324,74326,74328],{},[898,74319,4049],{},[898,74321,5245],{},[1655,74323,1657],{},[898,74325,2132],{},[1655,74327,2869],{},[898,74329,1824],{},[902,74331,67838],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,74334,74335,3106,74337,74377],{},[38,74336,57462],{},[883,74338,74340],{"className":74339},[886],[888,74341,74342],{"xmlns":890},[892,74343,74344,74374],{},[895,74345,74346,74348,74350,74352,74364,74366,74368,74370,74372],{},[898,74347,2731],{},[898,74349,5245],{},[1655,74351,1657],{},[3615,74353,74354],{"scriptlevel":2552,"displaystyle":1663},[1949,74355,74356,74362],{},[895,74357,74358,74360],{},[898,74359,4049],{},[898,74361,5245],{},[898,74363,1824],{},[1655,74365,1657],{},[898,74367,2838],{},[1655,74369,1664],{"stretchy":1663},[898,74371,1824],{},[1655,74373,1677],{"stretchy":1663},[902,74375,74376],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,74379,74380,3106,74382,74418,74419,74434,74435,1719],{},[38,74381,57610],{},[883,74383,74385],{"className":74384},[886],[888,74386,74387],{"xmlns":890},[892,74388,74389,74415],{},[895,74390,74391,74393,74395,74397],{},[898,74392,2127],{},[898,74394,5245],{},[1655,74396,1657],{},[3615,74398,74399],{"scriptlevel":2552,"displaystyle":1663},[1949,74400,74401,74409],{},[895,74402,74403,74405,74407],{},[898,74404,2410],{"mathvariant":1943},[898,74406,4049],{},[898,74408,5245],{},[895,74410,74411,74413],{},[898,74412,2410],{"mathvariant":1943},[898,74414,1824],{},[902,74416,74417],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,74420,74422],{"className":74421},[886],[888,74423,74424],{"xmlns":890},[892,74425,74426,74432],{},[895,74427,74428,74430],{},[898,74429,4049],{},[898,74431,5245],{},[902,74433,5345],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,74436,74438],{"className":74437},[886],[888,74439,74440],{"xmlns":890},[892,74441,74442,74448],{},[895,74443,74444,74446],{},[898,74445,2731],{},[898,74447,5245],{},[902,74449,56571],{"encoding":904},[123,74451,74452,3106,74455,1343,74485,1719],{},[38,74453,74454],{},"Diferenciál příjmu\u002Fnákladů",[883,74456,74458],{"className":74457},[886],[888,74459,74460],{"xmlns":890},[892,74461,74462,74482],{},[895,74463,74464,74466,74468,74470,74472,74474,74476,74478,74480],{},[898,74465,2506],{"mathvariant":1943},[898,74467,4049],{},[898,74469,5245],{},[1655,74471,2357],{},[898,74473,2127],{},[898,74475,5245],{},[2031,74477,2435],{},[898,74479,2410],{"mathvariant":1943},[898,74481,1824],{},[902,74483,74484],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,74486,74488],{"className":74487},[886],[888,74489,74490],{"xmlns":890},[892,74491,74492,74512],{},[895,74493,74494,74496,74498,74500,74502,74504,74506,74508,74510],{},[898,74495,2506],{"mathvariant":1943},[898,74497,4049],{},[898,74499,4052],{},[1655,74501,2357],{},[898,74503,2127],{},[898,74505,4052],{},[2031,74507,2435],{},[898,74509,2410],{"mathvariant":1943},[898,74511,1824],{},[902,74513,74514],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,74516,74517,3106,74519,1719],{},[38,74518,59732],{},[883,74520,74522],{"className":74521},[886],[888,74523,74524],{"xmlns":890},[892,74525,74526,74552],{},[895,74527,74528,74530,74532,74534,74536,74538,74540,74542,74544,74546,74548,74550],{},[898,74529,4049],{},[898,74531,4052],{},[1655,74533,1657],{},[898,74535,2537],{},[898,74537,4052],{},[1655,74539,2346],{},[898,74541,4049],{},[898,74543,41465],{},[898,74545,4052],{},[1655,74547,1664],{"stretchy":1663},[898,74549,1824],{},[1655,74551,1677],{"stretchy":1663},[902,74553,74554],{"encoding":904},"TC = FC + TVC(Q)",[123,74556,74557,3106,74560,1343,74575,3106,74577,1343,74600,3106,74603,1719],{},[38,74558,74559],{},"Fixní náklady",[883,74561,74563],{"className":74562},[886],[888,74564,74565],{"xmlns":890},[892,74566,74567,74573],{},[895,74568,74569,74571],{},[898,74570,2537],{},[898,74572,4052],{},[902,74574,56617],{"encoding":904},[38,74576,59885],{},[883,74578,74580],{"className":74579},[886],[888,74581,74582],{"xmlns":890},[892,74583,74584,74598],{},[895,74585,74586,74588,74590,74592,74594,74596],{},[898,74587,4049],{},[898,74589,41465],{},[898,74591,4052],{},[1655,74593,1664],{"stretchy":1663},[898,74595,1824],{},[1655,74597,1677],{"stretchy":1663},[902,74599,59882],{"encoding":904},[38,74601,74602],{},"variabilní náklady na jednotku",[883,74604,74606],{"className":74605},[886],[888,74607,74608],{"xmlns":890},[892,74609,74610,74644],{},[895,74611,74612,74614,74616,74618,74620,74622,74624],{},[898,74613,41465],{},[898,74615,4052],{},[1655,74617,1664],{"stretchy":1663},[898,74619,1824],{},[1655,74621,1677],{"stretchy":1663},[1655,74623,1657],{},[3615,74625,74626],{"scriptlevel":2552,"displaystyle":1663},[1949,74627,74628,74642],{},[895,74629,74630,74632,74634,74636,74638,74640],{},[898,74631,4049],{},[898,74633,41465],{},[898,74635,4052],{},[1655,74637,1664],{"stretchy":1663},[898,74639,1824],{},[1655,74641,1677],{"stretchy":1663},[898,74643,1824],{},[902,74645,74646],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,74648,74649,3106,74651,1343,74681,3106,74684,1343,74716,3106,74719,1719],{},[38,74650,59893],{},[883,74652,74654],{"className":74653},[886],[888,74655,74656],{"xmlns":890},[892,74657,74658,74678],{},[895,74659,74660,74662,74664,74666],{},[898,74661,2731],{},[898,74663,4052],{},[1655,74665,1657],{},[3615,74667,74668],{"scriptlevel":2552,"displaystyle":1663},[1949,74669,74670,74676],{},[895,74671,74672,74674],{},[898,74673,4049],{},[898,74675,4052],{},[898,74677,1824],{},[902,74679,74680],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,74682,74683],{},"průměrné fixní",[883,74685,74687],{"className":74686},[886],[888,74688,74689],{"xmlns":890},[892,74690,74691,74713],{},[895,74692,74693,74695,74697,74699,74701],{},[898,74694,2731],{},[898,74696,2537],{},[898,74698,4052],{},[1655,74700,1657],{},[3615,74702,74703],{"scriptlevel":2552,"displaystyle":1663},[1949,74704,74705,74711],{},[895,74706,74707,74709],{},[898,74708,2537],{},[898,74710,4052],{},[898,74712,1824],{},[902,74714,74715],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,74717,74718],{},"průměrné variabilní",[883,74720,74722],{"className":74721},[886],[888,74723,74724],{"xmlns":890},[892,74725,74726,74750],{},[895,74727,74728,74730,74732,74734,74736],{},[898,74729,2731],{},[898,74731,41465],{},[898,74733,4052],{},[1655,74735,1657],{},[3615,74737,74738],{"scriptlevel":2552,"displaystyle":1663},[1949,74739,74740,74748],{},[895,74741,74742,74744,74746],{},[898,74743,4049],{},[898,74745,41465],{},[898,74747,4052],{},[898,74749,1824],{},[902,74751,74752],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,74754,74755,3106,74757,1719],{},[38,74756,61080],{},[883,74758,74760],{"className":74759},[886],[888,74761,74762],{"xmlns":890},[892,74763,74764,74790],{},[895,74765,74766,74768,74770,74772],{},[898,74767,2127],{},[898,74769,4052],{},[1655,74771,1657],{},[3615,74773,74774],{"scriptlevel":2552,"displaystyle":1663},[1949,74775,74776,74784],{},[895,74777,74778,74780,74782],{},[898,74779,2410],{"mathvariant":1943},[898,74781,4049],{},[898,74783,4052],{},[895,74785,74786,74788],{},[898,74787,2410],{"mathvariant":1943},[898,74789,1824],{},[902,74791,74792],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,74794,74795,3106,74797,74845,74846,74859,74860,1343,74875,1343,74892,1719],{},[38,74796,61978],{},[883,74798,74800],{"className":74799},[886],[888,74801,74802],{"xmlns":890},[892,74803,74804,74842],{},[895,74805,74806,74808,74810,74812,74814,74816,74818,74820,74822,74824,74826,74832,74834,74836],{},[898,74807,4049],{},[898,74809,4052],{},[1655,74811,1657],{},[898,74813,2537],{},[898,74815,4052],{},[1655,74817,2346],{},[898,74819,207],{},[898,74821,1824],{},[1655,74823,2346],{},[898,74825,2025],{},[2597,74827,74828,74830],{},[898,74829,1824],{},[1826,74831,1837],{},[1655,74833,2346],{},[898,74835,1789],{},[2597,74837,74838,74840],{},[898,74839,1824],{},[1826,74841,3472],{},[902,74843,74844],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,74847,74849],{"className":74848},[886],[888,74850,74851],{"xmlns":890},[892,74852,74853,74857],{},[895,74854,74855],{},[898,74856,900],{},[902,74858,900],{"encoding":904},"-průběhem ",[883,74861,74863],{"className":74862},[886],[888,74864,74865],{"xmlns":890},[892,74866,74867,74873],{},[895,74868,74869,74871],{},[898,74870,2731],{},[898,74872,4052],{},[902,74874,56686],{"encoding":904},[883,74876,74878],{"className":74877},[886],[888,74879,74880],{"xmlns":890},[892,74881,74882,74890],{},[895,74883,74884,74886,74888],{},[898,74885,2731],{},[898,74887,41465],{},[898,74889,4052],{},[902,74891,56437],{"encoding":904},[883,74893,74895],{"className":74894},[886],[888,74896,74897],{"xmlns":890},[892,74898,74899,74905],{},[895,74900,74901,74903],{},[898,74902,2127],{},[898,74904,4052],{},[902,74906,56418],{"encoding":904},[123,74908,74909,74911,74912,2494,74927,74968,74969,62623,74984,74999],{},[38,74910,63060],{},": v bodě minima ",[883,74913,74915],{"className":74914},[886],[888,74916,74917],{"xmlns":890},[892,74918,74919,74925],{},[895,74920,74921,74923],{},[898,74922,2731],{},[898,74924,4052],{},[902,74926,56686],{"encoding":904},[883,74928,74930],{"className":74929},[886],[888,74931,74932],{"xmlns":890},[892,74933,74934,74966],{},[895,74935,74936,74938,74940,74942,74948,74950,74952,74954,74956,74958,74964],{},[898,74937,2731],{},[898,74939,4052],{},[1655,74941,1664],{"stretchy":1663},[1820,74943,74944,74946],{},[898,74945,1824],{},[1826,74947,2552],{},[1655,74949,1677],{"stretchy":1663},[1655,74951,1657],{},[898,74953,2127],{},[898,74955,4052],{},[1655,74957,1664],{"stretchy":1663},[1820,74959,74960,74962],{},[898,74961,1824],{},[1826,74963,2552],{},[1655,74965,1677],{"stretchy":1663},[902,74967,63695],{"encoding":904},"; geometricky ",[883,74970,74972],{"className":74971},[886],[888,74973,74974],{"xmlns":890},[892,74975,74976,74982],{},[895,74977,74978,74980],{},[898,74979,2127],{},[898,74981,4052],{},[902,74983,56418],{"encoding":904},[883,74985,74987],{"className":74986},[886],[888,74988,74989],{"xmlns":890},[892,74990,74991,74997],{},[895,74992,74993,74995],{},[898,74994,2731],{},[898,74996,4052],{},[902,74998,56686],{"encoding":904}," v jejím minimu.",[123,75001,75002,74911,75004,2494,75021,1719],{},[38,75003,64410],{},[883,75005,75007],{"className":75006},[886],[888,75008,75009],{"xmlns":890},[892,75010,75011,75019],{},[895,75012,75013,75015,75017],{},[898,75014,2731],{},[898,75016,41465],{},[898,75018,4052],{},[902,75020,56437],{"encoding":904},[883,75022,75024],{"className":75023},[886],[888,75025,75026],{"xmlns":890},[892,75027,75028,75062],{},[895,75029,75030,75032,75034,75036,75038,75044,75046,75048,75050,75052,75054,75060],{},[898,75031,2731],{},[898,75033,41465],{},[898,75035,4052],{},[1655,75037,1664],{"stretchy":1663},[1820,75039,75040,75042],{},[898,75041,1824],{},[1826,75043,2552],{},[1655,75045,1677],{"stretchy":1663},[1655,75047,1657],{},[898,75049,2127],{},[898,75051,4052],{},[1655,75053,1664],{"stretchy":1663},[1820,75055,75056,75058],{},[898,75057,1824],{},[1826,75059,2552],{},[1655,75061,1677],{"stretchy":1663},[902,75063,70145],{"encoding":904},[123,75065,75066,3106,75068,75095],{},[38,75067,64589],{},[883,75069,75071],{"className":75070},[886],[888,75072,75073],{"xmlns":890},[892,75074,75075,75093],{},[895,75076,75077,75079,75081,75083,75085,75087,75089,75091],{},[898,75078,2132],{},[898,75080,5245],{},[1655,75082,1657],{},[898,75084,4049],{},[898,75086,5245],{},[1655,75088,2623],{},[898,75090,4049],{},[898,75092,4052],{},[902,75094,56326],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,75097,75098,2115,75100,75102,75103,75129,75130,75155],{},[38,75099,65451],{},[614,75101,64714],{},") — hodnoty ",[883,75104,75106],{"className":75105},[886],[888,75107,75108],{"xmlns":890},[892,75109,75110,75126],{},[895,75111,75112,75118,75120],{},[1820,75113,75114,75116],{},[898,75115,1824],{},[898,75117,2731],{},[1655,75119,1671],{"separator":1670},[1820,75121,75122,75124],{},[898,75123,1824],{},[898,75125,24379],{},[902,75127,75128],{"encoding":904},"Q_A, Q_B"," splňující ",[883,75131,75133],{"className":75132},[886],[888,75134,75135],{"xmlns":890},[892,75136,75137,75153],{},[895,75138,75139,75141,75143,75145,75147,75149,75151],{},[898,75140,2132],{},[898,75142,5245],{},[1655,75144,1664],{"stretchy":1663},[898,75146,1824],{},[1655,75148,1677],{"stretchy":1663},[1655,75150,1657],{},[1826,75152,2552],{},[902,75154,64991],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,75157,75158,75161],{},[38,75159,75160],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,75163,75164,75166,75167,2494,75184,75225],{},[38,75165,66505],{}," — v bodě maxima zisku ",[883,75168,75170],{"className":75169},[886],[888,75171,75172],{"xmlns":890},[892,75173,75174,75182],{},[895,75175,75176],{},[1820,75177,75178,75180],{},[898,75179,1824],{},[1826,75181,2552],{},[902,75183,39434],{"encoding":904},[883,75185,75187],{"className":75186},[886],[888,75188,75189],{"xmlns":890},[892,75190,75191,75223],{},[895,75192,75193,75195,75197,75199,75205,75207,75209,75211,75213,75215,75221],{},[898,75194,2127],{},[898,75196,5245],{},[1655,75198,1664],{"stretchy":1663},[1820,75200,75201,75203],{},[898,75202,1824],{},[1826,75204,2552],{},[1655,75206,1677],{"stretchy":1663},[1655,75208,1657],{},[898,75210,2127],{},[898,75212,4052],{},[1655,75214,1664],{"stretchy":1663},[1820,75216,75217,75219],{},[898,75218,1824],{},[1826,75220,2552],{},[1655,75222,1677],{"stretchy":1663},[902,75224,66771],{"encoding":904}," (3.13).",[123,75227,75228,21427,75230,2494,75249,75274],{},[38,75229,67798],{},[883,75231,75233],{"className":75232},[886],[888,75234,75235],{"xmlns":890},[892,75236,75237,75246],{},[895,75238,75239,75241,75243],{},[898,75240,2132],{},[1655,75242,1657],{},[2031,75244,75245],{},"konst",[902,75247,75248],{"encoding":904},"P = \\text{konst}",[883,75250,75252],{"className":75251},[886],[888,75253,75254],{"xmlns":890},[892,75255,75256,75272],{},[895,75257,75258,75260,75262,75264,75266,75268,75270],{},[898,75259,2132],{},[1655,75261,1657],{},[898,75263,2127],{},[898,75265,4052],{},[1655,75267,1664],{"stretchy":1663},[898,75269,1824],{},[1655,75271,1677],{"stretchy":1663},[902,75273,68492],{"encoding":904}," (3.14).",[123,75276,75277,75280,75281,75310,75311,75328],{},[38,75278,75279],{},"Shutdown point"," — bod ",[883,75282,75284],{"className":75283},[886],[888,75285,75286],{"xmlns":890},[892,75287,75288,75308],{},[895,75289,75290,75292,75298,75300,75306],{},[1655,75291,1664],{"stretchy":1663},[2597,75293,75294,75296],{},[898,75295,1824],{},[1655,75297,5603],{},[1655,75299,1671],{"separator":1670},[2597,75301,75302,75304],{},[898,75303,2132],{},[1655,75305,5603],{},[1655,75307,1677],{"stretchy":1663},[902,75309,68781],{"encoding":904}," v minimu ",[883,75312,75314],{"className":75313},[886],[888,75315,75316],{"xmlns":890},[892,75317,75318,75326],{},[895,75319,75320,75322,75324],{},[898,75321,2731],{},[898,75323,41465],{},[898,75325,4052],{},[902,75327,56437],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,75330,75331,3106,75334,7720,75369,69051,75390,75403,75404,75419,75420,1719],{},[38,75332,75333],{},"Funkce nabídky firmy",[883,75335,75337],{"className":75336},[886],[888,75338,75339],{"xmlns":890},[892,75340,75341,75367],{},[895,75342,75343,75345,75347,75349,75351,75353,75355,75357,75359,75361,75363,75365],{},[898,75344,2132],{},[1655,75346,1657],{},[898,75348,9920],{},[1655,75350,1664],{"stretchy":1663},[898,75352,1824],{},[1655,75354,1677],{"stretchy":1663},[1655,75356,1657],{},[898,75358,2127],{},[898,75360,4052],{},[1655,75362,1664],{"stretchy":1663},[898,75364,1824],{},[1655,75366,1677],{"stretchy":1663},[902,75368,70248],{"encoding":904},[883,75370,75372],{"className":75371},[886],[888,75373,75374],{"xmlns":890},[892,75375,75376,75388],{},[895,75377,75378,75380,75382],{},[898,75379,1824],{},[1655,75381,5734],{},[2597,75383,75384,75386],{},[898,75385,1824],{},[1655,75387,5603],{},[902,75389,69050],{"encoding":904},[883,75391,75393],{"className":75392},[886],[888,75394,75395],{"xmlns":890},[892,75396,75397,75401],{},[895,75398,75399],{},[1826,75400,2552],{},[902,75402,2552],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,75405,75407],{"className":75406},[886],[888,75408,75409],{"xmlns":890},[892,75410,75411,75417],{},[895,75412,75413,75415],{},[898,75414,2127],{},[898,75416,4052],{},[902,75418,56418],{"encoding":904}," nad minimem ",[883,75421,75423],{"className":75422},[886],[888,75424,75425],{"xmlns":890},[892,75426,75427,75435],{},[895,75428,75429,75431,75433],{},[898,75430,2731],{},[898,75432,41465],{},[898,75434,4052],{},[902,75436,56437],{"encoding":904},[123,75438,75439,8262,75441,75462,75463,1719],{},[38,75440,51205],{},[883,75442,75444],{"className":75443},[886],[888,75445,75446],{"xmlns":890},[892,75447,75448,75460],{},[895,75449,75450,75452,75454],{},[898,75451,2132],{},[1655,75453,1657],{},[2597,75455,75456,75458],{},[898,75457,2132],{},[1655,75459,5603],{},[902,75461,5606],{"encoding":904}," konstantní ⇒ ",[883,75464,75466],{"className":75465},[886],[888,75467,75468],{"xmlns":890},[892,75469,75470,75490],{},[895,75471,75472,75474,75476,75478,75480,75482,75484],{},[898,75473,2731],{},[898,75475,5245],{},[1655,75477,1657],{},[898,75479,2127],{},[898,75481,5245],{},[1655,75483,1657],{},[2597,75485,75486,75488],{},[898,75487,2132],{},[1655,75489,5603],{},[902,75491,59724],{"encoding":904},[123,75493,75494,75497],{},[38,75495,75496],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,75499,3187],{"id":3186},[120,75501,75502,75521,75533],{},[123,75503,75504,3106,75506,1343,75509,1343,75512,1343,75515,1343,75518],{},[38,75505,51849],{},[207,75507,13065],{"className":75508,"dataFsResolvedFilePath":800,"href":801},[210],[207,75510,3223],{"className":75511,"dataFsResolvedFilePath":848,"href":849},[210],[207,75513,3645],{"className":75514,"dataFsResolvedFilePath":764,"href":765},[210],[207,75516,775],{"className":75517,"dataFsResolvedFilePath":773,"href":774},[210],[207,75519,859],{"className":75520,"dataFsResolvedFilePath":857,"href":858},[210],[123,75522,75523,3106,75525,1343,75529],{},[38,75524,37829],{},[207,75526,75528],{"className":75527,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,75530,75532],{"className":75531,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,75534,75535,3106,75537],{},[38,75536,17329],{},[207,75538,17333],{"className":75539,"dataFsResolvedFilePath":3274,"href":3275},[210],{"title":641,"searchDepth":642,"depth":642,"links":75541},[75542,75543,75550,75556,75560,75561,75565,75566,75567,75568,75574,75575],{"id":52080,"depth":642,"text":1241},{"id":56864,"depth":642,"text":56865,"children":75544},[75545,75546,75547,75548,75549],{"id":56875,"depth":649,"text":56876},{"id":57461,"depth":649,"text":57462},{"id":57609,"depth":649,"text":57610},{"id":58351,"depth":649,"text":58352},{"id":59006,"depth":649,"text":59007},{"id":59727,"depth":642,"text":59728,"children":75551},[75552,75553,75554,75555],{"id":59731,"depth":649,"text":59732},{"id":59892,"depth":649,"text":59893},{"id":61079,"depth":649,"text":61080},{"id":61977,"depth":649,"text":61978},{"id":63059,"depth":642,"text":63060,"children":75557},[75558,75559],{"id":17537,"depth":649,"text":17538},{"id":64409,"depth":649,"text":64410},{"id":64583,"depth":642,"text":64584},{"id":66504,"depth":642,"text":66505,"children":75562},[75563,75564],{"id":66518,"depth":649,"text":17538},{"id":67797,"depth":649,"text":67798},{"id":68429,"depth":642,"text":68430},{"id":69895,"depth":642,"text":69896},{"id":51007,"depth":642,"text":51008},{"id":70356,"depth":642,"text":70357,"children":75569},[75570,75571,75572,75573],{"id":70360,"depth":649,"text":70361},{"id":71212,"depth":649,"text":71213},{"id":72758,"depth":649,"text":72759},{"id":74134,"depth":649,"text":74135},{"id":16844,"depth":642,"text":16845},{"id":3186,"depth":642,"text":3187},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":56246,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,75582,75583,56298,75584,75585,75586],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":75589,"title":75590,"body":75591,"course":1128,"courses":659,"created":10802,"description":641,"extension":661,"meta":87688,"navigation":664,"path":87689,"seo":87690,"sources":87691,"stem":87692,"tags":87693,"type":3252,"updated":677,"__hash__":87699},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":75592,"toc":87645},[75593,75596,75952,75956,75959,76027,76079,76089,76093,76127,76168,76192,76215,76244,76311,76418,76461,76518,76593,76638,76642,76650,76658,76661,76926,76977,77057,77127,77150,77178,77223,77245,77249,77256,77305,77331,77482,77485,77522,77685,77793,77797,77834,77909,77978,78097,78219,78300,78306,78347,78420,78513,78517,78553,78641,78755,78860,78945,79085,79089,79137,79182,79188,79192,79195,79246,79296,79303,79369,79502,79547,79551,79572,79951,80046,80063,80117,80121,80203,80287,80457,80460,80503,80570,80644,80648,80653,80722,80730,80739,80817,80883,80888,80983,81026,81031,81079,81084,81132,81250,81333,81371,81474,81533,81674,81678,81721,81794,81818,81872,81879,81881,81926,81971,81982,81987,82023,82085,82108,82117,82218,82285,82358,82365,82456,82518,82554,82611,82670,82855,82951,82955,82959,83038,83043,83167,83253,83259,83369,83406,83497,83595,83598,83602,83668,83705,83827,83879,83883,83911,83963,84037,84142,84166,84225,84229,84247,84390,84538,84540,84575,84579,84581,84671,84801,84927,85019,85094,85098,85214,85318,85508,85544,85638,85644,85757,86060,86066,86184,86283,86359,86361,87523,87525],[12,75594,75590],{"id":75595},"produkce-produkční-funkce-cobb-douglas-mrts",[5120,75597,75598],{},[724,75599,75600,5127,75602,75604,75605,38022,75618,75631,75632,17502,75645,2115,75647,75671,75672,3106,75674,2704,75708,3106,75711,75739,75740,2494,75760,75790,75791,2115,75794,75822,75823,75826,75827,75857,75858,75888,75889,3106,75892,75932,75933,75951],{},[883,75601,5126],{},[38,75603,859],{}," popisuje vztah mezi vstupy (práce ",[883,75606,75608],{"className":75607},[886],[888,75609,75610],{"xmlns":890},[892,75611,75612,75616],{},[895,75613,75614],{},[898,75615,1873],{},[902,75617,1873],{"encoding":904},[883,75619,75621],{"className":75620},[886],[888,75622,75623],{"xmlns":890},[892,75624,75625,75629],{},[895,75626,75627],{},[898,75628,1878],{},[902,75630,1878],{"encoding":904},") a výstupem ",[883,75633,75635],{"className":75634},[886],[888,75636,75637],{"xmlns":890},[892,75638,75639,75643],{},[895,75640,75641],{},[898,75642,1824],{},[902,75644,1824],{"encoding":904},[38,75646,38090],{},[883,75648,75650],{"className":75649},[886],[888,75651,75652],{"xmlns":890},[892,75653,75654,75668],{},[895,75655,75656,75658,75660,75662,75664,75666],{},[898,75657,1824],{},[1655,75659,1657],{},[898,75661,1824],{},[1655,75663,1664],{"stretchy":1663},[898,75665,1873],{},[1655,75667,1677],{"stretchy":1663},[902,75669,75670],{"encoding":904},"Q = Q(L)",") studujeme ",[614,75673,2114],{},[883,75675,75677],{"className":75676},[886],[888,75678,75679],{"xmlns":890},[892,75680,75681,75705],{},[895,75682,75683,75685,75691,75693,75699,75701,75703],{},[898,75684,2127],{},[1820,75686,75687,75689],{},[898,75688,2132],{},[898,75690,1873],{},[1655,75692,1657],{},[2597,75694,75695,75697],{},[898,75696,1824],{},[1655,75698,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,75700,1664],{"stretchy":1663},[898,75702,1873],{},[1655,75704,1677],{"stretchy":1663},[902,75706,75707],{"encoding":904},"MP_L = Q'(L)",[614,75709,75710],{},"průměrný produkt",[883,75712,75714],{"className":75713},[886],[888,75715,75716],{"xmlns":890},[892,75717,75718,75736],{},[895,75719,75720,75722,75728,75730,75732,75734],{},[898,75721,2731],{},[1820,75723,75724,75726],{},[898,75725,2132],{},[898,75727,1873],{},[1655,75729,1657],{},[898,75731,1824],{},[898,75733,5923],{"mathvariant":1943},[898,75735,1873],{},[902,75737,75738],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,75741,75743],{"className":75742},[886],[888,75744,75745],{"xmlns":890},[892,75746,75747,75757],{},[895,75748,75749,75751],{},[898,75750,2731],{},[1820,75752,75753,75755],{},[898,75754,2132],{},[898,75756,1873],{},[902,75758,75759],{"encoding":904},"AP_L",[883,75761,75763],{"className":75762},[886],[888,75764,75765],{"xmlns":890},[892,75766,75767,75787],{},[895,75768,75769,75771,75777,75779,75781],{},[898,75770,2127],{},[1820,75772,75773,75775],{},[898,75774,2132],{},[898,75776,1873],{},[1655,75778,1657],{},[898,75780,2731],{},[1820,75782,75783,75785],{},[898,75784,2132],{},[898,75786,1873],{},[902,75788,75789],{"encoding":904},"MP_L = AP_L",". Ve ",[38,75792,75793],{},"dvoufaktorovém modelu",[883,75795,75797],{"className":75796},[886],[888,75798,75799],{"xmlns":890},[892,75800,75801,75819],{},[895,75802,75803,75805,75807,75809,75811,75813,75815,75817],{},[898,75804,1824],{},[1655,75806,1657],{},[898,75808,1824],{},[1655,75810,1664],{"stretchy":1663},[898,75812,1873],{},[1655,75814,1671],{"separator":1670},[898,75816,1878],{},[1655,75818,1677],{"stretchy":1663},[902,75820,75821],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,75824,75825],{},"Cobb-Douglasovy"," funkce ",[883,75828,75830],{"className":75829},[886],[888,75831,75832],{"xmlns":890},[892,75833,75834,75854],{},[895,75835,75836,75838,75840,75842,75848],{},[898,75837,1824],{},[1655,75839,1657],{},[898,75841,2731],{},[2597,75843,75844,75846],{},[898,75845,1873],{},[898,75847,207],{},[2597,75849,75850,75852],{},[898,75851,1878],{},[898,75853,2025],{},[902,75855,75856],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,75859,75861],{"className":75860},[886],[888,75862,75863],{"xmlns":890},[892,75864,75865,75885],{},[895,75866,75867,75869,75875,75877,75879],{},[898,75868,2127],{},[1820,75870,75871,75873],{},[898,75872,2132],{},[898,75874,1873],{},[1655,75876,1671],{"separator":1670},[898,75878,2127],{},[1820,75880,75881,75883],{},[898,75882,2132],{},[898,75884,1878],{},[902,75886,75887],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,75890,75891],{},"mezní míru technické substituce",[883,75893,75895],{"className":75894},[886],[888,75896,75897],{"xmlns":890},[892,75898,75899,75929],{},[895,75900,75901,75903,75905,75907,75909,75911,75913,75919,75921,75923],{},[898,75902,2127],{},[898,75904,5245],{},[898,75906,4049],{},[898,75908,9920],{},[1655,75910,1657],{},[898,75912,2127],{},[1820,75914,75915,75917],{},[898,75916,2132],{},[898,75918,1873],{},[898,75920,5923],{"mathvariant":1943},[898,75922,2127],{},[1820,75924,75925,75927],{},[898,75926,2132],{},[898,75928,1878],{},[902,75930,75931],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,75934,75936],{"className":75935},[886],[888,75937,75938],{"xmlns":890},[892,75939,75940,75948],{},[895,75941,75942,75944,75946],{},[898,75943,207],{},[1655,75945,2346],{},[898,75947,2025],{},[902,75949,75950],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,75953,75955],{"id":75954},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,75957,75958],{},"Po prostudování kapitoly 5 student umí:",[120,75960,75961,75967,75977,75983,75989,75994,76000,76010,76015,76021],{},[123,75962,75963,75964,1671],{},"popsat ",[38,75965,75966],{},"jednofaktorový model produkce",[123,75968,75969,75970,2704,75973,75976],{},"vypočítat ",[38,75971,75972],{},"mezní",[38,75974,75975],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,75978,75979,75980,1671],{},"charakterizovat průběh ",[38,75981,75982],{},"křivky produkce",[123,75984,75985,75986,1671],{},"formulovat ",[38,75987,75988],{},"princip maximalizace průměrného produktu práce",[123,75990,75963,75991,1671],{},[38,75992,75993],{},"dvoufaktorový model produkce",[123,75995,75996,75997,1671],{},"uvést tvar ",[38,75998,75999],{},"Cobb–Douglasových produkčních funkcí",[123,76001,76002,76003,1343,76005,1343,76007,1671],{},"vyložit, co jsou ",[38,76004,25739],{},[38,76006,14782],{},[38,76008,76009],{},"klesající výnosy z rozsahu",[123,76011,75969,76012,75976],{},[38,76013,76014],{},"mezní produkty práce a kapitálu",[123,76016,76017,76018,1671],{},"najít ",[38,76019,76020],{},"izokvanty",[123,76022,75969,76023,76026],{},[38,76024,76025],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,76028,76029,76030,76033,76034,76037,76038,3106,76041,1343,76054,3106,76057,2704,76070,76073,76074,76076,76077,1719],{},"Každý proces produkce je určován ",[38,76031,76032],{},"faktory"," (též ",[38,76035,76036],{},"vstupy",") produkce. K hlavním patří ",[38,76039,76040],{},"práce",[883,76042,76044],{"className":76043},[886],[888,76045,76046],{"xmlns":890},[892,76047,76048,76052],{},[895,76049,76050],{},[898,76051,1873],{},[902,76053,1873],{"encoding":904},[38,76055,76056],{},"kapitál",[883,76058,76060],{"className":76059},[886],[888,76061,76062],{"xmlns":890},[892,76063,76064,76068],{},[895,76065,76066],{},[898,76067,1878],{},[902,76069,1878],{"encoding":904},[38,76071,76072],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,76075,38090],{}," (produkce závisí jen na práci); v opačném případě o ",[38,76078,75793],{},[724,76080,76081,76082,1343,76085,76088],{},"Související matematický aparát: ",[207,76083,3645],{"className":76084,"dataFsResolvedFilePath":764,"href":765},[210],[207,76086,784],{"className":76087,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,76090,76092],{"id":76091},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,76094,76095,76096,76109,76110,76123,76124],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,76097,76099],{"className":76098},[886],[888,76100,76101],{"xmlns":890},[892,76102,76103,76107],{},[895,76104,76105],{},[898,76106,1824],{},[902,76108,1824],{"encoding":904}," na práci ",[883,76111,76113],{"className":76112},[886],[888,76114,76115],{"xmlns":890},[892,76116,76117,76121],{},[895,76118,76119],{},[898,76120,1873],{},[902,76122,1873],{"encoding":904}," vyjadřuje ",[38,76125,76126],{},"produkční funkce",[883,76128,76130],{"className":76129},[886],[888,76131,76132],{"xmlns":890,"display":29192},[892,76133,76134,76165],{},[21880,76135,76136],{"width":29197},[21885,76137,76138,76140,76158,76160],{},[21888,76139],{"width":29202},[21888,76141,76142],{},[895,76143,76144,76146,76148,76150,76152,76154,76156],{},[898,76145,1824],{},[1655,76147,1657],{},[898,76149,1824],{},[1655,76151,1664],{"stretchy":1663},[898,76153,1873],{},[1655,76155,1677],{"stretchy":1663},[1655,76157,1671],{"separator":1670},[21888,76159],{"width":29202},[21888,76161,76162],{},[2031,76163,76164],{},"(5.1)",[902,76166,76167],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,76169,76170,76171,2115,76174,76177,76178,76191],{},"jejíž graf se nazývá ",[38,76172,76173],{},"křivka produkce",[614,76175,76176],{},"production curve","). Práce ",[883,76179,76181],{"className":76180},[886],[888,76182,76183],{"xmlns":890},[892,76184,76185,76189],{},[895,76186,76187],{},[898,76188,1873],{},[902,76190,1873],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,76193,76195,76196,1677],{"id":76194},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,76197,76199],{"className":76198},[886],[888,76200,76201],{"xmlns":890},[892,76202,76203,76213],{},[895,76204,76205,76207],{},[898,76206,2127],{},[1820,76208,76209,76211],{},[898,76210,2132],{},[898,76212,1873],{},[902,76214,2137],{"encoding":904},[724,76216,76217,2115,76220,76223,76224,76243],{},[38,76218,76219],{},"Mezní produkt práce",[614,76221,76222],{},"marginal product of labour",") ",[883,76225,76227],{"className":76226},[886],[888,76228,76229],{"xmlns":890},[892,76230,76231,76241],{},[895,76232,76233,76235],{},[898,76234,2127],{},[1820,76236,76237,76239],{},[898,76238,2132],{},[898,76240,1873],{},[902,76242,2137],{"encoding":904}," je derivace produkce podle práce:",[883,76245,76247],{"className":76246},[886],[888,76248,76249],{"xmlns":890,"display":29192},[892,76250,76251,76308],{},[21880,76252,76253],{"width":29197},[21885,76254,76255,76257,76301,76303],{},[21888,76256],{"width":29202},[21888,76258,76259],{},[895,76260,76261,76263,76269,76271,76285,76287,76293,76295,76297,76299],{},[898,76262,2127],{},[1820,76264,76265,76267],{},[898,76266,2132],{},[898,76268,1873],{},[1655,76270,1657],{},[1949,76272,76273,76279],{},[895,76274,76275,76277],{},[898,76276,2410],{},[898,76278,1824],{},[895,76280,76281,76283],{},[898,76282,2410],{},[898,76284,1873],{},[1655,76286,1657],{},[2597,76288,76289,76291],{},[898,76290,1824],{},[1655,76292,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,76294,1664],{"stretchy":1663},[898,76296,1873],{},[1655,76298,1677],{"stretchy":1663},[898,76300,1719],{"mathvariant":1943},[21888,76302],{"width":29202},[21888,76304,76305],{},[2031,76306,76307],{},"(5.2)",[902,76309,76310],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,76312,76313,76314,21071,76332,76360,76361,76378,76379,3962,76396,5171],{},"Pro pevnou hodnotu ",[883,76315,76317],{"className":76316},[886],[888,76318,76319],{"xmlns":890},[892,76320,76321,76329],{},[895,76322,76323],{},[2597,76324,76325,76327],{},[898,76326,1873],{},[1655,76328,5603],{},[902,76330,76331],{"encoding":904},"L^*",[883,76333,76335],{"className":76334},[886],[888,76336,76337],{"xmlns":890},[892,76338,76339,76357],{},[895,76340,76341,76347,76349,76355],{},[2597,76342,76343,76345],{},[898,76344,1824],{},[1655,76346,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,76348,1664],{"stretchy":1663},[2597,76350,76351,76353],{},[898,76352,1873],{},[1655,76354,5603],{},[1655,76356,1677],{"stretchy":1663},[902,76358,76359],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,76362,76364],{"className":76363},[886],[888,76365,76366],{"xmlns":890},[892,76367,76368,76376],{},[895,76369,76370],{},[2597,76371,76372,76374],{},[898,76373,1873],{},[1655,76375,5603],{},[902,76377,76331],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,76380,76382],{"className":76381},[886],[888,76383,76384],{"xmlns":890},[892,76385,76386,76394],{},[895,76387,76388],{},[2597,76389,76390,76392],{},[898,76391,1873],{},[1655,76393,5603],{},[902,76395,76331],{"encoding":904},[883,76397,76399],{"className":76398},[886],[888,76400,76401],{"xmlns":890},[892,76402,76403,76415],{},[895,76404,76405,76411,76413],{},[2597,76406,76407,76409],{},[898,76408,1873],{},[1655,76410,5603],{},[1655,76412,2346],{},[1826,76414,1828],{},[902,76416,76417],{"encoding":904},"L^*+1",[5120,76419,76420],{},[724,76421,76422,19149,76424,76443,76444,76447,76448,1719],{},[883,76423,5406],{},[883,76425,76427],{"className":76426},[886],[888,76428,76429],{"xmlns":890},[892,76430,76431,76441],{},[895,76432,76433,76435],{},[898,76434,2127],{},[1820,76436,76437,76439],{},[898,76438,2132],{},[898,76440,1873],{},[902,76442,2137],{"encoding":904}," odpovídá na otázku „",[38,76445,76446],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,76449,76451],{"className":76450},[886],[888,76452,76453],{"xmlns":890},[892,76454,76455,76459],{},[895,76456,76457],{},[898,76458,1873],{},[902,76460,1873],{"encoding":904},[724,76462,76463,76466,76467,76483,76484,3962,76497,76517],{},[38,76464,76465],{},"Přibližná změna produkce"," pro změnu práce o ",[883,76468,76470],{"className":76469},[886],[888,76471,76472],{"xmlns":890},[892,76473,76474,76480],{},[895,76475,76476,76478],{},[898,76477,2410],{},[898,76479,1873],{},[902,76481,76482],{"encoding":904},"dL"," (z ",[883,76485,76487],{"className":76486},[886],[888,76488,76489],{"xmlns":890},[892,76490,76491,76495],{},[895,76492,76493],{},[898,76494,1873],{},[902,76496,1873],{"encoding":904},[883,76498,76500],{"className":76499},[886],[888,76501,76502],{"xmlns":890},[892,76503,76504,76514],{},[895,76505,76506,76508,76510,76512],{},[898,76507,1873],{},[1655,76509,2346],{},[898,76511,2410],{},[898,76513,1873],{},[902,76515,76516],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,76519,76521],{"className":76520},[886],[888,76522,76523],{"xmlns":890,"display":29192},[892,76524,76525,76590],{},[21880,76526,76527],{"width":29197},[21885,76528,76529,76531,76583,76585],{},[21888,76530],{"width":29202},[21888,76532,76533],{},[895,76534,76535,76537,76539,76541,76543,76545,76547,76553,76555,76557,76559,76561,76563,76565,76567,76569,76575,76577,76579,76581],{},[898,76536,2506],{"mathvariant":1943},[898,76538,1824],{},[1655,76540,2357],{},[898,76542,2410],{},[898,76544,1824],{},[1655,76546,1657],{},[2597,76548,76549,76551],{},[898,76550,1824],{},[1655,76552,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,76554,1664],{"stretchy":1663},[898,76556,1873],{},[1655,76558,1677],{"stretchy":1663},[2031,76560,2435],{},[898,76562,2410],{},[898,76564,1873],{},[1655,76566,1657],{},[898,76568,2127],{},[1820,76570,76571,76573],{},[898,76572,2132],{},[898,76574,1873],{},[2031,76576,2435],{},[898,76578,2410],{},[898,76580,1873],{},[898,76582,1719],{"mathvariant":1943},[21888,76584],{"width":29202},[21888,76586,76587],{},[2031,76588,76589],{},"(5.3)",[902,76591,76592],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,76594,76595,76596,1719],{},"Skutečná změna je ",[883,76597,76599],{"className":76598},[886],[888,76600,76601],{"xmlns":890},[892,76602,76603,76635],{},[895,76604,76605,76607,76609,76611,76613,76615,76617,76619,76621,76623,76625,76627,76629,76631,76633],{},[898,76606,2506],{"mathvariant":1943},[898,76608,1824],{},[1655,76610,1657],{},[898,76612,1824],{},[1655,76614,1664],{"stretchy":1663},[898,76616,1873],{},[1655,76618,2346],{},[898,76620,2410],{},[898,76622,1873],{},[1655,76624,1677],{"stretchy":1663},[1655,76626,2623],{},[898,76628,1824],{},[1655,76630,1664],{"stretchy":1663},[898,76632,1873],{},[1655,76634,1677],{"stretchy":1663},[902,76636,76637],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,76639,76641],{"id":76640},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,76643,76644,2115,76647,4421],{},[38,76645,76646],{},"Zákon klesajících výnosů",[614,76648,76649],{},"law of diminishing marginal productivity",[5120,76651,76652],{},[724,76653,76654,76655,76657],{},"Roste-li postupně některý ze vstupů (",[614,76656,38086],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,76659,76660],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,76662,76663,76664,3106,76685,76704,76705,76755,76756,76758,76759,3106,76779,76798,76799,76755,76831,4199,76833,76852,76853,22720,76870,76904,76905,9349,76922,76925],{},"1° ",[38,76665,76666,76667,2086],{},"Do bodu ",[883,76668,76670],{"className":76669},[886],[888,76671,76672],{"xmlns":890},[892,76673,76674,76682],{},[895,76675,76676],{},[1820,76677,76678,76680],{},[898,76679,1873],{},[1826,76681,2552],{},[902,76683,76684],{"encoding":904},"L_0",[883,76686,76688],{"className":76687},[886],[888,76689,76690],{"xmlns":890},[892,76691,76692,76702],{},[895,76693,76694,76696],{},[898,76695,2127],{},[1820,76697,76698,76700],{},[898,76699,2132],{},[898,76701,1873],{},[902,76703,2137],{"encoding":904}," roste, tj. ",[883,76706,76708],{"className":76707},[886],[888,76709,76710],{"xmlns":890},[892,76711,76712,76752],{},[895,76713,76714,76716,76718,76724,76730,76732,76742,76744,76746,76748,76750],{},[1655,76715,1664],{"stretchy":1663},[898,76717,2127],{},[1820,76719,76720,76722],{},[898,76721,2132],{},[898,76723,1873],{},[2597,76725,76726,76728],{},[1655,76727,1677],{"stretchy":1663},[1655,76729,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,76731,1657],{},[2597,76733,76734,76736],{},[898,76735,1824],{},[895,76737,76738,76740],{},[1655,76739,1945],{"mathvariant":1943},[1655,76741,1945],{"mathvariant":1943},[1655,76743,1664],{"stretchy":1663},[898,76745,1873],{},[1655,76747,1677],{"stretchy":1663},[1655,76749,2969],{},[1826,76751,2552],{},[902,76753,76754],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,76757,38790],{},".\n2° ",[38,76760,76761,76762,2086],{},"Od bodu ",[883,76763,76765],{"className":76764},[886],[888,76766,76767],{"xmlns":890},[892,76768,76769,76777],{},[895,76770,76771],{},[1820,76772,76773,76775],{},[898,76774,1873],{},[1826,76776,2552],{},[902,76778,76684],{"encoding":904},[883,76780,76782],{"className":76781},[886],[888,76783,76784],{"xmlns":890},[892,76785,76786,76796],{},[895,76787,76788,76790],{},[898,76789,2127],{},[1820,76791,76792,76794],{},[898,76793,2132],{},[898,76795,1873],{},[902,76797,2137],{"encoding":904}," klesá, ",[883,76800,76802],{"className":76801},[886],[888,76803,76804],{"xmlns":890},[892,76805,76806,76828],{},[895,76807,76808,76818,76820,76822,76824,76826],{},[2597,76809,76810,76812],{},[898,76811,1824],{},[895,76813,76814,76816],{},[1655,76815,1945],{"mathvariant":1943},[1655,76817,1945],{"mathvariant":1943},[1655,76819,1664],{"stretchy":1663},[898,76821,1873],{},[1655,76823,1677],{"stretchy":1663},[1655,76825,3065],{},[1826,76827,2552],{},[902,76829,76830],{"encoding":904},"Q''(L) \u003C 0",[38,76832,39614],{},[883,76834,76836],{"className":76835},[886],[888,76837,76838],{"xmlns":890},[892,76839,76840,76850],{},[895,76841,76842,76844],{},[898,76843,2127],{},[1820,76845,76846,76848],{},[898,76847,2132],{},[898,76849,1873],{},[902,76851,2137],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,76854,76856],{"className":76855},[886],[888,76857,76858],{"xmlns":890},[892,76859,76860,76868],{},[895,76861,76862],{},[1820,76863,76864,76866],{},[898,76865,1873],{},[1826,76867,1828],{},[902,76869,14337],{"encoding":904},[883,76871,76873],{"className":76872},[886],[888,76874,76875],{"xmlns":890},[892,76876,76877,76901],{},[895,76878,76879,76881,76887,76889,76895,76897,76899],{},[898,76880,2127],{},[1820,76882,76883,76885],{},[898,76884,2132],{},[898,76886,1873],{},[1655,76888,1664],{"stretchy":1663},[1820,76890,76891,76893],{},[898,76892,1873],{},[1826,76894,1828],{},[1655,76896,1677],{"stretchy":1663},[1655,76898,1657],{},[1826,76900,2552],{},[902,76902,76903],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,76906,76908],{"className":76907},[886],[888,76909,76910],{"xmlns":890},[892,76911,76912,76920],{},[895,76913,76914],{},[1820,76915,76916,76918],{},[898,76917,1873],{},[1826,76919,2552],{},[902,76921,76684],{"encoding":904},[38,76923,76924],{},"inflexním bodem"," produkční funkce.",[724,76927,76928,76929,2494,76946,1719],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,76930,76932],{"className":76931},[886],[888,76933,76934],{"xmlns":890},[892,76935,76936,76944],{},[895,76937,76938],{},[1820,76939,76940,76942],{},[898,76941,1873],{},[1826,76943,2552],{},[902,76945,76684],{"encoding":904},[883,76947,76949],{"className":76948},[886],[888,76950,76951],{"xmlns":890},[892,76952,76953,76975],{},[895,76954,76955,76965,76967,76969,76971,76973],{},[2597,76956,76957,76959],{},[898,76958,1824],{},[895,76960,76961,76963],{},[1655,76962,1945],{"mathvariant":1943},[1655,76964,1945],{"mathvariant":1943},[1655,76966,1664],{"stretchy":1663},[898,76968,1873],{},[1655,76970,1677],{"stretchy":1663},[1655,76972,3065],{},[1826,76974,2552],{},[902,76976,76830],{"encoding":904},[724,76978,76979,3106,76982,6918,77022,1343,77039,77056],{},[38,76980,76981],{},"Typický polynom třetího stupně:",[883,76983,76985],{"className":76984},[886],[888,76986,76987],{"xmlns":890},[892,76988,76989,77019],{},[895,76990,76991,76993,76995,76997,76999,77001,77003,77009,77011,77013],{},[898,76992,1824],{},[1655,76994,1664],{"stretchy":1663},[898,76996,1873],{},[1655,76998,1677],{"stretchy":1663},[1655,77000,1657],{},[898,77002,207],{},[2597,77004,77005,77007],{},[898,77006,1873],{},[1826,77008,3472],{},[1655,77010,2346],{},[898,77012,2025],{},[2597,77014,77015,77017],{},[898,77016,1873],{},[1826,77018,1837],{},[902,77020,77021],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,77023,77025],{"className":77024},[886],[888,77026,77027],{"xmlns":890},[892,77028,77029,77037],{},[895,77030,77031,77033,77035],{},[898,77032,207],{},[1655,77034,3065],{},[1826,77036,2552],{},[902,77038,44211],{"encoding":904},[883,77040,77042],{"className":77041},[886],[888,77043,77044],{"xmlns":890},[892,77045,77046,77054],{},[895,77047,77048,77050,77052],{},[898,77049,2025],{},[1655,77051,2969],{},[1826,77053,2552],{},[902,77055,19940],{"encoding":904},". Pak",[883,77058,77060],{"className":77059},[886],[888,77061,77062],{"xmlns":890,"display":29192},[892,77063,77064,77124],{},[895,77065,77066,77072,77074,77076,77084,77092,77094,77096,77102,77104,77106,77114,77122],{},[1820,77067,77068,77070],{},[898,77069,1873],{},[1826,77071,2552],{},[1655,77073,1657],{},[1655,77075,2623],{},[3615,77077,77078],{"scriptlevel":2552,"displaystyle":1663},[1949,77079,77080,77082],{},[1826,77081,1828],{},[1826,77083,3472],{},[3615,77085,77086],{"scriptlevel":2552,"displaystyle":1663},[1949,77087,77088,77090],{},[898,77089,2025],{},[898,77091,207],{},[1655,77093,1671],{"separator":1670},[1967,77095],{"width":1969},[1820,77097,77098,77100],{},[898,77099,1873],{},[1826,77101,1828],{},[1655,77103,1657],{},[1655,77105,2623],{},[3615,77107,77108],{"scriptlevel":2552,"displaystyle":1663},[1949,77109,77110,77112],{},[1826,77111,1837],{},[1826,77113,3472],{},[3615,77115,77116],{"scriptlevel":2552,"displaystyle":1663},[1949,77117,77118,77120],{},[898,77119,2025],{},[898,77121,207],{},[898,77123,1719],{"mathvariant":1943},[902,77125,77126],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,77128,77130,77131,1677],{"id":77129},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,77132,77134],{"className":77133},[886],[888,77135,77136],{"xmlns":890},[892,77137,77138,77148],{},[895,77139,77140,77142],{},[898,77141,2731],{},[1820,77143,77144,77146],{},[898,77145,2132],{},[898,77147,1873],{},[902,77149,75759],{"encoding":904},[724,77151,77152,2115,77155,76223,77158,77177],{},[38,77153,77154],{},"Průměrný produkt práce",[614,77156,77157],{},"average product of labour",[883,77159,77161],{"className":77160},[886],[888,77162,77163],{"xmlns":890},[892,77164,77165,77175],{},[895,77166,77167,77169],{},[898,77168,2731],{},[1820,77170,77171,77173],{},[898,77172,2132],{},[898,77174,1873],{},[902,77176,75759],{"encoding":904}," je podíl produkce a práce:",[883,77179,77181],{"className":77180},[886],[888,77182,77183],{"xmlns":890,"display":29192},[892,77184,77185,77220],{},[21880,77186,77187],{"width":29197},[21885,77188,77189,77191,77213,77215],{},[21888,77190],{"width":29202},[21888,77192,77193],{},[895,77194,77195,77197,77203,77205,77211],{},[898,77196,2731],{},[1820,77198,77199,77201],{},[898,77200,2132],{},[898,77202,1873],{},[1655,77204,1657],{},[1949,77206,77207,77209],{},[898,77208,1824],{},[898,77210,1873],{},[898,77212,1719],{"mathvariant":1943},[21888,77214],{"width":29202},[21888,77216,77217],{},[2031,77218,77219],{},"(5.4)",[902,77221,77222],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,77224,77225,77226,1719],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,77227,77229],{"className":77228},[886],[888,77230,77231],{"xmlns":890},[892,77232,77233,77243],{},[895,77234,77235,77237],{},[898,77236,2731],{},[1820,77238,77239,77241],{},[898,77240,2132],{},[898,77242,1873],{},[902,77244,75759],{"encoding":904},[115,77246,77248],{"id":77247},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,77250,77251],{},[1723,77252],{"alt":77253,"className":77254,"src":77255},"imek-q-mpl-apl-tripanel",[210,1727],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[5120,77257,77258],{},[724,77259,77260,77263,77264,3902,77283,77300,77301],{},[38,77261,77262],{},"Princip:"," Má-li ",[883,77265,77267],{"className":77266},[886],[888,77268,77269],{"xmlns":890},[892,77270,77271,77281],{},[895,77272,77273,77275],{},[898,77274,2731],{},[1820,77276,77277,77279],{},[898,77278,2132],{},[898,77280,1873],{},[902,77282,75759],{"encoding":904},[883,77284,77286],{"className":77285},[886],[888,77287,77288],{"xmlns":890},[892,77289,77290,77298],{},[895,77291,77292],{},[1820,77293,77294,77296],{},[898,77295,1873],{},[1826,77297,2552],{},[902,77299,76684],{"encoding":904}," maximum, pak platí\n",[883,77302,77304],{"className":77303,"title":5450,"style":5451},[5449],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,77306,77307,77308,77311,77312,3106,77316,1719],{},"Slovně: ",[38,77309,77310],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,77313,77315],{"className":77314,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,77317,77319],{"className":77318},[886],[888,77320,77321],{"xmlns":890},[892,77322,77323,77329],{},[895,77324,77325,77327],{},[898,77326,2731],{},[898,77328,4052],{},[902,77330,56686],{"encoding":904},[5120,77332,77333,77357],{},[724,77334,77335,77337,77338],{},[883,77336,5821],{}," Postup — jak najít max ",[883,77339,77341],{"className":77340},[886],[888,77342,77343],{"xmlns":890},[892,77344,77345,77355],{},[895,77346,77347,77349],{},[898,77348,2731],{},[1820,77350,77351,77353],{},[898,77352,2132],{},[898,77354,1873],{},[902,77356,75759],{"encoding":904},[152,77358,77359,77397,77479],{},[123,77360,77361,77362,77396],{},"Napište ",[883,77363,77365],{"className":77364},[886],[888,77366,77367],{"xmlns":890},[892,77368,77369,77393],{},[895,77370,77371,77373,77379,77381,77383,77385,77387,77389,77391],{},[898,77372,2731],{},[1820,77374,77375,77377],{},[898,77376,2132],{},[898,77378,1873],{},[1655,77380,1657],{},[898,77382,1824],{},[1655,77384,1664],{"stretchy":1663},[898,77386,1873],{},[1655,77388,1677],{"stretchy":1663},[898,77390,5923],{"mathvariant":1943},[898,77392,1873],{},[902,77394,77395],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,77398,77399,77400,77432,77433,77436,77437,1719],{},"Položte ",[883,77401,77403],{"className":77402},[886],[888,77404,77405],{"xmlns":890},[892,77406,77407,77429],{},[895,77408,77409,77411,77413,77419,77425,77427],{},[1655,77410,1664],{"stretchy":1663},[898,77412,2731],{},[1820,77414,77415,77417],{},[898,77416,2132],{},[898,77418,1873],{},[2597,77420,77421,77423],{},[1655,77422,1677],{"stretchy":1663},[1655,77424,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,77426,1657],{},[1826,77428,2552],{},[902,77430,77431],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,77434,77435],{},"Zkratka:"," můžete rovnou řešit ",[883,77438,77440],{"className":77439},[886],[888,77441,77442],{"xmlns":890},[892,77443,77444,77476],{},[895,77445,77446,77448,77454,77456,77458,77460,77462,77464,77470,77472,77474],{},[898,77447,2127],{},[1820,77449,77450,77452],{},[898,77451,2132],{},[898,77453,1873],{},[1655,77455,1664],{"stretchy":1663},[898,77457,1873],{},[1655,77459,1677],{"stretchy":1663},[1655,77461,1657],{},[898,77463,2731],{},[1820,77465,77466,77468],{},[898,77467,2132],{},[898,77469,1873],{},[1655,77471,1664],{"stretchy":1663},[898,77473,1873],{},[1655,77475,1677],{"stretchy":1663},[902,77477,77478],{"encoding":904},"MP_L(L) = AP_L(L)",[123,77480,77481],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,77483,66627],{"id":77484},"odvození",[724,77486,77487,77488,77521],{},"Z ",[883,77489,77491],{"className":77490},[886],[888,77492,77493],{"xmlns":890},[892,77494,77495,77519],{},[895,77496,77497,77499,77505,77507,77509,77511,77513,77515,77517],{},[898,77498,2731],{},[1820,77500,77501,77503],{},[898,77502,2132],{},[898,77504,1873],{},[1655,77506,1657],{},[898,77508,1824],{},[1655,77510,1664],{"stretchy":1663},[898,77512,1873],{},[1655,77514,1677],{"stretchy":1663},[898,77516,5923],{"mathvariant":1943},[898,77518,1873],{},[902,77520,77395],{"encoding":904}," a derivace podílu:",[883,77523,77525],{"className":77524},[886],[888,77526,77527],{"xmlns":890,"display":29192},[892,77528,77529,77682],{},[895,77530,77531,77533,77535,77541,77547,77549,77551,77553,77555,77595,77597,77603,77637,77639,77645,77648,77650,77656,77658,77660,77662,77664,77666,77672,77674,77676,77678,77680],{},[1655,77532,1664],{"stretchy":1663},[898,77534,2731],{},[1820,77536,77537,77539],{},[898,77538,2132],{},[898,77540,1873],{},[2597,77542,77543,77545],{},[1655,77544,1677],{"stretchy":1663},[1655,77546,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,77548,1664],{"stretchy":1663},[898,77550,1873],{},[1655,77552,1677],{"stretchy":1663},[1655,77554,1657],{},[1949,77556,77557,77589],{},[895,77558,77559,77565,77567,77569,77571,77573,77575,77577,77579,77581,77583,77585,77587],{},[2597,77560,77561,77563],{},[898,77562,1824],{},[1655,77564,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,77566,1664],{"stretchy":1663},[898,77568,1873],{},[1655,77570,1677],{"stretchy":1663},[1655,77572,2869],{},[898,77574,1873],{},[1655,77576,2623],{},[898,77578,1824],{},[1655,77580,1664],{"stretchy":1663},[898,77582,1873],{},[1655,77584,1677],{"stretchy":1663},[1655,77586,2869],{},[1826,77588,1828],{},[2597,77590,77591,77593],{},[898,77592,1873],{},[1826,77594,1837],{},[1655,77596,1657],{},[1949,77598,77599,77601],{},[1826,77600,1828],{},[898,77602,1873],{},[895,77604,77605,77607,77613,77615,77617,77619,77621,77635],{},[1655,77606,1664],{"fence":1670},[2597,77608,77609,77611],{},[898,77610,1824],{},[1655,77612,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,77614,1664],{"stretchy":1663},[898,77616,1873],{},[1655,77618,1677],{"stretchy":1663},[1655,77620,2623],{},[1949,77622,77623,77633],{},[895,77624,77625,77627,77629,77631],{},[898,77626,1824],{},[1655,77628,1664],{"stretchy":1663},[898,77630,1873],{},[1655,77632,1677],{"stretchy":1663},[898,77634,1873],{},[1655,77636,1677],{"fence":1670},[1655,77638,1657],{},[1949,77640,77641,77643],{},[1826,77642,1828],{},[898,77644,1873],{},[1655,77646,1664],{"fence":1670,"stretchy":1670,"minsize":77647,"maxsize":77647},"1.2em",[898,77649,2127],{},[1820,77651,77652,77654],{},[898,77653,2132],{},[898,77655,1873],{},[1655,77657,1664],{"stretchy":1663},[898,77659,1873],{},[1655,77661,1677],{"stretchy":1663},[1655,77663,2623],{},[898,77665,2731],{},[1820,77667,77668,77670],{},[898,77669,2132],{},[898,77671,1873],{},[1655,77673,1664],{"stretchy":1663},[898,77675,1873],{},[1655,77677,1677],{"stretchy":1663},[1655,77679,1677],{"fence":1670,"stretchy":1670,"minsize":77647,"maxsize":77647},[898,77681,1719],{"mathvariant":1943},[902,77683,77684],{"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).",[724,77686,1735,77687,9349,77709,77792],{},[883,77688,77690],{"className":77689},[886],[888,77691,77692],{"xmlns":890},[892,77693,77694,77706],{},[895,77695,77696,77702,77704],{},[1820,77697,77698,77700],{},[898,77699,1873],{},[1826,77701,2552],{},[1655,77703,2969],{},[1826,77705,2552],{},[902,77707,77708],{"encoding":904},"L_0 > 0",[883,77710,77712],{"className":77711},[886],[888,77713,77714],{"xmlns":890},[892,77715,77716,77789],{},[895,77717,77718,77720,77722,77728,77734,77736,77742,77744,77746,77748,77751,77753,77759,77761,77767,77769,77771,77773,77779,77781,77787],{},[1655,77719,1664],{"stretchy":1663},[898,77721,2731],{},[1820,77723,77724,77726],{},[898,77725,2132],{},[898,77727,1873],{},[2597,77729,77730,77732],{},[1655,77731,1677],{"stretchy":1663},[1655,77733,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,77735,1664],{"stretchy":1663},[1820,77737,77738,77740],{},[898,77739,1873],{},[1826,77741,2552],{},[1655,77743,1677],{"stretchy":1663},[1655,77745,1657],{},[1826,77747,2552],{},[1655,77749,77750],{},"⇔",[898,77752,2127],{},[1820,77754,77755,77757],{},[898,77756,2132],{},[898,77758,1873],{},[1655,77760,1664],{"stretchy":1663},[1820,77762,77763,77765],{},[898,77764,1873],{},[1826,77766,2552],{},[1655,77768,1677],{"stretchy":1663},[1655,77770,1657],{},[898,77772,2731],{},[1820,77774,77775,77777],{},[898,77776,2132],{},[898,77778,1873],{},[1655,77780,1664],{"stretchy":1663},[1820,77782,77783,77785],{},[898,77784,1873],{},[1826,77786,2552],{},[1655,77788,1677],{"stretchy":1663},[902,77790,77791],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,77794,77796],{"id":77795},"příklad-51","Příklad 5.1",[724,77798,77799,77800,1719],{},"Je dána produkce ",[883,77801,77803],{"className":77802},[886],[888,77804,77805],{"xmlns":890},[892,77806,77807,77831],{},[895,77808,77809,77811,77813,77815,77821,77823,77825],{},[898,77810,1824],{},[1655,77812,1657],{},[1826,77814,3531],{},[2597,77816,77817,77819],{},[898,77818,1873],{},[1826,77820,1837],{},[1655,77822,2623],{},[1826,77824,4112],{},[2597,77826,77827,77829],{},[898,77828,1873],{},[1826,77830,3472],{},[902,77832,77833],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,77835,77836,58648,77839,77889,77890,1719],{},[38,77837,77838],{},"(a)",[883,77840,77842],{"className":77841},[886],[888,77843,77844],{"xmlns":890},[892,77845,77846,77886],{},[895,77847,77848,77850,77852,77854,77856,77858,77860,77862,77864,77866,77868,77870,77872,77874,77876,77878,77880,77882,77884],{},[898,77849,1873],{},[1655,77851,1657],{},[1826,77853,1837],{},[1655,77855,1671],{"separator":1670},[1826,77857,3524],{},[1655,77859,1671],{"separator":1670},[1826,77861,6834],{},[1655,77863,1671],{"separator":1670},[1826,77865,4136],{},[1655,77867,1671],{"separator":1670},[1826,77869,24072],{},[1655,77871,1671],{"separator":1670},[1826,77873,4969],{},[1655,77875,1671],{"separator":1670},[1826,77877,10282],{},[1655,77879,1671],{"separator":1670},[1826,77881,39472],{},[1655,77883,1671],{"separator":1670},[1826,77885,6253],{},[902,77887,77888],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,77891,77893],{"className":77892},[886],[888,77894,77895],{"xmlns":890},[892,77896,77897,77907],{},[895,77898,77899,77901],{},[898,77900,2127],{},[1820,77902,77903,77905],{},[898,77904,2132],{},[898,77906,1873],{},[902,77908,2137],{"encoding":904},[724,77910,77911,77912,36094],{},"Podle (5.2): ",[883,77913,77915],{"className":77914},[886],[888,77916,77917],{"xmlns":890},[892,77918,77919,77975],{},[895,77920,77921,77923,77929,77931,77937,77939,77941,77943,77945,77947,77949,77951,77953,77959,77961,77963,77965,77967,77969,77971,77973],{},[898,77922,2127],{},[1820,77924,77925,77927],{},[898,77926,2132],{},[898,77928,1873],{},[1655,77930,1657],{},[2597,77932,77933,77935],{},[898,77934,1824],{},[1655,77936,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,77938,1664],{"stretchy":1663},[898,77940,1873],{},[1655,77942,1677],{"stretchy":1663},[1655,77944,1657],{},[1826,77946,4771],{},[898,77948,1873],{},[1655,77950,2623],{},[1826,77952,20447],{},[2597,77954,77955,77957],{},[898,77956,1873],{},[1826,77958,1837],{},[1655,77960,1657],{},[898,77962,1873],{},[1655,77964,1664],{"stretchy":1663},[1826,77966,4771],{},[1655,77968,2623],{},[1826,77970,20447],{},[898,77972,1873],{},[1655,77974,1677],{"stretchy":1663},[902,77976,77977],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,77979,77980,78017],{},[19,77981,77982],{},[22,77983,77984,77999,78001,78003,78005,78007,78009,78011,78013,78015],{},[25,77985,77986],{},[883,77987,77989],{"className":77988},[886],[888,77990,77991],{"xmlns":890},[892,77992,77993,77997],{},[895,77994,77995],{},[898,77996,1873],{},[902,77998,1873],{"encoding":904},[25,78000,1837],{},[25,78002,3524],{},[25,78004,6834],{},[25,78006,4136],{},[25,78008,24072],{},[25,78010,4969],{},[25,78012,10282],{},[25,78014,39472],{},[25,78016,6253],{},[30,78018,78019],{},[22,78020,78021,78042,78045,78048,78051,78053,78056,78058,78060,78079],{},[35,78022,78023],{},[883,78024,78026],{"className":78025},[886],[888,78027,78028],{"xmlns":890},[892,78029,78030,78040],{},[895,78031,78032,78034],{},[898,78033,2127],{},[1820,78035,78036,78038],{},[898,78037,2132],{},[898,78039,1873],{},[902,78041,2137],{"encoding":904},[35,78043,78044],{},"21,6",[35,78046,78047],{},"45",[35,78049,78050],{},"57,6",[35,78052,4396],{},[35,78054,78055],{},"50,4",[35,78057,78044],{},[35,78059,2552],{},[35,78061,78062],{},[883,78063,78065],{"className":78064},[886],[888,78066,78067],{"xmlns":890},[892,78068,78069,78076],{},[895,78070,78071,78073],{},[1655,78072,2623],{},[1826,78074,78075],{},"12,6",[902,78077,78078],{"encoding":904},"-12{,}6",[35,78080,78081],{},[883,78082,78084],{"className":78083},[886],[888,78085,78086],{"xmlns":890},[892,78087,78088,78094],{},[895,78089,78090,78092],{},[1655,78091,2623],{},[1826,78093,46578],{},[902,78095,78096],{"encoding":904},"-75",[724,78098,78099,78118,78119,78137,78138,78155,78156,78174,78175,78199,78200,78218],{},[883,78100,78102],{"className":78101},[886],[888,78103,78104],{"xmlns":890},[892,78105,78106,78116],{},[895,78107,78108,78110],{},[898,78109,2127],{},[1820,78111,78112,78114],{},[898,78113,2132],{},[898,78115,1873],{},[902,78117,2137],{"encoding":904}," nabývá maxima pro ",[883,78120,78122],{"className":78121},[886],[888,78123,78124],{"xmlns":890},[892,78125,78126,78134],{},[895,78127,78128,78130,78132],{},[898,78129,1873],{},[1655,78131,1657],{},[1826,78133,4136],{},[902,78135,78136],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,78139,78141],{"className":78140},[886],[888,78142,78143],{"xmlns":890},[892,78144,78145,78153],{},[895,78146,78147,78149,78151],{},[898,78148,1873],{},[1655,78150,1657],{},[1826,78152,4136],{},[902,78154,78136],{"encoding":904}," přírůstky klesají, v ",[883,78157,78159],{"className":78158},[886],[888,78160,78161],{"xmlns":890},[892,78162,78163,78171],{},[895,78164,78165,78167,78169],{},[898,78166,1873],{},[1655,78168,1657],{},[1826,78170,10282],{},[902,78172,78173],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,78176,78178],{"className":78177},[886],[888,78179,78180],{"xmlns":890},[892,78181,78182,78196],{},[895,78183,78184,78186,78188,78190,78192,78194],{},[898,78185,1824],{},[1655,78187,1664],{"stretchy":1663},[1826,78189,10282],{},[1655,78191,1677],{"stretchy":1663},[1655,78193,1657],{},[1826,78195,24984],{},[902,78197,78198],{"encoding":904},"Q(20) = 800","), od ",[883,78201,78203],{"className":78202},[886],[888,78204,78205],{"xmlns":890},[892,78206,78207,78215],{},[895,78208,78209,78211,78213],{},[898,78210,1873],{},[1655,78212,2969],{},[1826,78214,10282],{},[902,78216,78217],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,78220,78221],{},[614,78222,78223,78224,78264,78265,3902,78283,1719],{},"Obrázek 5.1 — graf produkce ",[883,78225,78227],{"className":78226},[886],[888,78228,78229],{"xmlns":890},[892,78230,78231,78261],{},[895,78232,78233,78235,78237,78239,78241,78243,78245,78251,78253,78255],{},[898,78234,1824],{},[1655,78236,1664],{"stretchy":1663},[898,78238,1873],{},[1655,78240,1677],{"stretchy":1663},[1655,78242,1657],{},[1826,78244,3531],{},[2597,78246,78247,78249],{},[898,78248,1873],{},[1826,78250,1837],{},[1655,78252,2623],{},[1826,78254,4112],{},[2597,78256,78257,78259],{},[898,78258,1873],{},[1826,78260,3472],{},[902,78262,78263],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,78266,78268],{"className":78267},[886],[888,78269,78270],{"xmlns":890},[892,78271,78272,78280],{},[895,78273,78274,78276,78278],{},[898,78275,1824],{},[1655,78277,1657],{},[1826,78279,24984],{},[902,78281,78282],{"encoding":904},"Q = 800",[883,78284,78286],{"className":78285},[886],[888,78287,78288],{"xmlns":890},[892,78289,78290,78298],{},[895,78291,78292,78294,78296],{},[898,78293,1873],{},[1655,78295,1657],{},[1826,78297,10282],{},[902,78299,78173],{"encoding":904},[724,78301,78302,78305],{},[38,78303,78304],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,78307,78308,78309,1343,78327,2086],{},"Podle (5.3) s ",[883,78310,78312],{"className":78311},[886],[888,78313,78314],{"xmlns":890},[892,78315,78316,78324],{},[895,78317,78318,78320,78322],{},[898,78319,1873],{},[1655,78321,1657],{},[1826,78323,3531],{},[902,78325,78326],{"encoding":904},"L = 6",[883,78328,78330],{"className":78329},[886],[888,78331,78332],{"xmlns":890},[892,78333,78334,78344],{},[895,78335,78336,78338,78340,78342],{},[898,78337,2410],{},[898,78339,1873],{},[1655,78341,1657],{},[1826,78343,3472],{},[902,78345,78346],{"encoding":904},"dL = 3",[883,78348,78350],{"className":78349},[886],[888,78351,78352],{"xmlns":890,"display":29192},[892,78353,78354,78417],{},[895,78355,78356,78358,78360,78362,78364,78370,78372,78374,78376,78378,78380,78382,78384,78386,78388,78390,78392,78394,78396,78398,78400,78402,78404,78406,78408,78410,78412,78414],{},[898,78357,2410],{},[898,78359,1824],{},[1655,78361,1657],{},[898,78363,2127],{},[1820,78365,78366,78368],{},[898,78367,2132],{},[898,78369,1873],{},[1655,78371,1664],{"stretchy":1663},[1826,78373,3531],{},[1655,78375,1677],{"stretchy":1663},[1655,78377,2869],{},[1826,78379,3472],{},[1655,78381,1657],{},[1655,78383,1664],{"stretchy":1663},[1826,78385,4771],{},[1655,78387,2869],{},[1826,78389,3531],{},[1655,78391,2623],{},[1826,78393,20447],{},[1655,78395,2869],{},[1826,78397,6814],{},[1655,78399,1677],{"stretchy":1663},[1655,78401,2869],{},[1826,78403,3472],{},[1655,78405,1657],{},[1826,78407,78055],{},[1655,78409,2869],{},[1826,78411,3472],{},[1655,78413,1657],{},[1826,78415,78416],{},"151,2.",[902,78418,78419],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,78421,78422,78423,58878,78448,78462,78463,1719],{},"Produkce vzroste z ",[883,78424,78426],{"className":78425},[886],[888,78427,78428],{"xmlns":890},[892,78429,78430,78445],{},[895,78431,78432,78434,78436,78438,78440,78442],{},[898,78433,1824],{},[1655,78435,1664],{"stretchy":1663},[1826,78437,3531],{},[1655,78439,1677],{"stretchy":1663},[1655,78441,1657],{},[1826,78443,78444],{},"172,8",[902,78446,78447],{"encoding":904},"Q(6) = 172{,}8",[883,78449,78451],{"className":78450},[886],[888,78452,78453],{"xmlns":890},[892,78454,78455,78460],{},[895,78456,78457],{},[1826,78458,78459],{},"324",[902,78461,78459],{"encoding":904},". Skutečná hodnota: ",[883,78464,78466],{"className":78465},[886],[888,78467,78468],{"xmlns":890},[892,78469,78470,78510],{},[895,78471,78472,78474,78476,78478,78480,78482,78484,78486,78488,78490,78492,78494,78496,78498,78501,78503,78505,78507],{},[898,78473,2506],{"mathvariant":1943},[898,78475,1824],{},[1655,78477,1657],{},[898,78479,1824],{},[1655,78481,1664],{"stretchy":1663},[1826,78483,5250],{},[1655,78485,1677],{"stretchy":1663},[1655,78487,2623],{},[898,78489,1824],{},[1655,78491,1664],{"stretchy":1663},[1826,78493,3531],{},[1655,78495,1677],{"stretchy":1663},[1655,78497,1657],{},[1826,78499,78500],{},"340,2",[1655,78502,2623],{},[1826,78504,78444],{},[1655,78506,1657],{},[1826,78508,78509],{},"167,4",[902,78511,78512],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,78514,78516],{"id":78515},"příklad-52","Příklad 5.2",[724,78518,78519,78520,1719],{},"Ověříme princip (5.5) pro ",[883,78521,78523],{"className":78522},[886],[888,78524,78525],{"xmlns":890},[892,78526,78527,78551],{},[895,78528,78529,78531,78533,78535,78541,78543,78545],{},[898,78530,1824],{},[1655,78532,1657],{},[1826,78534,3531],{},[2597,78536,78537,78539],{},[898,78538,1873],{},[1826,78540,1837],{},[1655,78542,2623],{},[1826,78544,4112],{},[2597,78546,78547,78549],{},[898,78548,1873],{},[1826,78550,3472],{},[902,78552,77833],{"encoding":904},[883,78554,78556],{"className":78555},[886],[888,78557,78558],{"xmlns":890,"display":29192},[892,78559,78560,78638],{},[895,78561,78562,78564,78570,78572,78578,78580,78582,78584,78586,78588,78594,78596,78598,78600,78608,78610,78612,78614,78616,78618,78620,78622,78624,78626,78628,78634,78636],{},[898,78563,2731],{},[1820,78565,78566,78568],{},[898,78567,2132],{},[898,78569,1873],{},[1655,78571,1657],{},[1949,78573,78574,78576],{},[898,78575,1824],{},[898,78577,1873],{},[1655,78579,1657],{},[1826,78581,3531],{},[898,78583,1873],{},[1655,78585,2623],{},[1826,78587,4112],{},[2597,78589,78590,78592],{},[898,78591,1873],{},[1826,78593,1837],{},[1655,78595,1671],{"separator":1670},[1967,78597],{"width":16409},[898,78599,2731],{},[1935,78601,78602,78604,78606],{},[898,78603,2132],{},[898,78605,1873],{},[1655,78607,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,78609,1657],{},[1826,78611,3531],{},[1655,78613,2623],{},[1826,78615,20397],{},[898,78617,1873],{},[1655,78619,1657],{},[1826,78621,2552],{},[2031,78623,2783],{},[1655,78625,5238],{},[2031,78627,2783],{},[1820,78629,78630,78632],{},[898,78631,1873],{},[1826,78633,2552],{},[1655,78635,1657],{},[1826,78637,69409],{},[902,78639,78640],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,78642,78643,78679,78680,78698,78699,1719],{},[883,78644,78646],{"className":78645},[886],[888,78647,78648],{"xmlns":890},[892,78649,78650,78676],{},[895,78651,78652,78654,78666,78668,78670,78672,78674],{},[898,78653,2731],{},[1935,78655,78656,78658,78660],{},[898,78657,2132],{},[898,78659,1873],{},[895,78661,78662,78664],{},[1655,78663,1945],{"mathvariant":1943},[1655,78665,1945],{"mathvariant":1943},[1655,78667,1657],{},[1655,78669,2623],{},[1826,78671,20397],{},[1655,78673,3065],{},[1826,78675,2552],{},[902,78677,78678],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,78681,78683],{"className":78682},[886],[888,78684,78685],{"xmlns":890},[892,78686,78687,78695],{},[895,78688,78689,78691,78693],{},[898,78690,1873],{},[1655,78692,1657],{},[1826,78694,37370],{},[902,78696,78697],{"encoding":904},"L = 15"," je maximum, ",[883,78700,78702],{"className":78701},[886],[888,78703,78704],{"xmlns":890},[892,78705,78706,78752],{},[895,78707,78708,78710,78716,78718,78720,78722,78724,78726,78728,78730,78732,78734,78736,78739,78741,78744,78746,78748,78750],{},[898,78709,2731],{},[1820,78711,78712,78714],{},[898,78713,2132],{},[898,78715,1873],{},[1655,78717,1664],{"stretchy":1663},[1826,78719,37370],{},[1655,78721,1677],{"stretchy":1663},[1655,78723,1657],{},[1826,78725,3531],{},[1655,78727,2869],{},[1826,78729,37370],{},[1655,78731,2623],{},[1826,78733,4112],{},[1655,78735,2869],{},[1826,78737,78738],{},"225",[1655,78740,1657],{},[1826,78742,78743],{},"90",[1655,78745,2623],{},[1826,78747,78047],{},[1655,78749,1657],{},[1826,78751,78047],{},[902,78753,78754],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,78756,78757,43006,78813,78859],{},[883,78758,78760],{"className":78759},[886],[888,78761,78762],{"xmlns":890},[892,78763,78764,78810],{},[895,78765,78766,78768,78774,78776,78778,78780,78782,78784,78786,78788,78790,78792,78794,78796,78798,78801,78803,78806,78808],{},[898,78767,2127],{},[1820,78769,78770,78772],{},[898,78771,2132],{},[898,78773,1873],{},[1655,78775,1664],{"stretchy":1663},[1826,78777,37370],{},[1655,78779,1677],{"stretchy":1663},[1655,78781,1657],{},[1826,78783,4771],{},[1655,78785,2869],{},[1826,78787,37370],{},[1655,78789,2623],{},[1826,78791,20447],{},[1655,78793,2869],{},[1826,78795,78738],{},[1655,78797,1657],{},[1826,78799,78800],{},"180",[1655,78802,2623],{},[1826,78804,78805],{},"135",[1655,78807,1657],{},[1826,78809,78047],{},[902,78811,78812],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,78814,78816],{"className":78815},[886],[888,78817,78818],{"xmlns":890},[892,78819,78820,78856],{},[895,78821,78822,78824,78830,78832,78834,78836,78838,78840,78846,78848,78850,78852,78854],{},[898,78823,2127],{},[1820,78825,78826,78828],{},[898,78827,2132],{},[898,78829,1873],{},[1655,78831,1664],{"stretchy":1663},[1826,78833,37370],{},[1655,78835,1677],{"stretchy":1663},[1655,78837,1657],{},[898,78839,2731],{},[1820,78841,78842,78844],{},[898,78843,2132],{},[898,78845,1873],{},[1655,78847,1664],{"stretchy":1663},[1826,78849,37370],{},[1655,78851,1677],{"stretchy":1663},[1655,78853,1657],{},[1826,78855,78047],{},[902,78857,78858],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,78861,78862,78865,78866,18702,78895,1719],{},[38,78863,78864],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,78867,78869],{"className":78868},[886],[888,78870,78871],{"xmlns":890},[892,78872,78873,78893],{},[895,78874,78875,78877,78883,78885,78887],{},[898,78876,2127],{},[1820,78878,78879,78881],{},[898,78880,2132],{},[898,78882,1873],{},[1655,78884,1657],{},[898,78886,2731],{},[1820,78888,78889,78891],{},[898,78890,2132],{},[898,78892,1873],{},[902,78894,75789],{"encoding":904},[883,78896,78898],{"className":78897},[886],[888,78899,78900],{"xmlns":890},[892,78901,78902,78942],{},[895,78903,78904,78906,78908,78910,78912,78918,78920,78922,78924,78926,78928,78934,78936,78938,78940],{},[1826,78905,4771],{},[898,78907,1873],{},[1655,78909,2623],{},[1826,78911,20447],{},[2597,78913,78914,78916],{},[898,78915,1873],{},[1826,78917,1837],{},[1655,78919,1657],{},[1826,78921,3531],{},[898,78923,1873],{},[1655,78925,2623],{},[1826,78927,4112],{},[2597,78929,78930,78932],{},[898,78931,1873],{},[1826,78933,1837],{},[1655,78935,5238],{},[898,78937,1873],{},[1655,78939,1657],{},[1826,78941,37370],{},[902,78943,78944],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,78946,78947],{},[614,78948,78949,78950,78969,78970,13253,78988,79007,79008,79026,79027,79044,79045,79064,79065,79084],{},"Obrázek 5.3 — křivky ",[883,78951,78953],{"className":78952},[886],[888,78954,78955],{"xmlns":890},[892,78956,78957,78967],{},[895,78958,78959,78961],{},[898,78960,2127],{},[1820,78962,78963,78965],{},[898,78964,2132],{},[898,78966,1873],{},[902,78968,2137],{"encoding":904}," (max 60 při ",[883,78971,78973],{"className":78972},[886],[888,78974,78975],{"xmlns":890},[892,78976,78977,78985],{},[895,78978,78979,78981,78983],{},[898,78980,1873],{},[1655,78982,1657],{},[1826,78984,4136],{},[902,78986,78987],{"encoding":904},"L=10",[883,78989,78991],{"className":78990},[886],[888,78992,78993],{"xmlns":890},[892,78994,78995,79005],{},[895,78996,78997,78999],{},[898,78998,2731],{},[1820,79000,79001,79003],{},[898,79002,2132],{},[898,79004,1873],{},[902,79006,75759],{"encoding":904}," (max 45 při ",[883,79009,79011],{"className":79010},[886],[888,79012,79013],{"xmlns":890},[892,79014,79015,79023],{},[895,79016,79017,79019,79021],{},[898,79018,1873],{},[1655,79020,1657],{},[1826,79022,37370],{},[902,79024,79025],{"encoding":904},"L=15","), průsečík v ",[883,79028,79030],{"className":79029},[886],[888,79031,79032],{"xmlns":890},[892,79033,79034,79042],{},[895,79035,79036,79038,79040],{},[898,79037,1873],{},[1655,79039,1657],{},[1826,79041,37370],{},[902,79043,78697],{"encoding":904},". Nalevo od 15 leží ",[883,79046,79048],{"className":79047},[886],[888,79049,79050],{"xmlns":890},[892,79051,79052,79062],{},[895,79053,79054,79056],{},[898,79055,2127],{},[1820,79057,79058,79060],{},[898,79059,2132],{},[898,79061,1873],{},[902,79063,2137],{"encoding":904}," nad ",[883,79066,79068],{"className":79067},[886],[888,79069,79070],{"xmlns":890},[892,79071,79072,79082],{},[895,79073,79074,79076],{},[898,79075,2731],{},[1820,79077,79078,79080],{},[898,79079,2132],{},[898,79081,1873],{},[902,79083,75759],{"encoding":904},", napravo pod ní.",[115,79086,79088],{"id":79087},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,79090,79091,79092,3962,79105,3106,79108,7437,79121,3106,79124,2086],{},"V dvoufaktorovém modelu závisí produkce ",[883,79093,79095],{"className":79094},[886],[888,79096,79097],{"xmlns":890},[892,79098,79099,79103],{},[895,79100,79101],{},[898,79102,1824],{},[902,79104,1824],{"encoding":904},[38,79106,79107],{},"práci",[883,79109,79111],{"className":79110},[886],[888,79112,79113],{"xmlns":890},[892,79114,79115,79119],{},[895,79116,79117],{},[898,79118,1873],{},[902,79120,1873],{"encoding":904},[38,79122,79123],{},"kapitálu",[883,79125,79127],{"className":79126},[886],[888,79128,79129],{"xmlns":890},[892,79130,79131,79135],{},[895,79132,79133],{},[898,79134,1878],{},[902,79136,1878],{"encoding":904},[883,79138,79140],{"className":79139},[886],[888,79141,79142],{"xmlns":890,"display":29192},[892,79143,79144,79179],{},[21880,79145,79146],{"width":29197},[21885,79147,79148,79150,79172,79174],{},[21888,79149],{"width":29202},[21888,79151,79152],{},[895,79153,79154,79156,79158,79160,79162,79164,79166,79168,79170],{},[898,79155,1824],{},[1655,79157,1657],{},[898,79159,1824],{},[1655,79161,1664],{"stretchy":1663},[898,79163,1873],{},[1655,79165,1671],{"separator":1670},[898,79167,1878],{},[1655,79169,1677],{"stretchy":1663},[898,79171,1719],{"mathvariant":1943},[21888,79173],{"width":29202},[21888,79175,79176],{},[2031,79177,79178],{},"(5.6)",[902,79180,79181],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,79183,79184,79185,79187],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,79186,76126],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,79189,79191],{"id":79190},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,79193,79194],{},"Široce používané produkční funkce mají tvar",[883,79196,79198],{"className":79197},[886],[888,79199,79200],{"xmlns":890,"display":29192},[892,79201,79202,79243],{},[21880,79203,79204],{"width":29197},[21885,79205,79206,79208,79236,79238],{},[21888,79207],{"width":29202},[21888,79209,79210],{},[895,79211,79212,79214,79216,79218,79220,79226,79228,79234],{},[898,79213,1824],{},[1655,79215,1657],{},[898,79217,2731],{},[2031,79219,2435],{},[2597,79221,79222,79224],{},[898,79223,1873],{},[898,79225,207],{},[2031,79227,2435],{},[2597,79229,79230,79232],{},[898,79231,1878],{},[898,79233,2025],{},[1655,79235,1671],{"separator":1670},[21888,79237],{"width":29202},[21888,79239,79240],{},[2031,79241,79242],{},"(5.7)",[902,79244,79245],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,79247,5559,79248,79270,79271,79273,79274,1719],{},[883,79249,79251],{"className":79250},[886],[888,79252,79253],{"xmlns":890},[892,79254,79255,79267],{},[895,79256,79257,79259,79261,79263,79265],{},[898,79258,2731],{},[1655,79260,1671],{"separator":1670},[898,79262,207],{},[1655,79264,1671],{"separator":1670},[898,79266,2025],{},[902,79268,79269],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,79272,75825],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,79275,79277],{"className":79276},[886],[888,79278,79279],{"xmlns":890},[892,79280,79281,79293],{},[895,79282,79283,79285,79287,79289,79291],{},[898,79284,207],{},[1655,79286,1671],{"separator":1670},[898,79288,2025],{},[1655,79290,3065],{},[1826,79292,1828],{},[902,79294,79295],{"encoding":904},"a, b \u003C 1",[724,79297,79298],{},[1723,79299],{"alt":79300,"className":79301,"src":79302},"imek-vynosy-z-rozsahu-3typy",[210,1727],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,79304,79305,79306,79309,79310,3962,79323,79339,79340,3962,79353,2086],{},"Reflektují ekonomickou zákonitost, že ",[38,79307,79308],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,79311,79313],{"className":79312},[886],[888,79314,79315],{"xmlns":890},[892,79316,79317,79321],{},[895,79318,79319],{},[898,79320,1873],{},[902,79322,1873],{"encoding":904},[883,79324,79326],{"className":79325},[886],[888,79327,79328],{"xmlns":890},[892,79329,79330,79336],{},[895,79331,79332,79334],{},[898,79333,13166],{},[898,79335,1873],{},[902,79337,79338],{"encoding":904},"rL"," a kapitál z ",[883,79341,79343],{"className":79342},[886],[888,79344,79345],{"xmlns":890},[892,79346,79347,79351],{},[895,79348,79349],{},[898,79350,1878],{},[902,79352,1878],{"encoding":904},[883,79354,79356],{"className":79355},[886],[888,79357,79358],{"xmlns":890},[892,79359,79360,79366],{},[895,79361,79362,79364],{},[898,79363,13166],{},[898,79365,1878],{},[902,79367,79368],{"encoding":904},"rK",[883,79370,79372],{"className":79371},[886],[888,79373,79374],{"xmlns":890,"display":29192},[892,79375,79376,79499],{},[21880,79377,79378],{"width":29197},[21885,79379,79380,79382,79492,79494],{},[21888,79381],{"width":29202},[21888,79383,79384],{},[895,79385,79386,79388,79390,79392,79394,79396,79398,79400,79402,79404,79406,79408,79410,79412,79418,79420,79422,79424,79430,79432,79434,79436,79448,79450,79456,79462,79464,79476,79478,79480,79482,79484,79486,79488,79490],{},[898,79387,1824],{},[1655,79389,1664],{"stretchy":1663},[898,79391,13166],{},[898,79393,1873],{},[1655,79395,1671],{"separator":1670},[898,79397,13166],{},[898,79399,1878],{},[1655,79401,1677],{"stretchy":1663},[1655,79403,1657],{},[898,79405,2731],{},[1655,79407,1664],{"stretchy":1663},[898,79409,13166],{},[898,79411,1873],{},[2597,79413,79414,79416],{},[1655,79415,1677],{"stretchy":1663},[898,79417,207],{},[1655,79419,1664],{"stretchy":1663},[898,79421,13166],{},[898,79423,1878],{},[2597,79425,79426,79428],{},[1655,79427,1677],{"stretchy":1663},[898,79429,2025],{},[1655,79431,1657],{},[898,79433,2731],{},[2031,79435,2435],{},[2597,79437,79438,79440],{},[898,79439,13166],{},[895,79441,79442,79444,79446],{},[898,79443,207],{},[1655,79445,2346],{},[898,79447,2025],{},[2031,79449,2435],{},[2597,79451,79452,79454],{},[898,79453,1873],{},[898,79455,207],{},[2597,79457,79458,79460],{},[898,79459,1878],{},[898,79461,2025],{},[1655,79463,1657],{},[2597,79465,79466,79468],{},[898,79467,13166],{},[895,79469,79470,79472,79474],{},[898,79471,207],{},[1655,79473,2346],{},[898,79475,2025],{},[2031,79477,2435],{},[898,79479,1824],{},[1655,79481,1664],{"stretchy":1663},[898,79483,1873],{},[1655,79485,1671],{"separator":1670},[898,79487,1878],{},[1655,79489,1677],{"stretchy":1663},[898,79491,1719],{"mathvariant":1943},[21888,79493],{"width":29202},[21888,79495,79496],{},[2031,79497,79498],{},"(5.8)",[902,79500,79501],{"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}",[724,79503,79504,79505],{},"Volně: ",[38,79506,79507,79508,79521,79522,79546],{},"změní-li se vstupy ",[883,79509,79511],{"className":79510},[886],[888,79512,79513],{"xmlns":890},[892,79514,79515,79519],{},[895,79516,79517],{},[898,79518,13166],{},[902,79520,13166],{"encoding":904},"-krát, změní se výstup ",[883,79523,79525],{"className":79524},[886],[888,79526,79527],{"xmlns":890},[892,79528,79529,79543],{},[895,79530,79531],{},[2597,79532,79533,79535],{},[898,79534,13166],{},[895,79536,79537,79539,79541],{},[898,79538,207],{},[1655,79540,2346],{},[898,79542,2025],{},[902,79544,79545],{"encoding":904},"r^{a+b}","-krát.",[198,79548,79550],{"id":79549},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,79552,79553,79554,79571],{},"Součet exponentů ",[883,79555,79557],{"className":79556},[886],[888,79558,79559],{"xmlns":890},[892,79560,79561,79569],{},[895,79562,79563,79565,79567],{},[898,79564,207],{},[1655,79566,2346],{},[898,79568,2025],{},[902,79570,75950],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,79573,79574,79603],{},[19,79575,79576],{},[22,79577,79578,79581,79584,79601],{},[25,79579,79580],{},"Typ",[25,79582,79583],{},"Podmínka",[25,79585,79586,79587,79600],{},"Chování produkce při ",[883,79588,79590],{"className":79589},[886],[888,79591,79592],{"xmlns":890},[892,79593,79594,79598],{},[895,79595,79596],{},[898,79597,13166],{},[902,79599,13166],{"encoding":904},"-násobném zvýšení vstupů",[25,79602,4340],{},[30,79604,79605,79716,79831],{},[22,79606,79607,79615,79639,79672],{},[35,79608,76663,79609,2115,79612,1677],{},[38,79610,79611],{},"Konstantní",[614,79613,79614],{},"constant returns",[35,79616,79617],{},[883,79618,79620],{"className":79619},[886],[888,79621,79622],{"xmlns":890},[892,79623,79624,79636],{},[895,79625,79626,79628,79630,79632,79634],{},[898,79627,207],{},[1655,79629,2346],{},[898,79631,2025],{},[1655,79633,1657],{},[1826,79635,1828],{},[902,79637,79638],{"encoding":904},"a+b = 1",[35,79640,79641,79654,79655,3106,79658,79671],{},[883,79642,79644],{"className":79643},[886],[888,79645,79646],{"xmlns":890},[892,79647,79648,79652],{},[895,79649,79650],{},[898,79651,1824],{},[902,79653,1824],{"encoding":904}," vzroste ",[38,79656,79657],{},"přesně",[883,79659,79661],{"className":79660},[886],[888,79662,79663],{"xmlns":890},[892,79664,79665,79669],{},[895,79666,79667],{},[898,79668,13166],{},[902,79670,13166],{"encoding":904},"-krát",[35,79673,79674],{},[883,79675,79677],{"className":79676},[886],[888,79678,79679],{"xmlns":890},[892,79680,79681,79713],{},[895,79682,79683,79685,79687,79689,79701],{},[898,79684,1824],{},[1655,79686,1657],{},[1826,79688,1837],{},[2597,79690,79691,79693],{},[898,79692,1873],{},[895,79694,79695,79697,79699],{},[1826,79696,1828],{},[898,79698,5923],{"mathvariant":1943},[1826,79700,3639],{},[2597,79702,79703,79705],{},[898,79704,1878],{},[895,79706,79707,79709,79711],{},[1826,79708,3472],{},[898,79710,5923],{"mathvariant":1943},[1826,79712,3639],{},[902,79714,79715],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,79717,79718,79727,79751,79781],{},[35,79719,79720,79721,2115,79724,1677],{},"2° ",[38,79722,79723],{},"Rostoucí",[614,79725,79726],{},"increasing returns",[35,79728,79729],{},[883,79730,79732],{"className":79731},[886],[888,79733,79734],{"xmlns":890},[892,79735,79736,79748],{},[895,79737,79738,79740,79742,79744,79746],{},[898,79739,207],{},[1655,79741,2346],{},[898,79743,2025],{},[1655,79745,2969],{},[1826,79747,1828],{},[902,79749,79750],{"encoding":904},"a+b > 1",[35,79752,79753,79654,79766,52357,79768,79671],{},[883,79754,79756],{"className":79755},[886],[888,79757,79758],{"xmlns":890},[892,79759,79760,79764],{},[895,79761,79762],{},[898,79763,1824],{},[902,79765,1824],{"encoding":904},[38,79767,26396],{},[883,79769,79771],{"className":79770},[886],[888,79772,79773],{"xmlns":890},[892,79774,79775,79779],{},[895,79776,79777],{},[898,79778,13166],{},[902,79780,13166],{"encoding":904},[35,79782,79783,2115,79809,1677],{},[883,79784,79786],{"className":79785},[886],[888,79787,79788],{"xmlns":890},[892,79789,79790,79806],{},[895,79791,79792,79794,79796,79798,79800],{},[898,79793,1824],{},[1655,79795,1657],{},[1826,79797,25327],{},[898,79799,1873],{},[2597,79801,79802,79804],{},[898,79803,1878],{},[1826,79805,1837],{},[902,79807,79808],{"encoding":904},"Q = 7LK^2",[883,79810,79812],{"className":79811},[886],[888,79813,79814],{"xmlns":890},[892,79815,79816,79828],{},[895,79817,79818,79820,79822,79824,79826],{},[898,79819,207],{},[1655,79821,2346],{},[898,79823,2025],{},[1655,79825,1657],{},[1826,79827,3472],{},[902,79829,79830],{"encoding":904},"a+b = 3",[22,79832,79833,79842,79866,79897],{},[35,79834,79835,79836,2115,79839,1677],{},"3° ",[38,79837,79838],{},"Klesající",[614,79840,79841],{},"decreasing returns",[35,79843,79844],{},[883,79845,79847],{"className":79846},[886],[888,79848,79849],{"xmlns":890},[892,79850,79851,79863],{},[895,79852,79853,79855,79857,79859,79861],{},[898,79854,207],{},[1655,79856,2346],{},[898,79858,2025],{},[1655,79860,3065],{},[1826,79862,1828],{},[902,79864,79865],{"encoding":904},"a+b \u003C 1",[35,79867,79868,79654,79881,52357,79884,79671],{},[883,79869,79871],{"className":79870},[886],[888,79872,79873],{"xmlns":890},[892,79874,79875,79879],{},[895,79876,79877],{},[898,79878,1824],{},[902,79880,1824],{"encoding":904},[38,79882,79883],{},"méně",[883,79885,79887],{"className":79886},[886],[888,79888,79889],{"xmlns":890},[892,79890,79891,79895],{},[895,79892,79893],{},[898,79894,13166],{},[902,79896,13166],{"encoding":904},[35,79898,79899,2115,79929,1677],{},[883,79900,79902],{"className":79901},[886],[888,79903,79904],{"xmlns":890},[892,79905,79906,79926],{},[895,79907,79908,79910,79912,79914,79920],{},[898,79909,1824],{},[1655,79911,1657],{},[1826,79913,4136],{},[2597,79915,79916,79918],{},[898,79917,1873],{},[1826,79919,69337],{},[2597,79921,79922,79924],{},[898,79923,1878],{},[1826,79925,6258],{},[902,79927,79928],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,79930,79932],{"className":79931},[886],[888,79933,79934],{"xmlns":890},[892,79935,79936,79948],{},[895,79937,79938,79940,79942,79944,79946],{},[898,79939,207],{},[1655,79941,2346],{},[898,79943,2025],{},[1655,79945,1657],{},[1826,79947,15714],{},[902,79949,79950],{"encoding":904},"a+b = 0{,}8",[5120,79952,79953],{},[724,79954,79955,79957,79958,79975,79976,79979,79980,3106,79983,80019,80020,80042,80043,1719],{},[883,79956,5661],{}," Pozor\nSoučet ",[883,79959,79961],{"className":79960},[886],[888,79962,79963],{"xmlns":890},[892,79964,79965,79973],{},[895,79966,79967,79969,79971],{},[898,79968,207],{},[1655,79970,2346],{},[898,79972,2025],{},[902,79974,75950],{"encoding":904}," neudává velikost produkce, ale ",[38,79977,79978],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,79981,79982],{},"ryzí Cobb-Douglas",[883,79984,79986],{"className":79985},[886],[888,79987,79988],{"xmlns":890},[892,79989,79990,80016],{},[895,79991,79992,79994,79996,79998,80004],{},[898,79993,1824],{},[1655,79995,1657],{},[898,79997,2731],{},[2597,79999,80000,80002],{},[898,80001,1873],{},[898,80003,207],{},[2597,80005,80006,80008],{},[898,80007,1878],{},[895,80009,80010,80012,80014],{},[1826,80011,1828],{},[1655,80013,2623],{},[898,80015,207],{},[902,80017,80018],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,80021,80023],{"className":80022},[886],[888,80024,80025],{"xmlns":890},[892,80026,80027,80039],{},[895,80028,80029,80031,80033,80035,80037],{},[898,80030,2025],{},[1655,80032,1657],{},[1826,80034,1828],{},[1655,80036,2623],{},[898,80038,207],{},[902,80040,80041],{"encoding":904},"b = 1-a",", tedy vždy ",[38,80044,80045],{},"konstantní výnosy z rozsahu",[198,80047,80049,80050],{"id":80048},"parametr-efektivity-aa","Parametr efektivity ",[883,80051,80053],{"className":80052},[886],[888,80054,80055],{"xmlns":890},[892,80056,80057,80061],{},[895,80058,80059],{},[898,80060,2731],{},[902,80062,2731],{"encoding":904},[724,80064,80065,80066,80079,80080,80093,80094,80112,80113,80116],{},"Konstanta ",[883,80067,80069],{"className":80068},[886],[888,80070,80071],{"xmlns":890},[892,80072,80073,80077],{},[895,80074,80075],{},[898,80076,2731],{},[902,80078,2731],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,80081,80083],{"className":80082},[886],[888,80084,80085],{"xmlns":890},[892,80086,80087,80091],{},[895,80088,80089],{},[898,80090,1824],{},[902,80092,1824],{"encoding":904}," při pevně zadaných ",[883,80095,80097],{"className":80096},[886],[888,80098,80099],{"xmlns":890},[892,80100,80101,80109],{},[895,80102,80103,80105,80107],{},[898,80104,1873],{},[1655,80106,1671],{"separator":1670},[898,80108,1878],{},[902,80110,80111],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,80114,80115],{},"parametr efektivity"," — indikátor stavu technologie.",[198,80118,80120],{"id":80119},"příklad-53","Příklad 5.3",[724,80122,80123,80124,80019,80166,80168,80169,1719],{},"Produkční funkce ",[883,80125,80127],{"className":80126},[886],[888,80128,80129],{"xmlns":890},[892,80130,80131,80163],{},[895,80132,80133,80135,80137,80139,80151],{},[898,80134,1824],{},[1655,80136,1657],{},[1826,80138,1837],{},[2597,80140,80141,80143],{},[898,80142,1873],{},[895,80144,80145,80147,80149],{},[1826,80146,1828],{},[898,80148,5923],{"mathvariant":1943},[1826,80150,3639],{},[2597,80152,80153,80155],{},[898,80154,1878],{},[895,80156,80157,80159,80161],{},[1826,80158,3472],{},[898,80160,5923],{"mathvariant":1943},[1826,80162,3639],{},[902,80164,80165],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,80167,25739],{}," výnosy z rozsahu, neboť ",[883,80170,80172],{"className":80171},[886],[888,80173,80174],{"xmlns":890},[892,80175,80176,80200],{},[895,80177,80178,80186,80188,80196,80198],{},[3615,80179,80180],{"scriptlevel":2552,"displaystyle":1663},[1949,80181,80182,80184],{},[1826,80183,1828],{},[1826,80185,3639],{},[1655,80187,2346],{},[3615,80189,80190],{"scriptlevel":2552,"displaystyle":1663},[1949,80191,80192,80194],{},[1826,80193,3472],{},[1826,80195,3639],{},[1655,80197,1657],{},[1826,80199,1828],{},[902,80201,80202],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,80204,80205,80206,7437,80219,80232,80233,3106,80246,80286],{},"Změní-li se ",[883,80207,80209],{"className":80208},[886],[888,80210,80211],{"xmlns":890},[892,80212,80213,80217],{},[895,80214,80215],{},[898,80216,1873],{},[902,80218,1873],{"encoding":904},[883,80220,80222],{"className":80221},[886],[888,80223,80224],{"xmlns":890},[892,80225,80226,80230],{},[895,80227,80228],{},[898,80229,1878],{},[902,80231,1878],{"encoding":904}," čtyřnásobně, změní se ",[883,80234,80236],{"className":80235},[886],[888,80237,80238],{"xmlns":890},[892,80239,80240,80244],{},[895,80241,80242],{},[898,80243,1824],{},[902,80245,1824],{"encoding":904},[883,80247,80249],{"className":80248},[886],[888,80250,80251],{"xmlns":890},[892,80252,80253,80283],{},[895,80254,80255,80275,80277],{},[2597,80256,80257,80259],{},[1826,80258,3639],{},[895,80260,80261,80263,80265,80267,80269,80271,80273],{},[1826,80262,1828],{},[898,80264,5923],{"mathvariant":1943},[1826,80266,3639],{},[1655,80268,2346],{},[1826,80270,3472],{},[898,80272,5923],{"mathvariant":1943},[1826,80274,3639],{},[1655,80276,1657],{},[2597,80278,80279,80281],{},[1826,80280,3639],{},[1826,80282,1828],{},[902,80284,80285],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,80288,80290],{"className":80289},[886],[888,80291,80292],{"xmlns":890,"display":29192},[892,80293,80294,80454],{},[895,80295,80296,80298,80300,80302,80304,80306,80308,80310,80312,80314,80316,80318,80320,80322,80334,80336,80338,80340,80352,80354,80356,80358,80378,80390,80402,80404,80406,80408,80410,80422,80434,80436,80438,80440,80442,80444,80446,80448,80450,80452],{},[898,80297,1824],{},[1655,80299,1664],{"stretchy":1663},[1826,80301,3639],{},[898,80303,1873],{},[1655,80305,1671],{"separator":1670},[1826,80307,3639],{},[898,80309,1878],{},[1655,80311,1677],{"stretchy":1663},[1655,80313,1657],{},[1826,80315,1837],{},[1655,80317,1664],{"stretchy":1663},[1826,80319,3639],{},[898,80321,1873],{},[2597,80323,80324,80326],{},[1655,80325,1677],{"stretchy":1663},[895,80327,80328,80330,80332],{},[1826,80329,1828],{},[898,80331,5923],{"mathvariant":1943},[1826,80333,3639],{},[1655,80335,1664],{"stretchy":1663},[1826,80337,3639],{},[898,80339,1878],{},[2597,80341,80342,80344],{},[1655,80343,1677],{"stretchy":1663},[895,80345,80346,80348,80350],{},[1826,80347,3472],{},[898,80349,5923],{"mathvariant":1943},[1826,80351,3639],{},[1655,80353,1657],{},[1826,80355,1837],{},[1655,80357,2869],{},[2597,80359,80360,80362],{},[1826,80361,3639],{},[895,80363,80364,80366,80368,80370,80372,80374,80376],{},[1826,80365,1828],{},[898,80367,5923],{"mathvariant":1943},[1826,80369,3639],{},[1655,80371,2346],{},[1826,80373,3472],{},[898,80375,5923],{"mathvariant":1943},[1826,80377,3639],{},[2597,80379,80380,80382],{},[898,80381,1873],{},[895,80383,80384,80386,80388],{},[1826,80385,1828],{},[898,80387,5923],{"mathvariant":1943},[1826,80389,3639],{},[2597,80391,80392,80394],{},[898,80393,1878],{},[895,80395,80396,80398,80400],{},[1826,80397,3472],{},[898,80399,5923],{"mathvariant":1943},[1826,80401,3639],{},[1655,80403,1657],{},[1826,80405,3639],{},[1655,80407,2869],{},[1826,80409,1837],{},[2597,80411,80412,80414],{},[898,80413,1873],{},[895,80415,80416,80418,80420],{},[1826,80417,1828],{},[898,80419,5923],{"mathvariant":1943},[1826,80421,3639],{},[2597,80423,80424,80426],{},[898,80425,1878],{},[895,80427,80428,80430,80432],{},[1826,80429,3472],{},[898,80431,5923],{"mathvariant":1943},[1826,80433,3639],{},[1655,80435,1657],{},[1826,80437,3639],{},[2031,80439,2435],{},[898,80441,1824],{},[1655,80443,1664],{"stretchy":1663},[898,80445,1873],{},[1655,80447,1671],{"separator":1670},[898,80449,1878],{},[1655,80451,1677],{"stretchy":1663},[898,80453,1719],{"mathvariant":1943},[902,80455,80456],{"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).",[198,80458,80459],{"id":38305},"Homogenita",[724,80461,80462,80463,9349,80486,80502],{},"Funkce ",[883,80464,80466],{"className":80465},[886],[888,80467,80468],{"xmlns":890},[892,80469,80470,80484],{},[895,80471,80472,80474,80476,80478,80480,80482],{},[898,80473,1824],{},[1655,80475,1664],{"stretchy":1663},[898,80477,1873],{},[1655,80479,1671],{"separator":1670},[898,80481,1878],{},[1655,80483,1677],{"stretchy":1663},[902,80485,2085],{"encoding":904},[38,80487,80488,80489],{},"homogenní stupně ",[883,80490,80492],{"className":80491},[886],[888,80493,80494],{"xmlns":890},[892,80495,80496,80500],{},[895,80497,80498],{},[898,80499,37986],{},[902,80501,37986],{"encoding":904},", jestliže",[883,80504,80506],{"className":80505},[886],[888,80507,80508],{"xmlns":890,"display":29192},[892,80509,80510,80567],{},[21880,80511,80512],{"width":29197},[21885,80513,80514,80516,80560,80562],{},[21888,80515],{"width":29202},[21888,80517,80518],{},[895,80519,80520,80522,80524,80526,80528,80530,80532,80534,80536,80538,80544,80546,80548,80550,80552,80554,80556,80558],{},[898,80521,1824],{},[1655,80523,1664],{"stretchy":1663},[898,80525,13166],{},[898,80527,1873],{},[1655,80529,1671],{"separator":1670},[898,80531,13166],{},[898,80533,1878],{},[1655,80535,1677],{"stretchy":1663},[1655,80537,1657],{},[2597,80539,80540,80542],{},[898,80541,13166],{},[898,80543,37986],{},[2031,80545,2435],{},[898,80547,1824],{},[1655,80549,1664],{"stretchy":1663},[898,80551,1873],{},[1655,80553,1671],{"separator":1670},[898,80555,1878],{},[1655,80557,1677],{"stretchy":1663},[1655,80559,1671],{"separator":1670},[21888,80561],{"width":29202},[21888,80563,80564],{},[2031,80565,80566],{},"(5.10)",[902,80568,80569],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,80571,5559,80572,80590,80591,80609,80610,44762,80623,80626,80627,1719],{},[883,80573,80575],{"className":80574},[886],[888,80576,80577],{"xmlns":890},[892,80578,80579,80587],{},[895,80580,80581,80583,80585],{},[898,80582,37986],{},[1655,80584,5734],{},[1826,80586,2552],{},[902,80588,80589],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,80592,80594],{"className":80593},[886],[888,80595,80596],{"xmlns":890},[892,80597,80598,80606],{},[895,80599,80600,80602,80604],{},[898,80601,13166],{},[1655,80603,2969],{},[1826,80605,2552],{},[902,80607,80608],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,80611,80613],{"className":80612},[886],[888,80614,80615],{"xmlns":890},[892,80616,80617,80621],{},[895,80618,80619],{},[1826,80620,1828],{},[902,80622,1828],{"encoding":904},[38,80624,80625],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,80628,80630],{"className":80629},[886],[888,80631,80632],{"xmlns":890},[892,80633,80634,80642],{},[895,80635,80636,80638,80640],{},[898,80637,207],{},[1655,80639,2346],{},[898,80641,2025],{},[902,80643,75950],{"encoding":904},[115,80645,80647],{"id":80646},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,80649,80650],{},[38,80651,80652],{},"Ryzí Cobb-Douglasovy funkce:",[883,80654,80656],{"className":80655},[886],[888,80657,80658],{"xmlns":890,"display":29192},[892,80659,80660,80719],{},[21880,80661,80662],{"width":29197},[21885,80663,80664,80666,80712,80714],{},[21888,80665],{"width":29202},[21888,80667,80668],{},[895,80669,80670,80672,80674,80676,80678,80684,80686,80698,80700,80702,80704,80706,80708,80710],{},[898,80671,1824],{},[1655,80673,1657],{},[898,80675,2731],{},[2031,80677,2435],{},[2597,80679,80680,80682],{},[898,80681,1873],{},[898,80683,207],{},[2031,80685,2435],{},[2597,80687,80688,80690],{},[898,80689,1878],{},[895,80691,80692,80694,80696],{},[1826,80693,1828],{},[1655,80695,2623],{},[898,80697,207],{},[1655,80699,1671],{"separator":1670},[1967,80701],{"width":16409},[1826,80703,2552],{},[1655,80705,3065],{},[898,80707,207],{},[1655,80709,3065],{},[1826,80711,14385],{},[21888,80713],{"width":29202},[21888,80715,80716],{},[2031,80717,80718],{},"(5.9)",[902,80720,80721],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,80723,80724,80725,80727,80728,1719],{},"Mají vždy ",[38,80726,80045],{}," a jsou ",[38,80729,80625],{},[724,80731,80732,2115,80735,80738],{},[38,80733,80734],{},"CES produkční funkce",[614,80736,80737],{},"Constant Elasticity of Substitution",", 1961):",[883,80740,80742],{"className":80741},[886],[888,80743,80744],{"xmlns":890,"display":29192},[892,80745,80746,80814],{},[895,80747,80748,80750,80752,80754,80812],{},[898,80749,1824],{},[1655,80751,1657],{},[898,80753,2731],{},[2597,80755,80756,80800],{},[895,80757,80758,80760,80762,80764,80766,80768,80770,80772,80782,80784,80786,80788,80798],{},[1655,80759,2734],{"fence":1670},[1655,80761,1664],{"stretchy":1663},[1826,80763,1828],{},[1655,80765,2623],{},[898,80767,207],{},[1655,80769,1677],{"stretchy":1663},[2031,80771,2435],{},[2597,80773,80774,80776],{},[898,80775,1873],{},[895,80777,80778,80780],{},[1655,80779,2623],{},[898,80781,2025],{},[1655,80783,2346],{},[898,80785,207],{},[2031,80787,2435],{},[2597,80789,80790,80792],{},[898,80791,1878],{},[895,80793,80794,80796],{},[1655,80795,2623],{},[898,80797,2025],{},[1655,80799,2743],{"fence":1670},[895,80801,80802,80804],{},[1655,80803,2623],{},[3615,80805,80806],{"scriptlevel":2552,"displaystyle":1663},[1949,80807,80808,80810],{},[1826,80809,1828],{},[898,80811,2025],{},[1655,80813,1671],{"separator":1670},[902,80815,80816],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,80818,5559,80819,1343,80837,1343,80858,80882],{},[883,80820,80822],{"className":80821},[886],[888,80823,80824],{"xmlns":890},[892,80825,80826,80834],{},[895,80827,80828,80830,80832],{},[898,80829,2731],{},[1655,80831,2969],{},[1826,80833,2552],{},[902,80835,80836],{"encoding":904},"A > 0",[883,80838,80840],{"className":80839},[886],[888,80841,80842],{"xmlns":890},[892,80843,80844,80856],{},[895,80845,80846,80848,80850,80852,80854],{},[1826,80847,2552],{},[1655,80849,3065],{},[898,80851,207],{},[1655,80853,3065],{},[1826,80855,1828],{},[902,80857,19962],{"encoding":904},[883,80859,80861],{"className":80860},[886],[888,80862,80863],{"xmlns":890},[892,80864,80865,80879],{},[895,80866,80867,80869,80871,80873,80875,80877],{},[1655,80868,2623],{},[1826,80870,1828],{},[1655,80872,3065],{},[898,80874,2025],{},[1655,80876,4636],{"mathvariant":1943},[1826,80878,2552],{},[902,80880,80881],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,80884,80885],{},[38,80886,80887],{},"Další typy:",[120,80889,80890,80932],{},[123,80891,80892,3106,80895,80931],{},[38,80893,80894],{},"Lineární:",[883,80896,80898],{"className":80897},[886],[888,80899,80900],{"xmlns":890},[892,80901,80902,80928],{},[895,80903,80904,80906,80908,80910,80912,80914,80916,80918,80920,80922,80924,80926],{},[898,80905,1824],{},[1655,80907,1664],{"stretchy":1663},[898,80909,1873],{},[1655,80911,1671],{"separator":1670},[898,80913,1878],{},[1655,80915,1677],{"stretchy":1663},[1655,80917,1657],{},[898,80919,207],{},[898,80921,1873],{},[1655,80923,2346],{},[898,80925,2025],{},[898,80927,1878],{},[902,80929,80930],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,80933,80934,3106,80937,80982],{},[38,80935,80936],{},"Leontiefova:",[883,80938,80940],{"className":80939},[886],[888,80941,80942],{"xmlns":890},[892,80943,80944,80979],{},[895,80945,80946,80948,80950,80952,80954,80956,80958,80960,80963,80965,80967,80969,80971,80973,80975,80977],{},[898,80947,1824],{},[1655,80949,1664],{"stretchy":1663},[898,80951,1873],{},[1655,80953,1671],{"separator":1670},[898,80955,1878],{},[1655,80957,1677],{"stretchy":1663},[1655,80959,1657],{},[898,80961,80962],{},"min",[1655,80964,57326],{},[1655,80966,1664],{"stretchy":1663},[898,80968,207],{},[898,80970,1873],{},[1655,80972,1671],{"separator":1670},[898,80974,2025],{},[898,80976,1878],{},[1655,80978,1677],{"stretchy":1663},[902,80980,80981],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,80984,80986,80987,1343,81006,81025],{"id":80985},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,80988,80990],{"className":80989},[886],[888,80991,80992],{"xmlns":890},[892,80993,80994,81004],{},[895,80995,80996,80998],{},[898,80997,2127],{},[1820,80999,81000,81002],{},[898,81001,2132],{},[898,81003,1873],{},[902,81005,2137],{"encoding":904},[883,81007,81009],{"className":81008},[886],[888,81010,81011],{"xmlns":890},[892,81012,81013,81023],{},[895,81014,81015,81017],{},[898,81016,2127],{},[1820,81018,81019,81021],{},[898,81020,2132],{},[898,81022,1878],{},[902,81024,2182],{"encoding":904}," a totální diferenciál",[724,81027,81028],{},[38,81029,81030],{},"Mezní produkt práce:",[883,81032,81034],{"className":81033},[886],[888,81035,81036],{"xmlns":890,"display":29192},[892,81037,81038,81076],{},[895,81039,81040,81042,81048,81050,81058,81060,81074],{},[898,81041,2127],{},[1820,81043,81044,81046],{},[898,81045,2132],{},[898,81047,1873],{},[1655,81049,1657],{},[1935,81051,81052,81054,81056],{},[898,81053,1824],{},[898,81055,1873],{},[1655,81057,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,81059,1657],{},[1949,81061,81062,81068],{},[895,81063,81064,81066],{},[898,81065,1955],{"mathvariant":1943},[898,81067,1824],{},[895,81069,81070,81072],{},[898,81071,1955],{"mathvariant":1943},[898,81073,1873],{},[898,81075,1719],{"mathvariant":1943},[902,81077,81078],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,81080,81081],{},[38,81082,81083],{},"Mezní produkt kapitálu:",[883,81085,81087],{"className":81086},[886],[888,81088,81089],{"xmlns":890,"display":29192},[892,81090,81091,81129],{},[895,81092,81093,81095,81101,81103,81111,81113,81127],{},[898,81094,2127],{},[1820,81096,81097,81099],{},[898,81098,2132],{},[898,81100,1878],{},[1655,81102,1657],{},[1935,81104,81105,81107,81109],{},[898,81106,1824],{},[898,81108,1878],{},[1655,81110,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,81112,1657],{},[1949,81114,81115,81121],{},[895,81116,81117,81119],{},[898,81118,1955],{"mathvariant":1943},[898,81120,1824],{},[895,81122,81123,81125],{},[898,81124,1955],{"mathvariant":1943},[898,81126,1878],{},[898,81128,1719],{"mathvariant":1943},[902,81130,81131],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,81133,81134,81164,81165,81186,81187,81205,81206,81219,81220,1719],{},[883,81135,81137],{"className":81136},[886],[888,81138,81139],{"xmlns":890},[892,81140,81141,81161],{},[895,81142,81143,81145,81151,81153,81155,81157,81159],{},[898,81144,2127],{},[1820,81146,81147,81149],{},[898,81148,2132],{},[898,81150,1873],{},[1655,81152,1664],{"stretchy":1663},[898,81154,207],{},[1655,81156,1671],{"separator":1670},[898,81158,2025],{},[1655,81160,1677],{"stretchy":1663},[902,81162,81163],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,81166,81168],{"className":81167},[886],[888,81169,81170],{"xmlns":890},[892,81171,81172,81184],{},[895,81173,81174,81176,81178,81180,81182],{},[1655,81175,2734],{"stretchy":1663},[898,81177,207],{},[1655,81179,1671],{"separator":1670},[898,81181,2025],{},[1655,81183,2743],{"stretchy":1663},[902,81185,2939],{"encoding":904}," (na hladině ",[883,81188,81190],{"className":81189},[886],[888,81191,81192],{"xmlns":890},[892,81193,81194,81202],{},[895,81195,81196,81198,81200],{},[898,81197,1878],{},[1655,81199,1657],{},[898,81201,2025],{},[902,81203,81204],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,81207,81209],{"className":81208},[886],[888,81210,81211],{"xmlns":890},[892,81212,81213,81217],{},[895,81214,81215],{},[898,81216,1873],{},[902,81218,1873],{"encoding":904},". Analogicky ",[883,81221,81223],{"className":81222},[886],[888,81224,81225],{"xmlns":890},[892,81226,81227,81247],{},[895,81228,81229,81231,81237,81239,81241,81243,81245],{},[898,81230,2127],{},[1820,81232,81233,81235],{},[898,81234,2132],{},[898,81236,1878],{},[1655,81238,1664],{"stretchy":1663},[898,81240,207],{},[1655,81242,1671],{"separator":1670},[898,81244,2025],{},[1655,81246,1677],{"stretchy":1663},[902,81248,81249],{"encoding":904},"MP_K(a, b)",[5120,81251,81252,81256],{},[724,81253,81254,52345],{},[883,81255,5406],{},[120,81257,81258,81296],{},[123,81259,81260,27315,81279],{},[883,81261,81263],{"className":81262},[886],[888,81264,81265],{"xmlns":890},[892,81266,81267,81277],{},[895,81268,81269,81271],{},[898,81270,2127],{},[1820,81272,81273,81275],{},[898,81274,2132],{},[898,81276,1873],{},[902,81278,2137],{"encoding":904},[614,81280,81281,81282,81295],{},"„o kolik vzroste ",[883,81283,81285],{"className":81284},[886],[888,81286,81287],{"xmlns":890},[892,81288,81289,81293],{},[895,81290,81291],{},[898,81292,1824],{},[902,81294,1824],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,81297,81298,27315,81317],{},[883,81299,81301],{"className":81300},[886],[888,81302,81303],{"xmlns":890},[892,81304,81305,81315],{},[895,81306,81307,81309],{},[898,81308,2127],{},[1820,81310,81311,81313],{},[898,81312,2132],{},[898,81314,1878],{},[902,81316,2182],{"encoding":904},[614,81318,81281,81319,81332],{},[883,81320,81322],{"className":81321},[886],[888,81323,81324],{"xmlns":890},[892,81325,81326,81330],{},[895,81327,81328],{},[898,81329,1824],{},[902,81331,1824],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,81334,81335,81338,81339,81354,81355,2086],{},[38,81336,81337],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,81340,81342],{"className":81341},[886],[888,81343,81344],{"xmlns":890},[892,81345,81346,81352],{},[895,81347,81348,81350],{},[898,81349,2410],{},[898,81351,1873],{},[902,81353,76482],{"encoding":904}," a kapitálu o ",[883,81356,81358],{"className":81357},[886],[888,81359,81360],{"xmlns":890},[892,81361,81362,81368],{},[895,81363,81364,81366],{},[898,81365,2410],{},[898,81367,1878],{},[902,81369,81370],{"encoding":904},"dK",[883,81372,81374],{"className":81373},[886],[888,81375,81376],{"xmlns":890,"display":29192},[892,81377,81378,81471],{},[21880,81379,81380],{"width":29197},[21885,81381,81382,81384,81464,81466],{},[21888,81383],{"width":29202},[21888,81385,81386],{},[895,81387,81388,81390,81392,81394,81396,81398,81400,81408,81410,81412,81414,81416,81424,81426,81428,81430,81432,81434,81440,81442,81444,81446,81448,81450,81456,81458,81460,81462],{},[898,81389,2506],{"mathvariant":1943},[898,81391,1824],{},[1655,81393,2357],{},[898,81395,2410],{},[898,81397,1824],{},[1655,81399,1657],{},[1935,81401,81402,81404,81406],{},[898,81403,1824],{},[898,81405,1873],{},[1655,81407,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[2031,81409,2435],{},[898,81411,2410],{},[898,81413,1873],{},[1655,81415,2346],{},[1935,81417,81418,81420,81422],{},[898,81419,1824],{},[898,81421,1878],{},[1655,81423,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[2031,81425,2435],{},[898,81427,2410],{},[898,81429,1878],{},[1655,81431,1657],{},[898,81433,2127],{},[1820,81435,81436,81438],{},[898,81437,2132],{},[898,81439,1873],{},[2031,81441,2435],{},[898,81443,2410],{},[898,81445,1873],{},[1655,81447,2346],{},[898,81449,2127],{},[1820,81451,81452,81454],{},[898,81453,2132],{},[898,81455,1878],{},[2031,81457,2435],{},[898,81459,2410],{},[898,81461,1878],{},[898,81463,1719],{"mathvariant":1943},[21888,81465],{"width":29202},[21888,81467,81468],{},[2031,81469,81470],{},"(5.11)",[902,81472,81473],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,81475,81476,81477,1719],{},"Skutečná změna: ",[883,81478,81480],{"className":81479},[886],[888,81481,81482],{"xmlns":890},[892,81483,81484,81530],{},[895,81485,81486,81488,81490,81492,81494,81496,81498,81500,81502,81504,81506,81508,81510,81512,81514,81516,81518,81520,81522,81524,81526,81528],{},[898,81487,2506],{"mathvariant":1943},[898,81489,1824],{},[1655,81491,1657],{},[898,81493,1824],{},[1655,81495,1664],{"stretchy":1663},[898,81497,1873],{},[1655,81499,2346],{},[898,81501,2410],{},[898,81503,1873],{},[1655,81505,1671],{"separator":1670},[898,81507,1878],{},[1655,81509,2346],{},[898,81511,2410],{},[898,81513,1878],{},[1655,81515,1677],{"stretchy":1663},[1655,81517,2623],{},[898,81519,1824],{},[1655,81521,1664],{"stretchy":1663},[898,81523,1873],{},[1655,81525,1671],{"separator":1670},[898,81527,1878],{},[1655,81529,1677],{"stretchy":1663},[902,81531,81532],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,81534,81535,81537,81538,81556,81557,81570,81571,81590,81591,81623,81624,81656,81657,1719],{},[38,81536,76646],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,81539,81541],{"className":81540},[886],[888,81542,81543],{"xmlns":890},[892,81544,81545,81553],{},[895,81546,81547],{},[1820,81548,81549,81551],{},[898,81550,1878],{},[1826,81552,2552],{},[902,81554,81555],{"encoding":904},"K_0"," se od jistého ",[883,81558,81560],{"className":81559},[886],[888,81561,81562],{"xmlns":890},[892,81563,81564,81568],{},[895,81565,81566],{},[898,81567,1873],{},[902,81569,1873],{"encoding":904}," stane ",[883,81572,81574],{"className":81573},[886],[888,81575,81576],{"xmlns":890},[892,81577,81578,81588],{},[895,81579,81580,81582],{},[898,81581,2127],{},[1820,81583,81584,81586],{},[898,81585,2132],{},[898,81587,1873],{},[902,81589,2137],{"encoding":904}," klesající (",[883,81592,81594],{"className":81593},[886],[888,81595,81596],{"xmlns":890},[892,81597,81598,81620],{},[895,81599,81600,81616,81618],{},[1935,81601,81602,81604,81610],{},[898,81603,1824],{},[895,81605,81606,81608],{},[898,81607,1873],{},[898,81609,1873],{},[895,81611,81612,81614],{},[1655,81613,1945],{"mathvariant":1943},[1655,81615,1945],{"mathvariant":1943},[1655,81617,3065],{},[1826,81619,2552],{},[902,81621,81622],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,81625,81627],{"className":81626},[886],[888,81628,81629],{"xmlns":890},[892,81630,81631,81653],{},[895,81632,81633,81649,81651],{},[1935,81634,81635,81637,81643],{},[898,81636,1824],{},[895,81638,81639,81641],{},[898,81640,1878],{},[898,81642,1878],{},[895,81644,81645,81647],{},[1655,81646,1945],{"mathvariant":1943},[1655,81648,1945],{"mathvariant":1943},[1655,81650,3065],{},[1826,81652,2552],{},[902,81654,81655],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,81658,81660],{"className":81659},[886],[888,81661,81662],{"xmlns":890},[892,81663,81664,81672],{},[895,81665,81666],{},[1820,81667,81668,81670],{},[898,81669,1873],{},[1826,81671,2552],{},[902,81673,76684],{"encoding":904},[115,81675,81677],{"id":81676},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,81679,81680,81683,81684,81707,81708,31070],{},[38,81681,81682],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,81685,81687],{"className":81686},[886],[888,81688,81689],{"xmlns":890},[892,81690,81691,81705],{},[895,81692,81693,81695,81697,81699,81701,81703],{},[898,81694,1824],{},[1655,81696,1664],{"stretchy":1663},[898,81698,1873],{},[1655,81700,1671],{"separator":1670},[898,81702,1878],{},[1655,81704,1677],{"stretchy":1663},[902,81706,2085],{"encoding":904}," stupně ",[883,81709,81711],{"className":81710},[886],[888,81712,81713],{"xmlns":890},[892,81714,81715,81719],{},[895,81716,81717],{},[898,81718,37986],{},[902,81720,37986],{"encoding":904},[883,81722,81724],{"className":81723},[886],[888,81725,81726],{"xmlns":890,"display":29192},[892,81727,81728,81791],{},[21880,81729,81730],{"width":29197},[21885,81731,81732,81734,81784,81786],{},[21888,81733],{"width":29202},[21888,81735,81736],{},[895,81737,81738,81740,81742,81750,81752,81754,81756,81764,81766,81768,81770,81772,81774,81776,81778,81780,81782],{},[898,81739,1873],{},[2031,81741,2435],{},[1935,81743,81744,81746,81748],{},[898,81745,1824],{},[898,81747,1873],{},[1655,81749,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,81751,2346],{},[898,81753,1878],{},[2031,81755,2435],{},[1935,81757,81758,81760,81762],{},[898,81759,1824],{},[898,81761,1878],{},[1655,81763,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,81765,1657],{},[898,81767,37986],{},[2031,81769,2435],{},[898,81771,1824],{},[1655,81773,1664],{"stretchy":1663},[898,81775,1873],{},[1655,81777,1671],{"separator":1670},[898,81779,1878],{},[1655,81781,1677],{"stretchy":1663},[898,81783,1719],{"mathvariant":1943},[21888,81785],{"width":29202},[21888,81787,81788],{},[2031,81789,81790],{},"(5.12)",[902,81792,81793],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,81795,81796,81817],{},[38,81797,81798,81799],{},"Speciální případ ",[883,81800,81802],{"className":81801},[886],[888,81803,81804],{"xmlns":890},[892,81805,81806,81814],{},[895,81807,81808,81810,81812],{},[898,81809,37986],{},[1655,81811,1657],{},[1826,81813,1828],{},[902,81815,81816],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,81819,81821],{"className":81820},[886],[888,81822,81823],{"xmlns":890,"display":29192},[892,81824,81825,81869],{},[895,81826,81827,81829,81831,81833,81839,81841,81843,81845,81847,81853,81855,81857,81859,81861,81863,81865,81867],{},[898,81828,1873],{},[1655,81830,2869],{},[898,81832,2127],{},[1820,81834,81835,81837],{},[898,81836,2132],{},[898,81838,1873],{},[1655,81840,2346],{},[898,81842,1878],{},[1655,81844,2869],{},[898,81846,2127],{},[1820,81848,81849,81851],{},[898,81850,2132],{},[898,81852,1878],{},[1655,81854,1657],{},[898,81856,1824],{},[1655,81858,1664],{"stretchy":1663},[898,81860,1873],{},[1655,81862,1671],{"separator":1670},[898,81864,1878],{},[1655,81866,1677],{"stretchy":1663},[898,81868,1719],{"mathvariant":1943},[902,81870,81871],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,81873,81874,81875,81878],{},"Slovně — ",[38,81876,81877],{},"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).",[115,81880,1856],{"id":76020},[724,81882,81883,2115,81885,81888,81889,81911,81912,2086],{},[38,81884,1856],{},[614,81886,81887],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,81890,81892],{"className":81891},[886],[888,81893,81894],{"xmlns":890},[892,81895,81896,81908],{},[895,81897,81898,81900,81902,81904,81906],{},[1655,81899,2734],{"stretchy":1663},[898,81901,1873],{},[1655,81903,1671],{"separator":1670},[898,81905,1878],{},[1655,81907,2743],{"stretchy":1663},[902,81909,81910],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,81913,81915],{"className":81914},[886],[888,81916,81917],{"xmlns":890},[892,81918,81919,81924],{},[895,81920,81921],{},[898,81922,81923],{},"q",[902,81925,81923],{"encoding":904},[883,81927,81929],{"className":81928},[886],[888,81930,81931],{"xmlns":890,"display":29192},[892,81932,81933,81968],{},[21880,81934,81935],{"width":29197},[21885,81936,81937,81939,81961,81963],{},[21888,81938],{"width":29202},[21888,81940,81941],{},[895,81942,81943,81945,81947,81949,81951,81953,81955,81957,81959],{},[898,81944,1824],{},[1655,81946,1664],{"stretchy":1663},[898,81948,1873],{},[1655,81950,1671],{"separator":1670},[898,81952,1878],{},[1655,81954,1677],{"stretchy":1663},[1655,81956,1657],{},[898,81958,81923],{},[898,81960,1719],{"mathvariant":1943},[21888,81962],{"width":29202},[21888,81964,81965],{},[2031,81966,81967],{},"(5.13)",[902,81969,81970],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,81972,81973,81974,81977,81978,5171],{},"Jsou to ",[38,81975,81976],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,81979,81981],{"className":81980,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,81983,81984],{},[38,81985,81986],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,81988,81989,81994,81999,82004],{},[123,81990,81991,81993],{},[38,81992,13644],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,81995,81996,81998],{},[38,81997,38790],{}," (úloha 5.14);",[123,82000,82001,9672],{},[38,82002,82003],{},"neprotínají se",[123,82005,82006,82007,5607,82020,1719],{},"s rostoucím ",[883,82008,82010],{"className":82009},[886],[888,82011,82012],{"xmlns":890},[892,82013,82014,82018],{},[895,82015,82016],{},[898,82017,81923],{},[902,82019,81923],{"encoding":904},[38,82021,82022],{},"vzdalují od počátku",[724,82024,82025],{},[614,82026,82027,82028,82050,82051,1719],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,82029,82031],{"className":82030},[886],[888,82032,82033],{"xmlns":890},[892,82034,82035,82047],{},[895,82036,82037,82039,82041,82043,82045],{},[1655,82038,1664],{"stretchy":1663},[898,82040,1873],{},[1655,82042,1671],{"separator":1670},[898,82044,1878],{},[1655,82046,1677],{"stretchy":1663},[902,82048,82049],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,82052,82054],{"className":82053},[886],[888,82055,82056],{"xmlns":890},[892,82057,82058,82082],{},[895,82059,82060,82066,82068,82074,82076],{},[1820,82061,82062,82064],{},[898,82063,81923],{},[1826,82065,1828],{},[1655,82067,3065],{},[1820,82069,82070,82072],{},[898,82071,81923],{},[1826,82073,2552],{},[1655,82075,3065],{},[1820,82077,82078,82080],{},[898,82079,81923],{},[1826,82081,1837],{},[902,82083,82084],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,82086,82088,82089,1677],{"id":82087},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,82090,82092],{"className":82091},[886],[888,82093,82094],{"xmlns":890},[892,82095,82096,82106],{},[895,82097,82098,82100,82102,82104],{},[898,82099,2127],{},[898,82101,5245],{},[898,82103,4049],{},[898,82105,9920],{},[902,82107,2703],{"encoding":904},[724,82109,82110,2115,82113,82116],{},[38,82111,82112],{},"Mezní míra technické substituce",[614,82114,82115],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,82118,82120],{"className":82119},[886],[888,82121,82122],{"xmlns":890,"display":29192},[892,82123,82124,82215],{},[21880,82125,82126],{"width":29197},[21885,82127,82128,82130,82208,82210],{},[21888,82129],{"width":29202},[21888,82131,82132],{},[895,82133,82134,82136,82138,82140,82142,82144,82146,82148,82150,82152,82154,82156,82158,82160,82162,82164,82186,82188,82206],{},[898,82135,2127],{},[898,82137,5245],{},[898,82139,4049],{},[898,82141,9920],{},[1655,82143,1657],{},[898,82145,2127],{},[898,82147,5245],{},[898,82149,4049],{},[898,82151,9920],{},[1655,82153,1664],{"stretchy":1663},[898,82155,1873],{},[1655,82157,1671],{"separator":1670},[898,82159,1878],{},[1655,82161,1677],{"stretchy":1663},[1655,82163,1657],{},[1949,82165,82166,82176],{},[895,82167,82168,82170],{},[898,82169,2127],{},[1820,82171,82172,82174],{},[898,82173,2132],{},[898,82175,1873],{},[895,82177,82178,82180],{},[898,82179,2127],{},[1820,82181,82182,82184],{},[898,82183,2132],{},[898,82185,1878],{},[1655,82187,1657],{},[1949,82189,82190,82198],{},[1935,82191,82192,82194,82196],{},[898,82193,1824],{},[898,82195,1873],{},[1655,82197,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1935,82199,82200,82202,82204],{},[898,82201,1824],{},[898,82203,1878],{},[1655,82205,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[898,82207,1719],{"mathvariant":1943},[21888,82209],{"width":29202},[21888,82211,82212],{},[2031,82213,82214],{},"(5.14)",[902,82216,82217],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,82219,82220,3106,82222,82252,82253,82284],{},[38,82221,10462],{},[883,82223,82225],{"className":82224},[886],[888,82226,82227],{"xmlns":890},[892,82228,82229,82249],{},[895,82230,82231,82233,82235,82237,82239,82241,82243,82245,82247],{},[898,82232,2127],{},[898,82234,5245],{},[898,82236,4049],{},[898,82238,9920],{},[1655,82240,1664],{"stretchy":1663},[898,82242,1873],{},[1655,82244,1671],{"separator":1670},[898,82246,1878],{},[1655,82248,1677],{"stretchy":1663},[902,82250,82251],{"encoding":904},"MRTS(L, K)"," udává, ",[38,82254,82255,82256,82269,82270,82283],{},"o kolik se musí přibližně změnit kapitál ",[883,82257,82259],{"className":82258},[886],[888,82260,82261],{"xmlns":890},[892,82262,82263,82267],{},[895,82264,82265],{},[898,82266,1878],{},[902,82268,1878],{"encoding":904},", jestliže se práce ",[883,82271,82273],{"className":82272},[886],[888,82274,82275],{"xmlns":890},[892,82276,82277,82281],{},[895,82278,82279],{},[898,82280,1873],{},[902,82282,1873],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[5120,82286,82287],{},[724,82288,82289,19149,82291,82310,82311,82348,82349,82352,82353,82357],{},[883,82290,5406],{},[883,82292,82294],{"className":82293},[886],[888,82295,82296],{"xmlns":890},[892,82297,82298,82308],{},[895,82299,82300,82302,82304,82306],{},[898,82301,2127],{},[898,82303,5245],{},[898,82305,4049],{},[898,82307,9920],{},[902,82309,2703],{"encoding":904}," říká: ",[614,82312,82313,82314,82333,82334,82347],{},"„jednu jednotku práce musím nahradit přibližně ",[883,82315,82317],{"className":82316},[886],[888,82318,82319],{"xmlns":890},[892,82320,82321,82331],{},[895,82322,82323,82325,82327,82329],{},[898,82324,2127],{},[898,82326,5245],{},[898,82328,4049],{},[898,82330,9920],{},[902,82332,2703],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,82335,82337],{"className":82336},[886],[888,82338,82339],{"xmlns":890},[892,82340,82341,82345],{},[895,82342,82343],{},[898,82344,1824],{},[902,82346,1824],{"encoding":904}," zůstala stejná.\""," Je to ",[38,82350,82351],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,82354,82356],{"className":82355,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,82359,82360],{},[1723,82361],{"alt":82362,"className":82363,"src":82364},"imek-izokvanty-mrts",[210,1727],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,82366,82367,82370,82371,9349,82401,82423,82424,4421],{},[38,82368,82369],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,82372,82374],{"className":82373},[886],[888,82375,82376],{"xmlns":890},[892,82377,82378,82398],{},[895,82379,82380,82382,82388,82390,82396],{},[1655,82381,2734],{"stretchy":1663},[1820,82383,82384,82386],{},[898,82385,1873],{},[1826,82387,2552],{},[1655,82389,1671],{"separator":1670},[1820,82391,82392,82394],{},[898,82393,1878],{},[1826,82395,2552],{},[1655,82397,2743],{"stretchy":1663},[902,82399,82400],{"encoding":904},"[L_0, K_0]",[883,82402,82404],{"className":82403},[886],[888,82405,82406],{"xmlns":890},[892,82407,82408,82420],{},[895,82409,82410,82412,82414,82416,82418],{},[1655,82411,2623],{},[898,82413,2127],{},[898,82415,5245],{},[898,82417,4049],{},[898,82419,9920],{},[902,82421,82422],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,82425,82427],{"className":82426},[886],[888,82428,82429],{"xmlns":890},[892,82430,82431,82453],{},[895,82432,82433,82435,82437,82439,82441,82443,82445,82447],{},[898,82434,1824],{},[1655,82436,1664],{"stretchy":1663},[898,82438,1873],{},[1655,82440,1671],{"separator":1670},[898,82442,1878],{},[1655,82444,1677],{"stretchy":1663},[1655,82446,1657],{},[1820,82448,82449,82451],{},[898,82450,81923],{},[1826,82452,2552],{},[902,82454,82455],{"encoding":904},"Q(L,K) = q_0",[883,82457,82459],{"className":82458},[886],[888,82460,82461],{"xmlns":890,"display":29192},[892,82462,82463,82515],{},[895,82464,82465,82479,82481,82483,82501,82503,82505,82507,82509,82511,82513],{},[1949,82466,82467,82473],{},[895,82468,82469,82471],{},[898,82470,2410],{},[898,82472,1878],{},[895,82474,82475,82477],{},[898,82476,2410],{},[898,82478,1873],{},[1655,82480,1657],{},[1655,82482,2623],{},[1949,82484,82485,82493],{},[1935,82486,82487,82489,82491],{},[898,82488,1824],{},[898,82490,1873],{},[1655,82492,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1935,82494,82495,82497,82499],{},[898,82496,1824],{},[898,82498,1878],{},[1655,82500,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,82502,1657],{},[1655,82504,2623],{},[898,82506,2127],{},[898,82508,5245],{},[898,82510,4049],{},[898,82512,9920],{},[898,82514,1719],{"mathvariant":1943},[902,82516,82517],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,82519,82520,82521,82536,82537,82553],{},"Změní-li se práce o ",[883,82522,82524],{"className":82523},[886],[888,82525,82526],{"xmlns":890},[892,82527,82528,82534],{},[895,82529,82530,82532],{},[898,82531,2410],{},[898,82533,1873],{},[902,82535,76482],{"encoding":904},", lze pro odhad změny kapitálu ",[883,82538,82540],{"className":82539},[886],[888,82541,82542],{"xmlns":890},[892,82543,82544,82550],{},[895,82545,82546,82548],{},[898,82547,2506],{"mathvariant":1943},[898,82549,1878],{},[902,82551,82552],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,82555,82557],{"className":82556},[886],[888,82558,82559],{"xmlns":890,"display":29192},[892,82560,82561,82608],{},[21880,82562,82563],{"width":29197},[21885,82564,82565,82567,82601,82603],{},[21888,82566],{"width":29202},[21888,82568,82569],{},[895,82570,82571,82573,82575,82577,82579,82581,82583,82585,82587,82589,82591,82593,82595,82597,82599],{},[898,82572,2506],{"mathvariant":1943},[898,82574,1878],{},[1655,82576,2357],{},[898,82578,2410],{},[898,82580,1878],{},[1655,82582,1657],{},[1655,82584,2623],{},[898,82586,2127],{},[898,82588,5245],{},[898,82590,4049],{},[898,82592,9920],{},[2031,82594,2435],{},[898,82596,2410],{},[898,82598,1873],{},[1655,82600,1671],{"separator":1670},[21888,82602],{"width":29202},[21888,82604,82605],{},[2031,82606,82607],{},"(5.15)",[902,82609,82610],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,82612,82614],{"className":82613},[886],[888,82615,82616],{"xmlns":890,"display":29192},[892,82617,82618,82667],{},[21880,82619,82620],{"width":29197},[21885,82621,82622,82624,82660,82662],{},[21888,82623],{"width":29202},[21888,82625,82626],{},[895,82627,82628,82630,82632,82634,82652,82654,82656,82658],{},[898,82629,2410],{},[898,82631,1873],{},[1655,82633,1657],{},[1949,82635,82636,82642],{},[895,82637,82638,82640],{},[1655,82639,2623],{},[1826,82641,1828],{},[895,82643,82644,82646,82648,82650],{},[898,82645,2127],{},[898,82647,5245],{},[898,82649,4049],{},[898,82651,9920],{},[2031,82653,2435],{},[898,82655,2410],{},[898,82657,1878],{},[898,82659,1719],{"mathvariant":1943},[21888,82661],{"width":29202},[21888,82663,82664],{},[2031,82665,82666],{},"(5.16)",[902,82668,82669],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[5120,82671,82672,82696],{},[724,82673,82674,82676,82677],{},[883,82675,5821],{}," Postup — jak spočítat ",[883,82678,82680],{"className":82679},[886],[888,82681,82682],{"xmlns":890},[892,82683,82684,82694],{},[895,82685,82686,82688,82690,82692],{},[898,82687,2127],{},[898,82689,5245],{},[898,82691,4049],{},[898,82693,9920],{},[902,82695,2703],{"encoding":904},[152,82697,82698,82739,82782,82814],{},[123,82699,82700,82701,2704,82720,1719],{},"Vypočtěte parciální derivace ",[883,82702,82704],{"className":82703},[886],[888,82705,82706],{"xmlns":890},[892,82707,82708,82718],{},[895,82709,82710],{},[1935,82711,82712,82714,82716],{},[898,82713,1824],{},[898,82715,1873],{},[1655,82717,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,82719,2110],{"encoding":904},[883,82721,82723],{"className":82722},[886],[888,82724,82725],{"xmlns":890},[892,82726,82727,82737],{},[895,82728,82729],{},[1935,82730,82731,82733,82735],{},[898,82732,1824],{},[898,82734,1878],{},[1655,82736,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,82738,2159],{"encoding":904},[123,82740,66967,82741,82781],{},[883,82742,82744],{"className":82743},[886],[888,82745,82746],{"xmlns":890},[892,82747,82748,82778],{},[895,82749,82750,82752,82754,82756,82758,82760,82768,82770],{},[898,82751,2127],{},[898,82753,5245],{},[898,82755,4049],{},[898,82757,9920],{},[1655,82759,1657],{},[1935,82761,82762,82764,82766],{},[898,82763,1824],{},[898,82765,1873],{},[1655,82767,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[898,82769,5923],{"mathvariant":1943},[1935,82771,82772,82774,82776],{},[898,82773,1824],{},[898,82775,1878],{},[1655,82777,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,82779,82780],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,82783,82784,82785,1719],{},"Případně dosaďte konkrétní ",[883,82786,82788],{"className":82787},[886],[888,82789,82790],{"xmlns":890},[892,82791,82792,82812],{},[895,82793,82794,82796,82802,82804,82810],{},[1655,82795,2734],{"stretchy":1663},[1820,82797,82798,82800],{},[898,82799,1873],{},[1826,82801,2552],{},[1655,82803,1671],{"separator":1670},[1820,82805,82806,82808],{},[898,82807,1878],{},[1826,82809,2552],{},[1655,82811,2743],{"stretchy":1663},[902,82813,82400],{"encoding":904},[123,82815,82816,82817,82851,82852,82854],{},"Pro odhad substituce použijte ",[883,82818,82820],{"className":82819},[886],[888,82821,82822],{"xmlns":890},[892,82823,82824,82848],{},[895,82825,82826,82828,82830,82832,82834,82836,82838,82840,82842,82844,82846],{},[898,82827,2506],{"mathvariant":1943},[898,82829,1878],{},[1655,82831,2357],{},[1655,82833,2623],{},[898,82835,2127],{},[898,82837,5245],{},[898,82839,4049],{},[898,82841,9920],{},[1655,82843,2869],{},[898,82845,2506],{"mathvariant":1943},[898,82847,1873],{},[902,82849,82850],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,82853,53732],{}," — substituce, ne doplnění).",[724,82856,82857],{},[614,82858,82859,82860,82892,82893,3902,82906,16917,82935,82950],{},"Obrázek 5.7 — izokvanta ",[883,82861,82863],{"className":82862},[886],[888,82864,82865],{"xmlns":890},[892,82866,82867,82889],{},[895,82868,82869,82875,82877,82879,82881,82883,82885,82887],{},[1820,82870,82871,82873],{},[898,82872,81923],{},[1826,82874,2552],{},[1655,82876,1657],{},[898,82878,1824],{},[1655,82880,1664],{"stretchy":1663},[898,82882,1873],{},[1655,82884,1671],{"separator":1670},[898,82886,1878],{},[1655,82888,1677],{"stretchy":1663},[902,82890,82891],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,82894,82896],{"className":82895},[886],[888,82897,82898],{"xmlns":890},[892,82899,82900,82904],{},[895,82901,82902],{},[898,82903,19981],{},[902,82905,19981],{"encoding":904},[883,82907,82909],{"className":82908},[886],[888,82910,82911],{"xmlns":890},[892,82912,82913,82933],{},[895,82914,82915,82917,82923,82925,82931],{},[1655,82916,2734],{"stretchy":1663},[1820,82918,82919,82921],{},[898,82920,1873],{},[1826,82922,2552],{},[1655,82924,1671],{"separator":1670},[1820,82926,82927,82929],{},[898,82928,1878],{},[1826,82930,2552],{},[1655,82932,2743],{"stretchy":1663},[902,82934,82400],{"encoding":904},[883,82936,82938],{"className":82937},[886],[888,82939,82940],{"xmlns":890},[892,82941,82942,82948],{},[895,82943,82944,82946],{},[898,82945,2506],{"mathvariant":1943},[898,82947,1878],{},[902,82949,82552],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,82952,82954],{"id":82953},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,82956,82958],{"id":82957},"příklad-54","Příklad 5.4",[724,82960,77799,82961,1343,83003,1343,83020,1719],{},[883,82962,82964],{"className":82963},[886],[888,82965,82966],{"xmlns":890},[892,82967,82968,83000],{},[895,82969,82970,82972,82974,82976,82988],{},[898,82971,1824],{},[1655,82973,1657],{},[1826,82975,37370],{},[2597,82977,82978,82980],{},[898,82979,1873],{},[895,82981,82982,82984,82986],{},[1826,82983,1828],{},[898,82985,5923],{"mathvariant":1943},[1826,82987,1837],{},[2597,82989,82990,82992],{},[898,82991,1878],{},[895,82993,82994,82996,82998],{},[1826,82995,1828],{},[898,82997,5923],{"mathvariant":1943},[1826,82999,3472],{},[902,83001,83002],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,83004,83006],{"className":83005},[886],[888,83007,83008],{"xmlns":890},[892,83009,83010,83018],{},[895,83011,83012,83014,83016],{},[898,83013,1873],{},[1655,83015,1657],{},[1826,83017,10282],{},[902,83019,78173],{"encoding":904},[883,83021,83023],{"className":83022},[886],[888,83024,83025],{"xmlns":890},[892,83026,83027,83035],{},[895,83028,83029,83031,83033],{},[898,83030,1878],{},[1655,83032,1657],{},[1826,83034,4360],{},[902,83036,83037],{"encoding":904},"K = 100",[724,83039,83040],{},[38,83041,83042],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,83044,83046],{"className":83045},[886],[888,83047,83048],{"xmlns":890,"display":29192},[892,83049,83050,83164],{},[895,83051,83052,83054,83060,83062,83070,83072,83080,83094,83106,83108,83110,83112,83118,83120,83122,83124,83126,83128,83130,83138,83140,83150,83152,83159,83161],{},[898,83053,2127],{},[1820,83055,83056,83058],{},[898,83057,2132],{},[898,83059,1873],{},[1655,83061,1657],{},[1935,83063,83064,83066,83068],{},[898,83065,1824],{},[898,83067,1873],{},[1655,83069,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,83071,1657],{},[3615,83073,83074],{"scriptlevel":2552,"displaystyle":1663},[1949,83075,83076,83078],{},[1826,83077,37370],{},[1826,83079,1837],{},[2597,83081,83082,83084],{},[898,83083,1873],{},[895,83085,83086,83088,83090,83092],{},[1655,83087,2623],{},[1826,83089,1828],{},[898,83091,5923],{"mathvariant":1943},[1826,83093,1837],{},[2597,83095,83096,83098],{},[898,83097,1878],{},[895,83099,83100,83102,83104],{},[1826,83101,1828],{},[898,83103,5923],{"mathvariant":1943},[1826,83105,3472],{},[1655,83107,1671],{"separator":1670},[1967,83109],{"width":16409},[898,83111,2127],{},[1820,83113,83114,83116],{},[898,83115,2132],{},[898,83117,1873],{},[1655,83119,1664],{"stretchy":1663},[1826,83121,10282],{},[1655,83123,1671],{"separator":1670},[1826,83125,4360],{},[1655,83127,1677],{"stretchy":1663},[1655,83129,1657],{},[3615,83131,83132],{"scriptlevel":2552,"displaystyle":1663},[1949,83133,83134,83136],{},[1826,83135,37370],{},[1826,83137,1837],{},[1655,83139,2869],{},[3615,83141,83142],{"scriptlevel":2552,"displaystyle":1663},[1949,83143,83144,83146],{},[1826,83145,1828],{},[9364,83147,83148],{},[1826,83149,10282],{},[1655,83151,2869],{},[83153,83154,83155,83157],"mroot",{},[1826,83156,4360],{},[1826,83158,3472],{},[1655,83160,2357],{},[1826,83162,83163],{},"7,153.",[902,83165,83166],{"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.",[724,83168,83169,83170,45286,83192,2328,83209,83230,83231,83252],{},"Přibližná změna při ",[883,83171,83173],{"className":83172},[886],[888,83174,83175],{"xmlns":890},[892,83176,83177,83189],{},[895,83178,83179,83181,83183,83185,83187],{},[898,83180,1873],{},[1655,83182,2086],{},[1826,83184,10282],{},[1655,83186,4393],{},[1826,83188,39472],{},[902,83190,83191],{"encoding":904},"L: 20 \\to 21",[883,83193,83195],{"className":83194},[886],[888,83196,83197],{"xmlns":890},[892,83198,83199,83207],{},[895,83200,83201,83203,83205],{},[898,83202,1878],{},[1655,83204,1657],{},[1826,83206,4360],{},[902,83208,83037],{"encoding":904},[883,83210,83212],{"className":83211},[886],[888,83213,83214],{"xmlns":890},[892,83215,83216,83227],{},[895,83217,83218,83220,83222,83224],{},[898,83219,2506],{"mathvariant":1943},[898,83221,1824],{},[1655,83223,2357],{},[1826,83225,83226],{},"7,153",[902,83228,83229],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,83232,83234],{"className":83233},[886],[888,83235,83236],{"xmlns":890},[892,83237,83238,83249],{},[895,83239,83240,83242,83244,83246],{},[898,83241,2506],{"mathvariant":1943},[898,83243,1824],{},[1655,83245,2357],{},[1826,83247,83248],{},"26,888",[902,83250,83251],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,83254,83255,83258],{},[38,83256,83257],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,83260,83262],{"className":83261},[886],[888,83263,83264],{"xmlns":890,"display":29192},[892,83265,83266,83366],{},[895,83267,83268,83270,83276,83278,83286,83288,83290,83302,83316,83318,83320,83322,83328,83330,83332,83334,83336,83338,83340,83342,83346,83348,83361,83363],{},[898,83269,2127],{},[1820,83271,83272,83274],{},[898,83273,2132],{},[898,83275,1878],{},[1655,83277,1657],{},[1935,83279,83280,83282,83284],{},[898,83281,1824],{},[898,83283,1878],{},[1655,83285,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,83287,1657],{},[1826,83289,3524],{},[2597,83291,83292,83294],{},[898,83293,1873],{},[895,83295,83296,83298,83300],{},[1826,83297,1828],{},[898,83299,5923],{"mathvariant":1943},[1826,83301,1837],{},[2597,83303,83304,83306],{},[898,83305,1878],{},[895,83307,83308,83310,83312,83314],{},[1655,83309,2623],{},[1826,83311,1837],{},[898,83313,5923],{"mathvariant":1943},[1826,83315,3472],{},[1655,83317,1671],{"separator":1670},[1967,83319],{"width":16409},[898,83321,2127],{},[1820,83323,83324,83326],{},[898,83325,2132],{},[898,83327,1878],{},[1655,83329,1664],{"stretchy":1663},[1826,83331,10282],{},[1655,83333,1671],{"separator":1670},[1826,83335,4360],{},[1655,83337,1677],{"stretchy":1663},[1655,83339,1657],{},[1826,83341,3524],{},[9364,83343,83344],{},[1826,83345,10282],{},[1655,83347,2869],{},[3615,83349,83350],{"scriptlevel":2552,"displaystyle":1663},[1949,83351,83352,83354],{},[1826,83353,1828],{},[83153,83355,83356,83359],{},[1826,83357,83358],{},"10000",[1826,83360,3472],{},[1655,83362,2357],{},[1826,83364,83365],{},"4,525.",[902,83367,83368],{"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.",[724,83370,83371,83372,3962,83389,5171],{},"Produkce poklesne přibližně o 4,525 (z ",[883,83373,83375],{"className":83374},[886],[888,83376,83377],{"xmlns":890},[892,83378,83379,83386],{},[895,83380,83381,83383],{},[1655,83382,2357],{},[1826,83384,83385],{},"905,126",[902,83387,83388],{"encoding":904},"\\approx 905{,}126",[883,83390,83392],{"className":83391},[886],[888,83393,83394],{"xmlns":890},[892,83395,83396,83403],{},[895,83397,83398,83400],{},[1655,83399,2357],{},[1826,83401,83402],{},"900,601",[902,83404,83405],{"encoding":904},"\\approx 900{,}601",[724,83407,83408,4400,83455,1343,83477,5171],{},[38,83409,83410,83411,2704,83433],{},"(c) Změna ",[883,83412,83414],{"className":83413},[886],[888,83415,83416],{"xmlns":890},[892,83417,83418,83430],{},[895,83419,83420,83422,83424,83426,83428],{},[898,83421,1873],{},[1655,83423,2086],{},[1826,83425,10282],{},[1655,83427,4393],{},[1826,83429,37370],{},[902,83431,83432],{"encoding":904},"L: 20 \\to 15",[883,83434,83436],{"className":83435},[886],[888,83437,83438],{"xmlns":890},[892,83439,83440,83452],{},[895,83441,83442,83444,83446,83448,83450],{},[898,83443,1878],{},[1655,83445,2086],{},[1826,83447,4360],{},[1655,83449,4393],{},[1826,83451,10050],{},[902,83453,83454],{"encoding":904},"K: 100 \\to 150",[883,83456,83458],{"className":83457},[886],[888,83459,83460],{"xmlns":890},[892,83461,83462,83474],{},[895,83463,83464,83466,83468,83470,83472],{},[898,83465,2410],{},[898,83467,1873],{},[1655,83469,1657],{},[1655,83471,2623],{},[1826,83473,3524],{},[902,83475,83476],{"encoding":904},"dL = -5",[883,83478,83480],{"className":83479},[886],[888,83481,83482],{"xmlns":890},[892,83483,83484,83494],{},[895,83485,83486,83488,83490,83492],{},[898,83487,2410],{},[898,83489,1878],{},[1655,83491,1657],{},[1826,83493,4390],{},[902,83495,83496],{"encoding":904},"dK = 50",[883,83498,83500],{"className":83499},[886],[888,83501,83502],{"xmlns":890,"display":29192},[892,83503,83504,83592],{},[895,83505,83506,83508,83510,83512,83514,83520,83522,83524,83526,83528,83530,83532,83534,83536,83538,83540,83542,83544,83550,83552,83554,83556,83558,83560,83562,83564,83566,83568,83570,83572,83574,83576,83578,83580,83583,83585,83587,83589],{},[898,83507,2410],{},[898,83509,1824],{},[1655,83511,1657],{},[898,83513,2127],{},[1820,83515,83516,83518],{},[898,83517,2132],{},[898,83519,1873],{},[1655,83521,1664],{"stretchy":1663},[1826,83523,10282],{},[1655,83525,1671],{"separator":1670},[1826,83527,4360],{},[1655,83529,1677],{"stretchy":1663},[1655,83531,2869],{},[1655,83533,1664],{"stretchy":1663},[1655,83535,2623],{},[1826,83537,3524],{},[1655,83539,1677],{"stretchy":1663},[1655,83541,2346],{},[898,83543,2127],{},[1820,83545,83546,83548],{},[898,83547,2132],{},[898,83549,1878],{},[1655,83551,1664],{"stretchy":1663},[1826,83553,10282],{},[1655,83555,1671],{"separator":1670},[1826,83557,4360],{},[1655,83559,1677],{"stretchy":1663},[1655,83561,2869],{},[1826,83563,4390],{},[1655,83565,1657],{},[1826,83567,83226],{},[1655,83569,2869],{},[1655,83571,1664],{"stretchy":1663},[1655,83573,2623],{},[1826,83575,3524],{},[1655,83577,1677],{"stretchy":1663},[1655,83579,2346],{},[1826,83581,83582],{},"4,525",[1655,83584,2869],{},[1826,83586,4390],{},[1655,83588,2357],{},[1826,83590,83591],{},"190,485.",[902,83593,83594],{"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.",[724,83596,83597],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,83599,83601],{"id":83600},"příklad-55","Příklad 5.5",[724,83603,83604,83605,83641,83642,1719],{},"Pro produkci ",[883,83606,83608],{"className":83607},[886],[888,83609,83610],{"xmlns":890},[892,83611,83612,83638],{},[895,83613,83614,83616,83618,83620,83622,83624,83626,83628,83634],{},[898,83615,1824],{},[1655,83617,1664],{"stretchy":1663},[898,83619,1873],{},[1655,83621,1671],{"separator":1670},[898,83623,1878],{},[1655,83625,1677],{"stretchy":1663},[1655,83627,1657],{},[83153,83629,83630,83632],{},[898,83631,1873],{},[1826,83633,3472],{},[9364,83635,83636],{},[898,83637,1878],{},[902,83639,83640],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,83643,83645],{"className":83644},[886],[888,83646,83647],{"xmlns":890},[892,83648,83649,83665],{},[895,83650,83651,83657,83661,83663],{},[83153,83652,83653,83655],{},[898,83654,1873],{},[1826,83656,3472],{},[9364,83658,83659],{},[898,83660,1878],{},[1655,83662,1657],{},[898,83664,81923],{},[902,83666,83667],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,83669,83670,83671,1719],{},"Umocněním na druhou: ",[883,83672,83674],{"className":83673},[886],[888,83675,83676],{"xmlns":890},[892,83677,83678,83702],{},[895,83679,83680,83682,83684,83690,83692],{},[898,83681,1878],{},[1655,83683,1657],{},[2597,83685,83686,83688],{},[898,83687,81923],{},[1826,83689,1837],{},[898,83691,5923],{"mathvariant":1943},[83153,83693,83694,83700],{},[2597,83695,83696,83698],{},[898,83697,1873],{},[1826,83699,1837],{},[1826,83701,3472],{},[902,83703,83704],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,83706,83707,83747,83787],{},[123,83708,83709],{},[883,83710,83712],{"className":83711},[886],[888,83713,83714],{"xmlns":890},[892,83715,83716,83744],{},[895,83717,83718,83720,83722,83724,83726,83728,83730,83732,83734],{},[898,83719,81923],{},[1655,83721,1657],{},[1826,83723,1828],{},[1655,83725,5238],{},[898,83727,1878],{},[1655,83729,1657],{},[1826,83731,1828],{},[898,83733,5923],{"mathvariant":1943},[83153,83735,83736,83742],{},[2597,83737,83738,83740],{},[898,83739,1873],{},[1826,83741,1837],{},[1826,83743,3472],{},[902,83745,83746],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,83748,83749],{},[883,83750,83752],{"className":83751},[886],[888,83753,83754],{"xmlns":890},[892,83755,83756,83784],{},[895,83757,83758,83760,83762,83764,83766,83768,83770,83772,83774],{},[898,83759,81923],{},[1655,83761,1657],{},[1826,83763,1837],{},[1655,83765,5238],{},[898,83767,1878],{},[1655,83769,1657],{},[1826,83771,3639],{},[898,83773,5923],{"mathvariant":1943},[83153,83775,83776,83782],{},[2597,83777,83778,83780],{},[898,83779,1873],{},[1826,83781,1837],{},[1826,83783,3472],{},[902,83785,83786],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,83788,83789],{},[883,83790,83792],{"className":83791},[886],[888,83793,83794],{"xmlns":890},[892,83795,83796,83824],{},[895,83797,83798,83800,83802,83804,83806,83808,83810,83812,83814],{},[898,83799,81923],{},[1655,83801,1657],{},[1826,83803,3472],{},[1655,83805,5238],{},[898,83807,1878],{},[1655,83809,1657],{},[1826,83811,5250],{},[898,83813,5923],{"mathvariant":1943},[83153,83815,83816,83822],{},[2597,83817,83818,83820],{},[898,83819,1873],{},[1826,83821,1837],{},[1826,83823,3472],{},[902,83825,83826],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,83828,83829],{},[614,83830,83831,83832,7720,83853,1719],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,83833,83835],{"className":83834},[886],[888,83836,83837],{"xmlns":890},[892,83838,83839,83851],{},[895,83840,83841,83843,83845,83847,83849],{},[1655,83842,1664],{"stretchy":1663},[898,83844,1873],{},[1655,83846,1671],{"separator":1670},[898,83848,1878],{},[1655,83850,1677],{"stretchy":1663},[902,83852,82049],{"encoding":904},[883,83854,83856],{"className":83855},[886],[888,83857,83858],{"xmlns":890},[892,83859,83860,83876],{},[895,83861,83862,83864,83866,83868,83870,83872,83874],{},[898,83863,81923],{},[1655,83865,1657],{},[1826,83867,1828],{},[1655,83869,1671],{"separator":1670},[1826,83871,1837],{},[1655,83873,1671],{"separator":1670},[1826,83875,3472],{},[902,83877,83878],{"encoding":904},"q = 1, 2, 3",[198,83880,83882],{"id":83881},"příklad-56","Příklad 5.6",[724,83884,77799,83885,1719],{},[883,83886,83888],{"className":83887},[886],[888,83889,83890],{"xmlns":890},[892,83891,83892,83908],{},[895,83893,83894,83896,83898,83900,83902,83904],{},[898,83895,1824],{},[1655,83897,1657],{},[1826,83899,1837],{},[898,83901,1873],{},[1655,83903,2346],{},[9364,83905,83906],{},[898,83907,1878],{},[902,83909,83910],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,83912,83914],{"className":83913},[886],[888,83915,83916],{"xmlns":890,"display":29192},[892,83917,83918,83960],{},[895,83919,83920,83922,83928,83930,83932,83934,83936,83938,83944,83946,83958],{},[898,83921,2127],{},[1820,83923,83924,83926],{},[898,83925,2132],{},[898,83927,1873],{},[1655,83929,1657],{},[1826,83931,1837],{},[1655,83933,1671],{"separator":1670},[1967,83935],{"width":1969},[898,83937,2127],{},[1820,83939,83940,83942],{},[898,83941,2132],{},[898,83943,1878],{},[1655,83945,1657],{},[1949,83947,83948,83950],{},[1826,83949,1828],{},[895,83951,83952,83954],{},[1826,83953,1837],{},[9364,83955,83956],{},[898,83957,1878],{},[898,83959,1719],{"mathvariant":1943},[902,83961,83962],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,83964,83966],{"className":83965},[886],[888,83967,83968],{"xmlns":890,"display":29192},[892,83969,83970,84034],{},[895,83971,83972,83974,83976,83978,83980,83982,84004,84006,84024,84026,84028,84032],{},[898,83973,2127],{},[898,83975,5245],{},[898,83977,4049],{},[898,83979,9920],{},[1655,83981,1657],{},[1949,83983,83984,83994],{},[895,83985,83986,83988],{},[898,83987,2127],{},[1820,83989,83990,83992],{},[898,83991,2132],{},[898,83993,1873],{},[895,83995,83996,83998],{},[898,83997,2127],{},[1820,83999,84000,84002],{},[898,84001,2132],{},[898,84003,1878],{},[1655,84005,1657],{},[1949,84007,84008,84010],{},[1826,84009,1837],{},[3615,84011,84012],{"scriptlevel":2552,"displaystyle":1663},[1949,84013,84014,84016],{},[1826,84015,1828],{},[895,84017,84018,84020],{},[1826,84019,1837],{},[9364,84021,84022],{},[898,84023,1878],{},[1655,84025,1657],{},[1826,84027,3639],{},[9364,84029,84030],{},[898,84031,1878],{},[898,84033,1719],{"mathvariant":1943},[902,84035,84036],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,84038,84039,84040,84083,84084,84123,84124,1719],{},"Například ",[883,84041,84043],{"className":84042},[886],[888,84044,84045],{"xmlns":890},[892,84046,84047,84080],{},[895,84048,84049,84051,84053,84055,84057,84059,84061,84063,84065,84067,84069,84071,84075,84077],{},[898,84050,2127],{},[898,84052,5245],{},[898,84054,4049],{},[898,84056,9920],{},[1655,84058,1664],{"stretchy":1663},[1826,84060,3639],{},[1655,84062,1671],{"separator":1670},[1826,84064,25327],{},[1655,84066,1677],{"stretchy":1663},[1655,84068,1657],{},[1826,84070,3639],{},[9364,84072,84073],{},[1826,84074,25327],{},[1655,84076,2357],{},[1826,84078,84079],{},"10,58",[902,84081,84082],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,84085,84087],{"className":84086},[886],[888,84088,84089],{"xmlns":890},[892,84090,84091,84120],{},[895,84092,84093,84095,84097,84099,84101,84103,84105,84107,84109,84111,84115,84117],{},[898,84094,1824],{},[1655,84096,1664],{"stretchy":1663},[1826,84098,3639],{},[1655,84100,1671],{"separator":1670},[1826,84102,25327],{},[1655,84104,1677],{"stretchy":1663},[1655,84106,1657],{},[1826,84108,6834],{},[1655,84110,2346],{},[9364,84112,84113],{},[1826,84114,25327],{},[1655,84116,2357],{},[1826,84118,84119],{},"10,646",[902,84121,84122],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,84125,84127],{"className":84126},[886],[888,84128,84129],{"xmlns":890},[892,84130,84131,84139],{},[895,84132,84133,84135],{},[1826,84134,3639],{},[9364,84136,84137],{},[1826,84138,25327],{},[902,84140,84141],{"encoding":904},"4\\sqrt{7}",[724,84143,84144,84145,84165],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,84146,84148],{"className":84147},[886],[888,84149,84150],{"xmlns":890},[892,84151,84152,84162],{},[895,84153,84154,84156,84158,84160],{},[898,84155,2410],{},[898,84157,1873],{},[1655,84159,1657],{},[1826,84161,1837],{},[902,84163,84164],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,84167,84169],{"className":84168},[886],[888,84170,84171],{"xmlns":890,"display":29192},[892,84172,84173,84222],{},[895,84174,84175,84177,84179,84181,84183,84185,84187,84189,84191,84193,84195,84197,84199,84201,84203,84205,84207,84209,84211,84215,84217,84219],{},[898,84176,2410],{},[898,84178,1878],{},[1655,84180,1657],{},[1655,84182,2623],{},[898,84184,2127],{},[898,84186,5245],{},[898,84188,4049],{},[898,84190,9920],{},[1655,84192,1664],{"stretchy":1663},[1826,84194,3639],{},[1655,84196,1671],{"separator":1670},[1826,84198,25327],{},[1655,84200,1677],{"stretchy":1663},[1655,84202,2869],{},[1826,84204,1837],{},[1655,84206,1657],{},[1655,84208,2623],{},[1826,84210,6834],{},[9364,84212,84213],{},[1826,84214,25327],{},[1655,84216,2357],{},[1655,84218,2623],{},[1826,84220,84221],{},"21,17.",[902,84223,84224],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,84226,84228],{"id":84227},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,84230,84231,84232,1343,84234,2704,84236,84238,84239,84242,84243,84246],{},"Hlavními faktory produkce jsou ",[38,84233,76040],{},[38,84235,76056],{},[38,84237,76072],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,84240,84241],{},"jednofaktorový"," (pouze práce) a ",[38,84244,84245],{},"dvoufaktorový"," (práce + kapitál) model.",[724,84248,84249,84250,84253,84254,84256,84257,84259,84260,27315,84263,84282,84283,84300,84301,84318,84319,84341,84342,5607,84361,1719],{},"V ",[38,84251,84252],{},"1F modelu"," se definuje ",[38,84255,2114],{}," (derivace produkce podle práce) a ",[38,84258,75975],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,84261,84262],{},"zákonu klesajících výnosů",[883,84264,84266],{"className":84265},[886],[888,84267,84268],{"xmlns":890},[892,84269,84270,84280],{},[895,84271,84272,84274],{},[898,84273,2127],{},[1820,84275,84276,84278],{},[898,84277,2132],{},[898,84279,1873],{},[902,84281,2137],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,84284,84286],{"className":84285},[886],[888,84287,84288],{"xmlns":890},[892,84289,84290,84298],{},[895,84291,84292],{},[1820,84293,84294,84296],{},[898,84295,1873],{},[1826,84297,2552],{},[902,84299,76684],{"encoding":904}," klesá a v bodě ",[883,84302,84304],{"className":84303},[886],[888,84305,84306],{"xmlns":890},[892,84307,84308,84316],{},[895,84309,84310],{},[1820,84311,84312,84314],{},[898,84313,1873],{},[1826,84315,1828],{},[902,84317,14337],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,84320,84321,84322],{},"princip maximalizace ",[883,84323,84325],{"className":84324},[886],[888,84326,84327],{"xmlns":890},[892,84328,84329,84339],{},[895,84330,84331,84333],{},[898,84332,2731],{},[1820,84334,84335,84337],{},[898,84336,2132],{},[898,84338,1873],{},[902,84340,75759],{"encoding":904},": v bodě maxima ",[883,84343,84345],{"className":84344},[886],[888,84346,84347],{"xmlns":890},[892,84348,84349,84359],{},[895,84350,84351,84353],{},[898,84352,2731],{},[1820,84354,84355,84357],{},[898,84356,2132],{},[898,84358,1873],{},[902,84360,75759],{"encoding":904},[883,84362,84364],{"className":84363},[886],[888,84365,84366],{"xmlns":890},[892,84367,84368,84388],{},[895,84369,84370,84372,84378,84380,84382],{},[898,84371,2127],{},[1820,84373,84374,84376],{},[898,84375,2132],{},[898,84377,1873],{},[1655,84379,1657],{},[898,84381,2731],{},[1820,84383,84384,84386],{},[898,84385,2132],{},[898,84387,1873],{},[902,84389,75789],{"encoding":904},[724,84391,84392,84393,84396,84397,3106,84400,84429,84430,84447,84448,84451,84452,84481,84482,84484,84485,9349,84515,84537],{},"Ve ",[38,84394,84395],{},"2F modelu"," se obvykle používají ",[38,84398,84399],{},"Cobb-Douglasovy funkce",[883,84401,84403],{"className":84402},[886],[888,84404,84405],{"xmlns":890},[892,84406,84407,84427],{},[895,84408,84409,84411,84413,84415,84421],{},[898,84410,1824],{},[1655,84412,1657],{},[898,84414,2731],{},[2597,84416,84417,84419],{},[898,84418,1873],{},[898,84420,207],{},[2597,84422,84423,84425],{},[898,84424,1878],{},[898,84426,2025],{},[902,84428,75856],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,84431,84433],{"className":84432},[886],[888,84434,84435],{"xmlns":890},[892,84436,84437,84445],{},[895,84438,84439,84441,84443],{},[898,84440,207],{},[1655,84442,2346],{},[898,84444,2025],{},[902,84446,75950],{"encoding":904}," rozlišujeme ",[38,84449,84450],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,84453,84455],{"className":84454},[886],[888,84456,84457],{"xmlns":890},[892,84458,84459,84479],{},[895,84460,84461,84463,84469,84471,84473],{},[898,84462,2127],{},[1820,84464,84465,84467],{},[898,84466,2132],{},[898,84468,1873],{},[1655,84470,1671],{"separator":1670},[898,84472,2127],{},[1820,84474,84475,84477],{},[898,84476,2132],{},[898,84478,1878],{},[902,84480,75887],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,84483,1856],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,84486,84488],{"className":84487},[886],[888,84489,84490],{"xmlns":890},[892,84491,84492,84512],{},[895,84493,84494,84496,84502,84504,84506],{},[898,84495,2127],{},[1820,84497,84498,84500],{},[898,84499,2132],{},[898,84501,1873],{},[898,84503,5923],{"mathvariant":1943},[898,84505,2127],{},[1820,84507,84508,84510],{},[898,84509,2132],{},[898,84511,1878],{},[902,84513,84514],{"encoding":904},"MP_L\u002FMP_K",[38,84516,84517,84518,1677],{},"mezní míra technické substituce (",[883,84519,84521],{"className":84520},[886],[888,84522,84523],{"xmlns":890},[892,84524,84525,84535],{},[895,84526,84527,84529,84531,84533],{},[898,84528,2127],{},[898,84530,5245],{},[898,84532,4049],{},[898,84534,9920],{},[902,84536,2703],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,84539,51008],{"id":51007},[152,84541,84542,84545,84548,84551,84554,84557,84560,84563,84566,84569,84572],{},[123,84543,84544],{},"Jaké jsou faktory produkce?",[123,84546,84547],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,84549,84550],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,84552,84553],{},"Co udává mezní produkt práce?",[123,84555,84556],{},"Co musí respektovat průběh křivky produkce?",[123,84558,84559],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,84561,84562],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,84564,84565],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,84567,84568],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,84570,84571],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,84573,84574],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,84576,84578],{"id":84577},"úlohy-51517","Úlohy 5.1–5.17",[198,84580,41577],{"id":41576},[724,84582,84583,84586,84587,84609,84610,1343,84630,1343,84650,84670],{},[38,84584,84585],{},"5.1"," Je dána produkce ",[883,84588,84590],{"className":84589},[886],[888,84591,84592],{"xmlns":890},[892,84593,84594,84606],{},[895,84595,84596,84598,84600,84602],{},[898,84597,1824],{},[1655,84599,1657],{},[1826,84601,4136],{},[9364,84603,84604],{},[898,84605,1873],{},[902,84607,84608],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,84611,84613],{"className":84612},[886],[888,84614,84615],{"xmlns":890},[892,84616,84617,84627],{},[895,84618,84619,84621,84623,84625],{},[898,84620,1824],{},[1655,84622,1664],{"stretchy":1663},[1826,84624,1828],{},[1655,84626,1677],{"stretchy":1663},[902,84628,84629],{"encoding":904},"Q(1)",[883,84631,84633],{"className":84632},[886],[888,84634,84635],{"xmlns":890},[892,84636,84637,84647],{},[895,84638,84639,84641,84643,84645],{},[898,84640,1824],{},[1655,84642,1664],{"stretchy":1663},[1826,84644,3639],{},[1655,84646,1677],{"stretchy":1663},[902,84648,84649],{"encoding":904},"Q(4)",[883,84651,84653],{"className":84652},[886],[888,84654,84655],{"xmlns":890},[892,84656,84657,84667],{},[895,84658,84659,84661,84663,84665],{},[898,84660,1824],{},[1655,84662,1664],{"stretchy":1663},[1826,84664,5250],{},[1655,84666,1677],{"stretchy":1663},[902,84668,84669],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,84672,84673,84586,84676,84712,84713,84726,84727,84746,84747,84773,84774,3962,84787,84800],{},[38,84674,84675],{},"5.2",[883,84677,84679],{"className":84678},[886],[888,84680,84681],{"xmlns":890},[892,84682,84683,84709],{},[895,84684,84685,84687,84689,84691,84693,84699,84701,84703],{},[898,84686,1824],{},[1655,84688,1657],{},[1655,84690,2623],{},[1826,84692,4068],{},[2597,84694,84695,84697],{},[898,84696,1873],{},[1826,84698,3472],{},[1655,84700,2346],{},[1826,84702,5250],{},[2597,84704,84705,84707],{},[898,84706,1873],{},[1826,84708,1837],{},[902,84710,84711],{"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 ",[883,84714,84716],{"className":84715},[886],[888,84717,84718],{"xmlns":890},[892,84719,84720,84724],{},[895,84721,84722],{},[898,84723,1873],{},[902,84725,1873],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,84728,84730],{"className":84729},[886],[888,84731,84732],{"xmlns":890},[892,84733,84734,84744],{},[895,84735,84736,84738],{},[898,84737,2127],{},[1820,84739,84740,84742],{},[898,84741,2132],{},[898,84743,1873],{},[902,84745,2137],{"encoding":904},". (f) Vypočtěte ",[883,84748,84750],{"className":84749},[886],[888,84751,84752],{"xmlns":890},[892,84753,84754,84770],{},[895,84755,84756,84758,84764,84766,84768],{},[898,84757,2127],{},[1820,84759,84760,84762],{},[898,84761,2132],{},[898,84763,1873],{},[1655,84765,1664],{"stretchy":1663},[1826,84767,4136],{},[1655,84769,1677],{"stretchy":1663},[902,84771,84772],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,84775,84777],{"className":84776},[886],[888,84778,84779],{"xmlns":890},[892,84780,84781,84785],{},[895,84782,84783],{},[1826,84784,4136],{},[902,84786,4136],{"encoding":904},[883,84788,84790],{"className":84789},[886],[888,84791,84792],{"xmlns":890},[892,84793,84794,84798],{},[895,84795,84796],{},[1826,84797,43413],{},[902,84799,43413],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,84802,84803,84806,84807,84829,84830,84858,84859,84890,84891,1719],{},[38,84804,84805],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,84808,84810],{"className":84809},[886],[888,84811,84812],{"xmlns":890},[892,84813,84814,84826],{},[895,84815,84816,84818,84820,84822],{},[898,84817,1824],{},[1655,84819,1657],{},[1826,84821,16235],{},[9364,84823,84824],{},[898,84825,1873],{},[902,84827,84828],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,84831,84833],{"className":84832},[886],[888,84834,84835],{"xmlns":890},[892,84836,84837,84855],{},[895,84838,84839,84841,84843,84845,84849,84851,84853],{},[898,84840,1824],{},[1655,84842,1657],{},[1826,84844,31207],{},[9364,84846,84847],{},[898,84848,1873],{},[1655,84850,2623],{},[1826,84852,3639],{},[898,84854,1873],{},[902,84856,84857],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,84860,84862],{"className":84861},[886],[888,84863,84864],{"xmlns":890},[892,84865,84866,84887],{},[895,84867,84868,84870,84872,84874,84876,84878,84881],{},[898,84869,1824],{},[1655,84871,1657],{},[1826,84873,4390],{},[898,84875,1873],{},[1655,84877,2623],{},[1826,84879,84880],{},"0,01",[2597,84882,84883,84885],{},[898,84884,1873],{},[1826,84886,1837],{},[902,84888,84889],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,84892,84894],{"className":84893},[886],[888,84895,84896],{"xmlns":890},[892,84897,84898,84924],{},[895,84899,84900,84902,84904,84906,84908,84914,84916,84918],{},[898,84901,1824],{},[1655,84903,1657],{},[1655,84905,2623],{},[1826,84907,69337],{},[2597,84909,84910,84912],{},[898,84911,1873],{},[1826,84913,3472],{},[1655,84915,2346],{},[1826,84917,5250],{},[2597,84919,84920,84922],{},[898,84921,1873],{},[1826,84923,1837],{},[902,84925,84926],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,84928,84929,84932,84933,3902,84952,73324,84969,1719],{},[38,84930,84931],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,84934,84936],{"className":84935},[886],[888,84937,84938],{"xmlns":890},[892,84939,84940,84950],{},[895,84941,84942,84944],{},[898,84943,2731],{},[1820,84945,84946,84948],{},[898,84947,2132],{},[898,84949,1873],{},[902,84951,75759],{"encoding":904},[883,84953,84955],{"className":84954},[886],[888,84956,84957],{"xmlns":890},[892,84958,84959,84967],{},[895,84960,84961],{},[1820,84962,84963,84965],{},[898,84964,1873],{},[1826,84966,2552],{},[902,84968,76684],{"encoding":904},[883,84970,84972],{"className":84971},[886],[888,84973,84974],{"xmlns":890},[892,84975,84976,85016],{},[895,84977,84978,84980,84986,84988,84994,84996,84998,85000,85006,85008,85014],{},[898,84979,2731],{},[1820,84981,84982,84984],{},[898,84983,2132],{},[898,84985,1873],{},[1655,84987,1664],{"stretchy":1663},[1820,84989,84990,84992],{},[898,84991,1873],{},[1826,84993,2552],{},[1655,84995,1677],{"stretchy":1663},[1655,84997,1657],{},[898,84999,2127],{},[1820,85001,85002,85004],{},[898,85003,2132],{},[898,85005,1873],{},[1655,85007,1664],{"stretchy":1663},[1820,85009,85010,85012],{},[898,85011,1873],{},[1826,85013,2552],{},[1655,85015,1677],{"stretchy":1663},[902,85017,85018],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,85020,85021,84586,85024,22720,85060,85073,85074,85093],{},[38,85022,85023],{},"5.5",[883,85025,85027],{"className":85026},[886],[888,85028,85029],{"xmlns":890},[892,85030,85031,85057],{},[895,85032,85033,85035,85037,85039,85041,85047,85049,85051],{},[898,85034,1824],{},[1655,85036,1657],{},[1655,85038,2623],{},[1826,85040,4112],{},[2597,85042,85043,85045],{},[898,85044,1873],{},[1826,85046,3472],{},[1655,85048,2346],{},[1826,85050,4771],{},[2597,85052,85053,85055],{},[898,85054,1873],{},[1826,85056,1837],{},[902,85058,85059],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,85061,85063],{"className":85062},[886],[888,85064,85065],{"xmlns":890},[892,85066,85067,85071],{},[895,85068,85069],{},[898,85070,1873],{},[902,85072,1873],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,85075,85077],{"className":85076},[886],[888,85078,85079],{"xmlns":890},[892,85080,85081,85091],{},[895,85082,85083,85085],{},[898,85084,2731],{},[1820,85086,85087,85089],{},[898,85088,2132],{},[898,85090,1873],{},[902,85092,75759],{"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.",[198,85095,85097],{"id":85096},"dvoufaktorový-model","Dvoufaktorový model",[724,85099,85100,85103,85104,84829,85130,84858,85172,1719],{},[38,85101,85102],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,85105,85107],{"className":85106},[886],[888,85108,85109],{"xmlns":890},[892,85110,85111,85127],{},[895,85112,85113,85115,85117,85119,85121],{},[898,85114,1824],{},[1655,85116,1657],{},[1826,85118,25327],{},[898,85120,1873],{},[2597,85122,85123,85125],{},[898,85124,1878],{},[1826,85126,1837],{},[902,85128,85129],{"encoding":904},"Q = 7 L K^{2}",[883,85131,85133],{"className":85132},[886],[888,85134,85135],{"xmlns":890},[892,85136,85137,85169],{},[895,85138,85139,85141,85143,85145,85157],{},[898,85140,1824],{},[1655,85142,1657],{},[1826,85144,4390],{},[2597,85146,85147,85149],{},[898,85148,1873],{},[895,85150,85151,85153,85155],{},[1826,85152,1837],{},[898,85154,5923],{"mathvariant":1943},[1826,85156,3472],{},[2597,85158,85159,85161],{},[898,85160,1878],{},[895,85162,85163,85165,85167],{},[1826,85164,1828],{},[898,85166,5923],{"mathvariant":1943},[1826,85168,3472],{},[902,85170,85171],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,85173,85175],{"className":85174},[886],[888,85176,85177],{"xmlns":890},[892,85178,85179,85211],{},[895,85180,85181,85183,85185,85187,85199],{},[898,85182,1824],{},[1655,85184,1657],{},[1826,85186,4969],{},[2597,85188,85189,85191],{},[898,85190,1873],{},[895,85192,85193,85195,85197],{},[1826,85194,3472],{},[898,85196,5923],{"mathvariant":1943},[1826,85198,3524],{},[2597,85200,85201,85203],{},[898,85202,1878],{},[895,85204,85205,85207,85209],{},[1826,85206,1837],{},[898,85208,5923],{"mathvariant":1943},[1826,85210,3524],{},[902,85212,85213],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,85215,85216,84586,85219,85261,85262,1343,85280,85299,85300,85317],{},[38,85217,85218],{},"5.7",[883,85220,85222],{"className":85221},[886],[888,85223,85224],{"xmlns":890},[892,85225,85226,85258],{},[895,85227,85228,85230,85232,85234,85246],{},[898,85229,1824],{},[1655,85231,1657],{},[1826,85233,4136],{},[2597,85235,85236,85238],{},[898,85237,1873],{},[895,85239,85240,85242,85244],{},[1826,85241,1828],{},[898,85243,5923],{"mathvariant":1943},[1826,85245,1837],{},[2597,85247,85248,85250],{},[898,85249,1878],{},[895,85251,85252,85254,85256],{},[1826,85253,1828],{},[898,85255,5923],{"mathvariant":1943},[1826,85257,1837],{},[902,85259,85260],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,85263,85265],{"className":85264},[886],[888,85266,85267],{"xmlns":890},[892,85268,85269,85277],{},[895,85270,85271,85273,85275],{},[898,85272,1873],{},[1655,85274,1657],{},[1826,85276,21268],{},[902,85278,85279],{"encoding":904},"L = 400",[883,85281,85283],{"className":85282},[886],[888,85284,85285],{"xmlns":890},[892,85286,85287,85296],{},[895,85288,85289,85291,85293],{},[898,85290,1878],{},[1655,85292,1657],{},[1826,85294,85295],{},"17576",[902,85297,85298],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,85301,85303],{"className":85302},[886],[888,85304,85305],{"xmlns":890},[892,85306,85307,85315],{},[895,85308,85309,85311,85313],{},[898,85310,1873],{},[1655,85312,1671],{"separator":1670},[898,85314,1878],{},[902,85316,80111],{"encoding":904}," zdvojnásobí.",[724,85319,85320,85323,85324,85261,85355,1343,85373,70710,85391,85421,85422,85452,85453,3962,85466,85480,85481,3962,85494,85507],{},[38,85321,85322],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,85325,85327],{"className":85326},[886],[888,85328,85329],{"xmlns":890},[892,85330,85331,85352],{},[895,85332,85333,85335,85337,85340,85346],{},[898,85334,1824],{},[1655,85336,1657],{},[1826,85338,85339],{},"1,01",[2597,85341,85342,85344],{},[898,85343,1873],{},[1826,85345,24856],{},[2597,85347,85348,85350],{},[898,85349,1878],{},[1826,85351,24915],{},[902,85353,85354],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,85356,85358],{"className":85357},[886],[888,85359,85360],{"xmlns":890},[892,85361,85362,85370],{},[895,85363,85364,85366,85368],{},[898,85365,1873],{},[1655,85367,1657],{},[1826,85369,31869],{},[902,85371,85372],{"encoding":904},"L = 250",[883,85374,85376],{"className":85375},[886],[888,85377,85378],{"xmlns":890},[892,85379,85380,85388],{},[895,85381,85382,85384,85386],{},[898,85383,1878],{},[1655,85385,1657],{},[1826,85387,4057],{},[902,85389,85390],{"encoding":904},"K = 1000",[883,85392,85394],{"className":85393},[886],[888,85395,85396],{"xmlns":890},[892,85397,85398,85418],{},[895,85399,85400,85402,85408,85410,85412,85414,85416],{},[898,85401,2127],{},[1820,85403,85404,85406],{},[898,85405,2132],{},[898,85407,1873],{},[1655,85409,1664],{"stretchy":1663},[1826,85411,31869],{},[1655,85413,1671],{"separator":1670},[1826,85415,4057],{},[1655,85417,1677],{"stretchy":1663},[902,85419,85420],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,85423,85425],{"className":85424},[886],[888,85426,85427],{"xmlns":890},[892,85428,85429,85449],{},[895,85430,85431,85433,85439,85441,85443,85445,85447],{},[898,85432,2127],{},[1820,85434,85435,85437],{},[898,85436,2132],{},[898,85438,1878],{},[1655,85440,1664],{"stretchy":1663},[1826,85442,31869],{},[1655,85444,1671],{"separator":1670},[1826,85446,4057],{},[1655,85448,1677],{"stretchy":1663},[902,85450,85451],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,85454,85456],{"className":85455},[886],[888,85457,85458],{"xmlns":890},[892,85459,85460,85464],{},[895,85461,85462],{},[898,85463,1873],{},[902,85465,1873],{"encoding":904},[883,85467,85469],{"className":85468},[886],[888,85470,85471],{"xmlns":890},[892,85472,85473,85478],{},[895,85474,85475],{},[1826,85476,85477],{},"260",[902,85479,85477],{"encoding":904}," a současném poklesu ",[883,85482,85484],{"className":85483},[886],[888,85485,85486],{"xmlns":890},[892,85487,85488,85492],{},[895,85489,85490],{},[898,85491,1878],{},[902,85493,1878],{"encoding":904},[883,85495,85497],{"className":85496},[886],[888,85498,85499],{"xmlns":890},[892,85500,85501,85505],{},[895,85502,85503],{},[1826,85504,16316],{},[902,85506,16316],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,85509,85510,85513,85514,1719],{},[38,85511,85512],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,85515,85517],{"className":85516},[886],[888,85518,85519],{"xmlns":890},[892,85520,85521,85541],{},[895,85522,85523,85525,85527,85529,85535],{},[898,85524,1824],{},[1655,85526,1657],{},[1826,85528,4136],{},[2597,85530,85531,85533],{},[898,85532,1873],{},[1826,85534,69337],{},[2597,85536,85537,85539],{},[898,85538,1878],{},[1826,85540,6258],{},[902,85542,85543],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,85545,85546,85549,85550,81707,85573,2494,85586,2115,85636,5171],{},[38,85547,85548],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,85551,85553],{"className":85552},[886],[888,85554,85555],{"xmlns":890},[892,85556,85557,85571],{},[895,85558,85559,85561,85563,85565,85567,85569],{},[898,85560,1824],{},[1655,85562,1664],{"stretchy":1663},[898,85564,1873],{},[1655,85566,1671],{"separator":1670},[898,85568,1878],{},[1655,85570,1677],{"stretchy":1663},[902,85572,2085],{"encoding":904},[883,85574,85576],{"className":85575},[886],[888,85577,85578],{"xmlns":890},[892,85579,85580,85584],{},[895,85581,85582],{},[898,85583,37986],{},[902,85585,37986],{"encoding":904},[883,85587,85589],{"className":85588},[886],[888,85590,85591],{"xmlns":890},[892,85592,85593,85633],{},[895,85594,85595,85597,85605,85607,85609,85617,85619,85621,85623,85625,85627,85629,85631],{},[898,85596,1873],{},[1935,85598,85599,85601,85603],{},[898,85600,1824],{},[898,85602,1873],{},[1655,85604,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,85606,2346],{},[898,85608,1878],{},[1935,85610,85611,85613,85615],{},[898,85612,1824],{},[898,85614,1878],{},[1655,85616,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,85618,1657],{},[898,85620,37986],{},[898,85622,1824],{},[1655,85624,1664],{"stretchy":1663},[898,85626,1873],{},[1655,85628,1671],{"separator":1670},[898,85630,1878],{},[1655,85632,1677],{"stretchy":1663},[902,85634,85635],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,85637,81682],{},[724,85639,85640,85643],{},[38,85641,85642],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,85645,85646,84586,85649,85689,85690,1343,85712,1343,85734,85756],{},[38,85647,85648],{},"5.12",[883,85650,85652],{"className":85651},[886],[888,85653,85654],{"xmlns":890},[892,85655,85656,85686],{},[895,85657,85658,85660,85662,85674],{},[898,85659,1824],{},[1655,85661,1657],{},[2597,85663,85664,85666],{},[898,85665,1873],{},[895,85667,85668,85670,85672],{},[1826,85669,1828],{},[898,85671,5923],{"mathvariant":1943},[1826,85673,3472],{},[2597,85675,85676,85678],{},[898,85677,1878],{},[895,85679,85680,85682,85684],{},[1826,85681,1828],{},[898,85683,5923],{"mathvariant":1943},[1826,85685,3639],{},[902,85687,85688],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,85691,85693],{"className":85692},[886],[888,85694,85695],{"xmlns":890},[892,85696,85697,85709],{},[895,85698,85699,85705,85707],{},[1820,85700,85701,85703],{},[898,85702,81923],{},[1826,85704,2552],{},[1655,85706,1657],{},[1826,85708,1828],{},[902,85710,85711],{"encoding":904},"q_0 = 1",[883,85713,85715],{"className":85714},[886],[888,85716,85717],{"xmlns":890},[892,85718,85719,85731],{},[895,85720,85721,85727,85729],{},[1820,85722,85723,85725],{},[898,85724,81923],{},[1826,85726,1828],{},[1655,85728,1657],{},[1826,85730,1837],{},[902,85732,85733],{"encoding":904},"q_1 = 2",[883,85735,85737],{"className":85736},[886],[888,85738,85739],{"xmlns":890},[892,85740,85741,85753],{},[895,85742,85743,85749,85751],{},[1820,85744,85745,85747],{},[898,85746,81923],{},[1826,85748,1837],{},[1655,85750,1657],{},[1826,85752,3472],{},[902,85754,85755],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,85758,85759,84586,85762,85802,85803,1343,85831,1343,85859,1343,85887,1343,85916,1343,85945,1343,85974,1343,86003,1343,86032,1719],{},[38,85760,85761],{},"5.13",[883,85763,85765],{"className":85764},[886],[888,85766,85767],{"xmlns":890},[892,85768,85769,85799],{},[895,85770,85771,85773,85775,85787],{},[898,85772,1824],{},[1655,85774,1657],{},[2597,85776,85777,85779],{},[898,85778,1873],{},[895,85780,85781,85783,85785],{},[1826,85782,1828],{},[898,85784,5923],{"mathvariant":1943},[1826,85786,3472],{},[2597,85788,85789,85791],{},[898,85790,1878],{},[895,85792,85793,85795,85797],{},[1826,85794,1828],{},[898,85796,5923],{"mathvariant":1943},[1826,85798,1837],{},[902,85800,85801],{"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): ",[883,85804,85806],{"className":85805},[886],[888,85807,85808],{"xmlns":890},[892,85809,85810,85828],{},[895,85811,85812,85818,85820,85822,85824,85826],{},[1820,85813,85814,85816],{},[898,85815,2731],{},[1826,85817,1828],{},[1655,85819,2734],{"stretchy":1663},[1826,85821,1828],{},[1655,85823,9672],{"separator":1670},[1826,85825,1828],{},[1655,85827,2743],{"stretchy":1663},[902,85829,85830],{"encoding":904},"A_1[1; 1]",[883,85832,85834],{"className":85833},[886],[888,85835,85836],{"xmlns":890},[892,85837,85838,85856],{},[895,85839,85840,85846,85848,85850,85852,85854],{},[1820,85841,85842,85844],{},[898,85843,2731],{},[1826,85845,1837],{},[1655,85847,2734],{"stretchy":1663},[1826,85849,1828],{},[1655,85851,9672],{"separator":1670},[1826,85853,6834],{},[1655,85855,2743],{"stretchy":1663},[902,85857,85858],{"encoding":904},"A_2[1; 8]",[883,85860,85862],{"className":85861},[886],[888,85863,85864],{"xmlns":890},[892,85865,85866,85884],{},[895,85867,85868,85874,85876,85878,85880,85882],{},[1820,85869,85870,85872],{},[898,85871,2731],{},[1826,85873,3472],{},[1655,85875,2734],{"stretchy":1663},[1826,85877,1828],{},[1655,85879,9672],{"separator":1670},[1826,85881,67723],{},[1655,85883,2743],{"stretchy":1663},[902,85885,85886],{"encoding":904},"A_3[1; 27]",[883,85888,85890],{"className":85889},[886],[888,85891,85892],{"xmlns":890},[892,85893,85894,85913],{},[895,85895,85896,85902,85904,85906,85908,85911],{},[1820,85897,85898,85900],{},[898,85899,2731],{},[1826,85901,3639],{},[1655,85903,2734],{"stretchy":1663},[1826,85905,1837],{},[1655,85907,9672],{"separator":1670},[1826,85909,85910],{},"0,353",[1655,85912,2743],{"stretchy":1663},[902,85914,85915],{"encoding":904},"A_4[2; 0{,}353]",[883,85917,85919],{"className":85918},[886],[888,85920,85921],{"xmlns":890},[892,85922,85923,85942],{},[895,85924,85925,85931,85933,85935,85937,85940],{},[1820,85926,85927,85929],{},[898,85928,2731],{},[1826,85930,3524],{},[1655,85932,2734],{"stretchy":1663},[1826,85934,1837],{},[1655,85936,9672],{"separator":1670},[1826,85938,85939],{},"2,828",[1655,85941,2743],{"stretchy":1663},[902,85943,85944],{"encoding":904},"A_5[2; 2{,}828]",[883,85946,85948],{"className":85947},[886],[888,85949,85950],{"xmlns":890},[892,85951,85952,85971],{},[895,85953,85954,85960,85962,85964,85966,85969],{},[1820,85955,85956,85958],{},[898,85957,2731],{},[1826,85959,3531],{},[1655,85961,2734],{"stretchy":1663},[1826,85963,1837],{},[1655,85965,9672],{"separator":1670},[1826,85967,85968],{},"9,545",[1655,85970,2743],{"stretchy":1663},[902,85972,85973],{"encoding":904},"A_6[2; 9{,}545]",[883,85975,85977],{"className":85976},[886],[888,85978,85979],{"xmlns":890},[892,85980,85981,86000],{},[895,85982,85983,85989,85991,85993,85995,85998],{},[1820,85984,85985,85987],{},[898,85986,2731],{},[1826,85988,25327],{},[1655,85990,2734],{"stretchy":1663},[1826,85992,65685],{},[1655,85994,9672],{"separator":1670},[1826,85996,85997],{},"0,544",[1655,85999,2743],{"stretchy":1663},[902,86001,86002],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,86004,86006],{"className":86005},[886],[888,86007,86008],{"xmlns":890},[892,86009,86010,86029],{},[895,86011,86012,86018,86020,86022,86024,86027],{},[1820,86013,86014,86016],{},[898,86015,2731],{},[1826,86017,6834],{},[1655,86019,2734],{"stretchy":1663},[1826,86021,65685],{},[1655,86023,9672],{"separator":1670},[1826,86025,86026],{},"14,696",[1655,86028,2743],{"stretchy":1663},[902,86030,86031],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,86033,86035],{"className":86034},[886],[888,86036,86037],{"xmlns":890},[892,86038,86039,86057],{},[895,86040,86041,86047,86049,86051,86053,86055],{},[1820,86042,86043,86045],{},[898,86044,2731],{},[1826,86046,5250],{},[1655,86048,2734],{"stretchy":1663},[1826,86050,1837],{},[1655,86052,9672],{"separator":1670},[1826,86054,3524],{},[1655,86056,2743],{"stretchy":1663},[902,86058,86059],{"encoding":904},"A_9[2; 5]",[724,86061,86062,86065],{},[38,86063,86064],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,86067,86068,86071,86072,86102,86103,86116,86117,86130,86131,70443,86150,86169,86170,1719],{},[38,86069,86070],{},"5.15"," Produkce firmy je dána vztahem ",[883,86073,86075],{"className":86074},[886],[888,86076,86077],{"xmlns":890},[892,86078,86079,86099],{},[895,86080,86081,86083,86085,86087,86093],{},[898,86082,1824],{},[1655,86084,1657],{},[1826,86086,1837],{},[2597,86088,86089,86091],{},[898,86090,1873],{},[1826,86092,6258],{},[2597,86094,86095,86097],{},[898,86096,1878],{},[1826,86098,24915],{},[902,86100,86101],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,86104,86106],{"className":86105},[886],[888,86107,86108],{"xmlns":890},[892,86109,86110,86114],{},[895,86111,86112],{},[1826,86113,4360],{},[902,86115,4360],{"encoding":904}," pracovníků a disponuje-li ",[883,86118,86120],{"className":86119},[886],[888,86121,86122],{"xmlns":890},[892,86123,86124,86128],{},[895,86125,86126],{},[1826,86127,65561],{},[902,86129,65561],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,86132,86134],{"className":86133},[886],[888,86135,86136],{"xmlns":890},[892,86137,86138,86148],{},[895,86139,86140,86142,86144,86146],{},[898,86141,2127],{},[898,86143,5245],{},[898,86145,4049],{},[898,86147,9920],{},[902,86149,2703],{"encoding":904},[883,86151,86153],{"className":86152},[886],[888,86154,86155],{"xmlns":890},[892,86156,86157,86167],{},[895,86158,86159,86161,86163,86165],{},[898,86160,2127],{},[898,86162,5245],{},[898,86164,4049],{},[898,86166,9920],{},[902,86168,2703],{"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 ",[883,86171,86173],{"className":86172},[886],[888,86174,86175],{"xmlns":890},[892,86176,86177,86182],{},[895,86178,86179],{},[1826,86180,86181],{},"95",[902,86183,86181],{"encoding":904},[724,86185,86186,84586,86189,72117,86221,86240,86241,86254,86255,86268,86269,86282],{},[38,86187,86188],{},"5.16",[883,86190,86192],{"className":86191},[886],[888,86193,86194],{"xmlns":890},[892,86195,86196,86218],{},[895,86197,86198,86200,86202,86208,86210,86212],{},[898,86199,1824],{},[1655,86201,1657],{},[2597,86203,86204,86206],{},[898,86205,1878],{},[1826,86207,1837],{},[1655,86209,2346],{},[1826,86211,1837],{},[2597,86213,86214,86216],{},[898,86215,1873],{},[1826,86217,1837],{},[902,86219,86220],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,86222,86224],{"className":86223},[886],[888,86225,86226],{"xmlns":890},[892,86227,86228,86238],{},[895,86229,86230,86232,86234,86236],{},[898,86231,2127],{},[898,86233,5245],{},[898,86235,4049],{},[898,86237,9920],{},[902,86239,2703],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,86242,86244],{"className":86243},[886],[888,86245,86246],{"xmlns":890},[892,86247,86248,86252],{},[895,86249,86250],{},[1826,86251,4390],{},[902,86253,4390],{"encoding":904}," pracovníky a ",[883,86256,86258],{"className":86257},[886],[888,86259,86260],{"xmlns":890},[892,86261,86262,86266],{},[895,86263,86264],{},[1826,86265,78743],{},[902,86267,78743],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,86270,86272],{"className":86271},[886],[888,86273,86274],{"xmlns":890},[892,86275,86276,86280],{},[895,86277,86278],{},[1826,86279,47829],{},[902,86281,47829],{"encoding":904}," jednotek.",[724,86284,86285,86288,86289,2494,86319,1719],{},[38,86286,86287],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,86290,86292],{"className":86291},[886],[888,86293,86294],{"xmlns":890},[892,86295,86296,86316],{},[895,86297,86298,86300,86302,86304,86310],{},[898,86299,1824],{},[1655,86301,1657],{},[898,86303,2731],{},[2597,86305,86306,86308],{},[898,86307,1873],{},[898,86309,207],{},[2597,86311,86312,86314],{},[898,86313,1878],{},[898,86315,2025],{},[902,86317,86318],{"encoding":904},"Q = A L^{a} K^{b}",[883,86320,86322],{"className":86321},[886],[888,86323,86324],{"xmlns":890},[892,86325,86326,86356],{},[895,86327,86328,86330,86332,86334,86336,86338,86346,86348],{},[898,86329,2127],{},[898,86331,5245],{},[898,86333,4049],{},[898,86335,9920],{},[1655,86337,1657],{},[3615,86339,86340],{"scriptlevel":2552,"displaystyle":1663},[1949,86341,86342,86344],{},[898,86343,207],{},[898,86345,2025],{},[1655,86347,2869],{},[3615,86349,86350],{"scriptlevel":2552,"displaystyle":1663},[1949,86351,86352,86354],{},[898,86353,1878],{},[898,86355,1873],{},[902,86357,86358],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,86360,16845],{"id":16844},[120,86362,86363,86396,86423,86432,86482,86513,86566,86589,86644,86717,86795,86838,86870,86903,86944,87016,87077,87143,87160,87233,87299,87351,87407,87441,87484],{},[123,86364,86365,86368,86369,38022,86382,86395],{},[38,86366,86367],{},"Faktory (vstupy) produkce:"," práce ",[883,86370,86372],{"className":86371},[886],[888,86373,86374],{"xmlns":890},[892,86375,86376,86380],{},[895,86377,86378],{},[898,86379,1873],{},[902,86381,1873],{"encoding":904},[883,86383,86385],{"className":86384},[886],[888,86386,86387],{"xmlns":890},[892,86388,86389,86393],{},[895,86390,86391],{},[898,86392,1878],{},[902,86394,1878],{"encoding":904},", půda.",[123,86397,86398,8262,86400,1719],{},[38,86399,41577],{},[883,86401,86403],{"className":86402},[886],[888,86404,86405],{"xmlns":890},[892,86406,86407,86421],{},[895,86408,86409,86411,86413,86415,86417,86419],{},[898,86410,1824],{},[1655,86412,1657],{},[898,86414,1824],{},[1655,86416,1664],{"stretchy":1663},[898,86418,1873],{},[1655,86420,1677],{"stretchy":1663},[902,86422,75670],{"encoding":904},[123,86424,86425,2115,86427,13253,86430,1719],{},[38,86426,859],{},[614,86428,86429],{},"production function",[38,86431,76173],{},[123,86433,86434,3106,86436,1719],{},[38,86435,76219],{},[883,86437,86439],{"className":86438},[886],[888,86440,86441],{"xmlns":890},[892,86442,86443,86479],{},[895,86444,86445,86447,86453,86455,86457,86459,86461,86463,86465,86467,86473,86475,86477],{},[898,86446,2127],{},[1820,86448,86449,86451],{},[898,86450,2132],{},[898,86452,1873],{},[1655,86454,1657],{},[898,86456,2410],{},[898,86458,1824],{},[898,86460,5923],{"mathvariant":1943},[898,86462,2410],{},[898,86464,1873],{},[1655,86466,1657],{},[2597,86468,86469,86471],{},[898,86470,1824],{},[1655,86472,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,86474,1664],{"stretchy":1663},[898,86476,1873],{},[1655,86478,1677],{"stretchy":1663},[902,86480,86481],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,86483,86484,3106,86486,1719],{},[38,86485,77154],{},[883,86487,86489],{"className":86488},[886],[888,86490,86491],{"xmlns":890},[892,86492,86493,86511],{},[895,86494,86495,86497,86503,86505,86507,86509],{},[898,86496,2731],{},[1820,86498,86499,86501],{},[898,86500,2132],{},[898,86502,1873],{},[1655,86504,1657],{},[898,86506,1824],{},[898,86508,5923],{"mathvariant":1943},[898,86510,1873],{},[902,86512,75738],{"encoding":904},[123,86514,86515,86517,86518,2494,86535,1719],{},[38,86516,76641],{}," — od určitého ",[883,86519,86521],{"className":86520},[886],[888,86522,86523],{"xmlns":890},[892,86524,86525,86533],{},[895,86526,86527],{},[1820,86528,86529,86531],{},[898,86530,1873],{},[1826,86532,2552],{},[902,86534,76684],{"encoding":904},[883,86536,86538],{"className":86537},[886],[888,86539,86540],{"xmlns":890},[892,86541,86542,86564],{},[895,86543,86544,86554,86556,86558,86560,86562],{},[2597,86545,86546,86548],{},[898,86547,1824],{},[895,86549,86550,86552],{},[1655,86551,1945],{"mathvariant":1943},[1655,86553,1945],{"mathvariant":1943},[1655,86555,1664],{"stretchy":1663},[898,86557,1873],{},[1655,86559,1677],{"stretchy":1663},[1655,86561,3065],{},[1826,86563,2552],{},[902,86565,76830],{"encoding":904},[123,86567,86568,3106,86571,86588],{},[38,86569,86570],{},"Inflexní bod",[883,86572,86574],{"className":86573},[886],[888,86575,86576],{"xmlns":890},[892,86577,86578,86586],{},[895,86579,86580],{},[1820,86581,86582,86584],{},[898,86583,1873],{},[1826,86585,2552],{},[902,86587,76684],{"encoding":904}," — přechod z konvexity do konkavity.",[123,86590,86591,3106,86594,8262,86611,1719],{},[38,86592,86593],{},"Bod maxima produkce",[883,86595,86597],{"className":86596},[886],[888,86598,86599],{"xmlns":890},[892,86600,86601,86609],{},[895,86602,86603],{},[1820,86604,86605,86607],{},[898,86606,1873],{},[1826,86608,1828],{},[902,86610,14337],{"encoding":904},[883,86612,86614],{"className":86613},[886],[888,86615,86616],{"xmlns":890},[892,86617,86618,86642],{},[895,86619,86620,86622,86628,86630,86636,86638,86640],{},[898,86621,2127],{},[1820,86623,86624,86626],{},[898,86625,2132],{},[898,86627,1873],{},[1655,86629,1664],{"stretchy":1663},[1820,86631,86632,86634],{},[898,86633,1873],{},[1826,86635,1828],{},[1655,86637,1677],{"stretchy":1663},[1655,86639,1657],{},[1826,86641,2552],{},[902,86643,76903],{"encoding":904},[123,86645,86646,86668,86669,2494,86688,1719],{},[38,86647,86648,86649],{},"Princip maximalizace ",[883,86650,86652],{"className":86651},[886],[888,86653,86654],{"xmlns":890},[892,86655,86656,86666],{},[895,86657,86658,86660],{},[898,86659,2731],{},[1820,86661,86662,86664],{},[898,86663,2132],{},[898,86665,1873],{},[902,86667,75759],{"encoding":904}," — v bodě maxima ",[883,86670,86672],{"className":86671},[886],[888,86673,86674],{"xmlns":890},[892,86675,86676,86686],{},[895,86677,86678,86680],{},[898,86679,2731],{},[1820,86681,86682,86684],{},[898,86683,2132],{},[898,86685,1873],{},[902,86687,75759],{"encoding":904},[883,86689,86691],{"className":86690},[886],[888,86692,86693],{"xmlns":890},[892,86694,86695,86715],{},[895,86696,86697,86699,86705,86707,86709],{},[898,86698,2127],{},[1820,86700,86701,86703],{},[898,86702,2132],{},[898,86704,1873],{},[1655,86706,1657],{},[898,86708,2731],{},[1820,86710,86711,86713],{},[898,86712,2132],{},[898,86714,1873],{},[902,86716,75789],{"encoding":904},[123,86718,86719,3106,86722,1343,86761,1343,86778,1719],{},[38,86720,86721],{},"Polynomiální produkční funkce",[883,86723,86725],{"className":86724},[886],[888,86726,86727],{"xmlns":890},[892,86728,86729,86759],{},[895,86730,86731,86733,86735,86737,86739,86741,86743,86749,86751,86753],{},[898,86732,1824],{},[1655,86734,1664],{"stretchy":1663},[898,86736,1873],{},[1655,86738,1677],{"stretchy":1663},[1655,86740,1657],{},[898,86742,207],{},[2597,86744,86745,86747],{},[898,86746,1873],{},[1826,86748,3472],{},[1655,86750,2346],{},[898,86752,2025],{},[2597,86754,86755,86757],{},[898,86756,1873],{},[1826,86758,1837],{},[902,86760,77021],{"encoding":904},[883,86762,86764],{"className":86763},[886],[888,86765,86766],{"xmlns":890},[892,86767,86768,86776],{},[895,86769,86770,86772,86774],{},[898,86771,207],{},[1655,86773,3065],{},[1826,86775,2552],{},[902,86777,44211],{"encoding":904},[883,86779,86781],{"className":86780},[886],[888,86782,86783],{"xmlns":890},[892,86784,86785,86793],{},[895,86786,86787,86789,86791],{},[898,86788,2025],{},[1655,86790,2969],{},[1826,86792,2552],{},[902,86794,19940],{"encoding":904},[123,86796,86797,3106,86800,1719],{},[38,86798,86799],{},"Diferenciál produkce",[883,86801,86803],{"className":86802},[886],[888,86804,86805],{"xmlns":890},[892,86806,86807,86835],{},[895,86808,86809,86811,86813,86815,86817,86819,86821,86823,86829,86831,86833],{},[898,86810,2506],{"mathvariant":1943},[898,86812,1824],{},[1655,86814,2357],{},[898,86816,2410],{},[898,86818,1824],{},[1655,86820,1657],{},[898,86822,2127],{},[1820,86824,86825,86827],{},[898,86826,2132],{},[898,86828,1873],{},[2031,86830,2435],{},[898,86832,2410],{},[898,86834,1873],{},[902,86836,86837],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,86839,86840,8262,86842,1719],{},[38,86841,85097],{},[883,86843,86845],{"className":86844},[886],[888,86846,86847],{"xmlns":890},[892,86848,86849,86867],{},[895,86850,86851,86853,86855,86857,86859,86861,86863,86865],{},[898,86852,1824],{},[1655,86854,1657],{},[898,86856,1824],{},[1655,86858,1664],{"stretchy":1663},[898,86860,1873],{},[1655,86862,1671],{"separator":1670},[898,86864,1878],{},[1655,86866,1677],{"stretchy":1663},[902,86868,86869],{"encoding":904},"Q = Q(L, K)",[123,86871,86872,8262,86874,1719],{},[38,86873,79191],{},[883,86875,86877],{"className":86876},[886],[888,86878,86879],{"xmlns":890},[892,86880,86881,86901],{},[895,86882,86883,86885,86887,86889,86895],{},[898,86884,1824],{},[1655,86886,1657],{},[898,86888,2731],{},[2597,86890,86891,86893],{},[898,86892,1873],{},[898,86894,207],{},[2597,86896,86897,86899],{},[898,86898,1878],{},[898,86900,2025],{},[902,86902,75856],{"encoding":904},[123,86904,86905,8262,86908,86943],{},[38,86906,86907],{},"Ryzí Cobb-Douglas",[883,86909,86911],{"className":86910},[886],[888,86912,86913],{"xmlns":890},[892,86914,86915,86941],{},[895,86916,86917,86919,86921,86923,86929],{},[898,86918,1824],{},[1655,86920,1657],{},[898,86922,2731],{},[2597,86924,86925,86927],{},[898,86926,1873],{},[898,86928,207],{},[2597,86930,86931,86933],{},[898,86932,1878],{},[895,86934,86935,86937,86939],{},[1826,86936,1828],{},[1655,86938,2623],{},[898,86940,207],{},[902,86942,80018],{"encoding":904}," (konstantní výnosy).",[123,86945,86946,8262,86948,1719],{},[38,86947,80734],{},[883,86949,86951],{"className":86950},[886],[888,86952,86953],{"xmlns":890},[892,86954,86955,87013],{},[895,86956,86957,86959,86961,86963,86965,86967,86969,86971,86973,86975,86985,86987,86989,86999],{},[898,86958,1824],{},[1655,86960,1657],{},[898,86962,2731],{},[1655,86964,2734],{"stretchy":1663},[1655,86966,1664],{"stretchy":1663},[1826,86968,1828],{},[1655,86970,2623],{},[898,86972,207],{},[1655,86974,1677],{"stretchy":1663},[2597,86976,86977,86979],{},[898,86978,1873],{},[895,86980,86981,86983],{},[1655,86982,2623],{},[898,86984,2025],{},[1655,86986,2346],{},[898,86988,207],{},[2597,86990,86991,86993],{},[898,86992,1878],{},[895,86994,86995,86997],{},[1655,86996,2623],{},[898,86998,2025],{},[2597,87000,87001,87003],{},[1655,87002,2743],{"stretchy":1663},[895,87004,87005,87007,87009,87011],{},[1655,87006,2623],{},[1826,87008,1828],{},[898,87010,5923],{"mathvariant":1943},[898,87012,2025],{},[902,87014,87015],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,87017,87018,2115,87021,13253,87043,2115,87046,87076],{},[38,87019,87020],{},"Lineární",[883,87022,87024],{"className":87023},[886],[888,87025,87026],{"xmlns":890},[892,87027,87028,87040],{},[895,87029,87030,87032,87034,87036,87038],{},[898,87031,207],{},[898,87033,1873],{},[1655,87035,2346],{},[898,87037,2025],{},[898,87039,1878],{},[902,87041,87042],{"encoding":904},"aL + bK",[38,87044,87045],{},"Leontiefova",[883,87047,87049],{"className":87048},[886],[888,87050,87051],{"xmlns":890},[892,87052,87053,87073],{},[895,87054,87055,87057,87059,87061,87063,87065,87067,87069,87071],{},[898,87056,80962],{},[1655,87058,57326],{},[1655,87060,1664],{"stretchy":1663},[898,87062,207],{},[898,87064,1873],{},[1655,87066,1671],{"separator":1670},[898,87068,2025],{},[898,87070,1878],{},[1655,87072,1677],{"stretchy":1663},[902,87074,87075],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,87078,87079,8262,87095,1719],{},[38,87080,87081,87082],{},"Homogenita stupně ",[883,87083,87085],{"className":87084},[886],[888,87086,87087],{"xmlns":890},[892,87088,87089,87093],{},[895,87090,87091],{},[898,87092,37986],{},[902,87094,37986],{"encoding":904},[883,87096,87098],{"className":87097},[886],[888,87099,87100],{"xmlns":890},[892,87101,87102,87140],{},[895,87103,87104,87106,87108,87110,87112,87114,87116,87118,87120,87122,87128,87130,87132,87134,87136,87138],{},[898,87105,1824],{},[1655,87107,1664],{"stretchy":1663},[898,87109,13166],{},[898,87111,1873],{},[1655,87113,1671],{"separator":1670},[898,87115,13166],{},[898,87117,1878],{},[1655,87119,1677],{"stretchy":1663},[1655,87121,1657],{},[2597,87123,87124,87126],{},[898,87125,13166],{},[898,87127,37986],{},[898,87129,1824],{},[1655,87131,1664],{"stretchy":1663},[898,87133,1873],{},[1655,87135,1671],{"separator":1670},[898,87137,1878],{},[1655,87139,1677],{"stretchy":1663},[902,87141,87142],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,87144,87145,80116],{},[38,87146,80049,87147],{},[883,87148,87150],{"className":87149},[886],[888,87151,87152],{"xmlns":890},[892,87153,87154,87158],{},[895,87155,87156],{},[898,87157,2731],{},[902,87159,2731],{"encoding":904},[123,87161,87162,87164,87165,87187,87188,87210,87211,5171],{},[38,87163,79550],{}," — konstantní (",[883,87166,87168],{"className":87167},[886],[888,87169,87170],{"xmlns":890},[892,87171,87172,87184],{},[895,87173,87174,87176,87178,87180,87182],{},[898,87175,207],{},[1655,87177,2346],{},[898,87179,2025],{},[1655,87181,1657],{},[1826,87183,1828],{},[902,87185,87186],{"encoding":904},"a+b=1","), rostoucí (",[883,87189,87191],{"className":87190},[886],[888,87192,87193],{"xmlns":890},[892,87194,87195,87207],{},[895,87196,87197,87199,87201,87203,87205],{},[898,87198,207],{},[1655,87200,2346],{},[898,87202,2025],{},[1655,87204,2969],{},[1826,87206,1828],{},[902,87208,87209],{"encoding":904},"a+b>1","), klesající (",[883,87212,87214],{"className":87213},[886],[888,87215,87216],{"xmlns":890},[892,87217,87218,87230],{},[895,87219,87220,87222,87224,87226,87228],{},[898,87221,207],{},[1655,87223,2346],{},[898,87225,2025],{},[1655,87227,3065],{},[1826,87229,1828],{},[902,87231,87232],{"encoding":904},"a+b\u003C1",[123,87234,87235,3106,87237,1343,87267,3106,87269,1719],{},[38,87236,76219],{},[883,87238,87240],{"className":87239},[886],[888,87241,87242],{"xmlns":890},[892,87243,87244,87264],{},[895,87245,87246,87248,87254,87256],{},[898,87247,2127],{},[1820,87249,87250,87252],{},[898,87251,2132],{},[898,87253,1873],{},[1655,87255,1657],{},[1935,87257,87258,87260,87262],{},[898,87259,1824],{},[898,87261,1873],{},[1655,87263,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,87265,87266],{"encoding":904},"MP_L = Q'_L",[38,87268,79123],{},[883,87270,87272],{"className":87271},[886],[888,87273,87274],{"xmlns":890},[892,87275,87276,87296],{},[895,87277,87278,87280,87286,87288],{},[898,87279,2127],{},[1820,87281,87282,87284],{},[898,87283,2132],{},[898,87285,1878],{},[1655,87287,1657],{},[1935,87289,87290,87292,87294],{},[898,87291,1824],{},[898,87293,1878],{},[1655,87295,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,87297,87298],{"encoding":904},"MP_K = Q'_K",[123,87300,87301,3106,87303,1719],{},[38,87302,81337],{},[883,87304,87306],{"className":87305},[886],[888,87307,87308],{"xmlns":890},[892,87309,87310,87348],{},[895,87311,87312,87314,87316,87318,87320,87326,87328,87330,87332,87334,87336,87342,87344,87346],{},[898,87313,2410],{},[898,87315,1824],{},[1655,87317,1657],{},[898,87319,2127],{},[1820,87321,87322,87324],{},[898,87323,2132],{},[898,87325,1873],{},[2031,87327,2435],{},[898,87329,2410],{},[898,87331,1873],{},[1655,87333,2346],{},[898,87335,2127],{},[1820,87337,87338,87340],{},[898,87339,2132],{},[898,87341,1878],{},[2031,87343,2435],{},[898,87345,2410],{},[898,87347,1878],{},[902,87349,87350],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,87352,87353,8262,87355,1719],{},[38,87354,81682],{},[883,87356,87358],{"className":87357},[886],[888,87359,87360],{"xmlns":890},[892,87361,87362,87404],{},[895,87363,87364,87366,87374,87376,87378,87386,87388,87390,87392,87394,87396,87398,87400,87402],{},[898,87365,1873],{},[1935,87367,87368,87370,87372],{},[898,87369,1824],{},[898,87371,1873],{},[1655,87373,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,87375,2346],{},[898,87377,1878],{},[1935,87379,87380,87382,87384],{},[898,87381,1824],{},[898,87383,1878],{},[1655,87385,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,87387,1657],{},[898,87389,37986],{},[2031,87391,2435],{},[898,87393,1824],{},[1655,87395,1664],{"stretchy":1663},[898,87397,1873],{},[1655,87399,1671],{"separator":1670},[898,87401,1878],{},[1655,87403,1677],{"stretchy":1663},[902,87405,87406],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,87408,87409,87412,87413,1719],{},[38,87410,87411],{},"Izokvanta"," — křivka ",[883,87414,87416],{"className":87415},[886],[888,87417,87418],{"xmlns":890},[892,87419,87420,87438],{},[895,87421,87422,87424,87426,87428,87430,87432,87434,87436],{},[898,87423,1824],{},[1655,87425,1664],{"stretchy":1663},[898,87427,1873],{},[1655,87429,1671],{"separator":1670},[898,87431,1878],{},[1655,87433,1677],{"stretchy":1663},[1655,87435,1657],{},[898,87437,81923],{},[902,87439,87440],{"encoding":904},"Q(L, K) = q",[123,87442,87443,3106,87445,1719],{},[38,87444,82112],{},[883,87446,87448],{"className":87447},[886],[888,87449,87450],{"xmlns":890},[892,87451,87452,87482],{},[895,87453,87454,87456,87458,87460,87462,87464,87466,87472,87474,87476],{},[898,87455,2127],{},[898,87457,5245],{},[898,87459,4049],{},[898,87461,9920],{},[1655,87463,1657],{},[898,87465,2127],{},[1820,87467,87468,87470],{},[898,87469,2132],{},[898,87471,1873],{},[898,87473,5923],{"mathvariant":1943},[898,87475,2127],{},[1820,87477,87478,87480],{},[898,87479,2132],{},[898,87481,1878],{},[902,87483,75931],{"encoding":904},[123,87485,87486,3106,87489,1719],{},[38,87487,87488],{},"Substituční vztah",[883,87490,87492],{"className":87491},[886],[888,87493,87494],{"xmlns":890},[892,87495,87496,87520],{},[895,87497,87498,87500,87502,87504,87506,87508,87510,87512,87514,87516,87518],{},[898,87499,2506],{"mathvariant":1943},[898,87501,1878],{},[1655,87503,2357],{},[1655,87505,2623],{},[898,87507,2127],{},[898,87509,5245],{},[898,87511,4049],{},[898,87513,9920],{},[2031,87515,2435],{},[898,87517,2410],{},[898,87519,1873],{},[902,87521,87522],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,87524,3187],{"id":3186},[120,87526,87527,87624,87631,87638],{},[123,87528,87529,3106,87531,87534,87535,1343,87538,87541,87542,87545,87546,87565,87566,19774,87585,87588,87589,87608,87609,5171],{},[38,87530,51849],{},[207,87532,784],{"className":87533,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,87536,3645],{"className":87537,"dataFsResolvedFilePath":764,"href":765},[210],[207,87539,793],{"className":87540,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,87543,880],{"className":87544,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,87547,87549],{"className":87548},[886],[888,87550,87551],{"xmlns":890},[892,87552,87553,87563],{},[895,87554,87555,87557,87559,87561],{},[898,87556,2127],{},[898,87558,5245],{},[898,87560,4049],{},[898,87562,9920],{},[902,87564,2703],{"encoding":904}," ↔ ",[883,87567,87569],{"className":87568},[886],[888,87570,87571],{"xmlns":890},[892,87572,87573,87583],{},[895,87574,87575,87577,87579,87581],{},[898,87576,2127],{},[898,87578,5245],{},[898,87580,4052],{},[898,87582,9920],{},[902,87584,2708],{"encoding":904},[207,87586,5078],{"className":87587,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,87590,87592],{"className":87591},[886],[888,87593,87594],{"xmlns":890},[892,87595,87596,87606],{},[895,87597,87598,87600],{},[898,87599,2731],{},[1820,87601,87602,87604],{},[898,87603,2132],{},[898,87605,1873],{},[902,87607,75759],{"encoding":904}," ↔ min ",[883,87610,87612],{"className":87611},[886],[888,87613,87614],{"xmlns":890},[892,87615,87616,87622],{},[895,87617,87618,87620],{},[898,87619,2731],{},[898,87621,4052],{},[902,87623,56686],{"encoding":904},[123,87625,87626,3106,87628,1719],{},[38,87627,3194],{},[207,87629,3223],{"className":87630,"dataFsResolvedFilePath":848,"href":849},[210],[123,87632,87633,3106,87635,1719],{},[38,87634,17338],{},[207,87636,1094],{"className":87637,"dataFsResolvedFilePath":838,"href":839},[210],[123,87639,87640,3106,87642,1719],{},[38,87641,17329],{},[207,87643,17333],{"className":87644,"dataFsResolvedFilePath":3274,"href":3275},[210],{"title":641,"searchDepth":642,"depth":642,"links":87646},[87647,87648,87649,87653,87655,87660,87661,87668,87669,87671,87672,87673,87675,87680,87681,87682,87686,87687],{"id":75954,"depth":642,"text":75955},{"id":76091,"depth":642,"text":76092},{"id":76194,"depth":642,"text":87650,"children":87651},"Mezní produkt práce (MPLMP_L)",[87652],{"id":76640,"depth":649,"text":76641},{"id":77129,"depth":642,"text":87654},"Průměrný produkt práce (APLAP_L)",{"id":77247,"depth":642,"text":77248,"children":87656},[87657,87658,87659],{"id":77484,"depth":649,"text":66627},{"id":77795,"depth":649,"text":77796},{"id":78515,"depth":649,"text":78516},{"id":79087,"depth":642,"text":79088},{"id":79190,"depth":642,"text":79191,"children":87662},[87663,87664,87666,87667],{"id":79549,"depth":649,"text":79550},{"id":80048,"depth":649,"text":87665},"Parametr efektivity AA",{"id":80119,"depth":649,"text":80120},{"id":38305,"depth":649,"text":80459},{"id":80646,"depth":642,"text":80647},{"id":80985,"depth":642,"text":87670},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":81676,"depth":642,"text":81677},{"id":76020,"depth":642,"text":1856},{"id":82087,"depth":642,"text":87674},"Mezní míra technické substituce (MRTSMRTS)",{"id":82953,"depth":642,"text":82954,"children":87676},[87677,87678,87679],{"id":82957,"depth":649,"text":82958},{"id":83600,"depth":649,"text":83601},{"id":83881,"depth":649,"text":83882},{"id":84227,"depth":642,"text":84228},{"id":51007,"depth":642,"text":51008},{"id":84577,"depth":642,"text":84578,"children":87683},[87684,87685],{"id":41576,"depth":649,"text":41577},{"id":85096,"depth":649,"text":85097},{"id":16844,"depth":642,"text":16845},{"id":3186,"depth":642,"text":3187},{},"\u002Ftopics\u002Fprodukce",{"title":75590,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,1891,87694,87695,87696,76020,87697,87698],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":87701,"title":87702,"body":87703,"course":1128,"courses":659,"created":10802,"description":641,"extension":661,"meta":96650,"navigation":664,"path":96651,"seo":96652,"sources":96653,"stem":96654,"tags":96655,"type":3252,"updated":677,"__hash__":96658},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":87704,"toc":96624},[87705,87708,87710,87907,87916,87920,87923,87976,87980,87992,87996,87999,88016,88139,88145,88289,88299,88303,88338,88376,88424,88481,88541,88583,89159,89163,89246,89355,89448,89706,89709,89762,89873,89955,89959,89970,90203,90258,90264,90304,90367,90378,90569,90675,90828,90876,90881,90995,91033,91159,91205,91232,91309,91384,91464,91594,91655,91743,91747,91750,91819,91902,91909,91969,92279,92283,92289,92342,92358,92409,92547,92623,92736,93053,93057,93064,93224,93283,93287,93309,93406,93527,93641,93664,93727,93784,94036,94044,94048,94055,94309,94359,94415,94418,94582,94586,94684,94686,94718,94722,94855,95097,95281,95449,95756,95889,96076,96088,96090,96525,96527],[12,87706,87702],{"id":87707},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,87709,13131],{"id":13130},[724,87711,87712,3106,87714,87745,87746,87749,87750,87780,87781,87799,87800,87840,87841,87844,87845,87858,87859,29379,87862,87875,87876,87889,87890,87903,87904,1719],{},[38,87713,880],{},[883,87715,87717],{"className":87716},[886],[888,87718,87719],{"xmlns":890},[892,87720,87721,87743],{},[895,87722,87723,87725,87727,87733,87735,87741],{},[898,87724,900],{},[1655,87726,1664],{"stretchy":1663},[1820,87728,87729,87731],{},[898,87730,1824],{},[1826,87732,1828],{},[1655,87734,1671],{"separator":1670},[1820,87736,87737,87739],{},[898,87738,1824],{},[1826,87740,1837],{},[1655,87742,1677],{"stretchy":1663},[902,87744,17469],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,87747,87748],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,87751,87753],{"className":87752},[886],[888,87754,87755],{"xmlns":890},[892,87756,87757,87777],{},[895,87758,87759,87761,87767,87769],{},[898,87760,2127],{},[1820,87762,87763,87765],{},[898,87764,900],{},[898,87766,18916],{},[1655,87768,1657],{},[1935,87770,87771,87773,87775],{},[898,87772,900],{},[898,87774,18916],{},[1655,87776,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,87778,87779],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,87782,87784],{"className":87783},[886],[888,87785,87786],{"xmlns":890},[892,87787,87788,87796],{},[895,87789,87790,87792,87794],{},[898,87791,900],{},[1655,87793,1657],{},[898,87795,1789],{},[902,87797,87798],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,87801,87803],{"className":87802},[886],[888,87804,87805],{"xmlns":890},[892,87806,87807,87837],{},[895,87808,87809,87811,87813,87815,87817,87819,87821,87827,87829,87831],{},[898,87810,2127],{},[898,87812,5245],{},[898,87814,4052],{},[898,87816,9920],{},[1655,87818,1657],{},[898,87820,2127],{},[1820,87822,87823,87825],{},[898,87824,900],{},[1826,87826,1828],{},[898,87828,5923],{"mathvariant":1943},[898,87830,2127],{},[1820,87832,87833,87835],{},[898,87834,900],{},[1826,87836,1837],{},[902,87838,87839],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,87842,87843],{},"teorii užitečnosti"," — funkce ",[883,87846,87848],{"className":87847},[886],[888,87849,87850],{"xmlns":890},[892,87851,87852,87856],{},[895,87853,87854],{},[898,87855,900],{},[902,87857,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,87860,87861],{},"Optimalizaci spotřebitele",[883,87863,87865],{"className":87864},[886],[888,87866,87867],{"xmlns":890},[892,87868,87869,87873],{},[895,87870,87871],{},[898,87872,900],{},[902,87874,900],{"encoding":904}," při rozpočtu, min ",[883,87877,87879],{"className":87878},[886],[888,87880,87881],{"xmlns":890},[892,87882,87883,87887],{},[895,87884,87885],{},[898,87886,5502],{},[902,87888,5502],{"encoding":904}," při dané ",[883,87891,87893],{"className":87892},[886],[888,87894,87895],{"xmlns":890},[892,87896,87897,87901],{},[895,87898,87899],{},[898,87900,900],{},[902,87902,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,87905,913],{"className":87906,"dataFsResolvedFilePath":911,"href":912},[210],[724,87908,87909,87910,87912,87913,1719],{},"Kapitola 6 knihy ",[614,87911,17333],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,87914,37880],{"className":87915,"dataFsResolvedFilePath":911,"href":912},[210],[115,87917,87919],{"id":87918},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,87921,87922],{},"Po prostudování této kapitoly byste měli umět:",[120,87924,87925,87931,87940,87945,87948,87954,87960,87963,87969],{},[123,87926,87927,87928,1671],{},"vyložit, co se rozumí termínem ",[38,87929,87930],{},"užitečnost",[123,87932,87933,87934,2704,87937,1671],{},"definovat pojmy ",[38,87935,87936],{},"svazek zboží",[38,87938,87939],{},"funkce užitečnosti",[123,87941,75969,87942,75976],{},[38,87943,87944],{},"mezní užitečnosti",[123,87946,87947],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,87949,75996,87950,87953],{},[38,87951,87952],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,87955,76017,87956,87959],{},[38,87957,87958],{},"křivky užitečnosti"," (indiferenční křivky),",[123,87961,87962],{},"vyjmenovat jejich základní vlastnosti,",[123,87964,75969,87965,87968],{},[38,87966,87967],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,87970,87971,87972,87975],{},"řešit ",[38,87973,87974],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,87977,87979],{"id":87978},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,87981,87982,87983,87987,87988,87991],{},"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 ",[207,87984,87986],{"className":87985,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,87989,87990],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,87993,87995],{"id":87994},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,87997,87998],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,88000,88001,88007],{},[123,88002,88003,88006],{},[38,88004,88005],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,88008,88009,88012,88013,88015],{},[38,88010,88011],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,88014,87748],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[5120,88017,88018],{},[724,88019,88020,88022,88023,88026,88027,3106,88040,88043,88044,2704,88057,88076,88077,1343,88103,88130,88131,88134,88135,88138],{},[883,88021,5661],{}," Pozor — ordinalisté užitečnost ",[38,88024,88025],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,88028,88030],{"className":88029},[886],[888,88031,88032],{"xmlns":890},[892,88033,88034,88038],{},[895,88035,88036],{},[898,88037,900],{},[902,88039,900],{"encoding":904},[38,88041,88042],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,88045,88047],{"className":88046},[886],[888,88048,88049],{"xmlns":890},[892,88050,88051,88055],{},[895,88052,88053],{},[898,88054,900],{},[902,88056,900],{"encoding":904},[883,88058,88060],{"className":88059},[886],[888,88061,88062],{"xmlns":890},[892,88063,88064,88073],{},[895,88065,88066],{},[9633,88067,88068,88070],{"accent":1670},[898,88069,900],{},[1655,88071,88072],{},"~",[902,88074,88075],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,88078,88080],{"className":88079},[886],[888,88081,88082],{"xmlns":890},[892,88083,88084,88100],{},[895,88085,88086,88092,88094],{},[9633,88087,88088,88090],{"accent":1670},[898,88089,900],{},[1655,88091,88072],{},[1655,88093,1657],{},[2597,88095,88096,88098],{},[898,88097,900],{},[1826,88099,1837],{},[902,88101,88102],{"encoding":904},"\\tilde U = U^2",[883,88104,88106],{"className":88105},[886],[888,88107,88108],{"xmlns":890},[892,88109,88110,88127],{},[895,88111,88112,88118,88120,88123,88125],{},[9633,88113,88114,88116],{"accent":1670},[898,88115,900],{},[1655,88117,88072],{},[1655,88119,1657],{},[898,88121,88122],{},"ln",[1655,88124,57326],{},[898,88126,900],{},[902,88128,88129],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,88132,88133],{},"porovnání"," mezi svazky a ",[38,88136,88137],{},"poměry"," mezních veličin.",[724,88140,88141,88142,2086],{},"Ordinalistický přístup vychází z ",[38,88143,88144],{},"pěti hlavních předpokladů",[152,88146,88147,88153,88159,88277,88283],{},[123,88148,88149,88152],{},[38,88150,88151],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,88154,88155,88158],{},[38,88156,88157],{},"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.",[123,88160,88161,88164,88165,62867,88178,88191,88192,62867,88205,4199,88218,88221,88222,2704,88241,63696,88259,1719],{},[38,88162,88163],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,88166,88168],{"className":88167},[886],[888,88169,88170],{"xmlns":890},[892,88171,88172,88176],{},[895,88173,88174],{},[898,88175,2731],{},[902,88177,2731],{"encoding":904},[883,88179,88181],{"className":88180},[886],[888,88182,88183],{"xmlns":890},[892,88184,88185,88189],{},[895,88186,88187],{},[898,88188,24379],{},[902,88190,24379],{"encoding":904},", nebude jindy preferovat ",[883,88193,88195],{"className":88194},[886],[888,88196,88197],{"xmlns":890},[892,88198,88199,88203],{},[895,88200,88201],{},[898,88202,24379],{},[902,88204,24379],{"encoding":904},[883,88206,88208],{"className":88207},[886],[888,88209,88210],{"xmlns":890},[892,88211,88212,88216],{},[895,88213,88214],{},[898,88215,2731],{},[902,88217,2731],{"encoding":904},[38,88219,88220],{},"Tranzitivita",": pokud ",[883,88223,88225],{"className":88224},[886],[888,88226,88227],{"xmlns":890},[892,88228,88229,88238],{},[895,88230,88231,88233,88236],{},[898,88232,2731],{},[1655,88234,88235],{},"≻",[898,88237,24379],{},[902,88239,88240],{"encoding":904},"A \\succ B",[883,88242,88244],{"className":88243},[886],[888,88245,88246],{"xmlns":890},[892,88247,88248,88256],{},[895,88249,88250,88252,88254],{},[898,88251,24379],{},[1655,88253,88235],{},[898,88255,4052],{},[902,88257,88258],{"encoding":904},"B \\succ C",[883,88260,88262],{"className":88261},[886],[888,88263,88264],{"xmlns":890},[892,88265,88266,88274],{},[895,88267,88268,88270,88272],{},[898,88269,2731],{},[1655,88271,88235],{},[898,88273,4052],{},[902,88275,88276],{"encoding":904},"A \\succ C",[123,88278,88279,88282],{},[38,88280,88281],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,88284,88285,88288],{},[38,88286,88287],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,88290,88291,88292,88295,88296,1719],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,88293,88294],{},"preference"," a na příbuzné ",[614,88297,88298],{},"funkci užitečnosti",[115,88300,88302],{"id":88301},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,88304,88305,88306,88319,88320,88323,88324,88337],{},"Uvažujme ",[883,88307,88309],{"className":88308},[886],[888,88310,88311],{"xmlns":890},[892,88312,88313,88317],{},[895,88314,88315],{},[898,88316,37986],{},[902,88318,37986],{"encoding":904}," různých zboží. ",[38,88321,88322],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,88325,88327],{"className":88326},[886],[888,88328,88329],{"xmlns":890},[892,88330,88331,88335],{},[895,88332,88333],{},[898,88334,37986],{},[902,88336,37986],{"encoding":904},"-tice",[724,88339,88340],{},[883,88341,88343],{"className":88342},[886],[888,88344,88345],{"xmlns":890},[892,88346,88347,88373],{},[895,88348,88349,88351,88357,88359,88361,88363,88369,88371],{},[1655,88350,1664],{"stretchy":1663},[1820,88352,88353,88355],{},[898,88354,1824],{},[1826,88356,1828],{},[1655,88358,1671],{"separator":1670},[1655,88360,1715],{},[1655,88362,1671],{"separator":1670},[1820,88364,88365,88367],{},[898,88366,1824],{},[898,88368,37986],{},[1655,88370,1677],{"stretchy":1663},[1655,88372,1671],{"separator":1670},[902,88374,88375],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,88377,5559,88378,88395,88396,88409,88410,88413,88414,88417,88418,88421,88422,2086],{},[883,88379,88381],{"className":88380},[886],[888,88382,88383],{"xmlns":890},[892,88384,88385,88393],{},[895,88386,88387],{},[1820,88388,88389,88391],{},[898,88390,1824],{},[898,88392,18916],{},[902,88394,48664],{"encoding":904}," značí množství ",[883,88397,88399],{"className":88398},[886],[888,88400,88401],{"xmlns":890},[892,88402,88403,88407],{},[895,88404,88405],{},[898,88406,18916],{},[902,88408,18916],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,88411,88412],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,88415,88416],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,88419,88420],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,88423,88298],{},[883,88425,88427],{"className":88426},[886],[888,88428,88429],{"xmlns":890,"display":29192},[892,88430,88431,88478],{},[21880,88432,88433],{"width":29197},[21885,88434,88435,88437,88471,88473],{},[21888,88436],{"width":29202},[21888,88438,88439],{},[895,88440,88441,88443,88445,88447,88449,88455,88457,88459,88461,88467,88469],{},[898,88442,900],{},[1655,88444,1657],{},[898,88446,900],{},[1655,88448,1664],{"stretchy":1663},[1820,88450,88451,88453],{},[898,88452,1824],{},[1826,88454,1828],{},[1655,88456,1671],{"separator":1670},[1655,88458,1715],{},[1655,88460,1671],{"separator":1670},[1820,88462,88463,88465],{},[898,88464,1824],{},[898,88466,37986],{},[1655,88468,1677],{"stretchy":1663},[1655,88470,1671],{"separator":1670},[21888,88472],{"width":29202},[21888,88474,88475],{},[2031,88476,88477],{},"(6.1)",[902,88479,88480],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,88482,5559,88483,88513,88514,88536,88537,88540],{},[883,88484,88486],{"className":88485},[886],[888,88487,88488],{"xmlns":890},[892,88489,88490,88510],{},[895,88491,88492,88498,88500,88502,88504],{},[1820,88493,88494,88496],{},[898,88495,1824],{},[1826,88497,1828],{},[1655,88499,1671],{"separator":1670},[1655,88501,1715],{},[1655,88503,1671],{"separator":1670},[1820,88505,88506,88508],{},[898,88507,1824],{},[898,88509,37986],{},[902,88511,88512],{"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 ",[883,88515,88517],{"className":88516},[886],[888,88518,88519],{"xmlns":890},[892,88520,88521,88533],{},[895,88522,88523,88525,88527],{},[898,88524,900],{},[1655,88526,1671],{"separator":1670},[9633,88528,88529,88531],{"accent":1670},[898,88530,900],{},[1655,88532,88072],{},[902,88534,88535],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,88538,88539],{},"monotónní transformace"," zachovávající pořadí.",[724,88542,88543,88544,8262,88547,1719],{},"Dále se omezíme na funkce pro ",[38,88545,88546],{},"dvě zboží",[883,88548,88550],{"className":88549},[886],[888,88551,88552],{"xmlns":890},[892,88553,88554,88580],{},[895,88555,88556,88558,88560,88562,88564,88570,88572,88578],{},[898,88557,900],{},[1655,88559,1657],{},[898,88561,900],{},[1655,88563,1664],{"stretchy":1663},[1820,88565,88566,88568],{},[898,88567,1824],{},[1826,88569,1828],{},[1655,88571,1671],{"separator":1670},[1820,88573,88574,88576],{},[898,88575,1824],{},[1826,88577,1837],{},[1655,88579,1677],{"stretchy":1663},[902,88581,88582],{"encoding":904},"U = U(Q_1, Q_2)",[5120,88584,88585,88660],{},[724,88586,88587,88589,88590,2086],{},[883,88588,53821],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,88591,88593],{"className":88592},[886],[888,88594,88595],{"xmlns":890},[892,88596,88597,88657],{},[895,88598,88599,88601,88603,88605,88607,88613,88615,88621,88623,88629,88631,88633,88635],{},[898,88600,900],{},[1655,88602,1657],{},[898,88604,900],{},[1655,88606,1664],{"stretchy":1663},[1820,88608,88609,88611],{},[898,88610,1824],{},[1826,88612,1828],{},[1655,88614,1671],{"separator":1670},[1820,88616,88617,88619],{},[898,88618,1824],{},[1826,88620,1837],{},[1655,88622,1671],{"separator":1670},[1820,88624,88625,88627],{},[898,88626,1824],{},[1826,88628,3472],{},[1655,88630,1677],{"stretchy":1663},[1655,88632,1657],{},[1826,88634,1837],{},[9364,88636,88637],{},[895,88638,88639,88645,88651],{},[1820,88640,88641,88643],{},[898,88642,1824],{},[1826,88644,1828],{},[1820,88646,88647,88649],{},[898,88648,1824],{},[1826,88650,1837],{},[1820,88652,88653,88655],{},[898,88654,1824],{},[1826,88656,3472],{},[902,88658,88659],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,88661,88662,88855],{},[123,88663,88664,88665,88691,88692,14063,88718,2704,88777,6838,88837,9672],{},"svazek ",[883,88666,88668],{"className":88667},[886],[888,88669,88670],{"xmlns":890},[892,88671,88672,88688],{},[895,88673,88674,88676,88678,88680,88682,88684,88686],{},[1655,88675,1664],{"stretchy":1663},[1826,88677,42988],{},[1655,88679,1671],{"separator":1670},[1826,88681,3639],{},[1655,88683,1671],{"separator":1670},[1826,88685,42966],{},[1655,88687,1677],{"stretchy":1663},[902,88689,88690],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,88693,88695],{"className":88694},[886],[888,88696,88697],{"xmlns":890},[892,88698,88699,88715],{},[895,88700,88701,88703,88705,88707,88709,88711,88713],{},[1655,88702,1664],{"stretchy":1663},[1826,88704,5250],{},[1655,88706,1671],{"separator":1670},[1826,88708,5250],{},[1655,88710,1671],{"separator":1670},[1826,88712,67723],{},[1655,88714,1677],{"stretchy":1663},[902,88716,88717],{"encoding":904},"(9, 9, 27)",[883,88719,88721],{"className":88720},[886],[888,88722,88723],{"xmlns":890},[892,88724,88725,88774],{},[895,88726,88727,88729,88731,88733,88735,88737,88739,88741,88743,88745,88747,88761,88763,88765,88770,88772],{},[898,88728,900],{},[1655,88730,1664],{"stretchy":1663},[1826,88732,42988],{},[1655,88734,1671],{"separator":1670},[1826,88736,3639],{},[1655,88738,1671],{"separator":1670},[1826,88740,42966],{},[1655,88742,1677],{"stretchy":1663},[1655,88744,1657],{},[1826,88746,1837],{},[9364,88748,88749],{},[895,88750,88751,88753,88755,88757,88759],{},[1826,88752,42988],{},[1655,88754,2869],{},[1826,88756,3639],{},[1655,88758,2869],{},[1826,88760,42966],{},[1655,88762,1657],{},[1826,88764,1837],{},[9364,88766,88767],{},[1826,88768,88769],{},"4096",[1655,88771,1657],{},[1826,88773,6866],{},[902,88775,88776],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,88778,88780],{"className":88779},[886],[888,88781,88782],{"xmlns":890},[892,88783,88784,88834],{},[895,88785,88786,88788,88790,88792,88794,88796,88798,88800,88802,88804,88806,88820,88822,88824,88829,88831],{},[898,88787,900],{},[1655,88789,1664],{"stretchy":1663},[1826,88791,5250],{},[1655,88793,1671],{"separator":1670},[1826,88795,5250],{},[1655,88797,1671],{"separator":1670},[1826,88799,67723],{},[1655,88801,1677],{"stretchy":1663},[1655,88803,1657],{},[1826,88805,1837],{},[9364,88807,88808],{},[895,88809,88810,88812,88814,88816,88818],{},[1826,88811,5250],{},[1655,88813,2869],{},[1826,88815,5250],{},[1655,88817,2869],{},[1826,88819,67723],{},[1655,88821,1657],{},[1826,88823,1837],{},[9364,88825,88826],{},[1826,88827,88828],{},"2187",[1655,88830,7147],{},[1826,88832,88833],{},"93,53",[902,88835,88836],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,88838,88840],{"className":88839},[886],[888,88841,88842],{"xmlns":890},[892,88843,88844,88852],{},[895,88845,88846,88848,88850],{},[1826,88847,6866],{},[1655,88849,2969],{},[1826,88851,88833],{},[902,88853,88854],{"encoding":904},"128 > 93{,}53",[123,88856,88857,88858,2704,88884,88910,88911,2704,88951,88992,88993,89039,89040,2704,89066,4118,89092,2704,89110,89128,89129,1719],{},"svazky ",[883,88859,88861],{"className":88860},[886],[888,88862,88863],{"xmlns":890},[892,88864,88865,88881],{},[895,88866,88867,88869,88871,88873,88875,88877,88879],{},[1655,88868,1664],{"stretchy":1663},[1826,88870,3639],{},[1655,88872,1671],{"separator":1670},[1826,88874,6834],{},[1655,88876,1671],{"separator":1670},[1826,88878,1837],{},[1655,88880,1677],{"stretchy":1663},[902,88882,88883],{"encoding":904},"(4, 8, 2)",[883,88885,88887],{"className":88886},[886],[888,88888,88889],{"xmlns":890},[892,88890,88891,88907],{},[895,88892,88893,88895,88897,88899,88901,88903,88905],{},[1655,88894,1664],{"stretchy":1663},[1826,88896,42966],{},[1655,88898,1671],{"separator":1670},[1826,88900,1828],{},[1655,88902,1671],{"separator":1670},[1826,88904,3639],{},[1655,88906,1677],{"stretchy":1663},[902,88908,88909],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,88912,88914],{"className":88913},[886],[888,88915,88916],{"xmlns":890},[892,88917,88918,88948],{},[895,88919,88920,88922,88924,88926,88928,88930,88932,88934,88936,88938,88940,88944,88946],{},[898,88921,900],{},[1655,88923,1664],{"stretchy":1663},[1826,88925,3639],{},[1655,88927,1671],{"separator":1670},[1826,88929,6834],{},[1655,88931,1671],{"separator":1670},[1826,88933,1837],{},[1655,88935,1677],{"stretchy":1663},[1655,88937,1657],{},[1826,88939,1837],{},[9364,88941,88942],{},[1826,88943,42966],{},[1655,88945,1657],{},[1826,88947,42988],{},[902,88949,88950],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,88952,88954],{"className":88953},[886],[888,88955,88956],{"xmlns":890},[892,88957,88958,88989],{},[895,88959,88960,88962,88964,88966,88968,88970,88972,88974,88976,88978,88980,88985,88987],{},[898,88961,900],{},[1655,88963,1664],{"stretchy":1663},[1826,88965,42966],{},[1655,88967,1671],{"separator":1670},[1826,88969,1828],{},[1655,88971,1671],{"separator":1670},[1826,88973,3639],{},[1655,88975,1677],{"stretchy":1663},[1655,88977,1657],{},[1826,88979,1837],{},[9364,88981,88982],{},[1826,88983,88984],{},"256",[1655,88986,1657],{},[1826,88988,73485],{},[902,88990,88991],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,88994,88996],{"className":88995},[886],[888,88997,88998],{"xmlns":890},[892,88999,89000,89036],{},[895,89001,89002,89004,89006,89008,89010,89012,89014,89016,89018,89020,89022,89024,89026,89028,89030,89032,89034],{},[898,89003,900],{},[1655,89005,1664],{"stretchy":1663},[1826,89007,3639],{},[1655,89009,1671],{"separator":1670},[1826,89011,6834],{},[1655,89013,1671],{"separator":1670},[1826,89015,1837],{},[1655,89017,1677],{"stretchy":1663},[1655,89019,1657],{},[898,89021,900],{},[1655,89023,1664],{"stretchy":1663},[1826,89025,42966],{},[1655,89027,1671],{"separator":1670},[1826,89029,1828],{},[1655,89031,1671],{"separator":1670},[1826,89033,3639],{},[1655,89035,1677],{"stretchy":1663},[902,89037,89038],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,89041,89043],{"className":89042},[886],[888,89044,89045],{"xmlns":890},[892,89046,89047,89063],{},[895,89048,89049,89051,89053,89055,89057,89059,89061],{},[1826,89050,3639],{},[1655,89052,2869],{},[1826,89054,6834],{},[1655,89056,2869],{},[1826,89058,1837],{},[1655,89060,1657],{},[1826,89062,42966],{},[902,89064,89065],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,89067,89069],{"className":89068},[886],[888,89070,89071],{"xmlns":890},[892,89072,89073,89089],{},[895,89074,89075,89077,89079,89081,89083,89085,89087],{},[1826,89076,42966],{},[1655,89078,2869],{},[1826,89080,1828],{},[1655,89082,2869],{},[1826,89084,3639],{},[1655,89086,1657],{},[1826,89088,88984],{},[902,89090,89091],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,89093,89095],{"className":89094},[886],[888,89096,89097],{"xmlns":890},[892,89098,89099,89107],{},[895,89100,89101,89103,89105],{},[898,89102,900],{},[1655,89104,1657],{},[1826,89106,42988],{},[902,89108,89109],{"encoding":904},"U = 16",[883,89111,89113],{"className":89112},[886],[888,89114,89115],{"xmlns":890},[892,89116,89117,89125],{},[895,89118,89119,89121,89123],{},[898,89120,900],{},[1655,89122,1657],{},[1826,89124,73485],{},[902,89126,89127],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,89130,89132],{"className":89131},[886],[888,89133,89134],{"xmlns":890},[892,89135,89136,89156],{},[895,89137,89138,89144,89150],{},[1820,89139,89140,89142],{},[898,89141,1824],{},[1826,89143,1828],{},[1820,89145,89146,89148],{},[898,89147,1824],{},[1826,89149,1837],{},[1820,89151,89152,89154],{},[898,89153,1824],{},[1826,89155,3472],{},[902,89157,89158],{"encoding":904},"Q_1 Q_2 Q_3",[115,89160,89162],{"id":89161},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,89164,89165,89166,9349,89201,3106,89204,42940,89221,2115,89238,89241,89242,89245],{},"Pro funkci užitečnosti ",[883,89167,89169],{"className":89168},[886],[888,89170,89171],{"xmlns":890},[892,89172,89173,89199],{},[895,89174,89175,89177,89179,89181,89183,89189,89191,89197],{},[898,89176,900],{},[1655,89178,1657],{},[898,89180,900],{},[1655,89182,1664],{"stretchy":1663},[1820,89184,89185,89187],{},[898,89186,1824],{},[1826,89188,1828],{},[1655,89190,1671],{"separator":1670},[1820,89192,89193,89195],{},[898,89194,1824],{},[1826,89196,1837],{},[1655,89198,1677],{"stretchy":1663},[902,89200,88582],{"encoding":904},[38,89202,89203],{},"mezní užitečnost",[883,89205,89207],{"className":89206},[886],[888,89208,89209],{"xmlns":890},[892,89210,89211,89219],{},[895,89212,89213],{},[1820,89214,89215,89217],{},[898,89216,1824],{},[1826,89218,1828],{},[902,89220,30128],{"encoding":904},[883,89222,89224],{"className":89223},[886],[888,89225,89226],{"xmlns":890},[892,89227,89228,89236],{},[895,89229,89230],{},[1820,89231,89232,89234],{},[898,89233,1824],{},[1826,89235,1837],{},[902,89237,30147],{"encoding":904},[38,89239,89240],{},"marginal utility",") parciální ",[207,89243,1145],{"className":89244,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,89247,89249],{"className":89248},[886],[888,89250,89251],{"xmlns":890,"display":29192},[892,89252,89253,89352],{},[21880,89254,89255],{"width":29197},[21885,89256,89257,89259,89345,89347],{},[21888,89258],{"width":29202},[21888,89260,89261],{},[895,89262,89263,89265,89271,89273,89281,89283,89301,89303,89305,89307,89313,89315,89323,89325,89343],{},[898,89264,2127],{},[1820,89266,89267,89269],{},[898,89268,900],{},[1826,89270,1828],{},[1655,89272,1657],{},[1935,89274,89275,89277,89279],{},[898,89276,900],{},[1826,89278,1828],{},[1655,89280,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,89282,1657],{},[1949,89284,89285,89291],{},[895,89286,89287,89289],{},[898,89288,1955],{"mathvariant":1943},[898,89290,900],{},[895,89292,89293,89295],{},[898,89294,1955],{"mathvariant":1943},[1820,89296,89297,89299],{},[898,89298,1824],{},[1826,89300,1828],{},[1655,89302,1671],{"separator":1670},[1967,89304],{"width":16409},[898,89306,2127],{},[1820,89308,89309,89311],{},[898,89310,900],{},[1826,89312,1837],{},[1655,89314,1657],{},[1935,89316,89317,89319,89321],{},[898,89318,900],{},[1826,89320,1837],{},[1655,89322,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,89324,1657],{},[1949,89326,89327,89333],{},[895,89328,89329,89331],{},[898,89330,1955],{"mathvariant":1943},[898,89332,900],{},[895,89334,89335,89337],{},[898,89336,1955],{"mathvariant":1943},[1820,89338,89339,89341],{},[898,89340,1824],{},[1826,89342,1837],{},[898,89344,1719],{"mathvariant":1943},[21888,89346],{"width":29202},[21888,89348,89349],{},[2031,89350,89351],{},"(6.2)",[902,89353,89354],{"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}",[724,89356,89357,89358,89392,89393,89423,89424,3106,89427,1719],{},"Pro pevné ",[883,89359,89361],{"className":89360},[886],[888,89362,89363],{"xmlns":890},[892,89364,89365,89389],{},[895,89366,89367,89373,89375,89377,89379,89385,89387],{},[1820,89368,89369,89371],{},[898,89370,1824],{},[1826,89372,1828],{},[1655,89374,1657],{},[898,89376,207],{},[1655,89378,1671],{"separator":1670},[1820,89380,89381,89383],{},[898,89382,1824],{},[1826,89384,1837],{},[1655,89386,1657],{},[898,89388,2025],{},[902,89390,89391],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,89394,89396],{"className":89395},[886],[888,89397,89398],{"xmlns":890},[892,89399,89400,89420],{},[895,89401,89402,89404,89410,89412,89414,89416,89418],{},[898,89403,2127],{},[1820,89405,89406,89408],{},[898,89407,900],{},[1826,89409,1828],{},[1655,89411,1664],{"stretchy":1663},[898,89413,207],{},[1655,89415,1671],{"separator":1670},[898,89417,2025],{},[1655,89419,1677],{"stretchy":1663},[902,89421,89422],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,89425,89426],{},"v bodě (na hladině)",[883,89428,89430],{"className":89429},[886],[888,89431,89432],{"xmlns":890},[892,89433,89434,89446],{},[895,89435,89436,89438,89440,89442,89444],{},[1655,89437,2734],{"stretchy":1663},[898,89439,207],{},[1655,89441,1671],{"separator":1670},[898,89443,2025],{},[1655,89445,2743],{"stretchy":1663},[902,89447,2939],{"encoding":904},[5120,89449,89450],{},[724,89451,89452,89454,89455,89485,89514,89515,3888,89528,3902,89545,89566,89567,3948,89584,3962,89597,89614,89615,89637,89638,89667,89668,7720,89688,89705],{},[883,89453,5406],{}," Intuice — co říká ",[883,89456,89458],{"className":89457},[886],[888,89459,89460],{"xmlns":890},[892,89461,89462,89482],{},[895,89463,89464,89466,89472,89474,89476,89478,89480],{},[898,89465,2127],{},[1820,89467,89468,89470],{},[898,89469,900],{},[1826,89471,1828],{},[1655,89473,1664],{"stretchy":1663},[898,89475,207],{},[1655,89477,1671],{"separator":1670},[898,89479,2025],{},[1655,89481,1677],{"stretchy":1663},[902,89483,89484],{"encoding":904},"MU_1(a,b)",[883,89486,89488],{"className":89487},[886],[888,89489,89490],{"xmlns":890},[892,89491,89492,89512],{},[895,89493,89494,89496,89502,89504,89506,89508,89510],{},[898,89495,2127],{},[1820,89497,89498,89500],{},[898,89499,900],{},[1826,89501,1828],{},[1655,89503,1664],{"stretchy":1663},[898,89505,207],{},[1655,89507,1671],{"separator":1670},[898,89509,2025],{},[1655,89511,1677],{"stretchy":1663},[902,89513,89422],{"encoding":904}," je rychlost změny ",[883,89516,89518],{"className":89517},[886],[888,89519,89520],{"xmlns":890},[892,89521,89522,89526],{},[895,89523,89524],{},[898,89525,900],{},[902,89527,900],{"encoding":904},[883,89529,89531],{"className":89530},[886],[888,89532,89533],{"xmlns":890},[892,89534,89535,89543],{},[895,89536,89537],{},[1820,89538,89539,89541],{},[898,89540,1824],{},[1826,89542,1828],{},[902,89544,30128],{"encoding":904},[883,89546,89548],{"className":89547},[886],[888,89549,89550],{"xmlns":890},[892,89551,89552,89564],{},[895,89553,89554,89556,89558,89560,89562],{},[1655,89555,2734],{"stretchy":1663},[898,89557,207],{},[1655,89559,1671],{"separator":1670},[898,89561,2025],{},[1655,89563,2743],{"stretchy":1663},[902,89565,2939],{"encoding":904},". Přibližně: změní-li se ",[883,89568,89570],{"className":89569},[886],[888,89571,89572],{"xmlns":890},[892,89573,89574,89582],{},[895,89575,89576],{},[1820,89577,89578,89580],{},[898,89579,1824],{},[1826,89581,1828],{},[902,89583,30128],{"encoding":904},[883,89585,89587],{"className":89586},[886],[888,89588,89589],{"xmlns":890},[892,89590,89591,89595],{},[895,89592,89593],{},[898,89594,207],{},[902,89596,207],{"encoding":904},[883,89598,89600],{"className":89599},[886],[888,89601,89602],{"xmlns":890},[892,89603,89604,89612],{},[895,89605,89606,89608,89610],{},[898,89607,207],{},[1655,89609,2346],{},[1826,89611,1828],{},[902,89613,3980],{"encoding":904}," při pevném ",[883,89616,89618],{"className":89617},[886],[888,89619,89620],{"xmlns":890},[892,89621,89622,89634],{},[895,89623,89624,89630,89632],{},[1820,89625,89626,89628],{},[898,89627,1824],{},[1826,89629,1837],{},[1655,89631,1657],{},[898,89633,2025],{},[902,89635,89636],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,89639,89641],{"className":89640},[886],[888,89642,89643],{"xmlns":890},[892,89644,89645,89665],{},[895,89646,89647,89649,89655,89657,89659,89661,89663],{},[898,89648,2127],{},[1820,89650,89651,89653],{},[898,89652,900],{},[1826,89654,1828],{},[1655,89656,1664],{"stretchy":1663},[898,89658,207],{},[1655,89660,1671],{"separator":1670},[898,89662,2025],{},[1655,89664,1677],{"stretchy":1663},[902,89666,89422],{"encoding":904},". Stejně tak ",[883,89669,89671],{"className":89670},[886],[888,89672,89673],{"xmlns":890},[892,89674,89675,89685],{},[895,89676,89677,89679],{},[898,89678,2127],{},[1820,89680,89681,89683],{},[898,89682,900],{},[1826,89684,1837],{},[902,89686,89687],{"encoding":904},"MU_2",[883,89689,89691],{"className":89690},[886],[888,89692,89693],{"xmlns":890},[892,89694,89695,89703],{},[895,89696,89697],{},[1820,89698,89699,89701],{},[898,89700,1824],{},[1826,89702,1837],{},[902,89704,30147],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,89707,81337],{"id":89708},"totální-diferenciál",[724,89710,89711,89712,49466,89728,89758,89759,2086],{},"Přibližnou změnu užitečnosti ",[883,89713,89715],{"className":89714},[886],[888,89716,89717],{"xmlns":890},[892,89718,89719,89725],{},[895,89720,89721,89723],{},[898,89722,2506],{"mathvariant":1943},[898,89724,900],{},[902,89726,89727],{"encoding":904},"\\Delta U",[883,89729,89731],{"className":89730},[886],[888,89732,89733],{"xmlns":890},[892,89734,89735,89755],{},[895,89736,89737,89739,89745,89747,89749],{},[898,89738,2410],{"mathvariant":1943},[1820,89740,89741,89743],{},[898,89742,1824],{},[1826,89744,1828],{},[1655,89746,1671],{"separator":1670},[898,89748,2410],{"mathvariant":1943},[1820,89750,89751,89753],{},[898,89752,1824],{},[1826,89754,1837],{},[902,89756,89757],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,89760,89761],{},"totálního diferenciálu",[883,89763,89765],{"className":89764},[886],[888,89766,89767],{"xmlns":890,"display":29192},[892,89768,89769,89870],{},[21880,89770,89771],{"width":29197},[21885,89772,89773,89775,89863,89865],{},[21888,89774],{"width":29202},[21888,89776,89777],{},[895,89778,89779,89781,89783,89785,89787,89789,89791,89799,89801,89807,89809,89817,89819,89825,89827,89829,89835,89837,89843,89845,89847,89853,89855,89861],{},[898,89780,2506],{"mathvariant":1943},[898,89782,900],{},[1655,89784,2357],{},[898,89786,2410],{"mathvariant":1943},[898,89788,900],{},[1655,89790,1657],{},[1935,89792,89793,89795,89797],{},[898,89794,900],{},[1826,89796,1828],{},[1655,89798,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[898,89800,2410],{"mathvariant":1943},[1820,89802,89803,89805],{},[898,89804,1824],{},[1826,89806,1828],{},[1655,89808,2346],{},[1935,89810,89811,89813,89815],{},[898,89812,900],{},[1826,89814,1837],{},[1655,89816,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[898,89818,2410],{"mathvariant":1943},[1820,89820,89821,89823],{},[898,89822,1824],{},[1826,89824,1837],{},[1655,89826,1657],{},[898,89828,2127],{},[1820,89830,89831,89833],{},[898,89832,900],{},[1826,89834,1828],{},[898,89836,2410],{"mathvariant":1943},[1820,89838,89839,89841],{},[898,89840,1824],{},[1826,89842,1828],{},[1655,89844,2346],{},[898,89846,2127],{},[1820,89848,89849,89851],{},[898,89850,900],{},[1826,89852,1837],{},[898,89854,2410],{"mathvariant":1943},[1820,89856,89857,89859],{},[898,89858,1824],{},[1826,89860,1837],{},[898,89862,1719],{"mathvariant":1943},[21888,89864],{"width":29202},[21888,89866,89867],{},[2031,89868,89869],{},"(6.3)",[902,89871,89872],{"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}",[724,89874,76595,89875,1719],{},[883,89876,89878],{"className":89877},[886],[888,89879,89880],{"xmlns":890},[892,89881,89882,89952],{},[895,89883,89884,89886,89888,89890,89892,89894,89900,89902,89904,89910,89912,89918,89920,89922,89928,89930,89932,89934,89936,89942,89944,89950],{},[898,89885,2506],{"mathvariant":1943},[898,89887,900],{},[1655,89889,1657],{},[898,89891,900],{},[1655,89893,1664],{"stretchy":1663},[1820,89895,89896,89898],{},[898,89897,1824],{},[1826,89899,1828],{},[1655,89901,2346],{},[898,89903,2410],{"mathvariant":1943},[1820,89905,89906,89908],{},[898,89907,1824],{},[1826,89909,1828],{},[1655,89911,1671],{"separator":1670},[1820,89913,89914,89916],{},[898,89915,1824],{},[1826,89917,1837],{},[1655,89919,2346],{},[898,89921,2410],{"mathvariant":1943},[1820,89923,89924,89926],{},[898,89925,1824],{},[1826,89927,1837],{},[1655,89929,1677],{"stretchy":1663},[1655,89931,2623],{},[898,89933,900],{},[1655,89935,1664],{"stretchy":1663},[1820,89937,89938,89940],{},[898,89939,1824],{},[1826,89941,1828],{},[1655,89943,1671],{"separator":1670},[1820,89945,89946,89948],{},[898,89947,1824],{},[1826,89949,1837],{},[1655,89951,1677],{"stretchy":1663},[902,89953,89954],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,89956,89958],{"id":89957},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,89960,89961,89962,89965,89966,89969],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,89963,89964],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,89967,89968],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,89971,89972,89975,89976,42940,90002,90028,90029,1343,90061,90093,90094,2704,90148,90202],{},[38,89973,89974],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,89977,89979],{"className":89978},[886],[888,89980,89981],{"xmlns":890},[892,89982,89983,89999],{},[895,89984,89985,89991,89993],{},[1820,89986,89987,89989],{},[898,89988,1824],{},[1826,89990,1837],{},[1655,89992,1657],{},[1820,89994,89995,89997],{},[898,89996,207],{},[1826,89998,2552],{},[902,90000,90001],{"encoding":904},"Q_2 = a_0",[883,90003,90005],{"className":90004},[886],[888,90006,90007],{"xmlns":890},[892,90008,90009,90025],{},[895,90010,90011,90017,90019],{},[1820,90012,90013,90015],{},[898,90014,1824],{},[1826,90016,1828],{},[1655,90018,1657],{},[1820,90020,90021,90023],{},[898,90022,2025],{},[1826,90024,2552],{},[902,90026,90027],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,90030,90032],{"className":90031},[886],[888,90033,90034],{"xmlns":890},[892,90035,90036,90058],{},[895,90037,90038,90040,90042,90048,90050,90056],{},[898,90039,900],{},[1655,90041,1664],{"stretchy":1663},[1820,90043,90044,90046],{},[898,90045,1824],{},[1826,90047,1828],{},[1655,90049,1671],{"separator":1670},[1820,90051,90052,90054],{},[898,90053,207],{},[1826,90055,2552],{},[1655,90057,1677],{"stretchy":1663},[902,90059,90060],{"encoding":904},"U(Q_1, a_0)",[883,90062,90064],{"className":90063},[886],[888,90065,90066],{"xmlns":890},[892,90067,90068,90090],{},[895,90069,90070,90072,90074,90080,90082,90088],{},[898,90071,900],{},[1655,90073,1664],{"stretchy":1663},[1820,90075,90076,90078],{},[898,90077,2025],{},[1826,90079,2552],{},[1655,90081,1671],{"separator":1670},[1820,90083,90084,90086],{},[898,90085,1824],{},[1826,90087,1837],{},[1655,90089,1677],{"stretchy":1663},[902,90091,90092],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,90095,90097],{"className":90096},[886],[888,90098,90099],{"xmlns":890},[892,90100,90101,90145],{},[895,90102,90103,90141,90143],{},[3615,90104,90105],{"scriptlevel":2552,"displaystyle":1670},[1949,90106,90107,90131],{},[895,90108,90109,90111,90113,90115,90121,90123,90129],{},[898,90110,2410],{"mathvariant":1943},[898,90112,900],{},[1655,90114,1664],{"stretchy":1663},[1820,90116,90117,90119],{},[898,90118,1824],{},[1826,90120,1828],{},[1655,90122,1671],{"separator":1670},[1820,90124,90125,90127],{},[898,90126,207],{},[1826,90128,2552],{},[1655,90130,1677],{"stretchy":1663},[895,90132,90133,90135],{},[898,90134,2410],{"mathvariant":1943},[1820,90136,90137,90139],{},[898,90138,1824],{},[1826,90140,1828],{},[1655,90142,2969],{},[1826,90144,2552],{},[902,90146,90147],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,90149,90151],{"className":90150},[886],[888,90152,90153],{"xmlns":890},[892,90154,90155,90199],{},[895,90156,90157,90195,90197],{},[3615,90158,90159],{"scriptlevel":2552,"displaystyle":1670},[1949,90160,90161,90185],{},[895,90162,90163,90165,90167,90169,90175,90177,90183],{},[898,90164,2410],{"mathvariant":1943},[898,90166,900],{},[1655,90168,1664],{"stretchy":1663},[1820,90170,90171,90173],{},[898,90172,2025],{},[1826,90174,2552],{},[1655,90176,1671],{"separator":1670},[1820,90178,90179,90181],{},[898,90180,1824],{},[1826,90182,1837],{},[1655,90184,1677],{"stretchy":1663},[895,90186,90187,90189],{},[898,90188,2410],{"mathvariant":1943},[1820,90190,90191,90193],{},[898,90192,1824],{},[1826,90194,1837],{},[1655,90196,2969],{},[1826,90198,2552],{},[902,90200,90201],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,90204,90206],{"className":90205},[886],[888,90207,90208],{"xmlns":890,"display":29192},[892,90209,90210,90255],{},[21880,90211,90212],{"width":29197},[21885,90213,90214,90216,90248,90250],{},[21888,90215],{"width":29202},[21888,90217,90218],{},[895,90219,90220,90228,90230,90232,90234,90236,90244,90246],{},[1935,90221,90222,90224,90226],{},[898,90223,900],{},[1826,90225,1828],{},[1655,90227,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,90229,2969],{},[1826,90231,2552],{},[1655,90233,1671],{"separator":1670},[1967,90235],{"width":16409},[1935,90237,90238,90240,90242],{},[898,90239,900],{},[1826,90241,1837],{},[1655,90243,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,90245,2969],{},[1826,90247,13585],{},[21888,90249],{"width":29202},[21888,90251,90252],{},[2031,90253,90254],{},"(6.4)",[902,90256,90257],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,90259,90260,90261,90263],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,90262,53803],{}," — užitečnost roste s množstvím každého zboží.",[724,90265,90266,90269,90270,90300,90301,2086],{},[38,90267,90268],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,90271,90273],{"className":90272},[886],[888,90274,90275],{"xmlns":890},[892,90276,90277,90297],{},[895,90278,90279,90287,90289],{},[1935,90280,90281,90283,90285],{},[898,90282,900],{},[1826,90284,1828],{},[1655,90286,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,90288,1671],{"separator":1670},[1935,90290,90291,90293,90295],{},[898,90292,900],{},[1826,90294,1837],{},[1655,90296,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,90298,90299],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,90302,90303],{},"záporné",[883,90305,90307],{"className":90306},[886],[888,90308,90309],{"xmlns":890,"display":29192},[892,90310,90311,90364],{},[21880,90312,90313],{"width":29197},[21885,90314,90315,90317,90357,90359],{},[21888,90316],{"width":29202},[21888,90318,90319],{},[895,90320,90321,90333,90335,90337,90339,90341,90353,90355],{},[1935,90322,90323,90325,90327],{},[898,90324,900],{},[1826,90326,4176],{},[895,90328,90329,90331],{},[1655,90330,1945],{"mathvariant":1943},[1655,90332,1945],{"mathvariant":1943},[1655,90334,3065],{},[1826,90336,2552],{},[1655,90338,1671],{"separator":1670},[1967,90340],{"width":16409},[1935,90342,90343,90345,90347],{},[898,90344,900],{},[1826,90346,33672],{},[895,90348,90349,90351],{},[1655,90350,1945],{"mathvariant":1943},[1655,90352,1945],{"mathvariant":1943},[1655,90354,3065],{},[1826,90356,13585],{},[21888,90358],{"width":29202},[21888,90360,90361],{},[2031,90362,90363],{},"(6.5)",[902,90365,90366],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,90368,90369,90370,90373,90374,1719],{},"Podmínka (6.5) je známa jako ",[38,90371,90372],{},"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 ",[207,90375,90377],{"className":90376,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,90379,90380,90381,2704,90413,90445,90446,2704,90472,90498,90499,90527,90528,2704,90530,90532,90533,90568],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,90382,90384],{"className":90383},[886],[888,90385,90386],{"xmlns":890},[892,90387,90388,90410],{},[895,90389,90390,90392,90394,90400,90402,90408],{},[898,90391,900],{},[1655,90393,1664],{"stretchy":1663},[1820,90395,90396,90398],{},[898,90397,1824],{},[1826,90399,1828],{},[1655,90401,1671],{"separator":1670},[1820,90403,90404,90406],{},[898,90405,2025],{},[1826,90407,2552],{},[1655,90409,1677],{"stretchy":1663},[902,90411,90412],{"encoding":904},"U(Q_1, b_0)",[883,90414,90416],{"className":90415},[886],[888,90417,90418],{"xmlns":890},[892,90419,90420,90442],{},[895,90421,90422,90424,90426,90432,90434,90440],{},[898,90423,900],{},[1655,90425,1664],{"stretchy":1663},[1820,90427,90428,90430],{},[898,90429,207],{},[1826,90431,2552],{},[1655,90433,1671],{"separator":1670},[1820,90435,90436,90438],{},[898,90437,1824],{},[1826,90439,1837],{},[1655,90441,1677],{"stretchy":1663},[902,90443,90444],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,90447,90449],{"className":90448},[886],[888,90450,90451],{"xmlns":890},[892,90452,90453,90469],{},[895,90454,90455,90457,90459,90461,90467],{},[1655,90456,1664],{"stretchy":1663},[898,90458,900],{},[1655,90460,1671],{"separator":1670},[1820,90462,90463,90465],{},[898,90464,1824],{},[1826,90466,1828],{},[1655,90468,1677],{"stretchy":1663},[902,90470,90471],{"encoding":904},"(U, Q_1)",[883,90473,90475],{"className":90474},[886],[888,90476,90477],{"xmlns":890},[892,90478,90479,90495],{},[895,90480,90481,90483,90485,90487,90493],{},[1655,90482,1664],{"stretchy":1663},[898,90484,900],{},[1655,90486,1671],{"separator":1670},[1820,90488,90489,90491],{},[898,90490,1824],{},[1826,90492,1837],{},[1655,90494,1677],{"stretchy":1663},[902,90496,90497],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,90500,90502],{"className":90501},[886],[888,90503,90504],{"xmlns":890},[892,90505,90506,90524],{},[895,90507,90508,90510,90512,90514,90516,90518,90520,90522],{},[898,90509,900],{},[1655,90511,1664],{"stretchy":1663},[1826,90513,2552],{},[1655,90515,1671],{"separator":1670},[1826,90517,2552],{},[1655,90519,1677],{"stretchy":1663},[1655,90521,1657],{},[1826,90523,2552],{},[902,90525,90526],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,90529,14782],{},[38,90531,39614],{},". Typický tvar grafu ",[883,90534,90536],{"className":90535},[886],[888,90537,90538],{"xmlns":890},[892,90539,90540,90566],{},[895,90541,90542,90544,90546,90548,90550,90556,90558,90564],{},[898,90543,900],{},[1655,90545,1657],{},[898,90547,900],{},[1655,90549,1664],{"stretchy":1663},[1820,90551,90552,90554],{},[898,90553,1824],{},[1826,90555,1828],{},[1655,90557,1671],{"separator":1670},[1820,90559,90560,90562],{},[898,90561,1824],{},[1826,90563,1837],{},[1655,90565,1677],{"stretchy":1663},[902,90567,88582],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,90570,90571],{},[614,90572,90573,90574,89614,90602,90623,90624,89614,90652,90674],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,90575,90577],{"className":90576},[886],[888,90578,90579],{"xmlns":890},[892,90580,90581,90599],{},[895,90582,90583,90585,90587,90593,90595,90597],{},[898,90584,900],{},[1655,90586,1664],{"stretchy":1663},[1820,90588,90589,90591],{},[898,90590,1824],{},[1826,90592,1828],{},[1655,90594,1671],{"separator":1670},[898,90596,2025],{},[1655,90598,1677],{"stretchy":1663},[902,90600,90601],{"encoding":904},"U(Q_1, b)",[883,90603,90605],{"className":90604},[886],[888,90606,90607],{"xmlns":890},[892,90608,90609,90621],{},[895,90610,90611,90617,90619],{},[1820,90612,90613,90615],{},[898,90614,1824],{},[1826,90616,1837],{},[1655,90618,1657],{},[898,90620,2025],{},[902,90622,89636],{"encoding":904}," (vlevo) a ",[883,90625,90627],{"className":90626},[886],[888,90628,90629],{"xmlns":890},[892,90630,90631,90649],{},[895,90632,90633,90635,90637,90639,90641,90647],{},[898,90634,900],{},[1655,90636,1664],{"stretchy":1663},[898,90638,207],{},[1655,90640,1671],{"separator":1670},[1820,90642,90643,90645],{},[898,90644,1824],{},[1826,90646,1837],{},[1655,90648,1677],{"stretchy":1663},[902,90650,90651],{"encoding":904},"U(a, Q_2)",[883,90653,90655],{"className":90654},[886],[888,90656,90657],{"xmlns":890},[892,90658,90659,90671],{},[895,90660,90661,90667,90669],{},[1820,90662,90663,90665],{},[898,90664,1824],{},[1826,90666,1828],{},[1655,90668,1657],{},[898,90670,207],{},[902,90672,90673],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,90676,90677],{},[614,90678,90679,90680,90715,90716,90746,90747,2704,90770,90792,90793,1719],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,90681,90683],{"className":90682},[886],[888,90684,90685],{"xmlns":890},[892,90686,90687,90713],{},[895,90688,90689,90691,90693,90695,90697,90703,90705,90711],{},[898,90690,900],{},[1655,90692,1657],{},[898,90694,900],{},[1655,90696,1664],{"stretchy":1663},[1820,90698,90699,90701],{},[898,90700,1824],{},[1826,90702,1828],{},[1655,90704,1671],{"separator":1670},[1820,90706,90707,90709],{},[898,90708,1824],{},[1826,90710,1837],{},[1655,90712,1677],{"stretchy":1663},[902,90714,88582],{"encoding":904}," nad rovinou ",[883,90717,90719],{"className":90718},[886],[888,90720,90721],{"xmlns":890},[892,90722,90723,90743],{},[895,90724,90725,90727,90733,90735,90741],{},[1655,90726,1664],{"stretchy":1663},[1820,90728,90729,90731],{},[898,90730,1824],{},[1826,90732,1828],{},[1655,90734,1671],{"separator":1670},[1820,90736,90737,90739],{},[898,90738,1824],{},[1826,90740,1837],{},[1655,90742,1677],{"stretchy":1663},[902,90744,90745],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,90748,90750],{"className":90749},[886],[888,90751,90752],{"xmlns":890},[892,90753,90754,90767],{},[895,90755,90756,90762,90764],{},[1820,90757,90758,90760],{},[898,90759,1824],{},[1826,90761,1828],{},[1655,90763,1657],{},[2031,90765,90766],{},"const",[902,90768,90769],{"encoding":904},"Q_1 = \\text{const}",[883,90771,90773],{"className":90772},[886],[888,90774,90775],{"xmlns":890},[892,90776,90777,90789],{},[895,90778,90779,90785,90787],{},[1820,90780,90781,90783],{},[898,90782,1824],{},[1826,90784,1837],{},[1655,90786,1657],{},[2031,90788,90766],{},[902,90790,90791],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,90794,90796],{"className":90795},[886],[888,90797,90798],{"xmlns":890},[892,90799,90800,90826],{},[895,90801,90802,90804,90806,90812,90814,90820,90822,90824],{},[898,90803,900],{},[1655,90805,1664],{"stretchy":1663},[1820,90807,90808,90810],{},[898,90809,1824],{},[1826,90811,1828],{},[1655,90813,1671],{"separator":1670},[1820,90815,90816,90818],{},[898,90817,1824],{},[1826,90819,1837],{},[1655,90821,1677],{"stretchy":1663},[1655,90823,1657],{},[898,90825,1789],{},[902,90827,1846],{"encoding":904},[198,90829,90831,90832],{"id":90830},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,90833,90835],{"className":90834},[886],[888,90836,90837],{"xmlns":890},[892,90838,90839,90873],{},[895,90840,90841,90843,90845,90859],{},[898,90842,900],{},[1655,90844,1657],{},[1935,90846,90847,90849,90851],{},[898,90848,1824],{},[1826,90850,1828],{},[895,90852,90853,90855,90857],{},[1826,90854,1828],{},[898,90856,5923],{"mathvariant":1943},[1826,90858,1837],{},[1935,90860,90861,90863,90865],{},[898,90862,1824],{},[1826,90864,1837],{},[895,90866,90867,90869,90871],{},[1826,90868,1828],{},[898,90870,5923],{"mathvariant":1943},[1826,90872,3472],{},[902,90874,90875],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,90877,90878],{},[38,90879,90880],{},"Ověření (6.4) a (6.5).",[883,90882,90884],{"className":90883},[886],[888,90885,90886],{"xmlns":890,"display":29192},[892,90887,90888,90992],{},[895,90889,90890,90898,90900,90908,90924,90938,90940,90942,90950,90952,90960,90974,90990],{},[1935,90891,90892,90894,90896],{},[898,90893,900],{},[1826,90895,1828],{},[1655,90897,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,90899,1657],{},[3615,90901,90902],{"scriptlevel":2552,"displaystyle":1663},[1949,90903,90904,90906],{},[1826,90905,1828],{},[1826,90907,1837],{},[1935,90909,90910,90912,90914],{},[898,90911,1824],{},[1826,90913,1828],{},[895,90915,90916,90918,90920,90922],{},[1655,90917,2623],{},[1826,90919,1828],{},[898,90921,5923],{"mathvariant":1943},[1826,90923,1837],{},[1935,90925,90926,90928,90930],{},[898,90927,1824],{},[1826,90929,1837],{},[895,90931,90932,90934,90936],{},[1826,90933,1828],{},[898,90935,5923],{"mathvariant":1943},[1826,90937,3472],{},[1655,90939,1671],{"separator":1670},[1967,90941],{"width":16409},[1935,90943,90944,90946,90948],{},[898,90945,900],{},[1826,90947,1837],{},[1655,90949,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,90951,1657],{},[3615,90953,90954],{"scriptlevel":2552,"displaystyle":1663},[1949,90955,90956,90958],{},[1826,90957,1828],{},[1826,90959,3472],{},[1935,90961,90962,90964,90966],{},[898,90963,1824],{},[1826,90965,1828],{},[895,90967,90968,90970,90972],{},[1826,90969,1828],{},[898,90971,5923],{"mathvariant":1943},[1826,90973,1837],{},[1935,90975,90976,90978,90980],{},[898,90977,1824],{},[1826,90979,1837],{},[895,90981,90982,90984,90986,90988],{},[1655,90983,2623],{},[1826,90985,1837],{},[898,90987,5923],{"mathvariant":1943},[1826,90989,3472],{},[1655,90991,1671],{"separator":1670},[902,90993,90994],{"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},",[724,90996,90997,90998,91032],{},"zřejmě ",[883,90999,91001],{"className":91000},[886],[888,91002,91003],{"xmlns":890},[892,91004,91005,91029],{},[895,91006,91007,91015,91017,91025,91027],{},[1935,91008,91009,91011,91013],{},[898,91010,900],{},[1826,91012,1828],{},[1655,91014,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,91016,1671],{"separator":1670},[1935,91018,91019,91021,91023],{},[898,91020,900],{},[1826,91022,1837],{},[1655,91024,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,91026,2969],{},[1826,91028,2552],{},[902,91030,91031],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,91034,91036],{"className":91035},[886],[888,91037,91038],{"xmlns":890,"display":29192},[892,91039,91040,91156],{},[895,91041,91042,91054,91056,91058,91066,91082,91096,91098,91100,91112,91114,91116,91124,91138,91154],{},[1935,91043,91044,91046,91048],{},[898,91045,900],{},[1826,91047,4176],{},[895,91049,91050,91052],{},[1655,91051,1945],{"mathvariant":1943},[1655,91053,1945],{"mathvariant":1943},[1655,91055,1657],{},[1655,91057,2623],{},[3615,91059,91060],{"scriptlevel":2552,"displaystyle":1663},[1949,91061,91062,91064],{},[1826,91063,1828],{},[1826,91065,3639],{},[1935,91067,91068,91070,91072],{},[898,91069,1824],{},[1826,91071,1828],{},[895,91073,91074,91076,91078,91080],{},[1655,91075,2623],{},[1826,91077,3472],{},[898,91079,5923],{"mathvariant":1943},[1826,91081,1837],{},[1935,91083,91084,91086,91088],{},[898,91085,1824],{},[1826,91087,1837],{},[895,91089,91090,91092,91094],{},[1826,91091,1828],{},[898,91093,5923],{"mathvariant":1943},[1826,91095,3472],{},[1655,91097,1671],{"separator":1670},[1967,91099],{"width":16409},[1935,91101,91102,91104,91106],{},[898,91103,900],{},[1826,91105,33672],{},[895,91107,91108,91110],{},[1655,91109,1945],{"mathvariant":1943},[1655,91111,1945],{"mathvariant":1943},[1655,91113,1657],{},[1655,91115,2623],{},[3615,91117,91118],{"scriptlevel":2552,"displaystyle":1663},[1949,91119,91120,91122],{},[1826,91121,1837],{},[1826,91123,5250],{},[1935,91125,91126,91128,91130],{},[898,91127,1824],{},[1826,91129,1828],{},[895,91131,91132,91134,91136],{},[1826,91133,1828],{},[898,91135,5923],{"mathvariant":1943},[1826,91137,1837],{},[1935,91139,91140,91142,91144],{},[898,91141,1824],{},[1826,91143,1837],{},[895,91145,91146,91148,91150,91152],{},[1655,91147,2623],{},[1826,91149,3524],{},[898,91151,5923],{"mathvariant":1943},[1826,91153,3472],{},[1655,91155,1671],{"separator":1670},[902,91157,91158],{"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},",[724,91160,91161,91162,91204],{},"opět ",[883,91163,91165],{"className":91164},[886],[888,91166,91167],{"xmlns":890},[892,91168,91169,91201],{},[895,91170,91171,91183,91185,91197,91199],{},[1935,91172,91173,91175,91177],{},[898,91174,900],{},[1826,91176,4176],{},[895,91178,91179,91181],{},[1655,91180,1945],{"mathvariant":1943},[1655,91182,1945],{"mathvariant":1943},[1655,91184,1671],{"separator":1670},[1935,91186,91187,91189,91191],{},[898,91188,900],{},[1826,91190,33672],{},[895,91192,91193,91195],{},[1655,91194,1945],{"mathvariant":1943},[1655,91196,1945],{"mathvariant":1943},[1655,91198,3065],{},[1826,91200,2552],{},[902,91202,91203],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,91206,91207],{},[38,91208,91209,91210,1719],{},"(a) Mezní užitečnosti v bodě ",[883,91211,91213],{"className":91212},[886],[888,91214,91215],{"xmlns":890},[892,91216,91217,91229],{},[895,91218,91219,91221,91223,91225,91227],{},[1655,91220,2734],{"stretchy":1663},[1826,91222,4360],{},[1655,91224,1671],{"separator":1670},[1826,91226,9624],{},[1655,91228,2743],{"stretchy":1663},[902,91230,91231],{"encoding":904},"[100, 200]",[883,91233,91235],{"className":91234},[886],[888,91236,91237],{"xmlns":890,"display":29192},[892,91238,91239,91306],{},[895,91240,91241,91243,91249,91251,91253,91255,91257,91259,91261,91269,91271,91285,91287,91299,91301,91304],{},[898,91242,2127],{},[1820,91244,91245,91247],{},[898,91246,900],{},[1826,91248,1828],{},[1655,91250,1664],{"stretchy":1663},[1826,91252,4360],{},[1655,91254,1671],{"separator":1670},[1826,91256,9624],{},[1655,91258,1677],{"stretchy":1663},[1655,91260,1657],{},[3615,91262,91263],{"scriptlevel":2552,"displaystyle":1663},[1949,91264,91265,91267],{},[1826,91266,1828],{},[1826,91268,1837],{},[1655,91270,2869],{},[2597,91272,91273,91275],{},[1826,91274,4360],{},[895,91276,91277,91279,91281,91283],{},[1655,91278,2623],{},[1826,91280,1828],{},[898,91282,5923],{"mathvariant":1943},[1826,91284,1837],{},[1655,91286,2869],{},[2597,91288,91289,91291],{},[1826,91290,9624],{},[895,91292,91293,91295,91297],{},[1826,91294,1828],{},[898,91296,5923],{"mathvariant":1943},[1826,91298,3472],{},[1655,91300,7147],{},[1826,91302,91303],{},"0,4204",[1655,91305,1671],{"separator":1670},[902,91307,91308],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,91310,91312],{"className":91311},[886],[888,91313,91314],{"xmlns":890,"display":29192},[892,91315,91316,91381],{},[895,91317,91318,91320,91326,91328,91330,91332,91334,91336,91338,91346,91348,91360,91362,91376,91378],{},[898,91319,2127],{},[1820,91321,91322,91324],{},[898,91323,900],{},[1826,91325,1837],{},[1655,91327,1664],{"stretchy":1663},[1826,91329,4360],{},[1655,91331,1671],{"separator":1670},[1826,91333,9624],{},[1655,91335,1677],{"stretchy":1663},[1655,91337,1657],{},[3615,91339,91340],{"scriptlevel":2552,"displaystyle":1663},[1949,91341,91342,91344],{},[1826,91343,1828],{},[1826,91345,3472],{},[1655,91347,2869],{},[2597,91349,91350,91352],{},[1826,91351,4360],{},[895,91353,91354,91356,91358],{},[1826,91355,1828],{},[898,91357,5923],{"mathvariant":1943},[1826,91359,1837],{},[1655,91361,2869],{},[2597,91363,91364,91366],{},[1826,91365,9624],{},[895,91367,91368,91370,91372,91374],{},[1655,91369,2623],{},[1826,91371,1837],{},[898,91373,5923],{"mathvariant":1943},[1826,91375,3472],{},[1655,91377,7147],{},[1826,91379,91380],{},"0,63067.",[902,91382,91383],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,91385,91386,3106,91388,91423,91424,91445,91446,91463],{},[614,91387,10462],{},[883,91389,91391],{"className":91390},[886],[888,91392,91393],{"xmlns":890},[892,91394,91395,91420],{},[895,91396,91397,91399,91405,91407,91409,91411,91413,91415,91417],{},[898,91398,2127],{},[1820,91400,91401,91403],{},[898,91402,900],{},[1826,91404,1837],{},[1655,91406,1664],{"stretchy":1663},[1826,91408,4360],{},[1655,91410,1671],{"separator":1670},[1826,91412,9624],{},[1655,91414,1677],{"stretchy":1663},[1655,91416,7147],{},[1826,91418,91419],{},"0,63067",[902,91421,91422],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,91425,91427],{"className":91426},[886],[888,91428,91429],{"xmlns":890},[892,91430,91431,91443],{},[895,91432,91433,91435,91437,91439,91441],{},[1655,91434,2734],{"stretchy":1663},[1826,91436,4360],{},[1655,91438,1671],{"separator":1670},[1826,91440,9624],{},[1655,91442,2743],{"stretchy":1663},[902,91444,91231],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,91447,91449],{"className":91448},[886],[888,91450,91451],{"xmlns":890},[892,91452,91453,91461],{},[895,91454,91455],{},[1820,91456,91457,91459],{},[898,91458,1824],{},[1826,91460,1837],{},[902,91462,30147],{"encoding":904}," přibližně o 0,63067.",[724,91465,91466,91485,91486,40310,91507,91524,91525,91551,91552,91569,91570,4421],{},[38,91467,91468,91469,91484],{},"(b) Odhad změny ",[883,91470,91472],{"className":91471},[886],[888,91473,91474],{"xmlns":890},[892,91475,91476,91482],{},[895,91477,91478,91480],{},[898,91479,2506],{"mathvariant":1943},[898,91481,900],{},[902,91483,89727],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,91487,91489],{"className":91488},[886],[888,91490,91491],{"xmlns":890},[892,91492,91493,91505],{},[895,91494,91495,91497,91499,91501,91503],{},[1655,91496,2734],{"stretchy":1663},[1826,91498,4360],{},[1655,91500,1671],{"separator":1670},[1826,91502,9624],{},[1655,91504,2743],{"stretchy":1663},[902,91506,91231],{"encoding":904},[883,91508,91510],{"className":91509},[886],[888,91511,91512],{"xmlns":890},[892,91513,91514,91522],{},[895,91515,91516],{},[1820,91517,91518,91520],{},[898,91519,1824],{},[1826,91521,1828],{},[902,91523,30128],{"encoding":904}," na 98 (tj. ",[883,91526,91528],{"className":91527},[886],[888,91529,91530],{"xmlns":890},[892,91531,91532,91548],{},[895,91533,91534,91536,91542,91544,91546],{},[898,91535,2410],{"mathvariant":1943},[1820,91537,91538,91540],{},[898,91539,1824],{},[1826,91541,1828],{},[1655,91543,1657],{},[1655,91545,2623],{},[1826,91547,1837],{},[902,91549,91550],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,91553,91555],{"className":91554},[886],[888,91556,91557],{"xmlns":890},[892,91558,91559,91567],{},[895,91560,91561],{},[1820,91562,91563,91565],{},[898,91564,1824],{},[1826,91566,1837],{},[902,91568,30147],{"encoding":904}," o 3 (tj. ",[883,91571,91573],{"className":91572},[886],[888,91574,91575],{"xmlns":890},[892,91576,91577,91591],{},[895,91578,91579,91581,91587,91589],{},[898,91580,2410],{"mathvariant":1943},[1820,91582,91583,91585],{},[898,91584,1824],{},[1826,91586,1837],{},[1655,91588,1657],{},[1826,91590,3472],{},[902,91592,91593],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,91595,91597],{"className":91596},[886],[888,91598,91599],{"xmlns":890,"display":29192},[892,91600,91601,91652],{},[895,91602,91603,91605,91607,91609,91611,91613,91615,91617,91619,91621,91623,91625,91627,91629,91631,91633,91635,91637,91639,91642,91644,91647,91649],{},[898,91604,2506],{"mathvariant":1943},[898,91606,900],{},[1655,91608,2357],{},[898,91610,2410],{"mathvariant":1943},[898,91612,900],{},[1655,91614,1657],{},[1826,91616,91303],{},[1655,91618,2869],{},[1655,91620,1664],{"stretchy":1663},[1655,91622,2623],{},[1826,91624,1837],{},[1655,91626,1677],{"stretchy":1663},[1655,91628,2346],{},[1826,91630,91419],{},[1655,91632,2869],{},[1826,91634,3472],{},[1655,91636,1657],{},[1655,91638,2623],{},[1826,91640,91641],{},"0,8408",[1655,91643,2346],{},[1826,91645,91646],{},"1,89201",[1655,91648,7147],{},[1826,91650,91651],{},"1,05.",[902,91653,91654],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,91656,91657,91658,91661,91662,91713,91714,1719],{},"Užitečnost se tedy zvýší přibližně o ",[38,91659,91660],{},"1,05",". Skutečná změna je ",[883,91663,91665],{"className":91664},[886],[888,91666,91667],{"xmlns":890},[892,91668,91669,91710],{},[895,91670,91671,91673,91675,91677,91679,91681,91684,91686,91689,91691,91693,91695,91697,91699,91701,91703,91705,91707],{},[898,91672,2506],{"mathvariant":1943},[898,91674,900],{},[1655,91676,1657],{},[898,91678,900],{},[1655,91680,1664],{"stretchy":1663},[1826,91682,91683],{},"98",[1655,91685,1671],{"separator":1670},[1826,91687,91688],{},"203",[1655,91690,1677],{"stretchy":1663},[1655,91692,2623],{},[898,91694,900],{},[1655,91696,1664],{"stretchy":1663},[1826,91698,4360],{},[1655,91700,1671],{"separator":1670},[1826,91702,9624],{},[1655,91704,1677],{"stretchy":1663},[1655,91706,7147],{},[1826,91708,91709],{},"1,031",[902,91711,91712],{"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 ",[883,91715,91717],{"className":91716},[886],[888,91718,91719],{"xmlns":890},[892,91720,91721,91741],{},[895,91722,91723,91725,91731,91733,91735],{},[898,91724,2410],{"mathvariant":1943},[1820,91726,91727,91729],{},[898,91728,1824],{},[1826,91730,1828],{},[1655,91732,1671],{"separator":1670},[898,91734,2410],{"mathvariant":1943},[1820,91736,91737,91739],{},[898,91738,1824],{},[1826,91740,1837],{},[902,91742,89757],{"encoding":904},[115,91744,91746],{"id":91745},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,91748,91749],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,91751,91753],{"className":91752},[886],[888,91754,91755],{"xmlns":890,"display":29192},[892,91756,91757,91816],{},[21880,91758,91759],{"width":29197},[21885,91760,91761,91763,91809,91811],{},[21888,91762],{"width":29202},[21888,91764,91765],{},[895,91766,91767,91769,91771,91777,91779,91785,91787,91789,91797,91799,91807],{},[898,91768,900],{},[1655,91770,1664],{"stretchy":1663},[1820,91772,91773,91775],{},[898,91774,1824],{},[1826,91776,1828],{},[1655,91778,1671],{"separator":1670},[1820,91780,91781,91783],{},[898,91782,1824],{},[1826,91784,1837],{},[1655,91786,1677],{"stretchy":1663},[1655,91788,1657],{},[1935,91790,91791,91793,91795],{},[898,91792,1824],{},[1826,91794,1828],{},[898,91796,207],{},[1655,91798,2869],{},[1935,91800,91801,91803,91805],{},[898,91802,1824],{},[1826,91804,1837],{},[898,91806,2025],{},[1655,91808,1671],{"separator":1670},[21888,91810],{"width":29202},[21888,91812,91813],{},[2031,91814,91815],{},"(6.6)",[902,91817,91818],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,91820,5559,91821,91839,91840,91842,91843,91847,91848,91878,91879,91901],{},[883,91822,91824],{"className":91823},[886],[888,91825,91826],{"xmlns":890},[892,91827,91828,91836],{},[895,91829,91830,91832,91834],{},[898,91831,207],{},[1655,91833,1671],{"separator":1670},[898,91835,2025],{},[902,91837,91838],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,91841,75825],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,91844,91846],{"className":91845,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,91849,91851],{"className":91850},[886],[888,91852,91853],{"xmlns":890},[892,91854,91855,91875],{},[895,91856,91857,91859,91861,91863,91865,91867,91869,91871,91873],{},[898,91858,207],{},[1655,91860,1671],{"separator":1670},[898,91862,2025],{},[1655,91864,7753],{},[1655,91866,1664],{"stretchy":1663},[1826,91868,2552],{},[1655,91870,1671],{"separator":1670},[1826,91872,1828],{},[1655,91874,1677],{"stretchy":1663},[902,91876,91877],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,91880,91882],{"className":91881},[886],[888,91883,91884],{"xmlns":890},[892,91885,91886,91898],{},[895,91887,91888,91890,91892,91894,91896],{},[898,91889,2025],{},[1655,91891,1657],{},[1826,91893,1828],{},[1655,91895,2623],{},[898,91897,207],{},[902,91899,91900],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,91903,91904],{},[1723,91905],{"alt":91906,"className":91907,"src":91908},"imek-cobb-douglas-3d-plus-ic",[210,1727],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,91910,91912],{"className":91911},[886],[888,91913,91914],{"xmlns":890,"display":29192},[892,91915,91916,91966],{},[895,91917,91918,91920,91922,91928,91930,91936,91938,91940,91948,91950,91964],{},[898,91919,900],{},[1655,91921,1664],{"stretchy":1663},[1820,91923,91924,91926],{},[898,91925,1824],{},[1826,91927,1828],{},[1655,91929,1671],{"separator":1670},[1820,91931,91932,91934],{},[898,91933,1824],{},[1826,91935,1837],{},[1655,91937,1677],{"stretchy":1663},[1655,91939,1657],{},[1935,91941,91942,91944,91946],{},[898,91943,1824],{},[1826,91945,1828],{},[898,91947,207],{},[1655,91949,2869],{},[1935,91951,91952,91954,91956],{},[898,91953,1824],{},[1826,91955,1837],{},[895,91957,91958,91960,91962],{},[1826,91959,1828],{},[1655,91961,2623],{},[898,91963,207],{},[898,91965,1719],{"mathvariant":1943},[902,91967,91968],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[5120,91970,91971,92020,92142,92276],{},[724,91972,91973,91975,91976],{},[883,91974,53821],{}," Příklad 6.3 — ověření vlastností pro ",[883,91977,91979],{"className":91978},[886],[888,91980,91981],{"xmlns":890},[892,91982,91983,92017],{},[895,91984,91985,91987,91989,92003],{},[898,91986,900],{},[1655,91988,1657],{},[1935,91990,91991,91993,91995],{},[898,91992,1824],{},[1826,91994,1828],{},[895,91996,91997,91999,92001],{},[1826,91998,1828],{},[898,92000,5923],{"mathvariant":1943},[1826,92002,3639],{},[1935,92004,92005,92007,92009],{},[898,92006,1824],{},[1826,92008,1837],{},[895,92010,92011,92013,92015],{},[1826,92012,3472],{},[898,92014,5923],{"mathvariant":1943},[1826,92016,3639],{},[902,92018,92019],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,92021,92023],{"className":92022},[886],[888,92024,92025],{"xmlns":890,"display":29192},[892,92026,92027,92139],{},[895,92028,92029,92037,92039,92047,92063,92077,92079,92081,92083,92085,92093,92095,92103,92117,92133,92135,92137],{},[1935,92030,92031,92033,92035],{},[898,92032,900],{},[1826,92034,1828],{},[1655,92036,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,92038,1657],{},[3615,92040,92041],{"scriptlevel":2552,"displaystyle":1663},[1949,92042,92043,92045],{},[1826,92044,1828],{},[1826,92046,3639],{},[1935,92048,92049,92051,92053],{},[898,92050,1824],{},[1826,92052,1828],{},[895,92054,92055,92057,92059,92061],{},[1655,92056,2623],{},[1826,92058,3472],{},[898,92060,5923],{"mathvariant":1943},[1826,92062,3639],{},[1935,92064,92065,92067,92069],{},[898,92066,1824],{},[1826,92068,1837],{},[895,92070,92071,92073,92075],{},[1826,92072,3472],{},[898,92074,5923],{"mathvariant":1943},[1826,92076,3639],{},[1655,92078,2969],{},[1826,92080,2552],{},[1655,92082,1671],{"separator":1670},[1967,92084],{"width":16409},[1935,92086,92087,92089,92091],{},[898,92088,900],{},[1826,92090,1837],{},[1655,92092,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,92094,1657],{},[3615,92096,92097],{"scriptlevel":2552,"displaystyle":1663},[1949,92098,92099,92101],{},[1826,92100,3472],{},[1826,92102,3639],{},[1935,92104,92105,92107,92109],{},[898,92106,1824],{},[1826,92108,1828],{},[895,92110,92111,92113,92115],{},[1826,92112,1828],{},[898,92114,5923],{"mathvariant":1943},[1826,92116,3639],{},[1935,92118,92119,92121,92123],{},[898,92120,1824],{},[1826,92122,1837],{},[895,92124,92125,92127,92129,92131],{},[1655,92126,2623],{},[1826,92128,1828],{},[898,92130,5923],{"mathvariant":1943},[1826,92132,3639],{},[1655,92134,2969],{},[1826,92136,2552],{},[1655,92138,1671],{"separator":1670},[902,92140,92141],{"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,",[883,92143,92145],{"className":92144},[886],[888,92146,92147],{"xmlns":890,"display":29192},[892,92148,92149,92273],{},[895,92150,92151,92163,92165,92167,92175,92191,92205,92207,92209,92211,92213,92225,92227,92229,92237,92251,92267,92269,92271],{},[1935,92152,92153,92155,92157],{},[898,92154,900],{},[1826,92156,4176],{},[895,92158,92159,92161],{},[1655,92160,1945],{"mathvariant":1943},[1655,92162,1945],{"mathvariant":1943},[1655,92164,1657],{},[1655,92166,2623],{},[3615,92168,92169],{"scriptlevel":2552,"displaystyle":1663},[1949,92170,92171,92173],{},[1826,92172,3472],{},[1826,92174,42988],{},[1935,92176,92177,92179,92181],{},[898,92178,1824],{},[1826,92180,1828],{},[895,92182,92183,92185,92187,92189],{},[1655,92184,2623],{},[1826,92186,25327],{},[898,92188,5923],{"mathvariant":1943},[1826,92190,3639],{},[1935,92192,92193,92195,92197],{},[898,92194,1824],{},[1826,92196,1837],{},[895,92198,92199,92201,92203],{},[1826,92200,3472],{},[898,92202,5923],{"mathvariant":1943},[1826,92204,3639],{},[1655,92206,3065],{},[1826,92208,2552],{},[1655,92210,1671],{"separator":1670},[1967,92212],{"width":16409},[1935,92214,92215,92217,92219],{},[898,92216,900],{},[1826,92218,33672],{},[895,92220,92221,92223],{},[1655,92222,1945],{"mathvariant":1943},[1655,92224,1945],{"mathvariant":1943},[1655,92226,1657],{},[1655,92228,2623],{},[3615,92230,92231],{"scriptlevel":2552,"displaystyle":1663},[1949,92232,92233,92235],{},[1826,92234,3472],{},[1826,92236,42988],{},[1935,92238,92239,92241,92243],{},[898,92240,1824],{},[1826,92242,1828],{},[895,92244,92245,92247,92249],{},[1826,92246,1828],{},[898,92248,5923],{"mathvariant":1943},[1826,92250,3639],{},[1935,92252,92253,92255,92257],{},[898,92254,1824],{},[1826,92256,1837],{},[895,92258,92259,92261,92263,92265],{},[1655,92260,2623],{},[1826,92262,3524],{},[898,92264,5923],{"mathvariant":1943},[1826,92266,3639],{},[1655,92268,3065],{},[1826,92270,2552],{},[1655,92272,1671],{"separator":1670},[902,92274,92275],{"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,",[724,92277,92278],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,92280,92282],{"id":92281},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,92284,92285,92288],{},[38,92286,92287],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,92290,92292],{"className":92291},[886],[888,92293,92294],{"xmlns":890,"display":29192},[892,92295,92296,92339],{},[21880,92297,92298],{"width":29197},[21885,92299,92300,92302,92332,92334],{},[21888,92301],{"width":29202},[21888,92303,92304],{},[895,92305,92306,92308,92310,92316,92318,92324,92326,92328,92330],{},[898,92307,900],{},[1655,92309,1664],{"stretchy":1663},[1820,92311,92312,92314],{},[898,92313,1824],{},[1826,92315,1828],{},[1655,92317,1671],{"separator":1670},[1820,92319,92320,92322],{},[898,92321,1824],{},[1826,92323,1837],{},[1655,92325,1677],{"stretchy":1663},[1655,92327,1657],{},[898,92329,1789],{},[1655,92331,1671],{"separator":1670},[21888,92333],{"width":29202},[21888,92335,92336],{},[2031,92337,92338],{},"(6.7)",[902,92340,92341],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,92343,5559,92344,92357],{},[883,92345,92347],{"className":92346},[886],[888,92348,92349],{"xmlns":890},[892,92350,92351,92355],{},[895,92352,92353],{},[898,92354,1789],{},[902,92356,1789],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,92359,92361],{"className":92360},[886],[888,92362,92363],{"xmlns":890,"display":29192},[892,92364,92365,92406],{},[21880,92366,92367],{"width":29197},[21885,92368,92369,92371,92399,92401],{},[21888,92370],{"width":29202},[21888,92372,92373],{},[895,92374,92375,92383,92385,92393,92395,92397],{},[1935,92376,92377,92379,92381],{},[898,92378,1824],{},[1826,92380,1828],{},[898,92382,207],{},[1655,92384,2869],{},[1935,92386,92387,92389,92391],{},[898,92388,1824],{},[1826,92390,1837],{},[898,92392,2025],{},[1655,92394,1657],{},[898,92396,1789],{},[898,92398,1719],{"mathvariant":1943},[21888,92400],{"width":29202},[21888,92402,92403],{},[2031,92404,92405],{},"(6.8)",[902,92407,92408],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,92410,92411,92412,5607,92442,3106,92445,92458,92459,92494,92495,92512,92513,92542,92543,92546],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,92413,92415],{"className":92414},[886],[888,92416,92417],{"xmlns":890},[892,92418,92419,92439],{},[895,92420,92421,92423,92429,92431,92437],{},[1655,92422,2734],{"stretchy":1663},[1820,92424,92425,92427],{},[898,92426,1824],{},[1826,92428,1828],{},[1655,92430,1671],{"separator":1670},[1820,92432,92433,92435],{},[898,92434,1824],{},[1826,92436,1837],{},[1655,92438,2743],{"stretchy":1663},[902,92440,92441],{"encoding":904},"[Q_1, Q_2]",[38,92443,92444],{},"stejnou úrovní uspokojení",[883,92446,92448],{"className":92447},[886],[888,92449,92450],{"xmlns":890},[892,92451,92452,92456],{},[895,92453,92454],{},[898,92455,1789],{},[902,92457,1789],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,92460,92462],{"className":92461},[886],[888,92463,92464],{"xmlns":890},[892,92465,92466,92492],{},[895,92467,92468,92470,92472,92474,92476,92482,92484,92490],{},[898,92469,900],{},[1655,92471,1657],{},[898,92473,900],{},[1655,92475,1664],{"stretchy":1663},[1820,92477,92478,92480],{},[898,92479,1824],{},[1826,92481,1828],{},[1655,92483,1671],{"separator":1670},[1820,92485,92486,92488],{},[898,92487,1824],{},[1826,92489,1837],{},[1655,92491,1677],{"stretchy":1663},[902,92493,88582],{"encoding":904}," s rovinami ",[883,92496,92498],{"className":92497},[886],[888,92499,92500],{"xmlns":890},[892,92501,92502,92510],{},[895,92503,92504,92506,92508],{},[898,92505,900],{},[1655,92507,1657],{},[898,92509,1789],{},[902,92511,87798],{"encoding":904}," rovnoběžnými s rovinou ",[883,92514,92516],{"className":92515},[886],[888,92517,92518],{"xmlns":890},[892,92519,92520,92540],{},[895,92521,92522,92524,92530,92532,92538],{},[1655,92523,1664],{"stretchy":1663},[1820,92525,92526,92528],{},[898,92527,1824],{},[1826,92529,1828],{},[1655,92531,1671],{"separator":1670},[1820,92533,92534,92536],{},[898,92535,1824],{},[1826,92537,1837],{},[1655,92539,1677],{"stretchy":1663},[902,92541,90745],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,92544,92545],{},"izokvantami"," produkčních funkcí.",[724,92548,92549],{},[614,92550,92551,92552,90623,92570,92588,92589,1719],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,92553,92555],{"className":92554},[886],[888,92556,92557],{"xmlns":890},[892,92558,92559,92567],{},[895,92560,92561,92563,92565],{},[898,92562,207],{},[1655,92564,3065],{},[898,92566,2025],{},[902,92568,92569],{"encoding":904},"a \u003C b",[883,92571,92573],{"className":92572},[886],[888,92574,92575],{"xmlns":890},[892,92576,92577,92585],{},[895,92578,92579,92581,92583],{},[898,92580,207],{},[1655,92582,2969],{},[898,92584,2025],{},[902,92586,92587],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,92590,92592],{"className":92591},[886],[888,92593,92594],{"xmlns":890},[892,92595,92596,92620],{},[895,92597,92598,92604,92606,92612,92614],{},[1820,92599,92600,92602],{},[898,92601,1789],{},[1826,92603,2552],{},[1655,92605,3065],{},[1820,92607,92608,92610],{},[898,92609,1789],{},[1826,92611,1828],{},[1655,92613,3065],{},[1820,92615,92616,92618],{},[898,92617,1789],{},[1826,92619,1837],{},[902,92621,92622],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,92624,92625],{},[614,92626,92627,92628,92657,92658,92716,92717,92735],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,92629,92631],{"className":92630},[886],[888,92632,92633],{"xmlns":890},[892,92634,92635,92655],{},[895,92636,92637,92639,92645,92647,92653],{},[1655,92638,1664],{"stretchy":1663},[1820,92640,92641,92643],{},[898,92642,1824],{},[1826,92644,1828],{},[1655,92646,1671],{"separator":1670},[1820,92648,92649,92651],{},[898,92650,1824],{},[1826,92652,1837],{},[1655,92654,1677],{"stretchy":1663},[902,92656,90745],{"encoding":904},"; body ",[883,92659,92661],{"className":92660},[886],[888,92662,92663],{"xmlns":890},[892,92664,92665,92713],{},[895,92666,92667,92669,92671,92673,92679,92681,92687,92689,92691,92693,92695,92697,92703,92705,92711],{},[898,92668,2731],{},[1655,92670,1657],{},[1655,92672,2734],{"stretchy":1663},[1820,92674,92675,92677],{},[898,92676,207],{},[1826,92678,1828],{},[1655,92680,1671],{"separator":1670},[1820,92682,92683,92685],{},[898,92684,207],{},[1826,92686,1837],{},[1655,92688,2743],{"stretchy":1663},[1655,92690,1671],{"separator":1670},[898,92692,24379],{},[1655,92694,1657],{},[1655,92696,2734],{"stretchy":1663},[1820,92698,92699,92701],{},[898,92700,2025],{},[1826,92702,1828],{},[1655,92704,1671],{"separator":1670},[1820,92706,92707,92709],{},[898,92708,2025],{},[1826,92710,1837],{},[1655,92712,2743],{"stretchy":1663},[902,92714,92715],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,92718,92720],{"className":92719},[886],[888,92721,92722],{"xmlns":890},[892,92723,92724,92732],{},[895,92725,92726,92728,92730],{},[898,92727,4052],{},[1655,92729,1671],{"separator":1670},[898,92731,2838],{},[902,92733,92734],{"encoding":904},"C, D"," na vyšší hladině.",[5120,92737,92738],{},[724,92739,92740,92742,92743,92805,92806,92850,92851,92885,92886,27315,92904,92885,92958,27315,92976,93052],{},[883,92741,53821],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,92744,92746],{"className":92745},[886],[888,92747,92748],{"xmlns":890},[892,92749,92750,92802],{},[895,92751,92752,92754,92756,92762,92764,92770,92772,92774,92788],{},[898,92753,900],{},[1655,92755,1664],{"stretchy":1663},[1820,92757,92758,92760],{},[898,92759,1824],{},[1826,92761,1828],{},[1655,92763,1671],{"separator":1670},[1820,92765,92766,92768],{},[898,92767,1824],{},[1826,92769,1837],{},[1655,92771,1677],{"stretchy":1663},[1655,92773,1657],{},[1935,92775,92776,92778,92780],{},[898,92777,1824],{},[1826,92779,1828],{},[895,92781,92782,92784,92786],{},[1826,92783,1828],{},[898,92785,5923],{"mathvariant":1943},[1826,92787,3639],{},[1935,92789,92790,92792,92794],{},[898,92791,1824],{},[1826,92793,1837],{},[895,92795,92796,92798,92800],{},[1826,92797,3472],{},[898,92799,5923],{"mathvariant":1943},[1826,92801,3639],{},[902,92803,92804],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,92807,92809],{"className":92808},[886],[888,92810,92811],{"xmlns":890},[892,92812,92813,92847],{},[895,92814,92815,92829,92843,92845],{},[1935,92816,92817,92819,92821],{},[898,92818,1824],{},[1826,92820,1828],{},[895,92822,92823,92825,92827],{},[1826,92824,1828],{},[898,92826,5923],{"mathvariant":1943},[1826,92828,3639],{},[1935,92830,92831,92833,92835],{},[898,92832,1824],{},[1826,92834,1837],{},[895,92836,92837,92839,92841],{},[1826,92838,3472],{},[898,92840,5923],{"mathvariant":1943},[1826,92842,3639],{},[1655,92844,1657],{},[898,92846,1789],{},[902,92848,92849],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,92852,92854],{"className":92853},[886],[888,92855,92856],{"xmlns":890},[892,92857,92858,92882],{},[895,92859,92860,92866,92874,92876],{},[1820,92861,92862,92864],{},[898,92863,1824],{},[1826,92865,1828],{},[1935,92867,92868,92870,92872],{},[898,92869,1824],{},[1826,92871,1837],{},[1826,92873,3472],{},[1655,92875,1657],{},[2597,92877,92878,92880],{},[898,92879,1789],{},[1826,92881,3639],{},[902,92883,92884],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,92887,92889],{"className":92888},[886],[888,92890,92891],{"xmlns":890},[892,92892,92893,92901],{},[895,92894,92895,92897,92899],{},[898,92896,1789],{},[1655,92898,1657],{},[1826,92900,1828],{},[902,92902,92903],{"encoding":904},"c = 1",[883,92905,92907],{"className":92906},[886],[888,92908,92909],{"xmlns":890},[892,92910,92911,92955],{},[895,92912,92913,92919,92921,92937,92939],{},[1820,92914,92915,92917],{},[898,92916,1824],{},[1826,92918,1837],{},[1655,92920,1657],{},[1935,92922,92923,92925,92927],{},[898,92924,1824],{},[1826,92926,1828],{},[895,92928,92929,92931,92933,92935],{},[1655,92930,2623],{},[1826,92932,1828],{},[898,92934,5923],{"mathvariant":1943},[1826,92936,3472],{},[1655,92938,1657],{},[3615,92940,92941],{"scriptlevel":2552,"displaystyle":1670},[1949,92942,92943,92945],{},[1826,92944,1828],{},[83153,92946,92947,92953],{},[1820,92948,92949,92951],{},[898,92950,1824],{},[1826,92952,1828],{},[1826,92954,3472],{},[902,92956,92957],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,92959,92961],{"className":92960},[886],[888,92962,92963],{"xmlns":890},[892,92964,92965,92973],{},[895,92966,92967,92969,92971],{},[898,92968,1789],{},[1655,92970,1657],{},[1826,92972,1837],{},[902,92974,92975],{"encoding":904},"c = 2",[883,92977,92979],{"className":92978},[886],[888,92980,92981],{"xmlns":890},[892,92982,92983,93049],{},[895,92984,92985,92991,92993,93005,93007,93023,93025],{},[1820,92986,92987,92989],{},[898,92988,1824],{},[1826,92990,1837],{},[1655,92992,1657],{},[2597,92994,92995,92997],{},[1826,92996,1837],{},[895,92998,92999,93001,93003],{},[1826,93000,3639],{},[898,93002,5923],{"mathvariant":1943},[1826,93004,3472],{},[1655,93006,2869],{},[1935,93008,93009,93011,93013],{},[898,93010,1824],{},[1826,93012,1828],{},[895,93014,93015,93017,93019,93021],{},[1655,93016,2623],{},[1826,93018,1828],{},[898,93020,5923],{"mathvariant":1943},[1826,93022,3472],{},[1655,93024,1657],{},[3615,93026,93027],{"scriptlevel":2552,"displaystyle":1670},[1949,93028,93029,93039],{},[895,93030,93031,93033],{},[1826,93032,1837],{},[83153,93034,93035,93037],{},[1826,93036,1837],{},[1826,93038,3472],{},[83153,93040,93041,93047],{},[1820,93042,93043,93045],{},[898,93044,1824],{},[1826,93046,1828],{},[1826,93048,3472],{},[902,93050,93051],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,93054,93056],{"id":93055},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,93058,93059],{},[1723,93060],{"alt":93061,"className":93062,"src":93063},"imek-ic-4vlastnosti-anotovane",[210,1727],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[5120,93065,93066,93075,93122,93166,93172,93178],{},[724,93067,93068,93070,93071,93074],{},[883,93069,5661],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,93072,93073],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,93076,93077],{},[883,93078,93080],{"className":93079},[886],[888,93081,93082],{"xmlns":890},[892,93083,93084,93119],{},[895,93085,93086,93089,93091,93093,93095,93097,93115,93117],{},[898,93087,93088],{"mathvariant":1943},"tg",[1655,93090,57326],{},[898,93092,19988],{},[1655,93094,1657],{},[1655,93096,2623],{},[1949,93098,93099,93107],{},[1935,93100,93101,93103,93105],{},[898,93102,900],{},[1826,93104,1828],{},[1655,93106,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1935,93108,93109,93111,93113],{},[898,93110,900],{},[1826,93112,1837],{},[1655,93114,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,93116,3065],{},[1826,93118,2552],{},[902,93120,93121],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,93123,93124,93125,93165],{},"(derivace implicitně zadané funkce ",[883,93126,93128],{"className":93127},[886],[888,93129,93130],{"xmlns":890},[892,93131,93132,93162],{},[895,93133,93134,93136,93138,93144,93146,93152,93154,93156,93158,93160],{},[898,93135,900],{},[1655,93137,1664],{"stretchy":1663},[1820,93139,93140,93142],{},[898,93141,1824],{},[1826,93143,1828],{},[1655,93145,1671],{"separator":1670},[1820,93147,93148,93150],{},[898,93149,1824],{},[1826,93151,1837],{},[1655,93153,1677],{"stretchy":1663},[1655,93155,2623],{},[898,93157,1789],{},[1655,93159,1657],{},[1826,93161,2552],{},[902,93163,93164],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,93167,93168,93171],{},[38,93169,93170],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,93173,93174,93177],{},[38,93175,93176],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,93179,93180,93183,93184,93202,93203,93219,93220,93223],{},[38,93181,93182],{},"4° Konvexní."," Pro každé dva body ",[883,93185,93187],{"className":93186},[886],[888,93188,93189],{"xmlns":890},[892,93190,93191,93199],{},[895,93192,93193,93195,93197],{},[898,93194,2731],{},[1655,93196,1671],{"separator":1670},[898,93198,24379],{},[902,93200,93201],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,93204,93206],{"className":93205},[886],[888,93207,93208],{"xmlns":890},[892,93209,93210,93216],{},[895,93211,93212,93214],{},[898,93213,2731],{},[898,93215,24379],{},[902,93217,93218],{"encoding":904},"AB"," ve ",[38,93221,93222],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,93225,93226],{},[614,93227,93228,93229,93264,93265,1719],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,93230,93232],{"className":93231},[886],[888,93233,93234],{"xmlns":890},[892,93235,93236,93262],{},[895,93237,93238,93240,93242,93248,93250,93256,93258,93260],{},[898,93239,900],{},[1655,93241,1664],{"stretchy":1663},[1820,93243,93244,93246],{},[898,93245,1824],{},[1826,93247,1828],{},[1655,93249,1671],{"separator":1670},[1820,93251,93252,93254],{},[898,93253,1824],{},[1826,93255,1837],{},[1655,93257,1677],{"stretchy":1663},[1655,93259,1657],{},[898,93261,1789],{},[902,93263,1846],{"encoding":904}," s tečnou se sklonem ",[883,93266,93268],{"className":93267},[886],[888,93269,93270],{"xmlns":890},[892,93271,93272,93280],{},[895,93273,93274,93276,93278],{},[898,93275,93088],{"mathvariant":1943},[1655,93277,57326],{},[898,93279,19988],{},[902,93281,93282],{"encoding":904},"\\operatorname{tg}\\alpha",[115,93284,93286],{"id":93285},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,93288,93289,3106,93292,2115,93305,93308],{},[38,93290,93291],{},"Mezní míra komoditní substituce",[883,93293,93295],{"className":93294},[886],[888,93296,93297],{"xmlns":890},[892,93298,93299,93303],{},[895,93300,93301],{},[2031,93302,2708],{},[902,93304,29364],{"encoding":904},[38,93306,93307],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,93310,93312],{"className":93311},[886],[888,93313,93314],{"xmlns":890,"display":29192},[892,93315,93316,93403],{},[21880,93317,93318],{"width":29197},[21885,93319,93320,93322,93396,93398],{},[21888,93321],{"width":29202},[21888,93323,93324],{},[895,93325,93326,93328,93330,93332,93334,93340,93342,93348,93350,93352,93374,93376,93394],{},[2031,93327,2708],{},[1655,93329,1657],{},[2031,93331,2708],{},[1655,93333,1664],{"stretchy":1663},[1820,93335,93336,93338],{},[898,93337,1824],{},[1826,93339,1828],{},[1655,93341,1671],{"separator":1670},[1820,93343,93344,93346],{},[898,93345,1824],{},[1826,93347,1837],{},[1655,93349,1677],{"stretchy":1663},[1655,93351,1657],{},[1949,93353,93354,93364],{},[895,93355,93356,93358],{},[898,93357,2127],{},[1820,93359,93360,93362],{},[898,93361,900],{},[1826,93363,1828],{},[895,93365,93366,93368],{},[898,93367,2127],{},[1820,93369,93370,93372],{},[898,93371,900],{},[1826,93373,1837],{},[1655,93375,1657],{},[1949,93377,93378,93386],{},[1935,93379,93380,93382,93384],{},[898,93381,900],{},[1826,93383,1828],{},[1655,93385,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1935,93387,93388,93390,93392],{},[898,93389,900],{},[1826,93391,1837],{},[1655,93393,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[898,93395,1719],{"mathvariant":1943},[21888,93397],{"width":29202},[21888,93399,93400],{},[2031,93401,93402],{},"(6.9)",[902,93404,93405],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,93407,93408,93409,93443,93444,93476,93477,93512,93513,93526],{},"Geometricky: ",[883,93410,93412],{"className":93411},[886],[888,93413,93414],{"xmlns":890},[892,93415,93416,93440],{},[895,93417,93418,93420],{},[1655,93419,2623],{},[3615,93421,93422],{"scriptlevel":2552,"displaystyle":1663},[1949,93423,93424,93432],{},[1935,93425,93426,93428,93430],{},[898,93427,900],{},[1826,93429,1828],{},[1655,93431,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1935,93433,93434,93436,93438],{},[898,93435,900],{},[1826,93437,1837],{},[1655,93439,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,93441,93442],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,93445,93447],{"className":93446},[886],[888,93448,93449],{"xmlns":890},[892,93450,93451,93473],{},[895,93452,93453,93459,93461,93463,93465,93471],{},[1820,93454,93455,93457],{},[898,93456,1824],{},[1826,93458,1837],{},[1655,93460,1657],{},[898,93462,1660],{},[1655,93464,1664],{"stretchy":1663},[1820,93466,93467,93469],{},[898,93468,1824],{},[1826,93470,1828],{},[1655,93472,1677],{"stretchy":1663},[902,93474,93475],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,93478,93480],{"className":93479},[886],[888,93481,93482],{"xmlns":890},[892,93483,93484,93510],{},[895,93485,93486,93488,93490,93496,93498,93504,93506,93508],{},[898,93487,900],{},[1655,93489,1664],{"stretchy":1663},[1820,93491,93492,93494],{},[898,93493,1824],{},[1826,93495,1828],{},[1655,93497,1671],{"separator":1670},[1820,93499,93500,93502],{},[898,93501,1824],{},[1826,93503,1837],{},[1655,93505,1677],{"stretchy":1663},[1655,93507,1657],{},[898,93509,1789],{},[902,93511,1846],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,93514,93516],{"className":93515},[886],[888,93517,93518],{"xmlns":890},[892,93519,93520,93524],{},[895,93521,93522],{},[2031,93523,2708],{},[902,93525,29364],{"encoding":904}," chápeme jako velikost kompenzace.",[5120,93528,93529],{},[724,93530,93531,93533,93534,9349,93566,93604,93605,93622,93623,93640],{},[883,93532,5406],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,93535,93537],{"className":93536},[886],[888,93538,93539],{"xmlns":890},[892,93540,93541,93563],{},[895,93542,93543,93545,93547,93553,93555,93561],{},[2031,93544,2708],{},[1655,93546,1664],{"stretchy":1663},[1820,93548,93549,93551],{},[898,93550,1824],{},[1826,93552,1828],{},[1655,93554,1671],{"separator":1670},[1820,93556,93557,93559],{},[898,93558,1824],{},[1826,93560,1837],{},[1655,93562,1677],{"stretchy":1663},[902,93564,93565],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,93567,93568,93569,30129,93586,93603],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,93570,93572],{"className":93571},[886],[888,93573,93574],{"xmlns":890},[892,93575,93576,93584],{},[895,93577,93578],{},[1820,93579,93580,93582],{},[898,93581,1824],{},[1826,93583,1828],{},[902,93585,30128],{"encoding":904},[883,93587,93589],{"className":93588},[886],[888,93590,93591],{"xmlns":890},[892,93592,93593,93601],{},[895,93594,93595],{},[1820,93596,93597,93599],{},[898,93598,1824],{},[1826,93600,1837],{},[902,93602,30147],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,93606,93608],{"className":93607},[886],[888,93609,93610],{"xmlns":890},[892,93611,93612,93620],{},[895,93613,93614],{},[1820,93615,93616,93618],{},[898,93617,1824],{},[1826,93619,1837],{},[902,93621,30147],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,93624,93626],{"className":93625},[886],[888,93627,93628],{"xmlns":890},[892,93629,93630,93638],{},[895,93631,93632],{},[1820,93633,93634,93636],{},[898,93635,1824],{},[1826,93637,1828],{},[902,93639,30128],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,93642,93643,93644,31070],{},"Pro obecnou změnu ",[883,93645,93647],{"className":93646},[886],[888,93648,93649],{"xmlns":890},[892,93650,93651,93661],{},[895,93652,93653,93655],{},[898,93654,2410],{"mathvariant":1943},[1820,93656,93657,93659],{},[898,93658,1824],{},[1826,93660,1828],{},[902,93662,93663],{"encoding":904},"\\mathrm{d} Q_1",[883,93665,93667],{"className":93666},[886],[888,93668,93669],{"xmlns":890,"display":29192},[892,93670,93671,93724],{},[21880,93672,93673],{"width":29197},[21885,93674,93675,93677,93717,93719],{},[21888,93676],{"width":29202},[21888,93678,93679],{},[895,93680,93681,93683,93689,93691,93693,93699,93701,93703,93705,93707,93709,93715],{},[898,93682,2506],{"mathvariant":1943},[1820,93684,93685,93687],{},[898,93686,1824],{},[1826,93688,1837],{},[1655,93690,2357],{},[898,93692,2410],{"mathvariant":1943},[1820,93694,93695,93697],{},[898,93696,1824],{},[1826,93698,1837],{},[1655,93700,1657],{},[1655,93702,2623],{},[2031,93704,2708],{},[1655,93706,2869],{},[898,93708,2410],{"mathvariant":1943},[1820,93710,93711,93713],{},[898,93712,1824],{},[1826,93714,1828],{},[1655,93716,1671],{"separator":1670},[21888,93718],{"width":29202},[21888,93720,93721],{},[2031,93722,93723],{},"(6.10)",[902,93725,93726],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,93728,93730],{"className":93729},[886],[888,93731,93732],{"xmlns":890,"display":29192},[892,93733,93734,93781],{},[21880,93735,93736],{"width":29197},[21885,93737,93738,93740,93774,93776],{},[21888,93739],{"width":29202},[21888,93741,93742],{},[895,93743,93744,93746,93752,93754,93756,93762,93764,93766,93772],{},[898,93745,2410],{"mathvariant":1943},[1820,93747,93748,93750],{},[898,93749,1824],{},[1826,93751,1828],{},[1655,93753,1657],{},[1655,93755,2623],{},[1949,93757,93758,93760],{},[1826,93759,1828],{},[2031,93761,2708],{},[2031,93763,2435],{},[898,93765,2410],{"mathvariant":1943},[1820,93767,93768,93770],{},[898,93769,1824],{},[1826,93771,1837],{},[898,93773,1719],{"mathvariant":1943},[21888,93775],{"width":29202},[21888,93777,93778],{},[2031,93779,93780],{},"(6.11)",[902,93782,93783],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[5120,93785,93786,93852,93969],{},[724,93787,93788,93790,93791,31070],{},[883,93789,53821],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,93792,93794],{"className":93793},[886],[888,93795,93796],{"xmlns":890},[892,93797,93798,93850],{},[895,93799,93800,93802,93804,93810,93812,93818,93820,93822,93836],{},[898,93801,900],{},[1655,93803,1664],{"stretchy":1663},[1820,93805,93806,93808],{},[898,93807,1824],{},[1826,93809,1828],{},[1655,93811,1671],{"separator":1670},[1820,93813,93814,93816],{},[898,93815,1824],{},[1826,93817,1837],{},[1655,93819,1677],{"stretchy":1663},[1655,93821,1657],{},[1935,93823,93824,93826,93828],{},[898,93825,1824],{},[1826,93827,1828],{},[895,93829,93830,93832,93834],{},[1826,93831,1828],{},[898,93833,5923],{"mathvariant":1943},[1826,93835,1837],{},[1935,93837,93838,93840,93842],{},[898,93839,1824],{},[1826,93841,1837],{},[895,93843,93844,93846,93848],{},[1826,93845,1828],{},[898,93847,5923],{"mathvariant":1943},[1826,93849,1837],{},[902,93851,31069],{"encoding":904},[724,93853,93854],{},[883,93855,93857],{"className":93856},[886],[888,93858,93859],{"xmlns":890},[892,93860,93861,93967],{},[895,93862,93863,93865,93867,93949,93951,93965],{},[2031,93864,2708],{},[1655,93866,1657],{},[1949,93868,93869,93909],{},[895,93870,93871,93879,93895],{},[3615,93872,93873],{"scriptlevel":2552,"displaystyle":1663},[1949,93874,93875,93877],{},[1826,93876,1828],{},[1826,93878,1837],{},[1935,93880,93881,93883,93885],{},[898,93882,1824],{},[1826,93884,1828],{},[895,93886,93887,93889,93891,93893],{},[1655,93888,2623],{},[1826,93890,1828],{},[898,93892,5923],{"mathvariant":1943},[1826,93894,1837],{},[1935,93896,93897,93899,93901],{},[898,93898,1824],{},[1826,93900,1837],{},[895,93902,93903,93905,93907],{},[1826,93904,1828],{},[898,93906,5923],{"mathvariant":1943},[1826,93908,1837],{},[895,93910,93911,93919,93933],{},[3615,93912,93913],{"scriptlevel":2552,"displaystyle":1663},[1949,93914,93915,93917],{},[1826,93916,1828],{},[1826,93918,1837],{},[1935,93920,93921,93923,93925],{},[898,93922,1824],{},[1826,93924,1828],{},[895,93926,93927,93929,93931],{},[1826,93928,1828],{},[898,93930,5923],{"mathvariant":1943},[1826,93932,1837],{},[1935,93934,93935,93937,93939],{},[898,93936,1824],{},[1826,93938,1837],{},[895,93940,93941,93943,93945,93947],{},[1655,93942,2623],{},[1826,93944,1828],{},[898,93946,5923],{"mathvariant":1943},[1826,93948,1837],{},[1655,93950,1657],{},[1949,93952,93953,93959],{},[1820,93954,93955,93957],{},[898,93956,1824],{},[1826,93958,1837],{},[1820,93960,93961,93963],{},[898,93962,1824],{},[1826,93964,1828],{},[898,93966,1719],{"mathvariant":1943},[902,93968,31188],{"encoding":904},[724,93970,31191,93971,4199,94014,31239,94016,94035],{},[883,93972,93974],{"className":93973},[886],[888,93975,93976],{"xmlns":890},[892,93977,93978,94012],{},[895,93979,93980,93982,93984,93986,93988,93990,93992,93994,94002,94004],{},[2031,93981,2708],{},[1655,93983,1664],{"stretchy":1663},[1826,93985,31207],{},[1655,93987,1671],{"separator":1670},[1826,93989,16235],{},[1655,93991,1677],{"stretchy":1663},[1655,93993,1657],{},[3615,93995,93996],{"scriptlevel":2552,"displaystyle":1663},[1949,93997,93998,94000],{},[1826,93999,16235],{},[1826,94001,31207],{},[1655,94003,1657],{},[3615,94005,94006],{"scriptlevel":2552,"displaystyle":1663},[1949,94007,94008,94010],{},[1826,94009,3524],{},[1826,94011,3472],{},[902,94013,31236],{"encoding":904},[614,94015,10462],{},[883,94017,94019],{"className":94018},[886],[888,94020,94021],{"xmlns":890},[892,94022,94023,94033],{},[895,94024,94025],{},[3615,94026,94027],{"scriptlevel":2552,"displaystyle":1663},[1949,94028,94029,94031],{},[1826,94030,3524],{},[1826,94032,3472],{},[902,94034,31259],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,94037,94038,94039,94043],{},"(Paralelou je ",[207,94040,94042],{"className":94041,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,94045,94047],{"id":94046},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,94049,94050,94051,94054],{},"Rámcově se v kapitole 6 studují ",[38,94052,94053],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,94056,94057,94193],{},[123,94058,94059,94061,94062,2251,94093,3106,94096,94145,94146,1719],{},[38,94060,29378],{}," — maximalizace ",[883,94063,94065],{"className":94064},[886],[888,94066,94067],{"xmlns":890},[892,94068,94069,94091],{},[895,94070,94071,94073,94075,94081,94083,94089],{},[898,94072,900],{},[1655,94074,1664],{"stretchy":1663},[1820,94076,94077,94079],{},[898,94078,1824],{},[1826,94080,1828],{},[1655,94082,1671],{"separator":1670},[1820,94084,94085,94087],{},[898,94086,1824],{},[1826,94088,1837],{},[1655,94090,1677],{"stretchy":1663},[902,94092,17469],{"encoding":904},[38,94094,94095],{},"rozpočtovém omezení",[883,94097,94099],{"className":94098},[886],[888,94100,94101],{"xmlns":890},[892,94102,94103,94143],{},[895,94104,94105,94111,94113,94121,94127,94129,94137],{},[2597,94106,94107,94109],{},[898,94108,10375],{},[1655,94110,5603],{},[1655,94112,1657],{},[1935,94114,94115,94117,94119],{},[898,94116,2132],{},[1826,94118,1828],{},[1655,94120,5603],{},[1820,94122,94123,94125],{},[898,94124,1824],{},[1826,94126,1828],{},[1655,94128,2346],{},[1935,94130,94131,94133,94135],{},[898,94132,2132],{},[1826,94134,1837],{},[1655,94136,5603],{},[1820,94138,94139,94141],{},[898,94140,1824],{},[1826,94142,1837],{},[902,94144,18424],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,94147,94149],{"className":94148},[886],[888,94150,94151],{"xmlns":890},[892,94152,94153,94191],{},[895,94154,94155,94161,94163,94169,94171,94177,94179,94185,94187,94189],{},[1820,94156,94157,94159],{},[898,94158,1824],{},[898,94160,18916],{},[1655,94162,1657],{},[1820,94164,94165,94167],{},[898,94166,2838],{},[898,94168,18916],{},[1655,94170,1664],{"stretchy":1663},[1820,94172,94173,94175],{},[898,94174,2132],{},[1826,94176,1828],{},[1655,94178,1671],{"separator":1670},[1820,94180,94181,94183],{},[898,94182,2132],{},[1826,94184,1837],{},[1655,94186,1671],{"separator":1670},[898,94188,10375],{},[1655,94190,1677],{"stretchy":1663},[902,94192,37581],{"encoding":904},[123,94194,94195,29027,94198,29070,94244,94261,94262,1719],{},[38,94196,94197],{},"Duální úloha",[883,94199,94201],{"className":94200},[886],[888,94202,94203],{"xmlns":890},[892,94204,94205,94241],{},[895,94206,94207,94209,94211,94219,94225,94227,94235],{},[898,94208,5502],{},[1655,94210,1657],{},[1935,94212,94213,94215,94217],{},[898,94214,2132],{},[1826,94216,1828],{},[1655,94218,5603],{},[1820,94220,94221,94223],{},[898,94222,1824],{},[1826,94224,1828],{},[1655,94226,2346],{},[1935,94228,94229,94231,94233],{},[898,94230,2132],{},[1826,94232,1837],{},[1655,94234,5603],{},[1820,94236,94237,94239],{},[898,94238,1824],{},[1826,94240,1837],{},[902,94242,94243],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,94245,94247],{"className":94246},[886],[888,94248,94249],{"xmlns":890},[892,94250,94251,94259],{},[895,94252,94253],{},[2597,94254,94255,94257],{},[898,94256,900],{},[1655,94258,5603],{},[902,94260,29088],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,94263,94265],{"className":94264},[886],[888,94266,94267],{"xmlns":890},[892,94268,94269,94307],{},[895,94270,94271,94277,94279,94285,94287,94293,94295,94301,94303,94305],{},[1820,94272,94273,94275],{},[898,94274,1824],{},[898,94276,18916],{},[1655,94278,1657],{},[1820,94280,94281,94283],{},[898,94282,2838],{},[898,94284,18916],{},[1655,94286,1664],{"stretchy":1663},[1820,94288,94289,94291],{},[898,94290,2132],{},[1826,94292,1828],{},[1655,94294,1671],{"separator":1670},[1820,94296,94297,94299],{},[898,94298,2132],{},[1826,94300,1837],{},[1655,94302,1671],{"separator":1670},[898,94304,900],{},[1655,94306,1677],{"stretchy":1663},[902,94308,18949],{"encoding":904},[724,94310,94311,94312,94315,94316,3106,94319,94358],{},"Obě úlohy se řeší ",[207,94313,29093],{"className":94314,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,94317,94318],{},"tentýž bod dotyku",[883,94320,94322],{"className":94321},[886],[888,94323,94324],{"xmlns":890},[892,94325,94326,94356],{},[895,94327,94328,94334,94336,94344,94346,94354],{},[2597,94329,94330,94332],{},[898,94331,1824],{},[1655,94333,5603],{},[1655,94335,2734],{"stretchy":1663},[1935,94337,94338,94340,94342],{},[898,94339,1824],{},[1826,94341,1828],{},[1655,94343,5603],{},[1655,94345,1671],{"separator":1670},[1935,94347,94348,94350,94352],{},[898,94349,1824],{},[1826,94351,1837],{},[1655,94353,5603],{},[1655,94355,2743],{"stretchy":1663},[902,94357,29453],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,94360,94362],{"className":94361},[886],[888,94363,94364],{"xmlns":890,"display":29192},[892,94365,94366,94412],{},[895,94367,94368,94370,94372,94390,94392,94410],{},[2031,94369,2708],{},[1655,94371,1657],{},[1949,94373,94374,94382],{},[1935,94375,94376,94378,94380],{},[898,94377,900],{},[1826,94379,1828],{},[1655,94381,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1935,94383,94384,94386,94388],{},[898,94385,900],{},[1826,94387,1837],{},[1655,94389,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,94391,1657],{},[1949,94393,94394,94402],{},[1935,94395,94396,94398,94400],{},[898,94397,2132],{},[1826,94399,1828],{},[1655,94401,5603],{},[1935,94403,94404,94406,94408],{},[898,94405,2132],{},[1826,94407,1837],{},[1655,94409,5603],{},[898,94411,1719],{"mathvariant":1943},[902,94413,94414],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,94416,94417],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[5120,94419,94420],{},[724,94421,94422,94424,94425,94428,94429,94432,94433,94460,94461,94495,94496,94530,94531,94574,94575,94578,94579,1719],{},[883,94423,5406],{}," Pro detailní postup viz ",[207,94426,37880],{"className":94427,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,94430,94431],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,94434,94436],{"className":94435},[886],[888,94437,94438],{"xmlns":890},[892,94439,94440,94458],{},[895,94441,94442,94444,94446,94452],{},[898,94443,900],{},[1655,94445,1657],{},[1820,94447,94448,94450],{},[898,94449,1824],{},[1826,94451,1828],{},[1820,94453,94454,94456],{},[898,94455,1824],{},[1826,94457,1837],{},[902,94459,31352],{"encoding":904}," s výsledkem ",[883,94462,94464],{"className":94463},[886],[888,94465,94466],{"xmlns":890},[892,94467,94468,94492],{},[895,94469,94470,94476,94478,94480,94482,94488,94490],{},[1820,94471,94472,94474],{},[898,94473,1824],{},[1826,94475,1828],{},[1655,94477,1657],{},[1826,94479,6253],{},[1655,94481,1671],{"separator":1670},[1820,94483,94484,94486],{},[898,94485,1824],{},[1826,94487,1837],{},[1655,94489,1657],{},[1826,94491,4136],{},[902,94493,94494],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,94497,94499],{"className":94498},[886],[888,94500,94501],{"xmlns":890},[892,94502,94503,94527],{},[895,94504,94505,94511,94513,94515,94517,94523,94525],{},[1820,94506,94507,94509],{},[898,94508,1824],{},[1826,94510,1828],{},[1655,94512,1657],{},[1826,94514,3639],{},[1655,94516,1671],{"separator":1670},[1820,94518,94519,94521],{},[898,94520,1824],{},[1826,94522,1837],{},[1655,94524,1657],{},[1826,94526,1828],{},[902,94528,94529],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,94532,94534],{"className":94533},[886],[888,94535,94536],{"xmlns":890},[892,94537,94538,94572],{},[895,94539,94540,94542,94544,94558],{},[898,94541,900],{},[1655,94543,1657],{},[1935,94545,94546,94548,94550],{},[898,94547,1824],{},[1826,94549,1828],{},[895,94551,94552,94554,94556],{},[1826,94553,1828],{},[898,94555,5923],{"mathvariant":1943},[1826,94557,1837],{},[1935,94559,94560,94562,94564],{},[898,94561,1824],{},[1826,94563,1837],{},[895,94565,94566,94568,94570],{},[1826,94567,1828],{},[898,94569,5923],{"mathvariant":1943},[1826,94571,1837],{},[902,94573,34285],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,94576,94577],{},"6.8–6.13"," jsou na stránce ",[207,94580,28893],{"className":94581,"dataFsResolvedFilePath":911,"href":912},[210],[115,94583,94585],{"id":94584},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,94587,94588,94589,94602,94603,94605,94606,94608,94609,94611,94612,94614,94615,94617,94618,94620,94621,3106,94623,94658,94659,94672,94673,94676,94677,94680,94681,1719],{},"Každá ",[883,94590,94592],{"className":94591},[886],[888,94593,94594],{"xmlns":890},[892,94595,94596,94600],{},[895,94597,94598],{},[898,94599,37986],{},[902,94601,37986],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,94604,87936],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,94607,88420],{}," a současně ",[38,94610,87939],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,94613,87944],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,94616,53803],{}," (6.4) a druhé parciální derivace ",[38,94619,90303],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,94622,1804],{},[883,94624,94626],{"className":94625},[886],[888,94627,94628],{"xmlns":890},[892,94629,94630,94656],{},[895,94631,94632,94634,94636,94642,94644,94650,94652,94654],{},[898,94633,900],{},[1655,94635,1664],{"stretchy":1663},[1820,94637,94638,94640],{},[898,94639,1824],{},[1826,94641,1828],{},[1655,94643,1671],{"separator":1670},[1820,94645,94646,94648],{},[898,94647,1824],{},[1826,94649,1837],{},[1655,94651,1677],{"stretchy":1663},[1655,94653,1657],{},[898,94655,1789],{},[902,94657,1846],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,94660,94662],{"className":94661},[886],[888,94663,94664],{"xmlns":890},[892,94665,94666,94670],{},[895,94667,94668],{},[2031,94669,2708],{},[902,94671,29364],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,94674,94675],{},"maximalizace užitečnosti"," a duální ",[38,94678,94679],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,94682,37880],{"className":94683,"dataFsResolvedFilePath":911,"href":912},[210],[115,94685,51008],{"id":51007},[152,94687,94688,94691,94694,94697,94700,94703,94706,94709,94712,94715],{},[123,94689,94690],{},"Co se zahrnuje pod termín užitečnost?",[123,94692,94693],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,94695,94696],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,94698,94699],{},"Jak se vypočítá mezní užitečnost?",[123,94701,94702],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,94704,94705],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,94707,94708],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,94710,94711],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,94713,94714],{},"Proč mají křivky užitečnosti záporný sklon?",[123,94716,94717],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,94719,94721],{"id":94720},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,94723,94724,94727,94728,84609,94770,1343,94798,1343,94826,94854],{},[38,94725,94726],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,94729,94731],{"className":94730},[886],[888,94732,94733],{"xmlns":890},[892,94734,94735,94767],{},[895,94736,94737,94739,94741,94747,94749,94751,94757,94759,94761],{},[898,94738,900],{},[1655,94740,1657],{},[1820,94742,94743,94745],{},[898,94744,1824],{},[1826,94746,1828],{},[1655,94748,2346],{},[1826,94750,65685],{},[1820,94752,94753,94755],{},[898,94754,1824],{},[1826,94756,1837],{},[1655,94758,2346],{},[1826,94760,1837],{},[1820,94762,94763,94765],{},[898,94764,1824],{},[1826,94766,3472],{},[902,94768,94769],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,94771,94773],{"className":94772},[886],[888,94774,94775],{"xmlns":890},[892,94776,94777,94795],{},[895,94778,94779,94781,94783,94785,94787,94789,94791,94793],{},[898,94780,900],{},[1655,94782,1664],{"stretchy":1663},[1826,94784,3639],{},[1655,94786,1671],{"separator":1670},[1826,94788,1837],{},[1655,94790,1671],{"separator":1670},[1826,94792,1837],{},[1655,94794,1677],{"stretchy":1663},[902,94796,94797],{"encoding":904},"U(4, 2, 2)",[883,94799,94801],{"className":94800},[886],[888,94802,94803],{"xmlns":890},[892,94804,94805,94823],{},[895,94806,94807,94809,94811,94813,94815,94817,94819,94821],{},[898,94808,900],{},[1655,94810,1664],{"stretchy":1663},[1826,94812,1828],{},[1655,94814,1671],{"separator":1670},[1826,94816,3639],{},[1655,94818,1671],{"separator":1670},[1826,94820,1837],{},[1655,94822,1677],{"stretchy":1663},[902,94824,94825],{"encoding":904},"U(1, 4, 2)",[883,94827,94829],{"className":94828},[886],[888,94830,94831],{"xmlns":890},[892,94832,94833,94851],{},[895,94834,94835,94837,94839,94841,94843,94845,94847,94849],{},[898,94836,900],{},[1655,94838,1664],{"stretchy":1663},[1826,94840,1837],{},[1655,94842,1671],{"separator":1670},[1826,94844,3472],{},[1655,94846,1671],{"separator":1670},[1826,94848,1828],{},[1655,94850,1677],{"stretchy":1663},[902,94852,94853],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,94856,94857,94860,94861,94913,94914,1343,94940,1343,94966,1343,94992,1343,95018,1343,95044,1343,95070,95096],{},[38,94858,94859],{},"6.2"," Je dána užitečnost ",[883,94862,94864],{"className":94863},[886],[888,94865,94866],{"xmlns":890},[892,94867,94868,94910],{},[895,94869,94870,94872,94874,94876,94890,94904],{},[898,94871,900],{},[1655,94873,1657],{},[1826,94875,1837],{},[1935,94877,94878,94880,94882],{},[898,94879,1824],{},[1826,94881,1828],{},[895,94883,94884,94886,94888],{},[1826,94885,1828],{},[898,94887,5923],{"mathvariant":1943},[1826,94889,3472],{},[1935,94891,94892,94894,94896],{},[898,94893,1824],{},[1826,94895,1837],{},[895,94897,94898,94900,94902],{},[1826,94899,1828],{},[898,94901,5923],{"mathvariant":1943},[1826,94903,1837],{},[1820,94905,94906,94908],{},[898,94907,1824],{},[1826,94909,3472],{},[902,94911,94912],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,94915,94917],{"className":94916},[886],[888,94918,94919],{"xmlns":890},[892,94920,94921,94937],{},[895,94922,94923,94925,94927,94929,94931,94933,94935],{},[1655,94924,1664],{"stretchy":1663},[1826,94926,6814],{},[1655,94928,1671],{"separator":1670},[1826,94930,67723],{},[1655,94932,1671],{"separator":1670},[1826,94934,4136],{},[1655,94936,1677],{"stretchy":1663},[902,94938,94939],{"encoding":904},"(36, 27, 10)",[883,94941,94943],{"className":94942},[886],[888,94944,94945],{"xmlns":890},[892,94946,94947,94963],{},[895,94948,94949,94951,94953,94955,94957,94959,94961],{},[1655,94950,1664],{"stretchy":1663},[1826,94952,42966],{},[1655,94954,1671],{"separator":1670},[1826,94956,6834],{},[1655,94958,1671],{"separator":1670},[1826,94960,10282],{},[1655,94962,1677],{"stretchy":1663},[902,94964,94965],{"encoding":904},"(64, 8, 20)",[883,94967,94969],{"className":94968},[886],[888,94970,94971],{"xmlns":890},[892,94972,94973,94989],{},[895,94974,94975,94977,94979,94981,94983,94985,94987],{},[1655,94976,1664],{"stretchy":1663},[1826,94978,6253],{},[1655,94980,1671],{"separator":1670},[1826,94982,42966],{},[1655,94984,1671],{"separator":1670},[1826,94986,6834],{},[1655,94988,1677],{"stretchy":1663},[902,94990,94991],{"encoding":904},"(25, 64, 8)",[883,94993,94995],{"className":94994},[886],[888,94996,94997],{"xmlns":890},[892,94998,94999,95015],{},[895,95000,95001,95003,95005,95007,95009,95011,95013],{},[1655,95002,1664],{"stretchy":1663},[1826,95004,3639],{},[1655,95006,1671],{"separator":1670},[1826,95008,73655],{},[1655,95010,1671],{"separator":1670},[1826,95012,3531],{},[1655,95014,1677],{"stretchy":1663},[902,95016,95017],{"encoding":904},"(4, 125, 6)",[883,95019,95021],{"className":95020},[886],[888,95022,95023],{"xmlns":890},[892,95024,95025,95041],{},[895,95026,95027,95029,95031,95033,95035,95037,95039],{},[1655,95028,1664],{"stretchy":1663},[1826,95030,5250],{},[1655,95032,1671],{"separator":1670},[1826,95034,6460],{},[1655,95036,1671],{"separator":1670},[1826,95038,4771],{},[1655,95040,1677],{"stretchy":1663},[902,95042,95043],{"encoding":904},"(9, 40, 12)",[883,95045,95047],{"className":95046},[886],[888,95048,95049],{"xmlns":890},[892,95050,95051,95067],{},[895,95052,95053,95055,95057,95059,95061,95063,95065],{},[1655,95054,1664],{"stretchy":1663},[1826,95056,5250],{},[1655,95058,1671],{"separator":1670},[1826,95060,42966],{},[1655,95062,1671],{"separator":1670},[1826,95064,3524],{},[1655,95066,1677],{"stretchy":1663},[902,95068,95069],{"encoding":904},"(9, 64, 5)",[883,95071,95073],{"className":95072},[886],[888,95074,95075],{"xmlns":890},[892,95076,95077,95093],{},[895,95078,95079,95081,95083,95085,95087,95089,95091],{},[1655,95080,1664],{"stretchy":1663},[1826,95082,42966],{},[1655,95084,1671],{"separator":1670},[1826,95086,6834],{},[1655,95088,1671],{"separator":1670},[1826,95090,4136],{},[1655,95092,1677],{"stretchy":1663},[902,95094,95095],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,95098,95099,94860,95102,95145,95146,95180,95181,7720,95211,95244,95245,95262,95263,95280],{},[38,95100,95101],{},"6.3",[883,95103,95105],{"className":95104},[886],[888,95106,95107],{"xmlns":890},[892,95108,95109,95143],{},[895,95110,95111,95113,95115,95129],{},[898,95112,900],{},[1655,95114,1657],{},[1935,95116,95117,95119,95121],{},[898,95118,1824],{},[1826,95120,1828],{},[895,95122,95123,95125,95127],{},[1826,95124,1828],{},[898,95126,5923],{"mathvariant":1943},[1826,95128,1837],{},[1935,95130,95131,95133,95135],{},[898,95132,1824],{},[1826,95134,1837],{},[895,95136,95137,95139,95141],{},[1826,95138,1828],{},[898,95140,5923],{"mathvariant":1943},[1826,95142,1837],{},[902,95144,34285],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,95147,95149],{"className":95148},[886],[888,95150,95151],{"xmlns":890},[892,95152,95153,95177],{},[895,95154,95155,95161,95163,95165,95167,95173,95175],{},[1820,95156,95157,95159],{},[898,95158,1824],{},[1826,95160,1828],{},[1655,95162,1657],{},[1826,95164,4390],{},[1655,95166,1671],{"separator":1670},[1820,95168,95169,95171],{},[898,95170,1824],{},[1826,95172,1837],{},[1655,95174,1657],{},[1826,95176,47829],{},[902,95178,95179],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,95182,95184],{"className":95183},[886],[888,95185,95186],{"xmlns":890},[892,95187,95188,95208],{},[895,95189,95190,95192,95198,95200,95202],{},[898,95191,2127],{},[1820,95193,95194,95196],{},[898,95195,900],{},[1826,95197,1828],{},[1655,95199,1671],{"separator":1670},[898,95201,2127],{},[1820,95203,95204,95206],{},[898,95205,900],{},[1826,95207,1837],{},[902,95209,95210],{"encoding":904},"MU_1, MU_2",[883,95212,95214],{"className":95213},[886],[888,95215,95216],{"xmlns":890},[892,95217,95218,95242],{},[895,95219,95220,95226,95228,95230,95232,95238,95240],{},[1820,95221,95222,95224],{},[898,95223,1824],{},[1826,95225,1828],{},[1655,95227,1657],{},[1826,95229,4390],{},[1655,95231,1671],{"separator":1670},[1820,95233,95234,95236],{},[898,95235,1824],{},[1826,95237,1837],{},[1655,95239,1657],{},[1826,95241,47829],{},[902,95243,95179],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,95246,95248],{"className":95247},[886],[888,95249,95250],{"xmlns":890},[892,95251,95252,95260],{},[895,95253,95254],{},[1820,95255,95256,95258],{},[898,95257,1824],{},[1826,95259,1828],{},[902,95261,30128],{"encoding":904}," na 60 a poklesu ",[883,95264,95266],{"className":95265},[886],[888,95267,95268],{"xmlns":890},[892,95269,95270,95278],{},[895,95271,95272],{},[1820,95273,95274,95276],{},[898,95275,1824],{},[1826,95277,1837],{},[902,95279,30147],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,95282,95283,95286,95287,95348,95349,1719],{},[38,95284,95285],{},"6.4"," Je dána funkce ",[883,95288,95290],{"className":95289},[886],[888,95291,95292],{"xmlns":890},[892,95293,95294,95346],{},[895,95295,95296,95298,95300,95306,95308,95314,95316,95318,95332],{},[898,95297,900],{},[1655,95299,1664],{"stretchy":1663},[1820,95301,95302,95304],{},[898,95303,1824],{},[1826,95305,1828],{},[1655,95307,1671],{"separator":1670},[1820,95309,95310,95312],{},[898,95311,1824],{},[1826,95313,1837],{},[1655,95315,1677],{"stretchy":1663},[1655,95317,1657],{},[1935,95319,95320,95322,95324],{},[898,95321,1824],{},[1826,95323,1828],{},[895,95325,95326,95328,95330],{},[1826,95327,1828],{},[898,95329,5923],{"mathvariant":1943},[1826,95331,1837],{},[1935,95333,95334,95336,95338],{},[898,95335,1824],{},[1826,95337,1837],{},[895,95339,95340,95342,95344],{},[1826,95341,1828],{},[898,95343,5923],{"mathvariant":1943},[1826,95345,1837],{},[902,95347,31069],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,95350,95352],{"className":95351},[886],[888,95353,95354],{"xmlns":890},[892,95355,95356,95446],{},[895,95357,95358,95360,95362,95368,95370,95372,95374,95376,95378,95380,95386,95388,95390,95392,95394,95396,95398,95400,95402,95408,95410,95412,95414,95416,95418,95420,95426,95428,95430,95432,95434,95436,95438,95444],{},[898,95359,900],{},[1655,95361,1664],{"stretchy":1663},[1820,95363,95364,95366],{},[898,95365,1824],{},[1826,95367,1828],{},[1655,95369,1671],{"separator":1670},[1826,95371,1828],{},[1655,95373,1677],{"stretchy":1663},[1655,95375,1671],{"separator":1670},[898,95377,900],{},[1655,95379,1664],{"stretchy":1663},[1820,95381,95382,95384],{},[898,95383,1824],{},[1826,95385,1828],{},[1655,95387,1671],{"separator":1670},[1826,95389,1837],{},[1655,95391,1677],{"stretchy":1663},[1655,95393,1671],{"separator":1670},[898,95395,900],{},[1655,95397,1664],{"stretchy":1663},[1826,95399,1828],{},[1655,95401,1671],{"separator":1670},[1820,95403,95404,95406],{},[898,95405,1824],{},[1826,95407,1837],{},[1655,95409,1677],{"stretchy":1663},[1655,95411,1671],{"separator":1670},[898,95413,900],{},[1655,95415,1664],{"stretchy":1663},[1826,95417,1837],{},[1655,95419,1671],{"separator":1670},[1820,95421,95422,95424],{},[898,95423,1824],{},[1826,95425,1837],{},[1655,95427,1677],{"stretchy":1663},[1655,95429,1671],{"separator":1670},[898,95431,900],{},[1655,95433,1664],{"stretchy":1663},[1826,95435,3472],{},[1655,95437,1671],{"separator":1670},[1820,95439,95440,95442],{},[898,95441,1824],{},[1826,95443,1837],{},[1655,95445,1677],{"stretchy":1663},[902,95447,95448],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,95450,95451,94860,95454,95498,95499,95607,95608,1343,95633,1343,95658,95700,95701,1343,95730,95755],{},[38,95452,95453],{},"6.5",[883,95455,95457],{"className":95456},[886],[888,95458,95459],{"xmlns":890},[892,95460,95461,95495],{},[895,95462,95463,95465,95467,95481],{},[898,95464,900],{},[1655,95466,1657],{},[1935,95468,95469,95471,95473],{},[898,95470,1824],{},[1826,95472,1828],{},[895,95474,95475,95477,95479],{},[1826,95476,1837],{},[898,95478,5923],{"mathvariant":1943},[1826,95480,3472],{},[1935,95482,95483,95485,95487],{},[898,95484,1824],{},[1826,95486,1837],{},[895,95488,95489,95491,95493],{},[1826,95490,1828],{},[898,95492,5923],{"mathvariant":1943},[1826,95494,3472],{},[902,95496,95497],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,95500,95502],{"className":95501},[886],[888,95503,95504],{"xmlns":890},[892,95505,95506,95604],{},[895,95507,95508,95510,95512,95518,95520,95526,95528,95530,95532,95534,95536,95538,95544,95546,95548,95550,95552,95554,95556,95562,95564,95566,95568,95570,95572,95574,95576,95578,95584,95586,95588,95590,95592,95594,95596,95602],{},[898,95509,900],{},[1655,95511,1664],{"stretchy":1663},[1820,95513,95514,95516],{},[898,95515,1824],{},[1826,95517,1828],{},[1655,95519,1671],{"separator":1670},[1820,95521,95522,95524],{},[898,95523,1824],{},[1826,95525,1837],{},[1655,95527,1677],{"stretchy":1663},[1655,95529,1657],{},[1826,95531,1837],{},[1655,95533,1671],{"separator":1670},[898,95535,900],{},[1655,95537,1664],{"stretchy":1663},[1820,95539,95540,95542],{},[898,95541,1824],{},[1826,95543,1828],{},[1655,95545,1671],{"separator":1670},[1826,95547,3472],{},[1655,95549,1677],{"stretchy":1663},[1655,95551,1671],{"separator":1670},[898,95553,900],{},[1655,95555,1664],{"stretchy":1663},[1820,95557,95558,95560],{},[898,95559,1824],{},[1826,95561,1828],{},[1655,95563,1671],{"separator":1670},[1826,95565,1837],{},[1655,95567,1677],{"stretchy":1663},[1655,95569,1671],{"separator":1670},[898,95571,900],{},[1655,95573,1664],{"stretchy":1663},[1826,95575,1837],{},[1655,95577,1671],{"separator":1670},[1820,95579,95580,95582],{},[898,95581,1824],{},[1826,95583,1837],{},[1655,95585,1677],{"stretchy":1663},[1655,95587,1671],{"separator":1670},[898,95589,900],{},[1655,95591,1664],{"stretchy":1663},[1826,95593,3472],{},[1655,95595,1671],{"separator":1670},[1820,95597,95598,95600],{},[898,95599,1824],{},[1826,95601,1837],{},[1655,95603,1677],{"stretchy":1663},[902,95605,95606],{"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 ",[883,95609,95611],{"className":95610},[886],[888,95612,95613],{"xmlns":890},[892,95614,95615,95630],{},[895,95616,95617,95619,95621,95623,95625,95628],{},[898,95618,2731],{},[1655,95620,2734],{"stretchy":1663},[1826,95622,65685],{},[1655,95624,9672],{"separator":1670},[1826,95626,95627],{},"3,555",[1655,95629,2743],{"stretchy":1663},[902,95631,95632],{"encoding":904},"A[1{,}5; 3{,}555]",[883,95634,95636],{"className":95635},[886],[888,95637,95638],{"xmlns":890},[892,95639,95640,95655],{},[895,95641,95642,95644,95646,95648,95650,95653],{},[898,95643,24379],{},[1655,95645,2734],{"stretchy":1663},[1826,95647,54325],{},[1655,95649,9672],{"separator":1670},[1826,95651,95652],{},"1,28",[1655,95654,2743],{"stretchy":1663},[902,95656,95657],{"encoding":904},"B[2{,}5; 1{,}28]",[883,95659,95661],{"className":95660},[886],[888,95662,95663],{"xmlns":890},[892,95664,95665,95697],{},[895,95666,95667,95669,95671,95673,95675,95677,95679,95685,95687,95689,95691,95693,95695],{},[898,95668,4052],{},[1655,95670,2734],{"stretchy":1663},[1826,95672,1837],{},[1655,95674,9672],{"separator":1670},[898,95676,900],{},[1655,95678,1664],{"stretchy":1663},[1820,95680,95681,95683],{},[898,95682,1824],{},[1826,95684,1828],{},[1655,95686,1671],{"separator":1670},[1826,95688,3472],{},[1655,95690,1677],{"stretchy":1663},[1655,95692,1657],{},[1826,95694,3472],{},[1655,95696,2743],{"stretchy":1663},[902,95698,95699],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,95702,95704],{"className":95703},[886],[888,95705,95706],{"xmlns":890},[892,95707,95708,95727],{},[895,95709,95710,95712,95714,95716,95718,95720,95722,95725],{},[898,95711,2838],{},[1655,95713,2734],{"stretchy":1663},[1826,95715,3472],{},[1655,95717,9672],{"separator":1670},[1826,95719,1828],{},[1655,95721,9672],{"separator":1670},[1826,95723,95724],{},"0,832",[1655,95726,2743],{"stretchy":1663},[902,95728,95729],{"encoding":904},"D[3; 1; 0{,}832]",[883,95731,95733],{"className":95732},[886],[888,95734,95735],{"xmlns":890},[892,95736,95737,95752],{},[895,95738,95739,95741,95743,95745,95747,95750],{},[898,95740,5502],{},[1655,95742,2734],{"stretchy":1663},[1826,95744,54325],{},[1655,95746,9672],{"separator":1670},[1826,95748,95749],{},"4,32",[1655,95751,2743],{"stretchy":1663},[902,95753,95754],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,95757,95758,94860,95761,95804,95805,7720,95818,95852,95853,95870,95871,95888],{},[38,95759,95760],{},"6.6",[883,95762,95764],{"className":95763},[886],[888,95765,95766],{"xmlns":890},[892,95767,95768,95802],{},[895,95769,95770,95772,95774,95788],{},[898,95771,900],{},[1655,95773,1657],{},[1935,95775,95776,95778,95780],{},[898,95777,1824],{},[1826,95779,1828],{},[895,95781,95782,95784,95786],{},[1826,95783,1837],{},[898,95785,5923],{"mathvariant":1943},[1826,95787,3472],{},[1935,95789,95790,95792,95794],{},[898,95791,1824],{},[1826,95793,1837],{},[895,95795,95796,95798,95800],{},[1826,95797,1828],{},[898,95799,5923],{"mathvariant":1943},[1826,95801,3472],{},[902,95803,95497],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,95806,95808],{"className":95807},[886],[888,95809,95810],{"xmlns":890},[892,95811,95812,95816],{},[895,95813,95814],{},[2031,95815,2708],{},[902,95817,29364],{"encoding":904},[883,95819,95821],{"className":95820},[886],[888,95822,95823],{"xmlns":890},[892,95824,95825,95849],{},[895,95826,95827,95833,95835,95837,95839,95845,95847],{},[1820,95828,95829,95831],{},[898,95830,1824],{},[1826,95832,1828],{},[1655,95834,1657],{},[1826,95836,4360],{},[1655,95838,1671],{"separator":1670},[1820,95840,95841,95843],{},[898,95842,1824],{},[1826,95844,1837],{},[1655,95846,1657],{},[1826,95848,9624],{},[902,95850,95851],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,95854,95856],{"className":95855},[886],[888,95857,95858],{"xmlns":890},[892,95859,95860,95868],{},[895,95861,95862],{},[1820,95863,95864,95866],{},[898,95865,1824],{},[1826,95867,1828],{},[902,95869,30128],{"encoding":904},", poklesne-li ",[883,95872,95874],{"className":95873},[886],[888,95875,95876],{"xmlns":890},[892,95877,95878,95886],{},[895,95879,95880],{},[1820,95881,95882,95884],{},[898,95883,1824],{},[1826,95885,1837],{},[902,95887,30147],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,95890,95891,95894,95895,95912,95913,95930,95931,95963,95964,95989,95990,96003,96004,1343,96028,1343,96052,1719],{},[38,95892,95893],{},"6.7"," Míra uspokojení z nákupu množství ",[883,95896,95898],{"className":95897},[886],[888,95899,95900],{"xmlns":890},[892,95901,95902,95910],{},[895,95903,95904],{},[1820,95905,95906,95908],{},[898,95907,1824],{},[1826,95909,1828],{},[902,95911,30128],{"encoding":904}," nealko nápojů a množství ",[883,95914,95916],{"className":95915},[886],[888,95917,95918],{"xmlns":890},[892,95919,95920,95928],{},[895,95921,95922],{},[1820,95923,95924,95926],{},[898,95925,1824],{},[1826,95927,1837],{},[902,95929,30147],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,95932,95934],{"className":95933},[886],[888,95935,95936],{"xmlns":890},[892,95937,95938,95960],{},[895,95939,95940,95942,95944],{},[898,95941,900],{},[1655,95943,1657],{},[9364,95945,95946],{},[895,95947,95948,95954],{},[1820,95949,95950,95952],{},[898,95951,1824],{},[1826,95953,1828],{},[1820,95955,95956,95958],{},[898,95957,1824],{},[1826,95959,1837],{},[902,95961,95962],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,95965,95967],{"className":95966},[886],[888,95968,95969],{"xmlns":890},[892,95970,95971,95987],{},[895,95972,95973,95979,95981],{},[1820,95974,95975,95977],{},[898,95976,1824],{},[1826,95978,1828],{},[1655,95980,1671],{"separator":1670},[1820,95982,95983,95985],{},[898,95984,1824],{},[1826,95986,1837],{},[902,95988,36748],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,95991,95993],{"className":95992},[886],[888,95994,95995],{"xmlns":890},[892,95996,95997,96001],{},[895,95998,95999],{},[2031,96000,2708],{},[902,96002,29364],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,96005,96007],{"className":96006},[886],[888,96008,96009],{"xmlns":890},[892,96010,96011,96025],{},[895,96012,96013,96015,96017,96019,96021,96023],{},[2031,96014,2708],{},[1655,96016,1664],{"stretchy":1663},[1826,96018,3524],{},[1655,96020,1671],{"separator":1670},[1826,96022,10282],{},[1655,96024,1677],{"stretchy":1663},[902,96026,96027],{"encoding":904},"\\text{MRCS}(5, 20)",[883,96029,96031],{"className":96030},[886],[888,96032,96033],{"xmlns":890},[892,96034,96035,96049],{},[895,96036,96037,96039,96041,96043,96045,96047],{},[2031,96038,2708],{},[1655,96040,1664],{"stretchy":1663},[1826,96042,10282],{},[1655,96044,1671],{"separator":1670},[1826,96046,3524],{},[1655,96048,1677],{"stretchy":1663},[902,96050,96051],{"encoding":904},"\\text{MRCS}(20, 5)",[883,96053,96055],{"className":96054},[886],[888,96056,96057],{"xmlns":890},[892,96058,96059,96073],{},[895,96060,96061,96063,96065,96067,96069,96071],{},[2031,96062,2708],{},[1655,96064,1664],{"stretchy":1663},[1826,96066,1837],{},[1655,96068,1671],{"separator":1670},[1826,96070,4390],{},[1655,96072,1677],{"stretchy":1663},[902,96074,96075],{"encoding":904},"\\text{MRCS}(2, 50)",[5120,96077,96078],{},[724,96079,96080,96082,96083,1719],{},[883,96081,5821],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,96084,96087],{"className":96085,"dataFsResolvedFilePath":911,"href":96086},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,96089,16845],{"id":16844},[120,96091,96092,96098,96103,96109,96162,96172,96218,96273,96336,96393,96448,96487],{},[123,96093,96094,96097],{},[38,96095,96096],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,96099,96100,96102],{},[38,96101,87995],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,96104,96105,96108],{},[38,96106,96107],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,96110,96111,96113,96114,96127,96128,1719],{},[38,96112,88322],{}," — uspořádaná ",[883,96115,96117],{"className":96116},[886],[888,96118,96119],{"xmlns":890},[892,96120,96121,96125],{},[895,96122,96123],{},[898,96124,37986],{},[902,96126,37986],{"encoding":904},"-tice ",[883,96129,96131],{"className":96130},[886],[888,96132,96133],{"xmlns":890},[892,96134,96135,96159],{},[895,96136,96137,96139,96145,96147,96149,96151,96157],{},[1655,96138,1664],{"stretchy":1663},[1820,96140,96141,96143],{},[898,96142,1824],{},[1826,96144,1828],{},[1655,96146,1671],{"separator":1670},[1655,96148,1715],{},[1655,96150,1671],{"separator":1670},[1820,96152,96153,96155],{},[898,96154,1824],{},[898,96156,37986],{},[1655,96158,1677],{"stretchy":1663},[902,96160,96161],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,96163,96164,96167,96168,96171],{},[38,96165,96166],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,96169,96170],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,96173,96174,3106,96177,96217],{},[38,96175,96176],{},"Funkce užitečnosti",[883,96178,96180],{"className":96179},[886],[888,96181,96182],{"xmlns":890},[892,96183,96184,96214],{},[895,96185,96186,96188,96190,96192,96194,96200,96202,96204,96206,96212],{},[898,96187,900],{},[1655,96189,1657],{},[898,96191,900],{},[1655,96193,1664],{"stretchy":1663},[1820,96195,96196,96198],{},[898,96197,1824],{},[1826,96199,1828],{},[1655,96201,1671],{"separator":1670},[1655,96203,1715],{},[1655,96205,1671],{"separator":1670},[1820,96207,96208,96210],{},[898,96209,1824],{},[898,96211,37986],{},[1655,96213,1677],{"stretchy":1663},[902,96215,96216],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,96219,96220,3106,96223,96252,96253,3106,96256,96272],{},[38,96221,96222],{},"Mezní užitečnost",[883,96224,96226],{"className":96225},[886],[888,96227,96228],{"xmlns":890},[892,96229,96230,96250],{},[895,96231,96232,96234,96240,96242],{},[898,96233,2127],{},[1820,96235,96236,96238],{},[898,96237,900],{},[898,96239,18916],{},[1655,96241,1657],{},[1935,96243,96244,96246,96248],{},[898,96245,900],{},[898,96247,18916],{},[1655,96249,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[902,96251,87779],{"encoding":904}," — vzorec (6.2); ",[38,96254,96255],{},"totální diferenciál",[883,96257,96259],{"className":96258},[886],[888,96260,96261],{"xmlns":890},[892,96262,96263,96269],{},[895,96264,96265,96267],{},[898,96266,2410],{"mathvariant":1943},[898,96268,900],{},[902,96270,96271],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,96274,96275,96277,96278,96302,96303,96335],{},[38,96276,89958],{}," — (6.4) ",[883,96279,96281],{"className":96280},[886],[888,96282,96283],{"xmlns":890},[892,96284,96285,96299],{},[895,96286,96287,96295,96297],{},[1935,96288,96289,96291,96293],{},[898,96290,900],{},[898,96292,18916],{},[1655,96294,1945],{"mathvariant":1943,"lspace":1944,"rspace":1944},[1655,96296,2969],{},[1826,96298,2552],{},[902,96300,96301],{"encoding":904},"U'_i > 0",", (6.5) ",[883,96304,96306],{"className":96305},[886],[888,96307,96308],{"xmlns":890},[892,96309,96310,96332],{},[895,96311,96312,96328,96330],{},[1935,96313,96314,96316,96322],{},[898,96315,900],{},[895,96317,96318,96320],{},[898,96319,18916],{},[898,96321,18916],{},[895,96323,96324,96326],{},[1655,96325,1945],{"mathvariant":1943},[1655,96327,1945],{"mathvariant":1943},[1655,96329,3065],{},[1826,96331,2552],{},[902,96333,96334],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,96337,96338,3106,96340,96371,96372,1719],{},[38,96339,91746],{},[883,96341,96343],{"className":96342},[886],[888,96344,96345],{"xmlns":890},[892,96346,96347,96369],{},[895,96348,96349,96351,96353,96361],{},[898,96350,900],{},[1655,96352,1657],{},[1935,96354,96355,96357,96359],{},[898,96356,1824],{},[1826,96358,1828],{},[898,96360,207],{},[1935,96362,96363,96365,96367],{},[898,96364,1824],{},[1826,96366,1837],{},[898,96368,2025],{},[902,96370,36929],{"encoding":904}," — (6.6), speciálně ",[883,96373,96375],{"className":96374},[886],[888,96376,96377],{"xmlns":890},[892,96378,96379,96391],{},[895,96380,96381,96383,96385,96387,96389],{},[898,96382,2025],{},[1655,96384,1657],{},[1826,96386,1828],{},[1655,96388,2623],{},[898,96390,207],{},[902,96392,91900],{"encoding":904},[123,96394,96395,3106,96398,96433,96434,96447],{},[38,96396,96397],{},"Křivky užitečnosti (indiferenční)",[883,96399,96401],{"className":96400},[886],[888,96402,96403],{"xmlns":890},[892,96404,96405,96431],{},[895,96406,96407,96409,96411,96417,96419,96425,96427,96429],{},[898,96408,900],{},[1655,96410,1664],{"stretchy":1663},[1820,96412,96413,96415],{},[898,96414,1824],{},[1826,96416,1828],{},[1655,96418,1671],{"separator":1670},[1820,96420,96421,96423],{},[898,96422,1824],{},[1826,96424,1837],{},[1655,96426,1677],{"stretchy":1663},[1655,96428,1657],{},[898,96430,1789],{},[902,96432,1846],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,96435,96437],{"className":96436},[886],[888,96438,96439],{"xmlns":890},[892,96440,96441,96445],{},[895,96442,96443],{},[898,96444,900],{},[902,96446,900],{"encoding":904},", konvexní.",[123,96449,96450,3106,96452,96486],{},[38,96451,93291],{},[883,96453,96455],{"className":96454},[886],[888,96456,96457],{"xmlns":890},[892,96458,96459,96483],{},[895,96460,96461,96463,96465,96467,96473,96475,96477],{},[2031,96462,2708],{},[1655,96464,1657],{},[898,96466,2127],{},[1820,96468,96469,96471],{},[898,96470,900],{},[1826,96472,1828],{},[898,96474,5923],{"mathvariant":1943},[898,96476,2127],{},[1820,96478,96479,96481],{},[898,96480,900],{},[1826,96482,1837],{},[902,96484,96485],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,96488,96489,3106,96492,1847,96521,96524],{},[38,96490,96491],{},"Podmínka optimality",[883,96493,96495],{"className":96494},[886],[888,96496,96497],{"xmlns":890},[892,96498,96499,96519],{},[895,96500,96501,96503,96505,96511,96513],{},[2031,96502,2708],{},[1655,96504,1657],{},[1820,96506,96507,96509],{},[898,96508,2132],{},[1826,96510,1828],{},[898,96512,5923],{"mathvariant":1943},[1820,96514,96515,96517],{},[898,96516,2132],{},[1826,96518,1837],{},[902,96520,29124],{"encoding":904},[207,96522,37880],{"className":96523,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,96526,3187],{"id":3186},[120,96528,96529,96566,96607,96617],{},[123,96530,96531,3106,96534,96537,96538,96551,96552,96565],{},[38,96532,96533],{},"Navazující téma:",[207,96535,913],{"className":96536,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,96539,96541],{"className":96540},[886],[888,96542,96543],{"xmlns":890},[892,96544,96545,96549],{},[895,96546,96547],{},[898,96548,900],{},[902,96550,900],{"encoding":904},", min ",[883,96553,96555],{"className":96554},[886],[888,96556,96557],{"xmlns":890},[892,96558,96559,96563],{},[895,96560,96561],{},[898,96562,5502],{},[902,96564,5502],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,96567,96568,3106,96571,3219,96574,87534,96577,96580,96581,96584,96585,19774,96603,96606],{},[38,96569,96570],{},"Související pojmy:",[207,96572,784],{"className":96573,"dataFsResolvedFilePath":782,"href":783},[210],[207,96575,3645],{"className":96576,"dataFsResolvedFilePath":764,"href":765},[210],[207,96578,3214],{"className":96579,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,96582,13065],{"className":96583,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,96586,96588],{"className":96587},[886],[888,96589,96590],{"xmlns":890},[892,96591,96592,96600],{},[895,96593,96594],{},[1820,96595,96596,96598],{},[898,96597,2838],{},[898,96599,18916],{},[902,96601,96602],{"encoding":904},"D_i",[207,96604,793],{"className":96605,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,96608,96609,3106,96611,1343,96614],{},[38,96610,37829],{},[207,96612,1094],{"className":96613,"dataFsResolvedFilePath":838,"href":839},[210],[207,96615,1101],{"className":96616,"dataFsResolvedFilePath":868,"href":869},[210],[123,96618,96619,3106,96621],{},[38,96620,17329],{},[207,96622,17333],{"className":96623,"dataFsResolvedFilePath":3274,"href":3275},[210],{"title":641,"searchDepth":642,"depth":642,"links":96625},[96626,96627,96628,96631,96632,96635,96639,96640,96643,96644,96645,96646,96647,96648,96649],{"id":13130,"depth":642,"text":13131},{"id":87918,"depth":642,"text":87919},{"id":87978,"depth":642,"text":87979,"children":96629},[96630],{"id":87994,"depth":649,"text":87995},{"id":88301,"depth":642,"text":88302},{"id":89161,"depth":642,"text":89162,"children":96633},[96634],{"id":89708,"depth":649,"text":81337},{"id":89957,"depth":642,"text":89958,"children":96636},[96637],{"id":90830,"depth":649,"text":96638},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":91745,"depth":642,"text":91746},{"id":92281,"depth":642,"text":92282,"children":96641},[96642],{"id":93055,"depth":649,"text":93056},{"id":93285,"depth":642,"text":93286},{"id":94046,"depth":642,"text":94047},{"id":94584,"depth":642,"text":94585},{"id":51007,"depth":642,"text":51008},{"id":94720,"depth":642,"text":94721},{"id":16844,"depth":642,"text":16845},{"id":3186,"depth":642,"text":3187},{},"\u002Ftopics\u002Fuzitecnost",{"title":87702,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,1851,96656,87696,3251,96657],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":96660,"title":757,"body":96661,"course":1128,"courses":659,"created":1129,"description":96934,"extension":661,"meta":96935,"navigation":664,"path":96936,"seo":96937,"sources":96938,"stem":96939,"tags":96940,"type":3252,"updated":677,"__hash__":96946},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":96662,"toc":96926},[96663,96666,96673,96680,96684,96694,96696,96730,96734,96777,96780,96838,96842,96872,96876,96897,96899],[12,96664,757],{"id":96665},"základy-matematické-ekonomie",[724,96667,96668,96669,96672],{},"Úvodní pojmy a princip modelování v ",[207,96670,17506],{"className":96671,"dataFsResolvedFilePath":3274,"href":3275},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,96674,96675],{},[1723,96676],{"alt":96677,"className":96678,"src":96679},"imek-model-promenne",[210,1727],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,96681,96683],{"id":96682},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,96685,96686,96689,96690,96693],{},[38,96687,96688],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,96691,96692],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,96695,16845],{"id":16844},[120,96697,96698,96704,96710,96716,96725],{},[123,96699,96700,96703],{},[38,96701,96702],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,96705,96706,96709],{},[38,96707,96708],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,96711,96712,96715],{},[38,96713,96714],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,96717,96718,8262,96721,96724],{},[38,96719,96720],{},"Ceteris paribus",[614,96722,96723],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,96726,96727,96729],{},[38,96728,51761],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,96731,96733],{"id":96732},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,96735,96736,96776],{},[883,96737,96739],{"className":96738},[886],[888,96740,96741],{"xmlns":890},[892,96742,96743,96773],{},[895,96744,96745,96747,96749,96751,96753,96755,96757,96759,96761,96763,96765,96767,96769,96771],{},[898,96746,1824],{},[1655,96748,1657],{},[898,96750,2838],{},[1655,96752,1664],{"stretchy":1663},[898,96754,2132],{},[1655,96756,1671],{"separator":1670},[898,96758,10375],{},[1655,96760,1671],{"separator":1670},[898,96762,19420],{},[1655,96764,1671],{"separator":1670},[898,96766,900],{},[1655,96768,1671],{"separator":1670},[1655,96770,1715],{},[1655,96772,1677],{"stretchy":1663},[902,96774,96775],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,96778,96779],{},"Zjednodušení:",[120,96781,96782,96810],{},[123,96783,96784,3106,96787],{},[38,96785,96786],{},"Jednofaktorový model:",[883,96788,96790],{"className":96789},[886],[888,96791,96792],{"xmlns":890},[892,96793,96794,96808],{},[895,96795,96796,96798,96800,96802,96804,96806],{},[898,96797,1824],{},[1655,96799,1657],{},[898,96801,2838],{},[1655,96803,1664],{"stretchy":1663},[898,96805,2132],{},[1655,96807,1677],{"stretchy":1663},[902,96809,5442],{"encoding":904},[123,96811,96812,3106,96815],{},[38,96813,96814],{},"Inverzní zápis:",[883,96816,96818],{"className":96817},[886],[888,96819,96820],{"xmlns":890},[892,96821,96822,96836],{},[895,96823,96824,96826,96828,96830,96832,96834],{},[898,96825,2132],{},[1655,96827,1657],{},[898,96829,2838],{},[1655,96831,1664],{"stretchy":1663},[898,96833,1824],{},[1655,96835,1677],{"stretchy":1663},[902,96837,5889],{"encoding":904},[115,96839,96841],{"id":96840},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,96843,96844,96853],{},[123,96845,96846,96849,96850,5171],{},[38,96847,96848],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,96851,17365],{"className":96852,"dataFsResolvedFilePath":800,"href":801},[210],[123,96854,96855,96858,96859,96862,96863,96866,96867,96871],{},[38,96856,96857],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,96860,1145],{"className":96861,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,96864,17378],{"className":96865,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,96868,96870],{"className":96869,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,96873,96875],{"id":96874},"konvence-z-přednášek","Konvence z přednášek",[120,96877,96878,96885,96891],{},[123,96879,96880,96881,96884],{},"Symbol ",[96882,96883,2357],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,96886,96887,96888,1719],{},"Numerické výsledky ",[38,96889,96890],{},"na 3 desetinná místa",[123,96892,5147,96893,96896],{},[614,96894,96895],{},"jednotková změna"," má standardní význam (změna o 1).",[115,96898,3187],{"id":3186},[120,96900,96901,96906,96914],{},[123,96902,96903,96905],{},[38,96904,3194],{}," —",[123,96907,96908,3106,96910],{},[38,96909,3202],{},[207,96911,96913],{"className":96912,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,96915,96916,3106,96918,1343,96922],{},[38,96917,3210],{},[207,96919,96921],{"className":96920,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,96923,96925],{"className":96924,"dataFsResolvedFilePath":3274,"href":3275},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":96927},[96928,96929,96930,96931,96932,96933],{"id":96682,"depth":642,"text":96683},{"id":16844,"depth":642,"text":16845},{"id":96732,"depth":642,"text":96733},{"id":96840,"depth":642,"text":96841},{"id":96874,"depth":642,"text":96875},{"id":3186,"depth":642,"text":3187},"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":96934},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,96941,96942,96943,96944,96945],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":96948,"title":96949,"body":96950,"course":1128,"courses":659,"created":10802,"description":641,"extension":661,"meta":101222,"navigation":664,"path":101223,"seo":101224,"sources":101225,"stem":101226,"tags":101227,"type":3252,"updated":677,"__hash__":101231},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":96951,"toc":101205},[96952,96955,97049,97053,97075,97089,97141,97143,97147,97210,97253,97272,97435,97534,97537,97604,97608,97737,97776,97806,97918,97963,98029,98082,98158,98214,98216,98220,98284,98328,98348,98509,98512,98596,98693,98696,98762,98766,98815,98841,98946,99010,99015,99111,99158,99160,99163,99185,99227,99234,99267,99269,99340,99394,99503,99507,99596,99672,99936,99974,99976,99980,99983,99990,100301,100304,100362,100542,100571,100573,100577,100583,100721,100730,100732,100734,101159,101161,101163],[12,96953,96949],{"id":96954},"zdanění-trhu-dopady-daně-na-rovnováhu",[5120,96956,96957],{},[724,96958,96959,43754,96961,96974,96975,96978,96979,96981,96982,96985,96986,97007,97008,97031,97032,97035,97036,1719],{},[883,96960,5406],{},[883,96962,96964],{"className":96963},[886],[888,96965,96966],{"xmlns":890},[892,96967,96968,96972],{},[895,96969,96970],{},[898,96971,4049],{},[902,96973,4049],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,96976,96977],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,96980,87986],{}," (je-li uložena spotřebiteli). Výsledné ",[38,96983,96984],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,96987,96989],{"className":96988},[886],[888,96990,96991],{"xmlns":890},[892,96992,96993,97005],{},[895,96994,96995],{},[1820,96996,96997,96999],{},[898,96998,4049],{},[895,97000,97001,97003],{},[898,97002,43803],{},[898,97004,724],{},[902,97006,43808],{"encoding":904}," (spotřebitel) a ",[883,97009,97011],{"className":97010},[886],[888,97012,97013],{"xmlns":890},[892,97014,97015,97029],{},[895,97016,97017],{},[1820,97018,97019,97021],{},[898,97020,4049],{},[895,97022,97023,97025,97027],{},[898,97024,43826],{},[898,97026,1674],{},[898,97028,13166],{},[902,97030,43833],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,97033,97034],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,97037,97039],{"className":97038},[886],[888,97040,97041],{"xmlns":890},[892,97042,97043,97047],{},[895,97044,97045],{},[898,97046,4049],{},[902,97048,4049],{"encoding":904},[115,97050,97052],{"id":97051},"dvě-formy-zdanění","Dvě formy zdanění",[724,97054,97055,97056,97074],{},"Uvažujme jednotkovou daň ",[883,97057,97059],{"className":97058},[886],[888,97060,97061],{"xmlns":890},[892,97062,97063,97071],{},[895,97064,97065,97067,97069],{},[898,97066,4049],{},[1655,97068,2969],{},[1826,97070,2552],{},[902,97072,97073],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,97076,97077,97083],{},[123,97078,97079,97082],{},[38,97080,97081],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,97084,97085,97088],{},[38,97086,97087],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,97090,97091,97092,97105,97106,97109,97110,1719],{},"V obou případech dochází k posunu jedné z křivek o ",[883,97093,97095],{"className":97094},[886],[888,97096,97097],{"xmlns":890},[892,97098,97099,97103],{},[895,97100,97101],{},[898,97102,4049],{},[902,97104,4049],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,97107,97108],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,97111,97113],{"className":97112},[886],[888,97114,97115],{"xmlns":890},[892,97116,97117,97139],{},[895,97118,97119,97121,97123,97129,97131,97137],{},[898,97120,5502],{},[1655,97122,2734],{"stretchy":1663},[2597,97124,97125,97127],{},[898,97126,1824],{},[898,97128,5502],{},[1655,97130,1671],{"separator":1670},[2597,97132,97133,97135],{},[898,97134,2132],{},[898,97136,5502],{},[1655,97138,2743],{"stretchy":1663},[902,97140,42493],{"encoding":904},[38096,97142],{},[115,97144,97146],{"id":97145},"daň-uložená-výrobci","Daň uložená výrobci",[724,97148,97149,97150,97163,97164,97181,97182,97209],{},"Je-li daň ",[883,97151,97153],{"className":97152},[886],[888,97154,97155],{"xmlns":890},[892,97156,97157,97161],{},[895,97158,97159],{},[898,97160,4049],{},[902,97162,4049],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,97165,97167],{"className":97166},[886],[888,97168,97169],{"xmlns":890},[892,97170,97171,97179],{},[895,97172,97173,97175,97177],{},[898,97174,2132],{},[1655,97176,2623],{},[898,97178,4049],{},[902,97180,42248],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,97183,97185],{"className":97184},[886],[888,97186,97187],{"xmlns":890},[892,97188,97189,97207],{},[895,97190,97191,97193,97195,97197,97199,97201,97203,97205],{},[898,97192,2132],{},[1655,97194,2623],{},[898,97196,4049],{},[1655,97198,1657],{},[898,97200,9920],{},[1655,97202,1664],{"stretchy":1663},[898,97204,1824],{},[1655,97206,1677],{"stretchy":1663},[902,97208,42277],{"encoding":904}," nová funkce nabídky:",[883,97211,97213],{"className":97212},[886],[888,97214,97215],{"xmlns":890,"display":29192},[892,97216,97217,97251],{},[895,97218,97219,97221,97223,97229,97231,97233,97235,97237,97239,97241,97243,97245,97247,97249],{},[898,97220,2132],{},[1655,97222,1657],{},[1820,97224,97225,97227],{},[898,97226,9920],{},[1826,97228,1828],{},[1655,97230,1664],{"stretchy":1663},[898,97232,1824],{},[1655,97234,1677],{"stretchy":1663},[1655,97236,1657],{},[898,97238,9920],{},[1655,97240,1664],{"stretchy":1663},[898,97242,1824],{},[1655,97244,1677],{"stretchy":1663},[1655,97246,2346],{},[898,97248,4049],{},[898,97250,1719],{"mathvariant":1943},[902,97252,42322],{"encoding":904},[724,97254,97255,97256,3106,97269,97271],{},"Nabídka se tedy posouvá o ",[883,97257,97259],{"className":97258},[886],[888,97260,97261],{"xmlns":890},[892,97262,97263,97267],{},[895,97264,97265],{},[898,97266,4049],{},[902,97268,4049],{"encoding":904},[38,97270,42355],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,97273,97274,97275,97315,97316,2704,97344,97372,97373,97392,97393,97417,97418,5171],{},"Nový rovnovážný bod ",[883,97276,97278],{"className":97277},[886],[888,97279,97280],{"xmlns":890},[892,97281,97282,97312],{},[895,97283,97284,97290,97292,97300,97302,97310],{},[1820,97285,97286,97288],{},[898,97287,5502],{},[1826,97289,1828],{},[1655,97291,2734],{"stretchy":1663},[1935,97293,97294,97296,97298],{},[898,97295,1824],{},[1826,97297,1828],{},[898,97299,5502],{},[1655,97301,1671],{"separator":1670},[1935,97303,97304,97306,97308],{},[898,97305,2132],{},[1826,97307,1828],{},[898,97309,5502],{},[1655,97311,2743],{"stretchy":1663},[902,97313,97314],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,97317,97319],{"className":97318},[886],[888,97320,97321],{"xmlns":890},[892,97322,97323,97341],{},[895,97324,97325,97333,97335],{},[1935,97326,97327,97329,97331],{},[898,97328,1824],{},[1826,97330,1828],{},[898,97332,5502],{},[1655,97334,3065],{},[2597,97336,97337,97339],{},[898,97338,1824],{},[898,97340,5502],{},[902,97342,97343],{"encoding":904},"Q_1^E \u003C Q^E",[883,97345,97347],{"className":97346},[886],[888,97348,97349],{"xmlns":890},[892,97350,97351,97369],{},[895,97352,97353,97361,97363],{},[1935,97354,97355,97357,97359],{},[898,97356,2132],{},[1826,97358,1828],{},[898,97360,5502],{},[1655,97362,2969],{},[2597,97364,97365,97367],{},[898,97366,2132],{},[898,97368,5502],{},[902,97370,97371],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,97374,97376],{"className":97375},[886],[888,97377,97378],{"xmlns":890},[892,97379,97380,97390],{},[895,97381,97382],{},[1935,97383,97384,97386,97388],{},[898,97385,2132],{},[1826,97387,1828],{},[898,97389,5502],{},[902,97391,48983],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,97394,97396],{"className":97395},[886],[888,97397,97398],{"xmlns":890},[892,97399,97400,97414],{},[895,97401,97402,97410,97412],{},[1935,97403,97404,97406,97408],{},[898,97405,2132],{},[1826,97407,1828],{},[898,97409,5502],{},[1655,97411,2623],{},[898,97413,4049],{},[902,97415,97416],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,97419,97421],{"className":97420},[886],[888,97422,97423],{"xmlns":890},[892,97424,97425,97433],{},[895,97426,97427],{},[2597,97428,97429,97431],{},[898,97430,2132],{},[898,97432,5502],{},[902,97434,42592],{"encoding":904},[724,97436,97437],{},[614,97438,97439,97440,97470,97471,97484,97485,6918,97502,97515,97516,1719],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,97441,97443],{"className":97442},[886],[888,97444,97445],{"xmlns":890},[892,97446,97447,97467],{},[895,97448,97449,97451,97453,97459,97461,97463,97465],{},[898,97450,9920],{},[1655,97452,4393],{},[1820,97454,97455,97457],{},[898,97456,9920],{},[1826,97458,1828],{},[1655,97460,1657],{},[898,97462,9920],{},[1655,97464,2346],{},[898,97466,4049],{},[902,97468,97469],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,97472,97474],{"className":97473},[886],[888,97475,97476],{"xmlns":890},[892,97477,97478,97482],{},[895,97479,97480],{},[898,97481,4049],{},[902,97483,4049],{"encoding":904},". Průsečík ",[883,97486,97488],{"className":97487},[886],[888,97489,97490],{"xmlns":890},[892,97491,97492,97500],{},[895,97493,97494],{},[1820,97495,97496,97498],{},[898,97497,9920],{},[1826,97499,1828],{},[902,97501,42123],{"encoding":904},[883,97503,97505],{"className":97504},[886],[888,97506,97507],{"xmlns":890},[892,97508,97509,97513],{},[895,97510,97511],{},[898,97512,2838],{},[902,97514,2838],{"encoding":904}," je nový rovnovážný bod ",[883,97517,97519],{"className":97518},[886],[888,97520,97521],{"xmlns":890},[892,97522,97523,97531],{},[895,97524,97525],{},[1820,97526,97527,97529],{},[898,97528,5502],{},[1826,97530,1828],{},[902,97532,97533],{"encoding":904},"E_1",[198,97535,46429],{"id":97536},"příklad-29",[724,97538,97539,42781,97541,42816,97565,97585,97586,97603],{},[38,97540,39059],{},[883,97542,97544],{"className":97543},[886],[888,97545,97546],{"xmlns":890},[892,97547,97548,97562],{},[895,97549,97550,97552,97554,97556,97558,97560],{},[898,97551,2132],{},[1655,97553,1657],{},[1826,97555,4771],{},[1655,97557,2623],{},[1826,97559,1837],{},[898,97561,1824],{},[902,97563,97564],{"encoding":904},"P = 12 - 2Q",[883,97566,97568],{"className":97567},[886],[888,97569,97570],{"xmlns":890},[892,97571,97572,97582],{},[895,97573,97574,97576,97578,97580],{},[898,97575,2132],{},[1655,97577,1657],{},[1826,97579,3639],{},[898,97581,1824],{},[902,97583,97584],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,97587,97589],{"className":97588},[886],[888,97590,97591],{"xmlns":890},[892,97592,97593,97601],{},[895,97594,97595,97597,97599],{},[898,97596,4049],{},[1655,97598,1657],{},[1826,97600,3531],{},[902,97602,42394],{"encoding":904}," Kč.",[724,97605,97606],{},[38,97607,39091],{},[724,97609,97610,97613,97614,6818,97640,6838,97660,1343,97682,97712,97713,1719],{},[614,97611,97612],{},"Bez daně."," Z rovnosti ",[883,97615,97617],{"className":97616},[886],[888,97618,97619],{"xmlns":890},[892,97620,97621,97637],{},[895,97622,97623,97625,97627,97629,97631,97633,97635],{},[1826,97624,4771],{},[1655,97626,2623],{},[1826,97628,1837],{},[898,97630,1824],{},[1655,97632,1657],{},[1826,97634,3639],{},[898,97636,1824],{},[902,97638,97639],{"encoding":904},"12 - 2Q = 4Q",[883,97641,97643],{"className":97642},[886],[888,97644,97645],{"xmlns":890},[892,97646,97647,97657],{},[895,97648,97649,97651,97653,97655],{},[1826,97650,3531],{},[898,97652,1824],{},[1655,97654,1657],{},[1826,97656,4771],{},[902,97658,97659],{"encoding":904},"6Q = 12",[883,97661,97663],{"className":97662},[886],[888,97664,97665],{"xmlns":890},[892,97666,97667,97679],{},[895,97668,97669,97675,97677],{},[2597,97670,97671,97673],{},[898,97672,1824],{},[898,97674,5502],{},[1655,97676,1657],{},[1826,97678,1837],{},[902,97680,97681],{"encoding":904},"Q^E = 2",[883,97683,97685],{"className":97684},[886],[888,97686,97687],{"xmlns":890},[892,97688,97689,97709],{},[895,97690,97691,97697,97699,97701,97703,97705,97707],{},[2597,97692,97693,97695],{},[898,97694,2132],{},[898,97696,5502],{},[1655,97698,1657],{},[1826,97700,3639],{},[1655,97702,2869],{},[1826,97704,1837],{},[1655,97706,1657],{},[1826,97708,6834],{},[902,97710,97711],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,97714,97716],{"className":97715},[886],[888,97717,97718],{"xmlns":890},[892,97719,97720,97734],{},[895,97721,97722,97724,97726,97728,97730,97732],{},[898,97723,5502],{},[1655,97725,2734],{"stretchy":1663},[1826,97727,1837],{},[1655,97729,1671],{"separator":1670},[1826,97731,6834],{},[1655,97733,2743],{"stretchy":1663},[902,97735,97736],{"encoding":904},"E[2, 8]",[724,97738,97739,97742,97743,97775],{},[614,97740,97741],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,97744,97746],{"className":97745},[886],[888,97747,97748],{"xmlns":890},[892,97749,97750,97772],{},[895,97751,97752,97758,97760,97762,97764,97766,97768,97770],{},[1820,97753,97754,97756],{},[898,97755,9920],{},[1826,97757,1828],{},[1655,97759,2086],{},[898,97761,2132],{},[1655,97763,1657],{},[1826,97765,3639],{},[898,97767,1824],{},[1655,97769,2346],{},[1826,97771,3531],{},[902,97773,97774],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,97777,97779],{"className":97778},[886],[888,97780,97781],{"xmlns":890,"display":29192},[892,97782,97783,97803],{},[895,97784,97785,97787,97789,97791,97793,97795,97797,97799,97801],{},[1826,97786,4771],{},[1655,97788,2623],{},[1826,97790,1837],{},[898,97792,1824],{},[1655,97794,1657],{},[1826,97796,3639],{},[898,97798,1824],{},[1655,97800,2346],{},[1826,97802,3531],{},[902,97804,97805],{"encoding":904},"12 - 2Q = 4Q + 6",[724,97807,97808,97809,6838,97829,1343,97853,97889,97890,1719],{},"plyne ",[883,97810,97812],{"className":97811},[886],[888,97813,97814],{"xmlns":890},[892,97815,97816,97826],{},[895,97817,97818,97820,97822,97824],{},[1826,97819,3531],{},[898,97821,1824],{},[1655,97823,1657],{},[1826,97825,3531],{},[902,97827,97828],{"encoding":904},"6Q = 6",[883,97830,97832],{"className":97831},[886],[888,97833,97834],{"xmlns":890},[892,97835,97836,97850],{},[895,97837,97838,97846,97848],{},[1935,97839,97840,97842,97844],{},[898,97841,1824],{},[1826,97843,1828],{},[898,97845,5502],{},[1655,97847,1657],{},[1826,97849,1828],{},[902,97851,97852],{"encoding":904},"Q_1^E = 1",[883,97854,97856],{"className":97855},[886],[888,97857,97858],{"xmlns":890},[892,97859,97860,97886],{},[895,97861,97862,97870,97872,97874,97876,97878,97880,97882,97884],{},[1935,97863,97864,97866,97868],{},[898,97865,2132],{},[1826,97867,1828],{},[898,97869,5502],{},[1655,97871,1657],{},[1826,97873,3639],{},[1655,97875,2869],{},[1826,97877,1828],{},[1655,97879,2346],{},[1826,97881,3531],{},[1655,97883,1657],{},[1826,97885,4136],{},[902,97887,97888],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,97891,97893],{"className":97892},[886],[888,97894,97895],{"xmlns":890},[892,97896,97897,97915],{},[895,97898,97899,97905,97907,97909,97911,97913],{},[1820,97900,97901,97903],{},[898,97902,5502],{},[1826,97904,1828],{},[1655,97906,2734],{"stretchy":1663},[1826,97908,1828],{},[1655,97910,1671],{"separator":1670},[1826,97912,4136],{},[1655,97914,2743],{"stretchy":1663},[902,97916,97917],{"encoding":904},"E_1[1, 10]",[724,97919,97920,97923,97924,97948,97949,97962],{},[614,97921,97922],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,97925,97927],{"className":97926},[886],[888,97928,97929],{"xmlns":890},[892,97930,97931,97945],{},[895,97932,97933,97941,97943],{},[1935,97934,97935,97937,97939],{},[898,97936,2132],{},[1826,97938,1828],{},[898,97940,5502],{},[1655,97942,1657],{},[1826,97944,4136],{},[902,97946,97947],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,97950,97952],{"className":97951},[886],[888,97953,97954],{"xmlns":890},[892,97955,97956,97960],{},[895,97957,97958],{},[1826,97959,6834],{},[902,97961,6834],{"encoding":904},", navýšení je",[883,97964,97966],{"className":97965},[886],[888,97967,97968],{"xmlns":890,"display":29192},[892,97969,97970,98026],{},[895,97971,97972,97982,97984,97992,97994,98000,98002,98004,98006,98008,98010,98012,98014,98024],{},[1820,97973,97974,97976],{},[898,97975,4049],{},[895,97977,97978,97980],{},[898,97979,43803],{},[898,97981,724],{},[1655,97983,1657],{},[1935,97985,97986,97988,97990],{},[898,97987,2132],{},[1826,97989,1828],{},[898,97991,5502],{},[1655,97993,2623],{},[2597,97995,97996,97998],{},[898,97997,2132],{},[898,97999,5502],{},[1655,98001,1657],{},[1826,98003,4136],{},[1655,98005,2623],{},[1826,98007,6834],{},[1655,98009,1657],{},[1826,98011,1837],{},[2031,98013,2033],{},[895,98015,98016,98018],{},[2031,98017,1878],{},[9633,98019,98020,98022],{"accent":1670},[2031,98021,1789],{},[1655,98023,26184],{},[898,98025,1719],{"mathvariant":1943},[902,98027,98028],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,98030,98031,98032,97948,98068,98081],{},"Výrobci zůstává čistá cena ",[883,98033,98035],{"className":98034},[886],[888,98036,98037],{"xmlns":890},[892,98038,98039,98065],{},[895,98040,98041,98049,98051,98053,98055,98057,98059,98061,98063],{},[1935,98042,98043,98045,98047],{},[898,98044,2132],{},[1826,98046,1828],{},[898,98048,5502],{},[1655,98050,2623],{},[898,98052,4049],{},[1655,98054,1657],{},[1826,98056,4136],{},[1655,98058,2623],{},[1826,98060,3531],{},[1655,98062,1657],{},[1826,98064,3639],{},[902,98066,98067],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,98069,98071],{"className":98070},[886],[888,98072,98073],{"xmlns":890},[892,98074,98075,98079],{},[895,98076,98077],{},[1826,98078,6834],{},[902,98080,6834],{"encoding":904},", pokles je",[883,98083,98085],{"className":98084},[886],[888,98086,98087],{"xmlns":890,"display":29192},[892,98088,98089,98155],{},[895,98090,98091,98103,98105,98111,98113,98115,98123,98125,98127,98129,98131,98133,98135,98137,98139,98141,98143,98153],{},[1820,98092,98093,98095],{},[898,98094,4049],{},[895,98096,98097,98099,98101],{},[898,98098,43826],{},[898,98100,1674],{},[898,98102,13166],{},[1655,98104,1657],{},[2597,98106,98107,98109],{},[898,98108,2132],{},[898,98110,5502],{},[1655,98112,2623],{},[1655,98114,1664],{"stretchy":1663},[1935,98116,98117,98119,98121],{},[898,98118,2132],{},[1826,98120,1828],{},[898,98122,5502],{},[1655,98124,2623],{},[898,98126,4049],{},[1655,98128,1677],{"stretchy":1663},[1655,98130,1657],{},[1826,98132,6834],{},[1655,98134,2623],{},[1826,98136,3639],{},[1655,98138,1657],{},[1826,98140,3639],{},[2031,98142,2033],{},[895,98144,98145,98147],{},[2031,98146,1878],{},[9633,98148,98149,98151],{"accent":1670},[2031,98150,1789],{},[1655,98152,26184],{},[898,98154,1719],{"mathvariant":1943},[902,98156,98157],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,98159,98160,98161,98213],{},"Kontrola: ",[883,98162,98164],{"className":98163},[886],[888,98165,98166],{"xmlns":890},[892,98167,98168,98210],{},[895,98169,98170,98180,98182,98194,98196,98198,98200,98202,98204,98206,98208],{},[1820,98171,98172,98174],{},[898,98173,4049],{},[895,98175,98176,98178],{},[898,98177,43803],{},[898,98179,724],{},[1655,98181,2346],{},[1820,98183,98184,98186],{},[898,98185,4049],{},[895,98187,98188,98190,98192],{},[898,98189,43826],{},[898,98191,1674],{},[898,98193,13166],{},[1655,98195,1657],{},[1826,98197,1837],{},[1655,98199,2346],{},[1826,98201,3639],{},[1655,98203,1657],{},[1826,98205,3531],{},[1655,98207,1657],{},[898,98209,4049],{},[902,98211,98212],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[38096,98215],{},[115,98217,98219],{"id":98218},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,98221,97149,98222,98235,98236,98254,98255,98283],{},[883,98223,98225],{"className":98224},[886],[888,98226,98227],{"xmlns":890},[892,98228,98229,98233],{},[895,98230,98231],{},[898,98232,4049],{},[902,98234,4049],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,98237,98239],{"className":98238},[886],[888,98240,98241],{"xmlns":890},[892,98242,98243,98251],{},[895,98244,98245,98247,98249],{},[898,98246,2132],{},[1655,98248,2346],{},[898,98250,4049],{},[902,98252,98253],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,98256,98258],{"className":98257},[886],[888,98259,98260],{"xmlns":890},[892,98261,98262,98280],{},[895,98263,98264,98266,98268,98270,98272,98274,98276,98278],{},[898,98265,2132],{},[1655,98267,2346],{},[898,98269,4049],{},[1655,98271,1657],{},[898,98273,2838],{},[1655,98275,1664],{"stretchy":1663},[898,98277,1824],{},[1655,98279,1677],{"stretchy":1663},[902,98281,98282],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,98285,98287],{"className":98286},[886],[888,98288,98289],{"xmlns":890,"display":29192},[892,98290,98291,98325],{},[895,98292,98293,98295,98297,98303,98305,98307,98309,98311,98313,98315,98317,98319,98321,98323],{},[898,98294,2132],{},[1655,98296,1657],{},[1820,98298,98299,98301],{},[898,98300,2838],{},[1826,98302,1837],{},[1655,98304,1664],{"stretchy":1663},[898,98306,1824],{},[1655,98308,1677],{"stretchy":1663},[1655,98310,1657],{},[898,98312,2838],{},[1655,98314,1664],{"stretchy":1663},[898,98316,1824],{},[1655,98318,1677],{"stretchy":1663},[1655,98320,2623],{},[898,98322,4049],{},[898,98324,1719],{"mathvariant":1943},[902,98326,98327],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,98329,98330,98331,3106,98344,98347],{},"Poptávka se tedy posouvá o ",[883,98332,98334],{"className":98333},[886],[888,98335,98336],{"xmlns":890},[892,98337,98338,98342],{},[895,98339,98340],{},[898,98341,4049],{},[902,98343,4049],{"encoding":904},[38,98345,98346],{},"svisle dolů",". Nabídka se nemění.",[724,98349,97274,98350,97315,98390,2704,98418,98446,98447,98466,98467,98491,98492,5171],{},[883,98351,98353],{"className":98352},[886],[888,98354,98355],{"xmlns":890},[892,98356,98357,98387],{},[895,98358,98359,98365,98367,98375,98377,98385],{},[1820,98360,98361,98363],{},[898,98362,5502],{},[1826,98364,1837],{},[1655,98366,2734],{"stretchy":1663},[1935,98368,98369,98371,98373],{},[898,98370,1824],{},[1826,98372,1837],{},[898,98374,5502],{},[1655,98376,1671],{"separator":1670},[1935,98378,98379,98381,98383],{},[898,98380,2132],{},[1826,98382,1837],{},[898,98384,5502],{},[1655,98386,2743],{"stretchy":1663},[902,98388,98389],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,98391,98393],{"className":98392},[886],[888,98394,98395],{"xmlns":890},[892,98396,98397,98415],{},[895,98398,98399,98407,98409],{},[1935,98400,98401,98403,98405],{},[898,98402,1824],{},[1826,98404,1837],{},[898,98406,5502],{},[1655,98408,3065],{},[2597,98410,98411,98413],{},[898,98412,1824],{},[898,98414,5502],{},[902,98416,98417],{"encoding":904},"Q_2^E \u003C Q^E",[883,98419,98421],{"className":98420},[886],[888,98422,98423],{"xmlns":890},[892,98424,98425,98443],{},[895,98426,98427,98435,98437],{},[1935,98428,98429,98431,98433],{},[898,98430,2132],{},[1826,98432,1837],{},[898,98434,5502],{},[1655,98436,3065],{},[2597,98438,98439,98441],{},[898,98440,2132],{},[898,98442,5502],{},[902,98444,98445],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,98448,98450],{"className":98449},[886],[888,98451,98452],{"xmlns":890},[892,98453,98454,98464],{},[895,98455,98456],{},[1935,98457,98458,98460,98462],{},[898,98459,2132],{},[1826,98461,1837],{},[898,98463,5502],{},[902,98465,49044],{"encoding":904},", spotřebitel platí celkem ",[883,98468,98470],{"className":98469},[886],[888,98471,98472],{"xmlns":890},[892,98473,98474,98488],{},[895,98475,98476,98484,98486],{},[1935,98477,98478,98480,98482],{},[898,98479,2132],{},[1826,98481,1837],{},[898,98483,5502],{},[1655,98485,2346],{},[898,98487,4049],{},[902,98489,98490],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,98493,98495],{"className":98494},[886],[888,98496,98497],{"xmlns":890},[892,98498,98499,98507],{},[895,98500,98501],{},[2597,98502,98503,98505],{},[898,98504,2132],{},[898,98506,5502],{},[902,98508,42592],{"encoding":904},[724,98510,98511],{},"Daňové břemeno:",[883,98513,98515],{"className":98514},[886],[888,98516,98517],{"xmlns":890,"display":29192},[892,98518,98519,98593],{},[895,98520,98521,98531,98533,98535,98543,98545,98547,98549,98551,98557,98559,98561,98573,98575,98581,98583,98591],{},[1820,98522,98523,98525],{},[898,98524,4049],{},[895,98526,98527,98529],{},[898,98528,43803],{},[898,98530,724],{},[1655,98532,1657],{},[1655,98534,1664],{"stretchy":1663},[1935,98536,98537,98539,98541],{},[898,98538,2132],{},[1826,98540,1837],{},[898,98542,5502],{},[1655,98544,2346],{},[898,98546,4049],{},[1655,98548,1677],{"stretchy":1663},[1655,98550,2623],{},[2597,98552,98553,98555],{},[898,98554,2132],{},[898,98556,5502],{},[1655,98558,1671],{"separator":1670},[1967,98560],{"width":1969},[1820,98562,98563,98565],{},[898,98564,4049],{},[895,98566,98567,98569,98571],{},[898,98568,43826],{},[898,98570,1674],{},[898,98572,13166],{},[1655,98574,1657],{},[2597,98576,98577,98579],{},[898,98578,2132],{},[898,98580,5502],{},[1655,98582,2623],{},[1935,98584,98585,98587,98589],{},[898,98586,2132],{},[1826,98588,1837],{},[898,98590,5502],{},[898,98592,1719],{"mathvariant":1943},[902,98594,98595],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,98597,98598],{},[614,98599,98600,98601,98631,98632,97484,98645,6918,98662,97515,98675,1719],{},"Obrázek 2.19: Posun ",[883,98602,98604],{"className":98603},[886],[888,98605,98606],{"xmlns":890},[892,98607,98608,98628],{},[895,98609,98610,98612,98614,98620,98622,98624,98626],{},[898,98611,2838],{},[1655,98613,4393],{},[1820,98615,98616,98618],{},[898,98617,2838],{},[1826,98619,1837],{},[1655,98621,1657],{},[898,98623,2838],{},[1655,98625,2623],{},[898,98627,4049],{},[902,98629,98630],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,98633,98635],{"className":98634},[886],[888,98636,98637],{"xmlns":890},[892,98638,98639,98643],{},[895,98640,98641],{},[898,98642,4049],{},[902,98644,4049],{"encoding":904},[883,98646,98648],{"className":98647},[886],[888,98649,98650],{"xmlns":890},[892,98651,98652,98660],{},[895,98653,98654],{},[1820,98655,98656,98658],{},[898,98657,2838],{},[1826,98659,1837],{},[902,98661,39453],{"encoding":904},[883,98663,98665],{"className":98664},[886],[888,98666,98667],{"xmlns":890},[892,98668,98669,98673],{},[895,98670,98671],{},[898,98672,9920],{},[902,98674,9920],{"encoding":904},[883,98676,98678],{"className":98677},[886],[888,98679,98680],{"xmlns":890},[892,98681,98682,98690],{},[895,98683,98684],{},[1820,98685,98686,98688],{},[898,98687,5502],{},[1826,98689,1837],{},[902,98691,98692],{"encoding":904},"E_2",[198,98694,46509],{"id":98695},"příklad-210",[724,98697,98698,98700,98701,42816,98724,98743,98744,98761],{},[38,98699,39059],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,98702,98704],{"className":98703},[886],[888,98705,98706],{"xmlns":890},[892,98707,98708,98722],{},[895,98709,98710,98712,98714,98716,98718,98720],{},[898,98711,2132],{},[1655,98713,1657],{},[1826,98715,4771],{},[1655,98717,2623],{},[1826,98719,1837],{},[898,98721,1824],{},[902,98723,97564],{"encoding":904},[883,98725,98727],{"className":98726},[886],[888,98728,98729],{"xmlns":890},[892,98730,98731,98741],{},[895,98732,98733,98735,98737,98739],{},[898,98734,2132],{},[1655,98736,1657],{},[1826,98738,3639],{},[898,98740,1824],{},[902,98742,97584],{"encoding":904},". Daň ",[883,98745,98747],{"className":98746},[886],[888,98748,98749],{"xmlns":890},[892,98750,98751,98759],{},[895,98752,98753,98755,98757],{},[898,98754,4049],{},[1655,98756,1657],{},[1826,98758,3531],{},[902,98760,42394],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,98763,98764],{},[38,98765,39091],{},[724,98767,98768,98769,97775],{},"Nová poptávka je ",[883,98770,98772],{"className":98771},[886],[888,98773,98774],{"xmlns":890},[892,98775,98776,98812],{},[895,98777,98778,98784,98786,98788,98790,98792,98794,98796,98798,98800,98802,98804,98806,98808,98810],{},[1820,98779,98780,98782],{},[898,98781,2838],{},[1826,98783,1837],{},[1655,98785,2086],{},[898,98787,2132],{},[1655,98789,1657],{},[1826,98791,4771],{},[1655,98793,2623],{},[1826,98795,1837],{},[898,98797,1824],{},[1655,98799,2623],{},[1826,98801,3531],{},[1655,98803,1657],{},[1826,98805,3531],{},[1655,98807,2623],{},[1826,98809,1837],{},[898,98811,1824],{},[902,98813,98814],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,98816,98818],{"className":98817},[886],[888,98819,98820],{"xmlns":890,"display":29192},[892,98821,98822,98838],{},[895,98823,98824,98826,98828,98830,98832,98834,98836],{},[1826,98825,3531],{},[1655,98827,2623],{},[1826,98829,1837],{},[898,98831,1824],{},[1655,98833,1657],{},[1826,98835,3639],{},[898,98837,1824],{},[902,98839,98840],{"encoding":904},"6 - 2Q = 4Q",[724,98842,97808,98843,6838,98862,1343,98886,97889,98918,1719],{},[883,98844,98846],{"className":98845},[886],[888,98847,98848],{"xmlns":890},[892,98849,98850,98860],{},[895,98851,98852,98854,98856,98858],{},[1826,98853,3531],{},[898,98855,1824],{},[1655,98857,1657],{},[1826,98859,3531],{},[902,98861,97828],{"encoding":904},[883,98863,98865],{"className":98864},[886],[888,98866,98867],{"xmlns":890},[892,98868,98869,98883],{},[895,98870,98871,98879,98881],{},[1935,98872,98873,98875,98877],{},[898,98874,1824],{},[1826,98876,1837],{},[898,98878,5502],{},[1655,98880,1657],{},[1826,98882,1828],{},[902,98884,98885],{"encoding":904},"Q_2^E = 1",[883,98887,98889],{"className":98888},[886],[888,98890,98891],{"xmlns":890},[892,98892,98893,98915],{},[895,98894,98895,98903,98905,98907,98909,98911,98913],{},[1935,98896,98897,98899,98901],{},[898,98898,2132],{},[1826,98900,1837],{},[898,98902,5502],{},[1655,98904,1657],{},[1826,98906,3639],{},[1655,98908,2869],{},[1826,98910,1828],{},[1655,98912,1657],{},[1826,98914,3639],{},[902,98916,98917],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,98919,98921],{"className":98920},[886],[888,98922,98923],{"xmlns":890},[892,98924,98925,98943],{},[895,98926,98927,98933,98935,98937,98939,98941],{},[1820,98928,98929,98931],{},[898,98930,5502],{},[1826,98932,1837],{},[1655,98934,2734],{"stretchy":1663},[1826,98936,1828],{},[1655,98938,1671],{"separator":1670},[1826,98940,3639],{},[1655,98942,2743],{"stretchy":1663},[902,98944,98945],{"encoding":904},"E_2[1, 4]",[724,98947,98948,98949,98985,98986,97603],{},"Spotřebitel platí celkem ",[883,98950,98952],{"className":98951},[886],[888,98953,98954],{"xmlns":890},[892,98955,98956,98982],{},[895,98957,98958,98966,98968,98970,98972,98974,98976,98978,98980],{},[1935,98959,98960,98962,98964],{},[898,98961,2132],{},[1826,98963,1837],{},[898,98965,5502],{},[1655,98967,2346],{},[898,98969,4049],{},[1655,98971,1657],{},[1826,98973,3639],{},[1655,98975,2346],{},[1826,98977,3531],{},[1655,98979,1657],{},[1826,98981,4136],{},[902,98983,98984],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,98987,98989],{"className":98988},[886],[888,98990,98991],{"xmlns":890},[892,98992,98993,99007],{},[895,98994,98995,99003,99005],{},[1935,98996,98997,98999,99001],{},[898,98998,2132],{},[1826,99000,1837],{},[898,99002,5502],{},[1655,99004,1657],{},[1826,99006,3639],{},[902,99008,99009],{"encoding":904},"P_2^E = 4",[724,99011,99012],{},[614,99013,99014],{},"Rozklad daňového břemene:",[883,99016,99018],{"className":99017},[886],[888,99019,99020],{"xmlns":890,"display":29192},[892,99021,99022,99108],{},[895,99023,99024,99034,99036,99038,99040,99042,99044,99046,99048,99050,99052,99054,99056,99066,99068,99070,99082,99084,99086,99088,99090,99092,99094,99096,99106],{},[1820,99025,99026,99028],{},[898,99027,4049],{},[895,99029,99030,99032],{},[898,99031,43803],{},[898,99033,724],{},[1655,99035,1657],{},[1655,99037,1664],{"stretchy":1663},[1826,99039,3639],{},[1655,99041,2346],{},[1826,99043,3531],{},[1655,99045,1677],{"stretchy":1663},[1655,99047,2623],{},[1826,99049,6834],{},[1655,99051,1657],{},[1826,99053,1837],{},[2031,99055,2033],{},[895,99057,99058,99060],{},[2031,99059,1878],{},[9633,99061,99062,99064],{"accent":1670},[2031,99063,1789],{},[1655,99065,26184],{},[1655,99067,1671],{"separator":1670},[1967,99069],{"width":1969},[1820,99071,99072,99074],{},[898,99073,4049],{},[895,99075,99076,99078,99080],{},[898,99077,43826],{},[898,99079,1674],{},[898,99081,13166],{},[1655,99083,1657],{},[1826,99085,6834],{},[1655,99087,2623],{},[1826,99089,3639],{},[1655,99091,1657],{},[1826,99093,3639],{},[2031,99095,2033],{},[895,99097,99098,99100],{},[2031,99099,1878],{},[9633,99101,99102,99104],{"accent":1670},[2031,99103,1789],{},[1655,99105,26184],{},[898,99107,1719],{"mathvariant":1943},[902,99109,99110],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,99112,99113,99114,1719],{},"Opět ",[883,99115,99117],{"className":99116},[886],[888,99118,99119],{"xmlns":890},[892,99120,99121,99155],{},[895,99122,99123,99133,99135,99147,99149,99151,99153],{},[1820,99124,99125,99127],{},[898,99126,4049],{},[895,99128,99129,99131],{},[898,99130,43803],{},[898,99132,724],{},[1655,99134,2346],{},[1820,99136,99137,99139],{},[898,99138,4049],{},[895,99140,99141,99143,99145],{},[898,99142,43826],{},[898,99144,1674],{},[898,99146,13166],{},[1655,99148,1657],{},[1826,99150,3531],{},[1655,99152,1657],{},[898,99154,4049],{},[902,99156,99157],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[38096,99159],{},[115,99161,43784],{"id":99162},"daňové-břemeno",[724,99164,99165,2115,99167,99170,99171,99184],{},[38,99166,43784],{},[614,99168,99169],{},"tax burden",") je rozdělení zaplacené daně ",[883,99172,99174],{"className":99173},[886],[888,99175,99176],{"xmlns":890},[892,99177,99178,99182],{},[895,99179,99180],{},[898,99181,4049],{},[902,99183,4049],{"encoding":904}," mezi spotřebitele a výrobce:",[883,99186,99188],{"className":99187},[886],[888,99189,99190],{"xmlns":890,"display":29192},[892,99191,99192,99224],{},[895,99193,99194,99196,99198,99208,99210,99222],{},[898,99195,4049],{},[1655,99197,1657],{},[1820,99199,99200,99202],{},[898,99201,4049],{},[895,99203,99204,99206],{},[898,99205,43803],{},[898,99207,724],{},[1655,99209,2346],{},[1820,99211,99212,99214],{},[898,99213,4049],{},[895,99215,99216,99218,99220],{},[898,99217,43826],{},[898,99219,1674],{},[898,99221,13166],{},[898,99223,1719],{"mathvariant":1943},[902,99225,99226],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,99228,99229],{},[1723,99230],{"alt":99231,"className":99232,"src":99233},"imek-dan-rozklad-bremene-sklony",[210,1727],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[5120,99235,99236],{},[724,99237,99238,99240,99241,2704,99254,1719],{},[883,99239,5406],{}," 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 ",[883,99242,99244],{"className":99243},[886],[888,99245,99246],{"xmlns":890},[892,99247,99248,99252],{},[895,99249,99250],{},[898,99251,2838],{},[902,99253,2838],{"encoding":904},[883,99255,99257],{"className":99256},[886],[888,99258,99259],{"xmlns":890},[892,99260,99261,99265],{},[895,99262,99263],{},[898,99264,9920],{},[902,99266,9920],{"encoding":904},[198,99268,3729],{"id":3728},[724,99270,99271,99272,99293,99294,99307,99308,99325,99326,99339],{},"V grafu ",[883,99273,99275],{"className":99274},[886],[888,99276,99277],{"xmlns":890},[892,99278,99279,99291],{},[895,99280,99281,99283,99285,99287,99289],{},[1655,99282,1664],{"stretchy":1663},[898,99284,1824],{},[1655,99286,1671],{"separator":1670},[898,99288,2132],{},[1655,99290,1677],{"stretchy":1663},[902,99292,38817],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,99295,99297],{"className":99296},[886],[888,99298,99299],{"xmlns":890},[892,99300,99301,99305],{},[895,99302,99303],{},[898,99304,4049],{},[902,99306,4049],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,99309,99311],{"className":99310},[886],[888,99312,99313],{"xmlns":890},[892,99314,99315,99323],{},[895,99316,99317],{},[2597,99318,99319,99321],{},[898,99320,2132],{},[898,99322,5502],{},[902,99324,42592],{"encoding":904},", rozdělí se úsečka ",[883,99327,99329],{"className":99328},[886],[888,99330,99331],{"xmlns":890},[892,99332,99333,99337],{},[895,99334,99335],{},[898,99336,4049],{},[902,99338,4049],{"encoding":904}," na dvě části:",[120,99341,99342,99367],{},[123,99343,99344,99345,99366],{},"horní část odpovídá ",[883,99346,99348],{"className":99347},[886],[888,99349,99350],{"xmlns":890},[892,99351,99352,99364],{},[895,99353,99354],{},[1820,99355,99356,99358],{},[898,99357,4049],{},[895,99359,99360,99362],{},[898,99361,43803],{},[898,99363,724],{},[902,99365,43808],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,99368,99369,99370,99393],{},"dolní část odpovídá ",[883,99371,99373],{"className":99372},[886],[888,99374,99375],{"xmlns":890},[892,99376,99377,99391],{},[895,99378,99379],{},[1820,99380,99381,99383],{},[898,99382,4049],{},[895,99384,99385,99387,99389],{},[898,99386,43826],{},[898,99388,1674],{},[898,99390,13166],{},[902,99392,43833],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,99395,99396],{},[614,99397,99398,99399,3962,99412,99433,99434,99457,99458,2704,99479,99502],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,99400,99402],{"className":99401},[886],[888,99403,99404],{"xmlns":890},[892,99405,99406,99410],{},[895,99407,99408],{},[898,99409,4049],{},[902,99411,4049],{"encoding":904},[883,99413,99415],{"className":99414},[886],[888,99416,99417],{"xmlns":890},[892,99418,99419,99431],{},[895,99420,99421],{},[1820,99422,99423,99425],{},[898,99424,4049],{},[895,99426,99427,99429],{},[898,99428,43803],{},[898,99430,724],{},[902,99432,43808],{"encoding":904}," (nahoře) a ",[883,99435,99437],{"className":99436},[886],[888,99438,99439],{"xmlns":890},[892,99440,99441,99455],{},[895,99442,99443],{},[1820,99444,99445,99447],{},[898,99446,4049],{},[895,99448,99449,99451,99453],{},[898,99450,43826],{},[898,99452,1674],{},[898,99454,13166],{},[902,99456,43833],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,99459,99461],{"className":99460},[886],[888,99462,99463],{"xmlns":890},[892,99464,99465,99477],{},[895,99466,99467],{},[1820,99468,99469,99471],{},[898,99470,4049],{},[895,99472,99473,99475],{},[898,99474,43803],{},[898,99476,724],{},[902,99478,43808],{"encoding":904},[883,99480,99482],{"className":99481},[886],[888,99483,99484],{"xmlns":890},[892,99485,99486,99500],{},[895,99487,99488],{},[1820,99489,99490,99492],{},[898,99491,4049],{},[895,99493,99494,99496,99498],{},[898,99495,43826],{},[898,99497,1674],{},[898,99499,13166],{},[902,99501,43833],{"encoding":904}," je v obou případech stejná.",[198,99504,99506],{"id":99505},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,99508,99509,99510,99513,99514,2115,99537,99554,99555,2115,99578,99595],{},"Platí obecně: ",[38,99511,99512],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,99515,99517],{"className":99516},[886],[888,99518,99519],{"xmlns":890},[892,99520,99521,99535],{},[895,99522,99523,99525,99527,99529,99531,99533],{},[898,99524,2132],{},[1655,99526,1657],{},[898,99528,207],{},[898,99530,1824],{},[1655,99532,2346],{},[898,99534,2025],{},[902,99536,38186],{"encoding":904},[883,99538,99540],{"className":99539},[886],[888,99541,99542],{"xmlns":890},[892,99543,99544,99552],{},[895,99545,99546,99548,99550],{},[898,99547,207],{},[1655,99549,3065],{},[1826,99551,2552],{},[902,99553,44211],{"encoding":904},") a lineární nabídku ",[883,99556,99558],{"className":99557},[886],[888,99559,99560],{"xmlns":890},[892,99561,99562,99576],{},[895,99563,99564,99566,99568,99570,99572,99574],{},[898,99565,2132],{},[1655,99567,1657],{},[898,99569,1789],{},[898,99571,1824],{},[1655,99573,2346],{},[898,99575,2410],{},[902,99577,41368],{"encoding":904},[883,99579,99581],{"className":99580},[886],[888,99582,99583],{"xmlns":890},[892,99584,99585,99593],{},[895,99586,99587,99589,99591],{},[898,99588,1789],{},[1655,99590,2969],{},[1826,99592,2552],{},[902,99594,41386],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,99597,99599],{"className":99598},[886],[888,99600,99601],{"xmlns":890,"display":29192},[892,99602,99603,99669],{},[895,99604,99605,99629,99631,99641,99643,99667],{},[1949,99606,99607,99617],{},[1820,99608,99609,99611],{},[898,99610,4049],{},[895,99612,99613,99615],{},[898,99614,43803],{},[898,99616,724],{},[1820,99618,99619,99621],{},[898,99620,4049],{},[895,99622,99623,99625,99627],{},[898,99624,43826],{},[898,99626,1674],{},[898,99628,13166],{},[1655,99630,1657],{},[1949,99632,99633,99635],{},[898,99634,1789],{},[895,99636,99637,99639],{},[1655,99638,2623],{},[898,99640,207],{},[1655,99642,1657],{},[1949,99644,99645,99657],{},[895,99646,99647,99650,99653,99655],{},[898,99648,99649],{"mathvariant":1943},"∣",[2031,99651,99652],{},"sklon ",[898,99654,9920],{},[898,99656,99649],{"mathvariant":1943},[895,99658,99659,99661,99663,99665],{},[898,99660,99649],{"mathvariant":1943},[2031,99662,99652],{},[898,99664,2838],{},[898,99666,99649],{"mathvariant":1943},[898,99668,1719],{"mathvariant":1943},[902,99670,99671],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[5120,99673,99674,99679],{},[724,99675,99676,99678],{},[883,99677,5821],{}," Postup výpočtu rozkladu",[152,99680,99681,99716,99769,99848],{},[123,99682,99683,99684,99715],{},"Spočti rovnovážný bod ",[883,99685,99687],{"className":99686},[886],[888,99688,99689],{"xmlns":890},[892,99690,99691,99713],{},[895,99692,99693,99695,99697,99703,99705,99711],{},[898,99694,5502],{},[1655,99696,2734],{"stretchy":1663},[2597,99698,99699,99701],{},[898,99700,1824],{},[898,99702,5502],{},[1655,99704,1671],{"separator":1670},[2597,99706,99707,99709],{},[898,99708,2132],{},[898,99710,5502],{},[1655,99712,2743],{"stretchy":1663},[902,99714,42493],{"encoding":904}," bez daně.",[123,99717,99718,99719,1348,99744,5171],{},"Urči posunutou křivku (",[883,99720,99722],{"className":99721},[886],[888,99723,99724],{"xmlns":890},[892,99725,99726,99742],{},[895,99727,99728,99734,99736,99738,99740],{},[1820,99729,99730,99732],{},[898,99731,9920],{},[1826,99733,1828],{},[1655,99735,1657],{},[898,99737,9920],{},[1655,99739,2346],{},[898,99741,4049],{},[902,99743,43880],{"encoding":904},[883,99745,99747],{"className":99746},[886],[888,99748,99749],{"xmlns":890},[892,99750,99751,99767],{},[895,99752,99753,99759,99761,99763,99765],{},[1820,99754,99755,99757],{},[898,99756,2838],{},[1826,99758,1837],{},[1655,99760,1657],{},[898,99762,2838],{},[1655,99764,2623],{},[898,99766,4049],{},[902,99768,43911],{"encoding":904},[123,99770,99771,99772,5163,99791,13253,99810,5163,99829,5171],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,99773,99775],{"className":99774},[886],[888,99776,99777],{"xmlns":890},[892,99778,99779,99789],{},[895,99780,99781],{},[1935,99782,99783,99785,99787],{},[898,99784,1824],{},[1826,99786,1828],{},[898,99788,5502],{},[902,99790,48962],{"encoding":904},[883,99792,99794],{"className":99793},[886],[888,99795,99796],{"xmlns":890},[892,99797,99798,99808],{},[895,99799,99800],{},[1935,99801,99802,99804,99806],{},[898,99803,1824],{},[1826,99805,1837],{},[898,99807,5502],{},[902,99809,49024],{"encoding":904},[883,99811,99813],{"className":99812},[886],[888,99814,99815],{"xmlns":890},[892,99816,99817,99827],{},[895,99818,99819],{},[1935,99820,99821,99823,99825],{},[898,99822,2132],{},[1826,99824,1828],{},[898,99826,5502],{},[902,99828,48983],{"encoding":904},[883,99830,99832],{"className":99831},[886],[888,99833,99834],{"xmlns":890},[892,99835,99836,99846],{},[895,99837,99838],{},[1935,99839,99840,99842,99844],{},[898,99841,2132],{},[1826,99843,1837],{},[898,99845,5502],{},[902,99847,49044],{"encoding":904},[123,99849,99850,99851,2704,99872,99895,99896,1719],{},"Dopočítej ",[883,99852,99854],{"className":99853},[886],[888,99855,99856],{"xmlns":890},[892,99857,99858,99870],{},[895,99859,99860],{},[1820,99861,99862,99864],{},[898,99863,4049],{},[895,99865,99866,99868],{},[898,99867,43803],{},[898,99869,724],{},[902,99871,43808],{"encoding":904},[883,99873,99875],{"className":99874},[886],[888,99876,99877],{"xmlns":890},[892,99878,99879,99893],{},[895,99880,99881],{},[1820,99882,99883,99885],{},[898,99884,4049],{},[895,99886,99887,99889,99891],{},[898,99888,43826],{},[898,99890,1674],{},[898,99892,13166],{},[902,99894,43833],{"encoding":904}," z definice, vždy ověř ",[883,99897,99899],{"className":99898},[886],[888,99900,99901],{"xmlns":890},[892,99902,99903,99933],{},[895,99904,99905,99915,99917,99929,99931],{},[1820,99906,99907,99909],{},[898,99908,4049],{},[895,99910,99911,99913],{},[898,99912,43803],{},[898,99914,724],{},[1655,99916,2346],{},[1820,99918,99919,99921],{},[898,99920,4049],{},[895,99922,99923,99925,99927],{},[898,99924,43826],{},[898,99926,1674],{},[898,99928,13166],{},[1655,99930,1657],{},[898,99932,4049],{},[902,99934,99935],{"encoding":904},"T_{sp} + T_{vyr} = T",[5120,99937,99938],{},[724,99939,99940,99942,99943,99946,99947,2704,99960,99973],{},[883,99941,5661],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,99944,99945],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,99948,99950],{"className":99949},[886],[888,99951,99952],{"xmlns":890},[892,99953,99954,99958],{},[895,99955,99956],{},[898,99957,2838],{},[902,99959,2838],{"encoding":904},[883,99961,99963],{"className":99962},[886],[888,99964,99965],{"xmlns":890},[892,99966,99967,99971],{},[895,99968,99969],{},[898,99970,9920],{},[902,99972,9920],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[38096,99975],{},[115,99977,99979],{"id":99978},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,99981,99982],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,99984,99985],{},[1723,99986],{"alt":99987,"className":99988,"src":99989},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,1727],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,99991,99992,100004],{},[19,99993,99994],{},[22,99995,99996,99998,100001],{},[25,99997,55422],{},[25,99999,100000],{},"(a) daň výrobci",[25,100002,100003],{},"(b) daň spotřebiteli",[30,100005,100006,100061,100128,100188],{},[22,100007,100008,100011,100036],{},[35,100009,100010],{},"Rovnovážné množství",[35,100012,100013],{},[883,100014,100016],{"className":100015},[886],[888,100017,100018],{"xmlns":890},[892,100019,100020,100034],{},[895,100021,100022,100030,100032],{},[1935,100023,100024,100026,100028],{},[898,100025,1824],{},[1826,100027,1828],{},[898,100029,5502],{},[1655,100031,1657],{},[1826,100033,1828],{},[902,100035,97852],{"encoding":904},[35,100037,100038],{},[883,100039,100041],{"className":100040},[886],[888,100042,100043],{"xmlns":890},[892,100044,100045,100059],{},[895,100046,100047,100055,100057],{},[1935,100048,100049,100051,100053],{},[898,100050,1824],{},[1826,100052,1837],{},[898,100054,5502],{},[1655,100056,1657],{},[1826,100058,1828],{},[902,100060,98885],{"encoding":904},[22,100062,100063,100066,100091],{},[35,100064,100065],{},"Cena placená spotřebitelem",[35,100067,100068],{},[883,100069,100071],{"className":100070},[886],[888,100072,100073],{"xmlns":890},[892,100074,100075,100089],{},[895,100076,100077,100085,100087],{},[1935,100078,100079,100081,100083],{},[898,100080,2132],{},[1826,100082,1828],{},[898,100084,5502],{},[1655,100086,1657],{},[1826,100088,4136],{},[902,100090,97947],{"encoding":904},[35,100092,100093],{},[883,100094,100096],{"className":100095},[886],[888,100097,100098],{"xmlns":890},[892,100099,100100,100126],{},[895,100101,100102,100110,100112,100114,100116,100118,100120,100122,100124],{},[1935,100103,100104,100106,100108],{},[898,100105,2132],{},[1826,100107,1837],{},[898,100109,5502],{},[1655,100111,2346],{},[898,100113,4049],{},[1655,100115,1657],{},[1826,100117,3639],{},[1655,100119,2346],{},[1826,100121,3531],{},[1655,100123,1657],{},[1826,100125,4136],{},[902,100127,98984],{"encoding":904},[22,100129,100130,100133,100163],{},[35,100131,100132],{},"Cena přijímaná výrobcem",[35,100134,100135],{},[883,100136,100138],{"className":100137},[886],[888,100139,100140],{"xmlns":890},[892,100141,100142,100160],{},[895,100143,100144,100152,100154,100156,100158],{},[1935,100145,100146,100148,100150],{},[898,100147,2132],{},[1826,100149,1828],{},[898,100151,5502],{},[1655,100153,2623],{},[898,100155,4049],{},[1655,100157,1657],{},[1826,100159,3639],{},[902,100161,100162],{"encoding":904},"P_1^E - T = 4",[35,100164,100165],{},[883,100166,100168],{"className":100167},[886],[888,100169,100170],{"xmlns":890},[892,100171,100172,100186],{},[895,100173,100174,100182,100184],{},[1935,100175,100176,100178,100180],{},[898,100177,2132],{},[1826,100179,1837],{},[898,100181,5502],{},[1655,100183,1657],{},[1826,100185,3639],{},[902,100187,99009],{"encoding":904},[22,100189,100190,100193,100247],{},[35,100191,100192],{},"Rozklad břemene",[35,100194,100195,1343,100220],{},[883,100196,100198],{"className":100197},[886],[888,100199,100200],{"xmlns":890},[892,100201,100202,100218],{},[895,100203,100204,100214,100216],{},[1820,100205,100206,100208],{},[898,100207,4049],{},[895,100209,100210,100212],{},[898,100211,43803],{},[898,100213,724],{},[1655,100215,1657],{},[1826,100217,1837],{},[902,100219,44102],{"encoding":904},[883,100221,100223],{"className":100222},[886],[888,100224,100225],{"xmlns":890},[892,100226,100227,100245],{},[895,100228,100229,100241,100243],{},[1820,100230,100231,100233],{},[898,100232,4049],{},[895,100234,100235,100237,100239],{},[898,100236,43826],{},[898,100238,1674],{},[898,100240,13166],{},[1655,100242,1657],{},[1826,100244,3639],{},[902,100246,44131],{"encoding":904},[35,100248,100249,1343,100274],{},[883,100250,100252],{"className":100251},[886],[888,100253,100254],{"xmlns":890},[892,100255,100256,100272],{},[895,100257,100258,100268,100270],{},[1820,100259,100260,100262],{},[898,100261,4049],{},[895,100263,100264,100266],{},[898,100265,43803],{},[898,100267,724],{},[1655,100269,1657],{},[1826,100271,1837],{},[902,100273,44102],{"encoding":904},[883,100275,100277],{"className":100276},[886],[888,100278,100279],{"xmlns":890},[892,100280,100281,100299],{},[895,100282,100283,100295,100297],{},[1820,100284,100285,100287],{},[898,100286,4049],{},[895,100288,100289,100291,100293],{},[898,100290,43826],{},[898,100292,1674],{},[898,100294,13166],{},[1655,100296,1657],{},[1826,100298,3639],{},[902,100300,44131],{"encoding":904},[724,100302,100303],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,100305,100307],{"className":100306},[886],[888,100308,100309],{"xmlns":890,"display":29192},[892,100310,100311,100359],{},[895,100312,100313,100321,100323,100331,100333,100335,100343,100345,100347,100349,100357],{},[1935,100314,100315,100317,100319],{},[898,100316,1824],{},[1826,100318,1828],{},[898,100320,5502],{},[1655,100322,1657],{},[1935,100324,100325,100327,100329],{},[898,100326,1824],{},[1826,100328,1837],{},[898,100330,5502],{},[1655,100332,1671],{"separator":1670},[1967,100334],{"width":1969},[1935,100336,100337,100339,100341],{},[898,100338,2132],{},[1826,100340,1828],{},[898,100342,5502],{},[1655,100344,2623],{},[898,100346,4049],{},[1655,100348,1657],{},[1935,100350,100351,100353,100355],{},[898,100352,2132],{},[1826,100354,1837],{},[898,100356,5502],{},[898,100358,1719],{"mathvariant":1943},[902,100360,100361],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[5120,100363,100364,100383,100537],{},[724,100365,100366,100368,100369,100382],{},[883,100367,5821],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,100370,100372],{"className":100371},[886],[888,100373,100374],{"xmlns":890},[892,100375,100376,100380],{},[895,100377,100378],{},[898,100379,4049],{},[902,100381,4049],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,100384,100385,100417,100453,100490],{},[123,100386,100387,100388,1671],{},"rovnovážná množství obou režimů, ",[883,100389,100391],{"className":100390},[886],[888,100392,100393],{"xmlns":890},[892,100394,100395,100415],{},[895,100396,100397,100405,100407],{},[1935,100398,100399,100401,100403],{},[898,100400,1824],{},[1826,100402,1828],{},[898,100404,5502],{},[1655,100406,1657],{},[1935,100408,100409,100411,100413],{},[898,100410,1824],{},[1826,100412,1837],{},[898,100414,5502],{},[902,100416,44034],{"encoding":904},[123,100418,100419,100420,1671],{},"čistá cena přijímaná výrobcem, ",[883,100421,100423],{"className":100422},[886],[888,100424,100425],{"xmlns":890},[892,100426,100427,100451],{},[895,100428,100429,100437,100439,100441,100443],{},[1935,100430,100431,100433,100435],{},[898,100432,2132],{},[1826,100434,1828],{},[898,100436,5502],{},[1655,100438,2623],{},[898,100440,4049],{},[1655,100442,1657],{},[1935,100444,100445,100447,100449],{},[898,100446,2132],{},[1826,100448,1837],{},[898,100450,5502],{},[902,100452,44068],{"encoding":904},[123,100454,100455,100456,1671],{},"celková cena placená spotřebitelem, ",[883,100457,100459],{"className":100458},[886],[888,100460,100461],{"xmlns":890},[892,100462,100463,100487],{},[895,100464,100465,100473,100475,100483,100485],{},[1935,100466,100467,100469,100471],{},[898,100468,2132],{},[1826,100470,1828],{},[898,100472,5502],{},[1655,100474,1657],{},[1935,100476,100477,100479,100481],{},[898,100478,2132],{},[1826,100480,1837],{},[898,100482,5502],{},[1655,100484,2346],{},[898,100486,4049],{},[902,100488,100489],{"encoding":904},"P_1^E = P_2^E + T",[123,100491,100492,100493,2704,100514,1719],{},"rozklad daňového břemene ",[883,100494,100496],{"className":100495},[886],[888,100497,100498],{"xmlns":890},[892,100499,100500,100512],{},[895,100501,100502],{},[1820,100503,100504,100506],{},[898,100505,4049],{},[895,100507,100508,100510],{},[898,100509,43803],{},[898,100511,724],{},[902,100513,43808],{"encoding":904},[883,100515,100517],{"className":100516},[886],[888,100518,100519],{"xmlns":890},[892,100520,100521,100535],{},[895,100522,100523],{},[1820,100524,100525,100527],{},[898,100526,4049],{},[895,100528,100529,100531,100533],{},[898,100530,43826],{},[898,100532,1674],{},[898,100534,13166],{},[902,100536,43833],{"encoding":904},[724,100538,100539,100540,1719],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,100541,36323],{},[724,100543,100544,100545,2704,100558,5171],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,100546,100548],{"className":100547},[886],[888,100549,100550],{"xmlns":890},[892,100551,100552,100556],{},[895,100553,100554],{},[898,100555,2838],{},[902,100557,2838],{"encoding":904},[883,100559,100561],{"className":100560},[886],[888,100562,100563],{"xmlns":890},[892,100564,100565,100569],{},[895,100566,100567],{},[898,100568,9920],{},[902,100570,9920],{"encoding":904},[38096,100572],{},[115,100574,100576],{"id":100575},"úlohy","Úlohy",[724,100578,100579,100580,4421],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,100581,17365],{"className":100582,"dataFsResolvedFilePath":800,"href":801},[210],[120,100584,100585,100615,100646],{},[123,100586,100587,100590,100591,100614],{},[38,100588,100589],{},"Úloha 2.4"," — Poptávka ",[883,100592,100594],{"className":100593},[886],[888,100595,100596],{"xmlns":890},[892,100597,100598,100612],{},[895,100599,100600,100602,100604,100606,100608,100610],{},[898,100601,2132],{},[1655,100603,1657],{},[1826,100605,4771],{},[1655,100607,2623],{},[1826,100609,1837],{},[898,100611,1824],{},[902,100613,97564],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,100616,100617,100620,100621,100645],{},[38,100618,100619],{},"Úloha 2.9"," — Nabídka ",[883,100622,100624],{"className":100623},[886],[888,100625,100626],{"xmlns":890},[892,100627,100628,100642],{},[895,100629,100630,100632,100634,100636,100638,100640],{},[898,100631,2132],{},[1655,100633,1657],{},[1826,100635,6258],{},[898,100637,1824],{},[1655,100639,2346],{},[1826,100641,37370],{},[902,100643,100644],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,100647,100648,100651,100652,2704,100678,100702,100703,100720],{},[38,100649,100650],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,100653,100655],{"className":100654},[886],[888,100656,100657],{"xmlns":890},[892,100658,100659,100675],{},[895,100660,100661,100663,100665,100667,100669,100671,100673],{},[898,100662,2132],{},[1655,100664,1657],{},[1655,100666,2623],{},[1826,100668,3639],{},[898,100670,1824],{},[1655,100672,2346],{},[1826,100674,47829],{},[902,100676,100677],{"encoding":904},"P = -4Q + 80",[883,100679,100681],{"className":100680},[886],[888,100682,100683],{"xmlns":890},[892,100684,100685,100699],{},[895,100686,100687,100689,100691,100693,100695,100697],{},[898,100688,2132],{},[1655,100690,1657],{},[1826,100692,3472],{},[898,100694,1824],{},[1655,100696,2346],{},[1826,100698,4136],{},[902,100700,100701],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,100704,100706],{"className":100705},[886],[888,100707,100708],{"xmlns":890},[892,100709,100710,100718],{},[895,100711,100712,100714,100716],{},[898,100713,4049],{},[1655,100715,1657],{},[1826,100717,25327],{},[902,100719,48941],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,100722,100723,100724,100726,100727,100729],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,100725,46354],{}," (posun poptávky při zdanění kupujícího) a ",[38,100728,46388],{}," (posun nabídky při zdanění výrobce).",[38096,100731],{},[115,100733,16845],{"id":16844},[120,100735,100736,100755,100813,100870,100953,100999,101042,101087,101153],{},[123,100737,100738,3106,100741,100754],{},[38,100739,100740],{},"Jednotková daň",[883,100742,100744],{"className":100743},[886],[888,100745,100746],{"xmlns":890},[892,100747,100748,100752],{},[895,100749,100750],{},[898,100751,4049],{},[902,100753,4049],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,100756,100757,100759,100760,100798,100799,100812],{},[38,100758,97146],{}," — posun nabídky ",[883,100761,100763],{"className":100762},[886],[888,100764,100765],{"xmlns":890},[892,100766,100767,100795],{},[895,100768,100769,100775,100777,100779,100781,100783,100785,100787,100789,100791,100793],{},[1820,100770,100771,100773],{},[898,100772,9920],{},[1826,100774,1828],{},[1655,100776,1664],{"stretchy":1663},[898,100778,1824],{},[1655,100780,1677],{"stretchy":1663},[1655,100782,1657],{},[898,100784,9920],{},[1655,100786,1664],{"stretchy":1663},[898,100788,1824],{},[1655,100790,1677],{"stretchy":1663},[1655,100792,2346],{},[898,100794,4049],{},[902,100796,100797],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,100800,100802],{"className":100801},[886],[888,100803,100804],{"xmlns":890},[892,100805,100806,100810],{},[895,100807,100808],{},[898,100809,4049],{},[902,100811,4049],{"encoding":904}," svisle nahoru)",[123,100814,100815,100817,100818,100798,100856,100869],{},[38,100816,98219],{}," — posun poptávky ",[883,100819,100821],{"className":100820},[886],[888,100822,100823],{"xmlns":890},[892,100824,100825,100853],{},[895,100826,100827,100833,100835,100837,100839,100841,100843,100845,100847,100849,100851],{},[1820,100828,100829,100831],{},[898,100830,2838],{},[1826,100832,1837],{},[1655,100834,1664],{"stretchy":1663},[898,100836,1824],{},[1655,100838,1677],{"stretchy":1663},[1655,100840,1657],{},[898,100842,2838],{},[1655,100844,1664],{"stretchy":1663},[898,100846,1824],{},[1655,100848,1677],{"stretchy":1663},[1655,100850,2623],{},[898,100852,4049],{},[902,100854,100855],{"encoding":904},"D_2(Q) = D(Q) - T",[883,100857,100859],{"className":100858},[886],[888,100860,100861],{"xmlns":890},[892,100862,100863,100867],{},[895,100864,100865],{},[898,100866,4049],{},[902,100868,4049],{"encoding":904}," svisle dolů)",[123,100871,100872,8262,100875,42940,100914],{},[38,100873,100874],{},"Rovnovážný bod s daní",[883,100876,100878],{"className":100877},[886],[888,100879,100880],{"xmlns":890},[892,100881,100882,100912],{},[895,100883,100884,100890,100892,100900,100902,100910],{},[1820,100885,100886,100888],{},[898,100887,5502],{},[1826,100889,1828],{},[1655,100891,2734],{"stretchy":1663},[1935,100893,100894,100896,100898],{},[898,100895,1824],{},[1826,100897,1828],{},[898,100899,5502],{},[1655,100901,1671],{"separator":1670},[1935,100903,100904,100906,100908],{},[898,100905,2132],{},[1826,100907,1828],{},[898,100909,5502],{},[1655,100911,2743],{"stretchy":1663},[902,100913,97314],{"encoding":904},[883,100915,100917],{"className":100916},[886],[888,100918,100919],{"xmlns":890},[892,100920,100921,100951],{},[895,100922,100923,100929,100931,100939,100941,100949],{},[1820,100924,100925,100927],{},[898,100926,5502],{},[1826,100928,1837],{},[1655,100930,2734],{"stretchy":1663},[1935,100932,100933,100935,100937],{},[898,100934,1824],{},[1826,100936,1837],{},[898,100938,5502],{},[1655,100940,1671],{"separator":1670},[1935,100942,100943,100945,100947],{},[898,100944,2132],{},[1826,100946,1837],{},[898,100948,5502],{},[1655,100950,2743],{"stretchy":1663},[902,100952,98389],{"encoding":904},[123,100954,100955,2115,100957,100959,100960],{},[38,100956,43784],{},[614,100958,99169],{},") — rozklad ",[883,100961,100963],{"className":100962},[886],[888,100964,100965],{"xmlns":890},[892,100966,100967,100997],{},[895,100968,100969,100971,100973,100983,100985],{},[898,100970,4049],{},[1655,100972,1657],{},[1820,100974,100975,100977],{},[898,100976,4049],{},[895,100978,100979,100981],{},[898,100980,43803],{},[898,100982,724],{},[1655,100984,2346],{},[1820,100986,100987,100989],{},[898,100988,4049],{},[895,100990,100991,100993,100995],{},[898,100992,43826],{},[898,100994,1674],{},[898,100996,13166],{},[902,100998,43970],{"encoding":904},[123,101000,101001,101024,101025,1677],{},[38,101002,101003],{},[883,101004,101006],{"className":101005},[886],[888,101007,101008],{"xmlns":890},[892,101009,101010,101022],{},[895,101011,101012],{},[1820,101013,101014,101016],{},[898,101015,4049],{},[895,101017,101018,101020],{},[898,101019,43803],{},[898,101021,724],{},[902,101023,43808],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,101026,101028],{"className":101027},[886],[888,101029,101030],{"xmlns":890},[892,101031,101032,101040],{},[895,101033,101034],{},[2597,101035,101036,101038],{},[898,101037,2132],{},[898,101039,5502],{},[902,101041,42592],{"encoding":904},[123,101043,101044,101069,101070,1677],{},[38,101045,101046],{},[883,101047,101049],{"className":101048},[886],[888,101050,101051],{"xmlns":890},[892,101052,101053,101067],{},[895,101054,101055],{},[1820,101056,101057,101059],{},[898,101058,4049],{},[895,101060,101061,101063,101065],{},[898,101062,43826],{},[898,101064,1674],{},[898,101066,13166],{},[902,101068,43833],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,101071,101073],{"className":101072},[886],[888,101074,101075],{"xmlns":890},[892,101076,101077,101085],{},[895,101078,101079],{},[2597,101080,101081,101083],{},[898,101082,2132],{},[898,101084,5502],{},[902,101086,42592],{"encoding":904},[123,101088,101089,8262,101091,1343,101120],{},[38,101090,51600],{},[883,101092,101094],{"className":101093},[886],[888,101095,101096],{"xmlns":890},[892,101097,101098,101118],{},[895,101099,101100,101108,101110],{},[1935,101101,101102,101104,101106],{},[898,101103,1824],{},[1826,101105,1828],{},[898,101107,5502],{},[1655,101109,1657],{},[1935,101111,101112,101114,101116],{},[898,101113,1824],{},[1826,101115,1837],{},[898,101117,5502],{},[902,101119,44034],{"encoding":904},[883,101121,101123],{"className":101122},[886],[888,101124,101125],{"xmlns":890},[892,101126,101127,101151],{},[895,101128,101129,101137,101139,101141,101143],{},[1935,101130,101131,101133,101135],{},[898,101132,2132],{},[1826,101134,1828],{},[898,101136,5502],{},[1655,101138,2623],{},[898,101140,4049],{},[1655,101142,1657],{},[1935,101144,101145,101147,101149],{},[898,101146,2132],{},[1826,101148,1837],{},[898,101150,5502],{},[902,101152,44068],{"encoding":904},[123,101154,101155,101158],{},[38,101156,101157],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[38096,101160],{},[115,101162,3187],{"id":3186},[120,101164,101165,101173,101191,101198],{},[123,101166,101167,3106,101170],{},[38,101168,101169],{},"Kontext (hub):",[207,101171,802],{"className":101172,"dataFsResolvedFilePath":800,"href":801},[210],[123,101174,101175,3106,101177,101180,101181,19774,101183,101186,101187,101190],{},[38,101176,51849],{},[207,101178,820],{"className":101179,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,101182,56160],{},[207,101184,3645],{"className":101185,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,101188,3223],{"className":101189,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,101192,101193,3106,101195],{},[38,101194,51884],{},[207,101196,51888],{"className":101197,"dataFsResolvedFilePath":745,"href":746},[210],[123,101199,101200,3106,101202],{},[38,101201,17329],{},[207,101203,17333],{"className":101204,"dataFsResolvedFilePath":3274,"href":3275},[210],{"title":641,"searchDepth":642,"depth":642,"links":101206},[101207,101208,101211,101214,101218,101219,101220,101221],{"id":97051,"depth":642,"text":97052},{"id":97145,"depth":642,"text":97146,"children":101209},[101210],{"id":97536,"depth":649,"text":46429},{"id":98218,"depth":642,"text":98219,"children":101212},[101213],{"id":98695,"depth":649,"text":46509},{"id":99162,"depth":642,"text":43784,"children":101215},[101216,101217],{"id":3728,"depth":649,"text":3729},{"id":99505,"depth":649,"text":99506},{"id":99978,"depth":642,"text":99979},{"id":100575,"depth":642,"text":100576},{"id":16844,"depth":642,"text":16845},{"id":3186,"depth":642,"text":3187},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":96949,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,51949,101228,101229,101230,17365],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[101233,101235,101237,101241,101245,101248,101252,101256],{"slug":1145,"path":765,"title":3262,"snippet":101234},"… 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