[{"data":1,"prerenderedAt":100793},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-imek-kniha":1626,"course-stats-imek":2690,"course-topics-imek":2694,"backlinks-imek-kniha":100780,"related-imek-kniha":100787},{"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":2689},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":2676,"description":2677,"extension":661,"meta":2678,"navigation":664,"path":2679,"seo":2680,"sources":2681,"stem":2682,"tags":2683,"type":2687,"updated":677,"__hash__":2688},"summaries\u002Fsummaries\u002Fimek-kniha.md","Kniha — *Úvod do matematické ekonomie pro ekonomy*",{"type":9,"value":1631,"toc":2656},[1632,1638,1656,1665,1669,1676,1686,1697,1704,1818,1825,1832,1877,1883,1890,2144,2150,2157,2356,2362,2369,2413,2419,2423,2426,2549,2553,2596,2600,2617,2621],[12,1633,1635,1636],{"id":1634},"kniha-úvod-do-matematické-ekonomie-pro-ekonomy","Kniha — ",[614,1637,1031],{},[724,1639,1640,1641,1647,1648,1651,1652,1655],{},"Doporučená literatura k předmětu ",[207,1642,1646],{"className":1643,"href":1644,"dataFsResolvedFilePath":1645},[210],"\u002Fwiki\u002Fimek","courses\u002Fimek.md","Matematická ekonomie",", autor ",[38,1649,1650],{},"I. Mezník",", vydavatelství FP VUT \u002F CERM, Brno 2017. Studentské naskenované fotografie pokrývají ",[38,1653,1654],{},"kapitoly 2 až 7"," (stran 34–144, celkem 107 unikátních stran).",[724,1657,1658,1659,1664],{},"Text je hlavním zdrojem obsahu pro většinu topiců ImeK — kniha poskytuje podrobný matematický a ekonomický výklad, všechny pracovní příklady (s plnými řešeními), soubory úloh k samostatnému řešení i otázky k sebehodnocení. Obsah byl strojově přepsán do strukturovaných českých studijních materiálů v ",[207,1660,1663],{"className":1661,"href":1662},[210],"\u002Fwiki\u002F#Pokrytí topiců","#Pokrytí topiců",".",[115,1666,1668],{"id":1667},"pokrytí-podle-kapitol","Pokrytí podle kapitol",[198,1670,1672,1673],{"id":1671},"kapitola-2-poptávka-nabídka-tržní-rovnováha-str-3463","Kapitola 2 — Poptávka, nabídka, tržní rovnováha ",[614,1674,1675],{},"(str. 34–63)",[724,1677,1678,1679,1682,1683,1664],{},"Obecný vícefaktorový a jednofaktorový model poptávky a nabídky, zákon klesající poptávky, lineární modely, posun poptávky a nabídky (Engelova funkce, zdanění), tržní rovnováha jako průsečík D a S, pravidla komparativní statiky, multiplikátory pro mikroekonomické proměnné, přebytek spotřebitele a výrobce. Obsahuje ",[38,1680,1681],{},"Příklady 2.1–2.13"," a ",[38,1684,1685],{},"Úlohy 2.1–2.18",[724,1687,1688,1689,1343,1693,1664],{},"Topiky: ",[207,1690,1692],{"className":1691,"href":801,"dataFsResolvedFilePath":800},[210],"poptavka-nabidka",[207,1694,1696],{"className":1695,"href":819,"dataFsResolvedFilePath":818},[210],"prebytek-spotrebitele-vyrobce",[198,1698,1700,1701],{"id":1699},"kapitola-3-příjem-náklady-zisk-nabídka-firmy-str-6681","Kapitola 3 — Příjem, náklady, zisk, nabídka firmy ",[614,1702,1703],{},"(str. 66–81)",[724,1705,1706,1707,1734,1735,1767,1768,1790,1791,1811,1812,1343,1815,1664],{},"Celkový, průměrný a mezní příjem (TR, AR, MR); celkové, fixní, variabilní, průměrné a mezní náklady (TC, FC, TVC, AC, AFC, AVC, MC); princip minimalizace průměrných nákladů (",[883,1708,1710],{"className":1709},[886],[888,1711,1712],{"xmlns":890},[892,1713,1714,1731],{},[895,1715,1716,1719,1722,1726,1729],{},[898,1717,1718],{},"A",[898,1720,1721],{},"C",[1723,1724,1725],"mo",{},"=",[898,1727,1728],{},"M",[898,1730,1721],{},[902,1732,1733],{"encoding":904},"AC = MC"," v minimu); zisk ",[883,1736,1738],{"className":1737},[886],[888,1739,1740],{"xmlns":890},[892,1741,1742,1764],{},[895,1743,1744,1747,1750,1752,1755,1757,1760,1762],{},[898,1745,1746],{},"P",[898,1748,1749],{},"R",[1723,1751,1725],{},[898,1753,1754],{},"T",[898,1756,1749],{},[1723,1758,1759],{},"−",[898,1761,1754],{},[898,1763,1721],{},[902,1765,1766],{"encoding":904},"PR = TR - TC"," a body zvratu; princip maximalizace zisku (",[883,1769,1771],{"className":1770},[886],[888,1772,1773],{"xmlns":890},[892,1774,1775,1787],{},[895,1776,1777,1779,1781,1783,1785],{},[898,1778,1728],{},[898,1780,1749],{},[1723,1782,1725],{},[898,1784,1728],{},[898,1786,1721],{},[902,1788,1789],{"encoding":904},"MR = MC","); konstrukce křivky nabídky firmy (",[883,1792,1794],{"className":1793},[886],[888,1795,1796],{"xmlns":890},[892,1797,1798,1808],{},[895,1799,1800,1802,1804,1806],{},[898,1801,1746],{},[1723,1803,1725],{},[898,1805,1728],{},[898,1807,1721],{},[902,1809,1810],{"encoding":904},"P = MC"," nad minimem AVC). ",[38,1813,1814],{},"Příklady 3.1–3.12",[38,1816,1817],{},"Úlohy 3.1–3.28",[724,1819,1820,1821,1664],{},"Topic: ",[207,1822,1824],{"className":1823,"href":828,"dataFsResolvedFilePath":827},[210],"prijem-naklady-zisk",[198,1826,1828,1829],{"id":1827},"kapitola-4-elasticita-str-8396","Kapitola 4 — Elasticita ",[614,1830,1831],{},"(str. 83–96)",[724,1833,1834,1835,1849,1850,1870,1871,1343,1874,1664],{},"Pojem elasticity jako míry citlivosti na procentní změnu, cenová elasticita poptávky i nabídky, tři pravidla o vztahu ",[883,1836,1838],{"className":1837},[886],[888,1839,1840],{"xmlns":890},[892,1841,1842,1847],{},[895,1843,1844],{},[898,1845,1846],{},"E",[902,1848,1846],{"encoding":904}," a celkového příjmu (u lineární poptávky max TR v bodě ",[883,1851,1853],{"className":1852},[886],[888,1854,1855],{"xmlns":890},[892,1856,1857,1867],{},[895,1858,1859,1861,1863],{},[898,1860,1846],{},[1723,1862,1725],{},[1864,1865,1866],"mn",{},"1",[902,1868,1869],{"encoding":904},"E = 1","), křížová a důchodová elasticita. ",[38,1872,1873],{},"Příklady 4.1–4.8",[38,1875,1876],{},"Úlohy 4.1–4.21",[724,1878,1820,1879,1664],{},[207,1880,1882],{"className":1881,"href":849,"dataFsResolvedFilePath":848},[210],"elasticita",[198,1884,1886,1887],{"id":1885},"kapitola-5-produkce-str-97111","Kapitola 5 — Produkce ",[614,1888,1889],{},"(str. 97–111)",[724,1891,1892,1893,1918,1919,1940,1941,1961,1962,1981,1982,2012,2013,2040,2041,2073,2074,2093,2094,2137,2138,1343,2141,1664],{},"Jednofaktorový model ",[883,1894,1896],{"className":1895},[886],[888,1897,1898],{"xmlns":890},[892,1899,1900,1915],{},[895,1901,1902,1905,1909,1912],{},[898,1903,1904],{},"Q",[1723,1906,1908],{"stretchy":1907},"false","(",[898,1910,1911],{},"L",[1723,1913,1914],{"stretchy":1907},")",[902,1916,1917],{"encoding":904},"Q(L)"," s mezním produktem práce ",[883,1920,1922],{"className":1921},[886],[888,1923,1924],{"xmlns":890},[892,1925,1926,1937],{},[895,1927,1928,1930],{},[898,1929,1728],{},[1931,1932,1933,1935],"msub",{},[898,1934,1746],{},[898,1936,1911],{},[902,1938,1939],{"encoding":904},"MP_L",", průměrným produktem ",[883,1942,1944],{"className":1943},[886],[888,1945,1946],{"xmlns":890},[892,1947,1948,1958],{},[895,1949,1950,1952],{},[898,1951,1718],{},[1931,1953,1954,1956],{},[898,1955,1746],{},[898,1957,1911],{},[902,1959,1960],{"encoding":904},"AP_L"," a principem maximalizace ",[883,1963,1965],{"className":1964},[886],[888,1966,1967],{"xmlns":890},[892,1968,1969,1979],{},[895,1970,1971,1973],{},[898,1972,1718],{},[1931,1974,1975,1977],{},[898,1976,1746],{},[898,1978,1911],{},[902,1980,1960],{"encoding":904}," (",[883,1983,1985],{"className":1984},[886],[888,1986,1987],{"xmlns":890},[892,1988,1989,2009],{},[895,1990,1991,1993,1999,2001,2003],{},[898,1992,1728],{},[1931,1994,1995,1997],{},[898,1996,1746],{},[898,1998,1911],{},[1723,2000,1725],{},[898,2002,1718],{},[1931,2004,2005,2007],{},[898,2006,1746],{},[898,2008,1911],{},[902,2010,2011],{"encoding":904},"MP_L = AP_L"," v max); dvoufaktorový model ",[883,2014,2016],{"className":2015},[886],[888,2017,2018],{"xmlns":890},[892,2019,2020,2037],{},[895,2021,2022,2024,2026,2028,2032,2035],{},[898,2023,1904],{},[1723,2025,1908],{"stretchy":1907},[898,2027,1911],{},[1723,2029,2031],{"separator":2030},"true",",",[898,2033,2034],{},"K",[1723,2036,1914],{"stretchy":1907},[902,2038,2039],{"encoding":904},"Q(L,K)","; Cobb-Douglasova produkční funkce ",[883,2042,2044],{"className":2043},[886],[888,2045,2046],{"xmlns":890},[892,2047,2048,2070],{},[895,2049,2050,2052,2054,2056,2063],{},[898,2051,1904],{},[1723,2053,1725],{},[898,2055,1718],{},[2057,2058,2059,2061],"msup",{},[898,2060,1911],{},[898,2062,207],{},[2057,2064,2065,2067],{},[898,2066,2034],{},[898,2068,2069],{},"b",[902,2071,2072],{"encoding":904},"Q = AL^a K^b",", výnosy z rozsahu podle ",[883,2075,2077],{"className":2076},[886],[888,2078,2079],{"xmlns":890},[892,2080,2081,2090],{},[895,2082,2083,2085,2088],{},[898,2084,207],{},[1723,2086,2087],{},"+",[898,2089,2069],{},[902,2091,2092],{"encoding":904},"a + b","; CES funkce; Eulerova věta; izokvanty; mezní míra technické substituce ",[883,2095,2097],{"className":2096},[886],[888,2098,2099],{"xmlns":890},[892,2100,2101,2134],{},[895,2102,2103,2105,2107,2109,2112,2114,2116,2122,2126,2128],{},[898,2104,1728],{},[898,2106,1749],{},[898,2108,1754],{},[898,2110,2111],{},"S",[1723,2113,1725],{},[898,2115,1728],{},[1931,2117,2118,2120],{},[898,2119,1746],{},[898,2121,1911],{},[898,2123,2125],{"mathvariant":2124},"normal","\u002F",[898,2127,1728],{},[1931,2129,2130,2132],{},[898,2131,1746],{},[898,2133,2034],{},[902,2135,2136],{"encoding":904},"MRTS = MP_L\u002FMP_K",". ",[38,2139,2140],{},"Příklady 5.1–5.6",[38,2142,2143],{},"Úlohy 5.1–5.17",[724,2145,1820,2146,1664],{},[207,2147,2149],{"className":2148,"href":858,"dataFsResolvedFilePath":857},[210],"produkce",[198,2151,2153,2154],{"id":2152},"kapitola-6-užitečnost-str-113131","Kapitola 6 — Užitečnost ",[614,2155,2156],{},"(str. 113–131)",[724,2158,2159,2160,2198,2199,2233,2234,1682,2260,2293,2294,2335,2336,2349,2350,1343,2353,1664],{},"Pojetí užitečnosti (kardinalistický vs. ordinalistický přístup, předpoklady spotřebitele); funkce užitečnosti ",[883,2161,2163],{"className":2162},[886],[888,2164,2165],{"xmlns":890},[892,2166,2167,2195],{},[895,2168,2169,2171,2173,2179,2181,2184,2186,2193],{},[898,2170,900],{},[1723,2172,1908],{"stretchy":1907},[1931,2174,2175,2177],{},[898,2176,1904],{},[1864,2178,1866],{},[1723,2180,2031],{"separator":2030},[1723,2182,2183],{},"…",[1723,2185,2031],{"separator":2030},[1931,2187,2188,2190],{},[898,2189,1904],{},[898,2191,2192],{},"n",[1723,2194,1914],{"stretchy":1907},[902,2196,2197],{"encoding":904},"U(Q_1, \\dots, Q_n)",", mezní užitečnost ",[883,2200,2202],{"className":2201},[886],[888,2203,2204],{"xmlns":890},[892,2205,2206,2230],{},[895,2207,2208,2210,2217,2219],{},[898,2209,1728],{},[1931,2211,2212,2214],{},[898,2213,900],{},[898,2215,2216],{},"i",[1723,2218,1725],{},[2220,2221,2222,2224,2226],"msubsup",{},[898,2223,900],{},[898,2225,2216],{},[1723,2227,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},"0em","′",[902,2231,2232],{"encoding":904},"MU_i = U'_i",", vlastnosti ",[883,2235,2237],{"className":2236},[886],[888,2238,2239],{"xmlns":890},[892,2240,2241,2257],{},[895,2242,2243,2251,2254],{},[2220,2244,2245,2247,2249],{},[898,2246,900],{},[898,2248,2216],{},[1723,2250,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,2252,2253],{},">",[1864,2255,2256],{},"0",[902,2258,2259],{"encoding":904},"U'_i > 0",[883,2261,2263],{"className":2262},[886],[888,2264,2265],{"xmlns":890},[892,2266,2267,2290],{},[895,2268,2269,2285,2288],{},[2220,2270,2271,2273,2279],{},[898,2272,900],{},[895,2274,2275,2277],{},[898,2276,2216],{},[898,2278,2216],{},[895,2280,2281,2283],{},[1723,2282,2229],{"mathvariant":2124},[1723,2284,2229],{"mathvariant":2124},[1723,2286,2287],{},"\u003C",[1864,2289,2256],{},[902,2291,2292],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti); Cobb-Douglasova funkce užitečnosti; indiferenční křivky a jejich 4 vlastnosti; mezní míra komoditní substituce ",[883,2295,2297],{"className":2296},[886],[888,2298,2299],{"xmlns":890},[892,2300,2301,2332],{},[895,2302,2303,2305,2307,2309,2311,2313,2315,2321,2323,2325],{},[898,2304,1728],{},[898,2306,1749],{},[898,2308,1721],{},[898,2310,2111],{},[1723,2312,1725],{},[898,2314,1728],{},[1931,2316,2317,2319],{},[898,2318,900],{},[1864,2320,1866],{},[898,2322,2125],{"mathvariant":2124},[898,2324,1728],{},[1931,2326,2327,2329],{},[898,2328,900],{},[1864,2330,2331],{},"2",[902,2333,2334],{"encoding":904},"MRCS = MU_1\u002FMU_2","; optimalizace spotřebitele Lagrangeovou metodou (maximalizace ",[883,2337,2339],{"className":2338},[886],[888,2340,2341],{"xmlns":890},[892,2342,2343,2347],{},[895,2344,2345],{},[898,2346,900],{},[902,2348,900],{"encoding":904}," za rozpočtového omezení i duální minimalizace výdajů). ",[38,2351,2352],{},"Příklady 6.1–6.8",[38,2354,2355],{},"Úlohy 6.1–6.13",[724,2357,1820,2358,1664],{},[207,2359,2361],{"className":2360,"href":879,"dataFsResolvedFilePath":878},[210],"uzitecnost",[198,2363,2365,2366],{"id":2364},"kapitola-7-národní-důchod-str-133144","Kapitola 7 — Národní důchod ",[614,2367,2368],{},"(str. 133–144)",[724,2370,2371,2372,2390,2391,2409,2410,1664],{},"Zjednodušený makroekonomický model, GNP a národní důchod, funkce spotřeby a úspor, mezní sklon ke spotřebě ",[883,2373,2375],{"className":2374},[886],[888,2376,2377],{"xmlns":890},[892,2378,2379,2387],{},[895,2380,2381,2383,2385],{},[898,2382,1728],{},[898,2384,1746],{},[898,2386,1721],{},[902,2388,2389],{"encoding":904},"MPC"," a k úsporám ",[883,2392,2394],{"className":2393},[886],[888,2395,2396],{"xmlns":890},[892,2397,2398,2406],{},[895,2399,2400,2402,2404],{},[898,2401,1728],{},[898,2403,1746],{},[898,2405,2111],{},[902,2407,2408],{"encoding":904},"MPS","; modely národní ekonomiky C-I (uzavřená bez vlády), C-I-G (s vládou), C-I-G-X (otevřená); multiplikátory pro makroekonomické proměnné; IS-LM analýza — křivky IS a LM, rovnovážný důchod a úroková míra. ",[38,2411,2412],{},"Příklady 7.1–7.6",[724,2414,1820,2415,1664],{},[207,2416,2418],{"className":2417,"href":935,"dataFsResolvedFilePath":934},[210],"narodni-duchod",[115,2420,2422],{"id":2421},"pokrytí-topiců","Pokrytí topiců",[724,2424,2425],{},"Obsah knihy byl sloučen s již existujícími přednáškovými shrnutími do následujících topic pages:",[16,2427,2428,2441],{},[19,2429,2430],{},[22,2431,2432,2435,2438],{},[25,2433,2434],{},"Topic",[25,2436,2437],{},"Zdroj (kniha)",[25,2439,2440],{},"Další zdroje",[30,2442,2443,2459,2472,2487,2503,2518,2534],{},[22,2444,2445,2450,2453],{},[35,2446,2447],{},[207,2448,1692],{"className":2449,"href":801,"dataFsResolvedFilePath":800},[210],[35,2451,2452],{},"Kap. 2",[35,2454,2455],{},[207,2456,2458],{"className":2457,"href":746,"dataFsResolvedFilePath":745},[210],"imek-blok-01",[22,2460,2461,2466,2469],{},[35,2462,2463],{},[207,2464,1696],{"className":2465,"href":819,"dataFsResolvedFilePath":818},[210],[35,2467,2468],{},"Kap. 2.5–2.6 (nové)",[35,2470,2471],{},"—",[22,2473,2474,2479,2482],{},[35,2475,2476],{},[207,2477,1824],{"className":2478,"href":828,"dataFsResolvedFilePath":827},[210],[35,2480,2481],{},"Kap. 3",[35,2483,2484],{},[207,2485,2458],{"className":2486,"href":746,"dataFsResolvedFilePath":745},[210],[22,2488,2489,2494,2497],{},[35,2490,2491],{},[207,2492,1882],{"className":2493,"href":849,"dataFsResolvedFilePath":848},[210],[35,2495,2496],{},"Kap. 4",[35,2498,2499],{},[207,2500,2502],{"className":2501,"href":839,"dataFsResolvedFilePath":838},[210],"imek-blok-02",[22,2504,2505,2510,2513],{},[35,2506,2507],{},[207,2508,2149],{"className":2509,"href":858,"dataFsResolvedFilePath":857},[210],[35,2511,2512],{},"Kap. 5",[35,2514,2515],{},[207,2516,2502],{"className":2517,"href":839,"dataFsResolvedFilePath":838},[210],[22,2519,2520,2525,2528],{},[35,2521,2522],{},[207,2523,2361],{"className":2524,"href":879,"dataFsResolvedFilePath":878},[210],[35,2526,2527],{},"Kap. 6",[35,2529,2530],{},[207,2531,2533],{"className":2532,"href":869,"dataFsResolvedFilePath":868},[210],"imek-blok-03",[22,2535,2536,2541,2544],{},[35,2537,2538],{},[207,2539,2418],{"className":2540,"href":935,"dataFsResolvedFilePath":934},[210],[35,2542,2543],{},"Kap. 7",[35,2545,2546],{},[207,2547,2533],{"className":2548,"href":869,"dataFsResolvedFilePath":868},[210],[115,2550,2552],{"id":2551},"co-kniha-neobsahuje-v-naskenovaných-stránkách","Co kniha neobsahuje (v naskenovaných stránkách)",[120,2554,2555,2581],{},[123,2556,2557,2560,2561,1343,2565,1343,2568,1343,2572,1343,2576,2580],{},[38,2558,2559],{},"Kapitola 1"," (str. 1–33) — pravděpodobně úvod \u002F matematický aparát (funkce, derivace, integrály, Lagrange). Teorie je pokryta v ",[207,2562,2564],{"className":2563,"href":756,"dataFsResolvedFilePath":755},[210],"zaklady-matematicke-ekonomie",[207,2566,1145],{"className":2567,"href":765,"dataFsResolvedFilePath":764},[210],[207,2569,2571],{"className":2570,"href":774,"dataFsResolvedFilePath":773},[210],"integral",[207,2573,2575],{"className":2574,"href":783,"dataFsResolvedFilePath":782},[210],"funkce-vice-promennych",[207,2577,2579],{"className":2578,"href":792,"dataFsResolvedFilePath":791},[210],"lagrangeova-metoda"," ze zdrojů ve vysokoškolských blocích.",[123,2582,2583,2584,2587,2588,2591,2592,2595],{},"Chybějící strany ve skenech: ",[38,2585,2586],{},"64, 65"," (konec teorie \u002F úvod kap. 3), ",[38,2589,2590],{},"82"," (začátek kap. 4), ",[38,2593,2594],{},"112"," (úvod kap. 6). Obsah byl pokud možno dovozen z kontextu sousedních stran a z přednášek.",[115,2597,2599],{"id":2598},"vlastní-úlohy-otázky","Vlastní úlohy \u002F otázky",[724,2601,2602,2603,1682,2606,2609,2610,1682,2613,2616],{},"Kniha obsahuje rozsáhlé soubory ",[38,2604,2605],{},"úloh k samostatnému řešení",[38,2607,2608],{},"otázek k sebehodnocení"," ke každé kapitole. Všechny jsou zachované verbatim v příslušných topic pages (sekce ",[614,2611,2612],{},"Úlohy X.x",[614,2614,2615],{},"Otázky k sebehodnocení",") a představují vysoce kvalitní studijní materiál pro přípravu ke zkoušce.",[115,2618,2620],{"id":2619},"navigace","Navigace",[120,2622,2623,2632,2642],{},[123,2624,2625,2628,2629],{},[38,2626,2627],{},"Kurz:"," ",[207,2630,1646],{"className":2631,"href":1644,"dataFsResolvedFilePath":1645},[210],[123,2633,2634,2628,2637,2641],{},[38,2635,2636],{},"Manifest skenu:",[2638,2639,2640],"code",{},"raw\u002Fimek\u002Fkniha_scanned\u002F_manifest.md"," (mapování fotografií → stránky)",[123,2643,2644,2628,2647,1343,2650,1343,2653],{},[38,2645,2646],{},"Přednášková shrnutí:",[207,2648,2458],{"className":2649,"href":746,"dataFsResolvedFilePath":745},[210],[207,2651,2502],{"className":2652,"href":839,"dataFsResolvedFilePath":838},[210],[207,2654,2533],{"className":2655,"href":869,"dataFsResolvedFilePath":868},[210],{"title":641,"searchDepth":642,"depth":642,"links":2657},[2658,2672,2673,2674,2675],{"id":1667,"depth":642,"text":1668,"children":2659},[2660,2662,2664,2666,2668,2670],{"id":1671,"depth":649,"text":2661},"Kapitola 2 — Poptávka, nabídka, tržní rovnováha (str. 34–63)",{"id":1699,"depth":649,"text":2663},"Kapitola 3 — Příjem, náklady, zisk, nabídka firmy (str. 66–81)",{"id":1827,"depth":649,"text":2665},"Kapitola 4 — Elasticita (str. 83–96)",{"id":1885,"depth":649,"text":2667},"Kapitola 5 — Produkce (str. 97–111)",{"id":2152,"depth":649,"text":2669},"Kapitola 6 — Užitečnost (str. 113–131)",{"id":2364,"depth":649,"text":2671},"Kapitola 7 — Národní důchod (str. 133–144)",{"id":2421,"depth":642,"text":2422},{"id":2551,"depth":642,"text":2552},{"id":2598,"depth":642,"text":2599},{"id":2619,"depth":642,"text":2620},"2026-04-22","Doporučená literatura k předmětu Matematická ekonomie, autor I. Mezník, vydavatelství FP VUT \u002F CERM, Brno 2017. Studentské naskenované fotografie pokrývají kapitoly 2 až 7 (stran 34–144, celkem 107 unikátních stran).",{},"\u002Fsummaries\u002Fimek-kniha",{"title":1629,"description":2677},[1138],"summaries\u002Fimek-kniha",[1128,2684,2685,2686,1142,1143],"kniha","meznik","uvod-do-matematicke-ekonomie","summary","y96KAueM4SX4d38JcXzZsLYGyBeElKYfkrfMaVP4EJQ","summaries",{"zapisku":1625,"topics":2691,"summaries":2692,"outputs":2693},15,5,1,[2695,4575,10275,11825,12696,16974,18580,28458,37452,51516,55808,75147,87254,96209,96495],{"id":2696,"title":2697,"body":2698,"course":1128,"courses":659,"created":1129,"description":4563,"extension":661,"meta":4564,"navigation":664,"path":4565,"seo":4566,"sources":4567,"stem":4568,"tags":4569,"type":4573,"updated":677,"__hash__":4574},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":2699,"toc":4546},[2700,2703,2722,2726,2805,2808,2934,3084,3087,3167,3171,3232,3282,3291,3295,3431,3482,3486,3527,3595,3665,3672,3676,3715,3787,3791,3872,3921,3965,3969,3973,4043,4047,4097,4174,4181,4184,4237,4507,4509],[12,2701,2697],{"id":2702},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,2704,2705,2706,2710,2711,2714,2715,2718,2719,1664],{},"Matematický aparát kurzu ",[207,2707,2709],{"className":2708,"dataFsResolvedFilePath":1645,"href":1644},[210],"ImeK",". Bez derivace se neobejdou ",[38,2712,2713],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,2716,2717],{},"maximalizace zisku"," ani ",[38,2720,2721],{},"minimalizace nákladů",[115,2723,2725],{"id":2724},"funkce-a-polynomy","Funkce a polynomy",[724,2727,2728,2729,2756,2757,2770,2771,2784,2785,1664],{},"Funkce jedné proměnné ",[883,2730,2732],{"className":2731},[886],[888,2733,2734],{"xmlns":890},[892,2735,2736,2753],{},[895,2737,2738,2741,2743,2746,2748,2751],{},[898,2739,2740],{},"y",[1723,2742,1725],{},[898,2744,2745],{},"f",[1723,2747,1908],{"stretchy":1907},[898,2749,2750],{},"x",[1723,2752,1914],{"stretchy":1907},[902,2754,2755],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,2758,2760],{"className":2759},[886],[888,2761,2762],{"xmlns":890},[892,2763,2764,2768],{},[895,2765,2766],{},[898,2767,2750],{},[902,2769,2750],{"encoding":904}," (nezávislá) → ",[883,2772,2774],{"className":2773},[886],[888,2775,2776],{"xmlns":890},[892,2777,2778,2782],{},[895,2779,2780],{},[898,2781,2740],{},[902,2783,2740],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,2786,2788],{"className":2787},[886],[888,2789,2790],{"xmlns":890},[892,2791,2792,2802],{},[895,2793,2794,2796,2798,2800],{},[898,2795,2745],{},[1723,2797,1908],{"stretchy":1907},[898,2799,207],{},[1723,2801,1914],{"stretchy":1907},[902,2803,2804],{"encoding":904},"f(a)",[724,2806,2807],{},"Polynomy:",[120,2809,2810,2841,2882],{},[123,2811,2812],{},[152,2813,2814],{},[123,2815,2816,2817],{},"stupně: ",[883,2818,2820],{"className":2819},[886],[888,2821,2822],{"xmlns":890},[892,2823,2824,2838],{},[895,2825,2826,2828,2830,2832,2834,2836],{},[898,2827,2740],{},[1723,2829,1725],{},[898,2831,207],{},[898,2833,2750],{},[1723,2835,2087],{},[898,2837,2069],{},[902,2839,2840],{"encoding":904},"y = ax + b",[123,2842,2843],{},[152,2844,2845],{"start":642},[123,2846,2816,2847],{},[883,2848,2850],{"className":2849},[886],[888,2851,2852],{"xmlns":890},[892,2853,2854,2879],{},[895,2855,2856,2858,2860,2862,2868,2870,2872,2874,2876],{},[898,2857,2740],{},[1723,2859,1725],{},[898,2861,207],{},[2057,2863,2864,2866],{},[898,2865,2750],{},[1864,2867,2331],{},[1723,2869,2087],{},[898,2871,2069],{},[898,2873,2750],{},[1723,2875,2087],{},[898,2877,2878],{},"c",[902,2880,2881],{"encoding":904},"y = ax^2 + bx + c",[123,2883,2884],{},[152,2885,2886],{"start":649},[123,2887,2816,2888],{},[883,2889,2891],{"className":2890},[886],[888,2892,2893],{"xmlns":890},[892,2894,2895,2931],{},[895,2896,2897,2899,2901,2903,2910,2912,2914,2920,2922,2924,2926,2928],{},[898,2898,2740],{},[1723,2900,1725],{},[898,2902,207],{},[2057,2904,2905,2907],{},[898,2906,2750],{},[1864,2908,2909],{},"3",[1723,2911,2087],{},[898,2913,2069],{},[2057,2915,2916,2918],{},[898,2917,2750],{},[1864,2919,2331],{},[1723,2921,2087],{},[898,2923,2878],{},[898,2925,2750],{},[1723,2927,2087],{},[898,2929,2930],{},"d",[902,2932,2933],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,2935,2936,2628,2939,2995,2996,3034,3035,1664],{},[38,2937,2938],{},"Příklad rozkladu:",[883,2940,2942],{"className":2941},[886],[888,2943,2944],{"xmlns":890},[892,2945,2946,2992],{},[895,2947,2948,2950,2952,2958,2960,2963,2965,2967,2970,2972,2974,2976,2978,2980,2982,2984,2986,2988,2990],{},[898,2949,2740],{},[1723,2951,1725],{},[2057,2953,2954,2956],{},[898,2955,2750],{},[1864,2957,2331],{},[1723,2959,1759],{},[1864,2961,2962],{},"5",[898,2964,2750],{},[1723,2966,2087],{},[1864,2968,2969],{},"6",[1723,2971,1725],{},[1723,2973,1908],{"stretchy":1907},[898,2975,2750],{},[1723,2977,1759],{},[1864,2979,2331],{},[1723,2981,1914],{"stretchy":1907},[1723,2983,1908],{"stretchy":1907},[898,2985,2750],{},[1723,2987,1759],{},[1864,2989,2909],{},[1723,2991,1914],{"stretchy":1907},[902,2993,2994],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,2997,2999],{"className":2998},[886],[888,3000,3001],{"xmlns":890},[892,3002,3003,3031],{},[895,3004,3005,3011,3013,3015,3017,3021,3027,3029],{},[1931,3006,3007,3009],{},[898,3008,2750],{},[1864,3010,1866],{},[1723,3012,1725],{},[1864,3014,2331],{},[1723,3016,2031],{"separator":2030},[3018,3019,3020],"mtext",{}," ",[1931,3022,3023,3025],{},[898,3024,2750],{},[1864,3026,2331],{},[1723,3028,1725],{},[1864,3030,2909],{},[902,3032,3033],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,3036,3038],{"className":3037},[886],[888,3039,3040],{"xmlns":890},[892,3041,3042,3081],{},[895,3043,3044,3046,3048,3050,3052,3054,3064,3070,3072],{},[898,3045,2740],{},[1723,3047,1725],{},[1723,3049,1908],{"stretchy":1907},[898,3051,2750],{},[1723,3053,1759],{},[3055,3056,3057],"mstyle",{"scriptlevel":2256,"displaystyle":1907},[3058,3059,3060,3062],"mfrac",{},[1864,3061,2962],{},[1864,3063,2331],{},[2057,3065,3066,3068],{},[1723,3067,1914],{"stretchy":1907},[1864,3069,2331],{},[1723,3071,1759],{},[3055,3073,3074],{"scriptlevel":2256,"displaystyle":1907},[3058,3075,3076,3078],{},[1864,3077,1866],{},[1864,3079,3080],{},"4",[902,3082,3083],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,3085,3086],{"id":1145},"Derivace",[724,3088,3089,3090,1348,3114,3142,3143,1664],{},"Označení ",[883,3091,3093],{"className":3092},[886],[888,3094,3095],{"xmlns":890},[892,3096,3097,3111],{},[895,3098,3099,3105,3107,3109],{},[2057,3100,3101,3103],{},[898,3102,2745],{},[1723,3104,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,3106,1908],{"stretchy":1907},[898,3108,2750],{},[1723,3110,1914],{"stretchy":1907},[902,3112,3113],{"encoding":904},"f'(x)",[883,3115,3117],{"className":3116},[886],[888,3118,3119],{"xmlns":890},[892,3120,3121,3139],{},[895,3122,3123],{},[3055,3124,3125],{"scriptlevel":2256,"displaystyle":2030},[3058,3126,3127,3133],{},[895,3128,3129,3131],{},[898,3130,2930],{},[898,3132,2740],{},[895,3134,3135,3137],{},[898,3136,2930],{},[898,3138,2750],{},[902,3140,3141],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,3144,3146],{"className":3145},[886],[888,3147,3148],{"xmlns":890},[892,3149,3150,3164],{},[895,3151,3152,3158,3160,3162],{},[2057,3153,3154,3156],{},[898,3155,2745],{},[1723,3157,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,3159,1908],{"stretchy":1907},[898,3161,207],{},[1723,3163,1914],{"stretchy":1907},[902,3165,3166],{"encoding":904},"f'(a)",[198,3168,3170],{"id":3169},"geometrická-interpretace","Geometrická interpretace",[724,3172,3173,3196,3197,3200,3201,3231],{},[883,3174,3176],{"className":3175},[886],[888,3177,3178],{"xmlns":890},[892,3179,3180,3194],{},[895,3181,3182,3188,3190,3192],{},[2057,3183,3184,3186],{},[898,3185,2745],{},[1723,3187,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,3189,1908],{"stretchy":1907},[898,3191,207],{},[1723,3193,1914],{"stretchy":1907},[902,3195,3166],{"encoding":904}," = ",[38,3198,3199],{},"sklon tečny"," ke grafu funkce v bodě ",[883,3202,3204],{"className":3203},[886],[888,3205,3206],{"xmlns":890},[892,3207,3208,3228],{},[895,3209,3210,3213,3215,3217,3219,3221,3223,3225],{},[1723,3211,3212],{"stretchy":1907},"[",[898,3214,207],{},[1723,3216,2031],{"separator":2030},[898,3218,2745],{},[1723,3220,1908],{"stretchy":1907},[898,3222,207],{},[1723,3224,1914],{"stretchy":1907},[1723,3226,3227],{"stretchy":1907},"]",[902,3229,3230],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,3233,3234],{},[883,3235,3237],{"className":3236},[886],[888,3238,3239],{"xmlns":890},[892,3240,3241,3279],{},[895,3242,3243,3245,3247,3249,3251,3253,3255,3257,3263,3265,3267,3269,3271,3273,3275,3277],{},[898,3244,2740],{},[1723,3246,1759],{},[898,3248,2745],{},[1723,3250,1908],{"stretchy":1907},[898,3252,207],{},[1723,3254,1914],{"stretchy":1907},[1723,3256,1725],{},[2057,3258,3259,3261],{},[898,3260,2745],{},[1723,3262,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,3264,1908],{"stretchy":1907},[898,3266,207],{},[1723,3268,1914],{"stretchy":1907},[1723,3270,1908],{"stretchy":1907},[898,3272,2750],{},[1723,3274,1759],{},[898,3276,207],{},[1723,3278,1914],{"stretchy":1907},[902,3280,3281],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,3283,3284],{},[3285,3286],"img",{"alt":3287,"className":3288,"src":3290},"imek-derivace-tecna",[210,3289],"wikilink-broken","\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,3292,3294],{"id":3293},"inženýrská-interpretace","Inženýrská interpretace",[724,3296,3297,3196,3320,2628,3323,3336,3337,3350,3351,3369,3370,3383,3384,3397,3398,3411,3412,3430],{},[883,3298,3300],{"className":3299},[886],[888,3301,3302],{"xmlns":890},[892,3303,3304,3318],{},[895,3305,3306,3312,3314,3316],{},[2057,3307,3308,3310],{},[898,3309,2745],{},[1723,3311,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,3313,1908],{"stretchy":1907},[898,3315,207],{},[1723,3317,1914],{"stretchy":1907},[902,3319,3166],{"encoding":904},[38,3321,3322],{},"rychlost změny",[883,3324,3326],{"className":3325},[886],[888,3327,3328],{"xmlns":890},[892,3329,3330,3334],{},[895,3331,3332],{},[898,3333,2740],{},[902,3335,2740],{"encoding":904}," vzhledem k ",[883,3338,3340],{"className":3339},[886],[888,3341,3342],{"xmlns":890},[892,3343,3344,3348],{},[895,3345,3346],{},[898,3347,2750],{},[902,3349,2750],{"encoding":904}," v bodě ",[883,3352,3354],{"className":3353},[886],[888,3355,3356],{"xmlns":890},[892,3357,3358,3366],{},[895,3359,3360,3362,3364],{},[898,3361,2750],{},[1723,3363,1725],{},[898,3365,207],{},[902,3367,3368],{"encoding":904},"x = a","; přibližná změna ",[883,3371,3373],{"className":3372},[886],[888,3374,3375],{"xmlns":890},[892,3376,3377,3381],{},[895,3378,3379],{},[898,3380,2740],{},[902,3382,2740],{"encoding":904}," při změně ",[883,3385,3387],{"className":3386},[886],[888,3388,3389],{"xmlns":890},[892,3390,3391,3395],{},[895,3392,3393],{},[898,3394,2750],{},[902,3396,2750],{"encoding":904}," z ",[883,3399,3401],{"className":3400},[886],[888,3402,3403],{"xmlns":890},[892,3404,3405,3409],{},[895,3406,3407],{},[898,3408,207],{},[902,3410,207],{"encoding":904}," na ",[883,3413,3415],{"className":3414},[886],[888,3416,3417],{"xmlns":890},[892,3418,3419,3427],{},[895,3420,3421,3423,3425],{},[898,3422,207],{},[1723,3424,2087],{},[1864,3426,1866],{},[902,3428,3429],{"encoding":904},"a+1",":",[724,3432,3433],{},[883,3434,3436],{"className":3435},[886],[888,3437,3438],{"xmlns":890},[892,3439,3440,3479],{},[895,3441,3442,3444,3446,3448,3450,3452,3454,3457,3459,3461,3463,3465,3467,3473,3475,3477],{},[898,3443,2745],{},[1723,3445,1908],{"stretchy":1907},[898,3447,207],{},[1723,3449,2087],{},[1864,3451,1866],{},[1723,3453,1914],{"stretchy":1907},[1723,3455,3456],{},"≈",[898,3458,2745],{},[1723,3460,1908],{"stretchy":1907},[898,3462,207],{},[1723,3464,1914],{"stretchy":1907},[1723,3466,2087],{},[2057,3468,3469,3471],{},[898,3470,2745],{},[1723,3472,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,3474,1908],{"stretchy":1907},[898,3476,207],{},[1723,3478,1914],{"stretchy":1907},[902,3480,3481],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,3483,3485],{"id":3484},"příklad-mezní-náklady","Příklad — mezní náklady",[724,3487,3488,3489,1664],{},"Celkové náklady ",[883,3490,3492],{"className":3491},[886],[888,3493,3494],{"xmlns":890},[892,3495,3496,3524],{},[895,3497,3498,3500,3502,3504,3507,3509,3511,3513,3515,3518],{},[898,3499,1754],{},[898,3501,1721],{},[1723,3503,1725],{},[1864,3505,3506],{},"1000",[1723,3508,2087],{},[1864,3510,2331],{},[898,3512,1904],{},[1723,3514,2087],{},[1864,3516,3517],{},"0,1",[2057,3519,3520,3522],{},[898,3521,1904],{},[1864,3523,2331],{},[902,3525,3526],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,3528,3529,3530,3567,3568,1664],{},"Mezní náklady: ",[883,3531,3533],{"className":3532},[886],[888,3534,3535],{"xmlns":890},[892,3536,3537,3564],{},[895,3538,3539,3541,3543,3545,3547,3553,3555,3557,3559,3562],{},[898,3540,1728],{},[898,3542,1721],{},[1723,3544,1725],{},[898,3546,1754],{},[2057,3548,3549,3551],{},[898,3550,1721],{},[1723,3552,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,3554,1725],{},[1864,3556,2331],{},[1723,3558,2087],{},[1864,3560,3561],{},"0,2",[898,3563,1904],{},[902,3565,3566],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,3569,3571],{"className":3570},[886],[888,3572,3573],{"xmlns":890},[892,3574,3575,3592],{},[895,3576,3577,3579,3581,3583,3586,3588,3590],{},[898,3578,1728],{},[898,3580,1721],{},[1723,3582,1908],{"stretchy":1907},[1864,3584,3585],{},"10",[1723,3587,1914],{"stretchy":1907},[1723,3589,1725],{},[1864,3591,3080],{},[902,3593,3594],{"encoding":904},"MC(10) = 4",[724,3596,3597,2628,3600,2137,3649,2628,3652,1664],{},[38,3598,3599],{},"Skutečný přírůstek:",[883,3601,3603],{"className":3602},[886],[888,3604,3605],{"xmlns":890},[892,3606,3607,3646],{},[895,3608,3609,3612,3614,3616,3618,3620,3622,3624,3627,3629,3631,3633,3635,3637,3639,3641,3643],{},[898,3610,3611],{"mathvariant":2124},"Δ",[898,3613,1754],{},[898,3615,1721],{},[1723,3617,1725],{},[898,3619,1754],{},[898,3621,1721],{},[1723,3623,1908],{"stretchy":1907},[1864,3625,3626],{},"11",[1723,3628,1914],{"stretchy":1907},[1723,3630,1759],{},[898,3632,1754],{},[898,3634,1721],{},[1723,3636,1908],{"stretchy":1907},[1864,3638,3585],{},[1723,3640,1914],{"stretchy":1907},[1723,3642,1725],{},[1864,3644,3645],{},"4,2",[902,3647,3648],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",[38,3650,3651],{},"Přibližný (lineární):",[883,3653,3655],{"className":3654},[886],[888,3656,3657],{"xmlns":890},[892,3658,3659,3663],{},[895,3660,3661],{},[1864,3662,3080],{},[902,3664,3080],{"encoding":904},[724,3666,3667,3668,3671],{},"(Viz aplikace v ",[207,3669,1824],{"className":3670,"dataFsResolvedFilePath":827,"href":828},[210],".)",[115,3673,3675],{"id":3674},"diferenciál","Diferenciál",[724,3677,3678],{},[883,3679,3681],{"className":3680},[886],[888,3682,3683],{"xmlns":890},[892,3684,3685,3712],{},[895,3686,3687,3689,3691,3693,3699,3701,3703,3705,3708,3710],{},[898,3688,2930],{},[898,3690,2745],{},[1723,3692,1725],{},[2057,3694,3695,3697],{},[898,3696,2745],{},[1723,3698,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,3700,1908],{"stretchy":1907},[898,3702,2750],{},[1723,3704,1914],{"stretchy":1907},[3018,3706,3707],{}," ",[898,3709,2930],{},[898,3711,2750],{},[902,3713,3714],{"encoding":904},"df = f'(x)\\, dx",[724,3716,3717,3718,3734,3735,3783,3784,1664],{},"Pro malá ",[883,3719,3721],{"className":3720},[886],[888,3722,3723],{"xmlns":890},[892,3724,3725,3731],{},[895,3726,3727,3729],{},[898,3728,2930],{},[898,3730,2750],{},[902,3732,3733],{"encoding":904},"dx"," platí: ",[883,3736,3738],{"className":3737},[886],[888,3739,3740],{"xmlns":890},[892,3741,3742,3780],{},[895,3743,3744,3746,3748,3750,3752,3754,3756,3758,3760,3762,3764,3766,3768,3770,3772,3774,3776,3778],{},[898,3745,3611],{"mathvariant":2124},[898,3747,2745],{},[1723,3749,1725],{},[898,3751,2745],{},[1723,3753,1908],{"stretchy":1907},[898,3755,2750],{},[1723,3757,2087],{},[898,3759,2930],{},[898,3761,2750],{},[1723,3763,1914],{"stretchy":1907},[1723,3765,1759],{},[898,3767,2745],{},[1723,3769,1908],{"stretchy":1907},[898,3771,2750],{},[1723,3773,1914],{"stretchy":1907},[1723,3775,3456],{},[898,3777,2930],{},[898,3779,2745],{},[902,3781,3782],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,3785,3786],{},"lineární odhad přírůstku",[198,3788,3790],{"id":3789},"příklad","Příklad",[724,3792,3793,3824,3825,3850,3851,3871],{},[883,3794,3796],{"className":3795},[886],[888,3797,3798],{"xmlns":890},[892,3799,3800,3821],{},[895,3801,3802,3804,3806,3808,3811,3813,3815],{},[898,3803,1754],{},[898,3805,1721],{},[1723,3807,1725],{},[1864,3809,3810],{},"100",[1723,3812,2087],{},[1864,3814,3517],{},[2057,3816,3817,3819],{},[898,3818,1904],{},[1864,3820,2331],{},[902,3822,3823],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,3826,3828],{"className":3827},[886],[888,3829,3830],{"xmlns":890},[892,3831,3832,3847],{},[895,3833,3834,3836,3838,3841,3844],{},[898,3835,1904],{},[1723,3837,3430],{},[1864,3839,3840],{},"50",[1723,3842,3843],{},"→",[1864,3845,3846],{},"60",[902,3848,3849],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,3852,3854],{"className":3853},[886],[888,3855,3856],{"xmlns":890},[892,3857,3858,3868],{},[895,3859,3860,3862,3864,3866],{},[898,3861,2930],{},[898,3863,1904],{},[1723,3865,1725],{},[1864,3867,3585],{},[902,3869,3870],{"encoding":904},"dQ = 10","):",[724,3873,3874],{},[883,3875,3877],{"className":3876},[886],[888,3878,3879],{"xmlns":890},[892,3880,3881,3918],{},[895,3882,3883,3885,3887,3889,3891,3893,3895,3898,3900,3902,3904,3906,3908,3910,3912,3914,3916],{},[898,3884,2930],{},[898,3886,1754],{},[898,3888,1721],{},[1723,3890,1725],{},[1864,3892,3561],{},[898,3894,1904],{},[1723,3896,3897],{},"⋅",[898,3899,2930],{},[898,3901,1904],{},[1723,3903,1725],{},[1864,3905,3561],{},[1723,3907,3897],{},[1864,3909,3840],{},[1723,3911,3897],{},[1864,3913,3585],{},[1723,3915,1725],{},[1864,3917,3810],{},[902,3919,3920],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,3922,3923,3924,3947,3948,3964],{},"Přesná změna: ",[883,3925,3927],{"className":3926},[886],[888,3928,3929],{"xmlns":890},[892,3930,3931,3944],{},[895,3932,3933,3935,3937,3939,3941],{},[898,3934,3611],{"mathvariant":2124},[898,3936,1754],{},[898,3938,1721],{},[1723,3940,1725],{},[1864,3942,3943],{},"110",[902,3945,3946],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,3949,3951],{"className":3950},[886],[888,3952,3953],{"xmlns":890},[892,3954,3955,3961],{},[895,3956,3957,3959],{},[898,3958,1754],{},[898,3960,1721],{},[902,3962,3963],{"encoding":904},"TC"," je konvexní.",[115,3966,3968],{"id":3967},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,3970,3972],{"id":3971},"nutná-podmínka","Nutná podmínka",[724,3974,3975,3976,3350,3996,4009,4010,4038,4039,4042],{},"Má-li ",[883,3977,3979],{"className":3978},[886],[888,3980,3981],{"xmlns":890},[892,3982,3983,3993],{},[895,3984,3985,3987,3989,3991],{},[898,3986,2745],{},[1723,3988,1908],{"stretchy":1907},[898,3990,2750],{},[1723,3992,1914],{"stretchy":1907},[902,3994,3995],{"encoding":904},"f(x)",[883,3997,3999],{"className":3998},[886],[888,4000,4001],{"xmlns":890},[892,4002,4003,4007],{},[895,4004,4005],{},[898,4006,207],{},[902,4008,207],{"encoding":904}," extrém, pak ",[883,4011,4013],{"className":4012},[886],[888,4014,4015],{"xmlns":890},[892,4016,4017,4035],{},[895,4018,4019,4025,4027,4029,4031,4033],{},[2057,4020,4021,4023],{},[898,4022,2745],{},[1723,4024,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,4026,1908],{"stretchy":1907},[898,4028,207],{},[1723,4030,1914],{"stretchy":1907},[1723,4032,1725],{},[1864,4034,2256],{},[902,4036,4037],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,4040,4041],{},"stacionární"," (podezřelé) body.",[198,4044,4046],{"id":4045},"postačující-podmínka","Postačující podmínka",[724,4048,4049,4050,4063,4064,3430],{},"Pro stacionární bod ",[883,4051,4053],{"className":4052},[886],[888,4054,4055],{"xmlns":890},[892,4056,4057,4061],{},[895,4058,4059],{},[898,4060,207],{},[902,4062,207],{"encoding":904},", je-li ",[883,4065,4067],{"className":4066},[886],[888,4068,4069],{"xmlns":890},[892,4070,4071,4094],{},[895,4072,4073,4083,4085,4087,4089,4092],{},[2057,4074,4075,4077],{},[898,4076,2745],{},[895,4078,4079,4081],{},[1723,4080,2229],{"mathvariant":2124},[1723,4082,2229],{"mathvariant":2124},[1723,4084,1908],{"stretchy":1907},[898,4086,207],{},[1723,4088,1914],{"stretchy":1907},[1723,4090,4091],{"mathvariant":2124},"≠",[1864,4093,2256],{},[902,4095,4096],{"encoding":904},"f''(a) \\neq 0",[120,4098,4099,4137],{},[123,4100,4101,4133,4134],{},[883,4102,4104],{"className":4103},[886],[888,4105,4106],{"xmlns":890},[892,4107,4108,4130],{},[895,4109,4110,4120,4122,4124,4126,4128],{},[2057,4111,4112,4114],{},[898,4113,2745],{},[895,4115,4116,4118],{},[1723,4117,2229],{"mathvariant":2124},[1723,4119,2229],{"mathvariant":2124},[1723,4121,1908],{"stretchy":1907},[898,4123,207],{},[1723,4125,1914],{"stretchy":1907},[1723,4127,2253],{},[1864,4129,2256],{},[902,4131,4132],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,4135,4136],{},"lokální minimum",[123,4138,4139,4133,4171],{},[883,4140,4142],{"className":4141},[886],[888,4143,4144],{"xmlns":890},[892,4145,4146,4168],{},[895,4147,4148,4158,4160,4162,4164,4166],{},[2057,4149,4150,4152],{},[898,4151,2745],{},[895,4153,4154,4156],{},[1723,4155,2229],{"mathvariant":2124},[1723,4157,2229],{"mathvariant":2124},[1723,4159,1908],{"stretchy":1907},[898,4161,207],{},[1723,4163,1914],{"stretchy":1907},[1723,4165,2287],{},[1864,4167,2256],{},[902,4169,4170],{"encoding":904},"f''(a) \u003C 0",[38,4172,4173],{},"lokální maximum",[724,4175,4176],{},[3285,4177],{"alt":4178,"className":4179,"src":4180},"imek-extremy-1d",[210,3289],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,4182,3790],{"id":4183},"příklad-1",[724,4185,4186],{},[883,4187,4189],{"className":4188},[886],[888,4190,4191],{"xmlns":890},[892,4192,4193,4234],{},[895,4194,4195,4197,4199,4201,4203,4205,4207,4213,4215,4217,4223,4225,4228,4230,4232],{},[898,4196,2745],{},[1723,4198,1908],{"stretchy":1907},[898,4200,2750],{},[1723,4202,1914],{"stretchy":1907},[1723,4204,1725],{},[1864,4206,2331],{},[2057,4208,4209,4211],{},[898,4210,2750],{},[1864,4212,2909],{},[1723,4214,1759],{},[1864,4216,2909],{},[2057,4218,4219,4221],{},[898,4220,2750],{},[1864,4222,2331],{},[1723,4224,1759],{},[1864,4226,4227],{},"12",[898,4229,2750],{},[1723,4231,2087],{},[1864,4233,2909],{},[902,4235,4236],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,4238,4239,4350,4390,4453],{},[123,4240,4241,4313,4314],{},[883,4242,4244],{"className":4243},[886],[888,4245,4246],{"xmlns":890},[892,4247,4248,4310],{},[895,4249,4250,4256,4258,4260,4262,4264,4266,4272,4274,4276,4278,4280,4282,4284,4286,4288,4290,4292,4294,4296,4298,4300,4302,4304,4306,4308],{},[2057,4251,4252,4254],{},[898,4253,2745],{},[1723,4255,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,4257,1908],{"stretchy":1907},[898,4259,2750],{},[1723,4261,1914],{"stretchy":1907},[1723,4263,1725],{},[1864,4265,2969],{},[2057,4267,4268,4270],{},[898,4269,2750],{},[1864,4271,2331],{},[1723,4273,1759],{},[1864,4275,2969],{},[898,4277,2750],{},[1723,4279,1759],{},[1864,4281,4227],{},[1723,4283,1725],{},[1864,4285,2969],{},[1723,4287,1908],{"stretchy":1907},[898,4289,2750],{},[1723,4291,2087],{},[1864,4293,1866],{},[1723,4295,1914],{"stretchy":1907},[1723,4297,1908],{"stretchy":1907},[898,4299,2750],{},[1723,4301,1759],{},[1864,4303,2331],{},[1723,4305,1914],{"stretchy":1907},[1723,4307,1725],{},[1864,4309,2256],{},[902,4311,4312],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,4315,4317],{"className":4316},[886],[888,4318,4319],{"xmlns":890},[892,4320,4321,4347],{},[895,4322,4323,4329,4331,4333,4335,4337,4343,4345],{},[1931,4324,4325,4327],{},[898,4326,2750],{},[1864,4328,1866],{},[1723,4330,1725],{},[1723,4332,1759],{},[1864,4334,1866],{},[1723,4336,2031],{"separator":2030},[1931,4338,4339,4341],{},[898,4340,2750],{},[1864,4342,2331],{},[1723,4344,1725],{},[1864,4346,2331],{},[902,4348,4349],{"encoding":904},"x_1 = -1, x_2 = 2",[123,4351,4352],{},[883,4353,4355],{"className":4354},[886],[888,4356,4357],{"xmlns":890},[892,4358,4359,4387],{},[895,4360,4361,4371,4373,4375,4377,4379,4381,4383,4385],{},[2057,4362,4363,4365],{},[898,4364,2745],{},[895,4366,4367,4369],{},[1723,4368,2229],{"mathvariant":2124},[1723,4370,2229],{"mathvariant":2124},[1723,4372,1908],{"stretchy":1907},[898,4374,2750],{},[1723,4376,1914],{"stretchy":1907},[1723,4378,1725],{},[1864,4380,4227],{},[898,4382,2750],{},[1723,4384,1759],{},[1864,4386,2969],{},[902,4388,4389],{"encoding":904},"f''(x) = 12x - 6",[123,4391,4392,4133,4433,4436,4437],{},[883,4393,4395],{"className":4394},[886],[888,4396,4397],{"xmlns":890},[892,4398,4399,4430],{},[895,4400,4401,4411,4413,4415,4417,4419,4421,4423,4426,4428],{},[2057,4402,4403,4405],{},[898,4404,2745],{},[895,4406,4407,4409],{},[1723,4408,2229],{"mathvariant":2124},[1723,4410,2229],{"mathvariant":2124},[1723,4412,1908],{"stretchy":1907},[1723,4414,1759],{},[1864,4416,1866],{},[1723,4418,1914],{"stretchy":1907},[1723,4420,1725],{},[1723,4422,1759],{},[1864,4424,4425],{},"18",[1723,4427,2287],{},[1864,4429,2256],{},[902,4431,4432],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,4434,4435],{},"maximum"," v ",[883,4438,4440],{"className":4439},[886],[888,4441,4442],{"xmlns":890},[892,4443,4444,4450],{},[895,4445,4446,4448],{},[1723,4447,1759],{},[1864,4449,1866],{},[902,4451,4452],{"encoding":904},"-1",[123,4454,4455,4133,4491,4436,4494],{},[883,4456,4458],{"className":4457},[886],[888,4459,4460],{"xmlns":890},[892,4461,4462,4488],{},[895,4463,4464,4474,4476,4478,4480,4482,4484,4486],{},[2057,4465,4466,4468],{},[898,4467,2745],{},[895,4469,4470,4472],{},[1723,4471,2229],{"mathvariant":2124},[1723,4473,2229],{"mathvariant":2124},[1723,4475,1908],{"stretchy":1907},[1864,4477,2331],{},[1723,4479,1914],{"stretchy":1907},[1723,4481,1725],{},[1864,4483,4425],{},[1723,4485,2253],{},[1864,4487,2256],{},[902,4489,4490],{"encoding":904},"f''(2) = 18 > 0",[38,4492,4493],{},"minimum",[883,4495,4497],{"className":4496},[886],[888,4498,4499],{"xmlns":890},[892,4500,4501,4505],{},[895,4502,4503],{},[1864,4504,2331],{},[902,4506,2331],{"encoding":904},[115,4508,2620],{"id":2619},[120,4510,4511,4519,4527],{},[123,4512,4513,2628,4516],{},[38,4514,4515],{},"Předchozí:",[207,4517,757],{"className":4518,"dataFsResolvedFilePath":755,"href":756},[210],[123,4520,4521,2628,4524],{},[38,4522,4523],{},"Navazující:",[207,4525,775],{"className":4526,"dataFsResolvedFilePath":773,"href":774},[210],[123,4528,4529,2628,4532,4535,4536,4540,4541,4545],{},[38,4530,4531],{},"Souvislosti:",[207,4533,784],{"className":4534,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,4537,4539],{"className":4538,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,4542,4544],{"className":4543,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":4547},[4548,4549,4554,4557,4562],{"id":2724,"depth":642,"text":2725},{"id":1145,"depth":642,"text":3086,"children":4550},[4551,4552,4553],{"id":3169,"depth":649,"text":3170},{"id":3293,"depth":649,"text":3294},{"id":3484,"depth":649,"text":3485},{"id":3674,"depth":642,"text":3675,"children":4555},[4556],{"id":3789,"depth":649,"text":3790},{"id":3967,"depth":642,"text":3968,"children":4558},[4559,4560,4561],{"id":3971,"depth":649,"text":3972},{"id":4045,"depth":649,"text":4046},{"id":4183,"depth":649,"text":3790},{"id":2619,"depth":642,"text":2620},"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":2697,"description":4563},[1135],"topics\u002Fderivace",[1128,1145,4570,4571,4572],"diferencial","extremy","mezni-naklady","topic","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":4576,"title":4577,"body":4578,"course":1128,"courses":659,"created":2676,"description":641,"extension":661,"meta":10264,"navigation":664,"path":10265,"seo":10266,"sources":10267,"stem":10268,"tags":10269,"type":4573,"updated":677,"__hash__":10274},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":4579,"toc":10237},[4580,4583,4605,4609,4635,4639,4680,4770,4814,4818,4842,4849,4853,4863,4875,4879,4908,4917,4972,4978,4981,4987,5014,5020,5118,5277,5567,5571,5651,5657,5661,5759,5825,5993,5997,6075,6106,6133,6139,6171,6249,6336,6340,6403,6409,6412,6418,6532,6617,6661,6665,6711,6718,7035,7040,7064,7093,7160,7257,7261,7268,7275,7346,7466,7550,7553,7559,7886,7890,8053,8061,8197,8205,8443,8451,8454,8459,8715,8719,8893,9027,9064,9108,9111,9241,9331,9349,9353,9360,9366,9426,9429,9453,9456,9462,9465,9471,9474,9478,9516,9574,9763,9767,9840,9846,9853,9857,9863,10004,10008,10014,10050,10055,10232],[12,4581,4577],{"id":4582},"elasticita-poptávky-a-nabídky",[4584,4585,4586],"blockquote",{},[724,4587,4588,4591,4592,4594,4595,4598,4599,1682,4602,1664],{},[883,4589,4590],{},"!abstract"," TL;DR\n",[38,4593,4544],{}," 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: ",[38,4596,4597],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,4600,4601],{},"křížově-cenovou elasticitu",[38,4603,4604],{},"důchodovou elasticitu",[115,4606,4608],{"id":4607},"úvod-motivace","Úvod — motivace",[724,4610,4611,4612,4614,4615,4618,4619,4622,4623,4626,4627,4630,4631,4634],{},"Termín ",[614,4613,1882],{}," (alternativně ",[614,4616,4617],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,4620,4621],{},"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 ",[614,4624,4625],{},"cenové elasticity poptávky"," (resp. ",[614,4628,4629],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,4632,3086],{"className":4633,"dataFsResolvedFilePath":764,"href":765},[210],").",[198,4636,4638],{"id":4637},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,4640,4641,4642,4660,4661,4679],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,4643,4645],{"className":4644},[886],[888,4646,4647],{"xmlns":890},[892,4648,4649,4657],{},[895,4650,4651,4653,4655],{},[898,4652,1746],{},[1723,4654,1725],{},[1864,4656,3585],{},[902,4658,4659],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,4662,4664],{"className":4663},[886],[888,4665,4666],{"xmlns":890},[892,4667,4668,4676],{},[895,4669,4670,4672,4674],{},[898,4671,1904],{},[1723,4673,1725],{},[1864,4675,3810],{},[902,4677,4678],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,4681,4682,4727],{},[123,4683,4684,4687,4688,4726],{},[38,4685,4686],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,4689,4691],{"className":4690},[886],[888,4692,4693],{"xmlns":890},[892,4694,4695,4723],{},[895,4696,4697,4700,4703,4705,4707,4709,4711,4714,4716,4718,4720],{},[3018,4698,4699],{},"  ",[1723,4701,4702],{},"⇒",[3018,4704,4699],{},[898,4706,1754],{},[898,4708,1749],{},[1723,4710,1725],{},[1864,4712,4713],{},"9",[1723,4715,3897],{},[1864,4717,3943],{},[1723,4719,1725],{},[1864,4721,4722],{},"990",[902,4724,4725],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,4728,4729,4732,4733,4769],{},[38,4730,4731],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,4734,4736],{"className":4735},[886],[888,4737,4738],{"xmlns":890},[892,4739,4740,4766],{},[895,4741,4742,4744,4746,4748,4750,4752,4754,4756,4758,4761,4763],{},[3018,4743,4699],{},[1723,4745,4702],{},[3018,4747,4699],{},[898,4749,1754],{},[898,4751,1749],{},[1723,4753,1725],{},[1864,4755,4713],{},[1723,4757,3897],{},[1864,4759,4760],{},"120",[1723,4762,1725],{},[1864,4764,4765],{},"1080",[902,4767,4768],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,4771,4772,4773,4776,4777,4780,4781,4784,4785,4788,4789,4792,4793,4809,4810,4813],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,4774,4775],{},"nerozumné",", na Trhu 2 ",[38,4778,4779],{},"rozumné",". Trh 2 je ",[38,4782,4783],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,4786,4787],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,4790,4791],{},"neelastická"," a vyššího ",[883,4794,4796],{"className":4795},[886],[888,4797,4798],{"xmlns":890},[892,4799,4800,4806],{},[895,4801,4802,4804],{},[898,4803,1754],{},[898,4805,1749],{},[902,4807,4808],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,4811,4812],{},"zvýšením"," ceny.",[198,4815,4817],{"id":4816},"hypotéza-41","Hypotéza 4.1",[4584,4819,4820],{},[724,4821,4822,4823],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,4824,4826],{"className":4825},[886],[888,4827,4828],{"xmlns":890},[892,4829,4830,4839],{},[895,4831,4832,4834,4837],{},[1723,4833,1908],{"stretchy":1907},[1864,4835,4836],{},"4.1",[1723,4838,1914],{"stretchy":1907},[902,4840,4841],{"encoding":904},"(4.1)",[724,4843,4844,4845,4848],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,4846,4847],{},"procentní změny"," obou faktorů.",[115,4850,4852],{"id":4851},"pojem-elasticity","Pojem elasticity",[724,4854,4855,4856,4858,4859,4862],{},"Obecně ",[38,4857,1882],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,4860,4861],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[4584,4864,4865],{},[724,4866,4867,4870,4871,4874],{},[883,4868,4869],{},"!info"," Intuice\nElasticitu lze číst jako ",[38,4872,4873],{},"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.",[115,4876,4878],{"id":4877},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,4880,4881,4882,4907],{},"Nechť ",[883,4883,4885],{"className":4884},[886],[888,4886,4887],{"xmlns":890},[892,4888,4889,4904],{},[895,4890,4891,4893,4895,4898,4900,4902],{},[898,4892,1904],{},[1723,4894,1725],{},[898,4896,4897],{},"D",[1723,4899,1908],{"stretchy":1907},[898,4901,1746],{},[1723,4903,1914],{"stretchy":1907},[902,4905,4906],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,4909,4910],{},[883,4911,4916],{"className":4912,"title":4914,"style":4915},[4913],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,4918,4919,4920,1682,4936,4952,4953,4971],{},"Znaménko minus je korekce: změny ",[883,4921,4923],{"className":4922},[886],[888,4924,4925],{"xmlns":890},[892,4926,4927,4933],{},[895,4928,4929,4931],{},[898,4930,3611],{"mathvariant":2124},[898,4932,1904],{},[902,4934,4935],{"encoding":904},"\\Delta Q",[883,4937,4939],{"className":4938},[886],[888,4940,4941],{"xmlns":890},[892,4942,4943,4949],{},[895,4944,4945,4947],{},[898,4946,3611],{"mathvariant":2124},[898,4948,1746],{},[902,4950,4951],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,4954,4956],{"className":4955},[886],[888,4957,4958],{"xmlns":890},[892,4959,4960,4968],{},[895,4961,4962],{},[2057,4963,4964,4966],{},[898,4965,1846],{},[898,4967,1718],{},[902,4969,4970],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,4973,4974],{},[883,4975,4977],{"className":4976,"title":4914,"style":4915},[4913],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,4979,4980],{},"Po dosazení:",[724,4982,4983],{},[883,4984,4986],{"className":4985,"title":4914,"style":4915},[4913],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,4988,4989,4990,5010,5011,5013],{},"Limitním přechodem ",[883,4991,4993],{"className":4992},[886],[888,4994,4995],{"xmlns":890},[892,4996,4997,5007],{},[895,4998,4999,5001,5003,5005],{},[898,5000,3611],{"mathvariant":2124},[898,5002,1746],{},[1723,5004,3843],{},[1864,5006,2256],{},[902,5008,5009],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,5012,4625],{}," (price elasticity of demand):",[724,5015,5016],{},[883,5017,5019],{"className":5018,"title":4914,"style":4915},[4913],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,5021,5022,5023,5046,5047,5070,5071,5095,5096,5117],{},"kde ",[883,5024,5026],{"className":5025},[886],[888,5027,5028],{"xmlns":890},[892,5029,5030,5044],{},[895,5031,5032,5034,5036,5038,5040,5042],{},[898,5033,1904],{},[1723,5035,1725],{},[898,5037,4897],{},[1723,5039,1908],{"stretchy":1907},[898,5041,1746],{},[1723,5043,1914],{"stretchy":1907},[902,5045,4906],{"encoding":904},". Pro pevnou cenu ",[883,5048,5050],{"className":5049},[886],[888,5051,5052],{"xmlns":890},[892,5053,5054,5067],{},[895,5055,5056,5058,5060],{},[898,5057,1746],{},[1723,5059,1725],{},[2057,5061,5062,5064],{},[898,5063,1746],{},[1723,5065,5066],{},"∗",[902,5068,5069],{"encoding":904},"P = P^*"," se ",[883,5072,5074],{"className":5073},[886],[888,5075,5076],{"xmlns":890},[892,5077,5078,5092],{},[895,5079,5080,5082,5084,5090],{},[898,5081,1846],{},[1723,5083,1908],{"stretchy":1907},[2057,5085,5086,5088],{},[898,5087,1746],{},[1723,5089,5066],{},[1723,5091,1914],{"stretchy":1907},[902,5093,5094],{"encoding":904},"E(P^*)"," nazývá ",[614,5097,5098,5099],{},"elasticita poptávky při ceně ",[883,5100,5102],{"className":5101},[886],[888,5103,5104],{"xmlns":890},[892,5105,5106,5114],{},[895,5107,5108],{},[2057,5109,5110,5112],{},[898,5111,1746],{},[1723,5113,5066],{},[902,5115,5116],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[4584,5119,5120],{},[724,5121,5122,5125,5126,5144,5145,5173,5174,5203,5204,1343,5222,1343,5240,5257,5258,5273,5274,1664],{},[883,5123,5124],{},"!warning"," Pozor na znaménko\nV (4.5) je ",[38,5127,5128,5129],{},"explicitní ",[883,5130,5132],{"className":5131},[886],[888,5133,5134],{"xmlns":890},[892,5135,5136,5142],{},[895,5137,5138,5140],{},[1723,5139,1759],{},[1864,5141,1866],{},[902,5143,4452],{"encoding":904}," právě proto, že ",[883,5146,5148],{"className":5147},[886],[888,5149,5150],{"xmlns":890},[892,5151,5152,5170],{},[895,5153,5154,5160,5162,5164,5166,5168],{},[2057,5155,5156,5158],{},[898,5157,1904],{},[1723,5159,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,5161,1908],{"stretchy":1907},[898,5163,1746],{},[1723,5165,1914],{"stretchy":1907},[1723,5167,2287],{},[1864,5169,2256],{},[902,5171,5172],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,5175,5177],{"className":5176},[886],[888,5178,5179],{"xmlns":890},[892,5180,5181,5200],{},[895,5182,5183,5185,5187,5193,5195,5198],{},[898,5184,1846],{},[1723,5186,1908],{"stretchy":1907},[2057,5188,5189,5191],{},[898,5190,1746],{},[1723,5192,5066],{},[1723,5194,1914],{"stretchy":1907},[1723,5196,5197],{},"≥",[1864,5199,2256],{},[902,5201,5202],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,5205,5207],{"className":5206},[886],[888,5208,5209],{"xmlns":890},[892,5210,5211,5219],{},[895,5212,5213,5215,5217],{},[898,5214,1846],{},[1723,5216,2253],{},[1864,5218,1866],{},[902,5220,5221],{"encoding":904},"E > 1",[883,5223,5225],{"className":5224},[886],[888,5226,5227],{"xmlns":890},[892,5228,5229,5237],{},[895,5230,5231,5233,5235],{},[898,5232,1846],{},[1723,5234,2287],{},[1864,5236,1866],{},[902,5238,5239],{"encoding":904},"E \u003C 1",[883,5241,5243],{"className":5242},[886],[888,5244,5245],{"xmlns":890},[892,5246,5247,5255],{},[895,5248,5249,5251,5253],{},[898,5250,1846],{},[1723,5252,1725],{},[1864,5254,1866],{},[902,5256,1869],{"encoding":904},". V některých starších pramenech se ",[883,5259,5261],{"className":5260},[886],[888,5262,5263],{"xmlns":890},[892,5264,5265,5271],{},[895,5266,5267,5269],{},[1723,5268,1759],{},[1864,5270,1866],{},[902,5272,4452],{"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 ",[38,5275,5276],{},"absolutní hodnotou",[4584,5278,5279,5299],{},[724,5280,5281,5284,5285,5298],{},[883,5282,5283],{},"!tip"," Postup: jak spočítat ",[883,5286,5288],{"className":5287},[886],[888,5289,5290],{"xmlns":890},[892,5291,5292,5296],{},[895,5293,5294],{},[898,5295,1846],{},[902,5297,1846],{"encoding":904}," v bodě",[152,5300,5301,5353,5392,5445,5510],{},[123,5302,5303,5304,5327,5328,5352],{},"Zapište ",[883,5305,5307],{"className":5306},[886],[888,5308,5309],{"xmlns":890},[892,5310,5311,5325],{},[895,5312,5313,5315,5317,5319,5321,5323],{},[898,5314,1904],{},[1723,5316,1725],{},[898,5318,4897],{},[1723,5320,1908],{"stretchy":1907},[898,5322,1746],{},[1723,5324,1914],{"stretchy":1907},[902,5326,4906],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,5329,5331],{"className":5330},[886],[888,5332,5333],{"xmlns":890},[892,5334,5335,5349],{},[895,5336,5337,5339,5341,5343,5345,5347],{},[898,5338,1746],{},[1723,5340,1725],{},[898,5342,4897],{},[1723,5344,1908],{"stretchy":1907},[898,5346,1904],{},[1723,5348,1914],{"stretchy":1907},[902,5350,5351],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,5354,5355,5356,1664],{},"Spočítejte derivaci ",[883,5357,5359],{"className":5358},[886],[888,5360,5361],{"xmlns":890},[892,5362,5363,5389],{},[895,5364,5365,5371,5373,5375,5377,5379,5381,5383,5385,5387],{},[2057,5366,5367,5369],{},[898,5368,1904],{},[1723,5370,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,5372,1908],{"stretchy":1907},[898,5374,1746],{},[1723,5376,1914],{"stretchy":1907},[1723,5378,1725],{},[898,5380,2930],{"mathvariant":2124},[898,5382,1904],{},[898,5384,2125],{"mathvariant":2124},[898,5386,2930],{"mathvariant":2124},[898,5388,1746],{},[902,5390,5391],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,5393,5394,5395,5412,5413,1664],{},"Dosaďte zadanou cenu ",[883,5396,5398],{"className":5397},[886],[888,5399,5400],{"xmlns":890},[892,5401,5402,5410],{},[895,5403,5404],{},[2057,5405,5406,5408],{},[898,5407,1746],{},[1723,5409,5066],{},[902,5411,5116],{"encoding":904}," a dopočítejte odpovídající ",[883,5414,5416],{"className":5415},[886],[888,5417,5418],{"xmlns":890},[892,5419,5420,5442],{},[895,5421,5422,5428,5430,5432,5434,5440],{},[2057,5423,5424,5426],{},[898,5425,1904],{},[1723,5427,5066],{},[1723,5429,1725],{},[898,5431,4897],{},[1723,5433,1908],{"stretchy":1907},[2057,5435,5436,5438],{},[898,5437,1746],{},[1723,5439,5066],{},[1723,5441,1914],{"stretchy":1907},[902,5443,5444],{"encoding":904},"Q^* = D(P^*)",[123,5446,5447,5448,1664],{},"Dosaďte do (4.5): ",[883,5449,5451],{"className":5450},[886],[888,5452,5453],{"xmlns":890},[892,5454,5455,5507],{},[895,5456,5457,5459,5461,5467,5469,5471,5473,5489,5491,5497,5499,5505],{},[898,5458,1846],{},[1723,5460,1908],{"stretchy":1907},[2057,5462,5463,5465],{},[898,5464,1746],{},[1723,5466,5066],{},[1723,5468,1914],{"stretchy":1907},[1723,5470,1725],{},[1723,5472,1759],{},[3055,5474,5475],{"scriptlevel":2256,"displaystyle":2030},[3058,5476,5477,5483],{},[2057,5478,5479,5481],{},[898,5480,1746],{},[1723,5482,5066],{},[2057,5484,5485,5487],{},[898,5486,1904],{},[1723,5488,5066],{},[3018,5490,3707],{},[2057,5492,5493,5495],{},[898,5494,1904],{},[1723,5496,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,5498,1908],{"stretchy":1907},[2057,5500,5501,5503],{},[898,5502,1746],{},[1723,5504,5066],{},[1723,5506,1914],{"stretchy":1907},[902,5508,5509],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,5511,5512,5513,5530,5531,5548,5549,5566],{},"Klasifikujte: ",[883,5514,5516],{"className":5515},[886],[888,5517,5518],{"xmlns":890},[892,5519,5520,5528],{},[895,5521,5522,5524,5526],{},[898,5523,1846],{},[1723,5525,2253],{},[1864,5527,1866],{},[902,5529,5221],{"encoding":904}," elastická, ",[883,5532,5534],{"className":5533},[886],[888,5535,5536],{"xmlns":890},[892,5537,5538,5546],{},[895,5539,5540,5542,5544],{},[898,5541,1846],{},[1723,5543,1725],{},[1864,5545,1866],{},[902,5547,1869],{"encoding":904}," jednotková, ",[883,5550,5552],{"className":5551},[886],[888,5553,5554],{"xmlns":890},[892,5555,5556,5564],{},[895,5557,5558,5560,5562],{},[898,5559,1846],{},[1723,5561,2287],{},[1864,5563,1866],{},[902,5565,5239],{"encoding":904}," neelastická.",[198,5568,5570],{"id":5569},"interpretace-46","Interpretace (4.6)",[4584,5572,5573],{},[724,5574,5575,5576,5599,5600,5613,5614,5631,5632],{},"Číslo ",[883,5577,5579],{"className":5578},[886],[888,5580,5581],{"xmlns":890},[892,5582,5583,5597],{},[895,5584,5585,5587,5589,5595],{},[898,5586,1846],{},[1723,5588,1908],{"stretchy":1907},[2057,5590,5591,5593],{},[898,5592,1746],{},[1723,5594,5066],{},[1723,5596,1914],{"stretchy":1907},[902,5598,5094],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,5601,5603],{"className":5602},[886],[888,5604,5605],{"xmlns":890},[892,5606,5607,5611],{},[895,5608,5609],{},[898,5610,1904],{},[902,5612,1904],{"encoding":904},", jestliže se cena ",[883,5615,5617],{"className":5616},[886],[888,5618,5619],{"xmlns":890},[892,5620,5621,5629],{},[895,5622,5623],{},[2057,5624,5625,5627],{},[898,5626,1746],{},[1723,5628,5066],{},[902,5630,5116],{"encoding":904}," změní o 1 %. ",[883,5633,5635],{"className":5634},[886],[888,5636,5637],{"xmlns":890},[892,5638,5639,5648],{},[895,5640,5641,5643,5646],{},[1723,5642,1908],{"stretchy":1907},[1864,5644,5645],{},"4.6",[1723,5647,1914],{"stretchy":1907},[902,5649,5650],{"encoding":904},"(4.6)",[724,5652,5653,5656],{},[38,5654,5655],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,5658,5660],{"id":5659},"příklad-41","Příklad 4.1",[724,5662,5663,5664,5698,5699,1343,5725,3430],{},"Poptávka ",[883,5665,5667],{"className":5666},[886],[888,5668,5669],{"xmlns":890},[892,5670,5671,5695],{},[895,5672,5673,5675,5677,5679,5681,5683,5685,5687,5689,5691,5693],{},[898,5674,1746],{},[1723,5676,1725],{},[898,5678,4897],{},[1723,5680,1908],{"stretchy":1907},[898,5682,1904],{},[1723,5684,1914],{"stretchy":1907},[1723,5686,1725],{},[1864,5688,3840],{},[1723,5690,1759],{},[1864,5692,2331],{},[898,5694,1904],{},[902,5696,5697],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,5700,5702],{"className":5701},[886],[888,5703,5704],{"xmlns":890},[892,5705,5706,5722],{},[895,5707,5708,5710,5712,5715,5717,5720],{},[898,5709,1904],{},[1723,5711,1725],{},[1864,5713,5714],{},"25",[1723,5716,1759],{},[1864,5718,5719],{},"0,5",[898,5721,1746],{},[902,5723,5724],{"encoding":904},"Q = 25 - 0{,}5P",[883,5726,5728],{"className":5727},[886],[888,5729,5730],{"xmlns":890},[892,5731,5732,5756],{},[895,5733,5734,5750,5752,5754],{},[3055,5735,5736],{"scriptlevel":2256,"displaystyle":2030},[3058,5737,5738,5744],{},[895,5739,5740,5742],{},[898,5741,2930],{"mathvariant":2124},[898,5743,1904],{},[895,5745,5746,5748],{},[898,5747,2930],{"mathvariant":2124},[898,5749,1746],{},[1723,5751,1725],{},[1723,5753,1759],{},[1864,5755,5719],{},[902,5757,5758],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,5760,5761],{},[883,5762,5764],{"className":5763},[886],[888,5765,5766],{"xmlns":890},[892,5767,5768,5822],{},[895,5769,5770,5772,5774,5776,5790,5792,5794,5796,5798,5800,5802,5820],{},[898,5771,1846],{},[1723,5773,1725],{},[1723,5775,1759],{},[3058,5777,5778,5780],{},[898,5779,1746],{},[895,5781,5782,5784,5786,5788],{},[1864,5783,5714],{},[1723,5785,1759],{},[1864,5787,5719],{},[898,5789,1746],{},[1723,5791,3897],{},[1723,5793,1908],{"stretchy":1907},[1723,5795,1759],{},[1864,5797,5719],{},[1723,5799,1914],{"stretchy":1907},[1723,5801,1725],{},[3058,5803,5804,5810],{},[895,5805,5806,5808],{},[1864,5807,5719],{},[898,5809,1746],{},[895,5811,5812,5814,5816,5818],{},[1864,5813,5714],{},[1723,5815,1759],{},[1864,5817,5719],{},[898,5819,1746],{},[898,5821,1664],{"mathvariant":2124},[902,5823,5824],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,5826,5827,5828,1343,5852,1343,5882,1343,5906,5931,5932,5955,5956,3411,5974,4634],{},"Potom ",[883,5829,5831],{"className":5830},[886],[888,5832,5833],{"xmlns":890},[892,5834,5835,5849],{},[895,5836,5837,5839,5841,5843,5845,5847],{},[898,5838,1846],{},[1723,5840,1908],{"stretchy":1907},[1864,5842,2256],{},[1723,5844,1914],{"stretchy":1907},[1723,5846,1725],{},[1864,5848,2256],{},[902,5850,5851],{"encoding":904},"E(0)=0",[883,5853,5855],{"className":5854},[886],[888,5856,5857],{"xmlns":890},[892,5858,5859,5879],{},[895,5860,5861,5863,5865,5867,5869,5871],{},[898,5862,1846],{},[1723,5864,1908],{"stretchy":1907},[1864,5866,3585],{},[1723,5868,1914],{"stretchy":1907},[1723,5870,1725],{},[3055,5872,5873],{"scriptlevel":2256,"displaystyle":1907},[3058,5874,5875,5877],{},[1864,5876,1866],{},[1864,5878,3080],{},[902,5880,5881],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,5883,5885],{"className":5884},[886],[888,5886,5887],{"xmlns":890},[892,5888,5889,5903],{},[895,5890,5891,5893,5895,5897,5899,5901],{},[898,5892,1846],{},[1723,5894,1908],{"stretchy":1907},[1864,5896,5714],{},[1723,5898,1914],{"stretchy":1907},[1723,5900,1725],{},[1864,5902,1866],{},[902,5904,5905],{"encoding":904},"E(25)=1",[883,5907,5909],{"className":5908},[886],[888,5910,5911],{"xmlns":890},[892,5912,5913,5928],{},[895,5914,5915,5917,5919,5922,5924,5926],{},[898,5916,1846],{},[1723,5918,1908],{"stretchy":1907},[1864,5920,5921],{},"40",[1723,5923,1914],{"stretchy":1907},[1723,5925,1725],{},[1864,5927,3080],{},[902,5929,5930],{"encoding":904},"E(40)=4",". Např. ",[883,5933,5935],{"className":5934},[886],[888,5936,5937],{"xmlns":890},[892,5938,5939,5953],{},[895,5940,5941,5943,5945,5947,5949,5951],{},[898,5942,1846],{},[1723,5944,1908],{"stretchy":1907},[1864,5946,5921],{},[1723,5948,1914],{"stretchy":1907},[1723,5950,1725],{},[1864,5952,3080],{},[902,5954,5930],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,5957,5959],{"className":5958},[886],[888,5960,5961],{"xmlns":890},[892,5962,5963,5971],{},[895,5964,5965,5967,5969],{},[898,5966,1904],{},[1723,5968,1725],{},[1864,5970,2962],{},[902,5972,5973],{"encoding":904},"Q=5",[883,5975,5977],{"className":5976},[886],[888,5978,5979],{"xmlns":890},[892,5980,5981,5990],{},[895,5982,5983,5985,5987],{},[898,5984,1904],{},[1723,5986,1725],{},[1864,5988,5989],{},"4,8",[902,5991,5992],{"encoding":904},"Q=4{,}8",[198,5994,5996],{"id":5995},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,5998,5999,6055],{},[123,6000,6001,6004,6005,6022,6023,1664],{},[38,6002,6003],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,6006,6008],{"className":6007},[886],[888,6009,6010],{"xmlns":890},[892,6011,6012,6020],{},[895,6013,6014],{},[2057,6015,6016,6018],{},[898,6017,1846],{},[898,6019,1718],{},[902,6021,4970],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,6024,6026],{"className":6025},[886],[888,6027,6028],{"xmlns":890},[892,6029,6030,6052],{},[895,6031,6032,6035,6037,6039,6041,6043,6045,6047,6049],{},[1723,6033,6034],{"stretchy":1907},"⟨",[898,6036,1746],{},[1723,6038,2031],{"separator":2030},[3018,6040,3707],{},[898,6042,1746],{},[1723,6044,2087],{},[898,6046,3611],{"mathvariant":2124},[898,6048,1746],{},[1723,6050,6051],{"stretchy":1907},"⟩",[902,6053,6054],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,6056,6057,6060,6061,6074],{},[38,6058,6059],{},"Bodová"," (okamžitá) elasticita: ",[883,6062,6064],{"className":6063},[886],[888,6065,6066],{"xmlns":890},[892,6067,6068,6072],{},[895,6069,6070],{},[898,6071,1846],{},[902,6073,1846],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,6076,6078,6079,6092,6093],{"id":6077},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,6080,6082],{"className":6081},[886],[888,6083,6084],{"xmlns":890},[892,6085,6086,6090],{},[895,6087,6088],{},[898,6089,1746],{},[902,6091,1746],{"encoding":904}," jako funkce ",[883,6094,6096],{"className":6095},[886],[888,6097,6098],{"xmlns":890},[892,6099,6100,6104],{},[895,6101,6102],{},[898,6103,1904],{},[902,6105,1904],{"encoding":904},[724,6107,6108,6109,6132],{},"Pokud je poptávka zadaná ve tvaru ",[883,6110,6112],{"className":6111},[886],[888,6113,6114],{"xmlns":890},[892,6115,6116,6130],{},[895,6117,6118,6120,6122,6124,6126,6128],{},[898,6119,1746],{},[1723,6121,1725],{},[898,6123,4897],{},[1723,6125,1908],{"stretchy":1907},[898,6127,1904],{},[1723,6129,1914],{"stretchy":1907},[902,6131,5351],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,6134,6135],{},[883,6136,6138],{"className":6137,"title":4914,"style":4915},[4913],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,6140,6141,2628,6144,6170],{},[38,6142,6143],{},"Příklad 4.3.",[883,6145,6147],{"className":6146},[886],[888,6148,6149],{"xmlns":890},[892,6150,6151,6167],{},[895,6152,6153,6155,6157,6159,6161],{},[898,6154,1746],{},[1723,6156,1725],{},[1864,6158,3810],{},[1723,6160,1759],{},[2057,6162,6163,6165],{},[898,6164,1904],{},[1864,6166,2331],{},[902,6168,6169],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,6172,6173],{},[883,6174,6176],{"className":6175},[886],[888,6177,6178],{"xmlns":890},[892,6179,6180,6246],{},[895,6181,6182,6184,6186,6188,6204,6206,6218,6220,6244],{},[898,6183,1846],{},[1723,6185,1725],{},[1723,6187,1759],{},[3058,6189,6190,6202],{},[895,6191,6192,6194,6196],{},[1864,6193,3810],{},[1723,6195,1759],{},[2057,6197,6198,6200],{},[898,6199,1904],{},[1864,6201,2331],{},[898,6203,1904],{},[1723,6205,3897],{},[3058,6207,6208,6210],{},[1864,6209,1866],{},[895,6211,6212,6214,6216],{},[1723,6213,1759],{},[1864,6215,2331],{},[898,6217,1904],{},[1723,6219,1725],{},[3058,6221,6222,6234],{},[895,6223,6224,6226,6228],{},[1864,6225,3810],{},[1723,6227,1759],{},[2057,6229,6230,6232],{},[898,6231,1904],{},[1864,6233,2331],{},[895,6235,6236,6238],{},[1864,6237,2331],{},[2057,6239,6240,6242],{},[898,6241,1904],{},[1864,6243,2331],{},[898,6245,1664],{"mathvariant":2124},[902,6247,6248],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,6250,6251,6252,6279,6280,6299,6300,1664],{},"Z rovnice ",[883,6253,6255],{"className":6254},[886],[888,6256,6257],{"xmlns":890},[892,6258,6259,6276],{},[895,6260,6261,6263,6265,6271,6273],{},[1864,6262,3810],{},[1723,6264,1759],{},[2057,6266,6267,6269],{},[898,6268,1904],{},[1864,6270,2331],{},[1723,6272,1725],{},[1864,6274,6275],{},"36",[902,6277,6278],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,6281,6283],{"className":6282},[886],[888,6284,6285],{"xmlns":890},[892,6286,6287,6296],{},[895,6288,6289,6291,6293],{},[898,6290,1904],{},[1723,6292,1725],{},[1864,6294,6295],{},"8",[902,6297,6298],{"encoding":904},"Q = 8",", tedy ",[883,6301,6303],{"className":6302},[886],[888,6304,6305],{"xmlns":890},[892,6306,6307,6333],{},[895,6308,6309,6311,6313,6315,6317,6319,6328,6330],{},[898,6310,1846],{},[1723,6312,1908],{"stretchy":1907},[1864,6314,6295],{},[1723,6316,1914],{"stretchy":1907},[1723,6318,1725],{},[3055,6320,6321],{"scriptlevel":2256,"displaystyle":1907},[3058,6322,6323,6325],{},[1864,6324,6275],{},[1864,6326,6327],{},"128",[1723,6329,1725],{},[1864,6331,6332],{},"0,281",[902,6334,6335],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,6337,6339],{"id":6338},"přibližné-změny","Přibližné změny",[724,6341,6342,6343,6379,6380,6402],{},"Diferenciál ",[883,6344,6346],{"className":6345},[886],[888,6347,6348],{"xmlns":890},[892,6349,6350,6376],{},[895,6351,6352,6354,6356,6358,6364,6366,6368,6370,6372,6374],{},[898,6353,2930],{"mathvariant":2124},[898,6355,1904],{},[1723,6357,1725],{},[2057,6359,6360,6362],{},[898,6361,1904],{},[1723,6363,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,6365,1908],{"stretchy":1907},[898,6367,1746],{},[1723,6369,1914],{"stretchy":1907},[3018,6371,3707],{},[898,6373,2930],{"mathvariant":2124},[898,6375,1746],{},[902,6377,6378],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,6381,6383],{"className":6382},[886],[888,6384,6385],{"xmlns":890},[892,6386,6387,6399],{},[895,6388,6389,6391,6393,6395,6397],{},[898,6390,2930],{"mathvariant":2124},[898,6392,1746],{},[1723,6394,1725],{},[898,6396,3611],{"mathvariant":2124},[898,6398,1746],{},[902,6400,6401],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,6404,6405],{},[883,6406,6408],{"className":6407,"title":4914,"style":4915},[4913],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,6410,6411],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,6413,6414],{},[883,6415,6417],{"className":6416,"title":4914,"style":4915},[4913],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,6419,6420,2628,6423,6458,6459,6478,6479,6513,6514,6531],{},[38,6421,6422],{},"Příklad 4.5.",[883,6424,6426],{"className":6425},[886],[888,6427,6428],{"xmlns":890},[892,6429,6430,6455],{},[895,6431,6432,6434,6436,6438,6444,6446,6448,6450,6452],{},[898,6433,1746],{},[1723,6435,1725],{},[1723,6437,1759],{},[2057,6439,6440,6442],{},[898,6441,1904],{},[1864,6443,2331],{},[1723,6445,1759],{},[1864,6447,3080],{},[898,6449,1904],{},[1723,6451,2087],{},[1864,6453,6454],{},"96",[902,6456,6457],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,6460,6462],{"className":6461},[886],[888,6463,6464],{"xmlns":890},[892,6465,6466,6475],{},[895,6467,6468,6470,6472],{},[898,6469,1746],{},[1723,6471,1725],{},[1864,6473,6474],{},"51",[902,6476,6477],{"encoding":904},"P=51",". Z rovnice ",[883,6480,6482],{"className":6481},[886],[888,6483,6484],{"xmlns":890},[892,6485,6486,6510],{},[895,6487,6488,6490,6492,6494,6500,6502,6504,6506,6508],{},[1864,6489,6474],{},[1723,6491,1725],{},[1723,6493,1759],{},[2057,6495,6496,6498],{},[898,6497,1904],{},[1864,6499,2331],{},[1723,6501,1759],{},[1864,6503,3080],{},[898,6505,1904],{},[1723,6507,2087],{},[1864,6509,6454],{},[902,6511,6512],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,6515,6517],{"className":6516},[886],[888,6518,6519],{"xmlns":890},[892,6520,6521,6529],{},[895,6522,6523,6525,6527],{},[898,6524,1904],{},[1723,6526,1725],{},[1864,6528,2962],{},[902,6530,5973],{"encoding":904},". Elasticita:",[724,6533,6534],{},[883,6535,6537],{"className":6536},[886],[888,6538,6539],{"xmlns":890},[892,6540,6541,6614],{},[895,6542,6543,6545,6547,6585,6587,6591,6593,6595,6597,6599,6601,6608,6611],{},[898,6544,1846],{},[1723,6546,1725],{},[3058,6548,6549,6569],{},[895,6550,6551,6553,6559,6561,6563,6565,6567],{},[1723,6552,1759],{},[2057,6554,6555,6557],{},[898,6556,1904],{},[1864,6558,2331],{},[1723,6560,1759],{},[1864,6562,3080],{},[898,6564,1904],{},[1723,6566,2087],{},[1864,6568,6454],{},[895,6570,6571,6573,6575,6577,6579,6581,6583],{},[898,6572,1904],{},[1723,6574,1908],{"stretchy":1907},[1864,6576,2331],{},[898,6578,1904],{},[1723,6580,2087],{},[1864,6582,3080],{},[1723,6584,1914],{"stretchy":1907},[1723,6586,2031],{"separator":2030},[6588,6589],"mspace",{"width":6590},"2em",[898,6592,1846],{},[1723,6594,1908],{"stretchy":1907},[1864,6596,2962],{},[1723,6598,1914],{"stretchy":1907},[1723,6600,1725],{},[3058,6602,6603,6605],{},[1864,6604,6474],{},[1864,6606,6607],{},"70",[1723,6609,6610],{},"≐",[1864,6612,6613],{},"0,728.",[902,6615,6616],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,6618,6619,6620,1664],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,6621,6623],{"className":6622},[886],[888,6624,6625],{"xmlns":890},[892,6626,6627,6658],{},[895,6628,6629,6631,6633,6636,6638,6640,6643,6645,6647,6649,6651,6654,6656],{},[898,6630,3611],{"mathvariant":2124},[898,6632,1904],{},[898,6634,6635],{"mathvariant":2124},"%",[1723,6637,3456],{},[1723,6639,1759],{},[1864,6641,6642],{},"0,728",[1723,6644,3897],{},[1864,6646,2331],{},[1723,6648,1725],{},[1723,6650,1759],{},[1864,6652,6653],{},"1,456",[3018,6655,3707],{},[898,6657,6635],{"mathvariant":2124},[902,6659,6660],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,6662,6664],{"id":6663},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,6666,6667,6668,6691,6692,3430],{},"V závislosti na hodnotě ",[883,6669,6671],{"className":6670},[886],[888,6672,6673],{"xmlns":890},[892,6674,6675,6689],{},[895,6676,6677,6679,6681,6687],{},[898,6678,1846],{},[1723,6680,1908],{"stretchy":1907},[2057,6682,6683,6685],{},[898,6684,1746],{},[1723,6686,5066],{},[1723,6688,1914],{"stretchy":1907},[902,6690,5094],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,6693,6695],{"className":6694},[886],[888,6696,6697],{"xmlns":890},[892,6698,6699,6708],{},[895,6700,6701,6703,6706],{},[1723,6702,1908],{"stretchy":1907},[1864,6704,6705],{},"4.7",[1723,6707,1914],{"stretchy":1907},[902,6709,6710],{"encoding":904},"(4.7)",[724,6712,6713],{},[3285,6714],{"alt":6715,"className":6716,"src":6717},"imek-typy-elasticity-5panelu",[210,3289],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,6719,6720,6759],{},[19,6721,6722],{},[22,6723,6724,6750,6753,6756],{},[25,6725,6726,6727],{},"Hodnota ",[883,6728,6730],{"className":6729},[886],[888,6731,6732],{"xmlns":890},[892,6733,6734,6748],{},[895,6735,6736,6738,6740,6746],{},[898,6737,1846],{},[1723,6739,1908],{"stretchy":1907},[2057,6741,6742,6744],{},[898,6743,1746],{},[1723,6745,5066],{},[1723,6747,1914],{"stretchy":1907},[902,6749,5094],{"encoding":904},[25,6751,6752],{},"Typ poptávky",[25,6754,6755],{},"Termín",[25,6757,6758],{},"Význam",[30,6760,6761,6794,6856,6931,6988],{},[22,6762,6763,6783,6788,6791],{},[35,6764,6765],{},[883,6766,6768],{"className":6767},[886],[888,6769,6770],{"xmlns":890},[892,6771,6772,6780],{},[895,6773,6774,6776,6778],{},[898,6775,1846],{},[1723,6777,1725],{},[1864,6779,2256],{},[902,6781,6782],{"encoding":904},"E = 0",[35,6784,6785],{},[38,6786,6787],{},"dokonale neelastická",[35,6789,6790],{},"perfectly inelastic",[35,6792,6793],{},"množství se nemění bez ohledu na cenu",[22,6795,6796,6820,6824,6827],{},[35,6797,6798],{},[883,6799,6801],{"className":6800},[886],[888,6802,6803],{"xmlns":890},[892,6804,6805,6817],{},[895,6806,6807,6809,6811,6813,6815],{},[1864,6808,2256],{},[1723,6810,2287],{},[898,6812,1846],{},[1723,6814,2287],{},[1864,6816,1866],{},[902,6818,6819],{"encoding":904},"0 \u003C E \u003C 1",[35,6821,6822],{},[38,6823,4791],{},[35,6825,6826],{},"inelastic",[35,6828,6829,6842,6843],{},[883,6830,6832],{"className":6831},[886],[888,6833,6834],{"xmlns":890},[892,6835,6836,6840],{},[895,6837,6838],{},[898,6839,1904],{},[902,6841,1904],{"encoding":904}," se mění pomaleji než ",[883,6844,6846],{"className":6845},[886],[888,6847,6848],{"xmlns":890},[892,6849,6850,6854],{},[895,6851,6852],{},[898,6853,1746],{},[902,6855,1746],{"encoding":904},[22,6857,6858,6877,6882,6885],{},[35,6859,6860],{},[883,6861,6863],{"className":6862},[886],[888,6864,6865],{"xmlns":890},[892,6866,6867,6875],{},[895,6868,6869,6871,6873],{},[898,6870,1846],{},[1723,6872,1725],{},[1864,6874,1866],{},[902,6876,1869],{"encoding":904},[35,6878,6879],{},[38,6880,6881],{},"jednotkově elastická",[35,6883,6884],{},"unit elastic",[35,6886,6887,6900,6901,6914,6915,6930],{},[883,6888,6890],{"className":6889},[886],[888,6891,6892],{"xmlns":890},[892,6893,6894,6898],{},[895,6895,6896],{},[898,6897,1904],{},[902,6899,1904],{"encoding":904}," i ",[883,6902,6904],{"className":6903},[886],[888,6905,6906],{"xmlns":890},[892,6907,6908,6912],{},[895,6909,6910],{},[898,6911,1746],{},[902,6913,1746],{"encoding":904}," se mění stejně rychle; ",[883,6916,6918],{"className":6917},[886],[888,6919,6920],{"xmlns":890},[892,6921,6922,6928],{},[895,6923,6924,6926],{},[898,6925,1754],{},[898,6927,1749],{},[902,6929,4808],{"encoding":904}," má maximum",[22,6932,6933,6952,6956,6959],{},[35,6934,6935],{},[883,6936,6938],{"className":6937},[886],[888,6939,6940],{"xmlns":890},[892,6941,6942,6950],{},[895,6943,6944,6946,6948],{},[898,6945,1846],{},[1723,6947,2253],{},[1864,6949,1866],{},[902,6951,5221],{"encoding":904},[35,6953,6954],{},[38,6955,4787],{},[35,6957,6958],{},"elastic",[35,6960,6961,6974,6975],{},[883,6962,6964],{"className":6963},[886],[888,6965,6966],{"xmlns":890},[892,6967,6968,6972],{},[895,6969,6970],{},[898,6971,1904],{},[902,6973,1904],{"encoding":904}," se mění rychleji než ",[883,6976,6978],{"className":6977},[886],[888,6979,6980],{"xmlns":890},[892,6981,6982,6986],{},[895,6983,6984],{},[898,6985,1746],{},[902,6987,1746],{"encoding":904},[22,6989,6990,7011,7016,7019],{},[35,6991,6992],{},[883,6993,6995],{"className":6994},[886],[888,6996,6997],{"xmlns":890},[892,6998,6999,7008],{},[895,7000,7001,7003,7005],{},[898,7002,1846],{},[1723,7004,3843],{},[898,7006,7007],{"mathvariant":2124},"∞",[902,7009,7010],{"encoding":904},"E \\to \\infty",[35,7012,7013],{},[38,7014,7015],{},"dokonale elastická",[35,7017,7018],{},"perfectly elastic",[35,7020,7021,7022],{},"sebemenší změna ceny úplně mění ",[883,7023,7025],{"className":7024},[886],[888,7026,7027],{"xmlns":890},[892,7028,7029,7033],{},[895,7030,7031],{},[898,7032,1904],{},[902,7034,1904],{"encoding":904},[724,7036,7037],{},[38,7038,7039],{},"Pravidlo růstu elasticity s cenou:",[4584,7041,7042],{},[724,7043,7044,7045],{},"S rostoucí cenou elasticita poptávky roste. ",[883,7046,7048],{"className":7047},[886],[888,7049,7050],{"xmlns":890},[892,7051,7052,7061],{},[895,7053,7054,7056,7059],{},[1723,7055,1908],{"stretchy":1907},[1864,7057,7058],{},"4.8",[1723,7060,1914],{"stretchy":1907},[902,7062,7063],{"encoding":904},"(4.8)",[724,7065,7066,7067,7070,7071,7074,7075,7092],{},"Z toho plyne, že při ",[614,7068,7069],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,7072,7073],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,7076,7078],{"className":7077},[886],[888,7079,7080],{"xmlns":890},[892,7081,7082,7090],{},[895,7083,7084],{},[2057,7085,7086,7088],{},[898,7087,1746],{},[1723,7089,5066],{},[902,7091,5116],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[4584,7094,7095,7100],{},[724,7096,7097,7099],{},[883,7098,5283],{}," Postup: jak klasifikovat poptávku",[152,7101,7102,7129,7132],{},[123,7103,7104,7105,7128],{},"Spočítejte ",[883,7106,7108],{"className":7107},[886],[888,7109,7110],{"xmlns":890},[892,7111,7112,7126],{},[895,7113,7114,7116,7118,7124],{},[898,7115,1846],{},[1723,7117,1908],{"stretchy":1907},[2057,7119,7120,7122],{},[898,7121,1746],{},[1723,7123,5066],{},[1723,7125,1914],{"stretchy":1907},[902,7127,5094],{"encoding":904}," dle (4.5).",[123,7130,7131],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,7133,7134,7135,7159],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,7136,7138],{"className":7137},[886],[888,7139,7140],{"xmlns":890},[892,7141,7142,7156],{},[895,7143,7144,7146,7148,7150,7152,7154],{},[898,7145,1846],{},[1723,7147,1908],{"stretchy":1907},[898,7149,1746],{},[1723,7151,1914],{"stretchy":1907},[1723,7153,1725],{},[1864,7155,1866],{},[902,7157,7158],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,7161,7162,7165,7166,7183,7184,7202,7203,7230,7231,1664],{},[38,7163,7164],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,7167,7169],{"className":7168},[886],[888,7170,7171],{"xmlns":890},[892,7172,7173,7181],{},[895,7174,7175,7177,7179],{},[898,7176,1846],{},[1723,7178,1725],{},[1864,7180,1866],{},[902,7182,1869],{"encoding":904}," pro ",[883,7185,7187],{"className":7186},[886],[888,7188,7189],{"xmlns":890},[892,7190,7191,7199],{},[895,7192,7193,7195,7197],{},[898,7194,1746],{},[1723,7196,1725],{},[1864,7198,5714],{},[902,7200,7201],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,7204,7206],{"className":7205},[886],[888,7207,7208],{"xmlns":890},[892,7209,7210,7227],{},[895,7211,7212,7214,7217,7219,7221,7223,7225],{},[898,7213,1746],{},[1723,7215,7216],{},"∈",[1723,7218,6034],{"stretchy":1907},[1864,7220,2256],{},[1723,7222,2031],{"separator":2030},[1864,7224,5714],{},[1723,7226,1914],{"stretchy":1907},[902,7228,7229],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,7232,7234],{"className":7233},[886],[888,7235,7236],{"xmlns":890},[892,7237,7238,7254],{},[895,7239,7240,7242,7244,7246,7248,7250,7252],{},[898,7241,1746],{},[1723,7243,7216],{},[1723,7245,1908],{"stretchy":1907},[1864,7247,5714],{},[1723,7249,2031],{"separator":2030},[1864,7251,3840],{},[1723,7253,6051],{"stretchy":1907},[902,7255,7256],{"encoding":904},"P \\in (25, 50\\rangle",[115,7258,7260],{"id":7259},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,7262,7263],{},[3285,7264],{"alt":7265,"className":7266,"src":7267},"imek-elasticita-tr",[210,3289],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,7269,7270],{},[3285,7271],{"alt":7272,"className":7273,"src":7274},"imek-elasticita-podel-linearni-poptavky",[210,3289],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,7276,7277,7278,7328,7329,7345],{},"Pro celkový příjem platí ",[883,7279,7281],{"className":7280},[886],[888,7282,7283],{"xmlns":890},[892,7284,7285,7325],{},[895,7286,7287,7289,7291,7293,7295,7297,7299,7301,7303,7305,7307,7309,7311,7313,7315,7317,7319,7321,7323],{},[898,7288,1754],{},[898,7290,1749],{},[1723,7292,1725],{},[898,7294,1754],{},[898,7296,1749],{},[1723,7298,1908],{"stretchy":1907},[898,7300,1904],{},[1723,7302,1914],{"stretchy":1907},[1723,7304,1725],{},[898,7306,1746],{},[1723,7308,3897],{},[898,7310,1904],{},[1723,7312,1725],{},[898,7314,1904],{},[1723,7316,3897],{},[898,7318,4897],{},[1723,7320,1908],{"stretchy":1907},[898,7322,1904],{},[1723,7324,1914],{"stretchy":1907},[902,7326,7327],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,7330,7332],{"className":7331},[886],[888,7333,7334],{"xmlns":890},[892,7335,7336,7342],{},[895,7337,7338,7340],{},[898,7339,1728],{},[898,7341,1749],{},[902,7343,7344],{"encoding":904},"MR"," odvodíme:",[724,7347,7348],{},[883,7349,7351],{"className":7350},[886],[888,7352,7353],{"xmlns":890},[892,7354,7355,7463],{},[895,7356,7357,7359,7361,7363,7365,7371,7373,7375,7377,7379,7381,7383,7385,7387,7389,7391,7393,7399,7401,7403,7405,7407,7409,7411,7413,7427,7429,7431],{},[898,7358,1728],{},[898,7360,1749],{},[1723,7362,1725],{},[898,7364,1754],{},[2057,7366,7367,7369],{},[898,7368,1749],{},[1723,7370,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,7372,1908],{"stretchy":1907},[898,7374,1904],{},[1723,7376,1914],{"stretchy":1907},[1723,7378,1725],{},[898,7380,4897],{},[1723,7382,1908],{"stretchy":1907},[898,7384,1904],{},[1723,7386,1914],{"stretchy":1907},[1723,7388,2087],{},[898,7390,1904],{},[3018,7392,3707],{},[2057,7394,7395,7397],{},[898,7396,4897],{},[1723,7398,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,7400,1908],{"stretchy":1907},[898,7402,1904],{},[1723,7404,1914],{"stretchy":1907},[1723,7406,1725],{},[898,7408,1746],{},[1723,7410,2087],{},[898,7412,1904],{},[3058,7414,7415,7421],{},[895,7416,7417,7419],{},[898,7418,2930],{"mathvariant":2124},[898,7420,1746],{},[895,7422,7423,7425],{},[898,7424,2930],{"mathvariant":2124},[898,7426,1904],{},[1723,7428,1725],{},[898,7430,1746],{},[895,7432,7433,7435,7437,7439,7445,7447,7461],{},[1723,7434,1908],{"fence":2030},[1864,7436,1866],{},[1723,7438,2087],{},[3058,7440,7441,7443],{},[898,7442,1904],{},[898,7444,1746],{},[1723,7446,3897],{},[3058,7448,7449,7455],{},[895,7450,7451,7453],{},[898,7452,2930],{"mathvariant":2124},[898,7454,1746],{},[895,7456,7457,7459],{},[898,7458,2930],{"mathvariant":2124},[898,7460,1904],{},[1723,7462,1914],{"fence":2030},[902,7464,7465],{"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)",[724,7467,7468],{},[883,7469,7471],{"className":7470},[886],[888,7472,7473],{"xmlns":890},[892,7474,7475,7547],{},[895,7476,7477,7479,7481,7523,7525,7527],{},[1723,7478,1725],{},[898,7480,1746],{},[895,7482,7483,7485,7487,7489,7521],{},[1723,7484,1908],{"fence":2030},[1864,7486,1866],{},[1723,7488,2087],{},[3058,7490,7491,7493],{},[1864,7492,1866],{},[895,7494,7495,7503,7505],{},[3055,7496,7497],{"scriptlevel":2256,"displaystyle":1907},[3058,7498,7499,7501],{},[898,7500,1746],{},[898,7502,1904],{},[1723,7504,3897],{},[3055,7506,7507],{"scriptlevel":2256,"displaystyle":1907},[3058,7508,7509,7515],{},[895,7510,7511,7513],{},[898,7512,2930],{"mathvariant":2124},[898,7514,1904],{},[895,7516,7517,7519],{},[898,7518,2930],{"mathvariant":2124},[898,7520,1746],{},[1723,7522,1914],{"fence":2030},[1723,7524,1725],{},[898,7526,1746],{},[895,7528,7529,7531,7533,7535,7545],{},[1723,7530,1908],{"fence":2030},[1864,7532,1866],{},[1723,7534,2087],{},[3058,7536,7537,7539],{},[1864,7538,1866],{},[895,7540,7541,7543],{},[1723,7542,1759],{},[898,7544,1846],{},[1723,7546,1914],{"fence":2030},[902,7548,7549],{"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)",[724,7551,7552],{},"a tedy",[724,7554,7555],{},[883,7556,7558],{"className":7557,"title":4914,"style":4915},[4913],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[4584,7560,7561,7630,7880],{},[724,7562,7563,7565,7566,7600,7601,7616,7617,3430],{},[883,7564,4869],{}," Intuice: vztah ",[883,7567,7569],{"className":7568},[886],[888,7570,7571],{"xmlns":890},[892,7572,7573,7597],{},[895,7574,7575,7577,7579,7581,7583,7585,7587,7589,7591,7593,7595],{},[898,7576,1728],{},[898,7578,1749],{},[1723,7580,1725],{},[898,7582,1746],{},[1723,7584,1908],{"stretchy":1907},[1864,7586,1866],{},[1723,7588,1759],{},[1864,7590,1866],{},[898,7592,2125],{"mathvariant":2124},[898,7594,1846],{},[1723,7596,1914],{"stretchy":1907},[902,7598,7599],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,7602,7604],{"className":7603},[886],[888,7605,7606],{"xmlns":890},[892,7607,7608,7614],{},[895,7609,7610,7612],{},[898,7611,1728],{},[898,7613,1749],{},[902,7615,7344],{"encoding":904}," jednoznačně určuje hodnota ",[883,7618,7620],{"className":7619},[886],[888,7621,7622],{"xmlns":890},[892,7623,7624,7628],{},[895,7625,7626],{},[898,7627,1846],{},[902,7629,1846],{"encoding":904},[120,7631,7632,7742,7811],{},[123,7633,7634,7651,7652,2628,7666,2628,7692,2628,7705,7725,7726,7741],{},[883,7635,7637],{"className":7636},[886],[888,7638,7639],{"xmlns":890},[892,7640,7641,7649],{},[895,7642,7643,7645,7647],{},[898,7644,1846],{},[1723,7646,2253],{},[1864,7648,1866],{},[902,7650,5221],{"encoding":904}," (elastická) ",[883,7653,7655],{"className":7654},[886],[888,7656,7657],{"xmlns":890},[892,7658,7659,7663],{},[895,7660,7661],{},[1723,7662,4702],{},[902,7664,7665],{"encoding":904},"\\Rightarrow",[883,7667,7669],{"className":7668},[886],[888,7670,7671],{"xmlns":890},[892,7672,7673,7689],{},[895,7674,7675,7677,7679,7681,7683,7685,7687],{},[1864,7676,1866],{},[1723,7678,1759],{},[1864,7680,1866],{},[898,7682,2125],{"mathvariant":2124},[898,7684,1846],{},[1723,7686,2253],{},[1864,7688,2256],{},[902,7690,7691],{"encoding":904},"1 - 1\u002FE > 0",[883,7693,7695],{"className":7694},[886],[888,7696,7697],{"xmlns":890},[892,7698,7699,7703],{},[895,7700,7701],{},[1723,7702,4702],{},[902,7704,7665],{"encoding":904},[883,7706,7708],{"className":7707},[886],[888,7709,7710],{"xmlns":890},[892,7711,7712,7722],{},[895,7713,7714,7716,7718,7720],{},[898,7715,1728],{},[898,7717,1749],{},[1723,7719,2253],{},[1864,7721,2256],{},[902,7723,7724],{"encoding":904},"MR > 0"," — ",[883,7727,7729],{"className":7728},[886],[888,7730,7731],{"xmlns":890},[892,7732,7733,7739],{},[895,7734,7735,7737],{},[898,7736,1754],{},[898,7738,1749],{},[902,7740,4808],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,7743,7744,7761,7762,2628,7775,7725,7795,7810],{},[883,7745,7747],{"className":7746},[886],[888,7748,7749],{"xmlns":890},[892,7750,7751,7759],{},[895,7752,7753,7755,7757],{},[898,7754,1846],{},[1723,7756,1725],{},[1864,7758,1866],{},[902,7760,1869],{"encoding":904}," (jednotková) ",[883,7763,7765],{"className":7764},[886],[888,7766,7767],{"xmlns":890},[892,7768,7769,7773],{},[895,7770,7771],{},[1723,7772,4702],{},[902,7774,7665],{"encoding":904},[883,7776,7778],{"className":7777},[886],[888,7779,7780],{"xmlns":890},[892,7781,7782,7792],{},[895,7783,7784,7786,7788,7790],{},[898,7785,1728],{},[898,7787,1749],{},[1723,7789,1725],{},[1864,7791,2256],{},[902,7793,7794],{"encoding":904},"MR = 0",[883,7796,7798],{"className":7797},[886],[888,7799,7800],{"xmlns":890},[892,7801,7802,7808],{},[895,7803,7804,7806],{},[898,7805,1754],{},[898,7807,1749],{},[902,7809,4808],{"encoding":904}," je extrém (maximum).",[123,7812,7813,7830,7831,2628,7844,7725,7864,7879],{},[883,7814,7816],{"className":7815},[886],[888,7817,7818],{"xmlns":890},[892,7819,7820,7828],{},[895,7821,7822,7824,7826],{},[898,7823,1846],{},[1723,7825,2287],{},[1864,7827,1866],{},[902,7829,5239],{"encoding":904}," (neelastická) ",[883,7832,7834],{"className":7833},[886],[888,7835,7836],{"xmlns":890},[892,7837,7838,7842],{},[895,7839,7840],{},[1723,7841,4702],{},[902,7843,7665],{"encoding":904},[883,7845,7847],{"className":7846},[886],[888,7848,7849],{"xmlns":890},[892,7850,7851,7861],{},[895,7852,7853,7855,7857,7859],{},[898,7854,1728],{},[898,7856,1749],{},[1723,7858,2287],{},[1864,7860,2256],{},[902,7862,7863],{"encoding":904},"MR \u003C 0",[883,7865,7867],{"className":7866},[886],[888,7868,7869],{"xmlns":890},[892,7870,7871,7877],{},[895,7872,7873,7875],{},[898,7874,1754],{},[898,7876,1749],{},[902,7878,4808],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,7881,7882,7883,1664],{},"Viz také ",[207,7884,4539],{"className":7885,"dataFsResolvedFilePath":827,"href":828},[210],[198,7887,7889],{"id":7888},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,7891,7892,7912,7913,7939,7940,7955,7956,7969,7970,7983,7984,7997,7998,8014,8015,2628,8030,8033,8034,8014,8050,1664],{},[38,7893,7894,7895,4634],{},"(a) Poptávka elastická (",[883,7896,7898],{"className":7897},[886],[888,7899,7900],{"xmlns":890},[892,7901,7902,7910],{},[895,7903,7904,7906,7908],{},[898,7905,1846],{},[1723,7907,2253],{},[1864,7909,1866],{},[902,7911,5221],{"encoding":904}," Z (4.12) plyne ",[883,7914,7916],{"className":7915},[886],[888,7917,7918],{"xmlns":890},[892,7919,7920,7936],{},[895,7921,7922,7924,7926,7928,7930,7932,7934],{},[898,7923,1728],{},[898,7925,1749],{},[1723,7927,1908],{"stretchy":1907},[898,7929,1904],{},[1723,7931,1914],{"stretchy":1907},[1723,7933,2253],{},[1864,7935,2256],{},[902,7937,7938],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,7941,7943],{"className":7942},[886],[888,7944,7945],{"xmlns":890},[892,7946,7947,7953],{},[895,7948,7949,7951],{},[898,7950,1754],{},[898,7952,1749],{},[902,7954,4808],{"encoding":904}," je rostoucí funkcí ",[883,7957,7959],{"className":7958},[886],[888,7960,7961],{"xmlns":890},[892,7962,7963,7967],{},[895,7964,7965],{},[898,7966,1904],{},[902,7968,1904],{"encoding":904},". Avšak růst ",[883,7971,7973],{"className":7972},[886],[888,7974,7975],{"xmlns":890},[892,7976,7977,7981],{},[895,7978,7979],{},[898,7980,1904],{},[902,7982,1904],{"encoding":904}," je odezvou na pokles ceny ",[883,7985,7987],{"className":7986},[886],[888,7988,7989],{"xmlns":890},[892,7990,7991,7995],{},[895,7992,7993],{},[898,7994,1746],{},[902,7996,1746],{"encoding":904},". Tudíž s ",[614,7999,8000,8001],{},"poklesem ceny ",[883,8002,8004],{"className":8003},[886],[888,8005,8006],{"xmlns":890},[892,8007,8008,8012],{},[895,8009,8010],{},[898,8011,1746],{},[902,8013,1746],{"encoding":904}," celkový příjem ",[883,8016,8018],{"className":8017},[886],[888,8019,8020],{"xmlns":890},[892,8021,8022,8028],{},[895,8023,8024,8026],{},[898,8025,1754],{},[898,8027,1749],{},[902,8029,4808],{"encoding":904},[614,8031,8032],{},"roste"," a s ",[614,8035,8036,8037],{},"růstem ceny ",[883,8038,8040],{"className":8039},[886],[888,8041,8042],{"xmlns":890},[892,8043,8044,8048],{},[895,8045,8046],{},[898,8047,1746],{},[902,8049,1746],{"encoding":904},[614,8051,8052],{},"klesá",[4584,8054,8055],{},[724,8056,8057,8060],{},[38,8058,8059],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,8062,8063,7912,8083,1343,8109,8124,8125,8138,8139,8152,8153,8166,8167,8014,8180,2628,8195,1664],{},[38,8064,8065,8066,4634],{},"(b) Poptávka neelastická (",[883,8067,8069],{"className":8068},[886],[888,8070,8071],{"xmlns":890},[892,8072,8073,8081],{},[895,8074,8075,8077,8079],{},[898,8076,1846],{},[1723,8078,2287],{},[1864,8080,1866],{},[902,8082,5239],{"encoding":904},[883,8084,8086],{"className":8085},[886],[888,8087,8088],{"xmlns":890},[892,8089,8090,8106],{},[895,8091,8092,8094,8096,8098,8100,8102,8104],{},[898,8093,1728],{},[898,8095,1749],{},[1723,8097,1908],{"stretchy":1907},[898,8099,1904],{},[1723,8101,1914],{"stretchy":1907},[1723,8103,2287],{},[1864,8105,2256],{},[902,8107,8108],{"encoding":904},"MR(Q) \u003C 0",[883,8110,8112],{"className":8111},[886],[888,8113,8114],{"xmlns":890},[892,8115,8116,8122],{},[895,8117,8118,8120],{},[898,8119,1754],{},[898,8121,1749],{},[902,8123,4808],{"encoding":904}," je klesající funkce ",[883,8126,8128],{"className":8127},[886],[888,8129,8130],{"xmlns":890},[892,8131,8132,8136],{},[895,8133,8134],{},[898,8135,1904],{},[902,8137,1904],{"encoding":904},", tj. s růstem ",[883,8140,8142],{"className":8141},[886],[888,8143,8144],{"xmlns":890},[892,8145,8146,8150],{},[895,8147,8148],{},[898,8149,1904],{},[902,8151,1904],{"encoding":904}," (s poklesem ceny ",[883,8154,8156],{"className":8155},[886],[888,8157,8158],{"xmlns":890},[892,8159,8160,8164],{},[895,8161,8162],{},[898,8163,1746],{},[902,8165,1746],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,8168,8170],{"className":8169},[886],[888,8171,8172],{"xmlns":890},[892,8173,8174,8178],{},[895,8175,8176],{},[898,8177,1746],{},[902,8179,1746],{"encoding":904},[883,8181,8183],{"className":8182},[886],[888,8184,8185],{"xmlns":890},[892,8186,8187,8193],{},[895,8188,8189,8191],{},[898,8190,1754],{},[898,8192,1749],{},[902,8194,4808],{"encoding":904},[614,8196,8032],{},[4584,8198,8199],{},[724,8200,8201,8204],{},[38,8202,8203],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,8206,8207,7912,8227,8246,8247,8262,8263,8333,8334,1682,8362,8395,8396,6299,8424,8439,8440,1664],{},[38,8208,8209,8210,4634],{},"(c) Jednotková elasticita (",[883,8211,8213],{"className":8212},[886],[888,8214,8215],{"xmlns":890},[892,8216,8217,8225],{},[895,8218,8219,8221,8223],{},[898,8220,1846],{},[1723,8222,1725],{},[1864,8224,1866],{},[902,8226,1869],{"encoding":904},[883,8228,8230],{"className":8229},[886],[888,8231,8232],{"xmlns":890},[892,8233,8234,8244],{},[895,8235,8236,8238,8240,8242],{},[898,8237,1728],{},[898,8239,1749],{},[1723,8241,1725],{},[1864,8243,2256],{},[902,8245,7794],{"encoding":904}," — nutná podmínka extrému ",[883,8248,8250],{"className":8249},[886],[888,8251,8252],{"xmlns":890},[892,8253,8254,8260],{},[895,8255,8256,8258],{},[898,8257,1754],{},[898,8259,1749],{},[902,8261,4808],{"encoding":904},". Dále ",[883,8264,8266],{"className":8265},[886],[888,8267,8268],{"xmlns":890},[892,8269,8270,8330],{},[895,8271,8272,8274,8284,8286,8288,8294,8296,8302,8304,8306,8308,8310,8312,8314,8324,8326,8328],{},[898,8273,1754],{},[2057,8275,8276,8278],{},[898,8277,1749],{},[895,8279,8280,8282],{},[1723,8281,2229],{"mathvariant":2124},[1723,8283,2229],{"mathvariant":2124},[1723,8285,1725],{},[898,8287,1728],{},[2057,8289,8290,8292],{},[898,8291,1749],{},[1723,8293,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,8295,1725],{},[2057,8297,8298,8300],{},[898,8299,4897],{},[1723,8301,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,8303,1908],{"stretchy":1907},[898,8305,1904],{},[1723,8307,1914],{"stretchy":1907},[1723,8309,2087],{},[898,8311,1904],{},[3018,8313,3707],{},[2057,8315,8316,8318],{},[898,8317,4897],{},[895,8319,8320,8322],{},[1723,8321,2229],{"mathvariant":2124},[1723,8323,2229],{"mathvariant":2124},[1723,8325,1908],{"stretchy":1907},[898,8327,1904],{},[1723,8329,1914],{"stretchy":1907},[902,8331,8332],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,8335,8337],{"className":8336},[886],[888,8338,8339],{"xmlns":890},[892,8340,8341,8359],{},[895,8342,8343,8349,8351,8353,8355,8357],{},[2057,8344,8345,8347],{},[898,8346,4897],{},[1723,8348,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,8350,1908],{"stretchy":1907},[898,8352,1904],{},[1723,8354,1914],{"stretchy":1907},[1723,8356,2287],{},[1864,8358,2256],{},[902,8360,8361],{"encoding":904},"D'(Q) \u003C 0",[883,8363,8365],{"className":8364},[886],[888,8366,8367],{"xmlns":890},[892,8368,8369,8392],{},[895,8370,8371,8381,8383,8385,8387,8390],{},[2057,8372,8373,8375],{},[898,8374,4897],{},[895,8376,8377,8379],{},[1723,8378,2229],{"mathvariant":2124},[1723,8380,2229],{"mathvariant":2124},[1723,8382,1908],{"stretchy":1907},[898,8384,1904],{},[1723,8386,1914],{"stretchy":1907},[1723,8388,8389],{},"≤",[1864,8391,2256],{},[902,8393,8394],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,8397,8399],{"className":8398},[886],[888,8400,8401],{"xmlns":890},[892,8402,8403,8421],{},[895,8404,8405,8407,8417,8419],{},[898,8406,1754],{},[2057,8408,8409,8411],{},[898,8410,1749],{},[895,8412,8413,8415],{},[1723,8414,2229],{"mathvariant":2124},[1723,8416,2229],{"mathvariant":2124},[1723,8418,2287],{},[1864,8420,2256],{},[902,8422,8423],{"encoding":904},"TR'' \u003C 0",[883,8425,8427],{"className":8426},[886],[888,8428,8429],{"xmlns":890},[892,8430,8431,8437],{},[895,8432,8433,8435],{},[898,8434,1754],{},[898,8436,1749],{},[902,8438,4808],{"encoding":904}," nabývá ",[38,8441,8442],{},"maxima",[4584,8444,8445],{},[724,8446,8447,8450],{},[38,8448,8449],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,8452,8453],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,8455,8456],{},[38,8457,8458],{},"Souhrnná tabulka Pravidel 1–3:",[16,8460,8461,8565],{},[19,8462,8463],{},[22,8464,8465,8468,8483,8500,8531,8562],{},[25,8466,8467],{},"Charakter poptávky",[25,8469,8470],{},[883,8471,8473],{"className":8472},[886],[888,8474,8475],{"xmlns":890},[892,8476,8477,8481],{},[895,8478,8479],{},[898,8480,1846],{},[902,8482,1846],{"encoding":904},[25,8484,8485],{},[883,8486,8488],{"className":8487},[886],[888,8489,8490],{"xmlns":890},[892,8491,8492,8498],{},[895,8493,8494,8496],{},[898,8495,1728],{},[898,8497,1749],{},[902,8499,7344],{"encoding":904},[25,8501,8502,8503,2628,8516],{},"Pokles ceny ",[883,8504,8506],{"className":8505},[886],[888,8507,8508],{"xmlns":890},[892,8509,8510,8514],{},[895,8511,8512],{},[1723,8513,4702],{},[902,8515,7665],{"encoding":904},[883,8517,8519],{"className":8518},[886],[888,8520,8521],{"xmlns":890},[892,8522,8523,8529],{},[895,8524,8525,8527],{},[898,8526,1754],{},[898,8528,1749],{},[902,8530,4808],{"encoding":904},[25,8532,8533,8534,2628,8547],{},"Růst ceny ",[883,8535,8537],{"className":8536},[886],[888,8538,8539],{"xmlns":890},[892,8540,8541,8545],{},[895,8542,8543],{},[1723,8544,4702],{},[902,8546,7665],{"encoding":904},[883,8548,8550],{"className":8549},[886],[888,8551,8552],{"xmlns":890},[892,8553,8554,8560],{},[895,8555,8556,8558],{},[898,8557,1754],{},[898,8559,1749],{},[902,8561,4808],{"encoding":904},[25,8563,8564],{},"Doporučení",[30,8566,8567,8616,8666],{},[22,8568,8569,8571,8589,8607,8609,8611],{},[35,8570,4787],{},[35,8572,8573],{},[883,8574,8576],{"className":8575},[886],[888,8577,8578],{"xmlns":890},[892,8579,8580,8586],{},[895,8581,8582,8584],{},[1723,8583,2253],{},[1864,8585,1866],{},[902,8587,8588],{"encoding":904},"> 1",[35,8590,8591],{},[883,8592,8594],{"className":8593},[886],[888,8595,8596],{"xmlns":890},[892,8597,8598,8604],{},[895,8599,8600,8602],{},[1723,8601,2253],{},[1864,8603,2256],{},[902,8605,8606],{"encoding":904},"> 0",[35,8608,8032],{},[35,8610,8052],{},[35,8612,8613],{},[38,8614,8615],{},"snížit cenu",[22,8617,8618,8621,8639,8657,8659,8661],{},[35,8619,8620],{},"jednotková",[35,8622,8623],{},[883,8624,8626],{"className":8625},[886],[888,8627,8628],{"xmlns":890},[892,8629,8630,8636],{},[895,8631,8632,8634],{},[1723,8633,1725],{},[1864,8635,1866],{},[902,8637,8638],{"encoding":904},"= 1",[35,8640,8641],{},[883,8642,8644],{"className":8643},[886],[888,8645,8646],{"xmlns":890},[892,8647,8648,8654],{},[895,8649,8650,8652],{},[1723,8651,1725],{},[1864,8653,2256],{},[902,8655,8656],{"encoding":904},"= 0",[35,8658,4435],{},[35,8660,4435],{},[35,8662,8663],{},[38,8664,8665],{},"držet cenu",[22,8667,8668,8670,8688,8706,8708,8710],{},[35,8669,4791],{},[35,8671,8672],{},[883,8673,8675],{"className":8674},[886],[888,8676,8677],{"xmlns":890},[892,8678,8679,8685],{},[895,8680,8681,8683],{},[1723,8682,2287],{},[1864,8684,1866],{},[902,8686,8687],{"encoding":904},"\u003C 1",[35,8689,8690],{},[883,8691,8693],{"className":8692},[886],[888,8694,8695],{"xmlns":890},[892,8696,8697,8703],{},[895,8698,8699,8701],{},[1723,8700,2287],{},[1864,8702,2256],{},[902,8704,8705],{"encoding":904},"\u003C 0",[35,8707,8052],{},[35,8709,8032],{},[35,8711,8712],{},[38,8713,8714],{},"zvýšit cenu",[198,8716,8718],{"id":8717},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,8720,8721,8722,8747,8748,8770,8771,8784,8785,8798,8799,8812,8813,6299,8840,8892],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,8723,8725],{"className":8724},[886],[888,8726,8727],{"xmlns":890},[892,8728,8729,8745],{},[895,8730,8731,8733,8735,8737,8739],{},[898,8732,1746],{},[1723,8734,1725],{},[1864,8736,3810],{},[1723,8738,1759],{},[2057,8740,8741,8743],{},[898,8742,1904],{},[1864,8744,2331],{},[902,8746,6169],{"encoding":904},". Reálné cenové rozpětí je ",[883,8749,8751],{"className":8750},[886],[888,8752,8753],{"xmlns":890},[892,8754,8755,8767],{},[895,8756,8757,8759,8761,8763,8765],{},[1723,8758,6034],{"stretchy":1907},[1864,8760,1866],{},[1723,8762,2031],{"separator":2030},[1864,8764,3810],{},[1723,8766,6051],{"stretchy":1907},[902,8768,8769],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,8772,8774],{"className":8773},[886],[888,8775,8776],{"xmlns":890},[892,8777,8778,8782],{},[895,8779,8780],{},[898,8781,1904],{},[902,8783,1904],{"encoding":904}," jako funkci ",[883,8786,8788],{"className":8787},[886],[888,8789,8790],{"xmlns":890},[892,8791,8792,8796],{},[895,8793,8794],{},[898,8795,1746],{},[902,8797,1746],{"encoding":904},"; pro nezáporné ",[883,8800,8802],{"className":8801},[886],[888,8803,8804],{"xmlns":890},[892,8805,8806,8810],{},[895,8807,8808],{},[898,8809,1904],{},[902,8811,1904],{"encoding":904}," je ",[883,8814,8816],{"className":8815},[886],[888,8817,8818],{"xmlns":890},[892,8819,8820,8837],{},[895,8821,8822,8824,8826],{},[898,8823,1904],{},[1723,8825,1725],{},[8827,8828,8829],"msqrt",{},[895,8830,8831,8833,8835],{},[1864,8832,3810],{},[1723,8834,1759],{},[898,8836,1746],{},[902,8838,8839],{"encoding":904},"Q = \\sqrt{100 - P}",[883,8841,8843],{"className":8842},[886],[888,8844,8845],{"xmlns":890},[892,8846,8847,8889],{},[895,8848,8849,8865,8867,8869],{},[3055,8850,8851],{"scriptlevel":2256,"displaystyle":2030},[3058,8852,8853,8859],{},[895,8854,8855,8857],{},[898,8856,2930],{"mathvariant":2124},[898,8858,1904],{},[895,8860,8861,8863],{},[898,8862,2930],{"mathvariant":2124},[898,8864,1746],{},[1723,8866,1725],{},[1723,8868,1759],{},[3055,8870,8871],{"scriptlevel":2256,"displaystyle":2030},[3058,8872,8873,8875],{},[1864,8874,1866],{},[895,8876,8877,8879],{},[1864,8878,2331],{},[8827,8880,8881],{},[895,8882,8883,8885,8887],{},[1864,8884,3810],{},[1723,8886,1759],{},[898,8888,1746],{},[902,8890,8891],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,8894,8895],{},[883,8896,8898],{"className":8897},[886],[888,8899,8900],{"xmlns":890},[892,8901,8902,9024],{},[895,8903,8904,8906,8908,8910,8912,8914,8916,8922,8924,8938,8940,8942,8956,8958,8984,8986,9004,9006,9022],{},[898,8905,1846],{},[1723,8907,1908],{"stretchy":1907},[898,8909,1746],{},[1723,8911,1914],{"stretchy":1907},[1723,8913,1725],{},[1723,8915,1759],{},[3058,8917,8918,8920],{},[898,8919,1746],{},[898,8921,1904],{},[1723,8923,3897],{},[3058,8925,8926,8932],{},[895,8927,8928,8930],{},[898,8929,2930],{"mathvariant":2124},[898,8931,1904],{},[895,8933,8934,8936],{},[898,8935,2930],{"mathvariant":2124},[898,8937,1746],{},[1723,8939,1725],{},[1723,8941,1759],{},[3058,8943,8944,8946],{},[898,8945,1746],{},[8827,8947,8948],{},[895,8949,8950,8952,8954],{},[1864,8951,3810],{},[1723,8953,1759],{},[898,8955,1746],{},[1723,8957,3897],{},[895,8959,8960,8962,8964,8982],{},[1723,8961,1908],{"fence":2030},[1723,8963,1759],{},[3058,8965,8966,8968],{},[1864,8967,1866],{},[895,8969,8970,8972],{},[1864,8971,2331],{},[8827,8973,8974],{},[895,8975,8976,8978,8980],{},[1864,8977,3810],{},[1723,8979,1759],{},[898,8981,1746],{},[1723,8983,1914],{"fence":2030},[1723,8985,1725],{},[3058,8987,8988,8990],{},[898,8989,1746],{},[895,8991,8992,8994,8996,8998,9000,9002],{},[1864,8993,2331],{},[1723,8995,1908],{"stretchy":1907},[1864,8997,3810],{},[1723,8999,1759],{},[898,9001,1746],{},[1723,9003,1914],{"stretchy":1907},[1723,9005,1725],{},[3058,9007,9008,9014],{},[895,9009,9010,9012],{},[1864,9011,5719],{},[898,9013,1746],{},[895,9015,9016,9018,9020],{},[1864,9017,3810],{},[1723,9019,1759],{},[898,9021,1746],{},[898,9023,1664],{"mathvariant":2124},[902,9025,9026],{"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}.",[724,9028,9029,9030,3430],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,9031,9033],{"className":9032},[886],[888,9034,9035],{"xmlns":890},[892,9036,9037,9061],{},[895,9038,9039,9057,9059],{},[3055,9040,9041],{"scriptlevel":2256,"displaystyle":2030},[3058,9042,9043,9049],{},[895,9044,9045,9047],{},[1864,9046,5719],{},[898,9048,1746],{},[895,9050,9051,9053,9055],{},[1864,9052,3810],{},[1723,9054,1759],{},[898,9056,1746],{},[1723,9058,1725],{},[1864,9060,1866],{},[902,9062,9063],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,9065,9066],{},[883,9067,9069],{"className":9068},[886],[888,9070,9071],{"xmlns":890},[892,9072,9073,9105],{},[895,9074,9075,9081,9083,9090,9092,9095,9103],{},[2057,9076,9077,9079],{},[898,9078,1746],{},[1723,9080,5066],{},[1723,9082,1725],{},[3058,9084,9085,9088],{},[1864,9086,9087],{},"200",[1864,9089,2909],{},[1723,9091,6610],{},[1864,9093,9094],{},"66,",[9096,9097,9098,9100],"mover",{"accent":2030},[1864,9099,2969],{},[1723,9101,9102],{"stretchy":2030},"‾",[898,9104,1664],{"mathvariant":2124},[902,9106,9107],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,9109,9110],{},"S využitím vlastnosti (4.8):",[120,9112,9113,9159,9201],{},[123,9114,9115,9116,9151,9152,9154,9155,9158],{},"Při cenách ",[883,9117,9119],{"className":9118},[886],[888,9120,9121],{"xmlns":890},[892,9122,9123,9148],{},[895,9124,9125,9127,9129,9131,9133,9136,9138,9140,9146],{},[898,9126,1746],{},[1723,9128,7216],{},[1723,9130,6034],{"stretchy":1907},[1864,9132,1866],{},[1723,9134,9135],{"separator":2030},";",[3018,9137,3707],{},[1864,9139,9094],{},[9096,9141,9142,9144],{"accent":2030},[1864,9143,2969],{},[1723,9145,9102],{"stretchy":2030},[1723,9147,1914],{"stretchy":1907},[902,9149,9150],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,9153,4791],{}," — dle ",[614,9156,9157],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,9160,9115,9161,9151,9195,9154,9197,9200],{},[883,9162,9164],{"className":9163},[886],[888,9165,9166],{"xmlns":890},[892,9167,9168,9192],{},[895,9169,9170,9172,9174,9176,9178,9184,9186,9188,9190],{},[898,9171,1746],{},[1723,9173,7216],{},[1723,9175,1908],{"stretchy":1907},[1864,9177,9094],{},[9096,9179,9180,9182],{"accent":2030},[1864,9181,2969],{},[1723,9183,9102],{"stretchy":2030},[1723,9185,9135],{"separator":2030},[3018,9187,3707],{},[1864,9189,3810],{},[1723,9191,6051],{"stretchy":1907},[902,9193,9194],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,9196,4787],{},[614,9198,9199],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,9202,9203,9204,9207,9208,9236,9237,9240],{},"Dle ",[614,9205,9206],{},"Pravidla 3"," je při ceně ",[883,9209,9211],{"className":9210},[886],[888,9212,9213],{"xmlns":890},[892,9214,9215,9233],{},[895,9216,9217,9223,9225,9227],{},[2057,9218,9219,9221],{},[898,9220,1746],{},[1723,9222,5066],{},[1723,9224,1725],{},[1864,9226,9094],{},[9096,9228,9229,9231],{"accent":2030},[1864,9230,2969],{},[1723,9232,9102],{"stretchy":2030},[902,9234,9235],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,9238,9239],{},"maxima celkového příjmu"," ve výši",[724,9242,9243],{},[883,9244,9246],{"className":9245},[886],[888,9247,9248],{"xmlns":890},[892,9249,9250,9328],{},[895,9251,9252,9254,9256,9258,9264,9266,9268,9274,9276,9290,9292,9298,9300,9308,9310,9323,9325],{},[898,9253,1754],{},[898,9255,1749],{},[1723,9257,1908],{"stretchy":1907},[2057,9259,9260,9262],{},[898,9261,1746],{},[1723,9263,5066],{},[1723,9265,1914],{"stretchy":1907},[1723,9267,1725],{},[2057,9269,9270,9272],{},[898,9271,1746],{},[1723,9273,5066],{},[1723,9275,3897],{},[8827,9277,9278],{},[895,9279,9280,9282,9284],{},[1864,9281,3810],{},[1723,9283,1759],{},[2057,9285,9286,9288],{},[898,9287,1746],{},[1723,9289,5066],{},[1723,9291,1725],{},[3058,9293,9294,9296],{},[1864,9295,9087],{},[1864,9297,2909],{},[1723,9299,3897],{},[8827,9301,9302],{},[3058,9303,9304,9306],{},[1864,9305,3810],{},[1864,9307,2909],{},[1723,9309,1725],{},[3058,9311,9312,9315],{},[1864,9313,9314],{},"2000",[895,9316,9317,9319],{},[1864,9318,2909],{},[8827,9320,9321],{},[1864,9322,2909],{},[1723,9324,6610],{},[1864,9326,9327],{},"384,9.",[902,9329,9330],{"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.",[724,9332,9333,9334,1664],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,9335,9337],{"className":9336},[886],[888,9338,9339],{"xmlns":890},[892,9340,9341,9347],{},[895,9342,9343,9345],{},[898,9344,1754],{},[898,9346,1749],{},[902,9348,4808],{"encoding":904},[115,9350,9352],{"id":9351},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,9354,9355,9356,9359],{},"Analogicky se definuje ",[38,9357,9358],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,9361,9362],{},[883,9363,9365],{"className":9364,"title":4914,"style":4915},[4913],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,9367,5022,9368,9392,9393,9425],{},[883,9369,9371],{"className":9370},[886],[888,9372,9373],{"xmlns":890},[892,9374,9375,9389],{},[895,9376,9377,9379,9381,9383,9385,9387],{},[898,9378,1904],{},[1723,9380,1725],{},[898,9382,2111],{},[1723,9384,1908],{"stretchy":1907},[898,9386,1746],{},[1723,9388,1914],{"stretchy":1907},[902,9390,9391],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,9394,9396],{"className":9395},[886],[888,9397,9398],{"xmlns":890},[892,9399,9400,9422],{},[895,9401,9402,9418,9420],{},[3055,9403,9404],{"scriptlevel":2256,"displaystyle":2030},[3058,9405,9406,9412],{},[895,9407,9408,9410],{},[898,9409,2930],{"mathvariant":2124},[898,9411,1904],{},[895,9413,9414,9416],{},[898,9415,2930],{"mathvariant":2124},[898,9417,1746],{},[1723,9419,2253],{},[1864,9421,2256],{},[902,9423,9424],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,9427,9428],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[4584,9430,9431],{},[724,9432,9433,9434],{},"S rostoucí cenou elasticita nabídky roste. ",[883,9435,9437],{"className":9436},[886],[888,9438,9439],{"xmlns":890},[892,9440,9441,9450],{},[895,9442,9443,9445,9448],{},[1723,9444,1908],{"stretchy":1907},[1864,9446,9447],{},"4.14",[1723,9449,1914],{"stretchy":1907},[902,9451,9452],{"encoding":904},"(4.14)",[724,9454,9455],{},"Pro nominální změny platí",[724,9457,9458],{},[883,9459,9461],{"className":9460,"title":4914,"style":4915},[4913],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,9463,9464],{},"a pro procentní změny",[724,9466,9467],{},[883,9468,9470],{"className":9469,"title":4914,"style":4915},[4913],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,9472,9473],{},"(bez znaménka minus).",[198,9475,9477],{"id":9476},"příklad-47","Příklad 4.7",[724,9479,9480,9481,3430],{},"Nabídka ",[883,9482,9484],{"className":9483},[886],[888,9485,9486],{"xmlns":890},[892,9487,9488,9513],{},[895,9489,9490,9492,9494,9496,9502,9504,9506,9508,9510],{},[898,9491,1904],{},[1723,9493,1725],{},[1864,9495,3517],{},[2057,9497,9498,9500],{},[898,9499,1746],{},[1864,9501,2331],{},[1723,9503,2087],{},[1864,9505,2962],{},[898,9507,1746],{},[1723,9509,2087],{},[1864,9511,9512],{},"150",[902,9514,9515],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,9517,9518],{},[883,9519,9521],{"className":9520},[886],[888,9522,9523],{"xmlns":890},[892,9524,9525,9571],{},[895,9526,9527,9529,9531,9555,9557,9559,9561,9563,9565,9567,9569],{},[898,9528,1846],{},[1723,9530,1725],{},[3058,9532,9533,9535],{},[898,9534,1746],{},[895,9536,9537,9539,9545,9547,9549,9551,9553],{},[1864,9538,3517],{},[2057,9540,9541,9543],{},[898,9542,1746],{},[1864,9544,2331],{},[1723,9546,2087],{},[1864,9548,2962],{},[898,9550,1746],{},[1723,9552,2087],{},[1864,9554,9512],{},[3018,9556,3707],{},[1723,9558,1908],{"stretchy":1907},[1864,9560,3561],{},[898,9562,1746],{},[1723,9564,2087],{},[1864,9566,2962],{},[1723,9568,1914],{"stretchy":1907},[898,9570,1664],{"mathvariant":2124},[902,9572,9573],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,9575,5827,9576,1343,9606,1343,9633,9669,9670,9695,9696,9714,9715,1664],{},[883,9577,9579],{"className":9578},[886],[888,9580,9581],{"xmlns":890},[892,9582,9583,9603],{},[895,9584,9585,9587,9589,9591,9593,9595],{},[898,9586,1846],{},[1723,9588,1908],{"stretchy":1907},[1864,9590,3585],{},[1723,9592,1914],{"stretchy":1907},[1723,9594,1725],{},[3055,9596,9597],{"scriptlevel":2256,"displaystyle":1907},[3058,9598,9599,9601],{},[1864,9600,1866],{},[1864,9602,2909],{},[902,9604,9605],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,9607,9609],{"className":9608},[886],[888,9610,9611],{"xmlns":890},[892,9612,9613,9630],{},[895,9614,9615,9617,9619,9624,9626,9628],{},[898,9616,1846],{},[1723,9618,1908],{"stretchy":1907},[8827,9620,9621],{},[1864,9622,9623],{},"1500",[1723,9625,1914],{"stretchy":1907},[1723,9627,1725],{},[1864,9629,1866],{},[902,9631,9632],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,9634,9636],{"className":9635},[886],[888,9637,9638],{"xmlns":890},[892,9639,9640,9666],{},[895,9641,9642,9644,9646,9648,9650,9652,9661,9663],{},[898,9643,1846],{},[1723,9645,1908],{"stretchy":1907},[1864,9647,3810],{},[1723,9649,1914],{"stretchy":1907},[1723,9651,1725],{},[3055,9653,9654],{"scriptlevel":2256,"displaystyle":1907},[3058,9655,9656,9658],{},[1864,9657,3840],{},[1864,9659,9660],{},"33",[1723,9662,6610],{},[1864,9664,9665],{},"1,515",[902,9667,9668],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,9671,9673],{"className":9672},[886],[888,9674,9675],{"xmlns":890},[892,9676,9677,9692],{},[895,9678,9679,9681,9683,9687,9689],{},[898,9680,1746],{},[1723,9682,2253],{},[8827,9684,9685],{},[1864,9686,9623],{},[1723,9688,3456],{},[1864,9690,9691],{},"38,7",[902,9693,9694],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,9697,9699],{"className":9698},[886],[888,9700,9701],{"xmlns":890},[892,9702,9703,9711],{},[895,9704,9705,9707,9709],{},[898,9706,1746],{},[1723,9708,2287],{},[1864,9710,9691],{},[902,9712,9713],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,9716,9718],{"className":9717},[886],[888,9719,9720],{"xmlns":890},[892,9721,9722,9760],{},[895,9723,9724,9726,9728,9730,9732,9740,9742,9745,9747,9750,9756,9758],{},[898,9725,3611],{"mathvariant":2124},[898,9727,1904],{},[898,9729,6635],{"mathvariant":2124},[1723,9731,3456],{},[3055,9733,9734],{"scriptlevel":2256,"displaystyle":1907},[3058,9735,9736,9738],{},[1864,9737,1866],{},[1864,9739,2909],{},[1723,9741,3897],{},[1864,9743,9744],{},"20",[1723,9746,1725],{},[1864,9748,9749],{},"6,",[9096,9751,9752,9754],{"accent":2030},[1864,9753,2969],{},[1723,9755,9102],{"stretchy":2030},[3018,9757,3707],{},[898,9759,6635],{"mathvariant":2124},[902,9761,9762],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,9764,9766],{"id":9765},"vícefaktorový-model","Vícefaktorový model",[724,9768,9769,9770,9783,9784,2628,9787,9800,9801,2628,9804,9822,9823,2628,9826,3430],{},"Předpokládejme, že poptávané množství ",[883,9771,9773],{"className":9772},[886],[888,9774,9775],{"xmlns":890},[892,9776,9777,9781],{},[895,9778,9779],{},[898,9780,1904],{},[902,9782,1904],{"encoding":904}," závisí na ",[38,9785,9786],{},"ceně základního zboží",[883,9788,9790],{"className":9789},[886],[888,9791,9792],{"xmlns":890},[892,9793,9794,9798],{},[895,9795,9796],{},[898,9797,1746],{},[902,9799,1746],{"encoding":904},", na ",[38,9802,9803],{},"ceně alternativního zboží",[883,9805,9807],{"className":9806},[886],[888,9808,9809],{"xmlns":890},[892,9810,9811,9819],{},[895,9812,9813],{},[1931,9814,9815,9817],{},[898,9816,1746],{},[898,9818,1718],{},[902,9820,9821],{"encoding":904},"P_A"," a na ",[38,9824,9825],{},"důchodu",[883,9827,9829],{"className":9828},[886],[888,9830,9831],{"xmlns":890},[892,9832,9833,9838],{},[895,9834,9835],{},[898,9836,9837],{},"Y",[902,9839,9837],{"encoding":904},[724,9841,9842],{},[883,9843,9845],{"className":9844,"title":4914,"style":4915},[4913],"Q = D(P, P_A, Y). \\tag{4.17}",[724,9847,9848,9849,9852],{},"V analogii jednofaktorového modelu pracujeme s ",[38,9850,9851],{},"parciálními derivacemi"," funkce poptávky.",[198,9854,9856],{"id":9855},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,9858,9859],{},[883,9860,9862],{"className":9861,"title":4914,"style":4915},[4913],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,9864,5022,9865,9885,9886,9899,9900,2137,9922,2628,9925,9971,9972,9985,9986,10003],{},[883,9866,9868],{"className":9867},[886],[888,9869,9870],{"xmlns":890},[892,9871,9872,9882],{},[895,9873,9874],{},[2220,9875,9876,9878,9880],{},[898,9877,1904],{},[898,9879,1746],{},[1723,9881,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,9883,9884],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,9887,9889],{"className":9888},[886],[888,9890,9891],{"xmlns":890},[892,9892,9893,9897],{},[895,9894,9895],{},[898,9896,1746],{},[902,9898,1746],{"encoding":904},". Vždy ",[883,9901,9903],{"className":9902},[886],[888,9904,9905],{"xmlns":890},[892,9906,9907,9919],{},[895,9908,9909,9915,9917],{},[1931,9910,9911,9913],{},[898,9912,1846],{},[898,9914,1746],{},[1723,9916,5197],{},[1864,9918,2256],{},[902,9920,9921],{"encoding":904},"E_P \\ge 0",[614,9923,9924],{},"Interpretace:",[883,9926,9928],{"className":9927},[886],[888,9929,9930],{"xmlns":890},[892,9931,9932,9968],{},[895,9933,9934,9940,9942,9948,9950,9958,9960,9966],{},[1931,9935,9936,9938],{},[898,9937,1846],{},[898,9939,1746],{},[1723,9941,1908],{"stretchy":1907},[2057,9943,9944,9946],{},[898,9945,1746],{},[1723,9947,5066],{},[1723,9949,2031],{"separator":2030},[2220,9951,9952,9954,9956],{},[898,9953,1746],{},[898,9955,1718],{},[1723,9957,5066],{},[1723,9959,2031],{"separator":2030},[2057,9961,9962,9964],{},[898,9963,9837],{},[1723,9965,5066],{},[1723,9967,1914],{"stretchy":1907},[902,9969,9970],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,9973,9975],{"className":9974},[886],[888,9976,9977],{"xmlns":890},[892,9978,9979,9983],{},[895,9980,9981],{},[898,9982,1904],{},[902,9984,1904],{"encoding":904}," při 1% změně ",[883,9987,9989],{"className":9988},[886],[888,9990,9991],{"xmlns":890},[892,9992,9993,10001],{},[895,9994,9995],{},[2057,9996,9997,9999],{},[898,9998,1746],{},[1723,10000,5066],{},[902,10002,5116],{"encoding":904},", ceteris paribus.",[198,10005,10007],{"id":10006},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,10009,10010],{},[883,10011,10013],{"className":10012,"title":4914,"style":4915},[4913],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,10015,10016,9971,10018,10031,10032,10049],{},[614,10017,9924],{},[883,10019,10021],{"className":10020},[886],[888,10022,10023],{"xmlns":890},[892,10024,10025,10029],{},[895,10026,10027],{},[898,10028,1904],{},[902,10030,1904],{"encoding":904}," základního zboží při 1% změně ceny ",[883,10033,10035],{"className":10034},[886],[888,10036,10037],{"xmlns":890},[892,10038,10039,10047],{},[895,10040,10041],{},[1931,10042,10043,10045],{},[898,10044,1746],{},[898,10046,1718],{},[902,10048,9821],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,10051,10052],{},[38,10053,10054],{},"Znaménko závisí na povaze alternativního zboží:",[120,10056,10057,10145],{},[123,10058,10059,10060,10063,10064,10081,10082,2628,10095,1664],{},"Je-li alternativní zboží ",[38,10061,10062],{},"komplement",", růst ",[883,10065,10067],{"className":10066},[886],[888,10068,10069],{"xmlns":890},[892,10070,10071,10079],{},[895,10072,10073],{},[1931,10074,10075,10077],{},[898,10076,1746],{},[898,10078,1718],{},[902,10080,9821],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,10083,10085],{"className":10084},[886],[888,10086,10087],{"xmlns":890},[892,10088,10089,10093],{},[895,10090,10091],{},[898,10092,1904],{},[902,10094,1904],{"encoding":904},[883,10096,10098],{"className":10097},[886],[888,10099,10100],{"xmlns":890},[892,10101,10102,10142],{},[895,10103,10104,10106,10108,10120,10122,10124,10126,10128,10138,10140],{},[1723,10105,4702],{},[3018,10107,4699],{},[2220,10109,10110,10112,10118],{},[898,10111,1904],{},[1931,10113,10114,10116],{},[898,10115,1746],{},[898,10117,1718],{},[1723,10119,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,10121,2287],{},[1864,10123,2256],{},[1723,10125,2031],{"separator":2030},[3018,10127,4699],{},[1931,10129,10130,10132],{},[898,10131,1846],{},[1931,10133,10134,10136],{},[898,10135,1746],{},[898,10137,1718],{},[1723,10139,2287],{},[1864,10141,2256],{},[902,10143,10144],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,10146,10059,10147,10063,10150,10167,10168,10181,10182,1664],{},[38,10148,10149],{},"substitut",[883,10151,10153],{"className":10152},[886],[888,10154,10155],{"xmlns":890},[892,10156,10157,10165],{},[895,10158,10159],{},[1931,10160,10161,10163],{},[898,10162,1746],{},[898,10164,1718],{},[902,10166,9821],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,10169,10171],{"className":10170},[886],[888,10172,10173],{"xmlns":890},[892,10174,10175,10179],{},[895,10176,10177],{},[898,10178,1904],{},[902,10180,1904],{"encoding":904}," roste ",[883,10183,10185],{"className":10184},[886],[888,10186,10187],{"xmlns":890},[892,10188,10189,10229],{},[895,10190,10191,10193,10195,10207,10209,10211,10213,10215,10225,10227],{},[1723,10192,4702],{},[3018,10194,4699],{},[2220,10196,10197,10199,10205],{},[898,10198,1904],{},[1931,10200,10201,10203],{},[898,10202,1746],{},[898,10204,1718],{},[1723,10206,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,10208,2253],{},[1864,10210,2256],{},[1723,10212,2031],{"separator":2030},[3018,10214,4699],{},[1931,10216,10217,10219],{},[898,10218,1846],{},[1931,10220,10221,10223],{},[898,10222,1746],{},[898,10224,1718],{},[1723,10226,2253],{},[1864,10228,2256],{},[902,10230,10231],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,10233,10236],{"className":10234,"title":10235,"style":4915},[4913],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":10238},[10239,10243,10244,10252,10253,10257,10260],{"id":4607,"depth":642,"text":4608,"children":10240},[10241,10242],{"id":4637,"depth":649,"text":4638},{"id":4816,"depth":649,"text":4817},{"id":4851,"depth":642,"text":4852},{"id":4877,"depth":642,"text":4878,"children":10245},[10246,10247,10248,10249,10251],{"id":5569,"depth":649,"text":5570},{"id":5659,"depth":649,"text":5660},{"id":5995,"depth":649,"text":5996},{"id":6077,"depth":649,"text":10250},"Výpočet, je-li dáno PP jako funkce QQ",{"id":6338,"depth":649,"text":6339},{"id":6663,"depth":642,"text":6664},{"id":7259,"depth":642,"text":7260,"children":10254},[10255,10256],{"id":7888,"depth":649,"text":7889},{"id":8717,"depth":649,"text":8718},{"id":9351,"depth":642,"text":9352,"children":10258},[10259],{"id":9476,"depth":649,"text":9477},{"id":9765,"depth":642,"text":9766,"children":10261},[10262,10263],{"id":9855,"depth":649,"text":9856},{"id":10006,"depth":649,"text":10007},{},"\u002Ftopics\u002Felasticita",{"title":4577,"description":641},[1138,1136],"topics\u002Felasticita",[1128,1882,10270,10271,10272,10273],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":10276,"title":10277,"body":10278,"course":1128,"courses":659,"created":1129,"description":11813,"extension":661,"meta":11814,"navigation":664,"path":11815,"seo":11816,"sources":11817,"stem":11818,"tags":11819,"type":4573,"updated":677,"__hash__":11824},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":10279,"toc":11798},[10280,10283,10356,10363,10367,10431,10516,10520,10547,10614,10669,10673,10700,10791,10793,10825,10996,11000,11070,11118,11122,11183,11289,11304,11308,11310,11338,11403,11405,11412,11500,11525,11723,11727,11763,11765],[12,10281,10277],{"id":10282},"kalkul-funkcí-více-proměnných",[724,10284,10285,10286,10289,10290,1343,10319,1664],{},"Většina ekonomických veličin závisí na ",[38,10287,10288],{},"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 ",[883,10291,10293],{"className":10292},[886],[888,10294,10295],{"xmlns":890},[892,10296,10297,10316],{},[895,10298,10299,10302,10304,10306,10308,10310,10312,10314],{},[898,10300,10301],{},"z",[1723,10303,1725],{},[898,10305,2745],{},[1723,10307,1908],{"stretchy":1907},[898,10309,2750],{},[1723,10311,2031],{"separator":2030},[898,10313,2740],{},[1723,10315,1914],{"stretchy":1907},[902,10317,10318],{"encoding":904},"z = f(x, y)",[883,10320,10322],{"className":10321},[886],[888,10323,10324],{"xmlns":890},[892,10325,10326,10353],{},[895,10327,10328,10331,10333,10335,10337,10339,10341,10343,10345,10347,10349,10351],{},[898,10329,10330],{},"w",[1723,10332,1725],{},[898,10334,2745],{},[1723,10336,1908],{"stretchy":1907},[898,10338,2750],{},[1723,10340,2031],{"separator":2030},[898,10342,2740],{},[1723,10344,2031],{"separator":2030},[898,10346,10301],{},[1723,10348,1914],{"stretchy":1907},[1723,10350,2031],{"separator":2030},[1723,10352,2183],{},[902,10354,10355],{"encoding":904},"w = f(x, y, z), \\ldots",[724,10357,10358],{},[3285,10359],{"alt":10360,"className":10361,"src":10362},"imek-funkce-2d-vrstevnice",[210,3289],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,10364,10366],{"id":10365},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,10368,10369,10370,10397,10398,10426,10427,10430],{},"Pro ",[883,10371,10373],{"className":10372},[886],[888,10374,10375],{"xmlns":890},[892,10376,10377,10395],{},[895,10378,10379,10381,10383,10385,10387,10389,10391,10393],{},[898,10380,10301],{},[1723,10382,1725],{},[898,10384,2745],{},[1723,10386,1908],{"stretchy":1907},[898,10388,2750],{},[1723,10390,2031],{"separator":2030},[898,10392,2740],{},[1723,10394,1914],{"stretchy":1907},[902,10396,10318],{"encoding":904}," se křivkou s předpisem ",[883,10399,10401],{"className":10400},[886],[888,10402,10403],{"xmlns":890},[892,10404,10405,10423],{},[895,10406,10407,10409,10411,10413,10415,10417,10419,10421],{},[898,10408,2745],{},[1723,10410,1908],{"stretchy":1907},[898,10412,2750],{},[1723,10414,2031],{"separator":2030},[898,10416,2740],{},[1723,10418,1914],{"stretchy":1907},[1723,10420,1725],{},[898,10422,2878],{},[902,10424,10425],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,10428,10429],{},"vrstevnice"," funkce. V ekonomii:",[120,10432,10433,10479],{},[123,10434,10435,10438,10439,10475,10476,1664],{},[38,10436,10437],{},"Indiferenční křivky"," užitečnosti ",[883,10440,10442],{"className":10441},[886],[888,10443,10444],{"xmlns":890},[892,10445,10446,10472],{},[895,10447,10448,10450,10452,10458,10460,10466,10468,10470],{},[898,10449,900],{},[1723,10451,1908],{"stretchy":1907},[1931,10453,10454,10456],{},[898,10455,1904],{},[1864,10457,1866],{},[1723,10459,2031],{"separator":2030},[1931,10461,10462,10464],{},[898,10463,1904],{},[1864,10465,2331],{},[1723,10467,1914],{"stretchy":1907},[1723,10469,1725],{},[898,10471,2878],{},[902,10473,10474],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,10477,2361],{"className":10478,"dataFsResolvedFilePath":878,"href":879},[210],[123,10480,10481,10484,10485,10475,10513,1664],{},[38,10482,10483],{},"Izokvanty"," produkce ",[883,10486,10488],{"className":10487},[886],[888,10489,10490],{"xmlns":890},[892,10491,10492,10510],{},[895,10493,10494,10496,10498,10500,10502,10504,10506,10508],{},[898,10495,1904],{},[1723,10497,1908],{"stretchy":1907},[898,10499,1911],{},[1723,10501,2031],{"separator":2030},[898,10503,2034],{},[1723,10505,1914],{"stretchy":1907},[1723,10507,1725],{},[898,10509,2878],{},[902,10511,10512],{"encoding":904},"Q(L, K) = c",[207,10514,2149],{"className":10515,"dataFsResolvedFilePath":857,"href":858},[210],[115,10517,10519],{"id":10518},"parciální-derivace","Parciální derivace",[724,10521,10369,10522,10546],{},[883,10523,10525],{"className":10524},[886],[888,10526,10527],{"xmlns":890},[892,10528,10529,10543],{},[895,10530,10531,10533,10535,10537,10539,10541],{},[898,10532,2745],{},[1723,10534,1908],{"stretchy":1907},[898,10536,2750],{},[1723,10538,2031],{"separator":2030},[898,10540,2740],{},[1723,10542,1914],{"stretchy":1907},[902,10544,10545],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,10548,10549],{},[883,10550,10552],{"className":10551},[886],[888,10553,10554],{"xmlns":890},[892,10555,10556,10611],{},[895,10557,10558,10566,10568,10583,10585,10587,10595,10597],{},[2220,10559,10560,10562,10564],{},[898,10561,2745],{},[898,10563,2750],{},[1723,10565,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,10567,1725],{},[3058,10569,10570,10577],{},[895,10571,10572,10575],{},[898,10573,10574],{"mathvariant":2124},"∂",[898,10576,2745],{},[895,10578,10579,10581],{},[898,10580,10574],{"mathvariant":2124},[898,10582,2750],{},[1723,10584,2031],{"separator":2030},[6588,10586],{"width":6590},[2220,10588,10589,10591,10593],{},[898,10590,2745],{},[898,10592,2740],{},[1723,10594,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,10596,1725],{},[3058,10598,10599,10605],{},[895,10600,10601,10603],{},[898,10602,10574],{"mathvariant":2124},[898,10604,2745],{},[895,10606,10607,10609],{},[898,10608,10574],{"mathvariant":2124},[898,10610,2740],{},[902,10612,10613],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,10615,10616,10617,1664],{},"Hodnoty v bodě: ",[883,10618,10620],{"className":10619},[886],[888,10621,10622],{"xmlns":890},[892,10623,10624,10666],{},[895,10625,10626,10634,10636,10638,10640,10642,10644,10646,10648,10656,10658,10660,10662,10664],{},[2220,10627,10628,10630,10632],{},[898,10629,2745],{},[898,10631,2750],{},[1723,10633,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,10635,1908],{"stretchy":1907},[898,10637,207],{},[1723,10639,2031],{"separator":2030},[898,10641,2069],{},[1723,10643,1914],{"stretchy":1907},[1723,10645,2031],{"separator":2030},[3018,10647,3020],{},[2220,10649,10650,10652,10654],{},[898,10651,2745],{},[898,10653,2740],{},[1723,10655,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,10657,1908],{"stretchy":1907},[898,10659,207],{},[1723,10661,2031],{"separator":2030},[898,10663,2069],{},[1723,10665,1914],{"stretchy":1907},[902,10667,10668],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,10670,10672],{"id":10671},"ekonomické-značení","Ekonomické značení",[724,10674,10675,10676,3430],{},"Pro produkční funkci ",[883,10677,10679],{"className":10678},[886],[888,10680,10681],{"xmlns":890},[892,10682,10683,10697],{},[895,10684,10685,10687,10689,10691,10693,10695],{},[898,10686,1904],{},[1723,10688,1908],{"stretchy":1907},[898,10690,1911],{},[1723,10692,2031],{"separator":2030},[898,10694,2034],{},[1723,10696,1914],{"stretchy":1907},[902,10698,10699],{"encoding":904},"Q(L, K)",[120,10701,10702,10746],{},[123,10703,10704,3196,10724,1981,10727,1914],{},[883,10705,10707],{"className":10706},[886],[888,10708,10709],{"xmlns":890},[892,10710,10711,10721],{},[895,10712,10713],{},[2220,10714,10715,10717,10719],{},[898,10716,1904],{},[898,10718,1911],{},[1723,10720,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,10722,10723],{"encoding":904},"Q'_L",[38,10725,10726],{},"mezní produkt práce",[883,10728,10730],{"className":10729},[886],[888,10731,10732],{"xmlns":890},[892,10733,10734,10744],{},[895,10735,10736,10738],{},[898,10737,1728],{},[1931,10739,10740,10742],{},[898,10741,1746],{},[898,10743,1911],{},[902,10745,1939],{"encoding":904},[123,10747,10748,3196,10768,1981,10771,1914],{},[883,10749,10751],{"className":10750},[886],[888,10752,10753],{"xmlns":890},[892,10754,10755,10765],{},[895,10756,10757],{},[2220,10758,10759,10761,10763],{},[898,10760,1904],{},[898,10762,2034],{},[1723,10764,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,10766,10767],{"encoding":904},"Q'_K",[38,10769,10770],{},"mezní produkt kapitálu",[883,10772,10774],{"className":10773},[886],[888,10775,10776],{"xmlns":890},[892,10777,10778,10788],{},[895,10779,10780,10782],{},[898,10781,1728],{},[1931,10783,10784,10786],{},[898,10785,1746],{},[898,10787,2034],{},[902,10789,10790],{"encoding":904},"MP_K",[198,10792,3294],{"id":3293},[724,10794,10795,3430],{},[883,10796,10798],{"className":10797},[886],[888,10799,10800],{"xmlns":890},[892,10801,10802,10822],{},[895,10803,10804,10812,10814,10816,10818,10820],{},[2220,10805,10806,10808,10810],{},[898,10807,2745],{},[898,10809,2750],{},[1723,10811,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,10813,1908],{"stretchy":1907},[898,10815,207],{},[1723,10817,2031],{"separator":2030},[898,10819,2069],{},[1723,10821,1914],{"stretchy":1907},[902,10823,10824],{"encoding":904},"f'_x(a, b)",[120,10826,10827,10885],{},[123,10828,10829,10830,10843,10844,10857,10858,10884],{},"rychlost změny ",[883,10831,10833],{"className":10832},[886],[888,10834,10835],{"xmlns":890},[892,10836,10837,10841],{},[895,10838,10839],{},[898,10840,2745],{},[902,10842,2745],{"encoding":904}," vůči ",[883,10845,10847],{"className":10846},[886],[888,10848,10849],{"xmlns":890},[892,10850,10851,10855],{},[895,10852,10853],{},[898,10854,2750],{},[902,10856,2750],{"encoding":904}," při ",[883,10859,10861],{"className":10860},[886],[888,10862,10863],{"xmlns":890},[892,10864,10865,10881],{},[895,10866,10867,10869,10871,10873,10875,10877,10879],{},[898,10868,2750],{},[1723,10870,1725],{},[898,10872,207],{},[1723,10874,2031],{"separator":2030},[898,10876,2740],{},[1723,10878,1725],{},[898,10880,2069],{},[902,10882,10883],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,10886,10887,10888,3383,10901,10914,10915,10933,10934,1664],{},"přibližná změna ",[883,10889,10891],{"className":10890},[886],[888,10892,10893],{"xmlns":890},[892,10894,10895,10899],{},[895,10896,10897],{},[898,10898,2745],{},[902,10900,2745],{"encoding":904},[883,10902,10904],{"className":10903},[886],[888,10905,10906],{"xmlns":890},[892,10907,10908,10912],{},[895,10909,10910],{},[898,10911,2750],{},[902,10913,2750],{"encoding":904}," o 1 (a pevném ",[883,10916,10918],{"className":10917},[886],[888,10919,10920],{"xmlns":890},[892,10921,10922,10930],{},[895,10923,10924,10926,10928],{},[898,10925,2740],{},[1723,10927,1725],{},[898,10929,2069],{},[902,10931,10932],{"encoding":904},"y = b","): ",[883,10935,10937],{"className":10936},[886],[888,10938,10939],{"xmlns":890},[892,10940,10941,10993],{},[895,10942,10943,10945,10947,10949,10951,10953,10955,10957,10959,10961,10963,10965,10967,10969,10971,10973,10975,10983,10985,10987,10989,10991],{},[898,10944,2745],{},[1723,10946,1908],{"stretchy":1907},[898,10948,207],{},[1723,10950,2087],{},[1864,10952,1866],{},[1723,10954,2031],{"separator":2030},[898,10956,2069],{},[1723,10958,1914],{"stretchy":1907},[1723,10960,3456],{},[898,10962,2745],{},[1723,10964,1908],{"stretchy":1907},[898,10966,207],{},[1723,10968,2031],{"separator":2030},[898,10970,2069],{},[1723,10972,1914],{"stretchy":1907},[1723,10974,2087],{},[2220,10976,10977,10979,10981],{},[898,10978,2745],{},[898,10980,2750],{},[1723,10982,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,10984,1908],{"stretchy":1907},[898,10986,207],{},[1723,10988,2031],{"separator":2030},[898,10990,2069],{},[1723,10992,1914],{"stretchy":1907},[902,10994,10995],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,10997,10999],{"id":10998},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,11001,11002],{},[883,11003,11005],{"className":11004},[886],[888,11006,11007],{"xmlns":890},[892,11008,11009,11067],{},[895,11010,11011,11013,11015,11017,11025,11027,11029,11031,11033,11035,11037,11039,11041,11043,11051,11053,11055,11057,11059,11061,11063,11065],{},[898,11012,2930],{},[898,11014,2745],{},[1723,11016,1725],{},[2220,11018,11019,11021,11023],{},[898,11020,2745],{},[898,11022,2750],{},[1723,11024,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,11026,1908],{"stretchy":1907},[898,11028,2750],{},[1723,11030,2031],{"separator":2030},[898,11032,2740],{},[1723,11034,1914],{"stretchy":1907},[3018,11036,3707],{},[898,11038,2930],{},[898,11040,2750],{},[1723,11042,2087],{},[2220,11044,11045,11047,11049],{},[898,11046,2745],{},[898,11048,2740],{},[1723,11050,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,11052,1908],{"stretchy":1907},[898,11054,2750],{},[1723,11056,2031],{"separator":2030},[898,11058,2740],{},[1723,11060,1914],{"stretchy":1907},[3018,11062,3707],{},[898,11064,2930],{},[898,11066,2740],{},[902,11068,11069],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,11071,3717,11072,11094,11095,11117],{},[883,11073,11075],{"className":11074},[886],[888,11076,11077],{"xmlns":890},[892,11078,11079,11091],{},[895,11080,11081,11083,11085,11087,11089],{},[898,11082,2930],{},[898,11084,2750],{},[1723,11086,2031],{"separator":2030},[898,11088,2930],{},[898,11090,2740],{},[902,11092,11093],{"encoding":904},"dx, dy"," platí ",[883,11096,11098],{"className":11097},[886],[888,11099,11100],{"xmlns":890},[892,11101,11102,11114],{},[895,11103,11104,11106,11108,11110,11112],{},[898,11105,3611],{"mathvariant":2124},[898,11107,2745],{},[1723,11109,3456],{},[898,11111,2930],{},[898,11113,2745],{},[902,11115,11116],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,11119,11121],{"id":11120},"implicitní-funkce","Implicitní funkce",[724,11123,11124,11125,11154,11155,11168,11169,11182],{},"Je-li vztah dán rovnicí ",[883,11126,11128],{"className":11127},[886],[888,11129,11130],{"xmlns":890},[892,11131,11132,11151],{},[895,11133,11134,11137,11139,11141,11143,11145,11147,11149],{},[898,11135,11136],{},"F",[1723,11138,1908],{"stretchy":1907},[898,11140,2750],{},[1723,11142,2031],{"separator":2030},[898,11144,2740],{},[1723,11146,1914],{"stretchy":1907},[1723,11148,1725],{},[1864,11150,2256],{},[902,11152,11153],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,11156,11158],{"className":11157},[886],[888,11159,11160],{"xmlns":890},[892,11161,11162,11166],{},[895,11163,11164],{},[898,11165,2740],{},[902,11167,2740],{"encoding":904}," podle ",[883,11170,11172],{"className":11171},[886],[888,11173,11174],{"xmlns":890},[892,11175,11176,11180],{},[895,11177,11178],{},[898,11179,2750],{},[902,11181,2750],{"encoding":904}," (nebo naopak):",[724,11184,11185],{},[883,11186,11188],{"className":11187},[886],[888,11189,11190],{"xmlns":890},[892,11191,11192,11286],{},[895,11193,11194,11200,11202,11216,11218,11220,11238,11240,11242,11248,11250,11264,11266,11268],{},[2057,11195,11196,11198],{},[898,11197,2740],{},[1723,11199,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,11201,1725],{},[3058,11203,11204,11210],{},[895,11205,11206,11208],{},[898,11207,2930],{},[898,11209,2740],{},[895,11211,11212,11214],{},[898,11213,2930],{},[898,11215,2750],{},[1723,11217,1725],{},[1723,11219,1759],{},[3058,11221,11222,11230],{},[2220,11223,11224,11226,11228],{},[898,11225,11136],{},[898,11227,2750],{},[1723,11229,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[2220,11231,11232,11234,11236],{},[898,11233,11136],{},[898,11235,2740],{},[1723,11237,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,11239,2031],{"separator":2030},[6588,11241],{"width":6590},[2057,11243,11244,11246],{},[898,11245,2750],{},[1723,11247,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,11249,1725],{},[3058,11251,11252,11258],{},[895,11253,11254,11256],{},[898,11255,2930],{},[898,11257,2750],{},[895,11259,11260,11262],{},[898,11261,2930],{},[898,11263,2740],{},[1723,11265,1725],{},[1723,11267,1759],{},[3058,11269,11270,11278],{},[2220,11271,11272,11274,11276],{},[898,11273,11136],{},[898,11275,2740],{},[1723,11277,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[2220,11279,11280,11282,11284],{},[898,11281,11136],{},[898,11283,2750],{},[1723,11285,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,11287,11288],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,11290,11291,11292,11295,11296,1682,11300,1664],{},"Tato vzorec dává ",[38,11293,11294],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,11297,11299],{"className":11298,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,11301,11303],{"className":11302,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,11305,11307],{"id":11306},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,11309,3972],{"id":3971},[724,11311,11312,11313,11337],{},"V bodě extrému ",[883,11314,11316],{"className":11315},[886],[888,11317,11318],{"xmlns":890},[892,11319,11320,11334],{},[895,11321,11322,11324,11326,11328,11330,11332],{},[898,11323,1718],{},[1723,11325,3212],{"stretchy":1907},[898,11327,207],{},[1723,11329,2031],{"separator":2030},[898,11331,2069],{},[1723,11333,3227],{"stretchy":1907},[902,11335,11336],{"encoding":904},"A[a, b]"," musí platit současně:",[724,11339,11340],{},[883,11341,11343],{"className":11342},[886],[888,11344,11345],{"xmlns":890},[892,11346,11347,11400],{},[895,11348,11349,11357,11359,11361,11363,11365,11367,11369,11371,11373,11376,11378,11386,11388,11390,11392,11394,11396,11398],{},[2220,11350,11351,11353,11355],{},[898,11352,2745],{},[898,11354,2750],{},[1723,11356,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,11358,1908],{"stretchy":1907},[898,11360,207],{},[1723,11362,2031],{"separator":2030},[898,11364,2069],{},[1723,11366,1914],{"stretchy":1907},[1723,11368,1725],{},[1864,11370,2256],{},[3018,11372,4699],{},[1723,11374,11375],{},"∧",[3018,11377,4699],{},[2220,11379,11380,11382,11384],{},[898,11381,2745],{},[898,11383,2740],{},[1723,11385,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,11387,1908],{"stretchy":1907},[898,11389,207],{},[1723,11391,2031],{"separator":2030},[898,11393,2069],{},[1723,11395,1914],{"stretchy":1907},[1723,11397,1725],{},[1864,11399,2256],{},[902,11401,11402],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,11404,4046],{"id":4045},[724,11406,11407,11408,11411],{},"Definujeme ",[38,11409,11410],{},"diskriminant"," (Hessián zjednodušeně):",[724,11413,11414],{},[883,11415,11417],{"className":11416},[886],[888,11418,11419],{"xmlns":890},[892,11420,11421,11497],{},[895,11422,11423,11425,11427,11429,11431,11433,11435,11437,11453,11455,11471,11473,11475,11491],{},[898,11424,4897],{},[1723,11426,1908],{"stretchy":1907},[898,11428,2750],{},[1723,11430,2031],{"separator":2030},[898,11432,2740],{},[1723,11434,1914],{"stretchy":1907},[1723,11436,1725],{},[2220,11438,11439,11441,11447],{},[898,11440,2745],{},[895,11442,11443,11445],{},[898,11444,2750],{},[898,11446,2750],{},[895,11448,11449,11451],{},[1723,11450,2229],{"mathvariant":2124},[1723,11452,2229],{"mathvariant":2124},[1723,11454,3897],{},[2220,11456,11457,11459,11465],{},[898,11458,2745],{},[895,11460,11461,11463],{},[898,11462,2740],{},[898,11464,2740],{},[895,11466,11467,11469],{},[1723,11468,2229],{"mathvariant":2124},[1723,11470,2229],{"mathvariant":2124},[1723,11472,1759],{},[1723,11474,1908],{"stretchy":1907},[2220,11476,11477,11479,11485],{},[898,11478,2745],{},[895,11480,11481,11483],{},[898,11482,2750],{},[898,11484,2740],{},[895,11486,11487,11489],{},[1723,11488,2229],{"mathvariant":2124},[1723,11490,2229],{"mathvariant":2124},[2057,11492,11493,11495],{},[1723,11494,1914],{"stretchy":1907},[1864,11496,2331],{},[902,11498,11499],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,11501,11502,11503,3430],{},"V podezřelém bodě ",[883,11504,11506],{"className":11505},[886],[888,11507,11508],{"xmlns":890},[892,11509,11510,11522],{},[895,11511,11512,11514,11516,11518,11520],{},[1723,11513,3212],{"stretchy":1907},[898,11515,207],{},[1723,11517,2031],{"separator":2030},[898,11519,2069],{},[1723,11521,3227],{"stretchy":1907},[902,11523,11524],{"encoding":904},"[a, b]",[152,11526,11527,11654,11690],{},[123,11528,11529,11559,11560],{},[38,11530,11531,3430],{},[883,11532,11534],{"className":11533},[886],[888,11535,11536],{"xmlns":890},[892,11537,11538,11556],{},[895,11539,11540,11542,11544,11546,11548,11550,11552,11554],{},[898,11541,4897],{},[1723,11543,1908],{"stretchy":1907},[898,11545,207],{},[1723,11547,2031],{"separator":2030},[898,11549,2069],{},[1723,11551,1914],{"stretchy":1907},[1723,11553,2253],{},[1864,11555,2256],{},[902,11557,11558],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,11561,11562,11608],{},[123,11563,11564,4133,11606],{},[883,11565,11567],{"className":11566},[886],[888,11568,11569],{"xmlns":890},[892,11570,11571,11603],{},[895,11572,11573,11589,11591,11593,11595,11597,11599,11601],{},[2220,11574,11575,11577,11583],{},[898,11576,2745],{},[895,11578,11579,11581],{},[898,11580,2750],{},[898,11582,2750],{},[895,11584,11585,11587],{},[1723,11586,2229],{"mathvariant":2124},[1723,11588,2229],{"mathvariant":2124},[1723,11590,1908],{"stretchy":1907},[898,11592,207],{},[1723,11594,2031],{"separator":2030},[898,11596,2069],{},[1723,11598,1914],{"stretchy":1907},[1723,11600,2253],{},[1864,11602,2256],{},[902,11604,11605],{"encoding":904},"f''_{xx}(a, b) > 0",[38,11607,4493],{},[123,11609,11610,4133,11652],{},[883,11611,11613],{"className":11612},[886],[888,11614,11615],{"xmlns":890},[892,11616,11617,11649],{},[895,11618,11619,11635,11637,11639,11641,11643,11645,11647],{},[2220,11620,11621,11623,11629],{},[898,11622,2745],{},[895,11624,11625,11627],{},[898,11626,2750],{},[898,11628,2750],{},[895,11630,11631,11633],{},[1723,11632,2229],{"mathvariant":2124},[1723,11634,2229],{"mathvariant":2124},[1723,11636,1908],{"stretchy":1907},[898,11638,207],{},[1723,11640,2031],{"separator":2030},[898,11642,2069],{},[1723,11644,1914],{"stretchy":1907},[1723,11646,2287],{},[1864,11648,2256],{},[902,11650,11651],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,11653,4435],{},[123,11655,11656,2628,11686,11689],{},[38,11657,11658,3430],{},[883,11659,11661],{"className":11660},[886],[888,11662,11663],{"xmlns":890},[892,11664,11665,11683],{},[895,11666,11667,11669,11671,11673,11675,11677,11679,11681],{},[898,11668,4897],{},[1723,11670,1908],{"stretchy":1907},[898,11672,207],{},[1723,11674,2031],{"separator":2030},[898,11676,2069],{},[1723,11678,1914],{"stretchy":1907},[1723,11680,2287],{},[1864,11682,2256],{},[902,11684,11685],{"encoding":904},"D(a, b) \u003C 0",[38,11687,11688],{},"sedlo"," (v daném bodě extrém není).",[123,11691,11692,11722],{},[38,11693,11694,3430],{},[883,11695,11697],{"className":11696},[886],[888,11698,11699],{"xmlns":890},[892,11700,11701,11719],{},[895,11702,11703,11705,11707,11709,11711,11713,11715,11717],{},[898,11704,4897],{},[1723,11706,1908],{"stretchy":1907},[898,11708,207],{},[1723,11710,2031],{"separator":2030},[898,11712,2069],{},[1723,11714,1914],{"stretchy":1907},[1723,11716,1725],{},[1864,11718,2256],{},[902,11720,11721],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,11724,11726],{"id":11725},"vázané-extrémy","Vázané extrémy",[724,11728,11729,11730,11759,11760,1664],{},"Pro extrémy s omezující podmínkou ",[883,11731,11733],{"className":11732},[886],[888,11734,11735],{"xmlns":890},[892,11736,11737,11756],{},[895,11738,11739,11742,11744,11746,11748,11750,11752,11754],{},[898,11740,11741],{},"g",[1723,11743,1908],{"stretchy":1907},[898,11745,2750],{},[1723,11747,2031],{"separator":2030},[898,11749,2740],{},[1723,11751,1914],{"stretchy":1907},[1723,11753,1725],{},[1864,11755,2256],{},[902,11757,11758],{"encoding":904},"g(x, y) = 0"," se používá ",[207,11761,793],{"className":11762,"dataFsResolvedFilePath":791,"href":792},[210],[115,11764,2620],{"id":2619},[120,11766,11767,11774,11781],{},[123,11768,11769,2628,11771],{},[38,11770,4515],{},[207,11772,775],{"className":11773,"dataFsResolvedFilePath":773,"href":774},[210],[123,11775,11776,2628,11778],{},[38,11777,4523],{},[207,11779,793],{"className":11780,"dataFsResolvedFilePath":791,"href":792},[210],[123,11782,11783,2628,11785,11789,11790,11793,11794,11797],{},[38,11784,4531],{},[207,11786,11788],{"className":11787,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,11791,880],{"className":11792,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,11795,4544],{"className":11796,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":11799},[11800,11801,11805,11806,11807,11811,11812],{"id":10365,"depth":642,"text":10366},{"id":10518,"depth":642,"text":10519,"children":11802},[11803,11804],{"id":10671,"depth":649,"text":10672},{"id":3293,"depth":649,"text":3294},{"id":10998,"depth":642,"text":10999},{"id":11120,"depth":642,"text":11121},{"id":11306,"depth":642,"text":11307,"children":11808},[11809,11810],{"id":3971,"depth":649,"text":3972},{"id":4045,"depth":649,"text":4046},{"id":11725,"depth":642,"text":11726},{"id":2619,"depth":642,"text":2620},"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":10277,"description":11813},[1135],"topics\u002Ffunkce-vice-promennych",[1128,11820,4570,11821,11822,11823],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":11826,"title":775,"body":11827,"course":1128,"courses":659,"created":1129,"description":12683,"extension":661,"meta":12684,"navigation":664,"path":12685,"seo":12686,"sources":12687,"stem":12688,"tags":12689,"type":4573,"updated":677,"__hash__":12695},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":11828,"toc":12673},[11829,11832,11843,11847,11892,11972,11976,12052,12094,12101,12105,12109,12138,12196,12243,12281,12285,12335,12387,12439,12483,12486,12489,12561,12564,12636,12643,12645],[12,11830,775],{"id":11831},"integrál",[724,11833,11834,11835,11838,11839,11842],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,11836,11837],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,11840,11841],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,11844,11846],{"id":11845},"neurčitý-integrál","Neurčitý integrál",[724,11848,11849],{},[883,11850,11852],{"className":11851},[886],[888,11853,11854],{"xmlns":890},[892,11855,11856,11889],{},[895,11857,11858,11860,11862,11864,11866,11868,11871,11873,11875,11877,11879,11881,11883,11885,11887],{},[898,11859,11136],{},[1723,11861,1908],{"stretchy":1907},[898,11863,2750],{},[1723,11865,1914],{"stretchy":1907},[1723,11867,1725],{},[1723,11869,11870],{},"∫",[898,11872,2745],{},[1723,11874,1908],{"stretchy":1907},[898,11876,2750],{},[1723,11878,1914],{"stretchy":1907},[3018,11880,3707],{},[898,11882,2930],{},[898,11884,2750],{},[1723,11886,2087],{},[898,11888,1721],{},[902,11890,11891],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,11893,5022,11894,2137,11928,8812,11941,11944,11945,1343,11958,11971],{},[883,11895,11897],{"className":11896},[886],[888,11898,11899],{"xmlns":890},[892,11900,11901,11925],{},[895,11902,11903,11909,11911,11913,11915,11917,11919,11921,11923],{},[2057,11904,11905,11907],{},[898,11906,11136],{},[1723,11908,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,11910,1908],{"stretchy":1907},[898,11912,2750],{},[1723,11914,1914],{"stretchy":1907},[1723,11916,1725],{},[898,11918,2745],{},[1723,11920,1908],{"stretchy":1907},[898,11922,2750],{},[1723,11924,1914],{"stretchy":1907},[902,11926,11927],{"encoding":904},"F'(x) = f(x)",[883,11929,11931],{"className":11930},[886],[888,11932,11933],{"xmlns":890},[892,11934,11935,11939],{},[895,11936,11937],{},[898,11938,11136],{},[902,11940,11136],{"encoding":904},[38,11942,11943],{},"primitivní funkce"," k ",[883,11946,11948],{"className":11947},[886],[888,11949,11950],{"xmlns":890},[892,11951,11952,11956],{},[895,11953,11954],{},[898,11955,2745],{},[902,11957,2745],{"encoding":904},[883,11959,11961],{"className":11960},[886],[888,11962,11963],{"xmlns":890},[892,11964,11965,11969],{},[895,11966,11967],{},[898,11968,1721],{},[902,11970,1721],{"encoding":904}," konstanta.",[115,11973,11975],{"id":11974},"určitý-integrál","Určitý integrál",[724,11977,11978],{},[883,11979,11981],{"className":11980},[886],[888,11982,11983],{"xmlns":890},[892,11984,11985,12049],{},[895,11986,11987,11995,11997,11999,12001,12003,12005,12007,12009,12011,12013,12015,12017,12019,12021,12029,12031,12033,12035,12037,12039,12041,12043,12045,12047],{},[2220,11988,11989,11991,11993],{},[1723,11990,11870],{},[898,11992,207],{},[898,11994,2069],{},[898,11996,2745],{},[1723,11998,1908],{"stretchy":1907},[898,12000,2750],{},[1723,12002,1914],{"stretchy":1907},[3018,12004,3707],{},[898,12006,2930],{},[898,12008,2750],{},[1723,12010,1725],{},[1723,12012,3212],{"stretchy":1907},[898,12014,11136],{},[1723,12016,1908],{"stretchy":1907},[898,12018,2750],{},[1723,12020,1914],{"stretchy":1907},[2220,12022,12023,12025,12027],{},[1723,12024,3227],{"stretchy":1907},[898,12026,207],{},[898,12028,2069],{},[1723,12030,1725],{},[898,12032,11136],{},[1723,12034,1908],{"stretchy":1907},[898,12036,2069],{},[1723,12038,1914],{"stretchy":1907},[1723,12040,1759],{},[898,12042,11136],{},[1723,12044,1908],{"stretchy":1907},[898,12046,207],{},[1723,12048,1914],{"stretchy":1907},[902,12050,12051],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,12053,12054,12055,2628,12058,12071,12072,12093],{},"Geometricky ",[38,12056,12057],{},"plocha pod grafem",[883,12059,12061],{"className":12060},[886],[888,12062,12063],{"xmlns":890},[892,12064,12065,12069],{},[895,12066,12067],{},[898,12068,2745],{},[902,12070,2745],{"encoding":904}," na intervalu ",[883,12073,12075],{"className":12074},[886],[888,12076,12077],{"xmlns":890},[892,12078,12079,12091],{},[895,12080,12081,12083,12085,12087,12089],{},[1723,12082,3212],{"stretchy":1907},[898,12084,207],{},[1723,12086,2031],{"separator":2030},[898,12088,2069],{},[1723,12090,3227],{"stretchy":1907},[902,12092,11524],{"encoding":904}," (orientovaná).",[724,12095,12096],{},[3285,12097],{"alt":12098,"className":12099,"src":12100},"imek-integral-plocha",[210,3289],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,12102,12104],{"id":12103},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,12106,12108],{"id":12107},"příklad-tr-z-mr","Příklad — TR z MR",[724,12110,12111,12112,1664],{},"Mezní příjem ",[883,12113,12115],{"className":12114},[886],[888,12116,12117],{"xmlns":890},[892,12118,12119,12135],{},[895,12120,12121,12123,12125,12127,12129,12131,12133],{},[898,12122,1728],{},[898,12124,1749],{},[1723,12126,1725],{},[1864,12128,3810],{},[1723,12130,1759],{},[1864,12132,2331],{},[898,12134,1904],{},[902,12136,12137],{"encoding":904},"MR = 100 - 2Q",[724,12139,12140],{},[883,12141,12143],{"className":12142},[886],[888,12144,12145],{"xmlns":890},[892,12146,12147,12193],{},[895,12148,12149,12151,12153,12155,12157,12159,12161,12163,12165,12167,12169,12171,12173,12175,12177,12179,12181,12183,12189,12191],{},[898,12150,1754],{},[898,12152,1749],{},[1723,12154,1725],{},[1723,12156,11870],{},[1723,12158,1908],{"stretchy":1907},[1864,12160,3810],{},[1723,12162,1759],{},[1864,12164,2331],{},[898,12166,1904],{},[1723,12168,1914],{"stretchy":1907},[3018,12170,3707],{},[898,12172,2930],{},[898,12174,1904],{},[1723,12176,1725],{},[1864,12178,3810],{},[898,12180,1904],{},[1723,12182,1759],{},[2057,12184,12185,12187],{},[898,12186,1904],{},[1864,12188,2331],{},[1723,12190,2087],{},[898,12192,2878],{},[902,12194,12195],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,12197,12198,12199,4133,12225,3430],{},"Okrajová podmínka ",[883,12200,12202],{"className":12201},[886],[888,12203,12204],{"xmlns":890},[892,12205,12206,12222],{},[895,12207,12208,12210,12212,12214,12216,12218,12220],{},[898,12209,1754],{},[898,12211,1749],{},[1723,12213,1908],{"stretchy":1907},[1864,12215,2256],{},[1723,12217,1914],{"stretchy":1907},[1723,12219,1725],{},[1864,12221,2256],{},[902,12223,12224],{"encoding":904},"TR(0) = 0",[883,12226,12228],{"className":12227},[886],[888,12229,12230],{"xmlns":890},[892,12231,12232,12240],{},[895,12233,12234,12236,12238],{},[898,12235,2878],{},[1723,12237,1725],{},[1864,12239,2256],{},[902,12241,12242],{"encoding":904},"c = 0",[724,12244,12245],{},[883,12246,12248],{"className":12247},[886],[888,12249,12250],{"xmlns":890},[892,12251,12252,12278],{},[895,12253,12254,12256,12258,12260,12262,12264,12266,12268,12270,12272],{},[898,12255,1754],{},[898,12257,1749],{},[1723,12259,1908],{"stretchy":1907},[898,12261,1904],{},[1723,12263,1914],{"stretchy":1907},[1723,12265,1725],{},[1864,12267,3810],{},[898,12269,1904],{},[1723,12271,1759],{},[2057,12273,12274,12276],{},[898,12275,1904],{},[1864,12277,2331],{},[902,12279,12280],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,12282,12284],{"id":12283},"příklad-tc-z-mc","Příklad — TC z MC",[724,12286,12287,12288,12314,12315,1664],{},"Mezní náklady ",[883,12289,12291],{"className":12290},[886],[888,12292,12293],{"xmlns":890},[892,12294,12295,12311],{},[895,12296,12297,12299,12301,12303,12305,12307,12309],{},[898,12298,1728],{},[898,12300,1721],{},[1723,12302,1725],{},[1864,12304,2331],{},[1723,12306,2087],{},[1864,12308,3561],{},[898,12310,1904],{},[902,12312,12313],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,12316,12318],{"className":12317},[886],[888,12319,12320],{"xmlns":890},[892,12321,12322,12332],{},[895,12323,12324,12326,12328,12330],{},[898,12325,11136],{},[898,12327,1721],{},[1723,12329,1725],{},[1864,12331,3810],{},[902,12333,12334],{"encoding":904},"FC = 100",[724,12336,12337],{},[883,12338,12340],{"className":12339},[886],[888,12341,12342],{"xmlns":890},[892,12343,12344,12384],{},[895,12345,12346,12348,12350,12352,12354,12356,12358,12360,12362,12364,12366,12368,12370,12372,12374,12380,12382],{},[898,12347,1754],{},[898,12349,1721],{},[1723,12351,1725],{},[1723,12353,11870],{},[898,12355,1728],{},[898,12357,1721],{},[3018,12359,3707],{},[898,12361,2930],{},[898,12363,1904],{},[1723,12365,1725],{},[1864,12367,2331],{},[898,12369,1904],{},[1723,12371,2087],{},[1864,12373,3517],{},[2057,12375,12376,12378],{},[898,12377,1904],{},[1864,12379,2331],{},[1723,12381,2087],{},[898,12383,2878],{},[902,12385,12386],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,12388,12198,12389,4133,12421,3430],{},[883,12390,12392],{"className":12391},[886],[888,12393,12394],{"xmlns":890},[892,12395,12396,12418],{},[895,12397,12398,12400,12402,12404,12406,12408,12410,12412,12414,12416],{},[898,12399,1754],{},[898,12401,1721],{},[1723,12403,1908],{"stretchy":1907},[1864,12405,2256],{},[1723,12407,1914],{"stretchy":1907},[1723,12409,1725],{},[898,12411,11136],{},[898,12413,1721],{},[1723,12415,1725],{},[1864,12417,3810],{},[902,12419,12420],{"encoding":904},"TC(0) = FC = 100",[883,12422,12424],{"className":12423},[886],[888,12425,12426],{"xmlns":890},[892,12427,12428,12436],{},[895,12429,12430,12432,12434],{},[898,12431,2878],{},[1723,12433,1725],{},[1864,12435,3810],{},[902,12437,12438],{"encoding":904},"c = 100",[724,12440,12441],{},[883,12442,12444],{"className":12443},[886],[888,12445,12446],{"xmlns":890},[892,12447,12448,12480],{},[895,12449,12450,12452,12454,12456,12458,12460,12462,12464,12466,12468,12470,12472,12474],{},[898,12451,1754],{},[898,12453,1721],{},[1723,12455,1908],{"stretchy":1907},[898,12457,1904],{},[1723,12459,1914],{"stretchy":1907},[1723,12461,1725],{},[1864,12463,3810],{},[1723,12465,2087],{},[1864,12467,2331],{},[898,12469,1904],{},[1723,12471,2087],{},[1864,12473,3517],{},[2057,12475,12476,12478],{},[898,12477,1904],{},[1864,12479,2331],{},[902,12481,12482],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,12484,820],{"id":12485},"přebytek-spotřebitele-a-výrobce",[724,12487,12488],{},"Přebytek spotřebitele:",[724,12490,12491],{},[883,12492,12494],{"className":12493},[886],[888,12495,12496],{"xmlns":890},[892,12497,12498,12558],{},[895,12499,12500,12502,12504,12506,12512,12514,12516,12528,12530,12532,12534,12536,12538,12540,12542,12544,12550,12552],{},[898,12501,1721],{},[898,12503,2111],{},[1723,12505,1908],{"stretchy":1907},[1931,12507,12508,12510],{},[898,12509,1904],{},[1864,12511,2256],{},[1723,12513,1914],{"stretchy":1907},[1723,12515,1725],{},[2220,12517,12518,12520,12522],{},[1723,12519,11870],{},[1864,12521,2256],{},[1931,12523,12524,12526],{},[898,12525,1904],{},[1864,12527,2256],{},[898,12529,4897],{},[1723,12531,1908],{"stretchy":1907},[898,12533,1904],{},[1723,12535,1914],{"stretchy":1907},[3018,12537,3707],{},[898,12539,2930],{},[898,12541,1904],{},[1723,12543,1759],{},[1931,12545,12546,12548],{},[898,12547,1746],{},[1864,12549,2256],{},[3018,12551,3707],{},[1931,12553,12554,12556],{},[898,12555,1904],{},[1864,12557,2256],{},[902,12559,12560],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,12562,12563],{},"Přebytek výrobce:",[724,12565,12566],{},[883,12567,12569],{"className":12568},[886],[888,12570,12571],{"xmlns":890},[892,12572,12573,12633],{},[895,12574,12575,12577,12579,12581,12587,12589,12591,12597,12599,12605,12607,12619,12621,12623,12625,12627,12629,12631],{},[898,12576,1746],{},[898,12578,2111],{},[1723,12580,1908],{"stretchy":1907},[1931,12582,12583,12585],{},[898,12584,1904],{},[1864,12586,2256],{},[1723,12588,1914],{"stretchy":1907},[1723,12590,1725],{},[1931,12592,12593,12595],{},[898,12594,1746],{},[1864,12596,2256],{},[3018,12598,3707],{},[1931,12600,12601,12603],{},[898,12602,1904],{},[1864,12604,2256],{},[1723,12606,1759],{},[2220,12608,12609,12611,12613],{},[1723,12610,11870],{},[1864,12612,2256],{},[1931,12614,12615,12617],{},[898,12616,1904],{},[1864,12618,2256],{},[898,12620,2111],{},[1723,12622,1908],{"stretchy":1907},[898,12624,1904],{},[1723,12626,1914],{"stretchy":1907},[3018,12628,3707],{},[898,12630,2930],{},[898,12632,1904],{},[902,12634,12635],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,12637,12638,12639,1664],{},"Detailně viz ",[207,12640,12642],{"className":12641,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,12644,2620],{"id":2619},[120,12646,12647,12654,12661],{},[123,12648,12649,2628,12651],{},[38,12650,4515],{},[207,12652,766],{"className":12653,"dataFsResolvedFilePath":764,"href":765},[210],[123,12655,12656,2628,12658],{},[38,12657,4523],{},[207,12659,784],{"className":12660,"dataFsResolvedFilePath":782,"href":783},[210],[123,12662,12663,2628,12665,12668,12669,12672],{},[38,12664,4531],{},[207,12666,4539],{"className":12667,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,12670,12642],{"className":12671,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":12674},[12675,12676,12677,12682],{"id":11845,"depth":642,"text":11846},{"id":11974,"depth":642,"text":11975},{"id":12103,"depth":642,"text":12104,"children":12678},[12679,12680,12681],{"id":12107,"depth":649,"text":12108},{"id":12283,"depth":649,"text":12284},{"id":12485,"depth":649,"text":820},{"id":2619,"depth":642,"text":2620},"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":12683},[1135],"topics\u002Fintegral",[1128,2571,12690,12691,12692,12693,12694],"neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":12697,"title":12698,"body":12699,"course":1128,"courses":659,"created":2676,"description":641,"extension":661,"meta":16962,"navigation":664,"path":16963,"seo":16964,"sources":16965,"stem":16966,"tags":16967,"type":4573,"updated":677,"__hash__":16973},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":12700,"toc":16950},[12701,12704,12708,12852,12859,12863,12933,12971,13074,13078,13108,13174,13221,13224,13293,13296,13331,13367,13371,13419,13426,13472,13518,13521,13600,13697,13780,13784,13828,13858,13864,13893,13915,13965,14018,14084,14087,14153,14182,14241,14257,14344,14442,14573,14577,14734,14883,15263,15267,15270,15329,15332,15418,15446,15484,15487,15524,15564,15598,15600,15637,15669,15767,15772,15896,15948,16030,16169,16173,16293,16300,16411,16418,16422,16897,16899],[12,12702,12698],{"id":12703},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,12705,12707],{"id":12706},"tldr","TL;DR",[724,12709,12710,12713,12714,1981,12717,12730,12731,12745,12746,12749,12750,1343,12753,12756,12757,1343,12760,12763,12764,2628,12767,12797,12798,12801,12802,1343,12816,12829,12830,12833,12834,4634],{},[38,12711,12712],{},"IS-LM"," je makroekonomický model se ",[38,12715,12716],{},"dvěma neznámými",[883,12718,12720],{"className":12719},[886],[888,12721,12722],{"xmlns":890},[892,12723,12724,12728],{},[895,12725,12726],{},[898,12727,9837],{},[902,12729,9837],{"encoding":904}," — národní důchod a ",[883,12732,12734],{"className":12733},[886],[888,12735,12736],{"xmlns":890},[892,12737,12738,12743],{},[895,12739,12740],{},[898,12741,12742],{},"r",[902,12744,12742],{"encoding":904}," — úroková míra) a ",[38,12747,12748],{},"dvěma trhy",": trhem zboží (křivka ",[38,12751,12752],{},"IS",[614,12754,12755],{},"Investment = Savings",") a trhem peněz (křivka ",[38,12758,12759],{},"LM",[614,12761,12762],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,12765,12766],{},"simultánní rovnováhu",[883,12768,12770],{"className":12769},[886],[888,12771,12772],{"xmlns":890},[892,12773,12774,12794],{},[895,12775,12776,12778,12784,12786,12792],{},[1723,12777,1908],{"stretchy":1907},[2057,12779,12780,12782],{},[898,12781,9837],{},[898,12783,1846],{},[1723,12785,2031],{"separator":2030},[2057,12787,12788,12790],{},[898,12789,12742],{},[898,12791,1846],{},[1723,12793,1914],{"stretchy":1907},[902,12795,12796],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,12799,12800],{},"fiskální politiky"," (posun IS změnou ",[883,12803,12805],{"className":12804},[886],[888,12806,12807],{"xmlns":890},[892,12808,12809,12814],{},[895,12810,12811],{},[898,12812,12813],{},"G",[902,12815,12813],{"encoding":904},[883,12817,12819],{"className":12818},[886],[888,12820,12821],{"xmlns":890},[892,12822,12823,12827],{},[895,12824,12825],{},[898,12826,1754],{},[902,12828,1754],{"encoding":904},") a ",[38,12831,12832],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,12835,12837],{"className":12836},[886],[888,12838,12839],{"xmlns":890},[892,12840,12841,12849],{},[895,12842,12843],{},[2057,12844,12845,12847],{},[898,12846,1728],{},[1723,12848,5066],{},[902,12850,12851],{"encoding":904},"M^*",[724,12853,12854],{},[3285,12855],{"alt":12856,"className":12857,"src":12858},"imek-is-lm-model",[210,3289],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,12860,12862],{"id":12861},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,12864,12865,12866,12870,12871,1981,12874,12897,12898,12901,12902,12918,12919,12932],{},"V modelech ",[207,12867,12869],{"className":12868,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,12872,12873],{},"investice pokládány za konstantní",[883,12875,12877],{"className":12876},[886],[888,12878,12879],{"xmlns":890},[892,12880,12881,12894],{},[895,12882,12883,12886,12888],{},[898,12884,12885],{},"I",[1723,12887,1725],{},[2057,12889,12890,12892],{},[898,12891,12885],{},[1723,12893,5066],{},[902,12895,12896],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,12899,12900],{},"ceně peněz",", tedy na ",[38,12903,12904,12905],{},"úrokové míře ",[883,12906,12908],{"className":12907},[886],[888,12909,12910],{"xmlns":890},[892,12911,12912,12916],{},[895,12913,12914],{},[898,12915,12742],{},[902,12917,12742],{"encoding":904},": čím vyšší ",[883,12920,12922],{"className":12921},[886],[888,12923,12924],{"xmlns":890},[892,12925,12926,12930],{},[895,12927,12928],{},[898,12929,12742],{},[902,12931,12742],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,12934,12935,12965],{},[123,12936,12937,2628,12940,12964],{},[38,12938,12939],{},"funkci investic",[883,12941,12943],{"className":12942},[886],[888,12944,12945],{"xmlns":890},[892,12946,12947,12961],{},[895,12948,12949,12951,12953,12955,12957,12959],{},[898,12950,12885],{},[1723,12952,1725],{},[898,12954,12885],{},[1723,12956,1908],{"stretchy":1907},[898,12958,12742],{},[1723,12960,1914],{"stretchy":1907},[902,12962,12963],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,12966,12967,12970],{},[38,12968,12969],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[4584,12972,12973],{},[724,12974,12975,12977,12978,12997,12998,13025,13026,13039,13040,13069,13070,13073],{},[883,12976,5124],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,12979,12981],{"className":12980},[886],[888,12982,12983],{"xmlns":890},[892,12984,12985,12994],{},[895,12986,12987,12989,12992],{},[898,12988,1721],{},[3018,12990,12991],{},"-",[898,12993,12885],{},[902,12995,12996],{"encoding":904},"C\\text{-}I"," až ",[883,12999,13001],{"className":13000},[886],[888,13002,13003],{"xmlns":890},[892,13004,13005,13022],{},[895,13006,13007,13009,13011,13013,13015,13017,13019],{},[898,13008,1721],{},[3018,13010,12991],{},[898,13012,12885],{},[3018,13014,12991],{},[898,13016,12813],{},[3018,13018,12991],{},[898,13020,13021],{},"X",[902,13023,13024],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,13027,13029],{"className":13028},[886],[888,13030,13031],{"xmlns":890},[892,13032,13033,13037],{},[895,13034,13035],{},[898,13036,9837],{},[902,13038,9837],{"encoding":904},". V IS-LM jsou ",[38,13041,13042,13043,1682,13056],{},"dvě neznámé ",[883,13044,13046],{"className":13045},[886],[888,13047,13048],{"xmlns":890},[892,13049,13050,13054],{},[895,13051,13052],{},[898,13053,9837],{},[902,13055,9837],{"encoding":904},[883,13057,13059],{"className":13058},[886],[888,13060,13061],{"xmlns":890},[892,13062,13063,13067],{},[895,13064,13065],{},[898,13066,12742],{},[902,13068,12742],{"encoding":904},", a proto potřebujeme ",[38,13071,13072],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,13075,13077],{"id":13076},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,13079,13080,13081,13094,13095,3430],{},"Lineární závislost investic ",[883,13082,13084],{"className":13083},[886],[888,13085,13086],{"xmlns":890},[892,13087,13088,13092],{},[895,13089,13090],{},[898,13091,12885],{},[902,13093,12885],{"encoding":904}," na úrokové míře ",[883,13096,13098],{"className":13097},[886],[888,13099,13100],{"xmlns":890},[892,13101,13102,13106],{},[895,13103,13104],{},[898,13105,12742],{},[902,13107,12742],{"encoding":904},[724,13109,13110],{},[883,13111,13113],{"className":13112},[886],[888,13114,13115],{"xmlns":890},[892,13116,13117,13171],{},[895,13118,13119,13121,13123,13125,13127,13129,13131,13133,13135,13137,13139,13141,13143,13145,13147,13149,13151,13153,13155,13157,13159,13162,13164,13166,13169],{},[898,13120,12885],{},[1723,13122,1725],{},[898,13124,12885],{},[1723,13126,1908],{"stretchy":1907},[898,13128,12742],{},[1723,13130,1914],{"stretchy":1907},[1723,13132,1725],{},[898,13134,2878],{},[898,13136,12742],{},[1723,13138,2087],{},[898,13140,2930],{},[1723,13142,2031],{"separator":2030},[6588,13144],{"width":6590},[898,13146,2878],{},[1723,13148,2287],{},[1864,13150,2256],{},[1723,13152,2031],{"separator":2030},[3018,13154,3020],{},[898,13156,2930],{},[1723,13158,2253],{},[1864,13160,13161],{},"0.",[6588,13163],{"width":6590},[1723,13165,1908],{"stretchy":1907},[1864,13167,13168],{},"7.11",[1723,13170,1914],{"stretchy":1907},[902,13172,13173],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,13175,13176,13197],{},[123,13177,13178,13196],{},[883,13179,13181],{"className":13180},[886],[888,13182,13183],{"xmlns":890},[892,13184,13185,13193],{},[895,13186,13187,13189,13191],{},[898,13188,2930],{},[1723,13190,2253],{},[1864,13192,2256],{},[902,13194,13195],{"encoding":904},"d > 0"," zřejmé,",[123,13198,13199,13217,13218,1664],{},[883,13200,13202],{"className":13201},[886],[888,13203,13204],{"xmlns":890},[892,13205,13206,13214],{},[895,13207,13208,13210,13212],{},[898,13209,2878],{},[1723,13211,2287],{},[1864,13213,2256],{},[902,13215,13216],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,13219,13220],{},"klesající",[724,13222,13223],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,13225,13226],{},[883,13227,13229],{"className":13228},[886],[888,13230,13231],{"xmlns":890},[892,13232,13233,13290],{},[895,13234,13235,13237,13239,13241,13243,13245,13247,13249,13251,13253,13255,13257,13259,13261,13263,13265,13267,13269,13271,13273,13275,13277,13279,13281,13283,13285,13288],{},[898,13236,1721],{},[1723,13238,1725],{},[898,13240,1721],{},[1723,13242,1908],{"stretchy":1907},[898,13244,9837],{},[1723,13246,1914],{"stretchy":1907},[1723,13248,1725],{},[898,13250,207],{},[898,13252,9837],{},[1723,13254,2087],{},[898,13256,2069],{},[1723,13258,2031],{"separator":2030},[6588,13260],{"width":6590},[1864,13262,2256],{},[1723,13264,2287],{},[898,13266,207],{},[1723,13268,2287],{},[1864,13270,1866],{},[1723,13272,2031],{"separator":2030},[3018,13274,3020],{},[898,13276,2069],{},[1723,13278,2253],{},[1864,13280,13161],{},[6588,13282],{"width":6590},[1723,13284,1908],{"stretchy":1907},[1864,13286,13287],{},"7.12",[1723,13289,1914],{"stretchy":1907},[902,13291,13292],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,13294,13295],{},"Podmínka rovnováhy na trhu zboží:",[724,13297,13298],{},[883,13299,13301],{"className":13300},[886],[888,13302,13303],{"xmlns":890},[892,13304,13305,13328],{},[895,13306,13307,13309,13311,13313,13315,13317,13319,13321,13323,13326],{},[898,13308,9837],{},[1723,13310,1725],{},[898,13312,1721],{},[1723,13314,2087],{},[898,13316,12885],{},[898,13318,1664],{"mathvariant":2124},[6588,13320],{"width":6590},[1723,13322,1908],{"stretchy":1907},[1864,13324,13325],{},"7.13",[1723,13327,1914],{"stretchy":1907},[902,13329,13330],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,13332,13333,13334,2628,13337,13363,13364,1664],{},"To dává ",[38,13335,13336],{},"tři rovnice o čtyřech neznámých",[883,13338,13340],{"className":13339},[886],[888,13341,13342],{"xmlns":890},[892,13343,13344,13360],{},[895,13345,13346,13348,13350,13352,13354,13356,13358],{},[898,13347,9837],{},[1723,13349,2031],{"separator":2030},[898,13351,1721],{},[1723,13353,2031],{"separator":2030},[898,13355,12885],{},[1723,13357,2031],{"separator":2030},[898,13359,12742],{},[902,13361,13362],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,13365,13366],{},"rovnováhy na trhu peněz",[115,13368,13370],{"id":13369},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,13372,13373,13374,6279,13396,13414,13415,13418],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,13375,13377],{"className":13376},[886],[888,13378,13379],{"xmlns":890},[892,13380,13381,13393],{},[895,13382,13383,13385,13387,13389,13391],{},[898,13384,9837],{},[1723,13386,1725],{},[898,13388,1721],{},[1723,13390,2087],{},[898,13392,2111],{},[902,13394,13395],{"encoding":904},"Y = C + S",[883,13397,13399],{"className":13398},[886],[888,13400,13401],{"xmlns":890},[892,13402,13403,13411],{},[895,13404,13405,13407,13409],{},[898,13406,12885],{},[1723,13408,1725],{},[898,13410,2111],{},[902,13412,13413],{"encoding":904},"I = S"," (plánované ",[38,13416,13417],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,13420,13421],{},[3285,13422],{"alt":13423,"className":13424,"src":13425},"imek-odvozeni-is-4panelu",[210,3289],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,13427,13428],{},[883,13429,13431],{"className":13430},[886],[888,13432,13433],{"xmlns":890},[892,13434,13435,13469],{},[895,13436,13437,13439,13441,13443,13445,13447,13449,13451,13453,13455,13457,13459,13461,13463,13465,13467],{},[898,13438,9837],{},[1723,13440,1725],{},[1723,13442,1908],{"stretchy":1907},[898,13444,207],{},[898,13446,9837],{},[1723,13448,2087],{},[898,13450,2069],{},[1723,13452,1914],{"stretchy":1907},[1723,13454,2087],{},[1723,13456,1908],{"stretchy":1907},[898,13458,2878],{},[898,13460,12742],{},[1723,13462,2087],{},[898,13464,2930],{},[1723,13466,1914],{"stretchy":1907},[1723,13468,2031],{"separator":2030},[902,13470,13471],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,13473,13474],{},[883,13475,13477],{"className":13476},[886],[888,13478,13479],{"xmlns":890},[892,13480,13481,13515],{},[895,13482,13483,13485,13487,13489,13491,13493,13495,13497,13499,13501,13503,13505,13507,13509,13511,13513],{},[1723,13484,1908],{"stretchy":1907},[1864,13486,1866],{},[1723,13488,1759],{},[898,13490,207],{},[1723,13492,1914],{"stretchy":1907},[898,13494,9837],{},[1723,13496,1759],{},[898,13498,2878],{},[898,13500,12742],{},[1723,13502,1759],{},[898,13504,2069],{},[1723,13506,1759],{},[898,13508,2930],{},[1723,13510,1725],{},[1864,13512,2256],{},[1723,13514,2031],{"separator":2030},[902,13516,13517],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,13519,13520],{},"odkud",[724,13522,13523],{},[883,13524,13526],{"className":13525},[886],[888,13527,13528],{"xmlns":890},[892,13529,13530,13597],{},[895,13531,13532,13588,13590,13592,13595],{},[13533,13534,13536],"menclose",{"notation":13535},"box",[3055,13537,13538],{"scriptlevel":2256,"displaystyle":1907},[3055,13539,13540],{"scriptlevel":2256,"displaystyle":1907},[3055,13541,13542],{"scriptlevel":2256,"displaystyle":2030},[895,13543,13544,13546,13548,13550,13562,13564,13566,13568,13586],{},[3018,13545,3707],{},[898,13547,9837],{},[1723,13549,1725],{},[3058,13551,13552,13554],{},[898,13553,2878],{},[895,13555,13556,13558,13560],{},[1864,13557,1866],{},[1723,13559,1759],{},[898,13561,207],{},[3018,13563,3707],{},[898,13565,12742],{},[1723,13567,2087],{},[3058,13569,13570,13578],{},[895,13571,13572,13574,13576],{},[898,13573,2069],{},[1723,13575,2087],{},[898,13577,2930],{},[895,13579,13580,13582,13584],{},[1864,13581,1866],{},[1723,13583,1759],{},[898,13585,207],{},[3018,13587,3707],{},[6588,13589],{"width":6590},[1723,13591,1908],{"stretchy":1907},[1864,13593,13594],{},"7.14",[1723,13596,1914],{"stretchy":1907},[902,13598,13599],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,13601,13602,13603,1981,13606,13609,13610,13613,13614,13616,13617,13639,13640,13668,13669,13690,13691,13693,13694,13696],{},"Tento vztah se nazývá ",[38,13604,13605],{},"funkce IS",[614,13607,13608],{},"IS schedule",") a její graf ",[38,13611,13612],{},"křivka IS",". Křivka je ",[38,13615,13220],{}," přímka v rovině ",[883,13618,13620],{"className":13619},[886],[888,13621,13622],{"xmlns":890},[892,13623,13624,13636],{},[895,13625,13626,13628,13630,13632,13634],{},[1723,13627,1908],{"stretchy":1907},[898,13629,12742],{},[1723,13631,2031],{"separator":2030},[898,13633,9837],{},[1723,13635,1914],{"stretchy":1907},[902,13637,13638],{"encoding":904},"(r, Y)",", neboť ",[883,13641,13643],{"className":13642},[886],[888,13644,13645],{"xmlns":890},[892,13646,13647,13665],{},[895,13648,13649,13661,13663],{},[3058,13650,13651,13653],{},[898,13652,2878],{},[895,13654,13655,13657,13659],{},[1864,13656,1866],{},[1723,13658,1759],{},[898,13660,207],{},[1723,13662,2287],{},[1864,13664,2256],{},[902,13666,13667],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,13670,13672],{"className":13671},[886],[888,13673,13674],{"xmlns":890},[892,13675,13676,13688],{},[895,13677,13678,13680,13682,13684,13686],{},[1723,13679,1908],{"stretchy":1907},[898,13681,12742],{},[1723,13683,2031],{"separator":2030},[898,13685,9837],{},[1723,13687,1914],{"stretchy":1907},[902,13689,13638],{"encoding":904},", pro které plánované ",[38,13692,12885],{},"nvestment = ",[38,13695,2111],{},"avings.",[4584,13698,13699],{},[724,13700,13701,13703,13704,13717,13718,2628,13721,13734,13735,13748,13749,1682,13762,13775,13776,13779],{},[883,13702,4869],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,13705,13707],{"className":13706},[886],[888,13708,13709],{"xmlns":890},[892,13710,13711,13715],{},[895,13712,13713],{},[898,13714,12742],{},[902,13716,12742],{"encoding":904}," → levnější úvěr → ",[38,13719,13720],{},"více investic",[883,13722,13724],{"className":13723},[886],[888,13725,13726],{"xmlns":890},[892,13727,13728,13732],{},[895,13729,13730],{},[898,13731,12885],{},[902,13733,12885],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,13736,13738],{"className":13737},[886],[888,13739,13740],{"xmlns":890},[892,13741,13742,13746],{},[895,13743,13744],{},[898,13745,9837],{},[902,13747,9837],{"encoding":904},". Vztah mezi ",[883,13750,13752],{"className":13751},[886],[888,13753,13754],{"xmlns":890},[892,13755,13756,13760],{},[895,13757,13758],{},[898,13759,12742],{},[902,13761,12742],{"encoding":904},[883,13763,13765],{"className":13764},[886],[888,13766,13767],{"xmlns":890},[892,13768,13769,13773],{},[895,13770,13771],{},[898,13772,9837],{},[902,13774,9837],{"encoding":904}," na trhu zboží je proto ",[38,13777,13778],{},"nepřímý"," (klesající křivka).",[115,13781,13783],{"id":13782},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,13785,13786,13787,13805,13806,2137,13824,13827],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,13788,13790],{"className":13789},[886],[888,13791,13792],{"xmlns":890},[892,13793,13794,13802],{},[895,13795,13796],{},[2057,13797,13798,13800],{},[898,13799,1728],{},[898,13801,4897],{},[902,13803,13804],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,13807,13809],{"className":13808},[886],[888,13810,13811],{"xmlns":890},[892,13812,13813,13821],{},[895,13814,13815],{},[2057,13816,13817,13819],{},[898,13818,1728],{},[898,13820,2111],{},[902,13822,13823],{"encoding":904},"M^S",[38,13825,13826],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,13829,13830],{},[883,13831,13833],{"className":13832},[886],[888,13834,13835],{"xmlns":890},[892,13836,13837,13855],{},[895,13838,13839,13845,13847,13853],{},[2057,13840,13841,13843],{},[898,13842,1728],{},[898,13844,2111],{},[1723,13846,1725],{},[2057,13848,13849,13851],{},[898,13850,1728],{},[1723,13852,5066],{},[898,13854,1664],{"mathvariant":2124},[902,13856,13857],{"encoding":904},"M^S = M^*.",[724,13859,13860,13863],{},[38,13861,13862],{},"Poptávka"," po penězích má tři zdroje:",[120,13865,13866,13875,13884],{},[123,13867,13868,1981,13871,13874],{},[38,13869,13870],{},"transakční poptávka",[614,13872,13873],{},"transactions demand",") — peníze pro nákup zboží,",[123,13876,13877,1981,13880,13883],{},[38,13878,13879],{},"opatrnostní poptávka",[614,13881,13882],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,13885,13886,1981,13889,13892],{},[38,13887,13888],{},"spekulační poptávka",[614,13890,13891],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,13894,13895,13896,13914],{},"Součet transakční a opatrnostní poptávky ",[883,13897,13899],{"className":13898},[886],[888,13900,13901],{"xmlns":890},[892,13902,13903,13911],{},[895,13904,13905],{},[1931,13906,13907,13909],{},[898,13908,1911],{},[1864,13910,1866],{},[902,13912,13913],{"encoding":904},"L_1"," je úměrný důchodu:",[724,13916,13917],{},[883,13918,13920],{"className":13919},[886],[888,13921,13922],{"xmlns":890},[892,13923,13924,13962],{},[895,13925,13926,13932,13934,13941,13943,13945,13947,13949,13951,13957,13959],{},[1931,13927,13928,13930],{},[898,13929,1911],{},[1864,13931,1866],{},[1723,13933,1725],{},[1931,13935,13936,13939],{},[898,13937,13938],{},"k",[1864,13940,1866],{},[898,13942,9837],{},[1723,13944,2031],{"separator":2030},[6588,13946],{"width":6590},[1864,13948,2256],{},[1723,13950,2287],{},[1931,13952,13953,13955],{},[898,13954,13938],{},[1864,13956,1866],{},[1723,13958,2287],{},[1864,13960,13961],{},"1.",[902,13963,13964],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,13966,13967,13968,13986,13987,1343,14000,14017],{},"Spekulační poptávka ",[883,13969,13971],{"className":13970},[886],[888,13972,13973],{"xmlns":890},[892,13974,13975,13983],{},[895,13976,13977],{},[1931,13978,13979,13981],{},[898,13980,1911],{},[1864,13982,2331],{},[902,13984,13985],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,13988,13990],{"className":13989},[886],[888,13991,13992],{"xmlns":890},[892,13993,13994,13998],{},[895,13995,13996],{},[898,13997,12742],{},[902,13999,12742],{"encoding":904},[883,14001,14003],{"className":14002},[886],[888,14004,14005],{"xmlns":890},[892,14006,14007,14015],{},[895,14008,14009],{},[1931,14010,14011,14013],{},[898,14012,1911],{},[1864,14014,2331],{},[902,14016,13985],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,14019,14020],{},[883,14021,14023],{"className":14022},[886],[888,14024,14025],{"xmlns":890},[892,14026,14027,14081],{},[895,14028,14029,14035,14037,14043,14045,14047,14053,14055,14057,14063,14065,14067,14069,14071,14077,14079],{},[1931,14030,14031,14033],{},[898,14032,1911],{},[1864,14034,2331],{},[1723,14036,1725],{},[1931,14038,14039,14041],{},[898,14040,13938],{},[1864,14042,2331],{},[898,14044,12742],{},[1723,14046,2087],{},[1931,14048,14049,14051],{},[898,14050,13938],{},[1864,14052,2909],{},[1723,14054,2031],{"separator":2030},[6588,14056],{"width":6590},[1931,14058,14059,14061],{},[898,14060,13938],{},[1864,14062,2331],{},[1723,14064,2287],{},[1864,14066,2256],{},[1723,14068,2031],{"separator":2030},[3018,14070,3020],{},[1931,14072,14073,14075],{},[898,14074,13938],{},[1864,14076,2909],{},[1723,14078,2253],{},[1864,14080,13161],{},[902,14082,14083],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,14085,14086],{},"Celková poptávka po penězích:",[724,14088,14089],{},[883,14090,14092],{"className":14091},[886],[888,14093,14094],{"xmlns":890},[892,14095,14096,14150],{},[895,14097,14098,14104,14106,14112,14114,14120,14122,14128,14130,14132,14138,14140,14142,14148],{},[2057,14099,14100,14102],{},[898,14101,1728],{},[898,14103,4897],{},[1723,14105,1725],{},[1931,14107,14108,14110],{},[898,14109,1911],{},[1864,14111,1866],{},[1723,14113,2087],{},[1931,14115,14116,14118],{},[898,14117,1911],{},[1864,14119,2331],{},[1723,14121,1725],{},[1931,14123,14124,14126],{},[898,14125,13938],{},[1864,14127,1866],{},[898,14129,9837],{},[1723,14131,2087],{},[1931,14133,14134,14136],{},[898,14135,13938],{},[1864,14137,2331],{},[898,14139,12742],{},[1723,14141,2087],{},[1931,14143,14144,14146],{},[898,14145,13938],{},[1864,14147,2909],{},[898,14149,1664],{"mathvariant":2124},[902,14151,14152],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,14154,14155,14156,3430],{},"Podmínka rovnováhy na trhu peněz ",[883,14157,14159],{"className":14158},[886],[888,14160,14161],{"xmlns":890},[892,14162,14163,14179],{},[895,14164,14165,14171,14173],{},[2057,14166,14167,14169],{},[898,14168,1728],{},[898,14170,4897],{},[1723,14172,1725],{},[2057,14174,14175,14177],{},[898,14176,1728],{},[1723,14178,5066],{},[902,14180,14181],{"encoding":904},"M^D = M^*",[724,14183,14184],{},[883,14185,14187],{"className":14186},[886],[888,14188,14189],{"xmlns":890},[892,14190,14191,14238],{},[895,14192,14193,14199,14201,14207,14209,14211,14217,14219,14221,14227,14229,14231,14233,14236],{},[2057,14194,14195,14197],{},[898,14196,1728],{},[1723,14198,5066],{},[1723,14200,1725],{},[1931,14202,14203,14205],{},[898,14204,13938],{},[1864,14206,1866],{},[898,14208,9837],{},[1723,14210,2087],{},[1931,14212,14213,14215],{},[898,14214,13938],{},[1864,14216,2331],{},[898,14218,12742],{},[1723,14220,2087],{},[1931,14222,14223,14225],{},[898,14224,13938],{},[1864,14226,2909],{},[1723,14228,2031],{"separator":2030},[6588,14230],{"width":6590},[1723,14232,1908],{"stretchy":1907},[1864,14234,14235],{},"7.15",[1723,14237,1914],{"stretchy":1907},[902,14239,14240],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,14242,14243,14244,3871],{},"po úpravě (vyjádření ",[883,14245,14247],{"className":14246},[886],[888,14248,14249],{"xmlns":890},[892,14250,14251,14255],{},[895,14252,14253],{},[898,14254,9837],{},[902,14256,9837],{"encoding":904},[724,14258,14259],{},[883,14260,14262],{"className":14261},[886],[888,14263,14264],{"xmlns":890},[892,14265,14266,14341],{},[895,14267,14268,14332,14334,14336,14339],{},[13533,14269,14270],{"notation":13535},[3055,14271,14272],{"scriptlevel":2256,"displaystyle":1907},[3055,14273,14274],{"scriptlevel":2256,"displaystyle":1907},[3055,14275,14276],{"scriptlevel":2256,"displaystyle":2030},[895,14277,14278,14280,14282,14284,14286,14300,14302,14304,14306,14330],{},[3018,14279,3707],{},[898,14281,9837],{},[1723,14283,1725],{},[1723,14285,1759],{},[3058,14287,14288,14294],{},[1931,14289,14290,14292],{},[898,14291,13938],{},[1864,14293,2331],{},[1931,14295,14296,14298],{},[898,14297,13938],{},[1864,14299,1866],{},[3018,14301,3707],{},[898,14303,12742],{},[1723,14305,2087],{},[3058,14307,14308,14324],{},[895,14309,14310,14316,14318],{},[2057,14311,14312,14314],{},[898,14313,1728],{},[1723,14315,5066],{},[1723,14317,1759],{},[1931,14319,14320,14322],{},[898,14321,13938],{},[1864,14323,2909],{},[1931,14325,14326,14328],{},[898,14327,13938],{},[1864,14329,1866],{},[3018,14331,3707],{},[6588,14333],{"width":6590},[1723,14335,1908],{"stretchy":1907},[1864,14337,14338],{},"7.16",[1723,14340,1914],{"stretchy":1907},[902,14342,14343],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,14345,13602,14346,1981,14349,14352,14353,13613,14356,13616,14359,13639,14380,14412,14413,14435,14436,14438,14439,14441],{},[38,14347,14348],{},"funkce LM",[614,14350,14351],{},"LM schedule","), její graf ",[38,14354,14355],{},"křivka LM",[38,14357,14358],{},"rostoucí",[883,14360,14362],{"className":14361},[886],[888,14363,14364],{"xmlns":890},[892,14365,14366,14378],{},[895,14367,14368,14370,14372,14374,14376],{},[1723,14369,1908],{"stretchy":1907},[898,14371,12742],{},[1723,14373,2031],{"separator":2030},[898,14375,9837],{},[1723,14377,1914],{"stretchy":1907},[902,14379,13638],{"encoding":904},[883,14381,14383],{"className":14382},[886],[888,14384,14385],{"xmlns":890},[892,14386,14387,14409],{},[895,14388,14389,14391,14405,14407],{},[1723,14390,1759],{},[3058,14392,14393,14399],{},[1931,14394,14395,14397],{},[898,14396,13938],{},[1864,14398,2331],{},[1931,14400,14401,14403],{},[898,14402,13938],{},[1864,14404,1866],{},[1723,14406,2253],{},[1864,14408,2256],{},[902,14410,14411],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,14414,14416],{"className":14415},[886],[888,14417,14418],{"xmlns":890},[892,14419,14420,14432],{},[895,14421,14422,14428,14430],{},[1931,14423,14424,14426],{},[898,14425,13938],{},[1864,14427,2331],{},[1723,14429,2287],{},[1864,14431,2256],{},[902,14433,14434],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,14437,1911],{},"iquidity of ",[38,14440,1728],{},"oney.",[4584,14443,14444],{},[724,14445,14446,14448,14449,14462,14463,14491,14492,14509,14510,14523,14524,14541,14542,1682,14555,14568,14569,14572],{},[883,14447,4869],{}," Intuice — proč LM roste\nVyšší důchod ",[883,14450,14452],{"className":14451},[886],[888,14453,14454],{"xmlns":890},[892,14455,14456,14460],{},[895,14457,14458],{},[898,14459,9837],{},[902,14461,9837],{"encoding":904}," → větší transakční poptávka po penězích ",[883,14464,14466],{"className":14465},[886],[888,14467,14468],{"xmlns":890},[892,14469,14470,14488],{},[895,14471,14472,14478,14480,14486],{},[1931,14473,14474,14476],{},[898,14475,1911],{},[1864,14477,1866],{},[1723,14479,1725],{},[1931,14481,14482,14484],{},[898,14483,13938],{},[1864,14485,1866],{},[898,14487,9837],{},[902,14489,14490],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,14493,14495],{"className":14494},[886],[888,14496,14497],{"xmlns":890},[892,14498,14499,14507],{},[895,14500,14501],{},[2057,14502,14503,14505],{},[898,14504,1728],{},[1723,14506,5066],{},[902,14508,12851],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,14511,14513],{"className":14512},[886],[888,14514,14515],{"xmlns":890},[892,14516,14517,14521],{},[895,14518,14519],{},[898,14520,12742],{},[902,14522,12742],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,14525,14527],{"className":14526},[886],[888,14528,14529],{"xmlns":890},[892,14530,14531,14539],{},[895,14532,14533],{},[1931,14534,14535,14537],{},[898,14536,1911],{},[1864,14538,2331],{},[902,14540,13985],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,14543,14545],{"className":14544},[886],[888,14546,14547],{"xmlns":890},[892,14548,14549,14553],{},[895,14550,14551],{},[898,14552,9837],{},[902,14554,9837],{"encoding":904},[883,14556,14558],{"className":14557},[886],[888,14559,14560],{"xmlns":890},[892,14561,14562,14566],{},[895,14563,14564],{},[898,14565,12742],{},[902,14567,12742],{"encoding":904}," na trhu peněz je proto ",[38,14570,14571],{},"přímý"," (rostoucí křivka).",[115,14574,14576],{"id":14575},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,14578,14579,14580,14583,14584,2628,14587,1682,14605,2628,14608,14626,14627,14645,14646,14664,14665,14681,14682,1682,14697,14712,14713,1664],{},"Řešením ",[38,14581,14582],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,14585,14586],{},"rovnovážný důchod",[883,14588,14590],{"className":14589},[886],[888,14591,14592],{"xmlns":890},[892,14593,14594,14602],{},[895,14595,14596],{},[2057,14597,14598,14600],{},[898,14599,9837],{},[898,14601,1846],{},[902,14603,14604],{"encoding":904},"Y^E",[38,14606,14607],{},"rovnovážnou úrokovou míru",[883,14609,14611],{"className":14610},[886],[888,14612,14613],{"xmlns":890},[892,14614,14615,14623],{},[895,14616,14617],{},[2057,14618,14619,14621],{},[898,14620,12742],{},[898,14622,1846],{},[902,14624,14625],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,14628,14630],{"className":14629},[886],[888,14631,14632],{"xmlns":890},[892,14633,14634,14642],{},[895,14635,14636],{},[2057,14637,14638,14640],{},[898,14639,12885],{},[898,14641,1846],{},[902,14643,14644],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,14647,14649],{"className":14648},[886],[888,14650,14651],{"xmlns":890},[892,14652,14653,14661],{},[895,14654,14655],{},[2057,14656,14657,14659],{},[898,14658,1721],{},[898,14660,1846],{},[902,14662,14663],{"encoding":904},"C^E",". Graficky jde o ",[38,14666,14667,14668],{},"průsečík ",[883,14669,14671],{"className":14670},[886],[888,14672,14673],{"xmlns":890},[892,14674,14675,14679],{},[895,14676,14677],{},[898,14678,1846],{},[902,14680,1846],{"encoding":904}," křivek ",[883,14683,14685],{"className":14684},[886],[888,14686,14687],{"xmlns":890},[892,14688,14689,14695],{},[895,14690,14691,14693],{},[898,14692,12885],{},[898,14694,2111],{},[902,14696,12752],{"encoding":904},[883,14698,14700],{"className":14699},[886],[888,14701,14702],{"xmlns":890},[892,14703,14704,14710],{},[895,14705,14706,14708],{},[898,14707,1911],{},[898,14709,1728],{},[902,14711,12759],{"encoding":904}," v rovině ",[883,14714,14716],{"className":14715},[886],[888,14717,14718],{"xmlns":890},[892,14719,14720,14732],{},[895,14721,14722,14724,14726,14728,14730],{},[1723,14723,1908],{"stretchy":1907},[898,14725,12742],{},[1723,14727,2031],{"separator":2030},[898,14729,9837],{},[1723,14731,1914],{"stretchy":1907},[902,14733,13638],{"encoding":904},[724,14735,14736],{},[614,14737,14738,14739,14760,14761,14776,14777,14792,14793,14806,14807,14824,14825,12829,14838,14824,14855,14868,14869,14882],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,14740,14742],{"className":14741},[886],[888,14743,14744],{"xmlns":890},[892,14745,14746,14758],{},[895,14747,14748,14750,14752,14754,14756],{},[1723,14749,1908],{"stretchy":1907},[898,14751,12742],{},[1723,14753,2031],{"separator":2030},[898,14755,9837],{},[1723,14757,1914],{"stretchy":1907},[902,14759,13638],{"encoding":904},". Rostoucí přímka ",[883,14762,14764],{"className":14763},[886],[888,14765,14766],{"xmlns":890},[892,14767,14768,14774],{},[895,14769,14770,14772],{},[898,14771,1911],{},[898,14773,1728],{},[902,14775,12759],{"encoding":904}," a klesající přímka ",[883,14778,14780],{"className":14779},[886],[888,14781,14782],{"xmlns":890},[892,14783,14784,14790],{},[895,14785,14786,14788],{},[898,14787,12885],{},[898,14789,2111],{},[902,14791,12752],{"encoding":904}," se protínají v bodě ",[883,14794,14796],{"className":14795},[886],[888,14797,14798],{"xmlns":890},[892,14799,14800,14804],{},[895,14801,14802],{},[898,14803,1846],{},[902,14805,1846],{"encoding":904}," se souřadnicemi ",[883,14808,14810],{"className":14809},[886],[888,14811,14812],{"xmlns":890},[892,14813,14814,14822],{},[895,14815,14816],{},[2057,14817,14818,14820],{},[898,14819,12742],{},[898,14821,1846],{},[902,14823,14625],{"encoding":904}," (na ose ",[883,14826,14828],{"className":14827},[886],[888,14829,14830],{"xmlns":890},[892,14831,14832,14836],{},[895,14833,14834],{},[898,14835,12742],{},[902,14837,12742],{"encoding":904},[883,14839,14841],{"className":14840},[886],[888,14842,14843],{"xmlns":890},[892,14844,14845,14853],{},[895,14846,14847],{},[2057,14848,14849,14851],{},[898,14850,9837],{},[898,14852,1846],{},[902,14854,14604],{"encoding":904},[883,14856,14858],{"className":14857},[886],[888,14859,14860],{"xmlns":890},[892,14861,14862,14866],{},[895,14863,14864],{},[898,14865,9837],{},[902,14867,9837],{"encoding":904},"); tečkované čáry z ",[883,14870,14872],{"className":14871},[886],[888,14873,14874],{"xmlns":890},[892,14875,14876,14880],{},[895,14877,14878],{},[898,14879,1846],{},[902,14881,1846],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[4584,14884,14885,14890],{},[724,14886,14887,14889],{},[883,14888,5283],{}," Postup — jak najít IS-LM rovnováhu",[152,14891,14892,14968,15036,15094,15167],{},[123,14893,14894,14897,14898,1682,14918,14938,14939,1682,14952,14965,14966,1664],{},[38,14895,14896],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,14899,14901],{"className":14900},[886],[888,14902,14903],{"xmlns":890},[892,14904,14905,14915],{},[895,14906,14907,14909,14911,14913],{},[898,14908,1721],{},[1723,14910,1908],{"stretchy":1907},[898,14912,9837],{},[1723,14914,1914],{"stretchy":1907},[902,14916,14917],{"encoding":904},"C(Y)",[883,14919,14921],{"className":14920},[886],[888,14922,14923],{"xmlns":890},[892,14924,14925,14935],{},[895,14926,14927,14929,14931,14933],{},[898,14928,12885],{},[1723,14930,1908],{"stretchy":1907},[898,14932,12742],{},[1723,14934,1914],{"stretchy":1907},[902,14936,14937],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,14940,14942],{"className":14941},[886],[888,14943,14944],{"xmlns":890},[892,14945,14946,14950],{},[895,14947,14948],{},[898,14949,9837],{},[902,14951,9837],{"encoding":904},[883,14953,14955],{"className":14954},[886],[888,14956,14957],{"xmlns":890},[892,14958,14959,14963],{},[895,14960,14961],{},[898,14962,12742],{},[902,14964,12742],{"encoding":904}," — dostaneš rovnici ",[38,14967,12752],{},[123,14969,14970,14973,14974,1682,14991,15008,15009,14965,15034,1664],{},[38,14971,14972],{},"Z trhu peněz (7.15)"," dosaď ",[883,14975,14977],{"className":14976},[886],[888,14978,14979],{"xmlns":890},[892,14980,14981,14989],{},[895,14982,14983],{},[1931,14984,14985,14987],{},[898,14986,1911],{},[1864,14988,1866],{},[902,14990,13913],{"encoding":904},[883,14992,14994],{"className":14993},[886],[888,14995,14996],{"xmlns":890},[892,14997,14998,15006],{},[895,14999,15000],{},[1931,15001,15002,15004],{},[898,15003,1911],{},[1864,15005,2331],{},[902,15007,13985],{"encoding":904}," a vztah ",[883,15010,15012],{"className":15011},[886],[888,15013,15014],{"xmlns":890},[892,15015,15016,15032],{},[895,15017,15018,15024,15026],{},[2057,15019,15020,15022],{},[898,15021,1728],{},[898,15023,4897],{},[1723,15025,1725],{},[2057,15027,15028,15030],{},[898,15029,1728],{},[1723,15031,5066],{},[902,15033,14181],{"encoding":904},[38,15035,12759],{},[123,15037,15038,15041,15042,1682,15055,15068,15069,15093],{},[38,15039,15040],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,15043,15045],{"className":15044},[886],[888,15046,15047],{"xmlns":890},[892,15048,15049,15053],{},[895,15050,15051],{},[898,15052,9837],{},[902,15054,9837],{"encoding":904},[883,15056,15058],{"className":15057},[886],[888,15059,15060],{"xmlns":890},[892,15061,15062,15066],{},[895,15063,15064],{},[898,15065,12742],{},[902,15067,12742],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,15070,15072],{"className":15071},[886],[888,15073,15074],{"xmlns":890},[892,15075,15076,15090],{},[895,15077,15078,15080,15082,15084,15086,15088],{},[898,15079,9837],{},[1723,15081,1725],{},[898,15083,2745],{},[1723,15085,1908],{"stretchy":1907},[898,15087,12742],{},[1723,15089,1914],{"stretchy":1907},[902,15091,15092],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,15095,15096,2628,15099,1682,15133,1664],{},[38,15097,15098],{},"Zpětně dopočítej",[883,15100,15102],{"className":15101},[886],[888,15103,15104],{"xmlns":890},[892,15105,15106,15130],{},[895,15107,15108,15114,15116,15118,15120,15126,15128],{},[2057,15109,15110,15112],{},[898,15111,1721],{},[898,15113,1846],{},[1723,15115,1725],{},[898,15117,207],{},[3018,15119,3707],{},[2057,15121,15122,15124],{},[898,15123,9837],{},[898,15125,1846],{},[1723,15127,2087],{},[898,15129,2069],{},[902,15131,15132],{"encoding":904},"C^E = a\\,Y^E + b",[883,15134,15136],{"className":15135},[886],[888,15137,15138],{"xmlns":890},[892,15139,15140,15164],{},[895,15141,15142,15148,15150,15152,15154,15160,15162],{},[2057,15143,15144,15146],{},[898,15145,12885],{},[898,15147,1846],{},[1723,15149,1725],{},[898,15151,2878],{},[3018,15153,3707],{},[2057,15155,15156,15158],{},[898,15157,12742],{},[898,15159,1846],{},[1723,15161,2087],{},[898,15163,2930],{},[902,15165,15166],{"encoding":904},"I^E = c\\,r^E + d",[123,15168,15169,15172,15173,15207,15208,15262],{},[38,15170,15171],{},"Ověř:"," musí platit ",[883,15174,15176],{"className":15175},[886],[888,15177,15178],{"xmlns":890},[892,15179,15180,15204],{},[895,15181,15182,15188,15190,15196,15198],{},[2057,15183,15184,15186],{},[898,15185,9837],{},[898,15187,1846],{},[1723,15189,1725],{},[2057,15191,15192,15194],{},[898,15193,1721],{},[898,15195,1846],{},[1723,15197,2087],{},[2057,15199,15200,15202],{},[898,15201,12885],{},[898,15203,1846],{},[902,15205,15206],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,15209,15211],{"className":15210},[886],[888,15212,15213],{"xmlns":890},[892,15214,15215,15259],{},[895,15216,15217,15223,15225,15231,15237,15239,15245,15251,15253],{},[2057,15218,15219,15221],{},[898,15220,1728],{},[1723,15222,5066],{},[1723,15224,1725],{},[1931,15226,15227,15229],{},[898,15228,13938],{},[1864,15230,1866],{},[2057,15232,15233,15235],{},[898,15234,9837],{},[898,15236,1846],{},[1723,15238,2087],{},[1931,15240,15241,15243],{},[898,15242,13938],{},[1864,15244,2331],{},[2057,15246,15247,15249],{},[898,15248,12742],{},[898,15250,1846],{},[1723,15252,2087],{},[1931,15254,15255,15257],{},[898,15256,13938],{},[1864,15258,2909],{},[902,15260,15261],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,15264,15266],{"id":15265},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,15268,15269],{},"Pro trh zboží jsou dány:",[120,15271,15272,15300],{},[123,15273,15274,15275,2031],{},"spotřeba ",[883,15276,15278],{"className":15277},[886],[888,15279,15280],{"xmlns":890},[892,15281,15282,15297],{},[895,15283,15284,15286,15288,15291,15293,15295],{},[898,15285,1721],{},[1723,15287,1725],{},[1864,15289,15290],{},"0,8",[898,15292,9837],{},[1723,15294,2087],{},[1864,15296,3810],{},[902,15298,15299],{"encoding":904},"C = 0{,}8Y + 100",[123,15301,15302,15303,1664],{},"investice ",[883,15304,15306],{"className":15305},[886],[888,15307,15308],{"xmlns":890},[892,15309,15310,15326],{},[895,15311,15312,15314,15316,15318,15320,15322,15324],{},[898,15313,12885],{},[1723,15315,1725],{},[1723,15317,1759],{},[1864,15319,9744],{},[898,15321,12742],{},[1723,15323,2087],{},[1864,15325,3506],{},[902,15327,15328],{"encoding":904},"I = -20r + 1000",[724,15330,15331],{},"Pro trh peněz:",[120,15333,15334,15360,15392],{},[123,15335,15336,2031],{},[883,15337,15339],{"className":15338},[886],[888,15340,15341],{"xmlns":890},[892,15342,15343,15357],{},[895,15344,15345,15351,15353,15355],{},[1931,15346,15347,15349],{},[898,15348,1911],{},[1864,15350,1866],{},[1723,15352,1725],{},[1864,15354,3517],{},[898,15356,9837],{},[902,15358,15359],{"encoding":904},"L_1 = 0{,}1Y",[123,15361,15362,2031],{},[883,15363,15365],{"className":15364},[886],[888,15366,15367],{"xmlns":890},[892,15368,15369,15389],{},[895,15370,15371,15377,15379,15381,15383,15385,15387],{},[1931,15372,15373,15375],{},[898,15374,1911],{},[1864,15376,2331],{},[1723,15378,1725],{},[1723,15380,1759],{},[1864,15382,5714],{},[898,15384,12742],{},[1723,15386,2087],{},[1864,15388,9314],{},[902,15390,15391],{"encoding":904},"L_2 = -25r + 2000",[123,15393,15394,15395,1664],{},"nabídka peněz ",[883,15396,15398],{"className":15397},[886],[888,15399,15400],{"xmlns":890},[892,15401,15402,15415],{},[895,15403,15404,15410,15412],{},[2057,15405,15406,15408],{},[898,15407,1728],{},[1723,15409,5066],{},[1723,15411,1725],{},[1864,15413,15414],{},"2375",[902,15416,15417],{"encoding":904},"M^* = 2375",[724,15419,15420,15423,15424,3430],{},[38,15421,15422],{},"Funkce IS"," — dosazením do (7.13) ",[883,15425,15427],{"className":15426},[886],[888,15428,15429],{"xmlns":890},[892,15430,15431,15443],{},[895,15432,15433,15435,15437,15439,15441],{},[898,15434,9837],{},[1723,15436,1725],{},[898,15438,1721],{},[1723,15440,2087],{},[898,15442,12885],{},[902,15444,15445],{"encoding":904},"Y = C + I",[724,15447,15448],{},[883,15449,15451],{"className":15450},[886],[888,15452,15453],{"xmlns":890},[892,15454,15455,15481],{},[895,15456,15457,15459,15461,15463,15465,15467,15469,15471,15473,15475,15477,15479],{},[898,15458,9837],{},[1723,15460,1725],{},[1864,15462,15290],{},[898,15464,9837],{},[1723,15466,2087],{},[1864,15468,3810],{},[1723,15470,1759],{},[1864,15472,9744],{},[898,15474,12742],{},[1723,15476,2087],{},[1864,15478,3506],{},[1723,15480,2031],{"separator":2030},[902,15482,15483],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,15485,15486],{},"tj.",[724,15488,15489],{},[883,15490,15492],{"className":15491},[886],[888,15493,15494],{"xmlns":890},[892,15495,15496,15521],{},[895,15497,15498,15500,15502,15504,15506,15508,15510,15513,15515,15517,15519],{},[1864,15499,3561],{},[898,15501,9837],{},[1723,15503,2087],{},[1864,15505,9744],{},[898,15507,12742],{},[1723,15509,1725],{},[1864,15511,15512],{},"1100.",[6588,15514],{"width":6590},[1723,15516,1908],{"stretchy":1907},[3018,15518,12752],{},[1723,15520,1914],{"stretchy":1907},[902,15522,15523],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,15525,15526,15529,15530,3430],{},[38,15527,15528],{},"Funkce LM"," — dosazením do (7.15) ",[883,15531,15533],{"className":15532},[886],[888,15534,15535],{"xmlns":890},[892,15536,15537,15561],{},[895,15538,15539,15545,15547,15553,15555],{},[2057,15540,15541,15543],{},[898,15542,1728],{},[1723,15544,5066],{},[1723,15546,1725],{},[1931,15548,15549,15551],{},[898,15550,1911],{},[1864,15552,1866],{},[1723,15554,2087],{},[1931,15556,15557,15559],{},[898,15558,1911],{},[1864,15560,2331],{},[902,15562,15563],{"encoding":904},"M^* = L_1 + L_2",[724,15565,15566],{},[883,15567,15569],{"className":15568},[886],[888,15570,15571],{"xmlns":890},[892,15572,15573,15595],{},[895,15574,15575,15577,15579,15581,15583,15585,15587,15589,15591,15593],{},[1864,15576,15414],{},[1723,15578,1725],{},[1864,15580,3517],{},[898,15582,9837],{},[1723,15584,1759],{},[1864,15586,5714],{},[898,15588,12742],{},[1723,15590,2087],{},[1864,15592,9314],{},[1723,15594,2031],{"separator":2030},[902,15596,15597],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,15599,15486],{},[724,15601,15602],{},[883,15603,15605],{"className":15604},[886],[888,15606,15607],{"xmlns":890},[892,15608,15609,15634],{},[895,15610,15611,15613,15615,15617,15619,15621,15623,15626,15628,15630,15632],{},[1864,15612,3517],{},[898,15614,9837],{},[1723,15616,1759],{},[1864,15618,5714],{},[898,15620,12742],{},[1723,15622,1725],{},[1864,15624,15625],{},"375.",[6588,15627],{"width":6590},[1723,15629,1908],{"stretchy":1907},[3018,15631,12759],{},[1723,15633,1914],{"stretchy":1907},[902,15635,15636],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,15638,15639,15642,15643,15668],{},[38,15640,15641],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,15644,15646],{"className":15645},[886],[888,15647,15648],{"xmlns":890},[892,15649,15650,15665],{},[895,15651,15652,15654,15656,15659,15661,15663],{},[898,15653,9837],{},[1723,15655,1725],{},[1864,15657,15658],{},"5500",[1723,15660,1759],{},[1864,15662,3810],{},[898,15664,12742],{},[902,15666,15667],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,15670,15671],{},[883,15672,15674],{"className":15673},[886],[888,15675,15676],{"xmlns":890},[892,15677,15678,15764],{},[895,15679,15680,15682,15684,15686,15688,15690,15692,15694,15696,15698,15700,15702,15705,15707,15710,15712,15715,15717,15719,15721,15723,15725,15727,15729,15731,15733,15735,15737,15740,15742,15744,15747,15749,15751,15753,15759,15761],{},[1864,15681,3517],{},[1723,15683,1908],{"stretchy":1907},[1864,15685,15658],{},[1723,15687,1759],{},[1864,15689,3810],{},[898,15691,12742],{},[1723,15693,1914],{"stretchy":1907},[1723,15695,1759],{},[1864,15697,5714],{},[898,15699,12742],{},[1723,15701,1725],{},[1864,15703,15704],{},"375",[3018,15706,4699],{},[1723,15708,15709],{},"⟹",[3018,15711,4699],{},[1864,15713,15714],{},"550",[1723,15716,1759],{},[1864,15718,3585],{},[898,15720,12742],{},[1723,15722,1759],{},[1864,15724,5714],{},[898,15726,12742],{},[1723,15728,1725],{},[1864,15730,15704],{},[3018,15732,4699],{},[1723,15734,15709],{},[3018,15736,4699],{},[1864,15738,15739],{},"35",[898,15741,12742],{},[1723,15743,1725],{},[1864,15745,15746],{},"175",[3018,15748,4699],{},[1723,15750,15709],{},[3018,15752,4699],{},[2057,15754,15755,15757],{},[898,15756,12742],{},[898,15758,1846],{},[1723,15760,1725],{},[1864,15762,15763],{},"5.",[902,15765,15766],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,15768,15769],{},[38,15770,15771],{},"Zpětné dosazení:",[120,15773,15774,15820,15857],{},[123,15775,15776,2031],{},[883,15777,15779],{"className":15778},[886],[888,15780,15781],{"xmlns":890},[892,15782,15783,15817],{},[895,15784,15785,15791,15793,15795,15797,15799,15801,15803,15805,15807,15809,15812,15814],{},[2057,15786,15787,15789],{},[898,15788,9837],{},[898,15790,1846],{},[1723,15792,1725],{},[1864,15794,15658],{},[1723,15796,1759],{},[1864,15798,3810],{},[1723,15800,3897],{},[1864,15802,2962],{},[1723,15804,1725],{},[1864,15806,15658],{},[1723,15808,1759],{},[1864,15810,15811],{},"500",[1723,15813,1725],{},[1864,15815,15816],{},"5000",[902,15818,15819],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,15821,15822,2031],{},[883,15823,15825],{"className":15824},[886],[888,15826,15827],{"xmlns":890},[892,15828,15829,15854],{},[895,15830,15831,15837,15839,15841,15843,15845,15847,15849,15851],{},[2057,15832,15833,15835],{},[898,15834,1721],{},[898,15836,1846],{},[1723,15838,1725],{},[1864,15840,15290],{},[1723,15842,3897],{},[1864,15844,15816],{},[1723,15846,2087],{},[1864,15848,3810],{},[1723,15850,1725],{},[1864,15852,15853],{},"4100",[902,15855,15856],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,15858,15859,1664],{},[883,15860,15862],{"className":15861},[886],[888,15863,15864],{"xmlns":890},[892,15865,15866,15893],{},[895,15867,15868,15874,15876,15878,15880,15882,15884,15886,15888,15890],{},[2057,15869,15870,15872],{},[898,15871,12885],{},[898,15873,1846],{},[1723,15875,1725],{},[1723,15877,1759],{},[1864,15879,9744],{},[1723,15881,3897],{},[1864,15883,2962],{},[1723,15885,2087],{},[1864,15887,3506],{},[1723,15889,1725],{},[1864,15891,15892],{},"900",[902,15894,15895],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,15897,15898,2628,15901,15947],{},[38,15899,15900],{},"Ověření:",[883,15902,15904],{"className":15903},[886],[888,15905,15906],{"xmlns":890},[892,15907,15908,15944],{},[895,15909,15910,15916,15918,15924,15926,15928,15930,15932,15934,15936,15938],{},[2057,15911,15912,15914],{},[898,15913,1721],{},[898,15915,1846],{},[1723,15917,2087],{},[2057,15919,15920,15922],{},[898,15921,12885],{},[898,15923,1846],{},[1723,15925,1725],{},[1864,15927,15853],{},[1723,15929,2087],{},[1864,15931,15892],{},[1723,15933,1725],{},[1864,15935,15816],{},[1723,15937,1725],{},[2057,15939,15940,15942],{},[898,15941,9837],{},[898,15943,1846],{},[902,15945,15946],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,15949,15950],{},[883,15951,15953],{"className":15952},[886],[888,15954,15955],{"xmlns":890},[892,15956,15957,16027],{},[895,15958,15959],{},[13533,15960,15961],{"notation":13535},[3055,15962,15963],{"scriptlevel":2256,"displaystyle":1907},[3055,15964,15965],{"scriptlevel":2256,"displaystyle":1907},[3055,15966,15967],{"scriptlevel":2256,"displaystyle":2030},[895,15968,15969,15971,15977,15979,15981,15983,15986,15992,15994,15996,15998,16000,16006,16008,16010,16012,16014,16020,16022,16025],{},[3018,15970,3707],{},[2057,15972,15973,15975],{},[898,15974,9837],{},[898,15976,1846],{},[1723,15978,1725],{},[1864,15980,15816],{},[1723,15982,2031],{"separator":2030},[6588,15984],{"width":15985},"1em",[2057,15987,15988,15990],{},[898,15989,12742],{},[898,15991,1846],{},[1723,15993,1725],{},[1864,15995,2962],{},[1723,15997,2031],{"separator":2030},[6588,15999],{"width":15985},[2057,16001,16002,16004],{},[898,16003,1721],{},[898,16005,1846],{},[1723,16007,1725],{},[1864,16009,15853],{},[1723,16011,2031],{"separator":2030},[6588,16013],{"width":15985},[2057,16015,16016,16018],{},[898,16017,12885],{},[898,16019,1846],{},[1723,16021,1725],{},[1864,16023,16024],{},"900.",[3018,16026,3707],{},[902,16028,16029],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,16031,16032],{},[614,16033,16034,16035,16048,16049,16062,16063,16078,16079,16092,16093,16108,16109,16122,16123,16136,16137,1664],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,16036,16038],{"className":16037},[886],[888,16039,16040],{"xmlns":890},[892,16041,16042,16046],{},[895,16043,16044],{},[898,16045,9837],{},[902,16047,9837],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,16050,16052],{"className":16051},[886],[888,16053,16054],{"xmlns":890},[892,16055,16056,16060],{},[895,16057,16058],{},[898,16059,12742],{},[902,16061,12742],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,16064,16066],{"className":16065},[886],[888,16067,16068],{"xmlns":890},[892,16069,16070,16076],{},[895,16071,16072,16074],{},[898,16073,1911],{},[898,16075,1728],{},[902,16077,12759],{"encoding":904}," stoupá z oblasti nízkých ",[883,16080,16082],{"className":16081},[886],[888,16083,16084],{"xmlns":890},[892,16085,16086,16090],{},[895,16087,16088],{},[898,16089,12742],{},[902,16091,12742],{"encoding":904},", přímka ",[883,16094,16096],{"className":16095},[886],[888,16097,16098],{"xmlns":890},[892,16099,16100,16106],{},[895,16101,16102,16104],{},[898,16103,12885],{},[898,16105,2111],{},[902,16107,12752],{"encoding":904}," klesá a protíná osu ",[883,16110,16112],{"className":16111},[886],[888,16113,16114],{"xmlns":890},[892,16115,16116,16120],{},[895,16117,16118],{},[898,16119,12742],{},[902,16121,12742],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,16124,16126],{"className":16125},[886],[888,16127,16128],{"xmlns":890},[892,16129,16130,16134],{},[895,16131,16132],{},[898,16133,1846],{},[902,16135,1846],{"encoding":904}," leží v bodě ",[883,16138,16140],{"className":16139},[886],[888,16141,16142],{"xmlns":890},[892,16143,16144,16166],{},[895,16145,16146,16148,16150,16152,16154,16156,16158,16160,16162,16164],{},[1723,16147,3212],{"stretchy":1907},[898,16149,12742],{},[1723,16151,1725],{},[1864,16153,2962],{},[1723,16155,2031],{"separator":2030},[3018,16157,3020],{},[898,16159,9837],{},[1723,16161,1725],{},[1864,16163,15816],{},[1723,16165,3227],{"stretchy":1907},[902,16167,16168],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,16170,16172],{"id":16171},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,16174,16175,16178,16179,16192,16193,7725,16206,16209,16210,16228,16229,16246,16247,16264,16265,16278,16279,16292],{},[38,16176,16177],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,16180,16182],{"className":16181},[886],[888,16183,16184],{"xmlns":890},[892,16185,16186,16190],{},[895,16187,16188],{},[898,16189,12813],{},[902,16191,12813],{"encoding":904}," nebo snížení daní ",[883,16194,16196],{"className":16195},[886],[888,16197,16198],{"xmlns":890},[892,16199,16200,16204],{},[895,16201,16202],{},[898,16203,1754],{},[902,16205,1754],{"encoding":904},[38,16207,16208],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,16211,16213],{"className":16212},[886],[888,16214,16215],{"xmlns":890},[892,16216,16217,16225],{},[895,16218,16219],{},[2057,16220,16221,16223],{},[898,16222,1846],{},[1723,16224,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,16226,16227],{"encoding":904},"E'"," má vyšší ",[883,16230,16232],{"className":16231},[886],[888,16233,16234],{"xmlns":890},[892,16235,16236,16244],{},[895,16237,16238],{},[2057,16239,16240,16242],{},[898,16241,9837],{},[898,16243,1846],{},[902,16245,14604],{"encoding":904}," i vyšší ",[883,16248,16250],{"className":16249},[886],[888,16251,16252],{"xmlns":890},[892,16253,16254,16262],{},[895,16255,16256],{},[2057,16257,16258,16260],{},[898,16259,12742],{},[898,16261,1846],{},[902,16263,14625],{"encoding":904}," (vyšší ",[883,16266,16268],{"className":16267},[886],[888,16269,16270],{"xmlns":890},[892,16271,16272,16276],{},[895,16273,16274],{},[898,16275,9837],{},[902,16277,9837],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,16280,16282],{"className":16281},[886],[888,16283,16284],{"xmlns":890},[892,16285,16286,16290],{},[895,16287,16288],{},[898,16289,12742],{},[902,16291,12742],{"encoding":904}," nahoru).",[724,16294,16295],{},[3285,16296],{"alt":16297,"className":16298,"src":16299},"imek-posun-is-lm-politiky",[210,3289],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,16301,16302,16305,16306,16323,16324,16327,16328,16345,16346,16363,16364,16377,16378,16397,16398,4634],{},[38,16303,16304],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,16307,16309],{"className":16308},[886],[888,16310,16311],{"xmlns":890},[892,16312,16313,16321],{},[895,16314,16315],{},[2057,16316,16317,16319],{},[898,16318,1728],{},[1723,16320,5066],{},[902,16322,12851],{"encoding":904}," národní bankou — ",[38,16325,16326],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,16329,16331],{"className":16330},[886],[888,16332,16333],{"xmlns":890},[892,16334,16335,16343],{},[895,16336,16337],{},[2057,16338,16339,16341],{},[898,16340,12742],{},[898,16342,1846],{},[902,16344,14625],{"encoding":904}," a vyšší ",[883,16347,16349],{"className":16348},[886],[888,16350,16351],{"xmlns":890},[892,16352,16353,16361],{},[895,16354,16355],{},[2057,16356,16357,16359],{},[898,16358,9837],{},[898,16360,1846],{},[902,16362,14604],{"encoding":904}," (nižší ",[883,16365,16367],{"className":16366},[886],[888,16368,16369],{"xmlns":890},[892,16370,16371,16375],{},[895,16372,16373],{},[898,16374,12742],{},[902,16376,12742],{"encoding":904}," povzbuzuje investice ",[883,16379,16381],{"className":16380},[886],[888,16382,16383],{"xmlns":890},[892,16384,16385,16395],{},[895,16386,16387,16389,16391,16393],{},[898,16388,12885],{},[1723,16390,1908],{"stretchy":1907},[898,16392,12742],{},[1723,16394,1914],{"stretchy":1907},[902,16396,14937],{"encoding":904},", ty zvedají ",[883,16399,16401],{"className":16400},[886],[888,16402,16403],{"xmlns":890},[892,16404,16405,16409],{},[895,16406,16407],{},[898,16408,9837],{},[902,16410,9837],{"encoding":904},[724,16412,16413,16414,16417],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,16415,16416],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,16419,16421],{"id":16420},"klíčové-pojmy","Klíčové pojmy",[120,16423,16424,16497,16543,16625,16675,16742,16799,16840,16873],{},[123,16425,16426,7725,16459,1343,16476,16493,16494,16496],{},[38,16427,16428,16429],{},"Funkce investic ",[883,16430,16432],{"className":16431},[886],[888,16433,16434],{"xmlns":890},[892,16435,16436,16456],{},[895,16437,16438,16440,16442,16444,16446,16448,16450,16452,16454],{},[898,16439,12885],{},[1723,16441,1908],{"stretchy":1907},[898,16443,12742],{},[1723,16445,1914],{"stretchy":1907},[1723,16447,1725],{},[898,16449,2878],{},[898,16451,12742],{},[1723,16453,2087],{},[898,16455,2930],{},[902,16457,16458],{"encoding":904},"I(r) = cr + d",[883,16460,16462],{"className":16461},[886],[888,16463,16464],{"xmlns":890},[892,16465,16466,16474],{},[895,16467,16468,16470,16472],{},[898,16469,2878],{},[1723,16471,2287],{},[1864,16473,2256],{},[902,16475,13216],{"encoding":904},[883,16477,16479],{"className":16478},[886],[888,16480,16481],{"xmlns":890},[892,16482,16483,16491],{},[895,16484,16485,16487,16489],{},[898,16486,2930],{},[1723,16488,2253],{},[1864,16490,2256],{},[902,16492,13195],{"encoding":904},"; ",[38,16495,13220],{}," funkce úrokové míry.",[123,16498,16499,16502,16503,16524,16525,16542],{},[38,16500,16501],{},"Trh zboží"," — rovnováha ",[883,16504,16506],{"className":16505},[886],[888,16507,16508],{"xmlns":890},[892,16509,16510,16522],{},[895,16511,16512,16514,16516,16518,16520],{},[898,16513,9837],{},[1723,16515,1725],{},[898,16517,1721],{},[1723,16519,2087],{},[898,16521,12885],{},[902,16523,15445],{"encoding":904},", ekvivalentně ",[883,16526,16528],{"className":16527},[886],[888,16529,16530],{"xmlns":890},[892,16531,16532,16540],{},[895,16533,16534,16536,16538],{},[898,16535,12885],{},[1723,16537,1725],{},[898,16539,2111],{},[902,16541,13413],{"encoding":904}," (investice = úspory).",[123,16544,16545,1981,16548,16550,16551,16601,16602,13616,16604,1664],{},[38,16546,16547],{},"Křivka IS",[614,16549,12755],{},") — ",[883,16552,16554],{"className":16553},[886],[888,16555,16556],{"xmlns":890},[892,16557,16558,16598],{},[895,16559,16560,16562,16564,16576,16578,16580],{},[898,16561,9837],{},[1723,16563,1725],{},[3058,16565,16566,16568],{},[898,16567,2878],{},[895,16569,16570,16572,16574],{},[1864,16571,1866],{},[1723,16573,1759],{},[898,16575,207],{},[898,16577,12742],{},[1723,16579,2087],{},[3058,16581,16582,16590],{},[895,16583,16584,16586,16588],{},[898,16585,2069],{},[1723,16587,2087],{},[898,16589,2930],{},[895,16591,16592,16594,16596],{},[1864,16593,1866],{},[1723,16595,1759],{},[898,16597,207],{},[902,16599,16600],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,16603,13220],{},[883,16605,16607],{"className":16606},[886],[888,16608,16609],{"xmlns":890},[892,16610,16611,16623],{},[895,16612,16613,16615,16617,16619,16621],{},[1723,16614,1908],{"stretchy":1907},[898,16616,12742],{},[1723,16618,2031],{"separator":2030},[898,16620,9837],{},[1723,16622,1914],{"stretchy":1907},[902,16624,13638],{"encoding":904},[123,16626,16627,16502,16630,16656,16657,1664],{},[38,16628,16629],{},"Trh peněz",[883,16631,16633],{"className":16632},[886],[888,16634,16635],{"xmlns":890},[892,16636,16637,16653],{},[895,16638,16639,16645,16647],{},[2057,16640,16641,16643],{},[898,16642,1728],{},[898,16644,4897],{},[1723,16646,1725],{},[2057,16648,16649,16651],{},[898,16650,1728],{},[898,16652,2111],{},[902,16654,16655],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,16658,16660],{"className":16659},[886],[888,16661,16662],{"xmlns":890},[892,16663,16664,16672],{},[895,16665,16666],{},[2057,16667,16668,16670],{},[898,16669,1728],{},[1723,16671,5066],{},[902,16673,16674],{"encoding":904},"M^* ",[123,16676,16677,7725,16680,1664],{},[38,16678,16679],{},"Transakční, opatrnostní, spekulační poptávka",[883,16681,16683],{"className":16682},[886],[888,16684,16685],{"xmlns":890},[892,16686,16687,16739],{},[895,16688,16689,16695,16697,16703,16705,16711,16713,16719,16721,16723,16729,16731,16733],{},[2057,16690,16691,16693],{},[898,16692,1728],{},[898,16694,4897],{},[1723,16696,1725],{},[1931,16698,16699,16701],{},[898,16700,1911],{},[1864,16702,1866],{},[1723,16704,2087],{},[1931,16706,16707,16709],{},[898,16708,1911],{},[1864,16710,2331],{},[1723,16712,1725],{},[1931,16714,16715,16717],{},[898,16716,13938],{},[1864,16718,1866],{},[898,16720,9837],{},[1723,16722,2087],{},[1931,16724,16725,16727],{},[898,16726,13938],{},[1864,16728,2331],{},[898,16730,12742],{},[1723,16732,2087],{},[1931,16734,16735,16737],{},[898,16736,13938],{},[1864,16738,2909],{},[902,16740,16741],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,16743,16744,1981,16747,16550,16749,16795,16796,16798],{},[38,16745,16746],{},"Křivka LM",[614,16748,12762],{},[883,16750,16752],{"className":16751},[886],[888,16753,16754],{"xmlns":890},[892,16755,16756,16792],{},[895,16757,16758,16764,16766,16772,16774,16776,16782,16784,16786],{},[2057,16759,16760,16762],{},[898,16761,1728],{},[1723,16763,5066],{},[1723,16765,1725],{},[1931,16767,16768,16770],{},[898,16769,13938],{},[1864,16771,1866],{},[898,16773,9837],{},[1723,16775,2087],{},[1931,16777,16778,16780],{},[898,16779,13938],{},[1864,16781,2331],{},[898,16783,12742],{},[1723,16785,2087],{},[1931,16787,16788,16790],{},[898,16789,13938],{},[1864,16791,2909],{},[902,16793,16794],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,16797,14358],{}," přímka.",[123,16800,16801,16804,16805,16839],{},[38,16802,16803],{},"Simultánní rovnováha"," — průsečík ",[883,16806,16808],{"className":16807},[886],[888,16809,16810],{"xmlns":890},[892,16811,16812,16836],{},[895,16813,16814,16816,16818,16820,16826,16828,16834],{},[898,16815,1846],{},[1723,16817,1725],{},[1723,16819,1908],{"stretchy":1907},[2057,16821,16822,16824],{},[898,16823,12742],{},[898,16825,1846],{},[1723,16827,2031],{"separator":2030},[2057,16829,16830,16832],{},[898,16831,9837],{},[898,16833,1846],{},[1723,16835,1914],{"stretchy":1907},[902,16837,16838],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,16841,16842,16845,16846,1343,16859,16872],{},[38,16843,16844],{},"Fiskální politika"," — nástroje ",[883,16847,16849],{"className":16848},[886],[888,16850,16851],{"xmlns":890},[892,16852,16853,16857],{},[895,16854,16855],{},[898,16856,12813],{},[902,16858,12813],{"encoding":904},[883,16860,16862],{"className":16861},[886],[888,16863,16864],{"xmlns":890},[892,16865,16866,16870],{},[895,16867,16868],{},[898,16869,1754],{},[902,16871,1754],{"encoding":904}," posouvající křivku IS.",[123,16874,16875,16878,16879,16896],{},[38,16876,16877],{},"Monetární politika"," — nástroj ",[883,16880,16882],{"className":16881},[886],[888,16883,16884],{"xmlns":890},[892,16885,16886,16894],{},[895,16887,16888],{},[2057,16889,16890,16892],{},[898,16891,1728],{},[1723,16893,5066],{},[902,16895,12851],{"encoding":904}," posouvající křivku LM.",[115,16898,2620],{"id":2619},[120,16900,16901,16908,16916,16925],{},[123,16902,16903,2628,16905],{},[38,16904,2627],{},[207,16906,1646],{"className":16907,"dataFsResolvedFilePath":1645,"href":1644},[210],[123,16909,16910,2628,16913],{},[38,16911,16912],{},"Přednáška:",[207,16914,2533],{"className":16915,"dataFsResolvedFilePath":868,"href":869},[210],[123,16917,16918,2628,16921,16924],{},[38,16919,16920],{},"Nadřazené téma:",[207,16922,2418],{"className":16923,"dataFsResolvedFilePath":934,"href":935},[210]," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,16926,16927,16930],{},[38,16928,16929],{},"Související:",[120,16931,16932,16938,16944],{},[123,16933,16934,16937],{},[207,16935,1692],{"className":16936,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,16939,16940,16943],{},[207,16941,1145],{"className":16942,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,16945,16946,16949],{},[207,16947,2575],{"className":16948,"dataFsResolvedFilePath":782,"href":783},[210]," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":16951},[16952,16953,16954,16955,16956,16957,16958,16959,16960,16961],{"id":12706,"depth":642,"text":12707},{"id":12861,"depth":642,"text":12862},{"id":13076,"depth":642,"text":13077},{"id":13369,"depth":642,"text":13370},{"id":13782,"depth":642,"text":13783},{"id":14575,"depth":642,"text":14576},{"id":15265,"depth":642,"text":15266},{"id":16171,"depth":642,"text":16172},{"id":16420,"depth":642,"text":16421},{"id":2619,"depth":642,"text":2620},{},"\u002Ftopics\u002Fis-lm",{"title":12698,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,16968,1143,16969,16970,16971,16972,2418],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":16975,"title":16976,"body":16977,"course":659,"courses":18569,"created":1129,"description":18570,"extension":661,"meta":18571,"navigation":664,"path":18572,"seo":18573,"sources":18574,"stem":18575,"tags":18576,"type":4573,"updated":677,"__hash__":18579},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":16978,"toc":18557},[16979,16982,17078,17085,17105,17109,17114,17177,17196,17198,17201,17337,17339,17549,17583,17720,17724,17788,17804,17832,17836,17934,17938,17942,17995,18101,18315,18319,18362,18468,18519,18521],[12,16980,16976],{"id":16981},"lagrangeova-metoda-vázané-extrémy",[724,16983,16984,16985,4626,17008,17040,17041,17044,17045,17072,17073,17077],{},"Hledáme extrém funkce ",[883,16986,16988],{"className":16987},[886],[888,16989,16990],{"xmlns":890},[892,16991,16992,17006],{},[895,16993,16994,16996,16998,17000,17002,17004],{},[898,16995,2745],{},[1723,16997,1908],{"stretchy":1907},[898,16999,2750],{},[1723,17001,2031],{"separator":2030},[898,17003,2740],{},[1723,17005,1914],{"stretchy":1907},[902,17007,10545],{"encoding":904},[883,17009,17011],{"className":17010},[886],[888,17012,17013],{"xmlns":890},[892,17014,17015,17037],{},[895,17016,17017,17019,17021,17027,17029,17035],{},[898,17018,900],{},[1723,17020,1908],{"stretchy":1907},[1931,17022,17023,17025],{},[898,17024,1904],{},[1864,17026,1866],{},[1723,17028,2031],{"separator":2030},[1931,17030,17031,17033],{},[898,17032,1904],{},[1864,17034,2331],{},[1723,17036,1914],{"stretchy":1907},[902,17038,17039],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,17042,17043],{},"podmíněný"," rovnicí ",[883,17046,17048],{"className":17047},[886],[888,17049,17050],{"xmlns":890},[892,17051,17052,17070],{},[895,17053,17054,17056,17058,17060,17062,17064,17066,17068],{},[898,17055,11741],{},[1723,17057,1908],{"stretchy":1907},[898,17059,2750],{},[1723,17061,2031],{"separator":2030},[898,17063,2740],{},[1723,17065,1914],{"stretchy":1907},[1723,17067,1725],{},[1864,17069,2256],{},[902,17071,11758],{"encoding":904},". V ",[207,17074,17076],{"className":17075,"dataFsResolvedFilePath":1645,"href":1644},[210],"matematické ekonomii"," se používá pro:",[724,17079,17080],{},[3285,17081],{"alt":17082,"className":17083,"src":17084},"imek-lagrange-tecnost",[210,3289],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,17086,17087,17096,17102],{},[123,17088,17089,17092,17093,1914],{},[38,17090,17091],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,17094,2361],{"className":17095,"dataFsResolvedFilePath":878,"href":879},[210],[123,17097,17098,17101],{},[38,17099,17100],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,17103,17104],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,17106,17108],{"id":17107},"princip","Princip",[724,17110,11407,17111,3430],{},[38,17112,17113],{},"Lagrangeovu funkci",[724,17115,17116],{},[883,17117,17119],{"className":17118},[886],[888,17120,17121],{"xmlns":890},[892,17122,17123,17174],{},[895,17124,17125,17127,17129,17131,17133,17135,17137,17140,17142,17144,17146,17148,17150,17152,17154,17156,17158,17160,17162,17164,17166,17168,17170,17172],{},[898,17126,1911],{},[1723,17128,1908],{"stretchy":1907},[898,17130,2750],{},[1723,17132,2031],{"separator":2030},[898,17134,2740],{},[1723,17136,2031],{"separator":2030},[898,17138,17139],{},"λ",[1723,17141,1914],{"stretchy":1907},[1723,17143,1725],{},[898,17145,2745],{},[1723,17147,1908],{"stretchy":1907},[898,17149,2750],{},[1723,17151,2031],{"separator":2030},[898,17153,2740],{},[1723,17155,1914],{"stretchy":1907},[1723,17157,2087],{},[898,17159,17139],{},[3018,17161,3707],{},[898,17163,11741],{},[1723,17165,1908],{"stretchy":1907},[898,17167,2750],{},[1723,17169,2031],{"separator":2030},[898,17171,2740],{},[1723,17173,1914],{"stretchy":1907},[902,17175,17176],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,17178,5022,17179,8812,17193,1664],{},[883,17180,17182],{"className":17181},[886],[888,17183,17184],{"xmlns":890},[892,17185,17186,17190],{},[895,17187,17188],{},[898,17189,17139],{},[902,17191,17192],{"encoding":904},"\\lambda",[38,17194,17195],{},"Lagrangeův multiplikátor",[115,17197,3972],{"id":3971},[724,17199,17200],{},"Řešíme soustavu:",[724,17202,17203,17251,17299],{},[883,17204,17206],{"className":17205},[886],[888,17207,17208],{"xmlns":890},[892,17209,17210,17248],{},[895,17211,17212,17220,17222,17230,17232,17234,17236,17244,17246],{},[2220,17213,17214,17216,17218],{},[898,17215,1911],{},[898,17217,2750],{},[1723,17219,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,17221,1725],{},[2220,17223,17224,17226,17228],{},[898,17225,2745],{},[898,17227,2750],{},[1723,17229,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,17231,2087],{},[898,17233,17139],{},[3018,17235,3707],{},[2220,17237,17238,17240,17242],{},[898,17239,11741],{},[898,17241,2750],{},[1723,17243,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,17245,1725],{},[1864,17247,2256],{},[902,17249,17250],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,17252,17254],{"className":17253},[886],[888,17255,17256],{"xmlns":890},[892,17257,17258,17296],{},[895,17259,17260,17268,17270,17278,17280,17282,17284,17292,17294],{},[2220,17261,17262,17264,17266],{},[898,17263,1911],{},[898,17265,2740],{},[1723,17267,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,17269,1725],{},[2220,17271,17272,17274,17276],{},[898,17273,2745],{},[898,17275,2740],{},[1723,17277,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,17279,2087],{},[898,17281,17139],{},[3018,17283,3707],{},[2220,17285,17286,17288,17290],{},[898,17287,11741],{},[898,17289,2740],{},[1723,17291,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,17293,1725],{},[1864,17295,2256],{},[902,17297,17298],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,17300,17302],{"className":17301},[886],[888,17303,17304],{"xmlns":890},[892,17305,17306,17334],{},[895,17307,17308,17316,17318,17320,17322,17324,17326,17328,17330,17332],{},[2220,17309,17310,17312,17314],{},[898,17311,1911],{},[898,17313,17139],{},[1723,17315,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,17317,1725],{},[898,17319,11741],{},[1723,17321,1908],{"stretchy":1907},[898,17323,2750],{},[1723,17325,2031],{"separator":2030},[898,17327,2740],{},[1723,17329,1914],{"stretchy":1907},[1723,17331,1725],{},[1864,17333,2256],{},[902,17335,17336],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,17338,4046],{"id":4045},[724,17340,17341],{},[883,17342,17344],{"className":17343},[886],[888,17345,17346],{"xmlns":890},[892,17347,17348,17546],{},[895,17349,17350,17352,17354,17356,17358,17360,17362,17364,17366,17368,17370,17386,17388,17390,17406,17408,17410,17418,17424,17426,17428,17444,17446,17448,17464,17466,17468,17476,17482,17484,17486,17488,17504,17506,17508,17524,17526,17528,17536,17538],{},[898,17351,4897],{},[1723,17353,1908],{"stretchy":1907},[898,17355,2750],{},[1723,17357,2031],{"separator":2030},[898,17359,2740],{},[1723,17361,2031],{"separator":2030},[898,17363,17139],{},[1723,17365,1914],{"stretchy":1907},[1723,17367,1725],{},[1723,17369,1908],{"stretchy":1907},[2220,17371,17372,17374,17380],{},[898,17373,2745],{},[895,17375,17376,17378],{},[898,17377,2750],{},[898,17379,2750],{},[895,17381,17382,17384],{},[1723,17383,2229],{"mathvariant":2124},[1723,17385,2229],{"mathvariant":2124},[1723,17387,2087],{},[898,17389,17139],{},[2220,17391,17392,17394,17400],{},[898,17393,11741],{},[895,17395,17396,17398],{},[898,17397,2750],{},[898,17399,2750],{},[895,17401,17402,17404],{},[1723,17403,2229],{"mathvariant":2124},[1723,17405,2229],{"mathvariant":2124},[1723,17407,1914],{"stretchy":1907},[1723,17409,1908],{"stretchy":1907},[2220,17411,17412,17414,17416],{},[898,17413,11741],{},[898,17415,2740],{},[1723,17417,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[2057,17419,17420,17422],{},[1723,17421,1914],{"stretchy":1907},[1864,17423,2331],{},[1723,17425,2087],{},[1723,17427,1908],{"stretchy":1907},[2220,17429,17430,17432,17438],{},[898,17431,2745],{},[895,17433,17434,17436],{},[898,17435,2740],{},[898,17437,2740],{},[895,17439,17440,17442],{},[1723,17441,2229],{"mathvariant":2124},[1723,17443,2229],{"mathvariant":2124},[1723,17445,2087],{},[898,17447,17139],{},[2220,17449,17450,17452,17458],{},[898,17451,11741],{},[895,17453,17454,17456],{},[898,17455,2740],{},[898,17457,2740],{},[895,17459,17460,17462],{},[1723,17461,2229],{"mathvariant":2124},[1723,17463,2229],{"mathvariant":2124},[1723,17465,1914],{"stretchy":1907},[1723,17467,1908],{"stretchy":1907},[2220,17469,17470,17472,17474],{},[898,17471,11741],{},[898,17473,2750],{},[1723,17475,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[2057,17477,17478,17480],{},[1723,17479,1914],{"stretchy":1907},[1864,17481,2331],{},[1723,17483,1759],{},[1864,17485,2331],{},[1723,17487,1908],{"stretchy":1907},[2220,17489,17490,17492,17498],{},[898,17491,2745],{},[895,17493,17494,17496],{},[898,17495,2750],{},[898,17497,2740],{},[895,17499,17500,17502],{},[1723,17501,2229],{"mathvariant":2124},[1723,17503,2229],{"mathvariant":2124},[1723,17505,2087],{},[898,17507,17139],{},[2220,17509,17510,17512,17518],{},[898,17511,11741],{},[895,17513,17514,17516],{},[898,17515,2750],{},[898,17517,2740],{},[895,17519,17520,17522],{},[1723,17521,2229],{"mathvariant":2124},[1723,17523,2229],{"mathvariant":2124},[1723,17525,1914],{"stretchy":1907},[3018,17527,3707],{},[2220,17529,17530,17532,17534],{},[898,17531,11741],{},[898,17533,2750],{},[1723,17535,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[3018,17537,3707],{},[2220,17539,17540,17542,17544],{},[898,17541,11741],{},[898,17543,2740],{},[1723,17545,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,17547,17548],{"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",[724,17550,17551,17552,17582],{},"Je-li ",[883,17553,17555],{"className":17554},[886],[888,17556,17557],{"xmlns":890},[892,17558,17559,17579],{},[895,17560,17561,17563,17565,17567,17569,17571,17577],{},[1723,17562,3212],{"stretchy":1907},[898,17564,207],{},[1723,17566,2031],{"separator":2030},[898,17568,2069],{},[1723,17570,2031],{"separator":2030},[1931,17572,17573,17575],{},[898,17574,17139],{},[1864,17576,2256],{},[1723,17578,3227],{"stretchy":1907},[902,17580,17581],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,17584,17585,17653],{},[123,17586,17587,4133,17623,17625,17626],{},[883,17588,17590],{"className":17589},[886],[888,17591,17592],{"xmlns":890},[892,17593,17594,17620],{},[895,17595,17596,17598,17600,17602,17604,17606,17608,17614,17616,17618],{},[898,17597,4897],{},[1723,17599,1908],{"stretchy":1907},[898,17601,207],{},[1723,17603,2031],{"separator":2030},[898,17605,2069],{},[1723,17607,2031],{"separator":2030},[1931,17609,17610,17612],{},[898,17611,17139],{},[1864,17613,2256],{},[1723,17615,1914],{"stretchy":1907},[1723,17617,2287],{},[1864,17619,2256],{},[902,17621,17622],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,17624,4435],{}," vázané podmínkou ",[883,17627,17629],{"className":17628},[886],[888,17630,17631],{"xmlns":890},[892,17632,17633,17651],{},[895,17634,17635,17637,17639,17641,17643,17645,17647,17649],{},[898,17636,11741],{},[1723,17638,1908],{"stretchy":1907},[898,17640,2750],{},[1723,17642,2031],{"separator":2030},[898,17644,2740],{},[1723,17646,1914],{"stretchy":1907},[1723,17648,1725],{},[1864,17650,2256],{},[902,17652,11758],{"encoding":904},[123,17654,17655,4133,17691,17625,17693],{},[883,17656,17658],{"className":17657},[886],[888,17659,17660],{"xmlns":890},[892,17661,17662,17688],{},[895,17663,17664,17666,17668,17670,17672,17674,17676,17682,17684,17686],{},[898,17665,4897],{},[1723,17667,1908],{"stretchy":1907},[898,17669,207],{},[1723,17671,2031],{"separator":2030},[898,17673,2069],{},[1723,17675,2031],{"separator":2030},[1931,17677,17678,17680],{},[898,17679,17139],{},[1864,17681,2256],{},[1723,17683,1914],{"stretchy":1907},[1723,17685,2253],{},[1864,17687,2256],{},[902,17689,17690],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,17692,4493],{},[883,17694,17696],{"className":17695},[886],[888,17697,17698],{"xmlns":890},[892,17699,17700,17718],{},[895,17701,17702,17704,17706,17708,17710,17712,17714,17716],{},[898,17703,11741],{},[1723,17705,1908],{"stretchy":1907},[898,17707,2750],{},[1723,17709,2031],{"separator":2030},[898,17711,2740],{},[1723,17713,1914],{"stretchy":1907},[1723,17715,1725],{},[1864,17717,2256],{},[902,17719,11758],{"encoding":904},[115,17721,17723],{"id":17722},"význam-multiplikátoru","Význam multiplikátoru",[724,17725,17726],{},[883,17727,17729],{"className":17728},[886],[888,17730,17731],{"xmlns":890},[892,17732,17733,17785],{},[895,17734,17735,17737,17739,17761,17763],{},[898,17736,17139],{},[1723,17738,1725],{},[3058,17740,17741,17749],{},[2220,17742,17743,17745,17747],{},[898,17744,2745],{},[898,17746,2750],{},[1723,17748,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[895,17750,17751,17753],{},[1723,17752,1759],{},[2220,17754,17755,17757,17759],{},[898,17756,11741],{},[898,17758,2750],{},[1723,17760,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,17762,1725],{},[3058,17764,17765,17773],{},[2220,17766,17767,17769,17771],{},[898,17768,2745],{},[898,17770,2740],{},[1723,17772,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[895,17774,17775,17777],{},[1723,17776,1759],{},[2220,17778,17779,17781,17783],{},[898,17780,11741],{},[898,17782,2740],{},[1723,17784,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,17786,17787],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,17789,17790,17803],{},[883,17791,17793],{"className":17792},[886],[888,17794,17795],{"xmlns":890},[892,17796,17797,17801],{},[895,17798,17799],{},[898,17800,17139],{},[902,17802,17192],{"encoding":904}," udává:",[120,17805,17806,17812],{},[123,17807,17808,17809],{},"konstantní ",[38,17810,17811],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,17813,17814,17817,17818,17831],{},[38,17815,17816],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,17819,17821],{"className":17820},[886],[888,17822,17823],{"xmlns":890},[892,17824,17825,17829],{},[895,17826,17827],{},[898,17828,2745],{},[902,17830,2745],{"encoding":904},", uvolní-li se omezení o jednotku",[115,17833,17835],{"id":17834},"alternativní-postup","Alternativní postup",[724,17837,17838,17839,17866,17867,17891,17892,17916,17917,17930,17931,1664],{},"Lze-li z ",[883,17840,17842],{"className":17841},[886],[888,17843,17844],{"xmlns":890},[892,17845,17846,17864],{},[895,17847,17848,17850,17852,17854,17856,17858,17860,17862],{},[898,17849,11741],{},[1723,17851,1908],{"stretchy":1907},[898,17853,2750],{},[1723,17855,2031],{"separator":2030},[898,17857,2740],{},[1723,17859,1914],{"stretchy":1907},[1723,17861,1725],{},[1864,17863,2256],{},[902,17865,11758],{"encoding":904}," vyjádřit ",[883,17868,17870],{"className":17869},[886],[888,17871,17872],{"xmlns":890},[892,17873,17874,17888],{},[895,17875,17876,17878,17880,17882,17884,17886],{},[898,17877,2740],{},[1723,17879,1725],{},[898,17881,2740],{},[1723,17883,1908],{"stretchy":1907},[898,17885,2750],{},[1723,17887,1914],{"stretchy":1907},[902,17889,17890],{"encoding":904},"y = y(x)"," (nebo ",[883,17893,17895],{"className":17894},[886],[888,17896,17897],{"xmlns":890},[892,17898,17899,17913],{},[895,17900,17901,17903,17905,17907,17909,17911],{},[898,17902,2750],{},[1723,17904,1725],{},[898,17906,2750],{},[1723,17908,1908],{"stretchy":1907},[898,17910,2740],{},[1723,17912,1914],{"stretchy":1907},[902,17914,17915],{"encoding":904},"x = x(y)","), dosadíme do ",[883,17918,17920],{"className":17919},[886],[888,17921,17922],{"xmlns":890},[892,17923,17924,17928],{},[895,17925,17926],{},[898,17927,2745],{},[902,17929,2745],{"encoding":904}," a převedeme na ",[38,17932,17933],{},"extrém funkce jedné proměnné",[115,17935,17937],{"id":17936},"použití-v-imek","Použití v ImeK",[198,17939,17941],{"id":17940},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,17943,17944,17945,1664],{},"Rozpočtové omezení: ",[883,17946,17948],{"className":17947},[886],[888,17949,17950],{"xmlns":890},[892,17951,17952,17992],{},[895,17953,17954,17960,17962,17970,17976,17978,17986],{},[2057,17955,17956,17958],{},[898,17957,9837],{},[1723,17959,5066],{},[1723,17961,1725],{},[2220,17963,17964,17966,17968],{},[898,17965,1746],{},[1864,17967,1866],{},[1723,17969,5066],{},[1931,17971,17972,17974],{},[898,17973,1904],{},[1864,17975,1866],{},[1723,17977,2087],{},[2220,17979,17980,17982,17984],{},[898,17981,1746],{},[1864,17983,2331],{},[1723,17985,5066],{},[1931,17987,17988,17990],{},[898,17989,1904],{},[1864,17991,2331],{},[902,17993,17994],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,17996,17997],{},[883,17998,18000],{"className":17999},[886],[888,18001,18002],{"xmlns":890},[892,18003,18004,18098],{},[895,18005,18006,18008,18010,18016,18018,18024,18026,18028,18030,18032,18034,18036,18042,18044,18050,18052,18054,18056,18058,18064,18066,18074,18080,18082,18090,18096],{},[898,18007,1911],{},[1723,18009,1908],{"stretchy":1907},[1931,18011,18012,18014],{},[898,18013,1904],{},[1864,18015,1866],{},[1723,18017,2031],{"separator":2030},[1931,18019,18020,18022],{},[898,18021,1904],{},[1864,18023,2331],{},[1723,18025,2031],{"separator":2030},[898,18027,17139],{},[1723,18029,1914],{"stretchy":1907},[1723,18031,1725],{},[898,18033,900],{},[1723,18035,1908],{"stretchy":1907},[1931,18037,18038,18040],{},[898,18039,1904],{},[1864,18041,1866],{},[1723,18043,2031],{"separator":2030},[1931,18045,18046,18048],{},[898,18047,1904],{},[1864,18049,2331],{},[1723,18051,1914],{"stretchy":1907},[1723,18053,2087],{},[898,18055,17139],{},[1723,18057,1908],{"stretchy":1907},[2057,18059,18060,18062],{},[898,18061,9837],{},[1723,18063,5066],{},[1723,18065,1759],{},[2220,18067,18068,18070,18072],{},[898,18069,1746],{},[1864,18071,1866],{},[1723,18073,5066],{},[1931,18075,18076,18078],{},[898,18077,1904],{},[1864,18079,1866],{},[1723,18081,1759],{},[2220,18083,18084,18086,18088],{},[898,18085,1746],{},[1864,18087,2331],{},[1723,18089,5066],{},[1931,18091,18092,18094],{},[898,18093,1904],{},[1864,18095,2331],{},[1723,18097,1914],{"stretchy":1907},[902,18099,18100],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,18102,18103,18104,1343,18136,1343,18168,18217,18218,18272,18273,1664],{},"Soustava: ",[883,18105,18107],{"className":18106},[886],[888,18108,18109],{"xmlns":890},[892,18110,18111,18133],{},[895,18112,18113,18121,18123,18125],{},[2220,18114,18115,18117,18119],{},[898,18116,900],{},[1864,18118,1866],{},[1723,18120,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,18122,1725],{},[898,18124,17139],{},[2220,18126,18127,18129,18131],{},[898,18128,1746],{},[1864,18130,1866],{},[1723,18132,5066],{},[902,18134,18135],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,18137,18139],{"className":18138},[886],[888,18140,18141],{"xmlns":890},[892,18142,18143,18165],{},[895,18144,18145,18153,18155,18157],{},[2220,18146,18147,18149,18151],{},[898,18148,900],{},[1864,18150,2331],{},[1723,18152,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,18154,1725],{},[898,18156,17139],{},[2220,18158,18159,18161,18163],{},[898,18160,1746],{},[1864,18162,2331],{},[1723,18164,5066],{},[902,18166,18167],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,18169,18171],{"className":18170},[886],[888,18172,18173],{"xmlns":890},[892,18174,18175,18215],{},[895,18176,18177,18183,18185,18193,18199,18201,18209],{},[2057,18178,18179,18181],{},[898,18180,9837],{},[1723,18182,5066],{},[1723,18184,1725],{},[2220,18186,18187,18189,18191],{},[898,18188,1746],{},[1864,18190,1866],{},[1723,18192,5066],{},[1931,18194,18195,18197],{},[898,18196,1904],{},[1864,18198,1866],{},[1723,18200,2087],{},[2220,18202,18203,18205,18207],{},[898,18204,1746],{},[1864,18206,2331],{},[1723,18208,5066],{},[1931,18210,18211,18213],{},[898,18212,1904],{},[1864,18214,2331],{},[902,18216,17994],{"encoding":904},". Z prvních dvou: ",[883,18219,18221],{"className":18220},[886],[888,18222,18223],{"xmlns":890},[892,18224,18225,18269],{},[895,18226,18227,18247,18249],{},[3055,18228,18229],{"scriptlevel":2256,"displaystyle":1907},[3058,18230,18231,18239],{},[2220,18232,18233,18235,18237],{},[898,18234,900],{},[1864,18236,1866],{},[1723,18238,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[2220,18240,18241,18243,18245],{},[898,18242,900],{},[1864,18244,2331],{},[1723,18246,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,18248,1725],{},[3055,18250,18251],{"scriptlevel":2256,"displaystyle":1907},[3058,18252,18253,18261],{},[2220,18254,18255,18257,18259],{},[898,18256,1746],{},[1864,18258,1866],{},[1723,18260,5066],{},[2220,18262,18263,18265,18267],{},[898,18264,1746],{},[1864,18266,2331],{},[1723,18268,5066],{},[902,18270,18271],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,18274,18276],{"className":18275},[886],[888,18277,18278],{"xmlns":890},[892,18279,18280,18312],{},[895,18281,18282,18284,18286,18288,18290,18292],{},[898,18283,1728],{},[898,18285,1749],{},[898,18287,1721],{},[898,18289,2111],{},[1723,18291,1725],{},[3055,18293,18294],{"scriptlevel":2256,"displaystyle":1907},[3058,18295,18296,18304],{},[2220,18297,18298,18300,18302],{},[898,18299,1746],{},[1864,18301,1866],{},[1723,18303,5066],{},[2220,18305,18306,18308,18310],{},[898,18307,1746],{},[1864,18309,2331],{},[1723,18311,5066],{},[902,18313,18314],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,18316,18318],{"id":18317},"minimalizace-výdajů","Minimalizace výdajů",[724,18320,18321,18322,1664],{},"Podmínka dané užitečnosti ",[883,18323,18325],{"className":18324},[886],[888,18326,18327],{"xmlns":890},[892,18328,18329,18359],{},[895,18330,18331,18337,18339,18341,18343,18349,18351,18357],{},[2057,18332,18333,18335],{},[898,18334,900],{},[1723,18336,5066],{},[1723,18338,1725],{},[898,18340,900],{},[1723,18342,1908],{"stretchy":1907},[1931,18344,18345,18347],{},[898,18346,1904],{},[1864,18348,1866],{},[1723,18350,2031],{"separator":2030},[1931,18352,18353,18355],{},[898,18354,1904],{},[1864,18356,2331],{},[1723,18358,1914],{"stretchy":1907},[902,18360,18361],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,18363,18364],{},[883,18365,18367],{"className":18366},[886],[888,18368,18369],{"xmlns":890},[892,18370,18371,18465],{},[895,18372,18373,18375,18377,18383,18385,18391,18393,18395,18397,18399,18407,18413,18415,18423,18429,18431,18433,18435,18441,18443,18445,18447,18453,18455,18461,18463],{},[898,18374,1911],{},[1723,18376,1908],{"stretchy":1907},[1931,18378,18379,18381],{},[898,18380,1904],{},[1864,18382,1866],{},[1723,18384,2031],{"separator":2030},[1931,18386,18387,18389],{},[898,18388,1904],{},[1864,18390,2331],{},[1723,18392,2031],{"separator":2030},[898,18394,17139],{},[1723,18396,1914],{"stretchy":1907},[1723,18398,1725],{},[2220,18400,18401,18403,18405],{},[898,18402,1746],{},[1864,18404,1866],{},[1723,18406,5066],{},[1931,18408,18409,18411],{},[898,18410,1904],{},[1864,18412,1866],{},[1723,18414,2087],{},[2220,18416,18417,18419,18421],{},[898,18418,1746],{},[1864,18420,2331],{},[1723,18422,5066],{},[1931,18424,18425,18427],{},[898,18426,1904],{},[1864,18428,2331],{},[1723,18430,2087],{},[898,18432,17139],{},[1723,18434,1908],{"stretchy":1907},[2057,18436,18437,18439],{},[898,18438,900],{},[1723,18440,5066],{},[1723,18442,1759],{},[898,18444,900],{},[1723,18446,1908],{"stretchy":1907},[1931,18448,18449,18451],{},[898,18450,1904],{},[1864,18452,1866],{},[1723,18454,2031],{"separator":2030},[1931,18456,18457,18459],{},[898,18458,1904],{},[1864,18460,2331],{},[1723,18462,1914],{"stretchy":1907},[1723,18464,1914],{"stretchy":1907},[902,18466,18467],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,18469,18470,18471,1664],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,18472,18474],{"className":18473},[886],[888,18475,18476],{"xmlns":890},[892,18477,18478,18516],{},[895,18479,18480,18486,18488,18494,18496,18502,18504,18510,18512,18514],{},[1931,18481,18482,18484],{},[898,18483,1904],{},[898,18485,2216],{},[1723,18487,1725],{},[1931,18489,18490,18492],{},[898,18491,4897],{},[898,18493,2216],{},[1723,18495,1908],{"stretchy":1907},[1931,18497,18498,18500],{},[898,18499,1746],{},[1864,18501,1866],{},[1723,18503,2031],{"separator":2030},[1931,18505,18506,18508],{},[898,18507,1746],{},[1864,18509,2331],{},[1723,18511,2031],{"separator":2030},[898,18513,900],{},[1723,18515,1914],{"stretchy":1907},[902,18517,18518],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,18520,2620],{"id":2619},[120,18522,18523,18530,18537,18546],{},[123,18524,18525,2628,18527],{},[38,18526,4515],{},[207,18528,784],{"className":18529,"dataFsResolvedFilePath":782,"href":783},[210],[123,18531,18532,2628,18534],{},[38,18533,4523],{},[207,18535,12642],{"className":18536,"dataFsResolvedFilePath":800,"href":801},[210],[123,18538,18539,2628,18542,18545],{},[38,18540,18541],{},"Aplikace v kurzu:",[207,18543,880],{"className":18544,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,18547,18548,2628,18550,1343,18553,18556],{},[38,18549,4531],{},[207,18551,936],{"className":18552,"dataFsResolvedFilePath":934,"href":935},[210],[207,18554,1400],{"className":18555,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":18558},[18559,18560,18561,18562,18563,18564,18568],{"id":17107,"depth":642,"text":17108},{"id":3971,"depth":642,"text":3972},{"id":4045,"depth":642,"text":4046},{"id":17722,"depth":642,"text":17723},{"id":17834,"depth":642,"text":17835},{"id":17936,"depth":642,"text":17937,"children":18565},[18566,18567],{"id":17940,"depth":649,"text":17941},{"id":18317,"depth":649,"text":18318},{"id":2619,"depth":642,"text":2620},[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":16976,"description":18570},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,18577,18578],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":18581,"title":936,"body":18582,"course":1128,"courses":659,"created":2676,"description":641,"extension":661,"meta":28448,"navigation":664,"path":28449,"seo":28450,"sources":28451,"stem":28452,"tags":28453,"type":4573,"updated":677,"__hash__":28457},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":18583,"toc":28410},[18584,18587,18589,18712,18846,18850,18853,18966,18970,18998,19045,19048,19114,19159,19162,19188,19219,19223,19227,19271,19315,19377,19432,19435,19439,19442,19489,19586,19692,19698,19775,19804,19943,19947,19976,20026,20173,20263,20267,20293,20331,20357,20395,20457,20532,20610,20668,20734,20778,20782,20840,20889,20934,21147,21267,21273,21277,21300,21304,21311,21315,21346,21381,21385,21435,21523,21565,21586,21648,21708,21712,21783,21851,21923,22038,22086,22090,22093,22134,22173,22196,22310,22474,22482,22509,22539,22542,22619,22772,22856,23195,23199,23323,23459,23595,23648,23651,23901,23982,23986,23989,24047,24079,24082,24131,24134,24205,24401,24405,24556,24786,24824,24877,24923,24926,24982,25031,25235,25325,25329,25345,25352,25521,25525,25596,25677,25758,25837,25983,26071,26075,26258,26389,26434,26531,26535,27274,27276,28327,28329],[12,18585,936],{"id":18586},"národní-důchod",[115,18588,12707],{"id":12706},[724,18590,18591,18592,2628,18596,18599,18600,2628,18603,18616,18617,18620,18621,18624,18625,18628,18629,18631,18632,2628,18634,18651,18652,18669,18670,18673,18674,4634],{},"Kapitola 7 ",[207,18593,18595],{"className":18594,"dataFsResolvedFilePath":1645,"href":1644},[210],"Matematické ekonomie",[38,18597,18598],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,18601,18602],{},"národním důchodem",[883,18604,18606],{"className":18605},[886],[888,18607,18608],{"xmlns":890},[892,18609,18610,18614],{},[895,18611,18612],{},[898,18613,9837],{},[902,18615,9837],{"encoding":904},". Budují se postupně bohatší modely — ",[38,18618,18619],{},"C-I"," (jen spotřeba a investice) → ",[38,18622,18623],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,18626,18627],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,18630,12712],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,18633,14586],{},[883,18635,18637],{"className":18636},[886],[888,18638,18639],{"xmlns":890},[892,18640,18641,18649],{},[895,18642,18643],{},[2057,18644,18645,18647],{},[898,18646,9837],{},[898,18648,1846],{},[902,18650,14604],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,18653,18655],{"className":18654},[886],[888,18656,18657],{"xmlns":890},[892,18658,18659,18667],{},[895,18660,18661],{},[2057,18662,18663,18665],{},[898,18664,9837],{},[898,18666,1846],{},[902,18668,14604],{"encoding":904}," na exogenní veličiny popisují ",[38,18671,18672],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,18675,18677],{"className":18676},[886],[888,18678,18679],{"xmlns":890},[892,18680,18681,18709],{},[895,18682,18683,18685,18687,18689,18691,18693,18695,18697,18699,18701,18703,18705,18707],{},[1864,18684,1866],{},[898,18686,2125],{"mathvariant":2124},[1723,18688,1908],{"stretchy":1907},[1864,18690,1866],{},[1723,18692,1759],{},[898,18694,207],{},[1723,18696,1914],{"stretchy":1907},[1723,18698,1725],{},[1864,18700,1866],{},[898,18702,2125],{"mathvariant":2124},[898,18704,1728],{},[898,18706,1746],{},[898,18708,2111],{},[902,18710,18711],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[4584,18713,18714],{},[724,18715,18716,18718,18719,18722,18723,18740,18741,18771,18772,18819,18820,18822,18823,18845],{},[883,18717,4869],{}," Intuice\n",[38,18720,18721],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,18724,18726],{"className":18725},[886],[888,18727,18728],{"xmlns":890},[892,18729,18730,18738],{},[895,18731,18732,18734,18736],{},[898,18733,1728],{},[898,18735,1746],{},[898,18737,1721],{},[902,18739,2389],{"encoding":904}," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,18742,18744],{"className":18743},[886],[888,18745,18746],{"xmlns":890},[892,18747,18748,18768],{},[895,18749,18750,18752,18754,18756,18758,18760,18762,18764,18766],{},[898,18751,1728],{},[898,18753,1746],{},[898,18755,2111],{},[1723,18757,1725],{},[1864,18759,1866],{},[1723,18761,1759],{},[898,18763,1728],{},[898,18765,1746],{},[898,18767,1721],{},[902,18769,18770],{"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 ",[883,18773,18775],{"className":18774},[886],[888,18776,18777],{"xmlns":890},[892,18778,18779,18816],{},[895,18780,18781,18783,18785,18787,18789,18795,18797,18800,18802,18804,18806,18808,18810,18812,18814],{},[1864,18782,1866],{},[1723,18784,2087],{},[898,18786,207],{},[1723,18788,2087],{},[2057,18790,18791,18793],{},[898,18792,207],{},[1864,18794,2331],{},[1723,18796,2087],{},[1723,18798,18799],{},"⋯",[1723,18801,1725],{},[1864,18803,1866],{},[898,18805,2125],{"mathvariant":2124},[1723,18807,1908],{"stretchy":1907},[1864,18809,1866],{},[1723,18811,1759],{},[898,18813,207],{},[1723,18815,1914],{"stretchy":1907},[902,18817,18818],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,18821,12712],{}," 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 ",[883,18824,18826],{"className":18825},[886],[888,18827,18828],{"xmlns":890},[892,18829,18830,18842],{},[895,18831,18832,18834,18836,18838,18840],{},[1723,18833,1908],{"stretchy":1907},[898,18835,9837],{},[1723,18837,2031],{"separator":2030},[898,18839,12742],{},[1723,18841,1914],{"stretchy":1907},[902,18843,18844],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,18847,18849],{"id":18848},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,18851,18852],{},"Po prostudování kapitoly by čtenář měl umět:",[120,18854,18855,18858,18861,18864,18867,18870,18873,18963],{},[123,18856,18857],{},"popsat zjednodušený model národní ekonomiky,",[123,18859,18860],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,18862,18863],{},"popsat lineární model spotřeby a úspor,",[123,18865,18866],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,18868,18869],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,18871,18872],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,18874,18875,18876,1343,18893,1343,18915,1682,18940,18962],{},"popsat modely ",[883,18877,18879],{"className":18878},[886],[888,18880,18881],{"xmlns":890},[892,18882,18883,18891],{},[895,18884,18885,18887,18889],{},[898,18886,1721],{},[3018,18888,12991],{},[898,18890,12885],{},[902,18892,12996],{"encoding":904},[883,18894,18896],{"className":18895},[886],[888,18897,18898],{"xmlns":890},[892,18899,18900,18912],{},[895,18901,18902,18904,18906,18908,18910],{},[898,18903,1721],{},[3018,18905,12991],{},[898,18907,12885],{},[3018,18909,12991],{},[898,18911,12813],{},[902,18913,18914],{"encoding":904},"C\\text{-}I\\text{-}G",[883,18916,18918],{"className":18917},[886],[888,18919,18920],{"xmlns":890},[892,18921,18922,18938],{},[895,18923,18924,18926,18928,18930,18932,18934,18936],{},[898,18925,1721],{},[3018,18927,12991],{},[898,18929,12885],{},[3018,18931,12991],{},[898,18933,12813],{},[3018,18935,12991],{},[898,18937,13021],{},[902,18939,13024],{"encoding":904},[883,18941,18943],{"className":18942},[886],[888,18944,18945],{"xmlns":890},[892,18946,18947,18959],{},[895,18948,18949,18951,18953,18955,18957],{},[898,18950,12885],{},[898,18952,2111],{},[3018,18954,12991],{},[898,18956,1911],{},[898,18958,1728],{},[902,18960,18961],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,18964,18965],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,18967,18969],{"id":18968},"gnp-a-národní-důchod","GNP a národní důchod",[724,18971,18972,2628,18975,1981,18994,18997],{},[38,18973,18974],{},"Hrubý národní produkt",[883,18976,18978],{"className":18977},[886],[888,18979,18980],{"xmlns":890},[892,18981,18982,18991],{},[895,18983,18984,18986,18989],{},[898,18985,12813],{},[898,18987,18988],{},"N",[898,18990,1746],{},[902,18992,18993],{"encoding":904},"GNP",[614,18995,18996],{},"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:",[724,18999,19000],{},[883,19001,19003],{"className":19002},[886],[888,19004,19005],{"xmlns":890},[892,19006,19007,19042],{},[895,19008,19009,19011,19013,19015,19017,19019,19021,19023,19025,19027,19029,19031,19033,19035,19037,19040],{},[898,19010,12813],{},[898,19012,18988],{},[898,19014,1746],{},[1723,19016,1725],{},[898,19018,1721],{},[1723,19020,2087],{},[898,19022,12885],{},[1723,19024,2087],{},[898,19026,12813],{},[1723,19028,2087],{},[898,19030,13021],{},[1723,19032,2031],{"separator":2030},[6588,19034],{"width":6590},[1723,19036,1908],{"stretchy":1907},[1864,19038,19039],{},"7.1",[1723,19041,1914],{"stretchy":1907},[902,19043,19044],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,19046,19047],{},"kde",[120,19049,19050,19066,19082,19098],{},[123,19051,19052,19065],{},[883,19053,19055],{"className":19054},[886],[888,19056,19057],{"xmlns":890},[892,19058,19059,19063],{},[895,19060,19061],{},[898,19062,1721],{},[902,19064,1721],{"encoding":904}," — výdaje domácností na spotřebu,",[123,19067,19068,19081],{},[883,19069,19071],{"className":19070},[886],[888,19072,19073],{"xmlns":890},[892,19074,19075,19079],{},[895,19076,19077],{},[898,19078,12885],{},[902,19080,12885],{"encoding":904}," — hrubé domácí investice,",[123,19083,19084,19097],{},[883,19085,19087],{"className":19086},[886],[888,19088,19089],{"xmlns":890},[892,19090,19091,19095],{},[895,19092,19093],{},[898,19094,12813],{},[902,19096,12813],{"encoding":904}," — vládní výdaje,",[123,19099,19100,19113],{},[883,19101,19103],{"className":19102},[886],[888,19104,19105],{"xmlns":890},[892,19106,19107,19111],{},[895,19108,19109],{},[898,19110,13021],{},[902,19112,13021],{"encoding":904}," — čistý export.",[724,19115,19116,19117,19134,19135,19138,19139,2628,19142,1981,19155,19158],{},"K měření ",[883,19118,19120],{"className":19119},[886],[888,19121,19122],{"xmlns":890},[892,19123,19124,19132],{},[895,19125,19126,19128,19130],{},[898,19127,12813],{},[898,19129,18988],{},[898,19131,1746],{},[902,19133,18993],{"encoding":904}," se užívá ",[38,19136,19137],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,19140,19141],{},"národní důchod",[883,19143,19145],{"className":19144},[886],[888,19146,19147],{"xmlns":890},[892,19148,19149,19153],{},[895,19150,19151],{},[898,19152,9837],{},[902,19154,9837],{"encoding":904},[614,19156,19157],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,19160,19161],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,19163,19164],{},[883,19165,19167],{"className":19166},[886],[888,19168,19169],{"xmlns":890},[892,19170,19171,19185],{},[895,19172,19173,19175,19177,19179,19181,19183],{},[898,19174,12813],{},[898,19176,18988],{},[898,19178,1746],{},[1723,19180,3456],{},[898,19182,9837],{},[1723,19184,2031],{"separator":2030},[902,19186,19187],{"encoding":904},"GNP \\approx Y,",[724,19189,19190,19191,1981,19194,19197,19198,19211,19212,19215,19216,1664],{},"a užívá se společného názvu ",[38,19192,19193],{},"důchod",[614,19195,19196],{},"income",") s označením ",[883,19199,19201],{"className":19200},[886],[888,19202,19203],{"xmlns":890},[892,19204,19205,19209],{},[895,19206,19207],{},[898,19208,9837],{},[902,19210,9837],{"encoding":904},". Domácnosti důchod použijí ke ",[38,19213,19214],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,19217,19218],{},"úspor",[115,19220,19222],{"id":19221},"spotřeba-a-úspory","Spotřeba a úspory",[198,19224,19226],{"id":19225},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,19228,19229,19230,19243,19244,19257,19258,3430],{},"Jak spotřeba ",[883,19231,19233],{"className":19232},[886],[888,19234,19235],{"xmlns":890},[892,19236,19237,19241],{},[895,19238,19239],{},[898,19240,1721],{},[902,19242,1721],{"encoding":904},", tak úspory ",[883,19245,19247],{"className":19246},[886],[888,19248,19249],{"xmlns":890},[892,19250,19251,19255],{},[895,19252,19253],{},[898,19254,2111],{},[902,19256,2111],{"encoding":904}," závisejí na důchodu ",[883,19259,19261],{"className":19260},[886],[888,19262,19263],{"xmlns":890},[892,19264,19265,19269],{},[895,19266,19267],{},[898,19268,9837],{},[902,19270,9837],{"encoding":904},[724,19272,19273],{},[883,19274,19276],{"className":19275},[886],[888,19277,19278],{"xmlns":890},[892,19279,19280,19312],{},[895,19281,19282,19284,19286,19288,19290,19292,19294,19296,19298,19300,19302,19304,19306,19308,19310],{},[898,19283,1721],{},[1723,19285,1725],{},[898,19287,1721],{},[1723,19289,1908],{"stretchy":1907},[898,19291,9837],{},[1723,19293,1914],{"stretchy":1907},[1723,19295,2031],{"separator":2030},[6588,19297],{"width":6590},[898,19299,2111],{},[1723,19301,1725],{},[898,19303,2111],{},[1723,19305,1908],{"stretchy":1907},[898,19307,9837],{},[1723,19309,1914],{"stretchy":1907},[898,19311,1664],{"mathvariant":2124},[902,19313,19314],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,19316,19317,8812,19336,1981,19339,19342,19343,8812,19363,1981,19366,19369,19370,1682,19373,19376],{},[883,19318,19320],{"className":19319},[886],[888,19321,19322],{"xmlns":890},[892,19323,19324,19334],{},[895,19325,19326,19328,19330,19332],{},[898,19327,1721],{},[1723,19329,1908],{"stretchy":1907},[898,19331,9837],{},[1723,19333,1914],{"stretchy":1907},[902,19335,14917],{"encoding":904},[38,19337,19338],{},"funkce spotřeby",[614,19340,19341],{},"consumption function","), ",[883,19344,19346],{"className":19345},[886],[888,19347,19348],{"xmlns":890},[892,19349,19350,19360],{},[895,19351,19352,19354,19356,19358],{},[898,19353,2111],{},[1723,19355,1908],{"stretchy":1907},[898,19357,9837],{},[1723,19359,1914],{"stretchy":1907},[902,19361,19362],{"encoding":904},"S(Y)",[38,19364,19365],{},"funkce úspor",[614,19367,19368],{},"savings function","); jejich grafy se nazývají ",[38,19371,19372],{},"křivka spotřeby",[38,19374,19375],{},"křivka úspor",". Platí základní identita",[724,19378,19379],{},[883,19380,19382],{"className":19381},[886],[888,19383,19384],{"xmlns":890},[892,19385,19386,19429],{},[895,19387,19388,19390,19392,19394,19396,19398,19400,19402,19404,19406,19408,19410,19412,19414,19416,19418,19420,19422,19424,19427],{},[898,19389,9837],{},[1723,19391,1725],{},[898,19393,1721],{},[1723,19395,2087],{},[898,19397,2111],{},[1723,19399,1725],{},[898,19401,1721],{},[1723,19403,1908],{"stretchy":1907},[898,19405,9837],{},[1723,19407,1914],{"stretchy":1907},[1723,19409,2087],{},[898,19411,2111],{},[1723,19413,1908],{"stretchy":1907},[898,19415,9837],{},[1723,19417,1914],{"stretchy":1907},[898,19419,1664],{"mathvariant":2124},[6588,19421],{"width":6590},[1723,19423,1908],{"stretchy":1907},[1864,19425,19426],{},"7.2",[1723,19428,1914],{"stretchy":1907},[902,19430,19431],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,19433,19434],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,19436,19438],{"id":19437},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,19440,19441],{},"Nejjednodušší model předpokládá lineární tvar",[724,19443,19444],{},[883,19445,19447],{"className":19446},[886],[888,19448,19449],{"xmlns":890},[892,19450,19451,19486],{},[895,19452,19453,19455,19457,19459,19461,19463,19465,19467,19469,19471,19473,19475,19477,19479,19481,19484],{},[898,19454,1721],{},[1723,19456,1725],{},[898,19458,1721],{},[1723,19460,1908],{"stretchy":1907},[898,19462,9837],{},[1723,19464,1914],{"stretchy":1907},[1723,19466,1725],{},[898,19468,207],{},[898,19470,9837],{},[1723,19472,2087],{},[898,19474,2069],{},[1723,19476,2031],{"separator":2030},[6588,19478],{"width":6590},[1723,19480,1908],{"stretchy":1907},[1864,19482,19483],{},"7.3",[1723,19485,1914],{"stretchy":1907},[902,19487,19488],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,19490,5022,19491,1682,19509,19531,19532,19572,19573,1664],{},[883,19492,19494],{"className":19493},[886],[888,19495,19496],{"xmlns":890},[892,19497,19498,19506],{},[895,19499,19500,19502,19504],{},[898,19501,2069],{},[1723,19503,2253],{},[1864,19505,2256],{},[902,19507,19508],{"encoding":904},"b > 0",[883,19510,19512],{"className":19511},[886],[888,19513,19514],{"xmlns":890},[892,19515,19516,19528],{},[895,19517,19518,19520,19522,19524,19526],{},[1864,19519,2256],{},[1723,19521,2287],{},[898,19523,207],{},[1723,19525,2287],{},[1864,19527,1866],{},[902,19529,19530],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,19533,19535],{"className":19534},[886],[888,19536,19537],{"xmlns":890},[892,19538,19539,19569],{},[895,19540,19541,19543,19545,19552,19554,19557,19559,19561,19563,19565,19567],{},[898,19542,207],{},[1723,19544,1725],{},[895,19546,19547,19550],{},[898,19548,19549],{"mathvariant":2124},"t",[898,19551,11741],{"mathvariant":2124},[3018,19553,3707],{},[898,19555,19556],{},"α",[1723,19558,1725],{},[898,19560,3611],{"mathvariant":2124},[898,19562,1721],{},[898,19564,2125],{"mathvariant":2124},[898,19566,3611],{"mathvariant":2124},[898,19568,9837],{},[902,19570,19571],{"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 ",[883,19574,19576],{"className":19575},[886],[888,19577,19578],{"xmlns":890},[892,19579,19580,19584],{},[895,19581,19582],{},[898,19583,9837],{},[902,19585,9837],{"encoding":904},[724,19587,19588],{},[614,19589,19590,19591,19615,19616,19654,19655,19671,19672,1664],{},"Obrázek 7.1 — Přímka spotřeby ",[883,19592,19594],{"className":19593},[886],[888,19595,19596],{"xmlns":890},[892,19597,19598,19612],{},[895,19599,19600,19602,19604,19606,19608,19610],{},[898,19601,1721],{},[1723,19603,1725],{},[898,19605,207],{},[898,19607,9837],{},[1723,19609,2087],{},[898,19611,2069],{},[902,19613,19614],{"encoding":904},"C = aY + b"," se směrnicí ",[883,19617,19619],{"className":19618},[886],[888,19620,19621],{"xmlns":890},[892,19622,19623,19651],{},[895,19624,19625,19627,19629,19635,19637,19639,19641,19643,19645,19647,19649],{},[898,19626,207],{},[1723,19628,1725],{},[895,19630,19631,19633],{},[898,19632,19549],{"mathvariant":2124},[898,19634,11741],{"mathvariant":2124},[3018,19636,3707],{},[898,19638,19556],{},[1723,19640,1725],{},[898,19642,3611],{"mathvariant":2124},[898,19644,1721],{},[898,19646,2125],{"mathvariant":2124},[898,19648,3611],{"mathvariant":2124},[898,19650,9837],{},[902,19652,19653],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,19656,19658],{"className":19657},[886],[888,19659,19660],{"xmlns":890},[892,19661,19662,19668],{},[895,19663,19664,19666],{},[898,19665,3611],{"mathvariant":2124},[898,19667,1721],{},[902,19669,19670],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,19673,19675],{"className":19674},[886],[888,19676,19677],{"xmlns":890},[892,19678,19679,19689],{},[895,19680,19681,19683,19685,19687],{},[898,19682,3611],{"mathvariant":2124},[898,19684,9837],{},[1723,19686,1725],{},[1864,19688,1866],{},[902,19690,19691],{"encoding":904},"\\Delta Y = 1",[724,19693,19694,19695,3430],{},"Dosazením do (7.2) plyne ",[38,19696,19697],{},"lineární model úspor",[724,19699,19700],{},[883,19701,19703],{"className":19702},[886],[888,19704,19705],{"xmlns":890},[892,19706,19707,19772],{},[895,19708,19709,19711,19713,19715,19717,19719,19721,19723,19725,19727,19729,19731,19733,19735,19737,19739,19741,19743,19745,19747,19749,19751,19753,19755,19757,19759,19761,19763,19765,19767,19770],{},[898,19710,2111],{},[1723,19712,1725],{},[898,19714,9837],{},[1723,19716,1759],{},[898,19718,1721],{},[1723,19720,1908],{"stretchy":1907},[898,19722,9837],{},[1723,19724,1914],{"stretchy":1907},[1723,19726,1725],{},[898,19728,9837],{},[1723,19730,1759],{},[1723,19732,1908],{"stretchy":1907},[898,19734,207],{},[898,19736,9837],{},[1723,19738,2087],{},[898,19740,2069],{},[1723,19742,1914],{"stretchy":1907},[1723,19744,1725],{},[1723,19746,1908],{"stretchy":1907},[1864,19748,1866],{},[1723,19750,1759],{},[898,19752,207],{},[1723,19754,1914],{"stretchy":1907},[898,19756,9837],{},[1723,19758,1759],{},[898,19760,2069],{},[898,19762,1664],{"mathvariant":2124},[6588,19764],{"width":6590},[1723,19766,1908],{"stretchy":1907},[1864,19768,19769],{},"7.4",[1723,19771,1914],{"stretchy":1907},[902,19773,19774],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,19776,19777,19778,4634],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,19779,19781],{"className":19780},[886],[888,19782,19783],{"xmlns":890},[892,19784,19785,19801],{},[895,19786,19787,19789,19791,19793,19795,19797,19799],{},[1864,19788,2256],{},[1723,19790,2287],{},[1864,19792,1866],{},[1723,19794,1759],{},[898,19796,207],{},[1723,19798,2287],{},[1864,19800,1866],{},[902,19802,19803],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,19805,19806],{},[614,19807,19808,19809,1682,19832,19864,19865,3350,19878,19908,19909,3350,19927,1664],{},"Obrázek 7.2 — Přímky ",[883,19810,19812],{"className":19811},[886],[888,19813,19814],{"xmlns":890},[892,19815,19816,19830],{},[895,19817,19818,19820,19822,19824,19826,19828],{},[898,19819,1721],{},[1723,19821,1725],{},[898,19823,207],{},[898,19825,9837],{},[1723,19827,2087],{},[898,19829,2069],{},[902,19831,19614],{"encoding":904},[883,19833,19835],{"className":19834},[886],[888,19836,19837],{"xmlns":890},[892,19838,19839,19861],{},[895,19840,19841,19843,19845,19847,19849,19851,19853,19855,19857,19859],{},[898,19842,2111],{},[1723,19844,1725],{},[1723,19846,1908],{"stretchy":1907},[1864,19848,1866],{},[1723,19850,1759],{},[898,19852,207],{},[1723,19854,1914],{"stretchy":1907},[898,19856,9837],{},[1723,19858,1759],{},[898,19860,2069],{},[902,19862,19863],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,19866,19868],{"className":19867},[886],[888,19869,19870],{"xmlns":890},[892,19871,19872,19876],{},[895,19873,19874],{},[898,19875,9837],{},[902,19877,9837],{"encoding":904},[883,19879,19881],{"className":19880},[886],[888,19882,19883],{"xmlns":890},[892,19884,19885,19905],{},[895,19886,19887,19889,19891,19893,19895,19897,19899,19901,19903],{},[898,19888,9837],{},[1723,19890,1725],{},[898,19892,2069],{},[898,19894,2125],{"mathvariant":2124},[1723,19896,1908],{"stretchy":1907},[1864,19898,1866],{},[1723,19900,1759],{},[898,19902,207],{},[1723,19904,1914],{"stretchy":1907},[902,19906,19907],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,19910,19912],{"className":19911},[886],[888,19913,19914],{"xmlns":890},[892,19915,19916,19924],{},[895,19917,19918,19920,19922],{},[898,19919,1721],{},[1723,19921,2031],{"separator":2030},[898,19923,2111],{},[902,19925,19926],{"encoding":904},"C, S",[883,19928,19930],{"className":19929},[886],[888,19931,19932],{"xmlns":890},[892,19933,19934,19940],{},[895,19935,19936,19938],{},[1723,19937,1759],{},[898,19939,2069],{},[902,19941,19942],{"encoding":904},"-b",[198,19944,19946],{"id":19945},"příklad-71","Příklad 7.1",[724,19948,19949,19950,19975],{},"Pro spotřebu ",[883,19951,19953],{"className":19952},[886],[888,19954,19955],{"xmlns":890},[892,19956,19957,19972],{},[895,19958,19959,19961,19963,19966,19968,19970],{},[898,19960,1721],{},[1723,19962,1725],{},[1864,19964,19965],{},"0,4",[898,19967,9837],{},[1723,19969,2087],{},[1864,19971,3585],{},[902,19973,19974],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,19977,19978],{},[883,19979,19981],{"className":19980},[886],[888,19982,19983],{"xmlns":890},[892,19984,19985,20023],{},[895,19986,19987,19989,19991,19993,19995,19997,19999,20001,20003,20005,20007,20009,20011,20013,20016,20018,20020],{},[898,19988,2111],{},[1723,19990,1725],{},[898,19992,9837],{},[1723,19994,1759],{},[898,19996,1721],{},[1723,19998,1725],{},[898,20000,9837],{},[1723,20002,1759],{},[1864,20004,19965],{},[898,20006,9837],{},[1723,20008,1759],{},[1864,20010,3585],{},[1723,20012,1725],{},[1864,20014,20015],{},"0,6",[898,20017,9837],{},[1723,20019,1759],{},[1864,20021,20022],{},"10.",[902,20024,20025],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,20027,20028],{},[614,20029,20030,20031,1682,20054,20078,20079,8812,20092,20116,20117,8812,20134,20150,20151,1664],{},"Obrázek 7.3 — Přímky ",[883,20032,20034],{"className":20033},[886],[888,20035,20036],{"xmlns":890},[892,20037,20038,20052],{},[895,20039,20040,20042,20044,20046,20048,20050],{},[898,20041,1721],{},[1723,20043,1725],{},[1864,20045,19965],{},[898,20047,9837],{},[1723,20049,2087],{},[1864,20051,3585],{},[902,20053,19974],{"encoding":904},[883,20055,20057],{"className":20056},[886],[888,20058,20059],{"xmlns":890},[892,20060,20061,20075],{},[895,20062,20063,20065,20067,20069,20071,20073],{},[898,20064,2111],{},[1723,20066,1725],{},[1864,20068,20015],{},[898,20070,9837],{},[1723,20072,1759],{},[1864,20074,3585],{},[902,20076,20077],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,20080,20082],{"className":20081},[886],[888,20083,20084],{"xmlns":890},[892,20085,20086,20090],{},[895,20087,20088],{},[898,20089,9837],{},[902,20091,9837],{"encoding":904},[883,20093,20095],{"className":20094},[886],[888,20096,20097],{"xmlns":890},[892,20098,20099,20113],{},[895,20100,20101,20103,20106],{},[1723,20102,3456],{},[1864,20104,20105],{},"16,",[9096,20107,20108,20110],{"accent":2030},[1864,20109,2969],{},[1723,20111,20112],{},"ˉ",[902,20114,20115],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,20118,20120],{"className":20119},[886],[888,20121,20122],{"xmlns":890},[892,20123,20124,20132],{},[895,20125,20126,20128,20130],{},[898,20127,1721],{},[1723,20129,2031],{"separator":2030},[898,20131,2111],{},[902,20133,19926],{"encoding":904},[883,20135,20137],{"className":20136},[886],[888,20138,20139],{"xmlns":890},[892,20140,20141,20147],{},[895,20142,20143,20145],{},[1723,20144,1759],{},[1864,20146,3585],{},[902,20148,20149],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,20152,20154],{"className":20153},[886],[888,20155,20156],{"xmlns":890},[892,20157,20158,20170],{},[895,20159,20160,20162,20164,20166,20168],{},[1723,20161,1908],{"stretchy":1907},[1864,20163,2256],{},[1723,20165,2031],{"separator":2030},[1864,20167,3585],{},[1723,20169,1914],{"stretchy":1907},[902,20171,20172],{"encoding":904},"(0, 10)",[724,20174,20175,20176,8812,20194,20224,20225,1981,20228,20231,20232,8812,20256,1981,20259,20262],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,20177,20179],{"className":20178},[886],[888,20180,20181],{"xmlns":890},[892,20182,20183,20191],{},[895,20184,20185,20187,20189],{},[898,20186,9837],{},[1723,20188,1725],{},[1864,20190,2256],{},[902,20192,20193],{"encoding":904},"Y = 0",[883,20195,20197],{"className":20196},[886],[888,20198,20199],{"xmlns":890},[892,20200,20201,20221],{},[895,20202,20203,20205,20207,20209,20211,20213,20215,20217,20219],{},[898,20204,2111],{},[1723,20206,1908],{"stretchy":1907},[1864,20208,2256],{},[1723,20210,1914],{"stretchy":1907},[1723,20212,1725],{},[1723,20214,1759],{},[898,20216,2069],{},[1723,20218,2287],{},[1864,20220,2256],{},[902,20222,20223],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,20226,20227],{},"autonomních úsporách",[614,20229,20230],{},"autonomous savings","). Analogicky ",[883,20233,20235],{"className":20234},[886],[888,20236,20237],{"xmlns":890},[892,20238,20239,20253],{},[895,20240,20241,20243,20245,20247,20249,20251],{},[898,20242,1721],{},[1723,20244,1908],{"stretchy":1907},[1864,20246,2256],{},[1723,20248,1914],{"stretchy":1907},[1723,20250,1725],{},[898,20252,2069],{},[902,20254,20255],{"encoding":904},"C(0) = b",[38,20257,20258],{},"autonomní spotřeba",[614,20260,20261],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,20264,20266],{"id":20265},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,20268,20269,2628,20272,1981,20289,20292],{},[38,20270,20271],{},"Mezní sklon ke spotřebě",[883,20273,20275],{"className":20274},[886],[888,20276,20277],{"xmlns":890},[892,20278,20279,20287],{},[895,20280,20281,20283,20285],{},[898,20282,1728],{},[898,20284,1746],{},[898,20286,1721],{},[902,20288,2389],{"encoding":904},[614,20290,20291],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,20294,20295],{},[883,20296,20298],{"className":20297},[886],[888,20299,20300],{"xmlns":890},[892,20301,20302,20328],{},[895,20303,20304,20306,20308,20310,20312,20326],{},[898,20305,1728],{},[898,20307,1746],{},[898,20309,1721],{},[1723,20311,1725],{},[3058,20313,20314,20320],{},[895,20315,20316,20318],{},[898,20317,2930],{"mathvariant":2124},[898,20319,1721],{},[895,20321,20322,20324],{},[898,20323,2930],{"mathvariant":2124},[898,20325,9837],{},[898,20327,1664],{"mathvariant":2124},[902,20329,20330],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,20332,20333,2628,20336,1981,20353,20356],{},[38,20334,20335],{},"Mezní sklon k úsporám",[883,20337,20339],{"className":20338},[886],[888,20340,20341],{"xmlns":890},[892,20342,20343,20351],{},[895,20344,20345,20347,20349],{},[898,20346,1728],{},[898,20348,1746],{},[898,20350,2111],{},[902,20352,2408],{"encoding":904},[614,20354,20355],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,20358,20359],{},[883,20360,20362],{"className":20361},[886],[888,20363,20364],{"xmlns":890},[892,20365,20366,20392],{},[895,20367,20368,20370,20372,20374,20376,20390],{},[898,20369,1728],{},[898,20371,1746],{},[898,20373,2111],{},[1723,20375,1725],{},[3058,20377,20378,20384],{},[895,20379,20380,20382],{},[898,20381,2930],{"mathvariant":2124},[898,20383,2111],{},[895,20385,20386,20388],{},[898,20387,2930],{"mathvariant":2124},[898,20389,9837],{},[898,20391,1664],{"mathvariant":2124},[902,20393,20394],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,20396,20397,20398,20456],{},"Z (7.2) plyne ",[883,20399,20401],{"className":20400},[886],[888,20402,20403],{"xmlns":890},[892,20404,20405,20453],{},[895,20406,20407,20421,20423,20437,20439],{},[3058,20408,20409,20415],{},[895,20410,20411,20413],{},[898,20412,2930],{"mathvariant":2124},[898,20414,9837],{},[895,20416,20417,20419],{},[898,20418,2930],{"mathvariant":2124},[898,20420,9837],{},[1723,20422,1725],{},[3058,20424,20425,20431],{},[895,20426,20427,20429],{},[898,20428,2930],{"mathvariant":2124},[898,20430,1721],{},[895,20432,20433,20435],{},[898,20434,2930],{"mathvariant":2124},[898,20436,9837],{},[1723,20438,2087],{},[3058,20440,20441,20447],{},[895,20442,20443,20445],{},[898,20444,2930],{"mathvariant":2124},[898,20446,2111],{},[895,20448,20449,20451],{},[898,20450,2930],{"mathvariant":2124},[898,20452,9837],{},[902,20454,20455],{"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",[724,20458,20459],{},[883,20460,20462],{"className":20461},[886],[888,20463,20464],{"xmlns":890},[892,20465,20466,20529],{},[895,20467,20468,20520,20522,20524,20527],{},[13533,20469,20470],{"notation":13535},[3055,20471,20472],{"scriptlevel":2256,"displaystyle":1907},[3055,20473,20474],{"scriptlevel":2256,"displaystyle":1907},[3055,20475,20476],{"scriptlevel":2256,"displaystyle":2030},[895,20477,20478,20480,20482,20484,20486,20488,20490,20492,20494,20496,20498,20500,20502,20504,20506,20508,20510,20512,20514,20516,20518],{},[898,20479,1728],{},[898,20481,1746],{},[898,20483,1721],{},[1723,20485,2087],{},[898,20487,1728],{},[898,20489,1746],{},[898,20491,2111],{},[1723,20493,1725],{},[1864,20495,1866],{},[1723,20497,2031],{"separator":2030},[6588,20499],{"width":6590},[898,20501,1728],{},[898,20503,1746],{},[898,20505,2111],{},[1723,20507,1725],{},[1864,20509,1866],{},[1723,20511,1759],{},[898,20513,1728],{},[898,20515,1746],{},[898,20517,1721],{},[898,20519,1664],{"mathvariant":2124},[6588,20521],{"width":6590},[1723,20523,1908],{"stretchy":1907},[1864,20525,20526],{},"7.5",[1723,20528,1914],{"stretchy":1907},[902,20530,20531],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,20533,20534,2628,20537,20560,20561,1682,20583,20609],{},[38,20535,20536],{},"Pro lineární model",[883,20538,20540],{"className":20539},[886],[888,20541,20542],{"xmlns":890},[892,20543,20544,20558],{},[895,20545,20546,20548,20550,20552,20554,20556],{},[898,20547,1721],{},[1723,20549,1725],{},[898,20551,207],{},[898,20553,9837],{},[1723,20555,2087],{},[898,20557,2069],{},[902,20559,19614],{"encoding":904}," vychází ",[883,20562,20564],{"className":20563},[886],[888,20565,20566],{"xmlns":890},[892,20567,20568,20580],{},[895,20569,20570,20572,20574,20576,20578],{},[898,20571,1728],{},[898,20573,1746],{},[898,20575,1721],{},[1723,20577,1725],{},[898,20579,207],{},[902,20581,20582],{"encoding":904},"MPC = a",[883,20584,20586],{"className":20585},[886],[888,20587,20588],{"xmlns":890},[892,20589,20590,20606],{},[895,20591,20592,20594,20596,20598,20600,20602,20604],{},[898,20593,1728],{},[898,20595,1746],{},[898,20597,2111],{},[1723,20599,1725],{},[1864,20601,1866],{},[1723,20603,1759],{},[898,20605,207],{},[902,20607,20608],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,20611,20612,20615,20616,20638,20639,20667],{},[38,20613,20614],{},"Interpretace diferenciálem."," Pro pevné ",[883,20617,20619],{"className":20618},[886],[888,20620,20621],{"xmlns":890},[892,20622,20623,20635],{},[895,20624,20625,20627,20629],{},[898,20626,9837],{},[1723,20628,1725],{},[2057,20630,20631,20633],{},[898,20632,9837],{},[1723,20634,5066],{},[902,20636,20637],{"encoding":904},"Y = Y^*"," udává ",[883,20640,20642],{"className":20641},[886],[888,20643,20644],{"xmlns":890},[892,20645,20646,20664],{},[895,20647,20648,20650,20652,20654,20656,20662],{},[898,20649,1728],{},[898,20651,1746],{},[898,20653,1721],{},[1723,20655,1908],{"stretchy":1907},[2057,20657,20658,20660],{},[898,20659,9837],{},[1723,20661,5066],{},[1723,20663,1914],{"stretchy":1907},[902,20665,20666],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,20669,20670],{},[883,20671,20673],{"className":20672},[886],[888,20674,20675],{"xmlns":890},[892,20676,20677,20731],{},[895,20678,20679,20681,20683,20685,20687,20689,20691,20697,20699,20701,20703,20705,20707,20709,20711,20713,20715,20717,20719,20721,20723,20725,20727,20729],{},[898,20680,3611],{"mathvariant":2124},[898,20682,1721],{},[1723,20684,3456],{},[898,20686,2930],{"mathvariant":2124},[898,20688,1721],{},[1723,20690,1725],{},[2057,20692,20693,20695],{},[898,20694,1721],{},[1723,20696,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,20698,1908],{"stretchy":1907},[898,20700,9837],{},[1723,20702,1914],{"stretchy":1907},[3018,20704,3707],{},[898,20706,2930],{"mathvariant":2124},[898,20708,9837],{},[1723,20710,1725],{},[898,20712,1728],{},[898,20714,1746],{},[898,20716,1721],{},[1723,20718,1908],{"stretchy":1907},[898,20720,9837],{},[1723,20722,1914],{"stretchy":1907},[3018,20724,3707],{},[898,20726,2930],{"mathvariant":2124},[898,20728,9837],{},[898,20730,1664],{"mathvariant":2124},[902,20732,20733],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,20735,20736,20737,20773,20774,20777],{},"Analogicky ",[883,20738,20740],{"className":20739},[886],[888,20741,20742],{"xmlns":890},[892,20743,20744,20770],{},[895,20745,20746,20748,20750,20752,20754,20756,20758,20760,20762,20764,20766,20768],{},[898,20747,3611],{"mathvariant":2124},[898,20749,2111],{},[1723,20751,3456],{},[898,20753,1728],{},[898,20755,1746],{},[898,20757,2111],{},[1723,20759,1908],{"stretchy":1907},[898,20761,9837],{},[1723,20763,1914],{"stretchy":1907},[3018,20765,3707],{},[898,20767,2930],{"mathvariant":2124},[898,20769,9837],{},[902,20771,20772],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,20775,1145],{"className":20776,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,20779,20781],{"id":20780},"příklad-72","Příklad 7.2",[724,20783,19949,20784,20819,20820,20839],{},[883,20785,20787],{"className":20786},[886],[888,20788,20789],{"xmlns":890},[892,20790,20791,20816],{},[895,20792,20793,20795,20797,20800,20806,20808,20810,20812,20814],{},[898,20794,1721],{},[1723,20796,1725],{},[1864,20798,20799],{},"0,001",[2057,20801,20802,20804],{},[898,20803,9837],{},[1864,20805,2331],{},[1723,20807,2087],{},[1864,20809,3561],{},[898,20811,9837],{},[1723,20813,2087],{},[1864,20815,3840],{},[902,20817,20818],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,20821,20823],{"className":20822},[886],[888,20824,20825],{"xmlns":890},[892,20826,20827,20836],{},[895,20828,20829,20831,20833],{},[898,20830,9837],{},[1723,20832,2287],{},[1864,20834,20835],{},"400",[902,20837,20838],{"encoding":904},"Y \u003C 400",") platí",[724,20841,20842],{},[883,20843,20845],{"className":20844},[886],[888,20846,20847],{"xmlns":890},[892,20848,20849,20886],{},[895,20850,20851,20853,20855,20857,20859,20873,20875,20878,20880,20882,20884],{},[898,20852,1728],{},[898,20854,1746],{},[898,20856,1721],{},[1723,20858,1725],{},[3058,20860,20861,20867],{},[895,20862,20863,20865],{},[898,20864,2930],{"mathvariant":2124},[898,20866,1721],{},[895,20868,20869,20871],{},[898,20870,2930],{"mathvariant":2124},[898,20872,9837],{},[1723,20874,1725],{},[1864,20876,20877],{},"0,002",[898,20879,9837],{},[1723,20881,2087],{},[1864,20883,3561],{},[1723,20885,2031],{"separator":2030},[902,20887,20888],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,20890,20891],{},[883,20892,20894],{"className":20893},[886],[888,20895,20896],{"xmlns":890},[892,20897,20898,20931],{},[895,20899,20900,20902,20904,20906,20908,20910,20912,20914,20916,20918,20920,20922,20924,20926,20928],{},[898,20901,1728],{},[898,20903,1746],{},[898,20905,2111],{},[1723,20907,1725],{},[1864,20909,1866],{},[1723,20911,1759],{},[898,20913,1728],{},[898,20915,1746],{},[898,20917,1721],{},[1723,20919,1725],{},[1723,20921,1759],{},[1864,20923,20877],{},[898,20925,9837],{},[1723,20927,2087],{},[1864,20929,20930],{},"0,8.",[902,20932,20933],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,20935,20936,21016,21095],{},[123,20937,20938,1343,20966,20994,20995,8812,21013,1664],{},[883,20939,20941],{"className":20940},[886],[888,20942,20943],{"xmlns":890},[892,20944,20945,20963],{},[895,20946,20947,20949,20951,20953,20955,20957,20959,20961],{},[898,20948,1728],{},[898,20950,1746],{},[898,20952,1721],{},[1723,20954,1908],{"stretchy":1907},[1864,20956,3810],{},[1723,20958,1914],{"stretchy":1907},[1723,20960,1725],{},[1864,20962,19965],{},[902,20964,20965],{"encoding":904},"MPC(100) = 0{,}4",[883,20967,20969],{"className":20968},[886],[888,20970,20971],{"xmlns":890},[892,20972,20973,20991],{},[895,20974,20975,20977,20979,20981,20983,20985,20987,20989],{},[898,20976,1728],{},[898,20978,1746],{},[898,20980,2111],{},[1723,20982,1908],{"stretchy":1907},[1864,20984,3810],{},[1723,20986,1914],{"stretchy":1907},[1723,20988,1725],{},[1864,20990,20015],{},[902,20992,20993],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,20996,20998],{"className":20997},[886],[888,20999,21000],{"xmlns":890},[892,21001,21002,21010],{},[895,21003,21004,21006,21008],{},[898,21005,9837],{},[1723,21007,1725],{},[1864,21009,3810],{},[902,21011,21012],{"encoding":904},"Y = 100",[38,21014,21015],{},"větší sklon k úsporám",[123,21017,21018,1343,21046,20994,21074,8812,21092,1664],{},[883,21019,21021],{"className":21020},[886],[888,21022,21023],{"xmlns":890},[892,21024,21025,21043],{},[895,21026,21027,21029,21031,21033,21035,21037,21039,21041],{},[898,21028,1728],{},[898,21030,1746],{},[898,21032,1721],{},[1723,21034,1908],{"stretchy":1907},[1864,21036,9087],{},[1723,21038,1914],{"stretchy":1907},[1723,21040,1725],{},[1864,21042,20015],{},[902,21044,21045],{"encoding":904},"MPC(200) = 0{,}6",[883,21047,21049],{"className":21048},[886],[888,21050,21051],{"xmlns":890},[892,21052,21053,21071],{},[895,21054,21055,21057,21059,21061,21063,21065,21067,21069],{},[898,21056,1728],{},[898,21058,1746],{},[898,21060,2111],{},[1723,21062,1908],{"stretchy":1907},[1864,21064,9087],{},[1723,21066,1914],{"stretchy":1907},[1723,21068,1725],{},[1864,21070,19965],{},[902,21072,21073],{"encoding":904},"MPS(200) = 0{,}4",[883,21075,21077],{"className":21076},[886],[888,21078,21079],{"xmlns":890},[892,21080,21081,21089],{},[895,21082,21083,21085,21087],{},[898,21084,9837],{},[1723,21086,1725],{},[1864,21088,9087],{},[902,21090,21091],{"encoding":904},"Y = 200",[38,21093,21094],{},"větší sklon ke spotřebě",[123,21096,21097,21098,21116,21117,4634],{},"Přesně při ",[883,21099,21101],{"className":21100},[886],[888,21102,21103],{"xmlns":890},[892,21104,21105,21113],{},[895,21106,21107,21109,21111],{},[898,21108,9837],{},[1723,21110,1725],{},[1864,21112,9512],{},[902,21114,21115],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,21118,21120],{"className":21119},[886],[888,21121,21122],{"xmlns":890},[892,21123,21124,21144],{},[895,21125,21126,21128,21130,21132,21134,21136,21138,21140,21142],{},[898,21127,1728],{},[898,21129,1746],{},[898,21131,1721],{},[1723,21133,1725],{},[898,21135,1728],{},[898,21137,1746],{},[898,21139,2111],{},[1723,21141,1725],{},[1864,21143,5719],{},[902,21145,21146],{"encoding":904},"MPC = MPS = 0{,}5",[724,21148,21149,21150,21167,21168,21182,21183,3411,21196,21210,21211,21224,21225,21266],{},"Interpretace: při ",[883,21151,21153],{"className":21152},[886],[888,21154,21155],{"xmlns":890},[892,21156,21157,21165],{},[895,21158,21159,21161,21163],{},[898,21160,9837],{},[1723,21162,1725],{},[1864,21164,3810],{},[902,21166,21012],{"encoding":904}," se spotřeba mění ",[883,21169,21171],{"className":21170},[886],[888,21172,21173],{"xmlns":890},[892,21174,21175,21179],{},[895,21176,21177],{},[1864,21178,19965],{},[902,21180,21181],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,21184,21186],{"className":21185},[886],[888,21187,21188],{"xmlns":890},[892,21189,21190,21194],{},[895,21191,21192],{},[1864,21193,3810],{},[902,21195,3810],{"encoding":904},[883,21197,21199],{"className":21198},[886],[888,21200,21201],{"xmlns":890},[892,21202,21203,21208],{},[895,21204,21205],{},[1864,21206,21207],{},"101",[902,21209,21207],{"encoding":904},", změní se spotřeba přibližně o ",[883,21212,21214],{"className":21213},[886],[888,21215,21216],{"xmlns":890},[892,21217,21218,21222],{},[895,21219,21220],{},[1864,21221,19965],{},[902,21223,21181],{"encoding":904},". Skutečná změna ",[883,21226,21228],{"className":21227},[886],[888,21229,21230],{"xmlns":890},[892,21231,21232,21263],{},[895,21233,21234,21236,21238,21240,21242,21244,21246,21248,21250,21252,21254,21256,21258,21260],{},[898,21235,3611],{"mathvariant":2124},[898,21237,1721],{},[1723,21239,1725],{},[898,21241,1721],{},[1723,21243,1908],{"stretchy":1907},[1864,21245,21207],{},[1723,21247,1914],{"stretchy":1907},[1723,21249,1759],{},[898,21251,1721],{},[1723,21253,1908],{"stretchy":1907},[1864,21255,3810],{},[1723,21257,1914],{"stretchy":1907},[1723,21259,1725],{},[1864,21261,21262],{},"0,401",[902,21264,21265],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,21268,21269,21270],{},"Obecný trend: ",[38,21271,21272],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,21274,21276],{"id":21275},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,21278,21279,21280,1981,21283,21286,21287,1981,21290,12829,21293,1981,21296,21299],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,21281,21282],{},"makroekonomická rovnováha",[614,21284,21285],{},"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 ",[38,21288,21289],{},"agregátní poptávky",[614,21291,21292],{},"aggregate demand",[38,21294,21295],{},"agregátní nabídky",[614,21297,21298],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,21301,21303],{"id":21302},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,21305,21306],{},[3285,21307],{"alt":21308,"className":21309,"src":21310},"imek-keynesian-kriz",[210,3289],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,21312,21314],{"id":21313},"zadání-modelu","Zadání modelu",[724,21316,21317,21318,21331,21332,21345],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,21319,21321],{"className":21320},[886],[888,21322,21323],{"xmlns":890},[892,21324,21325,21329],{},[895,21326,21327],{},[898,21328,1721],{},[902,21330,1721],{"encoding":904}," a investice ",[883,21333,21335],{"className":21334},[886],[888,21336,21337],{"xmlns":890},[892,21338,21339,21343],{},[895,21340,21341],{},[898,21342,12885],{},[902,21344,12885],{"encoding":904},". Podmínka rovnováhy:",[724,21347,21348],{},[883,21349,21351],{"className":21350},[886],[888,21352,21353],{"xmlns":890},[892,21354,21355,21378],{},[895,21356,21357,21359,21361,21363,21365,21367,21369,21371,21373,21376],{},[898,21358,9837],{},[1723,21360,1725],{},[898,21362,1721],{},[1723,21364,2087],{},[898,21366,12885],{},[898,21368,1664],{"mathvariant":2124},[6588,21370],{"width":6590},[1723,21372,1908],{"stretchy":1907},[1864,21374,21375],{},"7.6",[1723,21377,1914],{"stretchy":1907},[902,21379,21380],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,21382,21384],{"id":21383},"soustava-rovnic","Soustava rovnic",[724,21386,21387,21388,21409,21410,21434],{},"Pro pevně zadané (plánované) investice ",[883,21389,21391],{"className":21390},[886],[888,21392,21393],{"xmlns":890},[892,21394,21395,21407],{},[895,21396,21397,21399,21401],{},[898,21398,12885],{},[1723,21400,1725],{},[2057,21402,21403,21405],{},[898,21404,12885],{},[1723,21406,5066],{},[902,21408,12896],{"encoding":904}," a funkci spotřeby ",[883,21411,21413],{"className":21412},[886],[888,21414,21415],{"xmlns":890},[892,21416,21417,21431],{},[895,21418,21419,21421,21423,21425,21427,21429],{},[898,21420,1721],{},[1723,21422,1725],{},[898,21424,1721],{},[1723,21426,1908],{"stretchy":1907},[898,21428,9837],{},[1723,21430,1914],{"stretchy":1907},[902,21432,21433],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,21436,21437],{},[883,21438,21440],{"className":21439},[886],[888,21441,21442],{"xmlns":890},[892,21443,21444,21520],{},[895,21445,21446,21511,21513,21515,21518],{},[21447,21448,21451,21483],"mtable",{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},"0.25em","right left",[21452,21453,21454,21461],"mtr",{},[21455,21456,21457],"mtd",{},[3055,21458,21459],{"scriptlevel":2256,"displaystyle":2030},[898,21460,9837],{},[21455,21462,21463],{},[3055,21464,21465],{"scriptlevel":2256,"displaystyle":2030},[895,21466,21467,21469,21471,21473,21475,21481],{},[895,21468],{},[1723,21470,1725],{},[898,21472,1721],{},[1723,21474,2087],{},[2057,21476,21477,21479],{},[898,21478,12885],{},[1723,21480,5066],{},[1723,21482,2031],{"separator":2030},[21452,21484,21485,21491],{},[21455,21486,21487],{},[3055,21488,21489],{"scriptlevel":2256,"displaystyle":2030},[898,21490,1721],{},[21455,21492,21493],{},[3055,21494,21495],{"scriptlevel":2256,"displaystyle":2030},[895,21496,21497,21499,21501,21503,21505,21507,21509],{},[895,21498],{},[1723,21500,1725],{},[898,21502,1721],{},[1723,21504,1908],{"stretchy":1907},[898,21506,9837],{},[1723,21508,1914],{"stretchy":1907},[1723,21510,2031],{"separator":2030},[6588,21512],{"width":6590},[1723,21514,1908],{"stretchy":1907},[1864,21516,21517],{},"7.7",[1723,21519,1914],{"stretchy":1907},[902,21521,21522],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,21524,21525,21526,2628,21528,1682,21545,2628,21548,1664],{},"jejímž řešením jsou ",[38,21527,14586],{},[883,21529,21531],{"className":21530},[886],[888,21532,21533],{"xmlns":890},[892,21534,21535,21543],{},[895,21536,21537],{},[2057,21538,21539,21541],{},[898,21540,9837],{},[898,21542,1846],{},[902,21544,14604],{"encoding":904},[38,21546,21547],{},"rovnovážná spotřeba",[883,21549,21551],{"className":21550},[886],[888,21552,21553],{"xmlns":890},[892,21554,21555,21563],{},[895,21556,21557],{},[2057,21558,21559,21561],{},[898,21560,1721],{},[898,21562,1846],{},[902,21564,14663],{"encoding":904},[198,21566,21568,21569],{"id":21567},"výpočet-yeye","Výpočet ",[883,21570,21572],{"className":21571},[886],[888,21573,21574],{"xmlns":890},[892,21575,21576,21584],{},[895,21577,21578],{},[2057,21579,21580,21582],{},[898,21581,9837],{},[898,21583,1846],{},[902,21585,14604],{"encoding":904},[724,21587,21588,21589,21612,21613,8395,21645],{},"Pro lineární spotřebu ",[883,21590,21592],{"className":21591},[886],[888,21593,21594],{"xmlns":890},[892,21595,21596,21610],{},[895,21597,21598,21600,21602,21604,21606,21608],{},[898,21599,1721],{},[1723,21601,1725],{},[898,21603,207],{},[898,21605,9837],{},[1723,21607,2087],{},[898,21609,2069],{},[902,21611,19614],{"encoding":904}," plyne z (7.7) rovnice ",[883,21614,21616],{"className":21615},[886],[888,21617,21618],{"xmlns":890},[892,21619,21620,21642],{},[895,21621,21622,21624,21626,21628,21630,21632,21634,21636],{},[898,21623,9837],{},[1723,21625,1725],{},[898,21627,207],{},[898,21629,9837],{},[1723,21631,2087],{},[898,21633,2069],{},[1723,21635,2087],{},[2057,21637,21638,21640],{},[898,21639,12885],{},[1723,21641,5066],{},[902,21643,21644],{"encoding":904},"Y = aY + b + I^*",[38,21646,21647],{},"redukovaný tvar",[724,21649,21650],{},[883,21651,21653],{"className":21652},[886],[888,21654,21655],{"xmlns":890},[892,21656,21657,21705],{},[895,21658,21659],{},[13533,21660,21661],{"notation":13535},[3055,21662,21663],{"scriptlevel":2256,"displaystyle":1907},[3055,21664,21665],{"scriptlevel":2256,"displaystyle":1907},[3055,21666,21667],{"scriptlevel":2256,"displaystyle":2030},[895,21668,21669,21671,21677,21679,21701,21703],{},[3018,21670,3707],{},[2057,21672,21673,21675],{},[898,21674,9837],{},[898,21676,1846],{},[1723,21678,1725],{},[3058,21680,21681,21693],{},[895,21682,21683,21685,21687],{},[898,21684,2069],{},[1723,21686,2087],{},[2057,21688,21689,21691],{},[898,21690,12885],{},[1723,21692,5066],{},[895,21694,21695,21697,21699],{},[1864,21696,1866],{},[1723,21698,1759],{},[898,21700,207],{},[898,21702,1664],{"mathvariant":2124},[3018,21704,3707],{},[902,21706,21707],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,21709,21711],{"id":21710},"příklad-73","Příklad 7.3",[724,21713,21714,21715,8812,21732,1682,21756,21782],{},"V modelu ",[883,21716,21718],{"className":21717},[886],[888,21719,21720],{"xmlns":890},[892,21721,21722,21730],{},[895,21723,21724,21726,21728],{},[898,21725,1721],{},[3018,21727,12991],{},[898,21729,12885],{},[902,21731,12996],{"encoding":904},[883,21733,21735],{"className":21734},[886],[888,21736,21737],{"xmlns":890},[892,21738,21739,21753],{},[895,21740,21741,21743,21745,21747,21749,21751],{},[898,21742,1721],{},[1723,21744,1725],{},[1864,21746,20015],{},[898,21748,9837],{},[1723,21750,2087],{},[1864,21752,3585],{},[902,21754,21755],{"encoding":904},"C = 0{,}6Y + 10",[883,21757,21759],{"className":21758},[886],[888,21760,21761],{"xmlns":890},[892,21762,21763,21779],{},[895,21764,21765,21767,21769,21771,21773],{},[898,21766,12885],{},[1723,21768,1725],{},[1864,21770,4227],{},[1723,21772,1725],{},[2057,21774,21775,21777],{},[898,21776,12885],{},[1723,21778,5066],{},[902,21780,21781],{"encoding":904},"I = 12 = I^*",". Soustava",[724,21784,21785],{},[883,21786,21788],{"className":21787},[886],[888,21789,21790],{"xmlns":890},[892,21791,21792,21848],{},[21447,21793,21794,21820],{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},[21452,21795,21796,21802],{},[21455,21797,21798],{},[3055,21799,21800],{"scriptlevel":2256,"displaystyle":2030},[898,21801,9837],{},[21455,21803,21804],{},[3055,21805,21806],{"scriptlevel":2256,"displaystyle":2030},[895,21807,21808,21810,21812,21814,21816,21818],{},[895,21809],{},[1723,21811,1725],{},[898,21813,1721],{},[1723,21815,2087],{},[1864,21817,4227],{},[1723,21819,2031],{"separator":2030},[21452,21821,21822,21828],{},[21455,21823,21824],{},[3055,21825,21826],{"scriptlevel":2256,"displaystyle":2030},[898,21827,1721],{},[21455,21829,21830],{},[3055,21831,21832],{"scriptlevel":2256,"displaystyle":2030},[895,21833,21834,21836,21838,21840,21842,21844,21846],{},[895,21835],{},[1723,21837,1725],{},[1864,21839,20015],{},[898,21841,9837],{},[1723,21843,2087],{},[1864,21845,3585],{},[1723,21847,2031],{"separator":2030},[902,21849,21850],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,21852,21853,21854,1343,21877,21900,21901,4634],{},"má řešení ",[883,21855,21857],{"className":21856},[886],[888,21858,21859],{"xmlns":890},[892,21860,21861,21874],{},[895,21862,21863,21869,21871],{},[2057,21864,21865,21867],{},[898,21866,9837],{},[898,21868,1846],{},[1723,21870,1725],{},[1864,21872,21873],{},"55",[902,21875,21876],{"encoding":904},"Y^E = 55",[883,21878,21880],{"className":21879},[886],[888,21881,21882],{"xmlns":890},[892,21883,21884,21897],{},[895,21885,21886,21892,21894],{},[2057,21887,21888,21890],{},[898,21889,1721],{},[898,21891,1846],{},[1723,21893,1725],{},[1864,21895,21896],{},"43",[902,21898,21899],{"encoding":904},"C^E = 43"," (a ",[883,21902,21904],{"className":21903},[886],[888,21905,21906],{"xmlns":890},[892,21907,21908,21920],{},[895,21909,21910,21916,21918],{},[2057,21911,21912,21914],{},[898,21913,2111],{},[898,21915,1846],{},[1723,21917,1725],{},[1864,21919,4227],{},[902,21921,21922],{"encoding":904},"S^E = 12",[724,21924,21925],{},[614,21926,21927,21928,21950,21951,12829,21972,21995,21996,1664],{},"Obrázek 7.5 — Přímky ",[883,21929,21931],{"className":21930},[886],[888,21932,21933],{"xmlns":890},[892,21934,21935,21947],{},[895,21936,21937,21939,21941,21943,21945],{},[898,21938,1721],{},[1723,21940,1725],{},[898,21942,9837],{},[1723,21944,1759],{},[1864,21946,4227],{},[902,21948,21949],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,21952,21954],{"className":21953},[886],[888,21955,21956],{"xmlns":890},[892,21957,21958,21970],{},[895,21959,21960,21962,21964,21966,21968],{},[898,21961,9837],{},[1723,21963,1725],{},[898,21965,1721],{},[1723,21967,2087],{},[898,21969,12885],{},[902,21971,15445],{"encoding":904},[883,21973,21975],{"className":21974},[886],[888,21976,21977],{"xmlns":890},[892,21978,21979,21993],{},[895,21980,21981,21983,21985,21987,21989,21991],{},[898,21982,1721],{},[1723,21984,1725],{},[1864,21986,20015],{},[898,21988,9837],{},[1723,21990,2087],{},[1864,21992,3585],{},[902,21994,21755],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,21997,21999],{"className":21998},[886],[888,22000,22001],{"xmlns":890},[892,22002,22003,22035],{},[895,22004,22005,22007,22013,22015,22021,22023,22025,22027,22029,22031,22033],{},[1723,22006,3212],{"stretchy":1907},[2057,22008,22009,22011],{},[898,22010,9837],{},[898,22012,1846],{},[1723,22014,2031],{"separator":2030},[2057,22016,22017,22019],{},[898,22018,1721],{},[898,22020,1846],{},[1723,22022,3227],{"stretchy":1907},[1723,22024,1725],{},[1723,22026,3212],{"stretchy":1907},[1864,22028,21873],{},[1723,22030,2031],{"separator":2030},[1864,22032,21896],{},[1723,22034,3227],{"stretchy":1907},[902,22036,22037],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,22039,22040,22043,22044,22061,22062,1664],{},[38,22041,22042],{},"Komentář k přechodu."," Model ",[883,22045,22047],{"className":22046},[886],[888,22048,22049],{"xmlns":890},[892,22050,22051,22059],{},[895,22052,22053,22055,22057],{},[898,22054,1721],{},[3018,22056,12991],{},[898,22058,12885],{},[902,22060,12996],{"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 ",[38,22063,22064,22065],{},"model ",[883,22066,22068],{"className":22067},[886],[888,22069,22070],{"xmlns":890},[892,22071,22072,22084],{},[895,22073,22074,22076,22078,22080,22082],{},[898,22075,1721],{},[3018,22077,12991],{},[898,22079,12885],{},[3018,22081,12991],{},[898,22083,12813],{},[902,22085,18914],{"encoding":904},[115,22087,22089],{"id":22088},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,22091,21314],{"id":22092},"zadání-modelu-1",[724,22094,22095,22096,22113,22114,2628,22117,1981,22130,22133],{},"Rozšíření modelu ",[883,22097,22099],{"className":22098},[886],[888,22100,22101],{"xmlns":890},[892,22102,22103,22111],{},[895,22104,22105,22107,22109],{},[898,22106,1721],{},[3018,22108,12991],{},[898,22110,12885],{},[902,22112,12996],{"encoding":904}," o ",[38,22115,22116],{},"vládní výdaje",[883,22118,22120],{"className":22119},[886],[888,22121,22122],{"xmlns":890},[892,22123,22124,22128],{},[895,22125,22126],{},[898,22127,12813],{},[902,22129,12813],{"encoding":904},[614,22131,22132],{},"government expenditure","). Podmínka rovnováhy:",[724,22135,22136],{},[883,22137,22139],{"className":22138},[886],[888,22140,22141],{"xmlns":890},[892,22142,22143,22170],{},[895,22144,22145,22147,22149,22151,22153,22155,22157,22159,22161,22163,22165,22168],{},[898,22146,9837],{},[1723,22148,1725],{},[898,22150,1721],{},[1723,22152,2087],{},[898,22154,12885],{},[1723,22156,2087],{},[898,22158,12813],{},[898,22160,1664],{"mathvariant":2124},[6588,22162],{"width":6590},[1723,22164,1908],{"stretchy":1907},[1864,22166,22167],{},"7.8",[1723,22169,1914],{"stretchy":1907},[902,22171,22172],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,22174,22175,22176,2628,22179,1981,22192,22195],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,22177,22178],{},"zdaněním domácností",[883,22180,22182],{"className":22181},[886],[888,22183,22184],{"xmlns":890},[892,22185,22186,22190],{},[895,22187,22188],{},[898,22189,1754],{},[902,22191,1754],{"encoding":904},[614,22193,22194],{},"taxation","). Zdanění bývá:",[120,22197,22198,22231,22256],{},[123,22199,22200,22201,2031],{},"úměrné důchodu: ",[883,22202,22204],{"className":22203},[886],[888,22205,22206],{"xmlns":890},[892,22207,22208,22228],{},[895,22209,22210,22212,22214,22216,22218,22220,22222,22224,22226],{},[898,22211,1754],{},[1723,22213,1725],{},[898,22215,1754],{},[1723,22217,1908],{"stretchy":1907},[898,22219,9837],{},[1723,22221,1914],{"stretchy":1907},[1723,22223,1725],{},[898,22225,19549],{},[898,22227,9837],{},[902,22229,22230],{"encoding":904},"T = T(Y) = tY",[123,22232,22233,22234,2031],{},"fixní: ",[883,22235,22237],{"className":22236},[886],[888,22238,22239],{"xmlns":890},[892,22240,22241,22253],{},[895,22242,22243,22245,22247],{},[898,22244,1754],{},[1723,22246,1725],{},[2057,22248,22249,22251],{},[898,22250,1754],{},[1723,22252,5066],{},[902,22254,22255],{"encoding":904},"T = T^*",[123,22257,22258,22259,22287,22288,1664],{},"kombinované: ",[883,22260,22262],{"className":22261},[886],[888,22263,22264],{"xmlns":890},[892,22265,22266,22284],{},[895,22267,22268,22270,22272,22278,22280,22282],{},[898,22269,1754],{},[1723,22271,1725],{},[2057,22273,22274,22276],{},[898,22275,1754],{},[1723,22277,5066],{},[1723,22279,2087],{},[898,22281,19549],{},[898,22283,9837],{},[902,22285,22286],{"encoding":904},"T = T^* + tY",", kde ",[883,22289,22291],{"className":22290},[886],[888,22292,22293],{"xmlns":890},[892,22294,22295,22307],{},[895,22296,22297,22299,22301,22303,22305],{},[1864,22298,2256],{},[1723,22300,8389],{},[898,22302,19549],{},[1723,22304,2287],{},[1864,22306,1866],{},[902,22308,22309],{"encoding":904},"0 \\le t \u003C 1",[4584,22311,22312],{},[724,22313,22314,22316,22317,22338,22339,22342,22343,22356,22357,12829,22383,2628,22386,22412,22413,22441,22442,1682,22455,22473],{},[883,22315,5124],{}," Pozor na disponibilní důchod\nV modelu ",[883,22318,22320],{"className":22319},[886],[888,22321,22322],{"xmlns":890},[892,22323,22324,22336],{},[895,22325,22326,22328,22330,22332,22334],{},[898,22327,1721],{},[3018,22329,12991],{},[898,22331,12885],{},[3018,22333,12991],{},[898,22335,12813],{},[902,22337,18914],{"encoding":904}," je nutné ",[38,22340,22341],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,22344,22346],{"className":22345},[886],[888,22347,22348],{"xmlns":890},[892,22349,22350,22354],{},[895,22351,22352],{},[898,22353,9837],{},[902,22355,9837],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,22358,22360],{"className":22359},[886],[888,22361,22362],{"xmlns":890},[892,22363,22364,22380],{},[895,22365,22366,22368,22370,22372,22374,22376,22378],{},[898,22367,9837],{},[1723,22369,1725],{},[898,22371,1721],{},[1723,22373,2087],{},[898,22375,12885],{},[1723,22377,2087],{},[898,22379,12813],{},[902,22381,22382],{"encoding":904},"Y = C + I + G",[38,22384,22385],{},"disponibilní důchod",[883,22387,22389],{"className":22388},[886],[888,22390,22391],{"xmlns":890},[892,22392,22393,22409],{},[895,22394,22395,22401,22403,22405,22407],{},[1931,22396,22397,22399],{},[898,22398,9837],{},[898,22400,4897],{},[1723,22402,1725],{},[898,22404,9837],{},[1723,22406,1759],{},[898,22408,1754],{},[902,22410,22411],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,22414,22416],{"className":22415},[886],[888,22417,22418],{"xmlns":890},[892,22419,22420,22438],{},[895,22421,22422,22424,22426,22428,22430,22436],{},[898,22423,1721],{},[1723,22425,1725],{},[898,22427,1721],{},[1723,22429,1908],{"stretchy":1907},[1931,22431,22432,22434],{},[898,22433,9837],{},[898,22435,4897],{},[1723,22437,1914],{"stretchy":1907},[902,22439,22440],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,22443,22445],{"className":22444},[886],[888,22446,22447],{"xmlns":890},[892,22448,22449,22453],{},[895,22450,22451],{},[898,22452,9837],{},[902,22454,9837],{"encoding":904},[883,22456,22458],{"className":22457},[886],[888,22459,22460],{"xmlns":890},[892,22461,22462,22470],{},[895,22463,22464],{},[1931,22465,22466,22468],{},[898,22467,9837],{},[898,22469,4897],{},[902,22471,22472],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,22475,22476,1981,22479,1914],{},[38,22477,22478],{},"Disponibilní důchod",[614,22480,22481],{},"disposable income",[724,22483,22484],{},[883,22485,22487],{"className":22486},[886],[888,22488,22489],{"xmlns":890},[892,22490,22491,22507],{},[895,22492,22493,22499,22501,22503,22505],{},[1931,22494,22495,22497],{},[898,22496,9837],{},[898,22498,4897],{},[1723,22500,1725],{},[898,22502,9837],{},[1723,22504,1759],{},[898,22506,1754],{},[902,22508,22411],{"encoding":904},[724,22510,22511,22512,1664],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,22513,22515],{"className":22514},[886],[888,22516,22517],{"xmlns":890},[892,22518,22519,22537],{},[895,22520,22521,22523,22525,22527,22529,22535],{},[898,22522,1721],{},[1723,22524,1725],{},[898,22526,1721],{},[1723,22528,1908],{"stretchy":1907},[1931,22530,22531,22533],{},[898,22532,9837],{},[898,22534,4897],{},[1723,22536,1914],{"stretchy":1907},[902,22538,22440],{"encoding":904},[198,22540,21384],{"id":22541},"soustava-rovnic-1",[724,22543,22544,22545,1343,22566,22588,22589,3430],{},"Pro pevně zadané ",[883,22546,22548],{"className":22547},[886],[888,22549,22550],{"xmlns":890},[892,22551,22552,22564],{},[895,22553,22554,22556,22558],{},[898,22555,12885],{},[1723,22557,1725],{},[2057,22559,22560,22562],{},[898,22561,12885],{},[1723,22563,5066],{},[902,22565,12896],{"encoding":904},[883,22567,22569],{"className":22568},[886],[888,22570,22571],{"xmlns":890},[892,22572,22573,22585],{},[895,22574,22575,22577,22579],{},[898,22576,12813],{},[1723,22578,1725],{},[2057,22580,22581,22583],{},[898,22582,12813],{},[1723,22584,5066],{},[902,22586,22587],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,22590,22592],{"className":22591},[886],[888,22593,22594],{"xmlns":890},[892,22595,22596,22616],{},[895,22597,22598,22600,22602,22604,22606,22612,22614],{},[898,22599,9837],{},[1723,22601,2031],{"separator":2030},[898,22603,1721],{},[1723,22605,2031],{"separator":2030},[1931,22607,22608,22610],{},[898,22609,9837],{},[898,22611,4897],{},[1723,22613,2031],{"separator":2030},[898,22615,1754],{},[902,22617,22618],{"encoding":904},"Y, C, Y_D, T",[724,22620,22621],{},[883,22622,22624],{"className":22623},[886],[888,22625,22626],{"xmlns":890},[892,22627,22628,22769],{},[895,22629,22630,22760,22762,22764,22767],{},[21447,22631,22632,22670,22698,22730],{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},[21452,22633,22634,22640],{},[21455,22635,22636],{},[3055,22637,22638],{"scriptlevel":2256,"displaystyle":2030},[898,22639,9837],{},[21455,22641,22642],{},[3055,22643,22644],{"scriptlevel":2256,"displaystyle":2030},[895,22645,22646,22648,22650,22652,22654,22660,22662,22668],{},[895,22647],{},[1723,22649,1725],{},[898,22651,1721],{},[1723,22653,2087],{},[2057,22655,22656,22658],{},[898,22657,12885],{},[1723,22659,5066],{},[1723,22661,2087],{},[2057,22663,22664,22666],{},[898,22665,12813],{},[1723,22667,5066],{},[1723,22669,2031],{"separator":2030},[21452,22671,22672,22678],{},[21455,22673,22674],{},[3055,22675,22676],{"scriptlevel":2256,"displaystyle":2030},[898,22677,1754],{},[21455,22679,22680],{},[3055,22681,22682],{"scriptlevel":2256,"displaystyle":2030},[895,22683,22684,22686,22688,22690,22692,22694,22696],{},[895,22685],{},[1723,22687,1725],{},[898,22689,1754],{},[1723,22691,1908],{"stretchy":1907},[898,22693,9837],{},[1723,22695,1914],{"stretchy":1907},[1723,22697,2031],{"separator":2030},[21452,22699,22700,22706],{},[21455,22701,22702],{},[3055,22703,22704],{"scriptlevel":2256,"displaystyle":2030},[898,22705,1721],{},[21455,22707,22708],{},[3055,22709,22710],{"scriptlevel":2256,"displaystyle":2030},[895,22711,22712,22714,22716,22718,22720,22726,22728],{},[895,22713],{},[1723,22715,1725],{},[898,22717,1721],{},[1723,22719,1908],{"stretchy":1907},[1931,22721,22722,22724],{},[898,22723,9837],{},[898,22725,4897],{},[1723,22727,1914],{"stretchy":1907},[1723,22729,2031],{"separator":2030},[21452,22731,22732,22742],{},[21455,22733,22734],{},[3055,22735,22736],{"scriptlevel":2256,"displaystyle":2030},[1931,22737,22738,22740],{},[898,22739,9837],{},[898,22741,4897],{},[21455,22743,22744],{},[3055,22745,22746],{"scriptlevel":2256,"displaystyle":2030},[895,22747,22748,22750,22752,22754,22756,22758],{},[895,22749],{},[1723,22751,1725],{},[898,22753,9837],{},[1723,22755,1759],{},[898,22757,1754],{},[1723,22759,2031],{"separator":2030},[6588,22761],{"width":6590},[1723,22763,1908],{"stretchy":1907},[1864,22765,22766],{},"7.9",[1723,22768,1914],{"stretchy":1907},[902,22770,22771],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,22773,22774,22775,22819,22820,1664],{},"s řešeními ",[883,22776,22778],{"className":22777},[886],[888,22779,22780],{"xmlns":890},[892,22781,22782,22816],{},[895,22783,22784,22790,22792,22798,22800,22806,22808],{},[2057,22785,22786,22788],{},[898,22787,9837],{},[898,22789,1846],{},[1723,22791,2031],{"separator":2030},[2057,22793,22794,22796],{},[898,22795,1721],{},[898,22797,1846],{},[1723,22799,2031],{"separator":2030},[2057,22801,22802,22804],{},[898,22803,1754],{},[898,22805,1846],{},[1723,22807,2031],{"separator":2030},[2220,22809,22810,22812,22814],{},[898,22811,9837],{},[898,22813,4897],{},[898,22815,1846],{},[902,22817,22818],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,22821,22823],{"className":22822},[886],[888,22824,22825],{"xmlns":890},[892,22826,22827,22853],{},[895,22828,22829,22835,22837,22845,22847],{},[2057,22830,22831,22833],{},[898,22832,2111],{},[898,22834,1846],{},[1723,22836,1725],{},[2220,22838,22839,22841,22843],{},[898,22840,9837],{},[898,22842,4897],{},[898,22844,1846],{},[1723,22846,1759],{},[2057,22848,22849,22851],{},[898,22850,1721],{},[898,22852,1846],{},[902,22854,22855],{"encoding":904},"S^E = Y_D^E - C^E",[4584,22857,22858,22863],{},[724,22859,22860,22862],{},[883,22861,5283],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,22864,22865,22888,22971,23026,23116],{},[123,22866,22867,22870,22871,1664],{},[38,22868,22869],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,22872,22874],{"className":22873},[886],[888,22875,22876],{"xmlns":890},[892,22877,22878,22886],{},[895,22879,22880],{},[1931,22881,22882,22884],{},[898,22883,9837],{},[898,22885,4897],{},[902,22887,22472],{"encoding":904},[123,22889,22890,22939,22940,22957,22958,1664],{},[38,22891,22892,22893,22913,22914],{},"Dosaď ",[883,22894,22896],{"className":22895},[886],[888,22897,22898],{"xmlns":890},[892,22899,22900,22910],{},[895,22901,22902,22904,22906,22908],{},[898,22903,1754],{},[1723,22905,1908],{"stretchy":1907},[898,22907,9837],{},[1723,22909,1914],{"stretchy":1907},[902,22911,22912],{"encoding":904},"T(Y)"," do ",[883,22915,22917],{"className":22916},[886],[888,22918,22919],{"xmlns":890},[892,22920,22921,22937],{},[895,22922,22923,22929,22931,22933,22935],{},[1931,22924,22925,22927],{},[898,22926,9837],{},[898,22928,4897],{},[1723,22930,1725],{},[898,22932,9837],{},[1723,22934,1759],{},[898,22936,1754],{},[902,22938,22411],{"encoding":904}," — dostaneš ",[883,22941,22943],{"className":22942},[886],[888,22944,22945],{"xmlns":890},[892,22946,22947,22955],{},[895,22948,22949],{},[1931,22950,22951,22953],{},[898,22952,9837],{},[898,22954,4897],{},[902,22956,22472],{"encoding":904}," jako lineární funkci ",[883,22959,22961],{"className":22960},[886],[888,22962,22963],{"xmlns":890},[892,22964,22965,22969],{},[895,22966,22967],{},[898,22968,9837],{},[902,22970,9837],{"encoding":904},[123,22972,22973,22939,23000,22957,23013,1664],{},[38,22974,22892,22975,22999],{},[883,22976,22978],{"className":22977},[886],[888,22979,22980],{"xmlns":890},[892,22981,22982,22996],{},[895,22983,22984,22990,22992,22994],{},[1931,22985,22986,22988],{},[898,22987,9837],{},[898,22989,4897],{},[1723,22991,1908],{"stretchy":1907},[898,22993,9837],{},[1723,22995,1914],{"stretchy":1907},[902,22997,22998],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,23001,23003],{"className":23002},[886],[888,23004,23005],{"xmlns":890},[892,23006,23007,23011],{},[895,23008,23009],{},[898,23010,1721],{},[902,23012,1721],{"encoding":904},[883,23014,23016],{"className":23015},[886],[888,23017,23018],{"xmlns":890},[892,23019,23020,23024],{},[895,23021,23022],{},[898,23023,9837],{},[902,23025,9837],{"encoding":904},[123,23027,23028,2628,23050,23084,23085,23098,23099,1664],{},[38,23029,22892,23030,23049],{},[883,23031,23033],{"className":23032},[886],[888,23034,23035],{"xmlns":890},[892,23036,23037,23047],{},[895,23038,23039,23041,23043,23045],{},[898,23040,1721],{},[1723,23042,1908],{"stretchy":1907},[898,23044,9837],{},[1723,23046,1914],{"stretchy":1907},[902,23048,14917],{"encoding":904}," do podmínky rovnováhy",[883,23051,23053],{"className":23052},[886],[888,23054,23055],{"xmlns":890},[892,23056,23057,23081],{},[895,23058,23059,23061,23063,23065,23067,23073,23075],{},[898,23060,9837],{},[1723,23062,1725],{},[898,23064,1721],{},[1723,23066,2087],{},[2057,23068,23069,23071],{},[898,23070,12885],{},[1723,23072,5066],{},[1723,23074,2087],{},[2057,23076,23077,23079],{},[898,23078,12813],{},[1723,23080,5066],{},[902,23082,23083],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,23086,23088],{"className":23087},[886],[888,23089,23090],{"xmlns":890},[892,23091,23092,23096],{},[895,23093,23094],{},[898,23095,9837],{},[902,23097,9837],{"encoding":904},", odtud ",[883,23100,23102],{"className":23101},[886],[888,23103,23104],{"xmlns":890},[892,23105,23106,23114],{},[895,23107,23108],{},[2057,23109,23110,23112],{},[898,23111,9837],{},[898,23113,1846],{},[902,23115,14604],{"encoding":904},[123,23117,23118,23121,23122,1343,23140,1343,23160,1343,23177,1664],{},[38,23119,23120],{},"Zpětným dosazením"," dopočítej ",[883,23123,23125],{"className":23124},[886],[888,23126,23127],{"xmlns":890},[892,23128,23129,23137],{},[895,23130,23131],{},[2057,23132,23133,23135],{},[898,23134,1754],{},[898,23136,1846],{},[902,23138,23139],{"encoding":904},"T^E",[883,23141,23143],{"className":23142},[886],[888,23144,23145],{"xmlns":890},[892,23146,23147,23157],{},[895,23148,23149],{},[2220,23150,23151,23153,23155],{},[898,23152,9837],{},[898,23154,4897],{},[898,23156,1846],{},[902,23158,23159],{"encoding":904},"Y_D^E",[883,23161,23163],{"className":23162},[886],[888,23164,23165],{"xmlns":890},[892,23166,23167,23175],{},[895,23168,23169],{},[2057,23170,23171,23173],{},[898,23172,1721],{},[898,23174,1846],{},[902,23176,14663],{"encoding":904},[883,23178,23180],{"className":23179},[886],[888,23181,23182],{"xmlns":890},[892,23183,23184,23192],{},[895,23185,23186],{},[2057,23187,23188,23190],{},[898,23189,2111],{},[898,23191,1846],{},[902,23193,23194],{"encoding":904},"S^E",[198,23196,23198],{"id":23197},"příklad-74","Příklad 7.4",[724,23200,21714,23201,23222,23223,1343,23254,1343,23278,1343,23300,23322],{},[883,23202,23204],{"className":23203},[886],[888,23205,23206],{"xmlns":890},[892,23207,23208,23220],{},[895,23209,23210,23212,23214,23216,23218],{},[898,23211,1721],{},[3018,23213,12991],{},[898,23215,12885],{},[3018,23217,12991],{},[898,23219,12813],{},[902,23221,18914],{"encoding":904}," jsou dány ",[883,23224,23226],{"className":23225},[886],[888,23227,23228],{"xmlns":890},[892,23229,23230,23251],{},[895,23231,23232,23234,23236,23239,23241,23247,23249],{},[898,23233,1721],{},[1723,23235,1725],{},[1864,23237,23238],{},"0,9",[3018,23240,3707],{},[1931,23242,23243,23245],{},[898,23244,9837],{},[898,23246,4897],{},[1723,23248,2087],{},[1864,23250,6607],{},[902,23252,23253],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,23255,23257],{"className":23256},[886],[888,23258,23259],{"xmlns":890},[892,23260,23261,23275],{},[895,23262,23263,23265,23267,23269,23271,23273],{},[898,23264,1754],{},[1723,23266,1725],{},[1864,23268,3561],{},[898,23270,9837],{},[1723,23272,2087],{},[1864,23274,5714],{},[902,23276,23277],{"encoding":904},"T = 0{,}2Y + 25",[883,23279,23281],{"className":23280},[886],[888,23282,23283],{"xmlns":890},[892,23284,23285,23297],{},[895,23286,23287,23293,23295],{},[2057,23288,23289,23291],{},[898,23290,12885],{},[1723,23292,5066],{},[1723,23294,1725],{},[1864,23296,15739],{},[902,23298,23299],{"encoding":904},"I^* = 35",[883,23301,23303],{"className":23302},[886],[888,23304,23305],{"xmlns":890},[892,23306,23307,23319],{},[895,23308,23309,23315,23317],{},[2057,23310,23311,23313],{},[898,23312,12813],{},[1723,23314,5066],{},[1723,23316,1725],{},[1864,23318,9744],{},[902,23320,23321],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,23324,23325],{},[883,23326,23328],{"className":23327},[886],[888,23329,23330],{"xmlns":890},[892,23331,23332,23456],{},[21447,23333,23334,23364,23392,23426],{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},[21452,23335,23336,23342],{},[21455,23337,23338],{},[3055,23339,23340],{"scriptlevel":2256,"displaystyle":2030},[898,23341,9837],{},[21455,23343,23344],{},[3055,23345,23346],{"scriptlevel":2256,"displaystyle":2030},[895,23347,23348,23350,23352,23354,23356,23358,23360,23362],{},[895,23349],{},[1723,23351,1725],{},[898,23353,1721],{},[1723,23355,2087],{},[1864,23357,15739],{},[1723,23359,2087],{},[1864,23361,9744],{},[1723,23363,2031],{"separator":2030},[21452,23365,23366,23372],{},[21455,23367,23368],{},[3055,23369,23370],{"scriptlevel":2256,"displaystyle":2030},[898,23371,1754],{},[21455,23373,23374],{},[3055,23375,23376],{"scriptlevel":2256,"displaystyle":2030},[895,23377,23378,23380,23382,23384,23386,23388,23390],{},[895,23379],{},[1723,23381,1725],{},[1864,23383,3561],{},[898,23385,9837],{},[1723,23387,2087],{},[1864,23389,5714],{},[1723,23391,2031],{"separator":2030},[21452,23393,23394,23400],{},[21455,23395,23396],{},[3055,23397,23398],{"scriptlevel":2256,"displaystyle":2030},[898,23399,1721],{},[21455,23401,23402],{},[3055,23403,23404],{"scriptlevel":2256,"displaystyle":2030},[895,23405,23406,23408,23410,23412,23414,23420,23422,23424],{},[895,23407],{},[1723,23409,1725],{},[1864,23411,23238],{},[3018,23413,3707],{},[1931,23415,23416,23418],{},[898,23417,9837],{},[898,23419,4897],{},[1723,23421,2087],{},[1864,23423,6607],{},[1723,23425,2031],{"separator":2030},[21452,23427,23428,23438],{},[21455,23429,23430],{},[3055,23431,23432],{"scriptlevel":2256,"displaystyle":2030},[1931,23433,23434,23436],{},[898,23435,9837],{},[898,23437,4897],{},[21455,23439,23440],{},[3055,23441,23442],{"scriptlevel":2256,"displaystyle":2030},[895,23443,23444,23446,23448,23450,23452,23454],{},[895,23445],{},[1723,23447,1725],{},[898,23449,9837],{},[1723,23451,1759],{},[898,23453,1754],{},[898,23455,1664],{"mathvariant":2124},[902,23457,23458],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,23460,23461,23464,23465,23519,23520,23566,23567,3430],{},[38,23462,23463],{},"Řešení."," Z definice ",[883,23466,23468],{"className":23467},[886],[888,23469,23470],{"xmlns":890},[892,23471,23472,23516],{},[895,23473,23474,23480,23482,23484,23486,23488,23490,23492,23494,23496,23498,23500,23502,23504,23506,23508,23510,23512,23514],{},[1931,23475,23476,23478],{},[898,23477,9837],{},[898,23479,4897],{},[1723,23481,1725],{},[898,23483,9837],{},[1723,23485,1759],{},[898,23487,1754],{},[1723,23489,1725],{},[898,23491,9837],{},[1723,23493,1759],{},[1723,23495,1908],{"stretchy":1907},[1864,23497,3561],{},[898,23499,9837],{},[1723,23501,2087],{},[1864,23503,5714],{},[1723,23505,1914],{"stretchy":1907},[1723,23507,1725],{},[1864,23509,15290],{},[898,23511,9837],{},[1723,23513,1759],{},[1864,23515,5714],{},[902,23517,23518],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,23521,23523],{"className":23522},[886],[888,23524,23525],{"xmlns":890},[892,23526,23527,23563],{},[895,23528,23529,23531,23533,23535,23537,23539,23541,23543,23545,23547,23549,23551,23553,23556,23558,23560],{},[898,23530,1721],{},[1723,23532,1725],{},[1864,23534,23238],{},[1723,23536,1908],{"stretchy":1907},[1864,23538,15290],{},[898,23540,9837],{},[1723,23542,1759],{},[1864,23544,5714],{},[1723,23546,1914],{"stretchy":1907},[1723,23548,2087],{},[1864,23550,6607],{},[1723,23552,1725],{},[1864,23554,23555],{},"0,72",[898,23557,9837],{},[1723,23559,2087],{},[1864,23561,23562],{},"47,5",[902,23564,23565],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,23568,23570],{"className":23569},[886],[888,23571,23572],{"xmlns":890},[892,23573,23574,23592],{},[895,23575,23576,23578,23580,23582,23584,23586,23588,23590],{},[898,23577,9837],{},[1723,23579,1725],{},[1864,23581,23555],{},[898,23583,9837],{},[1723,23585,2087],{},[1864,23587,23562],{},[1723,23589,2087],{},[1864,23591,21873],{},[902,23593,23594],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,23596,23597],{},[883,23598,23600],{"className":23599},[886],[888,23601,23602],{"xmlns":890},[892,23603,23604,23645],{},[895,23605,23606,23609,23611,23613,23616,23618,23620,23622,23628,23630,23640,23642],{},[1864,23607,23608],{},"0,28",[898,23610,9837],{},[1723,23612,1725],{},[1864,23614,23615],{},"102,5",[3018,23617,4699],{},[1723,23619,15709],{},[3018,23621,4699],{},[2057,23623,23624,23626],{},[898,23625,9837],{},[898,23627,1846],{},[1723,23629,1725],{},[3055,23631,23632],{"scriptlevel":2256,"displaystyle":1907},[3058,23633,23634,23637],{},[1864,23635,23636],{},"5125",[1864,23638,23639],{},"14",[1723,23641,6610],{},[1864,23643,23644],{},"366,071.",[902,23646,23647],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,23649,23650],{},"Rovnovážné veličiny:",[120,23652,23653,23688,23740,23794,23842],{},[123,23654,23655,2031],{},[883,23656,23658],{"className":23657},[886],[888,23659,23660],{"xmlns":890},[892,23661,23662,23685],{},[895,23663,23664,23670,23672,23680,23682],{},[2057,23665,23666,23668],{},[898,23667,9837],{},[898,23669,1846],{},[1723,23671,1725],{},[3055,23673,23674],{"scriptlevel":2256,"displaystyle":1907},[3058,23675,23676,23678],{},[1864,23677,23636],{},[1864,23679,23639],{},[1723,23681,6610],{},[1864,23683,23684],{},"366,071",[902,23686,23687],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,23689,23690,2031],{},[883,23691,23693],{"className":23692},[886],[888,23694,23695],{"xmlns":890},[892,23696,23697,23737],{},[895,23698,23699,23705,23707,23709,23711,23717,23719,23721,23723,23732,23734],{},[2057,23700,23701,23703],{},[898,23702,1754],{},[898,23704,1846],{},[1723,23706,1725],{},[1864,23708,3561],{},[3018,23710,3707],{},[2057,23712,23713,23715],{},[898,23714,9837],{},[898,23716,1846],{},[1723,23718,2087],{},[1864,23720,5714],{},[1723,23722,1725],{},[3055,23724,23725],{"scriptlevel":2256,"displaystyle":1907},[3058,23726,23727,23730],{},[1864,23728,23729],{},"1375",[1864,23731,23639],{},[1723,23733,6610],{},[1864,23735,23736],{},"98,214",[902,23738,23739],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,23741,23742,2031],{},[883,23743,23745],{"className":23744},[886],[888,23746,23747],{"xmlns":890},[892,23748,23749,23791],{},[895,23750,23751,23759,23761,23767,23769,23775,23777,23786,23788],{},[2220,23752,23753,23755,23757],{},[898,23754,9837],{},[898,23756,4897],{},[898,23758,1846],{},[1723,23760,1725],{},[2057,23762,23763,23765],{},[898,23764,9837],{},[898,23766,1846],{},[1723,23768,1759],{},[2057,23770,23771,23773],{},[898,23772,1754],{},[898,23774,1846],{},[1723,23776,1725],{},[3055,23778,23779],{"scriptlevel":2256,"displaystyle":1907},[3058,23780,23781,23784],{},[1864,23782,23783],{},"3750",[1864,23785,23639],{},[1723,23787,6610],{},[1864,23789,23790],{},"267,857",[902,23792,23793],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,23795,23796,2031],{},[883,23797,23799],{"className":23798},[886],[888,23800,23801],{"xmlns":890},[892,23802,23803,23839],{},[895,23804,23805,23811,23813,23819,23821,23823,23825,23834,23836],{},[2057,23806,23807,23809],{},[898,23808,1721],{},[898,23810,1846],{},[1723,23812,1725],{},[2057,23814,23815,23817],{},[898,23816,9837],{},[898,23818,1846],{},[1723,23820,1759],{},[1864,23822,21873],{},[1723,23824,1725],{},[3055,23826,23827],{"scriptlevel":2256,"displaystyle":1907},[3058,23828,23829,23832],{},[1864,23830,23831],{},"4355",[1864,23833,23639],{},[1723,23835,6610],{},[1864,23837,23838],{},"311,071",[902,23840,23841],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,23843,23844,23900],{},[883,23845,23847],{"className":23846},[886],[888,23848,23849],{"xmlns":890},[892,23850,23851,23897],{},[895,23852,23853,23859,23861,23869,23871,23877,23879,23881,23890,23892,23894],{},[2057,23854,23855,23857],{},[898,23856,2111],{},[898,23858,1846],{},[1723,23860,1725],{},[2220,23862,23863,23865,23867],{},[898,23864,9837],{},[898,23866,4897],{},[898,23868,1846],{},[1723,23870,1759],{},[2057,23872,23873,23875],{},[898,23874,1721],{},[898,23876,1846],{},[1723,23878,1725],{},[1723,23880,1759],{},[3055,23882,23883],{"scriptlevel":2256,"displaystyle":1907},[3058,23884,23885,23888],{},[1864,23886,23887],{},"605",[1864,23889,23639],{},[1723,23891,6610],{},[1723,23893,1759],{},[1864,23895,23896],{},"43,214",[902,23898,23899],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,23902,23903,22043,23905,23926,23927,23930,23931,23954,23955,1664],{},[38,23904,22042],{},[883,23906,23908],{"className":23907},[886],[888,23909,23910],{"xmlns":890},[892,23911,23912,23924],{},[895,23913,23914,23916,23918,23920,23922],{},[898,23915,1721],{},[3018,23917,12991],{},[898,23919,12885],{},[3018,23921,12991],{},[898,23923,12813],{},[902,23925,18914],{"encoding":904}," stále uvažuje ",[38,23928,23929],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,23932,23934],{"className":23933},[886],[888,23935,23936],{"xmlns":890},[892,23937,23938,23951],{},[895,23939,23940,23942,23944,23947,23949],{},[898,23941,13021],{},[1723,23943,1725],{},[898,23945,23946],{},"B",[1723,23948,1759],{},[898,23950,1728],{},[902,23952,23953],{"encoding":904},"X = B - M"," dává ",[38,23956,22064,23957],{},[883,23958,23960],{"className":23959},[886],[888,23961,23962],{"xmlns":890},[892,23963,23964,23980],{},[895,23965,23966,23968,23970,23972,23974,23976,23978],{},[898,23967,1721],{},[3018,23969,12991],{},[898,23971,12885],{},[3018,23973,12991],{},[898,23975,12813],{},[3018,23977,12991],{},[898,23979,13021],{},[902,23981,13024],{"encoding":904},[115,23983,23985],{"id":23984},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,23987,21314],{"id":23988},"zadání-modelu-2",[724,23990,23991,23992,2628,23995,22287,24016,24029,24030,12829,24033,24046],{},"Rozšíření o ",[38,23993,23994],{},"čistý export",[883,23996,23998],{"className":23997},[886],[888,23999,24000],{"xmlns":890},[892,24001,24002,24014],{},[895,24003,24004,24006,24008,24010,24012],{},[898,24005,13021],{},[1723,24007,1725],{},[898,24009,23946],{},[1723,24011,1759],{},[898,24013,1728],{},[902,24015,23953],{"encoding":904},[883,24017,24019],{"className":24018},[886],[888,24020,24021],{"xmlns":890},[892,24022,24023,24027],{},[895,24024,24025],{},[898,24026,23946],{},[902,24028,23946],{"encoding":904}," je hrubý export (",[614,24031,24032],{},"brutto export",[883,24034,24036],{"className":24035},[886],[888,24037,24038],{"xmlns":890},[892,24039,24040,24044],{},[895,24041,24042],{},[898,24043,1728],{},[902,24045,1728],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,24048,24049],{},[883,24050,24052],{"className":24051},[886],[888,24053,24054],{"xmlns":890},[892,24055,24056,24076],{},[895,24057,24058,24060,24062,24064,24066,24072,24074],{},[898,24059,1728],{},[1723,24061,1725],{},[898,24063,1728],{},[1723,24065,1908],{"stretchy":1907},[1931,24067,24068,24070],{},[898,24069,9837],{},[898,24071,4897],{},[1723,24073,1914],{"stretchy":1907},[898,24075,1664],{"mathvariant":2124},[902,24077,24078],{"encoding":904},"M = M(Y_D).",[724,24080,24081],{},"Podmínka rovnováhy:",[724,24083,24084],{},[883,24085,24087],{"className":24086},[886],[888,24088,24089],{"xmlns":890},[892,24090,24091,24128],{},[895,24092,24093,24095,24097,24099,24101,24103,24105,24107,24109,24111,24113,24115,24117,24119,24121,24124,24126],{},[898,24094,9837],{},[1723,24096,1725],{},[898,24098,1721],{},[1723,24100,2087],{},[898,24102,12885],{},[1723,24104,2087],{},[898,24106,12813],{},[1723,24108,2087],{},[898,24110,23946],{},[1723,24112,1759],{},[898,24114,1728],{},[898,24116,1664],{"mathvariant":2124},[6588,24118],{"width":6590},[1723,24120,1908],{"stretchy":1907},[1864,24122,24123],{},"7.10",[3018,24125,207],{},[1723,24127,1914],{"stretchy":1907},[902,24129,24130],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,24132,21384],{"id":24133},"soustava-rovnic-2",[724,24135,22544,24136,24170,24171,3430],{},[883,24137,24139],{"className":24138},[886],[888,24140,24141],{"xmlns":890},[892,24142,24143,24167],{},[895,24144,24145,24151,24153,24159,24161],{},[2057,24146,24147,24149],{},[898,24148,12885],{},[1723,24150,5066],{},[1723,24152,2031],{"separator":2030},[2057,24154,24155,24157],{},[898,24156,12813],{},[1723,24158,5066],{},[1723,24160,2031],{"separator":2030},[2057,24162,24163,24165],{},[898,24164,23946],{},[1723,24166,5066],{},[902,24168,24169],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,24172,24174],{"className":24173},[886],[888,24175,24176],{"xmlns":890},[892,24177,24178,24202],{},[895,24179,24180,24182,24184,24186,24188,24190,24192,24198,24200],{},[898,24181,9837],{},[1723,24183,2031],{"separator":2030},[898,24185,1721],{},[1723,24187,2031],{"separator":2030},[898,24189,1754],{},[1723,24191,2031],{"separator":2030},[1931,24193,24194,24196],{},[898,24195,9837],{},[898,24197,4897],{},[1723,24199,2031],{"separator":2030},[898,24201,1728],{},[902,24203,24204],{"encoding":904},"Y, C, T, Y_D, M",[724,24206,24207],{},[883,24208,24210],{"className":24209},[886],[888,24211,24212],{"xmlns":890},[892,24213,24214,24398],{},[895,24215,24216,24390,24392,24394,24396],{},[21447,24217,24218,24250,24280,24308,24340],{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},[21452,24219,24220,24226],{},[21455,24221,24222],{},[3055,24223,24224],{"scriptlevel":2256,"displaystyle":2030},[898,24225,1721],{},[21455,24227,24228],{},[3055,24229,24230],{"scriptlevel":2256,"displaystyle":2030},[895,24231,24232,24234,24236,24238,24240,24246,24248],{},[895,24233],{},[1723,24235,1725],{},[898,24237,1721],{},[1723,24239,1908],{"stretchy":1907},[1931,24241,24242,24244],{},[898,24243,9837],{},[898,24245,4897],{},[1723,24247,1914],{"stretchy":1907},[1723,24249,2031],{"separator":2030},[21452,24251,24252,24262],{},[21455,24253,24254],{},[3055,24255,24256],{"scriptlevel":2256,"displaystyle":2030},[1931,24257,24258,24260],{},[898,24259,9837],{},[898,24261,4897],{},[21455,24263,24264],{},[3055,24265,24266],{"scriptlevel":2256,"displaystyle":2030},[895,24267,24268,24270,24272,24274,24276,24278],{},[895,24269],{},[1723,24271,1725],{},[898,24273,9837],{},[1723,24275,1759],{},[898,24277,1754],{},[1723,24279,2031],{"separator":2030},[21452,24281,24282,24288],{},[21455,24283,24284],{},[3055,24285,24286],{"scriptlevel":2256,"displaystyle":2030},[898,24287,1754],{},[21455,24289,24290],{},[3055,24291,24292],{"scriptlevel":2256,"displaystyle":2030},[895,24293,24294,24296,24298,24300,24302,24304,24306],{},[895,24295],{},[1723,24297,1725],{},[898,24299,1754],{},[1723,24301,1908],{"stretchy":1907},[898,24303,9837],{},[1723,24305,1914],{"stretchy":1907},[1723,24307,2031],{"separator":2030},[21452,24309,24310,24316],{},[21455,24311,24312],{},[3055,24313,24314],{"scriptlevel":2256,"displaystyle":2030},[898,24315,1728],{},[21455,24317,24318],{},[3055,24319,24320],{"scriptlevel":2256,"displaystyle":2030},[895,24321,24322,24324,24326,24328,24330,24336,24338],{},[895,24323],{},[1723,24325,1725],{},[898,24327,1728],{},[1723,24329,1908],{"stretchy":1907},[1931,24331,24332,24334],{},[898,24333,9837],{},[898,24335,4897],{},[1723,24337,1914],{"stretchy":1907},[1723,24339,2031],{"separator":2030},[21452,24341,24342,24348],{},[21455,24343,24344],{},[3055,24345,24346],{"scriptlevel":2256,"displaystyle":2030},[898,24347,9837],{},[21455,24349,24350],{},[3055,24351,24352],{"scriptlevel":2256,"displaystyle":2030},[895,24353,24354,24356,24358,24360,24362,24368,24370,24376,24378,24384,24386,24388],{},[895,24355],{},[1723,24357,1725],{},[898,24359,1721],{},[1723,24361,2087],{},[2057,24363,24364,24366],{},[898,24365,12885],{},[1723,24367,5066],{},[1723,24369,2087],{},[2057,24371,24372,24374],{},[898,24373,12813],{},[1723,24375,5066],{},[1723,24377,2087],{},[2057,24379,24380,24382],{},[898,24381,23946],{},[1723,24383,5066],{},[1723,24385,1759],{},[898,24387,1728],{},[898,24389,1664],{"mathvariant":2124},[6588,24391],{"width":6590},[1723,24393,1908],{"stretchy":1907},[1864,24395,24123],{},[1723,24397,1914],{"stretchy":1907},[902,24399,24400],{"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)",[198,24402,24404],{"id":24403},"příklad-75","Příklad 7.5",[724,24406,24407,24408,1343,24440,1343,24467,1343,24488,1343,24510,1343,24532,24555],{},"Dáno: ",[883,24409,24411],{"className":24410},[886],[888,24412,24413],{"xmlns":890},[892,24414,24415,24437],{},[895,24416,24417,24419,24421,24424,24426,24432,24434],{},[898,24418,1721],{},[1723,24420,1725],{},[1864,24422,24423],{},"0,75",[3018,24425,3707],{},[1931,24427,24428,24430],{},[898,24429,9837],{},[898,24431,4897],{},[1723,24433,2087],{},[1864,24435,24436],{},"750",[902,24438,24439],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,24441,24443],{"className":24442},[886],[888,24444,24445],{"xmlns":890},[892,24446,24447,24464],{},[895,24448,24449,24451,24453,24456,24458],{},[898,24450,1728],{},[1723,24452,1725],{},[1864,24454,24455],{},"0,15",[3018,24457,3707],{},[1931,24459,24460,24462],{},[898,24461,9837],{},[898,24463,4897],{},[902,24465,24466],{"encoding":904},"M = 0{,}15\\,Y_D",[883,24468,24470],{"className":24469},[886],[888,24471,24472],{"xmlns":890},[892,24473,24474,24485],{},[895,24475,24476,24478,24480,24483],{},[898,24477,1754],{},[1723,24479,1725],{},[1864,24481,24482],{},"0,25",[898,24484,9837],{},[902,24486,24487],{"encoding":904},"T = 0{,}25Y",[883,24489,24491],{"className":24490},[886],[888,24492,24493],{"xmlns":890},[892,24494,24495,24507],{},[895,24496,24497,24503,24505],{},[2057,24498,24499,24501],{},[898,24500,12885],{},[1723,24502,5066],{},[1723,24504,1725],{},[1864,24506,15811],{},[902,24508,24509],{"encoding":904},"I^* = 500",[883,24511,24513],{"className":24512},[886],[888,24514,24515],{"xmlns":890},[892,24516,24517,24529],{},[895,24518,24519,24525,24527],{},[2057,24520,24521,24523],{},[898,24522,12813],{},[1723,24524,5066],{},[1723,24526,1725],{},[1864,24528,9512],{},[902,24530,24531],{"encoding":904},"G^* = 150",[883,24533,24535],{"className":24534},[886],[888,24536,24537],{"xmlns":890},[892,24538,24539,24552],{},[895,24540,24541,24547,24549],{},[2057,24542,24543,24545],{},[898,24544,23946],{},[1723,24546,5066],{},[1723,24548,1725],{},[1864,24550,24551],{},"800",[902,24553,24554],{"encoding":904},"B^* = 800",". Soustava:",[724,24557,24558],{},[883,24559,24561],{"className":24560},[886],[888,24562,24563],{"xmlns":890},[892,24564,24565,24783],{},[21447,24566,24567,24613,24655,24691,24733],{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},[21452,24568,24569,24585],{},[21455,24570,24571],{},[3055,24572,24573],{"scriptlevel":2256,"displaystyle":2030},[895,24574,24575,24577,24579,24581,24583],{},[1723,24576,1908],{"stretchy":1907},[898,24578,12742],{},[1864,24580,1866],{},[1723,24582,1914],{"stretchy":1907},[3018,24584,3020],{},[21455,24586,24587],{},[3055,24588,24589],{"scriptlevel":2256,"displaystyle":2030},[895,24590,24591,24593,24595,24597,24599,24601,24607,24609,24611],{},[895,24592],{},[898,24594,1721],{},[1723,24596,1725],{},[1864,24598,24423],{},[3018,24600,3707],{},[1931,24602,24603,24605],{},[898,24604,9837],{},[898,24606,4897],{},[1723,24608,2087],{},[1864,24610,24436],{},[1723,24612,2031],{"separator":2030},[21452,24614,24615,24631],{},[21455,24616,24617],{},[3055,24618,24619],{"scriptlevel":2256,"displaystyle":2030},[895,24620,24621,24623,24625,24627,24629],{},[1723,24622,1908],{"stretchy":1907},[898,24624,12742],{},[1864,24626,2331],{},[1723,24628,1914],{"stretchy":1907},[3018,24630,3020],{},[21455,24632,24633],{},[3055,24634,24635],{"scriptlevel":2256,"displaystyle":2030},[895,24636,24637,24639,24645,24647,24649,24651,24653],{},[895,24638],{},[1931,24640,24641,24643],{},[898,24642,9837],{},[898,24644,4897],{},[1723,24646,1725],{},[898,24648,9837],{},[1723,24650,1759],{},[898,24652,1754],{},[1723,24654,2031],{"separator":2030},[21452,24656,24657,24673],{},[21455,24658,24659],{},[3055,24660,24661],{"scriptlevel":2256,"displaystyle":2030},[895,24662,24663,24665,24667,24669,24671],{},[1723,24664,1908],{"stretchy":1907},[898,24666,12742],{},[1864,24668,2909],{},[1723,24670,1914],{"stretchy":1907},[3018,24672,3020],{},[21455,24674,24675],{},[3055,24676,24677],{"scriptlevel":2256,"displaystyle":2030},[895,24678,24679,24681,24683,24685,24687,24689],{},[895,24680],{},[898,24682,1754],{},[1723,24684,1725],{},[1864,24686,24482],{},[898,24688,9837],{},[1723,24690,2031],{"separator":2030},[21452,24692,24693,24709],{},[21455,24694,24695],{},[3055,24696,24697],{"scriptlevel":2256,"displaystyle":2030},[895,24698,24699,24701,24703,24705,24707],{},[1723,24700,1908],{"stretchy":1907},[898,24702,12742],{},[1864,24704,3080],{},[1723,24706,1914],{"stretchy":1907},[3018,24708,3020],{},[21455,24710,24711],{},[3055,24712,24713],{"scriptlevel":2256,"displaystyle":2030},[895,24714,24715,24717,24719,24721,24723,24725,24731],{},[895,24716],{},[898,24718,1728],{},[1723,24720,1725],{},[1864,24722,24455],{},[3018,24724,3707],{},[1931,24726,24727,24729],{},[898,24728,9837],{},[898,24730,4897],{},[1723,24732,2031],{"separator":2030},[21452,24734,24735,24751],{},[21455,24736,24737],{},[3055,24738,24739],{"scriptlevel":2256,"displaystyle":2030},[895,24740,24741,24743,24745,24747,24749],{},[1723,24742,1908],{"stretchy":1907},[898,24744,12742],{},[1864,24746,2962],{},[1723,24748,1914],{"stretchy":1907},[3018,24750,3020],{},[21455,24752,24753],{},[3055,24754,24755],{"scriptlevel":2256,"displaystyle":2030},[895,24756,24757,24759,24761,24763,24765,24767,24769,24771,24773,24775,24777,24779,24781],{},[895,24758],{},[898,24760,9837],{},[1723,24762,1725],{},[898,24764,1721],{},[1723,24766,2087],{},[1864,24768,15811],{},[1723,24770,2087],{},[1864,24772,9512],{},[1723,24774,2087],{},[1864,24776,24551],{},[1723,24778,1759],{},[898,24780,1728],{},[898,24782,1664],{"mathvariant":2124},[902,24784,24785],{"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}",[724,24787,24788,24789,24823],{},"Postupná substituce — z (r3) do (r2): ",[883,24790,24792],{"className":24791},[886],[888,24793,24794],{"xmlns":890},[892,24795,24796,24820],{},[895,24797,24798,24804,24806,24808,24810,24812,24814,24816,24818],{},[1931,24799,24800,24802],{},[898,24801,9837],{},[898,24803,4897],{},[1723,24805,1725],{},[898,24807,9837],{},[1723,24809,1759],{},[1864,24811,24482],{},[898,24813,9837],{},[1723,24815,1725],{},[1864,24817,24423],{},[898,24819,9837],{},[902,24821,24822],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,24825,24826],{},[883,24827,24829],{"className":24828},[886],[888,24830,24831],{"xmlns":890},[892,24832,24833,24874],{},[895,24834,24835,24837,24839,24841,24843,24845,24847,24849,24851,24853,24855,24857,24859,24861,24863,24866,24868,24870,24872],{},[1723,24836,1908],{"stretchy":1907},[898,24838,12742],{},[1864,24840,2969],{},[1723,24842,1914],{"stretchy":1907},[3018,24844,3020],{},[898,24846,1721],{},[1723,24848,1725],{},[1864,24850,24423],{},[1723,24852,3897],{},[1864,24854,24423],{},[898,24856,9837],{},[1723,24858,2087],{},[1864,24860,24436],{},[1723,24862,1725],{},[1864,24864,24865],{},"0,5625",[898,24867,9837],{},[1723,24869,2087],{},[1864,24871,24436],{},[1723,24873,2031],{"separator":2030},[902,24875,24876],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,24878,24879],{},[883,24880,24882],{"className":24881},[886],[888,24883,24884],{"xmlns":890},[892,24885,24886,24920],{},[895,24887,24888,24890,24892,24895,24897,24899,24901,24903,24905,24907,24909,24911,24913,24916,24918],{},[1723,24889,1908],{"stretchy":1907},[898,24891,12742],{},[1864,24893,24894],{},"7",[1723,24896,1914],{"stretchy":1907},[3018,24898,3020],{},[898,24900,1728],{},[1723,24902,1725],{},[1864,24904,24455],{},[1723,24906,3897],{},[1864,24908,24423],{},[898,24910,9837],{},[1723,24912,1725],{},[1864,24914,24915],{},"0,1125",[898,24917,9837],{},[898,24919,1664],{"mathvariant":2124},[902,24921,24922],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,24924,24925],{},"Dosazením do (r5):",[724,24927,24928],{},[883,24929,24931],{"className":24930},[886],[888,24932,24933],{"xmlns":890},[892,24934,24935,24979],{},[895,24936,24937,24939,24941,24943,24945,24947,24949,24951,24953,24955,24957,24959,24961,24963,24965,24967,24969,24972,24974,24976],{},[898,24938,9837],{},[1723,24940,1725],{},[1864,24942,24865],{},[898,24944,9837],{},[1723,24946,2087],{},[1864,24948,24436],{},[1723,24950,2087],{},[1864,24952,15811],{},[1723,24954,2087],{},[1864,24956,9512],{},[1723,24958,2087],{},[1864,24960,24551],{},[1723,24962,1759],{},[1864,24964,24915],{},[898,24966,9837],{},[1723,24968,1725],{},[1864,24970,24971],{},"0,45",[898,24973,9837],{},[1723,24975,2087],{},[1864,24977,24978],{},"2200.",[902,24980,24981],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,24983,24984,24985,6299,25007,25030],{},"Odtud ",[883,24986,24988],{"className":24987},[886],[888,24989,24990],{"xmlns":890},[892,24991,24992,25004],{},[895,24993,24994,24997,24999,25001],{},[1864,24995,24996],{},"0,55",[898,24998,9837],{},[1723,25000,1725],{},[1864,25002,25003],{},"2200",[902,25005,25006],{"encoding":904},"0{,}55Y = 2200",[883,25008,25010],{"className":25009},[886],[888,25011,25012],{"xmlns":890},[892,25013,25014,25027],{},[895,25015,25016,25022,25024],{},[2057,25017,25018,25020],{},[898,25019,9837],{},[898,25021,1846],{},[1723,25023,1725],{},[1864,25025,25026],{},"4000",[902,25028,25029],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,25032,25033,25056,25088,25123,25156,25192],{},[123,25034,25035,2031],{},[883,25036,25038],{"className":25037},[886],[888,25039,25040],{"xmlns":890},[892,25041,25042,25054],{},[895,25043,25044,25050,25052],{},[2057,25045,25046,25048],{},[898,25047,9837],{},[898,25049,1846],{},[1723,25051,1725],{},[1864,25053,25026],{},[902,25055,25029],{"encoding":904},[123,25057,25058,2031],{},[883,25059,25061],{"className":25060},[886],[888,25062,25063],{"xmlns":890},[892,25064,25065,25085],{},[895,25066,25067,25073,25075,25077,25079,25081,25083],{},[2057,25068,25069,25071],{},[898,25070,1754],{},[898,25072,1846],{},[1723,25074,1725],{},[1864,25076,24482],{},[1723,25078,3897],{},[1864,25080,25026],{},[1723,25082,1725],{},[1864,25084,3506],{},[902,25086,25087],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,25089,25090,2031],{},[883,25091,25093],{"className":25092},[886],[888,25094,25095],{"xmlns":890},[892,25096,25097,25120],{},[895,25098,25099,25107,25109,25111,25113,25115,25117],{},[2220,25100,25101,25103,25105],{},[898,25102,9837],{},[898,25104,4897],{},[898,25106,1846],{},[1723,25108,1725],{},[1864,25110,24423],{},[1723,25112,3897],{},[1864,25114,25026],{},[1723,25116,1725],{},[1864,25118,25119],{},"3000",[902,25121,25122],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,25124,25125,2031],{},[883,25126,25128],{"className":25127},[886],[888,25129,25130],{"xmlns":890},[892,25131,25132,25153],{},[895,25133,25134,25140,25142,25144,25146,25148,25150],{},[2057,25135,25136,25138],{},[898,25137,1728],{},[898,25139,1846],{},[1723,25141,1725],{},[1864,25143,24455],{},[1723,25145,3897],{},[1864,25147,25119],{},[1723,25149,1725],{},[1864,25151,25152],{},"450",[902,25154,25155],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,25157,25158,2031],{},[883,25159,25161],{"className":25160},[886],[888,25162,25163],{"xmlns":890},[892,25164,25165,25189],{},[895,25166,25167,25173,25175,25177,25179,25181,25183,25185,25187],{},[2057,25168,25169,25171],{},[898,25170,1721],{},[898,25172,1846],{},[1723,25174,1725],{},[1864,25176,24423],{},[1723,25178,3897],{},[1864,25180,25119],{},[1723,25182,2087],{},[1864,25184,24436],{},[1723,25186,1725],{},[1864,25188,25119],{},[902,25190,25191],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,25193,25194,25234],{},[883,25195,25197],{"className":25196},[886],[888,25198,25199],{"xmlns":890},[892,25200,25201,25231],{},[895,25202,25203,25209,25211,25219,25221,25227,25229],{},[2057,25204,25205,25207],{},[898,25206,2111],{},[898,25208,1846],{},[1723,25210,1725],{},[2220,25212,25213,25215,25217],{},[898,25214,9837],{},[898,25216,4897],{},[898,25218,1846],{},[1723,25220,1759],{},[2057,25222,25223,25225],{},[898,25224,1721],{},[898,25226,1846],{},[1723,25228,1725],{},[1864,25230,2256],{},[902,25232,25233],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,25236,25237,25239,25240,1343,25257,1682,25278,25303,25304,25307,25308,25321,25322,1664],{},[38,25238,22042],{}," Modely ",[883,25241,25243],{"className":25242},[886],[888,25244,25245],{"xmlns":890},[892,25246,25247,25255],{},[895,25248,25249,25251,25253],{},[898,25250,1721],{},[3018,25252,12991],{},[898,25254,12885],{},[902,25256,12996],{"encoding":904},[883,25258,25260],{"className":25259},[886],[888,25261,25262],{"xmlns":890},[892,25263,25264,25276],{},[895,25265,25266,25268,25270,25272,25274],{},[898,25267,1721],{},[3018,25269,12991],{},[898,25271,12885],{},[3018,25273,12991],{},[898,25275,12813],{},[902,25277,18914],{"encoding":904},[883,25279,25281],{"className":25280},[886],[888,25282,25283],{"xmlns":890},[892,25284,25285,25301],{},[895,25286,25287,25289,25291,25293,25295,25297,25299],{},[898,25288,1721],{},[3018,25290,12991],{},[898,25292,12885],{},[3018,25294,12991],{},[898,25296,12813],{},[3018,25298,12991],{},[898,25300,13021],{},[902,25302,13024],{"encoding":904}," pokládají investice za ",[38,25305,25306],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,25309,25311],{"className":25310},[886],[888,25312,25313],{"xmlns":890},[892,25314,25315,25319],{},[895,25316,25317],{},[898,25318,12742],{},[902,25320,12742],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,25323,25324],{},"model IS-LM",[115,25326,25328],{"id":25327},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,25330,25331,25332,25336,25337,25340,25341,25344],{},"V článku ",[207,25333,25335],{"className":25334,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,25338,25339],{},"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 ",[38,25342,25343],{},"výraznější"," než v mikroekonomických modelech.",[724,25346,25347],{},[3285,25348],{"alt":25349,"className":25350,"src":25351},"imek-multiplikatorovy-efekt-chain",[210,3289],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,25353,12865,25354,1343,25371,1343,25392,25417,25418,25421,25422,25440,25441,25459,25460,25478,25479,25482,25483,1343,25500,25517,25518,25520],{},[883,25355,25357],{"className":25356},[886],[888,25358,25359],{"xmlns":890},[892,25360,25361,25369],{},[895,25362,25363,25365,25367],{},[898,25364,1721],{},[3018,25366,12991],{},[898,25368,12885],{},[902,25370,12996],{"encoding":904},[883,25372,25374],{"className":25373},[886],[888,25375,25376],{"xmlns":890},[892,25377,25378,25390],{},[895,25379,25380,25382,25384,25386,25388],{},[898,25381,1721],{},[3018,25383,12991],{},[898,25385,12885],{},[3018,25387,12991],{},[898,25389,12813],{},[902,25391,18914],{"encoding":904},[883,25393,25395],{"className":25394},[886],[888,25396,25397],{"xmlns":890},[892,25398,25399,25415],{},[895,25400,25401,25403,25405,25407,25409,25411,25413],{},[898,25402,1721],{},[3018,25404,12991],{},[898,25406,12885],{},[3018,25408,12991],{},[898,25410,12813],{},[3018,25412,12991],{},[898,25414,13021],{},[902,25416,13024],{"encoding":904}," se vyšetřuje vliv změn ",[38,25419,25420],{},"exogenních"," veličin (plánovaných investic ",[883,25423,25425],{"className":25424},[886],[888,25426,25427],{"xmlns":890},[892,25428,25429,25437],{},[895,25430,25431],{},[2057,25432,25433,25435],{},[898,25434,12885],{},[1723,25436,5066],{},[902,25438,25439],{"encoding":904},"I^*",", vládních výdajů ",[883,25442,25444],{"className":25443},[886],[888,25445,25446],{"xmlns":890},[892,25447,25448,25456],{},[895,25449,25450],{},[2057,25451,25452,25454],{},[898,25453,12813],{},[1723,25455,5066],{},[902,25457,25458],{"encoding":904},"G^*",", exportu ",[883,25461,25463],{"className":25462},[886],[888,25464,25465],{"xmlns":890},[892,25466,25467,25475],{},[895,25468,25469],{},[2057,25470,25471,25473],{},[898,25472,23946],{},[1723,25474,5066],{},[902,25476,25477],{"encoding":904},"B^*",") na změny ",[38,25480,25481],{},"endogenních"," rovnovážných veličin (",[883,25484,25486],{"className":25485},[886],[888,25487,25488],{"xmlns":890},[892,25489,25490,25498],{},[895,25491,25492],{},[2057,25493,25494,25496],{},[898,25495,9837],{},[898,25497,1846],{},[902,25499,14604],{"encoding":904},[883,25501,25503],{"className":25502},[886],[888,25504,25505],{"xmlns":890},[892,25506,25507,25515],{},[895,25508,25509],{},[2057,25510,25511,25513],{},[898,25512,1721],{},[898,25514,1846],{},[902,25516,14663],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,25519,18672],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,25522,25524],{"id":25523},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,25526,21588,25527,25550,25551,25595],{},[883,25528,25530],{"className":25529},[886],[888,25531,25532],{"xmlns":890},[892,25533,25534,25548],{},[895,25535,25536,25538,25540,25542,25544,25546],{},[898,25537,1721],{},[1723,25539,1725],{},[898,25541,207],{},[898,25543,9837],{},[1723,25545,2087],{},[898,25547,2069],{},[902,25549,19614],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,25552,25554],{"className":25553},[886],[888,25555,25556],{"xmlns":890},[892,25557,25558,25592],{},[895,25559,25560,25566,25568],{},[2057,25561,25562,25564],{},[898,25563,9837],{},[898,25565,1846],{},[1723,25567,1725],{},[3055,25569,25570],{"scriptlevel":2256,"displaystyle":2030},[3058,25571,25572,25584],{},[895,25573,25574,25576,25578],{},[898,25575,2069],{},[1723,25577,2087],{},[2057,25579,25580,25582],{},[898,25581,12885],{},[1723,25583,5066],{},[895,25585,25586,25588,25590],{},[1864,25587,1866],{},[1723,25589,1759],{},[898,25591,207],{},[902,25593,25594],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,25597,25598],{},[883,25599,25601],{"className":25600},[886],[888,25602,25603],{"xmlns":890},[892,25604,25605,25674],{},[895,25606,25607,25625,25627,25657,25659],{},[3058,25608,25609,25619],{},[895,25610,25611,25613],{},[898,25612,10574],{"mathvariant":2124},[2057,25614,25615,25617],{},[898,25616,9837],{},[898,25618,1846],{},[895,25620,25621,25623],{},[898,25622,10574],{"mathvariant":2124},[898,25624,207],{},[1723,25626,1725],{},[3058,25628,25629,25641],{},[895,25630,25631,25633,25635],{},[898,25632,2069],{},[1723,25634,2087],{},[2057,25636,25637,25639],{},[898,25638,12885],{},[1723,25640,5066],{},[895,25642,25643,25645,25647,25649,25651],{},[1723,25644,1908],{"stretchy":1907},[1864,25646,1866],{},[1723,25648,1759],{},[898,25650,207],{},[2057,25652,25653,25655],{},[1723,25654,1914],{"stretchy":1907},[1864,25656,2331],{},[6588,25658],{"width":6590},[895,25660,25661,25664,25671],{},[3018,25662,25663],{},"(multiplik",[9096,25665,25666,25668],{"accent":2030},[3018,25667,207],{},[1723,25669,25670],{},"ˊ",[3018,25672,25673],{},"tor MPC)",[902,25675,25676],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,25678,25679],{},[883,25680,25682],{"className":25681},[886],[888,25683,25684],{"xmlns":890},[892,25685,25686,25755],{},[895,25687,25688,25706,25708,25720,25722],{},[3058,25689,25690,25700],{},[895,25691,25692,25694],{},[898,25693,10574],{"mathvariant":2124},[2057,25695,25696,25698],{},[898,25697,9837],{},[898,25699,1846],{},[895,25701,25702,25704],{},[898,25703,10574],{"mathvariant":2124},[898,25705,2069],{},[1723,25707,1725],{},[3058,25709,25710,25712],{},[1864,25711,1866],{},[895,25713,25714,25716,25718],{},[1864,25715,1866],{},[1723,25717,1759],{},[898,25719,207],{},[6588,25721],{"width":6590},[895,25723,25724,25726,25732,25735,25742,25745,25752],{},[3018,25725,25663],{},[9096,25727,25728,25730],{"accent":2030},[3018,25729,207],{},[1723,25731,25670],{},[3018,25733,25734],{},"tor autonomn",[9096,25736,25737,25740],{"accent":2030},[3018,25738,25739],{},"ı",[1723,25741,25670],{},[3018,25743,25744],{}," spot",[9096,25746,25747,25749],{"accent":2030},[3018,25748,12742],{},[1723,25750,25751],{},"ˇ",[3018,25753,25754],{},"eby)",[902,25756,25757],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,25759,25760],{},[883,25761,25763],{"className":25762},[886],[888,25764,25765],{"xmlns":890},[892,25766,25767,25834],{},[895,25768,25769,25791,25793,25805,25807,25819,25821],{},[3058,25770,25771,25781],{},[895,25772,25773,25775],{},[898,25774,10574],{"mathvariant":2124},[2057,25776,25777,25779],{},[898,25778,9837],{},[898,25780,1846],{},[895,25782,25783,25785],{},[898,25784,10574],{"mathvariant":2124},[2057,25786,25787,25789],{},[898,25788,12885],{},[1723,25790,5066],{},[1723,25792,1725],{},[3058,25794,25795,25797],{},[1864,25796,1866],{},[895,25798,25799,25801,25803],{},[1864,25800,1866],{},[1723,25802,1759],{},[898,25804,207],{},[1723,25806,1725],{},[3058,25808,25809,25811],{},[1864,25810,1866],{},[895,25812,25813,25815,25817],{},[898,25814,1728],{},[898,25816,1746],{},[898,25818,2111],{},[6588,25820],{"width":6590},[895,25822,25823,25825,25831],{},[3018,25824,25663],{},[9096,25826,25827,25829],{"accent":2030},[3018,25828,207],{},[1723,25830,25670],{},[3018,25832,25833],{},"tor investic)",[902,25835,25836],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[4584,25838,25839],{},[724,25840,25841,25843,25844,25847,25848,25861,25862,25879,25880,25898,25899,25943,25944,22113,25961,25964,25965,25982],{},[883,25842,4869],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,25845,25846],{},"důchodem","; z něj se utratí ",[883,25849,25851],{"className":25850},[886],[888,25852,25853],{"xmlns":890},[892,25854,25855,25859],{},[895,25856,25857],{},[898,25858,207],{},[902,25860,207],{"encoding":904}," Kč (= ",[883,25863,25865],{"className":25864},[886],[888,25866,25867],{"xmlns":890},[892,25868,25869,25877],{},[895,25870,25871,25873,25875],{},[898,25872,1728],{},[898,25874,1746],{},[898,25876,1721],{},[902,25878,2389],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,25881,25883],{"className":25882},[886],[888,25884,25885],{"xmlns":890},[892,25886,25887,25895],{},[895,25888,25889],{},[2057,25890,25891,25893],{},[898,25892,207],{},[1864,25894,2331],{},[902,25896,25897],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,25900,25902],{"className":25901},[886],[888,25903,25904],{"xmlns":890},[892,25905,25906,25940],{},[895,25907,25908,25910,25912,25914,25916,25922,25924,25926,25928],{},[1864,25909,1866],{},[1723,25911,2087],{},[898,25913,207],{},[1723,25915,2087],{},[2057,25917,25918,25920],{},[898,25919,207],{},[1864,25921,2331],{},[1723,25923,2087],{},[1723,25925,18799],{},[1723,25927,1725],{},[3058,25929,25930,25932],{},[1864,25931,1866],{},[895,25933,25934,25936,25938],{},[1864,25935,1866],{},[1723,25937,1759],{},[898,25939,207],{},[902,25941,25942],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,25945,25947],{"className":25946},[886],[888,25948,25949],{"xmlns":890},[892,25950,25951,25959],{},[895,25952,25953],{},[2057,25954,25955,25957],{},[898,25956,9837],{},[898,25958,1846],{},[902,25960,14604],{"encoding":904},[38,25962,25963],{},"více"," než korunu — čím vyšší ",[883,25966,25968],{"className":25967},[886],[888,25969,25970],{"xmlns":890},[892,25971,25972,25980],{},[895,25973,25974,25976,25978],{},[898,25975,1728],{},[898,25977,1746],{},[898,25979,1721],{},[902,25981,2389],{"encoding":904},", tím silnější multiplikační efekt.",[724,25984,25985,25988,25989,26015,26016,26019,26020,1682,26041,26066,26067,1664],{},[38,25986,25987],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,25990,25992],{"className":25991},[886],[888,25993,25994],{"xmlns":890},[892,25995,25996,26012],{},[895,25997,25998],{},[3055,25999,26000],{"scriptlevel":2256,"displaystyle":1907},[3058,26001,26002,26004],{},[1864,26003,1866],{},[895,26005,26006,26008,26010],{},[1864,26007,1866],{},[1723,26009,1759],{},[898,26011,207],{},[902,26013,26014],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,26017,26018],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,26021,26023],{"className":26022},[886],[888,26024,26025],{"xmlns":890},[892,26026,26027,26039],{},[895,26028,26029,26031,26033,26035,26037],{},[898,26030,1721],{},[3018,26032,12991],{},[898,26034,12885],{},[3018,26036,12991],{},[898,26038,12813],{},[902,26040,18914],{"encoding":904},[883,26042,26044],{"className":26043},[886],[888,26045,26046],{"xmlns":890},[892,26047,26048,26064],{},[895,26049,26050,26052,26054,26056,26058,26060,26062],{},[898,26051,1721],{},[3018,26053,12991],{},[898,26055,12885],{},[3018,26057,12991],{},[898,26059,12813],{},[3018,26061,12991],{},[898,26063,13021],{},[902,26065,13024],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,26068,26070],{"className":26069,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,26072,26074],{"id":26073},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,26076,12865,26077,1343,26094,1682,26115,12870,26140,1981,26143,26164,26165,2628,26168,26181,26182,6379,26211,26228,26229,26232,26233,26235,26236,26257],{},[883,26078,26080],{"className":26079},[886],[888,26081,26082],{"xmlns":890},[892,26083,26084,26092],{},[895,26085,26086,26088,26090],{},[898,26087,1721],{},[3018,26089,12991],{},[898,26091,12885],{},[902,26093,12996],{"encoding":904},[883,26095,26097],{"className":26096},[886],[888,26098,26099],{"xmlns":890},[892,26100,26101,26113],{},[895,26102,26103,26105,26107,26109,26111],{},[898,26104,1721],{},[3018,26106,12991],{},[898,26108,12885],{},[3018,26110,12991],{},[898,26112,12813],{},[902,26114,18914],{"encoding":904},[883,26116,26118],{"className":26117},[886],[888,26119,26120],{"xmlns":890},[892,26121,26122,26138],{},[895,26123,26124,26126,26128,26130,26132,26134,26136],{},[898,26125,1721],{},[3018,26127,12991],{},[898,26129,12885],{},[3018,26131,12991],{},[898,26133,12813],{},[3018,26135,12991],{},[898,26137,13021],{},[902,26139,13024],{"encoding":904},[38,26141,26142],{},"investice konstantní",[883,26144,26146],{"className":26145},[886],[888,26147,26148],{"xmlns":890},[892,26149,26150,26162],{},[895,26151,26152,26154,26156],{},[898,26153,12885],{},[1723,26155,1725],{},[2057,26157,26158,26160],{},[898,26159,12885],{},[1723,26161,5066],{},[902,26163,12896],{"encoding":904},"). Reálnější je předpoklad, že ",[38,26166,26167],{},"investice závisejí na úrokové míře",[883,26169,26171],{"className":26170},[886],[888,26172,26173],{"xmlns":890},[892,26174,26175,26179],{},[895,26176,26177],{},[898,26178,12742],{},[902,26180,12742],{"encoding":904}," — klesající funkce ",[883,26183,26185],{"className":26184},[886],[888,26186,26187],{"xmlns":890},[892,26188,26189,26209],{},[895,26190,26191,26193,26195,26197,26199,26201,26203,26205,26207],{},[898,26192,12885],{},[1723,26194,1908],{"stretchy":1907},[898,26196,12742],{},[1723,26198,1914],{"stretchy":1907},[1723,26200,1725],{},[898,26202,2878],{},[898,26204,12742],{},[1723,26206,2087],{},[898,26208,2930],{},[902,26210,16458],{"encoding":904},[883,26212,26214],{"className":26213},[886],[888,26215,26216],{"xmlns":890},[892,26217,26218,26226],{},[895,26219,26220,26222,26224],{},[898,26221,2878],{},[1723,26223,2287],{},[1864,26225,2256],{},[902,26227,13216],{"encoding":904},". Přidáním ",[38,26230,26231],{},"trhu peněz"," k trhu zboží vzniká model ",[38,26234,12712],{}," se dvěma neznámými ",[883,26237,26239],{"className":26238},[886],[888,26240,26241],{"xmlns":890},[892,26242,26243,26255],{},[895,26244,26245,26247,26249,26251,26253],{},[1723,26246,1908],{"stretchy":1907},[898,26248,9837],{},[1723,26250,2031],{"separator":2030},[898,26252,12742],{},[1723,26254,1914],{"stretchy":1907},[902,26256,18844],{"encoding":904}," a dvěma rovnicemi:",[120,26259,26260,26310],{},[123,26261,26262,1981,26264,26266,26267,26288,26289,1664],{},[38,26263,16547],{},[614,26265,12755],{},") — klesající přímka v rovině ",[883,26268,26270],{"className":26269},[886],[888,26271,26272],{"xmlns":890},[892,26273,26274,26286],{},[895,26275,26276,26278,26280,26282,26284],{},[1723,26277,1908],{"stretchy":1907},[898,26279,12742],{},[1723,26281,2031],{"separator":2030},[898,26283,9837],{},[1723,26285,1914],{"stretchy":1907},[902,26287,13638],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,26290,26292],{"className":26291},[886],[888,26293,26294],{"xmlns":890},[892,26295,26296,26308],{},[895,26297,26298,26300,26302,26304,26306],{},[898,26299,9837],{},[1723,26301,1725],{},[898,26303,1721],{},[1723,26305,2087],{},[898,26307,12885],{},[902,26309,15445],{"encoding":904},[123,26311,26312,1981,26314,26316,26317,22287,26342,26388],{},[38,26313,16746],{},[614,26315,12762],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,26318,26320],{"className":26319},[886],[888,26321,26322],{"xmlns":890},[892,26323,26324,26340],{},[895,26325,26326,26332,26334],{},[2057,26327,26328,26330],{},[898,26329,1728],{},[898,26331,4897],{},[1723,26333,1725],{},[2057,26335,26336,26338],{},[898,26337,1728],{},[1723,26339,5066],{},[902,26341,14181],{"encoding":904},[883,26343,26345],{"className":26344},[886],[888,26346,26347],{"xmlns":890},[892,26348,26349,26385],{},[895,26350,26351,26357,26359,26365,26367,26369,26375,26377,26379],{},[2057,26352,26353,26355],{},[898,26354,1728],{},[898,26356,4897],{},[1723,26358,1725],{},[1931,26360,26361,26363],{},[898,26362,13938],{},[1864,26364,1866],{},[898,26366,9837],{},[1723,26368,2087],{},[1931,26370,26371,26373],{},[898,26372,13938],{},[1864,26374,2331],{},[898,26376,12742],{},[1723,26378,2087],{},[1931,26380,26381,26383],{},[898,26382,13938],{},[1864,26384,2909],{},[902,26386,26387],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,26390,26391,2628,26394,26427,26428,26430,26431,26433],{},[38,26392,26393],{},"Simultánní rovnovážný bod",[883,26395,26397],{"className":26396},[886],[888,26398,26399],{"xmlns":890},[892,26400,26401,26425],{},[895,26402,26403,26405,26407,26409,26415,26417,26423],{},[898,26404,1846],{},[1723,26406,1725],{},[1723,26408,1908],{"stretchy":1907},[2057,26410,26411,26413],{},[898,26412,12742],{},[898,26414,1846],{},[1723,26416,2031],{"separator":2030},[2057,26418,26419,26421],{},[898,26420,9837],{},[898,26422,1846],{},[1723,26424,1914],{"stretchy":1907},[902,26426,16838],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,26429,12800],{}," (posun IS) a ",[38,26432,12832],{}," (posun LM).",[724,26435,26436],{},[38,26437,26438,26439,1343,26461,1343,26483,1343,26505,26527,26528,1664],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,26440,26442],{"className":26441},[886],[888,26443,26444],{"xmlns":890},[892,26445,26446,26458],{},[895,26447,26448,26454,26456],{},[2057,26449,26450,26452],{},[898,26451,9837],{},[898,26453,1846],{},[1723,26455,1725],{},[1864,26457,15816],{},[902,26459,26460],{"encoding":904},"Y^E = 5000",[883,26462,26464],{"className":26463},[886],[888,26465,26466],{"xmlns":890},[892,26467,26468,26480],{},[895,26469,26470,26476,26478],{},[2057,26471,26472,26474],{},[898,26473,12742],{},[898,26475,1846],{},[1723,26477,1725],{},[1864,26479,2962],{},[902,26481,26482],{"encoding":904},"r^E = 5",[883,26484,26486],{"className":26485},[886],[888,26487,26488],{"xmlns":890},[892,26489,26490,26502],{},[895,26491,26492,26498,26500],{},[2057,26493,26494,26496],{},[898,26495,1721],{},[898,26497,1846],{},[1723,26499,1725],{},[1864,26501,15853],{},[902,26503,26504],{"encoding":904},"C^E = 4100",[883,26506,26508],{"className":26507},[886],[888,26509,26510],{"xmlns":890},[892,26511,26512,26524],{},[895,26513,26514,26520,26522],{},[2057,26515,26516,26518],{},[898,26517,12885],{},[898,26519,1846],{},[1723,26521,1725],{},[1864,26523,15892],{},[902,26525,26526],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,26529,945],{"className":26530,"dataFsResolvedFilePath":943,"href":944},[210],[115,26532,26534],{"id":26533},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,26536,26537,26601,26712,26855,27097,27165],{},[123,26538,26539,26542,26543,26565,26566,26600],{},[38,26540,26541],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,26544,26546],{"className":26545},[886],[888,26547,26548],{"xmlns":890},[892,26549,26550,26562],{},[895,26551,26552,26554,26556,26558,26560],{},[898,26553,12813],{},[898,26555,18988],{},[898,26557,1746],{},[1723,26559,3456],{},[898,26561,9837],{},[902,26563,26564],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,26567,26569],{"className":26568},[886],[888,26570,26571],{"xmlns":890},[892,26572,26573,26597],{},[895,26574,26575,26577,26579,26581,26583,26585,26587,26589,26591,26593,26595],{},[898,26576,12813],{},[898,26578,18988],{},[898,26580,1746],{},[1723,26582,1725],{},[898,26584,1721],{},[1723,26586,2087],{},[898,26588,12885],{},[1723,26590,2087],{},[898,26592,12813],{},[1723,26594,2087],{},[898,26596,13021],{},[902,26598,26599],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,26602,26603,26605,26606,26627,26628,1343,26651,26682,26683,26696,26697,1664],{},[38,26604,19222],{}," splňují ",[883,26607,26609],{"className":26608},[886],[888,26610,26611],{"xmlns":890},[892,26612,26613,26625],{},[895,26614,26615,26617,26619,26621,26623],{},[898,26616,9837],{},[1723,26618,1725],{},[898,26620,1721],{},[1723,26622,2087],{},[898,26624,2111],{},[902,26626,13395],{"encoding":904}," (7.2); lineární model ",[883,26629,26631],{"className":26630},[886],[888,26632,26633],{"xmlns":890},[892,26634,26635,26649],{},[895,26636,26637,26639,26641,26643,26645,26647],{},[898,26638,1721],{},[1723,26640,1725],{},[898,26642,207],{},[898,26644,9837],{},[1723,26646,2087],{},[898,26648,2069],{},[902,26650,19614],{"encoding":904},[883,26652,26654],{"className":26653},[886],[888,26655,26656],{"xmlns":890},[892,26657,26658,26680],{},[895,26659,26660,26662,26664,26666,26668,26670,26672,26674,26676,26678],{},[898,26661,2111],{},[1723,26663,1725],{},[1723,26665,1908],{"stretchy":1907},[1864,26667,1866],{},[1723,26669,1759],{},[898,26671,207],{},[1723,26673,1914],{"stretchy":1907},[898,26675,9837],{},[1723,26677,1759],{},[898,26679,2069],{},[902,26681,19863],{"encoding":904}," s autonomní spotřebou ",[883,26684,26686],{"className":26685},[886],[888,26687,26688],{"xmlns":890},[892,26689,26690,26694],{},[895,26691,26692],{},[898,26693,2069],{},[902,26695,2069],{"encoding":904}," a autonomními úsporami ",[883,26698,26700],{"className":26699},[886],[888,26701,26702],{"xmlns":890},[892,26703,26704,26710],{},[895,26705,26706,26708],{},[1723,26707,1759],{},[898,26709,2069],{},[902,26711,19942],{"encoding":904},[123,26713,26714,2628,26717,1343,26747,26777,26778,26808,26809,1343,26830,1664],{},[38,26715,26716],{},"Mezní sklony",[883,26718,26720],{"className":26719},[886],[888,26721,26722],{"xmlns":890},[892,26723,26724,26744],{},[895,26725,26726,26728,26730,26732,26734,26736,26738,26740,26742],{},[898,26727,1728],{},[898,26729,1746],{},[898,26731,1721],{},[1723,26733,1725],{},[898,26735,2930],{"mathvariant":2124},[898,26737,1721],{},[898,26739,2125],{"mathvariant":2124},[898,26741,2930],{"mathvariant":2124},[898,26743,9837],{},[902,26745,26746],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,26748,26750],{"className":26749},[886],[888,26751,26752],{"xmlns":890},[892,26753,26754,26774],{},[895,26755,26756,26758,26760,26762,26764,26766,26768,26770,26772],{},[898,26757,1728],{},[898,26759,1746],{},[898,26761,2111],{},[1723,26763,1725],{},[898,26765,2930],{"mathvariant":2124},[898,26767,2111],{},[898,26769,2125],{"mathvariant":2124},[898,26771,2930],{"mathvariant":2124},[898,26773,9837],{},[902,26775,26776],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,26779,26781],{"className":26780},[886],[888,26782,26783],{"xmlns":890},[892,26784,26785,26805],{},[895,26786,26787,26789,26791,26793,26795,26797,26799,26801,26803],{},[898,26788,1728],{},[898,26790,1746],{},[898,26792,1721],{},[1723,26794,2087],{},[898,26796,1728],{},[898,26798,1746],{},[898,26800,2111],{},[1723,26802,1725],{},[1864,26804,1866],{},[902,26806,26807],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,26810,26812],{"className":26811},[886],[888,26813,26814],{"xmlns":890},[892,26815,26816,26828],{},[895,26817,26818,26820,26822,26824,26826],{},[898,26819,1728],{},[898,26821,1746],{},[898,26823,1721],{},[1723,26825,1725],{},[898,26827,207],{},[902,26829,20582],{"encoding":904},[883,26831,26833],{"className":26832},[886],[888,26834,26835],{"xmlns":890},[892,26836,26837,26853],{},[895,26838,26839,26841,26843,26845,26847,26849,26851],{},[898,26840,1728],{},[898,26842,1746],{},[898,26844,2111],{},[1723,26846,1725],{},[1864,26848,1866],{},[1723,26850,1759],{},[898,26852,207],{},[902,26854,20608],{"encoding":904},[123,26856,26857,26860,26861],{},[38,26858,26859],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,26862,26863,26951,27020],{},[123,26864,26865,26882,26883,26904,26905,2031],{},[883,26866,26868],{"className":26867},[886],[888,26869,26870],{"xmlns":890},[892,26871,26872,26880],{},[895,26873,26874,26876,26878],{},[898,26875,1721],{},[3018,26877,12991],{},[898,26879,12885],{},[902,26881,12996],{"encoding":904},": ",[883,26884,26886],{"className":26885},[886],[888,26887,26888],{"xmlns":890},[892,26889,26890,26902],{},[895,26891,26892,26894,26896,26898,26900],{},[898,26893,9837],{},[1723,26895,1725],{},[898,26897,1721],{},[1723,26899,2087],{},[898,26901,12885],{},[902,26903,15445],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,26906,26908],{"className":26907},[886],[888,26909,26910],{"xmlns":890},[892,26911,26912,26948],{},[895,26913,26914,26920,26922,26924,26926,26928,26934,26936,26938,26940,26942,26944,26946],{},[2057,26915,26916,26918],{},[898,26917,9837],{},[898,26919,1846],{},[1723,26921,1725],{},[1723,26923,1908],{"stretchy":1907},[898,26925,2069],{},[1723,26927,2087],{},[2057,26929,26930,26932],{},[898,26931,12885],{},[1723,26933,5066],{},[1723,26935,1914],{"stretchy":1907},[898,26937,2125],{"mathvariant":2124},[1723,26939,1908],{"stretchy":1907},[1864,26941,1866],{},[1723,26943,1759],{},[898,26945,207],{},[1723,26947,1914],{"stretchy":1907},[902,26949,26950],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,26952,26953,26974,26975,26994,26995,2031],{},[883,26954,26956],{"className":26955},[886],[888,26957,26958],{"xmlns":890},[892,26959,26960,26972],{},[895,26961,26962,26964,26966,26968,26970],{},[898,26963,1721],{},[3018,26965,12991],{},[898,26967,12885],{},[3018,26969,12991],{},[898,26971,12813],{},[902,26973,18914],{"encoding":904},": přidává vládu, zdanění ",[883,26976,26978],{"className":26977},[886],[888,26979,26980],{"xmlns":890},[892,26981,26982,26992],{},[895,26983,26984,26986,26988,26990],{},[898,26985,1754],{},[1723,26987,1908],{"stretchy":1907},[898,26989,9837],{},[1723,26991,1914],{"stretchy":1907},[902,26993,22912],{"encoding":904}," a disponibilní důchod ",[883,26996,26998],{"className":26997},[886],[888,26999,27000],{"xmlns":890},[892,27001,27002,27018],{},[895,27003,27004,27010,27012,27014,27016],{},[1931,27005,27006,27008],{},[898,27007,9837],{},[898,27009,4897],{},[1723,27011,1725],{},[898,27013,9837],{},[1723,27015,1759],{},[898,27017,1754],{},[902,27019,22411],{"encoding":904},[123,27021,27022,27047,27048,22287,27069,1664],{},[883,27023,27025],{"className":27024},[886],[888,27026,27027],{"xmlns":890},[892,27028,27029,27045],{},[895,27030,27031,27033,27035,27037,27039,27041,27043],{},[898,27032,1721],{},[3018,27034,12991],{},[898,27036,12885],{},[3018,27038,12991],{},[898,27040,12813],{},[3018,27042,12991],{},[898,27044,13021],{},[902,27046,13024],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,27049,27051],{"className":27050},[886],[888,27052,27053],{"xmlns":890},[892,27054,27055,27067],{},[895,27056,27057,27059,27061,27063,27065],{},[898,27058,13021],{},[1723,27060,1725],{},[898,27062,23946],{},[1723,27064,1759],{},[898,27066,1728],{},[902,27068,23953],{"encoding":904},[883,27070,27072],{"className":27071},[886],[888,27073,27074],{"xmlns":890},[892,27075,27076,27094],{},[895,27077,27078,27080,27082,27084,27086,27092],{},[898,27079,1728],{},[1723,27081,1725],{},[898,27083,1728],{},[1723,27085,1908],{"stretchy":1907},[1931,27087,27088,27090],{},[898,27089,9837],{},[898,27091,4897],{},[1723,27093,1914],{"stretchy":1907},[902,27095,27096],{"encoding":904},"M = M(Y_D)",[123,27098,27099,27102,27103,2628,27106,27164],{},[38,27100,27101],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,27104,27105],{},"multiplikátor investic",[883,27107,27109],{"className":27108},[886],[888,27110,27111],{"xmlns":890},[892,27112,27113,27161],{},[895,27114,27115,27117,27123,27125,27127,27133,27135,27137,27139,27141,27143,27145,27147,27149,27151,27153,27155,27157,27159],{},[898,27116,10574],{"mathvariant":2124},[2057,27118,27119,27121],{},[898,27120,9837],{},[898,27122,1846],{},[898,27124,2125],{"mathvariant":2124},[898,27126,10574],{"mathvariant":2124},[2057,27128,27129,27131],{},[898,27130,12885],{},[1723,27132,5066],{},[1723,27134,1725],{},[1864,27136,1866],{},[898,27138,2125],{"mathvariant":2124},[1723,27140,1908],{"stretchy":1907},[1864,27142,1866],{},[1723,27144,1759],{},[898,27146,207],{},[1723,27148,1914],{"stretchy":1907},[1723,27150,1725],{},[1864,27152,1866],{},[898,27154,2125],{"mathvariant":2124},[898,27156,1728],{},[898,27158,1746],{},[898,27160,2111],{},[902,27162,27163],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,27166,27167,27169,27170,27185,27186,19342,27203,27218,27219,27244,27245,1664],{},[38,27168,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,27171,27173],{"className":27172},[886],[888,27174,27175],{"xmlns":890},[892,27176,27177,27183],{},[895,27178,27179,27181],{},[898,27180,12885],{},[898,27182,2111],{},[902,27184,12752],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,27187,27189],{"className":27188},[886],[888,27190,27191],{"xmlns":890},[892,27192,27193,27201],{},[895,27194,27195,27197,27199],{},[898,27196,12885],{},[1723,27198,1725],{},[898,27200,2111],{},[902,27202,13413],{"encoding":904},[883,27204,27206],{"className":27205},[886],[888,27207,27208],{"xmlns":890},[892,27209,27210,27216],{},[895,27211,27212,27214],{},[898,27213,1911],{},[898,27215,1728],{},[902,27217,12759],{"encoding":904}," rovnováhu trhu peněz (",[883,27220,27222],{"className":27221},[886],[888,27223,27224],{"xmlns":890},[892,27225,27226,27242],{},[895,27227,27228,27234,27236],{},[2057,27229,27230,27232],{},[898,27231,1728],{},[898,27233,4897],{},[1723,27235,1725],{},[2057,27237,27238,27240],{},[898,27239,1728],{},[1723,27241,5066],{},[902,27243,14181],{"encoding":904},"); průsečík dává ",[883,27246,27248],{"className":27247},[886],[888,27249,27250],{"xmlns":890},[892,27251,27252,27272],{},[895,27253,27254,27256,27262,27264,27270],{},[1723,27255,1908],{"stretchy":1907},[2057,27257,27258,27260],{},[898,27259,9837],{},[898,27261,1846],{},[1723,27263,2031],{"separator":2030},[2057,27265,27266,27268],{},[898,27267,12742],{},[898,27269,1846],{},[1723,27271,1914],{"stretchy":1907},[902,27273,12796],{"encoding":904},[115,27275,16421],{"id":16420},[120,27277,27278,27316,27356,27446,27528,27582,27638,27697,27732,27737,27809,27884,27970,28032,28100,28158,28211,28250],{},[123,27279,27280,7725,27283,26600],{},[38,27281,27282],{},"Hrubý národní produkt (GNP)",[883,27284,27286],{"className":27285},[886],[888,27287,27288],{"xmlns":890},[892,27289,27290,27314],{},[895,27291,27292,27294,27296,27298,27300,27302,27304,27306,27308,27310,27312],{},[898,27293,12813],{},[898,27295,18988],{},[898,27297,1746],{},[1723,27299,1725],{},[898,27301,1721],{},[1723,27303,2087],{},[898,27305,12885],{},[1723,27307,2087],{},[898,27309,12813],{},[1723,27311,2087],{},[898,27313,13021],{},[902,27315,26599],{"encoding":904},[123,27317,27318,27334,27335,1664],{},[38,27319,27320,27321],{},"Národní důchod ",[883,27322,27324],{"className":27323},[886],[888,27325,27326],{"xmlns":890},[892,27327,27328,27332],{},[895,27329,27330],{},[898,27331,9837],{},[902,27333,9837],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,27336,27338],{"className":27337},[886],[888,27339,27340],{"xmlns":890},[892,27341,27342,27354],{},[895,27343,27344,27346,27348,27350,27352],{},[898,27345,12813],{},[898,27347,18988],{},[898,27349,1746],{},[1723,27351,3456],{},[898,27353,9837],{},[902,27355,26564],{"encoding":904},[123,27357,27358,27384,27385,1343,27408,1343,27429,1664],{},[38,27359,27360,27361],{},"Funkce spotřeby ",[883,27362,27364],{"className":27363},[886],[888,27365,27366],{"xmlns":890},[892,27367,27368,27382],{},[895,27369,27370,27372,27374,27376,27378,27380],{},[898,27371,1721],{},[1723,27373,1725],{},[898,27375,1721],{},[1723,27377,1908],{"stretchy":1907},[898,27379,9837],{},[1723,27381,1914],{"stretchy":1907},[902,27383,21433],{"encoding":904}," — lineární model ",[883,27386,27388],{"className":27387},[886],[888,27389,27390],{"xmlns":890},[892,27391,27392,27406],{},[895,27393,27394,27396,27398,27400,27402,27404],{},[898,27395,1721],{},[1723,27397,1725],{},[898,27399,207],{},[898,27401,9837],{},[1723,27403,2087],{},[898,27405,2069],{},[902,27407,19614],{"encoding":904},[883,27409,27411],{"className":27410},[886],[888,27412,27413],{"xmlns":890},[892,27414,27415,27427],{},[895,27416,27417,27419,27421,27423,27425],{},[1864,27418,2256],{},[1723,27420,2287],{},[898,27422,207],{},[1723,27424,2287],{},[1864,27426,1866],{},[902,27428,19530],{"encoding":904},[883,27430,27432],{"className":27431},[886],[888,27433,27434],{"xmlns":890},[892,27435,27436,27444],{},[895,27437,27438,27440,27442],{},[898,27439,2069],{},[1723,27441,2253],{},[1864,27443,2256],{},[902,27445,19508],{"encoding":904},[123,27447,27448,7725,27475,27496,27497,1664],{},[38,27449,27450,27451],{},"Funkce úspor ",[883,27452,27454],{"className":27453},[886],[888,27455,27456],{"xmlns":890},[892,27457,27458,27472],{},[895,27459,27460,27462,27464,27466,27468,27470],{},[898,27461,2111],{},[1723,27463,1725],{},[898,27465,2111],{},[1723,27467,1908],{"stretchy":1907},[898,27469,9837],{},[1723,27471,1914],{"stretchy":1907},[902,27473,27474],{"encoding":904},"S = S(Y)",[883,27476,27478],{"className":27477},[886],[888,27479,27480],{"xmlns":890},[892,27481,27482,27494],{},[895,27483,27484,27486,27488,27490,27492],{},[898,27485,9837],{},[1723,27487,1725],{},[898,27489,1721],{},[1723,27491,2087],{},[898,27493,2111],{},[902,27495,13395],{"encoding":904},"; lineární ",[883,27498,27500],{"className":27499},[886],[888,27501,27502],{"xmlns":890},[892,27503,27504,27526],{},[895,27505,27506,27508,27510,27512,27514,27516,27518,27520,27522,27524],{},[898,27507,2111],{},[1723,27509,1725],{},[1723,27511,1908],{"stretchy":1907},[1864,27513,1866],{},[1723,27515,1759],{},[898,27517,207],{},[1723,27519,1914],{"stretchy":1907},[898,27521,9837],{},[1723,27523,1759],{},[898,27525,2069],{},[902,27527,19863],{"encoding":904},[123,27529,27530,7725,27533,1343,27556,1664],{},[38,27531,27532],{},"Autonomní spotřeba\u002Fúspory",[883,27534,27536],{"className":27535},[886],[888,27537,27538],{"xmlns":890},[892,27539,27540,27554],{},[895,27541,27542,27544,27546,27548,27550,27552],{},[898,27543,1721],{},[1723,27545,1908],{"stretchy":1907},[1864,27547,2256],{},[1723,27549,1914],{"stretchy":1907},[1723,27551,1725],{},[898,27553,2069],{},[902,27555,20255],{"encoding":904},[883,27557,27559],{"className":27558},[886],[888,27560,27561],{"xmlns":890},[892,27562,27563,27579],{},[895,27564,27565,27567,27569,27571,27573,27575,27577],{},[898,27566,2111],{},[1723,27568,1908],{"stretchy":1907},[1864,27570,2256],{},[1723,27572,1914],{"stretchy":1907},[1723,27574,1725],{},[1723,27576,1759],{},[898,27578,2069],{},[902,27580,27581],{"encoding":904},"S(0) = -b",[123,27583,27584,27616,27617,4634],{},[38,27585,27586,27587],{},"Mezní sklon ke spotřebě ",[883,27588,27590],{"className":27589},[886],[888,27591,27592],{"xmlns":890},[892,27593,27594,27614],{},[895,27595,27596,27598,27600,27602,27604,27606,27608,27610,27612],{},[898,27597,1728],{},[898,27599,1746],{},[898,27601,1721],{},[1723,27603,1725],{},[898,27605,2930],{"mathvariant":2124},[898,27607,1721],{},[898,27609,2125],{"mathvariant":2124},[898,27611,2930],{"mathvariant":2124},[898,27613,9837],{},[902,27615,26746],{"encoding":904}," (v lineárním modelu ",[883,27618,27620],{"className":27619},[886],[888,27621,27622],{"xmlns":890},[892,27623,27624,27636],{},[895,27625,27626,27628,27630,27632,27634],{},[898,27627,1728],{},[898,27629,1746],{},[898,27631,1721],{},[1723,27633,1725],{},[898,27635,207],{},[902,27637,20582],{"encoding":904},[123,27639,27640,27616,27672,4634],{},[38,27641,27642,27643],{},"Mezní sklon k úsporám ",[883,27644,27646],{"className":27645},[886],[888,27647,27648],{"xmlns":890},[892,27649,27650,27670],{},[895,27651,27652,27654,27656,27658,27660,27662,27664,27666,27668],{},[898,27653,1728],{},[898,27655,1746],{},[898,27657,2111],{},[1723,27659,1725],{},[898,27661,2930],{"mathvariant":2124},[898,27663,2111],{},[898,27665,2125],{"mathvariant":2124},[898,27667,2930],{"mathvariant":2124},[898,27669,9837],{},[902,27671,26776],{"encoding":904},[883,27673,27675],{"className":27674},[886],[888,27676,27677],{"xmlns":890},[892,27678,27679,27695],{},[895,27680,27681,27683,27685,27687,27689,27691,27693],{},[898,27682,1728],{},[898,27684,1746],{},[898,27686,2111],{},[1723,27688,1725],{},[1864,27690,1866],{},[1723,27692,1759],{},[898,27694,207],{},[902,27696,20608],{"encoding":904},[123,27698,27699,2628,27702,27731],{},[38,27700,27701],{},"Vztah",[883,27703,27705],{"className":27704},[886],[888,27706,27707],{"xmlns":890},[892,27708,27709,27729],{},[895,27710,27711,27713,27715,27717,27719,27721,27723,27725,27727],{},[898,27712,1728],{},[898,27714,1746],{},[898,27716,1721],{},[1723,27718,2087],{},[898,27720,1728],{},[898,27722,1746],{},[898,27724,2111],{},[1723,27726,1725],{},[1864,27728,1866],{},[902,27730,26807],{"encoding":904}," (7.5).",[123,27733,27734,27736],{},[38,27735,21276],{}," — rovnováha agregátní poptávky a nabídky.",[123,27738,27739,27742,27743,16493,27764,1664],{},[38,27740,27741],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,27744,27746],{"className":27745},[886],[888,27747,27748],{"xmlns":890},[892,27749,27750,27762],{},[895,27751,27752,27754,27756,27758,27760],{},[898,27753,9837],{},[1723,27755,1725],{},[898,27757,1721],{},[1723,27759,2087],{},[898,27761,12885],{},[902,27763,15445],{"encoding":904},[883,27765,27767],{"className":27766},[886],[888,27768,27769],{"xmlns":890},[892,27770,27771,27807],{},[895,27772,27773,27779,27781,27783,27785,27787,27793,27795,27797,27799,27801,27803,27805],{},[2057,27774,27775,27777],{},[898,27776,9837],{},[898,27778,1846],{},[1723,27780,1725],{},[1723,27782,1908],{"stretchy":1907},[898,27784,2069],{},[1723,27786,2087],{},[2057,27788,27789,27791],{},[898,27790,12885],{},[1723,27792,5066],{},[1723,27794,1914],{"stretchy":1907},[898,27796,2125],{"mathvariant":2124},[1723,27798,1908],{"stretchy":1907},[1864,27800,1866],{},[1723,27802,1759],{},[898,27804,207],{},[1723,27806,1914],{"stretchy":1907},[902,27808,26950],{"encoding":904},[123,27810,27811,27814,27815,1343,27834,16493,27859,1664],{},[38,27812,27813],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,27816,27818],{"className":27817},[886],[888,27819,27820],{"xmlns":890},[892,27821,27822,27832],{},[895,27823,27824,27826,27828,27830],{},[898,27825,1754],{},[1723,27827,1908],{"stretchy":1907},[898,27829,9837],{},[1723,27831,1914],{"stretchy":1907},[902,27833,22912],{"encoding":904},[883,27835,27837],{"className":27836},[886],[888,27838,27839],{"xmlns":890},[892,27840,27841,27857],{},[895,27842,27843,27849,27851,27853,27855],{},[1931,27844,27845,27847],{},[898,27846,9837],{},[898,27848,4897],{},[1723,27850,1725],{},[898,27852,9837],{},[1723,27854,1759],{},[898,27856,1754],{},[902,27858,22411],{"encoding":904},[883,27860,27862],{"className":27861},[886],[888,27863,27864],{"xmlns":890},[892,27865,27866,27882],{},[895,27867,27868,27870,27872,27874,27876,27878,27880],{},[898,27869,9837],{},[1723,27871,1725],{},[898,27873,1721],{},[1723,27875,2087],{},[898,27877,12885],{},[1723,27879,2087],{},[898,27881,12813],{},[902,27883,22382],{"encoding":904},[123,27885,27886,27889,27890,27911,27912,16493,27936,1664],{},[38,27887,27888],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,27891,27893],{"className":27892},[886],[888,27894,27895],{"xmlns":890},[892,27896,27897,27909],{},[895,27898,27899,27901,27903,27905,27907],{},[898,27900,13021],{},[1723,27902,1725],{},[898,27904,23946],{},[1723,27906,1759],{},[898,27908,1728],{},[902,27910,23953],{"encoding":904},", importem ",[883,27913,27915],{"className":27914},[886],[888,27916,27917],{"xmlns":890},[892,27918,27919,27933],{},[895,27920,27921,27923,27925,27931],{},[898,27922,1728],{},[1723,27924,1908],{"stretchy":1907},[1931,27926,27927,27929],{},[898,27928,9837],{},[898,27930,4897],{},[1723,27932,1914],{"stretchy":1907},[902,27934,27935],{"encoding":904},"M(Y_D)",[883,27937,27939],{"className":27938},[886],[888,27940,27941],{"xmlns":890},[892,27942,27943,27967],{},[895,27944,27945,27947,27949,27951,27953,27955,27957,27959,27961,27963,27965],{},[898,27946,9837],{},[1723,27948,1725],{},[898,27950,1721],{},[1723,27952,2087],{},[898,27954,12885],{},[1723,27956,2087],{},[898,27958,12813],{},[1723,27960,2087],{},[898,27962,23946],{},[1723,27964,1759],{},[898,27966,1728],{},[902,27968,27969],{"encoding":904},"Y = C + I + G + B - M",[123,27971,27972,7725,27975,27164],{},[38,27973,27974],{},"Multiplikátor investic",[883,27976,27978],{"className":27977},[886],[888,27979,27980],{"xmlns":890},[892,27981,27982,28030],{},[895,27983,27984,27986,27992,27994,27996,28002,28004,28006,28008,28010,28012,28014,28016,28018,28020,28022,28024,28026,28028],{},[898,27985,10574],{"mathvariant":2124},[2057,27987,27988,27990],{},[898,27989,9837],{},[898,27991,1846],{},[898,27993,2125],{"mathvariant":2124},[898,27995,10574],{"mathvariant":2124},[2057,27997,27998,28000],{},[898,27999,12885],{},[1723,28001,5066],{},[1723,28003,1725],{},[1864,28005,1866],{},[898,28007,2125],{"mathvariant":2124},[1723,28009,1908],{"stretchy":1907},[1864,28011,1866],{},[1723,28013,1759],{},[898,28015,207],{},[1723,28017,1914],{"stretchy":1907},[1723,28019,1725],{},[1864,28021,1866],{},[898,28023,2125],{"mathvariant":2124},[898,28025,1728],{},[898,28027,1746],{},[898,28029,2111],{},[902,28031,27163],{"encoding":904},[123,28033,28034,7725,28065,1343,28082,28099],{},[38,28035,16428,28036],{},[883,28037,28039],{"className":28038},[886],[888,28040,28041],{"xmlns":890},[892,28042,28043,28063],{},[895,28044,28045,28047,28049,28051,28053,28055,28057,28059,28061],{},[898,28046,12885],{},[1723,28048,1908],{"stretchy":1907},[898,28050,12742],{},[1723,28052,1914],{"stretchy":1907},[1723,28054,1725],{},[898,28056,2878],{},[898,28058,12742],{},[1723,28060,2087],{},[898,28062,2930],{},[902,28064,16458],{"encoding":904},[883,28066,28068],{"className":28067},[886],[888,28069,28070],{"xmlns":890},[892,28071,28072,28080],{},[895,28073,28074,28076,28078],{},[898,28075,2878],{},[1723,28077,2287],{},[1864,28079,2256],{},[902,28081,13216],{"encoding":904},[883,28083,28085],{"className":28084},[886],[888,28086,28087],{"xmlns":890},[892,28088,28089,28097],{},[895,28090,28091,28093,28095],{},[898,28092,2930],{},[1723,28094,2253],{},[1864,28096,2256],{},[902,28098,13195],{"encoding":904},"; klesající.",[123,28101,28102,28104,28105,28107,28108,28157],{},[38,28103,16547],{}," — rovnováha na trhu zboží (",[614,28106,12755],{},"); ",[883,28109,28111],{"className":28110},[886],[888,28112,28113],{"xmlns":890},[892,28114,28115,28155],{},[895,28116,28117,28119,28121,28133,28135,28137],{},[898,28118,9837],{},[1723,28120,1725],{},[3058,28122,28123,28125],{},[898,28124,2878],{},[895,28126,28127,28129,28131],{},[1864,28128,1866],{},[1723,28130,1759],{},[898,28132,207],{},[898,28134,12742],{},[1723,28136,2087],{},[3058,28138,28139,28147],{},[895,28140,28141,28143,28145],{},[898,28142,2069],{},[1723,28144,2087],{},[898,28146,2930],{},[895,28148,28149,28151,28153],{},[1864,28150,1866],{},[1723,28152,1759],{},[898,28154,207],{},[902,28156,16600],{"encoding":904}," (7.14); klesající.",[123,28159,28160,28162,28163,28107,28165,28210],{},[38,28161,16746],{}," — rovnováha na trhu peněz (",[614,28164,12762],{},[883,28166,28168],{"className":28167},[886],[888,28169,28170],{"xmlns":890},[892,28171,28172,28208],{},[895,28173,28174,28180,28182,28188,28190,28192,28198,28200,28202],{},[2057,28175,28176,28178],{},[898,28177,1728],{},[1723,28179,5066],{},[1723,28181,1725],{},[1931,28183,28184,28186],{},[898,28185,13938],{},[1864,28187,1866],{},[898,28189,9837],{},[1723,28191,2087],{},[1931,28193,28194,28196],{},[898,28195,13938],{},[1864,28197,2331],{},[898,28199,12742],{},[1723,28201,2087],{},[1931,28203,28204,28206],{},[898,28205,13938],{},[1864,28207,2909],{},[902,28209,16794],{"encoding":904}," (7.15); rostoucí.",[123,28212,28213,7725,28216,1664],{},[38,28214,28215],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,28217,28219],{"className":28218},[886],[888,28220,28221],{"xmlns":890},[892,28222,28223,28247],{},[895,28224,28225,28231,28233,28239,28241],{},[2057,28226,28227,28229],{},[898,28228,1728],{},[898,28230,4897],{},[1723,28232,1725],{},[1931,28234,28235,28237],{},[898,28236,1911],{},[1864,28238,1866],{},[1723,28240,2087],{},[1931,28242,28243,28245],{},[898,28244,1911],{},[1864,28246,2331],{},[902,28248,28249],{"encoding":904},"M^D = L_1 + L_2",[123,28251,28252,16804,28254,14681,28267,1682,28282,28297,28298,1664],{},[38,28253,945],{},[883,28255,28257],{"className":28256},[886],[888,28258,28259],{"xmlns":890},[892,28260,28261,28265],{},[895,28262,28263],{},[898,28264,1846],{},[902,28266,1846],{"encoding":904},[883,28268,28270],{"className":28269},[886],[888,28271,28272],{"xmlns":890},[892,28273,28274,28280],{},[895,28275,28276,28278],{},[898,28277,12885],{},[898,28279,2111],{},[902,28281,12752],{"encoding":904},[883,28283,28285],{"className":28284},[886],[888,28286,28287],{"xmlns":890},[892,28288,28289,28295],{},[895,28290,28291,28293],{},[898,28292,1911],{},[898,28294,1728],{},[902,28296,12759],{"encoding":904}," určuje ",[883,28299,28301],{"className":28300},[886],[888,28302,28303],{"xmlns":890},[892,28304,28305,28325],{},[895,28306,28307,28309,28315,28317,28323],{},[1723,28308,1908],{"stretchy":1907},[2057,28310,28311,28313],{},[898,28312,9837],{},[898,28314,1846],{},[1723,28316,2031],{"separator":2030},[2057,28318,28319,28321],{},[898,28320,12742],{},[898,28322,1846],{},[1723,28324,1914],{"stretchy":1907},[902,28326,12796],{"encoding":904},[115,28328,2620],{"id":2619},[120,28330,28331,28338,28345],{},[123,28332,28333,2628,28335],{},[38,28334,2627],{},[207,28336,1646],{"className":28337,"dataFsResolvedFilePath":1645,"href":1644},[210],[123,28339,28340,2628,28342],{},[38,28341,16912],{},[207,28343,2533],{"className":28344,"dataFsResolvedFilePath":868,"href":869},[210],[123,28346,28347,28349],{},[38,28348,16929],{},[120,28350,28351,28357,28363,28369],{},[123,28352,28353,28356],{},[207,28354,16968],{"className":28355,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,28358,28359,28362],{},[207,28360,1692],{"className":28361,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,28364,28365,28368],{},[207,28366,1824],{"className":28367,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,28370,28371,28374,28375,1343,28392,28409],{},[207,28372,1145],{"className":28373,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,28376,28378],{"className":28377},[886],[888,28379,28380],{"xmlns":890},[892,28381,28382,28390],{},[895,28383,28384,28386,28388],{},[898,28385,1728],{},[898,28387,1746],{},[898,28389,1721],{},[902,28391,2389],{"encoding":904},[883,28393,28395],{"className":28394},[886],[888,28396,28397],{"xmlns":890},[892,28398,28399,28407],{},[895,28400,28401,28403,28405],{},[898,28402,1728],{},[898,28404,1746],{},[898,28406,2111],{},[902,28408,2408],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":28411},[28412,28413,28414,28415,28420,28423,28424,28431,28436,28441,28444,28445,28446,28447],{"id":12706,"depth":642,"text":12707},{"id":18848,"depth":642,"text":18849},{"id":18968,"depth":642,"text":18969},{"id":19221,"depth":642,"text":19222,"children":28416},[28417,28418,28419],{"id":19225,"depth":649,"text":19226},{"id":19437,"depth":649,"text":19438},{"id":19945,"depth":649,"text":19946},{"id":20265,"depth":642,"text":20266,"children":28421},[28422],{"id":20780,"depth":649,"text":20781},{"id":21275,"depth":642,"text":21276},{"id":21302,"depth":642,"text":21303,"children":28425},[28426,28427,28428,28430],{"id":21313,"depth":649,"text":21314},{"id":21383,"depth":649,"text":21384},{"id":21567,"depth":649,"text":28429},"Výpočet YEY^E",{"id":21710,"depth":649,"text":21711},{"id":22088,"depth":642,"text":22089,"children":28432},[28433,28434,28435],{"id":22092,"depth":649,"text":21314},{"id":22541,"depth":649,"text":21384},{"id":23197,"depth":649,"text":23198},{"id":23984,"depth":642,"text":23985,"children":28437},[28438,28439,28440],{"id":23988,"depth":649,"text":21314},{"id":24133,"depth":649,"text":21384},{"id":24403,"depth":649,"text":24404},{"id":25327,"depth":642,"text":25328,"children":28442},[28443],{"id":25523,"depth":649,"text":25524},{"id":26073,"depth":642,"text":26074},{"id":26533,"depth":642,"text":26534},{"id":16420,"depth":642,"text":16421},{"id":2619,"depth":642,"text":2620},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,2418,1143,28454,28455,28456,16968,18578],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":28459,"title":28460,"body":28461,"course":1128,"courses":659,"created":2676,"description":641,"extension":661,"meta":37441,"navigation":664,"path":37442,"seo":37443,"sources":37444,"stem":37445,"tags":37446,"type":4573,"updated":677,"__hash__":37451},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":28462,"toc":37410},[28463,28466,28468,28697,28701,28754,28824,28936,29095,29099,29215,29219,29222,29344,29347,29540,29564,29632,29796,29814,29880,30258,30262,30269,30513,30569,30573,30638,30756,30888,30920,31040,31122,31125,31247,31440,31661,31665,31705,31810,31867,31967,32144,32274,32327,32330,32417,32421,32597,32601,32604,32689,32692,32749,32854,32858,32979,32982,33165,33168,33276,33485,33805,33853,33926,34000,34002,34226,34461,34729,34733,34736,34841,34898,34932,34979,35012,35096,35098,35330,35463,35540,35662,35817,35821,35962,35969,36193,36204,36208,36212,36317,36459,36569,36668,36672,36831,36941,36943,37336,37338],[12,28464,28460],{"id":28465},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,28467,12707],{"id":12706},[724,28469,28470,28472,28473,28507,28508,28511,28512,28543,28544,28590,28591,28594,28595,28637,28638,28656,28657,28661,28662,28692,28693,28696],{},[38,28471,913],{}," řeší, jaký svazek zboží ",[883,28474,28476],{"className":28475},[886],[888,28477,28478],{"xmlns":890},[892,28479,28480,28504],{},[895,28481,28482,28484,28492,28494,28502],{},[1723,28483,3212],{"stretchy":1907},[2220,28485,28486,28488,28490],{},[898,28487,1904],{},[1864,28489,1866],{},[1723,28491,5066],{},[1723,28493,2031],{"separator":2030},[2220,28495,28496,28498,28500],{},[898,28497,1904],{},[1864,28499,2331],{},[1723,28501,5066],{},[1723,28503,3227],{"stretchy":1907},[902,28505,28506],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,28509,28510],{},"primární úloha"," — maximalizace užitečnosti ",[883,28513,28515],{"className":28514},[886],[888,28516,28517],{"xmlns":890},[892,28518,28519,28541],{},[895,28520,28521,28523,28525,28531,28533,28539],{},[898,28522,900],{},[1723,28524,1908],{"stretchy":1907},[1931,28526,28527,28529],{},[898,28528,1904],{},[1864,28530,1866],{},[1723,28532,2031],{"separator":2030},[1931,28534,28535,28537],{},[898,28536,1904],{},[1864,28538,2331],{},[1723,28540,1914],{"stretchy":1907},[902,28542,17039],{"encoding":904}," při rozpočtovém omezení ",[883,28545,28547],{"className":28546},[886],[888,28548,28549],{"xmlns":890},[892,28550,28551,28587],{},[895,28552,28553,28559,28561,28567,28573,28575,28581],{},[2057,28554,28555,28557],{},[898,28556,9837],{},[1723,28558,5066],{},[1723,28560,1725],{},[1931,28562,28563,28565],{},[898,28564,1746],{},[1864,28566,1866],{},[1931,28568,28569,28571],{},[898,28570,1904],{},[1864,28572,1866],{},[1723,28574,2087],{},[1931,28576,28577,28579],{},[898,28578,1746],{},[1864,28580,2331],{},[1931,28582,28583,28585],{},[898,28584,1904],{},[1864,28586,2331],{},[902,28588,28589],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,28592,28593],{},"duální úloha"," — minimalizace výdajů ",[883,28596,28598],{"className":28597},[886],[888,28599,28600],{"xmlns":890},[892,28601,28602,28634],{},[895,28603,28604,28606,28608,28614,28620,28622,28628],{},[898,28605,1846],{},[1723,28607,1725],{},[1931,28609,28610,28612],{},[898,28611,1746],{},[1864,28613,1866],{},[1931,28615,28616,28618],{},[898,28617,1904],{},[1864,28619,1866],{},[1723,28621,2087],{},[1931,28623,28624,28626],{},[898,28625,1746],{},[1864,28627,2331],{},[1931,28629,28630,28632],{},[898,28631,1904],{},[1864,28633,2331],{},[902,28635,28636],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,28639,28641],{"className":28640},[886],[888,28642,28643],{"xmlns":890},[892,28644,28645,28653],{},[895,28646,28647],{},[2057,28648,28649,28651],{},[898,28650,900],{},[1723,28652,5066],{},[902,28654,28655],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,28658,28660],{"className":28659,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,28663,28665],{"className":28664},[886],[888,28666,28667],{"xmlns":890},[892,28668,28669,28689],{},[895,28670,28671,28673,28675,28681,28683],{},[3018,28672,11303],{},[1723,28674,1725],{},[1931,28676,28677,28679],{},[898,28678,1746],{},[1864,28680,1866],{},[898,28682,2125],{"mathvariant":2124},[1931,28684,28685,28687],{},[898,28686,1746],{},[1864,28688,2331],{},[902,28690,28691],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,28694,28695],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,28698,28700],{"id":28699},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,28702,28703,28704,28722,28723,28753],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,28705,28707],{"className":28706},[886],[888,28708,28709],{"xmlns":890},[892,28710,28711,28719],{},[895,28712,28713],{},[2057,28714,28715,28717],{},[898,28716,9837],{},[1723,28718,5066],{},[902,28720,28721],{"encoding":904},"Y^*"," a ceny ",[883,28724,28726],{"className":28725},[886],[888,28727,28728],{"xmlns":890},[892,28729,28730,28750],{},[895,28731,28732,28740,28742],{},[2220,28733,28734,28736,28738],{},[898,28735,1746],{},[1864,28737,1866],{},[1723,28739,5066],{},[1723,28741,2031],{"separator":2030},[2220,28743,28744,28746,28748],{},[898,28745,1746],{},[1864,28747,2331],{},[1723,28749,5066],{},[902,28751,28752],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,28755,28757],{"className":28756},[886],[888,28758,28760],{"xmlns":890,"display":28759},"block",[892,28761,28762,28821],{},[21447,28763,28765],{"width":28764},"100%",[21452,28766,28767,28770,28814,28816],{},[21455,28768],{"width":28769},"50%",[21455,28771,28772],{},[895,28773,28774,28780,28782,28790,28796,28798,28806,28812],{},[2057,28775,28776,28778],{},[898,28777,9837],{},[1723,28779,5066],{},[1723,28781,1725],{},[2220,28783,28784,28786,28788],{},[898,28785,1746],{},[1864,28787,1866],{},[1723,28789,5066],{},[1931,28791,28792,28794],{},[898,28793,1904],{},[1864,28795,1866],{},[1723,28797,2087],{},[2220,28799,28800,28802,28804],{},[898,28801,1746],{},[1864,28803,2331],{},[1723,28805,5066],{},[1931,28807,28808,28810],{},[898,28809,1904],{},[1864,28811,2331],{},[1723,28813,2031],{"separator":2030},[21455,28815],{"width":28769},[21455,28817,28818],{},[3018,28819,28820],{},"(6.12)",[902,28822,28823],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,28825,28826,28827,28830,28831,1682,28867,28903,28904,28917,28918,28932,28933,1664],{},"geometricky ",[38,28828,28829],{},"rozpočtová přímka (budget line)"," procházející body ",[883,28832,28834],{"className":28833},[886],[888,28835,28836],{"xmlns":890},[892,28837,28838,28864],{},[895,28839,28840,28842,28848,28850,28858,28860,28862],{},[1723,28841,3212],{"stretchy":1907},[2057,28843,28844,28846],{},[898,28845,9837],{},[1723,28847,5066],{},[898,28849,2125],{"mathvariant":2124},[2220,28851,28852,28854,28856],{},[898,28853,1746],{},[1864,28855,1866],{},[1723,28857,5066],{},[1723,28859,2031],{"separator":2030},[1864,28861,2256],{},[1723,28863,3227],{"stretchy":1907},[902,28865,28866],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,28868,28870],{"className":28869},[886],[888,28871,28872],{"xmlns":890},[892,28873,28874,28900],{},[895,28875,28876,28878,28880,28882,28888,28890,28898],{},[1723,28877,3212],{"stretchy":1907},[1864,28879,2256],{},[1723,28881,2031],{"separator":2030},[2057,28883,28884,28886],{},[898,28885,9837],{},[1723,28887,5066],{},[898,28889,2125],{"mathvariant":2124},[2220,28891,28892,28894,28896],{},[898,28893,1746],{},[1864,28895,2331],{},[1723,28897,5066],{},[1723,28899,3227],{"stretchy":1907},[902,28901,28902],{"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 ",[883,28905,28907],{"className":28906},[886],[888,28908,28909],{"xmlns":890},[892,28910,28911,28915],{},[895,28912,28913],{},[898,28914,900],{},[902,28916,900],{"encoding":904},", indiferenční křivky a ",[883,28919,28921],{"className":28920},[886],[888,28922,28923],{"xmlns":890},[892,28924,28925,28929],{},[895,28926,28927],{},[3018,28928,11303],{},[902,28930,28931],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,28934,880],{"className":28935,"dataFsResolvedFilePath":878,"href":879},[210],[4584,28937,28938],{},[724,28939,28940,28942,28943,28946,28947,28960,28961,28963,28964,28977,28978,2628,28981,29021,29022,29039,29040,29057,29058,29075,29076,29094],{},[883,28941,5124],{}," Pozor — dvě úlohy, totéž řešení\n",[38,28944,28945],{},"Primární úloha"," (max ",[883,28948,28950],{"className":28949},[886],[888,28951,28952],{"xmlns":890},[892,28953,28954,28958],{},[895,28955,28956],{},[898,28957,900],{},[902,28959,900],{"encoding":904}," při pevném rozpočtu) a ",[38,28962,28593],{}," (min ",[883,28965,28967],{"className":28966},[886],[888,28968,28969],{"xmlns":890},[892,28970,28971,28975],{},[895,28972,28973],{},[898,28974,1846],{},[902,28976,1846],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,28979,28980],{},"tentýž bod",[883,28982,28984],{"className":28983},[886],[888,28985,28986],{"xmlns":890},[892,28987,28988,29018],{},[895,28989,28990,28996,28998,29006,29008,29016],{},[2057,28991,28992,28994],{},[898,28993,1904],{},[1723,28995,5066],{},[1723,28997,3212],{"stretchy":1907},[2220,28999,29000,29002,29004],{},[898,29001,1904],{},[1864,29003,1866],{},[1723,29005,5066],{},[1723,29007,2031],{"separator":2030},[2220,29009,29010,29012,29014],{},[898,29011,1904],{},[1864,29013,2331],{},[1723,29015,5066],{},[1723,29017,3227],{"stretchy":1907},[902,29019,29020],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,29023,29025],{"className":29024},[886],[888,29026,29027],{"xmlns":890},[892,29028,29029,29037],{},[895,29030,29031],{},[2057,29032,29033,29035],{},[898,29034,9837],{},[1723,29036,5066],{},[902,29038,28721],{"encoding":904}," a hledáme maximální ",[883,29041,29043],{"className":29042},[886],[888,29044,29045],{"xmlns":890},[892,29046,29047,29055],{},[895,29048,29049],{},[2057,29050,29051,29053],{},[898,29052,900],{},[1723,29054,5066],{},[902,29056,28655],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,29059,29061],{"className":29060},[886],[888,29062,29063],{"xmlns":890},[892,29064,29065,29073],{},[895,29066,29067],{},[2057,29068,29069,29071],{},[898,29070,900],{},[1723,29072,5066],{},[902,29074,28655],{"encoding":904}," a hledáme minimální ",[883,29077,29079],{"className":29078},[886],[888,29080,29081],{"xmlns":890},[892,29082,29083,29091],{},[895,29084,29085],{},[2057,29086,29087,29089],{},[898,29088,1846],{},[1723,29090,5066],{},[902,29092,29093],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,29096,29098],{"id":29097},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,29100,29101,29102,29133,29134,29210,29211,1664],{},"Úlohou je najít maximum ",[883,29103,29105],{"className":29104},[886],[888,29106,29107],{"xmlns":890},[892,29108,29109,29131],{},[895,29110,29111,29113,29115,29121,29123,29129],{},[898,29112,900],{},[1723,29114,1908],{"stretchy":1907},[1931,29116,29117,29119],{},[898,29118,1904],{},[1864,29120,1866],{},[1723,29122,2031],{"separator":2030},[1931,29124,29125,29127],{},[898,29126,1904],{},[1864,29128,2331],{},[1723,29130,1914],{"stretchy":1907},[902,29132,17039],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,29135,29137],{"className":29136},[886],[888,29138,29139],{"xmlns":890},[892,29140,29141,29207],{},[895,29142,29143,29145,29147,29153,29155,29161,29163,29165,29171,29173,29181,29187,29189,29197,29203,29205],{},[898,29144,11741],{},[1723,29146,1908],{"stretchy":1907},[1931,29148,29149,29151],{},[898,29150,1904],{},[1864,29152,1866],{},[1723,29154,2031],{"separator":2030},[1931,29156,29157,29159],{},[898,29158,1904],{},[1864,29160,2331],{},[1723,29162,1914],{"stretchy":1907},[1723,29164,1725],{},[2057,29166,29167,29169],{},[898,29168,9837],{},[1723,29170,5066],{},[1723,29172,1759],{},[2220,29174,29175,29177,29179],{},[898,29176,1746],{},[1864,29178,1866],{},[1723,29180,5066],{},[1931,29182,29183,29185],{},[898,29184,1904],{},[1864,29186,1866],{},[1723,29188,1759],{},[2220,29190,29191,29193,29195],{},[898,29192,1746],{},[1864,29194,2331],{},[1723,29196,5066],{},[1931,29198,29199,29201],{},[898,29200,1904],{},[1864,29202,2331],{},[1723,29204,1725],{},[1864,29206,2256],{},[902,29208,29209],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,29212,29214],{"className":29213,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,29216,29218],{"id":29217},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,29220,29221],{},"Sestavíme",[883,29223,29225],{"className":29224},[886],[888,29226,29227],{"xmlns":890,"display":28759},[892,29228,29229,29341],{},[21447,29230,29231],{"width":28764},[21452,29232,29233,29235,29334,29336],{},[21455,29234],{"width":28769},[21455,29236,29237],{},[895,29238,29239,29242,29244,29250,29252,29258,29260,29262,29264,29266,29268,29270,29276,29278,29284,29286,29288,29290,29292,29298,29300,29308,29314,29316,29324,29330,29332],{},[898,29240,1911],{"mathvariant":29241},"script",[1723,29243,1908],{"stretchy":1907},[1931,29245,29246,29248],{},[898,29247,1904],{},[1864,29249,1866],{},[1723,29251,2031],{"separator":2030},[1931,29253,29254,29256],{},[898,29255,1904],{},[1864,29257,2331],{},[1723,29259,2031],{"separator":2030},[898,29261,17139],{},[1723,29263,1914],{"stretchy":1907},[1723,29265,1725],{},[898,29267,900],{},[1723,29269,1908],{"stretchy":1907},[1931,29271,29272,29274],{},[898,29273,1904],{},[1864,29275,1866],{},[1723,29277,2031],{"separator":2030},[1931,29279,29280,29282],{},[898,29281,1904],{},[1864,29283,2331],{},[1723,29285,1914],{"stretchy":1907},[1723,29287,2087],{},[898,29289,17139],{},[1723,29291,1908],{"stretchy":1907},[2057,29293,29294,29296],{},[898,29295,9837],{},[1723,29297,5066],{},[1723,29299,1759],{},[2220,29301,29302,29304,29306],{},[898,29303,1746],{},[1864,29305,1866],{},[1723,29307,5066],{},[1931,29309,29310,29312],{},[898,29311,1904],{},[1864,29313,1866],{},[1723,29315,1759],{},[2220,29317,29318,29320,29322],{},[898,29319,1746],{},[1864,29321,2331],{},[1723,29323,5066],{},[1931,29325,29326,29328],{},[898,29327,1904],{},[1864,29329,2331],{},[1723,29331,1914],{"stretchy":1907},[898,29333,1664],{"mathvariant":2124},[21455,29335],{"width":28769},[21455,29337,29338],{},[3018,29339,29340],{},"(6.13)",[902,29342,29343],{"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}",[724,29345,29346],{},"Soustava prvního řádu:",[883,29348,29350],{"className":29349},[886],[888,29351,29352],{"xmlns":890,"display":28759},[892,29353,29354,29537],{},[21447,29355,29356],{"width":28764},[21452,29357,29358,29360,29530,29532],{},[21455,29359],{"width":28769},[21455,29361,29362],{},[21447,29363,29364,29414,29464],{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},[21452,29365,29366,29378],{},[21455,29367,29368],{},[3055,29369,29370],{"scriptlevel":2256,"displaystyle":2030},[2220,29371,29372,29374,29376],{},[898,29373,1911],{"mathvariant":29241},[1864,29375,1866],{},[1723,29377,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,29379,29380],{},[3055,29381,29382],{"scriptlevel":2256,"displaystyle":2030},[895,29383,29384,29386,29388,29396,29398,29400,29408,29410,29412],{},[895,29385],{},[1723,29387,1725],{},[2220,29389,29390,29392,29394],{},[898,29391,900],{},[1864,29393,1866],{},[1723,29395,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,29397,1759],{},[898,29399,17139],{},[2220,29401,29402,29404,29406],{},[898,29403,1746],{},[1864,29405,1866],{},[1723,29407,5066],{},[1723,29409,1725],{},[1864,29411,2256],{},[1723,29413,2031],{"separator":2030},[21452,29415,29416,29428],{},[21455,29417,29418],{},[3055,29419,29420],{"scriptlevel":2256,"displaystyle":2030},[2220,29421,29422,29424,29426],{},[898,29423,1911],{"mathvariant":29241},[1864,29425,2331],{},[1723,29427,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,29429,29430],{},[3055,29431,29432],{"scriptlevel":2256,"displaystyle":2030},[895,29433,29434,29436,29438,29446,29448,29450,29458,29460,29462],{},[895,29435],{},[1723,29437,1725],{},[2220,29439,29440,29442,29444],{},[898,29441,900],{},[1864,29443,2331],{},[1723,29445,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,29447,1759],{},[898,29449,17139],{},[2220,29451,29452,29454,29456],{},[898,29453,1746],{},[1864,29455,2331],{},[1723,29457,5066],{},[1723,29459,1725],{},[1864,29461,2256],{},[1723,29463,2031],{"separator":2030},[21452,29465,29466,29478],{},[21455,29467,29468],{},[3055,29469,29470],{"scriptlevel":2256,"displaystyle":2030},[2220,29471,29472,29474,29476],{},[898,29473,1911],{"mathvariant":29241},[898,29475,17139],{},[1723,29477,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,29479,29480],{},[3055,29481,29482],{"scriptlevel":2256,"displaystyle":2030},[895,29483,29484,29486,29488,29494,29496,29504,29510,29512,29520,29526,29528],{},[895,29485],{},[1723,29487,1725],{},[2057,29489,29490,29492],{},[898,29491,9837],{},[1723,29493,5066],{},[1723,29495,1759],{},[2220,29497,29498,29500,29502],{},[898,29499,1746],{},[1864,29501,1866],{},[1723,29503,5066],{},[1931,29505,29506,29508],{},[898,29507,1904],{},[1864,29509,1866],{},[1723,29511,1759],{},[2220,29513,29514,29516,29518],{},[898,29515,1746],{},[1864,29517,2331],{},[1723,29519,5066],{},[1931,29521,29522,29524],{},[898,29523,1904],{},[1864,29525,2331],{},[1723,29527,1725],{},[1864,29529,13161],{},[21455,29531],{"width":28769},[21455,29533,29534],{},[3018,29535,29536],{},"(6.14)",[902,29538,29539],{"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}",[724,29541,29542,29543,29546,29547,29560,29561,3430],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,29544,29545],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,29548,29550],{"className":29549},[886],[888,29551,29552],{"xmlns":890},[892,29553,29554,29558],{},[895,29555,29556],{},[898,29557,17139],{},[902,29559,17192],{"encoding":904}," dostáváme ",[38,29562,29563],{},"podmínku optimality",[883,29565,29567],{"className":29566},[886],[888,29568,29569],{"xmlns":890,"display":28759},[892,29570,29571,29629],{},[895,29572,29573],{},[13533,29574,29575],{"notation":13535},[3055,29576,29577],{"scriptlevel":2256,"displaystyle":1907},[3055,29578,29579],{"scriptlevel":2256,"displaystyle":1907},[3055,29580,29581],{"scriptlevel":2256,"displaystyle":2030},[895,29582,29583,29585,29587,29589,29607,29609,29627],{},[3018,29584,4699],{},[3018,29586,11303],{},[1723,29588,1725],{},[3058,29590,29591,29599],{},[2220,29592,29593,29595,29597],{},[898,29594,900],{},[1864,29596,1866],{},[1723,29598,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[2220,29600,29601,29603,29605],{},[898,29602,900],{},[1864,29604,2331],{},[1723,29606,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,29608,1725],{},[3058,29610,29611,29619],{},[2220,29612,29613,29615,29617],{},[898,29614,1746],{},[1864,29616,1866],{},[1723,29618,5066],{},[2220,29620,29621,29623,29625],{},[898,29622,1746],{},[1864,29624,2331],{},[1723,29626,5066],{},[3018,29628,4699],{},[902,29630,29631],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[4584,29633,29634],{},[724,29635,29636,29638,29639,29673,29674,29677,29678,29696,29697,29715,29716,29746,29747,29764,29765,29795],{},[883,29637,4869],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,29640,29642],{"className":29641},[886],[888,29643,29644],{"xmlns":890},[892,29645,29646,29670],{},[895,29647,29648,29650,29652,29660,29662],{},[3018,29649,11303],{},[1723,29651,1725],{},[2220,29653,29654,29656,29658],{},[898,29655,1746],{},[1864,29657,1866],{},[1723,29659,5066],{},[898,29661,2125],{"mathvariant":2124},[2220,29663,29664,29666,29668],{},[898,29665,1746],{},[1864,29667,2331],{},[1723,29669,5066],{},[902,29671,29672],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,29675,29676],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,29679,29681],{"className":29680},[886],[888,29682,29683],{"xmlns":890},[892,29684,29685,29693],{},[895,29686,29687],{},[1931,29688,29689,29691],{},[898,29690,1904],{},[1864,29692,1866],{},[902,29694,29695],{"encoding":904},"Q_1"," za ",[883,29698,29700],{"className":29699},[886],[888,29701,29702],{"xmlns":890},[892,29703,29704,29712],{},[895,29705,29706],{},[1931,29707,29708,29710],{},[898,29709,1904],{},[1864,29711,2331],{},[902,29713,29714],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,29717,29719],{"className":29718},[886],[888,29720,29721],{"xmlns":890},[892,29722,29723,29743],{},[895,29724,29725,29727,29729,29735,29737],{},[3018,29726,11303],{},[1723,29728,2253],{},[1931,29730,29731,29733],{},[898,29732,1746],{},[1864,29734,1866],{},[898,29736,2125],{"mathvariant":2124},[1931,29738,29739,29741],{},[898,29740,1746],{},[1864,29742,2331],{},[902,29744,29745],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,29748,29750],{"className":29749},[886],[888,29751,29752],{"xmlns":890},[892,29753,29754,29762],{},[895,29755,29756],{},[1931,29757,29758,29760],{},[898,29759,1904],{},[1864,29761,1866],{},[902,29763,29695],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,29766,29768],{"className":29767},[886],[888,29769,29770],{"xmlns":890},[892,29771,29772,29792],{},[895,29773,29774,29776,29778,29784,29786],{},[3018,29775,11303],{},[1723,29777,2287],{},[1931,29779,29780,29782],{},[898,29781,1746],{},[1864,29783,1866],{},[898,29785,2125],{"mathvariant":2124},[1931,29787,29788,29790],{},[898,29789,1746],{},[1864,29791,2331],{},[902,29793,29794],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,29797,29799,29800,29813],{"id":29798},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,29801,29803],{"className":29802},[886],[888,29804,29805],{"xmlns":890},[892,29806,29807,29811],{},[895,29808,29809],{},[898,29810,17139],{},[902,29812,17192],{"encoding":904}," — mezní užitečnost důchodu",[724,29815,29816,29817,29835,29836,29839,29840,29857,29858,29875,29876,29879],{},"Lagrangeův multiplikátor ",[883,29818,29820],{"className":29819},[886],[888,29821,29822],{"xmlns":890},[892,29823,29824,29832],{},[895,29825,29826],{},[2057,29827,29828,29830],{},[898,29829,17139],{},[1723,29831,5066],{},[902,29833,29834],{"encoding":904},"\\lambda^*"," představuje ",[38,29837,29838],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,29841,29843],{"className":29842},[886],[888,29844,29845],{"xmlns":890},[892,29846,29847,29855],{},[895,29848,29849],{},[2057,29850,29851,29853],{},[898,29852,900],{},[1723,29854,5066],{},[902,29856,28655],{"encoding":904}," při jednotkové změně důchodu ",[883,29859,29861],{"className":29860},[886],[888,29862,29863],{"xmlns":890},[892,29864,29865,29873],{},[895,29866,29867],{},[2057,29868,29869,29871],{},[898,29870,9837],{},[1723,29872,5066],{},[902,29874,28721],{"encoding":904},". Je to ",[38,29877,29878],{},"stínová cena"," rozpočtového omezení.",[4584,29881,29882,29887],{},[724,29883,29884,29886],{},[883,29885,5283],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,29888,29889,29949,30036,30072,30159],{},[123,29890,29891,29894,29895,1664],{},[38,29892,29893],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,29896,29898],{"className":29897},[886],[888,29899,29900],{"xmlns":890},[892,29901,29902,29946],{},[895,29903,29904,29910,29912,29920,29926,29928,29936,29942,29944],{},[2057,29905,29906,29908],{},[898,29907,9837],{},[1723,29909,5066],{},[1723,29911,1759],{},[2220,29913,29914,29916,29918],{},[898,29915,1746],{},[1864,29917,1866],{},[1723,29919,5066],{},[1931,29921,29922,29924],{},[898,29923,1904],{},[1864,29925,1866],{},[1723,29927,1759],{},[2220,29929,29930,29932,29934],{},[898,29931,1746],{},[1864,29933,2331],{},[1723,29935,5066],{},[1931,29937,29938,29940],{},[898,29939,1904],{},[1864,29941,2331],{},[1723,29943,1725],{},[1864,29945,2256],{},[902,29947,29948],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,29950,29951,2628,29954,1664],{},[38,29952,29953],{},"Sestav Lagrangeovu funkci",[883,29955,29957],{"className":29956},[886],[888,29958,29959],{"xmlns":890},[892,29960,29961,30033],{},[895,29962,29963,29965,29967,29969,29971,29977,29979,29985,29987,29989,29991,29993,29999,30001,30009,30015,30017,30025,30031],{},[898,29964,1911],{"mathvariant":29241},[1723,29966,1725],{},[898,29968,900],{},[1723,29970,1908],{"stretchy":1907},[1931,29972,29973,29975],{},[898,29974,1904],{},[1864,29976,1866],{},[1723,29978,2031],{"separator":2030},[1931,29980,29981,29983],{},[898,29982,1904],{},[1864,29984,2331],{},[1723,29986,1914],{"stretchy":1907},[1723,29988,2087],{},[898,29990,17139],{},[1723,29992,1908],{"stretchy":1907},[2057,29994,29995,29997],{},[898,29996,9837],{},[1723,29998,5066],{},[1723,30000,1759],{},[2220,30002,30003,30005,30007],{},[898,30004,1746],{},[1864,30006,1866],{},[1723,30008,5066],{},[1931,30010,30011,30013],{},[898,30012,1904],{},[1864,30014,1866],{},[1723,30016,1759],{},[2220,30018,30019,30021,30023],{},[898,30020,1746],{},[1864,30022,2331],{},[1723,30024,5066],{},[1931,30026,30027,30029],{},[898,30028,1904],{},[1864,30030,2331],{},[1723,30032,1914],{"stretchy":1907},[902,30034,30035],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,30037,30038,11168,30041,30071],{},[38,30039,30040],{},"Spočítej parciální derivace",[883,30042,30044],{"className":30043},[886],[888,30045,30046],{"xmlns":890},[892,30047,30048,30068],{},[895,30049,30050,30056,30058,30064,30066],{},[1931,30051,30052,30054],{},[898,30053,1904],{},[1864,30055,1866],{},[1723,30057,2031],{"separator":2030},[1931,30059,30060,30062],{},[898,30061,1904],{},[1864,30063,2331],{},[1723,30065,2031],{"separator":2030},[898,30067,17139],{},[902,30069,30070],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,30073,30074,30090,30091,30124,30125,1682,30142,1664],{},[38,30075,30076,30077],{},"Vyluč ",[883,30078,30080],{"className":30079},[886],[888,30081,30082],{"xmlns":890},[892,30083,30084,30088],{},[895,30085,30086],{},[898,30087,17139],{},[902,30089,17192],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,30092,30094],{"className":30093},[886],[888,30095,30096],{"xmlns":890},[892,30097,30098,30122],{},[895,30099,30100,30102,30104,30112,30114],{},[3018,30101,11303],{},[1723,30103,1725],{},[2220,30105,30106,30108,30110],{},[898,30107,1746],{},[1864,30109,1866],{},[1723,30111,5066],{},[898,30113,2125],{"mathvariant":2124},[2220,30115,30116,30118,30120],{},[898,30117,1746],{},[1864,30119,2331],{},[1723,30121,5066],{},[902,30123,29672],{"encoding":904},", která dá vztah mezi ",[883,30126,30128],{"className":30127},[886],[888,30129,30130],{"xmlns":890},[892,30131,30132,30140],{},[895,30133,30134],{},[1931,30135,30136,30138],{},[898,30137,1904],{},[1864,30139,1866],{},[902,30141,29695],{"encoding":904},[883,30143,30145],{"className":30144},[886],[888,30146,30147],{"xmlns":890},[892,30148,30149,30157],{},[895,30150,30151],{},[1931,30152,30153,30155],{},[898,30154,1904],{},[1864,30156,2331],{},[902,30158,29714],{"encoding":904},[123,30160,30161,30164,30165,30195,30196,30213,30214,1664],{},[38,30162,30163],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,30166,30168],{"className":30167},[886],[888,30169,30170],{"xmlns":890},[892,30171,30172,30192],{},[895,30173,30174,30182,30184],{},[2220,30175,30176,30178,30180],{},[898,30177,1904],{},[1864,30179,1866],{},[1723,30181,5066],{},[1723,30183,2031],{"separator":2030},[2220,30185,30186,30188,30190],{},[898,30187,1904],{},[1864,30189,2331],{},[1723,30191,5066],{},[902,30193,30194],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,30197,30199],{"className":30198},[886],[888,30200,30201],{"xmlns":890},[892,30202,30203,30211],{},[895,30204,30205],{},[2057,30206,30207,30209],{},[898,30208,17139],{},[1723,30210,5066],{},[902,30212,29834],{"encoding":904}," a maximální užitečnost ",[883,30215,30217],{"className":30216},[886],[888,30218,30219],{"xmlns":890},[892,30220,30221,30255],{},[895,30222,30223,30229,30231,30233,30235,30243,30245,30253],{},[2057,30224,30225,30227],{},[898,30226,900],{},[1723,30228,5066],{},[1723,30230,1725],{},[898,30232,900],{},[1723,30234,1908],{"stretchy":1907},[2220,30236,30237,30239,30241],{},[898,30238,1904],{},[1864,30240,1866],{},[1723,30242,5066],{},[1723,30244,2031],{"separator":2030},[2220,30246,30247,30249,30251],{},[898,30248,1904],{},[1864,30250,2331],{},[1723,30252,5066],{},[1723,30254,1914],{"stretchy":1907},[902,30256,30257],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,30259,30261],{"id":30260},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,30263,30264],{},[3285,30265],{"alt":30266,"className":30267,"src":30268},"imek-uzitecnost-optimum",[210,3289],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,30270,30271],{},[614,30272,30273,30274,30323,30324,1682,30352,30380,30381,30415,30416,30455,30456,30474,30475,30493,30494,30512],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,30275,30277],{"className":30276},[886],[888,30278,30279],{"xmlns":890},[892,30280,30281,30321],{},[895,30282,30283,30289,30291,30299,30305,30307,30315],{},[2057,30284,30285,30287],{},[898,30286,9837],{},[1723,30288,5066],{},[1723,30290,1725],{},[2220,30292,30293,30295,30297],{},[898,30294,1746],{},[1864,30296,1866],{},[1723,30298,5066],{},[1931,30300,30301,30303],{},[898,30302,1904],{},[1864,30304,1866],{},[1723,30306,2087],{},[2220,30308,30309,30311,30313],{},[898,30310,1746],{},[1864,30312,2331],{},[1723,30314,5066],{},[1931,30316,30317,30319],{},[898,30318,1904],{},[1864,30320,2331],{},[902,30322,17994],{"encoding":904}," protíná osy v ",[883,30325,30327],{"className":30326},[886],[888,30328,30329],{"xmlns":890},[892,30330,30331,30349],{},[895,30332,30333,30339,30341],{},[2057,30334,30335,30337],{},[898,30336,9837],{},[1723,30338,5066],{},[898,30340,2125],{"mathvariant":2124},[2220,30342,30343,30345,30347],{},[898,30344,1746],{},[1864,30346,1866],{},[1723,30348,5066],{},[902,30350,30351],{"encoding":904},"Y^*\u002FP_1^*",[883,30353,30355],{"className":30354},[886],[888,30356,30357],{"xmlns":890},[892,30358,30359,30377],{},[895,30360,30361,30367,30369],{},[2057,30362,30363,30365],{},[898,30364,9837],{},[1723,30366,5066],{},[898,30368,2125],{"mathvariant":2124},[2220,30370,30371,30373,30375],{},[898,30372,1746],{},[1864,30374,2331],{},[1723,30376,5066],{},[902,30378,30379],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,30382,30384],{"className":30383},[886],[888,30385,30386],{"xmlns":890},[892,30387,30388,30412],{},[895,30389,30390,30396,30398,30404,30406],{},[1931,30391,30392,30394],{},[898,30393,2878],{},[1864,30395,1866],{},[1723,30397,2287],{},[2057,30399,30400,30402],{},[898,30401,2878],{},[1723,30403,5066],{},[1723,30405,2287],{},[1931,30407,30408,30410],{},[898,30409,2878],{},[1864,30411,2331],{},[902,30413,30414],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,30417,30419],{"className":30418},[886],[888,30420,30421],{"xmlns":890},[892,30422,30423,30453],{},[895,30424,30425,30431,30433,30441,30443,30451],{},[2057,30426,30427,30429],{},[898,30428,1904],{},[1723,30430,5066],{},[1723,30432,3212],{"stretchy":1907},[2220,30434,30435,30437,30439],{},[898,30436,1904],{},[1864,30438,1866],{},[1723,30440,5066],{},[1723,30442,2031],{"separator":2030},[2220,30444,30445,30447,30449],{},[898,30446,1904],{},[1864,30448,2331],{},[1723,30450,5066],{},[1723,30452,3227],{"stretchy":1907},[902,30454,29020],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,30457,30459],{"className":30458},[886],[888,30460,30461],{"xmlns":890},[892,30462,30463,30471],{},[895,30464,30465],{},[2057,30466,30467,30469],{},[898,30468,2878],{},[1723,30470,5066],{},[902,30472,30473],{"encoding":904},"c^*",". Křivka ",[883,30476,30478],{"className":30477},[886],[888,30479,30480],{"xmlns":890},[892,30481,30482,30490],{},[895,30483,30484],{},[1931,30485,30486,30488],{},[898,30487,2878],{},[1864,30489,1866],{},[902,30491,30492],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,30495,30497],{"className":30496},[886],[888,30498,30499],{"xmlns":890},[892,30500,30501,30509],{},[895,30502,30503],{},[1931,30504,30505,30507],{},[898,30506,2878],{},[1864,30508,2331],{},[902,30510,30511],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,30514,30515,30516,30519,30520,30538,30539,30568],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,30517,30518],{},"dotýkají",", tj. mají v bodě ",[883,30521,30523],{"className":30522},[886],[888,30524,30525],{"xmlns":890},[892,30526,30527,30535],{},[895,30528,30529],{},[2057,30530,30531,30533],{},[898,30532,1904],{},[1723,30534,5066],{},[902,30536,30537],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,30540,30542],{"className":30541},[886],[888,30543,30544],{"xmlns":890},[892,30545,30546,30566],{},[895,30547,30548,30550,30552,30558,30560],{},[3018,30549,11303],{},[1723,30551,1725],{},[1931,30553,30554,30556],{},[898,30555,1746],{},[1864,30557,1866],{},[898,30559,2125],{"mathvariant":2124},[1931,30561,30562,30564],{},[898,30563,1746],{},[1864,30565,2331],{},[902,30567,28691],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,30570,30572],{"id":30571},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,30574,10369,30575,30637],{},[883,30576,30578],{"className":30577},[886],[888,30579,30580],{"xmlns":890},[892,30581,30582,30634],{},[895,30583,30584,30586,30588,30594,30596,30602,30604,30606,30620],{},[898,30585,900],{},[1723,30587,1908],{"stretchy":1907},[1931,30589,30590,30592],{},[898,30591,1904],{},[1864,30593,1866],{},[1723,30595,2031],{"separator":2030},[1931,30597,30598,30600],{},[898,30599,1904],{},[1864,30601,2331],{},[1723,30603,1914],{"stretchy":1907},[1723,30605,1725],{},[2220,30607,30608,30610,30612],{},[898,30609,1904],{},[1864,30611,1866],{},[895,30613,30614,30616,30618],{},[1864,30615,1866],{},[898,30617,2125],{"mathvariant":2124},[1864,30619,2331],{},[2220,30621,30622,30624,30626],{},[898,30623,1904],{},[1864,30625,2331],{},[895,30627,30628,30630,30632],{},[1864,30629,1866],{},[898,30631,2125],{"mathvariant":2124},[1864,30633,2331],{},[902,30635,30636],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,30639,30640],{},[883,30641,30643],{"className":30642},[886],[888,30644,30645],{"xmlns":890},[892,30646,30647,30753],{},[895,30648,30649,30651,30653,30735,30737,30751],{},[3018,30650,11303],{},[1723,30652,1725],{},[3058,30654,30655,30695],{},[895,30656,30657,30665,30681],{},[3055,30658,30659],{"scriptlevel":2256,"displaystyle":1907},[3058,30660,30661,30663],{},[1864,30662,1866],{},[1864,30664,2331],{},[2220,30666,30667,30669,30671],{},[898,30668,1904],{},[1864,30670,1866],{},[895,30672,30673,30675,30677,30679],{},[1723,30674,1759],{},[1864,30676,1866],{},[898,30678,2125],{"mathvariant":2124},[1864,30680,2331],{},[2220,30682,30683,30685,30687],{},[898,30684,1904],{},[1864,30686,2331],{},[895,30688,30689,30691,30693],{},[1864,30690,1866],{},[898,30692,2125],{"mathvariant":2124},[1864,30694,2331],{},[895,30696,30697,30705,30719],{},[3055,30698,30699],{"scriptlevel":2256,"displaystyle":1907},[3058,30700,30701,30703],{},[1864,30702,1866],{},[1864,30704,2331],{},[2220,30706,30707,30709,30711],{},[898,30708,1904],{},[1864,30710,1866],{},[895,30712,30713,30715,30717],{},[1864,30714,1866],{},[898,30716,2125],{"mathvariant":2124},[1864,30718,2331],{},[2220,30720,30721,30723,30725],{},[898,30722,1904],{},[1864,30724,2331],{},[895,30726,30727,30729,30731,30733],{},[1723,30728,1759],{},[1864,30730,1866],{},[898,30732,2125],{"mathvariant":2124},[1864,30734,2331],{},[1723,30736,1725],{},[3058,30738,30739,30745],{},[1931,30740,30741,30743],{},[898,30742,1904],{},[1864,30744,2331],{},[1931,30746,30747,30749],{},[898,30748,1904],{},[1864,30750,1866],{},[898,30752,1664],{"mathvariant":2124},[902,30754,30755],{"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}.",[724,30757,30758,30759,2137,30804,30806,30807,30827,30828,30858,30859,1664],{},"Tedy ",[883,30760,30762],{"className":30761},[886],[888,30763,30764],{"xmlns":890},[892,30765,30766,30801],{},[895,30767,30768,30770,30772,30775,30777,30779,30781,30783,30791,30793],{},[3018,30769,11303],{},[1723,30771,1908],{"stretchy":1907},[1864,30773,30774],{},"300",[1723,30776,2031],{"separator":2030},[1864,30778,15811],{},[1723,30780,1914],{"stretchy":1907},[1723,30782,1725],{},[3055,30784,30785],{"scriptlevel":2256,"displaystyle":1907},[3058,30786,30787,30789],{},[1864,30788,15811],{},[1864,30790,30774],{},[1723,30792,1725],{},[3055,30794,30795],{"scriptlevel":2256,"displaystyle":1907},[3058,30796,30797,30799],{},[1864,30798,2962],{},[1864,30800,2909],{},[902,30802,30803],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,30805,9924],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,30808,30810],{"className":30809},[886],[888,30811,30812],{"xmlns":890},[892,30813,30814,30824],{},[895,30815,30816],{},[3055,30817,30818],{"scriptlevel":2256,"displaystyle":1907},[3058,30819,30820,30822],{},[1864,30821,2962],{},[1864,30823,2909],{},[902,30825,30826],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,30829,30831],{"className":30830},[886],[888,30832,30833],{"xmlns":890},[892,30834,30835,30855],{},[895,30836,30837,30839,30841,30847,30849],{},[3018,30838,11303],{},[1723,30840,1725],{},[1931,30842,30843,30845],{},[898,30844,1904],{},[1864,30846,2331],{},[898,30848,2125],{"mathvariant":2124},[1931,30850,30851,30853],{},[898,30852,1904],{},[1864,30854,1866],{},[902,30856,30857],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,30860,30862],{"className":30861},[886],[888,30863,30864],{"xmlns":890},[892,30865,30866,30886],{},[895,30867,30868,30870,30872,30878,30880],{},[3018,30869,11303],{},[1723,30871,1725],{},[1931,30873,30874,30876],{},[898,30875,1746],{},[1864,30877,1866],{},[898,30879,2125],{"mathvariant":2124},[1931,30881,30882,30884],{},[898,30883,1746],{},[1864,30885,2331],{},[902,30887,28691],{"encoding":904},[115,30889,30891,30892],{"id":30890},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,30893,30895],{"className":30894},[886],[888,30896,30897],{"xmlns":890},[892,30898,30899,30917],{},[895,30900,30901,30903,30905,30911],{},[898,30902,900],{},[1723,30904,1725],{},[1931,30906,30907,30909],{},[898,30908,1904],{},[1864,30910,1866],{},[1931,30912,30913,30915],{},[898,30914,1904],{},[1864,30916,2331],{},[902,30918,30919],{"encoding":904},"U = Q_1 Q_2",[724,30921,30922,30923,1343,30969,1343,30993,1343,31017,31039],{},"Je dána ",[883,30924,30926],{"className":30925},[886],[888,30927,30928],{"xmlns":890},[892,30929,30930,30966],{},[895,30931,30932,30934,30936,30942,30944,30950,30952,30954,30960],{},[898,30933,900],{},[1723,30935,1908],{"stretchy":1907},[1931,30937,30938,30940],{},[898,30939,1904],{},[1864,30941,1866],{},[1723,30943,2031],{"separator":2030},[1931,30945,30946,30948],{},[898,30947,1904],{},[1864,30949,2331],{},[1723,30951,1914],{"stretchy":1907},[1723,30953,1725],{},[1931,30955,30956,30958],{},[898,30957,1904],{},[1864,30959,1866],{},[1931,30961,30962,30964],{},[898,30963,1904],{},[1864,30965,2331],{},[902,30967,30968],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,30970,30972],{"className":30971},[886],[888,30973,30974],{"xmlns":890},[892,30975,30976,30990],{},[895,30977,30978,30986,30988],{},[2220,30979,30980,30982,30984],{},[898,30981,1746],{},[1864,30983,1866],{},[1723,30985,5066],{},[1723,30987,1725],{},[1864,30989,2331],{},[902,30991,30992],{"encoding":904},"P_1^* = 2",[883,30994,30996],{"className":30995},[886],[888,30997,30998],{"xmlns":890},[892,30999,31000,31014],{},[895,31001,31002,31010,31012],{},[2220,31003,31004,31006,31008],{},[898,31005,1746],{},[1864,31007,2331],{},[1723,31009,5066],{},[1723,31011,1725],{},[1864,31013,2962],{},[902,31015,31016],{"encoding":904},"P_2^* = 5",[883,31018,31020],{"className":31019},[886],[888,31021,31022],{"xmlns":890},[892,31023,31024,31036],{},[895,31025,31026,31032,31034],{},[2057,31027,31028,31030],{},[898,31029,9837],{},[1723,31031,5066],{},[1723,31033,1725],{},[1864,31035,3810],{},[902,31037,31038],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,31041,31043],{"className":31042},[886],[888,31044,31045],{"xmlns":890,"display":28759},[892,31046,31047,31119],{},[895,31048,31049,31051,31053,31059,31061,31067,31069,31071,31073,31075,31081,31087,31089,31091,31093,31095,31097,31099,31105,31107,31109,31115,31117],{},[898,31050,1911],{"mathvariant":29241},[1723,31052,1908],{"stretchy":1907},[1931,31054,31055,31057],{},[898,31056,1904],{},[1864,31058,1866],{},[1723,31060,2031],{"separator":2030},[1931,31062,31063,31065],{},[898,31064,1904],{},[1864,31066,2331],{},[1723,31068,2031],{"separator":2030},[898,31070,17139],{},[1723,31072,1914],{"stretchy":1907},[1723,31074,1725],{},[1931,31076,31077,31079],{},[898,31078,1904],{},[1864,31080,1866],{},[1931,31082,31083,31085],{},[898,31084,1904],{},[1864,31086,2331],{},[1723,31088,2087],{},[898,31090,17139],{},[1723,31092,1908],{"stretchy":1907},[1864,31094,3810],{},[1723,31096,1759],{},[1864,31098,2331],{},[1931,31100,31101,31103],{},[898,31102,1904],{},[1864,31104,1866],{},[1723,31106,1759],{},[1864,31108,2962],{},[1931,31110,31111,31113],{},[898,31112,1904],{},[1864,31114,2331],{},[1723,31116,1914],{"stretchy":1907},[898,31118,1664],{"mathvariant":2124},[902,31120,31121],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,31123,31124],{},"Soustava:",[883,31126,31128],{"className":31127},[886],[888,31129,31130],{"xmlns":890,"display":28759},[892,31131,31132,31244],{},[21447,31133,31134,31168,31202],{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},[21452,31135,31136,31154],{},[21455,31137,31138],{},[3055,31139,31140],{"scriptlevel":2256,"displaystyle":2030},[895,31141,31142,31148,31150,31152],{},[1931,31143,31144,31146],{},[898,31145,1904],{},[1864,31147,2331],{},[1723,31149,1759],{},[1864,31151,2331],{},[898,31153,17139],{},[21455,31155,31156],{},[3055,31157,31158],{"scriptlevel":2256,"displaystyle":2030},[895,31159,31160,31162,31164,31166],{},[895,31161],{},[1723,31163,1725],{},[1864,31165,2256],{},[1723,31167,2031],{"separator":2030},[21452,31169,31170,31188],{},[21455,31171,31172],{},[3055,31173,31174],{"scriptlevel":2256,"displaystyle":2030},[895,31175,31176,31182,31184,31186],{},[1931,31177,31178,31180],{},[898,31179,1904],{},[1864,31181,1866],{},[1723,31183,1759],{},[1864,31185,2962],{},[898,31187,17139],{},[21455,31189,31190],{},[3055,31191,31192],{"scriptlevel":2256,"displaystyle":2030},[895,31193,31194,31196,31198,31200],{},[895,31195],{},[1723,31197,1725],{},[1864,31199,2256],{},[1723,31201,2031],{"separator":2030},[21452,31203,31204,31232],{},[21455,31205,31206],{},[3055,31207,31208],{"scriptlevel":2256,"displaystyle":2030},[895,31209,31210,31212,31214,31216,31222,31224,31226],{},[1864,31211,3810],{},[1723,31213,1759],{},[1864,31215,2331],{},[1931,31217,31218,31220],{},[898,31219,1904],{},[1864,31221,1866],{},[1723,31223,1759],{},[1864,31225,2962],{},[1931,31227,31228,31230],{},[898,31229,1904],{},[1864,31231,2331],{},[21455,31233,31234],{},[3055,31235,31236],{"scriptlevel":2256,"displaystyle":2030},[895,31237,31238,31240,31242],{},[895,31239],{},[1723,31241,1725],{},[1864,31243,13161],{},[902,31245,31246],{"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}",[724,31248,31249,31250,1343,31274,31298,31299,6299,31339,31357,31358,31408,31409,1664],{},"Z prvních dvou rovnic ",[883,31251,31253],{"className":31252},[886],[888,31254,31255],{"xmlns":890},[892,31256,31257,31271],{},[895,31258,31259,31265,31267,31269],{},[1931,31260,31261,31263],{},[898,31262,1904],{},[1864,31264,2331],{},[1723,31266,1725],{},[1864,31268,2331],{},[898,31270,17139],{},[902,31272,31273],{"encoding":904},"Q_2 = 2\\lambda",[883,31275,31277],{"className":31276},[886],[888,31278,31279],{"xmlns":890},[892,31280,31281,31295],{},[895,31282,31283,31289,31291,31293],{},[1931,31284,31285,31287],{},[898,31286,1904],{},[1864,31288,1866],{},[1723,31290,1725],{},[1864,31292,2962],{},[898,31294,17139],{},[902,31296,31297],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,31300,31302],{"className":31301},[886],[888,31303,31304],{"xmlns":890},[892,31305,31306,31336],{},[895,31307,31308,31310,31312,31314,31316,31318,31320,31322,31324,31326,31328,31330,31332,31334],{},[1864,31309,3810],{},[1723,31311,1725],{},[1864,31313,2331],{},[1723,31315,3897],{},[1864,31317,2962],{},[898,31319,17139],{},[1723,31321,2087],{},[1864,31323,2962],{},[1723,31325,3897],{},[1864,31327,2331],{},[898,31329,17139],{},[1723,31331,1725],{},[1864,31333,9744],{},[898,31335,17139],{},[902,31337,31338],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,31340,31342],{"className":31341},[886],[888,31343,31344],{"xmlns":890},[892,31345,31346,31354],{},[895,31347,31348,31350,31352],{},[898,31349,17139],{},[1723,31351,1725],{},[1864,31353,2962],{},[902,31355,31356],{"encoding":904},"\\lambda = 5",". Odtud ",[38,31359,31360,1343,31384],{},[883,31361,31363],{"className":31362},[886],[888,31364,31365],{"xmlns":890},[892,31366,31367,31381],{},[895,31368,31369,31377,31379],{},[2220,31370,31371,31373,31375],{},[898,31372,1904],{},[1864,31374,1866],{},[1723,31376,5066],{},[1723,31378,1725],{},[1864,31380,5714],{},[902,31382,31383],{"encoding":904},"Q_1^* = 25",[883,31385,31387],{"className":31386},[886],[888,31388,31389],{"xmlns":890},[892,31390,31391,31405],{},[895,31392,31393,31401,31403],{},[2220,31394,31395,31397,31399],{},[898,31396,1904],{},[1864,31398,2331],{},[1723,31400,5066],{},[1723,31402,1725],{},[1864,31404,3585],{},[902,31406,31407],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,31410,31412],{"className":31411},[886],[888,31413,31414],{"xmlns":890},[892,31415,31416,31437],{},[895,31417,31418,31424,31426,31428,31430,31432,31434],{},[2057,31419,31420,31422],{},[898,31421,900],{},[1723,31423,5066],{},[1723,31425,1725],{},[1864,31427,5714],{},[1723,31429,3897],{},[1864,31431,3585],{},[1723,31433,1725],{},[1864,31435,31436],{},"250",[902,31438,31439],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,31441,31442],{},[614,31443,31444,31445,28830,31483,1682,31507,31531,31532,31562,31563,31587,31588,31610,31611,1664],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,31446,31448],{"className":31447},[886],[888,31449,31450],{"xmlns":890},[892,31451,31452,31480],{},[895,31453,31454,31456,31458,31460,31466,31468,31470,31476,31478],{},[1864,31455,3810],{},[1723,31457,1759],{},[1864,31459,2331],{},[1931,31461,31462,31464],{},[898,31463,1904],{},[1864,31465,1866],{},[1723,31467,1759],{},[1864,31469,2962],{},[1931,31471,31472,31474],{},[898,31473,1904],{},[1864,31475,2331],{},[1723,31477,1725],{},[1864,31479,2256],{},[902,31481,31482],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,31484,31486],{"className":31485},[886],[888,31487,31488],{"xmlns":890},[892,31489,31490,31504],{},[895,31491,31492,31494,31496,31498,31500,31502],{},[898,31493,1718],{},[1723,31495,3212],{"stretchy":1907},[1864,31497,2256],{},[1723,31499,2031],{"separator":2030},[1864,31501,9744],{},[1723,31503,3227],{"stretchy":1907},[902,31505,31506],{"encoding":904},"A[0, 20]",[883,31508,31510],{"className":31509},[886],[888,31511,31512],{"xmlns":890},[892,31513,31514,31528],{},[895,31515,31516,31518,31520,31522,31524,31526],{},[898,31517,23946],{},[1723,31519,3212],{"stretchy":1907},[1864,31521,3840],{},[1723,31523,2031],{"separator":2030},[1864,31525,2256],{},[1723,31527,3227],{"stretchy":1907},[902,31529,31530],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,31533,31535],{"className":31534},[886],[888,31536,31537],{"xmlns":890},[892,31538,31539,31559],{},[895,31540,31541,31547,31549,31551,31553],{},[1931,31542,31543,31545],{},[898,31544,1904],{},[1864,31546,2331],{},[1723,31548,1725],{},[1864,31550,31436],{},[898,31552,2125],{"mathvariant":2124},[1931,31554,31555,31557],{},[898,31556,1904],{},[1864,31558,1866],{},[902,31560,31561],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,31564,31566],{"className":31565},[886],[888,31567,31568],{"xmlns":890},[892,31569,31570,31584],{},[895,31571,31572,31574,31576,31578,31580,31582],{},[898,31573,1846],{},[1723,31575,3212],{"stretchy":1907},[1864,31577,5714],{},[1723,31579,2031],{"separator":2030},[1864,31581,3585],{},[1723,31583,3227],{"stretchy":1907},[902,31585,31586],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,31589,31591],{"className":31590},[886],[888,31592,31593],{"xmlns":890},[892,31594,31595,31607],{},[895,31596,31597,31599],{},[1723,31598,1759],{},[3055,31600,31601],{"scriptlevel":2256,"displaystyle":1907},[3058,31602,31603,31605],{},[1864,31604,2331],{},[1864,31606,2962],{},[902,31608,31609],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,31612,31614],{"className":31613},[886],[888,31615,31616],{"xmlns":890},[892,31617,31618,31658],{},[895,31619,31620,31622,31624,31626,31628,31630,31632,31634,31636,31638,31646,31648,31650],{},[1723,31621,1759],{},[3018,31623,11303],{},[1723,31625,1908],{"stretchy":1907},[1864,31627,5714],{},[1723,31629,2031],{"separator":2030},[1864,31631,3585],{},[1723,31633,1914],{"stretchy":1907},[1723,31635,1725],{},[1723,31637,1759],{},[3055,31639,31640],{"scriptlevel":2256,"displaystyle":1907},[3058,31641,31642,31644],{},[1864,31643,3585],{},[1864,31645,5714],{},[1723,31647,1725],{},[1723,31649,1759],{},[3055,31651,31652],{"scriptlevel":2256,"displaystyle":1907},[3058,31653,31654,31656],{},[1864,31655,2331],{},[1864,31657,2962],{},[902,31659,31660],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,31662,31664],{"id":31663},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,31666,31667,31668,29696,31698,31701,31702,3430],{},"Považujeme-li v úloze ",[883,31669,31671],{"className":31670},[886],[888,31672,31673],{"xmlns":890},[892,31674,31675,31695],{},[895,31676,31677,31683,31685,31691,31693],{},[1931,31678,31679,31681],{},[898,31680,1746],{},[1864,31682,1866],{},[1723,31684,2031],{"separator":2030},[1931,31686,31687,31689],{},[898,31688,1746],{},[1864,31690,2331],{},[1723,31692,2031],{"separator":2030},[898,31694,9837],{},[902,31696,31697],{"encoding":904},"P_1, P_2, Y",[38,31699,31700],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,31703,31704],{},"Marshallovy poptávkové funkce",[883,31706,31708],{"className":31707},[886],[888,31709,31710],{"xmlns":890,"display":28759},[892,31711,31712,31807],{},[21447,31713,31714],{"width":28764},[21452,31715,31716,31718,31800,31802],{},[21455,31717],{"width":28769},[21455,31719,31720],{},[895,31721,31722,31728,31730,31736,31738,31744,31746,31752,31754,31756,31758,31760,31762,31768,31770,31776,31778,31784,31786,31792,31794,31796,31798],{},[1931,31723,31724,31726],{},[898,31725,1904],{},[1864,31727,1866],{},[1723,31729,1725],{},[1931,31731,31732,31734],{},[898,31733,4897],{},[1864,31735,1866],{},[1723,31737,1908],{"stretchy":1907},[1931,31739,31740,31742],{},[898,31741,1746],{},[1864,31743,1866],{},[1723,31745,2031],{"separator":2030},[1931,31747,31748,31750],{},[898,31749,1746],{},[1864,31751,2331],{},[1723,31753,2031],{"separator":2030},[898,31755,9837],{},[1723,31757,1914],{"stretchy":1907},[1723,31759,2031],{"separator":2030},[6588,31761],{"width":15985},[1931,31763,31764,31766],{},[898,31765,1904],{},[1864,31767,2331],{},[1723,31769,1725],{},[1931,31771,31772,31774],{},[898,31773,4897],{},[1864,31775,2331],{},[1723,31777,1908],{"stretchy":1907},[1931,31779,31780,31782],{},[898,31781,1746],{},[1864,31783,1866],{},[1723,31785,2031],{"separator":2030},[1931,31787,31788,31790],{},[898,31789,1746],{},[1864,31791,2331],{},[1723,31793,2031],{"separator":2030},[898,31795,9837],{},[1723,31797,1914],{"stretchy":1907},[1723,31799,2031],{"separator":2030},[21455,31801],{"width":28769},[21455,31803,31804],{},[3018,31805,31806],{},"(6.15)",[902,31808,31809],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,31811,31813],{"className":31812},[886],[888,31814,31815],{"xmlns":890,"display":28759},[892,31816,31817,31864],{},[21447,31818,31819],{"width":28764},[21452,31820,31821,31823,31857,31859],{},[21455,31822],{"width":28769},[21455,31824,31825],{},[895,31826,31827,31829,31831,31833,31835,31841,31843,31849,31851,31853,31855],{},[898,31828,17139],{},[1723,31830,1725],{},[898,31832,17139],{},[1723,31834,1908],{"stretchy":1907},[1931,31836,31837,31839],{},[898,31838,1746],{},[1864,31840,1866],{},[1723,31842,2031],{"separator":2030},[1931,31844,31845,31847],{},[898,31846,1746],{},[1864,31848,2331],{},[1723,31850,2031],{"separator":2030},[898,31852,9837],{},[1723,31854,1914],{"stretchy":1907},[898,31856,1664],{"mathvariant":2124},[21455,31858],{"width":28769},[21455,31860,31861],{},[3018,31862,31863],{},"(6.16)",[902,31865,31866],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,31868,31869,31899,31900,31966],{},[38,31870,31871,31872,1664],{},"Odvození pro ",[883,31873,31875],{"className":31874},[886],[888,31876,31877],{"xmlns":890},[892,31878,31879,31897],{},[895,31880,31881,31883,31885,31891],{},[898,31882,900],{},[1723,31884,1725],{},[1931,31886,31887,31889],{},[898,31888,1904],{},[1864,31890,1866],{},[1931,31892,31893,31895],{},[898,31894,1904],{},[1864,31896,2331],{},[902,31898,30919],{"encoding":904}," Lagrangeova funkce ",[883,31901,31903],{"className":31902},[886],[888,31904,31905],{"xmlns":890},[892,31906,31907,31963],{},[895,31908,31909,31911,31913,31919,31925,31927,31929,31931,31933,31935,31941,31947,31949,31955,31961],{},[898,31910,1911],{"mathvariant":29241},[1723,31912,1725],{},[1931,31914,31915,31917],{},[898,31916,1904],{},[1864,31918,1866],{},[1931,31920,31921,31923],{},[898,31922,1904],{},[1864,31924,2331],{},[1723,31926,2087],{},[898,31928,17139],{},[1723,31930,1908],{"stretchy":1907},[898,31932,9837],{},[1723,31934,1759],{},[1931,31936,31937,31939],{},[898,31938,1746],{},[1864,31940,1866],{},[1931,31942,31943,31945],{},[898,31944,1904],{},[1864,31946,1866],{},[1723,31948,1759],{},[1931,31950,31951,31953],{},[898,31952,1746],{},[1864,31954,2331],{},[1931,31956,31957,31959],{},[898,31958,1904],{},[1864,31960,2331],{},[1723,31962,1914],{"stretchy":1907},[902,31964,31965],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,31968,31970],{"className":31969},[886],[888,31971,31972],{"xmlns":890,"display":28759},[892,31973,31974,32141],{},[21447,31975,31976],{"width":28764},[21452,31977,31978,31980,32134,32136],{},[21455,31979],{"width":28769},[21455,31981,31982],{},[21447,31983,31984,32030,32076],{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},[21452,31985,31986,31998],{},[21455,31987,31988],{},[3055,31989,31990],{"scriptlevel":2256,"displaystyle":2030},[2220,31991,31992,31994,31996],{},[898,31993,1911],{"mathvariant":29241},[1864,31995,1866],{},[1723,31997,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,31999,32000],{},[3055,32001,32002],{"scriptlevel":2256,"displaystyle":2030},[895,32003,32004,32006,32008,32014,32016,32018,32024,32026,32028],{},[895,32005],{},[1723,32007,1725],{},[1931,32009,32010,32012],{},[898,32011,1904],{},[1864,32013,2331],{},[1723,32015,1759],{},[898,32017,17139],{},[1931,32019,32020,32022],{},[898,32021,1746],{},[1864,32023,1866],{},[1723,32025,1725],{},[1864,32027,2256],{},[1723,32029,2031],{"separator":2030},[21452,32031,32032,32044],{},[21455,32033,32034],{},[3055,32035,32036],{"scriptlevel":2256,"displaystyle":2030},[2220,32037,32038,32040,32042],{},[898,32039,1911],{"mathvariant":29241},[1864,32041,2331],{},[1723,32043,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,32045,32046],{},[3055,32047,32048],{"scriptlevel":2256,"displaystyle":2030},[895,32049,32050,32052,32054,32060,32062,32064,32070,32072,32074],{},[895,32051],{},[1723,32053,1725],{},[1931,32055,32056,32058],{},[898,32057,1904],{},[1864,32059,1866],{},[1723,32061,1759],{},[898,32063,17139],{},[1931,32065,32066,32068],{},[898,32067,1746],{},[1864,32069,2331],{},[1723,32071,1725],{},[1864,32073,2256],{},[1723,32075,2031],{"separator":2030},[21452,32077,32078,32090],{},[21455,32079,32080],{},[3055,32081,32082],{"scriptlevel":2256,"displaystyle":2030},[2220,32083,32084,32086,32088],{},[898,32085,1911],{"mathvariant":29241},[898,32087,17139],{},[1723,32089,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,32091,32092],{},[3055,32093,32094],{"scriptlevel":2256,"displaystyle":2030},[895,32095,32096,32098,32100,32102,32104,32110,32116,32118,32124,32130,32132],{},[895,32097],{},[1723,32099,1725],{},[898,32101,9837],{},[1723,32103,1759],{},[1931,32105,32106,32108],{},[898,32107,1746],{},[1864,32109,1866],{},[1931,32111,32112,32114],{},[898,32113,1904],{},[1864,32115,1866],{},[1723,32117,1759],{},[1931,32119,32120,32122],{},[898,32121,1746],{},[1864,32123,2331],{},[1931,32125,32126,32128],{},[898,32127,1904],{},[1864,32129,2331],{},[1723,32131,1725],{},[1864,32133,13161],{},[21455,32135],{"width":28769},[21455,32137,32138],{},[3018,32139,32140],{},"(6.17)",[902,32142,32143],{"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}",[724,32145,32146,32147,32175,32176,32204,32205,32273],{},"Z prvních dvou: ",[883,32148,32150],{"className":32149},[886],[888,32151,32152],{"xmlns":890},[892,32153,32154,32172],{},[895,32155,32156,32162,32164,32170],{},[1931,32157,32158,32160],{},[898,32159,1904],{},[1864,32161,2331],{},[1723,32163,1725],{},[1931,32165,32166,32168],{},[898,32167,1746],{},[1864,32169,1866],{},[898,32171,17139],{},[902,32173,32174],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,32177,32179],{"className":32178},[886],[888,32180,32181],{"xmlns":890},[892,32182,32183,32201],{},[895,32184,32185,32191,32193,32199],{},[1931,32186,32187,32189],{},[898,32188,1904],{},[1864,32190,1866],{},[1723,32192,1725],{},[1931,32194,32195,32197],{},[898,32196,1746],{},[1864,32198,2331],{},[898,32200,17139],{},[902,32202,32203],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,32206,32208],{"className":32207},[886],[888,32209,32210],{"xmlns":890},[892,32211,32212,32270],{},[895,32213,32214,32216,32218,32224,32226,32232,32234,32236,32242,32244,32250,32252,32254,32256,32262,32268],{},[898,32215,9837],{},[1723,32217,1725],{},[1931,32219,32220,32222],{},[898,32221,1746],{},[1864,32223,1866],{},[1723,32225,3897],{},[1931,32227,32228,32230],{},[898,32229,1746],{},[1864,32231,2331],{},[898,32233,17139],{},[1723,32235,2087],{},[1931,32237,32238,32240],{},[898,32239,1746],{},[1864,32241,2331],{},[1723,32243,3897],{},[1931,32245,32246,32248],{},[898,32247,1746],{},[1864,32249,1866],{},[898,32251,17139],{},[1723,32253,1725],{},[1864,32255,2331],{},[1931,32257,32258,32260],{},[898,32259,1746],{},[1864,32261,1866],{},[1931,32263,32264,32266],{},[898,32265,1746],{},[1864,32267,2331],{},[898,32269,17139],{},[902,32271,32272],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,32275,32277],{"className":32276},[886],[888,32278,32279],{"xmlns":890,"display":28759},[892,32280,32281,32324],{},[21447,32282,32283],{"width":28764},[21452,32284,32285,32287,32317,32319],{},[21455,32286],{"width":28769},[21455,32288,32289],{},[895,32290,32291,32293,32295,32315],{},[898,32292,17139],{},[1723,32294,1725],{},[3058,32296,32297,32299],{},[898,32298,9837],{},[895,32300,32301,32303,32309],{},[1864,32302,2331],{},[1931,32304,32305,32307],{},[898,32306,1746],{},[1864,32308,1866],{},[1931,32310,32311,32313],{},[898,32312,1746],{},[1864,32314,2331],{},[898,32316,1664],{"mathvariant":2124},[21455,32318],{"width":28769},[21455,32320,32321],{},[3018,32322,32323],{},"(6.20)",[902,32325,32326],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,32328,32329],{},"Zpětně:",[883,32331,32333],{"className":32332},[886],[888,32334,32335],{"xmlns":890,"display":28759},[892,32336,32337,32414],{},[21447,32338,32339],{"width":28764},[21452,32340,32341,32343,32407,32409],{},[21455,32342],{"width":28769},[21455,32344,32345],{},[13533,32346,32347],{"notation":13535},[3055,32348,32349],{"scriptlevel":2256,"displaystyle":1907},[3055,32350,32351],{"scriptlevel":2256,"displaystyle":1907},[3055,32352,32353],{"scriptlevel":2256,"displaystyle":2030},[895,32354,32355,32357,32363,32365,32379,32381,32383,32389,32391,32405],{},[3018,32356,4699],{},[1931,32358,32359,32361],{},[898,32360,1904],{},[1864,32362,1866],{},[1723,32364,1725],{},[3058,32366,32367,32369],{},[898,32368,9837],{},[895,32370,32371,32373],{},[1864,32372,2331],{},[1931,32374,32375,32377],{},[898,32376,1746],{},[1864,32378,1866],{},[1723,32380,2031],{"separator":2030},[6588,32382],{"width":15985},[1931,32384,32385,32387],{},[898,32386,1904],{},[1864,32388,2331],{},[1723,32390,1725],{},[3058,32392,32393,32395],{},[898,32394,9837],{},[895,32396,32397,32399],{},[1864,32398,2331],{},[1931,32400,32401,32403],{},[898,32402,1746],{},[1864,32404,2331],{},[3018,32406,4699],{},[21455,32408],{"width":28769},[21455,32410,32411],{},[3018,32412,32413],{},"(6.21)",[902,32415,32416],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,32418,32420],{"id":32419},"engelova-funkce","Engelova funkce",[724,32422,10369,32423,32426,32427,32430,32431,20560,32448,1343,32478,32508,32509,32543,32544,1343,32570,32596],{},[38,32424,32425],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,32428,32429],{},"Engelovou funkcí",": pro ",[883,32432,32434],{"className":32433},[886],[888,32435,32436],{"xmlns":890},[892,32437,32438,32446],{},[895,32439,32440,32442,32444],{},[898,32441,9837],{},[1723,32443,1725],{},[1864,32445,3810],{},[902,32447,21012],{"encoding":904},[883,32449,32451],{"className":32450},[886],[888,32452,32453],{"xmlns":890},[892,32454,32455,32475],{},[895,32456,32457,32463,32465,32467,32469],{},[1931,32458,32459,32461],{},[898,32460,1904],{},[1864,32462,1866],{},[1723,32464,1725],{},[1864,32466,3840],{},[898,32468,2125],{"mathvariant":2124},[1931,32470,32471,32473],{},[898,32472,1746],{},[1864,32474,1866],{},[902,32476,32477],{"encoding":904},"Q_1 = 50\u002FP_1",[883,32479,32481],{"className":32480},[886],[888,32482,32483],{"xmlns":890},[892,32484,32485,32505],{},[895,32486,32487,32493,32495,32497,32499],{},[1931,32488,32489,32491],{},[898,32490,1904],{},[1864,32492,2331],{},[1723,32494,1725],{},[1864,32496,3840],{},[898,32498,2125],{"mathvariant":2124},[1931,32500,32501,32503],{},[898,32502,1746],{},[1864,32504,2331],{},[902,32506,32507],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,32510,32512],{"className":32511},[886],[888,32513,32514],{"xmlns":890},[892,32515,32516,32540],{},[895,32517,32518,32524,32526,32528,32530,32536,32538],{},[1931,32519,32520,32522],{},[898,32521,1746],{},[1864,32523,1866],{},[1723,32525,1725],{},[1864,32527,3585],{},[1723,32529,2031],{"separator":2030},[1931,32531,32532,32534],{},[898,32533,1746],{},[1864,32535,2331],{},[1723,32537,1725],{},[1864,32539,9744],{},[902,32541,32542],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,32545,32547],{"className":32546},[886],[888,32548,32549],{"xmlns":890},[892,32550,32551,32567],{},[895,32552,32553,32559,32561,32563,32565],{},[1931,32554,32555,32557],{},[898,32556,1904],{},[1864,32558,1866],{},[1723,32560,1725],{},[898,32562,9837],{},[898,32564,2125],{"mathvariant":2124},[1864,32566,9744],{},[902,32568,32569],{"encoding":904},"Q_1 = Y\u002F20",[883,32571,32573],{"className":32572},[886],[888,32574,32575],{"xmlns":890},[892,32576,32577,32593],{},[895,32578,32579,32585,32587,32589,32591],{},[1931,32580,32581,32583],{},[898,32582,1904],{},[1864,32584,2331],{},[1723,32586,1725],{},[898,32588,9837],{},[898,32590,2125],{"mathvariant":2124},[1864,32592,5921],{},[902,32594,32595],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,32598,32600],{"id":32599},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,32602,32603],{},"Výdaje spotřebitele jsou",[883,32605,32607],{"className":32606},[886],[888,32608,32609],{"xmlns":890,"display":28759},[892,32610,32611,32686],{},[21447,32612,32613],{"width":28764},[21452,32614,32615,32617,32679,32681],{},[21455,32616],{"width":28769},[21455,32618,32619],{},[895,32620,32621,32623,32625,32627,32629,32635,32637,32643,32645,32647,32655,32661,32663,32671,32677],{},[898,32622,1846],{},[1723,32624,1725],{},[898,32626,1846],{},[1723,32628,1908],{"stretchy":1907},[1931,32630,32631,32633],{},[898,32632,1904],{},[1864,32634,1866],{},[1723,32636,2031],{"separator":2030},[1931,32638,32639,32641],{},[898,32640,1904],{},[1864,32642,2331],{},[1723,32644,1914],{"stretchy":1907},[1723,32646,1725],{},[2220,32648,32649,32651,32653],{},[898,32650,1746],{},[1864,32652,1866],{},[1723,32654,5066],{},[1931,32656,32657,32659],{},[898,32658,1904],{},[1864,32660,1866],{},[1723,32662,2087],{},[2220,32664,32665,32667,32669],{},[898,32666,1746],{},[1864,32668,2331],{},[1723,32670,5066],{},[1931,32672,32673,32675],{},[898,32674,1904],{},[1864,32676,2331],{},[1723,32678,2031],{"separator":2030},[21455,32680],{"width":28769},[21455,32682,32683],{},[3018,32684,32685],{},"(6.22)",[902,32687,32688],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,32690,32691],{},"a je pevně zadána hladina užitečnosti",[883,32693,32695],{"className":32694},[886],[888,32696,32697],{"xmlns":890,"display":28759},[892,32698,32699,32746],{},[21447,32700,32701],{"width":28764},[21452,32702,32703,32705,32739,32741],{},[21455,32704],{"width":28769},[21455,32706,32707],{},[895,32708,32709,32715,32717,32719,32721,32727,32729,32735,32737],{},[2057,32710,32711,32713],{},[898,32712,900],{},[1723,32714,5066],{},[1723,32716,1725],{},[898,32718,900],{},[1723,32720,1908],{"stretchy":1907},[1931,32722,32723,32725],{},[898,32724,1904],{},[1864,32726,1866],{},[1723,32728,2031],{"separator":2030},[1931,32730,32731,32733],{},[898,32732,1904],{},[1864,32734,2331],{},[1723,32736,1914],{"stretchy":1907},[898,32738,1664],{"mathvariant":2124},[21455,32740],{"width":28769},[21455,32742,32743],{},[3018,32744,32745],{},"(6.23)",[902,32747,32748],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,32750,32751,32754,32755,32787,32788,1664],{},[38,32752,32753],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,32756,32758],{"className":32757},[886],[888,32759,32760],{"xmlns":890},[892,32761,32762,32784],{},[895,32763,32764,32766,32768,32774,32776,32782],{},[898,32765,1846],{},[1723,32767,1908],{"stretchy":1907},[1931,32769,32770,32772],{},[898,32771,1904],{},[1864,32773,1866],{},[1723,32775,2031],{"separator":2030},[1931,32777,32778,32780],{},[898,32779,1904],{},[1864,32781,2331],{},[1723,32783,1914],{"stretchy":1907},[902,32785,32786],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,32789,32791],{"className":32790},[886],[888,32792,32793],{"xmlns":890},[892,32794,32795,32851],{},[895,32796,32797,32799,32801,32807,32809,32815,32817,32819,32825,32827,32829,32831,32837,32839,32845,32847,32849],{},[898,32798,11741],{},[1723,32800,1908],{"stretchy":1907},[1931,32802,32803,32805],{},[898,32804,1904],{},[1864,32806,1866],{},[1723,32808,2031],{"separator":2030},[1931,32810,32811,32813],{},[898,32812,1904],{},[1864,32814,2331],{},[1723,32816,1914],{"stretchy":1907},[1723,32818,1725],{},[2057,32820,32821,32823],{},[898,32822,900],{},[1723,32824,5066],{},[1723,32826,1759],{},[898,32828,900],{},[1723,32830,1908],{"stretchy":1907},[1931,32832,32833,32835],{},[898,32834,1904],{},[1864,32836,1866],{},[1723,32838,2031],{"separator":2030},[1931,32840,32841,32843],{},[898,32842,1904],{},[1864,32844,2331],{},[1723,32846,1914],{"stretchy":1907},[1723,32848,1725],{},[1864,32850,2256],{},[902,32852,32853],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,32855,32857],{"id":32856},"lagrangeova-funkce","Lagrangeova funkce",[883,32859,32861],{"className":32860},[886],[888,32862,32863],{"xmlns":890,"display":28759},[892,32864,32865,32976],{},[21447,32866,32867],{"width":28764},[21452,32868,32869,32871,32969,32971],{},[21455,32870],{"width":28769},[21455,32872,32873],{},[895,32874,32875,32877,32879,32885,32887,32893,32895,32897,32899,32901,32909,32915,32917,32925,32931,32933,32935,32937,32943,32945,32947,32949,32955,32957,32963,32965,32967],{},[898,32876,1911],{"mathvariant":29241},[1723,32878,1908],{"stretchy":1907},[1931,32880,32881,32883],{},[898,32882,1904],{},[1864,32884,1866],{},[1723,32886,2031],{"separator":2030},[1931,32888,32889,32891],{},[898,32890,1904],{},[1864,32892,2331],{},[1723,32894,2031],{"separator":2030},[898,32896,17139],{},[1723,32898,1914],{"stretchy":1907},[1723,32900,1725],{},[2220,32902,32903,32905,32907],{},[898,32904,1746],{},[1864,32906,1866],{},[1723,32908,5066],{},[1931,32910,32911,32913],{},[898,32912,1904],{},[1864,32914,1866],{},[1723,32916,2087],{},[2220,32918,32919,32921,32923],{},[898,32920,1746],{},[1864,32922,2331],{},[1723,32924,5066],{},[1931,32926,32927,32929],{},[898,32928,1904],{},[1864,32930,2331],{},[1723,32932,2087],{},[898,32934,17139],{},[1723,32936,1908],{"stretchy":1907},[2057,32938,32939,32941],{},[898,32940,900],{},[1723,32942,5066],{},[1723,32944,1759],{},[898,32946,900],{},[1723,32948,1908],{"stretchy":1907},[1931,32950,32951,32953],{},[898,32952,1904],{},[1864,32954,1866],{},[1723,32956,2031],{"separator":2030},[1931,32958,32959,32961],{},[898,32960,1904],{},[1864,32962,2331],{},[1723,32964,1914],{"stretchy":1907},[1723,32966,1914],{"stretchy":1907},[898,32968,1664],{"mathvariant":2124},[21455,32970],{"width":28769},[21455,32972,32973],{},[3018,32974,32975],{},"(6.24)",[902,32977,32978],{"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}",[724,32980,32981],{},"Soustava podmínek prvního řádu:",[883,32983,32985],{"className":32984},[886],[888,32986,32987],{"xmlns":890,"display":28759},[892,32988,32989,33162],{},[21447,32990,32991],{"width":28764},[21452,32992,32993,32995,33155,33157],{},[21455,32994],{"width":28769},[21455,32996,32997],{},[21447,32998,32999,33049,33099],{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},[21452,33000,33001,33013],{},[21455,33002,33003],{},[3055,33004,33005],{"scriptlevel":2256,"displaystyle":2030},[2220,33006,33007,33009,33011],{},[898,33008,1911],{"mathvariant":29241},[1864,33010,1866],{},[1723,33012,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,33014,33015],{},[3055,33016,33017],{"scriptlevel":2256,"displaystyle":2030},[895,33018,33019,33021,33023,33031,33033,33035,33043,33045,33047],{},[895,33020],{},[1723,33022,1725],{},[2220,33024,33025,33027,33029],{},[898,33026,1746],{},[1864,33028,1866],{},[1723,33030,5066],{},[1723,33032,1759],{},[898,33034,17139],{},[2220,33036,33037,33039,33041],{},[898,33038,900],{},[1864,33040,1866],{},[1723,33042,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,33044,1725],{},[1864,33046,2256],{},[1723,33048,2031],{"separator":2030},[21452,33050,33051,33063],{},[21455,33052,33053],{},[3055,33054,33055],{"scriptlevel":2256,"displaystyle":2030},[2220,33056,33057,33059,33061],{},[898,33058,1911],{"mathvariant":29241},[1864,33060,2331],{},[1723,33062,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,33064,33065],{},[3055,33066,33067],{"scriptlevel":2256,"displaystyle":2030},[895,33068,33069,33071,33073,33081,33083,33085,33093,33095,33097],{},[895,33070],{},[1723,33072,1725],{},[2220,33074,33075,33077,33079],{},[898,33076,1746],{},[1864,33078,2331],{},[1723,33080,5066],{},[1723,33082,1759],{},[898,33084,17139],{},[2220,33086,33087,33089,33091],{},[898,33088,900],{},[1864,33090,2331],{},[1723,33092,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,33094,1725],{},[1864,33096,2256],{},[1723,33098,2031],{"separator":2030},[21452,33100,33101,33113],{},[21455,33102,33103],{},[3055,33104,33105],{"scriptlevel":2256,"displaystyle":2030},[2220,33106,33107,33109,33111],{},[898,33108,1911],{"mathvariant":29241},[898,33110,17139],{},[1723,33112,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,33114,33115],{},[3055,33116,33117],{"scriptlevel":2256,"displaystyle":2030},[895,33118,33119,33121,33123,33129,33131,33133,33135,33141,33143,33149,33151,33153],{},[895,33120],{},[1723,33122,1725],{},[2057,33124,33125,33127],{},[898,33126,900],{},[1723,33128,5066],{},[1723,33130,1759],{},[898,33132,900],{},[1723,33134,1908],{"stretchy":1907},[1931,33136,33137,33139],{},[898,33138,1904],{},[1864,33140,1866],{},[1723,33142,2031],{"separator":2030},[1931,33144,33145,33147],{},[898,33146,1904],{},[1864,33148,2331],{},[1723,33150,1914],{"stretchy":1907},[1723,33152,1725],{},[1864,33154,13161],{},[21455,33156],{"width":28769},[21455,33158,33159],{},[3018,33160,33161],{},"(6.25)",[902,33163,33164],{"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}",[724,33166,33167],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,33169,33171],{"className":33170},[886],[888,33172,33173],{"xmlns":890,"display":28759},[892,33174,33175,33273],{},[21447,33176,33177],{"width":28764},[21452,33178,33179,33181,33266,33268],{},[21455,33180],{"width":28769},[21455,33182,33183],{},[895,33184,33185,33187,33189,33195,33197,33203,33205,33207,33209,33211,33213,33215,33264],{},[898,33186,4897],{},[1723,33188,1908],{"stretchy":1907},[1931,33190,33191,33193],{},[898,33192,1904],{},[1864,33194,1866],{},[1723,33196,2031],{"separator":2030},[1931,33198,33199,33201],{},[898,33200,1904],{},[1864,33202,2331],{},[1723,33204,2031],{"separator":2030},[898,33206,17139],{},[1723,33208,1914],{"stretchy":1907},[1723,33210,1725],{},[1723,33212,1759],{},[898,33214,17139],{},[895,33216,33217,33219,33231,33233,33246,33248,33250,33262],{},[1723,33218,1908],{"fence":2030},[2220,33220,33221,33223,33225],{},[898,33222,900],{},[1864,33224,3626],{},[895,33226,33227,33229],{},[1723,33228,2229],{"mathvariant":2124},[1723,33230,2229],{"mathvariant":2124},[1723,33232,2087],{},[2220,33234,33235,33237,33240],{},[898,33236,900],{},[1864,33238,33239],{},"22",[895,33241,33242,33244],{},[1723,33243,2229],{"mathvariant":2124},[1723,33245,2229],{"mathvariant":2124},[1723,33247,2087],{},[1864,33249,2331],{},[2220,33251,33252,33254,33256],{},[898,33253,900],{},[1864,33255,4227],{},[895,33257,33258,33260],{},[1723,33259,2229],{"mathvariant":2124},[1723,33261,2229],{"mathvariant":2124},[1723,33263,1914],{"fence":2030},[898,33265,1664],{"mathvariant":2124},[21455,33267],{"width":28769},[21455,33269,33270],{},[3018,33271,33272],{},"(6.26)",[902,33274,33275],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,33277,33278,33281,33282,33321,33322,33361,33362,33412,33413,33439,33440,33457,33458,33484],{},[38,33279,33280],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,33283,33285],{"className":33284},[886],[888,33286,33287],{"xmlns":890},[892,33288,33289,33319],{},[895,33290,33291,33297,33299,33307,33309,33317],{},[2057,33292,33293,33295],{},[898,33294,1904],{},[1723,33296,5066],{},[1723,33298,3212],{"stretchy":1907},[2220,33300,33301,33303,33305],{},[898,33302,1904],{},[1864,33304,1866],{},[1723,33306,5066],{},[1723,33308,2031],{"separator":2030},[2220,33310,33311,33313,33315],{},[898,33312,1904],{},[1864,33314,2331],{},[1723,33316,5066],{},[1723,33318,3227],{"stretchy":1907},[902,33320,29020],{"encoding":904}," dotyku křivky užitečnosti ",[883,33323,33325],{"className":33324},[886],[888,33326,33327],{"xmlns":890},[892,33328,33329,33359],{},[895,33330,33331,33337,33339,33341,33343,33349,33351,33357],{},[2057,33332,33333,33335],{},[898,33334,900],{},[1723,33336,5066],{},[1723,33338,1725],{},[898,33340,900],{},[1723,33342,1908],{"stretchy":1907},[1931,33344,33345,33347],{},[898,33346,1904],{},[1864,33348,1866],{},[1723,33350,2031],{"separator":2030},[1931,33352,33353,33355],{},[898,33354,1904],{},[1864,33356,2331],{},[1723,33358,1914],{"stretchy":1907},[902,33360,18361],{"encoding":904}," s přímkou výdajů ",[883,33363,33365],{"className":33364},[886],[888,33366,33367],{"xmlns":890},[892,33368,33369,33409],{},[895,33370,33371,33377,33379,33387,33393,33395,33403],{},[2057,33372,33373,33375],{},[898,33374,1846],{},[1723,33376,5066],{},[1723,33378,1725],{},[2220,33380,33381,33383,33385],{},[898,33382,1746],{},[1864,33384,1866],{},[1723,33386,5066],{},[1931,33388,33389,33391],{},[898,33390,1904],{},[1864,33392,1866],{},[1723,33394,2087],{},[2220,33396,33397,33399,33401],{},[898,33398,1746],{},[1864,33400,2331],{},[1723,33402,5066],{},[1931,33404,33405,33407],{},[898,33406,1904],{},[1864,33408,2331],{},[902,33410,33411],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,33414,33416],{"className":33415},[886],[888,33417,33418],{"xmlns":890},[892,33419,33420,33436],{},[895,33421,33422,33428,33430],{},[1931,33423,33424,33426],{},[898,33425,1846],{},[1864,33427,2256],{},[1723,33429,2287],{},[2057,33431,33432,33434],{},[898,33433,1846],{},[1723,33435,5066],{},[902,33437,33438],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,33441,33443],{"className":33442},[886],[888,33444,33445],{"xmlns":890},[892,33446,33447,33455],{},[895,33448,33449],{},[2057,33450,33451,33453],{},[898,33452,900],{},[1723,33454,5066],{},[902,33456,28655],{"encoding":904},", hladina ",[883,33459,33461],{"className":33460},[886],[888,33462,33463],{"xmlns":890},[892,33464,33465,33481],{},[895,33466,33467,33473,33475],{},[1931,33468,33469,33471],{},[898,33470,1846],{},[1864,33472,1866],{},[1723,33474,2253],{},[2057,33476,33477,33479],{},[898,33478,1846],{},[1723,33480,5066],{},[902,33482,33483],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[4584,33486,33487,33492],{},[724,33488,33489,33491],{},[883,33490,5283],{}," Postup — duální úloha (minimalizace výdajů)",[152,33493,33494,33544,33630,33670,33745],{},[123,33495,33496,2628,33499,33543],{},[38,33497,33498],{},"Zapiš vazbu",[883,33500,33502],{"className":33501},[886],[888,33503,33504],{"xmlns":890},[892,33505,33506,33540],{},[895,33507,33508,33514,33516,33518,33520,33526,33528,33534,33536,33538],{},[2057,33509,33510,33512],{},[898,33511,900],{},[1723,33513,5066],{},[1723,33515,1759],{},[898,33517,900],{},[1723,33519,1908],{"stretchy":1907},[1931,33521,33522,33524],{},[898,33523,1904],{},[1864,33525,1866],{},[1723,33527,2031],{"separator":2030},[1931,33529,33530,33532],{},[898,33531,1904],{},[1864,33533,2331],{},[1723,33535,1914],{"stretchy":1907},[1723,33537,1725],{},[1864,33539,2256],{},[902,33541,33542],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,33545,33546,2628,33548,1664],{},[38,33547,29953],{},[883,33549,33551],{"className":33550},[886],[888,33552,33553],{"xmlns":890},[892,33554,33555,33627],{},[895,33556,33557,33559,33561,33569,33575,33577,33585,33591,33593,33595,33597,33603,33605,33607,33609,33615,33617,33623,33625],{},[898,33558,1911],{"mathvariant":29241},[1723,33560,1725],{},[2220,33562,33563,33565,33567],{},[898,33564,1746],{},[1864,33566,1866],{},[1723,33568,5066],{},[1931,33570,33571,33573],{},[898,33572,1904],{},[1864,33574,1866],{},[1723,33576,2087],{},[2220,33578,33579,33581,33583],{},[898,33580,1746],{},[1864,33582,2331],{},[1723,33584,5066],{},[1931,33586,33587,33589],{},[898,33588,1904],{},[1864,33590,2331],{},[1723,33592,2087],{},[898,33594,17139],{},[1723,33596,1908],{"stretchy":1907},[2057,33598,33599,33601],{},[898,33600,900],{},[1723,33602,5066],{},[1723,33604,1759],{},[898,33606,900],{},[1723,33608,1908],{"stretchy":1907},[1931,33610,33611,33613],{},[898,33612,1904],{},[1864,33614,1866],{},[1723,33616,2031],{"separator":2030},[1931,33618,33619,33621],{},[898,33620,1904],{},[1864,33622,2331],{},[1723,33624,1914],{"stretchy":1907},[1723,33626,1914],{"stretchy":1907},[902,33628,33629],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,33631,33632,33635,33636,33669],{},[38,33633,33634],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,33637,33639],{"className":33638},[886],[888,33640,33641],{"xmlns":890},[892,33642,33643,33667],{},[895,33644,33645,33647,33649,33657,33659],{},[3018,33646,11303],{},[1723,33648,1725],{},[2220,33650,33651,33653,33655],{},[898,33652,1746],{},[1864,33654,1866],{},[1723,33656,5066],{},[898,33658,2125],{"mathvariant":2124},[2220,33660,33661,33663,33665],{},[898,33662,1746],{},[1864,33664,2331],{},[1723,33666,5066],{},[902,33668,29672],{"encoding":904}," (stejná jako u maximalizace!).",[123,33671,33672,2628,33675,33715,33716,1664],{},[38,33673,33674],{},"Dosaď do vazby",[883,33676,33678],{"className":33677},[886],[888,33679,33680],{"xmlns":890},[892,33681,33682,33712],{},[895,33683,33684,33686,33688,33694,33696,33702,33704,33706],{},[898,33685,900],{},[1723,33687,1908],{"stretchy":1907},[1931,33689,33690,33692],{},[898,33691,1904],{},[1864,33693,1866],{},[1723,33695,2031],{"separator":2030},[1931,33697,33698,33700],{},[898,33699,1904],{},[1864,33701,2331],{},[1723,33703,1914],{"stretchy":1907},[1723,33705,1725],{},[2057,33707,33708,33710],{},[898,33709,900],{},[1723,33711,5066],{},[902,33713,33714],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,33717,33719],{"className":33718},[886],[888,33720,33721],{"xmlns":890},[892,33722,33723,33743],{},[895,33724,33725,33733,33735],{},[2220,33726,33727,33729,33731],{},[898,33728,1904],{},[1864,33730,1866],{},[1723,33732,5066],{},[1723,33734,2031],{"separator":2030},[2220,33736,33737,33739,33741],{},[898,33738,1904],{},[1864,33740,2331],{},[1723,33742,5066],{},[902,33744,30194],{"encoding":904},[123,33746,33747,2628,33750,33804],{},[38,33748,33749],{},"Vypočítej minimální výdaje",[883,33751,33753],{"className":33752},[886],[888,33754,33755],{"xmlns":890},[892,33756,33757,33801],{},[895,33758,33759,33765,33767,33775,33783,33785,33793],{},[2057,33760,33761,33763],{},[898,33762,1846],{},[1723,33764,5066],{},[1723,33766,1725],{},[2220,33768,33769,33771,33773],{},[898,33770,1746],{},[1864,33772,1866],{},[1723,33774,5066],{},[2220,33776,33777,33779,33781],{},[898,33778,1904],{},[1864,33780,1866],{},[1723,33782,5066],{},[1723,33784,2087],{},[2220,33786,33787,33789,33791],{},[898,33788,1746],{},[1864,33790,2331],{},[1723,33792,5066],{},[2220,33794,33795,33797,33799],{},[898,33796,1904],{},[1864,33798,2331],{},[1723,33800,5066],{},[902,33802,33803],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,33806,33808,33809],{"id":33807},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,33810,33812],{"className":33811},[886],[888,33813,33814],{"xmlns":890},[892,33815,33816,33850],{},[895,33817,33818,33820,33822,33836],{},[898,33819,900],{},[1723,33821,1725],{},[2220,33823,33824,33826,33828],{},[898,33825,1904],{},[1864,33827,1866],{},[895,33829,33830,33832,33834],{},[1864,33831,1866],{},[898,33833,2125],{"mathvariant":2124},[1864,33835,2331],{},[2220,33837,33838,33840,33842],{},[898,33839,1904],{},[1864,33841,2331],{},[895,33843,33844,33846,33848],{},[1864,33845,1866],{},[898,33847,2125],{"mathvariant":2124},[1864,33849,2331],{},[902,33851,33852],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,33854,33855,33856,1343,33878,1343,33902,31039],{},"Dáno ",[883,33857,33859],{"className":33858},[886],[888,33860,33861],{"xmlns":890},[892,33862,33863,33875],{},[895,33864,33865,33871,33873],{},[2057,33866,33867,33869],{},[898,33868,900],{},[1723,33870,5066],{},[1723,33872,1725],{},[1864,33874,2331],{},[902,33876,33877],{"encoding":904},"U^* = 2",[883,33879,33881],{"className":33880},[886],[888,33882,33883],{"xmlns":890},[892,33884,33885,33899],{},[895,33886,33887,33895,33897],{},[2220,33888,33889,33891,33893],{},[898,33890,1746],{},[1864,33892,1866],{},[1723,33894,5066],{},[1723,33896,1725],{},[1864,33898,24482],{},[902,33900,33901],{"encoding":904},"P_1^* = 0{,}25",[883,33903,33905],{"className":33904},[886],[888,33906,33907],{"xmlns":890},[892,33908,33909,33923],{},[895,33910,33911,33919,33921],{},[2220,33912,33913,33915,33917],{},[898,33914,1746],{},[1864,33916,2331],{},[1723,33918,5066],{},[1723,33920,1725],{},[1864,33922,1866],{},[902,33924,33925],{"encoding":904},"P_2^* = 1",[883,33927,33929],{"className":33928},[886],[888,33930,33931],{"xmlns":890,"display":28759},[892,33932,33933,33997],{},[895,33934,33935,33937,33939,33941,33947,33949,33955,33957,33959,33961,33963,33965,33979,33993,33995],{},[898,33936,1911],{"mathvariant":29241},[1723,33938,1725],{},[1864,33940,24482],{},[1931,33942,33943,33945],{},[898,33944,1904],{},[1864,33946,1866],{},[1723,33948,2087],{},[1931,33950,33951,33953],{},[898,33952,1904],{},[1864,33954,2331],{},[1723,33956,2087],{},[898,33958,17139],{},[1723,33960,1908],{"stretchy":1907},[1864,33962,2331],{},[1723,33964,1759],{},[2220,33966,33967,33969,33971],{},[898,33968,1904],{},[1864,33970,1866],{},[895,33972,33973,33975,33977],{},[1864,33974,1866],{},[898,33976,2125],{"mathvariant":2124},[1864,33978,2331],{},[2220,33980,33981,33983,33985],{},[898,33982,1904],{},[1864,33984,2331],{},[895,33986,33987,33989,33991],{},[1864,33988,1866],{},[898,33990,2125],{"mathvariant":2124},[1864,33992,2331],{},[1723,33994,1914],{"stretchy":1907},[898,33996,1664],{"mathvariant":2124},[902,33998,33999],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,34001,31124],{},[883,34003,34005],{"className":34004},[886],[888,34006,34007],{"xmlns":890,"display":28759},[892,34008,34009,34223],{},[21447,34010,34011,34087,34163],{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},[21452,34012,34013,34025],{},[21455,34014,34015],{},[3055,34016,34017],{"scriptlevel":2256,"displaystyle":2030},[2220,34018,34019,34021,34023],{},[898,34020,1911],{"mathvariant":29241},[1864,34022,1866],{},[1723,34024,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,34026,34027],{},[3055,34028,34029],{"scriptlevel":2256,"displaystyle":2030},[895,34030,34031,34033,34035,34037,34039,34041,34043,34051,34067,34081,34083,34085],{},[895,34032],{},[1723,34034,1725],{},[1864,34036,24482],{},[1723,34038,1759],{},[898,34040,17139],{},[1723,34042,3897],{},[3055,34044,34045],{"scriptlevel":2256,"displaystyle":1907},[3058,34046,34047,34049],{},[1864,34048,1866],{},[1864,34050,2331],{},[2220,34052,34053,34055,34057],{},[898,34054,1904],{},[1864,34056,1866],{},[895,34058,34059,34061,34063,34065],{},[1723,34060,1759],{},[1864,34062,1866],{},[898,34064,2125],{"mathvariant":2124},[1864,34066,2331],{},[2220,34068,34069,34071,34073],{},[898,34070,1904],{},[1864,34072,2331],{},[895,34074,34075,34077,34079],{},[1864,34076,1866],{},[898,34078,2125],{"mathvariant":2124},[1864,34080,2331],{},[1723,34082,1725],{},[1864,34084,2256],{},[1723,34086,2031],{"separator":2030},[21452,34088,34089,34101],{},[21455,34090,34091],{},[3055,34092,34093],{"scriptlevel":2256,"displaystyle":2030},[2220,34094,34095,34097,34099],{},[898,34096,1911],{"mathvariant":29241},[1864,34098,2331],{},[1723,34100,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,34102,34103],{},[3055,34104,34105],{"scriptlevel":2256,"displaystyle":2030},[895,34106,34107,34109,34111,34113,34115,34117,34119,34127,34141,34157,34159,34161],{},[895,34108],{},[1723,34110,1725],{},[1864,34112,1866],{},[1723,34114,1759],{},[898,34116,17139],{},[1723,34118,3897],{},[3055,34120,34121],{"scriptlevel":2256,"displaystyle":1907},[3058,34122,34123,34125],{},[1864,34124,1866],{},[1864,34126,2331],{},[2220,34128,34129,34131,34133],{},[898,34130,1904],{},[1864,34132,1866],{},[895,34134,34135,34137,34139],{},[1864,34136,1866],{},[898,34138,2125],{"mathvariant":2124},[1864,34140,2331],{},[2220,34142,34143,34145,34147],{},[898,34144,1904],{},[1864,34146,2331],{},[895,34148,34149,34151,34153,34155],{},[1723,34150,1759],{},[1864,34152,1866],{},[898,34154,2125],{"mathvariant":2124},[1864,34156,2331],{},[1723,34158,1725],{},[1864,34160,2256],{},[1723,34162,2031],{"separator":2030},[21452,34164,34165,34177],{},[21455,34166,34167],{},[3055,34168,34169],{"scriptlevel":2256,"displaystyle":2030},[2220,34170,34171,34173,34175],{},[898,34172,1911],{"mathvariant":29241},[898,34174,17139],{},[1723,34176,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,34178,34179],{},[3055,34180,34181],{"scriptlevel":2256,"displaystyle":2030},[895,34182,34183,34185,34187,34189,34191,34205,34219,34221],{},[895,34184],{},[1723,34186,1725],{},[1864,34188,2331],{},[1723,34190,1759],{},[2220,34192,34193,34195,34197],{},[898,34194,1904],{},[1864,34196,1866],{},[895,34198,34199,34201,34203],{},[1864,34200,1866],{},[898,34202,2125],{"mathvariant":2124},[1864,34204,2331],{},[2220,34206,34207,34209,34211],{},[898,34208,1904],{},[1864,34210,2331],{},[895,34212,34213,34215,34217],{},[1864,34214,1866],{},[898,34216,2125],{"mathvariant":2124},[1864,34218,2331],{},[1723,34220,1725],{},[1864,34222,13161],{},[902,34224,34225],{"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}",[724,34227,34228,34229,18272,34259,34287,34288,6299,34350,1343,34400,34422,34423,1664],{},"Podílem prvních dvou rovnic: ",[883,34230,34232],{"className":34231},[886],[888,34233,34234],{"xmlns":890},[892,34235,34236,34256],{},[895,34237,34238,34240,34242,34248,34250],{},[1864,34239,24482],{},[1723,34241,1725],{},[1931,34243,34244,34246],{},[898,34245,1904],{},[1864,34247,2331],{},[898,34249,2125],{"mathvariant":2124},[1931,34251,34252,34254],{},[898,34253,1904],{},[1864,34255,1866],{},[902,34257,34258],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,34260,34262],{"className":34261},[886],[888,34263,34264],{"xmlns":890},[892,34265,34266,34284],{},[895,34267,34268,34274,34276,34278],{},[1931,34269,34270,34272],{},[898,34271,1904],{},[1864,34273,2331],{},[1723,34275,1725],{},[1864,34277,24482],{},[1931,34279,34280,34282],{},[898,34281,1904],{},[1864,34283,1866],{},[902,34285,34286],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,34289,34291],{"className":34290},[886],[888,34292,34293],{"xmlns":890},[892,34294,34295,34347],{},[895,34296,34297,34311,34313,34315,34321,34333,34335,34337,34343,34345],{},[2220,34298,34299,34301,34303],{},[898,34300,1904],{},[1864,34302,1866],{},[895,34304,34305,34307,34309],{},[1864,34306,1866],{},[898,34308,2125],{"mathvariant":2124},[1864,34310,2331],{},[1723,34312,1908],{"stretchy":1907},[1864,34314,24482],{},[1931,34316,34317,34319],{},[898,34318,1904],{},[1864,34320,1866],{},[2057,34322,34323,34325],{},[1723,34324,1914],{"stretchy":1907},[895,34326,34327,34329,34331],{},[1864,34328,1866],{},[898,34330,2125],{"mathvariant":2124},[1864,34332,2331],{},[1723,34334,1725],{},[1864,34336,5719],{},[1931,34338,34339,34341],{},[898,34340,1904],{},[1864,34342,1866],{},[1723,34344,1725],{},[1864,34346,2331],{},[902,34348,34349],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,34351,34352,1343,34376],{},[883,34353,34355],{"className":34354},[886],[888,34356,34357],{"xmlns":890},[892,34358,34359,34373],{},[895,34360,34361,34369,34371],{},[2220,34362,34363,34365,34367],{},[898,34364,1904],{},[1864,34366,1866],{},[1723,34368,5066],{},[1723,34370,1725],{},[1864,34372,3080],{},[902,34374,34375],{"encoding":904},"Q_1^* = 4",[883,34377,34379],{"className":34378},[886],[888,34380,34381],{"xmlns":890},[892,34382,34383,34397],{},[895,34384,34385,34393,34395],{},[2220,34386,34387,34389,34391],{},[898,34388,1904],{},[1864,34390,2331],{},[1723,34392,5066],{},[1723,34394,1725],{},[1864,34396,1866],{},[902,34398,34399],{"encoding":904},"Q_2^* = 1",[883,34401,34403],{"className":34402},[886],[888,34404,34405],{"xmlns":890},[892,34406,34407,34419],{},[895,34408,34409,34415,34417],{},[2057,34410,34411,34413],{},[898,34412,17139],{},[1723,34414,5066],{},[1723,34416,1725],{},[1864,34418,1866],{},[902,34420,34421],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,34424,34426],{"className":34425},[886],[888,34427,34428],{"xmlns":890},[892,34429,34430,34458],{},[895,34431,34432,34438,34440,34442,34444,34446,34448,34450,34452,34454,34456],{},[2057,34433,34434,34436],{},[898,34435,1846],{},[1723,34437,5066],{},[1723,34439,1725],{},[1864,34441,24482],{},[1723,34443,3897],{},[1864,34445,3080],{},[1723,34447,2087],{},[1864,34449,1866],{},[1723,34451,3897],{},[1864,34453,1866],{},[1723,34455,1725],{},[1864,34457,2331],{},[902,34459,34460],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,34462,34463,34466,34467,1343,34533,1343,34599,34665,34666,34703,34704,34726,34727,1664],{},[614,34464,34465],{},"Ověření postačující podmínky"," (6.26): ",[883,34468,34470],{"className":34469},[886],[888,34471,34472],{"xmlns":890},[892,34473,34474,34530],{},[895,34475,34476,34488,34490,34492,34500,34516],{},[2220,34477,34478,34480,34482],{},[898,34479,900],{},[1864,34481,3626],{},[895,34483,34484,34486],{},[1723,34485,2229],{"mathvariant":2124},[1723,34487,2229],{"mathvariant":2124},[1723,34489,1725],{},[1723,34491,1759],{},[3055,34493,34494],{"scriptlevel":2256,"displaystyle":1907},[3058,34495,34496,34498],{},[1864,34497,1866],{},[1864,34499,3080],{},[2220,34501,34502,34504,34506],{},[898,34503,1904],{},[1864,34505,1866],{},[895,34507,34508,34510,34512,34514],{},[1723,34509,1759],{},[1864,34511,2909],{},[898,34513,2125],{"mathvariant":2124},[1864,34515,2331],{},[2220,34517,34518,34520,34522],{},[898,34519,1904],{},[1864,34521,2331],{},[895,34523,34524,34526,34528],{},[1864,34525,1866],{},[898,34527,2125],{"mathvariant":2124},[1864,34529,2331],{},[902,34531,34532],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,34534,34536],{"className":34535},[886],[888,34537,34538],{"xmlns":890},[892,34539,34540,34596],{},[895,34541,34542,34554,34556,34558,34566,34580],{},[2220,34543,34544,34546,34548],{},[898,34545,900],{},[1864,34547,33239],{},[895,34549,34550,34552],{},[1723,34551,2229],{"mathvariant":2124},[1723,34553,2229],{"mathvariant":2124},[1723,34555,1725],{},[1723,34557,1759],{},[3055,34559,34560],{"scriptlevel":2256,"displaystyle":1907},[3058,34561,34562,34564],{},[1864,34563,1866],{},[1864,34565,3080],{},[2220,34567,34568,34570,34572],{},[898,34569,1904],{},[1864,34571,1866],{},[895,34573,34574,34576,34578],{},[1864,34575,1866],{},[898,34577,2125],{"mathvariant":2124},[1864,34579,2331],{},[2220,34581,34582,34584,34586],{},[898,34583,1904],{},[1864,34585,2331],{},[895,34587,34588,34590,34592,34594],{},[1723,34589,1759],{},[1864,34591,2909],{},[898,34593,2125],{"mathvariant":2124},[1864,34595,2331],{},[902,34597,34598],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,34600,34602],{"className":34601},[886],[888,34603,34604],{"xmlns":890},[892,34605,34606,34662],{},[895,34607,34608,34620,34622,34630,34646],{},[2220,34609,34610,34612,34614],{},[898,34611,900],{},[1864,34613,4227],{},[895,34615,34616,34618],{},[1723,34617,2229],{"mathvariant":2124},[1723,34619,2229],{"mathvariant":2124},[1723,34621,1725],{},[3055,34623,34624],{"scriptlevel":2256,"displaystyle":1907},[3058,34625,34626,34628],{},[1864,34627,1866],{},[1864,34629,3080],{},[2220,34631,34632,34634,34636],{},[898,34633,1904],{},[1864,34635,1866],{},[895,34637,34638,34640,34642,34644],{},[1723,34639,1759],{},[1864,34641,1866],{},[898,34643,2125],{"mathvariant":2124},[1864,34645,2331],{},[2220,34647,34648,34650,34652],{},[898,34649,1904],{},[1864,34651,2331],{},[895,34653,34654,34656,34658,34660],{},[1723,34655,1759],{},[1864,34657,1866],{},[898,34659,2125],{"mathvariant":2124},[1864,34661,2331],{},[902,34663,34664],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,34667,34669],{"className":34668},[886],[888,34670,34671],{"xmlns":890},[892,34672,34673,34700],{},[895,34674,34675,34677,34679,34681,34683,34685,34687,34689,34691,34693,34696,34698],{},[898,34676,4897],{},[1723,34678,1908],{"stretchy":1907},[1864,34680,3080],{},[1723,34682,2031],{"separator":2030},[1864,34684,1866],{},[1723,34686,2031],{"separator":2030},[1864,34688,1866],{},[1723,34690,1914],{"stretchy":1907},[1723,34692,1725],{},[1864,34694,34695],{},"0,28125",[1723,34697,2253],{},[1864,34699,2256],{},[902,34701,34702],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,34705,34707],{"className":34706},[886],[888,34708,34709],{"xmlns":890},[892,34710,34711,34723],{},[895,34712,34713,34715,34717,34719,34721],{},[1723,34714,3212],{"stretchy":1907},[1864,34716,3080],{},[1723,34718,2031],{"separator":2030},[1864,34720,1866],{},[1723,34722,3227],{"stretchy":1907},[902,34724,34725],{"encoding":904},"[4, 1]"," je vázané ",[38,34728,4493],{},[115,34730,34732],{"id":34731},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,34734,34735],{},"Obecně:",[883,34737,34739],{"className":34738},[886],[888,34740,34741],{"xmlns":890,"display":28759},[892,34742,34743,34838],{},[21447,34744,34745],{"width":28764},[21452,34746,34747,34749,34831,34833],{},[21455,34748],{"width":28769},[21455,34750,34751],{},[895,34752,34753,34759,34761,34767,34769,34775,34777,34783,34785,34787,34789,34791,34793,34799,34801,34807,34809,34815,34817,34823,34825,34827,34829],{},[1931,34754,34755,34757],{},[898,34756,1904],{},[1864,34758,1866],{},[1723,34760,1725],{},[1931,34762,34763,34765],{},[898,34764,4897],{},[1864,34766,1866],{},[1723,34768,1908],{"stretchy":1907},[1931,34770,34771,34773],{},[898,34772,1746],{},[1864,34774,1866],{},[1723,34776,2031],{"separator":2030},[1931,34778,34779,34781],{},[898,34780,1746],{},[1864,34782,2331],{},[1723,34784,2031],{"separator":2030},[898,34786,900],{},[1723,34788,1914],{"stretchy":1907},[1723,34790,2031],{"separator":2030},[6588,34792],{"width":15985},[1931,34794,34795,34797],{},[898,34796,1904],{},[1864,34798,2331],{},[1723,34800,1725],{},[1931,34802,34803,34805],{},[898,34804,4897],{},[1864,34806,2331],{},[1723,34808,1908],{"stretchy":1907},[1931,34810,34811,34813],{},[898,34812,1746],{},[1864,34814,1866],{},[1723,34816,2031],{"separator":2030},[1931,34818,34819,34821],{},[898,34820,1746],{},[1864,34822,2331],{},[1723,34824,2031],{"separator":2030},[898,34826,900],{},[1723,34828,1914],{"stretchy":1907},[1723,34830,2031],{"separator":2030},[21455,34832],{"width":28769},[21455,34834,34835],{},[3018,34836,34837],{},"(6.27)",[902,34839,34840],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,34842,34844],{"className":34843},[886],[888,34845,34846],{"xmlns":890,"display":28759},[892,34847,34848,34895],{},[21447,34849,34850],{"width":28764},[21452,34851,34852,34854,34888,34890],{},[21455,34853],{"width":28769},[21455,34855,34856],{},[895,34857,34858,34860,34862,34864,34866,34872,34874,34880,34882,34884,34886],{},[898,34859,17139],{},[1723,34861,1725],{},[898,34863,17139],{},[1723,34865,1908],{"stretchy":1907},[1931,34867,34868,34870],{},[898,34869,1746],{},[1864,34871,1866],{},[1723,34873,2031],{"separator":2030},[1931,34875,34876,34878],{},[898,34877,1746],{},[1864,34879,2331],{},[1723,34881,2031],{"separator":2030},[898,34883,900],{},[1723,34885,1914],{"stretchy":1907},[898,34887,1664],{"mathvariant":2124},[21455,34889],{"width":28769},[21455,34891,34892],{},[3018,34893,34894],{},"(6.28)",[902,34896,34897],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,34899,34900,34901,2628,34904,34917,34918,34931],{},"Hicksova poptávka závisí na ",[38,34902,34903],{},"hladině užitečnosti",[883,34905,34907],{"className":34906},[886],[888,34908,34909],{"xmlns":890},[892,34910,34911,34915],{},[895,34912,34913],{},[898,34914,900],{},[902,34916,900],{"encoding":904}," (nikoli na důchodu ",[883,34919,34921],{"className":34920},[886],[888,34922,34923],{"xmlns":890},[892,34924,34925,34929],{},[895,34926,34927],{},[898,34928,9837],{},[902,34930,9837],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,34933,34935,34936],{"id":34934},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,34937,34939],{"className":34938},[886],[888,34940,34941],{"xmlns":890},[892,34942,34943,34977],{},[895,34944,34945,34947,34949,34963],{},[898,34946,900],{},[1723,34948,1725],{},[2220,34950,34951,34953,34955],{},[898,34952,1904],{},[1864,34954,1866],{},[895,34956,34957,34959,34961],{},[1864,34958,1866],{},[898,34960,2125],{"mathvariant":2124},[1864,34962,2331],{},[2220,34964,34965,34967,34969],{},[898,34966,1904],{},[1864,34968,2331],{},[895,34970,34971,34973,34975],{},[1864,34972,1866],{},[898,34974,2125],{"mathvariant":2124},[1864,34976,2331],{},[902,34978,33852],{"encoding":904},[724,34980,34981,35011],{},[883,34982,34984],{"className":34983},[886],[888,34985,34986],{"xmlns":890},[892,34987,34988,35008],{},[895,34989,34990,34996,34998,35004,35006],{},[1931,34991,34992,34994],{},[898,34993,1746],{},[1864,34995,1866],{},[1723,34997,2031],{"separator":2030},[1931,34999,35000,35002],{},[898,35001,1746],{},[1864,35003,2331],{},[1723,35005,2031],{"separator":2030},[898,35007,900],{},[902,35009,35010],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,35013,35015],{"className":35014},[886],[888,35016,35017],{"xmlns":890,"display":28759},[892,35018,35019,35093],{},[895,35020,35021,35023,35025,35031,35037,35039,35045,35051,35053,35055,35057,35059,35061,35075,35089,35091],{},[898,35022,1911],{"mathvariant":29241},[1723,35024,1725],{},[1931,35026,35027,35029],{},[898,35028,1746],{},[1864,35030,1866],{},[1931,35032,35033,35035],{},[898,35034,1904],{},[1864,35036,1866],{},[1723,35038,2087],{},[1931,35040,35041,35043],{},[898,35042,1746],{},[1864,35044,2331],{},[1931,35046,35047,35049],{},[898,35048,1904],{},[1864,35050,2331],{},[1723,35052,2087],{},[898,35054,17139],{},[1723,35056,1908],{"stretchy":1907},[898,35058,900],{},[1723,35060,1759],{},[2220,35062,35063,35065,35067],{},[898,35064,1904],{},[1864,35066,1866],{},[895,35068,35069,35071,35073],{},[1864,35070,1866],{},[898,35072,2125],{"mathvariant":2124},[1864,35074,2331],{},[2220,35076,35077,35079,35081],{},[898,35078,1904],{},[1864,35080,2331],{},[895,35082,35083,35085,35087],{},[1864,35084,1866],{},[898,35086,2125],{"mathvariant":2124},[1864,35088,2331],{},[1723,35090,1914],{"stretchy":1907},[898,35092,1664],{"mathvariant":2124},[902,35094,35095],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,35097,31124],{},[883,35099,35101],{"className":35100},[886],[888,35102,35103],{"xmlns":890,"display":28759},[892,35104,35105,35327],{},[21447,35106,35107,35187,35267],{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},[21452,35108,35109,35121],{},[21455,35110,35111],{},[3055,35112,35113],{"scriptlevel":2256,"displaystyle":2030},[2220,35114,35115,35117,35119],{},[898,35116,1911],{"mathvariant":29241},[1864,35118,1866],{},[1723,35120,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,35122,35123],{},[3055,35124,35125],{"scriptlevel":2256,"displaystyle":2030},[895,35126,35127,35129,35131,35137,35139,35141,35143,35151,35167,35181,35183,35185],{},[895,35128],{},[1723,35130,1725],{},[1931,35132,35133,35135],{},[898,35134,1746],{},[1864,35136,1866],{},[1723,35138,1759],{},[898,35140,17139],{},[1723,35142,3897],{},[3055,35144,35145],{"scriptlevel":2256,"displaystyle":1907},[3058,35146,35147,35149],{},[1864,35148,1866],{},[1864,35150,2331],{},[2220,35152,35153,35155,35157],{},[898,35154,1904],{},[1864,35156,1866],{},[895,35158,35159,35161,35163,35165],{},[1723,35160,1759],{},[1864,35162,1866],{},[898,35164,2125],{"mathvariant":2124},[1864,35166,2331],{},[2220,35168,35169,35171,35173],{},[898,35170,1904],{},[1864,35172,2331],{},[895,35174,35175,35177,35179],{},[1864,35176,1866],{},[898,35178,2125],{"mathvariant":2124},[1864,35180,2331],{},[1723,35182,1725],{},[1864,35184,2256],{},[1723,35186,2031],{"separator":2030},[21452,35188,35189,35201],{},[21455,35190,35191],{},[3055,35192,35193],{"scriptlevel":2256,"displaystyle":2030},[2220,35194,35195,35197,35199],{},[898,35196,1911],{"mathvariant":29241},[1864,35198,2331],{},[1723,35200,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,35202,35203],{},[3055,35204,35205],{"scriptlevel":2256,"displaystyle":2030},[895,35206,35207,35209,35211,35217,35219,35221,35223,35231,35245,35261,35263,35265],{},[895,35208],{},[1723,35210,1725],{},[1931,35212,35213,35215],{},[898,35214,1746],{},[1864,35216,2331],{},[1723,35218,1759],{},[898,35220,17139],{},[1723,35222,3897],{},[3055,35224,35225],{"scriptlevel":2256,"displaystyle":1907},[3058,35226,35227,35229],{},[1864,35228,1866],{},[1864,35230,2331],{},[2220,35232,35233,35235,35237],{},[898,35234,1904],{},[1864,35236,1866],{},[895,35238,35239,35241,35243],{},[1864,35240,1866],{},[898,35242,2125],{"mathvariant":2124},[1864,35244,2331],{},[2220,35246,35247,35249,35251],{},[898,35248,1904],{},[1864,35250,2331],{},[895,35252,35253,35255,35257,35259],{},[1723,35254,1759],{},[1864,35256,1866],{},[898,35258,2125],{"mathvariant":2124},[1864,35260,2331],{},[1723,35262,1725],{},[1864,35264,2256],{},[1723,35266,2031],{"separator":2030},[21452,35268,35269,35281],{},[21455,35270,35271],{},[3055,35272,35273],{"scriptlevel":2256,"displaystyle":2030},[2220,35274,35275,35277,35279],{},[898,35276,1911],{"mathvariant":29241},[898,35278,17139],{},[1723,35280,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[21455,35282,35283],{},[3055,35284,35285],{"scriptlevel":2256,"displaystyle":2030},[895,35286,35287,35289,35291,35293,35295,35309,35323,35325],{},[895,35288],{},[1723,35290,1725],{},[898,35292,900],{},[1723,35294,1759],{},[2220,35296,35297,35299,35301],{},[898,35298,1904],{},[1864,35300,1866],{},[895,35302,35303,35305,35307],{},[1864,35304,1866],{},[898,35306,2125],{"mathvariant":2124},[1864,35308,2331],{},[2220,35310,35311,35313,35315],{},[898,35312,1904],{},[1864,35314,2331],{},[895,35316,35317,35319,35321],{},[1864,35318,1866],{},[898,35320,2125],{"mathvariant":2124},[1864,35322,2331],{},[1723,35324,1725],{},[1864,35326,13161],{},[902,35328,35329],{"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}",[724,35331,35332,35333,35403,35404,35462],{},"Podílem rovnic: ",[883,35334,35336],{"className":35335},[886],[888,35337,35338],{"xmlns":890},[892,35339,35340,35400],{},[895,35341,35342,35348,35350,35356,35358,35364,35366,35372,35374,35380,35386,35388,35394],{},[1931,35343,35344,35346],{},[898,35345,1746],{},[1864,35347,1866],{},[898,35349,2125],{"mathvariant":2124},[1931,35351,35352,35354],{},[898,35353,1746],{},[1864,35355,2331],{},[1723,35357,1725],{},[1931,35359,35360,35362],{},[898,35361,1904],{},[1864,35363,2331],{},[898,35365,2125],{"mathvariant":2124},[1931,35367,35368,35370],{},[898,35369,1904],{},[1864,35371,1866],{},[1723,35373,4702],{},[1931,35375,35376,35378],{},[898,35377,1746],{},[1864,35379,1866],{},[1931,35381,35382,35384],{},[898,35383,1904],{},[1864,35385,1866],{},[1723,35387,1725],{},[1931,35389,35390,35392],{},[898,35391,1746],{},[1864,35393,2331],{},[1931,35395,35396,35398],{},[898,35397,1904],{},[1864,35399,2331],{},[902,35401,35402],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,35405,35407],{"className":35406},[886],[888,35408,35409],{"xmlns":890},[892,35410,35411,35459],{},[895,35412,35413,35415,35417,35423,35429,35431,35437,35443,35445,35447,35453],{},[898,35414,1846],{},[1723,35416,1725],{},[1931,35418,35419,35421],{},[898,35420,1746],{},[1864,35422,1866],{},[1931,35424,35425,35427],{},[898,35426,1904],{},[1864,35428,1866],{},[1723,35430,2087],{},[1931,35432,35433,35435],{},[898,35434,1746],{},[1864,35436,2331],{},[1931,35438,35439,35441],{},[898,35440,1904],{},[1864,35442,2331],{},[1723,35444,1725],{},[1864,35446,2331],{},[1931,35448,35449,35451],{},[898,35450,1746],{},[1864,35452,1866],{},[1931,35454,35455,35457],{},[898,35456,1904],{},[1864,35458,1866],{},[902,35460,35461],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,35464,35466],{"className":35465},[886],[888,35467,35468],{"xmlns":890,"display":28759},[892,35469,35470,35537],{},[21447,35471,35472],{"width":28764},[21452,35473,35474,35476,35530,35532],{},[21455,35475],{"width":28769},[21455,35477,35478],{},[895,35479,35480,35486,35488,35502,35504,35506,35512,35514,35528],{},[1931,35481,35482,35484],{},[898,35483,1904],{},[1864,35485,1866],{},[1723,35487,1725],{},[3058,35489,35490,35492],{},[898,35491,1846],{},[895,35493,35494,35496],{},[1864,35495,2331],{},[1931,35497,35498,35500],{},[898,35499,1746],{},[1864,35501,1866],{},[1723,35503,2031],{"separator":2030},[6588,35505],{"width":15985},[1931,35507,35508,35510],{},[898,35509,1904],{},[1864,35511,2331],{},[1723,35513,1725],{},[3058,35515,35516,35518],{},[898,35517,1846],{},[895,35519,35520,35522],{},[1864,35521,2331],{},[1931,35523,35524,35526],{},[898,35525,1746],{},[1864,35527,2331],{},[898,35529,1664],{"mathvariant":2124},[21455,35531],{"width":28769},[21455,35533,35534],{},[3018,35535,35536],{},"(6.29)",[902,35538,35539],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,35541,35542,35543,18272,35625,35661],{},"Ze třetí rovnice ",[883,35544,35546],{"className":35545},[886],[888,35547,35548],{"xmlns":890},[892,35549,35550,35622],{},[895,35551,35552,35554,35556,35594,35596],{},[898,35553,900],{},[1723,35555,1725],{},[8827,35557,35558],{},[895,35559,35560,35576,35578],{},[3055,35561,35562],{"scriptlevel":2256,"displaystyle":1907},[3058,35563,35564,35566],{},[898,35565,1846],{},[895,35567,35568,35570],{},[1864,35569,2331],{},[1931,35571,35572,35574],{},[898,35573,1746],{},[1864,35575,1866],{},[1723,35577,3897],{},[3055,35579,35580],{"scriptlevel":2256,"displaystyle":1907},[3058,35581,35582,35584],{},[898,35583,1846],{},[895,35585,35586,35588],{},[1864,35587,2331],{},[1931,35589,35590,35592],{},[898,35591,1746],{},[1864,35593,2331],{},[1723,35595,1725],{},[3055,35597,35598],{"scriptlevel":2256,"displaystyle":1907},[3058,35599,35600,35602],{},[898,35601,1846],{},[895,35603,35604,35606],{},[1864,35605,2331],{},[8827,35607,35608],{},[895,35609,35610,35616],{},[1931,35611,35612,35614],{},[898,35613,1746],{},[1864,35615,1866],{},[1931,35617,35618,35620],{},[898,35619,1746],{},[1864,35621,2331],{},[902,35623,35624],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,35626,35628],{"className":35627},[886],[888,35629,35630],{"xmlns":890},[892,35631,35632,35658],{},[895,35633,35634,35636,35638,35640,35642],{},[898,35635,1846],{},[1723,35637,1725],{},[1864,35639,2331],{},[898,35641,900],{},[8827,35643,35644],{},[895,35645,35646,35652],{},[1931,35647,35648,35650],{},[898,35649,1746],{},[1864,35651,1866],{},[1931,35653,35654,35656],{},[898,35655,1746],{},[1864,35657,2331],{},[902,35659,35660],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,35663,35665],{"className":35664},[886],[888,35666,35667],{"xmlns":890,"display":28759},[892,35668,35669,35814],{},[21447,35670,35671],{"width":28764},[21452,35672,35673,35675,35807,35809],{},[21455,35674],{"width":28769},[21455,35676,35677],{},[13533,35678,35679],{"notation":13535},[3055,35680,35681],{"scriptlevel":2256,"displaystyle":1907},[3055,35682,35683],{"scriptlevel":2256,"displaystyle":1907},[3055,35684,35685],{"scriptlevel":2256,"displaystyle":2030},[895,35686,35687,35689,35695,35697,35699,35715,35717,35723,35725,35731,35733,35739,35741,35743,35745,35747,35749,35755,35757,35759,35775,35777,35783,35785,35791,35793,35799,35801,35803,35805],{},[3018,35688,4699],{},[1931,35690,35691,35693],{},[898,35692,1904],{},[1864,35694,1866],{},[1723,35696,1725],{},[898,35698,900],{},[8827,35700,35701],{},[3058,35702,35703,35709],{},[1931,35704,35705,35707],{},[898,35706,1746],{},[1864,35708,2331],{},[1931,35710,35711,35713],{},[898,35712,1746],{},[1864,35714,1866],{},[1723,35716,1725],{},[1931,35718,35719,35721],{},[898,35720,4897],{},[1864,35722,1866],{},[1723,35724,1908],{"stretchy":1907},[1931,35726,35727,35729],{},[898,35728,1746],{},[1864,35730,1866],{},[1723,35732,2031],{"separator":2030},[1931,35734,35735,35737],{},[898,35736,1746],{},[1864,35738,2331],{},[1723,35740,2031],{"separator":2030},[898,35742,900],{},[1723,35744,1914],{"stretchy":1907},[1723,35746,2031],{"separator":2030},[6588,35748],{"width":15985},[1931,35750,35751,35753],{},[898,35752,1904],{},[1864,35754,2331],{},[1723,35756,1725],{},[898,35758,900],{},[8827,35760,35761],{},[3058,35762,35763,35769],{},[1931,35764,35765,35767],{},[898,35766,1746],{},[1864,35768,1866],{},[1931,35770,35771,35773],{},[898,35772,1746],{},[1864,35774,2331],{},[1723,35776,1725],{},[1931,35778,35779,35781],{},[898,35780,4897],{},[1864,35782,2331],{},[1723,35784,1908],{"stretchy":1907},[1931,35786,35787,35789],{},[898,35788,1746],{},[1864,35790,1866],{},[1723,35792,2031],{"separator":2030},[1931,35794,35795,35797],{},[898,35796,1746],{},[1864,35798,2331],{},[1723,35800,2031],{"separator":2030},[898,35802,900],{},[1723,35804,1914],{"stretchy":1907},[3018,35806,4699],{},[21455,35808],{"width":28769},[21455,35810,35811],{},[3018,35812,35813],{},"(6.30)",[902,35815,35816],{"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}",[115,35818,35820],{"id":35819},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,35822,35823,35824,35837,35838,35855,35856,35869,35870,35887,35888,35891,35892,35931,35932,35961],{},"Primární (max ",[883,35825,35827],{"className":35826},[886],[888,35828,35829],{"xmlns":890},[892,35830,35831,35835],{},[895,35832,35833],{},[898,35834,900],{},[902,35836,900],{"encoding":904}," při rozpočtu ",[883,35839,35841],{"className":35840},[886],[888,35842,35843],{"xmlns":890},[892,35844,35845,35853],{},[895,35846,35847],{},[2057,35848,35849,35851],{},[898,35850,9837],{},[1723,35852,5066],{},[902,35854,28721],{"encoding":904},") a duální (min ",[883,35857,35859],{"className":35858},[886],[888,35860,35861],{"xmlns":890},[892,35862,35863,35867],{},[895,35864,35865],{},[898,35866,1846],{},[902,35868,1846],{"encoding":904}," při užitečnosti ",[883,35871,35873],{"className":35872},[886],[888,35874,35875],{"xmlns":890},[892,35876,35877,35885],{},[895,35878,35879],{},[2057,35880,35881,35883],{},[898,35882,900],{},[1723,35884,5066],{},[902,35886,28655],{"encoding":904},") úloha jsou ",[38,35889,35890],{},"ekvivalentní",": mají tentýž bod optima ",[883,35893,35895],{"className":35894},[886],[888,35896,35897],{"xmlns":890},[892,35898,35899,35929],{},[895,35900,35901,35907,35909,35917,35919,35927],{},[2057,35902,35903,35905],{},[898,35904,1904],{},[1723,35906,5066],{},[1723,35908,3212],{"stretchy":1907},[2220,35910,35911,35913,35915],{},[898,35912,1904],{},[1864,35914,1866],{},[1723,35916,5066],{},[1723,35918,2031],{"separator":2030},[2220,35920,35921,35923,35925],{},[898,35922,1904],{},[1864,35924,2331],{},[1723,35926,5066],{},[1723,35928,3227],{"stretchy":1907},[902,35930,29020],{"encoding":904}," a v obou platí ",[883,35933,35935],{"className":35934},[886],[888,35936,35937],{"xmlns":890},[892,35938,35939,35959],{},[895,35940,35941,35943,35945,35951,35953],{},[3018,35942,11303],{},[1723,35944,1725],{},[1931,35946,35947,35949],{},[898,35948,1746],{},[1864,35950,1866],{},[898,35952,2125],{"mathvariant":2124},[1931,35954,35955,35957],{},[898,35956,1746],{},[1864,35958,2331],{},[902,35960,28691],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,35963,35964],{},[3285,35965],{"alt":35966,"className":35967,"src":35968},"imek-primarni-vs-dualni",[210,3289],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,35970,35971,36082],{},[123,35972,35973,35976,35977,35990,35991,36031,36032,1664],{},[38,35974,35975],{},"Primární"," (Marshall): zadáno ",[883,35978,35980],{"className":35979},[886],[888,35981,35982],{"xmlns":890},[892,35983,35984,35988],{},[895,35985,35986],{},[898,35987,9837],{},[902,35989,9837],{"encoding":904},", hledáme maximální ",[883,35992,35994],{"className":35993},[886],[888,35995,35996],{"xmlns":890},[892,35997,35998,36028],{},[895,35999,36000,36006,36008,36014,36016,36022,36024,36026],{},[2057,36001,36002,36004],{},[898,36003,900],{},[1723,36005,5066],{},[1723,36007,1908],{"stretchy":1907},[1931,36009,36010,36012],{},[898,36011,1746],{},[1864,36013,1866],{},[1723,36015,2031],{"separator":2030},[1931,36017,36018,36020],{},[898,36019,1746],{},[1864,36021,2331],{},[1723,36023,2031],{"separator":2030},[898,36025,9837],{},[1723,36027,1914],{"stretchy":1907},[902,36029,36030],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,36033,36035],{"className":36034},[886],[888,36036,36037],{"xmlns":890},[892,36038,36039,36079],{},[895,36040,36041,36047,36049,36057,36059,36065,36067,36073,36075,36077],{},[1931,36042,36043,36045],{},[898,36044,1904],{},[898,36046,2216],{},[1723,36048,1725],{},[2220,36050,36051,36053,36055],{},[898,36052,4897],{},[898,36054,2216],{},[898,36056,1728],{},[1723,36058,1908],{"stretchy":1907},[1931,36060,36061,36063],{},[898,36062,1746],{},[1864,36064,1866],{},[1723,36066,2031],{"separator":2030},[1931,36068,36069,36071],{},[898,36070,1746],{},[1864,36072,2331],{},[1723,36074,2031],{"separator":2030},[898,36076,9837],{},[1723,36078,1914],{"stretchy":1907},[902,36080,36081],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,36083,36084,36087,36088,36101,36102,36031,36142,1664],{},[38,36085,36086],{},"Duální"," (Hicks): zadáno ",[883,36089,36091],{"className":36090},[886],[888,36092,36093],{"xmlns":890},[892,36094,36095,36099],{},[895,36096,36097],{},[898,36098,900],{},[902,36100,900],{"encoding":904},", hledáme minimální ",[883,36103,36105],{"className":36104},[886],[888,36106,36107],{"xmlns":890},[892,36108,36109,36139],{},[895,36110,36111,36117,36119,36125,36127,36133,36135,36137],{},[2057,36112,36113,36115],{},[898,36114,1846],{},[1723,36116,5066],{},[1723,36118,1908],{"stretchy":1907},[1931,36120,36121,36123],{},[898,36122,1746],{},[1864,36124,1866],{},[1723,36126,2031],{"separator":2030},[1931,36128,36129,36131],{},[898,36130,1746],{},[1864,36132,2331],{},[1723,36134,2031],{"separator":2030},[898,36136,900],{},[1723,36138,1914],{"stretchy":1907},[902,36140,36141],{"encoding":904},"E^*(P_1, P_2, U)",[883,36143,36145],{"className":36144},[886],[888,36146,36147],{"xmlns":890},[892,36148,36149,36190],{},[895,36150,36151,36157,36159,36168,36170,36176,36178,36184,36186,36188],{},[1931,36152,36153,36155],{},[898,36154,1904],{},[898,36156,2216],{},[1723,36158,1725],{},[2220,36160,36161,36163,36165],{},[898,36162,4897],{},[898,36164,2216],{},[898,36166,36167],{},"H",[1723,36169,1908],{"stretchy":1907},[1931,36171,36172,36174],{},[898,36173,1746],{},[1864,36175,1866],{},[1723,36177,2031],{"separator":2030},[1931,36179,36180,36182],{},[898,36181,1746],{},[1864,36183,2331],{},[1723,36185,2031],{"separator":2030},[898,36187,900],{},[1723,36189,1914],{"stretchy":1907},[902,36191,36192],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,36194,36195,36196,36199,36200,36203],{},"Proč se studují obě? Marshallova poptávka je ",[38,36197,36198],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,36201,36202],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,36205,36207],{"id":36206},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,36209,36211],{"id":36210},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,36213,36214,36217,36218,36250,36251,36289,36290,36316],{},[38,36215,36216],{},"6.8"," Jsou dány užitečnost ",[883,36219,36221],{"className":36220},[886],[888,36222,36223],{"xmlns":890},[892,36224,36225,36247],{},[895,36226,36227,36229,36231,36239],{},[898,36228,900],{},[1723,36230,1725],{},[2220,36232,36233,36235,36237],{},[898,36234,1904],{},[1864,36236,1866],{},[1864,36238,5719],{},[2220,36240,36241,36243,36245],{},[898,36242,1904],{},[1864,36244,2331],{},[1864,36246,5719],{},[902,36248,36249],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,36252,36254],{"className":36253},[886],[888,36255,36256],{"xmlns":890},[892,36257,36258,36286],{},[895,36259,36260,36268,36270,36272,36274,36282,36284],{},[2220,36261,36262,36264,36266],{},[898,36263,1746],{},[1864,36265,1866],{},[1723,36267,5066],{},[1723,36269,1725],{},[1864,36271,3080],{},[1723,36273,2031],{"separator":2030},[2220,36275,36276,36278,36280],{},[898,36277,1746],{},[1864,36279,2331],{},[1723,36281,5066],{},[1723,36283,1725],{},[1864,36285,3585],{},[902,36287,36288],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,36291,36293],{"className":36292},[886],[888,36294,36295],{"xmlns":890},[892,36296,36297,36313],{},[895,36298,36299,36305,36307],{},[1931,36300,36301,36303],{},[898,36302,1904],{},[1864,36304,1866],{},[1723,36306,2031],{"separator":2030},[1931,36308,36309,36311],{},[898,36310,1904],{},[1864,36312,2331],{},[902,36314,36315],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,36318,36319,36322,36323,36365,36366,36397,36398,36420,36421,1664],{},[38,36320,36321],{},"6.9"," Jsou dány rozpočtové omezení ",[883,36324,36326],{"className":36325},[886],[888,36327,36328],{"xmlns":890},[892,36329,36330,36362],{},[895,36331,36332,36334,36336,36342,36348,36350,36356],{},[898,36333,9837],{},[1723,36335,1725],{},[1931,36337,36338,36340],{},[898,36339,1746],{},[1864,36341,1866],{},[1931,36343,36344,36346],{},[898,36345,1904],{},[1864,36347,1866],{},[1723,36349,2087],{},[1931,36351,36352,36354],{},[898,36353,1746],{},[1864,36355,2331],{},[1931,36357,36358,36360],{},[898,36359,1904],{},[1864,36361,2331],{},[902,36363,36364],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,36367,36369],{"className":36368},[886],[888,36370,36371],{"xmlns":890},[892,36372,36373,36395],{},[895,36374,36375,36377,36379,36387],{},[898,36376,900],{},[1723,36378,1725],{},[2220,36380,36381,36383,36385],{},[898,36382,1904],{},[1864,36384,1866],{},[1864,36386,5719],{},[2220,36388,36389,36391,36393],{},[898,36390,1904],{},[1864,36392,2331],{},[1864,36394,5719],{},[902,36396,36249],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,36399,36401],{"className":36400},[886],[888,36402,36403],{"xmlns":890},[892,36404,36405,36417],{},[895,36406,36407,36413,36415],{},[2057,36408,36409,36411],{},[898,36410,9837],{},[1723,36412,5066],{},[1723,36414,1725],{},[1864,36416,15811],{},[902,36418,36419],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,36422,36424],{"className":36423},[886],[888,36425,36426],{"xmlns":890},[892,36427,36428,36456],{},[895,36429,36430,36438,36440,36442,36444,36452,36454],{},[2220,36431,36432,36434,36436],{},[898,36433,1746],{},[1864,36435,1866],{},[1723,36437,5066],{},[1723,36439,1725],{},[1864,36441,2962],{},[1723,36443,2031],{"separator":2030},[2220,36445,36446,36448,36450],{},[898,36447,1746],{},[1864,36449,2331],{},[1723,36451,5066],{},[1723,36453,1725],{},[1864,36455,3585],{},[902,36457,36458],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,36460,36461,36464,36465,22287,36497,36527,36528,1664],{},[38,36462,36463],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,36466,36468],{"className":36467},[886],[888,36469,36470],{"xmlns":890},[892,36471,36472,36494],{},[895,36473,36474,36476,36478,36486],{},[898,36475,900],{},[1723,36477,1725],{},[2220,36479,36480,36482,36484],{},[898,36481,1904],{},[1864,36483,1866],{},[898,36485,207],{},[2220,36487,36488,36490,36492],{},[898,36489,1904],{},[1864,36491,2331],{},[898,36493,2069],{},[902,36495,36496],{"encoding":904},"U = Q_1^a Q_2^b",[883,36498,36500],{"className":36499},[886],[888,36501,36502],{"xmlns":890},[892,36503,36504,36524],{},[895,36505,36506,36508,36510,36512,36514,36516,36518,36520,36522],{},[898,36507,207],{},[1723,36509,2031],{"separator":2030},[898,36511,2069],{},[1723,36513,7216],{},[1723,36515,6034],{"stretchy":1907},[1864,36517,2256],{},[1723,36519,2031],{"separator":2030},[1864,36521,1866],{},[1723,36523,6051],{"stretchy":1907},[902,36525,36526],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,36529,36531],{"className":36530},[886],[888,36532,36533],{"xmlns":890},[892,36534,36535,36567],{},[895,36536,36537,36539,36541,36547,36553,36555,36561],{},[898,36538,9837],{},[1723,36540,1725],{},[1931,36542,36543,36545],{},[898,36544,1746],{},[1864,36546,1866],{},[1931,36548,36549,36551],{},[898,36550,1904],{},[1864,36552,1866],{},[1723,36554,2087],{},[1931,36556,36557,36559],{},[898,36558,1746],{},[1864,36560,2331],{},[1931,36562,36563,36565],{},[898,36564,1904],{},[1864,36566,2331],{},[902,36568,36364],{"encoding":904},[724,36570,36571,36574,36575,22287,36609,36527,36627,1664],{},[38,36572,36573],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,36576,36578],{"className":36577},[886],[888,36579,36580],{"xmlns":890},[892,36581,36582,36606],{},[895,36583,36584,36586,36588,36596,36598],{},[898,36585,900],{},[1723,36587,1725],{},[2220,36589,36590,36592,36594],{},[898,36591,1904],{},[1864,36593,1866],{},[898,36595,207],{},[1723,36597,2087],{},[2220,36599,36600,36602,36604],{},[898,36601,1904],{},[1864,36603,2331],{},[898,36605,207],{},[902,36607,36608],{"encoding":904},"U = Q_1^a + Q_2^a",[883,36610,36612],{"className":36611},[886],[888,36613,36614],{"xmlns":890},[892,36615,36616,36624],{},[895,36617,36618,36620,36622],{},[898,36619,207],{},[1723,36621,4091],{"mathvariant":2124},[1864,36623,2256],{},[902,36625,36626],{"encoding":904},"a \\neq 0",[883,36628,36630],{"className":36629},[886],[888,36631,36632],{"xmlns":890},[892,36633,36634,36666],{},[895,36635,36636,36638,36640,36646,36652,36654,36660],{},[898,36637,9837],{},[1723,36639,1725],{},[1931,36641,36642,36644],{},[898,36643,1746],{},[1864,36645,1866],{},[1931,36647,36648,36650],{},[898,36649,1904],{},[1864,36651,1866],{},[1723,36653,2087],{},[1931,36655,36656,36658],{},[898,36657,1746],{},[1864,36659,2331],{},[1931,36661,36662,36664],{},[898,36663,1904],{},[1864,36665,2331],{},[902,36667,36364],{"encoding":904},[198,36669,36671],{"id":36670},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,36673,36674,36217,36677,1343,36704,36726,36727,1343,36750,36774,36775,36800,36801,1664],{},[38,36675,36676],{},"6.12",[883,36678,36680],{"className":36679},[886],[888,36681,36682],{"xmlns":890},[892,36683,36684,36702],{},[895,36685,36686,36688,36690,36696],{},[898,36687,900],{},[1723,36689,1725],{},[1931,36691,36692,36694],{},[898,36693,1904],{},[1864,36695,1866],{},[1931,36697,36698,36700],{},[898,36699,1904],{},[1864,36701,2331],{},[902,36703,30919],{"encoding":904},[883,36705,36707],{"className":36706},[886],[888,36708,36709],{"xmlns":890},[892,36710,36711,36723],{},[895,36712,36713,36719,36721],{},[2057,36714,36715,36717],{},[898,36716,900],{},[1723,36718,5066],{},[1723,36720,1725],{},[1864,36722,3585],{},[902,36724,36725],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,36728,36730],{"className":36729},[886],[888,36731,36732],{"xmlns":890},[892,36733,36734,36748],{},[895,36735,36736,36744,36746],{},[2220,36737,36738,36740,36742],{},[898,36739,1746],{},[1864,36741,1866],{},[1723,36743,5066],{},[1723,36745,1725],{},[1864,36747,2331],{},[902,36749,30992],{"encoding":904},[883,36751,36753],{"className":36752},[886],[888,36754,36755],{"xmlns":890},[892,36756,36757,36771],{},[895,36758,36759,36767,36769],{},[2220,36760,36761,36763,36765],{},[898,36762,1746],{},[1864,36764,2331],{},[1723,36766,5066],{},[1723,36768,1725],{},[1864,36770,3080],{},[902,36772,36773],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,36776,36778],{"className":36777},[886],[888,36779,36780],{"xmlns":890},[892,36781,36782,36798],{},[895,36783,36784,36790,36792],{},[1931,36785,36786,36788],{},[898,36787,1904],{},[1864,36789,1866],{},[1723,36791,2031],{"separator":2030},[1931,36793,36794,36796],{},[898,36795,1904],{},[1864,36797,2331],{},[902,36799,36315],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,36802,36804],{"className":36803},[886],[888,36805,36806],{"xmlns":890},[892,36807,36808,36828],{},[895,36809,36810,36812,36814,36820,36822],{},[898,36811,900],{},[1723,36813,1725],{},[1931,36815,36816,36818],{},[898,36817,1904],{},[1864,36819,1866],{},[1723,36821,3897],{},[1931,36823,36824,36826],{},[898,36825,1904],{},[1864,36827,2331],{},[902,36829,36830],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,36832,36833,36836,36837,36878,36879,36901,36902,1664],{},[38,36834,36835],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,36838,36840],{"className":36839},[886],[888,36841,36842],{"xmlns":890},[892,36843,36844,36876],{},[895,36845,36846,36848,36850,36856,36862,36864,36870],{},[898,36847,1846],{},[1723,36849,1725],{},[1931,36851,36852,36854],{},[898,36853,1746],{},[1864,36855,1866],{},[1931,36857,36858,36860],{},[898,36859,1904],{},[1864,36861,1866],{},[1723,36863,2087],{},[1931,36865,36866,36868],{},[898,36867,1746],{},[1864,36869,2331],{},[1931,36871,36872,36874],{},[898,36873,1904],{},[1864,36875,2331],{},[902,36877,28636],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,36880,36882],{"className":36881},[886],[888,36883,36884],{"xmlns":890},[892,36885,36886,36898],{},[895,36887,36888,36894,36896],{},[2057,36889,36890,36892],{},[898,36891,900],{},[1723,36893,5066],{},[1723,36895,1725],{},[1864,36897,5714],{},[902,36899,36900],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,36903,36905],{"className":36904},[886],[888,36906,36907],{"xmlns":890},[892,36908,36909,36938],{},[895,36910,36911,36919,36921,36923,36925,36933,36935],{},[2220,36912,36913,36915,36917],{},[898,36914,1746],{},[1864,36916,1866],{},[1723,36918,5066],{},[1723,36920,1725],{},[1864,36922,9744],{},[1723,36924,2031],{"separator":2030},[2220,36926,36927,36929,36931],{},[898,36928,1746],{},[1864,36930,2331],{},[1723,36932,5066],{},[1723,36934,1725],{},[1864,36936,36937],{},"15",[902,36939,36940],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,36942,16421],{"id":16420},[120,36944,36945,37002,37041,37061,37096,37150,37155,37161,37257,37302],{},[123,36946,36947,2628,36950,36999,37000,1664],{},[38,36948,36949],{},"Rozpočtové omezení (budget constraint)",[883,36951,36953],{"className":36952},[886],[888,36954,36955],{"xmlns":890},[892,36956,36957,36997],{},[895,36958,36959,36965,36967,36975,36981,36983,36991],{},[2057,36960,36961,36963],{},[898,36962,9837],{},[1723,36964,5066],{},[1723,36966,1725],{},[2220,36968,36969,36971,36973],{},[898,36970,1746],{},[1864,36972,1866],{},[1723,36974,5066],{},[1931,36976,36977,36979],{},[898,36978,1904],{},[1864,36980,1866],{},[1723,36982,2087],{},[2220,36984,36985,36987,36989],{},[898,36986,1746],{},[1864,36988,2331],{},[1723,36990,5066],{},[1931,36992,36993,36995],{},[898,36994,1904],{},[1864,36996,2331],{},[902,36998,17994],{"encoding":904}," — (6.12); ",[38,37001,28829],{},[123,37003,37004,37007,37008,1664],{},[38,37005,37006],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,37009,37011],{"className":37010},[886],[888,37012,37013],{"xmlns":890},[892,37014,37015,37039],{},[895,37016,37017,37019,37021,37029,37031],{},[3018,37018,11303],{},[1723,37020,1725],{},[2220,37022,37023,37025,37027],{},[898,37024,1746],{},[1864,37026,1866],{},[1723,37028,5066],{},[898,37030,2125],{"mathvariant":2124},[2220,37032,37033,37035,37037],{},[898,37034,1746],{},[1864,37036,2331],{},[1723,37038,5066],{},[902,37040,29672],{"encoding":904},[123,37042,37043,37058,37059,1664],{},[38,37044,29816,37045],{},[883,37046,37048],{"className":37047},[886],[888,37049,37050],{"xmlns":890},[892,37051,37052,37056],{},[895,37053,37054],{},[898,37055,17139],{},[902,37057,17192],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,37060,29838],{},[123,37062,37063,37066,37067,1664],{},[38,37064,37065],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,37068,37070],{"className":37069},[886],[888,37071,37072],{"xmlns":890},[892,37073,37074,37094],{},[895,37075,37076,37078,37080,37086,37088],{},[3018,37077,11303],{},[1723,37079,1725],{},[1931,37081,37082,37084],{},[898,37083,1746],{},[1864,37085,1866],{},[898,37087,2125],{"mathvariant":2124},[1931,37089,37090,37092],{},[898,37091,1746],{},[1864,37093,2331],{},[902,37095,28691],{"encoding":904},[123,37097,37098,7725,37101,37149],{},[38,37099,37100],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,37102,37104],{"className":37103},[886],[888,37105,37106],{"xmlns":890},[892,37107,37108,37146],{},[895,37109,37110,37116,37118,37124,37126,37132,37134,37140,37142,37144],{},[1931,37111,37112,37114],{},[898,37113,1904],{},[898,37115,2216],{},[1723,37117,1725],{},[1931,37119,37120,37122],{},[898,37121,4897],{},[898,37123,2216],{},[1723,37125,1908],{"stretchy":1907},[1931,37127,37128,37130],{},[898,37129,1746],{},[1864,37131,1866],{},[1723,37133,2031],{"separator":2030},[1931,37135,37136,37138],{},[898,37137,1746],{},[1864,37139,2331],{},[1723,37141,2031],{"separator":2030},[898,37143,9837],{},[1723,37145,1914],{"stretchy":1907},[902,37147,37148],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,37151,37152,37154],{},[38,37153,32420],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,37156,37157,37160],{},[38,37158,37159],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,37162,37163,7725,37165,37212,37213,37256],{},[38,37164,34732],{},[883,37166,37168],{"className":37167},[886],[888,37169,37170],{"xmlns":890},[892,37171,37172,37210],{},[895,37173,37174,37180,37182,37188,37190,37196,37198,37204,37206,37208],{},[1931,37175,37176,37178],{},[898,37177,1904],{},[898,37179,2216],{},[1723,37181,1725],{},[1931,37183,37184,37186],{},[898,37185,4897],{},[898,37187,2216],{},[1723,37189,1908],{"stretchy":1907},[1931,37191,37192,37194],{},[898,37193,1746],{},[1864,37195,1866],{},[1723,37197,2031],{"separator":2030},[1931,37199,37200,37202],{},[898,37201,1746],{},[1864,37203,2331],{},[1723,37205,2031],{"separator":2030},[898,37207,900],{},[1723,37209,1914],{"stretchy":1907},[902,37211,18518],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,37214,37216],{"className":37215},[886],[888,37217,37218],{"xmlns":890},[892,37219,37220,37254],{},[895,37221,37222,37224,37226,37240],{},[898,37223,900],{},[1723,37225,1725],{},[2220,37227,37228,37230,37232],{},[898,37229,1904],{},[1864,37231,1866],{},[895,37233,37234,37236,37238],{},[1864,37235,1866],{},[898,37237,2125],{"mathvariant":2124},[1864,37239,2331],{},[2220,37241,37242,37244,37246],{},[898,37243,1904],{},[1864,37245,2331],{},[895,37247,37248,37250,37252],{},[1864,37249,1866],{},[898,37251,2125],{"mathvariant":2124},[1864,37253,2331],{},[902,37255,33852],{"encoding":904},": (6.30).",[123,37258,37259,37301],{},[38,37260,37261,37262],{},"Bod dotyku ",[883,37263,37265],{"className":37264},[886],[888,37266,37267],{"xmlns":890},[892,37268,37269,37299],{},[895,37270,37271,37277,37279,37287,37289,37297],{},[2057,37272,37273,37275],{},[898,37274,1904],{},[1723,37276,5066],{},[1723,37278,3212],{"stretchy":1907},[2220,37280,37281,37283,37285],{},[898,37282,1904],{},[1864,37284,1866],{},[1723,37286,5066],{},[1723,37288,2031],{"separator":2030},[2220,37290,37291,37293,37295],{},[898,37292,1904],{},[1864,37294,2331],{},[1723,37296,5066],{},[1723,37298,3227],{"stretchy":1907},[902,37300,29020],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,37303,37304,37307,37308,37321,37322,37335],{},[38,37305,37306],{},"Dualita"," — ekvivalence max ",[883,37309,37311],{"className":37310},[886],[888,37312,37313],{"xmlns":890},[892,37314,37315,37319],{},[895,37316,37317],{},[898,37318,900],{},[902,37320,900],{"encoding":904}," a min ",[883,37323,37325],{"className":37324},[886],[888,37326,37327],{"xmlns":890},[892,37328,37329,37333],{},[895,37330,37331],{},[898,37332,1846],{},[902,37334,1846],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,37337,2620],{"id":2619},[120,37339,37340,37363,37379,37392,37403],{},[123,37341,37342,2628,37345,37348,37349,37362],{},[38,37343,37344],{},"Teorie před optimalizací:",[207,37346,880],{"className":37347,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,37350,37352],{"className":37351},[886],[888,37353,37354],{"xmlns":890},[892,37355,37356,37360],{},[895,37357,37358],{},[898,37359,900],{},[902,37361,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,37364,37365,2628,37368,37371,37372,37375,37376,1664],{},[38,37366,37367],{},"Matematický aparát:",[207,37369,793],{"className":37370,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,37373,784],{"className":37374,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,37377,3086],{"className":37378,"dataFsResolvedFilePath":764,"href":765},[210],[123,37380,37381,2628,37384,37387,37388,37391],{},[38,37382,37383],{},"Paralely:",[207,37385,11788],{"className":37386,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,37389,12642],{"className":37390,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,37393,37394,2628,37397,1343,37400],{},[38,37395,37396],{},"Přednášky:",[207,37398,1094],{"className":37399,"dataFsResolvedFilePath":838,"href":839},[210],[207,37401,1101],{"className":37402,"dataFsResolvedFilePath":868,"href":869},[210],[123,37404,37405,2628,37407],{},[38,37406,2627],{},[207,37408,1646],{"className":37409,"dataFsResolvedFilePath":1645,"href":1644},[210],{"title":641,"searchDepth":642,"depth":642,"links":37411},[37412,37413,37414,37419,37420,37421,37423,37426,37429,37431,37432,37434,37435,37439,37440],{"id":12706,"depth":642,"text":12707},{"id":28699,"depth":642,"text":28700},{"id":29097,"depth":642,"text":29098,"children":37415},[37416,37417],{"id":29217,"depth":649,"text":29218},{"id":29798,"depth":649,"text":37418},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":30260,"depth":642,"text":30261},{"id":30571,"depth":642,"text":30572},{"id":30890,"depth":642,"text":37422},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":31663,"depth":642,"text":31664,"children":37424},[37425],{"id":32419,"depth":649,"text":32420},{"id":32599,"depth":642,"text":32600,"children":37427},[37428],{"id":32856,"depth":649,"text":32857},{"id":33807,"depth":642,"text":37430},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":34731,"depth":642,"text":34732},{"id":34934,"depth":642,"text":37433},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":35819,"depth":642,"text":35820},{"id":36206,"depth":642,"text":36207,"children":37436},[37437,37438],{"id":36210,"depth":649,"text":36211},{"id":36670,"depth":649,"text":36671},{"id":16420,"depth":642,"text":16421},{"id":2619,"depth":642,"text":2620},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":28460,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,37447,1144,2361,37448,37449,37450],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":37453,"title":802,"body":37454,"course":1128,"courses":659,"created":2676,"description":641,"extension":661,"meta":51504,"navigation":664,"path":51505,"seo":51506,"sources":51507,"stem":51508,"tags":51509,"type":4573,"updated":677,"__hash__":51515},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":37455,"toc":51460},[37456,37459,37485,37489,37496,37647,37661,37664,37666,37753,37757,37793,37866,37887,38012,38022,38035,38039,38044,38074,38136,38145,38149,38211,38218,38239,38357,38435,38439,38442,38501,38616,38621,38653,38715,38763,38818,38822,38843,38867,38915,38919,38931,38935,39045,39049,39065,39106,39117,39276,39286,39291,39295,39417,39427,39434,39438,39516,39527,39607,39613,39620,39759,39766,39769,39826,39830,39908,39954,39998,40004,40117,40121,40124,40319,40323,40560,40563,40717,40870,40872,40874,40954,40957,41062,41131,41140,41144,41147,41208,41217,41221,41254,41332,41371,41375,41424,41478,41482,41511,41540,41592,41599,41653,41731,41735,41778,41845,41889,41993,42012,42014,42018,42126,42130,42198,42247,42254,42339,42343,42415,42420,42468,42657,42661,42666,42842,42847,42906,43011,43015,43042,43046,43053,43217,43304,43309,43311,43314,43414,43564,43636,43710,43712,43716,43730,43734,43867,43922,44034,44111,44115,44172,44275,44334,44495,44499,44574,44646,44744,44802,44896,44949,44970,45024,45029,45107,45155,45242,45280,45368,45521,45557,45611,45614,45616,45618,45666,45673,45681,45768,45777,45864,45871,45873,45877,46102,46104,46108,46112,46181,46232,46435,46441,46452,46520,46526,46948,46952,47016,47040,47236,47242,47256,47324,47327,47367,47591,47659,47961,48370,48447,48613,48619,48622,48697,49150,49201,49607,49712,50375,50378,50455,50463,50537,50568,50570,50573,50617,50619,50621,50625,50855,50859,50950,50955,51049,51054,51227,51231,51349,51354,51403,51405,51407],[12,37457,802],{"id":37458},"poptávka-nabídka-a-tržní-rovnováha",[4584,37460,37461],{},[724,37462,37463,37465,37466,37469,37470,37473,37474,37477,37478,37480,37481,37484],{},[883,37464,4869],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,37467,37468],{},"poptávka",") a výrobce (",[38,37471,37472],{},"nabídka","), jejich interakci v ",[38,37475,37476],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,37479,18672],{},"). Uzavírá ji pojem ",[38,37482,37483],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,37486,37488],{"id":37487},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,37490,37491,37492,37495],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,37493,37494],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,37497,37498,37515,37556,37572],{},[123,37499,37500,37501,37514],{},"cena ",[883,37502,37504],{"className":37503},[886],[888,37505,37506],{"xmlns":890},[892,37507,37508,37512],{},[895,37509,37510],{},[898,37511,1746],{},[902,37513,1746],{"encoding":904}," zkoumaného zboží,",[123,37516,37517,37518,2031],{},"ceny alternativních zboží ",[883,37519,37521],{"className":37520},[886],[888,37522,37523],{"xmlns":890},[892,37524,37525,37553],{},[895,37526,37527,37533,37535,37541,37543,37545,37547],{},[1931,37528,37529,37531],{},[898,37530,1746],{},[1864,37532,1866],{},[1723,37534,2031],{"separator":2030},[1931,37536,37537,37539],{},[898,37538,1746],{},[1864,37540,2331],{},[1723,37542,2031],{"separator":2030},[1723,37544,2183],{},[1723,37546,2031],{"separator":2030},[1931,37548,37549,37551],{},[898,37550,1746],{},[898,37552,2192],{},[902,37554,37555],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,37557,37558,37559,2031],{},"důchod ",[883,37560,37562],{"className":37561},[886],[888,37563,37564],{"xmlns":890},[892,37565,37566,37570],{},[895,37567,37568],{},[898,37569,9837],{},[902,37571,9837],{"encoding":904},[123,37573,37574,37575,37588,37589,37602,37603,37616,37617,37631,37632,37646],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,37576,37578],{"className":37577},[886],[888,37579,37580],{"xmlns":890},[892,37581,37582,37586],{},[895,37583,37584],{},[898,37585,1911],{},[902,37587,1911],{"encoding":904},", kapitál ",[883,37590,37592],{"className":37591},[886],[888,37593,37594],{"xmlns":890},[892,37595,37596,37600],{},[895,37597,37598],{},[898,37599,2034],{},[902,37601,2034],{"encoding":904},", půda ",[883,37604,37606],{"className":37605},[886],[888,37607,37608],{"xmlns":890},[892,37609,37610,37614],{},[895,37611,37612],{},[898,37613,1846],{},[902,37615,1846],{"encoding":904},"), technologie, počet výrobců ",[883,37618,37620],{"className":37619},[886],[888,37621,37622],{"xmlns":890},[892,37623,37624,37629],{},[895,37625,37626],{},[898,37627,37628],{},"O",[902,37630,37628],{"encoding":904},", počasí ",[883,37633,37635],{"className":37634},[886],[888,37636,37637],{"xmlns":890},[892,37638,37639,37644],{},[895,37640,37641],{},[898,37642,37643],{},"W",[902,37645,37643],{"encoding":904}," atd.",[724,37648,37649,37650,37653,37654,37657,37658,1664],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,37651,37652],{},"ceteris paribus","), hovoříme o ",[38,37655,37656],{},"jednofaktorovém modelu","; jinak jde o model ",[38,37659,37660],{},"vícefaktorový",[37662,37663],"hr",{},[115,37665,13862],{"id":37468},[4584,37667,37668],{},[724,37669,37670,37672,37673,37686,37687,37700,37701,37704,37705,37728,37729,1664],{},[883,37671,4869],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,37674,37676],{"className":37675},[886],[888,37677,37678],{"xmlns":890},[892,37679,37680,37684],{},[895,37681,37682],{},[898,37683,1904],{},[902,37685,1904],{"encoding":904}," na ceně ",[883,37688,37690],{"className":37689},[886],[888,37691,37692],{"xmlns":890},[892,37693,37694,37698],{},[895,37695,37696],{},[898,37697,1746],{},[902,37699,1746],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,37702,37703],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,37706,37708],{"className":37707},[886],[888,37709,37710],{"xmlns":890},[892,37711,37712,37726],{},[895,37713,37714,37716,37718,37720,37722,37724],{},[898,37715,1904],{},[1723,37717,1725],{},[898,37719,4897],{},[1723,37721,1908],{"stretchy":1907},[898,37723,1746],{},[1723,37725,1914],{"stretchy":1907},[902,37727,4906],{"encoding":904}," a jeho lineární verzí ",[883,37730,37732],{"className":37731},[886],[888,37733,37734],{"xmlns":890},[892,37735,37736,37750],{},[895,37737,37738,37740,37742,37744,37746,37748],{},[898,37739,1746],{},[1723,37741,1725],{},[898,37743,207],{},[898,37745,1904],{},[1723,37747,2087],{},[898,37749,2069],{},[902,37751,37752],{"encoding":904},"P = aQ + b",[198,37754,37756],{"id":37755},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,37758,37759,37760,37773,37774,37787,37788,1981,37790,3871],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,37761,37763],{"className":37762},[886],[888,37764,37765],{"xmlns":890},[892,37766,37767,37771],{},[895,37768,37769],{},[898,37770,1904],{},[902,37772,1904],{"encoding":904}," závisí na ceně ",[883,37775,37777],{"className":37776},[886],[888,37778,37779],{"xmlns":890},[892,37780,37781,37785],{},[895,37782,37783],{},[898,37784,1746],{},[902,37786,1746],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,37789,28695],{},[614,37791,37792],{},"demand function",[883,37794,37796],{"className":37795},[886],[888,37797,37798],{"xmlns":890,"display":28759},[892,37799,37800,37863],{},[21447,37801,37802],{"width":28764},[21452,37803,37804,37806,37856,37858],{},[21455,37805],{"width":28769},[21455,37807,37808],{},[895,37809,37810,37812,37814,37816,37818,37820,37822,37828,37830,37836,37838,37840,37842,37848,37850,37852,37854],{},[898,37811,1904],{},[1723,37813,1725],{},[898,37815,4897],{},[1723,37817,1908],{"stretchy":1907},[898,37819,1746],{},[1723,37821,2031],{"separator":2030},[1931,37823,37824,37826],{},[898,37825,1746],{},[1864,37827,1866],{},[1723,37829,2031],{"separator":2030},[1931,37831,37832,37834],{},[898,37833,1746],{},[1864,37835,2331],{},[1723,37837,2031],{"separator":2030},[1723,37839,2183],{},[1723,37841,2031],{"separator":2030},[1931,37843,37844,37846],{},[898,37845,1746],{},[898,37847,2192],{},[1723,37849,2031],{"separator":2030},[898,37851,9837],{},[1723,37853,1914],{"stretchy":1907},[898,37855,1664],{"mathvariant":2124},[21455,37857],{"width":28769},[21455,37859,37860],{},[3018,37861,37862],{},"(2.1)",[902,37864,37865],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,37867,37868,37869,37872,37873,37886],{},"Důležitou vlastností je ",[38,37870,37871],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,37874,37876],{"className":37875},[886],[888,37877,37878],{"xmlns":890},[892,37879,37880,37884],{},[895,37881,37882],{},[898,37883,12742],{},[902,37885,12742],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,37888,37890],{"className":37889},[886],[888,37891,37892],{"xmlns":890,"display":28759},[892,37893,37894,38009],{},[21447,37895,37896],{"width":28764},[21452,37897,37898,37900,38002,38004],{},[21455,37899],{"width":28769},[21455,37901,37902],{},[895,37903,37904,37906,37908,37910,37912,37914,37916,37918,37920,37926,37928,37930,37936,37938,37940,37942,37944,37950,37952,37954,37956,37958,37960,37962,37964,37966,37968,37974,37976,37982,37984,37986,37988,37994,37996,37998,38000],{},[898,37905,1904],{},[1723,37907,1725],{},[898,37909,4897],{},[1723,37911,1908],{"stretchy":1907},[898,37913,12742],{},[898,37915,1746],{},[1723,37917,2031],{"separator":2030},[898,37919,12742],{},[1931,37921,37922,37924],{},[898,37923,1746],{},[1864,37925,1866],{},[1723,37927,2031],{"separator":2030},[898,37929,12742],{},[1931,37931,37932,37934],{},[898,37933,1746],{},[1864,37935,2331],{},[1723,37937,2031],{"separator":2030},[1723,37939,2183],{},[1723,37941,2031],{"separator":2030},[898,37943,12742],{},[1931,37945,37946,37948],{},[898,37947,1746],{},[898,37949,2192],{},[1723,37951,2031],{"separator":2030},[898,37953,12742],{},[898,37955,9837],{},[1723,37957,1914],{"stretchy":1907},[1723,37959,1725],{},[898,37961,4897],{},[1723,37963,1908],{"stretchy":1907},[898,37965,1746],{},[1723,37967,2031],{"separator":2030},[1931,37969,37970,37972],{},[898,37971,1746],{},[1864,37973,1866],{},[1723,37975,2031],{"separator":2030},[1931,37977,37978,37980],{},[898,37979,1746],{},[1864,37981,2331],{},[1723,37983,2031],{"separator":2030},[1723,37985,2183],{},[1723,37987,2031],{"separator":2030},[1931,37989,37990,37992],{},[898,37991,1746],{},[898,37993,2192],{},[1723,37995,2031],{"separator":2030},[898,37997,9837],{},[1723,37999,1914],{"stretchy":1907},[898,38001,1664],{"mathvariant":2124},[21455,38003],{"width":28769},[21455,38005,38006],{},[3018,38007,38008],{},"(2.2)",[902,38010,38011],{"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}",[4584,38013,38014],{},[724,38015,38016,38018,38019,1664],{},[883,38017,5124],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,38020,38021],{},"v jednofaktorových modelech neplatí",[724,38023,38024,38025,1343,38028,1682,38031,38034],{},"Rozlišuje se poptávka ",[38,38026,38027],{},"individuální",[38,38029,38030],{},"tržní",[38,38032,38033],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,38036,38038],{"id":38037},"jednofaktorové-modely","Jednofaktorové modely",[38040,38041,38043],"h4",{"id":38042},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,38045,38046,38047,38060,38061,3430],{},"Poptávané množství ",[883,38048,38050],{"className":38049},[886],[888,38051,38052],{"xmlns":890},[892,38053,38054,38058],{},[895,38055,38056],{},[898,38057,1904],{},[902,38059,1904],{"encoding":904}," závisí pouze na ceně ",[883,38062,38064],{"className":38063},[886],[888,38065,38066],{"xmlns":890},[892,38067,38068,38072],{},[895,38069,38070],{},[898,38071,1746],{},[902,38073,1746],{"encoding":904},[883,38075,38077],{"className":38076},[886],[888,38078,38079],{"xmlns":890,"display":28759},[892,38080,38081,38133],{},[21447,38082,38083],{"width":28764},[21452,38084,38085,38087,38126,38128],{},[21455,38086],{"width":28769},[21455,38088,38089],{},[895,38090,38091,38093,38095,38097,38099,38101,38103,38105,38107,38110,38112,38114,38116,38118,38120,38122,38124],{},[898,38092,1904],{},[1723,38094,1725],{},[898,38096,4897],{},[1723,38098,1908],{"stretchy":1907},[898,38100,1746],{},[1723,38102,1914],{"stretchy":1907},[1723,38104,2031],{"separator":2030},[6588,38106],{"width":6590},[3018,38108,38109],{},"resp.",[6588,38111],{"width":6590},[898,38113,1746],{},[1723,38115,1725],{},[898,38117,4897],{},[1723,38119,1908],{"stretchy":1907},[898,38121,1904],{},[1723,38123,1914],{"stretchy":1907},[898,38125,1664],{"mathvariant":2124},[21455,38127],{"width":28769},[21455,38129,38130],{},[3018,38131,38132],{},"(2.3)",[902,38134,38135],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,38137,38138,38139,1981,38142,4634],{},"Graf této funkce se nazývá ",[38,38140,38141],{},"křivka poptávky",[614,38143,38144],{},"demand curve",[38040,38146,38148],{"id":38147},"zákon-klesající-poptávky","Zákon klesající poptávky",[4584,38150,38151],{},[724,38152,38153],{},[38,38154,38155,38156,38169,38170,38183,38184,38169,38197,38210],{},"Roste-li cena ",[883,38157,38159],{"className":38158},[886],[888,38160,38161],{"xmlns":890},[892,38162,38163,38167],{},[895,38164,38165],{},[898,38166,1746],{},[902,38168,1746],{"encoding":904},", pak množství ",[883,38171,38173],{"className":38172},[886],[888,38174,38175],{"xmlns":890},[892,38176,38177,38181],{},[895,38178,38179],{},[898,38180,1904],{},[902,38182,1904],{"encoding":904}," klesá; klesá-li cena ",[883,38185,38187],{"className":38186},[886],[888,38188,38189],{"xmlns":890},[892,38190,38191,38195],{},[895,38192,38193],{},[898,38194,1746],{},[902,38196,1746],{"encoding":904},[883,38198,38200],{"className":38199},[886],[888,38201,38202],{"xmlns":890},[892,38203,38204,38208],{},[895,38205,38206],{},[898,38207,1904],{},[902,38209,1904],{"encoding":904}," roste.",[724,38212,38213,38214,38217],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,38215,38216],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[4584,38219,38220,38225],{},[724,38221,38222,38224],{},[883,38223,4869],{}," Intuice — proč zákon platí",[120,38226,38227,38233],{},[123,38228,38229,38232],{},[38,38230,38231],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,38234,38235,38238],{},[38,38236,38237],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,38240,38241,38242,38255,38256,38269,38270,38296,38297,38323,38324,8812,38350,38353,38354,1664],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,38243,38245],{"className":38244},[886],[888,38246,38247],{"xmlns":890},[892,38248,38249,38253],{},[895,38250,38251],{},[898,38252,1746],{},[902,38254,1746],{"encoding":904}," se vynáší na svislou osu, množství ",[883,38257,38259],{"className":38258},[886],[888,38260,38261],{"xmlns":890},[892,38262,38263,38267],{},[895,38264,38265],{},[898,38266,1904],{},[902,38268,1904],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,38271,38273],{"className":38272},[886],[888,38274,38275],{"xmlns":890},[892,38276,38277,38293],{},[895,38278,38279,38281,38283,38285,38291],{},[1723,38280,3212],{"stretchy":1907},[1864,38282,2256],{},[1723,38284,2031],{"separator":2030},[1931,38286,38287,38289],{},[898,38288,1746],{},[1864,38290,2256],{},[1723,38292,3227],{"stretchy":1907},[902,38294,38295],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,38298,38300],{"className":38299},[886],[888,38301,38302],{"xmlns":890},[892,38303,38304,38320],{},[895,38305,38306,38308,38314,38316,38318],{},[1723,38307,3212],{"stretchy":1907},[1931,38309,38310,38312],{},[898,38311,1904],{},[1864,38313,2256],{},[1723,38315,2031],{"separator":2030},[1864,38317,2256],{},[1723,38319,3227],{"stretchy":1907},[902,38321,38322],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,38325,38327],{"className":38326},[886],[888,38328,38329],{"xmlns":890},[892,38330,38331,38347],{},[895,38332,38333,38335,38337,38339,38345],{},[1723,38334,1908],{"stretchy":1907},[1864,38336,2256],{},[1723,38338,2031],{"separator":2030},[1931,38340,38341,38343],{},[898,38342,1746],{},[1864,38344,2256],{},[1723,38346,1914],{"stretchy":1907},[902,38348,38349],{"encoding":904},"(0, P_0)",[38,38351,38352],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,38355,38356],{},"konvexní",[724,38358,38359],{},[614,38360,38361,38362,38384,38385,1682,38410,1664],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,38363,38365],{"className":38364},[886],[888,38366,38367],{"xmlns":890},[892,38368,38369,38381],{},[895,38370,38371,38373,38375,38377,38379],{},[1723,38372,1908],{"stretchy":1907},[898,38374,1904],{},[1723,38376,2031],{"separator":2030},[898,38378,1746],{},[1723,38380,1914],{"stretchy":1907},[902,38382,38383],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,38386,38388],{"className":38387},[886],[888,38389,38390],{"xmlns":890},[892,38391,38392,38408],{},[895,38393,38394,38396,38398,38400,38406],{},[1723,38395,3212],{"stretchy":1907},[1864,38397,2256],{},[1723,38399,2031],{"separator":2030},[1931,38401,38402,38404],{},[898,38403,1746],{},[1864,38405,2256],{},[1723,38407,3227],{"stretchy":1907},[902,38409,38295],{"encoding":904},[883,38411,38413],{"className":38412},[886],[888,38414,38415],{"xmlns":890},[892,38416,38417,38433],{},[895,38418,38419,38421,38427,38429,38431],{},[1723,38420,3212],{"stretchy":1907},[1931,38422,38423,38425],{},[898,38424,1904],{},[1864,38426,2256],{},[1723,38428,2031],{"separator":2030},[1864,38430,2256],{},[1723,38432,3227],{"stretchy":1907},[902,38434,38322],{"encoding":904},[38040,38436,38438],{"id":38437},"lineární-model-poptávky","Lineární model poptávky",[724,38440,38441],{},"Nejjednodušší závislostí je",[883,38443,38445],{"className":38444},[886],[888,38446,38447],{"xmlns":890,"display":28759},[892,38448,38449,38498],{},[21447,38450,38451],{"width":28764},[21452,38452,38453,38455,38491,38493],{},[21455,38454],{"width":28769},[21455,38456,38457],{},[895,38458,38459,38461,38463,38465,38467,38469,38471,38473,38475,38477,38479,38481,38483,38485,38487,38489],{},[898,38460,1746],{},[1723,38462,1725],{},[898,38464,207],{},[898,38466,1904],{},[1723,38468,2087],{},[898,38470,2069],{},[1723,38472,2031],{"separator":2030},[6588,38474],{"width":6590},[898,38476,207],{},[1723,38478,2287],{},[1864,38480,2256],{},[1723,38482,2031],{"separator":2030},[3018,38484,3020],{},[898,38486,2069],{},[1723,38488,2253],{},[1864,38490,13161],{},[21455,38492],{"width":28769},[21455,38494,38495],{},[3018,38496,38497],{},"(2.4)",[902,38499,38500],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,38502,38503,38504,22287,38540,1682,38564,8747,38590,38612,38613,1664],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,38505,38507],{"className":38506},[886],[888,38508,38509],{"xmlns":890},[892,38510,38511,38537],{},[895,38512,38513,38515,38517,38525,38527,38529],{},[898,38514,1904],{},[1723,38516,1725],{},[3055,38518,38519],{"scriptlevel":2256,"displaystyle":1907},[3058,38520,38521,38523],{},[1864,38522,1866],{},[898,38524,207],{},[898,38526,1746],{},[1723,38528,1759],{},[3055,38530,38531],{"scriptlevel":2256,"displaystyle":1907},[3058,38532,38533,38535],{},[898,38534,2069],{},[898,38536,207],{},[902,38538,38539],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,38541,38543],{"className":38542},[886],[888,38544,38545],{"xmlns":890},[892,38546,38547,38561],{},[895,38548,38549,38557,38559],{},[3055,38550,38551],{"scriptlevel":2256,"displaystyle":1907},[3058,38552,38553,38555],{},[1864,38554,1866],{},[898,38556,207],{},[1723,38558,2287],{},[1864,38560,2256],{},[902,38562,38563],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,38565,38567],{"className":38566},[886],[888,38568,38569],{"xmlns":890},[892,38570,38571,38587],{},[895,38572,38573,38575,38583,38585],{},[1723,38574,1759],{},[3055,38576,38577],{"scriptlevel":2256,"displaystyle":1907},[3058,38578,38579,38581],{},[898,38580,2069],{},[898,38582,207],{},[1723,38584,2253],{},[1864,38586,2256],{},[902,38588,38589],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,38591,38593],{"className":38592},[886],[888,38594,38595],{"xmlns":890},[892,38596,38597,38609],{},[895,38598,38599,38601,38603,38605,38607],{},[1723,38600,1908],{"stretchy":1907},[1864,38602,2256],{},[1723,38604,2031],{"separator":2030},[898,38606,2069],{},[1723,38608,1914],{"stretchy":1907},[902,38610,38611],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,38614,38615],{},"nedokonalé konkurenci",[38617,38618,38620],"h5",{"id":38619},"příklad-21","Příklad 2.1",[724,38622,38623,38626,38627,1664],{},[38,38624,38625],{},"Zadání:"," Lineární poptávka ",[883,38628,38630],{"className":38629},[886],[888,38631,38632],{"xmlns":890},[892,38633,38634,38650],{},[895,38635,38636,38638,38640,38642,38644,38646,38648],{},[898,38637,1746],{},[1723,38639,1725],{},[1723,38641,1759],{},[1864,38643,2331],{},[898,38645,1904],{},[1723,38647,2087],{},[1864,38649,3846],{},[902,38651,38652],{"encoding":904},"P = -2Q + 60",[724,38654,38655,38658,38659,38681,38682,1664],{},[38,38656,38657],{},"Řešení:"," Reálné cenové rozpětí je ",[883,38660,38662],{"className":38661},[886],[888,38663,38664],{"xmlns":890},[892,38665,38666,38678],{},[895,38667,38668,38670,38672,38674,38676],{},[1723,38669,1908],{"stretchy":1907},[1864,38671,2256],{},[1723,38673,2031],{"separator":2030},[1864,38675,3846],{},[1723,38677,1914],{"stretchy":1907},[902,38679,38680],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,38683,38685],{"className":38684},[886],[888,38686,38687],{"xmlns":890},[892,38688,38689,38712],{},[895,38690,38691,38693,38695,38697,38705,38707,38709],{},[898,38692,1904],{},[1723,38694,1725],{},[1723,38696,1759],{},[3055,38698,38699],{"scriptlevel":2256,"displaystyle":1907},[3058,38700,38701,38703],{},[1864,38702,1866],{},[1864,38704,2331],{},[898,38706,1746],{},[1723,38708,2087],{},[1864,38710,38711],{},"30",[902,38713,38714],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,38716,38717,38740],{},[19,38718,38719],{},[22,38720,38721,38736,38738],{},[25,38722,38723],{},[883,38724,38726],{"className":38725},[886],[888,38727,38728],{"xmlns":890},[892,38729,38730,38734],{},[895,38731,38732],{},[898,38733,1746],{},[902,38735,1746],{"encoding":904},[25,38737,5921],{},[25,38739,9744],{},[30,38741,38742],{},[22,38743,38744,38759,38761],{},[35,38745,38746],{},[883,38747,38749],{"className":38748},[886],[888,38750,38751],{"xmlns":890},[892,38752,38753,38757],{},[895,38754,38755],{},[898,38756,1904],{},[902,38758,1904],{"encoding":904},[35,38760,3585],{},[35,38762,9744],{},[724,38764,38765],{},[614,38766,38767,38768,1682,38790,1664],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,38769,38771],{"className":38770},[886],[888,38772,38773],{"xmlns":890},[892,38774,38775,38787],{},[895,38776,38777,38779,38781,38783,38785],{},[1723,38778,3212],{"stretchy":1907},[1864,38780,2256],{},[1723,38782,2031],{"separator":2030},[898,38784,2069],{},[1723,38786,3227],{"stretchy":1907},[902,38788,38789],{"encoding":904},"[0, b]",[883,38791,38793],{"className":38792},[886],[888,38794,38795],{"xmlns":890},[892,38796,38797,38815],{},[895,38798,38799,38801,38803,38805,38807,38809,38811,38813],{},[1723,38800,3212],{"stretchy":1907},[1723,38802,1759],{},[898,38804,2069],{},[898,38806,2125],{"mathvariant":2124},[898,38808,207],{},[1723,38810,2031],{"separator":2030},[1864,38812,2256],{},[1723,38814,3227],{"stretchy":1907},[902,38816,38817],{"encoding":904},"[-b\u002Fa, 0]",[38040,38819,38821],{"id":38820},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,38823,38824,38825,38842],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,38826,38828],{"className":38827},[886],[888,38829,38830],{"xmlns":890},[892,38831,38832,38840],{},[895,38833,38834],{},[2057,38835,38836,38838],{},[898,38837,1746],{},[1723,38839,5066],{},[902,38841,5116],{"encoding":904},", je funkce poptávky konstantní:",[883,38844,38846],{"className":38845},[886],[888,38847,38848],{"xmlns":890,"display":28759},[892,38849,38850,38864],{},[895,38851,38852,38854,38856,38862],{},[898,38853,1746],{},[1723,38855,1725],{},[2057,38857,38858,38860],{},[898,38859,1746],{},[1723,38861,5066],{},[898,38863,1664],{"mathvariant":2124},[902,38865,38866],{"encoding":904},"P = P^*.",[724,38868,38869],{},[614,38870,38871,38872,38893,38894,1664],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,38873,38875],{"className":38874},[886],[888,38876,38877],{"xmlns":890},[892,38878,38879,38891],{},[895,38880,38881,38883,38885,38887,38889],{},[1723,38882,1908],{"stretchy":1907},[898,38884,1904],{},[1723,38886,2031],{"separator":2030},[898,38888,1746],{},[1723,38890,1914],{"stretchy":1907},[902,38892,38383],{"encoding":904}," na úrovni ",[883,38895,38897],{"className":38896},[886],[888,38898,38899],{"xmlns":890},[892,38900,38901,38913],{},[895,38902,38903,38905,38907],{},[898,38904,1746],{},[1723,38906,1725],{},[2057,38908,38909,38911],{},[898,38910,1746],{},[1723,38912,5066],{},[902,38914,5069],{"encoding":904},[38040,38916,38918],{"id":38917},"giffenův-statek","Giffenův statek",[724,38920,38921,38922,38924,38925,38927,38928,1664],{},"Existují zboží, u nichž je křivka poptávky ",[38,38923,14358],{}," — tzv. ",[38,38926,38918],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,38929,38930],{},"podřadnému zboží",[38617,38932,38934],{"id":38933},"příklad-22","Příklad 2.2",[724,38936,38937,38940,38941,38959,38960,38982,38983,39001,39002,39020,39021,39044],{},[38,38938,38939],{},"Zadání a popis:"," Křivka ",[883,38942,38944],{"className":38943},[886],[888,38945,38946],{"xmlns":890},[892,38947,38948,38956],{},[895,38949,38950],{},[1931,38951,38952,38954],{},[898,38953,4897],{},[1864,38955,1866],{},[902,38957,38958],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,38961,38963],{"className":38962},[886],[888,38964,38965],{"xmlns":890},[892,38966,38967,38979],{},[895,38968,38969,38971,38973,38975,38977],{},[1723,38970,1908],{"stretchy":1907},[1864,38972,2256],{},[1723,38974,2031],{"separator":2030},[1864,38976,36937],{},[1723,38978,1914],{"stretchy":1907},[902,38980,38981],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,38984,38986],{"className":38985},[886],[888,38987,38988],{"xmlns":890},[892,38989,38990,38998],{},[895,38991,38992],{},[1931,38993,38994,38996],{},[898,38995,1904],{},[1864,38997,2256],{},[902,38999,39000],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,39003,39005],{"className":39004},[886],[888,39006,39007],{"xmlns":890},[892,39008,39009,39017],{},[895,39010,39011],{},[1931,39012,39013,39015],{},[898,39014,4897],{},[1864,39016,2331],{},[902,39018,39019],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,39022,39024],{"className":39023},[886],[888,39025,39026],{"xmlns":890},[892,39027,39028,39041],{},[895,39029,39030,39032,39034,39036,39039],{},[1723,39031,3212],{"stretchy":1907},[1864,39033,2256],{},[1723,39035,2031],{"separator":2030},[1864,39037,39038],{},"21",[1723,39040,3227],{"stretchy":1907},[902,39042,39043],{"encoding":904},"[0, 21]"," centů.",[198,39046,39048],{"id":39047},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,39050,39051,39052,3430],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,39053,39055],{"className":39054},[886],[888,39056,39057],{"xmlns":890},[892,39058,39059,39063],{},[895,39060,39061],{},[898,39062,9837],{},[902,39064,9837],{"encoding":904},[883,39066,39068],{"className":39067},[886],[888,39069,39070],{"xmlns":890,"display":28759},[892,39071,39072,39103],{},[21447,39073,39074],{"width":28764},[21452,39075,39076,39078,39096,39098],{},[21455,39077],{"width":28769},[21455,39079,39080],{},[895,39081,39082,39084,39086,39088,39090,39092,39094],{},[898,39083,1904],{},[1723,39085,1725],{},[898,39087,1846],{},[1723,39089,1908],{"stretchy":1907},[898,39091,9837],{},[1723,39093,1914],{"stretchy":1907},[898,39095,1664],{"mathvariant":2124},[21455,39097],{"width":28769},[21455,39099,39100],{},[3018,39101,39102],{},"(2.5)",[902,39104,39105],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,39107,39108,39109,39112,39113,39116],{},"Funkce se nazývá ",[38,39110,39111],{},"Engelova",", její graf ",[38,39114,39115],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,39118,39119,39251],{},[123,39120,39121,7725,39124,39137,39138,39151,39152,39169,39170],{},[38,39122,39123],{},"Normální (superior) zboží",[883,39125,39127],{"className":39126},[886],[888,39128,39129],{"xmlns":890},[892,39130,39131,39135],{},[895,39132,39133],{},[898,39134,1904],{},[902,39136,1904],{"encoding":904}," roste s ",[883,39139,39141],{"className":39140},[886],[888,39142,39143],{"xmlns":890},[892,39144,39145,39149],{},[895,39146,39147],{},[898,39148,9837],{},[902,39150,9837],{"encoding":904},", nepřesáhne hodnotu ",[883,39153,39155],{"className":39154},[886],[888,39156,39157],{"xmlns":890},[892,39158,39159,39167],{},[895,39160,39161],{},[1931,39162,39163,39165],{},[898,39164,1904],{},[1864,39166,2256],{},[902,39168,39000],{"encoding":904},":\n",[120,39171,39172,39204],{},[123,39173,39174,39177,39178,39181,39182,1664],{},[38,39175,39176],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,39179,39180],{},"konkávní"," křivka, autonomní spotřeba ",[883,39183,39185],{"className":39184},[886],[888,39186,39187],{"xmlns":890},[892,39188,39189,39201],{},[895,39190,39191,39197,39199],{},[1931,39192,39193,39195],{},[898,39194,1904],{},[1864,39196,1866],{},[1723,39198,2253],{},[1864,39200,2256],{},[902,39202,39203],{"encoding":904},"Q_1 > 0",[123,39205,39206,39209,39210,39228,39229,39231,39232,2628,39249,1664],{},[38,39207,39208],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,39211,39213],{"className":39212},[886],[888,39214,39215],{"xmlns":890},[892,39216,39217,39225],{},[895,39218,39219],{},[1931,39220,39221,39223],{},[898,39222,9837],{},[1864,39224,1866],{},[902,39226,39227],{"encoding":904},"Y_1",", křivka je nejprve ",[38,39230,38356],{}," a od ",[883,39233,39235],{"className":39234},[886],[888,39236,39237],{"xmlns":890},[892,39238,39239,39247],{},[895,39240,39241],{},[1931,39242,39243,39245],{},[898,39244,9837],{},[1864,39246,1866],{},[902,39248,39227],{"encoding":904},[38,39250,39180],{},[123,39252,39253,39256,39257,39275],{},[38,39254,39255],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,39258,39260],{"className":39259},[886],[888,39261,39262],{"xmlns":890},[892,39263,39264,39272],{},[895,39265,39266],{},[1931,39267,39268,39270],{},[898,39269,9837],{},[1864,39271,2256],{},[902,39273,39274],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,39277,39278,39279,39282,39283,4634],{},"Mírou citlivosti je ",[614,39280,39281],{},"důchodová elasticita"," (viz ",[207,39284,1882],{"className":39285,"dataFsResolvedFilePath":848,"href":849},[210],[724,39287,39288],{},[614,39289,39290],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[38040,39292,39294],{"id":39293},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[4584,39296,39297,39368,39411],{},[724,39298,39299,39301,39302,2628,39305,2628,39318,6379,39320,39333,39334,39337,39338,1664],{},[883,39300,5124],{}," Pozor — nezbytné ≠ podřadné\n",[38,39303,39304],{},"Nezbytné zboží:",[883,39306,39308],{"className":39307},[886],[888,39309,39310],{"xmlns":890},[892,39311,39312,39316],{},[895,39313,39314],{},[898,39315,1904],{},[902,39317,1904],{"encoding":904},[38,39319,8032],{},[883,39321,39323],{"className":39322},[886],[888,39324,39325],{"xmlns":890},[892,39326,39327,39331],{},[895,39328,39329],{},[898,39330,9837],{},[902,39332,9837],{"encoding":904},", ale ",[38,39335,39336],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,39339,39341],{"className":39340},[886],[888,39342,39343],{"xmlns":890},[892,39344,39345,39365],{},[895,39346,39347,39353,39355,39357,39359,39361,39363],{},[1931,39348,39349,39351],{},[898,39350,1846],{},[898,39352,9837],{},[1723,39354,7216],{},[1723,39356,1908],{"stretchy":1907},[1864,39358,2256],{},[1723,39360,2031],{"separator":2030},[1864,39362,1866],{},[1723,39364,1914],{"stretchy":1907},[902,39366,39367],{"encoding":904},"E_Y \\in (0, 1)",[724,39369,39370,2628,39373,2628,39386,39388,39389,1664],{},[38,39371,39372],{},"Podřadné zboží:",[883,39374,39376],{"className":39375},[886],[888,39377,39378],{"xmlns":890},[892,39379,39380,39384],{},[895,39381,39382],{},[898,39383,1904],{},[902,39385,1904],{"encoding":904},[38,39387,8052],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,39390,39392],{"className":39391},[886],[888,39393,39394],{"xmlns":890},[892,39395,39396,39408],{},[895,39397,39398,39404,39406],{},[1931,39399,39400,39402],{},[898,39401,1846],{},[898,39403,9837],{},[1723,39405,2287],{},[1864,39407,2256],{},[902,39409,39410],{"encoding":904},"E_Y \u003C 0",[724,39412,39413,39414,1664],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,39415,39416],{},"méně kusů, ne jen proporčně méně",[724,39418,39419,39422,39423,39426],{},[38,39420,39421],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,39424,39425],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,39428,39429],{},[3285,39430],{"alt":39431,"className":39432,"src":39433},"imek-engelovy-krivky-3typy",[210,3289],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[38617,39435,39437],{"id":39436},"české-příklady","České příklady",[16,39439,39440,39450],{},[19,39441,39442],{},[22,39443,39444,39447],{},[25,39445,39446],{},"Podřadné",[25,39448,39449],{},"Nahradí se za",[30,39451,39452,39460,39468,39476,39484,39492,39500,39508],{},[22,39453,39454,39457],{},[35,39455,39456],{},"Instantní polévky, ramen",[35,39458,39459],{},"Čerstvé jídlo, restaurace",[22,39461,39462,39465],{},[35,39463,39464],{},"MHD (autobus, tramvaj)",[35,39466,39467],{},"Vlastní auto, Uber, taxi",[22,39469,39470,39473],{},[35,39471,39472],{},"Mražené polotovary, pizza z mrazáku",[35,39474,39475],{},"Čerstvé suroviny, hotovky",[22,39477,39478,39481],{},[35,39479,39480],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,39482,39483],{},"Značkové produkty",[22,39485,39486,39489],{},[35,39487,39488],{},"Paštika Májka, obyčejný měkký salám",[35,39490,39491],{},"Kvalitní uzeniny, šunka od kosti",[22,39493,39494,39497],{},[35,39495,39496],{},"Second hand oblečení",[35,39498,39499],{},"Nové oblečení, značky",[22,39501,39502,39505],{},[35,39503,39504],{},"Krabicové víno, nejlevnější pivo",[35,39506,39507],{},"Lahvové víno, řemeslná piva",[22,39509,39510,39513],{},[35,39511,39512],{},"Ojetá auta nižších tříd",[35,39514,39515],{},"Nová auta, prémiové značky",[4584,39517,39518],{},[724,39519,39520,39522,39523,39526],{},[883,39521,5283],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,39524,39525],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,39528,39529,39532,39533,1981,39536,39558,39559,1981,39562,39583,39584,39602,39603,39606],{},[38,39530,39531],{},"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 ",[38,39534,39535],{},"luxus",[883,39537,39539],{"className":39538},[886],[888,39540,39541],{"xmlns":890},[892,39542,39543,39555],{},[895,39544,39545,39551,39553],{},[1931,39546,39547,39549],{},[898,39548,1846],{},[898,39550,9837],{},[1723,39552,2253],{},[1864,39554,1866],{},[902,39556,39557],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,39560,39561],{},"podřadné",[883,39563,39565],{"className":39564},[886],[888,39566,39567],{"xmlns":890},[892,39568,39569,39581],{},[895,39570,39571,39577,39579],{},[1931,39572,39573,39575],{},[898,39574,1846],{},[898,39576,9837],{},[1723,39578,2287],{},[1864,39580,2256],{},[902,39582,39410],{"encoding":904},"). Proto je ",[883,39585,39587],{"className":39586},[886],[888,39588,39589],{"xmlns":890},[892,39590,39591,39599],{},[895,39592,39593],{},[1931,39594,39595,39597],{},[898,39596,1846],{},[898,39598,9837],{},[902,39600,39601],{"encoding":904},"E_Y"," vždy ",[38,39604,39605],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,39608,39609,39610,39612],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,39611,38918],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,39614,39616,39617,1914],{"id":39615},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,39618,39619],{},"shift of demand",[724,39621,39622,39623,39641,39642,39659,39660,39673,39674,3411,39687,39709,39710,39727,39728,39754,39755,39758],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,39624,39626],{"className":39625},[886],[888,39627,39628],{"xmlns":890},[892,39629,39630,39638],{},[895,39631,39632],{},[1931,39633,39634,39636],{},[898,39635,1746],{},[1864,39637,2256],{},[902,39639,39640],{"encoding":904},"P_0"," odpovídá množství ",[883,39643,39645],{"className":39644},[886],[888,39646,39647],{"xmlns":890},[892,39648,39649,39657],{},[895,39650,39651],{},[1931,39652,39653,39655],{},[898,39654,1904],{},[1864,39656,2256],{},[902,39658,39000],{"encoding":904}," na křivce ",[883,39661,39663],{"className":39662},[886],[888,39664,39665],{"xmlns":890},[892,39666,39667,39671],{},[895,39668,39669],{},[898,39670,4897],{},[902,39672,4897],{"encoding":904},"; vzroste-li důchod z ",[883,39675,39677],{"className":39676},[886],[888,39678,39679],{"xmlns":890},[892,39680,39681,39685],{},[895,39682,39683],{},[898,39684,9837],{},[902,39686,9837],{"encoding":904},[883,39688,39690],{"className":39689},[886],[888,39691,39692],{"xmlns":890},[892,39693,39694,39706],{},[895,39695,39696,39702,39704],{},[1931,39697,39698,39700],{},[898,39699,9837],{},[1864,39701,1866],{},[1723,39703,2253],{},[898,39705,9837],{},[902,39707,39708],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,39711,39713],{"className":39712},[886],[888,39714,39715],{"xmlns":890},[892,39716,39717,39725],{},[895,39718,39719],{},[1931,39720,39721,39723],{},[898,39722,1746],{},[1864,39724,2256],{},[902,39726,39640],{"encoding":904}," odpovídá vyšší ",[883,39729,39731],{"className":39730},[886],[888,39732,39733],{"xmlns":890},[892,39734,39735,39751],{},[895,39736,39737,39743,39745],{},[1931,39738,39739,39741],{},[898,39740,1904],{},[1864,39742,1866],{},[1723,39744,2253],{},[1931,39746,39747,39749],{},[898,39748,1904],{},[1864,39750,2256],{},[902,39752,39753],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,39756,39757],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,39760,39761],{},[3285,39762],{"alt":39763,"className":39764,"src":39765},"imek-posun-vs-pohyb-po-krivce",[210,3289],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,39767,39768],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,39770,39771],{},[614,39772,39773,39774,14712,39804,39825],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,39775,39777],{"className":39776},[886],[888,39778,39779],{"xmlns":890},[892,39780,39781,39801],{},[895,39782,39783,39789,39791,39793,39795],{},[1931,39784,39785,39787],{},[898,39786,4897],{},[1864,39788,2331],{},[1723,39790,2031],{"separator":2030},[898,39792,4897],{},[1723,39794,2031],{"separator":2030},[1931,39796,39797,39799],{},[898,39798,4897],{},[1864,39800,1866],{},[902,39802,39803],{"encoding":904},"D_2, D, D_1",[883,39805,39807],{"className":39806},[886],[888,39808,39809],{"xmlns":890},[892,39810,39811,39823],{},[895,39812,39813,39815,39817,39819,39821],{},[1723,39814,1908],{"stretchy":1907},[898,39816,1904],{},[1723,39818,2031],{"separator":2030},[898,39820,1746],{},[1723,39822,1914],{"stretchy":1907},[902,39824,38383],{"encoding":904},", šipky naznačují posuny.",[38617,39827,39829],{"id":39828},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,39831,39832,39834,39835,39858,39859,39876,39877,39894,39895,1664],{},[38,39833,38625],{}," Poptávce ",[883,39836,39838],{"className":39837},[886],[888,39839,39840],{"xmlns":890},[892,39841,39842,39856],{},[895,39843,39844,39846,39848,39850,39852,39854],{},[898,39845,1746],{},[1723,39847,1725],{},[898,39849,4897],{},[1723,39851,1908],{"stretchy":1907},[898,39853,1904],{},[1723,39855,1914],{"stretchy":1907},[902,39857,5351],{"encoding":904}," odpovídá ceně ",[883,39860,39862],{"className":39861},[886],[888,39863,39864],{"xmlns":890},[892,39865,39866,39874],{},[895,39867,39868],{},[1931,39869,39870,39872],{},[898,39871,1746],{},[1864,39873,2256],{},[902,39875,39640],{"encoding":904}," množství ",[883,39878,39880],{"className":39879},[886],[888,39881,39882],{"xmlns":890},[892,39883,39884,39892],{},[895,39885,39886],{},[1931,39887,39888,39890],{},[898,39889,1904],{},[1864,39891,2256],{},[902,39893,39000],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,39896,39898],{"className":39897},[886],[888,39899,39900],{"xmlns":890},[892,39901,39902,39906],{},[895,39903,39904],{},[898,39905,1754],{},[902,39907,1754],{"encoding":904},[724,39909,39910,39912,39913,39930,39931,39953],{},[38,39911,38657],{}," Kupující nakupuje množství ",[883,39914,39916],{"className":39915},[886],[888,39917,39918],{"xmlns":890},[892,39919,39920,39928],{},[895,39921,39922],{},[1931,39923,39924,39926],{},[898,39925,1904],{},[1864,39927,1866],{},[902,39929,29695],{"encoding":904},", které odpovídá ceně ",[883,39932,39934],{"className":39933},[886],[888,39935,39936],{"xmlns":890},[892,39937,39938,39950],{},[895,39939,39940,39946,39948],{},[1931,39941,39942,39944],{},[898,39943,1746],{},[1864,39945,2256],{},[1723,39947,2087],{},[898,39949,1754],{},[902,39951,39952],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,39955,39957],{"className":39956},[886],[888,39958,39959],{"xmlns":890,"display":28759},[892,39960,39961,39995],{},[895,39962,39963,39965,39967,39973,39975,39977,39979,39981,39983,39985,39987,39989,39991,39993],{},[898,39964,1746],{},[1723,39966,1725],{},[1931,39968,39969,39971],{},[898,39970,4897],{},[1864,39972,1866],{},[1723,39974,1908],{"stretchy":1907},[898,39976,1904],{},[1723,39978,1914],{"stretchy":1907},[1723,39980,1725],{},[898,39982,4897],{},[1723,39984,1908],{"stretchy":1907},[898,39986,1904],{},[1723,39988,1914],{"stretchy":1907},[1723,39990,1759],{},[898,39992,1754],{},[1723,39994,2031],{"separator":2030},[902,39996,39997],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,39999,40000,40001,1664],{},"tj. dojde k ",[38,40002,40003],{},"posunu poptávky doleva",[724,40005,40006],{},[614,40007,40008,40009,40030,40031,1343,40048,1343,40061,40082,40083,1682,40100,1664],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,40010,40012],{"className":40011},[886],[888,40013,40014],{"xmlns":890},[892,40015,40016,40028],{},[895,40017,40018,40020,40022,40024,40026],{},[1723,40019,1908],{"stretchy":1907},[898,40021,1904],{},[1723,40023,2031],{"separator":2030},[898,40025,1746],{},[1723,40027,1914],{"stretchy":1907},[902,40029,38383],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,40032,40034],{"className":40033},[886],[888,40035,40036],{"xmlns":890},[892,40037,40038,40046],{},[895,40039,40040],{},[1931,40041,40042,40044],{},[898,40043,1746],{},[1864,40045,2256],{},[902,40047,39640],{"encoding":904},[883,40049,40051],{"className":40050},[886],[888,40052,40053],{"xmlns":890},[892,40054,40055,40059],{},[895,40056,40057],{},[898,40058,1754],{},[902,40060,1754],{"encoding":904},[883,40062,40064],{"className":40063},[886],[888,40065,40066],{"xmlns":890},[892,40067,40068,40080],{},[895,40069,40070,40076,40078],{},[1931,40071,40072,40074],{},[898,40073,1746],{},[1864,40075,2256],{},[1723,40077,2087],{},[898,40079,1754],{},[902,40081,39952],{"encoding":904},"; na vodorovné ",[883,40084,40086],{"className":40085},[886],[888,40087,40088],{"xmlns":890},[892,40089,40090,40098],{},[895,40091,40092],{},[1931,40093,40094,40096],{},[898,40095,1904],{},[1864,40097,1866],{},[902,40099,29695],{"encoding":904},[883,40101,40103],{"className":40102},[886],[888,40104,40105],{"xmlns":890},[892,40106,40107,40115],{},[895,40108,40109],{},[1931,40110,40111,40113],{},[898,40112,1904],{},[1864,40114,2256],{},[902,40116,39000],{"encoding":904},[198,40118,40120],{"id":40119},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,40122,40123],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,40125,40127],{"className":40126},[886],[888,40128,40129],{"xmlns":890,"display":28759},[892,40130,40131,40316],{},[21447,40132,40133],{"width":28764},[21452,40134,40135,40137,40309,40311],{},[21455,40136],{"width":28769},[21455,40138,40139],{},[21447,40140,40141,40225],{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},[21452,40142,40143,40153],{},[21455,40144,40145],{},[3055,40146,40147],{"scriptlevel":2256,"displaystyle":2030},[1931,40148,40149,40151],{},[898,40150,1904],{},[1864,40152,1866],{},[21455,40154,40155],{},[3055,40156,40157],{"scriptlevel":2256,"displaystyle":2030},[895,40158,40159,40161,40163,40169,40171,40177,40179,40185,40187,40189,40195,40197,40203,40209,40211,40217,40223],{},[895,40160],{},[1723,40162,1725],{},[1931,40164,40165,40167],{},[898,40166,4897],{},[1864,40168,1866],{},[1723,40170,1908],{"stretchy":1907},[1931,40172,40173,40175],{},[898,40174,1746],{},[1864,40176,1866],{},[1723,40178,2031],{"separator":2030},[1931,40180,40181,40183],{},[898,40182,1746],{},[1864,40184,2331],{},[1723,40186,1914],{"stretchy":1907},[1723,40188,1725],{},[1931,40190,40191,40193],{},[898,40192,207],{},[1864,40194,1866],{},[1723,40196,2087],{},[1931,40198,40199,40201],{},[898,40200,2069],{},[1864,40202,1866],{},[1931,40204,40205,40207],{},[898,40206,1746],{},[1864,40208,1866],{},[1723,40210,2087],{},[1931,40212,40213,40215],{},[898,40214,2878],{},[1864,40216,1866],{},[1931,40218,40219,40221],{},[898,40220,1746],{},[1864,40222,2331],{},[1723,40224,2031],{"separator":2030},[21452,40226,40227,40237],{},[21455,40228,40229],{},[3055,40230,40231],{"scriptlevel":2256,"displaystyle":2030},[1931,40232,40233,40235],{},[898,40234,1904],{},[1864,40236,2331],{},[21455,40238,40239],{},[3055,40240,40241],{"scriptlevel":2256,"displaystyle":2030},[895,40242,40243,40245,40247,40253,40255,40261,40263,40269,40271,40273,40279,40281,40287,40293,40295,40301,40307],{},[895,40244],{},[1723,40246,1725],{},[1931,40248,40249,40251],{},[898,40250,4897],{},[1864,40252,2331],{},[1723,40254,1908],{"stretchy":1907},[1931,40256,40257,40259],{},[898,40258,1746],{},[1864,40260,1866],{},[1723,40262,2031],{"separator":2030},[1931,40264,40265,40267],{},[898,40266,1746],{},[1864,40268,2331],{},[1723,40270,1914],{"stretchy":1907},[1723,40272,1725],{},[1931,40274,40275,40277],{},[898,40276,207],{},[1864,40278,2331],{},[1723,40280,2087],{},[1931,40282,40283,40285],{},[898,40284,2069],{},[1864,40286,2331],{},[1931,40288,40289,40291],{},[898,40290,1746],{},[1864,40292,1866],{},[1723,40294,2087],{},[1931,40296,40297,40299],{},[898,40298,2878],{},[1864,40300,2331],{},[1931,40302,40303,40305],{},[898,40304,1746],{},[1864,40306,2331],{},[898,40308,1664],{"mathvariant":2124},[21455,40310],{"width":28769},[21455,40312,40313],{},[3018,40314,40315],{},"(2.6)",[902,40317,40318],{"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}",[38040,40320,40322],{"id":40321},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,40324,40325,40372,40419],{},[123,40326,40327,1343,40349,40371],{},[883,40328,40330],{"className":40329},[886],[888,40331,40332],{"xmlns":890},[892,40333,40334,40346],{},[895,40335,40336,40342,40344],{},[1931,40337,40338,40340],{},[898,40339,207],{},[1864,40341,1866],{},[1723,40343,2253],{},[1864,40345,2256],{},[902,40347,40348],{"encoding":904},"a_1 > 0",[883,40350,40352],{"className":40351},[886],[888,40353,40354],{"xmlns":890},[892,40355,40356,40368],{},[895,40357,40358,40364,40366],{},[1931,40359,40360,40362],{},[898,40361,207],{},[1864,40363,2331],{},[1723,40365,2253],{},[1864,40367,2256],{},[902,40369,40370],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,40373,40374,1343,40396,40418],{},[883,40375,40377],{"className":40376},[886],[888,40378,40379],{"xmlns":890},[892,40380,40381,40393],{},[895,40382,40383,40389,40391],{},[1931,40384,40385,40387],{},[898,40386,2069],{},[1864,40388,1866],{},[1723,40390,2287],{},[1864,40392,2256],{},[902,40394,40395],{"encoding":904},"b_1 \u003C 0",[883,40397,40399],{"className":40398},[886],[888,40400,40401],{"xmlns":890},[892,40402,40403,40415],{},[895,40404,40405,40411,40413],{},[1931,40406,40407,40409],{},[898,40408,2878],{},[1864,40410,2331],{},[1723,40412,2287],{},[1864,40414,2256],{},[902,40416,40417],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,40420,40421,40422,1343,40439,40457,40458],{},"zkřížené koeficienty ",[883,40423,40425],{"className":40424},[886],[888,40426,40427],{"xmlns":890},[892,40428,40429,40437],{},[895,40430,40431],{},[1931,40432,40433,40435],{},[898,40434,2878],{},[1864,40436,1866],{},[902,40438,30492],{"encoding":904},[883,40440,40442],{"className":40441},[886],[888,40443,40444],{"xmlns":890},[892,40445,40446,40454],{},[895,40447,40448],{},[1931,40449,40450,40452],{},[898,40451,2069],{},[1864,40453,2331],{},[902,40455,40456],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,40459,40460,40510],{},[123,40461,40462,40465,40466,1343,40488,2031],{},[38,40463,40464],{},"substituty"," (máslo vs. margarín): ",[883,40467,40469],{"className":40468},[886],[888,40470,40471],{"xmlns":890},[892,40472,40473,40485],{},[895,40474,40475,40481,40483],{},[1931,40476,40477,40479],{},[898,40478,2878],{},[1864,40480,1866],{},[1723,40482,2253],{},[1864,40484,2256],{},[902,40486,40487],{"encoding":904},"c_1 > 0",[883,40489,40491],{"className":40490},[886],[888,40492,40493],{"xmlns":890},[892,40494,40495,40507],{},[895,40496,40497,40503,40505],{},[1931,40498,40499,40501],{},[898,40500,2069],{},[1864,40502,2331],{},[1723,40504,2253],{},[1864,40506,2256],{},[902,40508,40509],{"encoding":904},"b_2 > 0",[123,40511,40512,40515,40516,1343,40538,1664],{},[38,40513,40514],{},"komplementy"," (auto vs. benzín): ",[883,40517,40519],{"className":40518},[886],[888,40520,40521],{"xmlns":890},[892,40522,40523,40535],{},[895,40524,40525,40531,40533],{},[1931,40526,40527,40529],{},[898,40528,2878],{},[1864,40530,1866],{},[1723,40532,2287],{},[1864,40534,2256],{},[902,40536,40537],{"encoding":904},"c_1 \u003C 0",[883,40539,40541],{"className":40540},[886],[888,40542,40543],{"xmlns":890},[892,40544,40545,40557],{},[895,40546,40547,40553,40555],{},[1931,40548,40549,40551],{},[898,40550,2069],{},[1864,40552,2331],{},[1723,40554,2287],{},[1864,40556,2256],{},[902,40558,40559],{"encoding":904},"b_2 \u003C 0",[724,40561,40562],{},"Schematicky:",[724,40564,40565,40568],{},[38,40566,40567],{},"Substituty",[883,40569,40571],{"className":40570},[886],[888,40572,40573],{"xmlns":890},[892,40574,40575,40714],{},[895,40576,40577,40583,40585,40600,40602,40622,40624,40644,40646,40648,40654,40656,40670,40672,40692,40694],{},[1931,40578,40579,40581],{},[898,40580,1904],{},[1864,40582,1866],{},[1723,40584,1725],{},[898,40586,40587],{},[40588,40589,40590,40598],"munder",{},[1723,40591,40592],{},[1931,40593,40594,40596],{},[898,40595,207],{},[1864,40597,1866],{},[1723,40599,2087],{"lspace":2228,"rspace":2228},[1723,40601,2087],{},[898,40603,40604],{},[40588,40605,40606,40620],{},[1723,40607,40608,40614],{},[1931,40609,40610,40612],{},[898,40611,2069],{},[1864,40613,1866],{},[1931,40615,40616,40618],{},[898,40617,1746],{},[1864,40619,1866],{},[1723,40621,1759],{"lspace":2228,"rspace":2228},[1723,40623,2087],{},[898,40625,40626],{},[40588,40627,40628,40642],{},[1723,40629,40630,40636],{},[1931,40631,40632,40634],{},[898,40633,2878],{},[1864,40635,1866],{},[1931,40637,40638,40640],{},[898,40639,1746],{},[1864,40641,2331],{},[1723,40643,2087],{"lspace":2228,"rspace":2228},[1723,40645,2031],{"separator":2030},[6588,40647],{"width":6590},[1931,40649,40650,40652],{},[898,40651,1904],{},[1864,40653,2331],{},[1723,40655,1725],{},[898,40657,40658],{},[40588,40659,40660,40668],{},[1723,40661,40662],{},[1931,40663,40664,40666],{},[898,40665,207],{},[1864,40667,2331],{},[1723,40669,2087],{"lspace":2228,"rspace":2228},[1723,40671,2087],{},[898,40673,40674],{},[40588,40675,40676,40690],{},[1723,40677,40678,40684],{},[1931,40679,40680,40682],{},[898,40681,2069],{},[1864,40683,2331],{},[1931,40685,40686,40688],{},[898,40687,1746],{},[1864,40689,1866],{},[1723,40691,2087],{"lspace":2228,"rspace":2228},[1723,40693,2087],{},[898,40695,40696],{},[40588,40697,40698,40712],{},[1723,40699,40700,40706],{},[1931,40701,40702,40704],{},[898,40703,2878],{},[1864,40705,2331],{},[1931,40707,40708,40710],{},[898,40709,1746],{},[1864,40711,2331],{},[1723,40713,1759],{"lspace":2228,"rspace":2228},[902,40715,40716],{"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}",[724,40718,40719,40722],{},[38,40720,40721],{},"Komplementy",[883,40723,40725],{"className":40724},[886],[888,40726,40727],{"xmlns":890},[892,40728,40729,40867],{},[895,40730,40731,40737,40739,40753,40755,40775,40777,40797,40799,40801,40807,40809,40823,40825,40845,40847],{},[1931,40732,40733,40735],{},[898,40734,1904],{},[1864,40736,1866],{},[1723,40738,1725],{},[898,40740,40741],{},[40588,40742,40743,40751],{},[1723,40744,40745],{},[1931,40746,40747,40749],{},[898,40748,207],{},[1864,40750,1866],{},[1723,40752,2087],{"lspace":2228,"rspace":2228},[1723,40754,2087],{},[898,40756,40757],{},[40588,40758,40759,40773],{},[1723,40760,40761,40767],{},[1931,40762,40763,40765],{},[898,40764,2069],{},[1864,40766,1866],{},[1931,40768,40769,40771],{},[898,40770,1746],{},[1864,40772,1866],{},[1723,40774,1759],{"lspace":2228,"rspace":2228},[1723,40776,2087],{},[898,40778,40779],{},[40588,40780,40781,40795],{},[1723,40782,40783,40789],{},[1931,40784,40785,40787],{},[898,40786,2878],{},[1864,40788,1866],{},[1931,40790,40791,40793],{},[898,40792,1746],{},[1864,40794,2331],{},[1723,40796,1759],{"lspace":2228,"rspace":2228},[1723,40798,2031],{"separator":2030},[6588,40800],{"width":6590},[1931,40802,40803,40805],{},[898,40804,1904],{},[1864,40806,2331],{},[1723,40808,1725],{},[898,40810,40811],{},[40588,40812,40813,40821],{},[1723,40814,40815],{},[1931,40816,40817,40819],{},[898,40818,207],{},[1864,40820,2331],{},[1723,40822,2087],{"lspace":2228,"rspace":2228},[1723,40824,2087],{},[898,40826,40827],{},[40588,40828,40829,40843],{},[1723,40830,40831,40837],{},[1931,40832,40833,40835],{},[898,40834,2069],{},[1864,40836,2331],{},[1931,40838,40839,40841],{},[898,40840,1746],{},[1864,40842,1866],{},[1723,40844,1759],{"lspace":2228,"rspace":2228},[1723,40846,2087],{},[898,40848,40849],{},[40588,40850,40851,40865],{},[1723,40852,40853,40859],{},[1931,40854,40855,40857],{},[898,40856,2878],{},[1864,40858,2331],{},[1931,40860,40861,40863],{},[898,40862,1746],{},[1864,40864,2331],{},[1723,40866,1759],{"lspace":2228,"rspace":2228},[902,40868,40869],{"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}",[37662,40871],{},[115,40873,13826],{"id":37472},[4584,40875,40876],{},[724,40877,40878,40880,40881,37686,40894,37700,40907,40910,40911,6379,40935,40953],{},[883,40879,4869],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,40882,40884],{"className":40883},[886],[888,40885,40886],{"xmlns":890},[892,40887,40888,40892],{},[895,40889,40890],{},[898,40891,1904],{},[902,40893,1904],{"encoding":904},[883,40895,40897],{"className":40896},[886],[888,40898,40899],{"xmlns":890},[892,40900,40901,40905],{},[895,40902,40903],{},[898,40904,1746],{},[902,40906,1746],{"encoding":904},[38,40908,40909],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,40912,40914],{"className":40913},[886],[888,40915,40916],{"xmlns":890},[892,40917,40918,40932],{},[895,40919,40920,40922,40924,40926,40928,40930],{},[898,40921,1746],{},[1723,40923,1725],{},[898,40925,2878],{},[898,40927,1904],{},[1723,40929,2087],{},[898,40931,2930],{},[902,40933,40934],{"encoding":904},"P = cQ + d",[883,40936,40938],{"className":40937},[886],[888,40939,40940],{"xmlns":890},[892,40941,40942,40950],{},[895,40943,40944,40946,40948],{},[898,40945,2878],{},[1723,40947,2253],{},[1864,40949,2256],{},[902,40951,40952],{"encoding":904},"c > 0"," je standardní aproximací.",[198,40955,37756],{"id":40956},"obecný-vícefaktorový-model-1",[724,40958,40959,1981,40962,40965,40966,40979,40980,37588,40993,37602,41006,41019,41020,41034,41035,37631,41048,41061],{},[38,40960,40961],{},"Nabízené množství",[614,40963,40964],{},"quantity supplied",") závisí na ceně ",[883,40967,40969],{"className":40968},[886],[888,40970,40971],{"xmlns":890},[892,40972,40973,40977],{},[895,40974,40975],{},[898,40976,1746],{},[902,40978,1746],{"encoding":904},", cenách výrobních faktorů (práce ",[883,40981,40983],{"className":40982},[886],[888,40984,40985],{"xmlns":890},[892,40986,40987,40991],{},[895,40988,40989],{},[898,40990,1911],{},[902,40992,1911],{"encoding":904},[883,40994,40996],{"className":40995},[886],[888,40997,40998],{"xmlns":890},[892,40999,41000,41004],{},[895,41001,41002],{},[898,41003,2034],{},[902,41005,2034],{"encoding":904},[883,41007,41009],{"className":41008},[886],[888,41010,41011],{"xmlns":890},[892,41012,41013,41017],{},[895,41014,41015],{},[898,41016,1846],{},[902,41018,1846],{"encoding":904},"), očekávání ",[883,41021,41023],{"className":41022},[886],[888,41024,41025],{"xmlns":890},[892,41026,41027,41032],{},[895,41028,41029],{},[898,41030,41031],{},"V",[902,41033,41031],{"encoding":904},", počtu výrobců ",[883,41036,41038],{"className":41037},[886],[888,41039,41040],{"xmlns":890},[892,41041,41042,41046],{},[895,41043,41044],{},[898,41045,37628],{},[902,41047,37628],{"encoding":904},[883,41049,41051],{"className":41050},[886],[888,41052,41053],{"xmlns":890},[892,41054,41055,41059],{},[895,41056,41057],{},[898,41058,37643],{},[902,41060,37643],{"encoding":904}," a dalších:",[883,41063,41065],{"className":41064},[886],[888,41066,41067],{"xmlns":890,"display":28759},[892,41068,41069,41128],{},[21447,41070,41071],{"width":28764},[21452,41072,41073,41075,41121,41123],{},[21455,41074],{"width":28769},[21455,41076,41077],{},[895,41078,41079,41081,41083,41085,41087,41089,41091,41093,41095,41097,41099,41101,41103,41105,41107,41109,41111,41113,41115,41117,41119],{},[898,41080,1904],{},[1723,41082,1725],{},[898,41084,2111],{},[1723,41086,1908],{"stretchy":1907},[898,41088,1746],{},[1723,41090,2031],{"separator":2030},[898,41092,1911],{},[1723,41094,2031],{"separator":2030},[898,41096,2034],{},[1723,41098,2031],{"separator":2030},[898,41100,1846],{},[1723,41102,2031],{"separator":2030},[898,41104,41031],{},[1723,41106,2031],{"separator":2030},[898,41108,37628],{},[1723,41110,2031],{"separator":2030},[898,41112,37643],{},[1723,41114,2031],{"separator":2030},[1723,41116,2183],{},[1723,41118,1914],{"stretchy":1907},[898,41120,1664],{"mathvariant":2124},[21455,41122],{"width":28769},[21455,41124,41125],{},[3018,41126,41127],{},"(2.7)",[902,41129,41130],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,41132,39108,41133,1981,41136,41139],{},[38,41134,41135],{},"funkce nabídky",[614,41137,41138],{},"supply function",") v širším slova smyslu.",[198,41141,41143],{"id":41142},"jednofaktorový-model","Jednofaktorový model",[724,41145,41146],{},"V nejpřirozenějším jednofaktorovém modelu",[883,41148,41150],{"className":41149},[886],[888,41151,41152],{"xmlns":890,"display":28759},[892,41153,41154,41205],{},[21447,41155,41156],{"width":28764},[21452,41157,41158,41160,41198,41200],{},[21455,41159],{"width":28769},[21455,41161,41162],{},[895,41163,41164,41166,41168,41170,41172,41174,41176,41178,41180,41182,41184,41186,41188,41190,41192,41194,41196],{},[898,41165,1904],{},[1723,41167,1725],{},[898,41169,2111],{},[1723,41171,1908],{"stretchy":1907},[898,41173,1746],{},[1723,41175,1914],{"stretchy":1907},[1723,41177,2031],{"separator":2030},[6588,41179],{"width":6590},[3018,41181,38109],{},[6588,41183],{"width":6590},[898,41185,1746],{},[1723,41187,1725],{},[898,41189,2111],{},[1723,41191,1908],{"stretchy":1907},[898,41193,1904],{},[1723,41195,1914],{"stretchy":1907},[898,41197,1664],{"mathvariant":2124},[21455,41199],{"width":28769},[21455,41201,41202],{},[3018,41203,41204],{},"(2.8)",[902,41206,41207],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,41209,41210,41211,1981,41214,4634],{},"Graf je ",[38,41212,41213],{},"křivka nabídky",[614,41215,41216],{},"supply curve",[38040,41218,41220],{"id":41219},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[4584,41222,41223],{},[724,41224,41225],{},[38,41226,38155,41227,41240,41241,38210],{},[883,41228,41230],{"className":41229},[886],[888,41231,41232],{"xmlns":890},[892,41233,41234,41238],{},[895,41235,41236],{},[898,41237,1746],{},[902,41239,1746],{"encoding":904},", pak nabízené množství ",[883,41242,41244],{"className":41243},[886],[888,41245,41246],{"xmlns":890},[892,41247,41248,41252],{},[895,41249,41250],{},[898,41251,1904],{},[902,41253,1904],{"encoding":904},[724,41255,41256,41257,41282,41283,41313,41314,41331],{},"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 ",[883,41258,41260],{"className":41259},[886],[888,41261,41262],{"xmlns":890},[892,41263,41264,41280],{},[895,41265,41266,41268,41270,41272,41278],{},[1723,41267,3212],{"stretchy":1907},[1864,41269,2256],{},[1723,41271,2031],{"separator":2030},[1931,41273,41274,41276],{},[898,41275,1746],{},[1864,41277,2256],{},[1723,41279,3227],{"stretchy":1907},[902,41281,38295],{"encoding":904}," na svislé ose (případně z ",[883,41284,41286],{"className":41285},[886],[888,41287,41288],{"xmlns":890},[892,41289,41290,41310],{},[895,41291,41292,41294,41300,41302,41308],{},[1723,41293,3212],{"stretchy":1907},[1931,41295,41296,41298],{},[898,41297,1904],{},[1864,41299,1866],{},[1723,41301,2031],{"separator":2030},[1931,41303,41304,41306],{},[898,41305,1746],{},[1864,41307,1866],{},[1723,41309,3227],{"stretchy":1907},[902,41311,41312],{"encoding":904},"[Q_1, P_1]","), kde ",[883,41315,41317],{"className":41316},[886],[888,41318,41319],{"xmlns":890},[892,41320,41321,41329],{},[895,41322,41323],{},[1931,41324,41325,41327],{},[898,41326,1746],{},[1864,41328,2256],{},[902,41330,39640],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,41333,41334],{},[614,41335,41336,41337,4436,41350,1664],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,41338,41340],{"className":41339},[886],[888,41341,41342],{"xmlns":890},[892,41343,41344,41348],{},[895,41345,41346],{},[898,41347,2111],{},[902,41349,2111],{"encoding":904},[883,41351,41353],{"className":41352},[886],[888,41354,41355],{"xmlns":890},[892,41356,41357,41369],{},[895,41358,41359,41361,41363,41365,41367],{},[1723,41360,1908],{"stretchy":1907},[898,41362,1904],{},[1723,41364,2031],{"separator":2030},[898,41366,1746],{},[1723,41368,1914],{"stretchy":1907},[902,41370,38383],{"encoding":904},[38040,41372,41374],{"id":41373},"lineární-model-nabídky","Lineární model nabídky",[883,41376,41378],{"className":41377},[886],[888,41379,41380],{"xmlns":890,"display":28759},[892,41381,41382,41421],{},[21447,41383,41384],{"width":28764},[21452,41385,41386,41388,41414,41416],{},[21455,41387],{"width":28769},[21455,41389,41390],{},[895,41391,41392,41394,41396,41398,41400,41402,41404,41406,41408,41410,41412],{},[898,41393,1746],{},[1723,41395,1725],{},[898,41397,2878],{},[898,41399,1904],{},[1723,41401,2087],{},[898,41403,2930],{},[1723,41405,2031],{"separator":2030},[6588,41407],{"width":6590},[898,41409,2878],{},[1723,41411,2253],{},[1864,41413,13161],{},[21455,41415],{"width":28769},[21455,41417,41418],{},[3018,41419,41420],{},"(2.9)",[902,41422,41423],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,41425,41426,41427,41463,41464,41477],{},"Alternativně ",[883,41428,41430],{"className":41429},[886],[888,41431,41432],{"xmlns":890},[892,41433,41434,41460],{},[895,41435,41436,41438,41440,41448,41450,41452],{},[898,41437,1904],{},[1723,41439,1725],{},[3055,41441,41442],{"scriptlevel":2256,"displaystyle":1907},[3058,41443,41444,41446],{},[1864,41445,1866],{},[898,41447,2878],{},[898,41449,1746],{},[1723,41451,1759],{},[3055,41453,41454],{"scriptlevel":2256,"displaystyle":1907},[3058,41455,41456,41458],{},[898,41457,2930],{},[898,41459,2878],{},[902,41461,41462],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,41465,41467],{"className":41466},[886],[888,41468,41469],{"xmlns":890},[892,41470,41471,41475],{},[895,41472,41473],{},[898,41474,1746],{},[902,41476,1746],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[38617,41479,41481],{"id":41480},"příklad-25","Příklad 2.5",[724,41483,41484,41486,41487,1664],{},[38,41485,38625],{}," Lineární nabídka ",[883,41488,41490],{"className":41489},[886],[888,41491,41492],{"xmlns":890},[892,41493,41494,41508],{},[895,41495,41496,41498,41500,41502,41504,41506],{},[898,41497,1746],{},[1723,41499,1725],{},[1864,41501,5719],{},[898,41503,1904],{},[1723,41505,2087],{},[1864,41507,5714],{},[902,41509,41510],{"encoding":904},"P = 0{,}5Q + 25",[724,41512,41513,41515,41516,1664],{},[38,41514,38657],{}," Alternativní tvar ",[883,41517,41519],{"className":41518},[886],[888,41520,41521],{"xmlns":890},[892,41522,41523,41537],{},[895,41524,41525,41527,41529,41531,41533,41535],{},[898,41526,1904],{},[1723,41528,1725],{},[1864,41530,2331],{},[898,41532,1746],{},[1723,41534,1759],{},[1864,41536,3840],{},[902,41538,41539],{"encoding":904},"Q = 2P - 50",[16,41541,41542,41567],{},[19,41543,41544],{},[22,41545,41546,41561,41563,41565],{},[25,41547,41548],{},[883,41549,41551],{"className":41550},[886],[888,41552,41553],{"xmlns":890},[892,41554,41555,41559],{},[895,41556,41557],{},[898,41558,1746],{},[902,41560,1746],{"encoding":904},[25,41562,38711],{},[25,41564,15739],{},[25,41566,5921],{},[30,41568,41569],{},[22,41570,41571,41586,41588,41590],{},[35,41572,41573],{},[883,41574,41576],{"className":41575},[886],[888,41577,41578],{"xmlns":890},[892,41579,41580,41584],{},[895,41581,41582],{},[898,41583,1904],{},[902,41585,1904],{"encoding":904},[35,41587,3585],{},[35,41589,9744],{},[35,41591,38711],{},[198,41593,41595,41596,1914],{"id":41594},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,41597,41598],{},"shift of supply",[724,41600,41601,41602,41605,41606,41623,41624,41649,41650,1664],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,41603,41604],{},"doprava",": při stejné ceně ",[883,41607,41609],{"className":41608},[886],[888,41610,41611],{"xmlns":890},[892,41612,41613,41621],{},[895,41614,41615],{},[1931,41616,41617,41619],{},[898,41618,1746],{},[1864,41620,2256],{},[902,41622,39640],{"encoding":904}," vyrobí výrobce větší ",[883,41625,41627],{"className":41626},[886],[888,41628,41629],{"xmlns":890},[892,41630,41631,41647],{},[895,41632,41633,41639,41641],{},[1931,41634,41635,41637],{},[898,41636,1904],{},[1864,41638,1866],{},[1723,41640,2253],{},[1931,41642,41643,41645],{},[898,41644,1904],{},[1864,41646,2256],{},[902,41648,39753],{"encoding":904},"); zdražení vstupů posune křivku ",[38,41651,41652],{},"doleva",[724,41654,41655],{},[614,41656,41657,41658,41671,41672,41690,41691,41709,41710,1664],{},"Obrázek 2.11: Původní ",[883,41659,41661],{"className":41660},[886],[888,41662,41663],{"xmlns":890},[892,41664,41665,41669],{},[895,41666,41667],{},[898,41668,2111],{},[902,41670,2111],{"encoding":904},", posunuté ",[883,41673,41675],{"className":41674},[886],[888,41676,41677],{"xmlns":890},[892,41678,41679,41687],{},[895,41680,41681],{},[1931,41682,41683,41685],{},[898,41684,2111],{},[1864,41686,1866],{},[902,41688,41689],{"encoding":904},"S_1"," (doprava) a ",[883,41692,41694],{"className":41693},[886],[888,41695,41696],{"xmlns":890},[892,41697,41698,41706],{},[895,41699,41700],{},[1931,41701,41702,41704],{},[898,41703,2111],{},[1864,41705,2331],{},[902,41707,41708],{"encoding":904},"S_2"," (doleva) v ",[883,41711,41713],{"className":41712},[886],[888,41714,41715],{"xmlns":890},[892,41716,41717,41729],{},[895,41718,41719,41721,41723,41725,41727],{},[1723,41720,1908],{"stretchy":1907},[898,41722,1904],{},[1723,41724,2031],{"separator":2030},[898,41726,1746],{},[1723,41728,1914],{"stretchy":1907},[902,41730,38383],{"encoding":904},[38617,41732,41734],{"id":41733},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,41736,41737,41739,41740,41764,41765,1664],{},[38,41738,38625],{}," Nabídka ",[883,41741,41743],{"className":41742},[886],[888,41744,41745],{"xmlns":890},[892,41746,41747,41761],{},[895,41748,41749,41751,41753,41755,41757,41759],{},[898,41750,1746],{},[1723,41752,1725],{},[898,41754,2111],{},[1723,41756,1908],{"stretchy":1907},[898,41758,1904],{},[1723,41760,1914],{"stretchy":1907},[902,41762,41763],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,41766,41768],{"className":41767},[886],[888,41769,41770],{"xmlns":890},[892,41771,41772,41776],{},[895,41773,41774],{},[898,41775,1754],{},[902,41777,1754],{"encoding":904},[724,41779,41780,41782,41783,41796,41797,41815,41816,41844],{},[38,41781,38657],{}," Spotřebitel zaplatí ",[883,41784,41786],{"className":41785},[886],[888,41787,41788],{"xmlns":890},[892,41789,41790,41794],{},[895,41791,41792],{},[898,41793,1746],{},[902,41795,1746],{"encoding":904},", výrobce obdrží ",[883,41798,41800],{"className":41799},[886],[888,41801,41802],{"xmlns":890},[892,41803,41804,41812],{},[895,41805,41806,41808,41810],{},[898,41807,1746],{},[1723,41809,1759],{},[898,41811,1754],{},[902,41813,41814],{"encoding":904},"P - T",". Z podmínky ",[883,41817,41819],{"className":41818},[886],[888,41820,41821],{"xmlns":890},[892,41822,41823,41841],{},[895,41824,41825,41827,41829,41831,41833,41835,41837,41839],{},[898,41826,1746],{},[1723,41828,1759],{},[898,41830,1754],{},[1723,41832,1725],{},[898,41834,2111],{},[1723,41836,1908],{"stretchy":1907},[898,41838,1904],{},[1723,41840,1914],{"stretchy":1907},[902,41842,41843],{"encoding":904},"P - T = S(Q)"," plyne",[883,41846,41848],{"className":41847},[886],[888,41849,41850],{"xmlns":890,"display":28759},[892,41851,41852,41886],{},[895,41853,41854,41856,41858,41864,41866,41868,41870,41872,41874,41876,41878,41880,41882,41884],{},[898,41855,1746],{},[1723,41857,1725],{},[1931,41859,41860,41862],{},[898,41861,2111],{},[1864,41863,1866],{},[1723,41865,1908],{"stretchy":1907},[898,41867,1904],{},[1723,41869,1914],{"stretchy":1907},[1723,41871,1725],{},[898,41873,2111],{},[1723,41875,1908],{"stretchy":1907},[898,41877,1904],{},[1723,41879,1914],{"stretchy":1907},[1723,41881,2087],{},[898,41883,1754],{},[898,41885,1664],{"mathvariant":2124},[902,41887,41888],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,41890,41891,41892,41905,41906,2628,41919,41922,41923,1682,41943,8812,41961,1664],{},"Křivka ",[883,41893,41895],{"className":41894},[886],[888,41896,41897],{"xmlns":890},[892,41898,41899,41903],{},[895,41900,41901],{},[898,41902,2111],{},[902,41904,2111],{"encoding":904}," se tedy posune o ",[883,41907,41909],{"className":41908},[886],[888,41910,41911],{"xmlns":890},[892,41912,41913,41917],{},[895,41914,41915],{},[898,41916,1754],{},[902,41918,1754],{"encoding":904},[38,41920,41921],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,41924,41926],{"className":41925},[886],[888,41927,41928],{"xmlns":890},[892,41929,41930,41940],{},[895,41931,41932,41934,41936,41938],{},[898,41933,1746],{},[1723,41935,1725],{},[1864,41937,2331],{},[898,41939,1904],{},[902,41941,41942],{"encoding":904},"P = 2Q",[883,41944,41946],{"className":41945},[886],[888,41947,41948],{"xmlns":890},[892,41949,41950,41958],{},[895,41951,41952,41954,41956],{},[898,41953,1754],{},[1723,41955,1725],{},[1864,41957,2969],{},[902,41959,41960],{"encoding":904},"T = 6",[883,41962,41964],{"className":41963},[886],[888,41965,41966],{"xmlns":890},[892,41967,41968,41990],{},[895,41969,41970,41976,41978,41980,41982,41984,41986,41988],{},[1931,41971,41972,41974],{},[898,41973,2111],{},[1864,41975,1866],{},[1723,41977,3430],{},[898,41979,1746],{},[1723,41981,1725],{},[1864,41983,2331],{},[898,41985,1904],{},[1723,41987,2087],{},[1864,41989,2969],{},[902,41991,41992],{"encoding":904},"S_1: P = 2Q + 6",[724,41994,41995],{},[614,41996,41997,41998,42011],{},"Obrázek 2.12: Posun nabídky o ",[883,41999,42001],{"className":42000},[886],[888,42002,42003],{"xmlns":890},[892,42004,42005,42009],{},[895,42006,42007],{},[898,42008,1754],{},[902,42010,1754],{"encoding":904}," svisle nahoru.",[37662,42013],{},[115,42015,42017],{"id":42016},"tržní-rovnováha","Tržní rovnováha",[4584,42019,42020],{},[724,42021,42022,42024,42025,2628,42028,42060,42061,1343,42084,42107,42108,42111,42112,42125],{},[883,42023,4869],{}," TL;DR\nV ",[38,42026,42027],{},"rovnovážném bodě",[883,42029,42031],{"className":42030},[886],[888,42032,42033],{"xmlns":890},[892,42034,42035,42057],{},[895,42036,42037,42039,42041,42047,42049,42055],{},[898,42038,1846],{},[1723,42040,3212],{"stretchy":1907},[2057,42042,42043,42045],{},[898,42044,1904],{},[898,42046,1846],{},[1723,42048,2031],{"separator":2030},[2057,42050,42051,42053],{},[898,42052,1746],{},[898,42054,1846],{},[1723,42056,3227],{"stretchy":1907},[902,42058,42059],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,42062,42064],{"className":42063},[886],[888,42065,42066],{"xmlns":890},[892,42067,42068,42082],{},[895,42069,42070,42072,42074,42076,42078,42080],{},[898,42071,1746],{},[1723,42073,1725],{},[898,42075,4897],{},[1723,42077,1908],{"stretchy":1907},[898,42079,1904],{},[1723,42081,1914],{"stretchy":1907},[902,42083,5351],{"encoding":904},[883,42085,42087],{"className":42086},[886],[888,42088,42089],{"xmlns":890},[892,42090,42091,42105],{},[895,42092,42093,42095,42097,42099,42101,42103],{},[898,42094,1746],{},[1723,42096,1725],{},[898,42098,2111],{},[1723,42100,1908],{"stretchy":1907},[898,42102,1904],{},[1723,42104,1914],{"stretchy":1907},[902,42106,41763],{"encoding":904},". Čtyři ",[38,42109,42110],{},"pravidla komparativní statiky"," popisují, jak se ",[883,42113,42115],{"className":42114},[886],[888,42116,42117],{"xmlns":890},[892,42118,42119,42123],{},[895,42120,42121],{},[898,42122,1846],{},[902,42124,1846],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,42127,42129],{"id":42128},"definice","Definice",[724,42131,42132,1981,42134,42137,42138,2628,42141,42159,42160,42191,42192,1981,42195,4634],{},[38,42133,42017],{},[614,42135,42136],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,42139,42140],{},"rovnovážné ceně",[883,42142,42144],{"className":42143},[886],[888,42145,42146],{"xmlns":890},[892,42147,42148,42156],{},[895,42149,42150],{},[2057,42151,42152,42154],{},[898,42153,1746],{},[898,42155,1846],{},[902,42157,42158],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,42161,42163],{"className":42162},[886],[888,42164,42165],{"xmlns":890},[892,42166,42167,42189],{},[895,42168,42169,42171,42173,42179,42181,42187],{},[898,42170,1846],{},[1723,42172,3212],{"stretchy":1907},[2057,42174,42175,42177],{},[898,42176,1904],{},[898,42178,1846],{},[1723,42180,2031],{"separator":2030},[2057,42182,42183,42185],{},[898,42184,1746],{},[898,42186,1846],{},[1723,42188,3227],{"stretchy":1907},[902,42190,42059],{"encoding":904}," se nazývá ",[38,42193,42194],{},"rovnovážný bod",[614,42196,42197],{},"equilibrium point",[724,42199,42200,42201,1343,42224,1664],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,42202,42204],{"className":42203},[886],[888,42205,42206],{"xmlns":890},[892,42207,42208,42222],{},[895,42209,42210,42212,42214,42216,42218,42220],{},[898,42211,1746],{},[1723,42213,1725],{},[898,42215,4897],{},[1723,42217,1908],{"stretchy":1907},[898,42219,1904],{},[1723,42221,1914],{"stretchy":1907},[902,42223,5351],{"encoding":904},[883,42225,42227],{"className":42226},[886],[888,42228,42229],{"xmlns":890},[892,42230,42231,42245],{},[895,42232,42233,42235,42237,42239,42241,42243],{},[898,42234,1746],{},[1723,42236,1725],{},[898,42238,2111],{},[1723,42240,1908],{"stretchy":1907},[898,42242,1904],{},[1723,42244,1914],{"stretchy":1907},[902,42246,41763],{"encoding":904},[724,42248,42249],{},[3285,42250],{"alt":42251,"className":42252,"src":42253},"imek-poptavka-nabidka-rovnovaha",[210,3289],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,42255,42256],{},[614,42257,42258,42259,42272,42273,14712,42286,42307,42308,1664],{},"Obrázek 2.13: Klesající ",[883,42260,42262],{"className":42261},[886],[888,42263,42264],{"xmlns":890},[892,42265,42266,42270],{},[895,42267,42268],{},[898,42269,4897],{},[902,42271,4897],{"encoding":904}," a rostoucí ",[883,42274,42276],{"className":42275},[886],[888,42277,42278],{"xmlns":890},[892,42279,42280,42284],{},[895,42281,42282],{},[898,42283,2111],{},[902,42285,2111],{"encoding":904},[883,42287,42289],{"className":42288},[886],[888,42290,42291],{"xmlns":890},[892,42292,42293,42305],{},[895,42294,42295,42297,42299,42301,42303],{},[1723,42296,1908],{"stretchy":1907},[898,42298,1904],{},[1723,42300,2031],{"separator":2030},[898,42302,1746],{},[1723,42304,1914],{"stretchy":1907},[902,42306,38383],{"encoding":904}," protínající se v ",[883,42309,42311],{"className":42310},[886],[888,42312,42313],{"xmlns":890},[892,42314,42315,42337],{},[895,42316,42317,42319,42321,42327,42329,42335],{},[898,42318,1846],{},[1723,42320,3212],{"stretchy":1907},[2057,42322,42323,42325],{},[898,42324,1904],{},[898,42326,1846],{},[1723,42328,2031],{"separator":2030},[2057,42330,42331,42333],{},[898,42332,1746],{},[898,42334,1846],{},[1723,42336,3227],{"stretchy":1907},[902,42338,42059],{"encoding":904},[198,42340,42342],{"id":42341},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,42344,42345,42347,42348,42382,42383,1664],{},[38,42346,38625],{}," Poptávka ",[883,42349,42351],{"className":42350},[886],[888,42352,42353],{"xmlns":890},[892,42354,42355,42379],{},[895,42356,42357,42359,42361,42363,42369,42371,42373,42375,42377],{},[898,42358,1746],{},[1723,42360,1725],{},[1723,42362,1759],{},[2057,42364,42365,42367],{},[898,42366,1904],{},[1864,42368,2331],{},[1723,42370,1759],{},[1864,42372,3585],{},[898,42374,1904],{},[1723,42376,2087],{},[1864,42378,9512],{},[902,42380,42381],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,42384,42386],{"className":42385},[886],[888,42387,42388],{"xmlns":890},[892,42389,42390,42412],{},[895,42391,42392,42394,42396,42402,42404,42406,42408,42410],{},[898,42393,1746],{},[1723,42395,1725],{},[2057,42397,42398,42400],{},[898,42399,1904],{},[1864,42401,2331],{},[1723,42403,2087],{},[1864,42405,23639],{},[898,42407,1904],{},[1723,42409,2087],{},[1864,42411,33239],{},[902,42413,42414],{"encoding":904},"P = Q^2 + 14Q + 22",[724,42416,42417,42419],{},[38,42418,38657],{}," Z rovnosti",[883,42421,42423],{"className":42422},[886],[888,42424,42425],{"xmlns":890,"display":28759},[892,42426,42427,42465],{},[895,42428,42429,42431,42437,42439,42441,42443,42445,42447,42449,42455,42457,42459,42461,42463],{},[1723,42430,1759],{},[2057,42432,42433,42435],{},[898,42434,1904],{},[1864,42436,2331],{},[1723,42438,1759],{},[1864,42440,3585],{},[898,42442,1904],{},[1723,42444,2087],{},[1864,42446,9512],{},[1723,42448,1725],{},[2057,42450,42451,42453],{},[898,42452,1904],{},[1864,42454,2331],{},[1723,42456,2087],{},[1864,42458,23639],{},[898,42460,1904],{},[1723,42462,2087],{},[1864,42464,33239],{},[902,42466,42467],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,42469,42470,42471,42506,42507,42540,42541,42558,42559,42572,42573,1343,42595,42632,42633,1664],{},"dostaneme ",[883,42472,42474],{"className":42473},[886],[888,42475,42476],{"xmlns":890},[892,42477,42478,42503],{},[895,42479,42480,42482,42488,42490,42493,42495,42497,42499,42501],{},[1864,42481,2331],{},[2057,42483,42484,42486],{},[898,42485,1904],{},[1864,42487,2331],{},[1723,42489,2087],{},[1864,42491,42492],{},"24",[898,42494,1904],{},[1723,42496,1759],{},[1864,42498,6327],{},[1723,42500,1725],{},[1864,42502,2256],{},[902,42504,42505],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,42508,42510],{"className":42509},[886],[888,42511,42512],{"xmlns":890},[892,42513,42514,42537],{},[895,42515,42516,42522,42524,42526,42528,42530,42533,42535],{},[2057,42517,42518,42520],{},[898,42519,1904],{},[1864,42521,2331],{},[1723,42523,2087],{},[1864,42525,4227],{},[898,42527,1904],{},[1723,42529,1759],{},[1864,42531,42532],{},"64",[1723,42534,1725],{},[1864,42536,2256],{},[902,42538,42539],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,42542,42544],{"className":42543},[886],[888,42545,42546],{"xmlns":890},[892,42547,42548,42555],{},[895,42549,42550,42552],{},[1723,42551,1759],{},[1864,42553,42554],{},"16",[902,42556,42557],{"encoding":904},"-16"," (nevyhovuje) a ",[883,42560,42562],{"className":42561},[886],[888,42563,42564],{"xmlns":890},[892,42565,42566,42570],{},[895,42567,42568],{},[1864,42569,3080],{},[902,42571,3080],{"encoding":904},". Tedy ",[883,42574,42576],{"className":42575},[886],[888,42577,42578],{"xmlns":890},[892,42579,42580,42592],{},[895,42581,42582,42588,42590],{},[2057,42583,42584,42586],{},[898,42585,1904],{},[898,42587,1846],{},[1723,42589,1725],{},[1864,42591,3080],{},[902,42593,42594],{"encoding":904},"Q^E = 4",[883,42596,42598],{"className":42597},[886],[888,42599,42600],{"xmlns":890},[892,42601,42602,42629],{},[895,42603,42604,42610,42612,42614,42616,42618,42620,42622,42624,42626],{},[2057,42605,42606,42608],{},[898,42607,1746],{},[898,42609,1846],{},[1723,42611,1725],{},[1723,42613,1759],{},[1864,42615,42554],{},[1723,42617,1759],{},[1864,42619,5921],{},[1723,42621,2087],{},[1864,42623,9512],{},[1723,42625,1725],{},[1864,42627,42628],{},"94",[902,42630,42631],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,42634,42636],{"className":42635},[886],[888,42637,42638],{"xmlns":890},[892,42639,42640,42654],{},[895,42641,42642,42644,42646,42648,42650,42652],{},[898,42643,1846],{},[1723,42645,3212],{"stretchy":1907},[1864,42647,3080],{},[1723,42649,2031],{"separator":2030},[1864,42651,42628],{},[1723,42653,3227],{"stretchy":1907},[902,42655,42656],{"encoding":904},"E[4, 94]",[198,42658,42660],{"id":42659},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,42662,42663,42665],{},[38,42664,38625],{}," Poptávky a nabídky dvou zboží",[883,42667,42669],{"className":42668},[886],[888,42670,42671],{"xmlns":890,"display":28759},[892,42672,42673,42839],{},[21447,42674,42677,42765],{"rowspacing":21449,"columnalign":42675,"columnspacing":42676},"right left right left","0em 1em 0em",[21452,42678,42679,42689,42721,42731],{},[21455,42680,42681],{},[3055,42682,42683],{"scriptlevel":2256,"displaystyle":2030},[1931,42684,42685,42687],{},[898,42686,1904],{},[1864,42688,1866],{},[21455,42690,42691],{},[3055,42692,42693],{"scriptlevel":2256,"displaystyle":2030},[895,42694,42695,42697,42699,42701,42703,42705,42711,42713,42719],{},[895,42696],{},[1723,42698,1725],{},[1864,42700,5921],{},[1723,42702,1759],{},[1864,42704,2962],{},[1931,42706,42707,42709],{},[898,42708,1746],{},[1864,42710,1866],{},[1723,42712,1759],{},[1931,42714,42715,42717],{},[898,42716,1746],{},[1864,42718,2331],{},[1723,42720,2031],{"separator":2030},[21455,42722,42723],{},[3055,42724,42725],{"scriptlevel":2256,"displaystyle":2030},[1931,42726,42727,42729],{},[898,42728,1904],{},[1864,42730,2331],{},[21455,42732,42733],{},[3055,42734,42735],{"scriptlevel":2256,"displaystyle":2030},[895,42736,42737,42739,42741,42743,42745,42747,42753,42755,42757,42763],{},[895,42738],{},[1723,42740,1725],{},[1864,42742,3840],{},[1723,42744,1759],{},[1864,42746,2331],{},[1931,42748,42749,42751],{},[898,42750,1746],{},[1864,42752,1866],{},[1723,42754,1759],{},[1864,42756,3080],{},[1931,42758,42759,42761],{},[898,42760,1746],{},[1864,42762,2331],{},[1723,42764,2031],{"separator":2030},[21452,42766,42767,42777,42803,42813],{},[21455,42768,42769],{},[3055,42770,42771],{"scriptlevel":2256,"displaystyle":2030},[1931,42772,42773,42775],{},[898,42774,1904],{},[1864,42776,1866],{},[21455,42778,42779],{},[3055,42780,42781],{"scriptlevel":2256,"displaystyle":2030},[895,42782,42783,42785,42787,42789,42791,42793,42795,42801],{},[895,42784],{},[1723,42786,1725],{},[1723,42788,1759],{},[1864,42790,2909],{},[1723,42792,2087],{},[1864,42794,3080],{},[1931,42796,42797,42799],{},[898,42798,1746],{},[1864,42800,1866],{},[1723,42802,2031],{"separator":2030},[21455,42804,42805],{},[3055,42806,42807],{"scriptlevel":2256,"displaystyle":2030},[1931,42808,42809,42811],{},[898,42810,1904],{},[1864,42812,2331],{},[21455,42814,42815],{},[3055,42816,42817],{"scriptlevel":2256,"displaystyle":2030},[895,42818,42819,42821,42823,42825,42827,42829,42831,42837],{},[895,42820],{},[1723,42822,1725],{},[1723,42824,1759],{},[1864,42826,24894],{},[1723,42828,2087],{},[1864,42830,2909],{},[1931,42832,42833,42835],{},[898,42834,1746],{},[1864,42836,2331],{},[898,42838,1664],{"mathvariant":2124},[902,42840,42841],{"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}",[724,42843,42844,42846],{},[38,42845,38657],{}," Z rovností poptávek a nabídek dostaneme",[883,42848,42850],{"className":42849},[886],[888,42851,42852],{"xmlns":890,"display":28759},[892,42853,42854,42903],{},[895,42855,42856,42858,42864,42866,42872,42874,42876,42878,42880,42882,42888,42890,42892,42898,42900],{},[1864,42857,4713],{},[1931,42859,42860,42862],{},[898,42861,1746],{},[1864,42863,1866],{},[1723,42865,2087],{},[1931,42867,42868,42870],{},[898,42869,1746],{},[1864,42871,2331],{},[1723,42873,1725],{},[1864,42875,21896],{},[1723,42877,2031],{"separator":2030},[6588,42879],{"width":6590},[1864,42881,2331],{},[1931,42883,42884,42886],{},[898,42885,1746],{},[1864,42887,1866],{},[1723,42889,2087],{},[1864,42891,24894],{},[1931,42893,42894,42896],{},[898,42895,1746],{},[1864,42897,2331],{},[1723,42899,1725],{},[1864,42901,42902],{},"57.",[902,42904,42905],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,42907,42908,42909,1343,42933,42957,42958,1343,42983,43007,43008,43010],{},"Řešením je ",[883,42910,42912],{"className":42911},[886],[888,42913,42914],{"xmlns":890},[892,42915,42916,42930],{},[895,42917,42918,42926,42928],{},[2220,42919,42920,42922,42924],{},[898,42921,1746],{},[1864,42923,1866],{},[898,42925,1846],{},[1723,42927,1725],{},[1864,42929,3080],{},[902,42931,42932],{"encoding":904},"P_1^E = 4",[883,42934,42936],{"className":42935},[886],[888,42937,42938],{"xmlns":890},[892,42939,42940,42954],{},[895,42941,42942,42950,42952],{},[2220,42943,42944,42946,42948],{},[898,42945,1746],{},[1864,42947,2331],{},[898,42949,1846],{},[1723,42951,1725],{},[1864,42953,24894],{},[902,42955,42956],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,42959,42961],{"className":42960},[886],[888,42962,42963],{"xmlns":890},[892,42964,42965,42980],{},[895,42966,42967,42975,42977],{},[2220,42968,42969,42971,42973],{},[898,42970,1904],{},[1864,42972,1866],{},[898,42974,1846],{},[1723,42976,1725],{},[1864,42978,42979],{},"13",[902,42981,42982],{"encoding":904},"Q_1^E = 13",[883,42984,42986],{"className":42985},[886],[888,42987,42988],{"xmlns":890},[892,42989,42990,43004],{},[895,42991,42992,43000,43002],{},[2220,42993,42994,42996,42998],{},[898,42995,1904],{},[1864,42997,2331],{},[898,42999,1846],{},[1723,43001,1725],{},[1864,43003,23639],{},[902,43005,43006],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,43009,40514],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,43012,43014],{"id":43013},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,43016,43017,43018,43035,43036,1981,43039,4634],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,43019,43021],{"className":43020},[886],[888,43022,43023],{"xmlns":890},[892,43024,43025,43033],{},[895,43026,43027],{},[2057,43028,43029,43031],{},[898,43030,1746],{},[898,43032,1846],{},[902,43034,42158],{"encoding":904},"; mechanismus popisuje ",[38,43037,43038],{},"teorém pavučiny",[614,43040,43041],{},"cobweb model",[198,43043,43045],{"id":43044},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,43047,43048],{},[3285,43049],{"alt":43050,"className":43051,"src":43052},"imek-komparativni-statika-4pripady",[210,3289],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[4584,43054,43055,43096,43136,43176],{},[724,43056,43057,43060,43061,6900,43078,1664],{},[38,43058,43059],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,43062,43064],{"className":43063},[886],[888,43065,43066],{"xmlns":890},[892,43067,43068,43076],{},[895,43069,43070],{},[2057,43071,43072,43074],{},[898,43073,1746],{},[898,43075,1846],{},[902,43077,42158],{"encoding":904},[883,43079,43081],{"className":43080},[886],[888,43082,43083],{"xmlns":890},[892,43084,43085,43093],{},[895,43086,43087],{},[2057,43088,43089,43091],{},[898,43090,1904],{},[898,43092,1846],{},[902,43094,43095],{"encoding":904},"Q^E",[724,43097,43098,43101,43102,6900,43119,1664],{},[38,43099,43100],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,43103,43105],{"className":43104},[886],[888,43106,43107],{"xmlns":890},[892,43108,43109,43117],{},[895,43110,43111],{},[2057,43112,43113,43115],{},[898,43114,1746],{},[898,43116,1846],{},[902,43118,42158],{"encoding":904},[883,43120,43122],{"className":43121},[886],[888,43123,43124],{"xmlns":890},[892,43125,43126,43134],{},[895,43127,43128],{},[2057,43129,43130,43132],{},[898,43131,1904],{},[898,43133,1846],{},[902,43135,43095],{"encoding":904},[724,43137,43138,43141,43142,10063,43159,1664],{},[38,43139,43140],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,43143,43145],{"className":43144},[886],[888,43146,43147],{"xmlns":890},[892,43148,43149,43157],{},[895,43150,43151],{},[2057,43152,43153,43155],{},[898,43154,1746],{},[898,43156,1846],{},[902,43158,42158],{"encoding":904},[883,43160,43162],{"className":43161},[886],[888,43163,43164],{"xmlns":890},[892,43165,43166,43174],{},[895,43167,43168],{},[2057,43169,43170,43172],{},[898,43171,1904],{},[898,43173,1846],{},[902,43175,43095],{"encoding":904},[724,43177,43178,43181,43182,43199,43200,1664],{},[38,43179,43180],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,43183,43185],{"className":43184},[886],[888,43186,43187],{"xmlns":890},[892,43188,43189,43197],{},[895,43190,43191],{},[2057,43192,43193,43195],{},[898,43194,1746],{},[898,43196,1846],{},[902,43198,42158],{"encoding":904},", pokles ",[883,43201,43203],{"className":43202},[886],[888,43204,43205],{"xmlns":890},[892,43206,43207,43215],{},[895,43208,43209],{},[2057,43210,43211,43213],{},[898,43212,1904],{},[898,43214,1846],{},[902,43216,43095],{"encoding":904},[16,43218,43219,43264],{},[19,43220,43221],{},[22,43222,43223,43226,43245],{},[25,43224,43225],{},"Změna",[25,43227,43228],{},[883,43229,43231],{"className":43230},[886],[888,43232,43233],{"xmlns":890},[892,43234,43235,43243],{},[895,43236,43237],{},[2057,43238,43239,43241],{},[898,43240,1746],{},[898,43242,1846],{},[902,43244,42158],{"encoding":904},[25,43246,43247],{},[883,43248,43250],{"className":43249},[886],[888,43251,43252],{"xmlns":890},[892,43253,43254,43262],{},[895,43255,43256],{},[2057,43257,43258,43260],{},[898,43259,1904],{},[898,43261,1846],{},[902,43263,43095],{"encoding":904},[30,43265,43266,43276,43286,43295],{},[22,43267,43268,43271,43274],{},[35,43269,43270],{},"Růst poptávky",[35,43272,43273],{},"↑",[35,43275,43273],{},[22,43277,43278,43281,43284],{},[35,43279,43280],{},"Pokles poptávky",[35,43282,43283],{},"↓",[35,43285,43283],{},[22,43287,43288,43291,43293],{},[35,43289,43290],{},"Růst nabídky",[35,43292,43283],{},[35,43294,43273],{},[22,43296,43297,43300,43302],{},[35,43298,43299],{},"Pokles nabídky",[35,43301,43273],{},[35,43303,43283],{},[724,43305,43306],{},[614,43307,43308],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[37662,43310],{},[115,43312,811],{"id":43313},"zdanění-trhu",[4584,43315,43316,43405],{},[724,43317,43318,43320,43321,43334,43335,2137,43348,43351,43352,37469,43375,43400,43401,43404],{},[883,43319,4869],{}," TL;DR\nJednotková daň ",[883,43322,43324],{"className":43323},[886],[888,43325,43326],{"xmlns":890},[892,43327,43328,43332],{},[895,43329,43330],{},[898,43331,1754],{},[902,43333,1754],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,43336,43338],{"className":43337},[886],[888,43339,43340],{"xmlns":890},[892,43341,43342,43346],{},[895,43343,43344],{},[898,43345,1754],{},[902,43347,1754],{"encoding":904},[38,43349,43350],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,43353,43355],{"className":43354},[886],[888,43356,43357],{"xmlns":890},[892,43358,43359,43372],{},[895,43360,43361],{},[1931,43362,43363,43365],{},[898,43364,1754],{},[895,43366,43367,43370],{},[898,43368,43369],{},"s",[898,43371,724],{},[902,43373,43374],{"encoding":904},"T_{sp}",[883,43376,43378],{"className":43377},[886],[888,43379,43380],{"xmlns":890},[892,43381,43382,43397],{},[895,43383,43384],{},[1931,43385,43386,43388],{},[898,43387,1754],{},[895,43389,43390,43393,43395],{},[898,43391,43392],{},"v",[898,43394,2740],{},[898,43396,12742],{},[902,43398,43399],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,43402,43403],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,43406,43407],{},[614,43408,43409,43410,1664],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,43411,43413],{"className":43412,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,43415,43416,43417,43420,43421,43447,43448,43451,43452,43478,43479,43496,43497,43537,43538,1682,43551,1664],{},"Existují dvě formy zdanění — daň uložená ",[38,43418,43419],{},"výrobci"," (posun nabídky ",[883,43422,43424],{"className":43423},[886],[888,43425,43426],{"xmlns":890},[892,43427,43428,43444],{},[895,43429,43430,43436,43438,43440,43442],{},[1931,43431,43432,43434],{},[898,43433,2111],{},[1864,43435,1866],{},[1723,43437,1725],{},[898,43439,2111],{},[1723,43441,2087],{},[898,43443,1754],{},[902,43445,43446],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,43449,43450],{},"spotřebiteli"," (posun poptávky ",[883,43453,43455],{"className":43454},[886],[888,43456,43457],{"xmlns":890},[892,43458,43459,43475],{},[895,43460,43461,43467,43469,43471,43473],{},[1931,43462,43463,43465],{},[898,43464,4897],{},[1864,43466,2331],{},[1723,43468,1725],{},[898,43470,4897],{},[1723,43472,1759],{},[898,43474,1754],{},[902,43476,43477],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,43480,43482],{"className":43481},[886],[888,43483,43484],{"xmlns":890},[892,43485,43486,43494],{},[895,43487,43488],{},[2057,43489,43490,43492],{},[898,43491,1904],{},[898,43493,1846],{},[902,43495,43095],{"encoding":904}," klesá a vzniká rozklad daně ",[883,43498,43500],{"className":43499},[886],[888,43501,43502],{"xmlns":890},[892,43503,43504,43534],{},[895,43505,43506,43508,43510,43520,43522],{},[898,43507,1754],{},[1723,43509,1725],{},[1931,43511,43512,43514],{},[898,43513,1754],{},[895,43515,43516,43518],{},[898,43517,43369],{},[898,43519,724],{},[1723,43521,2087],{},[1931,43523,43524,43526],{},[898,43525,1754],{},[895,43527,43528,43530,43532],{},[898,43529,43392],{},[898,43531,2740],{},[898,43533,12742],{},[902,43535,43536],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,43539,43541],{"className":43540},[886],[888,43542,43543],{"xmlns":890},[892,43544,43545,43549],{},[895,43546,43547],{},[898,43548,4897],{},[902,43550,4897],{"encoding":904},[883,43552,43554],{"className":43553},[886],[888,43555,43556],{"xmlns":890},[892,43557,43558,43562],{},[895,43559,43560],{},[898,43561,2111],{},[902,43563,2111],{"encoding":904},[724,43565,43566,43567,43570,43571,1682,43601,43635],{},"Zásadním výsledkem kapitoly je ",[38,43568,43569],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,43572,43574],{"className":43573},[886],[888,43575,43576],{"xmlns":890},[892,43577,43578,43598],{},[895,43579,43580,43588,43590],{},[2220,43581,43582,43584,43586],{},[898,43583,1904],{},[1864,43585,1866],{},[898,43587,1846],{},[1723,43589,1725],{},[2220,43591,43592,43594,43596],{},[898,43593,1904],{},[1864,43595,2331],{},[898,43597,1846],{},[902,43599,43600],{"encoding":904},"Q_1^E = Q_2^E",[883,43602,43604],{"className":43603},[886],[888,43605,43606],{"xmlns":890},[892,43607,43608,43632],{},[895,43609,43610,43618,43620,43622,43624],{},[2220,43611,43612,43614,43616],{},[898,43613,1746],{},[1864,43615,1866],{},[898,43617,1846],{},[1723,43619,1759],{},[898,43621,1754],{},[1723,43623,1725],{},[2220,43625,43626,43628,43630],{},[898,43627,1746],{},[1864,43629,2331],{},[898,43631,1846],{},[902,43633,43634],{"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.",[724,43637,43638,43639,43642,43643,43669,43670,43698,43699,43702,43703,43706,43707,1664],{},"Podrobný výklad, Příklady ",[38,43640,43641],{},"2.9"," (daň výrobci, ",[883,43644,43646],{"className":43645},[886],[888,43647,43648],{"xmlns":890},[892,43649,43650,43666],{},[895,43651,43652,43662,43664],{},[1931,43653,43654,43656],{},[898,43655,1754],{},[895,43657,43658,43660],{},[898,43659,43369],{},[898,43661,724],{},[1723,43663,1725],{},[1864,43665,2331],{},[902,43667,43668],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,43671,43673],{"className":43672},[886],[888,43674,43675],{"xmlns":890},[892,43676,43677,43695],{},[895,43678,43679,43691,43693],{},[1931,43680,43681,43683],{},[898,43682,1754],{},[895,43684,43685,43687,43689],{},[898,43686,43392],{},[898,43688,2740],{},[898,43690,12742],{},[1723,43692,1725],{},[1864,43694,3080],{},[902,43696,43697],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,43700,43701],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,43704,43705],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,43708,43413],{"className":43709,"dataFsResolvedFilePath":809,"href":810},[210],[37662,43711],{},[115,43713,43715],{"id":43714},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[4584,43717,43718],{},[724,43719,43720,43722,43723,43726,43727,43729],{},[883,43721,4869],{}," TL;DR\nMultiplikátory jsou ",[38,43724,43725],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,43728,37652],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,43731,43733],{"id":43732},"redukovaný-tvar","Redukovaný tvar",[724,43735,43736,43737,1981,43760,1343,43778,12829,43795,1981,43818,43835,43836,43866],{},"Pro lineární model ",[883,43738,43740],{"className":43739},[886],[888,43741,43742],{"xmlns":890},[892,43743,43744,43758],{},[895,43745,43746,43748,43750,43752,43754,43756],{},[898,43747,1746],{},[1723,43749,1725],{},[898,43751,207],{},[898,43753,1904],{},[1723,43755,2087],{},[898,43757,2069],{},[902,43759,37752],{"encoding":904},[883,43761,43763],{"className":43762},[886],[888,43764,43765],{"xmlns":890},[892,43766,43767,43775],{},[895,43768,43769,43771,43773],{},[898,43770,207],{},[1723,43772,2287],{},[1864,43774,2256],{},[902,43776,43777],{"encoding":904},"a \u003C 0",[883,43779,43781],{"className":43780},[886],[888,43782,43783],{"xmlns":890},[892,43784,43785,43793],{},[895,43786,43787,43789,43791],{},[898,43788,2069],{},[1723,43790,2253],{},[1864,43792,2256],{},[902,43794,19508],{"encoding":904},[883,43796,43798],{"className":43797},[886],[888,43799,43800],{"xmlns":890},[892,43801,43802,43816],{},[895,43803,43804,43806,43808,43810,43812,43814],{},[898,43805,1746],{},[1723,43807,1725],{},[898,43809,2878],{},[898,43811,1904],{},[1723,43813,2087],{},[898,43815,2930],{},[902,43817,40934],{"encoding":904},[883,43819,43821],{"className":43820},[886],[888,43822,43823],{"xmlns":890},[892,43824,43825,43833],{},[895,43826,43827,43829,43831],{},[898,43828,2878],{},[1723,43830,2253],{},[1864,43832,2256],{},[902,43834,40952],{"encoding":904},") dává podmínka rovnováhy ",[883,43837,43839],{"className":43838},[886],[888,43840,43841],{"xmlns":890},[892,43842,43843,43863],{},[895,43844,43845,43847,43849,43851,43853,43855,43857,43859,43861],{},[898,43846,207],{},[898,43848,1904],{},[1723,43850,2087],{},[898,43852,2069],{},[1723,43854,1725],{},[898,43856,2878],{},[898,43858,1904],{},[1723,43860,2087],{},[898,43862,2930],{},[902,43864,43865],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,43868,43870],{"className":43869},[886],[888,43871,43872],{"xmlns":890,"display":28759},[892,43873,43874,43919],{},[21447,43875,43876],{"width":28764},[21452,43877,43878,43880,43912,43914],{},[21455,43879],{"width":28769},[21455,43881,43882],{},[895,43883,43884,43890,43892,43910],{},[2057,43885,43886,43888],{},[898,43887,1904],{},[898,43889,1846],{},[1723,43891,1725],{},[3058,43893,43894,43902],{},[895,43895,43896,43898,43900],{},[898,43897,2069],{},[1723,43899,1759],{},[898,43901,2930],{},[895,43903,43904,43906,43908],{},[898,43905,2878],{},[1723,43907,1759],{},[898,43909,207],{},[898,43911,1664],{"mathvariant":2124},[21455,43913],{"width":28769},[21455,43915,43916],{},[3018,43917,43918],{},"(2.10)",[902,43920,43921],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,43923,43924,43925,1981,43927,43930,43931,43948,43949,2628,43952,43978,43979,43992,43993,44011,44012,4634],{},"Vztah (2.10) je ",[38,43926,21647],{},[614,43928,43929],{},"reduced form",") pro ",[883,43932,43934],{"className":43933},[886],[888,43935,43936],{"xmlns":890},[892,43937,43938,43946],{},[895,43939,43940],{},[2057,43941,43942,43944],{},[898,43943,1904],{},[898,43945,1846],{},[902,43947,43095],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,43950,43951],{},"parametrů",[883,43953,43955],{"className":43954},[886],[888,43956,43957],{"xmlns":890},[892,43958,43959,43975],{},[895,43960,43961,43963,43965,43967,43969,43971,43973],{},[898,43962,207],{},[1723,43964,2031],{"separator":2030},[898,43966,2069],{},[1723,43968,2031],{"separator":2030},[898,43970,2878],{},[1723,43972,2031],{"separator":2030},[898,43974,2930],{},[902,43976,43977],{"encoding":904},"a, b, c, d",". Aby ",[883,43980,43982],{"className":43981},[886],[888,43983,43984],{"xmlns":890},[892,43985,43986,43990],{},[895,43987,43988],{},[898,43989,1846],{},[902,43991,1846],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,43994,43996],{"className":43995},[886],[888,43997,43998],{"xmlns":890},[892,43999,44000,44008],{},[895,44001,44002,44004,44006],{},[898,44003,2069],{},[1723,44005,2253],{},[898,44007,2930],{},[902,44009,44010],{"encoding":904},"b > d"," (neboť ",[883,44013,44015],{"className":44014},[886],[888,44016,44017],{"xmlns":890},[892,44018,44019,44031],{},[895,44020,44021,44023,44025,44027,44029],{},[898,44022,2878],{},[1723,44024,1759],{},[898,44026,207],{},[1723,44028,2253],{},[1864,44030,2256],{},[902,44032,44033],{"encoding":904},"c - a > 0",[724,44035,44036],{},[614,44037,44038,44039,44052,44053,44066,44067,19342,44080,42632,44097,44110],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,44040,44042],{"className":44041},[886],[888,44043,44044],{"xmlns":890},[892,44045,44046,44050],{},[895,44047,44048],{},[898,44049,2069],{},[902,44051,2069],{"encoding":904}," na ose ",[883,44054,44056],{"className":44055},[886],[888,44057,44058],{"xmlns":890},[892,44059,44060,44064],{},[895,44061,44062],{},[898,44063,1746],{},[902,44065,1746],{"encoding":904},") a nabídka (úsek ",[883,44068,44070],{"className":44069},[886],[888,44071,44072],{"xmlns":890},[892,44073,44074,44078],{},[895,44075,44076],{},[898,44077,2930],{},[902,44079,2930],{"encoding":904},[883,44081,44083],{"className":44082},[886],[888,44084,44085],{"xmlns":890},[892,44086,44087,44095],{},[895,44088,44089,44091,44093],{},[898,44090,2069],{},[1723,44092,2253],{},[898,44094,2930],{},[902,44096,44010],{"encoding":904},[883,44098,44100],{"className":44099},[886],[888,44101,44102],{"xmlns":890},[892,44103,44104,44108],{},[895,44105,44106],{},[898,44107,1846],{},[902,44109,1846],{"encoding":904}," v 1. kvadrantu.",[198,44112,44114],{"id":44113},"definice-multiplikátorů","Definice multiplikátorů",[724,44116,44117,44118,44143,44144,44157,44158,44171],{},"V komparativní statice jsou ",[883,44119,44121],{"className":44120},[886],[888,44122,44123],{"xmlns":890},[892,44124,44125,44141],{},[895,44126,44127,44129,44131,44133,44135,44137,44139],{},[898,44128,207],{},[1723,44130,2031],{"separator":2030},[898,44132,2069],{},[1723,44134,2031],{"separator":2030},[898,44136,2878],{},[1723,44138,2031],{"separator":2030},[898,44140,2930],{},[902,44142,43977],{"encoding":904}," exogenní proměnné a ",[883,44145,44147],{"className":44146},[886],[888,44148,44149],{"xmlns":890},[892,44150,44151,44155],{},[895,44152,44153],{},[898,44154,1904],{},[902,44156,1904],{"encoding":904}," endogenní. Přibližná změna ",[883,44159,44161],{"className":44160},[886],[888,44162,44163],{"xmlns":890},[892,44164,44165,44169],{},[895,44166,44167],{},[898,44168,1904],{},[902,44170,1904],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,44173,44175],{"className":44174},[886],[888,44176,44177],{"xmlns":890,"display":28759},[892,44178,44179,44272],{},[21447,44180,44181],{"width":28764},[21452,44182,44183,44185,44265,44267],{},[21455,44184],{"width":28769},[21455,44186,44187],{},[895,44188,44189,44191,44193,44195,44197,44199,44201,44209,44211,44213,44215,44217,44225,44227,44229,44231,44233,44241,44243,44245,44247,44249,44257,44259,44261,44263],{},[898,44190,3611],{"mathvariant":2124},[898,44192,1904],{},[1723,44194,3456],{},[898,44196,2930],{},[898,44198,1904],{},[1723,44200,1725],{},[2220,44202,44203,44205,44207],{},[898,44204,1904],{},[898,44206,207],{},[1723,44208,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[3018,44210,3707],{},[898,44212,2930],{},[898,44214,207],{},[1723,44216,2087],{},[2220,44218,44219,44221,44223],{},[898,44220,1904],{},[898,44222,2069],{},[1723,44224,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[3018,44226,3707],{},[898,44228,2930],{},[898,44230,2069],{},[1723,44232,2087],{},[2220,44234,44235,44237,44239],{},[898,44236,1904],{},[898,44238,2878],{},[1723,44240,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[3018,44242,3707],{},[898,44244,2930],{},[898,44246,2878],{},[1723,44248,2087],{},[2220,44250,44251,44253,44255],{},[898,44252,1904],{},[898,44254,2930],{},[1723,44256,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[3018,44258,3707],{},[898,44260,2930],{},[898,44262,2930],{},[898,44264,1664],{"mathvariant":2124},[21455,44266],{"width":28769},[21455,44268,44269],{},[3018,44270,44271],{},"(2.11)",[902,44273,44274],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,44276,44277,44278,44328,44329,1981,44331,3871],{},"Parciální derivace ",[883,44279,44281],{"className":44280},[886],[888,44282,44283],{"xmlns":890},[892,44284,44285,44325],{},[895,44286,44287,44295,44297,44305,44307,44315,44317],{},[2220,44288,44289,44291,44293],{},[898,44290,1904],{},[898,44292,207],{},[1723,44294,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,44296,2031],{"separator":2030},[2220,44298,44299,44301,44303],{},[898,44300,1904],{},[898,44302,2069],{},[1723,44304,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,44306,2031],{"separator":2030},[2220,44308,44309,44311,44313],{},[898,44310,1904],{},[898,44312,2878],{},[1723,44314,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,44316,2031],{"separator":2030},[2220,44318,44319,44321,44323],{},[898,44320,1904],{},[898,44322,2930],{},[1723,44324,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,44326,44327],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,44330,18672],{},[614,44332,44333],{},"multipliers",[883,44335,44337],{"className":44336},[886],[888,44338,44339],{"xmlns":890,"display":28759},[892,44340,44341,44492],{},[21447,44342,44343],{"width":28764},[21452,44344,44345,44347,44485,44487],{},[21455,44346],{"width":28769},[21455,44348,44349],{},[895,44350,44351,44359,44361,44387,44389,44391,44399,44401,44413,44415,44417,44425,44427,44429,44455,44457,44459,44467,44469,44471,44483],{},[2220,44352,44353,44355,44357],{},[898,44354,1904],{},[898,44356,207],{},[1723,44358,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,44360,1725],{},[3058,44362,44363,44371],{},[895,44364,44365,44367,44369],{},[898,44366,2069],{},[1723,44368,1759],{},[898,44370,2930],{},[895,44372,44373,44375,44377,44379,44381],{},[1723,44374,1908],{"stretchy":1907},[898,44376,2878],{},[1723,44378,1759],{},[898,44380,207],{},[2057,44382,44383,44385],{},[1723,44384,1914],{"stretchy":1907},[1864,44386,2331],{},[1723,44388,2031],{"separator":2030},[6588,44390],{"width":15985},[2220,44392,44393,44395,44397],{},[898,44394,1904],{},[898,44396,2069],{},[1723,44398,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,44400,1725],{},[3058,44402,44403,44405],{},[1864,44404,1866],{},[895,44406,44407,44409,44411],{},[898,44408,2878],{},[1723,44410,1759],{},[898,44412,207],{},[1723,44414,2031],{"separator":2030},[6588,44416],{"width":15985},[2220,44418,44419,44421,44423],{},[898,44420,1904],{},[898,44422,2878],{},[1723,44424,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,44426,1725],{},[1723,44428,1759],{},[3058,44430,44431,44439],{},[895,44432,44433,44435,44437],{},[898,44434,2069],{},[1723,44436,1759],{},[898,44438,2930],{},[895,44440,44441,44443,44445,44447,44449],{},[1723,44442,1908],{"stretchy":1907},[898,44444,2878],{},[1723,44446,1759],{},[898,44448,207],{},[2057,44450,44451,44453],{},[1723,44452,1914],{"stretchy":1907},[1864,44454,2331],{},[1723,44456,2031],{"separator":2030},[6588,44458],{"width":15985},[2220,44460,44461,44463,44465],{},[898,44462,1904],{},[898,44464,2930],{},[1723,44466,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,44468,1725],{},[1723,44470,1759],{},[3058,44472,44473,44475],{},[1864,44474,1866],{},[895,44476,44477,44479,44481],{},[898,44478,2878],{},[1723,44480,1759],{},[898,44482,207],{},[898,44484,1664],{"mathvariant":2124},[21455,44486],{"width":28769},[21455,44488,44489],{},[3018,44490,44491],{},"(2.12)",[902,44493,44494],{"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}",[198,44496,44498],{"id":44497},"znaménka-a-interpretace","Znaménka a interpretace",[724,44500,44501,44502,1343,44519,1343,44536,1343,44553,44570,44571,3871],{},"Za podmínek ",[883,44503,44505],{"className":44504},[886],[888,44506,44507],{"xmlns":890},[892,44508,44509,44517],{},[895,44510,44511,44513,44515],{},[898,44512,207],{},[1723,44514,2287],{},[1864,44516,2256],{},[902,44518,43777],{"encoding":904},[883,44520,44522],{"className":44521},[886],[888,44523,44524],{"xmlns":890},[892,44525,44526,44534],{},[895,44527,44528,44530,44532],{},[898,44529,2069],{},[1723,44531,2253],{},[1864,44533,2256],{},[902,44535,19508],{"encoding":904},[883,44537,44539],{"className":44538},[886],[888,44540,44541],{"xmlns":890},[892,44542,44543,44551],{},[895,44544,44545,44547,44549],{},[898,44546,2878],{},[1723,44548,2253],{},[1864,44550,2256],{},[902,44552,40952],{"encoding":904},[883,44554,44556],{"className":44555},[886],[888,44557,44558],{"xmlns":890},[892,44559,44560,44568],{},[895,44561,44562,44564,44566],{},[898,44563,2069],{},[1723,44565,2253],{},[898,44567,2930],{},[902,44569,44010],{"encoding":904}," platí (znaménka se ",[38,44572,44573],{},"nemění",[883,44575,44577],{"className":44576},[886],[888,44578,44579],{"xmlns":890,"display":28759},[892,44580,44581,44643],{},[895,44582,44583,44591,44593,44595,44597,44599,44607,44609,44611,44613,44615,44623,44625,44627,44629,44631,44639,44641],{},[2220,44584,44585,44587,44589],{},[898,44586,1904],{},[898,44588,207],{},[1723,44590,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,44592,2253],{},[1864,44594,2256],{},[1723,44596,2031],{"separator":2030},[6588,44598],{"width":6590},[2220,44600,44601,44603,44605],{},[898,44602,1904],{},[898,44604,2069],{},[1723,44606,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,44608,2253],{},[1864,44610,2256],{},[1723,44612,2031],{"separator":2030},[6588,44614],{"width":6590},[2220,44616,44617,44619,44621],{},[898,44618,1904],{},[898,44620,2878],{},[1723,44622,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,44624,2287],{},[1864,44626,2256],{},[1723,44628,2031],{"separator":2030},[6588,44630],{"width":6590},[2220,44632,44633,44635,44637],{},[898,44634,1904],{},[898,44636,2930],{},[1723,44638,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,44640,2287],{},[1864,44642,13161],{},[902,44644,44645],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,44647,44648,44707],{},[123,44649,44650,2628,44653,44673,44674,44691,44692,1343,44705,1664],{},[38,44651,44652],{},"Kvantitativní smysl:",[883,44654,44656],{"className":44655},[886],[888,44657,44658],{"xmlns":890},[892,44659,44660,44670],{},[895,44661,44662],{},[2220,44663,44664,44666,44668],{},[898,44665,1904],{},[898,44667,2750],{},[1723,44669,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,44671,44672],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,44675,44677],{"className":44676},[886],[888,44678,44679],{"xmlns":890},[892,44680,44681,44689],{},[895,44682,44683],{},[2057,44684,44685,44687],{},[898,44686,1904],{},[898,44688,1846],{},[902,44690,43095],{"encoding":904}," při jednotkové změně parametru ",[883,44693,44695],{"className":44694},[886],[888,44696,44697],{"xmlns":890},[892,44698,44699,44703],{},[895,44700,44701],{},[898,44702,2750],{},[902,44704,2750],{"encoding":904},[614,44706,37652],{},[123,44708,44709,44712,44713,44730,44731,1664],{},[38,44710,44711],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,44714,44716],{"className":44715},[886],[888,44717,44718],{"xmlns":890},[892,44719,44720,44728],{},[895,44721,44722],{},[2057,44723,44724,44726],{},[898,44725,1904],{},[898,44727,1846],{},[902,44729,43095],{"encoding":904}," na růst ",[883,44732,44734],{"className":44733},[886],[888,44735,44736],{"xmlns":890},[892,44737,44738,44742],{},[895,44739,44740],{},[898,44741,2750],{},[902,44743,2750],{"encoding":904},[724,44745,44746,44747,44760,44761,44011,44778,4634],{},"Např. růst ",[883,44748,44750],{"className":44749},[886],[888,44751,44752],{"xmlns":890},[892,44753,44754,44758],{},[895,44755,44756],{},[898,44757,2878],{},[902,44759,2878],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,44762,44764],{"className":44763},[886],[888,44765,44766],{"xmlns":890},[892,44767,44768,44776],{},[895,44769,44770],{},[2057,44771,44772,44774],{},[898,44773,1904],{},[898,44775,1846],{},[902,44777,43095],{"encoding":904},[883,44779,44781],{"className":44780},[886],[888,44782,44783],{"xmlns":890},[892,44784,44785,44799],{},[895,44786,44787,44795,44797],{},[2220,44788,44789,44791,44793],{},[898,44790,1904],{},[898,44792,2878],{},[1723,44794,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,44796,2287],{},[1864,44798,2256],{},[902,44800,44801],{"encoding":904},"Q'_c \u003C 0",[724,44803,44804],{},[614,44805,44806,44807,44827,44828,44852,44853,44875,44876,1664],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,44808,44810],{"className":44809},[886],[888,44811,44812],{"xmlns":890},[892,44813,44814,44824],{},[895,44815,44816,44818,44820,44822],{},[898,44817,2878],{},[898,44819,1904],{},[1723,44821,2087],{},[898,44823,2930],{},[902,44825,44826],{"encoding":904},"cQ + d"," na strmější ",[883,44829,44831],{"className":44830},[886],[888,44832,44833],{"xmlns":890},[892,44834,44835,44849],{},[895,44836,44837,44843,44845,44847],{},[1931,44838,44839,44841],{},[898,44840,2878],{},[1864,44842,1866],{},[898,44844,1904],{},[1723,44846,2087],{},[898,44848,2930],{},[902,44850,44851],{"encoding":904},"c_1 Q + d"," (při ",[883,44854,44856],{"className":44855},[886],[888,44857,44858],{"xmlns":890},[892,44859,44860,44872],{},[895,44861,44862,44868,44870],{},[1931,44863,44864,44866],{},[898,44865,2878],{},[1864,44867,1866],{},[1723,44869,2253],{},[898,44871,2878],{},[902,44873,44874],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,44877,44879],{"className":44878},[886],[888,44880,44881],{"xmlns":890},[892,44882,44883,44893],{},[895,44884,44885,44891],{},[2057,44886,44887,44889],{},[898,44888,1904],{},[898,44890,1846],{},[1723,44892,43283],{},[902,44894,44895],{"encoding":904},"Q^E \\downarrow",[724,44897,44898,44899,44931,44932,1664],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,44900,44902],{"className":44901},[886],[888,44903,44904],{"xmlns":890},[892,44905,44906,44928],{},[895,44907,44908,44910,44912,44914,44922,44924,44926],{},[898,44909,3611],{"mathvariant":2124},[898,44911,1904],{},[1723,44913,3456],{},[2220,44915,44916,44918,44920],{},[898,44917,1904],{},[898,44919,2069],{},[1723,44921,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[3018,44923,3707],{},[898,44925,2930],{},[898,44927,2069],{},[902,44929,44930],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,44933,44935],{"className":44934},[886],[888,44936,44937],{"xmlns":890},[892,44938,44939,44947],{},[895,44940,44941],{},[2057,44942,44943,44945],{},[898,44944,1746],{},[898,44946,1846],{},[902,44948,42158],{"encoding":904},[198,44950,44952,44953],{"id":44951},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,44954,44956],{"className":44955},[886],[888,44957,44958],{"xmlns":890},[892,44959,44960,44968],{},[895,44961,44962],{},[2057,44963,44964,44966],{},[898,44965,1904],{},[898,44967,1846],{},[902,44969,43095],{"encoding":904},[724,44971,44972,42347,44974,42382,45000,1664],{},[38,44973,38625],{},[883,44975,44977],{"className":44976},[886],[888,44978,44979],{"xmlns":890},[892,44980,44981,44997],{},[895,44982,44983,44985,44987,44989,44991,44993,44995],{},[898,44984,1746],{},[1723,44986,1725],{},[1723,44988,1759],{},[1864,44990,2909],{},[898,44992,1904],{},[1723,44994,2087],{},[1864,44996,5921],{},[902,44998,44999],{"encoding":904},"P = -3Q + 40",[883,45001,45003],{"className":45002},[886],[888,45004,45005],{"xmlns":890},[892,45006,45007,45021],{},[895,45008,45009,45011,45013,45015,45017,45019],{},[898,45010,1746],{},[1723,45012,1725],{},[1864,45014,5719],{},[898,45016,1904],{},[1723,45018,2087],{},[1864,45020,3585],{},[902,45022,45023],{"encoding":904},"P = 0{,}5Q + 10",[724,45025,45026,45028],{},[38,45027,38657],{}," Rovnovážné množství",[883,45030,45032],{"className":45031},[886],[888,45033,45034],{"xmlns":890,"display":28759},[892,45035,45036,45104],{},[895,45037,45038,45044,45046,45064,45066,45090,45092,45099,45101],{},[2057,45039,45040,45042],{},[898,45041,1904],{},[898,45043,1846],{},[1723,45045,1725],{},[3058,45047,45048,45056],{},[895,45049,45050,45052,45054],{},[898,45051,2069],{},[1723,45053,1759],{},[898,45055,2930],{},[895,45057,45058,45060,45062],{},[898,45059,2878],{},[1723,45061,1759],{},[898,45063,207],{},[1723,45065,1725],{},[3058,45067,45068,45076],{},[895,45069,45070,45072,45074],{},[1864,45071,5921],{},[1723,45073,1759],{},[1864,45075,3585],{},[895,45077,45078,45080,45082,45084,45086,45088],{},[1864,45079,5719],{},[1723,45081,1759],{},[1723,45083,1908],{"stretchy":1907},[1723,45085,1759],{},[1864,45087,2909],{},[1723,45089,1914],{"stretchy":1907},[1723,45091,1725],{},[3058,45093,45094,45096],{},[1864,45095,38711],{},[1864,45097,45098],{},"3,5",[1723,45100,3456],{},[1864,45102,45103],{},"8,571.",[902,45105,45106],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,45108,45109,45154],{},[38,45110,45111,45112,3397,45125,3411,45139,45153],{},"(a) Změna ",[883,45113,45115],{"className":45114},[886],[888,45116,45117],{"xmlns":890},[892,45118,45119,45123],{},[895,45120,45121],{},[898,45122,2878],{},[902,45124,2878],{"encoding":904},[883,45126,45128],{"className":45127},[886],[888,45129,45130],{"xmlns":890},[892,45131,45132,45136],{},[895,45133,45134],{},[1864,45135,5719],{},[902,45137,45138],{"encoding":904},"0{,}5",[883,45140,45142],{"className":45141},[886],[888,45143,45144],{"xmlns":890},[892,45145,45146,45150],{},[895,45147,45148],{},[1864,45149,20015],{},[902,45151,45152],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,45156,45158],{"className":45157},[886],[888,45159,45160],{"xmlns":890,"display":28759},[892,45161,45162,45239],{},[895,45163,45164,45172,45174,45176,45178,45180,45182,45208,45210,45212,45214,45216,45218,45228,45230,45232,45234,45236],{},[2220,45165,45166,45168,45170],{},[898,45167,1904],{},[898,45169,2878],{},[1723,45171,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[3018,45173,3707],{},[898,45175,2930],{},[898,45177,2878],{},[1723,45179,1725],{},[1723,45181,1759],{},[3058,45183,45184,45192],{},[895,45185,45186,45188,45190],{},[898,45187,2069],{},[1723,45189,1759],{},[898,45191,2930],{},[895,45193,45194,45196,45198,45200,45202],{},[1723,45195,1908],{"stretchy":1907},[898,45197,2878],{},[1723,45199,1759],{},[898,45201,207],{},[2057,45203,45204,45206],{},[1723,45205,1914],{"stretchy":1907},[1864,45207,2331],{},[3018,45209,3707],{},[898,45211,2930],{},[898,45213,2878],{},[1723,45215,1725],{},[1723,45217,1759],{},[3058,45219,45220,45222],{},[1864,45221,38711],{},[2057,45223,45224,45226],{},[1864,45225,45098],{},[1864,45227,2331],{},[1723,45229,3897],{},[1864,45231,3517],{},[1723,45233,3456],{},[1723,45235,1759],{},[1864,45237,45238],{},"0,245.",[902,45240,45241],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,45243,45244,45245,1664],{},"Nové rovnovážné množství ",[883,45246,45248],{"className":45247},[886],[888,45249,45250],{"xmlns":890},[892,45251,45252,45277],{},[895,45253,45254,45262,45264,45267,45269,45272,45274],{},[2220,45255,45256,45258,45260],{},[898,45257,1904],{},[1864,45259,1866],{},[898,45261,1846],{},[1723,45263,3456],{},[1864,45265,45266],{},"8,571",[1723,45268,1759],{},[1864,45270,45271],{},"0,245",[1723,45273,1725],{},[1864,45275,45276],{},"8,326",[902,45278,45279],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,45281,45282,45367],{},[38,45283,45284,45285,1343,45305,1343,45327,1343,45347,1664],{},"(b) Současné změny ",[883,45286,45288],{"className":45287},[886],[888,45289,45290],{"xmlns":890},[892,45291,45292,45302],{},[895,45293,45294,45296,45298,45300],{},[898,45295,2930],{},[898,45297,207],{},[1723,45299,1725],{},[1864,45301,5719],{},[902,45303,45304],{"encoding":904},"da = 0{,}5",[883,45306,45308],{"className":45307},[886],[888,45309,45310],{"xmlns":890},[892,45311,45312,45324],{},[895,45313,45314,45316,45318,45320,45322],{},[898,45315,2930],{},[898,45317,2069],{},[1723,45319,1725],{},[1723,45321,1759],{},[1864,45323,2962],{},[902,45325,45326],{"encoding":904},"db = -5",[883,45328,45330],{"className":45329},[886],[888,45331,45332],{"xmlns":890},[892,45333,45334,45344],{},[895,45335,45336,45338,45340,45342],{},[898,45337,2930],{},[898,45339,2878],{},[1723,45341,1725],{},[1864,45343,3517],{},[902,45345,45346],{"encoding":904},"dc = 0{,}1",[883,45348,45350],{"className":45349},[886],[888,45351,45352],{"xmlns":890},[892,45353,45354,45364],{},[895,45355,45356,45358,45360,45362],{},[898,45357,2930],{},[898,45359,2930],{},[1723,45361,1725],{},[1864,45363,1866],{},[902,45365,45366],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,45369,45371],{"className":45370},[886],[888,45372,45373],{"xmlns":890,"display":28759},[892,45374,45375,45518],{},[21447,45376,45377,45459,45495],{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},[21452,45378,45379,45389],{},[21455,45380,45381],{},[3055,45382,45383],{"scriptlevel":2256,"displaystyle":2030},[895,45384,45385,45387],{},[898,45386,3611],{"mathvariant":2124},[898,45388,1904],{},[21455,45390,45391],{},[3055,45392,45393],{"scriptlevel":2256,"displaystyle":2030},[895,45394,45395,45397,45399,45409,45411,45413,45415,45421,45423,45425,45427,45429,45431,45433,45443,45445,45447,45449,45455,45457],{},[895,45396],{},[1723,45398,3456],{},[3058,45400,45401,45403],{},[1864,45402,38711],{},[2057,45404,45405,45407],{},[1864,45406,45098],{},[1864,45408,2331],{},[1723,45410,3897],{},[1864,45412,5719],{},[1723,45414,2087],{},[3058,45416,45417,45419],{},[1864,45418,1866],{},[1864,45420,45098],{},[1723,45422,3897],{},[1723,45424,1908],{"stretchy":1907},[1723,45426,1759],{},[1864,45428,2962],{},[1723,45430,1914],{"stretchy":1907},[1723,45432,1759],{},[3058,45434,45435,45437],{},[1864,45436,38711],{},[2057,45438,45439,45441],{},[1864,45440,45098],{},[1864,45442,2331],{},[1723,45444,3897],{},[1864,45446,3517],{},[1723,45448,1759],{},[3058,45450,45451,45453],{},[1864,45452,1866],{},[1864,45454,45098],{},[1723,45456,3897],{},[1864,45458,1866],{},[21452,45460,45461,45467],{},[21455,45462,45463],{},[3055,45464,45465],{"scriptlevel":2256,"displaystyle":2030},[895,45466],{},[21455,45468,45469],{},[3055,45470,45471],{"scriptlevel":2256,"displaystyle":2030},[895,45472,45473,45475,45477,45480,45482,45485,45487,45490,45492],{},[895,45474],{},[1723,45476,1725],{},[1864,45478,45479],{},"1,2245",[1723,45481,1759],{},[1864,45483,45484],{},"1,4286",[1723,45486,1759],{},[1864,45488,45489],{},"0,2449",[1723,45491,1759],{},[1864,45493,45494],{},"0,2857",[21452,45496,45497,45503],{},[21455,45498,45499],{},[3055,45500,45501],{"scriptlevel":2256,"displaystyle":2030},[895,45502],{},[21455,45504,45505],{},[3055,45506,45507],{"scriptlevel":2256,"displaystyle":2030},[895,45508,45509,45511,45513,45515],{},[895,45510],{},[1723,45512,3456],{},[1723,45514,1759],{},[1864,45516,45517],{},"0,735.",[902,45519,45520],{"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}",[724,45522,30758,45523,1664],{},[883,45524,45526],{"className":45525},[886],[888,45527,45528],{"xmlns":890},[892,45529,45530,45554],{},[895,45531,45532,45540,45542,45544,45546,45549,45551],{},[2220,45533,45534,45536,45538],{},[898,45535,1904],{},[1864,45537,1866],{},[898,45539,1846],{},[1723,45541,3456],{},[1864,45543,45266],{},[1723,45545,1759],{},[1864,45547,45548],{},"0,735",[1723,45550,1725],{},[1864,45552,45553],{},"7,836",[902,45555,45556],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[4584,45558,45559],{},[724,45560,45561,45563,45564,45587,45588,45610],{},[883,45562,5124],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,45565,45567],{"className":45566},[886],[888,45568,45569],{"xmlns":890},[892,45570,45571,45584],{},[895,45572,45573,45575,45577,45579,45581],{},[898,45574,3611],{"mathvariant":2124},[898,45576,1904],{},[1723,45578,3456],{},[1723,45580,1759],{},[1864,45582,45583],{},"2,69",[902,45585,45586],{"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 ",[883,45589,45591],{"className":45590},[886],[888,45592,45593],{"xmlns":890},[892,45594,45595,45607],{},[895,45596,45597,45599,45601,45603,45605],{},[898,45598,3611],{"mathvariant":2124},[898,45600,1904],{},[1723,45602,3456],{},[1723,45604,1759],{},[1864,45606,45548],{},[902,45608,45609],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,45612,45613],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[37662,45615],{},[115,45617,820],{"id":12485},[4584,45619,45620],{},[724,45621,45622,4591,45624,1981,45627,12829,45643,1981,45646,45662,45663,1664],{},[883,45623,4869],{},[38,45625,45626],{},"Přebytek spotřebitele",[883,45628,45630],{"className":45629},[886],[888,45631,45632],{"xmlns":890},[892,45633,45634,45640],{},[895,45635,45636,45638],{},[898,45637,1721],{},[898,45639,2111],{},[902,45641,45642],{"encoding":904},"CS",[38,45644,45645],{},"přebytek výrobce",[883,45647,45649],{"className":45648},[886],[888,45650,45651],{"xmlns":890},[892,45652,45653,45659],{},[895,45654,45655,45657],{},[898,45656,1746],{},[898,45658,2111],{},[902,45660,45661],{"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 ",[207,45664,1696],{"className":45665,"dataFsResolvedFilePath":818,"href":819},[210],[724,45667,45668],{},[3285,45669],{"alt":45670,"className":45671,"src":45672},"imek-prebytky-cs-ps",[210,3289],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,45674,45675,1981,45677,45680],{},[38,45676,45626],{},[614,45678,45679],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,45682,45684],{"className":45683},[886],[888,45685,45686],{"xmlns":890,"display":28759},[892,45687,45688,45765],{},[21447,45689,45690],{"width":28764},[21452,45691,45692,45694,45758,45760],{},[21455,45693],{"width":28769},[21455,45695,45696],{},[895,45697,45698,45700,45702,45704,45710,45712,45714,45726,45728,45730,45732,45734,45736,45738,45740,45742,45748,45750,45756],{},[898,45699,1721],{},[898,45701,2111],{},[1723,45703,1908],{"stretchy":1907},[1931,45705,45706,45708],{},[898,45707,1904],{},[1864,45709,2256],{},[1723,45711,1914],{"stretchy":1907},[1723,45713,1725],{},[2220,45715,45716,45718,45720],{},[1723,45717,11870],{},[1864,45719,2256],{},[1931,45721,45722,45724],{},[898,45723,1904],{},[1864,45725,2256],{},[898,45727,4897],{},[1723,45729,1908],{"stretchy":1907},[898,45731,1904],{},[1723,45733,1914],{"stretchy":1907},[3018,45735,3707],{},[898,45737,2930],{},[898,45739,1904],{},[1723,45741,1759],{},[1931,45743,45744,45746],{},[898,45745,1746],{},[1864,45747,2256],{},[3018,45749,3707],{},[1931,45751,45752,45754],{},[898,45753,1904],{},[1864,45755,2256],{},[898,45757,1664],{"mathvariant":2124},[21455,45759],{"width":28769},[21455,45761,45762],{},[3018,45763,45764],{},"(2.14)",[902,45766,45767],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,45769,45770,1981,45773,45776],{},[38,45771,45772],{},"Přebytek výrobce",[614,45774,45775],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,45778,45780],{"className":45779},[886],[888,45781,45782],{"xmlns":890,"display":28759},[892,45783,45784,45861],{},[21447,45785,45786],{"width":28764},[21452,45787,45788,45790,45854,45856],{},[21455,45789],{"width":28769},[21455,45791,45792],{},[895,45793,45794,45796,45798,45800,45806,45808,45810,45816,45818,45824,45826,45838,45840,45842,45844,45846,45848,45850,45852],{},[898,45795,1746],{},[898,45797,2111],{},[1723,45799,1908],{"stretchy":1907},[1931,45801,45802,45804],{},[898,45803,1904],{},[1864,45805,2256],{},[1723,45807,1914],{"stretchy":1907},[1723,45809,1725],{},[1931,45811,45812,45814],{},[898,45813,1746],{},[1864,45815,2256],{},[3018,45817,3707],{},[1931,45819,45820,45822],{},[898,45821,1904],{},[1864,45823,2256],{},[1723,45825,1759],{},[2220,45827,45828,45830,45832],{},[1723,45829,11870],{},[1864,45831,2256],{},[1931,45833,45834,45836],{},[898,45835,1904],{},[1864,45837,2256],{},[898,45839,2111],{},[1723,45841,1908],{"stretchy":1907},[898,45843,1904],{},[1723,45845,1914],{"stretchy":1907},[3018,45847,3707],{},[898,45849,2930],{},[898,45851,1904],{},[898,45853,1664],{"mathvariant":2124},[21455,45855],{"width":28769},[21455,45857,45858],{},[3018,45859,45860],{},"(2.15)",[902,45862,45863],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,45865,45866,45867,1664],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,45868,45870],{"className":45869,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[37662,45872],{},[115,45874,45876],{"id":45875},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,45878,45879,45910,45915,45921,45949,45955,45984,45990,46070,46096],{},[123,45880,45881,45883,45884,45909],{},[38,45882,38620],{}," — lineární poptávka ",[883,45885,45887],{"className":45886},[886],[888,45888,45889],{"xmlns":890},[892,45890,45891,45907],{},[895,45892,45893,45895,45897,45899,45901,45903,45905],{},[898,45894,1746],{},[1723,45896,1725],{},[1723,45898,1759],{},[1864,45900,2331],{},[898,45902,1904],{},[1723,45904,2087],{},[1864,45906,3846],{},[902,45908,38652],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,45911,45912,45914],{},[38,45913,38934],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,45916,45917,45920],{},[38,45918,45919],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,45922,45923,45925,45926,1664],{},[38,45924,41481],{}," — lineární nabídka ",[883,45927,45929],{"className":45928},[886],[888,45930,45931],{"xmlns":890},[892,45932,45933,45947],{},[895,45934,45935,45937,45939,45941,45943,45945],{},[898,45936,1746],{},[1723,45938,1725],{},[1864,45940,5719],{},[898,45942,1904],{},[1723,45944,2087],{},[1864,45946,5714],{},[902,45948,41510],{"encoding":904},[123,45950,45951,45954],{},[38,45952,45953],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,45956,45957,45960,45961,1664],{},[38,45958,45959],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,45962,45964],{"className":45963},[886],[888,45965,45966],{"xmlns":890},[892,45967,45968,45982],{},[895,45969,45970,45972,45974,45976,45978,45980],{},[898,45971,1846],{},[1723,45973,3212],{"stretchy":1907},[1864,45975,3080],{},[1723,45977,2031],{"separator":2030},[1864,45979,42628],{},[1723,45981,3227],{"stretchy":1907},[902,45983,42656],{"encoding":904},[123,45985,45986,45989],{},[38,45987,45988],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,45991,45992,45995,45996,46013,46014,1343,46039,46066,46067,3671],{},[38,45993,45994],{},"Příklad 2.9"," — daň ",[883,45997,45999],{"className":45998},[886],[888,46000,46001],{"xmlns":890},[892,46002,46003,46011],{},[895,46004,46005,46007,46009],{},[898,46006,1754],{},[1723,46008,1725],{},[1864,46010,2969],{},[902,46012,41960],{"encoding":904}," na výrobce; rozklad ",[883,46015,46017],{"className":46016},[886],[888,46018,46019],{"xmlns":890},[892,46020,46021,46037],{},[895,46022,46023,46033,46035],{},[1931,46024,46025,46027],{},[898,46026,1754],{},[895,46028,46029,46031],{},[898,46030,43369],{},[898,46032,724],{},[1723,46034,1725],{},[1864,46036,2331],{},[902,46038,43668],{"encoding":904},[883,46040,46042],{"className":46041},[886],[888,46043,46044],{"xmlns":890},[892,46045,46046,46064],{},[895,46047,46048,46060,46062],{},[1931,46049,46050,46052],{},[898,46051,1754],{},[895,46053,46054,46056,46058],{},[898,46055,43392],{},[898,46057,2740],{},[898,46059,12742],{},[1723,46061,1725],{},[1864,46063,3080],{},[902,46065,43697],{"encoding":904},". (Viz ",[207,46068,43413],{"className":46069,"dataFsResolvedFilePath":809,"href":810},[210],[123,46071,46072,45995,46075,46092,46093,3671],{},[38,46073,46074],{},"Příklad 2.10",[883,46076,46078],{"className":46077},[886],[888,46079,46080],{"xmlns":890},[892,46081,46082,46090],{},[895,46083,46084,46086,46088],{},[898,46085,1754],{},[1723,46087,1725],{},[1864,46089,2969],{},[902,46091,41960],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,46094,43413],{"className":46095,"dataFsResolvedFilePath":809,"href":810},[210],[123,46097,46098,46101],{},[38,46099,46100],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[37662,46103],{},[115,46105,46107],{"id":46106},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,46109,46111],{"id":46110},"základní-analýza-poptávky","Základní analýza poptávky",[724,46113,46114,46117,46118,46153,46154,46180],{},[38,46115,46116],{},"2.1"," Je dána poptávka ",[883,46119,46121],{"className":46120},[886],[888,46122,46123],{"xmlns":890},[892,46124,46125,46150],{},[895,46126,46127,46129,46131,46133,46135,46137,46139,46141,46144,46146,46148],{},[898,46128,1904],{},[1723,46130,1725],{},[898,46132,4897],{},[1723,46134,1908],{"stretchy":1907},[898,46136,1746],{},[1723,46138,1914],{"stretchy":1907},[1723,46140,1725],{},[1864,46142,46143],{},"75",[1723,46145,1759],{},[1864,46147,2962],{},[898,46149,1746],{},[902,46151,46152],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,46155,46157],{"className":46156},[886],[888,46158,46159],{"xmlns":890},[892,46160,46161,46177],{},[895,46162,46163,46165,46167,46169,46171,46173,46175],{},[1864,46164,2256],{},[1723,46166,2031],{"separator":2030},[1864,46168,2962],{},[1723,46170,2031],{"separator":2030},[1864,46172,3585],{},[1723,46174,2031],{"separator":2030},[1864,46176,36937],{},[902,46178,46179],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,46182,46183,46186,46187,46205,46206,3871],{},[38,46184,46185],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,46188,46190],{"className":46189},[886],[888,46191,46192],{"xmlns":890},[892,46193,46194,46202],{},[895,46195,46196,46198,46200],{},[898,46197,1746],{},[1723,46199,2031],{"separator":2030},[898,46201,1904],{},[902,46203,46204],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,46207,46209],{"className":46208},[886],[888,46210,46211],{"xmlns":890},[892,46212,46213,46229],{},[895,46214,46215,46217,46219,46221,46223,46225,46227],{},[898,46216,207],{},[1723,46218,2031],{"separator":2030},[898,46220,2069],{},[1723,46222,2031],{"separator":2030},[898,46224,2878],{},[1723,46226,2253],{},[1864,46228,2256],{},[902,46230,46231],{"encoding":904},"a, b, c > 0",[120,46233,46234,46267,46298,46333,46364,46399],{},[123,46235,46236,46237],{},"(a) ",[883,46238,46240],{"className":46239},[886],[888,46241,46242],{"xmlns":890},[892,46243,46244,46264],{},[895,46245,46246,46248,46250],{},[898,46247,1904],{},[1723,46249,1725],{},[3055,46251,46252],{"scriptlevel":2256,"displaystyle":2030},[3058,46253,46254,46256],{},[898,46255,207],{},[895,46257,46258,46260,46262],{},[898,46259,1746],{},[1723,46261,2087],{},[898,46263,2878],{},[902,46265,46266],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,46268,46269,46270],{},"(b) ",[883,46271,46273],{"className":46272},[886],[888,46274,46275],{"xmlns":890},[892,46276,46277,46295],{},[895,46278,46279,46281,46283],{},[898,46280,1904],{},[1723,46282,1725],{},[8827,46284,46285],{},[895,46286,46287,46289,46291,46293],{},[898,46288,207],{},[1723,46290,1759],{},[898,46292,2069],{},[898,46294,1904],{},[902,46296,46297],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,46299,46300,46301],{},"(c) ",[883,46302,46304],{"className":46303},[886],[888,46305,46306],{"xmlns":890},[892,46307,46308,46330],{},[895,46309,46310,46312,46314],{},[898,46311,1904],{},[1723,46313,1725],{},[3055,46315,46316],{"scriptlevel":2256,"displaystyle":2030},[3058,46317,46318,46328],{},[895,46319,46320,46322,46324],{},[898,46321,207],{},[1723,46323,1759],{},[8827,46325,46326],{},[898,46327,1746],{},[898,46329,2069],{},[902,46331,46332],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,46334,46335,46336],{},"(d) ",[883,46337,46339],{"className":46338},[886],[888,46340,46341],{"xmlns":890},[892,46342,46343,46361],{},[895,46344,46345,46347,46349,46351,46353,46355],{},[898,46346,1746],{},[1723,46348,1725],{},[898,46350,207],{},[1723,46352,1759],{},[898,46354,2069],{},[2057,46356,46357,46359],{},[898,46358,1904],{},[1864,46360,2331],{},[902,46362,46363],{"encoding":904},"P = a - bQ^2",[123,46365,46366,46367],{},"(e) ",[883,46368,46370],{"className":46369},[886],[888,46371,46372],{"xmlns":890},[892,46373,46374,46396],{},[895,46375,46376,46378,46380,46382,46392,46394],{},[898,46377,1904],{},[1723,46379,1725],{},[898,46381,2069],{},[2057,46383,46384,46386],{},[898,46385,1746],{},[895,46387,46388,46390],{},[1723,46389,1759],{},[898,46391,207],{},[1723,46393,2087],{},[898,46395,2878],{},[902,46397,46398],{"encoding":904},"Q = bP^{-a} + c",[123,46400,46401,46402],{},"(f) ",[883,46403,46405],{"className":46404},[886],[888,46406,46407],{"xmlns":890},[892,46408,46409,46432],{},[895,46410,46411,46413,46415,46417,46419],{},[898,46412,1904],{},[1723,46414,1725],{},[898,46416,207],{},[1723,46418,3897],{},[2057,46420,46421,46424],{},[898,46422,46423],{},"e",[895,46425,46426,46428,46430],{},[1723,46427,1759],{},[898,46429,2069],{},[898,46431,1746],{},[902,46433,46434],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,46436,46437,46440],{},[38,46438,46439],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,46442,46443,46446,46449],{},[123,46444,46445],{},"(a) Cena substitutu.",[123,46447,46448],{},"(b) Cena komplementu.",[123,46450,46451],{},"(c) Výdaje na reklamu.",[724,46453,46454,46117,46456,46490,46491,46519],{},[38,46455,25335],{},[883,46457,46459],{"className":46458},[886],[888,46460,46461],{"xmlns":890},[892,46462,46463,46487],{},[895,46464,46465,46467,46469,46471,46473,46475,46477,46479,46481,46483,46485],{},[898,46466,1746],{},[1723,46468,1725],{},[898,46470,4897],{},[1723,46472,1908],{"stretchy":1907},[898,46474,1904],{},[1723,46476,1914],{"stretchy":1907},[1723,46478,1725],{},[1864,46480,4227],{},[1723,46482,1759],{},[1864,46484,2331],{},[898,46486,1904],{},[902,46488,46489],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,46492,46494],{"className":46493},[886],[888,46495,46496],{"xmlns":890},[892,46497,46498,46516],{},[895,46499,46500,46502,46504,46510,46512,46514],{},[898,46501,1746],{},[1723,46503,1725],{},[2057,46505,46506,46508],{},[898,46507,4897],{},[1723,46509,5066],{},[1723,46511,1908],{"stretchy":1907},[898,46513,1904],{},[1723,46515,1914],{"stretchy":1907},[902,46517,46518],{"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.",[724,46521,46522,46525],{},[38,46523,46524],{},"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:",[120,46527,46528,46612,46688,46774,46862],{},[123,46529,46236,46530,1343,46570,1664],{},[883,46531,46533],{"className":46532},[886],[888,46534,46535],{"xmlns":890},[892,46536,46537,46567],{},[895,46538,46539,46545,46547,46549,46551,46553,46559,46561],{},[1931,46540,46541,46543],{},[898,46542,23946],{},[1864,46544,1866],{},[1723,46546,1725],{},[1864,46548,9744],{},[1723,46550,1759],{},[1864,46552,3080],{},[1931,46554,46555,46557],{},[898,46556,1718],{},[1864,46558,1866],{},[1723,46560,2087],{},[1931,46562,46563,46565],{},[898,46564,1718],{},[1864,46566,2331],{},[902,46568,46569],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,46571,46573],{"className":46572},[886],[888,46574,46575],{"xmlns":890},[892,46576,46577,46609],{},[895,46578,46579,46585,46587,46589,46591,46593,46599,46601,46603],{},[1931,46580,46581,46583],{},[898,46582,23946],{},[1864,46584,2331],{},[1723,46586,1725],{},[1864,46588,3585],{},[1723,46590,2087],{},[1864,46592,2331],{},[1931,46594,46595,46597],{},[898,46596,1718],{},[1864,46598,1866],{},[1723,46600,1759],{},[1864,46602,3080],{},[1931,46604,46605,46607],{},[898,46606,1718],{},[1864,46608,2331],{},[902,46610,46611],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,46613,46269,46614,1343,46656,1664],{},[883,46615,46617],{"className":46616},[886],[888,46618,46619],{"xmlns":890},[892,46620,46621,46653],{},[895,46622,46623,46629,46631,46633,46635,46637,46643,46645,46647],{},[1931,46624,46625,46627],{},[898,46626,23946],{},[1864,46628,1866],{},[1723,46630,1725],{},[1864,46632,3840],{},[1723,46634,1759],{},[1864,46636,3585],{},[1931,46638,46639,46641],{},[898,46640,1718],{},[1864,46642,1866],{},[1723,46644,1759],{},[1864,46646,2969],{},[1931,46648,46649,46651],{},[898,46650,1718],{},[1864,46652,2331],{},[902,46654,46655],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,46657,46659],{"className":46658},[886],[888,46660,46661],{"xmlns":890},[892,46662,46663,46685],{},[895,46664,46665,46671,46673,46675,46677,46679],{},[1931,46666,46667,46669],{},[898,46668,23946],{},[1864,46670,2331],{},[1723,46672,1725],{},[1864,46674,36937],{},[1723,46676,1759],{},[1864,46678,3585],{},[1931,46680,46681,46683],{},[898,46682,1718],{},[1864,46684,2331],{},[902,46686,46687],{"encoding":904},"B_2 = 15 - 10A_2",[123,46689,46300,46690,1343,46732,1664],{},[883,46691,46693],{"className":46692},[886],[888,46694,46695],{"xmlns":890},[892,46696,46697,46729],{},[895,46698,46699,46705,46707,46709,46711,46713,46719,46721,46723],{},[1931,46700,46701,46703],{},[898,46702,23946],{},[1864,46704,1866],{},[1723,46706,1725],{},[1864,46708,38711],{},[1723,46710,1759],{},[1864,46712,2331],{},[1931,46714,46715,46717],{},[898,46716,1718],{},[1864,46718,1866],{},[1723,46720,1759],{},[1864,46722,3080],{},[1931,46724,46725,46727],{},[898,46726,1718],{},[1864,46728,2331],{},[902,46730,46731],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,46733,46735],{"className":46734},[886],[888,46736,46737],{"xmlns":890},[892,46738,46739,46771],{},[895,46740,46741,46747,46749,46751,46753,46755,46761,46763,46765],{},[1931,46742,46743,46745],{},[898,46744,23946],{},[1864,46746,2331],{},[1723,46748,1725],{},[1864,46750,36937],{},[1723,46752,2087],{},[1864,46754,2331],{},[1931,46756,46757,46759],{},[898,46758,1718],{},[1864,46760,1866],{},[1723,46762,1759],{},[1864,46764,2331],{},[1931,46766,46767,46769],{},[898,46768,1718],{},[1864,46770,2331],{},[902,46772,46773],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,46775,46335,46776,1343,46820,1664],{},[883,46777,46779],{"className":46778},[886],[888,46780,46781],{"xmlns":890},[892,46782,46783,46817],{},[895,46784,46785,46791,46793,46795,46797,46799,46801,46807,46809,46811],{},[1931,46786,46787,46789],{},[898,46788,23946],{},[1864,46790,1866],{},[1723,46792,1725],{},[1723,46794,1759],{},[1864,46796,9744],{},[1723,46798,1759],{},[1864,46800,2331],{},[1931,46802,46803,46805],{},[898,46804,1718],{},[1864,46806,1866],{},[1723,46808,2087],{},[1864,46810,2909],{},[1931,46812,46813,46815],{},[898,46814,1718],{},[1864,46816,2331],{},[902,46818,46819],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,46821,46823],{"className":46822},[886],[888,46824,46825],{"xmlns":890},[892,46826,46827,46859],{},[895,46828,46829,46835,46837,46839,46841,46843,46849,46851,46853],{},[1931,46830,46831,46833],{},[898,46832,23946],{},[1864,46834,2331],{},[1723,46836,1725],{},[1864,46838,3585],{},[1723,46840,2087],{},[1864,46842,2331],{},[1931,46844,46845,46847],{},[898,46846,1718],{},[1864,46848,1866],{},[1723,46850,1759],{},[1864,46852,2331],{},[1931,46854,46855,46857],{},[898,46856,1718],{},[1864,46858,2331],{},[902,46860,46861],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,46863,46366,46864,1343,46906,1664],{},[883,46865,46867],{"className":46866},[886],[888,46868,46869],{"xmlns":890},[892,46870,46871,46903],{},[895,46872,46873,46879,46881,46883,46885,46887,46893,46895,46897],{},[1931,46874,46875,46877],{},[898,46876,23946],{},[1864,46878,1866],{},[1723,46880,1725],{},[1864,46882,9744],{},[1723,46884,2087],{},[1864,46886,2331],{},[1931,46888,46889,46891],{},[898,46890,1718],{},[1864,46892,1866],{},[1723,46894,2087],{},[1864,46896,3080],{},[1931,46898,46899,46901],{},[898,46900,1718],{},[1864,46902,2331],{},[902,46904,46905],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,46907,46909],{"className":46908},[886],[888,46910,46911],{"xmlns":890},[892,46912,46913,46945],{},[895,46914,46915,46921,46923,46925,46927,46929,46935,46937,46939],{},[1931,46916,46917,46919],{},[898,46918,23946],{},[1864,46920,2331],{},[1723,46922,1725],{},[1864,46924,5921],{},[1723,46926,1759],{},[1864,46928,2909],{},[1931,46930,46931,46933],{},[898,46932,1718],{},[1864,46934,1866],{},[1723,46936,2087],{},[1864,46938,2962],{},[1931,46940,46941,46943],{},[898,46942,1718],{},[1864,46944,2331],{},[902,46946,46947],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,46949,46951],{"id":46950},"základní-analýza-nabídky","Základní analýza nabídky",[724,46953,46954,46957,46958,46992,46993,47015],{},[38,46955,46956],{},"2.6"," Je dána nabídka ",[883,46959,46961],{"className":46960},[886],[888,46962,46963],{"xmlns":890},[892,46964,46965,46989],{},[895,46966,46967,46969,46971,46973,46975,46977,46979,46981,46983,46985,46987],{},[898,46968,1746],{},[1723,46970,1725],{},[898,46972,2111],{},[1723,46974,1908],{"stretchy":1907},[898,46976,1904],{},[1723,46978,1914],{"stretchy":1907},[1723,46980,1725],{},[1864,46982,9744],{},[1723,46984,2087],{},[1864,46986,3561],{},[898,46988,1904],{},[902,46990,46991],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,46994,46996],{"className":46995},[886],[888,46997,46998],{"xmlns":890},[892,46999,47000,47012],{},[895,47001,47002,47004,47006,47008,47010],{},[1864,47003,5714],{},[1723,47005,2031],{"separator":2030},[1864,47007,38711],{},[1723,47009,2031],{"separator":2030},[1864,47011,15739],{},[902,47013,47014],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,47017,47018,47021,47022,47039],{},[38,47019,47020],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,47023,47025],{"className":47024},[886],[888,47026,47027],{"xmlns":890},[892,47028,47029,47037],{},[895,47030,47031,47033,47035],{},[898,47032,1746],{},[1723,47034,2031],{"separator":2030},[898,47036,1904],{},[902,47038,46204],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,47041,47042,47068,47096,47129,47163,47199],{},[123,47043,46236,47044],{},[883,47045,47047],{"className":47046},[886],[888,47048,47049],{"xmlns":890},[892,47050,47051,47065],{},[895,47052,47053,47055,47057,47059,47061,47063],{},[898,47054,1746],{},[1723,47056,1725],{},[1864,47058,38711],{},[1723,47060,2087],{},[1864,47062,2331],{},[898,47064,1904],{},[902,47066,47067],{"encoding":904},"P = 30 + 2Q",[123,47069,46269,47070],{},[883,47071,47073],{"className":47072},[886],[888,47074,47075],{"xmlns":890},[892,47076,47077,47093],{},[895,47078,47079,47081,47083,47085,47087,47089,47091],{},[898,47080,1904],{},[1723,47082,1725],{},[1723,47084,1759],{},[1864,47086,2909],{},[1723,47088,2087],{},[1864,47090,4227],{},[898,47092,1746],{},[902,47094,47095],{"encoding":904},"Q = -3 + 12P",[123,47097,46300,47098],{},[883,47099,47101],{"className":47100},[886],[888,47102,47103],{"xmlns":890},[892,47104,47105,47127],{},[895,47106,47107,47109,47111,47117,47119,47121,47123,47125],{},[898,47108,1746],{},[1723,47110,1725],{},[2057,47112,47113,47115],{},[898,47114,1904],{},[1864,47116,2331],{},[1723,47118,2087],{},[1864,47120,23639],{},[898,47122,1904],{},[1723,47124,2087],{},[1864,47126,33239],{},[902,47128,42414],{"encoding":904},[123,47130,46335,47131],{},[883,47132,47134],{"className":47133},[886],[888,47135,47136],{"xmlns":890},[892,47137,47138,47160],{},[895,47139,47140,47142,47144,47150,47152,47154,47156,47158],{},[898,47141,1746],{},[1723,47143,1725],{},[2057,47145,47146,47148],{},[898,47147,1904],{},[1864,47149,2331],{},[1723,47151,2087],{},[1864,47153,2331],{},[898,47155,1904],{},[1723,47157,2087],{},[1864,47159,4227],{},[902,47161,47162],{"encoding":904},"P = Q^2 + 2Q + 12",[123,47164,46366,47165],{},[883,47166,47168],{"className":47167},[886],[888,47169,47170],{"xmlns":890},[892,47171,47172,47196],{},[895,47173,47174,47176,47178,47180,47182,47184,47186,47188,47190],{},[898,47175,1904],{},[1723,47177,1725],{},[1864,47179,9512],{},[1723,47181,2087],{},[1864,47183,2962],{},[898,47185,1746],{},[1723,47187,2087],{},[1864,47189,3517],{},[2057,47191,47192,47194],{},[898,47193,1746],{},[1864,47195,2331],{},[902,47197,47198],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,47200,46401,47201],{},[883,47202,47204],{"className":47203},[886],[888,47205,47206],{"xmlns":890},[892,47207,47208,47233],{},[895,47209,47210,47212,47214,47216,47218,47220,47222,47224,47227],{},[898,47211,1904],{},[1723,47213,1725],{},[1864,47215,24894],{},[1723,47217,2087],{},[1864,47219,3517],{},[898,47221,1746],{},[1723,47223,2087],{},[1864,47225,47226],{},"0,004",[2057,47228,47229,47231],{},[898,47230,1746],{},[1864,47232,2331],{},[902,47234,47235],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,47237,47238,47241],{},[38,47239,47240],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,47243,47244,47247,47250,47253],{},[123,47245,47246],{},"(a) Sníží ceny surovin — vstupů.",[123,47248,47249],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,47251,47252],{},"(c) Zvýší ceny všech energií.",[123,47254,47255],{},"(d) Sníží daňové odvody státu.",[724,47257,47258,46957,47260,47294,47295,47323],{},[38,47259,43641],{},[883,47261,47263],{"className":47262},[886],[888,47264,47265],{"xmlns":890},[892,47266,47267,47291],{},[895,47268,47269,47271,47273,47275,47277,47279,47281,47283,47285,47287,47289],{},[898,47270,1746],{},[1723,47272,1725],{},[898,47274,2111],{},[1723,47276,1908],{"stretchy":1907},[898,47278,1904],{},[1723,47280,1914],{"stretchy":1907},[1723,47282,1725],{},[1864,47284,5719],{},[898,47286,1904],{},[1723,47288,2087],{},[1864,47290,36937],{},[902,47292,47293],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,47296,47298],{"className":47297},[886],[888,47299,47300],{"xmlns":890},[892,47301,47302,47320],{},[895,47303,47304,47306,47308,47314,47316,47318],{},[898,47305,1746],{},[1723,47307,1725],{},[2057,47309,47310,47312],{},[898,47311,2111],{},[1723,47313,5066],{},[1723,47315,1908],{"stretchy":1907},[898,47317,1904],{},[1723,47319,1914],{"stretchy":1907},[902,47321,47322],{"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.",[198,47325,42017],{"id":47326},"tržní-rovnováha-1",[724,47328,47329,47331,47332,47349,47350,3430],{},[38,47330,43701],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,47333,47335],{"className":47334},[886],[888,47336,47337],{"xmlns":890},[892,47338,47339,47347],{},[895,47340,47341],{},[2057,47342,47343,47345],{},[898,47344,1904],{},[898,47346,1846],{},[902,47348,43095],{"encoding":904}," a rovnovážnou cenu ",[883,47351,47353],{"className":47352},[886],[888,47354,47355],{"xmlns":890},[892,47356,47357,47365],{},[895,47358,47359],{},[2057,47360,47361,47363],{},[898,47362,1746],{},[898,47364,1846],{},[902,47366,42158],{"encoding":904},[120,47368,47369,47422,47473,47532],{},[123,47370,46236,47371,1343,47398,1664],{},[883,47372,47374],{"className":47373},[886],[888,47375,47376],{"xmlns":890},[892,47377,47378,47395],{},[895,47379,47380,47382,47384,47386,47388,47390,47392],{},[898,47381,1746],{},[1723,47383,1725],{},[1723,47385,1759],{},[1864,47387,2962],{},[898,47389,1904],{},[1723,47391,2087],{},[1864,47393,47394],{},"80",[902,47396,47397],{"encoding":904},"P = -5Q + 80",[883,47399,47401],{"className":47400},[886],[888,47402,47403],{"xmlns":890},[892,47404,47405,47419],{},[895,47406,47407,47409,47411,47413,47415,47417],{},[898,47408,1746],{},[1723,47410,1725],{},[1864,47412,2331],{},[898,47414,1904],{},[1723,47416,2087],{},[1864,47418,3585],{},[902,47420,47421],{"encoding":904},"P = 2Q + 10",[123,47423,46269,47424,1343,47450,1664],{},[883,47425,47427],{"className":47426},[886],[888,47428,47429],{"xmlns":890},[892,47430,47431,47447],{},[895,47432,47433,47435,47437,47439,47441,47443,47445],{},[898,47434,1904],{},[1723,47436,1725],{},[1723,47438,1759],{},[1864,47440,5719],{},[898,47442,1746],{},[1723,47444,2087],{},[1864,47446,5714],{},[902,47448,47449],{"encoding":904},"Q = -0{,}5P + 25",[883,47451,47453],{"className":47452},[886],[888,47454,47455],{"xmlns":890},[892,47456,47457,47471],{},[895,47458,47459,47461,47463,47465,47467,47469],{},[898,47460,1904],{},[1723,47462,1725],{},[1864,47464,2331],{},[898,47466,1746],{},[1723,47468,1759],{},[1864,47470,3840],{},[902,47472,41539],{"encoding":904},[123,47474,46300,47475,1343,47501,1664],{},[883,47476,47478],{"className":47477},[886],[888,47479,47480],{"xmlns":890},[892,47481,47482,47498],{},[895,47483,47484,47486,47488,47490,47492,47494,47496],{},[898,47485,1746],{},[1723,47487,1725],{},[1723,47489,1759],{},[1864,47491,3080],{},[898,47493,1904],{},[1723,47495,2087],{},[1864,47497,4760],{},[902,47499,47500],{"encoding":904},"P = -4Q + 120",[883,47502,47504],{"className":47503},[886],[888,47505,47506],{"xmlns":890},[892,47507,47508,47529],{},[895,47509,47510,47512,47514,47522,47524,47526],{},[898,47511,1746],{},[1723,47513,1725],{},[3055,47515,47516],{"scriptlevel":2256,"displaystyle":1907},[3058,47517,47518,47520],{},[1864,47519,1866],{},[1864,47521,2909],{},[898,47523,1904],{},[1723,47525,2087],{},[1864,47527,47528],{},"29",[902,47530,47531],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,47533,46335,47534,1343,47563,1664],{},[883,47535,47537],{"className":47536},[886],[888,47538,47539],{"xmlns":890},[892,47540,47541,47560],{},[895,47542,47543,47545,47547,47549,47555,47557],{},[898,47544,1746],{},[1723,47546,1725],{},[1723,47548,1759],{},[2057,47550,47551,47553],{},[898,47552,1904],{},[1864,47554,2331],{},[1723,47556,2087],{},[1864,47558,47559],{},"52",[902,47561,47562],{"encoding":904},"P = -Q^2 + 52",[883,47564,47566],{"className":47565},[886],[888,47567,47568],{"xmlns":890},[892,47569,47570,47588],{},[895,47571,47572,47574,47576,47578,47584,47586],{},[898,47573,1746],{},[1723,47575,1725],{},[1864,47577,2331],{},[2057,47579,47580,47582],{},[898,47581,1904],{},[1864,47583,2331],{},[1723,47585,2087],{},[1864,47587,3585],{},[902,47589,47590],{"encoding":904},"P = 2Q^2 + 10",[724,47592,47593,47596,47597,47627,47628,47658],{},[38,47594,47595],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,47598,47600],{"className":47599},[886],[888,47601,47602],{"xmlns":890},[892,47603,47604,47624],{},[895,47605,47606,47614,47616],{},[2220,47607,47608,47610,47612],{},[898,47609,1904],{},[1864,47611,1866],{},[898,47613,1846],{},[1723,47615,2031],{"separator":2030},[2220,47617,47618,47620,47622],{},[898,47619,1904],{},[1864,47621,2331],{},[898,47623,1846],{},[902,47625,47626],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,47629,47631],{"className":47630},[886],[888,47632,47633],{"xmlns":890},[892,47634,47635,47655],{},[895,47636,47637,47645,47647],{},[2220,47638,47639,47641,47643],{},[898,47640,1746],{},[1864,47642,1866],{},[898,47644,1846],{},[1723,47646,2031],{"separator":2030},[2220,47648,47649,47651,47653],{},[898,47650,1746],{},[1864,47652,2331],{},[898,47654,1846],{},[902,47656,47657],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,47660,47661,47813],{},[123,47662,46236,47663,1343,47703,1343,47745,1343,47779,1664],{},[883,47664,47666],{"className":47665},[886],[888,47667,47668],{"xmlns":890},[892,47669,47670,47700],{},[895,47671,47672,47678,47680,47682,47684,47686,47692,47694],{},[1931,47673,47674,47676],{},[898,47675,1904],{},[1864,47677,1866],{},[1723,47679,1725],{},[1864,47681,3585],{},[1723,47683,1759],{},[1864,47685,2331],{},[1931,47687,47688,47690],{},[898,47689,1746],{},[1864,47691,1866],{},[1723,47693,2087],{},[1931,47695,47696,47698],{},[898,47697,1746],{},[1864,47699,2331],{},[902,47701,47702],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,47704,47706],{"className":47705},[886],[888,47707,47708],{"xmlns":890},[892,47709,47710,47742],{},[895,47711,47712,47718,47720,47722,47724,47726,47732,47734,47736],{},[1931,47713,47714,47716],{},[898,47715,1904],{},[1864,47717,2331],{},[1723,47719,1725],{},[1864,47721,2962],{},[1723,47723,2087],{},[1864,47725,2331],{},[1931,47727,47728,47730],{},[898,47729,1746],{},[1864,47731,1866],{},[1723,47733,1759],{},[1864,47735,2331],{},[1931,47737,47738,47740],{},[898,47739,1746],{},[1864,47741,2331],{},[902,47743,47744],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,47746,47748],{"className":47747},[886],[888,47749,47750],{"xmlns":890},[892,47751,47752,47776],{},[895,47753,47754,47760,47762,47764,47766,47768,47770],{},[1931,47755,47756,47758],{},[898,47757,1904],{},[1864,47759,1866],{},[1723,47761,1725],{},[1723,47763,1759],{},[1864,47765,2909],{},[1723,47767,2087],{},[1864,47769,2331],{},[1931,47771,47772,47774],{},[898,47773,1746],{},[1864,47775,1866],{},[902,47777,47778],{"encoding":904},"Q_1 = -3 + 2P_1",[883,47780,47782],{"className":47781},[886],[888,47783,47784],{"xmlns":890},[892,47785,47786,47810],{},[895,47787,47788,47794,47796,47798,47800,47802,47804],{},[1931,47789,47790,47792],{},[898,47791,1904],{},[1864,47793,2331],{},[1723,47795,1725],{},[1723,47797,1759],{},[1864,47799,2331],{},[1723,47801,2087],{},[1864,47803,2909],{},[1931,47805,47806,47808],{},[898,47807,1746],{},[1864,47809,2331],{},[902,47811,47812],{"encoding":904},"Q_2 = -2 + 3P_2",[123,47814,46269,47815,1343,47855,1343,47897,1343,47929,1664],{},[883,47816,47818],{"className":47817},[886],[888,47819,47820],{"xmlns":890},[892,47821,47822,47852],{},[895,47823,47824,47830,47832,47834,47836,47838,47844,47846],{},[1931,47825,47826,47828],{},[898,47827,1904],{},[1864,47829,1866],{},[1723,47831,1725],{},[1864,47833,3810],{},[1723,47835,1759],{},[1864,47837,2331],{},[1931,47839,47840,47842],{},[898,47841,1746],{},[1864,47843,1866],{},[1723,47845,2087],{},[1931,47847,47848,47850],{},[898,47849,1746],{},[1864,47851,2331],{},[902,47853,47854],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,47856,47858],{"className":47857},[886],[888,47859,47860],{"xmlns":890},[892,47861,47862,47894],{},[895,47863,47864,47870,47872,47874,47876,47878,47884,47886,47888],{},[1931,47865,47866,47868],{},[898,47867,1904],{},[1864,47869,2331],{},[1723,47871,1725],{},[1864,47873,2962],{},[1723,47875,2087],{},[1864,47877,2331],{},[1931,47879,47880,47882],{},[898,47881,1746],{},[1864,47883,1866],{},[1723,47885,1759],{},[1864,47887,2909],{},[1931,47889,47890,47892],{},[898,47891,1746],{},[1864,47893,2331],{},[902,47895,47896],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,47898,47900],{"className":47899},[886],[888,47901,47902],{"xmlns":890},[892,47903,47904,47926],{},[895,47905,47906,47912,47914,47916,47918,47920],{},[1931,47907,47908,47910],{},[898,47909,1904],{},[1864,47911,1866],{},[1723,47913,1725],{},[1723,47915,1759],{},[1864,47917,3585],{},[1723,47919,2087],{},[1931,47921,47922,47924],{},[898,47923,1746],{},[1864,47925,1866],{},[902,47927,47928],{"encoding":904},"Q_1 = -10 + P_1",[883,47930,47932],{"className":47931},[886],[888,47933,47934],{"xmlns":890},[892,47935,47936,47958],{},[895,47937,47938,47944,47946,47948,47950,47952],{},[1931,47939,47940,47942],{},[898,47941,1904],{},[1864,47943,2331],{},[1723,47945,1725],{},[1864,47947,2962],{},[1723,47949,2087],{},[1864,47951,2969],{},[1931,47953,47954,47956],{},[898,47955,1746],{},[1864,47957,2331],{},[902,47959,47960],{"encoding":904},"Q_2 = 5 + 6P_2",[724,47962,47963,47966,47967,1343,48015,1343,48061,48111,48112,1343,48144,1343,48178,22287,48212,1682,48230,48248,48249,48262,48263,48289,48290,47627,48330,1664],{},[38,47964,47965],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,47968,47970],{"className":47969},[886],[888,47971,47972],{"xmlns":890},[892,47973,47974,48012],{},[895,47975,47976,47982,47984,47986,47988,47994,47996,47998,48004,48006],{},[1931,47977,47978,47980],{},[898,47979,1904],{},[1864,47981,1866],{},[1723,47983,1725],{},[1864,47985,36937],{},[1723,47987,1759],{},[1931,47989,47990,47992],{},[898,47991,1746],{},[1864,47993,1866],{},[1723,47995,2087],{},[1864,47997,2331],{},[1931,47999,48000,48002],{},[898,48001,1746],{},[1864,48003,2331],{},[1723,48005,2087],{},[1931,48007,48008,48010],{},[898,48009,1746],{},[1864,48011,2909],{},[902,48013,48014],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,48016,48018],{"className":48017},[886],[888,48019,48020],{"xmlns":890},[892,48021,48022,48058],{},[895,48023,48024,48030,48032,48034,48036,48042,48044,48050,48052],{},[1931,48025,48026,48028],{},[898,48027,1904],{},[1864,48029,2331],{},[1723,48031,1725],{},[1864,48033,4713],{},[1723,48035,2087],{},[1931,48037,48038,48040],{},[898,48039,1746],{},[1864,48041,1866],{},[1723,48043,1759],{},[1931,48045,48046,48048],{},[898,48047,1746],{},[1864,48049,2331],{},[1723,48051,1759],{},[1931,48053,48054,48056],{},[898,48055,1746],{},[1864,48057,2909],{},[902,48059,48060],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,48062,48064],{"className":48063},[886],[888,48065,48066],{"xmlns":890},[892,48067,48068,48108],{},[895,48069,48070,48076,48078,48080,48082,48084,48090,48092,48098,48100,48102],{},[1931,48071,48072,48074],{},[898,48073,1904],{},[1864,48075,2909],{},[1723,48077,1725],{},[1864,48079,6295],{},[1723,48081,2087],{},[1864,48083,2331],{},[1931,48085,48086,48088],{},[898,48087,1746],{},[1864,48089,1866],{},[1723,48091,1759],{},[1931,48093,48094,48096],{},[898,48095,1746],{},[1864,48097,2331],{},[1723,48099,1759],{},[1864,48101,3080],{},[1931,48103,48104,48106],{},[898,48105,1746],{},[1864,48107,2909],{},[902,48109,48110],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,48113,48115],{"className":48114},[886],[888,48116,48117],{"xmlns":890},[892,48118,48119,48141],{},[895,48120,48121,48127,48129,48131,48133,48135],{},[1931,48122,48123,48125],{},[898,48124,1904],{},[1864,48126,1866],{},[1723,48128,1725],{},[1723,48130,1759],{},[1864,48132,24894],{},[1723,48134,2087],{},[1931,48136,48137,48139],{},[898,48138,1746],{},[1864,48140,1866],{},[902,48142,48143],{"encoding":904},"Q_1 = -7 + P_1",[883,48145,48147],{"className":48146},[886],[888,48148,48149],{"xmlns":890},[892,48150,48151,48175],{},[895,48152,48153,48159,48161,48163,48165,48167,48169],{},[1931,48154,48155,48157],{},[898,48156,1904],{},[1864,48158,2331],{},[1723,48160,1725],{},[1723,48162,1759],{},[1864,48164,3080],{},[1723,48166,2087],{},[1864,48168,3080],{},[1931,48170,48171,48173],{},[898,48172,1746],{},[1864,48174,2331],{},[902,48176,48177],{"encoding":904},"Q_2 = -4 + 4P_2",[883,48179,48181],{"className":48180},[886],[888,48182,48183],{"xmlns":890},[892,48184,48185,48209],{},[895,48186,48187,48193,48195,48197,48199,48201,48203],{},[1931,48188,48189,48191],{},[898,48190,1904],{},[1864,48192,2909],{},[1723,48194,1725],{},[1723,48196,1759],{},[1864,48198,2962],{},[1723,48200,2087],{},[1864,48202,2331],{},[1931,48204,48205,48207],{},[898,48206,1746],{},[1864,48208,2909],{},[902,48210,48211],{"encoding":904},"Q_3 = -5 + 2P_3",[883,48213,48215],{"className":48214},[886],[888,48216,48217],{"xmlns":890},[892,48218,48219,48227],{},[895,48220,48221],{},[1931,48222,48223,48225],{},[898,48224,1904],{},[898,48226,2216],{},[902,48228,48229],{"encoding":904},"Q_i",[883,48231,48233],{"className":48232},[886],[888,48234,48235],{"xmlns":890},[892,48236,48237,48245],{},[895,48238,48239],{},[1931,48240,48241,48243],{},[898,48242,1746],{},[898,48244,2216],{},[902,48246,48247],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,48250,48252],{"className":48251},[886],[888,48253,48254],{"xmlns":890},[892,48255,48256,48260],{},[895,48257,48258],{},[898,48259,2216],{},[902,48261,2216],{"encoding":904},"-tého zboží, ",[883,48264,48266],{"className":48265},[886],[888,48267,48268],{"xmlns":890},[892,48269,48270,48286],{},[895,48271,48272,48274,48276,48278,48280,48282,48284],{},[898,48273,2216],{},[1723,48275,1725],{},[1864,48277,1866],{},[1723,48279,2031],{"separator":2030},[1864,48281,2331],{},[1723,48283,2031],{"separator":2030},[1864,48285,2909],{},[902,48287,48288],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,48291,48293],{"className":48292},[886],[888,48294,48295],{"xmlns":890},[892,48296,48297,48327],{},[895,48298,48299,48307,48309,48317,48319],{},[2220,48300,48301,48303,48305],{},[898,48302,1904],{},[1864,48304,1866],{},[898,48306,1846],{},[1723,48308,2031],{"separator":2030},[2220,48310,48311,48313,48315],{},[898,48312,1904],{},[1864,48314,2331],{},[898,48316,1846],{},[1723,48318,2031],{"separator":2030},[2220,48320,48321,48323,48325],{},[898,48322,1904],{},[1864,48324,2909],{},[898,48326,1846],{},[902,48328,48329],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,48331,48333],{"className":48332},[886],[888,48334,48335],{"xmlns":890},[892,48336,48337,48367],{},[895,48338,48339,48347,48349,48357,48359],{},[2220,48340,48341,48343,48345],{},[898,48342,1746],{},[1864,48344,1866],{},[898,48346,1846],{},[1723,48348,2031],{"separator":2030},[2220,48350,48351,48353,48355],{},[898,48352,1746],{},[1864,48354,2331],{},[898,48356,1846],{},[1723,48358,2031],{"separator":2030},[2220,48360,48361,48363,48365],{},[898,48362,1746],{},[1864,48364,2909],{},[898,48366,1846],{},[902,48368,48369],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,48371,48372,48375,48376,48412,48413,1664],{},[38,48373,48374],{},"2.13"," Jsou dány poptávka ",[883,48377,48379],{"className":48378},[886],[888,48380,48381],{"xmlns":890},[892,48382,48383,48409],{},[895,48384,48385,48387,48389,48391,48393,48395,48397,48399,48401,48403,48405,48407],{},[898,48386,1746],{},[1723,48388,1725],{},[898,48390,4897],{},[1723,48392,1908],{"stretchy":1907},[898,48394,1904],{},[1723,48396,1914],{"stretchy":1907},[1723,48398,1725],{},[1723,48400,1759],{},[1864,48402,3080],{},[898,48404,1904],{},[1723,48406,2087],{},[1864,48408,47394],{},[902,48410,48411],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,48414,48416],{"className":48415},[886],[888,48417,48418],{"xmlns":890},[892,48419,48420,48444],{},[895,48421,48422,48424,48426,48428,48430,48432,48434,48436,48438,48440,48442],{},[898,48423,1746],{},[1723,48425,1725],{},[898,48427,2111],{},[1723,48429,1908],{"stretchy":1907},[898,48431,1904],{},[1723,48433,1914],{"stretchy":1907},[1723,48435,1725],{},[1864,48437,2909],{},[898,48439,1904],{},[1723,48441,2087],{},[1864,48443,3585],{},[902,48445,48446],{"encoding":904},"P = S(Q) = 3Q + 10",[120,48448,48449,48486,48550,48610],{},[123,48450,48451,48452,47349,48469,1664],{},"(a) Určete rovnovážné množství ",[883,48453,48455],{"className":48454},[886],[888,48456,48457],{"xmlns":890},[892,48458,48459,48467],{},[895,48460,48461],{},[2057,48462,48463,48465],{},[898,48464,1904],{},[898,48466,1846],{},[902,48468,43095],{"encoding":904},[883,48470,48472],{"className":48471},[886],[888,48473,48474],{"xmlns":890},[892,48475,48476,48484],{},[895,48477,48478],{},[2057,48479,48480,48482],{},[898,48481,1746],{},[898,48483,1846],{},[902,48485,42158],{"encoding":904},[123,48487,48488,48489,48507,48508,48528,48529,48549],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,48490,48492],{"className":48491},[886],[888,48493,48494],{"xmlns":890},[892,48495,48496,48504],{},[895,48497,48498,48500,48502],{},[898,48499,1754],{},[1723,48501,1725],{},[1864,48503,24894],{},[902,48505,48506],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,48509,48511],{"className":48510},[886],[888,48512,48513],{"xmlns":890},[892,48514,48515,48525],{},[895,48516,48517],{},[2220,48518,48519,48521,48523],{},[898,48520,1904],{},[1864,48522,1866],{},[898,48524,1846],{},[902,48526,48527],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,48530,48532],{"className":48531},[886],[888,48533,48534],{"xmlns":890},[892,48535,48536,48546],{},[895,48537,48538],{},[2220,48539,48540,48542,48544],{},[898,48541,1746],{},[1864,48543,1866],{},[898,48545,1846],{},[902,48547,48548],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,48551,48552,48553,48507,48570,48528,48590,48549],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,48554,48556],{"className":48555},[886],[888,48557,48558],{"xmlns":890},[892,48559,48560,48568],{},[895,48561,48562,48564,48566],{},[898,48563,1754],{},[1723,48565,1725],{},[1864,48567,24894],{},[902,48569,48506],{"encoding":904},[883,48571,48573],{"className":48572},[886],[888,48574,48575],{"xmlns":890},[892,48576,48577,48587],{},[895,48578,48579],{},[2220,48580,48581,48583,48585],{},[898,48582,1904],{},[1864,48584,2331],{},[898,48586,1846],{},[902,48588,48589],{"encoding":904},"Q_2^E",[883,48591,48593],{"className":48592},[886],[888,48594,48595],{"xmlns":890},[892,48596,48597,48607],{},[895,48598,48599],{},[2220,48600,48601,48603,48605],{},[898,48602,1746],{},[1864,48604,2331],{},[898,48606,1846],{},[902,48608,48609],{"encoding":904},"P_2^E",[123,48611,48612],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,48614,48615,48616,1664],{},"Viz též ",[207,48617,43413],{"className":48618,"dataFsResolvedFilePath":809,"href":810},[210],[198,48620,43715],{"id":48621},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,48623,48624,48375,48627,48412,48663,1664],{},[38,48625,48626],{},"2.14",[883,48628,48630],{"className":48629},[886],[888,48631,48632],{"xmlns":890},[892,48633,48634,48660],{},[895,48635,48636,48638,48640,48642,48644,48646,48648,48650,48652,48654,48656,48658],{},[898,48637,1746],{},[1723,48639,1725],{},[898,48641,207],{},[898,48643,1904],{},[1723,48645,2087],{},[898,48647,2069],{},[1723,48649,1725],{},[1723,48651,1759],{},[1864,48653,2331],{},[898,48655,1904],{},[1723,48657,2087],{},[1864,48659,3840],{},[902,48661,48662],{"encoding":904},"P = aQ + b = -2Q + 50",[883,48664,48666],{"className":48665},[886],[888,48667,48668],{"xmlns":890},[892,48669,48670,48694],{},[895,48671,48672,48674,48676,48678,48680,48682,48684,48686,48688,48690,48692],{},[898,48673,1746],{},[1723,48675,1725],{},[898,48677,2878],{},[898,48679,1904],{},[1723,48681,2087],{},[898,48683,2930],{},[1723,48685,1725],{},[1864,48687,20015],{},[898,48689,1904],{},[1723,48691,2087],{},[1864,48693,9744],{},[902,48695,48696],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,48698,48699,48735,48738,48824,48877,48957,49011],{},[123,48700,48451,48701,47349,48718,1664],{},[883,48702,48704],{"className":48703},[886],[888,48705,48706],{"xmlns":890},[892,48707,48708,48716],{},[895,48709,48710],{},[2057,48711,48712,48714],{},[898,48713,1904],{},[898,48715,1846],{},[902,48717,43095],{"encoding":904},[883,48719,48721],{"className":48720},[886],[888,48722,48723],{"xmlns":890},[892,48724,48725,48733],{},[895,48726,48727],{},[2057,48728,48729,48731],{},[898,48730,1746],{},[898,48732,1846],{},[902,48734,42158],{"encoding":904},[123,48736,48737],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,48739,48740,48741,48758,48759,3397,48772,3411,48788,48804,48805,1664],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,48742,48744],{"className":48743},[886],[888,48745,48746],{"xmlns":890},[892,48747,48748,48756],{},[895,48749,48750],{},[2057,48751,48752,48754],{},[898,48753,1904],{},[898,48755,1846],{},[902,48757,43095],{"encoding":904}," odpovídající změně ",[883,48760,48762],{"className":48761},[886],[888,48763,48764],{"xmlns":890},[892,48765,48766,48770],{},[895,48767,48768],{},[898,48769,207],{},[902,48771,207],{"encoding":904},[883,48773,48775],{"className":48774},[886],[888,48776,48777],{"xmlns":890},[892,48778,48779,48785],{},[895,48780,48781,48783],{},[1723,48782,1759],{},[1864,48784,2331],{},[902,48786,48787],{"encoding":904},"-2",[883,48789,48791],{"className":48790},[886],[888,48792,48793],{"xmlns":890},[892,48794,48795,48801],{},[895,48796,48797,48799],{},[1723,48798,1759],{},[1864,48800,2909],{},[902,48802,48803],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48806,48808],{"className":48807},[886],[888,48809,48810],{"xmlns":890},[892,48811,48812,48822],{},[895,48813,48814],{},[2220,48815,48816,48818,48820],{},[898,48817,1904],{},[1864,48819,1866],{},[898,48821,1846],{},[902,48823,48527],{"encoding":904},[123,48825,48826,48827,48758,48844,48857,48858,1664],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,48828,48830],{"className":48829},[886],[888,48831,48832],{"xmlns":890},[892,48833,48834,48842],{},[895,48835,48836],{},[2057,48837,48838,48840],{},[898,48839,1904],{},[898,48841,1846],{},[902,48843,43095],{"encoding":904},[883,48845,48847],{"className":48846},[886],[888,48848,48849],{"xmlns":890},[892,48850,48851,48855],{},[895,48852,48853],{},[898,48854,2069],{},[902,48856,2069],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48859,48861],{"className":48860},[886],[888,48862,48863],{"xmlns":890},[892,48864,48865,48875],{},[895,48866,48867],{},[2220,48868,48869,48871,48873],{},[898,48870,1904],{},[1864,48872,2331],{},[898,48874,1846],{},[902,48876,48589],{"encoding":904},[123,48878,48879,48880,48758,48897,3397,48910,3411,48923,48804,48937,1664],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,48881,48883],{"className":48882},[886],[888,48884,48885],{"xmlns":890},[892,48886,48887,48895],{},[895,48888,48889],{},[2057,48890,48891,48893],{},[898,48892,1904],{},[898,48894,1846],{},[902,48896,43095],{"encoding":904},[883,48898,48900],{"className":48899},[886],[888,48901,48902],{"xmlns":890},[892,48903,48904,48908],{},[895,48905,48906],{},[898,48907,2878],{},[902,48909,2878],{"encoding":904},[883,48911,48913],{"className":48912},[886],[888,48914,48915],{"xmlns":890},[892,48916,48917,48921],{},[895,48918,48919],{},[1864,48920,20015],{},[902,48922,45152],{"encoding":904},[883,48924,48926],{"className":48925},[886],[888,48927,48928],{"xmlns":890},[892,48929,48930,48934],{},[895,48931,48932],{},[1864,48933,15290],{},[902,48935,48936],{"encoding":904},"0{,}8",[883,48938,48940],{"className":48939},[886],[888,48941,48942],{"xmlns":890},[892,48943,48944,48954],{},[895,48945,48946],{},[2220,48947,48948,48950,48952],{},[898,48949,1904],{},[1864,48951,2909],{},[898,48953,1846],{},[902,48955,48956],{"encoding":904},"Q_3^E",[123,48958,48959,48960,48758,48977,48990,48991,1664],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,48961,48963],{"className":48962},[886],[888,48964,48965],{"xmlns":890},[892,48966,48967,48975],{},[895,48968,48969],{},[2057,48970,48971,48973],{},[898,48972,1904],{},[898,48974,1846],{},[902,48976,43095],{"encoding":904},[883,48978,48980],{"className":48979},[886],[888,48981,48982],{"xmlns":890},[892,48983,48984,48988],{},[895,48985,48986],{},[898,48987,2930],{},[902,48989,2930],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48992,48994],{"className":48993},[886],[888,48995,48996],{"xmlns":890},[892,48997,48998,49008],{},[895,48999,49000],{},[2220,49001,49002,49004,49006],{},[898,49003,1904],{},[1864,49005,3080],{},[898,49007,1846],{},[902,49009,49010],{"encoding":904},"Q_4^E",[123,49012,49013,49014,49031,49032,49045,49046,22113,49059,1343,49074,22113,49087,1682,49101,22113,49114,49129,49130,1664],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,49015,49017],{"className":49016},[886],[888,49018,49019],{"xmlns":890},[892,49020,49021,49029],{},[895,49022,49023],{},[2057,49024,49025,49027],{},[898,49026,1904],{},[898,49028,1846],{},[902,49030,43095],{"encoding":904}," odpovídající změnám ",[883,49033,49035],{"className":49034},[886],[888,49036,49037],{"xmlns":890},[892,49038,49039,49043],{},[895,49040,49041],{},[898,49042,207],{},[902,49044,207],{"encoding":904}," o 1, ",[883,49047,49049],{"className":49048},[886],[888,49050,49051],{"xmlns":890},[892,49052,49053,49057],{},[895,49054,49055],{},[898,49056,2069],{},[902,49058,2069],{"encoding":904},[883,49060,49062],{"className":49061},[886],[888,49063,49064],{"xmlns":890},[892,49065,49066,49072],{},[895,49067,49068,49070],{},[1723,49069,1759],{},[1864,49071,3585],{},[902,49073,20149],{"encoding":904},[883,49075,49077],{"className":49076},[886],[888,49078,49079],{"xmlns":890},[892,49080,49081,49085],{},[895,49082,49083],{},[898,49084,2878],{},[902,49086,2878],{"encoding":904},[883,49088,49090],{"className":49089},[886],[888,49091,49092],{"xmlns":890},[892,49093,49094,49098],{},[895,49095,49096],{},[1864,49097,3517],{},[902,49099,49100],{"encoding":904},"0{,}1",[883,49102,49104],{"className":49103},[886],[888,49105,49106],{"xmlns":890},[892,49107,49108,49112],{},[895,49109,49110],{},[898,49111,2930],{},[902,49113,2930],{"encoding":904},[883,49115,49117],{"className":49116},[886],[888,49118,49119],{"xmlns":890},[892,49120,49121,49127],{},[895,49122,49123,49125],{},[1723,49124,1759],{},[1864,49126,3585],{},[902,49128,20149],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,49131,49133],{"className":49132},[886],[888,49134,49135],{"xmlns":890},[892,49136,49137,49147],{},[895,49138,49139],{},[2220,49140,49141,49143,49145],{},[898,49142,1904],{},[1864,49144,2962],{},[898,49146,1846],{},[902,49148,49149],{"encoding":904},"Q_5^E",[724,49151,49152,48375,49155,48412,49178,1664],{},[38,49153,49154],{},"2.15",[883,49156,49158],{"className":49157},[886],[888,49159,49160],{"xmlns":890},[892,49161,49162,49176],{},[895,49163,49164,49166,49168,49170,49172,49174],{},[898,49165,1746],{},[1723,49167,1725],{},[898,49169,207],{},[898,49171,1904],{},[1723,49173,2087],{},[898,49175,2069],{},[902,49177,37752],{"encoding":904},[883,49179,49181],{"className":49180},[886],[888,49182,49183],{"xmlns":890},[892,49184,49185,49199],{},[895,49186,49187,49189,49191,49193,49195,49197],{},[898,49188,1746],{},[1723,49190,1725],{},[898,49192,2878],{},[898,49194,1904],{},[1723,49196,2087],{},[898,49198,2930],{},[902,49200,40934],{"encoding":904},[120,49202,49203,49278,49295,49404,49457,49511],{},[123,49204,49205,49206,49219,49220,49245,49246,49277],{},"(a) Odvoďte redukovaný tvar pro ",[883,49207,49209],{"className":49208},[886],[888,49210,49211],{"xmlns":890},[892,49212,49213,49217],{},[895,49214,49215],{},[898,49216,1746],{},[902,49218,1746],{"encoding":904},". Stanovte podmínky pro ",[883,49221,49223],{"className":49222},[886],[888,49224,49225],{"xmlns":890},[892,49226,49227,49243],{},[895,49228,49229,49231,49233,49235,49237,49239,49241],{},[898,49230,207],{},[1723,49232,2031],{"separator":2030},[898,49234,2069],{},[1723,49236,2031],{"separator":2030},[898,49238,2878],{},[1723,49240,2031],{"separator":2030},[898,49242,2930],{},[902,49244,43977],{"encoding":904}," tak, aby rovnovážný bod ",[883,49247,49249],{"className":49248},[886],[888,49250,49251],{"xmlns":890},[892,49252,49253,49275],{},[895,49254,49255,49257,49259,49265,49267,49273],{},[898,49256,1846],{},[1723,49258,3212],{"stretchy":1907},[2057,49260,49261,49263],{},[898,49262,1904],{},[898,49264,1846],{},[1723,49266,2031],{"separator":2030},[2057,49268,49269,49271],{},[898,49270,1746],{},[898,49272,1846],{},[1723,49274,3227],{"stretchy":1907},[902,49276,42059],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,49279,49280,49281,49294],{},"(b) Vypočtěte multiplikátory pro ",[883,49282,49284],{"className":49283},[886],[888,49285,49286],{"xmlns":890},[892,49287,49288,49292],{},[895,49289,49290],{},[898,49291,1746],{},[902,49293,1746],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,49296,49297,49298,1343,49318,1343,49336,1343,49354,49372,49373,49390,49391,1664],{},"(c) Pro hodnoty parametrů ",[883,49299,49301],{"className":49300},[886],[888,49302,49303],{"xmlns":890},[892,49304,49305,49315],{},[895,49306,49307,49309,49311,49313],{},[898,49308,207],{},[1723,49310,1725],{},[1723,49312,1759],{},[1864,49314,2331],{},[902,49316,49317],{"encoding":904},"a = -2",[883,49319,49321],{"className":49320},[886],[888,49322,49323],{"xmlns":890},[892,49324,49325,49333],{},[895,49326,49327,49329,49331],{},[898,49328,2069],{},[1723,49330,1725],{},[1864,49332,5921],{},[902,49334,49335],{"encoding":904},"b = 40",[883,49337,49339],{"className":49338},[886],[888,49340,49341],{"xmlns":890},[892,49342,49343,49351],{},[895,49344,49345,49347,49349],{},[898,49346,2878],{},[1723,49348,1725],{},[1864,49350,5719],{},[902,49352,49353],{"encoding":904},"c = 0{,}5",[883,49355,49357],{"className":49356},[886],[888,49358,49359],{"xmlns":890},[892,49360,49361,49369],{},[895,49362,49363,49365,49367],{},[898,49364,2930],{},[1723,49366,1725],{},[1864,49368,3585],{},[902,49370,49371],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,49374,49376],{"className":49375},[886],[888,49377,49378],{"xmlns":890},[892,49379,49380,49388],{},[895,49381,49382],{},[2057,49383,49384,49386],{},[898,49385,1746],{},[898,49387,1846],{},[902,49389,42158],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,49392,49394],{"className":49393},[886],[888,49395,49396],{"xmlns":890},[892,49397,49398,49402],{},[895,49399,49400],{},[898,49401,1746],{},[902,49403,1746],{"encoding":904},[123,49405,49406,49407,48758,49424,49437,49438,1664],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,49408,49410],{"className":49409},[886],[888,49411,49412],{"xmlns":890},[892,49413,49414,49422],{},[895,49415,49416],{},[2057,49417,49418,49420],{},[898,49419,1746],{},[898,49421,1846],{},[902,49423,42158],{"encoding":904},[883,49425,49427],{"className":49426},[886],[888,49428,49429],{"xmlns":890},[892,49430,49431,49435],{},[895,49432,49433],{},[898,49434,207],{},[902,49436,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,49439,49441],{"className":49440},[886],[888,49442,49443],{"xmlns":890},[892,49444,49445,49455],{},[895,49446,49447],{},[2220,49448,49449,49451,49453],{},[898,49450,1746],{},[1864,49452,1866],{},[898,49454,1846],{},[902,49456,48548],{"encoding":904},[123,49458,49459,49460,49477,49478,49491,49492,1664],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,49461,49463],{"className":49462},[886],[888,49464,49465],{"xmlns":890},[892,49466,49467,49475],{},[895,49468,49469],{},[2057,49470,49471,49473],{},[898,49472,1746],{},[898,49474,1846],{},[902,49476,42158],{"encoding":904}," odpovídající poklesu ",[883,49479,49481],{"className":49480},[886],[888,49482,49483],{"xmlns":890},[892,49484,49485,49489],{},[895,49486,49487],{},[898,49488,207],{},[902,49490,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,49493,49495],{"className":49494},[886],[888,49496,49497],{"xmlns":890},[892,49498,49499,49509],{},[895,49500,49501],{},[2220,49502,49503,49505,49507],{},[898,49504,1746],{},[1864,49506,2331],{},[898,49508,1846],{},[902,49510,48609],{"encoding":904},[123,49512,49513,49514,49031,49531,49544,49545,3411,49558,1682,49573,49586,49587,1664],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,49515,49517],{"className":49516},[886],[888,49518,49519],{"xmlns":890},[892,49520,49521,49529],{},[895,49522,49523],{},[2057,49524,49525,49527],{},[898,49526,1746],{},[898,49528,1846],{},[902,49530,42158],{"encoding":904},[883,49532,49534],{"className":49533},[886],[888,49535,49536],{"xmlns":890},[892,49537,49538,49542],{},[895,49539,49540],{},[898,49541,207],{},[902,49543,207],{"encoding":904}," na 35, ",[883,49546,49548],{"className":49547},[886],[888,49549,49550],{"xmlns":890},[892,49551,49552,49556],{},[895,49553,49554],{},[898,49555,2878],{},[902,49557,2878],{"encoding":904},[883,49559,49561],{"className":49560},[886],[888,49562,49563],{"xmlns":890},[892,49564,49565,49570],{},[895,49566,49567],{},[1864,49568,49569],{},"0,7",[902,49571,49572],{"encoding":904},"0{,}7",[883,49574,49576],{"className":49575},[886],[888,49577,49578],{"xmlns":890},[892,49579,49580,49584],{},[895,49581,49582],{},[898,49583,2930],{},[902,49585,2930],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,49588,49590],{"className":49589},[886],[888,49591,49592],{"xmlns":890},[892,49593,49594,49604],{},[895,49595,49596],{},[2220,49597,49598,49600,49602],{},[898,49599,1746],{},[1864,49601,2909],{},[898,49603,1846],{},[902,49605,49606],{"encoding":904},"P_3^E",[724,49608,49609,48375,49612,48412,49640,22287,49668,1682,49694,1664],{},[38,49610,49611],{},"2.16",[883,49613,49615],{"className":49614},[886],[888,49616,49617],{"xmlns":890},[892,49618,49619,49637],{},[895,49620,49621,49623,49625,49627,49629,49631],{},[898,49622,1746],{},[1723,49624,1725],{},[898,49626,207],{},[1723,49628,2087],{},[898,49630,2069],{},[2057,49632,49633,49635],{},[898,49634,1904],{},[1864,49636,2331],{},[902,49638,49639],{"encoding":904},"P = a + bQ^2",[883,49641,49643],{"className":49642},[886],[888,49644,49645],{"xmlns":890},[892,49646,49647,49665],{},[895,49648,49649,49651,49653,49655,49657,49659],{},[898,49650,1746],{},[1723,49652,1725],{},[898,49654,2878],{},[1723,49656,2087],{},[898,49658,2930],{},[2057,49660,49661,49663],{},[898,49662,1904],{},[1864,49664,2331],{},[902,49666,49667],{"encoding":904},"P = c + dQ^2",[883,49669,49671],{"className":49670},[886],[888,49672,49673],{"xmlns":890},[892,49674,49675,49691],{},[895,49676,49677,49679,49681,49683,49685,49687,49689],{},[898,49678,207],{},[1723,49680,2031],{"separator":2030},[898,49682,2878],{},[1723,49684,2031],{"separator":2030},[898,49686,2930],{},[1723,49688,2253],{},[1864,49690,2256],{},[902,49692,49693],{"encoding":904},"a, c, d > 0",[883,49695,49697],{"className":49696},[886],[888,49698,49699],{"xmlns":890},[892,49700,49701,49709],{},[895,49702,49703,49705,49707],{},[898,49704,2069],{},[1723,49706,2287],{},[1864,49708,2256],{},[902,49710,49711],{"encoding":904},"b \u003C 0",[120,49713,49714,49762,49778,49885,49937,49989,50098,50114,50213,50266],{},[123,49715,49205,49716,49729,49730,49761],{},[883,49717,49719],{"className":49718},[886],[888,49720,49721],{"xmlns":890},[892,49722,49723,49727],{},[895,49724,49725],{},[898,49726,1904],{},[902,49728,1904],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,49731,49733],{"className":49732},[886],[888,49734,49735],{"xmlns":890},[892,49736,49737,49759],{},[895,49738,49739,49741,49743,49749,49751,49757],{},[898,49740,1846],{},[1723,49742,3212],{"stretchy":1907},[2057,49744,49745,49747],{},[898,49746,1904],{},[898,49748,1846],{},[1723,49750,2031],{"separator":2030},[2057,49752,49753,49755],{},[898,49754,1746],{},[898,49756,1846],{},[1723,49758,3227],{"stretchy":1907},[902,49760,42059],{"encoding":904}," patřil do 1. kvadrantu.",[123,49763,49280,49764,49777],{},[883,49765,49767],{"className":49766},[886],[888,49768,49769],{"xmlns":890},[892,49770,49771,49775],{},[895,49772,49773],{},[898,49774,1904],{},[902,49776,1904],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,49779,49297,49780,1343,49798,1343,49818,1343,49836,49854,49855,49390,49872,1664],{},[883,49781,49783],{"className":49782},[886],[888,49784,49785],{"xmlns":890},[892,49786,49787,49795],{},[895,49788,49789,49791,49793],{},[898,49790,207],{},[1723,49792,1725],{},[1864,49794,3810],{},[902,49796,49797],{"encoding":904},"a = 100",[883,49799,49801],{"className":49800},[886],[888,49802,49803],{"xmlns":890},[892,49804,49805,49815],{},[895,49806,49807,49809,49811,49813],{},[898,49808,2069],{},[1723,49810,1725],{},[1723,49812,1759],{},[1864,49814,1866],{},[902,49816,49817],{"encoding":904},"b = -1",[883,49819,49821],{"className":49820},[886],[888,49822,49823],{"xmlns":890},[892,49824,49825,49833],{},[895,49826,49827,49829,49831],{},[898,49828,2878],{},[1723,49830,1725],{},[1864,49832,9744],{},[902,49834,49835],{"encoding":904},"c = 20",[883,49837,49839],{"className":49838},[886],[888,49840,49841],{"xmlns":890},[892,49842,49843,49851],{},[895,49844,49845,49847,49849],{},[898,49846,2930],{},[1723,49848,1725],{},[1864,49850,1866],{},[902,49852,49853],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,49856,49858],{"className":49857},[886],[888,49859,49860],{"xmlns":890},[892,49861,49862,49870],{},[895,49863,49864],{},[2057,49865,49866,49868],{},[898,49867,1904],{},[898,49869,1846],{},[902,49871,43095],{"encoding":904},[883,49873,49875],{"className":49874},[886],[888,49876,49877],{"xmlns":890},[892,49878,49879,49883],{},[895,49880,49881],{},[898,49882,1904],{},[902,49884,1904],{"encoding":904},[123,49886,48826,49887,48758,49904,49917,49918,1664],{},[883,49888,49890],{"className":49889},[886],[888,49891,49892],{"xmlns":890},[892,49893,49894,49902],{},[895,49895,49896],{},[2057,49897,49898,49900],{},[898,49899,1904],{},[898,49901,1846],{},[902,49903,43095],{"encoding":904},[883,49905,49907],{"className":49906},[886],[888,49908,49909],{"xmlns":890},[892,49910,49911,49915],{},[895,49912,49913],{},[898,49914,207],{},[902,49916,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49919,49921],{"className":49920},[886],[888,49922,49923],{"xmlns":890},[892,49924,49925,49935],{},[895,49926,49927],{},[2220,49928,49929,49931,49933],{},[898,49930,1904],{},[1864,49932,1866],{},[898,49934,1846],{},[902,49936,48527],{"encoding":904},[123,49938,48879,49939,48758,49956,49969,49970,1664],{},[883,49940,49942],{"className":49941},[886],[888,49943,49944],{"xmlns":890},[892,49945,49946,49954],{},[895,49947,49948],{},[2057,49949,49950,49952],{},[898,49951,1904],{},[898,49953,1846],{},[902,49955,43095],{"encoding":904},[883,49957,49959],{"className":49958},[886],[888,49960,49961],{"xmlns":890},[892,49962,49963,49967],{},[895,49964,49965],{},[898,49966,2878],{},[902,49968,2878],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49971,49973],{"className":49972},[886],[888,49974,49975],{"xmlns":890},[892,49976,49977,49987],{},[895,49978,49979],{},[2220,49980,49981,49983,49985],{},[898,49982,1904],{},[1864,49984,2331],{},[898,49986,1846],{},[902,49988,48589],{"encoding":904},[123,49990,48959,49991,49031,50008,50021,50022,3411,50035,50050,50051,50064,50065,50078,50079,1664],{},[883,49992,49994],{"className":49993},[886],[888,49995,49996],{"xmlns":890},[892,49997,49998,50006],{},[895,49999,50000],{},[2057,50001,50002,50004],{},[898,50003,1904],{},[898,50005,1846],{},[902,50007,43095],{"encoding":904},[883,50009,50011],{"className":50010},[886],[888,50012,50013],{"xmlns":890},[892,50014,50015,50019],{},[895,50016,50017],{},[898,50018,207],{},[902,50020,207],{"encoding":904}," na 110, poklesu ",[883,50023,50025],{"className":50024},[886],[888,50026,50027],{"xmlns":890},[892,50028,50029,50033],{},[895,50030,50031],{},[898,50032,2069],{},[902,50034,2069],{"encoding":904},[883,50036,50038],{"className":50037},[886],[888,50039,50040],{"xmlns":890},[892,50041,50042,50048],{},[895,50043,50044,50046],{},[1723,50045,1759],{},[1864,50047,2331],{},[902,50049,48787],{"encoding":904},", růstu ",[883,50052,50054],{"className":50053},[886],[888,50055,50056],{"xmlns":890},[892,50057,50058,50062],{},[895,50059,50060],{},[898,50061,2878],{},[902,50063,2878],{"encoding":904}," na 25 a růstu ",[883,50066,50068],{"className":50067},[886],[888,50069,50070],{"xmlns":890},[892,50071,50072,50076],{},[895,50073,50074],{},[898,50075,2930],{},[902,50077,2930],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,50080,50082],{"className":50081},[886],[888,50083,50084],{"xmlns":890},[892,50085,50086,50096],{},[895,50087,50088],{},[2220,50089,50090,50092,50094],{},[898,50091,1904],{},[1864,50093,2909],{},[898,50095,1846],{},[902,50097,48956],{"encoding":904},[123,50099,50100,50101,49777],{},"(i) Vypočtěte multiplikátory pro ",[883,50102,50104],{"className":50103},[886],[888,50105,50106],{"xmlns":890},[892,50107,50108,50112],{},[895,50109,50110],{},[898,50111,1746],{},[902,50113,1746],{"encoding":904},[123,50115,50116,50117,49390,50134,50147,50148,48758,50165,3411,50178,50193,50194,1664],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,50118,50120],{"className":50119},[886],[888,50121,50122],{"xmlns":890},[892,50123,50124,50132],{},[895,50125,50126],{},[2057,50127,50128,50130],{},[898,50129,1746],{},[898,50131,1846],{},[902,50133,42158],{"encoding":904},[883,50135,50137],{"className":50136},[886],[888,50138,50139],{"xmlns":890},[892,50140,50141,50145],{},[895,50142,50143],{},[898,50144,1746],{},[902,50146,1746],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,50149,50151],{"className":50150},[886],[888,50152,50153],{"xmlns":890},[892,50154,50155,50163],{},[895,50156,50157],{},[2057,50158,50159,50161],{},[898,50160,1746],{},[898,50162,1846],{},[902,50164,42158],{"encoding":904},[883,50166,50168],{"className":50167},[886],[888,50169,50170],{"xmlns":890},[892,50171,50172,50176],{},[895,50173,50174],{},[898,50175,207],{},[902,50177,207],{"encoding":904},[883,50179,50181],{"className":50180},[886],[888,50182,50183],{"xmlns":890},[892,50184,50185,50191],{},[895,50186,50187,50189],{},[1723,50188,1759],{},[1864,50190,2909],{},[902,50192,48803],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,50195,50197],{"className":50196},[886],[888,50198,50199],{"xmlns":890},[892,50200,50201,50211],{},[895,50202,50203],{},[2220,50204,50205,50207,50209],{},[898,50206,1746],{},[1864,50208,1866],{},[898,50210,1846],{},[902,50212,48548],{"encoding":904},[123,50214,50215,50216,48758,50233,50246,50247,1664],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,50217,50219],{"className":50218},[886],[888,50220,50221],{"xmlns":890},[892,50222,50223,50231],{},[895,50224,50225],{},[2057,50226,50227,50229],{},[898,50228,1746],{},[898,50230,1846],{},[902,50232,42158],{"encoding":904},[883,50234,50236],{"className":50235},[886],[888,50237,50238],{"xmlns":890},[892,50239,50240,50244],{},[895,50241,50242],{},[898,50243,207],{},[902,50245,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,50248,50250],{"className":50249},[886],[888,50251,50252],{"xmlns":890},[892,50253,50254,50264],{},[895,50255,50256],{},[2220,50257,50258,50260,50262],{},[898,50259,1746],{},[1864,50261,2331],{},[898,50263,1846],{},[902,50265,48609],{"encoding":904},[123,50267,50268,50269,49477,50286,50299,50300,3411,50313,50050,50328,50341,50342,50355,50356,1664],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,50270,50272],{"className":50271},[886],[888,50273,50274],{"xmlns":890},[892,50275,50276,50284],{},[895,50277,50278],{},[2057,50279,50280,50282],{},[898,50281,1746],{},[898,50283,1846],{},[902,50285,42158],{"encoding":904},[883,50287,50289],{"className":50288},[886],[888,50290,50291],{"xmlns":890},[892,50292,50293,50297],{},[895,50294,50295],{},[898,50296,207],{},[902,50298,207],{"encoding":904}," na 90, poklesu ",[883,50301,50303],{"className":50302},[886],[888,50304,50305],{"xmlns":890},[892,50306,50307,50311],{},[895,50308,50309],{},[898,50310,2069],{},[902,50312,2069],{"encoding":904},[883,50314,50316],{"className":50315},[886],[888,50317,50318],{"xmlns":890},[892,50319,50320,50326],{},[895,50321,50322,50324],{},[1723,50323,1759],{},[1864,50325,2909],{},[902,50327,48803],{"encoding":904},[883,50329,50331],{"className":50330},[886],[888,50332,50333],{"xmlns":890},[892,50334,50335,50339],{},[895,50336,50337],{},[898,50338,2878],{},[902,50340,2878],{"encoding":904}," na 30 a růstu ",[883,50343,50345],{"className":50344},[886],[888,50346,50347],{"xmlns":890},[892,50348,50349,50353],{},[895,50350,50351],{},[898,50352,2930],{},[902,50354,2930],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,50357,50359],{"className":50358},[886],[888,50360,50361],{"xmlns":890},[892,50362,50363,50373],{},[895,50364,50365],{},[2220,50366,50367,50369,50371],{},[898,50368,1746],{},[1864,50370,2909],{},[898,50372,1846],{},[902,50374,49606],{"encoding":904},[198,50376,820],{"id":50377},"přebytek-spotřebitele-a-výrobce-1",[724,50379,50380,48375,50383,48412,50419,1664],{},[38,50381,50382],{},"2.17",[883,50384,50386],{"className":50385},[886],[888,50387,50388],{"xmlns":890},[892,50389,50390,50416],{},[895,50391,50392,50394,50396,50398,50400,50402,50404,50406,50408,50410],{},[898,50393,1746],{},[1723,50395,1725],{},[898,50397,4897],{},[1723,50399,1908],{"stretchy":1907},[898,50401,1904],{},[1723,50403,1914],{"stretchy":1907},[1723,50405,1725],{},[1864,50407,15739],{},[1723,50409,1759],{},[2057,50411,50412,50414],{},[898,50413,1904],{},[1864,50415,2331],{},[902,50417,50418],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,50420,50422],{"className":50421},[886],[888,50423,50424],{"xmlns":890},[892,50425,50426,50452],{},[895,50427,50428,50430,50432,50434,50436,50438,50440,50442,50444,50446],{},[898,50429,1746],{},[1723,50431,1725],{},[898,50433,2111],{},[1723,50435,1908],{"stretchy":1907},[898,50437,1904],{},[1723,50439,1914],{"stretchy":1907},[1723,50441,1725],{},[1864,50443,2909],{},[1723,50445,2087],{},[2057,50447,50448,50450],{},[898,50449,1904],{},[1864,50451,2331],{},[902,50453,50454],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,50456,50457,50460],{},[123,50458,50459],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,50461,50462],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,50464,50465,48375,50468,48412,50502,1664],{},[38,50466,50467],{},"2.18",[883,50469,50471],{"className":50470},[886],[888,50472,50473],{"xmlns":890},[892,50474,50475,50499],{},[895,50476,50477,50479,50481,50483,50485,50487,50489,50491,50493,50495,50497],{},[898,50478,1746],{},[1723,50480,1725],{},[898,50482,4897],{},[1723,50484,1908],{"stretchy":1907},[898,50486,1904],{},[1723,50488,1914],{"stretchy":1907},[1723,50490,1725],{},[1864,50492,4425],{},[1723,50494,1759],{},[1864,50496,2331],{},[898,50498,1904],{},[902,50500,50501],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,50503,50505],{"className":50504},[886],[888,50506,50507],{"xmlns":890},[892,50508,50509,50535],{},[895,50510,50511,50513,50515,50517,50519,50521,50523,50525,50527,50529],{},[898,50512,1746],{},[1723,50514,1725],{},[898,50516,2111],{},[1723,50518,1908],{"stretchy":1907},[898,50520,1904],{},[1723,50522,1914],{"stretchy":1907},[1723,50524,1725],{},[1864,50526,2909],{},[1723,50528,2087],{},[2057,50530,50531,50533],{},[898,50532,1904],{},[1864,50534,2331],{},[902,50536,50454],{"encoding":904},[120,50538,50539,50559,50562,50565],{},[123,50540,50541,50542,1664],{},"(a) Vypočtěte rovnovážné množství ",[883,50543,50545],{"className":50544},[886],[888,50546,50547],{"xmlns":890},[892,50548,50549,50557],{},[895,50550,50551],{},[2057,50552,50553,50555],{},[898,50554,1904],{},[898,50556,1846],{},[902,50558,43095],{"encoding":904},[123,50560,50561],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,50563,50564],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,50566,50567],{},"(c) Graficky interpretujte.",[37662,50569],{},[115,50571,2615],{"id":50572},"otázky-k-sebehodnocení",[152,50574,50575,50578,50581,50584,50587,50590,50593,50596,50599,50602,50605,50608,50611,50614],{},[123,50576,50577],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,50579,50580],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,50582,50583],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,50585,50586],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,50588,50589],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,50591,50592],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,50594,50595],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,50597,50598],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,50600,50601],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,50603,50604],{},"K čemu slouží multiplikátory?",[123,50606,50607],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,50609,50610],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,50612,50613],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,50615,50616],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[37662,50618],{},[115,50620,16421],{"id":16420},[724,50622,50623],{},[38,50624,13862],{},[120,50626,50627,50662,50667,50697,50702,50765,50791,50796,50826,50835,50842,50848],{},[123,50628,50629,1981,50632,19342,50635,2628,50637,1343,50660],{},[38,50630,50631],{},"Poptávané množství",[614,50633,50634],{},"quantity demanded",[38,50636,28695],{},[883,50638,50640],{"className":50639},[886],[888,50641,50642],{"xmlns":890},[892,50643,50644,50658],{},[895,50645,50646,50648,50650,50652,50654,50656],{},[898,50647,1904],{},[1723,50649,1725],{},[898,50651,4897],{},[1723,50653,1908],{"stretchy":1907},[898,50655,1746],{},[1723,50657,1914],{"stretchy":1907},[902,50659,4906],{"encoding":904},[38,50661,38141],{},[123,50663,50664,50666],{},[38,50665,38148],{}," — substituční + důchodový efekt",[123,50668,50669,2628,50672],{},[38,50670,50671],{},"Reálné cenové rozpětí",[883,50673,50675],{"className":50674},[886],[888,50676,50677],{"xmlns":890},[892,50678,50679,50695],{},[895,50680,50681,50683,50685,50687,50693],{},[1723,50682,1908],{"stretchy":1907},[1864,50684,2256],{},[1723,50686,2031],{"separator":2030},[1931,50688,50689,50691],{},[898,50690,1746],{},[1864,50692,2256],{},[1723,50694,1914],{"stretchy":1907},[902,50696,38349],{"encoding":904},[123,50698,50699,11797],{},[38,50700,50701],{},"Homogenita poptávky",[123,50703,50704,2628,50707,1343,50730,1343,50747,50764],{},[38,50705,50706],{},"Lineární poptávka",[883,50708,50710],{"className":50709},[886],[888,50711,50712],{"xmlns":890},[892,50713,50714,50728],{},[895,50715,50716,50718,50720,50722,50724,50726],{},[898,50717,1746],{},[1723,50719,1725],{},[898,50721,207],{},[898,50723,1904],{},[1723,50725,2087],{},[898,50727,2069],{},[902,50729,37752],{"encoding":904},[883,50731,50733],{"className":50732},[886],[888,50734,50735],{"xmlns":890},[892,50736,50737,50745],{},[895,50738,50739,50741,50743],{},[898,50740,207],{},[1723,50742,2287],{},[1864,50744,2256],{},[902,50746,43777],{"encoding":904},[883,50748,50750],{"className":50749},[886],[888,50751,50752],{"xmlns":890},[892,50753,50754,50762],{},[895,50755,50756,50758,50760],{},[898,50757,2069],{},[1723,50759,2253],{},[1864,50761,2256],{},[902,50763,19508],{"encoding":904}," — nedokonalá konkurence",[123,50766,50767,7725,50770],{},[38,50768,50769],{},"Dokonalá konkurence",[883,50771,50773],{"className":50772},[886],[888,50774,50775],{"xmlns":890},[892,50776,50777,50789],{},[895,50778,50779,50781,50783],{},[898,50780,1746],{},[1723,50782,1725],{},[2057,50784,50785,50787],{},[898,50786,1746],{},[1723,50788,5066],{},[902,50790,5069],{"encoding":904},[123,50792,50793,50795],{},[38,50794,38918],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,50797,50798,2628,50800,1343,50824],{},[38,50799,32420],{},[883,50801,50803],{"className":50802},[886],[888,50804,50805],{"xmlns":890},[892,50806,50807,50821],{},[895,50808,50809,50811,50813,50815,50817,50819],{},[898,50810,1904],{},[1723,50812,1725],{},[898,50814,1846],{},[1723,50816,1908],{"stretchy":1907},[898,50818,9837],{},[1723,50820,1914],{"stretchy":1907},[902,50822,50823],{"encoding":904},"Q = E(Y)",[38,50825,39115],{},[123,50827,50828,50831,50832,50834],{},[38,50829,50830],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,50833,39561],{}," zboží",[123,50836,50837,1682,50839,50841],{},[38,50838,40567],{},[38,50840,40514],{}," — znaménka zkřížených koeficientů",[123,50843,50844,50847],{},[38,50845,50846],{},"Dvoukomoditní trh"," (2.6)",[123,50849,50850,1981,50853,1914],{},[38,50851,50852],{},"Posun poptávky",[614,50854,39619],{},[724,50856,50857],{},[38,50858,13826],{},[120,50860,50861,50894,50898,50943],{},[123,50862,50863,1981,50865,19342,50867,2628,50869,1343,50892],{},[38,50864,40961],{},[614,50866,40964],{},[38,50868,41135],{},[883,50870,50872],{"className":50871},[886],[888,50873,50874],{"xmlns":890},[892,50875,50876,50890],{},[895,50877,50878,50880,50882,50884,50886,50888],{},[898,50879,1904],{},[1723,50881,1725],{},[898,50883,2111],{},[1723,50885,1908],{"stretchy":1907},[898,50887,1746],{},[1723,50889,1914],{"stretchy":1907},[902,50891,9391],{"encoding":904},[38,50893,41213],{},[123,50895,50896],{},[38,50897,41220],{},[123,50899,50900,2628,50903,1343,50926],{},[38,50901,50902],{},"Lineární nabídka",[883,50904,50906],{"className":50905},[886],[888,50907,50908],{"xmlns":890},[892,50909,50910,50924],{},[895,50911,50912,50914,50916,50918,50920,50922],{},[898,50913,1746],{},[1723,50915,1725],{},[898,50917,2878],{},[898,50919,1904],{},[1723,50921,2087],{},[898,50923,2930],{},[902,50925,40934],{"encoding":904},[883,50927,50929],{"className":50928},[886],[888,50930,50931],{"xmlns":890},[892,50932,50933,50941],{},[895,50934,50935,50937,50939],{},[898,50936,2878],{},[1723,50938,2253],{},[1864,50940,2256],{},[902,50942,40952],{"encoding":904},[123,50944,50945,1981,50948,1914],{},[38,50946,50947],{},"Posun nabídky",[614,50949,41598],{},[724,50951,50952],{},[38,50953,50954],{},"Rovnováha a komparativní statika",[120,50956,50957,51036,51042],{},[123,50958,50959,1981,50961,19342,50963,2628,50966,1343,50983,2628,50986,1343,51003,2628,51005],{},[38,50960,42017],{},[614,50962,42136],{},[38,50964,50965],{},"rovnovážná cena",[883,50967,50969],{"className":50968},[886],[888,50970,50971],{"xmlns":890},[892,50972,50973,50981],{},[895,50974,50975],{},[2057,50976,50977,50979],{},[898,50978,1746],{},[898,50980,1846],{},[902,50982,42158],{"encoding":904},[38,50984,50985],{},"rovnovážné množství",[883,50987,50989],{"className":50988},[886],[888,50990,50991],{"xmlns":890},[892,50992,50993,51001],{},[895,50994,50995],{},[2057,50996,50997,50999],{},[898,50998,1904],{},[898,51000,1846],{},[902,51002,43095],{"encoding":904},[38,51004,42194],{},[883,51006,51008],{"className":51007},[886],[888,51009,51010],{"xmlns":890},[892,51011,51012,51034],{},[895,51013,51014,51016,51018,51024,51026,51032],{},[898,51015,1846],{},[1723,51017,3212],{"stretchy":1907},[2057,51019,51020,51022],{},[898,51021,1904],{},[898,51023,1846],{},[1723,51025,2031],{"separator":2030},[2057,51027,51028,51030],{},[898,51029,1746],{},[898,51031,1846],{},[1723,51033,3227],{"stretchy":1907},[902,51035,42059],{"encoding":904},[123,51037,51038,51041],{},[38,51039,51040],{},"Pravidla 1–4"," komparativní statiky",[123,51043,51044,1981,51047,1914],{},[38,51045,51046],{},"Teorém pavučiny",[614,51048,43041],{},[724,51050,51051],{},[38,51052,51053],{},"Zdanění",[120,51055,51056,51112,51160],{},[123,51057,51058,51060,51061,51086,51087,1914],{},[38,51059,51053],{}," — daň výrobci (",[883,51062,51064],{"className":51063},[886],[888,51065,51066],{"xmlns":890},[892,51067,51068,51084],{},[895,51069,51070,51076,51078,51080,51082],{},[1931,51071,51072,51074],{},[898,51073,2111],{},[1864,51075,1866],{},[1723,51077,1725],{},[898,51079,2111],{},[1723,51081,2087],{},[898,51083,1754],{},[902,51085,43446],{"encoding":904},") vs. daň spotřebiteli (",[883,51088,51090],{"className":51089},[886],[888,51091,51092],{"xmlns":890},[892,51093,51094,51110],{},[895,51095,51096,51102,51104,51106,51108],{},[1931,51097,51098,51100],{},[898,51099,4897],{},[1864,51101,2331],{},[1723,51103,1725],{},[898,51105,4897],{},[1723,51107,1759],{},[898,51109,1754],{},[902,51111,43477],{"encoding":904},[123,51113,51114,2628,51116,1343,51137],{},[38,51115,43350],{},[883,51117,51119],{"className":51118},[886],[888,51120,51121],{"xmlns":890},[892,51122,51123,51135],{},[895,51124,51125],{},[1931,51126,51127,51129],{},[898,51128,1754],{},[895,51130,51131,51133],{},[898,51132,43369],{},[898,51134,724],{},[902,51136,43374],{"encoding":904},[883,51138,51140],{"className":51139},[886],[888,51141,51142],{"xmlns":890},[892,51143,51144,51158],{},[895,51145,51146],{},[1931,51147,51148,51150],{},[898,51149,1754],{},[895,51151,51152,51154,51156],{},[898,51153,43392],{},[898,51155,2740],{},[898,51157,12742],{},[902,51159,43399],{"encoding":904},[123,51161,51162,2628,51165,1343,51194],{},[38,51163,51164],{},"Ekvivalence zdanění",[883,51166,51168],{"className":51167},[886],[888,51169,51170],{"xmlns":890},[892,51171,51172,51192],{},[895,51173,51174,51182,51184],{},[2220,51175,51176,51178,51180],{},[898,51177,1904],{},[1864,51179,1866],{},[898,51181,1846],{},[1723,51183,1725],{},[2220,51185,51186,51188,51190],{},[898,51187,1904],{},[1864,51189,2331],{},[898,51191,1846],{},[902,51193,43600],{"encoding":904},[883,51195,51197],{"className":51196},[886],[888,51198,51199],{"xmlns":890},[892,51200,51201,51225],{},[895,51202,51203,51211,51213,51215,51217],{},[2220,51204,51205,51207,51209],{},[898,51206,1746],{},[1864,51208,1866],{},[898,51210,1846],{},[1723,51212,1759],{},[898,51214,1754],{},[1723,51216,1725],{},[2220,51218,51219,51221,51223],{},[898,51220,1746],{},[1864,51222,2331],{},[898,51224,1846],{},[902,51226,43634],{"encoding":904},[724,51228,51229],{},[38,51230,27101],{},[120,51232,51233,51279,51310,51315,51321,51328],{},[123,51234,51235,2628,51237],{},[38,51236,43733],{},[883,51238,51240],{"className":51239},[886],[888,51241,51242],{"xmlns":890},[892,51243,51244,51276],{},[895,51245,51246,51252,51254,51256,51258,51260,51262,51264,51266,51268,51270,51272,51274],{},[2057,51247,51248,51250],{},[898,51249,1904],{},[898,51251,1846],{},[1723,51253,1725],{},[1723,51255,1908],{"stretchy":1907},[898,51257,2069],{},[1723,51259,1759],{},[898,51261,2930],{},[1723,51263,1914],{"stretchy":1907},[898,51265,2125],{"mathvariant":2124},[1723,51267,1908],{"stretchy":1907},[898,51269,2878],{},[1723,51271,1759],{},[898,51273,207],{},[1723,51275,1914],{"stretchy":1907},[902,51277,51278],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,51280,51281,2628,51284,51309],{},[38,51282,51283],{},"Parametry",[883,51285,51287],{"className":51286},[886],[888,51288,51289],{"xmlns":890},[892,51290,51291,51307],{},[895,51292,51293,51295,51297,51299,51301,51303,51305],{},[898,51294,207],{},[1723,51296,2031],{"separator":2030},[898,51298,2069],{},[1723,51300,2031],{"separator":2030},[898,51302,2878],{},[1723,51304,2031],{"separator":2030},[898,51306,2930],{},[902,51308,43977],{"encoding":904}," — exogenní proměnné",[123,51311,51312],{},[38,51313,51314],{},"Endogenní \u002F exogenní proměnná",[123,51316,51317,51320],{},[38,51318,51319],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,51322,51323,1343,51326],{},[38,51324,51325],{},"Komparativní statika",[38,51327,37652],{},[123,51329,51330,2628,51332,51348],{},[38,51331,3675],{},[883,51333,51335],{"className":51334},[886],[888,51336,51337],{"xmlns":890},[892,51338,51339,51345],{},[895,51340,51341,51343],{},[898,51342,2930],{},[898,51344,1904],{},[902,51346,51347],{"encoding":904},"dQ"," (2.11)",[724,51350,51351],{},[38,51352,51353],{},"Přebytky a ostatní",[120,51355,51356,51394],{},[123,51357,51358,2628,51360,51375,51376,2628,51378,51393],{},[38,51359,45626],{},[883,51361,51363],{"className":51362},[886],[888,51364,51365],{"xmlns":890},[892,51366,51367,51373],{},[895,51368,51369,51371],{},[898,51370,1721],{},[898,51372,2111],{},[902,51374,45642],{"encoding":904}," (2.14), ",[38,51377,45645],{},[883,51379,51381],{"className":51380},[886],[888,51382,51383],{"xmlns":890},[892,51384,51385,51391],{},[895,51386,51387,51389],{},[898,51388,1746],{},[898,51390,2111],{},[902,51392,45661],{"encoding":904}," (2.15)",[123,51395,51396,1343,51399,51402],{},[38,51397,51398],{},"Homo economicus",[38,51400,51401],{},"Marshallova formulace"," (1890)",[37662,51404],{},[115,51406,2620],{"id":2619},[120,51408,51409,51444,51453],{},[123,51410,51411,2628,51414,51417,51418,1343,51421,51424,51425,51428,51429,51432,51433,51436,51437,51440,51441],{},[38,51412,51413],{},"Související témata:",[207,51415,811],{"className":51416,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,51419,820],{"className":51420,"dataFsResolvedFilePath":818,"href":819},[210],[207,51422,3086],{"className":51423,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,51426,775],{"className":51427,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,51430,784],{"className":51431,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,51434,793],{"className":51435,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,51438,4544],{"className":51439,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,51442,4539],{"className":51443,"dataFsResolvedFilePath":827,"href":828},[210],[123,51445,51446,2628,51449],{},[38,51447,51448],{},"Shrnutí přednášek:",[207,51450,51452],{"className":51451,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,51454,51455,2628,51457],{},[38,51456,2627],{},[207,51458,1646],{"className":51459,"dataFsResolvedFilePath":1645,"href":1644},[210],{"title":641,"searchDepth":642,"depth":642,"links":51461},[51462,51463,51471,51477,51484,51485,51492,51493,51494,51501,51502,51503],{"id":37487,"depth":642,"text":37488},{"id":37468,"depth":642,"text":13862,"children":51464},[51465,51466,51467,51468,51470],{"id":37755,"depth":649,"text":37756},{"id":38037,"depth":649,"text":38038},{"id":39047,"depth":649,"text":39048},{"id":39615,"depth":649,"text":51469},"Posun poptávky (shift of demand)",{"id":40119,"depth":649,"text":40120},{"id":37472,"depth":642,"text":13826,"children":51472},[51473,51474,51475],{"id":40956,"depth":649,"text":37756},{"id":41142,"depth":649,"text":41143},{"id":41594,"depth":649,"text":51476},"Posun nabídky (shift of supply)",{"id":42016,"depth":642,"text":42017,"children":51478},[51479,51480,51481,51482,51483],{"id":42128,"depth":649,"text":42129},{"id":42341,"depth":649,"text":42342},{"id":42659,"depth":649,"text":42660},{"id":43013,"depth":649,"text":43014},{"id":43044,"depth":649,"text":43045},{"id":43313,"depth":642,"text":811},{"id":43714,"depth":642,"text":43715,"children":51486},[51487,51488,51489,51490],{"id":43732,"depth":649,"text":43733},{"id":44113,"depth":649,"text":44114},{"id":44497,"depth":649,"text":44498},{"id":44951,"depth":649,"text":51491},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":12485,"depth":642,"text":820},{"id":45875,"depth":642,"text":45876},{"id":46106,"depth":642,"text":46107,"children":51495},[51496,51497,51498,51499,51500],{"id":46110,"depth":649,"text":46111},{"id":46950,"depth":649,"text":46951},{"id":47326,"depth":649,"text":42017},{"id":48621,"depth":649,"text":43715},{"id":50377,"depth":649,"text":820},{"id":50572,"depth":642,"text":2615},{"id":16420,"depth":642,"text":16421},{"id":2619,"depth":642,"text":2620},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,51510,51511,51512,18578,51513,51514],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":51517,"title":820,"body":51518,"course":1128,"courses":659,"created":2676,"description":641,"extension":661,"meta":55797,"navigation":664,"path":55798,"seo":55799,"sources":55800,"stem":55801,"tags":55802,"type":4573,"updated":677,"__hash__":55807},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":51519,"toc":55775},[51520,51522,51590,51640,51642,51645,51903,51979,51984,51986,52005,52009,52085,52170,52172,52486,52579,52581,52600,52604,52678,52763,52766,52942,52947,52949,53369,53371,53375,53379,53615,53659,53759,53825,53828,53861,54037,54099,54229,54307,54418,54452,54650,54669,54688,54753,54757,54760,54805,54808,54926,54972,54974,54978,55326,55328,55330,55608,55610,55614,55649,55656,55729,55731,55733],[12,51521,820],{"id":12485},[4584,51523,51524],{},[724,51525,51526,4591,51528,1981,51530,51545,51546,1981,51548,51563,51564,51586,51587,1664],{},[883,51527,4590],{},[38,51529,45626],{},[883,51531,51533],{"className":51532},[886],[888,51534,51535],{"xmlns":890},[892,51536,51537,51543],{},[895,51538,51539,51541],{},[898,51540,1721],{},[898,51542,2111],{},[902,51544,45642],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,51547,45772],{},[883,51549,51551],{"className":51550},[886],[888,51552,51553],{"xmlns":890},[892,51554,51555,51561],{},[895,51556,51557,51559],{},[898,51558,1746],{},[898,51560,2111],{},[902,51562,45661],{"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 ",[883,51565,51567],{"className":51566},[886],[888,51568,51569],{"xmlns":890},[892,51570,51571,51583],{},[895,51572,51573,51575,51577,51579,51581],{},[898,51574,1721],{},[898,51576,2111],{},[1723,51578,2087],{},[898,51580,1746],{},[898,51582,2111],{},[902,51584,51585],{"encoding":904},"CS + PS"," měří ",[38,51588,51589],{},"celkový blahobyt trhu",[724,51591,51592,1981,51594,1343,51596,12829,51611,1981,51613,1343,51615,51630,51631,51635,51636,1664],{},[38,51593,45626],{},[614,51595,45679],{},[883,51597,51599],{"className":51598},[886],[888,51600,51601],{"xmlns":890},[892,51602,51603,51609],{},[895,51604,51605,51607],{},[898,51606,1721],{},[898,51608,2111],{},[902,51610,45642],{"encoding":904},[38,51612,45645],{},[614,51614,45775],{},[883,51616,51618],{"className":51617},[886],[888,51619,51620],{"xmlns":890},[892,51621,51622,51628],{},[895,51623,51624,51626],{},[898,51625,1746],{},[898,51627,2111],{},[902,51629,45661],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,51632,51634],{"className":51633,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,51637,51639],{"className":51638,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[37662,51641],{},[115,51643,1241],{"id":51644},"úvod",[724,51646,51647,51648,51671,51672,51695,51696,51713,51714,4626,51746,51778,51779,51805,51806,51809,51810,51813,51814,14712,51848,22287,51869,1664],{},"Je dána funkce poptávky ",[883,51649,51651],{"className":51650},[886],[888,51652,51653],{"xmlns":890},[892,51654,51655,51669],{},[895,51656,51657,51659,51661,51663,51665,51667],{},[898,51658,1746],{},[1723,51660,1725],{},[898,51662,4897],{},[1723,51664,1908],{"stretchy":1907},[898,51666,1904],{},[1723,51668,1914],{"stretchy":1907},[902,51670,5351],{"encoding":904},", resp. funkce nabídky ",[883,51673,51675],{"className":51674},[886],[888,51676,51677],{"xmlns":890},[892,51678,51679,51693],{},[895,51680,51681,51683,51685,51687,51689,51691],{},[898,51682,1746],{},[1723,51684,1725],{},[898,51686,2111],{},[1723,51688,1908],{"stretchy":1907},[898,51690,1904],{},[1723,51692,1914],{"stretchy":1907},[902,51694,41763],{"encoding":904},". Pro pevně zadané množství ",[883,51697,51699],{"className":51698},[886],[888,51700,51701],{"xmlns":890},[892,51702,51703,51711],{},[895,51704,51705],{},[1931,51706,51707,51709],{},[898,51708,1904],{},[1864,51710,2256],{},[902,51712,39000],{"encoding":904}," je odpovídající cena ",[883,51715,51717],{"className":51716},[886],[888,51718,51719],{"xmlns":890},[892,51720,51721,51743],{},[895,51722,51723,51729,51731,51733,51735,51741],{},[1931,51724,51725,51727],{},[898,51726,1746],{},[1864,51728,2256],{},[1723,51730,1725],{},[898,51732,4897],{},[1723,51734,1908],{"stretchy":1907},[1931,51736,51737,51739],{},[898,51738,1904],{},[1864,51740,2256],{},[1723,51742,1914],{"stretchy":1907},[902,51744,51745],{"encoding":904},"P_0 = D(Q_0)",[883,51747,51749],{"className":51748},[886],[888,51750,51751],{"xmlns":890},[892,51752,51753,51775],{},[895,51754,51755,51761,51763,51765,51767,51773],{},[1931,51756,51757,51759],{},[898,51758,1746],{},[1864,51760,2256],{},[1723,51762,1725],{},[898,51764,2111],{},[1723,51766,1908],{"stretchy":1907},[1931,51768,51769,51771],{},[898,51770,1904],{},[1864,51772,2256],{},[1723,51774,1914],{"stretchy":1907},[902,51776,51777],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,51780,51782],{"className":51781},[886],[888,51783,51784],{"xmlns":890},[892,51785,51786,51802],{},[895,51787,51788,51794,51796],{},[1931,51789,51790,51792],{},[898,51791,1746],{},[1864,51793,2256],{},[3018,51795,3707],{},[1931,51797,51798,51800],{},[898,51799,1904],{},[1864,51801,2256],{},[902,51803,51804],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,51807,51808],{},"výdaje spotřebitele",", nebo ",[38,51811,51812],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,51815,51817],{"className":51816},[886],[888,51818,51819],{"xmlns":890},[892,51820,51821,51845],{},[895,51822,51823,51825,51827,51833,51835,51837,51839],{},[1864,51824,2256],{},[3018,51826,3707],{},[1931,51828,51829,51831],{},[898,51830,1904],{},[1864,51832,2256],{},[3018,51834,3707],{},[898,51836,1718],{},[3018,51838,3707],{},[1931,51840,51841,51843],{},[898,51842,1746],{},[1864,51844,2256],{},[902,51846,51847],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,51849,51851],{"className":51850},[886],[888,51852,51853],{"xmlns":890},[892,51854,51855,51867],{},[895,51856,51857,51859,51861,51863,51865],{},[1723,51858,1908],{"stretchy":1907},[898,51860,1904],{},[1723,51862,2031],{"separator":2030},[898,51864,1746],{},[1723,51866,1914],{"stretchy":1907},[902,51868,38383],{"encoding":904},[883,51870,51872],{"className":51871},[886],[888,51873,51874],{"xmlns":890},[892,51875,51876,51900],{},[895,51877,51878,51880,51882,51884,51890,51892,51898],{},[898,51879,1718],{},[1723,51881,1725],{},[1723,51883,3212],{"stretchy":1907},[1931,51885,51886,51888],{},[898,51887,1904],{},[1864,51889,2256],{},[1723,51891,2031],{"separator":2030},[1931,51893,51894,51896],{},[898,51895,1746],{},[1864,51897,2256],{},[1723,51899,3227],{"stretchy":1907},[902,51901,51902],{"encoding":904},"A = [Q_0, P_0]",[4584,51904,51905,51910,51968],{},[724,51906,51907,51909],{},[883,51908,4869],{}," Intuice",[120,51911,51912,51940],{},[123,51913,51914,51915,51918,51919,51921,51922,51939],{},"Za jednotky zboží nakoupené ",[38,51916,51917],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,51920,25963],{}," než ",[883,51923,51925],{"className":51924},[886],[888,51926,51927],{"xmlns":890},[892,51928,51929,51937],{},[895,51930,51931],{},[1931,51932,51933,51935],{},[898,51934,1746],{},[1864,51936,2256],{},[902,51938,39640],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,51941,51942,51943,51945,51946,51949,51950,51967],{},"Za jednotky zboží prodané ",[38,51944,51917],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,51947,51948],{},"nižší"," cenu než ",[883,51951,51953],{"className":51952},[886],[888,51954,51955],{"xmlns":890},[892,51956,51957,51965],{},[895,51958,51959],{},[1931,51960,51961,51963],{},[898,51962,1746],{},[1864,51964,2256],{},[902,51966,39640],{"encoding":904}," — rozdíl je jeho přebytek.",[724,51969,51970,51971,51974,51975,51978],{},"Přebytek je tedy rozdíl mezi ",[614,51972,51973],{},"ochotou"," (platit \u002F prodávat) a ",[614,51976,51977],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,51980,51981],{},[3285,51982],{"alt":45670,"className":51983,"src":45672},[210,3289],[37662,51985],{},[115,51987,51989,51990,1914],{"id":51988},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,51991,51993],{"className":51992},[886],[888,51994,51995],{"xmlns":890},[892,51996,51997,52003],{},[895,51998,51999,52001],{},[898,52000,1721],{},[898,52002,2111],{},[902,52004,45642],{"encoding":904},[198,52006,52008],{"id":52007},"definice-vzorec-214","Definice (vzorec 2.14)",[724,52010,52011,52012,52035,52036,52053,52054,3430],{},"Pro poptávku ",[883,52013,52015],{"className":52014},[886],[888,52016,52017],{"xmlns":890},[892,52018,52019,52033],{},[895,52020,52021,52023,52025,52027,52029,52031],{},[898,52022,1746],{},[1723,52024,1725],{},[898,52026,4897],{},[1723,52028,1908],{"stretchy":1907},[898,52030,1904],{},[1723,52032,1914],{"stretchy":1907},[902,52034,5351],{"encoding":904}," a pevně zadané ",[883,52037,52039],{"className":52038},[886],[888,52040,52041],{"xmlns":890},[892,52042,52043,52051],{},[895,52044,52045],{},[1931,52046,52047,52049],{},[898,52048,1904],{},[1864,52050,2256],{},[902,52052,39000],{"encoding":904}," s cenou ",[883,52055,52057],{"className":52056},[886],[888,52058,52059],{"xmlns":890},[892,52060,52061,52083],{},[895,52062,52063,52069,52071,52073,52075,52081],{},[1931,52064,52065,52067],{},[898,52066,1746],{},[1864,52068,2256],{},[1723,52070,1725],{},[898,52072,4897],{},[1723,52074,1908],{"stretchy":1907},[1931,52076,52077,52079],{},[898,52078,1904],{},[1864,52080,2256],{},[1723,52082,1914],{"stretchy":1907},[902,52084,51745],{"encoding":904},[883,52086,52088],{"className":52087},[886],[888,52089,52090],{"xmlns":890,"display":28759},[892,52091,52092,52168],{},[21447,52093,52094],{"width":28764},[21452,52095,52096,52098,52162,52164],{},[21455,52097],{"width":28769},[21455,52099,52100],{},[895,52101,52102,52104,52106,52108,52114,52116,52118,52130,52132,52134,52136,52138,52140,52142,52144,52146,52152,52154,52160],{},[898,52103,1721],{},[898,52105,2111],{},[1723,52107,1908],{"stretchy":1907},[1931,52109,52110,52112],{},[898,52111,1904],{},[1864,52113,2256],{},[1723,52115,1914],{"stretchy":1907},[1723,52117,1725],{},[2220,52119,52120,52122,52124],{},[1723,52121,11870],{},[1864,52123,2256],{},[1931,52125,52126,52128],{},[898,52127,1904],{},[1864,52129,2256],{},[898,52131,4897],{},[1723,52133,1908],{"stretchy":1907},[898,52135,1904],{},[1723,52137,1914],{"stretchy":1907},[3018,52139,3707],{},[898,52141,2930],{},[898,52143,1904],{},[1723,52145,1759],{},[1931,52147,52148,52150],{},[898,52149,1746],{},[1864,52151,2256],{},[3018,52153,3707],{},[1931,52155,52156,52158],{},[898,52157,1904],{},[1864,52159,2256],{},[898,52161,1664],{"mathvariant":2124},[21455,52163],{"width":28769},[21455,52165,52166],{},[3018,52167,45764],{},[902,52169,45767],{"encoding":904},[198,52171,3170],{"id":3169},[120,52173,52174,52266,52328],{},[123,52175,52176,52216,52217,52243,52244,52247,52248,52265],{},[883,52177,52179],{"className":52178},[886],[888,52180,52181],{"xmlns":890},[892,52182,52183,52213],{},[895,52184,52185],{},[3055,52186,52187,52199,52201,52203,52205,52207,52209,52211],{"scriptlevel":2256,"displaystyle":2030},[2220,52188,52189,52191,52193],{},[1723,52190,11870],{},[1864,52192,2256],{},[1931,52194,52195,52197],{},[898,52196,1904],{},[1864,52198,2256],{},[898,52200,4897],{},[1723,52202,1908],{"stretchy":1907},[898,52204,1904],{},[1723,52206,1914],{"stretchy":1907},[3018,52208,3707],{},[898,52210,2930],{},[898,52212,1904],{},[902,52214,52215],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,52218,52220],{"className":52219},[886],[888,52221,52222],{"xmlns":890},[892,52223,52224,52240],{},[895,52225,52226,52228,52230,52232,52238],{},[1723,52227,3212],{"stretchy":1907},[1864,52229,2256],{},[1723,52231,2031],{"separator":2030},[1931,52233,52234,52236],{},[898,52235,1904],{},[1864,52237,2256],{},[1723,52239,3227],{"stretchy":1907},[902,52241,52242],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,52245,52246],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,52249,52251],{"className":52250},[886],[888,52252,52253],{"xmlns":890},[892,52254,52255,52263],{},[895,52256,52257],{},[1931,52258,52259,52261],{},[898,52260,1904],{},[1864,52262,2256],{},[902,52264,39000],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,52267,52268,52294,52295,4634],{},[883,52269,52271],{"className":52270},[886],[888,52272,52273],{"xmlns":890},[892,52274,52275,52291],{},[895,52276,52277,52283,52285],{},[1931,52278,52279,52281],{},[898,52280,1746],{},[1864,52282,2256],{},[3018,52284,3707],{},[1931,52286,52287,52289],{},[898,52288,1904],{},[1864,52290,2256],{},[902,52292,52293],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,52296,52298],{"className":52297},[886],[888,52299,52300],{"xmlns":890},[892,52301,52302,52326],{},[895,52303,52304,52306,52308,52314,52316,52318,52320],{},[1864,52305,2256],{},[3018,52307,3707],{},[1931,52309,52310,52312],{},[898,52311,1904],{},[1864,52313,2256],{},[3018,52315,3707],{},[898,52317,1718],{},[3018,52319,3707],{},[1931,52321,52322,52324],{},[898,52323,1746],{},[1864,52325,2256],{},[902,52327,51847],{"encoding":904},[123,52329,52330,52345,52346,52368,52369,52394,52395,22287,52421,1682,52453,1664],{},[883,52331,52333],{"className":52332},[886],[888,52334,52335],{"xmlns":890},[892,52336,52337,52343],{},[895,52338,52339,52341],{},[898,52340,1721],{},[898,52342,2111],{},[902,52344,45642],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,52347,52349],{"className":52348},[886],[888,52350,52351],{"xmlns":890},[892,52352,52353,52365],{},[895,52354,52355,52357,52359],{},[898,52356,1746],{},[1723,52358,1725],{},[1931,52360,52361,52363],{},[898,52362,1746],{},[1864,52364,2256],{},[902,52366,52367],{"encoding":904},"P = P_0"," v pásu ",[883,52370,52372],{"className":52371},[886],[888,52373,52374],{"xmlns":890},[892,52375,52376,52392],{},[895,52377,52378,52380,52382,52384,52390],{},[1723,52379,3212],{"stretchy":1907},[1864,52381,2256],{},[1723,52383,2031],{"separator":2030},[1931,52385,52386,52388],{},[898,52387,1904],{},[1864,52389,2256],{},[1723,52391,3227],{"stretchy":1907},[902,52393,52242],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,52396,52398],{"className":52397},[886],[888,52399,52400],{"xmlns":890},[892,52401,52402,52418],{},[895,52403,52404,52410,52412,52414,52416],{},[1931,52405,52406,52408],{},[898,52407,1746],{},[1864,52409,2256],{},[3018,52411,3707],{},[898,52413,23946],{},[3018,52415,3707],{},[898,52417,1718],{},[902,52419,52420],{"encoding":904},"P_0\\,B\\,A",[883,52422,52424],{"className":52423},[886],[888,52425,52426],{"xmlns":890},[892,52427,52428,52450],{},[895,52429,52430,52432,52434,52436,52438,52440,52442,52444,52446,52448],{},[898,52431,23946],{},[1723,52433,1725],{},[1723,52435,3212],{"stretchy":1907},[1864,52437,2256],{},[1723,52439,2031],{"separator":2030},[898,52441,4897],{},[1723,52443,1908],{"stretchy":1907},[1864,52445,2256],{},[1723,52447,1914],{"stretchy":1907},[1723,52449,3227],{"stretchy":1907},[902,52451,52452],{"encoding":904},"B = [0, D(0)]",[883,52454,52456],{"className":52455},[886],[888,52457,52458],{"xmlns":890},[892,52459,52460,52484],{},[895,52461,52462,52464,52466,52468,52474,52476,52482],{},[898,52463,1718],{},[1723,52465,1725],{},[1723,52467,3212],{"stretchy":1907},[1931,52469,52470,52472],{},[898,52471,1904],{},[1864,52473,2256],{},[1723,52475,2031],{"separator":2030},[1931,52477,52478,52480],{},[898,52479,1746],{},[1864,52481,2256],{},[1723,52483,3227],{"stretchy":1907},[902,52485,51902],{"encoding":904},[724,52487,52488],{},[614,52489,52490,52491,52504,52505,52538,52539,29835,52564,1664],{},"Obrázek 2.24: Křivka poptávky ",[883,52492,52494],{"className":52493},[886],[888,52495,52496],{"xmlns":890},[892,52497,52498,52502],{},[895,52499,52500],{},[898,52501,4897],{},[902,52503,4897],{"encoding":904},", bod ",[883,52506,52508],{"className":52507},[886],[888,52509,52510],{"xmlns":890},[892,52511,52512,52536],{},[895,52513,52514,52516,52518,52520,52526,52528,52534],{},[898,52515,1718],{},[1723,52517,1725],{},[1723,52519,3212],{"stretchy":1907},[1931,52521,52522,52524],{},[898,52523,1904],{},[1864,52525,2256],{},[1723,52527,2031],{"separator":2030},[1931,52529,52530,52532],{},[898,52531,1746],{},[1864,52533,2256],{},[1723,52535,3227],{"stretchy":1907},[902,52537,51902],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,52540,52542],{"className":52541},[886],[888,52543,52544],{"xmlns":890},[892,52545,52546,52562],{},[895,52547,52548,52554,52556,52558,52560],{},[1931,52549,52550,52552],{},[898,52551,1746],{},[1864,52553,2256],{},[3018,52555,3707],{},[898,52557,23946],{},[3018,52559,3707],{},[898,52561,1718],{},[902,52563,52420],{"encoding":904},[883,52565,52567],{"className":52566},[886],[888,52568,52569],{"xmlns":890},[892,52570,52571,52577],{},[895,52572,52573,52575],{},[898,52574,1721],{},[898,52576,2111],{},[902,52578,45642],{"encoding":904},[37662,52580],{},[115,52582,52584,52585,1914],{"id":52583},"přebytek-výrobce-psps","Přebytek výrobce (",[883,52586,52588],{"className":52587},[886],[888,52589,52590],{"xmlns":890},[892,52591,52592,52598],{},[895,52593,52594,52596],{},[898,52595,1746],{},[898,52597,2111],{},[902,52599,45661],{"encoding":904},[198,52601,52603],{"id":52602},"definice-vzorec-215","Definice (vzorec 2.15)",[724,52605,52606,52607,52035,52630,52053,52647,3430],{},"Analogicky — pro nabídku ",[883,52608,52610],{"className":52609},[886],[888,52611,52612],{"xmlns":890},[892,52613,52614,52628],{},[895,52615,52616,52618,52620,52622,52624,52626],{},[898,52617,1746],{},[1723,52619,1725],{},[898,52621,2111],{},[1723,52623,1908],{"stretchy":1907},[898,52625,1904],{},[1723,52627,1914],{"stretchy":1907},[902,52629,41763],{"encoding":904},[883,52631,52633],{"className":52632},[886],[888,52634,52635],{"xmlns":890},[892,52636,52637,52645],{},[895,52638,52639],{},[1931,52640,52641,52643],{},[898,52642,1904],{},[1864,52644,2256],{},[902,52646,39000],{"encoding":904},[883,52648,52650],{"className":52649},[886],[888,52651,52652],{"xmlns":890},[892,52653,52654,52676],{},[895,52655,52656,52662,52664,52666,52668,52674],{},[1931,52657,52658,52660],{},[898,52659,1746],{},[1864,52661,2256],{},[1723,52663,1725],{},[898,52665,2111],{},[1723,52667,1908],{"stretchy":1907},[1931,52669,52670,52672],{},[898,52671,1904],{},[1864,52673,2256],{},[1723,52675,1914],{"stretchy":1907},[902,52677,51777],{"encoding":904},[883,52679,52681],{"className":52680},[886],[888,52682,52683],{"xmlns":890,"display":28759},[892,52684,52685,52761],{},[21447,52686,52687],{"width":28764},[21452,52688,52689,52691,52755,52757],{},[21455,52690],{"width":28769},[21455,52692,52693],{},[895,52694,52695,52697,52699,52701,52707,52709,52711,52717,52719,52725,52727,52739,52741,52743,52745,52747,52749,52751,52753],{},[898,52696,1746],{},[898,52698,2111],{},[1723,52700,1908],{"stretchy":1907},[1931,52702,52703,52705],{},[898,52704,1904],{},[1864,52706,2256],{},[1723,52708,1914],{"stretchy":1907},[1723,52710,1725],{},[1931,52712,52713,52715],{},[898,52714,1746],{},[1864,52716,2256],{},[3018,52718,3707],{},[1931,52720,52721,52723],{},[898,52722,1904],{},[1864,52724,2256],{},[1723,52726,1759],{},[2220,52728,52729,52731,52733],{},[1723,52730,11870],{},[1864,52732,2256],{},[1931,52734,52735,52737],{},[898,52736,1904],{},[1864,52738,2256],{},[898,52740,2111],{},[1723,52742,1908],{"stretchy":1907},[898,52744,1904],{},[1723,52746,1914],{"stretchy":1907},[3018,52748,3707],{},[898,52750,2930],{},[898,52752,1904],{},[898,52754,1664],{"mathvariant":2124},[21455,52756],{"width":28769},[21455,52758,52759],{},[3018,52760,45860],{},[902,52762,45863],{"encoding":904},[198,52764,3170],{"id":52765},"geometrická-interpretace-1",[120,52767,52768,52816,52877],{},[123,52769,52770,7725,52795,52798,52799,1664],{},[883,52771,52773],{"className":52772},[886],[888,52774,52775],{"xmlns":890},[892,52776,52777,52793],{},[895,52778,52779,52785,52787],{},[1931,52780,52781,52783],{},[898,52782,1746],{},[1864,52784,2256],{},[3018,52786,3707],{},[1931,52788,52789,52791],{},[898,52790,1904],{},[1864,52792,2256],{},[902,52794,52293],{"encoding":904},[38,52796,52797],{},"tržba"," výrobce za prodané množství ",[883,52800,52802],{"className":52801},[886],[888,52803,52804],{"xmlns":890},[892,52805,52806,52814],{},[895,52807,52808],{},[1931,52809,52810,52812],{},[898,52811,1904],{},[1864,52813,2256],{},[902,52815,39000],{"encoding":904},[123,52817,52818,52858,52859,52876],{},[883,52819,52821],{"className":52820},[886],[888,52822,52823],{"xmlns":890},[892,52824,52825,52855],{},[895,52826,52827],{},[3055,52828,52829,52841,52843,52845,52847,52849,52851,52853],{"scriptlevel":2256,"displaystyle":2030},[2220,52830,52831,52833,52835],{},[1723,52832,11870],{},[1864,52834,2256],{},[1931,52836,52837,52839],{},[898,52838,1904],{},[1864,52840,2256],{},[898,52842,2111],{},[1723,52844,1908],{"stretchy":1907},[898,52846,1904],{},[1723,52848,1914],{"stretchy":1907},[3018,52850,3707],{},[898,52852,2930],{},[898,52854,1904],{},[902,52856,52857],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,52860,52862],{"className":52861},[886],[888,52863,52864],{"xmlns":890},[892,52865,52866,52874],{},[895,52867,52868],{},[1931,52869,52870,52872],{},[898,52871,1904],{},[1864,52873,2256],{},[902,52875,39000],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,52878,52879,52894,52895,52916,52917,1664],{},[883,52880,52882],{"className":52881},[886],[888,52883,52884],{"xmlns":890},[892,52885,52886,52892],{},[895,52887,52888,52890],{},[898,52889,1746],{},[898,52891,2111],{},[902,52893,45661],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,52896,52898],{"className":52897},[886],[888,52899,52900],{"xmlns":890},[892,52901,52902,52914],{},[895,52903,52904,52906,52908],{},[898,52905,1746],{},[1723,52907,1725],{},[1931,52909,52910,52912],{},[898,52911,1746],{},[1864,52913,2256],{},[902,52915,52367],{"encoding":904}," a křivkou nabídky v pásu ",[883,52918,52920],{"className":52919},[886],[888,52921,52922],{"xmlns":890},[892,52923,52924,52940],{},[895,52925,52926,52928,52930,52932,52938],{},[1723,52927,3212],{"stretchy":1907},[1864,52929,2256],{},[1723,52931,2031],{"separator":2030},[1931,52933,52934,52936],{},[898,52935,1904],{},[1864,52937,2256],{},[1723,52939,3227],{"stretchy":1907},[902,52941,52242],{"encoding":904},[724,52943,52944],{},[614,52945,52946],{},"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.",[37662,52948],{},[4584,52950,52951,52956],{},[724,52952,52953,52955],{},[883,52954,5283],{}," Postup výpočtu CS a PS",[152,52957,52958,53089,53199,53228,53362],{},[123,52959,52960,52961,52978,52979,53010,53011,53042,53043,1664],{},"Zjisti (nebo si zvol) množství ",[883,52962,52964],{"className":52963},[886],[888,52965,52966],{"xmlns":890},[892,52967,52968,52976],{},[895,52969,52970],{},[1931,52971,52972,52974],{},[898,52973,1904],{},[1864,52975,2256],{},[902,52977,39000],{"encoding":904}," a odpovídající cenu ",[883,52980,52982],{"className":52981},[886],[888,52983,52984],{"xmlns":890},[892,52985,52986,53008],{},[895,52987,52988,52994,52996,52998,53000,53006],{},[1931,52989,52990,52992],{},[898,52991,1746],{},[1864,52993,2256],{},[1723,52995,1725],{},[898,52997,4897],{},[1723,52999,1908],{"stretchy":1907},[1931,53001,53002,53004],{},[898,53003,1904],{},[1864,53005,2256],{},[1723,53007,1914],{"stretchy":1907},[902,53009,51745],{"encoding":904}," resp. ",[883,53012,53014],{"className":53013},[886],[888,53015,53016],{"xmlns":890},[892,53017,53018,53040],{},[895,53019,53020,53026,53028,53030,53032,53038],{},[1931,53021,53022,53024],{},[898,53023,1746],{},[1864,53025,2256],{},[1723,53027,1725],{},[898,53029,2111],{},[1723,53031,1908],{"stretchy":1907},[1931,53033,53034,53036],{},[898,53035,1904],{},[1864,53037,2256],{},[1723,53039,1914],{"stretchy":1907},[902,53041,51777],{"encoding":904},". V rovnováze platí ",[883,53044,53046],{"className":53045},[886],[888,53047,53048],{"xmlns":890},[892,53049,53050,53086],{},[895,53051,53052,53054,53056,53062,53064,53066,53068,53070,53076,53078,53080],{},[898,53053,4897],{},[1723,53055,1908],{"stretchy":1907},[2057,53057,53058,53060],{},[898,53059,1904],{},[898,53061,1846],{},[1723,53063,1914],{"stretchy":1907},[1723,53065,1725],{},[898,53067,2111],{},[1723,53069,1908],{"stretchy":1907},[2057,53071,53072,53074],{},[898,53073,1904],{},[898,53075,1846],{},[1723,53077,1914],{"stretchy":1907},[1723,53079,1725],{},[2057,53081,53082,53084],{},[898,53083,1746],{},[898,53085,1846],{},[902,53087,53088],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,53090,53091,53092,20819,53130,53145,53146,20819,53184,4634],{},"Spočti určitý integrál ",[883,53093,53095],{"className":53094},[886],[888,53096,53097],{"xmlns":890},[892,53098,53099,53127],{},[895,53100,53101,53113,53115,53117,53119,53121,53123,53125],{},[2220,53102,53103,53105,53107],{},[1723,53104,11870],{},[1864,53106,2256],{},[1931,53108,53109,53111],{},[898,53110,1904],{},[1864,53112,2256],{},[898,53114,4897],{},[1723,53116,1908],{"stretchy":1907},[898,53118,1904],{},[1723,53120,1914],{"stretchy":1907},[3018,53122,3707],{},[898,53124,2930],{},[898,53126,1904],{},[902,53128,53129],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,53131,53133],{"className":53132},[886],[888,53134,53135],{"xmlns":890},[892,53136,53137,53143],{},[895,53138,53139,53141],{},[898,53140,1721],{},[898,53142,2111],{},[902,53144,45642],{"encoding":904},") nebo ",[883,53147,53149],{"className":53148},[886],[888,53150,53151],{"xmlns":890},[892,53152,53153,53181],{},[895,53154,53155,53167,53169,53171,53173,53175,53177,53179],{},[2220,53156,53157,53159,53161],{},[1723,53158,11870],{},[1864,53160,2256],{},[1931,53162,53163,53165],{},[898,53164,1904],{},[1864,53166,2256],{},[898,53168,2111],{},[1723,53170,1908],{"stretchy":1907},[898,53172,1904],{},[1723,53174,1914],{"stretchy":1907},[3018,53176,3707],{},[898,53178,2930],{},[898,53180,1904],{},[902,53182,53183],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,53185,53187],{"className":53186},[886],[888,53188,53189],{"xmlns":890},[892,53190,53191,53197],{},[895,53192,53193,53195],{},[898,53194,1746],{},[898,53196,2111],{},[902,53198,45661],{"encoding":904},[123,53200,53201,53202,1664],{},"Sestav obdélník ",[883,53203,53205],{"className":53204},[886],[888,53206,53207],{"xmlns":890},[892,53208,53209,53225],{},[895,53210,53211,53217,53219],{},[1931,53212,53213,53215],{},[898,53214,1746],{},[1864,53216,2256],{},[1723,53218,3897],{},[1931,53220,53221,53223],{},[898,53222,1904],{},[1864,53224,2256],{},[902,53226,53227],{"encoding":904},"P_0 \\cdot Q_0",[123,53229,53230,53231],{},"Dosaď:\n",[120,53232,53233,53298],{},[123,53234,53235,53293,53294,53297],{},[883,53236,53238],{"className":53237},[886],[888,53239,53240],{"xmlns":890},[892,53241,53242,53290],{},[895,53243,53244,53246,53248,53250,53262,53264,53266,53268,53270,53272,53274,53276,53278,53284],{},[898,53245,1721],{},[898,53247,2111],{},[1723,53249,1725],{},[2220,53251,53252,53254,53256],{},[1723,53253,11870],{},[1864,53255,2256],{},[1931,53257,53258,53260],{},[898,53259,1904],{},[1864,53261,2256],{},[898,53263,4897],{},[1723,53265,1908],{"stretchy":1907},[898,53267,1904],{},[1723,53269,1914],{"stretchy":1907},[3018,53271,3707],{},[898,53273,2930],{},[898,53275,1904],{},[1723,53277,1759],{},[1931,53279,53280,53282],{},[898,53281,1746],{},[1864,53283,2256],{},[1931,53285,53286,53288],{},[898,53287,1904],{},[1864,53289,2256],{},[902,53291,53292],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,53295,53296],{},"mínus"," obdélník)",[123,53299,53300,53358,53359,53361],{},[883,53301,53303],{"className":53302},[886],[888,53304,53305],{"xmlns":890},[892,53306,53307,53355],{},[895,53308,53309,53311,53313,53315,53321,53327,53329,53341,53343,53345,53347,53349,53351,53353],{},[898,53310,1746],{},[898,53312,2111],{},[1723,53314,1725],{},[1931,53316,53317,53319],{},[898,53318,1746],{},[1864,53320,2256],{},[1931,53322,53323,53325],{},[898,53324,1904],{},[1864,53326,2256],{},[1723,53328,1759],{},[2220,53330,53331,53333,53335],{},[1723,53332,11870],{},[1864,53334,2256],{},[1931,53336,53337,53339],{},[898,53338,1904],{},[1864,53340,2256],{},[898,53342,2111],{},[1723,53344,1908],{"stretchy":1907},[898,53346,1904],{},[1723,53348,1914],{"stretchy":1907},[3018,53350,3707],{},[898,53352,2930],{},[898,53354,1904],{},[902,53356,53357],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,53360,53296],{}," integrál)",[123,53363,53364,53365,53368],{},"Kontrola znaménka: obě hodnoty musí být ",[38,53366,53367],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[37662,53370],{},[115,53372,53374],{"id":53373},"příklady","Příklady",[198,53376,53378],{"id":53377},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[4584,53380,53381],{},[724,53382,53383,53386,53387,48412,53410,53433,53434,1343,53454,1343,53471,1343,53488,53505,53506,53582,53583,53600,53601,53614],{},[883,53384,53385],{},"!example"," Zadání\nJsou dány poptávka ",[883,53388,53390],{"className":53389},[886],[888,53391,53392],{"xmlns":890},[892,53393,53394,53408],{},[895,53395,53396,53398,53400,53402,53404,53406],{},[898,53397,1746],{},[1723,53399,1725],{},[898,53401,207],{},[898,53403,1904],{},[1723,53405,2087],{},[898,53407,2069],{},[902,53409,37752],{"encoding":904},[883,53411,53413],{"className":53412},[886],[888,53414,53415],{"xmlns":890},[892,53416,53417,53431],{},[895,53418,53419,53421,53423,53425,53427,53429],{},[898,53420,1746],{},[1723,53422,1725],{},[898,53424,2878],{},[898,53426,1904],{},[1723,53428,2087],{},[898,53430,2930],{},[902,53432,40934],{"encoding":904}," s hodnotami ",[883,53435,53437],{"className":53436},[886],[888,53438,53439],{"xmlns":890},[892,53440,53441,53451],{},[895,53442,53443,53445,53447,53449],{},[898,53444,207],{},[1723,53446,1725],{},[1723,53448,1759],{},[1864,53450,2909],{},[902,53452,53453],{"encoding":904},"a = -3",[883,53455,53457],{"className":53456},[886],[888,53458,53459],{"xmlns":890},[892,53460,53461,53469],{},[895,53462,53463,53465,53467],{},[898,53464,2069],{},[1723,53466,1725],{},[1864,53468,5921],{},[902,53470,49335],{"encoding":904},[883,53472,53474],{"className":53473},[886],[888,53475,53476],{"xmlns":890},[892,53477,53478,53486],{},[895,53479,53480,53482,53484],{},[898,53481,2878],{},[1723,53483,1725],{},[1864,53485,5719],{},[902,53487,49353],{"encoding":904},[883,53489,53491],{"className":53490},[886],[888,53492,53493],{"xmlns":890},[892,53494,53495,53503],{},[895,53496,53497,53499,53501],{},[898,53498,2930],{},[1723,53500,1725],{},[1864,53502,3585],{},[902,53504,49371],{"encoding":904},".\nRovnovážné množství:\n",[883,53507,53509],{"className":53508},[886],[888,53510,53511],{"xmlns":890},[892,53512,53513,53579],{},[895,53514,53515,53521,53523,53541,53543,53567,53569,53575,53577],{},[2057,53516,53517,53519],{},[898,53518,1904],{},[898,53520,1846],{},[1723,53522,1725],{},[3058,53524,53525,53533],{},[895,53526,53527,53529,53531],{},[898,53528,2069],{},[1723,53530,1759],{},[898,53532,2930],{},[895,53534,53535,53537,53539],{},[898,53536,2878],{},[1723,53538,1759],{},[898,53540,207],{},[1723,53542,1725],{},[3058,53544,53545,53553],{},[895,53546,53547,53549,53551],{},[1864,53548,5921],{},[1723,53550,1759],{},[1864,53552,3585],{},[895,53554,53555,53557,53559,53561,53563,53565],{},[1864,53556,5719],{},[1723,53558,1759],{},[1723,53560,1908],{"stretchy":1907},[1723,53562,1759],{},[1864,53564,2909],{},[1723,53566,1914],{"stretchy":1907},[1723,53568,1725],{},[3058,53570,53571,53573],{},[1864,53572,38711],{},[1864,53574,45098],{},[1723,53576,6610],{},[1864,53578,45103],{},[902,53580,53581],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,53584,53586],{"className":53585},[886],[888,53587,53588],{"xmlns":890},[892,53589,53590,53598],{},[895,53591,53592],{},[2057,53593,53594,53596],{},[898,53595,1904],{},[898,53597,1846],{},[902,53599,43095],{"encoding":904}," (a) při změně samotného parametru ",[883,53602,53604],{"className":53603},[886],[888,53605,53606],{"xmlns":890},[892,53607,53608,53612],{},[895,53609,53610],{},[898,53611,2878],{},[902,53613,2878],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,53616,53617],{},[38,53618,53619,53620,3397,53633,3411,53646,10003],{},"Řešení (a) — změna ",[883,53621,53623],{"className":53622},[886],[888,53624,53625],{"xmlns":890},[892,53626,53627,53631],{},[895,53628,53629],{},[898,53630,2878],{},[902,53632,2878],{"encoding":904},[883,53634,53636],{"className":53635},[886],[888,53637,53638],{"xmlns":890},[892,53639,53640,53644],{},[895,53641,53642],{},[1864,53643,5719],{},[902,53645,45138],{"encoding":904},[883,53647,53649],{"className":53648},[886],[888,53650,53651],{"xmlns":890},[892,53652,53653,53657],{},[895,53654,53655],{},[1864,53656,20015],{},[902,53658,45152],{"encoding":904},[724,53660,53661,53662,53726,53727,3430],{},"Pomocí vzorce (2.13) pro ",[883,53663,53665],{"className":53664},[886],[888,53666,53667],{"xmlns":890},[892,53668,53669,53723],{},[895,53670,53671,53691,53693,53695],{},[3055,53672,53673],{"scriptlevel":2256,"displaystyle":2030},[3058,53674,53675,53685],{},[895,53676,53677,53679],{},[898,53678,10574],{"mathvariant":2124},[2057,53680,53681,53683],{},[898,53682,1904],{},[898,53684,1846],{},[895,53686,53687,53689],{},[898,53688,10574],{"mathvariant":2124},[898,53690,2878],{},[1723,53692,1725],{},[1723,53694,1759],{},[3055,53696,53697],{"scriptlevel":2256,"displaystyle":2030},[3058,53698,53699,53707],{},[895,53700,53701,53703,53705],{},[898,53702,2069],{},[1723,53704,1759],{},[898,53706,2930],{},[895,53708,53709,53711,53713,53715,53717],{},[1723,53710,1908],{"stretchy":1907},[898,53712,2878],{},[1723,53714,1759],{},[898,53716,207],{},[2057,53718,53719,53721],{},[1723,53720,1914],{"stretchy":1907},[1864,53722,2331],{},[902,53724,53725],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,53728,53730],{"className":53729},[886],[888,53731,53732],{"xmlns":890},[892,53733,53734,53756],{},[895,53735,53736,53738],{},[1723,53737,1759],{},[3055,53739,53740],{"scriptlevel":2256,"displaystyle":2030},[3058,53741,53742,53748],{},[2057,53743,53744,53746],{},[898,53745,1904],{},[898,53747,1846],{},[895,53749,53750,53752,53754],{},[898,53751,2878],{},[1723,53753,1759],{},[898,53755,207],{},[902,53757,53758],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,53760,53762],{"className":53761},[886],[888,53763,53764],{"xmlns":890,"display":28759},[892,53765,53766,53822],{},[895,53767,53768,53770,53776,53778,53780,53796,53798,53800,53802,53804,53806,53812,53814,53816,53818,53820],{},[898,53769,2930],{},[2057,53771,53772,53774],{},[898,53773,1904],{},[898,53775,1846],{},[1723,53777,1725],{},[1723,53779,1759],{},[3058,53781,53782,53788],{},[2057,53783,53784,53786],{},[898,53785,1904],{},[898,53787,1846],{},[895,53789,53790,53792,53794],{},[898,53791,2878],{},[1723,53793,1759],{},[898,53795,207],{},[3018,53797,3707],{},[898,53799,2930],{},[898,53801,2878],{},[1723,53803,1725],{},[1723,53805,1759],{},[3058,53807,53808,53810],{},[1864,53809,45266],{},[1864,53811,45098],{},[1723,53813,3897],{},[1864,53815,3517],{},[1723,53817,6610],{},[1723,53819,1759],{},[1864,53821,45238],{},[902,53823,53824],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,53826,53827],{},"Nové rovnovážné množství:",[883,53829,53831],{"className":53830},[886],[888,53832,53833],{"xmlns":890,"display":28759},[892,53834,53835,53858],{},[895,53836,53837,53845,53847,53849,53851,53853,53855],{},[2220,53838,53839,53841,53843],{},[898,53840,1904],{},[1864,53842,1866],{},[898,53844,1846],{},[1723,53846,3456],{},[1864,53848,45266],{},[1723,53850,1759],{},[1864,53852,45271],{},[1723,53854,1725],{},[1864,53856,53857],{},"8,326.",[902,53859,53860],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,53862,53863,2628,53866,1343,53893,1343,53915,1343,53937,6299,53959,1343,53978,1343,53999,1343,54018,1664],{},[38,53864,53865],{},"Řešení (b) — současná změna všech parametrů:",[883,53867,53869],{"className":53868},[886],[888,53870,53871],{"xmlns":890},[892,53872,53873,53890],{},[895,53874,53875,53877,53879,53881,53883,53885,53887],{},[898,53876,207],{},[1723,53878,3430],{},[1723,53880,1759],{},[1864,53882,2909],{},[1723,53884,3843],{},[1723,53886,1759],{},[1864,53888,53889],{},"2,5",[902,53891,53892],{"encoding":904},"a: -3 \\to -2{,}5",[883,53894,53896],{"className":53895},[886],[888,53897,53898],{"xmlns":890},[892,53899,53900,53912],{},[895,53901,53902,53904,53906,53908,53910],{},[898,53903,2069],{},[1723,53905,3430],{},[1864,53907,5921],{},[1723,53909,3843],{},[1864,53911,15739],{},[902,53913,53914],{"encoding":904},"b: 40 \\to 35",[883,53916,53918],{"className":53917},[886],[888,53919,53920],{"xmlns":890},[892,53921,53922,53934],{},[895,53923,53924,53926,53928,53930,53932],{},[898,53925,2878],{},[1723,53927,3430],{},[1864,53929,5719],{},[1723,53931,3843],{},[1864,53933,20015],{},[902,53935,53936],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,53938,53940],{"className":53939},[886],[888,53941,53942],{"xmlns":890},[892,53943,53944,53956],{},[895,53945,53946,53948,53950,53952,53954],{},[898,53947,2930],{},[1723,53949,3430],{},[1864,53951,3585],{},[1723,53953,3843],{},[1864,53955,3626],{},[902,53957,53958],{"encoding":904},"d: 10 \\to 11",[883,53960,53962],{"className":53961},[886],[888,53963,53964],{"xmlns":890},[892,53965,53966,53976],{},[895,53967,53968,53970,53972,53974],{},[898,53969,2930],{},[898,53971,207],{},[1723,53973,1725],{},[1864,53975,5719],{},[902,53977,45304],{"encoding":904},[883,53979,53981],{"className":53980},[886],[888,53982,53983],{"xmlns":890},[892,53984,53985,53997],{},[895,53986,53987,53989,53991,53993,53995],{},[898,53988,2930],{},[898,53990,2069],{},[1723,53992,1725],{},[1723,53994,1759],{},[1864,53996,2962],{},[902,53998,45326],{"encoding":904},[883,54000,54002],{"className":54001},[886],[888,54003,54004],{"xmlns":890},[892,54005,54006,54016],{},[895,54007,54008,54010,54012,54014],{},[898,54009,2930],{},[898,54011,2878],{},[1723,54013,1725],{},[1864,54015,3517],{},[902,54017,45346],{"encoding":904},[883,54019,54021],{"className":54020},[886],[888,54022,54023],{"xmlns":890},[892,54024,54025,54035],{},[895,54026,54027,54029,54031,54033],{},[898,54028,2930],{},[898,54030,2930],{},[1723,54032,1725],{},[1864,54034,1866],{},[902,54036,45366],{"encoding":904},[724,54038,54039,54040,54098],{},"Totální diferenciál ",[883,54041,54043],{"className":54042},[886],[888,54044,54045],{"xmlns":890},[892,54046,54047,54095],{},[895,54048,54049,54055,54057,54059,54061,54063,54065,54067,54069,54071,54073,54075],{},[2057,54050,54051,54053],{},[898,54052,1904],{},[898,54054,1846],{},[1723,54056,1908],{"stretchy":1907},[898,54058,207],{},[1723,54060,2031],{"separator":2030},[898,54062,2069],{},[1723,54064,2031],{"separator":2030},[898,54066,2878],{},[1723,54068,2031],{"separator":2030},[898,54070,2930],{},[1723,54072,1914],{"stretchy":1907},[1723,54074,1725],{},[3055,54076,54077],{"scriptlevel":2256,"displaystyle":2030},[3058,54078,54079,54087],{},[895,54080,54081,54083,54085],{},[898,54082,2069],{},[1723,54084,1759],{},[898,54086,2930],{},[895,54088,54089,54091,54093],{},[898,54090,2878],{},[1723,54092,1759],{},[898,54094,207],{},[902,54096,54097],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,54100,54102],{"className":54101},[886],[888,54103,54104],{"xmlns":890,"display":28759},[892,54105,54106,54226],{},[895,54107,54108,54110,54116,54118,54144,54146,54148,54150,54152,54164,54166,54168,54170,54172,54198,54200,54202,54204,54206,54218,54220,54222,54224],{},[898,54109,2930],{},[2057,54111,54112,54114],{},[898,54113,1904],{},[898,54115,1846],{},[1723,54117,1725],{},[3058,54119,54120,54128],{},[895,54121,54122,54124,54126],{},[898,54123,2069],{},[1723,54125,1759],{},[898,54127,2930],{},[895,54129,54130,54132,54134,54136,54138],{},[1723,54131,1908],{"stretchy":1907},[898,54133,2878],{},[1723,54135,1759],{},[898,54137,207],{},[2057,54139,54140,54142],{},[1723,54141,1914],{"stretchy":1907},[1864,54143,2331],{},[3018,54145,3707],{},[898,54147,2930],{},[898,54149,207],{},[1723,54151,2087],{},[3058,54153,54154,54156],{},[1864,54155,1866],{},[895,54157,54158,54160,54162],{},[898,54159,2878],{},[1723,54161,1759],{},[898,54163,207],{},[3018,54165,3707],{},[898,54167,2930],{},[898,54169,2069],{},[1723,54171,1759],{},[3058,54173,54174,54182],{},[895,54175,54176,54178,54180],{},[898,54177,2069],{},[1723,54179,1759],{},[898,54181,2930],{},[895,54183,54184,54186,54188,54190,54192],{},[1723,54185,1908],{"stretchy":1907},[898,54187,2878],{},[1723,54189,1759],{},[898,54191,207],{},[2057,54193,54194,54196],{},[1723,54195,1914],{"stretchy":1907},[1864,54197,2331],{},[3018,54199,3707],{},[898,54201,2930],{},[898,54203,2878],{},[1723,54205,1759],{},[3058,54207,54208,54210],{},[1864,54209,1866],{},[895,54211,54212,54214,54216],{},[898,54213,2878],{},[1723,54215,1759],{},[898,54217,207],{},[3018,54219,3707],{},[898,54221,2930],{},[898,54223,2930],{},[898,54225,1664],{"mathvariant":2124},[902,54227,54228],{"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.",[724,54230,54231,54232,1343,54254,1343,54285,3871],{},"Dosazením číselných hodnot (",[883,54233,54235],{"className":54234},[886],[888,54236,54237],{"xmlns":890},[892,54238,54239,54251],{},[895,54240,54241,54243,54245,54247,54249],{},[898,54242,2878],{},[1723,54244,1759],{},[898,54246,207],{},[1723,54248,1725],{},[1864,54250,45098],{},[902,54252,54253],{"encoding":904},"c - a = 3{,}5",[883,54255,54257],{"className":54256},[886],[888,54258,54259],{"xmlns":890},[892,54260,54261,54282],{},[895,54262,54263,54265,54267,54269,54271,54277,54279],{},[1723,54264,1908],{"stretchy":1907},[898,54266,2878],{},[1723,54268,1759],{},[898,54270,207],{},[2057,54272,54273,54275],{},[1723,54274,1914],{"stretchy":1907},[1864,54276,2331],{},[1723,54278,1725],{},[1864,54280,54281],{},"12,25",[902,54283,54284],{"encoding":904},"(c-a)^2 = 12{,}25",[883,54286,54288],{"className":54287},[886],[888,54289,54290],{"xmlns":890},[892,54291,54292,54304],{},[895,54293,54294,54296,54298,54300,54302],{},[898,54295,2069],{},[1723,54297,1759],{},[898,54299,2930],{},[1723,54301,1725],{},[1864,54303,38711],{},[902,54305,54306],{"encoding":904},"b - d = 30",[883,54308,54310],{"className":54309},[886],[888,54311,54312],{"xmlns":890,"display":28759},[892,54313,54314,54415],{},[895,54315,54316,54318,54324,54326,54334,54336,54338,54340,54342,54350,54352,54354,54356,54358,54360,54368,54370,54372,54374,54376,54384,54386,54388,54390,54392,54395,54397,54400,54402,54404,54406,54409,54411,54413],{},[898,54317,2930],{},[2057,54319,54320,54322],{},[898,54321,1904],{},[898,54323,1846],{},[1723,54325,3456],{},[3055,54327,54328],{"scriptlevel":2256,"displaystyle":1907},[3058,54329,54330,54332],{},[1864,54331,38711],{},[1864,54333,54281],{},[1723,54335,1908],{"stretchy":1907},[1864,54337,5719],{},[1723,54339,1914],{"stretchy":1907},[1723,54341,2087],{},[3055,54343,54344],{"scriptlevel":2256,"displaystyle":1907},[3058,54345,54346,54348],{},[1864,54347,1866],{},[1864,54349,45098],{},[1723,54351,1908],{"stretchy":1907},[1723,54353,1759],{},[1864,54355,2962],{},[1723,54357,1914],{"stretchy":1907},[1723,54359,1759],{},[3055,54361,54362],{"scriptlevel":2256,"displaystyle":1907},[3058,54363,54364,54366],{},[1864,54365,38711],{},[1864,54367,54281],{},[1723,54369,1908],{"stretchy":1907},[1864,54371,3517],{},[1723,54373,1914],{"stretchy":1907},[1723,54375,1759],{},[3055,54377,54378],{"scriptlevel":2256,"displaystyle":1907},[3058,54379,54380,54382],{},[1864,54381,1866],{},[1864,54383,45098],{},[1723,54385,1908],{"stretchy":1907},[1864,54387,1866],{},[1723,54389,1914],{"stretchy":1907},[1723,54391,6610],{},[1864,54393,54394],{},"1,224",[1723,54396,1759],{},[1864,54398,54399],{},"1,429",[1723,54401,1759],{},[1864,54403,45271],{},[1723,54405,1759],{},[1864,54407,54408],{},"0,286",[1723,54410,6610],{},[1723,54412,1759],{},[1864,54414,45517],{},[902,54416,54417],{"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.",[724,54419,30758,54420,1664],{},[883,54421,54423],{"className":54422},[886],[888,54424,54425],{"xmlns":890},[892,54426,54427,54449],{},[895,54428,54429,54437,54439,54441,54443,54445,54447],{},[2220,54430,54431,54433,54435],{},[898,54432,1904],{},[1864,54434,1866],{},[898,54436,1846],{},[1723,54438,3456],{},[1864,54440,45266],{},[1723,54442,1759],{},[1864,54444,45548],{},[1723,54446,6610],{},[1864,54448,45553],{},[902,54450,54451],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[4584,54453,54454],{},[724,54455,54456,54458,54459,54480,54481,54507,54508,54511,54512,54608,54609,54632,54633,54649],{},[883,54457,5124],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,54460,54462],{"className":54461},[886],[888,54463,54464],{"xmlns":890},[892,54465,54466,54478],{},[895,54467,54468,54470,54472,54474,54476],{},[898,54469,3611],{"mathvariant":2124},[898,54471,1904],{},[1723,54473,3456],{},[1723,54475,1759],{},[1864,54477,45583],{},[902,54479,45586],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,54482,54484],{"className":54483},[886],[888,54485,54486],{"xmlns":890},[892,54487,54488,54504],{},[895,54489,54490,54492,54498,54500,54502],{},[898,54491,2930],{},[2057,54493,54494,54496],{},[898,54495,1904],{},[898,54497,1846],{},[1723,54499,6610],{},[1723,54501,1759],{},[1864,54503,45548],{},[902,54505,54506],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,54509,54510],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,54513,54515],{"className":54514},[886],[888,54516,54517],{"xmlns":890},[892,54518,54519,54605],{},[895,54520,54521,54529,54531,54565,54567,54591,54593,54600,54602],{},[2220,54522,54523,54525,54527],{},[898,54524,1904],{},[1864,54526,1866],{},[898,54528,1846],{},[1723,54530,1725],{},[3058,54532,54533,54549],{},[895,54534,54535,54541,54543],{},[2057,54536,54537,54539],{},[898,54538,2069],{},[1723,54540,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,54542,1759],{},[2057,54544,54545,54547],{},[898,54546,2930],{},[1723,54548,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[895,54550,54551,54557,54559],{},[2057,54552,54553,54555],{},[898,54554,2878],{},[1723,54556,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,54558,1759],{},[2057,54560,54561,54563],{},[898,54562,207],{},[1723,54564,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,54566,1725],{},[3058,54568,54569,54577],{},[895,54570,54571,54573,54575],{},[1864,54572,15739],{},[1723,54574,1759],{},[1864,54576,3626],{},[895,54578,54579,54581,54583,54585,54587,54589],{},[1864,54580,20015],{},[1723,54582,1759],{},[1723,54584,1908],{"stretchy":1907},[1723,54586,1759],{},[1864,54588,53889],{},[1723,54590,1914],{"stretchy":1907},[1723,54592,1725],{},[3058,54594,54595,54597],{},[1864,54596,42492],{},[1864,54598,54599],{},"3,1",[1723,54601,6610],{},[1864,54603,54604],{},"7,742",[902,54606,54607],{"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 ",[883,54610,54612],{"className":54611},[886],[888,54613,54614],{"xmlns":890},[892,54615,54616,54629],{},[895,54617,54618,54620,54622,54624,54626],{},[898,54619,3611],{"mathvariant":2124},[898,54621,1904],{},[1723,54623,6610],{},[1723,54625,1759],{},[1864,54627,54628],{},"0,829",[902,54630,54631],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,54634,54636],{"className":54635},[886],[888,54637,54638],{"xmlns":890},[892,54639,54640,54646],{},[895,54641,54642,54644],{},[1723,54643,1759],{},[1864,54645,45583],{},[902,54647,54648],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,54651,54652],{},[614,54653,54654,54655,54668],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,54656,54658],{"className":54657},[886],[888,54659,54660],{"xmlns":890},[892,54661,54662,54666],{},[895,54663,54664],{},[898,54665,1904],{},[902,54667,1904],{"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.",[198,54670,54672,54673],{"id":54671},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,54674,54676],{"className":54675},[886],[888,54677,54678],{"xmlns":890},[892,54679,54680,54686],{},[895,54681,54682,54684],{},[898,54683,1746],{},[898,54685,2111],{},[902,54687,45661],{"encoding":904},[4584,54689,54690],{},[724,54691,54692,54694,54695,54729,54730,54752],{},[883,54693,53385],{}," Zadání\nPro nabídku ",[883,54696,54698],{"className":54697},[886],[888,54699,54700],{"xmlns":890},[892,54701,54702,54726],{},[895,54703,54704,54706,54708,54710,54712,54714,54716,54718,54720,54722,54724],{},[898,54705,1746],{},[1723,54707,1725],{},[898,54709,2111],{},[1723,54711,1908],{"stretchy":1907},[898,54713,1904],{},[1723,54715,1914],{"stretchy":1907},[1723,54717,1725],{},[1864,54719,3585],{},[1723,54721,2087],{},[1864,54723,2331],{},[898,54725,1904],{},[902,54727,54728],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,54731,54733],{"className":54732},[886],[888,54734,54735],{"xmlns":890},[892,54736,54737,54749],{},[895,54738,54739,54745,54747],{},[1931,54740,54741,54743],{},[898,54742,1904],{},[1864,54744,2256],{},[1723,54746,1725],{},[1864,54748,3585],{},[902,54750,54751],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,54754,54755],{},[38,54756,23463],{},[724,54758,54759],{},"Odpovídající cena:",[883,54761,54763],{"className":54762},[886],[888,54764,54765],{"xmlns":890,"display":28759},[892,54766,54767,54802],{},[895,54768,54769,54775,54777,54779,54781,54783,54785,54787,54789,54791,54793,54795,54797,54799],{},[1931,54770,54771,54773],{},[898,54772,1746],{},[1864,54774,2256],{},[1723,54776,1725],{},[898,54778,2111],{},[1723,54780,1908],{"stretchy":1907},[1864,54782,3585],{},[1723,54784,1914],{"stretchy":1907},[1723,54786,1725],{},[1864,54788,3585],{},[1723,54790,2087],{},[1864,54792,2331],{},[1723,54794,3897],{},[1864,54796,3585],{},[1723,54798,1725],{},[1864,54800,54801],{},"30.",[902,54803,54804],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,54806,54807],{},"Dle vzorce (2.15):",[883,54809,54811],{"className":54810},[886],[888,54812,54813],{"xmlns":890,"display":28759},[892,54814,54815,54923],{},[895,54816,54817,54819,54821,54823,54825,54827,54829,54835,54841,54843,54851,54853,54855,54857,54859,54861,54863,54865,54867,54869,54871,54873,54875,54877,54879,54882,54884,54886,54888,54894,54902,54904,54906,54908,54910,54912,54914,54916,54918,54920],{},[898,54818,1746],{},[898,54820,2111],{},[1723,54822,1908],{"stretchy":1907},[1864,54824,3585],{},[1723,54826,1914],{"stretchy":1907},[1723,54828,1725],{},[1931,54830,54831,54833],{},[898,54832,1746],{},[1864,54834,2256],{},[1931,54836,54837,54839],{},[898,54838,1904],{},[1864,54840,2256],{},[1723,54842,1759],{},[2220,54844,54845,54847,54849],{},[1723,54846,11870],{},[1864,54848,2256],{},[1864,54850,3585],{},[1723,54852,1908],{"stretchy":1907},[1864,54854,3585],{},[1723,54856,2087],{},[1864,54858,2331],{},[898,54860,1904],{},[1723,54862,1914],{"stretchy":1907},[3018,54864,3707],{},[898,54866,2930],{},[898,54868,1904],{},[1723,54870,1725],{},[1864,54872,3585],{},[1723,54874,3897],{},[1864,54876,38711],{},[1723,54878,1759],{},[1723,54880,3212],{"fence":1907,"stretchy":2030,"minsize":54881,"maxsize":54881},"1.8em",[1864,54883,3585],{},[898,54885,1904],{},[1723,54887,2087],{},[2057,54889,54890,54892],{},[898,54891,1904],{},[1864,54893,2331],{},[2220,54895,54896,54898,54900],{},[1723,54897,3227],{"fence":1907,"stretchy":2030,"minsize":54881,"maxsize":54881},[1864,54899,2256],{},[1864,54901,3585],{},[1723,54903,1725],{},[1864,54905,30774],{},[1723,54907,1759],{},[1723,54909,1908],{"stretchy":1907},[1864,54911,3810],{},[1723,54913,2087],{},[1864,54915,3810],{},[1723,54917,1914],{"stretchy":1907},[1723,54919,1725],{},[1864,54921,54922],{},"100.",[902,54924,54925],{"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.",[724,54927,54928,54929,54950,54951,54971],{},"Přebytek výrobce při množství ",[883,54930,54932],{"className":54931},[886],[888,54933,54934],{"xmlns":890},[892,54935,54936,54948],{},[895,54937,54938,54944,54946],{},[1931,54939,54940,54942],{},[898,54941,1904],{},[1864,54943,2256],{},[1723,54945,1725],{},[1864,54947,3585],{},[902,54949,54751],{"encoding":904}," je tedy ",[883,54952,54954],{"className":54953},[886],[888,54955,54956],{"xmlns":890},[892,54957,54958,54968],{},[895,54959,54960,54962,54964,54966],{},[898,54961,1746],{},[898,54963,2111],{},[1723,54965,1725],{},[1864,54967,3810],{},[902,54969,54970],{"encoding":904},"PS = 100"," (peněžních jednotek).",[37662,54973],{},[115,54975,54977],{"id":54976},"cheat-sheet","Cheat sheet",[16,54979,54980,54993],{},[19,54981,54982],{},[22,54983,54984,54987,54990],{},[25,54985,54986],{},"Veličina",[25,54988,54989],{},"Vzorec",[25,54991,54992],{},"Geometrie",[30,54994,54995,55113,55227,55295],{},[22,54996,54997,55025,55081],{},[35,54998,54999],{},[883,55000,55002],{"className":55001},[886],[888,55003,55004],{"xmlns":890},[892,55005,55006,55022],{},[895,55007,55008,55010,55012,55014,55020],{},[898,55009,1721],{},[898,55011,2111],{},[1723,55013,1908],{"stretchy":1907},[1931,55015,55016,55018],{},[898,55017,1904],{},[1864,55019,2256],{},[1723,55021,1914],{"stretchy":1907},[902,55023,55024],{"encoding":904},"CS(Q_0)",[35,55026,55027],{},[883,55028,55030],{"className":55029},[886],[888,55031,55032],{"xmlns":890},[892,55033,55034,55078],{},[895,55035,55036],{},[3055,55037,55038,55050,55052,55054,55056,55058,55060,55062,55064,55066,55072],{"scriptlevel":2256,"displaystyle":2030},[2220,55039,55040,55042,55044],{},[1723,55041,11870],{},[1864,55043,2256],{},[1931,55045,55046,55048],{},[898,55047,1904],{},[1864,55049,2256],{},[898,55051,4897],{},[1723,55053,1908],{"stretchy":1907},[898,55055,1904],{},[1723,55057,1914],{"stretchy":1907},[3018,55059,3707],{},[898,55061,2930],{},[898,55063,1904],{},[1723,55065,1759],{},[1931,55067,55068,55070],{},[898,55069,1746],{},[1864,55071,2256],{},[1931,55073,55074,55076],{},[898,55075,1904],{},[1864,55077,2256],{},[902,55079,55080],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,55082,55083,55084,55087,55088,55091,55092],{},"plocha ",[38,55085,55086],{},"pod"," křivkou poptávky, ",[38,55089,55090],{},"nad"," čárou ",[883,55093,55095],{"className":55094},[886],[888,55096,55097],{"xmlns":890},[892,55098,55099,55111],{},[895,55100,55101,55103,55105],{},[898,55102,1746],{},[1723,55104,1725],{},[1931,55106,55107,55109],{},[898,55108,1746],{},[1864,55110,2256],{},[902,55112,52367],{"encoding":904},[22,55114,55115,55143,55199],{},[35,55116,55117],{},[883,55118,55120],{"className":55119},[886],[888,55121,55122],{"xmlns":890},[892,55123,55124,55140],{},[895,55125,55126,55128,55130,55132,55138],{},[898,55127,1746],{},[898,55129,2111],{},[1723,55131,1908],{"stretchy":1907},[1931,55133,55134,55136],{},[898,55135,1904],{},[1864,55137,2256],{},[1723,55139,1914],{"stretchy":1907},[902,55141,55142],{"encoding":904},"PS(Q_0)",[35,55144,55145],{},[883,55146,55148],{"className":55147},[886],[888,55149,55150],{"xmlns":890},[892,55151,55152,55196],{},[895,55153,55154],{},[3055,55155,55156,55162,55168,55170,55182,55184,55186,55188,55190,55192,55194],{"scriptlevel":2256,"displaystyle":2030},[1931,55157,55158,55160],{},[898,55159,1746],{},[1864,55161,2256],{},[1931,55163,55164,55166],{},[898,55165,1904],{},[1864,55167,2256],{},[1723,55169,1759],{},[2220,55171,55172,55174,55176],{},[1723,55173,11870],{},[1864,55175,2256],{},[1931,55177,55178,55180],{},[898,55179,1904],{},[1864,55181,2256],{},[898,55183,2111],{},[1723,55185,1908],{"stretchy":1907},[898,55187,1904],{},[1723,55189,1914],{"stretchy":1907},[3018,55191,3707],{},[898,55193,2930],{},[898,55195,1904],{},[902,55197,55198],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,55200,55083,55201,55203,55204,55091,55206],{},[38,55202,55090],{}," křivkou nabídky, ",[38,55205,55086],{},[883,55207,55209],{"className":55208},[886],[888,55210,55211],{"xmlns":890},[892,55212,55213,55225],{},[895,55214,55215,55217,55219],{},[898,55216,1746],{},[1723,55218,1725],{},[1931,55220,55221,55223],{},[898,55222,1746],{},[1864,55224,2256],{},[902,55226,52367],{"encoding":904},[22,55228,55229,55232,55259],{},[35,55230,55231],{},"Výdaje \u002F tržby",[35,55233,55234],{},[883,55235,55237],{"className":55236},[886],[888,55238,55239],{"xmlns":890},[892,55240,55241,55257],{},[895,55242,55243,55249,55251],{},[1931,55244,55245,55247],{},[898,55246,1746],{},[1864,55248,2256],{},[1723,55250,3897],{},[1931,55252,55253,55255],{},[898,55254,1904],{},[1864,55256,2256],{},[902,55258,53227],{"encoding":904},[35,55260,55261,55262],{},"obdélník ",[883,55263,55265],{"className":55264},[886],[888,55266,55267],{"xmlns":890},[892,55268,55269,55293],{},[895,55270,55271,55273,55275,55281,55283,55285,55287],{},[1864,55272,2256],{},[3018,55274,3707],{},[1931,55276,55277,55279],{},[898,55278,1904],{},[1864,55280,2256],{},[3018,55282,3707],{},[898,55284,1718],{},[3018,55286,3707],{},[1931,55288,55289,55291],{},[898,55290,1746],{},[1864,55292,2256],{},[902,55294,51847],{"encoding":904},[22,55296,55297,55300,55323],{},[35,55298,55299],{},"Celkový přebytek",[35,55301,55302],{},[883,55303,55305],{"className":55304},[886],[888,55306,55307],{"xmlns":890},[892,55308,55309,55321],{},[895,55310,55311,55313,55315,55317,55319],{},[898,55312,1721],{},[898,55314,2111],{},[1723,55316,2087],{},[898,55318,1746],{},[898,55320,2111],{},[902,55322,51585],{"encoding":904},[35,55324,55325],{},"součet obou ploch v rovnováze",[37662,55327],{},[115,55329,16421],{"id":16420},[120,55331,55332,55354,55376,55420,55464,55527,55555],{},[123,55333,55334,1981,55336,1343,55351,55353],{},[38,55335,45626],{},[883,55337,55339],{"className":55338},[886],[888,55340,55341],{"xmlns":890},[892,55342,55343,55349],{},[895,55344,55345,55347],{},[898,55346,1721],{},[898,55348,2111],{},[902,55350,45642],{"encoding":904},[614,55352,45679],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,55355,55356,1981,55358,1343,55373,55375],{},[38,55357,45772],{},[883,55359,55361],{"className":55360},[886],[888,55362,55363],{"xmlns":890},[892,55364,55365,55371],{},[895,55366,55367,55369],{},[898,55368,1746],{},[898,55370,2111],{},[902,55372,45661],{"encoding":904},[614,55374,45775],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,55377,55378,7725,55381,1664],{},[38,55379,55380],{},"Ochota platit",[883,55382,55384],{"className":55383},[886],[888,55385,55386],{"xmlns":890},[892,55387,55388,55418],{},[895,55389,55390],{},[3055,55391,55392,55404,55406,55408,55410,55412,55414,55416],{"scriptlevel":2256,"displaystyle":2030},[2220,55393,55394,55396,55398],{},[1723,55395,11870],{},[1864,55397,2256],{},[1931,55399,55400,55402],{},[898,55401,1904],{},[1864,55403,2256],{},[898,55405,4897],{},[1723,55407,1908],{"stretchy":1907},[898,55409,1904],{},[1723,55411,1914],{"stretchy":1907},[3018,55413,3707],{},[898,55415,2930],{},[898,55417,1904],{},[902,55419,52215],{"encoding":904},[123,55421,55422,7725,55425,1664],{},[38,55423,55424],{},"Minimální cena výrobce",[883,55426,55428],{"className":55427},[886],[888,55429,55430],{"xmlns":890},[892,55431,55432,55462],{},[895,55433,55434],{},[3055,55435,55436,55448,55450,55452,55454,55456,55458,55460],{"scriptlevel":2256,"displaystyle":2030},[2220,55437,55438,55440,55442],{},[1723,55439,11870],{},[1864,55441,2256],{},[1931,55443,55444,55446],{},[898,55445,1904],{},[1864,55447,2256],{},[898,55449,2111],{},[1723,55451,1908],{"stretchy":1907},[898,55453,1904],{},[1723,55455,1914],{"stretchy":1907},[3018,55457,3707],{},[898,55459,2930],{},[898,55461,1904],{},[902,55463,52857],{"encoding":904},[123,55465,55466,7725,55469,53358,55494,4634],{},[38,55467,55468],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,55470,55472],{"className":55471},[886],[888,55473,55474],{"xmlns":890},[892,55475,55476,55492],{},[895,55477,55478,55484,55486],{},[1931,55479,55480,55482],{},[898,55481,1746],{},[1864,55483,2256],{},[3018,55485,3707],{},[1931,55487,55488,55490],{},[898,55489,1904],{},[1864,55491,2256],{},[902,55493,52293],{"encoding":904},[883,55495,55497],{"className":55496},[886],[888,55498,55499],{"xmlns":890},[892,55500,55501,55525],{},[895,55502,55503,55505,55507,55513,55515,55517,55519],{},[1864,55504,2256],{},[3018,55506,3707],{},[1931,55508,55509,55511],{},[898,55510,1904],{},[1864,55512,2256],{},[3018,55514,3707],{},[898,55516,1718],{},[3018,55518,3707],{},[1931,55520,55521,55523],{},[898,55522,1746],{},[1864,55524,2256],{},[902,55526,51847],{"encoding":904},[123,55528,55529,55532,55533,55554],{},[38,55530,55531],{},"Celkový přebytek trhu"," — součet ",[883,55534,55536],{"className":55535},[886],[888,55537,55538],{"xmlns":890},[892,55539,55540,55552],{},[895,55541,55542,55544,55546,55548,55550],{},[898,55543,1721],{},[898,55545,2111],{},[1723,55547,2087],{},[898,55549,1746],{},[898,55551,2111],{},[902,55553,51585],{"encoding":904}," v rovnovážném bodě.",[123,55556,55557,55559,55560,1343,55573,55586,55587,1664],{},[38,55558,3170],{}," — plochy ohraničené křivkami ",[883,55561,55563],{"className":55562},[886],[888,55564,55565],{"xmlns":890},[892,55566,55567,55571],{},[895,55568,55569],{},[898,55570,4897],{},[902,55572,4897],{"encoding":904},[883,55574,55576],{"className":55575},[886],[888,55577,55578],{"xmlns":890},[892,55579,55580,55584],{},[895,55581,55582],{},[898,55583,2111],{},[902,55585,2111],{"encoding":904}," a přímkou ",[883,55588,55590],{"className":55589},[886],[888,55591,55592],{"xmlns":890},[892,55593,55594,55606],{},[895,55595,55596,55598,55600],{},[898,55597,1746],{},[1723,55599,1725],{},[1931,55601,55602,55604],{},[898,55603,1746],{},[1864,55605,2256],{},[902,55607,52367],{"encoding":904},[37662,55609],{},[115,55611,55613],{"id":55612},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,55615,55616,55617,55630,55631,55648],{},"Uvalení jednotkové daně ",[883,55618,55620],{"className":55619},[886],[888,55621,55622],{"xmlns":890},[892,55623,55624,55628],{},[895,55625,55626],{},[898,55627,1754],{},[902,55629,1754],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,55632,55634],{"className":55633},[886],[888,55635,55636],{"xmlns":890},[892,55637,55638,55646],{},[895,55639,55640],{},[2057,55641,55642,55644],{},[898,55643,1904],{},[898,55645,1846],{},[902,55647,43095],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,55650,55651],{},[3285,55652],{"alt":55653,"className":55654,"src":55655},"imek-prebytky-s-dani-deadweight",[210,3289],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,55657,55658,55659,55674,55675,55690,55691,53358,55694,55718,55719,1981,55722,55725,55726,1664],{},"Přebytek spotřebitele ",[883,55660,55662],{"className":55661},[886],[888,55663,55664],{"xmlns":890},[892,55665,55666,55672],{},[895,55667,55668,55670],{},[898,55669,1721],{},[898,55671,2111],{},[902,55673,45642],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,55676,55678],{"className":55677},[886],[888,55679,55680],{"xmlns":890},[892,55681,55682,55688],{},[895,55683,55684,55686],{},[898,55685,1746],{},[898,55687,2111],{},[902,55689,45661],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,55692,55693],{},"daňový příjem",[883,55695,55697],{"className":55696},[886],[888,55698,55699],{"xmlns":890},[892,55700,55701,55715],{},[895,55702,55703,55705,55707],{},[898,55704,1754],{},[1723,55706,3897],{},[2220,55708,55709,55711,55713],{},[898,55710,1904],{},[1864,55712,1866],{},[898,55714,1846],{},[902,55716,55717],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,55720,55721],{},"mrtvá ztráta",[614,55723,55724],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,55727,811],{"className":55728,"dataFsResolvedFilePath":809,"href":810},[210],[37662,55730],{},[115,55732,2620],{"id":2619},[120,55734,55735,55742,55754,55761,55768],{},[123,55736,55737,2628,55739],{},[38,55738,16920],{},[207,55740,802],{"className":55741,"dataFsResolvedFilePath":800,"href":801},[210],[123,55743,55744,2628,55746,55749,55750,55753],{},[38,55745,37367],{},[207,55747,775],{"className":55748,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,55751,3086],{"className":55752,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,55755,55756,2628,55758],{},[38,55757,16929],{},[207,55759,4539],{"className":55760,"dataFsResolvedFilePath":827,"href":828},[210],[123,55762,55763,2628,55765],{},[38,55764,51448],{},[207,55766,51452],{"className":55767,"dataFsResolvedFilePath":745,"href":746},[210],[123,55769,55770,2628,55772],{},[38,55771,2627],{},[207,55773,1646],{"className":55774,"dataFsResolvedFilePath":1645,"href":1644},[210],{"title":641,"searchDepth":642,"depth":642,"links":55776},[55777,55778,55783,55788,55793,55794,55795,55796],{"id":51644,"depth":642,"text":1241},{"id":51988,"depth":642,"text":55779,"children":55780},"Přebytek spotřebitele (CSCS)",[55781,55782],{"id":52007,"depth":649,"text":52008},{"id":3169,"depth":649,"text":3170},{"id":52583,"depth":642,"text":55784,"children":55785},"Přebytek výrobce (PSPS)",[55786,55787],{"id":52602,"depth":649,"text":52603},{"id":52765,"depth":649,"text":3170},{"id":53373,"depth":642,"text":53374,"children":55789},[55790,55791],{"id":53377,"depth":649,"text":53378},{"id":54671,"depth":649,"text":55792},"Příklad 2.13 — numerický výpočet PSPS",{"id":54976,"depth":642,"text":54977},{"id":16420,"depth":642,"text":16421},{"id":55612,"depth":642,"text":55613},{"id":2619,"depth":642,"text":2620},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,51514,55803,55804,2571,1692,55805,55806],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":55809,"title":55810,"body":55811,"course":1128,"courses":659,"created":2676,"description":641,"extension":661,"meta":75135,"navigation":664,"path":75136,"seo":75137,"sources":75138,"stem":75139,"tags":75140,"type":4573,"updated":677,"__hash__":75146},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":55812,"toc":75099},[55813,55816,55999,56001,56092,56097,56423,56427,56434,56438,56483,56550,56581,56631,56666,56670,56729,56734,56800,56918,57020,57024,57047,57125,57168,57172,57201,57268,57274,57388,57392,57472,57509,57561,57759,57823,57910,57914,57917,57996,57999,58117,58136,58201,58205,58297,58365,58406,58460,58528,58565,58569,58627,58657,58868,58940,58992,59158,59251,59286,59290,59294,59331,59396,59451,59455,59478,59567,59671,59740,59744,59841,59954,60010,60064,60122,60183,60186,60222,60287,60317,60546,60604,60638,60642,60669,60748,60862,60883,60962,60964,61072,61076,61214,61536,61540,61543,61547,61596,61600,61854,62006,62013,62086,62270,62275,62618,62622,62645,62647,62668,62727,62737,62786,62928,63002,63097,63212,63310,63428,63432,63501,63506,63618,63763,63814,63926,63968,63972,63992,64053,64080,64142,64146,64168,64237,64517,64524,64554,64561,64754,64758,64836,64841,64917,64920,65008,65084,65151,65200,65303,65376,65497,65848,65961,66063,66067,66070,66077,66080,66116,66175,66184,66333,66557,66561,66624,66803,66895,66950,66954,67010,67080,67132,67153,67234,67237,67312,67356,67360,67401,67444,67470,67474,67545,67641,67703,67755,67858,67936,67959,67988,67992,68158,68275,68347,68662,68822,68826,68877,68938,68973,69003,69103,69145,69314,69319,69415,69453,69457,69576,69877,69879,69914,69917,69921,70049,70181,70503,70691,70769,70773,71078,71191,71337,71522,71628,71860,71975,72057,72176,72274,72315,72319,72374,72518,72672,72832,72925,73119,73431,73562,73691,73695,73767,73809,73860,73862,75057,75059],[12,55814,55810],{"id":55815},"příjem-náklady-zisk-a-nabídka-firmy",[4584,55817,55818],{},[724,55819,55820,4591,55822,2628,55825,55840,55841,2628,55844,55859,55860,2628,55863,55890,55891,55912,55913,55937,55938,55959,55960,55963,55964,55980,55981,1664],{},[883,55821,4590],{},[38,55823,55824],{},"Příjem",[883,55826,55828],{"className":55827},[886],[888,55829,55830],{"xmlns":890},[892,55831,55832,55838],{},[895,55833,55834,55836],{},[898,55835,1754],{},[898,55837,1749],{},[902,55839,4808],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,55842,55843],{},"náklady",[883,55845,55847],{"className":55846},[886],[888,55848,55849],{"xmlns":890},[892,55850,55851,55857],{},[895,55852,55853,55855],{},[898,55854,1754],{},[898,55856,1721],{},[902,55858,3963],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,55861,55862],{},"zisk",[883,55864,55866],{"className":55865},[886],[888,55867,55868],{"xmlns":890},[892,55869,55870,55888],{},[895,55871,55872,55874,55876,55878,55880,55882,55884,55886],{},[898,55873,1746],{},[898,55875,1749],{},[1723,55877,1725],{},[898,55879,1754],{},[898,55881,1749],{},[1723,55883,1759],{},[898,55885,1754],{},[898,55887,1721],{},[902,55889,1766],{"encoding":904}," jejich rozdíl. Kapitola pro každou ze tří veličin zavádí celkovou, průměrnou a mezní podobu, ukáže jejich grafický průběh (pro lineární poptávku a kubické náklady) a odvodí tři klíčové optimalizační principy: ",[883,55892,55894],{"className":55893},[886],[888,55895,55896],{"xmlns":890},[892,55897,55898,55910],{},[895,55899,55900,55902,55904,55906,55908],{},[898,55901,1718],{},[898,55903,1721],{},[1723,55905,1725],{},[898,55907,1728],{},[898,55909,1721],{},[902,55911,1733],{"encoding":904}," v minimu průměrných nákladů, ",[883,55914,55916],{"className":55915},[886],[888,55917,55918],{"xmlns":890},[892,55919,55920,55934],{},[895,55921,55922,55924,55926,55928,55930,55932],{},[898,55923,1718],{},[898,55925,41031],{},[898,55927,1721],{},[1723,55929,1725],{},[898,55931,1728],{},[898,55933,1721],{},[902,55935,55936],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,55939,55941],{"className":55940},[886],[888,55942,55943],{"xmlns":890},[892,55944,55945,55957],{},[895,55946,55947,55949,55951,55953,55955],{},[898,55948,1728],{},[898,55950,1749],{},[1723,55952,1725],{},[898,55954,1728],{},[898,55956,1721],{},[902,55958,1789],{"encoding":904}," v maximu zisku. Na závěr se sestaví ",[38,55961,55962],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,55965,55967],{"className":55966},[886],[888,55968,55969],{"xmlns":890},[892,55970,55971,55977],{},[895,55972,55973,55975],{},[898,55974,1728],{},[898,55976,1721],{},[902,55978,55979],{"encoding":904},"MC"," nad bodem minima ",[883,55982,55984],{"className":55983},[886],[888,55985,55986],{"xmlns":890},[892,55987,55988,55996],{},[895,55989,55990,55992,55994],{},[898,55991,1718],{},[898,55993,41031],{},[898,55995,1721],{},[902,55997,55998],{"encoding":904},"AVC",[115,56000,1241],{"id":51644},[724,56002,56003,56004,56007,56008,56010,56011,1343,56014,1343,56017,56019,56020,56023,56024,56027,56028,56031,56032,3397,56047,1348,56062,3397,56077,4634],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,56005,56006],{},"příjmem"," (revenue) a ",[38,56009,55843],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,56012,56013],{},"zisku",[38,56015,56016],{},"bodů zvratu",[38,56018,2717],{}," a konstrukcí ",[38,56021,56022],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,56025,1145],{"className":56026,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,56029,11831],{"className":56030,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,56033,56035],{"className":56034},[886],[888,56036,56037],{"xmlns":890},[892,56038,56039,56045],{},[895,56040,56041,56043],{},[898,56042,1754],{},[898,56044,1749],{},[902,56046,4808],{"encoding":904},[883,56048,56050],{"className":56049},[886],[888,56051,56052],{"xmlns":890},[892,56053,56054,56060],{},[895,56055,56056,56058],{},[898,56057,1728],{},[898,56059,1749],{},[902,56061,7344],{"encoding":904},[883,56063,56065],{"className":56064},[886],[888,56066,56067],{"xmlns":890},[892,56068,56069,56075],{},[895,56070,56071,56073],{},[898,56072,1754],{},[898,56074,1721],{},[902,56076,3963],{"encoding":904},[883,56078,56080],{"className":56079},[886],[888,56081,56082],{"xmlns":890},[892,56083,56084,56090],{},[895,56085,56086,56088],{},[898,56087,1728],{},[898,56089,1721],{},[902,56091,55979],{"encoding":904},[724,56093,56094],{},[38,56095,56096],{},"Cílové znalosti:",[120,56098,56099,56263,56266,56269,56362,56409,56416],{},[123,56100,56101,56102,1343,56117,1343,56133,1682,56148,1343,56163,1343,56179,1343,56197,1343,56215,1343,56232,1343,56248,9135],{},"odvodit a interpretovat funkce ",[883,56103,56105],{"className":56104},[886],[888,56106,56107],{"xmlns":890},[892,56108,56109,56115],{},[895,56110,56111,56113],{},[898,56112,1754],{},[898,56114,1749],{},[902,56116,4808],{"encoding":904},[883,56118,56120],{"className":56119},[886],[888,56121,56122],{"xmlns":890},[892,56123,56124,56130],{},[895,56125,56126,56128],{},[898,56127,1718],{},[898,56129,1749],{},[902,56131,56132],{"encoding":904},"AR",[883,56134,56136],{"className":56135},[886],[888,56137,56138],{"xmlns":890},[892,56139,56140,56146],{},[895,56141,56142,56144],{},[898,56143,1728],{},[898,56145,1749],{},[902,56147,7344],{"encoding":904},[883,56149,56151],{"className":56150},[886],[888,56152,56153],{"xmlns":890},[892,56154,56155,56161],{},[895,56156,56157,56159],{},[898,56158,1754],{},[898,56160,1721],{},[902,56162,3963],{"encoding":904},[883,56164,56166],{"className":56165},[886],[888,56167,56168],{"xmlns":890},[892,56169,56170,56176],{},[895,56171,56172,56174],{},[898,56173,11136],{},[898,56175,1721],{},[902,56177,56178],{"encoding":904},"FC",[883,56180,56182],{"className":56181},[886],[888,56183,56184],{"xmlns":890},[892,56185,56186,56194],{},[895,56187,56188,56190,56192],{},[898,56189,1754],{},[898,56191,41031],{},[898,56193,1721],{},[902,56195,56196],{"encoding":904},"TVC",[883,56198,56200],{"className":56199},[886],[888,56201,56202],{"xmlns":890},[892,56203,56204,56212],{},[895,56205,56206,56208,56210],{},[898,56207,1718],{},[898,56209,11136],{},[898,56211,1721],{},[902,56213,56214],{"encoding":904},"AFC",[883,56216,56218],{"className":56217},[886],[888,56219,56220],{"xmlns":890},[892,56221,56222,56230],{},[895,56223,56224,56226,56228],{},[898,56225,1718],{},[898,56227,41031],{},[898,56229,1721],{},[902,56231,55998],{"encoding":904},[883,56233,56235],{"className":56234},[886],[888,56236,56237],{"xmlns":890},[892,56238,56239,56245],{},[895,56240,56241,56243],{},[898,56242,1718],{},[898,56244,1721],{},[902,56246,56247],{"encoding":904},"AC",[883,56249,56251],{"className":56250},[886],[888,56252,56253],{"xmlns":890},[892,56254,56255,56261],{},[895,56256,56257,56259],{},[898,56258,1728],{},[898,56260,1721],{},[902,56262,55979],{"encoding":904},[123,56264,56265],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,56267,56268],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,56270,56271,56272,56275,56276,42506,56318,9135],{},"osvojit si ",[38,56273,56274],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,56277,56279],{"className":56278},[886],[888,56280,56281],{"xmlns":890},[892,56282,56283,56315],{},[895,56284,56285,56287,56289,56291,56297,56299,56301,56303,56305,56307,56313],{},[898,56286,1718],{},[898,56288,1721],{},[1723,56290,1908],{"stretchy":1907},[1931,56292,56293,56295],{},[898,56294,1904],{},[1864,56296,2256],{},[1723,56298,1914],{"stretchy":1907},[1723,56300,1725],{},[898,56302,1728],{},[898,56304,1721],{},[1723,56306,1908],{"stretchy":1907},[1931,56308,56309,56311],{},[898,56310,1904],{},[1864,56312,2256],{},[1723,56314,1914],{"stretchy":1907},[902,56316,56317],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,56319,56321],{"className":56320},[886],[888,56322,56323],{"xmlns":890},[892,56324,56325,56359],{},[895,56326,56327,56329,56331,56333,56335,56341,56343,56345,56347,56349,56351,56357],{},[898,56328,1718],{},[898,56330,41031],{},[898,56332,1721],{},[1723,56334,1908],{"stretchy":1907},[1931,56336,56337,56339],{},[898,56338,1904],{},[1864,56340,2256],{},[1723,56342,1914],{"stretchy":1907},[1723,56344,1725],{},[898,56346,1728],{},[898,56348,1721],{},[1723,56350,1908],{"stretchy":1907},[1931,56352,56353,56355],{},[898,56354,1904],{},[1864,56356,2256],{},[1723,56358,1914],{"stretchy":1907},[902,56360,56361],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,56363,56271,56364,56275,56367,9135],{},[38,56365,56366],{},"princip maximalizace zisku",[883,56368,56370],{"className":56369},[886],[888,56371,56372],{"xmlns":890},[892,56373,56374,56406],{},[895,56375,56376,56378,56380,56382,56388,56390,56392,56394,56396,56398,56404],{},[898,56377,1728],{},[898,56379,1749],{},[1723,56381,1908],{"stretchy":1907},[1931,56383,56384,56386],{},[898,56385,1904],{},[1864,56387,2256],{},[1723,56389,1914],{"stretchy":1907},[1723,56391,1725],{},[898,56393,1728],{},[898,56395,1721],{},[1723,56397,1908],{"stretchy":1907},[1931,56399,56400,56402],{},[898,56401,1904],{},[1864,56403,2256],{},[1723,56405,1914],{"stretchy":1907},[902,56407,56408],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,56410,56411,56412,56415],{},"stanovit ",[38,56413,56414],{},"body zvratu"," a interval zisku;",[123,56417,56418,56419,56422],{},"zkonstruovat ",[38,56420,56421],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,56424,56426],{"id":56425},"příjem-firmy","Příjem firmy",[724,56428,56429],{},[3285,56430],{"alt":56431,"className":56432,"src":56433},"imek-ar-mr-dvojnasobny-sklon",[210,3289],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,56435,56437],{"id":56436},"celkový-příjem","Celkový příjem",[724,56439,56440,56441,1981,56456,56459,56460,30637],{},"Celkový příjem ",[883,56442,56444],{"className":56443},[886],[888,56445,56446],{"xmlns":890},[892,56447,56448,56454],{},[895,56449,56450,56452],{},[898,56451,1754],{},[898,56453,1749],{},[902,56455,4808],{"encoding":904},[38,56457,56458],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,56461,56463],{"className":56462},[886],[888,56464,56465],{"xmlns":890},[892,56466,56467,56481],{},[895,56468,56469,56471,56473,56475,56477,56479],{},[898,56470,1746],{},[1723,56472,1725],{},[898,56474,4897],{},[1723,56476,1908],{"stretchy":1907},[898,56478,1904],{},[1723,56480,1914],{"stretchy":1907},[902,56482,5351],{"encoding":904},[883,56484,56486],{"className":56485},[886],[888,56487,56488],{"xmlns":890,"display":28759},[892,56489,56490,56547],{},[21447,56491,56492],{"width":28764},[21452,56493,56494,56496,56540,56542],{},[21455,56495],{"width":28769},[21455,56497,56498],{},[895,56499,56500,56502,56504,56506,56508,56510,56512,56514,56516,56518,56520,56522,56524,56526,56528,56530,56532,56534,56536,56538],{},[898,56501,1754],{},[898,56503,1749],{},[1723,56505,1725],{},[898,56507,1754],{},[898,56509,1749],{},[1723,56511,1908],{"stretchy":1907},[898,56513,1904],{},[1723,56515,1914],{"stretchy":1907},[1723,56517,1725],{},[898,56519,1746],{},[1723,56521,3897],{},[898,56523,1904],{},[1723,56525,1725],{},[898,56527,4897],{},[1723,56529,1908],{"stretchy":1907},[898,56531,1904],{},[1723,56533,1914],{"stretchy":1907},[1723,56535,3897],{},[898,56537,1904],{},[898,56539,1664],{"mathvariant":2124},[21455,56541],{"width":28769},[21455,56543,56544],{},[3018,56545,56546],{},"(3.1)",[902,56548,56549],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,56551,56552,56553,56556,56557,56580],{},"Graf funkce se nazývá ",[38,56554,56555],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,56558,56560],{"className":56559},[886],[888,56561,56562],{"xmlns":890},[892,56563,56564,56578],{},[895,56565,56566,56568,56570,56572,56574,56576],{},[898,56567,1746],{},[1723,56569,1725],{},[898,56571,207],{},[898,56573,1904],{},[1723,56575,2087],{},[898,56577,2069],{},[902,56579,37752],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,56582,56584],{"className":56583},[886],[888,56585,56586],{"xmlns":890,"display":28759},[892,56587,56588,56628],{},[895,56589,56590,56592,56594,56596,56598,56600,56602,56604,56606,56608,56610,56612,56614,56620,56622,56624,56626],{},[898,56591,1754],{},[898,56593,1749],{},[1723,56595,1725],{},[898,56597,1904],{},[1723,56599,1908],{"stretchy":1907},[898,56601,207],{},[898,56603,1904],{},[1723,56605,2087],{},[898,56607,2069],{},[1723,56609,1914],{"stretchy":1907},[1723,56611,1725],{},[898,56613,207],{},[2057,56615,56616,56618],{},[898,56617,1904],{},[1864,56619,2331],{},[1723,56621,2087],{},[898,56623,2069],{},[898,56625,1904],{},[1723,56627,2031],{"separator":2030},[902,56629,56630],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,56632,56633,56634,56647,56648,56665],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,56635,56637],{"className":56636},[886],[888,56638,56639],{"xmlns":890},[892,56640,56641,56645],{},[895,56642,56643],{},[898,56644,900],{},[902,56646,900],{"encoding":904}," (jelikož ",[883,56649,56651],{"className":56650},[886],[888,56652,56653],{"xmlns":890},[892,56654,56655,56663],{},[895,56656,56657,56659,56661],{},[898,56658,207],{},[1723,56660,2287],{},[1864,56662,2256],{},[902,56664,43777],{"encoding":904},") procházející počátkem.",[38040,56667,56669],{"id":56668},"příklad-31","Příklad 3.1",[724,56671,56672,56675,56676,56712,56713,56728],{},[38,56673,56674],{},"Zadání."," Pro poptávku ",[883,56677,56679],{"className":56678},[886],[888,56680,56681],{"xmlns":890},[892,56682,56683,56709],{},[895,56684,56685,56687,56689,56691,56693,56695,56697,56699,56701,56703,56705,56707],{},[898,56686,1746],{},[1723,56688,1725],{},[898,56690,4897],{},[1723,56692,1908],{"stretchy":1907},[898,56694,1904],{},[1723,56696,1914],{"stretchy":1907},[1723,56698,1725],{},[1723,56700,1759],{},[1864,56702,2331],{},[898,56704,1904],{},[1723,56706,2087],{},[1864,56708,3810],{},[902,56710,56711],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,56714,56716],{"className":56715},[886],[888,56717,56718],{"xmlns":890},[892,56719,56720,56726],{},[895,56721,56722,56724],{},[898,56723,1754],{},[898,56725,1749],{},[902,56727,4808],{"encoding":904}," a charakterizujte jeho křivku.",[724,56730,56731,56733],{},[38,56732,23463],{}," Celkový příjem je",[883,56735,56737],{"className":56736},[886],[888,56738,56739],{"xmlns":890,"display":28759},[892,56740,56741,56797],{},[895,56742,56743,56745,56747,56749,56751,56753,56755,56757,56759,56761,56763,56765,56767,56769,56771,56773,56775,56777,56779,56781,56783,56789,56791,56793,56795],{},[898,56744,1754],{},[898,56746,1749],{},[1723,56748,1725],{},[898,56750,1754],{},[898,56752,1749],{},[1723,56754,1908],{"stretchy":1907},[898,56756,1904],{},[1723,56758,1914],{"stretchy":1907},[1723,56760,1725],{},[898,56762,1904],{},[1723,56764,1908],{"stretchy":1907},[1723,56766,1759],{},[1864,56768,2331],{},[898,56770,1904],{},[1723,56772,2087],{},[1864,56774,3810],{},[1723,56776,1914],{"stretchy":1907},[1723,56778,1725],{},[1723,56780,1759],{},[1864,56782,2331],{},[2057,56784,56785,56787],{},[898,56786,1904],{},[1864,56788,2331],{},[1723,56790,2087],{},[1864,56792,3810],{},[898,56794,1904],{},[898,56796,1664],{"mathvariant":2124},[902,56798,56799],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,56801,56802,56803,1682,56825,56847,56848,56866,56867,1664],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,56804,56806],{"className":56805},[886],[888,56807,56808],{"xmlns":890},[892,56809,56810,56822],{},[895,56811,56812,56818,56820],{},[1931,56813,56814,56816],{},[898,56815,1904],{},[1864,56817,1866],{},[1723,56819,1725],{},[1864,56821,2256],{},[902,56823,56824],{"encoding":904},"Q_1 = 0",[883,56826,56828],{"className":56827},[886],[888,56829,56830],{"xmlns":890},[892,56831,56832,56844],{},[895,56833,56834,56840,56842],{},[1931,56835,56836,56838],{},[898,56837,1904],{},[1864,56839,2331],{},[1723,56841,1725],{},[1864,56843,3840],{},[902,56845,56846],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,56849,56851],{"className":56850},[886],[888,56852,56853],{"xmlns":890},[892,56854,56855,56863],{},[895,56856,56857,56859,56861],{},[898,56858,1904],{},[1723,56860,1725],{},[1864,56862,5714],{},[902,56864,56865],{"encoding":904},"Q = 25"," ve výši ",[883,56868,56870],{"className":56869},[886],[888,56871,56872],{"xmlns":890},[892,56873,56874,56915],{},[895,56875,56876,56878,56888,56890,56892,56894,56896,56899,56901,56903,56905,56907,56909,56911,56913],{},[898,56877,1754],{},[1931,56879,56880,56882,56885],{},[898,56881,1749],{},[898,56883,56884],{},"max",[1723,56886,56887],{},"⁡",[1723,56889,1725],{},[1723,56891,1759],{},[1864,56893,2331],{},[1723,56895,3897],{},[1864,56897,56898],{},"625",[1723,56900,2087],{},[1864,56902,3810],{},[1723,56904,3897],{},[1864,56906,5714],{},[1723,56908,1725],{},[1864,56910,1866],{},[3018,56912,3707],{},[1864,56914,31436],{},[902,56916,56917],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,56919,56920],{},[614,56921,56922,56923,56957,56958,1682,56971,56984,56985,3350,57003,1664],{},"Obrázek 3.1: Parabola ",[883,56924,56926],{"className":56925},[886],[888,56927,56928],{"xmlns":890},[892,56929,56930,56954],{},[895,56931,56932,56934,56936,56938,56940,56942,56948,56950,56952],{},[898,56933,1754],{},[898,56935,1749],{},[1723,56937,1725],{},[1723,56939,1759],{},[1864,56941,2331],{},[2057,56943,56944,56946],{},[898,56945,1904],{},[1864,56947,2331],{},[1723,56949,2087],{},[1864,56951,3810],{},[898,56953,1904],{},[902,56955,56956],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,56959,56961],{"className":56960},[886],[888,56962,56963],{"xmlns":890},[892,56964,56965,56969],{},[895,56966,56967],{},[1864,56968,2256],{},[902,56970,2256],{"encoding":904},[883,56972,56974],{"className":56973},[886],[888,56975,56976],{"xmlns":890},[892,56977,56978,56982],{},[895,56979,56980],{},[1864,56981,3840],{},[902,56983,3840],{"encoding":904}," a maximem ",[883,56986,56988],{"className":56987},[886],[888,56989,56990],{"xmlns":890},[892,56991,56992,57000],{},[895,56993,56994,56996,56998],{},[1864,56995,1866],{},[3018,56997,3707],{},[1864,56999,31436],{},[902,57001,57002],{"encoding":904},"1\\,250",[883,57004,57006],{"className":57005},[886],[888,57007,57008],{"xmlns":890},[892,57009,57010,57018],{},[895,57011,57012,57014,57016],{},[898,57013,1904],{},[1723,57015,1725],{},[1864,57017,5714],{},[902,57019,56865],{"encoding":904},[198,57021,57023],{"id":57022},"průměrný-příjem","Průměrný příjem",[724,57025,57026,2628,57028,1981,57043,57046],{},[38,57027,57023],{},[883,57029,57031],{"className":57030},[886],[888,57032,57033],{"xmlns":890},[892,57034,57035,57041],{},[895,57036,57037,57039],{},[898,57038,1718],{},[898,57040,1749],{},[902,57042,56132],{"encoding":904},[38,57044,57045],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,57048,57050],{"className":57049},[886],[888,57051,57052],{"xmlns":890,"display":28759},[892,57053,57054,57122],{},[895,57055,57056,57058,57060,57062,57064,57066,57068,57070,57072,57074,57090,57092,57110,57112,57114,57116,57118,57120],{},[898,57057,1718],{},[898,57059,1749],{},[1723,57061,1725],{},[898,57063,1718],{},[898,57065,1749],{},[1723,57067,1908],{"stretchy":1907},[898,57069,1904],{},[1723,57071,1914],{"stretchy":1907},[1723,57073,1725],{},[3058,57075,57076,57088],{},[895,57077,57078,57080,57082,57084,57086],{},[898,57079,1754],{},[898,57081,1749],{},[1723,57083,1908],{"stretchy":1907},[898,57085,1904],{},[1723,57087,1914],{"stretchy":1907},[898,57089,1904],{},[1723,57091,1725],{},[3058,57093,57094,57108],{},[895,57095,57096,57098,57100,57102,57104,57106],{},[898,57097,1904],{},[3018,57099,3707],{},[898,57101,4897],{},[1723,57103,1908],{"stretchy":1907},[898,57105,1904],{},[1723,57107,1914],{"stretchy":1907},[898,57109,1904],{},[1723,57111,1725],{},[898,57113,4897],{},[1723,57115,1908],{"stretchy":1907},[898,57117,1904],{},[1723,57119,1914],{"stretchy":1907},[898,57121,1664],{"mathvariant":2124},[902,57123,57124],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[4584,57126,57127],{},[724,57128,57129,57132,57133,1343,57136,1664],{},[883,57130,57131],{},"!note"," Klíčové pozorování\n",[38,57134,57135],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,57137,57139],{"className":57138},[886],[888,57140,57141],{"xmlns":890},[892,57142,57143,57165],{},[895,57144,57145,57147,57149,57151,57153,57155,57157,57159,57161,57163],{},[898,57146,1718],{},[898,57148,1749],{},[1723,57150,1908],{"stretchy":1907},[898,57152,1904],{},[1723,57154,1914],{"stretchy":1907},[1723,57156,1725],{},[898,57158,4897],{},[1723,57160,1908],{"stretchy":1907},[898,57162,1904],{},[1723,57164,1914],{"stretchy":1907},[902,57166,57167],{"encoding":904},"AR(Q) = D(Q)",[198,57169,57171],{"id":57170},"mezní-příjem","Mezní příjem",[724,57173,57174,57175,2628,57178,1981,57193,57196,57197,57200],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,57176,57177],{},"mezní příjem",[883,57179,57181],{"className":57180},[886],[888,57182,57183],{"xmlns":890},[892,57184,57185,57191],{},[895,57186,57187,57189],{},[898,57188,1728],{},[898,57190,1749],{},[902,57192,7344],{"encoding":904},[38,57194,57195],{},"marginal revenue","), definovaný jako ",[207,57198,1145],{"className":57199,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,57202,57204],{"className":57203},[886],[888,57205,57206],{"xmlns":890,"display":28759},[892,57207,57208,57265],{},[21447,57209,57210],{"width":28764},[21452,57211,57212,57214,57258,57260],{},[21455,57213],{"width":28769},[21455,57215,57216],{},[895,57217,57218,57220,57222,57224,57240,57242,57244,57250,57252,57254,57256],{},[898,57219,1728],{},[898,57221,1749],{},[1723,57223,1725],{},[3058,57225,57226,57234],{},[895,57227,57228,57230,57232],{},[898,57229,2930],{"mathvariant":2124},[898,57231,1754],{},[898,57233,1749],{},[895,57235,57236,57238],{},[898,57237,2930],{"mathvariant":2124},[898,57239,1904],{},[1723,57241,1725],{},[898,57243,1754],{},[2057,57245,57246,57248],{},[898,57247,1749],{},[1723,57249,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,57251,1908],{"stretchy":1907},[898,57253,1904],{},[1723,57255,1914],{"stretchy":1907},[898,57257,1664],{"mathvariant":2124},[21455,57259],{"width":28769},[21455,57261,57262],{},[3018,57263,57264],{},"(3.2)",[902,57266,57267],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,57269,57270,57271,57273],{},"Mezní příjem udává ",[38,57272,3322],{}," celkového příjmu vzhledem k množství.",[4584,57275,57276],{},[724,57277,57278,57280,57281,57307,57308,57325,57326,1664],{},[883,57279,4869],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,57282,57284],{"className":57283},[886],[888,57285,57286],{"xmlns":890},[892,57287,57288,57304],{},[895,57289,57290,57292,57294,57296,57302],{},[898,57291,1728],{},[898,57293,1749],{},[1723,57295,1908],{"stretchy":1907},[2057,57297,57298,57300],{},[898,57299,1904],{},[1723,57301,5066],{},[1723,57303,1914],{"stretchy":1907},[902,57305,57306],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,57309,57311],{"className":57310},[886],[888,57312,57313],{"xmlns":890},[892,57314,57315,57323],{},[895,57316,57317],{},[2057,57318,57319,57321],{},[898,57320,1904],{},[1723,57322,5066],{},[902,57324,30537],{"encoding":904},". Jinak řečeno: ",[883,57327,57329],{"className":57328},[886],[888,57330,57331],{"xmlns":890},[892,57332,57333,57385],{},[895,57334,57335,57337,57339,57341,57347,57349,57351,57353,57355,57357,57363,57365,57367,57369,57371,57373,57375,57377,57383],{},[898,57336,1728],{},[898,57338,1749],{},[1723,57340,1908],{"stretchy":1907},[2057,57342,57343,57345],{},[898,57344,1904],{},[1723,57346,5066],{},[1723,57348,1914],{"stretchy":1907},[1723,57350,3456],{},[898,57352,1754],{},[898,57354,1749],{},[1723,57356,1908],{"stretchy":1907},[2057,57358,57359,57361],{},[898,57360,1904],{},[1723,57362,5066],{},[1723,57364,2087],{},[1864,57366,1866],{},[1723,57368,1914],{"stretchy":1907},[1723,57370,1759],{},[898,57372,1754],{},[898,57374,1749],{},[1723,57376,1908],{"stretchy":1907},[2057,57378,57379,57381],{},[898,57380,1904],{},[1723,57382,5066],{},[1723,57384,1914],{"stretchy":1907},[902,57386,57387],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[38040,57389,57391],{"id":57390},"příklad-32","Příklad 3.2",[724,57393,57394,56675,57396,56712,57430,57445,57446,1664],{},[38,57395,56674],{},[883,57397,57399],{"className":57398},[886],[888,57400,57401],{"xmlns":890},[892,57402,57403,57427],{},[895,57404,57405,57407,57409,57411,57413,57415,57417,57419,57421,57423,57425],{},[898,57406,1746],{},[1723,57408,1725],{},[898,57410,4897],{},[1723,57412,1908],{"stretchy":1907},[898,57414,1904],{},[1723,57416,1914],{"stretchy":1907},[1723,57418,1725],{},[1864,57420,3810],{},[1723,57422,1759],{},[1864,57424,2331],{},[898,57426,1904],{},[902,57428,57429],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,57431,57433],{"className":57432},[886],[888,57434,57435],{"xmlns":890},[892,57436,57437,57443],{},[895,57438,57439,57441],{},[898,57440,1728],{},[898,57442,1749],{},[902,57444,7344],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,57447,57449],{"className":57448},[886],[888,57450,57451],{"xmlns":890},[892,57452,57453,57469],{},[895,57454,57455,57457,57459,57461,57463,57465,57467],{},[898,57456,1904],{},[1723,57458,1725],{},[1864,57460,36937],{},[1723,57462,2031],{"separator":2030},[1864,57464,42554],{},[1723,57466,2031],{"separator":2030},[1864,57468,9744],{},[902,57470,57471],{"encoding":904},"Q = 15, 16, 20",[724,57473,57474,2628,57476,57508],{},[38,57475,23463],{},[883,57477,57479],{"className":57478},[886],[888,57480,57481],{"xmlns":890},[892,57482,57483,57505],{},[895,57484,57485,57487,57489,57491,57493,57495,57497,57499],{},[898,57486,1754],{},[898,57488,1749],{},[1723,57490,1725],{},[1864,57492,3810],{},[898,57494,1904],{},[1723,57496,1759],{},[1864,57498,2331],{},[2057,57500,57501,57503],{},[898,57502,1904],{},[1864,57504,2331],{},[902,57506,57507],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,57510,57512],{"className":57511},[886],[888,57513,57514],{"xmlns":890,"display":28759},[892,57515,57516,57558],{},[895,57517,57518,57520,57522,57524,57526,57528,57530,57532,57534,57540,57546,57548,57550,57552,57554,57556],{},[898,57519,1728],{},[898,57521,1749],{},[1723,57523,1725],{},[1723,57525,1908],{"stretchy":1907},[1864,57527,3810],{},[898,57529,1904],{},[1723,57531,1759],{},[1864,57533,2331],{},[2057,57535,57536,57538],{},[898,57537,1904],{},[1864,57539,2331],{},[2057,57541,57542,57544],{},[1723,57543,1914],{"stretchy":1907},[1723,57545,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,57547,1725],{},[1864,57549,3810],{},[1723,57551,1759],{},[1864,57553,3080],{},[898,57555,1904],{},[898,57557,1664],{"mathvariant":2124},[902,57559,57560],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,57562,10369,57563,8812,57581,57607,57608,5070,57621,57636,57637,57650,57651,22113,57664,5070,57677,57692,57693,57706,57707,57738,57739,57758],{},[883,57564,57566],{"className":57565},[886],[888,57567,57568],{"xmlns":890},[892,57569,57570,57578],{},[895,57571,57572,57574,57576],{},[898,57573,1904],{},[1723,57575,1725],{},[1864,57577,36937],{},[902,57579,57580],{"encoding":904},"Q = 15",[883,57582,57584],{"className":57583},[886],[888,57585,57586],{"xmlns":890},[892,57587,57588,57604],{},[895,57589,57590,57592,57594,57596,57598,57600,57602],{},[898,57591,1728],{},[898,57593,1749],{},[1723,57595,1908],{"stretchy":1907},[1864,57597,36937],{},[1723,57599,1914],{"stretchy":1907},[1723,57601,1725],{},[1864,57603,5921],{},[902,57605,57606],{"encoding":904},"MR(15) = 40",": při množství ",[883,57609,57611],{"className":57610},[886],[888,57612,57613],{"xmlns":890},[892,57614,57615,57619],{},[895,57616,57617],{},[1864,57618,36937],{},[902,57620,36937],{"encoding":904},[883,57622,57624],{"className":57623},[886],[888,57625,57626],{"xmlns":890},[892,57627,57628,57634],{},[895,57629,57630,57632],{},[898,57631,1754],{},[898,57633,1749],{},[902,57635,4808],{"encoding":904}," mění asi ",[883,57638,57640],{"className":57639},[886],[888,57641,57642],{"xmlns":890},[892,57643,57644,57648],{},[895,57645,57646],{},[1864,57647,5921],{},[902,57649,5921],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,57652,57654],{"className":57653},[886],[888,57655,57656],{"xmlns":890},[892,57657,57658,57662],{},[895,57659,57660],{},[898,57661,1904],{},[902,57663,1904],{"encoding":904},[883,57665,57667],{"className":57666},[886],[888,57668,57669],{"xmlns":890},[892,57670,57671,57675],{},[895,57672,57673],{},[1864,57674,1866],{},[902,57676,1866],{"encoding":904},[883,57678,57680],{"className":57679},[886],[888,57681,57682],{"xmlns":890},[892,57683,57684,57690],{},[895,57685,57686,57688],{},[898,57687,1754],{},[898,57689,1749],{},[902,57691,4808],{"encoding":904}," zvýší přibližně o ",[883,57694,57696],{"className":57695},[886],[888,57697,57698],{"xmlns":890},[892,57699,57700,57704],{},[895,57701,57702],{},[1864,57703,5921],{},[902,57705,5921],{"encoding":904},", tj. ze skutečné hodnoty ",[883,57708,57710],{"className":57709},[886],[888,57711,57712],{"xmlns":890},[892,57713,57714,57735],{},[895,57715,57716,57718,57720,57722,57724,57726,57728,57730,57732],{},[898,57717,1754],{},[898,57719,1749],{},[1723,57721,1908],{"stretchy":1907},[1864,57723,36937],{},[1723,57725,1914],{"stretchy":1907},[1723,57727,1725],{},[1864,57729,1866],{},[3018,57731,3707],{},[1864,57733,57734],{},"050",[902,57736,57737],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,57740,57742],{"className":57741},[886],[888,57743,57744],{"xmlns":890},[892,57745,57746,57755],{},[895,57747,57748,57750,57752],{},[1864,57749,1866],{},[3018,57751,3707],{},[1864,57753,57754],{},"090",[902,57756,57757],{"encoding":904},"1\\,090",". Skutečná změna je",[883,57760,57762],{"className":57761},[886],[888,57763,57764],{"xmlns":890,"display":28759},[892,57765,57766,57820],{},[895,57767,57768,57770,57772,57774,57776,57778,57780,57782,57784,57786,57788,57790,57792,57794,57796,57798,57800,57802,57804,57807,57809,57811,57813,57815,57817],{},[898,57769,3611],{"mathvariant":2124},[898,57771,1754],{},[898,57773,1749],{},[1723,57775,1725],{},[898,57777,1754],{},[898,57779,1749],{},[1723,57781,1908],{"stretchy":1907},[1864,57783,42554],{},[1723,57785,1914],{"stretchy":1907},[1723,57787,1759],{},[898,57789,1754],{},[898,57791,1749],{},[1723,57793,1908],{"stretchy":1907},[1864,57795,36937],{},[1723,57797,1914],{"stretchy":1907},[1723,57799,1725],{},[1864,57801,1866],{},[3018,57803,3707],{},[1864,57805,57806],{},"088",[1723,57808,1759],{},[1864,57810,1866],{},[3018,57812,3707],{},[1864,57814,57734],{},[1723,57816,1725],{},[1864,57818,57819],{},"38.",[902,57821,57822],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,57824,57825,57826,1343,57852,2137,57878,57893,57894,57909],{},"Podobně ",[883,57827,57829],{"className":57828},[886],[888,57830,57831],{"xmlns":890},[892,57832,57833,57849],{},[895,57834,57835,57837,57839,57841,57843,57845,57847],{},[898,57836,1728],{},[898,57838,1749],{},[1723,57840,1908],{"stretchy":1907},[1864,57842,42554],{},[1723,57844,1914],{"stretchy":1907},[1723,57846,1725],{},[1864,57848,6275],{},[902,57850,57851],{"encoding":904},"MR(16) = 36",[883,57853,57855],{"className":57854},[886],[888,57856,57857],{"xmlns":890},[892,57858,57859,57875],{},[895,57860,57861,57863,57865,57867,57869,57871,57873],{},[898,57862,1728],{},[898,57864,1749],{},[1723,57866,1908],{"stretchy":1907},[1864,57868,9744],{},[1723,57870,1914],{"stretchy":1907},[1723,57872,1725],{},[1864,57874,9744],{},[902,57876,57877],{"encoding":904},"MR(20) = 20",[883,57879,57881],{"className":57880},[886],[888,57882,57883],{"xmlns":890},[892,57884,57885,57891],{},[895,57886,57887,57889],{},[898,57888,1728],{},[898,57890,1749],{},[902,57892,7344],{"encoding":904}," je klesající funkce — rychlost změny ",[883,57895,57897],{"className":57896},[886],[888,57898,57899],{"xmlns":890},[892,57900,57901,57907],{},[895,57902,57903,57905],{},[898,57904,1754],{},[898,57906,1749],{},[902,57908,4808],{"encoding":904}," s růstem množství klesá.",[198,57911,57913],{"id":57912},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,57915,57916],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,57918,57920],{"className":57919},[886],[888,57921,57922],{"xmlns":890,"display":28759},[892,57923,57924,57993],{},[21447,57925,57926],{"width":28764},[21452,57927,57928,57930,57986,57988],{},[21455,57929],{"width":28769},[21455,57931,57932],{},[895,57933,57934,57936,57938,57940,57942,57944,57946,57948,57950,57952,57954,57956,57958,57960,57966,57968,57970,57972,57974,57976,57978,57980,57982,57984],{},[898,57935,3611],{"mathvariant":2124},[898,57937,1754],{},[898,57939,1749],{},[3018,57941,4699],{},[1723,57943,3456],{},[3018,57945,4699],{},[898,57947,2930],{"mathvariant":2124},[898,57949,1754],{},[898,57951,1749],{},[1723,57953,1725],{},[1723,57955,1908],{"stretchy":1907},[898,57957,1754],{},[898,57959,1749],{},[2057,57961,57962,57964],{},[1723,57963,1914],{"stretchy":1907},[1723,57965,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[3018,57967,3707],{},[898,57969,2930],{"mathvariant":2124},[898,57971,1904],{},[1723,57973,1725],{},[898,57975,1728],{},[898,57977,1749],{},[3018,57979,3707],{},[898,57981,2930],{"mathvariant":2124},[898,57983,1904],{},[1723,57985,2031],{"separator":2030},[21455,57987],{"width":28769},[21455,57989,57990],{},[3018,57991,57992],{},"(3.3)",[902,57994,57995],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,57997,57998],{},"schematicky:",[883,58000,58002],{"className":58001},[886],[888,58003,58004],{"xmlns":890,"display":28759},[892,58005,58006,58114],{},[895,58007,58008,58046,58048,58050,58052,58081,58084,58112],{},[895,58009,58010,58013,58019,58022,58028,58031,58037,58043],{},[3018,58011,58012],{},"zm",[9096,58014,58015,58017],{"accent":2030},[3018,58016,46423],{},[1723,58018,25751],{},[3018,58020,58021],{},"na celkov",[9096,58023,58024,58026],{"accent":2030},[3018,58025,46423],{},[1723,58027,25670],{},[3018,58029,58030],{},"ho p",[9096,58032,58033,58035],{"accent":2030},[3018,58034,12742],{},[1723,58036,25751],{},[9096,58038,58039,58041],{"accent":2030},[3018,58040,25739],{},[1723,58042,25670],{},[3018,58044,58045],{},"jmu",[3018,58047,4699],{},[1723,58049,3456],{},[3018,58051,4699],{},[895,58053,58054,58057,58063,58066,58072,58078],{},[3018,58055,58056],{},"mezn",[9096,58058,58059,58061],{"accent":2030},[3018,58060,25739],{},[1723,58062,25670],{},[3018,58064,58065],{}," p",[9096,58067,58068,58070],{"accent":2030},[3018,58069,12742],{},[1723,58071,25751],{},[9096,58073,58074,58076],{"accent":2030},[3018,58075,25739],{},[1723,58077,25670],{},[3018,58079,58080],{},"jem",[1723,58082,58083],{},"×",[895,58085,58086,58088,58094,58097,58103,58106],{},[3018,58087,58012],{},[9096,58089,58090,58092],{"accent":2030},[3018,58091,46423],{},[1723,58093,25751],{},[3018,58095,58096],{},"na mno",[9096,58098,58099,58101],{"accent":2030},[3018,58100,10301],{},[1723,58102,25751],{},[3018,58104,58105],{},"stv",[9096,58107,58108,58110],{"accent":2030},[3018,58109,25739],{},[1723,58111,25670],{},[898,58113,1664],{"mathvariant":2124},[902,58115,58116],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,58118,58119,58120,58135],{},"Pro porovnání skutečná změna ",[883,58121,58123],{"className":58122},[886],[888,58124,58125],{"xmlns":890},[892,58126,58127,58133],{},[895,58128,58129,58131],{},[898,58130,1754],{},[898,58132,1749],{},[902,58134,4808],{"encoding":904}," je",[883,58137,58139],{"className":58138},[886],[888,58140,58141],{"xmlns":890,"display":28759},[892,58142,58143,58198],{},[21447,58144,58145],{"width":28764},[21452,58146,58147,58149,58191,58193],{},[21455,58148],{"width":28769},[21455,58150,58151],{},[895,58152,58153,58155,58157,58159,58161,58163,58165,58167,58169,58171,58173,58175,58177,58179,58181,58183,58185,58187,58189],{},[898,58154,3611],{"mathvariant":2124},[898,58156,1754],{},[898,58158,1749],{},[1723,58160,1725],{},[898,58162,1754],{},[898,58164,1749],{},[1723,58166,1908],{"stretchy":1907},[898,58168,1904],{},[1723,58170,2087],{},[898,58172,2930],{"mathvariant":2124},[898,58174,1904],{},[1723,58176,1914],{"stretchy":1907},[1723,58178,1759],{},[898,58180,1754],{},[898,58182,1749],{},[1723,58184,1908],{"stretchy":1907},[898,58186,1904],{},[1723,58188,1914],{"stretchy":1907},[898,58190,1664],{"mathvariant":2124},[21455,58192],{"width":28769},[21455,58194,58195],{},[3018,58196,58197],{},"(3.4)",[902,58199,58200],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[38040,58202,58204],{"id":58203},"příklad-33","Příklad 3.3",[724,58206,58207,58209,58210,58240,58241,3383,58256,3397,58269,3411,58282,58296],{},[38,58208,56674],{}," Pro ",[883,58211,58213],{"className":58212},[886],[888,58214,58215],{"xmlns":890},[892,58216,58217,58237],{},[895,58218,58219,58221,58223,58225,58227,58229,58231],{},[898,58220,1754],{},[898,58222,1749],{},[1723,58224,1725],{},[1864,58226,3810],{},[898,58228,1904],{},[1723,58230,1759],{},[2057,58232,58233,58235],{},[898,58234,1904],{},[1864,58236,2331],{},[902,58238,58239],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,58242,58244],{"className":58243},[886],[888,58245,58246],{"xmlns":890},[892,58247,58248,58254],{},[895,58249,58250,58252],{},[898,58251,1754],{},[898,58253,1749],{},[902,58255,4808],{"encoding":904},[883,58257,58259],{"className":58258},[886],[888,58260,58261],{"xmlns":890},[892,58262,58263,58267],{},[895,58264,58265],{},[898,58266,1904],{},[902,58268,1904],{"encoding":904},[883,58270,58272],{"className":58271},[886],[888,58273,58274],{"xmlns":890},[892,58275,58276,58280],{},[895,58277,58278],{},[1864,58279,3846],{},[902,58281,3846],{"encoding":904},[883,58283,58285],{"className":58284},[886],[888,58286,58287],{"xmlns":890},[892,58288,58289,58294],{},[895,58290,58291],{},[1864,58292,58293],{},"63",[902,58295,58293],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,58298,58299,2628,58301,58326,58327,1343,58345,3430],{},[38,58300,23463],{},[883,58302,58304],{"className":58303},[886],[888,58305,58306],{"xmlns":890},[892,58307,58308,58324],{},[895,58309,58310,58312,58314,58316,58318,58320,58322],{},[898,58311,1728],{},[898,58313,1749],{},[1723,58315,1725],{},[1864,58317,3810],{},[1723,58319,1759],{},[1864,58321,2331],{},[898,58323,1904],{},[902,58325,12137],{"encoding":904},", tedy při ",[883,58328,58330],{"className":58329},[886],[888,58331,58332],{"xmlns":890},[892,58333,58334,58342],{},[895,58335,58336,58338,58340],{},[898,58337,1904],{},[1723,58339,1725],{},[1864,58341,3846],{},[902,58343,58344],{"encoding":904},"Q = 60",[883,58346,58348],{"className":58347},[886],[888,58349,58350],{"xmlns":890},[892,58351,58352,58362],{},[895,58353,58354,58356,58358,58360],{},[898,58355,2930],{"mathvariant":2124},[898,58357,1904],{},[1723,58359,1725],{},[1864,58361,2909],{},[902,58363,58364],{"encoding":904},"\\mathrm{d}Q = 3",[883,58366,58368],{"className":58367},[886],[888,58369,58370],{"xmlns":890,"display":28759},[892,58371,58372,58403],{},[895,58373,58374,58376,58378,58380,58382,58384,58386,58388,58390,58392,58394,58396,58398,58400],{},[898,58375,2930],{"mathvariant":2124},[898,58377,1754],{},[898,58379,1749],{},[1723,58381,1725],{},[1723,58383,1908],{"stretchy":1907},[1864,58385,3810],{},[1723,58387,1759],{},[1864,58389,4760],{},[1723,58391,1914],{"stretchy":1907},[1723,58393,3897],{},[1864,58395,2909],{},[1723,58397,1725],{},[1723,58399,1759],{},[1864,58401,58402],{},"60.",[902,58404,58405],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,58407,58408,58409,58439,58440,58459],{},"Celkový příjem klesne z ",[883,58410,58412],{"className":58411},[886],[888,58413,58414],{"xmlns":890},[892,58415,58416,58436],{},[895,58417,58418,58420,58422,58424,58426,58428,58430,58432,58434],{},[898,58419,1754],{},[898,58421,1749],{},[1723,58423,1908],{"stretchy":1907},[1864,58425,3846],{},[1723,58427,1914],{"stretchy":1907},[1723,58429,1725],{},[1864,58431,2331],{},[3018,58433,3707],{},[1864,58435,20835],{},[902,58437,58438],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,58441,58443],{"className":58442},[886],[888,58444,58445],{"xmlns":890},[892,58446,58447,58456],{},[895,58448,58449,58451,58453],{},[1864,58450,2331],{},[3018,58452,3707],{},[1864,58454,58455],{},"340",[902,58457,58458],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,58461,58463],{"className":58462},[886],[888,58464,58465],{"xmlns":890,"display":28759},[892,58466,58467,58525],{},[895,58468,58469,58471,58473,58475,58477,58479,58481,58483,58485,58487,58489,58491,58493,58495,58497,58499,58501,58503,58505,58508,58510,58512,58514,58516,58518,58520,58523],{},[898,58470,3611],{"mathvariant":2124},[898,58472,1754],{},[898,58474,1749],{},[1723,58476,1725],{},[898,58478,1754],{},[898,58480,1749],{},[1723,58482,1908],{"stretchy":1907},[1864,58484,58293],{},[1723,58486,1914],{"stretchy":1907},[1723,58488,1759],{},[898,58490,1754],{},[898,58492,1749],{},[1723,58494,1908],{"stretchy":1907},[1864,58496,3846],{},[1723,58498,1914],{"stretchy":1907},[1723,58500,1725],{},[1864,58502,2331],{},[3018,58504,3707],{},[1864,58506,58507],{},"331",[1723,58509,1759],{},[1864,58511,2331],{},[3018,58513,3707],{},[1864,58515,20835],{},[1723,58517,1725],{},[1723,58519,1759],{},[1864,58521,58522],{},"69",[1723,58524,2031],{"separator":2030},[902,58526,58527],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,58529,58530,58531,58546,58547,1664],{},"tj. ",[883,58532,58534],{"className":58533},[886],[888,58535,58536],{"xmlns":890},[892,58537,58538,58544],{},[895,58539,58540,58542],{},[898,58541,1754],{},[898,58543,1749],{},[902,58545,4808],{"encoding":904}," klesne na ",[883,58548,58550],{"className":58549},[886],[888,58551,58552],{"xmlns":890},[892,58553,58554,58562],{},[895,58555,58556,58558,58560],{},[1864,58557,2331],{},[3018,58559,3707],{},[1864,58561,58507],{},[902,58563,58564],{"encoding":904},"2\\,331",[198,58566,58568],{"id":58567},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,58570,58571,58572,11094,58595,32273],{},"Obecně pro lineární poptávku ",[883,58573,58575],{"className":58574},[886],[888,58576,58577],{"xmlns":890},[892,58578,58579,58593],{},[895,58580,58581,58583,58585,58587,58589,58591],{},[898,58582,1746],{},[1723,58584,1725],{},[898,58586,207],{},[898,58588,1904],{},[1723,58590,2087],{},[898,58592,2069],{},[902,58594,37752],{"encoding":904},[883,58596,58598],{"className":58597},[886],[888,58599,58600],{"xmlns":890},[892,58601,58602,58624],{},[895,58603,58604,58606,58608,58610,58612,58618,58620,58622],{},[898,58605,1754],{},[898,58607,1749],{},[1723,58609,1725],{},[898,58611,207],{},[2057,58613,58614,58616],{},[898,58615,1904],{},[1864,58617,2331],{},[1723,58619,2087],{},[898,58621,2069],{},[898,58623,1904],{},[902,58625,58626],{"encoding":904},"TR = aQ^2 + bQ",[883,58628,58630],{"className":58629},[886],[888,58631,58632],{"xmlns":890,"display":28759},[892,58633,58634,58654],{},[895,58635,58636,58638,58640,58642,58644,58646,58648,58650,58652],{},[898,58637,1728],{},[898,58639,1749],{},[1723,58641,1725],{},[1864,58643,2331],{},[898,58645,207],{},[898,58647,1904],{},[1723,58649,2087],{},[898,58651,2069],{},[898,58653,1664],{"mathvariant":2124},[902,58655,58656],{"encoding":904},"MR = 2aQ + b.",[724,58658,58659,58660,58675,58676,58691,58692,58705,58706,1981,58709,58725,58726,58739,58740,58755,58756,58771,58772,58787,58788,3350,58801,58831,58832,58851,58852,58867],{},"Křivky ",[883,58661,58663],{"className":58662},[886],[888,58664,58665],{"xmlns":890},[892,58666,58667,58673],{},[895,58668,58669,58671],{},[898,58670,1728],{},[898,58672,1749],{},[902,58674,7344],{"encoding":904}," a poptávky (resp. ",[883,58677,58679],{"className":58678},[886],[888,58680,58681],{"xmlns":890},[892,58682,58683,58689],{},[895,58684,58685,58687],{},[898,58686,1718],{},[898,58688,1749],{},[902,58690,56132],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,58693,58695],{"className":58694},[886],[888,58696,58697],{"xmlns":890},[892,58698,58699,58703],{},[895,58700,58701],{},[898,58702,2069],{},[902,58704,2069],{"encoding":904},", přičemž ",[38,58707,58708],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,58710,58712],{"className":58711},[886],[888,58713,58714],{"xmlns":890},[892,58715,58716,58722],{},[895,58717,58718,58720],{},[1864,58719,2331],{},[898,58721,207],{},[902,58723,58724],{"encoding":904},"2a"," vs. ",[883,58727,58729],{"className":58728},[886],[888,58730,58731],{"xmlns":890},[892,58732,58733,58737],{},[895,58734,58735],{},[898,58736,207],{},[902,58738,207],{"encoding":904},", obrázek 3.2). ",[883,58741,58743],{"className":58742},[886],[888,58744,58745],{"xmlns":890},[892,58746,58747,58753],{},[895,58748,58749,58751],{},[898,58750,1728],{},[898,58752,1749],{},[902,58754,7344],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,58757,58759],{"className":58758},[886],[888,58760,58761],{"xmlns":890},[892,58762,58763,58769],{},[895,58764,58765,58767],{},[898,58766,1754],{},[898,58768,1749],{},[902,58770,4808],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,58773,58775],{"className":58774},[886],[888,58776,58777],{"xmlns":890},[892,58778,58779,58785],{},[895,58780,58781,58783],{},[898,58782,1728],{},[898,58784,1749],{},[902,58786,7344],{"encoding":904}," osu ",[883,58789,58791],{"className":58790},[886],[888,58792,58793],{"xmlns":890},[892,58794,58795,58799],{},[895,58796,58797],{},[898,58798,1904],{},[902,58800,1904],{"encoding":904},[883,58802,58804],{"className":58803},[886],[888,58805,58806],{"xmlns":890},[892,58807,58808,58828],{},[895,58809,58810,58812,58814,58816],{},[898,58811,1904],{},[1723,58813,1725],{},[1723,58815,1759],{},[3055,58817,58818],{"scriptlevel":2256,"displaystyle":1907},[3058,58819,58820,58822],{},[898,58821,2069],{},[895,58823,58824,58826],{},[1864,58825,2331],{},[898,58827,207],{},[902,58829,58830],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,58833,58835],{"className":58834},[886],[888,58836,58837],{"xmlns":890},[892,58838,58839,58849],{},[895,58840,58841,58843,58845,58847],{},[898,58842,1728],{},[898,58844,1749],{},[1723,58846,1725],{},[1864,58848,2256],{},[902,58850,7794],{"encoding":904},", a dále ",[883,58853,58855],{"className":58854},[886],[888,58856,58857],{"xmlns":890},[892,58858,58859,58865],{},[895,58860,58861,58863],{},[898,58862,1754],{},[898,58864,1749],{},[902,58866,4808],{"encoding":904}," klesá.",[724,58869,58870,58871,58877,58878,58910,58911,58939],{},"V případě ",[38,58872,58873],{},[207,58874,58876],{"className":58875,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,58879,58881],{"className":58880},[886],[888,58882,58883],{"xmlns":890},[892,58884,58885,58907],{},[895,58886,58887,58889,58891,58893,58895,58897,58899,58901],{},[898,58888,1746],{},[1723,58890,1725],{},[898,58892,4897],{},[1723,58894,1908],{"stretchy":1907},[898,58896,1904],{},[1723,58898,1914],{"stretchy":1907},[1723,58900,1725],{},[2057,58902,58903,58905],{},[898,58904,1746],{},[1723,58906,5066],{},[902,58908,58909],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,58912,58914],{"className":58913},[886],[888,58915,58916],{"xmlns":890},[892,58917,58918,58936],{},[895,58919,58920,58922,58924,58926,58928,58930],{},[898,58921,1754],{},[898,58923,1749],{},[1723,58925,1725],{},[898,58927,1904],{},[1723,58929,3897],{},[2057,58931,58932,58934],{},[898,58933,1746],{},[1723,58935,5066],{},[902,58937,58938],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,58941,58943],{"className":58942},[886],[888,58944,58945],{"xmlns":890,"display":28759},[892,58946,58947,58989],{},[895,58948,58949,58951,58953,58955,58957,58959,58961,58967,58969,58971,58985,58987],{},[898,58950,1728],{},[898,58952,1749],{},[1723,58954,1725],{},[898,58956,1718],{},[898,58958,1749],{},[1723,58960,1725],{},[2057,58962,58963,58965],{},[898,58964,1746],{},[1723,58966,5066],{},[6588,58968],{"width":15985},[1723,58970,1908],{"stretchy":1907},[895,58972,58973,58976,58982],{},[3018,58974,58975],{},"obr",[9096,58977,58978,58980],{"accent":2030},[3018,58979,207],{},[1723,58981,25670],{},[3018,58983,58984],{},"zek 3.4",[1723,58986,1914],{"stretchy":1907},[898,58988,1664],{"mathvariant":2124},[902,58990,58991],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,58993,58994],{},[614,58995,58996,58997,1682,59023,59051,59052,59065,59066,59081,59082,4436,59095,1343,59121,4436,59136,1664],{},"Obrázek 3.2: Přímky ",[883,58998,59000],{"className":58999},[886],[888,59001,59002],{"xmlns":890},[892,59003,59004,59020],{},[895,59005,59006,59008,59010,59012,59014,59016,59018],{},[898,59007,1718],{},[898,59009,1749],{},[1723,59011,1725],{},[898,59013,207],{},[898,59015,1904],{},[1723,59017,2087],{},[898,59019,2069],{},[902,59021,59022],{"encoding":904},"AR = aQ + b",[883,59024,59026],{"className":59025},[886],[888,59027,59028],{"xmlns":890},[892,59029,59030,59048],{},[895,59031,59032,59034,59036,59038,59040,59042,59044,59046],{},[898,59033,1728],{},[898,59035,1749],{},[1723,59037,1725],{},[1864,59039,2331],{},[898,59041,207],{},[898,59043,1904],{},[1723,59045,2087],{},[898,59047,2069],{},[902,59049,59050],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,59053,59055],{"className":59054},[886],[888,59056,59057],{"xmlns":890},[892,59058,59059,59063],{},[895,59060,59061],{},[898,59062,2069],{},[902,59064,2069],{"encoding":904}," se svislou osou, ",[883,59067,59069],{"className":59068},[886],[888,59070,59071],{"xmlns":890},[892,59072,59073,59079],{},[895,59074,59075,59077],{},[898,59076,1728],{},[898,59078,1749],{},[902,59080,7344],{"encoding":904}," protíná osu ",[883,59083,59085],{"className":59084},[886],[888,59086,59087],{"xmlns":890},[892,59088,59089,59093],{},[895,59090,59091],{},[898,59092,1904],{},[902,59094,1904],{"encoding":904},[883,59096,59098],{"className":59097},[886],[888,59099,59100],{"xmlns":890},[892,59101,59102,59118],{},[895,59103,59104,59106],{},[1723,59105,1759],{},[3055,59107,59108],{"scriptlevel":2256,"displaystyle":1907},[3058,59109,59110,59112],{},[898,59111,2069],{},[895,59113,59114,59116],{},[1864,59115,2331],{},[898,59117,207],{},[902,59119,59120],{"encoding":904},"-\\tfrac{b}{2a}",[883,59122,59124],{"className":59123},[886],[888,59125,59126],{"xmlns":890},[892,59127,59128,59134],{},[895,59129,59130,59132],{},[898,59131,1718],{},[898,59133,1749],{},[902,59135,56132],{"encoding":904},[883,59137,59139],{"className":59138},[886],[888,59140,59141],{"xmlns":890},[892,59142,59143,59155],{},[895,59144,59145,59147],{},[1723,59146,1759],{},[3055,59148,59149],{"scriptlevel":2256,"displaystyle":1907},[3058,59150,59151,59153],{},[898,59152,2069],{},[898,59154,207],{},[902,59156,59157],{"encoding":904},"-\\tfrac{b}{a}",[724,59159,59160],{},[614,59161,59162,59163,59194,59195,59224,59225,1664],{},"Obrázek 3.3: Parabola ",[883,59164,59166],{"className":59165},[886],[888,59167,59168],{"xmlns":890},[892,59169,59170,59192],{},[895,59171,59172,59174,59176,59178,59180,59186,59188,59190],{},[898,59173,1754],{},[898,59175,1749],{},[1723,59177,1725],{},[898,59179,207],{},[2057,59181,59182,59184],{},[898,59183,1904],{},[1864,59185,2331],{},[1723,59187,2087],{},[898,59189,2069],{},[898,59191,1904],{},[902,59193,58626],{"encoding":904}," s maximem v ",[883,59196,59198],{"className":59197},[886],[888,59199,59200],{"xmlns":890},[892,59201,59202,59222],{},[895,59203,59204,59206,59208,59210],{},[898,59205,1904],{},[1723,59207,1725],{},[1723,59209,1759],{},[3055,59211,59212],{"scriptlevel":2256,"displaystyle":1907},[3058,59213,59214,59216],{},[898,59215,2069],{},[895,59217,59218,59220],{},[1864,59219,2331],{},[898,59221,207],{},[902,59223,58830],{"encoding":904}," a nulou v ",[883,59226,59228],{"className":59227},[886],[888,59229,59230],{"xmlns":890},[892,59231,59232,59248],{},[895,59233,59234,59236,59238,59240],{},[898,59235,1904],{},[1723,59237,1725],{},[1723,59239,1759],{},[3055,59241,59242],{"scriptlevel":2256,"displaystyle":1907},[3058,59243,59244,59246],{},[898,59245,2069],{},[898,59247,207],{},[902,59249,59250],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,59252,59253],{},[614,59254,59255,59256,1664],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,59257,59259],{"className":59258},[886],[888,59260,59261],{"xmlns":890},[892,59262,59263,59283],{},[895,59264,59265,59267,59269,59271,59273,59275,59277],{},[898,59266,1718],{},[898,59268,1749],{},[1723,59270,1725],{},[898,59272,1728],{},[898,59274,1749],{},[1723,59276,1725],{},[2057,59278,59279,59281],{},[898,59280,1746],{},[1723,59282,5066],{},[902,59284,59285],{"encoding":904},"AR = MR = P^*",[115,59287,59289],{"id":59288},"náklady-firmy","Náklady firmy",[198,59291,59293],{"id":59292},"celkové-náklady","Celkové náklady",[724,59295,59296,2628,59298,1981,59313,59316,59317,59330],{},[38,59297,59293],{},[883,59299,59301],{"className":59300},[886],[888,59302,59303],{"xmlns":890},[892,59304,59305,59311],{},[895,59306,59307,59309],{},[898,59308,1754],{},[898,59310,1721],{},[902,59312,3963],{"encoding":904},[38,59314,59315],{},"total cost",") jsou veškeré náklady na realizaci ",[883,59318,59320],{"className":59319},[886],[888,59321,59322],{"xmlns":890},[892,59323,59324,59328],{},[895,59325,59326],{},[898,59327,1904],{},[902,59329,1904],{"encoding":904}," jednotek produkce:",[883,59332,59334],{"className":59333},[886],[888,59335,59336],{"xmlns":890,"display":28759},[892,59337,59338,59393],{},[21447,59339,59340],{"width":28764},[21452,59341,59342,59344,59386,59388],{},[21455,59343],{"width":28769},[21455,59345,59346],{},[895,59347,59348,59350,59352,59354,59356,59358,59360,59362,59364,59366,59368,59370,59372,59374,59376,59378,59380,59382,59384],{},[898,59349,1754],{},[898,59351,1721],{},[1723,59353,1725],{},[898,59355,1754],{},[898,59357,1721],{},[1723,59359,1908],{"stretchy":1907},[898,59361,1904],{},[1723,59363,1914],{"stretchy":1907},[1723,59365,1725],{},[898,59367,11136],{},[898,59369,1721],{},[1723,59371,2087],{},[898,59373,1754],{},[898,59375,41031],{},[898,59377,1721],{},[1723,59379,1908],{"stretchy":1907},[898,59381,1904],{},[1723,59383,1914],{"stretchy":1907},[1723,59385,2031],{"separator":2030},[21455,59387],{"width":28769},[21455,59389,59390],{},[3018,59391,59392],{},"(3.5)",[902,59394,59395],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,59397,5022,59398,59413,59414,1981,59417,12829,59420,59413,59444,1981,59447,59450],{},[883,59399,59401],{"className":59400},[886],[888,59402,59403],{"xmlns":890},[892,59404,59405,59411],{},[895,59406,59407,59409],{},[898,59408,11136],{},[898,59410,1721],{},[902,59412,56178],{"encoding":904}," jsou ",[38,59415,59416],{},"fixní náklady",[38,59418,59419],{},"fixed cost",[883,59421,59423],{"className":59422},[886],[888,59424,59425],{"xmlns":890},[892,59426,59427,59441],{},[895,59428,59429,59431,59433,59435,59437,59439],{},[898,59430,1754],{},[898,59432,41031],{},[898,59434,1721],{},[1723,59436,1908],{"stretchy":1907},[898,59438,1904],{},[1723,59440,1914],{"stretchy":1907},[902,59442,59443],{"encoding":904},"TVC(Q)",[38,59445,59446],{},"celkové variabilní náklady",[38,59448,59449],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,59452,59454],{"id":59453},"průměrné-náklady","Průměrné náklady",[724,59456,59457,2628,59459,1981,59474,59477],{},[38,59458,59454],{},[883,59460,59462],{"className":59461},[886],[888,59463,59464],{"xmlns":890},[892,59465,59466,59472],{},[895,59467,59468,59470],{},[898,59469,1718],{},[898,59471,1721],{},[902,59473,56247],{"encoding":904},[38,59475,59476],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,59479,59481],{"className":59480},[886],[888,59482,59483],{"xmlns":890,"display":28759},[892,59484,59485,59564],{},[21447,59486,59487],{"width":28764},[21452,59488,59489,59491,59557,59559],{},[21455,59490],{"width":28769},[21455,59492,59493],{},[895,59494,59495,59497,59499,59501,59503,59505,59507,59509,59511,59513,59523,59525,59535,59537,59555],{},[898,59496,1718],{},[898,59498,1721],{},[1723,59500,1725],{},[898,59502,1718],{},[898,59504,1721],{},[1723,59506,1908],{"stretchy":1907},[898,59508,1904],{},[1723,59510,1914],{"stretchy":1907},[1723,59512,1725],{},[3058,59514,59515,59521],{},[895,59516,59517,59519],{},[898,59518,1754],{},[898,59520,1721],{},[898,59522,1904],{},[1723,59524,1725],{},[3058,59526,59527,59533],{},[895,59528,59529,59531],{},[898,59530,11136],{},[898,59532,1721],{},[898,59534,1904],{},[1723,59536,2087],{},[3058,59538,59539,59553],{},[895,59540,59541,59543,59545,59547,59549,59551],{},[898,59542,1754],{},[898,59544,41031],{},[898,59546,1721],{},[1723,59548,1908],{"stretchy":1907},[898,59550,1904],{},[1723,59552,1914],{"stretchy":1907},[898,59554,1904],{},[1723,59556,2031],{"separator":2030},[21455,59558],{"width":28769},[21455,59560,59561],{},[3018,59562,59563],{},"(3.6)",[902,59565,59566],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,59568,5022,59569,59413,59593,2628,59596,1981,59613,12829,59616,59413,59648,2628,59651,1981,59668,3871],{},[883,59570,59572],{"className":59571},[886],[888,59573,59574],{"xmlns":890},[892,59575,59576,59590],{},[895,59577,59578],{},[3055,59579,59580],{"scriptlevel":2256,"displaystyle":1907},[3058,59581,59582,59588],{},[895,59583,59584,59586],{},[898,59585,11136],{},[898,59587,1721],{},[898,59589,1904],{},[902,59591,59592],{"encoding":904},"\\tfrac{FC}{Q}",[38,59594,59595],{},"průměrné fixní náklady",[883,59597,59599],{"className":59598},[886],[888,59600,59601],{"xmlns":890},[892,59602,59603,59611],{},[895,59604,59605,59607,59609],{},[898,59606,1718],{},[898,59608,11136],{},[898,59610,1721],{},[902,59612,56214],{"encoding":904},[38,59614,59615],{},"average fixed cost",[883,59617,59619],{"className":59618},[886],[888,59620,59621],{"xmlns":890},[892,59622,59623,59645],{},[895,59624,59625],{},[3055,59626,59627],{"scriptlevel":2256,"displaystyle":1907},[3058,59628,59629,59643],{},[895,59630,59631,59633,59635,59637,59639,59641],{},[898,59632,1754],{},[898,59634,41031],{},[898,59636,1721],{},[1723,59638,1908],{"stretchy":1907},[898,59640,1904],{},[1723,59642,1914],{"stretchy":1907},[898,59644,1904],{},[902,59646,59647],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,59649,59650],{},"průměrné variabilní náklady",[883,59652,59654],{"className":59653},[886],[888,59655,59656],{"xmlns":890},[892,59657,59658,59666],{},[895,59659,59660,59662,59664],{},[898,59661,1718],{},[898,59663,41031],{},[898,59665,1721],{},[902,59667,55998],{"encoding":904},[38,59669,59670],{},"average variable cost",[883,59672,59674],{"className":59673},[886],[888,59675,59676],{"xmlns":890,"display":28759},[892,59677,59678,59737],{},[21447,59679,59680],{"width":28764},[21452,59681,59682,59684,59730,59732],{},[21455,59683],{"width":28769},[21455,59685,59686],{},[895,59687,59688,59690,59692,59694,59696,59698,59700,59702,59704,59706,59708,59710,59728],{},[898,59689,1718],{},[898,59691,41031],{},[898,59693,1721],{},[1723,59695,1725],{},[898,59697,1718],{},[898,59699,41031],{},[898,59701,1721],{},[1723,59703,1908],{"stretchy":1907},[898,59705,1904],{},[1723,59707,1914],{"stretchy":1907},[1723,59709,1725],{},[3058,59711,59712,59726],{},[895,59713,59714,59716,59718,59720,59722,59724],{},[898,59715,1754],{},[898,59717,41031],{},[898,59719,1721],{},[1723,59721,1908],{"stretchy":1907},[898,59723,1904],{},[1723,59725,1914],{"stretchy":1907},[898,59727,1904],{},[898,59729,1664],{"mathvariant":2124},[21455,59731],{"width":28769},[21455,59733,59734],{},[3018,59735,59736],{},"(3.7)",[902,59738,59739],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[38040,59741,59743],{"id":59742},"příklad-34","Příklad 3.4",[724,59745,59746,58209,59748,1682,59773,56712,59797,1682,59812,59827,59828,1664],{},[38,59747,56674],{},[883,59749,59751],{"className":59750},[886],[888,59752,59753],{"xmlns":890},[892,59754,59755,59770],{},[895,59756,59757,59759,59761,59763,59765,59767],{},[898,59758,11136],{},[898,59760,1721],{},[1723,59762,1725],{},[1864,59764,1866],{},[3018,59766,3707],{},[1864,59768,59769],{},"000",[902,59771,59772],{"encoding":904},"FC = 1\\,000",[883,59774,59776],{"className":59775},[886],[888,59777,59778],{"xmlns":890},[892,59779,59780,59794],{},[895,59781,59782,59784,59786,59788,59790,59792],{},[898,59783,1754],{},[898,59785,41031],{},[898,59787,1721],{},[1723,59789,1725],{},[1864,59791,3080],{},[898,59793,1904],{},[902,59795,59796],{"encoding":904},"TVC = 4Q",[883,59798,59800],{"className":59799},[886],[888,59801,59802],{"xmlns":890},[892,59803,59804,59810],{},[895,59805,59806,59808],{},[898,59807,1754],{},[898,59809,1721],{},[902,59811,3963],{"encoding":904},[883,59813,59815],{"className":59814},[886],[888,59816,59817],{"xmlns":890},[892,59818,59819,59825],{},[895,59820,59821,59823],{},[898,59822,1718],{},[898,59824,1721],{},[902,59826,56247],{"encoding":904}," a jejich chování s rostoucím ",[883,59829,59831],{"className":59830},[886],[888,59832,59833],{"xmlns":890},[892,59834,59835,59839],{},[895,59836,59837],{},[898,59838,1904],{},[902,59840,1904],{"encoding":904},[724,59842,59843,2628,59845,1682,59875,59911,59912,5070,59925,59940,59941,3430],{},[38,59844,23463],{},[883,59846,59848],{"className":59847},[886],[888,59849,59850],{"xmlns":890},[892,59851,59852,59872],{},[895,59853,59854,59856,59858,59860,59862,59864,59866,59868,59870],{},[898,59855,1754],{},[898,59857,1721],{},[1723,59859,1725],{},[1864,59861,1866],{},[3018,59863,3707],{},[1864,59865,59769],{},[1723,59867,2087],{},[1864,59869,3080],{},[898,59871,1904],{},[902,59873,59874],{"encoding":904},"TC = 1\\,000 + 4Q",[883,59876,59878],{"className":59877},[886],[888,59879,59880],{"xmlns":890},[892,59881,59882,59908],{},[895,59883,59884,59886,59888,59890,59904,59906],{},[898,59885,1718],{},[898,59887,1721],{},[1723,59889,1725],{},[3055,59891,59892],{"scriptlevel":2256,"displaystyle":1907},[3058,59893,59894,59902],{},[895,59895,59896,59898,59900],{},[1864,59897,1866],{},[3018,59899,3707],{},[1864,59901,59769],{},[898,59903,1904],{},[1723,59905,2087],{},[1864,59907,3080],{},[902,59909,59910],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,59913,59915],{"className":59914},[886],[888,59916,59917],{"xmlns":890},[892,59918,59919,59923],{},[895,59920,59921],{},[898,59922,1904],{},[902,59924,1904],{"encoding":904},[883,59926,59928],{"className":59927},[886],[888,59929,59930],{"xmlns":890},[892,59931,59932,59938],{},[895,59933,59934,59936],{},[898,59935,1718],{},[898,59937,1721],{},[902,59939,56247],{"encoding":904}," blíží ",[883,59942,59944],{"className":59943},[886],[888,59945,59946],{"xmlns":890},[892,59947,59948,59952],{},[895,59949,59950],{},[1864,59951,3080],{},[902,59953,3080],{"encoding":904},[883,59955,59957],{"className":59956},[886],[888,59958,59959],{"xmlns":890,"display":28759},[892,59960,59961,60007],{},[895,59962,59963,59980,60002,60004],{},[40588,59964,59965,59972],{},[895,59966,59967,59970],{},[898,59968,59969],{},"lim",[1723,59971,56887],{},[895,59973,59974,59976,59978],{},[898,59975,1904],{},[1723,59977,3843],{},[898,59979,7007],{"mathvariant":2124},[895,59981,59982,59984,59996,59998,60000],{},[1723,59983,1908],{"fence":2030},[3058,59985,59986,59994],{},[895,59987,59988,59990,59992],{},[1864,59989,1866],{},[3018,59991,3707],{},[1864,59993,59769],{},[898,59995,1904],{},[1723,59997,2087],{},[1864,59999,3080],{},[1723,60001,1914],{"fence":2030},[1723,60003,1725],{},[1864,60005,60006],{},"4.",[902,60008,60009],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,60011,60012,60050,60051,1664],{},[883,60013,60015],{"className":60014},[886],[888,60016,60017],{"xmlns":890},[892,60018,60019,60047],{},[895,60020,60021,60023,60025,60027,60029,60043,60045],{},[898,60022,1718],{},[898,60024,11136],{},[898,60026,1721],{},[1723,60028,1725],{},[3055,60030,60031],{"scriptlevel":2256,"displaystyle":1907},[3058,60032,60033,60041],{},[895,60034,60035,60037,60039],{},[1864,60036,1866],{},[3018,60038,3707],{},[1864,60040,59769],{},[898,60042,1904],{},[1723,60044,3843],{},[1864,60046,2256],{},[902,60048,60049],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,60052,60054],{"className":60053},[886],[888,60055,60056],{"xmlns":890},[892,60057,60058,60062],{},[895,60059,60060],{},[898,60061,1904],{},[902,60063,1904],{"encoding":904},[724,60065,60066],{},[614,60067,60068,60069,60098,60099,1664],{},"Obrázek 3.5: Přímka ",[883,60070,60072],{"className":60071},[886],[888,60073,60074],{"xmlns":890},[892,60075,60076,60096],{},[895,60077,60078,60080,60082,60084,60086,60088,60090,60092,60094],{},[898,60079,1754],{},[898,60081,1721],{},[1723,60083,1725],{},[1864,60085,1866],{},[3018,60087,3707],{},[1864,60089,59769],{},[1723,60091,2087],{},[1864,60093,3080],{},[898,60095,1904],{},[902,60097,59874],{"encoding":904}," protínající svislou osu ve výši ",[883,60100,60102],{"className":60101},[886],[888,60103,60104],{"xmlns":890},[892,60105,60106,60120],{},[895,60107,60108,60110,60112,60114,60116,60118],{},[898,60109,11136],{},[898,60111,1721],{},[1723,60113,1725],{},[1864,60115,1866],{},[3018,60117,3707],{},[1864,60119,59769],{},[902,60121,59772],{"encoding":904},[724,60123,60124],{},[614,60125,60126,60127,60162,60163,1664],{},"Obrázek 3.6: Hyperbola ",[883,60128,60130],{"className":60129},[886],[888,60131,60132],{"xmlns":890},[892,60133,60134,60160],{},[895,60135,60136,60138,60140,60142,60156,60158],{},[898,60137,1718],{},[898,60139,1721],{},[1723,60141,1725],{},[3055,60143,60144],{"scriptlevel":2256,"displaystyle":1907},[3058,60145,60146,60154],{},[895,60147,60148,60150,60152],{},[1864,60149,1866],{},[3018,60151,3707],{},[1864,60153,59769],{},[898,60155,1904],{},[1723,60157,2087],{},[1864,60159,3080],{},[902,60161,59910],{"encoding":904}," s vodorovnou asymptotou ",[883,60164,60166],{"className":60165},[886],[888,60167,60168],{"xmlns":890},[892,60169,60170,60180],{},[895,60171,60172,60174,60176,60178],{},[898,60173,1718],{},[898,60175,1721],{},[1723,60177,1725],{},[1864,60179,3080],{},[902,60181,60182],{"encoding":904},"AC = 4",[724,60184,60185],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,60187,60189],{"className":60188},[886],[888,60190,60191],{"xmlns":890,"display":28759},[892,60192,60193,60219],{},[895,60194,60195,60197,60199,60201,60203,60205,60207,60209,60211,60213,60215,60217],{},[898,60196,1754],{},[898,60198,41031],{},[898,60200,1721],{},[1723,60202,1725],{},[898,60204,1904],{},[1723,60206,3897],{},[898,60208,41031],{},[898,60210,1721],{},[1723,60212,1908],{"stretchy":1907},[898,60214,1904],{},[1723,60216,1914],{"stretchy":1907},[1723,60218,2031],{"separator":2030},[902,60220,60221],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,60223,5022,60224,59413,60252,60255,60256,60286],{},[883,60225,60227],{"className":60226},[886],[888,60228,60229],{"xmlns":890},[892,60230,60231,60249],{},[895,60232,60233,60235,60237,60239,60241,60243,60245,60247],{},[898,60234,41031],{},[898,60236,1721],{},[1723,60238,1725],{},[898,60240,41031],{},[898,60242,1721],{},[1723,60244,1908],{"stretchy":1907},[898,60246,1904],{},[1723,60248,1914],{"stretchy":1907},[902,60250,60251],{"encoding":904},"VC = VC(Q)",[38,60253,60254],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,60257,60259],{"className":60258},[886],[888,60260,60261],{"xmlns":890},[892,60262,60263,60283],{},[895,60264,60265,60267,60269,60271,60273,60275,60277,60279,60281],{},[898,60266,1754],{},[898,60268,41031],{},[898,60270,1721],{},[1723,60272,1908],{"stretchy":1907},[898,60274,1904],{},[1723,60276,1914],{"stretchy":1907},[1723,60278,1725],{},[898,60280,207],{},[898,60282,1904],{},[902,60284,60285],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,60288,60290],{"className":60289},[886],[888,60291,60292],{"xmlns":890,"display":28759},[892,60293,60294,60314],{},[895,60295,60296,60298,60300,60302,60304,60306,60308,60310,60312],{},[898,60297,1754],{},[898,60299,1721],{},[1723,60301,1725],{},[898,60303,11136],{},[898,60305,1721],{},[1723,60307,2087],{},[898,60309,207],{},[898,60311,1904],{},[898,60313,1664],{"mathvariant":2124},[902,60315,60316],{"encoding":904},"TC = FC + aQ.",[724,60318,60319,60320,60335,60336,60351,60352,60375,60376,60410,60411,60162,60424,60437,60438,1682,60486,60530,60531,1664],{},"Křivkou ",[883,60321,60323],{"className":60322},[886],[888,60324,60325],{"xmlns":890},[892,60326,60327,60333],{},[895,60328,60329,60331],{},[898,60330,1754],{},[898,60332,1721],{},[902,60334,3963],{"encoding":904}," je přímka se svislým průsečíkem ",[883,60337,60339],{"className":60338},[886],[888,60340,60341],{"xmlns":890},[892,60342,60343,60349],{},[895,60344,60345,60347],{},[898,60346,11136],{},[898,60348,1721],{},[902,60350,56178],{"encoding":904}," a sklonem ",[883,60353,60355],{"className":60354},[886],[888,60356,60357],{"xmlns":890},[892,60358,60359,60372],{},[895,60360,60361,60364,60366,60368,60370],{},[898,60362,60363],{},"tan",[1723,60365,56887],{},[898,60367,19556],{},[1723,60369,1725],{},[898,60371,207],{},[902,60373,60374],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,60377,60379],{"className":60378},[886],[888,60380,60381],{"xmlns":890},[892,60382,60383,60407],{},[895,60384,60385,60387,60389,60391,60403,60405],{},[898,60386,1718],{},[898,60388,1721],{},[1723,60390,1725],{},[3055,60392,60393],{"scriptlevel":2256,"displaystyle":1907},[3058,60394,60395,60401],{},[895,60396,60397,60399],{},[898,60398,11136],{},[898,60400,1721],{},[898,60402,1904],{},[1723,60404,2087],{},[898,60406,207],{},[902,60408,60409],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,60412,60414],{"className":60413},[886],[888,60415,60416],{"xmlns":890},[892,60417,60418,60422],{},[895,60419,60420],{},[898,60421,1911],{},[902,60423,1911],{"encoding":904},[883,60425,60427],{"className":60426},[886],[888,60428,60429],{"xmlns":890},[892,60430,60431,60435],{},[895,60432,60433],{},[898,60434,207],{},[902,60436,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,60439,60441],{"className":60440},[886],[888,60442,60443],{"xmlns":890},[892,60444,60445,60483],{},[895,60446,60447,60467,60479,60481],{},[1931,60448,60449,60455],{},[895,60450,60451,60453],{},[898,60452,59969],{},[1723,60454,56887],{},[895,60456,60457,60459,60461],{},[898,60458,1904],{},[1723,60460,3843],{},[2057,60462,60463,60465],{},[1864,60464,2256],{},[1723,60466,2087],{},[3055,60468,60469],{"scriptlevel":2256,"displaystyle":1907},[3058,60470,60471,60477],{},[895,60472,60473,60475],{},[898,60474,11136],{},[898,60476,1721],{},[898,60478,1904],{},[1723,60480,1725],{},[898,60482,7007],{"mathvariant":2124},[902,60484,60485],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,60487,60489],{"className":60488},[886],[888,60490,60491],{"xmlns":890},[892,60492,60493,60527],{},[895,60494,60495,60511,60523,60525],{},[1931,60496,60497,60503],{},[895,60498,60499,60501],{},[898,60500,59969],{},[1723,60502,56887],{},[895,60504,60505,60507,60509],{},[898,60506,1904],{},[1723,60508,3843],{},[898,60510,7007],{"mathvariant":2124},[3055,60512,60513],{"scriptlevel":2256,"displaystyle":1907},[3058,60514,60515,60521],{},[895,60516,60517,60519],{},[898,60518,11136],{},[898,60520,1721],{},[898,60522,1904],{},[1723,60524,1725],{},[1864,60526,2256],{},[902,60528,60529],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,60532,60534],{"className":60533},[886],[888,60535,60536],{"xmlns":890},[892,60537,60538,60544],{},[895,60539,60540,60542],{},[898,60541,1718],{},[898,60543,1721],{},[902,60545,56247],{"encoding":904},[724,60547,60548],{},[614,60549,60550,60551,60566,60567,60582,60583,1664],{},"Obrázek 3.7: Přímka ",[883,60552,60554],{"className":60553},[886],[888,60555,60556],{"xmlns":890},[892,60557,60558,60564],{},[895,60559,60560,60562],{},[898,60561,1754],{},[898,60563,1721],{},[902,60565,3963],{"encoding":904}," s osovým průsečíkem ve výši ",[883,60568,60570],{"className":60569},[886],[888,60571,60572],{"xmlns":890},[892,60573,60574,60580],{},[895,60575,60576,60578],{},[898,60577,11136],{},[898,60579,1721],{},[902,60581,56178],{"encoding":904}," a se sklonem ",[883,60584,60586],{"className":60585},[886],[888,60587,60588],{"xmlns":890},[892,60589,60590,60602],{},[895,60591,60592,60594,60596,60598,60600],{},[898,60593,60363],{},[1723,60595,56887],{},[898,60597,19556],{},[1723,60599,1725],{},[898,60601,207],{},[902,60603,60374],{"encoding":904},[724,60605,60606],{},[614,60607,60608,60609,60624,60625,1664],{},"Obrázek 3.8: Klesající hyperbola ",[883,60610,60612],{"className":60611},[886],[888,60613,60614],{"xmlns":890},[892,60615,60616,60622],{},[895,60617,60618,60620],{},[898,60619,1718],{},[898,60621,1721],{},[902,60623,56247],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,60626,60628],{"className":60627},[886],[888,60629,60630],{"xmlns":890},[892,60631,60632,60636],{},[895,60633,60634],{},[898,60635,207],{},[902,60637,207],{"encoding":904},[198,60639,60641],{"id":60640},"mezní-náklady","Mezní náklady",[724,60643,60644,2628,60646,1981,60661,60664,60665,60668],{},[38,60645,60641],{},[883,60647,60649],{"className":60648},[886],[888,60650,60651],{"xmlns":890},[892,60652,60653,60659],{},[895,60654,60655,60657],{},[898,60656,1728],{},[898,60658,1721],{},[902,60660,55979],{"encoding":904},[38,60662,60663],{},"marginal cost",") jsou ",[207,60666,1145],{"className":60667,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,60670,60672],{"className":60671},[886],[888,60673,60674],{"xmlns":890,"display":28759},[892,60675,60676,60745],{},[21447,60677,60678],{"width":28764},[21452,60679,60680,60682,60738,60740],{},[21455,60681],{"width":28769},[21455,60683,60684],{},[895,60685,60686,60688,60690,60692,60694,60696,60698,60700,60702,60704,60720,60722,60724,60730,60732,60734,60736],{},[898,60687,1728],{},[898,60689,1721],{},[1723,60691,1725],{},[898,60693,1728],{},[898,60695,1721],{},[1723,60697,1908],{"stretchy":1907},[898,60699,1904],{},[1723,60701,1914],{"stretchy":1907},[1723,60703,1725],{},[3058,60705,60706,60714],{},[895,60707,60708,60710,60712],{},[898,60709,2930],{"mathvariant":2124},[898,60711,1754],{},[898,60713,1721],{},[895,60715,60716,60718],{},[898,60717,2930],{"mathvariant":2124},[898,60719,1904],{},[1723,60721,1725],{},[898,60723,1754],{},[2057,60725,60726,60728],{},[898,60727,1721],{},[1723,60729,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,60731,1908],{"stretchy":1907},[898,60733,1904],{},[1723,60735,1914],{"stretchy":1907},[898,60737,1664],{"mathvariant":2124},[21455,60739],{"width":28769},[21455,60741,60742],{},[3018,60743,60744],{},"(3.8)",[902,60746,60747],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[4584,60749,60750],{},[724,60751,60752,60754,60755,60781,60782,60799,60800,1664],{},[883,60753,4869],{}," Intuice — „kolik stojí další kus\"\n",[883,60756,60758],{"className":60757},[886],[888,60759,60760],{"xmlns":890},[892,60761,60762,60778],{},[895,60763,60764,60766,60768,60770,60776],{},[898,60765,1728],{},[898,60767,1721],{},[1723,60769,1908],{"stretchy":1907},[2057,60771,60772,60774],{},[898,60773,1904],{},[1723,60775,5066],{},[1723,60777,1914],{"stretchy":1907},[902,60779,60780],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,60783,60785],{"className":60784},[886],[888,60786,60787],{"xmlns":890},[892,60788,60789,60797],{},[895,60790,60791],{},[2057,60792,60793,60795],{},[898,60794,1904],{},[1723,60796,5066],{},[902,60798,30537],{"encoding":904},". Formálně ",[883,60801,60803],{"className":60802},[886],[888,60804,60805],{"xmlns":890},[892,60806,60807,60859],{},[895,60808,60809,60811,60813,60815,60821,60823,60825,60827,60829,60831,60837,60839,60841,60843,60845,60847,60849,60851,60857],{},[898,60810,1728],{},[898,60812,1721],{},[1723,60814,1908],{"stretchy":1907},[2057,60816,60817,60819],{},[898,60818,1904],{},[1723,60820,5066],{},[1723,60822,1914],{"stretchy":1907},[1723,60824,3456],{},[898,60826,1754],{},[898,60828,1721],{},[1723,60830,1908],{"stretchy":1907},[2057,60832,60833,60835],{},[898,60834,1904],{},[1723,60836,5066],{},[1723,60838,2087],{},[1864,60840,1866],{},[1723,60842,1914],{"stretchy":1907},[1723,60844,1759],{},[898,60846,1754],{},[898,60848,1721],{},[1723,60850,1908],{"stretchy":1907},[2057,60852,60853,60855],{},[898,60854,1904],{},[1723,60856,5066],{},[1723,60858,1914],{"stretchy":1907},[902,60860,60861],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,60863,60864,60865,3430],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,60866,60868],{"className":60867},[886],[888,60869,60870],{"xmlns":890},[892,60871,60872,60880],{},[895,60873,60874,60876,60878],{},[898,60875,3611],{"mathvariant":2124},[898,60877,1754],{},[898,60879,1721],{},[902,60881,60882],{"encoding":904},"\\Delta TC",[883,60884,60886],{"className":60885},[886],[888,60887,60888],{"xmlns":890,"display":28759},[892,60889,60890,60959],{},[21447,60891,60892],{"width":28764},[21452,60893,60894,60896,60952,60954],{},[21455,60895],{"width":28769},[21455,60897,60898],{},[895,60899,60900,60902,60904,60906,60908,60910,60912,60914,60916,60918,60920,60922,60924,60926,60932,60934,60936,60938,60940,60942,60944,60946,60948,60950],{},[898,60901,3611],{"mathvariant":2124},[898,60903,1754],{},[898,60905,1721],{},[3018,60907,4699],{},[1723,60909,3456],{},[3018,60911,4699],{},[898,60913,2930],{"mathvariant":2124},[898,60915,1754],{},[898,60917,1721],{},[1723,60919,1725],{},[1723,60921,1908],{"stretchy":1907},[898,60923,1754],{},[898,60925,1721],{},[2057,60927,60928,60930],{},[1723,60929,1914],{"stretchy":1907},[1723,60931,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[3018,60933,3707],{},[898,60935,2930],{"mathvariant":2124},[898,60937,1904],{},[1723,60939,1725],{},[898,60941,1728],{},[898,60943,1721],{},[3018,60945,3707],{},[898,60947,2930],{"mathvariant":2124},[898,60949,1904],{},[1723,60951,2031],{"separator":2030},[21455,60953],{"width":28769},[21455,60955,60956],{},[3018,60957,60958],{},"(3.9)",[902,60960,60961],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,60963,57998],{},[883,60965,60967],{"className":60966},[886],[888,60968,60969],{"xmlns":890,"display":28759},[892,60970,60971,61069],{},[895,60972,60973,61011,61013,61015,61017,61039,61041,61067],{},[895,60974,60975,60977,60983,60985,60991,60994,61000,61003],{},[3018,60976,58012],{},[9096,60978,60979,60981],{"accent":2030},[3018,60980,46423],{},[1723,60982,25751],{},[3018,60984,58021],{},[9096,60986,60987,60989],{"accent":2030},[3018,60988,2740],{},[1723,60990,25670],{},[3018,60992,60993],{},"ch n",[9096,60995,60996,60998],{"accent":2030},[3018,60997,207],{},[1723,60999,25670],{},[3018,61001,61002],{},"klad",[9096,61004,61005,61008],{"accent":2030},[3018,61006,61007],{},"u",[1723,61009,61010],{},"˚",[3018,61012,4699],{},[1723,61014,3456],{},[3018,61016,4699],{},[895,61018,61019,61021,61027,61030,61036],{},[3018,61020,58056],{},[9096,61022,61023,61025],{"accent":2030},[3018,61024,25739],{},[1723,61026,25670],{},[3018,61028,61029],{}," n",[9096,61031,61032,61034],{"accent":2030},[3018,61033,207],{},[1723,61035,25670],{},[3018,61037,61038],{},"klady",[1723,61040,58083],{},[895,61042,61043,61045,61051,61053,61059,61061],{},[3018,61044,58012],{},[9096,61046,61047,61049],{"accent":2030},[3018,61048,46423],{},[1723,61050,25751],{},[3018,61052,58096],{},[9096,61054,61055,61057],{"accent":2030},[3018,61056,10301],{},[1723,61058,25751],{},[3018,61060,58105],{},[9096,61062,61063,61065],{"accent":2030},[3018,61064,25739],{},[1723,61066,25670],{},[898,61068,1664],{"mathvariant":2124},[902,61070,61071],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[38040,61073,61075],{"id":61074},"příklad-35","Příklad 3.5",[724,61077,61078,58209,61080,56712,61116,61131,61132,61147,61148,3397,61161,3411,61174,61187,61188,3411,61201,1664],{},[38,61079,56674],{},[883,61081,61083],{"className":61082},[886],[888,61084,61085],{"xmlns":890},[892,61086,61087,61113],{},[895,61088,61089,61091,61093,61095,61097,61099,61101,61103,61105,61107],{},[898,61090,1754],{},[898,61092,1721],{},[1723,61094,1725],{},[1864,61096,9087],{},[1723,61098,2087],{},[1864,61100,2969],{},[898,61102,1904],{},[1723,61104,2087],{},[1864,61106,2331],{},[2057,61108,61109,61111],{},[898,61110,1904],{},[1864,61112,2331],{},[902,61114,61115],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,61117,61119],{"className":61118},[886],[888,61120,61121],{"xmlns":890},[892,61122,61123,61129],{},[895,61124,61125,61127],{},[898,61126,1728],{},[898,61128,1721],{},[902,61130,55979],{"encoding":904}," a odhadněte změny ",[883,61133,61135],{"className":61134},[886],[888,61136,61137],{"xmlns":890},[892,61138,61139,61145],{},[895,61140,61141,61143],{},[898,61142,1754],{},[898,61144,1721],{},[902,61146,3963],{"encoding":904}," při změnách ",[883,61149,61151],{"className":61150},[886],[888,61152,61153],{"xmlns":890},[892,61154,61155,61159],{},[895,61156,61157],{},[898,61158,1904],{},[902,61160,1904],{"encoding":904},[883,61162,61164],{"className":61163},[886],[888,61165,61166],{"xmlns":890},[892,61167,61168,61172],{},[895,61169,61170],{},[1864,61171,36937],{},[902,61173,36937],{"encoding":904},[883,61175,61177],{"className":61176},[886],[888,61178,61179],{"xmlns":890},[892,61180,61181,61185],{},[895,61182,61183],{},[1864,61184,42554],{},[902,61186,42554],{"encoding":904}," a z ",[883,61189,61191],{"className":61190},[886],[888,61192,61193],{"xmlns":890},[892,61194,61195,61199],{},[895,61196,61197],{},[1864,61198,36937],{},[902,61200,36937],{"encoding":904},[883,61202,61204],{"className":61203},[886],[888,61205,61206],{"xmlns":890},[892,61207,61208,61212],{},[895,61209,61210],{},[1864,61211,4227],{},[902,61213,4227],{"encoding":904},[724,61215,61216,2628,61218,2137,61244,1343,61271,61298,61299,61314,61315,61330,61331,61358,61359,61379,61380,21224,61401,61457,61458,3397,61471,3411,61484,8812,61497,1664],{},[38,61217,23463],{},[883,61219,61221],{"className":61220},[886],[888,61222,61223],{"xmlns":890},[892,61224,61225,61241],{},[895,61226,61227,61229,61231,61233,61235,61237,61239],{},[898,61228,1728],{},[898,61230,1721],{},[1723,61232,1725],{},[1864,61234,2969],{},[1723,61236,2087],{},[1864,61238,3080],{},[898,61240,1904],{},[902,61242,61243],{"encoding":904},"MC = 6 + 4Q",[883,61245,61247],{"className":61246},[886],[888,61248,61249],{"xmlns":890},[892,61250,61251,61268],{},[895,61252,61253,61255,61257,61259,61261,61263,61265],{},[898,61254,1728],{},[898,61256,1721],{},[1723,61258,1908],{"stretchy":1907},[1864,61260,36937],{},[1723,61262,1914],{"stretchy":1907},[1723,61264,1725],{},[1864,61266,61267],{},"66",[902,61269,61270],{"encoding":904},"MC(15) = 66",[883,61272,61274],{"className":61273},[886],[888,61275,61276],{"xmlns":890},[892,61277,61278,61295],{},[895,61279,61280,61282,61284,61286,61288,61290,61292],{},[898,61281,1728],{},[898,61283,1721],{},[1723,61285,1908],{"stretchy":1907},[1864,61287,9744],{},[1723,61289,1914],{"stretchy":1907},[1723,61291,1725],{},[1864,61293,61294],{},"86",[902,61296,61297],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,61300,61302],{"className":61301},[886],[888,61303,61304],{"xmlns":890},[892,61305,61306,61312],{},[895,61307,61308,61310],{},[898,61309,1754],{},[898,61311,1721],{},[902,61313,3963],{"encoding":904}," zvyšuje (",[883,61316,61318],{"className":61317},[886],[888,61319,61320],{"xmlns":890},[892,61321,61322,61328],{},[895,61323,61324,61326],{},[898,61325,1728],{},[898,61327,1721],{},[902,61329,55979],{"encoding":904}," je rostoucí). Z ",[883,61332,61334],{"className":61333},[886],[888,61335,61336],{"xmlns":890},[892,61337,61338,61355],{},[895,61339,61340,61342,61344,61346,61348,61350,61352],{},[898,61341,1754],{},[898,61343,1721],{},[1723,61345,1908],{"stretchy":1907},[1864,61347,36937],{},[1723,61349,1914],{"stretchy":1907},[1723,61351,1725],{},[1864,61353,61354],{},"740",[902,61356,61357],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,61360,61362],{"className":61361},[886],[888,61363,61364],{"xmlns":890},[892,61365,61366,61376],{},[895,61367,61368,61370,61372,61374],{},[898,61369,2930],{"mathvariant":2124},[898,61371,1904],{},[1723,61373,1725],{},[1864,61375,1866],{},[902,61377,61378],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,61381,61383],{"className":61382},[886],[888,61384,61385],{"xmlns":890},[892,61386,61387,61398],{},[895,61388,61389,61391,61393,61395],{},[898,61390,1754],{},[898,61392,1721],{},[1723,61394,3456],{},[1864,61396,61397],{},"806",[902,61399,61400],{"encoding":904},"TC \\approx 806",[883,61402,61404],{"className":61403},[886],[888,61405,61406],{"xmlns":890},[892,61407,61408,61454],{},[895,61409,61410,61412,61414,61416,61418,61420,61422,61424,61426,61428,61430,61432,61434,61436,61438,61440,61442,61445,61447,61449,61451],{},[898,61411,3611],{"mathvariant":2124},[898,61413,1754],{},[898,61415,1721],{},[1723,61417,1725],{},[898,61419,1754],{},[898,61421,1721],{},[1723,61423,1908],{"stretchy":1907},[1864,61425,42554],{},[1723,61427,1914],{"stretchy":1907},[1723,61429,1759],{},[898,61431,1754],{},[898,61433,1721],{},[1723,61435,1908],{"stretchy":1907},[1864,61437,36937],{},[1723,61439,1914],{"stretchy":1907},[1723,61441,1725],{},[1864,61443,61444],{},"808",[1723,61446,1759],{},[1864,61448,61354],{},[1723,61450,1725],{},[1864,61452,61453],{},"68",[902,61455,61456],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,61459,61461],{"className":61460},[886],[888,61462,61463],{"xmlns":890},[892,61464,61465,61469],{},[895,61466,61467],{},[898,61468,1904],{},[902,61470,1904],{"encoding":904},[883,61472,61474],{"className":61473},[886],[888,61475,61476],{"xmlns":890},[892,61477,61478,61482],{},[895,61479,61480],{},[1864,61481,36937],{},[902,61483,36937],{"encoding":904},[883,61485,61487],{"className":61486},[886],[888,61488,61489],{"xmlns":890},[892,61490,61491,61495],{},[895,61492,61493],{},[1864,61494,4227],{},[902,61496,4227],{"encoding":904},[883,61498,61500],{"className":61499},[886],[888,61501,61502],{"xmlns":890},[892,61503,61504,61533],{},[895,61505,61506,61508,61510,61512,61514,61516,61518,61520,61522,61524,61526,61528,61530],{},[898,61507,3611],{"mathvariant":2124},[898,61509,1754],{},[898,61511,1721],{},[1723,61513,3456],{},[1864,61515,61267],{},[1723,61517,3897],{},[1723,61519,1908],{"stretchy":1907},[1723,61521,1759],{},[1864,61523,2909],{},[1723,61525,1914],{"stretchy":1907},[1723,61527,1725],{},[1723,61529,1759],{},[1864,61531,61532],{},"198",[902,61534,61535],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,61537,61539],{"id":61538},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,61541,61542],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[38040,61544,61546],{"id":61545},"příklad-36","Příklad 3.6",[724,61548,61549,58209,61551,61595],{},[38,61550,56674],{},[883,61552,61554],{"className":61553},[886],[888,61555,61556],{"xmlns":890},[892,61557,61558,61592],{},[895,61559,61560,61562,61564,61566,61568,61570,61572,61574,61576,61578,61584,61586],{},[898,61561,1754],{},[898,61563,1721],{},[1723,61565,1725],{},[1864,61567,3810],{},[1723,61569,2087],{},[1864,61571,5714],{},[898,61573,1904],{},[1723,61575,1759],{},[1864,61577,2962],{},[2057,61579,61580,61582],{},[898,61581,1904],{},[1864,61583,2331],{},[1723,61585,2087],{},[2057,61587,61588,61590],{},[898,61589,1904],{},[1864,61591,2909],{},[902,61593,61594],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,61597,61598],{},[38,61599,23463],{},[883,61601,61603],{"className":61602},[886],[888,61604,61605],{"xmlns":890,"display":28759},[892,61606,61607,61851],{},[21447,61608,61609,61635,61683,61717,61759,61809],{"rowspacing":21449,"columnalign":21450,"columnspacing":2228},[21452,61610,61611,61621],{},[21455,61612,61613],{},[3055,61614,61615],{"scriptlevel":2256,"displaystyle":2030},[895,61616,61617,61619],{},[898,61618,11136],{},[898,61620,1721],{},[21455,61622,61623],{},[3055,61624,61625],{"scriptlevel":2256,"displaystyle":2030},[895,61626,61627,61629,61631,61633],{},[895,61628],{},[1723,61630,1725],{},[1864,61632,3810],{},[1723,61634,2031],{"separator":2030},[21452,61636,61637,61649],{},[21455,61638,61639],{},[3055,61640,61641],{"scriptlevel":2256,"displaystyle":2030},[895,61642,61643,61645,61647],{},[898,61644,1754],{},[898,61646,41031],{},[898,61648,1721],{},[21455,61650,61651],{},[3055,61652,61653],{"scriptlevel":2256,"displaystyle":2030},[895,61654,61655,61657,61659,61661,61663,61665,61667,61673,61675,61681],{},[895,61656],{},[1723,61658,1725],{},[1864,61660,5714],{},[898,61662,1904],{},[1723,61664,1759],{},[1864,61666,2962],{},[2057,61668,61669,61671],{},[898,61670,1904],{},[1864,61672,2331],{},[1723,61674,2087],{},[2057,61676,61677,61679],{},[898,61678,1904],{},[1864,61680,2909],{},[1723,61682,2031],{"separator":2030},[21452,61684,61685,61697],{},[21455,61686,61687],{},[3055,61688,61689],{"scriptlevel":2256,"displaystyle":2030},[895,61690,61691,61693,61695],{},[898,61692,1718],{},[898,61694,11136],{},[898,61696,1721],{},[21455,61698,61699],{},[3055,61700,61701],{"scriptlevel":2256,"displaystyle":2030},[895,61702,61703,61705,61707,61715],{},[895,61704],{},[1723,61706,1725],{},[3055,61708,61709],{"scriptlevel":2256,"displaystyle":1907},[3058,61710,61711,61713],{},[1864,61712,3810],{},[898,61714,1904],{},[1723,61716,2031],{"separator":2030},[21452,61718,61719,61731],{},[21455,61720,61721],{},[3055,61722,61723],{"scriptlevel":2256,"displaystyle":2030},[895,61724,61725,61727,61729],{},[898,61726,1718],{},[898,61728,41031],{},[898,61730,1721],{},[21455,61732,61733],{},[3055,61734,61735],{"scriptlevel":2256,"displaystyle":2030},[895,61736,61737,61739,61741,61743,61745,61747,61749,61751,61757],{},[895,61738],{},[1723,61740,1725],{},[1864,61742,5714],{},[1723,61744,1759],{},[1864,61746,2962],{},[898,61748,1904],{},[1723,61750,2087],{},[2057,61752,61753,61755],{},[898,61754,1904],{},[1864,61756,2331],{},[1723,61758,2031],{"separator":2030},[21452,61760,61761,61771],{},[21455,61762,61763],{},[3055,61764,61765],{"scriptlevel":2256,"displaystyle":2030},[895,61766,61767,61769],{},[898,61768,1718],{},[898,61770,1721],{},[21455,61772,61773],{},[3055,61774,61775],{"scriptlevel":2256,"displaystyle":2030},[895,61776,61777,61779,61781,61789,61791,61793,61795,61797,61799,61801,61807],{},[895,61778],{},[1723,61780,1725],{},[3055,61782,61783],{"scriptlevel":2256,"displaystyle":1907},[3058,61784,61785,61787],{},[1864,61786,3810],{},[898,61788,1904],{},[1723,61790,2087],{},[1864,61792,5714],{},[1723,61794,1759],{},[1864,61796,2962],{},[898,61798,1904],{},[1723,61800,2087],{},[2057,61802,61803,61805],{},[898,61804,1904],{},[1864,61806,2331],{},[1723,61808,2031],{"separator":2030},[21452,61810,61811,61821],{},[21455,61812,61813],{},[3055,61814,61815],{"scriptlevel":2256,"displaystyle":2030},[895,61816,61817,61819],{},[898,61818,1728],{},[898,61820,1721],{},[21455,61822,61823],{},[3055,61824,61825],{"scriptlevel":2256,"displaystyle":2030},[895,61826,61827,61829,61831,61833,61835,61837,61839,61841,61843,61849],{},[895,61828],{},[1723,61830,1725],{},[1864,61832,5714],{},[1723,61834,1759],{},[1864,61836,3585],{},[898,61838,1904],{},[1723,61840,2087],{},[1864,61842,2909],{},[2057,61844,61845,61847],{},[898,61846,1904],{},[1864,61848,2331],{},[898,61850,1664],{"mathvariant":2124},[902,61852,61853],{"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}",[724,61855,61856,61857,16493,61872,16493,61887,61902,61903,61918,61919,1343,61937,61918,61954,1343,61972,61918,61987,62005],{},"Význačné body ",[883,61858,61860],{"className":61859},[886],[888,61861,61862],{"xmlns":890},[892,61863,61864,61869],{},[895,61865,61866],{},[1864,61867,61868],{},"1,67",[902,61870,61871],{"encoding":904},"1{,}67",[883,61873,61875],{"className":61874},[886],[888,61876,61877],{"xmlns":890},[892,61878,61879,61884],{},[895,61880,61881],{},[1864,61882,61883],{},"2,50",[902,61885,61886],{"encoding":904},"2{,}50",[883,61888,61890],{"className":61889},[886],[888,61891,61892],{"xmlns":890},[892,61893,61894,61899],{},[895,61895,61896],{},[1864,61897,61898],{},"4,73",[902,61900,61901],{"encoding":904},"4{,}73"," odpovídají: ",[883,61904,61906],{"className":61905},[886],[888,61907,61908],{"xmlns":890},[892,61909,61910,61916],{},[895,61911,61912,61914],{},[898,61913,1728],{},[898,61915,1721],{},[902,61917,55979],{"encoding":904}," minimum v ",[883,61920,61922],{"className":61921},[886],[888,61923,61924],{"xmlns":890},[892,61925,61926,61934],{},[895,61927,61928,61930,61932],{},[898,61929,1904],{},[1723,61931,6610],{},[1864,61933,61868],{},[902,61935,61936],{"encoding":904},"Q \\doteq 1{,}67",[883,61938,61940],{"className":61939},[886],[888,61941,61942],{"xmlns":890},[892,61943,61944,61952],{},[895,61945,61946,61948,61950],{},[898,61947,1718],{},[898,61949,41031],{},[898,61951,1721],{},[902,61953,55998],{"encoding":904},[883,61955,61957],{"className":61956},[886],[888,61958,61959],{"xmlns":890},[892,61960,61961,61969],{},[895,61962,61963,61965,61967],{},[898,61964,1904],{},[1723,61966,1725],{},[1864,61968,61883],{},[902,61970,61971],{"encoding":904},"Q = 2{,}50",[883,61973,61975],{"className":61974},[886],[888,61976,61977],{"xmlns":890},[892,61978,61979,61985],{},[895,61980,61981,61983],{},[898,61982,1718],{},[898,61984,1721],{},[902,61986,56247],{"encoding":904},[883,61988,61990],{"className":61989},[886],[888,61991,61992],{"xmlns":890},[892,61993,61994,62002],{},[895,61995,61996,61998,62000],{},[898,61997,1904],{},[1723,61999,6610],{},[1864,62001,61898],{},[902,62003,62004],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,62007,62008],{},[3285,62009],{"alt":62010,"className":62011,"src":62012},"imek-ac-avc-mc",[210,3289],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,62014,62015],{},[614,62016,62017,62018,1682,62033,62050,62051,16493,62070,62085],{},"Obrázek 3.9: Kubické křivky ",[883,62019,62021],{"className":62020},[886],[888,62022,62023],{"xmlns":890},[892,62024,62025,62031],{},[895,62026,62027,62029],{},[898,62028,1754],{},[898,62030,1721],{},[902,62032,3963],{"encoding":904},[883,62034,62036],{"className":62035},[886],[888,62037,62038],{"xmlns":890},[892,62039,62040,62048],{},[895,62041,62042,62044,62046],{},[898,62043,1754],{},[898,62045,41031],{},[898,62047,1721],{},[902,62049,56196],{"encoding":904}," rostoucí od bodu ",[883,62052,62054],{"className":62053},[886],[888,62055,62056],{"xmlns":890},[892,62057,62058,62068],{},[895,62059,62060,62062,62064,62066],{},[898,62061,11136],{},[898,62063,1721],{},[1723,62065,1725],{},[1864,62067,3810],{},[902,62069,12334],{"encoding":904},[883,62071,62073],{"className":62072},[886],[888,62074,62075],{"xmlns":890},[892,62076,62077,62083],{},[895,62078,62079,62081],{},[898,62080,11136],{},[898,62082,1721],{},[902,62084,56178],{"encoding":904}," je vodorovná přímka.",[724,62087,62088],{},[614,62089,62090,62091,1343,62106,1343,62123,29894,62138,62151,62152,2137,62169,62184,62185,6900,62202,62217,62218,26882,62231,1343,62244,1343,62257,1664],{},"Obrázek 3.10: Křivky ",[883,62092,62094],{"className":62093},[886],[888,62095,62096],{"xmlns":890},[892,62097,62098,62104],{},[895,62099,62100,62102],{},[898,62101,1718],{},[898,62103,1721],{},[902,62105,56247],{"encoding":904},[883,62107,62109],{"className":62108},[886],[888,62110,62111],{"xmlns":890},[892,62112,62113,62121],{},[895,62114,62115,62117,62119],{},[898,62116,1718],{},[898,62118,41031],{},[898,62120,1721],{},[902,62122,55998],{"encoding":904},[883,62124,62126],{"className":62125},[886],[888,62127,62128],{"xmlns":890},[892,62129,62130,62136],{},[895,62131,62132,62134],{},[898,62133,1728],{},[898,62135,1721],{},[902,62137,55979],{"encoding":904},[883,62139,62141],{"className":62140},[886],[888,62142,62143],{"xmlns":890},[892,62144,62145,62149],{},[895,62146,62147],{},[898,62148,900],{},[902,62150,900],{"encoding":904}," a klesající hyperbola ",[883,62153,62155],{"className":62154},[886],[888,62156,62157],{"xmlns":890},[892,62158,62159,62167],{},[895,62160,62161,62163,62165],{},[898,62162,1718],{},[898,62164,11136],{},[898,62166,1721],{},[902,62168,56214],{"encoding":904},[883,62170,62172],{"className":62171},[886],[888,62173,62174],{"xmlns":890},[892,62175,62176,62182],{},[895,62177,62178,62180],{},[898,62179,1728],{},[898,62181,1721],{},[902,62183,55979],{"encoding":904}," protíná ",[883,62186,62188],{"className":62187},[886],[888,62189,62190],{"xmlns":890},[892,62191,62192,62200],{},[895,62193,62194,62196,62198],{},[898,62195,1718],{},[898,62197,41031],{},[898,62199,1721],{},[902,62201,55998],{"encoding":904},[883,62203,62205],{"className":62204},[886],[888,62206,62207],{"xmlns":890},[892,62208,62209,62215],{},[895,62210,62211,62213],{},[898,62212,1718],{},[898,62214,1721],{},[902,62216,56247],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,62219,62221],{"className":62220},[886],[888,62222,62223],{"xmlns":890},[892,62224,62225,62229],{},[895,62226,62227],{},[898,62228,1904],{},[902,62230,1904],{"encoding":904},[883,62232,62234],{"className":62233},[886],[888,62235,62236],{"xmlns":890},[892,62237,62238,62242],{},[895,62239,62240],{},[1864,62241,61868],{},[902,62243,61871],{"encoding":904},[883,62245,62247],{"className":62246},[886],[888,62248,62249],{"xmlns":890},[892,62250,62251,62255],{},[895,62252,62253],{},[1864,62254,61883],{},[902,62256,61886],{"encoding":904},[883,62258,62260],{"className":62259},[886],[888,62261,62262],{"xmlns":890},[892,62263,62264,62268],{},[895,62265,62266],{},[1864,62267,61898],{},[902,62269,61901],{"encoding":904},[724,62271,62272],{},[38,62273,62274],{},"Standardní vlastnosti:",[120,62276,62277,62312,62376,62444,62494,62514],{},[123,62278,62279,1682,62294,62311],{},[883,62280,62282],{"className":62281},[886],[888,62283,62284],{"xmlns":890},[892,62285,62286,62292],{},[895,62287,62288,62290],{},[898,62289,1754],{},[898,62291,1721],{},[902,62293,3963],{"encoding":904},[883,62295,62297],{"className":62296},[886],[888,62298,62299],{"xmlns":890},[892,62300,62301,62309],{},[895,62302,62303,62305,62307],{},[898,62304,1754],{},[898,62306,41031],{},[898,62308,1721],{},[902,62310,56196],{"encoding":904}," jsou kubické funkce;",[123,62313,62314,1343,62329,1343,62346,62361,62362,62375],{},[883,62315,62317],{"className":62316},[886],[888,62318,62319],{"xmlns":890},[892,62320,62321,62327],{},[895,62322,62323,62325],{},[898,62324,1718],{},[898,62326,1721],{},[902,62328,56247],{"encoding":904},[883,62330,62332],{"className":62331},[886],[888,62333,62334],{"xmlns":890},[892,62335,62336,62344],{},[895,62337,62338,62340,62342],{},[898,62339,1718],{},[898,62341,41031],{},[898,62343,1721],{},[902,62345,55998],{"encoding":904},[883,62347,62349],{"className":62348},[886],[888,62350,62351],{"xmlns":890},[892,62352,62353,62359],{},[895,62354,62355,62357],{},[898,62356,1728],{},[898,62358,1721],{},[902,62360,55979],{"encoding":904}," jsou křivky tvaru ",[883,62363,62365],{"className":62364},[886],[888,62366,62367],{"xmlns":890},[892,62368,62369,62373],{},[895,62370,62371],{},[898,62372,900],{},[902,62374,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,62377,62378,62393,62394,1343,62411,62428,62429,9135],{},[883,62379,62381],{"className":62380},[886],[888,62382,62383],{"xmlns":890},[892,62384,62385,62391],{},[895,62386,62387,62389],{},[898,62388,1728],{},[898,62390,1721],{},[902,62392,55979],{"encoding":904}," nabývá minima před ",[883,62395,62397],{"className":62396},[886],[888,62398,62399],{"xmlns":890},[892,62400,62401,62409],{},[895,62402,62403,62405,62407],{},[898,62404,1718],{},[898,62406,41031],{},[898,62408,1721],{},[902,62410,55998],{"encoding":904},[883,62412,62414],{"className":62413},[886],[888,62415,62416],{"xmlns":890},[892,62417,62418,62426],{},[895,62419,62420,62422,62424],{},[898,62421,1718],{},[898,62423,41031],{},[898,62425,1721],{},[902,62427,55998],{"encoding":904}," před ",[883,62430,62432],{"className":62431},[886],[888,62433,62434],{"xmlns":890},[892,62435,62436,62442],{},[895,62437,62438,62440],{},[898,62439,1718],{},[898,62441,1721],{},[902,62443,56247],{"encoding":904},[123,62445,62446,62184,62461,1682,62476,62493],{},[883,62447,62449],{"className":62448},[886],[888,62450,62451],{"xmlns":890},[892,62452,62453,62459],{},[895,62454,62455,62457],{},[898,62456,1728],{},[898,62458,1721],{},[902,62460,55979],{"encoding":904},[883,62462,62464],{"className":62463},[886],[888,62465,62466],{"xmlns":890},[892,62467,62468,62474],{},[895,62469,62470,62472],{},[898,62471,1718],{},[898,62473,1721],{},[902,62475,56247],{"encoding":904},[883,62477,62479],{"className":62478},[886],[888,62480,62481],{"xmlns":890},[892,62482,62483,62491],{},[895,62484,62485,62487,62489],{},[898,62486,1718],{},[898,62488,41031],{},[898,62490,1721],{},[902,62492,55998],{"encoding":904}," zdola právě v jejich minimech;",[123,62495,62496,62513],{},[883,62497,62499],{"className":62498},[886],[888,62500,62501],{"xmlns":890},[892,62502,62503,62511],{},[895,62504,62505,62507,62509],{},[898,62506,1718],{},[898,62508,11136],{},[898,62510,1721],{},[902,62512,56214],{"encoding":904}," je hyperbola, stále klesající;",[123,62515,62516,62548,62549,1682,62564,62581,62582,62595,62596,4634],{},[883,62517,62519],{"className":62518},[886],[888,62520,62521],{"xmlns":890},[892,62522,62523,62545],{},[895,62524,62525,62527,62529,62531,62533,62535,62537,62539,62541,62543],{},[898,62526,1718],{},[898,62528,1721],{},[1723,62530,1725],{},[898,62532,1718],{},[898,62534,11136],{},[898,62536,1721],{},[1723,62538,2087],{},[898,62540,1718],{},[898,62542,41031],{},[898,62544,1721],{},[902,62546,62547],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,62550,62552],{"className":62551},[886],[888,62553,62554],{"xmlns":890},[892,62555,62556,62562],{},[895,62557,62558,62560],{},[898,62559,1718],{},[898,62561,1721],{},[902,62563,56247],{"encoding":904},[883,62565,62567],{"className":62566},[886],[888,62568,62569],{"xmlns":890},[892,62570,62571,62579],{},[895,62572,62573,62575,62577],{},[898,62574,1718],{},[898,62576,41031],{},[898,62578,1721],{},[902,62580,55998],{"encoding":904}," klesá s rostoucím ",[883,62583,62585],{"className":62584},[886],[888,62586,62587],{"xmlns":890},[892,62588,62589,62593],{},[895,62590,62591],{},[898,62592,1904],{},[902,62594,1904],{"encoding":904}," (protože ",[883,62597,62599],{"className":62598},[886],[888,62600,62601],{"xmlns":890},[892,62602,62603,62615],{},[895,62604,62605,62607,62609,62611,62613],{},[898,62606,1718],{},[898,62608,11136],{},[898,62610,1721],{},[1723,62612,3843],{},[1864,62614,2256],{},[902,62616,62617],{"encoding":904},"AFC \\to 0",[115,62619,62621],{"id":62620},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,62623,62624,62625,62628,62629,62644],{},"Častou optimalizační úlohou je ",[38,62626,62627],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,62630,62632],{"className":62631},[886],[888,62633,62634],{"xmlns":890},[892,62635,62636,62642],{},[895,62637,62638,62640],{},[898,62639,1718],{},[898,62641,1721],{},[902,62643,56247],{"encoding":904}," minimální.",[198,62646,17108],{"id":17107},[724,62648,62649,62650,62667],{},"Mají-li průměrné náklady minimum v bodě ",[883,62651,62653],{"className":62652},[886],[888,62654,62655],{"xmlns":890},[892,62656,62657,62665],{},[895,62658,62659],{},[1931,62660,62661,62663],{},[898,62662,1904],{},[1864,62664,2256],{},[902,62666,39000],{"encoding":904},", pak platí",[883,62669,62671],{"className":62670},[886],[888,62672,62673],{"xmlns":890,"display":28759},[892,62674,62675,62724],{},[21447,62676,62677],{"width":28764},[21452,62678,62679,62681,62717,62719],{},[21455,62680],{"width":28769},[21455,62682,62683],{},[895,62684,62685,62687,62689,62691,62697,62699,62701,62703,62705,62707,62713,62715],{},[898,62686,1718],{},[898,62688,1721],{},[1723,62690,1908],{"stretchy":1907},[1931,62692,62693,62695],{},[898,62694,1904],{},[1864,62696,2256],{},[1723,62698,1914],{"stretchy":1907},[1723,62700,1725],{},[898,62702,1728],{},[898,62704,1721],{},[1723,62706,1908],{"stretchy":1907},[1931,62708,62709,62711],{},[898,62710,1904],{},[1864,62712,2256],{},[1723,62714,1914],{"stretchy":1907},[898,62716,1664],{"mathvariant":2124},[21455,62718],{"width":28769},[21455,62720,62721],{},[3018,62722,62723],{},"(3.10)",[902,62725,62726],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[4584,62728,62729],{},[724,62730,62731,62733,62734],{},[883,62732,57131],{}," Princip\n",[38,62735,62736],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,62738,62739,62742,62743,62785],{},[38,62740,62741],{},"Odvození."," Z ",[883,62744,62746],{"className":62745},[886],[888,62747,62748],{"xmlns":890},[892,62749,62750,62782],{},[895,62751,62752,62754,62756,62758,62760,62762,62764],{},[898,62753,1718],{},[898,62755,1721],{},[1723,62757,1908],{"stretchy":1907},[898,62759,1904],{},[1723,62761,1914],{"stretchy":1907},[1723,62763,1725],{},[3055,62765,62766],{"scriptlevel":2256,"displaystyle":1907},[3058,62767,62768,62780],{},[895,62769,62770,62772,62774,62776,62778],{},[898,62771,1754],{},[898,62773,1721],{},[1723,62775,1908],{"stretchy":1907},[898,62777,1904],{},[1723,62779,1914],{"stretchy":1907},[898,62781,1904],{},[902,62783,62784],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,62787,62789],{"className":62788},[886],[888,62790,62791],{"xmlns":890,"display":28759},[892,62792,62793,62925],{},[895,62794,62795,62797,62803,62805,62807,62809,62811,62851,62853,62893,62895,62923],{},[898,62796,1718],{},[2057,62798,62799,62801],{},[898,62800,1721],{},[1723,62802,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,62804,1908],{"stretchy":1907},[898,62806,1904],{},[1723,62808,1914],{"stretchy":1907},[1723,62810,1725],{},[3058,62812,62813,62845],{},[895,62814,62815,62817,62823,62825,62827,62829,62831,62833,62835,62837,62839,62841,62843],{},[898,62816,1754],{},[2057,62818,62819,62821],{},[898,62820,1721],{},[1723,62822,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,62824,1908],{"stretchy":1907},[898,62826,1904],{},[1723,62828,1914],{"stretchy":1907},[1723,62830,3897],{},[898,62832,1904],{},[1723,62834,1759],{},[898,62836,1754],{},[898,62838,1721],{},[1723,62840,1908],{"stretchy":1907},[898,62842,1904],{},[1723,62844,1914],{"stretchy":1907},[2057,62846,62847,62849],{},[898,62848,1904],{},[1864,62850,2331],{},[1723,62852,1725],{},[3058,62854,62855,62887],{},[895,62856,62857,62859,62861,62863,62865,62867,62869,62871,62873,62875,62877,62879,62881,62883,62885],{},[898,62858,1728],{},[898,62860,1721],{},[1723,62862,1908],{"stretchy":1907},[898,62864,1904],{},[1723,62866,1914],{"stretchy":1907},[1723,62868,3897],{},[898,62870,1904],{},[1723,62872,1759],{},[898,62874,1718],{},[898,62876,1721],{},[1723,62878,1908],{"stretchy":1907},[898,62880,1904],{},[1723,62882,1914],{"stretchy":1907},[1723,62884,3897],{},[898,62886,1904],{},[2057,62888,62889,62891],{},[898,62890,1904],{},[1864,62892,2331],{},[1723,62894,1725],{},[3058,62896,62897,62921],{},[895,62898,62899,62901,62903,62905,62907,62909,62911,62913,62915,62917,62919],{},[898,62900,1728],{},[898,62902,1721],{},[1723,62904,1908],{"stretchy":1907},[898,62906,1904],{},[1723,62908,1914],{"stretchy":1907},[1723,62910,1759],{},[898,62912,1718],{},[898,62914,1721],{},[1723,62916,1908],{"stretchy":1907},[898,62918,1904],{},[1723,62920,1914],{"stretchy":1907},[898,62922,1904],{},[898,62924,1664],{"mathvariant":2124},[902,62926,62927],{"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}.",[724,62929,62930,62931,3350,62946,8812,62968,57508],{},"Nutnou podmínkou minima ",[883,62932,62934],{"className":62933},[886],[888,62935,62936],{"xmlns":890},[892,62937,62938,62944],{},[895,62939,62940,62942],{},[898,62941,1718],{},[898,62943,1721],{},[902,62945,56247],{"encoding":904},[883,62947,62949],{"className":62948},[886],[888,62950,62951],{"xmlns":890},[892,62952,62953,62965],{},[895,62954,62955,62961,62963],{},[1931,62956,62957,62959],{},[898,62958,1904],{},[1864,62960,2256],{},[1723,62962,2253],{},[1864,62964,2256],{},[902,62966,62967],{"encoding":904},"Q_0 > 0",[883,62969,62971],{"className":62970},[886],[888,62972,62973],{"xmlns":890},[892,62974,62975,62999],{},[895,62976,62977,62979,62985,62987,62993,62995,62997],{},[898,62978,1718],{},[2057,62980,62981,62983],{},[898,62982,1721],{},[1723,62984,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,62986,1908],{"stretchy":1907},[1931,62988,62989,62991],{},[898,62990,1904],{},[1864,62992,2256],{},[1723,62994,1914],{"stretchy":1907},[1723,62996,1725],{},[1864,62998,2256],{},[902,63000,63001],{"encoding":904},"AC'(Q_0) = 0",[883,63003,63005],{"className":63004},[886],[888,63006,63007],{"xmlns":890,"display":28759},[892,63008,63009,63094],{},[895,63010,63011,63051,63053,63055,63057,63060,63062,63064,63066,63068,63074,63076,63078,63080,63082,63084,63090,63092],{},[3058,63012,63013,63045],{},[895,63014,63015,63017,63019,63021,63027,63029,63031,63033,63035,63037,63043],{},[898,63016,1728],{},[898,63018,1721],{},[1723,63020,1908],{"stretchy":1907},[1931,63022,63023,63025],{},[898,63024,1904],{},[1864,63026,2256],{},[1723,63028,1914],{"stretchy":1907},[1723,63030,1759],{},[898,63032,1718],{},[898,63034,1721],{},[1723,63036,1908],{"stretchy":1907},[1931,63038,63039,63041],{},[898,63040,1904],{},[1864,63042,2256],{},[1723,63044,1914],{"stretchy":1907},[1931,63046,63047,63049],{},[898,63048,1904],{},[1864,63050,2256],{},[1723,63052,1725],{},[1864,63054,2256],{},[6588,63056],{"width":15985},[1723,63058,63059],{},"⟺",[6588,63061],{"width":15985},[898,63063,1728],{},[898,63065,1721],{},[1723,63067,1908],{"stretchy":1907},[1931,63069,63070,63072],{},[898,63071,1904],{},[1864,63073,2256],{},[1723,63075,1914],{"stretchy":1907},[1723,63077,1725],{},[898,63079,1718],{},[898,63081,1721],{},[1723,63083,1908],{"stretchy":1907},[1931,63085,63086,63088],{},[898,63087,1904],{},[1864,63089,2256],{},[1723,63091,1914],{"stretchy":1907},[898,63093,1664],{"mathvariant":2124},[902,63095,63096],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,63098,63099,2628,63102,62184,63117,63132,63133,63148,63149,8812,63166,63188,63189,63211],{},[38,63100,63101],{},"Geometrická interpretace.",[883,63103,63105],{"className":63104},[886],[888,63106,63107],{"xmlns":890},[892,63108,63109,63115],{},[895,63110,63111,63113],{},[898,63112,1728],{},[898,63114,1721],{},[902,63116,55979],{"encoding":904},[883,63118,63120],{"className":63119},[886],[888,63121,63122],{"xmlns":890},[892,63123,63124,63130],{},[895,63125,63126,63128],{},[898,63127,1718],{},[898,63129,1721],{},[902,63131,56247],{"encoding":904}," právě v bodě minima ",[883,63134,63136],{"className":63135},[886],[888,63137,63138],{"xmlns":890},[892,63139,63140,63146],{},[895,63141,63142,63144],{},[898,63143,1718],{},[898,63145,1721],{},[902,63147,56247],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,63150,63152],{"className":63151},[886],[888,63153,63154],{"xmlns":890},[892,63155,63156,63164],{},[895,63157,63158],{},[1931,63159,63160,63162],{},[898,63161,1904],{},[1864,63163,2256],{},[902,63165,39000],{"encoding":904},[883,63167,63169],{"className":63168},[886],[888,63170,63171],{"xmlns":890},[892,63172,63173,63185],{},[895,63174,63175,63177,63179,63181,63183],{},[898,63176,1728],{},[898,63178,1721],{},[1723,63180,2287],{},[898,63182,1718],{},[898,63184,1721],{},[902,63186,63187],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,63190,63192],{"className":63191},[886],[888,63193,63194],{"xmlns":890},[892,63195,63196,63208],{},[895,63197,63198,63200,63202,63204,63206],{},[898,63199,1728],{},[898,63201,1721],{},[1723,63203,2253],{},[898,63205,1718],{},[898,63207,1721],{},[902,63209,63210],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,63213,63214,63215,63257,63258,63275,63276,1664],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,63216,63218],{"className":63217},[886],[888,63219,63220],{"xmlns":890},[892,63221,63222,63254],{},[895,63223,63224,63226,63228,63230,63236,63238,63240,63242,63244,63246,63252],{},[898,63225,1718],{},[898,63227,1721],{},[1723,63229,1908],{"stretchy":1907},[1931,63231,63232,63234],{},[898,63233,1904],{},[1864,63235,2256],{},[1723,63237,1914],{"stretchy":1907},[1723,63239,1725],{},[898,63241,1728],{},[898,63243,1721],{},[1723,63245,1908],{"stretchy":1907},[1931,63247,63248,63250],{},[898,63249,1904],{},[1864,63251,2256],{},[1723,63253,1914],{"stretchy":1907},[902,63255,63256],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,63259,63261],{"className":63260},[886],[888,63262,63263],{"xmlns":890},[892,63264,63265,63273],{},[895,63266,63267],{},[1931,63268,63269,63271],{},[898,63270,1904],{},[1864,63272,2256],{},[902,63274,39000],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,63277,63279],{"className":63278},[886],[888,63280,63281],{"xmlns":890},[892,63282,63283,63307],{},[895,63284,63285,63287,63289,63291,63293,63295,63297,63299,63301,63303,63305],{},[898,63286,1718],{},[898,63288,1721],{},[1723,63290,1908],{"stretchy":1907},[898,63292,1904],{},[1723,63294,1914],{"stretchy":1907},[1723,63296,1725],{},[898,63298,1728],{},[898,63300,1721],{},[1723,63302,1908],{"stretchy":1907},[898,63304,1904],{},[1723,63306,1914],{"stretchy":1907},[902,63308,63309],{"encoding":904},"AC(Q) = MC(Q)",[4584,63311,63312],{},[724,63313,63314,63316,63317,11094,63335,63356,63357,11094,63360,63381,63382,63397,63398,58725,63413,4634],{},[883,63315,5124],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,63318,63319,63320],{},"minimum ",[883,63321,63323],{"className":63322},[886],[888,63324,63325],{"xmlns":890},[892,63326,63327,63333],{},[895,63328,63329,63331],{},[898,63330,1718],{},[898,63332,1721],{},[902,63334,56247],{"encoding":904},[883,63336,63338],{"className":63337},[886],[888,63339,63340],{"xmlns":890},[892,63341,63342,63354],{},[895,63343,63344,63346,63348,63350,63352],{},[898,63345,1718],{},[898,63347,1721],{},[1723,63349,1725],{},[898,63351,1728],{},[898,63353,1721],{},[902,63355,1733],{"encoding":904},", pro ",[38,63358,63359],{},"maximum zisku",[883,63361,63363],{"className":63362},[886],[888,63364,63365],{"xmlns":890},[892,63366,63367,63379],{},[895,63368,63369,63371,63373,63375,63377],{},[898,63370,1728],{},[898,63372,1749],{},[1723,63374,1725],{},[898,63376,1728],{},[898,63378,1721],{},[902,63380,1789],{"encoding":904},". Obě podmínky využívají ",[883,63383,63385],{"className":63384},[886],[888,63386,63387],{"xmlns":890},[892,63388,63389,63395],{},[895,63390,63391,63393],{},[898,63392,1728],{},[898,63394,1721],{},[902,63396,55979],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,63399,63401],{"className":63400},[886],[888,63402,63403],{"xmlns":890},[892,63404,63405,63411],{},[895,63406,63407,63409],{},[898,63408,1718],{},[898,63410,1721],{},[902,63412,56247],{"encoding":904},[883,63414,63416],{"className":63415},[886],[888,63417,63418],{"xmlns":890},[892,63419,63420,63426],{},[895,63421,63422,63424],{},[898,63423,1728],{},[898,63425,1749],{},[902,63427,7344],{"encoding":904},[38040,63429,63431],{"id":63430},"příklad-37","Příklad 3.7",[724,63433,63434,58209,63436,63470,63471,63484,63485,63500],{},[38,63435,56674],{},[883,63437,63439],{"className":63438},[886],[888,63440,63441],{"xmlns":890},[892,63442,63443,63467],{},[895,63444,63445,63447,63449,63451,63457,63459,63461,63463,63465],{},[898,63446,1754],{},[898,63448,1721],{},[1723,63450,1725],{},[2057,63452,63453,63455],{},[898,63454,1904],{},[1864,63456,2331],{},[1723,63458,2087],{},[1864,63460,2909],{},[898,63462,1904],{},[1723,63464,2087],{},[1864,63466,6275],{},[902,63468,63469],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,63472,63474],{"className":63473},[886],[888,63475,63476],{"xmlns":890},[892,63477,63478,63482],{},[895,63479,63480],{},[898,63481,1904],{},[902,63483,1904],{"encoding":904}," minimalizující ",[883,63486,63488],{"className":63487},[886],[888,63489,63490],{"xmlns":890},[892,63491,63492,63498],{},[895,63493,63494,63496],{},[898,63495,1718],{},[898,63497,1721],{},[902,63499,56247],{"encoding":904}," a ověřte princip (3.10).",[724,63502,63503,63505],{},[38,63504,23463],{}," Přímý výpočet:",[883,63507,63509],{"className":63508},[886],[888,63510,63511],{"xmlns":890,"display":28759},[892,63512,63513,63615],{},[895,63514,63515,63517,63519,63521,63543,63545,63547,63549,63551,63553,63559,63561,63563,63565,63567,63569,63575,63577,63579,63581,63591,63593,63613],{},[898,63516,1718],{},[898,63518,1721],{},[1723,63520,1725],{},[3058,63522,63523,63541],{},[895,63524,63525,63531,63533,63535,63537,63539],{},[2057,63526,63527,63529],{},[898,63528,1904],{},[1864,63530,2331],{},[1723,63532,2087],{},[1864,63534,2909],{},[898,63536,1904],{},[1723,63538,2087],{},[1864,63540,6275],{},[898,63542,1904],{},[1723,63544,1725],{},[898,63546,1904],{},[1723,63548,2087],{},[1864,63550,2909],{},[1723,63552,2087],{},[3058,63554,63555,63557],{},[1864,63556,6275],{},[898,63558,1904],{},[1723,63560,2031],{"separator":2030},[6588,63562],{"width":6590},[1723,63564,1908],{"stretchy":1907},[898,63566,1718],{},[898,63568,1721],{},[2057,63570,63571,63573],{},[1723,63572,1914],{"stretchy":1907},[1723,63574,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,63576,1725],{},[1864,63578,1866],{},[1723,63580,1759],{},[3058,63582,63583,63585],{},[1864,63584,6275],{},[2057,63586,63587,63589],{},[898,63588,1904],{},[1864,63590,2331],{},[1723,63592,1725],{},[3058,63594,63595,63607],{},[895,63596,63597,63603,63605],{},[2057,63598,63599,63601],{},[898,63600,1904],{},[1864,63602,2331],{},[1723,63604,1759],{},[1864,63606,6275],{},[2057,63608,63609,63611],{},[898,63610,1904],{},[1864,63612,2331],{},[898,63614,1664],{"mathvariant":2124},[902,63616,63617],{"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}.",[724,63619,63620,63660,63661,63685,63686,63736,63737,1664],{},[883,63621,63623],{"className":63622},[886],[888,63624,63625],{"xmlns":890},[892,63626,63627,63657],{},[895,63628,63629,63631,63633,63635,63641,63643,63645,63647,63653,63655],{},[1723,63630,1908],{"stretchy":1907},[898,63632,1718],{},[898,63634,1721],{},[2057,63636,63637,63639],{},[1723,63638,1914],{"stretchy":1907},[1723,63640,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,63642,1725],{},[1864,63644,2256],{},[1723,63646,4702],{},[1931,63648,63649,63651],{},[898,63650,1904],{},[1864,63652,1866],{},[1723,63654,1725],{},[1864,63656,2969],{},[902,63658,63659],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,63662,63664],{"className":63663},[886],[888,63665,63666],{"xmlns":890},[892,63667,63668,63682],{},[895,63669,63670,63676,63678,63680],{},[1931,63671,63672,63674],{},[898,63673,1904],{},[1864,63675,2331],{},[1723,63677,1725],{},[1723,63679,1759],{},[1864,63681,2969],{},[902,63683,63684],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,63687,63689],{"className":63688},[886],[888,63690,63691],{"xmlns":890},[892,63692,63693,63733],{},[895,63694,63695,63697,63699,63701,63711,63713,63715,63717,63719,63727,63729,63731],{},[1723,63696,1908],{"stretchy":1907},[898,63698,1718],{},[898,63700,1721],{},[2057,63702,63703,63705],{},[1723,63704,1914],{"stretchy":1907},[895,63706,63707,63709],{},[1723,63708,2229],{"mathvariant":2124},[1723,63710,2229],{"mathvariant":2124},[1723,63712,1908],{"stretchy":1907},[1864,63714,2969],{},[1723,63716,1914],{"stretchy":1907},[1723,63718,1725],{},[3055,63720,63721],{"scriptlevel":2256,"displaystyle":1907},[3058,63722,63723,63725],{},[1864,63724,1866],{},[1864,63726,2909],{},[1723,63728,2253],{},[1864,63730,2256],{},[1723,63732,4702],{},[902,63734,63735],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,63738,63740],{"className":63739},[886],[888,63741,63742],{"xmlns":890},[892,63743,63744,63760],{},[895,63745,63746,63748,63750,63752,63754,63756,63758],{},[898,63747,1718],{},[898,63749,1721],{},[1723,63751,1908],{"stretchy":1907},[1864,63753,2969],{},[1723,63755,1914],{"stretchy":1907},[1723,63757,1725],{},[1864,63759,36937],{},[902,63761,63762],{"encoding":904},"AC(6) = 15",[724,63764,63765,63766,63792,63793,3430],{},"Pomocí principu: ",[883,63767,63769],{"className":63768},[886],[888,63770,63771],{"xmlns":890},[892,63772,63773,63789],{},[895,63774,63775,63777,63779,63781,63783,63785,63787],{},[898,63776,1728],{},[898,63778,1721],{},[1723,63780,1725],{},[1864,63782,2331],{},[898,63784,1904],{},[1723,63786,2087],{},[1864,63788,2909],{},[902,63790,63791],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,63794,63796],{"className":63795},[886],[888,63797,63798],{"xmlns":890},[892,63799,63800,63812],{},[895,63801,63802,63804,63806,63808,63810],{},[898,63803,1718],{},[898,63805,1721],{},[1723,63807,1725],{},[898,63809,1728],{},[898,63811,1721],{},[902,63813,1733],{"encoding":904},[883,63815,63817],{"className":63816},[886],[888,63818,63819],{"xmlns":890,"display":28759},[892,63820,63821,63923],{},[895,63822,63823,63845,63847,63849,63851,63853,63855,63857,63859,63861,63867,63869,63871,63873,63875,63877,63879,63881,63887,63889,63891,63893,63895,63897,63899,63905,63907,63909,63911,63913,63915,63917,63919,63921],{},[3058,63824,63825,63843],{},[895,63826,63827,63833,63835,63837,63839,63841],{},[2057,63828,63829,63831],{},[898,63830,1904],{},[1864,63832,2331],{},[1723,63834,2087],{},[1864,63836,2909],{},[898,63838,1904],{},[1723,63840,2087],{},[1864,63842,6275],{},[898,63844,1904],{},[1723,63846,1725],{},[1864,63848,2331],{},[898,63850,1904],{},[1723,63852,2087],{},[1864,63854,2909],{},[3018,63856,4699],{},[1723,63858,4702],{},[3018,63860,4699],{},[2057,63862,63863,63865],{},[898,63864,1904],{},[1864,63866,2331],{},[1723,63868,2087],{},[1864,63870,2909],{},[898,63872,1904],{},[1723,63874,2087],{},[1864,63876,6275],{},[1723,63878,1725],{},[1864,63880,2331],{},[2057,63882,63883,63885],{},[898,63884,1904],{},[1864,63886,2331],{},[1723,63888,2087],{},[1864,63890,2909],{},[898,63892,1904],{},[3018,63894,4699],{},[1723,63896,4702],{},[3018,63898,4699],{},[2057,63900,63901,63903],{},[898,63902,1904],{},[1864,63904,2331],{},[1723,63906,1725],{},[1864,63908,6275],{},[3018,63910,4699],{},[1723,63912,4702],{},[3018,63914,4699],{},[898,63916,1904],{},[1723,63918,1725],{},[1864,63920,2969],{},[1723,63922,2031],{"separator":2030},[902,63924,63925],{"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,",[724,63927,63928,63929,63967],{},"a ",[883,63930,63932],{"className":63931},[886],[888,63933,63934],{"xmlns":890},[892,63935,63936,63964],{},[895,63937,63938,63940,63942,63944,63946,63948,63950,63952,63954,63956,63958,63960,63962],{},[898,63939,1718],{},[898,63941,1721],{},[1723,63943,1908],{"stretchy":1907},[1864,63945,2969],{},[1723,63947,1914],{"stretchy":1907},[1723,63949,1725],{},[898,63951,1728],{},[898,63953,1721],{},[1723,63955,1908],{"stretchy":1907},[1864,63957,2969],{},[1723,63959,1914],{"stretchy":1907},[1723,63961,1725],{},[1864,63963,36937],{},[902,63965,63966],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,63969,63971],{"id":63970},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,63973,63974,63975,3430],{},"Analogicky pro ",[883,63976,63978],{"className":63977},[886],[888,63979,63980],{"xmlns":890},[892,63981,63982,63990],{},[895,63983,63984,63986,63988],{},[898,63985,1718],{},[898,63987,41031],{},[898,63989,1721],{},[902,63991,55998],{"encoding":904},[883,63993,63995],{"className":63994},[886],[888,63996,63997],{"xmlns":890,"display":28759},[892,63998,63999,64050],{},[21447,64000,64001],{"width":28764},[21452,64002,64003,64005,64043,64045],{},[21455,64004],{"width":28769},[21455,64006,64007],{},[895,64008,64009,64011,64013,64015,64017,64023,64025,64027,64029,64031,64033,64039,64041],{},[898,64010,1718],{},[898,64012,41031],{},[898,64014,1721],{},[1723,64016,1908],{"stretchy":1907},[1931,64018,64019,64021],{},[898,64020,1904],{},[1864,64022,2256],{},[1723,64024,1914],{"stretchy":1907},[1723,64026,1725],{},[898,64028,1728],{},[898,64030,1721],{},[1723,64032,1908],{"stretchy":1907},[1931,64034,64035,64037],{},[898,64036,1904],{},[1864,64038,2256],{},[1723,64040,1914],{"stretchy":1907},[898,64042,1664],{"mathvariant":2124},[21455,64044],{"width":28769},[21455,64046,64047],{},[3018,64048,64049],{},"(3.11)",[902,64051,64052],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[4584,64054,64055],{},[724,64056,64057,62733,64059],{},[883,64058,57131],{},[38,64060,64061,64062,64079],{},"V bodě minima průměrných variabilních nákladů se ",[883,64063,64065],{"className":64064},[886],[888,64066,64067],{"xmlns":890},[892,64068,64069,64077],{},[895,64070,64071,64073,64075],{},[898,64072,1718],{},[898,64074,41031],{},[898,64076,1721],{},[902,64078,55998],{"encoding":904}," rovnají mezním nákladům.",[724,64081,64082,64083,64105,64106,1664],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,64084,64086],{"className":64085},[886],[888,64087,64088],{"xmlns":890},[892,64089,64090,64102],{},[895,64091,64092,64098,64100],{},[1931,64093,64094,64096],{},[898,64095,1904],{},[1864,64097,2256],{},[1723,64099,1725],{},[1864,64101,53889],{},[902,64103,64104],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,64107,64109],{"className":64108},[886],[888,64110,64111],{"xmlns":890},[892,64112,64113,64139],{},[895,64114,64115,64117,64119,64121,64123,64125,64127,64129,64131,64133,64135,64137],{},[898,64116,1718],{},[898,64118,41031],{},[898,64120,1721],{},[1723,64122,1908],{"stretchy":1907},[898,64124,1904],{},[1723,64126,1914],{"stretchy":1907},[1723,64128,1725],{},[898,64130,1728],{},[898,64132,1721],{},[1723,64134,1908],{"stretchy":1907},[898,64136,1904],{},[1723,64138,1914],{"stretchy":1907},[902,64140,64141],{"encoding":904},"AVC(Q) = MC(Q)",[115,64143,64145],{"id":64144},"zisk-a-body-zvratu","Zisk a body zvratu",[724,64147,64148,2628,64151,64167],{},[38,64149,64150],{},"Zisk",[883,64152,64154],{"className":64153},[886],[888,64155,64156],{"xmlns":890},[892,64157,64158,64164],{},[895,64159,64160,64162],{},[898,64161,1746],{},[898,64163,1749],{},[902,64165,64166],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,64169,64171],{"className":64170},[886],[888,64172,64173],{"xmlns":890,"display":28759},[892,64174,64175,64234],{},[21447,64176,64177],{"width":28764},[21452,64178,64179,64181,64227,64229],{},[21455,64180],{"width":28769},[21455,64182,64183],{},[895,64184,64185,64187,64189,64191,64193,64195,64197,64199,64201,64203,64205,64207,64209,64211,64213,64215,64217,64219,64221,64223,64225],{},[898,64186,1746],{},[898,64188,1749],{},[1723,64190,1725],{},[898,64192,1746],{},[898,64194,1749],{},[1723,64196,1908],{"stretchy":1907},[898,64198,1904],{},[1723,64200,1914],{"stretchy":1907},[1723,64202,1725],{},[898,64204,1754],{},[898,64206,1749],{},[1723,64208,1908],{"stretchy":1907},[898,64210,1904],{},[1723,64212,1914],{"stretchy":1907},[1723,64214,1759],{},[898,64216,1754],{},[898,64218,1721],{},[1723,64220,1908],{"stretchy":1907},[898,64222,1904],{},[1723,64224,1914],{"stretchy":1907},[898,64226,1664],{"mathvariant":2124},[21455,64228],{"width":28769},[21455,64230,64231],{},[3018,64232,64233],{},"(3.12)",[902,64235,64236],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,64238,64239,64240,1682,64255,44328,64270,64272,64273,64276,64277,64293,64294,64309,64310,64325,64326,1343,64339,64352,64353,1343,64371,64389,64390,1981,64393,64396,64397,1348,64419,8812,64441,64463,64464,8812,64494,64516],{},"Body rovnosti ",[883,64241,64243],{"className":64242},[886],[888,64244,64245],{"xmlns":890},[892,64246,64247,64253],{},[895,64248,64249,64251],{},[898,64250,1754],{},[898,64252,1749],{},[902,64254,4808],{"encoding":904},[883,64256,64258],{"className":64257},[886],[888,64259,64260],{"xmlns":890},[892,64261,64262,64268],{},[895,64263,64264,64266],{},[898,64265,1754],{},[898,64267,1721],{},[902,64269,3963],{"encoding":904},[38,64271,56414],{}," (též vyrovnání, ",[614,64274,64275],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,64278,64280],{"className":64279},[886],[888,64281,64282],{"xmlns":890},[892,64283,64284,64290],{},[895,64285,64286,64288],{},[898,64287,41031],{},[898,64289,1721],{},[902,64291,64292],{"encoding":904},"VC",") je ",[883,64295,64297],{"className":64296},[886],[888,64298,64299],{"xmlns":890},[892,64300,64301,64307],{},[895,64302,64303,64305],{},[898,64304,1754],{},[898,64306,1749],{},[902,64308,4808],{"encoding":904}," kvadratická a ",[883,64311,64313],{"className":64312},[886],[888,64314,64315],{"xmlns":890},[892,64316,64317,64323],{},[895,64318,64319,64321],{},[898,64320,1754],{},[898,64322,1721],{},[902,64324,3963],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,64327,64329],{"className":64328},[886],[888,64330,64331],{"xmlns":890},[892,64332,64333,64337],{},[895,64334,64335],{},[898,64336,1718],{},[902,64338,1718],{"encoding":904},[883,64340,64342],{"className":64341},[886],[888,64343,64344],{"xmlns":890},[892,64345,64346,64350],{},[895,64347,64348],{},[898,64349,23946],{},[902,64351,23946],{"encoding":904}," odpovídajících množstvím ",[883,64354,64356],{"className":64355},[886],[888,64357,64358],{"xmlns":890},[892,64359,64360,64368],{},[895,64361,64362],{},[1931,64363,64364,64366],{},[898,64365,1904],{},[898,64367,1718],{},[902,64369,64370],{"encoding":904},"Q_A",[883,64372,64374],{"className":64373},[886],[888,64375,64376],{"xmlns":890},[892,64377,64378,64386],{},[895,64379,64380],{},[1931,64381,64382,64384],{},[898,64383,1904],{},[898,64385,23946],{},[902,64387,64388],{"encoding":904},"Q_B"," — firma je na ",[38,64391,64392],{},"prahu rentability",[614,64394,64395],{},"break even","). Pro ",[883,64398,64400],{"className":64399},[886],[888,64401,64402],{"xmlns":890},[892,64403,64404,64416],{},[895,64405,64406,64408,64410],{},[898,64407,1904],{},[1723,64409,2287],{},[1931,64411,64412,64414],{},[898,64413,1904],{},[898,64415,1718],{},[902,64417,64418],{"encoding":904},"Q \u003C Q_A",[883,64420,64422],{"className":64421},[886],[888,64423,64424],{"xmlns":890},[892,64425,64426,64438],{},[895,64427,64428,64430,64432],{},[898,64429,1904],{},[1723,64431,2253],{},[1931,64433,64434,64436],{},[898,64435,1904],{},[898,64437,23946],{},[902,64439,64440],{"encoding":904},"Q > Q_B",[883,64442,64444],{"className":64443},[886],[888,64445,64446],{"xmlns":890},[892,64447,64448,64460],{},[895,64449,64450,64452,64454,64456,64458],{},[898,64451,1754],{},[898,64453,1721],{},[1723,64455,2253],{},[898,64457,1754],{},[898,64459,1749],{},[902,64461,64462],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,64465,64467],{"className":64466},[886],[888,64468,64469],{"xmlns":890},[892,64470,64471,64491],{},[895,64472,64473,64479,64481,64483,64485],{},[1931,64474,64475,64477],{},[898,64476,1904],{},[898,64478,1718],{},[1723,64480,2287],{},[898,64482,1904],{},[1723,64484,2287],{},[1931,64486,64487,64489],{},[898,64488,1904],{},[898,64490,23946],{},[902,64492,64493],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,64495,64497],{"className":64496},[886],[888,64498,64499],{"xmlns":890},[892,64500,64501,64513],{},[895,64502,64503,64505,64507,64509,64511],{},[898,64504,1754],{},[898,64506,1749],{},[1723,64508,2253],{},[898,64510,1754],{},[898,64512,1721],{},[902,64514,64515],{"encoding":904},"TR > TC"," (zisk).",[4584,64518,64519],{},[724,64520,64521,64523],{},[883,64522,4869],{}," 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.",[724,64525,64526,64527,64553],{},"Body zvratu jsou řešení rovnice ",[883,64528,64530],{"className":64529},[886],[888,64531,64532],{"xmlns":890},[892,64533,64534,64550],{},[895,64535,64536,64538,64540,64542,64544,64546,64548],{},[898,64537,1746],{},[898,64539,1749],{},[1723,64541,1908],{"stretchy":1907},[898,64543,1904],{},[1723,64545,1914],{"stretchy":1907},[1723,64547,1725],{},[1864,64549,2256],{},[902,64551,64552],{"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.",[724,64555,64556],{},[3285,64557],{"alt":64558,"className":64559,"src":64560},"imek-tr-tc-body-zvratu",[210,3289],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,64562,64563],{},[614,64564,64565,64566,64581,64582,64597,64598,1682,64611,44052,64624,64637,64638,1682,64655,64672,64673,64693,64694,1682,64709,7183,64724,64753],{},"Obrázek 3.11: Body zvratu — křivky ",[883,64567,64569],{"className":64568},[886],[888,64570,64571],{"xmlns":890},[892,64572,64573,64579],{},[895,64574,64575,64577],{},[898,64576,1754],{},[898,64578,1749],{},[902,64580,4808],{"encoding":904}," (obrácená parabola) a ",[883,64583,64585],{"className":64584},[886],[888,64586,64587],{"xmlns":890},[892,64588,64589,64595],{},[895,64590,64591,64593],{},[898,64592,1754],{},[898,64594,1721],{},[902,64596,3963],{"encoding":904}," (přímka) se protínají v bodech ",[883,64599,64601],{"className":64600},[886],[888,64602,64603],{"xmlns":890},[892,64604,64605,64609],{},[895,64606,64607],{},[898,64608,1718],{},[902,64610,1718],{"encoding":904},[883,64612,64614],{"className":64613},[886],[888,64615,64616],{"xmlns":890},[892,64617,64618,64622],{},[895,64619,64620],{},[898,64621,23946],{},[902,64623,23946],{"encoding":904},[883,64625,64627],{"className":64626},[886],[888,64628,64629],{"xmlns":890},[892,64630,64631,64635],{},[895,64632,64633],{},[898,64634,1904],{},[902,64636,1904],{"encoding":904}," v hodnotách ",[883,64639,64641],{"className":64640},[886],[888,64642,64643],{"xmlns":890},[892,64644,64645,64653],{},[895,64646,64647],{},[1931,64648,64649,64651],{},[898,64650,1904],{},[898,64652,1718],{},[902,64654,64370],{"encoding":904},[883,64656,64658],{"className":64657},[886],[888,64659,64660],{"xmlns":890},[892,64661,64662,64670],{},[895,64663,64664],{},[1931,64665,64666,64668],{},[898,64667,1904],{},[898,64669,23946],{},[902,64671,64388],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,64674,64676],{"className":64675},[886],[888,64677,64678],{"xmlns":890},[892,64679,64680,64690],{},[895,64681,64682],{},[1931,64683,64684,64686,64688],{},[898,64685,1904],{},[898,64687,56884],{},[1723,64689,56887],{},[902,64691,64692],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,64695,64697],{"className":64696},[886],[888,64698,64699],{"xmlns":890},[892,64700,64701,64707],{},[895,64702,64703,64705],{},[898,64704,1754],{},[898,64706,1749],{},[902,64708,4808],{"encoding":904},[883,64710,64712],{"className":64711},[886],[888,64713,64714],{"xmlns":890},[892,64715,64716,64722],{},[895,64717,64718,64720],{},[898,64719,1754],{},[898,64721,1721],{},[902,64723,3963],{"encoding":904},[883,64725,64727],{"className":64726},[886],[888,64728,64729],{"xmlns":890},[892,64730,64731,64751],{},[895,64732,64733,64739,64741,64743,64745],{},[1931,64734,64735,64737],{},[898,64736,1904],{},[898,64738,1718],{},[1723,64740,2287],{},[898,64742,1904],{},[1723,64744,2287],{},[1931,64746,64747,64749],{},[898,64748,1904],{},[898,64750,23946],{},[902,64752,64493],{"encoding":904}," vyznačuje zisk.",[38040,64755,64757],{"id":64756},"příklad-38","Příklad 3.8",[724,64759,64760,64762,64763,1343,64783,1343,64809,64835],{},[38,64761,56674],{}," Dáno ",[883,64764,64766],{"className":64765},[886],[888,64767,64768],{"xmlns":890},[892,64769,64770,64780],{},[895,64771,64772,64774,64776,64778],{},[898,64773,11136],{},[898,64775,1721],{},[1723,64777,1725],{},[1864,64779,3080],{},[902,64781,64782],{"encoding":904},"FC = 4",[883,64784,64786],{"className":64785},[886],[888,64787,64788],{"xmlns":890},[892,64789,64790,64806],{},[895,64791,64792,64794,64796,64798,64800],{},[898,64793,1754],{},[898,64795,41031],{},[898,64797,1721],{},[1723,64799,1725],{},[2057,64801,64802,64804],{},[898,64803,1904],{},[1864,64805,2331],{},[902,64807,64808],{"encoding":904},"TVC = Q^2",[883,64810,64812],{"className":64811},[886],[888,64813,64814],{"xmlns":890},[892,64815,64816,64832],{},[895,64817,64818,64820,64822,64824,64826,64828,64830],{},[898,64819,1746],{},[1723,64821,1725],{},[1723,64823,1759],{},[1864,64825,2331],{},[898,64827,1904],{},[1723,64829,2087],{},[1864,64831,4713],{},[902,64833,64834],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,64837,64838,64840],{},[38,64839,23463],{}," Celkové náklady a příjem:",[883,64842,64844],{"className":64843},[886],[888,64845,64846],{"xmlns":890,"display":28759},[892,64847,64848,64914],{},[895,64849,64850,64852,64854,64856,64858,64860,64866,64868,64870,64872,64874,64876,64878,64880,64882,64884,64886,64888,64890,64892,64894,64896,64898,64900,64906,64908,64910,64912],{},[898,64851,1754],{},[898,64853,1721],{},[1723,64855,1725],{},[1864,64857,3080],{},[1723,64859,2087],{},[2057,64861,64862,64864],{},[898,64863,1904],{},[1864,64865,2331],{},[1723,64867,2031],{"separator":2030},[6588,64869],{"width":6590},[898,64871,1754],{},[898,64873,1749],{},[1723,64875,1725],{},[898,64877,1904],{},[1723,64879,3897],{},[1723,64881,1908],{"stretchy":1907},[1723,64883,1759],{},[1864,64885,2331],{},[898,64887,1904],{},[1723,64889,2087],{},[1864,64891,4713],{},[1723,64893,1914],{"stretchy":1907},[1723,64895,1725],{},[1723,64897,1759],{},[1864,64899,2331],{},[2057,64901,64902,64904],{},[898,64903,1904],{},[1864,64905,2331],{},[1723,64907,2087],{},[1864,64909,4713],{},[898,64911,1904],{},[898,64913,1664],{"mathvariant":2124},[902,64915,64916],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,64918,64919],{},"Zisk dle (3.12):",[883,64921,64923],{"className":64922},[886],[888,64924,64925],{"xmlns":890,"display":28759},[892,64926,64927,65005],{},[895,64928,64929,64931,64933,64935,64937,64939,64941,64943,64945,64947,64949,64951,64953,64959,64961,64963,64965,64967,64969,64971,64973,64975,64981,64983,64985,64987,64989,64995,64997,64999,65001,65003],{},[898,64930,1746],{},[898,64932,1749],{},[1723,64934,1725],{},[898,64936,1754],{},[898,64938,1749],{},[1723,64940,1759],{},[898,64942,1754],{},[898,64944,1721],{},[1723,64946,1725],{},[1723,64948,1908],{"stretchy":1907},[1723,64950,1759],{},[1864,64952,2331],{},[2057,64954,64955,64957],{},[898,64956,1904],{},[1864,64958,2331],{},[1723,64960,2087],{},[1864,64962,4713],{},[898,64964,1904],{},[1723,64966,1914],{"stretchy":1907},[1723,64968,1759],{},[1723,64970,1908],{"stretchy":1907},[1864,64972,3080],{},[1723,64974,2087],{},[2057,64976,64977,64979],{},[898,64978,1904],{},[1864,64980,2331],{},[1723,64982,1914],{"stretchy":1907},[1723,64984,1725],{},[1723,64986,1759],{},[1864,64988,2909],{},[2057,64990,64991,64993],{},[898,64992,1904],{},[1864,64994,2331],{},[1723,64996,2087],{},[1864,64998,4713],{},[898,65000,1904],{},[1723,65002,1759],{},[1864,65004,60006],{},[902,65006,65007],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,65009,65010,65013,65014,18272,65050,3430],{},[38,65011,65012],{},"Body zvratu"," jsou kořeny rovnice ",[883,65015,65017],{"className":65016},[886],[888,65018,65019],{"xmlns":890},[892,65020,65021,65047],{},[895,65022,65023,65025,65027,65033,65035,65037,65039,65041,65043,65045],{},[1723,65024,1759],{},[1864,65026,2909],{},[2057,65028,65029,65031],{},[898,65030,1904],{},[1864,65032,2331],{},[1723,65034,2087],{},[1864,65036,4713],{},[898,65038,1904],{},[1723,65040,1759],{},[1864,65042,3080],{},[1723,65044,1725],{},[1864,65046,2256],{},[902,65048,65049],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,65051,65053],{"className":65052},[886],[888,65054,65055],{"xmlns":890},[892,65056,65057,65081],{},[895,65058,65059,65061,65067,65069,65071,65073,65075,65077,65079],{},[1864,65060,2909],{},[2057,65062,65063,65065],{},[898,65064,1904],{},[1864,65066,2331],{},[1723,65068,1759],{},[1864,65070,4713],{},[898,65072,1904],{},[1723,65074,2087],{},[1864,65076,3080],{},[1723,65078,1725],{},[1864,65080,2256],{},[902,65082,65083],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,65085,65087],{"className":65086},[886],[888,65088,65089],{"xmlns":890,"display":28759},[892,65090,65091,65148],{},[895,65092,65093,65105,65107,65130,65132,65146],{},[1931,65094,65095,65097],{},[898,65096,1904],{},[895,65098,65099,65101,65103],{},[1864,65100,1866],{},[1723,65102,2031],{"separator":2030},[1864,65104,2331],{},[1723,65106,1725],{},[3058,65108,65109,65128],{},[895,65110,65111,65113,65116],{},[1864,65112,4713],{},[1723,65114,65115],{},"±",[8827,65117,65118],{},[895,65119,65120,65123,65125],{},[1864,65121,65122],{},"81",[1723,65124,1759],{},[1864,65126,65127],{},"48",[1864,65129,2969],{},[1723,65131,1725],{},[3058,65133,65134,65144],{},[895,65135,65136,65138,65140],{},[1864,65137,4713],{},[1723,65139,65115],{},[8827,65141,65142],{},[1864,65143,9660],{},[1864,65145,2969],{},[1723,65147,2031],{"separator":2030},[902,65149,65150],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,65152,65153,65154,1682,65177,1664],{},"numericky ",[883,65155,65157],{"className":65156},[886],[888,65158,65159],{"xmlns":890},[892,65160,65161,65174],{},[895,65162,65163,65169,65171],{},[1931,65164,65165,65167],{},[898,65166,1904],{},[1864,65168,1866],{},[1723,65170,6610],{},[1864,65172,65173],{},"0,543",[902,65175,65176],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,65178,65180],{"className":65179},[886],[888,65181,65182],{"xmlns":890},[892,65183,65184,65197],{},[895,65185,65186,65192,65194],{},[1931,65187,65188,65190],{},[898,65189,1904],{},[1864,65191,2331],{},[1723,65193,6610],{},[1864,65195,65196],{},"2,457",[902,65198,65199],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,65201,65202,2628,65205,8262,65250,18272,65284,65302],{},[38,65203,65204],{},"Maximum zisku.",[883,65206,65208],{"className":65207},[886],[888,65209,65210],{"xmlns":890},[892,65211,65212,65247],{},[895,65213,65214,65216,65222,65224,65226,65228,65230,65232,65234,65236,65238,65240,65242,65244],{},[898,65215,1746],{},[2057,65217,65218,65220],{},[898,65219,1749],{},[1723,65221,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,65223,1725],{},[1723,65225,1759],{},[1864,65227,2969],{},[898,65229,1904],{},[1723,65231,2087],{},[1864,65233,4713],{},[1723,65235,1725],{},[1864,65237,2256],{},[1723,65239,4702],{},[898,65241,1904],{},[1723,65243,1725],{},[1864,65245,65246],{},"1,5",[902,65248,65249],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,65251,65253],{"className":65252},[886],[888,65254,65255],{"xmlns":890},[892,65256,65257,65281],{},[895,65258,65259,65261,65271,65273,65275,65277,65279],{},[898,65260,1746],{},[2057,65262,65263,65265],{},[898,65264,1749],{},[895,65266,65267,65269],{},[1723,65268,2229],{"mathvariant":2124},[1723,65270,2229],{"mathvariant":2124},[1723,65272,1725],{},[1723,65274,1759],{},[1864,65276,2969],{},[1723,65278,2287],{},[1864,65280,2256],{},[902,65282,65283],{"encoding":904},"PR'' = -6 \u003C 0",[883,65285,65287],{"className":65286},[886],[888,65288,65289],{"xmlns":890},[892,65290,65291,65299],{},[895,65292,65293,65295,65297],{},[898,65294,1904],{},[1723,65296,1725],{},[1864,65298,65246],{},[902,65300,65301],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,65304,65306],{"className":65305},[886],[888,65307,65308],{"xmlns":890,"display":28759},[892,65309,65310,65373],{},[895,65311,65312,65314,65316,65318,65320,65322,65324,65326,65328,65330,65332,65334,65340,65342,65344,65346,65348,65350,65352,65354,65356,65359,65361,65364,65366,65368,65370],{},[898,65313,1746],{},[898,65315,1749],{},[1723,65317,1908],{"stretchy":1907},[1864,65319,65246],{},[1723,65321,1914],{"stretchy":1907},[1723,65323,1725],{},[1723,65325,1759],{},[1864,65327,2909],{},[1723,65329,3897],{},[1723,65331,1908],{"stretchy":1907},[1864,65333,65246],{},[2057,65335,65336,65338],{},[1723,65337,1914],{"stretchy":1907},[1864,65339,2331],{},[1723,65341,2087],{},[1864,65343,4713],{},[1723,65345,3897],{},[1864,65347,65246],{},[1723,65349,1759],{},[1864,65351,3080],{},[1723,65353,1725],{},[1723,65355,1759],{},[1864,65357,65358],{},"6,75",[1723,65360,2087],{},[1864,65362,65363],{},"13,5",[1723,65365,1759],{},[1864,65367,3080],{},[1723,65369,1725],{},[1864,65371,65372],{},"2,75.",[902,65374,65375],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,65377,65378,65379,1343,65424,65477,65478,65496],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,65380,65382],{"className":65381},[886],[888,65383,65384],{"xmlns":890},[892,65385,65386,65421],{},[895,65387,65388,65390,65396,65398,65400,65402,65404,65406,65408,65410,65412,65414,65416,65418],{},[898,65389,1754],{},[2057,65391,65392,65394],{},[898,65393,1749],{},[1723,65395,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,65397,1725],{},[1723,65399,1759],{},[1864,65401,3080],{},[898,65403,1904],{},[1723,65405,2087],{},[1864,65407,4713],{},[1723,65409,1725],{},[1864,65411,2256],{},[1723,65413,4702],{},[898,65415,1904],{},[1723,65417,1725],{},[1864,65419,65420],{},"2,25",[902,65422,65423],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,65425,65427],{"className":65426},[886],[888,65428,65429],{"xmlns":890},[892,65430,65431,65474],{},[895,65432,65433,65435,65443,65445,65447,65449,65451,65453,65455,65461,65463,65465,65467,65469,65471],{},[898,65434,1754],{},[1931,65436,65437,65439,65441],{},[898,65438,1749],{},[898,65440,56884],{},[1723,65442,56887],{},[1723,65444,1725],{},[1723,65446,1759],{},[1864,65448,2331],{},[1723,65450,3897],{},[1723,65452,1908],{"stretchy":1907},[1864,65454,65420],{},[2057,65456,65457,65459],{},[1723,65458,1914],{"stretchy":1907},[1864,65460,2331],{},[1723,65462,2087],{},[1864,65464,4713],{},[1723,65466,3897],{},[1864,65468,65420],{},[1723,65470,1725],{},[1864,65472,65473],{},"10,125",[902,65475,65476],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,65479,65481],{"className":65480},[886],[888,65482,65483],{"xmlns":890},[892,65484,65485,65493],{},[895,65486,65487,65489,65491],{},[898,65488,1904],{},[1723,65490,1725],{},[1864,65492,65420],{},[902,65494,65495],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[4584,65498,65499],{},[724,65500,65501,65503,65504,1343,65526,65548,65549,1343,65566,65587,65588,65620,65621,65659,65660,3397,65678,65695,65696,1682,65724,65758,65759,8395,65797,1682,65821,1664],{},[883,65502,5124],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,65505,65507],{"className":65506},[886],[888,65508,65509],{"xmlns":890},[892,65510,65511,65523],{},[895,65512,65513,65519,65521],{},[1931,65514,65515,65517],{},[898,65516,1904],{},[1864,65518,1866],{},[1723,65520,1725],{},[1864,65522,5719],{},[902,65524,65525],{"encoding":904},"Q_1 = 0{,}5",[883,65527,65529],{"className":65528},[886],[888,65530,65531],{"xmlns":890},[892,65532,65533,65545],{},[895,65534,65535,65541,65543],{},[1931,65536,65537,65539],{},[898,65538,1904],{},[1864,65540,2331],{},[1723,65542,1725],{},[1864,65544,3080],{},[902,65546,65547],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,65550,65552],{"className":65551},[886],[888,65553,65554],{"xmlns":890},[892,65555,65556,65564],{},[895,65557,65558,65560,65562],{},[898,65559,1904],{},[1723,65561,1725],{},[1864,65563,65420],{},[902,65565,65495],{"encoding":904},[883,65567,65569],{"className":65568},[886],[888,65570,65571],{"xmlns":890},[892,65572,65573,65584],{},[895,65574,65575,65577,65579,65581],{},[898,65576,1746],{},[898,65578,1749],{},[1723,65580,1725],{},[1864,65582,65583],{},"6,125",[902,65585,65586],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,65589,65591],{"className":65590},[886],[888,65592,65593],{"xmlns":890},[892,65594,65595,65617],{},[895,65596,65597,65599,65605,65607,65609,65611,65613,65615],{},[898,65598,1746],{},[2057,65600,65601,65603],{},[898,65602,1749],{},[1723,65604,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,65606,1725],{},[1723,65608,1759],{},[1864,65610,3080],{},[898,65612,1904],{},[1723,65614,2087],{},[1864,65616,4713],{},[902,65618,65619],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,65622,65624],{"className":65623},[886],[888,65625,65626],{"xmlns":890},[892,65627,65628,65656],{},[895,65629,65630,65632,65634,65636,65638,65640,65646,65648,65650,65652,65654],{},[898,65631,1746],{},[898,65633,1749],{},[1723,65635,1725],{},[1723,65637,1759],{},[1864,65639,2331],{},[2057,65641,65642,65644],{},[898,65643,1904],{},[1864,65645,2331],{},[1723,65647,2087],{},[1864,65649,4713],{},[898,65651,1904],{},[1723,65653,1759],{},[1864,65655,3080],{},[902,65657,65658],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,65661,65663],{"className":65662},[886],[888,65664,65665],{"xmlns":890},[892,65666,65667,65675],{},[895,65668,65669],{},[2057,65670,65671,65673],{},[898,65672,1904],{},[1864,65674,2331],{},[902,65676,65677],{"encoding":904},"Q^2",[883,65679,65681],{"className":65680},[886],[888,65682,65683],{"xmlns":890},[892,65684,65685,65693],{},[895,65686,65687,65689,65691],{},[898,65688,1754],{},[898,65690,41031],{},[898,65692,1721],{},[902,65694,56196],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,65697,65699],{"className":65698},[886],[888,65700,65701],{"xmlns":890},[892,65702,65703,65721],{},[895,65704,65705,65707,65709,65711,65713,65715],{},[898,65706,1754],{},[898,65708,1721],{},[1723,65710,1725],{},[1864,65712,3080],{},[1723,65714,2087],{},[2057,65716,65717,65719],{},[898,65718,1904],{},[1864,65720,2331],{},[902,65722,65723],{"encoding":904},"TC = 4 + Q^2",[883,65725,65727],{"className":65726},[886],[888,65728,65729],{"xmlns":890},[892,65730,65731,65755],{},[895,65732,65733,65735,65737,65739,65741,65743,65749,65751,65753],{},[898,65734,1754],{},[898,65736,1749],{},[1723,65738,1725],{},[1723,65740,1759],{},[1864,65742,2331],{},[2057,65744,65745,65747],{},[898,65746,1904],{},[1864,65748,2331],{},[1723,65750,2087],{},[1864,65752,4713],{},[898,65754,1904],{},[902,65756,65757],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,65760,65762],{"className":65761},[886],[888,65763,65764],{"xmlns":890},[892,65765,65766,65794],{},[895,65767,65768,65770,65772,65774,65776,65778,65784,65786,65788,65790,65792],{},[898,65769,1746],{},[898,65771,1749],{},[1723,65773,1725],{},[1723,65775,1759],{},[1864,65777,2909],{},[2057,65779,65780,65782],{},[898,65781,1904],{},[1864,65783,2331],{},[1723,65785,2087],{},[1864,65787,4713],{},[898,65789,1904],{},[1723,65791,1759],{},[1864,65793,3080],{},[902,65795,65796],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,65798,65800],{"className":65799},[886],[888,65801,65802],{"xmlns":890},[892,65803,65804,65818],{},[895,65805,65806,65814,65816],{},[1931,65807,65808,65810,65812],{},[898,65809,1904],{},[898,65811,56884],{},[1723,65813,56887],{},[1723,65815,1725],{},[1864,65817,65246],{},[902,65819,65820],{"encoding":904},"Q_{\\max} = 1{,}5",[883,65822,65824],{"className":65823},[886],[888,65825,65826],{"xmlns":890},[892,65827,65828,65845],{},[895,65829,65830,65832,65840,65842],{},[898,65831,1746],{},[1931,65833,65834,65836,65838],{},[898,65835,1749],{},[898,65837,56884],{},[1723,65839,56887],{},[1723,65841,1725],{},[1864,65843,65844],{},"2,75",[902,65846,65847],{"encoding":904},"PR_{\\max} = 2{,}75",[724,65849,65850],{},[614,65851,65852,65853,65880,65881,65914,65915,1343,65938,1664],{},"Obrázek 3.12: Graf ",[883,65854,65856],{"className":65855},[886],[888,65857,65858],{"xmlns":890},[892,65859,65860,65878],{},[895,65861,65862,65864,65866,65868,65870,65872],{},[898,65863,1754],{},[898,65865,1721],{},[1723,65867,1725],{},[1864,65869,3080],{},[1723,65871,2087],{},[2057,65873,65874,65876],{},[898,65875,1904],{},[1864,65877,2331],{},[902,65879,65723],{"encoding":904}," (parabola) a ",[883,65882,65884],{"className":65883},[886],[888,65885,65886],{"xmlns":890},[892,65887,65888,65912],{},[895,65889,65890,65892,65894,65896,65898,65900,65906,65908,65910],{},[898,65891,1754],{},[898,65893,1749],{},[1723,65895,1725],{},[1723,65897,1759],{},[1864,65899,2331],{},[2057,65901,65902,65904],{},[898,65903,1904],{},[1864,65905,2331],{},[1723,65907,2087],{},[1864,65909,4713],{},[898,65911,1904],{},[902,65913,65757],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,65916,65918],{"className":65917},[886],[888,65919,65920],{"xmlns":890},[892,65921,65922,65935],{},[895,65923,65924,65930,65932],{},[1931,65925,65926,65928],{},[898,65927,1904],{},[1864,65929,1866],{},[1723,65931,6610],{},[1864,65933,65934],{},"0,54",[902,65936,65937],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,65939,65941],{"className":65940},[886],[888,65942,65943],{"xmlns":890},[892,65944,65945,65958],{},[895,65946,65947,65953,65955],{},[1931,65948,65949,65951],{},[898,65950,1904],{},[1864,65952,2331],{},[1723,65954,6610],{},[1864,65956,65957],{},"2,46",[902,65959,65960],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,65962,65963],{},[614,65964,65965,65966,59194,66003,66020,66021,1343,66042,1664],{},"Obrázek 3.13: Graf zisku ",[883,65967,65969],{"className":65968},[886],[888,65970,65971],{"xmlns":890},[892,65972,65973,66001],{},[895,65974,65975,65977,65979,65981,65983,65985,65991,65993,65995,65997,65999],{},[898,65976,1746],{},[898,65978,1749],{},[1723,65980,1725],{},[1723,65982,1759],{},[1864,65984,2909],{},[2057,65986,65987,65989],{},[898,65988,1904],{},[1864,65990,2331],{},[1723,65992,2087],{},[1864,65994,4713],{},[898,65996,1904],{},[1723,65998,1759],{},[1864,66000,3080],{},[902,66002,65796],{"encoding":904},[883,66004,66006],{"className":66005},[886],[888,66007,66008],{"xmlns":890},[892,66009,66010,66018],{},[895,66011,66012,66014,66016],{},[898,66013,1904],{},[1723,66015,1725],{},[1864,66017,65246],{},[902,66019,65301],{"encoding":904}," a nulami ",[883,66022,66024],{"className":66023},[886],[888,66025,66026],{"xmlns":890},[892,66027,66028,66040],{},[895,66029,66030,66036,66038],{},[1931,66031,66032,66034],{},[898,66033,1904],{},[1864,66035,1866],{},[1723,66037,6610],{},[1864,66039,65934],{},[902,66041,65937],{"encoding":904},[883,66043,66045],{"className":66044},[886],[888,66046,66047],{"xmlns":890},[892,66048,66049,66061],{},[895,66050,66051,66057,66059],{},[1931,66052,66053,66055],{},[898,66054,1904],{},[1864,66056,2331],{},[1723,66058,6610],{},[1864,66060,65957],{},[902,66062,65960],{"encoding":904},[115,66064,66066],{"id":66065},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,66068,66069],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,66071,66072],{},[3285,66073],{"alt":66074,"className":66075,"src":66076},"imek-max-zisku-dva-pohledy",[210,3289],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,66078,17108],{"id":66079},"princip-1",[724,66081,66082,66083,3350,66098,66115],{},"Má-li zisk ",[883,66084,66086],{"className":66085},[886],[888,66087,66088],{"xmlns":890},[892,66089,66090,66096],{},[895,66091,66092,66094],{},[898,66093,1746],{},[898,66095,1749],{},[902,66097,64166],{"encoding":904},[883,66099,66101],{"className":66100},[886],[888,66102,66103],{"xmlns":890},[892,66104,66105,66113],{},[895,66106,66107],{},[1931,66108,66109,66111],{},[898,66110,1904],{},[1864,66112,2256],{},[902,66114,39000],{"encoding":904}," maximum, pak platí",[883,66117,66119],{"className":66118},[886],[888,66120,66121],{"xmlns":890,"display":28759},[892,66122,66123,66172],{},[21447,66124,66125],{"width":28764},[21452,66126,66127,66129,66165,66167],{},[21455,66128],{"width":28769},[21455,66130,66131],{},[895,66132,66133,66135,66137,66139,66145,66147,66149,66151,66153,66155,66161,66163],{},[898,66134,1728],{},[898,66136,1749],{},[1723,66138,1908],{"stretchy":1907},[1931,66140,66141,66143],{},[898,66142,1904],{},[1864,66144,2256],{},[1723,66146,1914],{"stretchy":1907},[1723,66148,1725],{},[898,66150,1728],{},[898,66152,1721],{},[1723,66154,1908],{"stretchy":1907},[1931,66156,66157,66159],{},[898,66158,1904],{},[1864,66160,2256],{},[1723,66162,1914],{"stretchy":1907},[898,66164,1664],{"mathvariant":2124},[21455,66166],{"width":28769},[21455,66168,66169],{},[3018,66170,66171],{},"(3.13)",[902,66173,66174],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[4584,66176,66177],{},[724,66178,66179,62733,66181],{},[883,66180,57131],{},[38,66182,66183],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,66185,66186,66189,66190,8812,66217,18272,66291,1664],{},[38,66187,66188],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,66191,66193],{"className":66192},[886],[888,66194,66195],{"xmlns":890},[892,66196,66197,66215],{},[895,66198,66199,66201,66203,66205,66207,66209,66211,66213],{},[898,66200,1746],{},[898,66202,1749],{},[1723,66204,1725],{},[898,66206,1754],{},[898,66208,1749],{},[1723,66210,1759],{},[898,66212,1754],{},[898,66214,1721],{},[902,66216,1766],{"encoding":904},[883,66218,66220],{"className":66219},[886],[888,66221,66222],{"xmlns":890},[892,66223,66224,66288],{},[895,66225,66226,66228,66234,66236,66242,66244,66246,66248,66254,66256,66262,66264,66266,66268,66274,66276,66282,66284,66286],{},[898,66227,1746],{},[2057,66229,66230,66232],{},[898,66231,1749],{},[1723,66233,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,66235,1908],{"stretchy":1907},[1931,66237,66238,66240],{},[898,66239,1904],{},[1864,66241,2256],{},[1723,66243,1914],{"stretchy":1907},[1723,66245,1725],{},[898,66247,1754],{},[2057,66249,66250,66252],{},[898,66251,1749],{},[1723,66253,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,66255,1908],{"stretchy":1907},[1931,66257,66258,66260],{},[898,66259,1904],{},[1864,66261,2256],{},[1723,66263,1914],{"stretchy":1907},[1723,66265,1759],{},[898,66267,1754],{},[2057,66269,66270,66272],{},[898,66271,1721],{},[1723,66273,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,66275,1908],{"stretchy":1907},[1931,66277,66278,66280],{},[898,66279,1904],{},[1864,66281,2256],{},[1723,66283,1914],{"stretchy":1907},[1723,66285,1725],{},[1864,66287,2256],{},[902,66289,66290],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,66292,66294],{"className":66293},[886],[888,66295,66296],{"xmlns":890},[892,66297,66298,66330],{},[895,66299,66300,66302,66304,66306,66312,66314,66316,66318,66320,66322,66328],{},[898,66301,1728],{},[898,66303,1749],{},[1723,66305,1908],{"stretchy":1907},[1931,66307,66308,66310],{},[898,66309,1904],{},[1864,66311,2256],{},[1723,66313,1914],{"stretchy":1907},[1723,66315,1725],{},[898,66317,1728],{},[898,66319,1721],{},[1723,66321,1908],{"stretchy":1907},[1931,66323,66324,66326],{},[898,66325,1904],{},[1864,66327,2256],{},[1723,66329,1914],{"stretchy":1907},[902,66331,66332],{"encoding":904},"MR(Q_0) = MC(Q_0)",[4584,66334,66335,66340],{},[724,66336,66337,66339],{},[883,66338,5283],{}," Postup — jak najít maximum zisku",[152,66341,66342,66406,66461,66498,66526],{},[123,66343,66344,66345,1682,66360,66375,66376,4634],{},"Sestavte ",[883,66346,66348],{"className":66347},[886],[888,66349,66350],{"xmlns":890},[892,66351,66352,66358],{},[895,66353,66354,66356],{},[898,66355,1754],{},[898,66357,1749],{},[902,66359,4808],{"encoding":904},[883,66361,66363],{"className":66362},[886],[888,66364,66365],{"xmlns":890},[892,66366,66367,66373],{},[895,66368,66369,66371],{},[898,66370,1754],{},[898,66372,1721],{},[902,66374,3963],{"encoding":904}," ze zadání (typicky ",[883,66377,66379],{"className":66378},[886],[888,66380,66381],{"xmlns":890},[892,66382,66383,66403],{},[895,66384,66385,66387,66389,66391,66393,66395,66397,66399,66401],{},[898,66386,1754],{},[898,66388,1749],{},[1723,66390,1725],{},[898,66392,1746],{},[1723,66394,1908],{"stretchy":1907},[898,66396,1904],{},[1723,66398,1914],{"stretchy":1907},[1723,66400,3897],{},[898,66402,1904],{},[902,66404,66405],{"encoding":904},"TR = P(Q) \\cdot Q",[123,66407,66408,66409,1682,66435,1664],{},"Vypočtěte ",[883,66410,66412],{"className":66411},[886],[888,66413,66414],{"xmlns":890},[892,66415,66416,66432],{},[895,66417,66418,66420,66422,66424,66426],{},[898,66419,1728],{},[898,66421,1749],{},[1723,66423,1725],{},[898,66425,1754],{},[2057,66427,66428,66430],{},[898,66429,1749],{},[1723,66431,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,66433,66434],{"encoding":904},"MR = TR'",[883,66436,66438],{"className":66437},[886],[888,66439,66440],{"xmlns":890},[892,66441,66442,66458],{},[895,66443,66444,66446,66448,66450,66452],{},[898,66445,1728],{},[898,66447,1721],{},[1723,66449,1725],{},[898,66451,1754],{},[2057,66453,66454,66456],{},[898,66455,1721],{},[1723,66457,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,66459,66460],{"encoding":904},"MC = TC'",[123,66462,66463,66464,1664],{},"Řešte rovnici ",[883,66465,66467],{"className":66466},[886],[888,66468,66469],{"xmlns":890},[892,66470,66471,66495],{},[895,66472,66473,66475,66477,66479,66481,66483,66485,66487,66489,66491,66493],{},[898,66474,1728],{},[898,66476,1749],{},[1723,66478,1908],{"stretchy":1907},[898,66480,1904],{},[1723,66482,1914],{"stretchy":1907},[1723,66484,1725],{},[898,66486,1728],{},[898,66488,1721],{},[1723,66490,1908],{"stretchy":1907},[898,66492,1904],{},[1723,66494,1914],{"stretchy":1907},[902,66496,66497],{"encoding":904},"MR(Q) = MC(Q)",[123,66499,66500,66501,66525],{},"Ověřte druhou derivaci ",[883,66502,66504],{"className":66503},[886],[888,66505,66506],{"xmlns":890},[892,66507,66508,66522],{},[895,66509,66510,66512],{},[898,66511,1746],{},[2057,66513,66514,66516],{},[898,66515,1749],{},[895,66517,66518,66520],{},[1723,66519,2229],{"mathvariant":2124},[1723,66521,2229],{"mathvariant":2124},[902,66523,66524],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,66527,66528,66529,66556],{},"Dosaďte do ",[883,66530,66532],{"className":66531},[886],[888,66533,66534],{"xmlns":890},[892,66535,66536,66554],{},[895,66537,66538,66540,66542,66544,66546,66548,66550,66552],{},[898,66539,1746],{},[898,66541,1749],{},[1723,66543,1725],{},[898,66545,1754],{},[898,66547,1749],{},[1723,66549,1759],{},[898,66551,1754],{},[898,66553,1721],{},[902,66555,1766],{"encoding":904}," pro hodnotu maxima.",[38040,66558,66560],{"id":66559},"příklad-39","Příklad 3.9",[724,66562,66563,56675,66565,1682,66587,66623],{},[38,66564,56674],{},[883,66566,66568],{"className":66567},[886],[888,66569,66570],{"xmlns":890},[892,66571,66572,66584],{},[895,66573,66574,66576,66578,66580,66582],{},[898,66575,1746],{},[1723,66577,1725],{},[1864,66579,38711],{},[1723,66581,1759],{},[898,66583,1904],{},[902,66585,66586],{"encoding":904},"P = 30 - Q",[883,66588,66590],{"className":66589},[886],[888,66591,66592],{"xmlns":890},[892,66593,66594,66620],{},[895,66595,66596,66598,66600,66602,66604,66610,66612,66614,66616,66618],{},[898,66597,1754],{},[898,66599,1721],{},[1723,66601,1725],{},[1864,66603,5719],{},[2057,66605,66606,66608],{},[898,66607,1904],{},[1864,66609,2331],{},[1723,66611,2087],{},[1864,66613,2969],{},[898,66615,1904],{},[1723,66617,2087],{},[1864,66619,24894],{},[902,66621,66622],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,66625,66626,2628,66628,1343,66658,66696,66697,16493,66741,66775,66776,1664],{},[38,66627,23463],{},[883,66629,66631],{"className":66630},[886],[888,66632,66633],{"xmlns":890},[892,66634,66635,66655],{},[895,66636,66637,66639,66641,66643,66645,66647,66649],{},[898,66638,1754],{},[898,66640,1749],{},[1723,66642,1725],{},[1864,66644,38711],{},[898,66646,1904],{},[1723,66648,1759],{},[2057,66650,66651,66653],{},[898,66652,1904],{},[1864,66654,2331],{},[902,66656,66657],{"encoding":904},"TR = 30Q - Q^2",[883,66659,66661],{"className":66660},[886],[888,66662,66663],{"xmlns":890},[892,66664,66665,66693],{},[895,66666,66667,66669,66671,66673,66675,66677,66683,66685,66687,66689,66691],{},[898,66668,1746],{},[898,66670,1749],{},[1723,66672,1725],{},[1723,66674,1759],{},[1864,66676,65246],{},[2057,66678,66679,66681],{},[898,66680,1904],{},[1864,66682,2331],{},[1723,66684,2087],{},[1864,66686,42492],{},[898,66688,1904],{},[1723,66690,1759],{},[1864,66692,24894],{},[902,66694,66695],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,66698,66700],{"className":66699},[886],[888,66701,66702],{"xmlns":890},[892,66703,66704,66738],{},[895,66705,66706,66708,66714,66716,66718,66720,66722,66724,66726,66728,66730,66732,66734,66736],{},[898,66707,1746],{},[2057,66709,66710,66712],{},[898,66711,1749],{},[1723,66713,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,66715,1725],{},[1723,66717,1759],{},[1864,66719,2909],{},[898,66721,1904],{},[1723,66723,2087],{},[1864,66725,42492],{},[1723,66727,1725],{},[1864,66729,2256],{},[1723,66731,4702],{},[898,66733,1904],{},[1723,66735,1725],{},[1864,66737,6295],{},[902,66739,66740],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,66742,66744],{"className":66743},[886],[888,66745,66746],{"xmlns":890},[892,66747,66748,66772],{},[895,66749,66750,66752,66762,66764,66766,66768,66770],{},[898,66751,1746],{},[2057,66753,66754,66756],{},[898,66755,1749],{},[895,66757,66758,66760],{},[1723,66759,2229],{"mathvariant":2124},[1723,66761,2229],{"mathvariant":2124},[1723,66763,1725],{},[1723,66765,1759],{},[1864,66767,2909],{},[1723,66769,2287],{},[1864,66771,2256],{},[902,66773,66774],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,66777,66779],{"className":66778},[886],[888,66780,66781],{"xmlns":890},[892,66782,66783,66800],{},[895,66784,66785,66787,66789,66791,66793,66795,66797],{},[898,66786,1746],{},[898,66788,1749],{},[1723,66790,1908],{"stretchy":1907},[1864,66792,6295],{},[1723,66794,1914],{"stretchy":1907},[1723,66796,1725],{},[1864,66798,66799],{},"89",[902,66801,66802],{"encoding":904},"PR(8) = 89",[724,66804,66805,66806,1343,66832,16493,66856,66894],{},"Ověření principu: ",[883,66807,66809],{"className":66808},[886],[888,66810,66811],{"xmlns":890},[892,66812,66813,66829],{},[895,66814,66815,66817,66819,66821,66823,66825,66827],{},[898,66816,1728],{},[898,66818,1749],{},[1723,66820,1725],{},[1864,66822,38711],{},[1723,66824,1759],{},[1864,66826,2331],{},[898,66828,1904],{},[902,66830,66831],{"encoding":904},"MR = 30 - 2Q",[883,66833,66835],{"className":66834},[886],[888,66836,66837],{"xmlns":890},[892,66838,66839,66853],{},[895,66840,66841,66843,66845,66847,66849,66851],{},[898,66842,1728],{},[898,66844,1721],{},[1723,66846,1725],{},[898,66848,1904],{},[1723,66850,2087],{},[1864,66852,2969],{},[902,66854,66855],{"encoding":904},"MC = Q + 6",[883,66857,66859],{"className":66858},[886],[888,66860,66861],{"xmlns":890},[892,66862,66863,66891],{},[895,66864,66865,66867,66869,66871,66873,66875,66877,66879,66881,66883,66885,66887,66889],{},[898,66866,1728],{},[898,66868,1749],{},[1723,66870,1908],{"stretchy":1907},[1864,66872,6295],{},[1723,66874,1914],{"stretchy":1907},[1723,66876,1725],{},[1864,66878,23639],{},[1723,66880,1725],{},[898,66882,1728],{},[898,66884,1721],{},[1723,66886,1908],{"stretchy":1907},[1864,66888,6295],{},[1723,66890,1914],{"stretchy":1907},[902,66892,66893],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,66896,66897,66898,66931,66932,66949],{},"V řadě případů — má-li rovnice ",[883,66899,66901],{"className":66900},[886],[888,66902,66903],{"xmlns":890},[892,66904,66905,66929],{},[895,66906,66907,66909,66911,66913,66915,66917,66919,66921,66923,66925,66927],{},[898,66908,1728],{},[898,66910,1749],{},[1723,66912,1908],{"stretchy":1907},[898,66914,1904],{},[1723,66916,1914],{"stretchy":1907},[1723,66918,1725],{},[898,66920,1728],{},[898,66922,1721],{},[1723,66924,1908],{"stretchy":1907},[898,66926,1904],{},[1723,66928,1914],{"stretchy":1907},[902,66930,66497],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,66933,66935],{"className":66934},[886],[888,66936,66937],{"xmlns":890},[892,66938,66939,66947],{},[895,66940,66941],{},[1931,66942,66943,66945],{},[898,66944,1904],{},[1864,66946,2256],{},[902,66948,39000],{"encoding":904}," — není třeba provádět test druhé derivace.",[38040,66951,66953],{"id":66952},"příklad-310","Příklad 3.10",[724,66955,66956,66958,66959,66963,66964,66977,66978,67009],{},[38,66957,56674],{}," Firma vyrábí minipočítače v ",[207,66960,66962],{"className":66961,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,66965,66967],{"className":66966},[886],[888,66968,66969],{"xmlns":890},[892,66970,66971,66975],{},[895,66972,66973],{},[1864,66974,15892],{},[902,66976,15892],{"encoding":904}," EUR\u002Fks. ",[883,66979,66981],{"className":66980},[886],[888,66982,66983],{"xmlns":890},[892,66984,66985,67006],{},[895,66986,66987,66989,66991,66993,66995,66997,67000],{},[898,66988,1754],{},[898,66990,1721],{},[1723,66992,1725],{},[1864,66994,3840],{},[1723,66996,2087],{},[1864,66998,66999],{},"28",[2057,67001,67002,67004],{},[898,67003,1904],{},[1864,67005,2331],{},[902,67007,67008],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,67011,67012,2628,67014,1343,67036,1343,67056,67079],{},[38,67013,23463],{},[883,67015,67017],{"className":67016},[886],[888,67018,67019],{"xmlns":890},[892,67020,67021,67033],{},[895,67022,67023,67025,67027,67029,67031],{},[898,67024,1754],{},[898,67026,1749],{},[1723,67028,1725],{},[1864,67030,15892],{},[898,67032,1904],{},[902,67034,67035],{"encoding":904},"TR = 900Q",[883,67037,67039],{"className":67038},[886],[888,67040,67041],{"xmlns":890},[892,67042,67043,67053],{},[895,67044,67045,67047,67049,67051],{},[898,67046,1728],{},[898,67048,1749],{},[1723,67050,1725],{},[1864,67052,15892],{},[902,67054,67055],{"encoding":904},"MR = 900",[883,67057,67059],{"className":67058},[886],[888,67060,67061],{"xmlns":890},[892,67062,67063,67076],{},[895,67064,67065,67067,67069,67071,67074],{},[898,67066,1728],{},[898,67068,1721],{},[1723,67070,1725],{},[1864,67072,67073],{},"56",[898,67075,1904],{},[902,67077,67078],{"encoding":904},"MC = 56Q",". Z principu:",[883,67081,67083],{"className":67082},[886],[888,67084,67085],{"xmlns":890,"display":28759},[892,67086,67087,67129],{},[895,67088,67089,67091,67093,67095,67097,67099,67101,67103,67105,67107,67115,67117,67120,67122,67124,67126],{},[1864,67090,15892],{},[1723,67092,1725],{},[1864,67094,67073],{},[898,67096,1904],{},[3018,67098,4699],{},[1723,67100,4702],{},[3018,67102,4699],{},[898,67104,1904],{},[1723,67106,1725],{},[3055,67108,67109],{"scriptlevel":2256,"displaystyle":1907},[3058,67110,67111,67113],{},[1864,67112,15892],{},[1864,67114,67073],{},[1723,67116,6610],{},[1864,67118,67119],{},"16,07",[3018,67121,4699],{},[1723,67123,3456],{},[3018,67125,4699],{},[1864,67127,67128],{},"16.",[902,67130,67131],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,67133,67134,67135,3430],{},"Zisk při ",[883,67136,67138],{"className":67137},[886],[888,67139,67140],{"xmlns":890},[892,67141,67142,67150],{},[895,67143,67144,67146,67148],{},[898,67145,1904],{},[1723,67147,1725],{},[1864,67149,42554],{},[902,67151,67152],{"encoding":904},"Q = 16",[883,67154,67156],{"className":67155},[886],[888,67157,67158],{"xmlns":890,"display":28759},[892,67159,67160,67231],{},[895,67161,67162,67164,67166,67168,67170,67172,67174,67176,67178,67180,67182,67184,67186,67188,67190,67192,67198,67200,67202,67204,67206,67208,67210,67212,67214,67217,67219,67221,67223,67226,67229],{},[898,67163,1746],{},[898,67165,1749],{},[1723,67167,1908],{"stretchy":1907},[1864,67169,42554],{},[1723,67171,1914],{"stretchy":1907},[1723,67173,1725],{},[1864,67175,15892],{},[1723,67177,3897],{},[1864,67179,42554],{},[1723,67181,1759],{},[1723,67183,1908],{"stretchy":1907},[1864,67185,3840],{},[1723,67187,2087],{},[1864,67189,66999],{},[1723,67191,3897],{},[2057,67193,67194,67196],{},[1864,67195,42554],{},[1864,67197,2331],{},[1723,67199,1914],{"stretchy":1907},[1723,67201,1725],{},[1864,67203,23639],{},[3018,67205,3707],{},[1864,67207,20835],{},[1723,67209,1759],{},[1864,67211,24894],{},[3018,67213,3707],{},[1864,67215,67216],{},"218",[1723,67218,1725],{},[1864,67220,24894],{},[3018,67222,3707],{},[1864,67224,67225],{},"182",[3018,67227,67228],{}," EUR",[898,67230,1664],{"mathvariant":2124},[902,67232,67233],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,67235,67236],{},"Pro srovnání při původních 30 ks:",[883,67238,67240],{"className":67239},[886],[888,67241,67242],{"xmlns":890,"display":28759},[892,67243,67244,67309],{},[895,67245,67246,67248,67250,67252,67254,67256,67258,67260,67262,67264,67266,67268,67270,67272,67274,67276,67278,67280,67282,67285,67287,67289,67291,67293,67295,67297,67299,67301,67303,67305,67307],{},[898,67247,1746],{},[898,67249,1749],{},[1723,67251,1908],{"stretchy":1907},[1864,67253,38711],{},[1723,67255,1914],{"stretchy":1907},[1723,67257,1725],{},[1864,67259,15892],{},[1723,67261,3897],{},[1864,67263,38711],{},[1723,67265,1759],{},[1723,67267,1908],{"stretchy":1907},[1864,67269,3840],{},[1723,67271,2087],{},[1864,67273,66999],{},[1723,67275,3897],{},[1864,67277,15892],{},[1723,67279,1914],{"stretchy":1907},[1723,67281,1725],{},[1864,67283,67284],{},"27",[3018,67286,3707],{},[1864,67288,59769],{},[1723,67290,1759],{},[1864,67292,5714],{},[3018,67294,3707],{},[1864,67296,31436],{},[1723,67298,1725],{},[1864,67300,1866],{},[3018,67302,3707],{},[1864,67304,24436],{},[3018,67306,67228],{},[898,67308,1664],{"mathvariant":2124},[902,67310,67311],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,67313,67314,67317,67318,67336,67337,67355],{},[38,67315,67316],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,67319,67321],{"className":67320},[886],[888,67322,67323],{"xmlns":890},[892,67324,67325,67333],{},[895,67326,67327,67329,67331],{},[1864,67328,24894],{},[3018,67330,3707],{},[1864,67332,67225],{},[902,67334,67335],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,67338,67340],{"className":67339},[886],[888,67341,67342],{"xmlns":890},[892,67343,67344,67352],{},[895,67345,67346,67348,67350],{},[1864,67347,1866],{},[3018,67349,3707],{},[1864,67351,24436],{},[902,67353,67354],{"encoding":904},"1\\,750"," EUR.",[198,67357,67359],{"id":67358},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,67361,67362,67363,63257,67376,67400],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,67364,67366],{"className":67365},[886],[888,67367,67368],{"xmlns":890},[892,67369,67370,67374],{},[895,67371,67372],{},[898,67373,1746],{},[902,67375,1746],{"encoding":904},[883,67377,67379],{"className":67378},[886],[888,67380,67381],{"xmlns":890},[892,67382,67383,67397],{},[895,67384,67385,67387,67389,67391,67393,67395],{},[898,67386,1754],{},[898,67388,1749],{},[1723,67390,1725],{},[898,67392,1746],{},[1723,67394,3897],{},[898,67396,1904],{},[902,67398,67399],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,67402,67404],{"className":67403},[886],[888,67405,67406],{"xmlns":890,"display":28759},[892,67407,67408,67441],{},[21447,67409,67410],{"width":28764},[21452,67411,67412,67414,67434,67436],{},[21455,67413],{"width":28769},[21455,67415,67416],{},[895,67417,67418,67420,67422,67424,67426,67428,67430,67432],{},[898,67419,1746],{},[1723,67421,1725],{},[898,67423,1728],{},[898,67425,1721],{},[1723,67427,1908],{"stretchy":1907},[898,67429,1904],{},[1723,67431,1914],{"stretchy":1907},[898,67433,1664],{"mathvariant":2124},[21455,67435],{"width":28769},[21455,67437,67438],{},[3018,67439,67440],{},"(3.14)",[902,67442,67443],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,67445,67446,67447,1664],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,67448,67450],{"className":67449},[886],[888,67451,67452],{"xmlns":890},[892,67453,67454,67468],{},[895,67455,67456,67458],{},[898,67457,1746],{},[2057,67459,67460,67462],{},[898,67461,1749],{},[895,67463,67464,67466],{},[1723,67465,2229],{"mathvariant":2124},[1723,67467,2229],{"mathvariant":2124},[902,67469,66524],{"encoding":904},[38040,67471,67473],{"id":67472},"příklad-311","Příklad 3.11",[724,67475,67476,58209,67478,67525,67526,67544],{},[38,67477,56674],{},[883,67479,67481],{"className":67480},[886],[888,67482,67483],{"xmlns":890},[892,67484,67485,67522],{},[895,67486,67487,67489,67491,67493,67496,67502,67504,67506,67512,67514,67516,67518,67520],{},[898,67488,1754],{},[898,67490,1721],{},[1723,67492,1725],{},[1864,67494,67495],{},"0,04",[2057,67497,67498,67500],{},[898,67499,1904],{},[1864,67501,2909],{},[1723,67503,1759],{},[1864,67505,23238],{},[2057,67507,67508,67510],{},[898,67509,1904],{},[1864,67511,2331],{},[1723,67513,2087],{},[1864,67515,3585],{},[898,67517,1904],{},[1723,67519,2087],{},[1864,67521,2962],{},[902,67523,67524],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,67527,67529],{"className":67528},[886],[888,67530,67531],{"xmlns":890},[892,67532,67533,67541],{},[895,67534,67535,67537,67539],{},[898,67536,1746],{},[1723,67538,1725],{},[1864,67540,3080],{},[902,67542,67543],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,67546,67547,67549,67550,18272,67592,67626,67627,3430],{},[38,67548,23463],{}," Z (3.14): ",[883,67551,67553],{"className":67552},[886],[888,67554,67555],{"xmlns":890},[892,67556,67557,67589],{},[895,67558,67559,67561,67563,67565,67568,67574,67576,67579,67581,67583,67585,67587],{},[898,67560,1728],{},[898,67562,1721],{},[1723,67564,1725],{},[1864,67566,67567],{},"0,12",[2057,67569,67570,67572],{},[898,67571,1904],{},[1864,67573,2331],{},[1723,67575,1759],{},[1864,67577,67578],{},"1,8",[898,67580,1904],{},[1723,67582,2087],{},[1864,67584,3585],{},[1723,67586,1725],{},[1864,67588,3080],{},[902,67590,67591],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,67593,67595],{"className":67594},[886],[888,67596,67597],{"xmlns":890},[892,67598,67599,67623],{},[895,67600,67601,67603,67609,67611,67613,67615,67617,67619,67621],{},[1864,67602,67567],{},[2057,67604,67605,67607],{},[898,67606,1904],{},[1864,67608,2331],{},[1723,67610,1759],{},[1864,67612,67578],{},[898,67614,1904],{},[1723,67616,2087],{},[1864,67618,2969],{},[1723,67620,1725],{},[1864,67622,2256],{},[902,67624,67625],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,67628,67630],{"className":67629},[886],[888,67631,67632],{"xmlns":890},[892,67633,67634,67638],{},[895,67635,67636],{},[1864,67637,67567],{},[902,67639,67640],{"encoding":904},"0{,}12",[883,67642,67644],{"className":67643},[886],[888,67645,67646],{"xmlns":890,"display":28759},[892,67647,67648,67700],{},[895,67649,67650,67656,67658,67660,67662,67664,67666,67668,67670,67672,67674,67676,67682,67684,67686,67688,67690,67696,67698],{},[2057,67651,67652,67654],{},[898,67653,1904],{},[1864,67655,2331],{},[1723,67657,1759],{},[1864,67659,36937],{},[898,67661,1904],{},[1723,67663,2087],{},[1864,67665,3840],{},[1723,67667,1725],{},[1864,67669,2256],{},[3018,67671,4699],{},[1723,67673,4702],{},[3018,67675,4699],{},[1931,67677,67678,67680],{},[898,67679,1904],{},[1864,67681,1866],{},[1723,67683,1725],{},[1864,67685,2962],{},[1723,67687,2031],{"separator":2030},[3018,67689,4699],{},[1931,67691,67692,67694],{},[898,67693,1904],{},[1864,67695,2331],{},[1723,67697,1725],{},[1864,67699,20022],{},[902,67701,67702],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,67704,67705,67706,3430],{},"Dále ",[883,67707,67709],{"className":67708},[886],[888,67710,67711],{"xmlns":890},[892,67712,67713,67752],{},[895,67714,67715,67717,67727,67729,67731,67733,67739,67741,67743,67746,67748,67750],{},[898,67716,1746],{},[2057,67718,67719,67721],{},[898,67720,1749],{},[895,67722,67723,67725],{},[1723,67724,2229],{"mathvariant":2124},[1723,67726,2229],{"mathvariant":2124},[1723,67728,1725],{},[1723,67730,1759],{},[898,67732,1728],{},[2057,67734,67735,67737],{},[898,67736,1721],{},[1723,67738,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,67740,1725],{},[1723,67742,1759],{},[1864,67744,67745],{},"0,24",[898,67747,1904],{},[1723,67749,2087],{},[1864,67751,67578],{},[902,67753,67754],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,67756,67757,67807],{},[123,67758,67759,67803,67804,67806],{},[883,67760,67762],{"className":67761},[886],[888,67763,67764],{"xmlns":890},[892,67765,67766,67800],{},[895,67767,67768,67770,67780,67782,67784,67786,67788,67790,67792,67794,67796,67798],{},[898,67769,1746],{},[2057,67771,67772,67774],{},[898,67773,1749],{},[895,67775,67776,67778],{},[1723,67777,2229],{"mathvariant":2124},[1723,67779,2229],{"mathvariant":2124},[1723,67781,1908],{"stretchy":1907},[1864,67783,2962],{},[1723,67785,1914],{"stretchy":1907},[1723,67787,1725],{},[1864,67789,20015],{},[1723,67791,2253],{},[1864,67793,2256],{},[3018,67795,4699],{},[1723,67797,4702],{},[3018,67799,4699],{},[902,67801,67802],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,67805,4493],{}," zisku (minimalizace ztráty);",[123,67808,67809,67803,67855,67857],{},[883,67810,67812],{"className":67811},[886],[888,67813,67814],{"xmlns":890},[892,67815,67816,67852],{},[895,67817,67818,67820,67830,67832,67834,67836,67838,67840,67842,67844,67846,67848,67850],{},[898,67819,1746],{},[2057,67821,67822,67824],{},[898,67823,1749],{},[895,67825,67826,67828],{},[1723,67827,2229],{"mathvariant":2124},[1723,67829,2229],{"mathvariant":2124},[1723,67831,1908],{"stretchy":1907},[1864,67833,3585],{},[1723,67835,1914],{"stretchy":1907},[1723,67837,1725],{},[1723,67839,1759],{},[1864,67841,20015],{},[1723,67843,2287],{},[1864,67845,2256],{},[3018,67847,4699],{},[1723,67849,4702],{},[3018,67851,4699],{},[902,67853,67854],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,67856,4435],{}," zisku, avšak",[883,67859,67861],{"className":67860},[886],[888,67862,67863],{"xmlns":890,"display":28759},[892,67864,67865,67933],{},[895,67866,67867,67869,67871,67873,67875,67877,67879,67881,67883,67885,67887,67889,67891,67893,67895,67897,67899,67901,67903,67905,67907,67909,67911,67913,67915,67917,67919,67921,67923,67925,67927,67929,67931],{},[898,67868,1746],{},[898,67870,1749],{},[1723,67872,1908],{"stretchy":1907},[1864,67874,3585],{},[1723,67876,1914],{"stretchy":1907},[1723,67878,1725],{},[1864,67880,3080],{},[1723,67882,3897],{},[1864,67884,3585],{},[1723,67886,1759],{},[1723,67888,1908],{"stretchy":1907},[1864,67890,67495],{},[1723,67892,3897],{},[1864,67894,1866],{},[3018,67896,3707],{},[1864,67898,59769],{},[1723,67900,1759],{},[1864,67902,23238],{},[1723,67904,3897],{},[1864,67906,3810],{},[1723,67908,2087],{},[1864,67910,3810],{},[1723,67912,2087],{},[1864,67914,2962],{},[1723,67916,1914],{"stretchy":1907},[1723,67918,1725],{},[1864,67920,5921],{},[1723,67922,1759],{},[1864,67924,21873],{},[1723,67926,1725],{},[1723,67928,1759],{},[1864,67930,36937],{},[1723,67932,2031],{"separator":2030},[902,67934,67935],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,67937,67938,67939,1664],{},"tj. ztráta větší než ",[883,67940,67942],{"className":67941},[886],[888,67943,67944],{"xmlns":890},[892,67945,67946,67956],{},[895,67947,67948,67950,67952,67954],{},[898,67949,11136],{},[898,67951,1721],{},[1723,67953,1725],{},[1864,67955,2962],{},[902,67957,67958],{"encoding":904},"FC = 5",[724,67960,67961,67964,67965,67968,67969,1664],{},[38,67962,67963],{},"Závěr:"," firma by měla ",[38,67966,67967],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,67970,67972],{"className":67971},[886],[888,67973,67974],{"xmlns":890},[892,67975,67976,67986],{},[895,67977,67978,67980,67982,67984],{},[898,67979,11136],{},[898,67981,1721],{},[1723,67983,1725],{},[1864,67985,2962],{},[902,67987,67958],{"encoding":904},[115,67989,67991],{"id":67990},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,67993,67994,67995,67997,67998,68013,68014,68027,68028,68054,68055,68068,68069,68086,68087,3350,68104,68107,68108,68128,68129,68144,68145,3430],{},"Důležitým završením analýzy je konstrukce ",[38,67996,55962],{},". S nabízeným množstvím rostou mezní náklady ",[883,67999,68001],{"className":68000},[886],[888,68002,68003],{"xmlns":890},[892,68004,68005,68011],{},[895,68006,68007,68009],{},[898,68008,1728],{},[898,68010,1721],{},[902,68012,55979],{"encoding":904}," a tyto určují cenu ",[883,68015,68017],{"className":68016},[886],[888,68018,68019],{"xmlns":890},[892,68020,68021,68025],{},[895,68022,68023],{},[898,68024,1746],{},[902,68026,1746],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,68029,68031],{"className":68030},[886],[888,68032,68033],{"xmlns":890},[892,68034,68035,68051],{},[895,68036,68037,68039,68041,68043,68045,68047,68049],{},[898,68038,1746],{},[1723,68040,1725],{},[898,68042,1728],{},[898,68044,1721],{},[1723,68046,1908],{"stretchy":1907},[898,68048,1904],{},[1723,68050,1914],{"stretchy":1907},[902,68052,68053],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,68056,68058],{"className":68057},[886],[888,68059,68060],{"xmlns":890},[892,68061,68062,68066],{},[895,68063,68064],{},[898,68065,1746],{},[902,68067,1746],{"encoding":904}," však nemůže být nižší než ",[883,68070,68072],{"className":68071},[886],[888,68073,68074],{"xmlns":890},[892,68075,68076,68084],{},[895,68077,68078],{},[2057,68079,68080,68082],{},[898,68081,1746],{},[1723,68083,5066],{},[902,68085,5116],{"encoding":904}," odpovídající množství ",[883,68088,68090],{"className":68089},[886],[888,68091,68092],{"xmlns":890},[892,68093,68094,68102],{},[895,68095,68096],{},[2057,68097,68098,68100],{},[898,68099,1904],{},[1723,68101,5066],{},[902,68103,30537],{"encoding":904},[38,68105,68106],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,68109,68111],{"className":68110},[886],[888,68112,68113],{"xmlns":890},[892,68114,68115,68125],{},[895,68116,68117,68119],{},[1864,68118,2256],{},[2057,68120,68121,68123],{},[898,68122,1904],{},[1723,68124,5066],{},[902,68126,68127],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,68130,68132],{"className":68131},[886],[888,68133,68134],{"xmlns":890},[892,68135,68136,68142],{},[895,68137,68138,68140],{},[898,68139,1728],{},[898,68141,1721],{},[902,68143,55979],{"encoding":904}," nad bodem ",[883,68146,68148],{"className":68147},[886],[888,68149,68150],{"xmlns":890},[892,68151,68152,68156],{},[895,68153,68154],{},[898,68155,1718],{},[902,68157,1718],{"encoding":904},[883,68159,68161],{"className":68160},[886],[888,68162,68163],{"xmlns":890,"display":28759},[892,68164,68165,68272],{},[21447,68166,68167],{"width":28764},[21452,68168,68169,68171,68265,68267],{},[21455,68170],{"width":28769},[21455,68172,68173],{},[895,68174,68175,68177,68179,68181,68183,68185,68187,68189],{},[898,68176,1746],{},[1723,68178,1725],{},[898,68180,2111],{},[1723,68182,1908],{"stretchy":1907},[898,68184,1904],{},[1723,68186,1914],{"stretchy":1907},[1723,68188,1725],{},[895,68190,68191,68194],{},[1723,68192,68193],{"fence":2030},"{",[21447,68195,68198,68237],{"rowspacing":68196,"columnalign":68197,"columnspacing":15985},"0.36em","left left",[21452,68199,68200,68216],{},[21455,68201,68202],{},[3055,68203,68204],{"scriptlevel":2256,"displaystyle":1907},[895,68205,68206,68208,68210,68212,68214],{},[898,68207,1728],{},[898,68209,1721],{},[1723,68211,1908],{"stretchy":1907},[898,68213,1904],{},[1723,68215,1914],{"stretchy":1907},[21455,68217,68218],{},[3055,68219,68220],{"scriptlevel":2256,"displaystyle":1907},[895,68221,68222,68225,68227,68229,68235],{},[3018,68223,68224],{},"pro ",[898,68226,1904],{},[1723,68228,5197],{},[2057,68230,68231,68233],{},[898,68232,1904],{},[1723,68234,5066],{},[1723,68236,2031],{"separator":2030},[21452,68238,68239,68245],{},[21455,68240,68241],{},[3055,68242,68243],{"scriptlevel":2256,"displaystyle":1907},[1864,68244,2256],{},[21455,68246,68247],{},[3055,68248,68249],{"scriptlevel":2256,"displaystyle":1907},[895,68250,68251,68253,68255,68257,68263],{},[3018,68252,68224],{},[898,68254,1904],{},[1723,68256,2287],{},[2057,68258,68259,68261],{},[898,68260,1904],{},[1723,68262,5066],{},[1723,68264,2031],{"separator":2030},[21455,68266],{"width":28769},[21455,68268,68269],{},[3018,68270,68271],{},"(3.15)",[902,68273,68274],{"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}",[724,68276,5022,68277,68294,68295,68312,68313,42191,68343,68346],{},[883,68278,68280],{"className":68279},[886],[888,68281,68282],{"xmlns":890},[892,68283,68284,68292],{},[895,68285,68286],{},[2057,68287,68288,68290],{},[898,68289,1904],{},[1723,68291,5066],{},[902,68293,30537],{"encoding":904}," je bod minima ",[883,68296,68298],{"className":68297},[886],[888,68299,68300],{"xmlns":890},[892,68301,68302,68310],{},[895,68303,68304,68306,68308],{},[898,68305,1718],{},[898,68307,41031],{},[898,68309,1721],{},[902,68311,55998],{"encoding":904},". Bod ",[883,68314,68316],{"className":68315},[886],[888,68317,68318],{"xmlns":890},[892,68319,68320,68340],{},[895,68321,68322,68324,68330,68332,68338],{},[1723,68323,1908],{"stretchy":1907},[2057,68325,68326,68328],{},[898,68327,1904],{},[1723,68329,5066],{},[1723,68331,2031],{"separator":2030},[2057,68333,68334,68336],{},[898,68335,1746],{},[1723,68337,5066],{},[1723,68339,1914],{"stretchy":1907},[902,68341,68342],{"encoding":904},"(Q^*, P^*)",[38,68344,68345],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[4584,68348,68349,68354],{},[724,68350,68351,68353],{},[883,68352,5283],{}," Postup — jak odvodit nabídku firmy",[152,68355,68356,68405,68500,68555,68626],{},[123,68357,68358,68359,1682,68381,1664],{},"Ze zadaných nákladů určete ",[883,68360,68362],{"className":68361},[886],[888,68363,68364],{"xmlns":890},[892,68365,68366,68378],{},[895,68367,68368,68370,68372,68374,68376],{},[898,68369,1728],{},[898,68371,1721],{},[1723,68373,1908],{"stretchy":1907},[898,68375,1904],{},[1723,68377,1914],{"stretchy":1907},[902,68379,68380],{"encoding":904},"MC(Q)",[883,68382,68384],{"className":68383},[886],[888,68385,68386],{"xmlns":890},[892,68387,68388,68402],{},[895,68389,68390,68392,68394,68396,68398,68400],{},[898,68391,1718],{},[898,68393,41031],{},[898,68395,1721],{},[1723,68397,1908],{"stretchy":1907},[898,68399,1904],{},[1723,68401,1914],{"stretchy":1907},[902,68403,68404],{"encoding":904},"AVC(Q)",[123,68406,68407,68408,68425,68426,68443,68444,68476,68477,4634],{},"Najděte ",[883,68409,68411],{"className":68410},[886],[888,68412,68413],{"xmlns":890},[892,68414,68415,68423],{},[895,68416,68417],{},[2057,68418,68419,68421],{},[898,68420,1904],{},[1723,68422,5066],{},[902,68424,30537],{"encoding":904}," jako bod minima ",[883,68427,68429],{"className":68428},[886],[888,68430,68431],{"xmlns":890},[892,68432,68433,68441],{},[895,68434,68435,68437,68439],{},[898,68436,1718],{},[898,68438,41031],{},[898,68440,1721],{},[902,68442,55998],{"encoding":904}," (řešením ",[883,68445,68447],{"className":68446},[886],[888,68448,68449],{"xmlns":890},[892,68450,68451,68473],{},[895,68452,68453,68455,68457,68463,68465,68467,68469,68471],{},[898,68454,1718],{},[898,68456,41031],{},[2057,68458,68459,68461],{},[898,68460,1721],{},[1723,68462,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,68464,1908],{"stretchy":1907},[898,68466,1904],{},[1723,68468,1914],{"stretchy":1907},[1723,68470,1725],{},[1864,68472,2256],{},[902,68474,68475],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,68478,68480],{"className":68479},[886],[888,68481,68482],{"xmlns":890},[892,68483,68484,68498],{},[895,68485,68486,68488,68490,68492,68494,68496],{},[898,68487,1718],{},[898,68489,41031],{},[898,68491,1721],{},[1723,68493,1725],{},[898,68495,1728],{},[898,68497,1721],{},[902,68499,55936],{"encoding":904},[123,68501,66408,68502,68554],{},[883,68503,68505],{"className":68504},[886],[888,68506,68507],{"xmlns":890},[892,68508,68509,68551],{},[895,68510,68511,68517,68519,68521,68523,68525,68531,68533,68535,68537,68539,68541,68543,68549],{},[2057,68512,68513,68515],{},[898,68514,1746],{},[1723,68516,5066],{},[1723,68518,1725],{},[898,68520,1728],{},[898,68522,1721],{},[1723,68524,1908],{"stretchy":1907},[2057,68526,68527,68529],{},[898,68528,1904],{},[1723,68530,5066],{},[1723,68532,1914],{"stretchy":1907},[1723,68534,1725],{},[898,68536,1718],{},[898,68538,41031],{},[898,68540,1721],{},[1723,68542,1908],{"stretchy":1907},[2057,68544,68545,68547],{},[898,68546,1904],{},[1723,68548,5066],{},[1723,68550,1914],{"stretchy":1907},[902,68552,68553],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,68556,68557,68558,7183,68590,68612,68613,1664],{},"Zapište nabídku: ",[883,68559,68561],{"className":68560},[886],[888,68562,68563],{"xmlns":890},[892,68564,68565,68587],{},[895,68566,68567,68569,68571,68573,68575,68577,68579,68581,68583,68585],{},[898,68568,2111],{},[1723,68570,1908],{"stretchy":1907},[898,68572,1904],{},[1723,68574,1914],{"stretchy":1907},[1723,68576,1725],{},[898,68578,1728],{},[898,68580,1721],{},[1723,68582,1908],{"stretchy":1907},[898,68584,1904],{},[1723,68586,1914],{"stretchy":1907},[902,68588,68589],{"encoding":904},"S(Q) = MC(Q)",[883,68591,68593],{"className":68592},[886],[888,68594,68595],{"xmlns":890},[892,68596,68597,68609],{},[895,68598,68599,68601,68603],{},[898,68600,1904],{},[1723,68602,5197],{},[2057,68604,68605,68607],{},[898,68606,1904],{},[1723,68608,5066],{},[902,68610,68611],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,68614,68616],{"className":68615},[886],[888,68617,68618],{"xmlns":890},[892,68619,68620,68624],{},[895,68621,68622],{},[1864,68623,2256],{},[902,68625,2256],{"encoding":904},[123,68627,68628,68629,68661],{},"V případě potřeby vyjádřete inverzi ",[883,68630,68632],{"className":68631},[886],[888,68633,68634],{"xmlns":890},[892,68635,68636,68658],{},[895,68637,68638,68640,68642,68652,68654,68656],{},[898,68639,1904],{},[1723,68641,1725],{},[2057,68643,68644,68646],{},[898,68645,2111],{},[895,68647,68648,68650],{},[1723,68649,1759],{},[1864,68651,1866],{},[1723,68653,1908],{"stretchy":1907},[898,68655,1746],{},[1723,68657,1914],{"stretchy":1907},[902,68659,68660],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,68663,68664],{},[614,68665,68666,68667,1343,68682,1682,68699,29894,68714,68727,68728,68753,68754,68767,68768,68785,68786,68803,68804,68821],{},"Obrázek 3.14: Křivky ",[883,68668,68670],{"className":68669},[886],[888,68671,68672],{"xmlns":890},[892,68673,68674,68680],{},[895,68675,68676,68678],{},[898,68677,1718],{},[898,68679,1721],{},[902,68681,56247],{"encoding":904},[883,68683,68685],{"className":68684},[886],[888,68686,68687],{"xmlns":890},[892,68688,68689,68697],{},[895,68690,68691,68693,68695],{},[898,68692,1718],{},[898,68694,41031],{},[898,68696,1721],{},[902,68698,55998],{"encoding":904},[883,68700,68702],{"className":68701},[886],[888,68703,68704],{"xmlns":890},[892,68705,68706,68712],{},[895,68707,68708,68710],{},[898,68709,1728],{},[898,68711,1721],{},[902,68713,55979],{"encoding":904},[883,68715,68717],{"className":68716},[886],[888,68718,68719],{"xmlns":890},[892,68720,68721,68725],{},[895,68722,68723],{},[898,68724,900],{},[902,68726,900],{"encoding":904},"; křivka nabídky ",[883,68729,68731],{"className":68730},[886],[888,68732,68733],{"xmlns":890},[892,68734,68735,68751],{},[895,68736,68737,68739,68741,68743,68745,68747,68749],{},[898,68738,1746],{},[1723,68740,1725],{},[898,68742,1728],{},[898,68744,1721],{},[1723,68746,1908],{"stretchy":1907},[898,68748,1904],{},[1723,68750,1914],{"stretchy":1907},[902,68752,68053],{"encoding":904}," začíná v bodě ",[883,68755,68757],{"className":68756},[886],[888,68758,68759],{"xmlns":890},[892,68760,68761,68765],{},[895,68762,68763],{},[898,68764,1718],{},[902,68766,1718],{"encoding":904}," odpovídajícím minimu ",[883,68769,68771],{"className":68770},[886],[888,68772,68773],{"xmlns":890},[892,68774,68775,68783],{},[895,68776,68777,68779,68781],{},[898,68778,1718],{},[898,68780,41031],{},[898,68782,1721],{},[902,68784,55998],{"encoding":904}," při ceně ",[883,68787,68789],{"className":68788},[886],[888,68790,68791],{"xmlns":890},[892,68792,68793,68801],{},[895,68794,68795],{},[2057,68796,68797,68799],{},[898,68798,1746],{},[1723,68800,5066],{},[902,68802,5116],{"encoding":904}," (minimální cena nabídky); pod ",[883,68805,68807],{"className":68806},[886],[888,68808,68809],{"xmlns":890},[892,68810,68811,68819],{},[895,68812,68813],{},[2057,68814,68815,68817],{},[898,68816,1904],{},[1723,68818,5066],{},[902,68820,30537],{"encoding":904}," je nabídka nulová.",[38040,68823,68825],{"id":68824},"příklad-312","Příklad 3.12",[724,68827,68828,58209,68830,68876],{},[38,68829,56674],{},[883,68831,68833],{"className":68832},[886],[888,68834,68835],{"xmlns":890},[892,68836,68837,68873],{},[895,68838,68839,68841,68843,68845,68847,68853,68855,68857,68863,68865,68867,68869,68871],{},[898,68840,1754],{},[898,68842,1721],{},[1723,68844,1725],{},[1864,68846,3517],{},[2057,68848,68849,68851],{},[898,68850,1904],{},[1864,68852,2909],{},[1723,68854,1759],{},[1864,68856,2331],{},[2057,68858,68859,68861],{},[898,68860,1904],{},[1864,68862,2331],{},[1723,68864,2087],{},[1864,68866,36937],{},[898,68868,1904],{},[1723,68870,2087],{},[1864,68872,3585],{},[902,68874,68875],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,68878,68879,2628,68881,68918,68919,3430],{},[38,68880,23463],{},[883,68882,68884],{"className":68883},[886],[888,68885,68886],{"xmlns":890},[892,68887,68888,68915],{},[895,68889,68890,68892,68894,68896,68899,68905,68907,68909,68911,68913],{},[898,68891,1728],{},[898,68893,1721],{},[1723,68895,1725],{},[1864,68897,68898],{},"0,3",[2057,68900,68901,68903],{},[898,68902,1904],{},[1864,68904,2331],{},[1723,68906,1759],{},[1864,68908,3080],{},[898,68910,1904],{},[1723,68912,2087],{},[1864,68914,36937],{},[902,68916,68917],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,68920,68922],{"className":68921},[886],[888,68923,68924],{"xmlns":890},[892,68925,68926,68936],{},[895,68927,68928,68930,68932,68934],{},[898,68929,1746],{},[1723,68931,1725],{},[898,68933,1728],{},[898,68935,1721],{},[902,68937,1810],{"encoding":904},[883,68939,68941],{"className":68940},[886],[888,68942,68943],{"xmlns":890,"display":28759},[892,68944,68945,68970],{},[895,68946,68947,68949,68951,68953,68959,68961,68963,68965,68967],{},[898,68948,1746],{},[1723,68950,1725],{},[1864,68952,68898],{},[2057,68954,68955,68957],{},[898,68956,1904],{},[1864,68958,2331],{},[1723,68960,1759],{},[1864,68962,3080],{},[898,68964,1904],{},[1723,68966,2087],{},[1864,68968,68969],{},"15.",[902,68971,68972],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,68974,68975,68976,6092,68989,69002],{},"Vyjádření ",[883,68977,68979],{"className":68978},[886],[888,68980,68981],{"xmlns":890},[892,68982,68983,68987],{},[895,68984,68985],{},[898,68986,1904],{},[902,68988,1904],{"encoding":904},[883,68990,68992],{"className":68991},[886],[888,68993,68994],{"xmlns":890},[892,68995,68996,69000],{},[895,68997,68998],{},[898,68999,1746],{},[902,69001,1746],{"encoding":904}," doplněním na čtverec:",[883,69004,69006],{"className":69005},[886],[888,69007,69008],{"xmlns":890,"display":28759},[892,69009,69010,69100],{},[895,69011,69012,69014,69016,69018,69056,69058,69060,69082,69084,69098],{},[898,69013,1746],{},[1723,69015,1725],{},[1864,69017,68898],{},[895,69019,69020,69022,69044,69046,69054],{},[1723,69021,1908],{"fence":2030},[2057,69023,69024,69042],{},[895,69025,69026,69028,69030,69032,69040],{},[1723,69027,1908],{"fence":2030},[898,69029,1904],{},[1723,69031,1759],{},[3055,69033,69034],{"scriptlevel":2256,"displaystyle":1907},[3058,69035,69036,69038],{},[1864,69037,9744],{},[1864,69039,2909],{},[1723,69041,1914],{"fence":2030},[1864,69043,2331],{},[1723,69045,2087],{},[3055,69047,69048],{"scriptlevel":2256,"displaystyle":1907},[3058,69049,69050,69052],{},[1864,69051,3840],{},[1864,69053,4713],{},[1723,69055,1914],{"fence":2030},[1723,69057,2031],{"separator":2030},[6588,69059],{"width":6590},[2057,69061,69062,69080],{},[895,69063,69064,69066,69068,69070,69078],{},[1723,69065,1908],{"fence":2030},[898,69067,1904],{},[1723,69069,1759],{},[3055,69071,69072],{"scriptlevel":2256,"displaystyle":1907},[3058,69073,69074,69076],{},[1864,69075,9744],{},[1864,69077,2909],{},[1723,69079,1914],{"fence":2030},[1864,69081,2331],{},[1723,69083,1725],{},[3058,69085,69086,69096],{},[895,69087,69088,69090,69092,69094],{},[1864,69089,38711],{},[898,69091,1746],{},[1723,69093,1759],{},[1864,69095,3840],{},[1864,69097,4713],{},[1723,69099,2031],{"separator":2030},[902,69101,69102],{"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},",[883,69104,69106],{"className":69105},[886],[888,69107,69108],{"xmlns":890,"display":28759},[892,69109,69110,69142],{},[895,69111,69112,69114,69116,69122,69124,69140],{},[898,69113,1904],{},[1723,69115,1725],{},[3058,69117,69118,69120],{},[1864,69119,9744],{},[1864,69121,2909],{},[1723,69123,2087],{},[3058,69125,69126,69138],{},[8827,69127,69128],{},[895,69129,69130,69132,69134,69136],{},[1864,69131,38711],{},[898,69133,1746],{},[1723,69135,1759],{},[1864,69137,3840],{},[1864,69139,2909],{},[898,69141,1664],{"mathvariant":2124},[902,69143,69144],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,69146,67705,69147,1343,69185,1343,69233,69267,69268,1664],{},[883,69148,69150],{"className":69149},[886],[888,69151,69152],{"xmlns":890},[892,69153,69154,69182],{},[895,69155,69156,69158,69160,69162,69164,69166,69172,69174,69176,69178,69180],{},[898,69157,1718],{},[898,69159,41031],{},[898,69161,1721],{},[1723,69163,1725],{},[1864,69165,3517],{},[2057,69167,69168,69170],{},[898,69169,1904],{},[1864,69171,2331],{},[1723,69173,1759],{},[1864,69175,2331],{},[898,69177,1904],{},[1723,69179,2087],{},[1864,69181,36937],{},[902,69183,69184],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,69186,69188],{"className":69187},[886],[888,69189,69190],{"xmlns":890},[892,69191,69192,69230],{},[895,69193,69194,69196,69198,69204,69206,69208,69210,69212,69214,69216,69218,69220,69226,69228],{},[898,69195,1718],{},[898,69197,41031],{},[2057,69199,69200,69202],{},[898,69201,1721],{},[1723,69203,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,69205,1725],{},[1864,69207,3561],{},[898,69209,1904],{},[1723,69211,1759],{},[1864,69213,2331],{},[1723,69215,1725],{},[1864,69217,2256],{},[1723,69219,4702],{},[2057,69221,69222,69224],{},[898,69223,1904],{},[1723,69225,5066],{},[1723,69227,1725],{},[1864,69229,3585],{},[902,69231,69232],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,69234,69236],{"className":69235},[886],[888,69237,69238],{"xmlns":890},[892,69239,69240,69264],{},[895,69241,69242,69244,69246,69256,69258,69260,69262],{},[898,69243,1718],{},[898,69245,41031],{},[2057,69247,69248,69250],{},[898,69249,1721],{},[895,69251,69252,69254],{},[1723,69253,2229],{"mathvariant":2124},[1723,69255,2229],{"mathvariant":2124},[1723,69257,1725],{},[1864,69259,3561],{},[1723,69261,2253],{},[1864,69263,2256],{},[902,69265,69266],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,69269,69271],{"className":69270},[886],[888,69272,69273],{"xmlns":890},[892,69274,69275,69311],{},[895,69276,69277,69283,69285,69287,69289,69291,69293,69295,69297,69299,69301,69303,69305,69307,69309],{},[2057,69278,69279,69281],{},[898,69280,1746],{},[1723,69282,5066],{},[1723,69284,1725],{},[898,69286,1728],{},[898,69288,1721],{},[1723,69290,1908],{"stretchy":1907},[1864,69292,3585],{},[1723,69294,1914],{"stretchy":1907},[1723,69296,1725],{},[1864,69298,38711],{},[1723,69300,1759],{},[1864,69302,5921],{},[1723,69304,2087],{},[1864,69306,36937],{},[1723,69308,1725],{},[1864,69310,2962],{},[902,69312,69313],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,69315,69316],{},[38,69317,69318],{},"Závěr.",[883,69320,69322],{"className":69321},[886],[888,69323,69324],{"xmlns":890,"display":28759},[892,69325,69326,69412],{},[895,69327,69328,69330,69332,69334,69336,69338,69340,69342],{},[898,69329,1746],{},[1723,69331,1725],{},[898,69333,2111],{},[1723,69335,1908],{"stretchy":1907},[898,69337,1904],{},[1723,69339,1914],{"stretchy":1907},[1723,69341,1725],{},[895,69343,69344,69346],{},[1723,69345,68193],{"fence":2030},[21447,69347,69348,69390],{"rowspacing":68196,"columnalign":68197,"columnspacing":15985},[21452,69349,69350,69374],{},[21455,69351,69352],{},[3055,69353,69354],{"scriptlevel":2256,"displaystyle":1907},[895,69355,69356,69358,69364,69366,69368,69370,69372],{},[1864,69357,68898],{},[2057,69359,69360,69362],{},[898,69361,1904],{},[1864,69363,2331],{},[1723,69365,1759],{},[1864,69367,3080],{},[898,69369,1904],{},[1723,69371,2087],{},[1864,69373,36937],{},[21455,69375,69376],{},[3055,69377,69378],{"scriptlevel":2256,"displaystyle":1907},[895,69379,69380,69382,69384,69386,69388],{},[3018,69381,68224],{},[898,69383,1904],{},[1723,69385,5197],{},[1864,69387,3585],{},[1723,69389,2031],{"separator":2030},[21452,69391,69392,69398],{},[21455,69393,69394],{},[3055,69395,69396],{"scriptlevel":2256,"displaystyle":1907},[1864,69397,2256],{},[21455,69399,69400],{},[3055,69401,69402],{"scriptlevel":2256,"displaystyle":1907},[895,69403,69404,69406,69408,69410],{},[3018,69405,68224],{},[898,69407,1904],{},[1723,69409,2287],{},[1864,69411,20022],{},[902,69413,69414],{"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}",[724,69416,69417],{},[614,69418,69419,69420,69435,69436,1664],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,69421,69423],{"className":69422},[886],[888,69424,69425],{"xmlns":890},[892,69426,69427,69433],{},[895,69428,69429,69431],{},[898,69430,1728],{},[898,69432,1721],{},[902,69434,55979],{"encoding":904}," ležící nad minimem ",[883,69437,69439],{"className":69438},[886],[888,69440,69441],{"xmlns":890},[892,69442,69443,69451],{},[895,69444,69445,69447,69449],{},[898,69446,1718],{},[898,69448,41031],{},[898,69450,1721],{},[902,69452,55998],{"encoding":904},[115,69454,69456],{"id":69455},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,69458,69459,69460,69464,69465,69480,69481,69501,69502,1682,69505,69508,69509,69511,69512,20638,69534,69536,69537,1682,69539,59413,69542,2628,69545,42506,69560,69575],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,69461,69463],{"className":69462,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,69466,69468],{"className":69467},[886],[888,69469,69470],{"xmlns":890},[892,69471,69472,69478],{},[895,69473,69474,69476],{},[898,69475,1754],{},[898,69477,1749],{},[902,69479,4808],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,69482,69484],{"className":69483},[886],[888,69485,69486],{"xmlns":890},[892,69487,69488,69498],{},[895,69489,69490,69492,69494,69496],{},[898,69491,1754],{},[898,69493,1749],{},[898,69495,2125],{"mathvariant":2124},[898,69497,1904],{},[902,69499,69500],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,69503,69504],{},"fixních",[38,69506,69507],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,69510,65012],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,69513,69515],{"className":69514},[886],[888,69516,69517],{"xmlns":890},[892,69518,69519,69531],{},[895,69520,69521,69523,69525,69527,69529],{},[898,69522,1754],{},[898,69524,1749],{},[1723,69526,1759],{},[898,69528,1754],{},[898,69530,1721],{},[902,69532,69533],{"encoding":904},"TR - TC",[38,69535,55862],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,69538,57171],{},[38,69540,69541],{},"mezní náklady",[207,69543,1145],{"className":69544,"dataFsResolvedFilePath":764,"href":765},[210],[883,69546,69548],{"className":69547},[886],[888,69549,69550],{"xmlns":890},[892,69551,69552,69558],{},[895,69553,69554,69556],{},[898,69555,1754],{},[898,69557,1749],{},[902,69559,4808],{"encoding":904},[883,69561,69563],{"className":69562},[886],[888,69564,69565],{"xmlns":890},[892,69566,69567,69573],{},[895,69568,69569,69571],{},[898,69570,1754],{},[898,69572,1721],{},[902,69574,3963],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,69577,69578,69640,69706,69768],{},[123,69579,69580,69583,69584,11094,69599,1664],{},[38,69581,69582],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,69585,69587],{"className":69586},[886],[888,69588,69589],{"xmlns":890},[892,69590,69591,69597],{},[895,69592,69593,69595],{},[898,69594,1718],{},[898,69596,1721],{},[902,69598,56247],{"encoding":904},[883,69600,69602],{"className":69601},[886],[888,69603,69604],{"xmlns":890},[892,69605,69606,69638],{},[895,69607,69608,69610,69612,69614,69620,69622,69624,69626,69628,69630,69636],{},[898,69609,1718],{},[898,69611,1721],{},[1723,69613,1908],{"stretchy":1907},[1931,69615,69616,69618],{},[898,69617,1904],{},[1864,69619,2256],{},[1723,69621,1914],{"stretchy":1907},[1723,69623,1725],{},[898,69625,1728],{},[898,69627,1721],{},[1723,69629,1908],{"stretchy":1907},[1931,69631,69632,69634],{},[898,69633,1904],{},[1864,69635,2256],{},[1723,69637,1914],{"stretchy":1907},[902,69639,63256],{"encoding":904},[123,69641,69642,69583,69645,11094,69662,1664],{},[38,69643,69644],{},"Princip minimalizace průměrných variabilních nákladů:",[883,69646,69648],{"className":69647},[886],[888,69649,69650],{"xmlns":890},[892,69651,69652,69660],{},[895,69653,69654,69656,69658],{},[898,69655,1718],{},[898,69657,41031],{},[898,69659,1721],{},[902,69661,55998],{"encoding":904},[883,69663,69665],{"className":69664},[886],[888,69666,69667],{"xmlns":890},[892,69668,69669,69703],{},[895,69670,69671,69673,69675,69677,69679,69685,69687,69689,69691,69693,69695,69701],{},[898,69672,1718],{},[898,69674,41031],{},[898,69676,1721],{},[1723,69678,1908],{"stretchy":1907},[1931,69680,69681,69683],{},[898,69682,1904],{},[1864,69684,2256],{},[1723,69686,1914],{"stretchy":1907},[1723,69688,1725],{},[898,69690,1728],{},[898,69692,1721],{},[1723,69694,1908],{"stretchy":1907},[1931,69696,69697,69699],{},[898,69698,1904],{},[1864,69700,2256],{},[1723,69702,1914],{"stretchy":1907},[902,69704,69705],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,69707,69708,69711,69712,11094,69727,1664],{},[38,69709,69710],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,69713,69715],{"className":69714},[886],[888,69716,69717],{"xmlns":890},[892,69718,69719,69725],{},[895,69720,69721,69723],{},[898,69722,1746],{},[898,69724,1749],{},[902,69726,64166],{"encoding":904},[883,69728,69730],{"className":69729},[886],[888,69731,69732],{"xmlns":890},[892,69733,69734,69766],{},[895,69735,69736,69738,69740,69742,69748,69750,69752,69754,69756,69758,69764],{},[898,69737,1728],{},[898,69739,1749],{},[1723,69741,1908],{"stretchy":1907},[1931,69743,69744,69746],{},[898,69745,1904],{},[1864,69747,2256],{},[1723,69749,1914],{"stretchy":1907},[1723,69751,1725],{},[898,69753,1728],{},[898,69755,1721],{},[1723,69757,1908],{"stretchy":1907},[1931,69759,69760,69762],{},[898,69761,1904],{},[1864,69763,2256],{},[1723,69765,1914],{"stretchy":1907},[902,69767,66332],{"encoding":904},[123,69769,69770,2628,69773,7183,69809,68612,69830,22287,69843,68294,69860,1664],{},[38,69771,69772],{},"Funkce nabídky firmy:",[883,69774,69776],{"className":69775},[886],[888,69777,69778],{"xmlns":890},[892,69779,69780,69806],{},[895,69781,69782,69784,69786,69788,69790,69792,69794,69796,69798,69800,69802,69804],{},[898,69783,1746],{},[1723,69785,1725],{},[898,69787,2111],{},[1723,69789,1908],{"stretchy":1907},[898,69791,1904],{},[1723,69793,1914],{"stretchy":1907},[1723,69795,1725],{},[898,69797,1728],{},[898,69799,1721],{},[1723,69801,1908],{"stretchy":1907},[898,69803,1904],{},[1723,69805,1914],{"stretchy":1907},[902,69807,69808],{"encoding":904},"P = S(Q) = MC(Q)",[883,69810,69812],{"className":69811},[886],[888,69813,69814],{"xmlns":890},[892,69815,69816,69828],{},[895,69817,69818,69820,69822],{},[898,69819,1904],{},[1723,69821,5197],{},[2057,69823,69824,69826],{},[898,69825,1904],{},[1723,69827,5066],{},[902,69829,68611],{"encoding":904},[883,69831,69833],{"className":69832},[886],[888,69834,69835],{"xmlns":890},[892,69836,69837,69841],{},[895,69838,69839],{},[1864,69840,2256],{},[902,69842,2256],{"encoding":904},[883,69844,69846],{"className":69845},[886],[888,69847,69848],{"xmlns":890},[892,69849,69850,69858],{},[895,69851,69852],{},[2057,69853,69854,69856],{},[898,69855,1904],{},[1723,69857,5066],{},[902,69859,30537],{"encoding":904},[883,69861,69863],{"className":69862},[886],[888,69864,69865],{"xmlns":890},[892,69866,69867,69875],{},[895,69868,69869,69871,69873],{},[898,69870,1718],{},[898,69872,41031],{},[898,69874,1721],{},[902,69876,55998],{"encoding":904},[115,69878,2615],{"id":50572},[152,69880,69881,69884,69887,69890,69893,69896,69899,69902,69905,69908,69911],{},[123,69882,69883],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,69885,69886],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,69888,69889],{},"Jak se vypočte mezní příjem a co udává?",[123,69891,69892],{},"Z jakých složek se skládají celkové náklady?",[123,69894,69895],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,69897,69898],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,69900,69901],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,69903,69904],{},"Jak se vypočte zisk?",[123,69906,69907],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,69909,69910],{},"Co jsou body zvratu? Jak se najdou?",[123,69912,69913],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,69915,1817],{"id":69916},"úlohy-31328",[198,69918,69920],{"id":69919},"příjem-3135","Příjem (3.1–3.5)",[724,69922,69923,46117,69926,69954,69955,69970,69971,69986,69987,70002,70003,1343,70018,1343,70033,70048],{},[38,69924,69925],{},"3.1",[883,69927,69929],{"className":69928},[886],[888,69930,69931],{"xmlns":890},[892,69932,69933,69951],{},[895,69934,69935,69937,69939,69941,69943,69945,69947,69949],{},[898,69936,1746],{},[1723,69938,1725],{},[898,69940,4897],{},[1723,69942,1908],{"stretchy":1907},[898,69944,1904],{},[1723,69946,1914],{"stretchy":1907},[1723,69948,1725],{},[1864,69950,3810],{},[902,69952,69953],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,69956,69958],{"className":69957},[886],[888,69959,69960],{"xmlns":890},[892,69961,69962,69968],{},[895,69963,69964,69966],{},[898,69965,1754],{},[898,69967,1749],{},[902,69969,4808],{"encoding":904},", průměrný příjem ",[883,69972,69974],{"className":69973},[886],[888,69975,69976],{"xmlns":890},[892,69977,69978,69984],{},[895,69979,69980,69982],{},[898,69981,1718],{},[898,69983,1749],{},[902,69985,56132],{"encoding":904}," a mezní příjem ",[883,69988,69990],{"className":69989},[886],[888,69991,69992],{"xmlns":890},[892,69993,69994,70000],{},[895,69995,69996,69998],{},[898,69997,1728],{},[898,69999,1749],{},[902,70001,7344],{"encoding":904},". (c) Vypočtěte ",[883,70004,70006],{"className":70005},[886],[888,70007,70008],{"xmlns":890},[892,70009,70010,70016],{},[895,70011,70012,70014],{},[898,70013,1754],{},[898,70015,1749],{},[902,70017,4808],{"encoding":904},[883,70019,70021],{"className":70020},[886],[888,70022,70023],{"xmlns":890},[892,70024,70025,70031],{},[895,70026,70027,70029],{},[898,70028,1718],{},[898,70030,1749],{},[902,70032,56132],{"encoding":904},[883,70034,70036],{"className":70035},[886],[888,70037,70038],{"xmlns":890},[892,70039,70040,70046],{},[895,70041,70042,70044],{},[898,70043,1728],{},[898,70045,1749],{},[902,70047,7344],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,70050,70051,46117,70054,69954,70090,69970,70105,69986,70120,70002,70135,1343,70150,1343,70165,70180],{},[38,70052,70053],{},"3.2",[883,70055,70057],{"className":70056},[886],[888,70058,70059],{"xmlns":890},[892,70060,70061,70087],{},[895,70062,70063,70065,70067,70069,70071,70073,70075,70077,70079,70081,70083,70085],{},[898,70064,1746],{},[1723,70066,1725],{},[898,70068,4897],{},[1723,70070,1908],{"stretchy":1907},[898,70072,1904],{},[1723,70074,1914],{"stretchy":1907},[1723,70076,1725],{},[1723,70078,1759],{},[1864,70080,5719],{},[898,70082,1904],{},[1723,70084,2087],{},[1864,70086,9744],{},[902,70088,70089],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,70091,70093],{"className":70092},[886],[888,70094,70095],{"xmlns":890},[892,70096,70097,70103],{},[895,70098,70099,70101],{},[898,70100,1754],{},[898,70102,1749],{},[902,70104,4808],{"encoding":904},[883,70106,70108],{"className":70107},[886],[888,70109,70110],{"xmlns":890},[892,70111,70112,70118],{},[895,70113,70114,70116],{},[898,70115,1718],{},[898,70117,1749],{},[902,70119,56132],{"encoding":904},[883,70121,70123],{"className":70122},[886],[888,70124,70125],{"xmlns":890},[892,70126,70127,70133],{},[895,70128,70129,70131],{},[898,70130,1728],{},[898,70132,1749],{},[902,70134,7344],{"encoding":904},[883,70136,70138],{"className":70137},[886],[888,70139,70140],{"xmlns":890},[892,70141,70142,70148],{},[895,70143,70144,70146],{},[898,70145,1754],{},[898,70147,1749],{},[902,70149,4808],{"encoding":904},[883,70151,70153],{"className":70152},[886],[888,70154,70155],{"xmlns":890},[892,70156,70157,70163],{},[895,70158,70159,70161],{},[898,70160,1718],{},[898,70162,1749],{},[902,70164,56132],{"encoding":904},[883,70166,70168],{"className":70167},[886],[888,70169,70170],{"xmlns":890},[892,70171,70172,70178],{},[895,70173,70174,70176],{},[898,70175,1728],{},[898,70177,1749],{},[902,70179,7344],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,70182,70183,46117,70186,70223,70224,69970,70239,69986,70254,70269,70270,7183,70285,70311,70312,70327,70328,1343,70343,7183,70358,70311,70383,70398,70399,70412,70413,70428,70429,70444,70445,1343,70458,1343,70473,1343,70488,1664],{},[38,70184,70185],{},"3.3",[883,70187,70189],{"className":70188},[886],[888,70190,70191],{"xmlns":890},[892,70192,70193,70220],{},[895,70194,70195,70197,70199,70201,70203,70205,70207,70209,70212,70214],{},[898,70196,1746],{},[1723,70198,1725],{},[898,70200,4897],{},[1723,70202,1908],{"stretchy":1907},[898,70204,1904],{},[1723,70206,1914],{"stretchy":1907},[1723,70208,1725],{},[1864,70210,70211],{},"1200",[1723,70213,1759],{},[2057,70215,70216,70218],{},[898,70217,1904],{},[1864,70219,2331],{},[902,70221,70222],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,70225,70227],{"className":70226},[886],[888,70228,70229],{"xmlns":890},[892,70230,70231,70237],{},[895,70232,70233,70235],{},[898,70234,1754],{},[898,70236,1749],{},[902,70238,4808],{"encoding":904},[883,70240,70242],{"className":70241},[886],[888,70243,70244],{"xmlns":890},[892,70245,70246,70252],{},[895,70247,70248,70250],{},[898,70249,1718],{},[898,70251,1749],{},[902,70253,56132],{"encoding":904},[883,70255,70257],{"className":70256},[886],[888,70258,70259],{"xmlns":890},[892,70260,70261,70267],{},[895,70262,70263,70265],{},[898,70264,1728],{},[898,70266,1749],{},[902,70268,7344],{"encoding":904},". (b) Vypočtěte ",[883,70271,70273],{"className":70272},[886],[888,70274,70275],{"xmlns":890},[892,70276,70277,70283],{},[895,70278,70279,70281],{},[898,70280,1754],{},[898,70282,1749],{},[902,70284,4808],{"encoding":904},[883,70286,70288],{"className":70287},[886],[888,70289,70290],{"xmlns":890},[892,70291,70292,70308],{},[895,70293,70294,70296,70298,70300,70302,70304,70306],{},[898,70295,1904],{},[1723,70297,1725],{},[1864,70299,3585],{},[1723,70301,2031],{"separator":2030},[1864,70303,9744],{},[1723,70305,2031],{"separator":2030},[1864,70307,38711],{},[902,70309,70310],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,70313,70315],{"className":70314},[886],[888,70316,70317],{"xmlns":890},[892,70318,70319,70325],{},[895,70320,70321,70323],{},[898,70322,1754],{},[898,70324,1749],{},[902,70326,4808],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,70329,70331],{"className":70330},[886],[888,70332,70333],{"xmlns":890},[892,70334,70335,70341],{},[895,70336,70337,70339],{},[898,70338,1718],{},[898,70340,1749],{},[902,70342,56132],{"encoding":904},[883,70344,70346],{"className":70345},[886],[888,70347,70348],{"xmlns":890},[892,70349,70350,70356],{},[895,70351,70352,70354],{},[898,70353,1728],{},[898,70355,1749],{},[902,70357,7344],{"encoding":904},[883,70359,70361],{"className":70360},[886],[888,70362,70363],{"xmlns":890},[892,70364,70365,70381],{},[895,70366,70367,70369,70371,70373,70375,70377,70379],{},[898,70368,1904],{},[1723,70370,1725],{},[1864,70372,3585],{},[1723,70374,2031],{"separator":2030},[1864,70376,9744],{},[1723,70378,2031],{"separator":2030},[1864,70380,38711],{},[902,70382,70310],{"encoding":904},[883,70384,70386],{"className":70385},[886],[888,70387,70388],{"xmlns":890},[892,70389,70390,70396],{},[895,70391,70392,70394],{},[898,70393,1728],{},[898,70395,1749],{},[902,70397,7344],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,70400,70402],{"className":70401},[886],[888,70403,70404],{"xmlns":890},[892,70405,70406,70410],{},[895,70407,70408],{},[898,70409,1904],{},[902,70411,1904],{"encoding":904},", které maximalizuje ",[883,70414,70416],{"className":70415},[886],[888,70417,70418],{"xmlns":890},[892,70419,70420,70426],{},[895,70421,70422,70424],{},[898,70423,1754],{},[898,70425,1749],{},[902,70427,4808],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,70430,70432],{"className":70431},[886],[888,70433,70434],{"xmlns":890},[892,70435,70436,70442],{},[895,70437,70438,70440],{},[898,70439,1754],{},[898,70441,1749],{},[902,70443,4808],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,70446,70448],{"className":70447},[886],[888,70449,70450],{"xmlns":890},[892,70451,70452,70456],{},[895,70453,70454],{},[898,70455,4897],{},[902,70457,4897],{"encoding":904},[883,70459,70461],{"className":70460},[886],[888,70462,70463],{"xmlns":890},[892,70464,70465,70471],{},[895,70466,70467,70469],{},[898,70468,1754],{},[898,70470,1749],{},[902,70472,4808],{"encoding":904},[883,70474,70476],{"className":70475},[886],[888,70477,70478],{"xmlns":890},[892,70479,70480,70486],{},[895,70481,70482,70484],{},[898,70483,1718],{},[898,70485,1749],{},[902,70487,56132],{"encoding":904},[883,70489,70491],{"className":70490},[886],[888,70492,70493],{"xmlns":890},[892,70494,70495,70501],{},[895,70496,70497,70499],{},[898,70498,1728],{},[898,70500,1749],{},[902,70502,7344],{"encoding":904},[724,70504,70505,70508,70509,70539,70540,70555,70556,10857,70569,1343,70587,1343,70604,70622,70623,70645,70646,70661,70662,70675,70676,1664],{},[38,70506,70507],{},"3.4"," Je dán celkový příjem ",[883,70510,70512],{"className":70511},[886],[888,70513,70514],{"xmlns":890},[892,70515,70516,70536],{},[895,70517,70518,70520,70522,70524,70526,70528,70530],{},[898,70519,1754],{},[898,70521,1749],{},[1723,70523,1725],{},[1864,70525,70211],{},[898,70527,1904],{},[1723,70529,1759],{},[2057,70531,70532,70534],{},[898,70533,1904],{},[1864,70535,2909],{},[902,70537,70538],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,70541,70543],{"className":70542},[886],[888,70544,70545],{"xmlns":890},[892,70546,70547,70553],{},[895,70548,70549,70551],{},[898,70550,1754],{},[898,70552,1749],{},[902,70554,4808],{"encoding":904}," vzhledem ke ",[883,70557,70559],{"className":70558},[886],[888,70560,70561],{"xmlns":890},[892,70562,70563,70567],{},[895,70564,70565],{},[898,70566,1904],{},[902,70568,1904],{"encoding":904},[883,70570,70572],{"className":70571},[886],[888,70573,70574],{"xmlns":890},[892,70575,70576,70584],{},[895,70577,70578,70580,70582],{},[898,70579,1904],{},[1723,70581,1725],{},[1864,70583,2962],{},[902,70585,70586],{"encoding":904},"Q = 5",[883,70588,70590],{"className":70589},[886],[888,70591,70592],{"xmlns":890},[892,70593,70594,70602],{},[895,70595,70596,70598,70600],{},[898,70597,1904],{},[1723,70599,1725],{},[1864,70601,6295],{},[902,70603,6298],{"encoding":904},[883,70605,70607],{"className":70606},[886],[888,70608,70609],{"xmlns":890},[892,70610,70611,70619],{},[895,70612,70613,70615,70617],{},[898,70614,1904],{},[1723,70616,1725],{},[1864,70618,4227],{},[902,70620,70621],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,70624,70626],{"className":70625},[886],[888,70627,70628],{"xmlns":890},[892,70629,70630,70642],{},[895,70631,70632,70634,70636,70638,70640],{},[898,70633,1728],{},[898,70635,1749],{},[1723,70637,1908],{"stretchy":1907},[1864,70639,3585],{},[1723,70641,1914],{"stretchy":1907},[902,70643,70644],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,70647,70649],{"className":70648},[886],[888,70650,70651],{"xmlns":890},[892,70652,70653,70659],{},[895,70654,70655,70657],{},[898,70656,1754],{},[898,70658,1749],{},[902,70660,4808],{"encoding":904},", jestliže se ",[883,70663,70665],{"className":70664},[886],[888,70666,70667],{"xmlns":890},[892,70668,70669,70673],{},[895,70670,70671],{},[898,70672,1904],{},[902,70674,1904],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,70677,70679],{"className":70678},[886],[888,70680,70681],{"xmlns":890},[892,70682,70683,70689],{},[895,70684,70685,70687],{},[898,70686,1754],{},[898,70688,1749],{},[902,70690,4808],{"encoding":904},[724,70692,70693,70696,70697,70723,70724,70739,70740,70661,70755,70768],{},[38,70694,70695],{},"3.5"," Je dán mezní příjem ",[883,70698,70700],{"className":70699},[886],[888,70701,70702],{"xmlns":890},[892,70703,70704,70720],{},[895,70705,70706,70708,70710,70712,70714,70716,70718],{},[898,70707,1728],{},[898,70709,1749],{},[1723,70711,1725],{},[1723,70713,1759],{},[898,70715,1904],{},[1723,70717,2087],{},[1864,70719,9744],{},[902,70721,70722],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,70725,70727],{"className":70726},[886],[888,70728,70729],{"xmlns":890},[892,70730,70731,70737],{},[895,70732,70733,70735],{},[898,70734,1754],{},[898,70736,1749],{},[902,70738,4808],{"encoding":904},". (b) Vypočtěte změnu ",[883,70741,70743],{"className":70742},[886],[888,70744,70745],{"xmlns":890},[892,70746,70747,70753],{},[895,70748,70749,70751],{},[898,70750,1754],{},[898,70752,1749],{},[902,70754,4808],{"encoding":904},[883,70756,70758],{"className":70757},[886],[888,70759,70760],{"xmlns":890},[892,70761,70762,70766],{},[895,70763,70764],{},[898,70765,1904],{},[902,70767,1904],{"encoding":904}," změní z 8 na 12.",[198,70770,70772],{"id":70771},"náklady-36316","Náklady (3.6–3.16)",[724,70774,70775,70778,70779,70819,70820,70835,70836,70853,70854,70871,70872,70887,70888,70903,70904,70269,70919,1343,70934,1343,70951,1343,70968,1343,70983,1343,70998,7183,71013,71031,71032,1343,71047,1343,71062,71077],{},[38,70776,70777],{},"3.6"," Jsou dány celkové náklady ",[883,70780,70782],{"className":70781},[886],[888,70783,70784],{"xmlns":890},[892,70785,70786,70816],{},[895,70787,70788,70790,70792,70794,70796,70798,70800,70802,70804],{},[898,70789,1754],{},[898,70791,1721],{},[1723,70793,1725],{},[1864,70795,3810],{},[1723,70797,2087],{},[1864,70799,2331],{},[898,70801,1904],{},[1723,70803,2087],{},[3055,70805,70806],{"scriptlevel":2256,"displaystyle":1907},[3058,70807,70808,70814],{},[2057,70809,70810,70812],{},[898,70811,1904],{},[1864,70813,2331],{},[1864,70815,3585],{},[902,70817,70818],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,70821,70823],{"className":70822},[886],[888,70824,70825],{"xmlns":890},[892,70826,70827,70833],{},[895,70828,70829,70831],{},[898,70830,11136],{},[898,70832,1721],{},[902,70834,56178],{"encoding":904},", celkové variabilní náklady ",[883,70837,70839],{"className":70838},[886],[888,70840,70841],{"xmlns":890},[892,70842,70843,70851],{},[895,70844,70845,70847,70849],{},[898,70846,1754],{},[898,70848,41031],{},[898,70850,1721],{},[902,70852,56196],{"encoding":904},", průměrné variabilní náklady ",[883,70855,70857],{"className":70856},[886],[888,70858,70859],{"xmlns":890},[892,70860,70861,70869],{},[895,70862,70863,70865,70867],{},[898,70864,1718],{},[898,70866,41031],{},[898,70868,1721],{},[902,70870,55998],{"encoding":904},", variabilní náklady na jednotku ",[883,70873,70875],{"className":70874},[886],[888,70876,70877],{"xmlns":890},[892,70878,70879,70885],{},[895,70880,70881,70883],{},[898,70882,41031],{},[898,70884,1721],{},[902,70886,64292],{"encoding":904},", průměrné náklady ",[883,70889,70891],{"className":70890},[886],[888,70892,70893],{"xmlns":890},[892,70894,70895,70901],{},[895,70896,70897,70899],{},[898,70898,1718],{},[898,70900,1721],{},[902,70902,56247],{"encoding":904}," a mezní náklady ",[883,70905,70907],{"className":70906},[886],[888,70908,70909],{"xmlns":890},[892,70910,70911,70917],{},[895,70912,70913,70915],{},[898,70914,1728],{},[898,70916,1721],{},[902,70918,55979],{"encoding":904},[883,70920,70922],{"className":70921},[886],[888,70923,70924],{"xmlns":890},[892,70925,70926,70932],{},[895,70927,70928,70930],{},[898,70929,1754],{},[898,70931,1721],{},[902,70933,3963],{"encoding":904},[883,70935,70937],{"className":70936},[886],[888,70938,70939],{"xmlns":890},[892,70940,70941,70949],{},[895,70942,70943,70945,70947],{},[898,70944,1754],{},[898,70946,41031],{},[898,70948,1721],{},[902,70950,56196],{"encoding":904},[883,70952,70954],{"className":70953},[886],[888,70955,70956],{"xmlns":890},[892,70957,70958,70966],{},[895,70959,70960,70962,70964],{},[898,70961,1718],{},[898,70963,41031],{},[898,70965,1721],{},[902,70967,55998],{"encoding":904},[883,70969,70971],{"className":70970},[886],[888,70972,70973],{"xmlns":890},[892,70974,70975,70981],{},[895,70976,70977,70979],{},[898,70978,41031],{},[898,70980,1721],{},[902,70982,64292],{"encoding":904},[883,70984,70986],{"className":70985},[886],[888,70987,70988],{"xmlns":890},[892,70989,70990,70996],{},[895,70991,70992,70994],{},[898,70993,1718],{},[898,70995,1721],{},[902,70997,56247],{"encoding":904},[883,70999,71001],{"className":71000},[886],[888,71002,71003],{"xmlns":890},[892,71004,71005,71011],{},[895,71006,71007,71009],{},[898,71008,1728],{},[898,71010,1721],{},[902,71012,55979],{"encoding":904},[883,71014,71016],{"className":71015},[886],[888,71017,71018],{"xmlns":890},[892,71019,71020,71028],{},[895,71021,71022,71024,71026],{},[898,71023,1904],{},[1723,71025,1725],{},[1864,71027,3840],{},[902,71029,71030],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,71033,71035],{"className":71034},[886],[888,71036,71037],{"xmlns":890},[892,71038,71039,71045],{},[895,71040,71041,71043],{},[898,71042,1754],{},[898,71044,1721],{},[902,71046,3963],{"encoding":904},[883,71048,71050],{"className":71049},[886],[888,71051,71052],{"xmlns":890},[892,71053,71054,71060],{},[895,71055,71056,71058],{},[898,71057,1718],{},[898,71059,1721],{},[902,71061,56247],{"encoding":904},[883,71063,71065],{"className":71064},[886],[888,71066,71067],{"xmlns":890},[892,71068,71069,71075],{},[895,71070,71071,71073],{},[898,71072,1728],{},[898,71074,1721],{},[902,71076,55979],{"encoding":904}," rostou, resp. klesají.",[724,71079,71080,71083,71084,70903,71114,71129,71130,71145,71146,1343,71161,1343,71176,1664],{},[38,71081,71082],{},"3.7"," Jsou dány průměrné náklady ",[883,71085,71087],{"className":71086},[886],[888,71088,71089],{"xmlns":890},[892,71090,71091,71111],{},[895,71092,71093,71095,71097,71099,71107,71109],{},[898,71094,1718],{},[898,71096,1721],{},[1723,71098,1725],{},[3055,71100,71101],{"scriptlevel":2256,"displaystyle":1907},[3058,71102,71103,71105],{},[1864,71104,3810],{},[898,71106,1904],{},[1723,71108,2087],{},[1864,71110,9744],{},[902,71112,71113],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,71115,71117],{"className":71116},[886],[888,71118,71119],{"xmlns":890},[892,71120,71121,71127],{},[895,71122,71123,71125],{},[898,71124,1728],{},[898,71126,1721],{},[902,71128,55979],{"encoding":904},". (a) Určete celkové náklady ",[883,71131,71133],{"className":71132},[886],[888,71134,71135],{"xmlns":890},[892,71136,71137,71143],{},[895,71138,71139,71141],{},[898,71140,1754],{},[898,71142,1721],{},[902,71144,3963],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,71147,71149],{"className":71148},[886],[888,71150,71151],{"xmlns":890},[892,71152,71153,71159],{},[895,71154,71155,71157],{},[898,71156,1718],{},[898,71158,1721],{},[902,71160,56247],{"encoding":904},[883,71162,71164],{"className":71163},[886],[888,71165,71166],{"xmlns":890},[892,71167,71168,71174],{},[895,71169,71170,71172],{},[898,71171,1754],{},[898,71173,1721],{},[902,71175,3963],{"encoding":904},[883,71177,71179],{"className":71178},[886],[888,71180,71181],{"xmlns":890},[892,71182,71183,71189],{},[895,71184,71185,71187],{},[898,71186,1728],{},[898,71188,1721],{},[902,71190,55979],{"encoding":904},[724,71192,71193,70778,71196,71240,71241,1343,71258,1343,71273,1343,71290,1343,71305,1343,71322,1664],{},[38,71194,71195],{},"3.8",[883,71197,71199],{"className":71198},[886],[888,71200,71201],{"xmlns":890},[892,71202,71203,71237],{},[895,71204,71205,71207,71209,71211,71213,71215,71217,71219,71221,71223,71229,71231],{},[898,71206,1754],{},[898,71208,1721],{},[1723,71210,1725],{},[1864,71212,47394],{},[1723,71214,2087],{},[1864,71216,38711],{},[898,71218,1904],{},[1723,71220,1759],{},[1864,71222,2969],{},[2057,71224,71225,71227],{},[898,71226,1904],{},[1864,71228,2331],{},[1723,71230,2087],{},[2057,71232,71233,71235],{},[898,71234,1904],{},[1864,71236,2909],{},[902,71238,71239],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,71242,71244],{"className":71243},[886],[888,71245,71246],{"xmlns":890},[892,71247,71248,71256],{},[895,71249,71250,71252,71254],{},[898,71251,1754],{},[898,71253,41031],{},[898,71255,1721],{},[902,71257,56196],{"encoding":904},[883,71259,71261],{"className":71260},[886],[888,71262,71263],{"xmlns":890},[892,71264,71265,71271],{},[895,71266,71267,71269],{},[898,71268,11136],{},[898,71270,1721],{},[902,71272,56178],{"encoding":904},[883,71274,71276],{"className":71275},[886],[888,71277,71278],{"xmlns":890},[892,71279,71280,71288],{},[895,71281,71282,71284,71286],{},[898,71283,1718],{},[898,71285,41031],{},[898,71287,1721],{},[902,71289,55998],{"encoding":904},[883,71291,71293],{"className":71292},[886],[888,71294,71295],{"xmlns":890},[892,71296,71297,71303],{},[895,71298,71299,71301],{},[898,71300,1718],{},[898,71302,1721],{},[902,71304,56247],{"encoding":904},[883,71306,71308],{"className":71307},[886],[888,71309,71310],{"xmlns":890},[892,71311,71312,71320],{},[895,71313,71314,71316,71318],{},[898,71315,1718],{},[898,71317,11136],{},[898,71319,1721],{},[902,71321,56214],{"encoding":904},[883,71323,71325],{"className":71324},[886],[888,71326,71327],{"xmlns":890},[892,71328,71329,71335],{},[895,71330,71331,71333],{},[898,71332,1728],{},[898,71334,1721],{},[902,71336,55979],{"encoding":904},[724,71338,71339,70778,71342,71372,71373,70555,71388,7183,71401,1343,71419,1343,71437,70622,71455,70645,71477,71492,71493,71506,71507,1664],{},[38,71340,71341],{},"3.9",[883,71343,71345],{"className":71344},[886],[888,71346,71347],{"xmlns":890},[892,71348,71349,71369],{},[895,71350,71351,71353,71355,71357,71359,71361,71363],{},[898,71352,1754],{},[898,71354,1721],{},[1723,71356,1725],{},[1864,71358,15811],{},[1723,71360,2087],{},[1864,71362,20015],{},[2057,71364,71365,71367],{},[898,71366,1904],{},[1864,71368,2331],{},[902,71370,71371],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,71374,71376],{"className":71375},[886],[888,71377,71378],{"xmlns":890},[892,71379,71380,71386],{},[895,71381,71382,71384],{},[898,71383,1754],{},[898,71385,1721],{},[902,71387,3963],{"encoding":904},[883,71389,71391],{"className":71390},[886],[888,71392,71393],{"xmlns":890},[892,71394,71395,71399],{},[895,71396,71397],{},[898,71398,1904],{},[902,71400,1904],{"encoding":904},[883,71402,71404],{"className":71403},[886],[888,71405,71406],{"xmlns":890},[892,71407,71408,71416],{},[895,71409,71410,71412,71414],{},[898,71411,1904],{},[1723,71413,1725],{},[1864,71415,3585],{},[902,71417,71418],{"encoding":904},"Q = 10",[883,71420,71422],{"className":71421},[886],[888,71423,71424],{"xmlns":890},[892,71425,71426,71434],{},[895,71427,71428,71430,71432],{},[898,71429,1904],{},[1723,71431,1725],{},[1864,71433,9744],{},[902,71435,71436],{"encoding":904},"Q = 20",[883,71438,71440],{"className":71439},[886],[888,71441,71442],{"xmlns":890},[892,71443,71444,71452],{},[895,71445,71446,71448,71450],{},[898,71447,1904],{},[1723,71449,1725],{},[1864,71451,38711],{},[902,71453,71454],{"encoding":904},"Q = 30",[883,71456,71458],{"className":71457},[886],[888,71459,71460],{"xmlns":890},[892,71461,71462,71474],{},[895,71463,71464,71466,71468,71470,71472],{},[898,71465,1728],{},[898,71467,1721],{},[1723,71469,1908],{"stretchy":1907},[1864,71471,36937],{},[1723,71473,1914],{"stretchy":1907},[902,71475,71476],{"encoding":904},"MC(15)",[883,71478,71480],{"className":71479},[886],[888,71481,71482],{"xmlns":890},[892,71483,71484,71490],{},[895,71485,71486,71488],{},[898,71487,1754],{},[898,71489,1721],{},[902,71491,3963],{"encoding":904}," v důsledku změny ",[883,71494,71496],{"className":71495},[886],[888,71497,71498],{"xmlns":890},[892,71499,71500,71504],{},[895,71501,71502],{},[898,71503,1904],{},[902,71505,1904],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,71508,71510],{"className":71509},[886],[888,71511,71512],{"xmlns":890},[892,71513,71514,71520],{},[895,71515,71516,71518],{},[898,71517,1754],{},[898,71519,1721],{},[902,71521,3963],{"encoding":904},[724,71523,71524,71527,71528,71129,71564,71579,71580,70739,71599,71492,71614,71627],{},[38,71525,71526],{},"3.10"," Jsou dány mezní náklady ",[883,71529,71531],{"className":71530},[886],[888,71532,71533],{"xmlns":890},[892,71534,71535,71561],{},[895,71536,71537,71539,71541,71543,71545,71547,71549,71551,71553,71555],{},[898,71538,1728],{},[898,71540,1721],{},[1723,71542,1725],{},[1864,71544,3846],{},[1723,71546,1759],{},[1864,71548,42554],{},[898,71550,1904],{},[1723,71552,2087],{},[1864,71554,65246],{},[2057,71556,71557,71559],{},[898,71558,1904],{},[1864,71560,2331],{},[902,71562,71563],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,71565,71567],{"className":71566},[886],[888,71568,71569],{"xmlns":890},[892,71570,71571,71577],{},[895,71572,71573,71575],{},[898,71574,1754],{},[898,71576,1721],{},[902,71578,3963],{"encoding":904},", jestliže fixní náklady ",[883,71581,71583],{"className":71582},[886],[888,71584,71585],{"xmlns":890},[892,71586,71587,71597],{},[895,71588,71589,71591,71593,71595],{},[898,71590,11136],{},[898,71592,1721],{},[1723,71594,1725],{},[1864,71596,3810],{},[902,71598,12334],{"encoding":904},[883,71600,71602],{"className":71601},[886],[888,71603,71604],{"xmlns":890},[892,71605,71606,71612],{},[895,71607,71608,71610],{},[898,71609,1754],{},[898,71611,1721],{},[902,71613,3963],{"encoding":904},[883,71615,71617],{"className":71616},[886],[888,71618,71619],{"xmlns":890},[892,71620,71621,71625],{},[895,71622,71623],{},[898,71624,1904],{},[902,71626,1904],{"encoding":904}," z 15 na 20.",[724,71629,71630,70778,71633,71676,71677,71690,71691,71706,71707,71722,71723,71690,71736,71706,71753,71770,71771,71690,71784,71706,71799,71814,71815,71835,71836,71859],{},[38,71631,71632],{},"3.11",[883,71634,71636],{"className":71635},[886],[888,71637,71638],{"xmlns":890},[892,71639,71640,71674],{},[895,71641,71642,71644,71646,71648,71650,71652,71654,71656,71658,71660,71666,71668],{},[898,71643,1754],{},[898,71645,1721],{},[1723,71647,1725],{},[1864,71649,3810],{},[1723,71651,2087],{},[1864,71653,5714],{},[898,71655,1904],{},[1723,71657,1759],{},[1864,71659,2962],{},[2057,71661,71662,71664],{},[898,71663,1904],{},[1864,71665,2331],{},[1723,71667,2087],{},[2057,71669,71670,71672],{},[898,71671,1904],{},[1864,71673,2909],{},[902,71675,61594],{"encoding":904},". (a) Určete ",[883,71678,71680],{"className":71679},[886],[888,71681,71682],{"xmlns":890},[892,71683,71684,71688],{},[895,71685,71686],{},[898,71687,1904],{},[902,71689,1904],{"encoding":904},", které minimalizuje ",[883,71692,71694],{"className":71693},[886],[888,71695,71696],{"xmlns":890},[892,71697,71698,71704],{},[895,71699,71700,71702],{},[898,71701,1728],{},[898,71703,1721],{},[902,71705,55979],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,71708,71710],{"className":71709},[886],[888,71711,71712],{"xmlns":890},[892,71713,71714,71720],{},[895,71715,71716,71718],{},[898,71717,1728],{},[898,71719,1721],{},[902,71721,55979],{"encoding":904},". (b) Určete ",[883,71724,71726],{"className":71725},[886],[888,71727,71728],{"xmlns":890},[892,71729,71730,71734],{},[895,71731,71732],{},[898,71733,1904],{},[902,71735,1904],{"encoding":904},[883,71737,71739],{"className":71738},[886],[888,71740,71741],{"xmlns":890},[892,71742,71743,71751],{},[895,71744,71745,71747,71749],{},[898,71746,1718],{},[898,71748,41031],{},[898,71750,1721],{},[902,71752,55998],{"encoding":904},[883,71754,71756],{"className":71755},[886],[888,71757,71758],{"xmlns":890},[892,71759,71760,71768],{},[895,71761,71762,71764,71766],{},[898,71763,1718],{},[898,71765,41031],{},[898,71767,1721],{},[902,71769,55998],{"encoding":904},". (c) Určete ",[883,71772,71774],{"className":71773},[886],[888,71775,71776],{"xmlns":890},[892,71777,71778,71782],{},[895,71779,71780],{},[898,71781,1904],{},[902,71783,1904],{"encoding":904},[883,71785,71787],{"className":71786},[886],[888,71788,71789],{"xmlns":890},[892,71790,71791,71797],{},[895,71792,71793,71795],{},[898,71794,1718],{},[898,71796,1721],{},[902,71798,56247],{"encoding":904},[883,71800,71802],{"className":71801},[886],[888,71803,71804],{"xmlns":890},[892,71805,71806,71812],{},[895,71807,71808,71810],{},[898,71809,1718],{},[898,71811,1721],{},[902,71813,56247],{"encoding":904}," (rada: hledaný kořen ",[883,71816,71818],{"className":71817},[886],[888,71819,71820],{"xmlns":890},[892,71821,71822,71832],{},[895,71823,71824,71826],{},[898,71825,1718],{},[2057,71827,71828,71830],{},[898,71829,1721],{},[1723,71831,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,71833,71834],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,71837,71839],{"className":71838},[886],[888,71840,71841],{"xmlns":890},[892,71842,71843,71856],{},[895,71844,71845,71847,71850,71852,71854],{},[1723,71846,1908],{"stretchy":1907},[1864,71848,71849],{},"4,7",[1723,71851,9135],{"separator":2030},[1864,71853,5989],{},[1723,71855,1914],{"stretchy":1907},[902,71857,71858],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,71861,71862,71865,71866,3350,71894,71911,71912,22287,71953,71974],{},[38,71863,71864],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,71867,71869],{"className":71868},[886],[888,71870,71871],{"xmlns":890},[892,71872,71873,71891],{},[895,71874,71875,71877,71879,71881,71883,71885,71887,71889],{},[898,71876,1718],{},[898,71878,1721],{},[1723,71880,1725],{},[898,71882,1718],{},[898,71884,1721],{},[1723,71886,1908],{"stretchy":1907},[898,71888,1904],{},[1723,71890,1914],{"stretchy":1907},[902,71892,71893],{"encoding":904},"AC = AC(Q)",[883,71895,71897],{"className":71896},[886],[888,71898,71899],{"xmlns":890},[892,71900,71901,71909],{},[895,71902,71903],{},[1931,71904,71905,71907],{},[898,71906,1904],{},[1864,71908,2256],{},[902,71910,39000],{"encoding":904}," minimum, pak platí ",[883,71913,71915],{"className":71914},[886],[888,71916,71917],{"xmlns":890},[892,71918,71919,71951],{},[895,71920,71921,71923,71925,71927,71933,71935,71937,71939,71941,71943,71949],{},[898,71922,1718],{},[898,71924,1721],{},[1723,71926,1908],{"stretchy":1907},[1931,71928,71929,71931],{},[898,71930,1904],{},[1864,71932,2256],{},[1723,71934,1914],{"stretchy":1907},[1723,71936,1725],{},[898,71938,1728],{},[898,71940,1721],{},[1723,71942,1908],{"stretchy":1907},[1931,71944,71945,71947],{},[898,71946,1904],{},[1864,71948,2256],{},[1723,71950,1914],{"stretchy":1907},[902,71952,63256],{"encoding":904},[883,71954,71956],{"className":71955},[886],[888,71957,71958],{"xmlns":890},[892,71959,71960,71972],{},[895,71961,71962,71964,71966,71968,71970],{},[898,71963,1728],{},[898,71965,1721],{},[1723,71967,1908],{"stretchy":1907},[898,71969,1904],{},[1723,71971,1914],{"stretchy":1907},[902,71973,68380],{"encoding":904}," jsou mezní náklady.",[724,71976,71977,70778,71980,71240,72014,71690,72027,71706,72042,1664],{},[38,71978,71979],{},"3.13",[883,71981,71983],{"className":71982},[886],[888,71984,71985],{"xmlns":890},[892,71986,71987,72011],{},[895,71988,71989,71991,71993,71995,72001,72003,72005,72007,72009],{},[898,71990,1754],{},[898,71992,1721],{},[1723,71994,1725],{},[2057,71996,71997,71999],{},[898,71998,1904],{},[1864,72000,2331],{},[1723,72002,2087],{},[1864,72004,2331],{},[898,72006,1904],{},[1723,72008,2087],{},[1864,72010,5714],{},[902,72012,72013],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,72015,72017],{"className":72016},[886],[888,72018,72019],{"xmlns":890},[892,72020,72021,72025],{},[895,72022,72023],{},[898,72024,1904],{},[902,72026,1904],{"encoding":904},[883,72028,72030],{"className":72029},[886],[888,72031,72032],{"xmlns":890},[892,72033,72034,72040],{},[895,72035,72036,72038],{},[898,72037,1718],{},[898,72039,1721],{},[902,72041,56247],{"encoding":904},[883,72043,72045],{"className":72044},[886],[888,72046,72047],{"xmlns":890},[892,72048,72049,72055],{},[895,72050,72051,72053],{},[898,72052,1718],{},[898,72054,1721],{},[902,72056,56247],{"encoding":904},[724,72058,72059,72062,72063,3350,72095,71911,72112,22287,72155,71974],{},[38,72060,72061],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,72064,72066],{"className":72065},[886],[888,72067,72068],{"xmlns":890},[892,72069,72070,72092],{},[895,72071,72072,72074,72076,72078,72080,72082,72084,72086,72088,72090],{},[898,72073,1718],{},[898,72075,41031],{},[898,72077,1721],{},[1723,72079,1725],{},[898,72081,1718],{},[898,72083,41031],{},[898,72085,1721],{},[1723,72087,1908],{"stretchy":1907},[898,72089,1904],{},[1723,72091,1914],{"stretchy":1907},[902,72093,72094],{"encoding":904},"AVC = AVC(Q)",[883,72096,72098],{"className":72097},[886],[888,72099,72100],{"xmlns":890},[892,72101,72102,72110],{},[895,72103,72104],{},[1931,72105,72106,72108],{},[898,72107,1904],{},[1864,72109,2256],{},[902,72111,39000],{"encoding":904},[883,72113,72115],{"className":72114},[886],[888,72116,72117],{"xmlns":890},[892,72118,72119,72153],{},[895,72120,72121,72123,72125,72127,72129,72135,72137,72139,72141,72143,72145,72151],{},[898,72122,1718],{},[898,72124,41031],{},[898,72126,1721],{},[1723,72128,1908],{"stretchy":1907},[1931,72130,72131,72133],{},[898,72132,1904],{},[1864,72134,2256],{},[1723,72136,1914],{"stretchy":1907},[1723,72138,1725],{},[898,72140,1728],{},[898,72142,1721],{},[1723,72144,1908],{"stretchy":1907},[1931,72146,72147,72149],{},[898,72148,1904],{},[1864,72150,2256],{},[1723,72152,1914],{"stretchy":1907},[902,72154,69705],{"encoding":904},[883,72156,72158],{"className":72157},[886],[888,72159,72160],{"xmlns":890},[892,72161,72162,72174],{},[895,72163,72164,72166,72168,72170,72172],{},[898,72165,1728],{},[898,72167,1721],{},[1723,72169,1908],{"stretchy":1907},[898,72171,1904],{},[1723,72173,1914],{"stretchy":1907},[902,72175,68380],{"encoding":904},[724,72177,72178,70778,72181,71240,72227,71690,72240,71706,72257,1664],{},[38,72179,72180],{},"3.15",[883,72182,72184],{"className":72183},[886],[888,72185,72186],{"xmlns":890},[892,72187,72188,72224],{},[895,72189,72190,72192,72194,72196,72198,72200,72202,72204,72206,72208,72214,72216,72218],{},[898,72191,1754],{},[898,72193,1721],{},[1723,72195,1725],{},[1864,72197,3840],{},[1723,72199,2087],{},[1864,72201,36937],{},[898,72203,1904],{},[1723,72205,1759],{},[1864,72207,2331],{},[2057,72209,72210,72212],{},[898,72211,1904],{},[1864,72213,2331],{},[1723,72215,2087],{},[1864,72217,3561],{},[2057,72219,72220,72222],{},[898,72221,1904],{},[1864,72223,2909],{},[902,72225,72226],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,72228,72230],{"className":72229},[886],[888,72231,72232],{"xmlns":890},[892,72233,72234,72238],{},[895,72235,72236],{},[898,72237,1904],{},[902,72239,1904],{"encoding":904},[883,72241,72243],{"className":72242},[886],[888,72244,72245],{"xmlns":890},[892,72246,72247,72255],{},[895,72248,72249,72251,72253],{},[898,72250,1718],{},[898,72252,41031],{},[898,72254,1721],{},[902,72256,55998],{"encoding":904},[883,72258,72260],{"className":72259},[886],[888,72261,72262],{"xmlns":890},[892,72263,72264,72272],{},[895,72265,72266,72268,72270],{},[898,72267,1718],{},[898,72269,41031],{},[898,72271,1721],{},[902,72273,55998],{"encoding":904},[724,72275,72276,72279,72280,72293,72294,72314],{},[38,72277,72278],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,72281,72283],{"className":72282},[886],[888,72284,72285],{"xmlns":890},[892,72286,72287,72291],{},[895,72288,72289],{},[898,72290,2750],{},[902,72292,2750],{"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 ",[883,72295,72297],{"className":72296},[886],[888,72298,72299],{"xmlns":890},[892,72300,72301,72311],{},[895,72302,72303,72305,72307,72309],{},[1864,72304,3585],{},[3018,72306,3707],{},[1864,72308,59769],{},[898,72310,2750],{},[902,72312,72313],{"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.",[198,72316,72318],{"id":72317},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,72320,72321,72324,72325,1682,72347,72373],{},[38,72322,72323],{},"3.17"," Jsou dány ",[883,72326,72328],{"className":72327},[886],[888,72329,72330],{"xmlns":890},[892,72331,72332,72344],{},[895,72333,72334,72336,72338,72340,72342],{},[898,72335,1754],{},[898,72337,1749],{},[1723,72339,1725],{},[1864,72341,3585],{},[898,72343,1904],{},[902,72345,72346],{"encoding":904},"TR = 10Q",[883,72348,72350],{"className":72349},[886],[888,72351,72352],{"xmlns":890},[892,72353,72354,72370],{},[895,72355,72356,72358,72360,72362,72364,72366,72368],{},[898,72357,1754],{},[898,72359,1721],{},[1723,72361,1725],{},[1864,72363,3810],{},[1723,72365,2087],{},[1864,72367,2962],{},[898,72369,1904],{},[902,72371,72372],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,72375,72376,72379,72380,6900,72395,72410,72411,1343,72433,22287,72460,72482,72483,72517],{},[38,72377,72378],{},"3.18"," Odvoďte, že jestliže ",[883,72381,72383],{"className":72382},[886],[888,72384,72385],{"xmlns":890},[892,72386,72387,72393],{},[895,72388,72389,72391],{},[898,72390,1754],{},[898,72392,1749],{},[902,72394,4808],{"encoding":904},[883,72396,72398],{"className":72397},[886],[888,72399,72400],{"xmlns":890},[892,72401,72402,72408],{},[895,72403,72404,72406],{},[898,72405,1754],{},[898,72407,1721],{},[902,72409,3963],{"encoding":904}," jsou lineární tvaru ",[883,72412,72414],{"className":72413},[886],[888,72415,72416],{"xmlns":890},[892,72417,72418,72430],{},[895,72419,72420,72422,72424,72426,72428],{},[898,72421,1754],{},[898,72423,1749],{},[1723,72425,1725],{},[898,72427,724],{},[898,72429,1904],{},[902,72431,72432],{"encoding":904},"TR = pQ",[883,72434,72436],{"className":72435},[886],[888,72437,72438],{"xmlns":890},[892,72439,72440,72457],{},[895,72441,72442,72444,72446,72448,72451,72453,72455],{},[898,72443,1754],{},[898,72445,1721],{},[1723,72447,1725],{},[898,72449,72450],{},"m",[1723,72452,2087],{},[898,72454,2192],{},[898,72456,1904],{},[902,72458,72459],{"encoding":904},"TC = m + nQ",[883,72461,72463],{"className":72462},[886],[888,72464,72465],{"xmlns":890},[892,72466,72467,72479],{},[895,72468,72469,72471,72473,72475,72477],{},[898,72470,72450],{},[1723,72472,2031],{"separator":2030},[898,72474,2192],{},[1723,72476,2031],{"separator":2030},[898,72478,724],{},[902,72480,72481],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,72484,72486],{"className":72485},[886],[888,72487,72488],{"xmlns":890},[892,72489,72490,72514],{},[895,72491,72492,72498,72500],{},[2057,72493,72494,72496],{},[898,72495,1904],{},[1723,72497,5066],{},[1723,72499,1725],{},[3055,72501,72502],{"scriptlevel":2256,"displaystyle":1907},[3058,72503,72504,72506],{},[898,72505,72450],{},[895,72507,72508,72510,72512],{},[898,72509,724],{},[1723,72511,1759],{},[898,72513,2192],{},[902,72515,72516],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,72519,72520,72324,72523,1682,72557,71676,72583,72596,72597,70428,72612,72627,72628,70412,72641,70428,72656,72671],{},[38,72521,72522],{},"3.19",[883,72524,72526],{"className":72525},[886],[888,72527,72528],{"xmlns":890},[892,72529,72530,72554],{},[895,72531,72532,72534,72536,72538,72540,72542,72548,72550,72552],{},[898,72533,1754],{},[898,72535,1749],{},[1723,72537,1725],{},[1723,72539,1759],{},[1864,72541,2331],{},[2057,72543,72544,72546],{},[898,72545,1904],{},[1864,72547,2331],{},[1723,72549,2087],{},[1864,72551,23639],{},[898,72553,1904],{},[902,72555,72556],{"encoding":904},"TR = -2Q^2 + 14Q",[883,72558,72560],{"className":72559},[886],[888,72561,72562],{"xmlns":890},[892,72563,72564,72580],{},[895,72565,72566,72568,72570,72572,72574,72576,72578],{},[898,72567,1754],{},[898,72569,1721],{},[1723,72571,1725],{},[1864,72573,2331],{},[898,72575,1904],{},[1723,72577,2087],{},[1864,72579,3585],{},[902,72581,72582],{"encoding":904},"TC = 2Q + 10",[883,72584,72586],{"className":72585},[886],[888,72587,72588],{"xmlns":890},[892,72589,72590,72594],{},[895,72591,72592],{},[898,72593,1904],{},[902,72595,1904],{"encoding":904},", které maximalizuje zisk ",[883,72598,72600],{"className":72599},[886],[888,72601,72602],{"xmlns":890},[892,72603,72604,72610],{},[895,72605,72606,72608],{},[898,72607,1746],{},[898,72609,1749],{},[902,72611,64166],{"encoding":904},[883,72613,72615],{"className":72614},[886],[888,72616,72617],{"xmlns":890},[892,72618,72619,72625],{},[895,72620,72621,72623],{},[898,72622,1746],{},[898,72624,1749],{},[902,72626,64166],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,72629,72631],{"className":72630},[886],[888,72632,72633],{"xmlns":890},[892,72634,72635,72639],{},[895,72636,72637],{},[898,72638,1904],{},[902,72640,1904],{"encoding":904},[883,72642,72644],{"className":72643},[886],[888,72645,72646],{"xmlns":890},[892,72647,72648,72654],{},[895,72649,72650,72652],{},[898,72651,1754],{},[898,72653,1749],{},[902,72655,4808],{"encoding":904},[883,72657,72659],{"className":72658},[886],[888,72660,72661],{"xmlns":890},[892,72662,72663,72669],{},[895,72664,72665,72667],{},[898,72666,1754],{},[898,72668,1749],{},[902,72670,4808],{"encoding":904},". (d) Graficky interpretujte.",[724,72673,72674,48375,72677,1343,72703,1343,72722,71676,72742,72596,72755,70428,72770,72785,72786,72808,72809,71859],{},[38,72675,72676],{},"3.20",[883,72678,72680],{"className":72679},[886],[888,72681,72682],{"xmlns":890},[892,72683,72684,72700],{},[895,72685,72686,72688,72690,72692,72694],{},[898,72687,1746],{},[1723,72689,1725],{},[1864,72691,20835],{},[1723,72693,1759],{},[2057,72695,72696,72698],{},[898,72697,1904],{},[1864,72699,2331],{},[902,72701,72702],{"encoding":904},"P = 400 - Q^2",[883,72704,72706],{"className":72705},[886],[888,72707,72708],{"xmlns":890},[892,72709,72710,72720],{},[895,72711,72712,72714,72716,72718],{},[898,72713,11136],{},[898,72715,1721],{},[1723,72717,1725],{},[1864,72719,3810],{},[902,72721,12334],{"encoding":904},[883,72723,72725],{"className":72724},[886],[888,72726,72727],{"xmlns":890},[892,72728,72729,72739],{},[895,72730,72731,72733,72735,72737],{},[898,72732,1728],{},[898,72734,1721],{},[1723,72736,1725],{},[1864,72738,9744],{},[902,72740,72741],{"encoding":904},"MC = 20",[883,72743,72745],{"className":72744},[886],[888,72746,72747],{"xmlns":890},[892,72748,72749,72753],{},[895,72750,72751],{},[898,72752,1904],{},[902,72754,1904],{"encoding":904},[883,72756,72758],{"className":72757},[886],[888,72759,72760],{"xmlns":890},[892,72761,72762,72768],{},[895,72763,72764,72766],{},[898,72765,1746],{},[898,72767,1749],{},[902,72769,64166],{"encoding":904},[883,72771,72773],{"className":72772},[886],[888,72774,72775],{"xmlns":890},[892,72776,72777,72783],{},[895,72778,72779,72781],{},[898,72780,1746],{},[898,72782,1749],{},[902,72784,64166],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,72787,72789],{"className":72788},[886],[888,72790,72791],{"xmlns":890},[892,72792,72793,72805],{},[895,72794,72795,72797,72799,72801,72803],{},[1723,72796,1908],{"stretchy":1907},[1864,72798,2256],{},[1723,72800,2031],{"separator":2030},[1864,72802,1866],{},[1723,72804,1914],{"stretchy":1907},[902,72806,72807],{"encoding":904},"(0, 1)",", druhý do ",[883,72810,72812],{"className":72811},[886],[888,72813,72814],{"xmlns":890},[892,72815,72816,72829],{},[895,72817,72818,72820,72823,72825,72827],{},[1723,72819,1908],{"stretchy":1907},[1864,72821,72822],{},"19",[1723,72824,2031],{"separator":2030},[1864,72826,9744],{},[1723,72828,1914],{"stretchy":1907},[902,72830,72831],{"encoding":904},"(19, 20)",[724,72833,72834,72837,72838,3350,72866,72883,72884,1664],{},[38,72835,72836],{},"3.21"," Dokažte, že má-li zisk ",[883,72839,72841],{"className":72840},[886],[888,72842,72843],{"xmlns":890},[892,72844,72845,72863],{},[895,72846,72847,72849,72851,72853,72855,72857,72859,72861],{},[898,72848,1746],{},[898,72850,1749],{},[1723,72852,1725],{},[898,72854,1746],{},[898,72856,1749],{},[1723,72858,1908],{"stretchy":1907},[898,72860,1904],{},[1723,72862,1914],{"stretchy":1907},[902,72864,72865],{"encoding":904},"PR = PR(Q)",[883,72867,72869],{"className":72868},[886],[888,72870,72871],{"xmlns":890},[892,72872,72873,72881],{},[895,72874,72875],{},[1931,72876,72877,72879],{},[898,72878,1904],{},[1864,72880,2256],{},[902,72882,39000],{"encoding":904}," maximum, pak platí ",[883,72885,72887],{"className":72886},[886],[888,72888,72889],{"xmlns":890},[892,72890,72891,72923],{},[895,72892,72893,72895,72897,72899,72905,72907,72909,72911,72913,72915,72921],{},[898,72894,1728],{},[898,72896,1749],{},[1723,72898,1908],{"stretchy":1907},[1931,72900,72901,72903],{},[898,72902,1904],{},[1864,72904,2256],{},[1723,72906,1914],{"stretchy":1907},[1723,72908,1725],{},[898,72910,1728],{},[898,72912,1721],{},[1723,72914,1908],{"stretchy":1907},[1931,72916,72917,72919],{},[898,72918,1904],{},[1864,72920,2256],{},[1723,72922,1914],{"stretchy":1907},[902,72924,66332],{"encoding":904},[724,72926,72927,72930,72931,1682,72946,56712,72961,72596,72974,72989,72990,1343,73017,73054,73055,1343,73082,1664],{},[38,72928,72929],{},"3.22"," Pro zadané ",[883,72932,72934],{"className":72933},[886],[888,72935,72936],{"xmlns":890},[892,72937,72938,72944],{},[895,72939,72940,72942],{},[898,72941,1728],{},[898,72943,1749],{},[902,72945,7344],{"encoding":904},[883,72947,72949],{"className":72948},[886],[888,72950,72951],{"xmlns":890},[892,72952,72953,72959],{},[895,72954,72955,72957],{},[898,72956,1728],{},[898,72958,1721],{},[902,72960,55979],{"encoding":904},[883,72962,72964],{"className":72963},[886],[888,72965,72966],{"xmlns":890},[892,72967,72968,72972],{},[895,72969,72970],{},[898,72971,1904],{},[902,72973,1904],{"encoding":904},[883,72975,72977],{"className":72976},[886],[888,72978,72979],{"xmlns":890},[892,72980,72981,72987],{},[895,72982,72983,72985],{},[898,72984,1746],{},[898,72986,1749],{},[902,72988,64166],{"encoding":904},". (a) ",[883,72991,72993],{"className":72992},[886],[888,72994,72995],{"xmlns":890},[892,72996,72997,73014],{},[895,72998,72999,73001,73003,73005,73008,73010,73012],{},[898,73000,1728],{},[898,73002,1749],{},[1723,73004,1725],{},[1864,73006,73007],{},"236",[1723,73009,1759],{},[1864,73011,42554],{},[898,73013,1904],{},[902,73015,73016],{"encoding":904},"MR = 236 - 16Q",[883,73018,73020],{"className":73019},[886],[888,73021,73022],{"xmlns":890},[892,73023,73024,73051],{},[895,73025,73026,73028,73030,73032,73034,73040,73042,73045,73047,73049],{},[898,73027,1728],{},[898,73029,1721],{},[1723,73031,1725],{},[1864,73033,2909],{},[2057,73035,73036,73038],{},[898,73037,1904],{},[1864,73039,2331],{},[1723,73041,1759],{},[1864,73043,73044],{},"32",[898,73046,1904],{},[1723,73048,2087],{},[1864,73050,6454],{},[902,73052,73053],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,73056,73058],{"className":73057},[886],[888,73059,73060],{"xmlns":890},[892,73061,73062,73079],{},[895,73063,73064,73066,73068,73070,73073,73075,73077],{},[898,73065,1728],{},[898,73067,1749],{},[1723,73069,1725],{},[1864,73071,73072],{},"280",[1723,73074,1759],{},[1864,73076,9744],{},[898,73078,1904],{},[902,73080,73081],{"encoding":904},"MR = 280 - 20Q",[883,73083,73085],{"className":73084},[886],[888,73086,73087],{"xmlns":890},[892,73088,73089,73116],{},[895,73090,73091,73093,73095,73097,73100,73106,73108,73110,73112,73114],{},[898,73092,1728],{},[898,73094,1721],{},[1723,73096,1725],{},[1864,73098,73099],{},"1,6",[2057,73101,73102,73104],{},[898,73103,1904],{},[1864,73105,2331],{},[1723,73107,1759],{},[1864,73109,36937],{},[898,73111,1904],{},[1723,73113,2087],{},[1864,73115,3846],{},[902,73117,73118],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,73120,73121,72930,73124,1682,73139,56712,73154,70412,73167,70428,73182,72989,73197,1343,73228,73054,73264,1343,73296,73340,73341,1343,73373,1664],{},[38,73122,73123],{},"3.23",[883,73125,73127],{"className":73126},[886],[888,73128,73129],{"xmlns":890},[892,73130,73131,73137],{},[895,73132,73133,73135],{},[898,73134,1754],{},[898,73136,1749],{},[902,73138,4808],{"encoding":904},[883,73140,73142],{"className":73141},[886],[888,73143,73144],{"xmlns":890},[892,73145,73146,73152],{},[895,73147,73148,73150],{},[898,73149,1754],{},[898,73151,1721],{},[902,73153,3963],{"encoding":904},[883,73155,73157],{"className":73156},[886],[888,73158,73159],{"xmlns":890},[892,73160,73161,73165],{},[895,73162,73163],{},[898,73164,1904],{},[902,73166,1904],{"encoding":904},[883,73168,73170],{"className":73169},[886],[888,73171,73172],{"xmlns":890},[892,73173,73174,73180],{},[895,73175,73176,73178],{},[898,73177,1746],{},[898,73179,1749],{},[902,73181,64166],{"encoding":904},[883,73183,73185],{"className":73184},[886],[888,73186,73187],{"xmlns":890},[892,73188,73189,73195],{},[895,73190,73191,73193],{},[898,73192,1746],{},[898,73194,1749],{},[902,73196,64166],{"encoding":904},[883,73198,73200],{"className":73199},[886],[888,73201,73202],{"xmlns":890},[892,73203,73204,73225],{},[895,73205,73206,73208,73210,73212,73215,73217,73219],{},[898,73207,1754],{},[898,73209,1749],{},[1723,73211,1725],{},[1864,73213,73214],{},"125",[898,73216,1904],{},[1723,73218,1759],{},[2057,73220,73221,73223],{},[898,73222,1904],{},[1864,73224,2331],{},[902,73226,73227],{"encoding":904},"TR = 125Q - Q^2",[883,73229,73231],{"className":73230},[886],[888,73232,73233],{"xmlns":890},[892,73234,73235,73261],{},[895,73236,73237,73239,73241,73243,73245,73247,73249,73251,73253,73255],{},[898,73238,1754],{},[898,73240,1721],{},[1723,73242,1725],{},[1864,73244,15811],{},[1723,73246,2087],{},[1864,73248,2962],{},[898,73250,1904],{},[1723,73252,2087],{},[1864,73254,5719],{},[2057,73256,73257,73259],{},[898,73258,1904],{},[1864,73260,2331],{},[902,73262,73263],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,73265,73267],{"className":73266},[886],[888,73268,73269],{"xmlns":890},[892,73270,73271,73293],{},[895,73272,73273,73275,73277,73279,73281,73283,73285,73287],{},[898,73274,1754],{},[898,73276,1749],{},[1723,73278,1725],{},[1864,73280,9744],{},[898,73282,1904],{},[1723,73284,1759],{},[1864,73286,2331],{},[2057,73288,73289,73291],{},[898,73290,1904],{},[1864,73292,2331],{},[902,73294,73295],{"encoding":904},"TR = 20Q - 2Q^2",[883,73297,73299],{"className":73298},[886],[888,73300,73301],{"xmlns":890},[892,73302,73303,73337],{},[895,73304,73305,73307,73309,73311,73313,73315,73317,73319,73321,73323,73329,73331],{},[898,73306,1754],{},[898,73308,1721],{},[1723,73310,1725],{},[1864,73312,2331],{},[1723,73314,2087],{},[1864,73316,9744],{},[898,73318,1904],{},[1723,73320,1759],{},[1864,73322,6295],{},[2057,73324,73325,73327],{},[898,73326,1904],{},[1864,73328,2331],{},[1723,73330,2087],{},[2057,73332,73333,73335],{},[898,73334,1904],{},[1864,73336,2909],{},[902,73338,73339],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,73342,73344],{"className":73343},[886],[888,73345,73346],{"xmlns":890},[892,73347,73348,73370],{},[895,73349,73350,73352,73354,73356,73358,73360,73362,73364],{},[898,73351,1754],{},[898,73353,1749],{},[1723,73355,1725],{},[1864,73357,3080],{},[898,73359,1904],{},[1723,73361,1759],{},[1864,73363,24482],{},[2057,73365,73366,73368],{},[898,73367,1904],{},[1864,73369,2331],{},[902,73371,73372],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,73374,73376],{"className":73375},[886],[888,73377,73378],{"xmlns":890},[892,73379,73380,73428],{},[895,73381,73382,73384,73386,73388,73390,73392,73394,73396,73398,73414,73416],{},[898,73383,1754],{},[898,73385,1721],{},[1723,73387,1725],{},[1864,73389,3080],{},[1723,73391,2087],{},[1864,73393,2331],{},[898,73395,1904],{},[1723,73397,1759],{},[3055,73399,73400],{"scriptlevel":2256,"displaystyle":1907},[3058,73401,73402,73412],{},[895,73403,73404,73406],{},[1864,73405,2909],{},[2057,73407,73408,73410],{},[898,73409,1904],{},[1864,73411,2331],{},[1864,73413,3585],{},[1723,73415,2087],{},[3055,73417,73418],{"scriptlevel":2256,"displaystyle":1907},[3058,73419,73420,73426],{},[2057,73421,73422,73424],{},[898,73423,1904],{},[1864,73425,2909],{},[1864,73427,9744],{},[902,73429,73430],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,73432,73433,73436,73437,73467,73468,73500,73501,22287,73531,73561],{},[38,73434,73435],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,73438,73440],{"className":73439},[886],[888,73441,73442],{"xmlns":890},[892,73443,73444,73464],{},[895,73445,73446,73452,73454,73456,73458],{},[1931,73447,73448,73450],{},[898,73449,1746],{},[1864,73451,1866],{},[1723,73453,1725],{},[1864,73455,15811],{},[1723,73457,1759],{},[1931,73459,73460,73462],{},[898,73461,1904],{},[1864,73463,1866],{},[902,73465,73466],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,73469,73471],{"className":73470},[886],[888,73472,73473],{"xmlns":890},[892,73474,73475,73497],{},[895,73476,73477,73483,73485,73487,73489,73491],{},[1931,73478,73479,73481],{},[898,73480,1746],{},[1864,73482,2331],{},[1723,73484,1725],{},[1864,73486,30774],{},[1723,73488,1759],{},[1864,73490,65246],{},[1931,73492,73493,73495],{},[898,73494,1904],{},[1864,73496,2331],{},[902,73498,73499],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,73502,73504],{"className":73503},[886],[888,73505,73506],{"xmlns":890},[892,73507,73508,73528],{},[895,73509,73510,73512,73514,73516,73518,73520,73522,73524,73526],{},[898,73511,1754],{},[898,73513,1721],{},[1723,73515,1725],{},[1864,73517,3840],{},[3018,73519,3707],{},[1864,73521,59769],{},[1723,73523,2087],{},[1864,73525,9744],{},[898,73527,1904],{},[902,73529,73530],{"encoding":904},"TC = 50\\,000 + 20Q",[883,73532,73534],{"className":73533},[886],[888,73535,73536],{"xmlns":890},[892,73537,73538,73558],{},[895,73539,73540,73542,73544,73550,73552],{},[898,73541,1904],{},[1723,73543,1725],{},[1931,73545,73546,73548],{},[898,73547,1904],{},[1864,73549,1866],{},[1723,73551,2087],{},[1931,73553,73554,73556],{},[898,73555,1904],{},[1864,73557,2331],{},[902,73559,73560],{"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.",[724,73563,73564,73567,73568,73598,73599,73500,73631,22287,73661,73690],{},[38,73565,73566],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,73569,73571],{"className":73570},[886],[888,73572,73573],{"xmlns":890},[892,73574,73575,73595],{},[895,73576,73577,73583,73585,73587,73589],{},[1931,73578,73579,73581],{},[898,73580,1746],{},[1864,73582,1866],{},[1723,73584,1725],{},[1864,73586,30774],{},[1723,73588,1759],{},[1931,73590,73591,73593],{},[898,73592,1904],{},[1864,73594,1866],{},[902,73596,73597],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,73600,73602],{"className":73601},[886],[888,73603,73604],{"xmlns":890},[892,73605,73606,73628],{},[895,73607,73608,73614,73616,73618,73620,73622],{},[1931,73609,73610,73612],{},[898,73611,1746],{},[1864,73613,2331],{},[1723,73615,1725],{},[1864,73617,9087],{},[1723,73619,1759],{},[1864,73621,5719],{},[1931,73623,73624,73626],{},[898,73625,1904],{},[1864,73627,2331],{},[902,73629,73630],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,73632,73634],{"className":73633},[886],[888,73635,73636],{"xmlns":890},[892,73637,73638,73658],{},[895,73639,73640,73642,73644,73646,73648,73650,73652,73654,73656],{},[898,73641,1754],{},[898,73643,1721],{},[1723,73645,1725],{},[1864,73647,2962],{},[3018,73649,3707],{},[1864,73651,59769],{},[1723,73653,2087],{},[1864,73655,3810],{},[898,73657,1904],{},[902,73659,73660],{"encoding":904},"TC = 5\\,000 + 100Q",[883,73662,73664],{"className":73663},[886],[888,73665,73666],{"xmlns":890},[892,73667,73668,73688],{},[895,73669,73670,73672,73674,73680,73682],{},[898,73671,1904],{},[1723,73673,1725],{},[1931,73675,73676,73678],{},[898,73677,1904],{},[1864,73679,1866],{},[1723,73681,2087],{},[1931,73683,73684,73686],{},[898,73685,1904],{},[1864,73687,2331],{},[902,73689,73560],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,73692,73694],{"id":73693},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,73696,73697,73700,73701,73748,73749,73766],{},[38,73698,73699],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,73702,73704],{"className":73703},[886],[888,73705,73706],{"xmlns":890},[892,73707,73708,73745],{},[895,73709,73710,73712,73714,73716,73718,73721,73727,73729,73732,73738,73740,73743],{},[898,73711,1754],{},[898,73713,41031],{},[898,73715,1721],{},[1723,73717,1725],{},[1864,73719,73720],{},"0,85",[2057,73722,73723,73725],{},[898,73724,1904],{},[1864,73726,2909],{},[1723,73728,1759],{},[1864,73730,73731],{},"11,9",[2057,73733,73734,73736],{},[898,73735,1904],{},[1864,73737,2331],{},[1723,73739,2087],{},[1864,73741,73742],{},"102",[898,73744,1904],{},[902,73746,73747],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,73750,73752],{"className":73751},[886],[888,73753,73754],{"xmlns":890},[892,73755,73756,73764],{},[895,73757,73758],{},[2057,73759,73760,73762],{},[898,73761,1746],{},[1723,73763,5066],{},[902,73765,5116],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,73768,73769,71527,73772,73808],{},[38,73770,73771],{},"3.27",[883,73773,73775],{"className":73774},[886],[888,73776,73777],{"xmlns":890},[892,73778,73779,73805],{},[895,73780,73781,73783,73785,73787,73789,73795,73797,73799,73801,73803],{},[898,73782,1728],{},[898,73784,1721],{},[1723,73786,1725],{},[1864,73788,3645],{},[2057,73790,73791,73793],{},[898,73792,1904],{},[1864,73794,2331],{},[1723,73796,1759],{},[1864,73798,65127],{},[898,73800,1904],{},[1723,73802,2087],{},[1864,73804,31436],{},[902,73806,73807],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,73810,73811,70778,73814,73808],{},[38,73812,73813],{},"3.28",[883,73815,73817],{"className":73816},[886],[888,73818,73819],{"xmlns":890},[892,73820,73821,73857],{},[895,73822,73823,73825,73827,73829,73831,73837,73839,73841,73847,73849,73851,73853,73855],{},[898,73824,1754],{},[898,73826,1721],{},[1723,73828,1725],{},[1864,73830,5719],{},[2057,73832,73833,73835],{},[898,73834,1904],{},[1864,73836,2909],{},[1723,73838,1759],{},[1864,73840,24894],{},[2057,73842,73843,73845],{},[898,73844,1904],{},[1864,73846,2331],{},[1723,73848,2087],{},[1864,73850,3846],{},[898,73852,1904],{},[1723,73854,2087],{},[1864,73856,15811],{},[902,73858,73859],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,73861,16421],{"id":16420},[120,73863,73864,73892,73937,74009,74074,74114,74206,74312,74352,74466,74559,74623,74655,74715,74721,74785,74834,74888,74996,75051],{},[123,73865,73866,2628,73868,73891],{},[38,73867,56437],{},[883,73869,73871],{"className":73870},[886],[888,73872,73873],{"xmlns":890},[892,73874,73875,73889],{},[895,73876,73877,73879,73881,73883,73885,73887],{},[898,73878,1754],{},[898,73880,1749],{},[1723,73882,1725],{},[898,73884,1746],{},[1723,73886,3897],{},[898,73888,1904],{},[902,73890,67399],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,73893,73894,2628,73896,73936],{},[38,73895,57023],{},[883,73897,73899],{"className":73898},[886],[888,73900,73901],{"xmlns":890},[892,73902,73903,73933],{},[895,73904,73905,73907,73909,73911,73923,73925,73927,73929,73931],{},[898,73906,1718],{},[898,73908,1749],{},[1723,73910,1725],{},[3055,73912,73913],{"scriptlevel":2256,"displaystyle":1907},[3058,73914,73915,73921],{},[895,73916,73917,73919],{},[898,73918,1754],{},[898,73920,1749],{},[898,73922,1904],{},[1723,73924,1725],{},[898,73926,4897],{},[1723,73928,1908],{"stretchy":1907},[898,73930,1904],{},[1723,73932,1914],{"stretchy":1907},[902,73934,73935],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,73938,73939,2628,73941,73977,73978,73993,73994,1664],{},[38,73940,57171],{},[883,73942,73944],{"className":73943},[886],[888,73945,73946],{"xmlns":890},[892,73947,73948,73974],{},[895,73949,73950,73952,73954,73956],{},[898,73951,1728],{},[898,73953,1749],{},[1723,73955,1725],{},[3055,73957,73958],{"scriptlevel":2256,"displaystyle":1907},[3058,73959,73960,73968],{},[895,73961,73962,73964,73966],{},[898,73963,2930],{"mathvariant":2124},[898,73965,1754],{},[898,73967,1749],{},[895,73969,73970,73972],{},[898,73971,2930],{"mathvariant":2124},[898,73973,1904],{},[902,73975,73976],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,73979,73981],{"className":73980},[886],[888,73982,73983],{"xmlns":890},[892,73984,73985,73991],{},[895,73986,73987,73989],{},[898,73988,1754],{},[898,73990,1749],{},[902,73992,4808],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,73995,73997],{"className":73996},[886],[888,73998,73999],{"xmlns":890},[892,74000,74001,74007],{},[895,74002,74003,74005],{},[898,74004,1718],{},[898,74006,1749],{},[902,74008,56132],{"encoding":904},[123,74010,74011,2628,74014,1343,74044,1664],{},[38,74012,74013],{},"Diferenciál příjmu\u002Fnákladů",[883,74015,74017],{"className":74016},[886],[888,74018,74019],{"xmlns":890},[892,74020,74021,74041],{},[895,74022,74023,74025,74027,74029,74031,74033,74035,74037,74039],{},[898,74024,3611],{"mathvariant":2124},[898,74026,1754],{},[898,74028,1749],{},[1723,74030,3456],{},[898,74032,1728],{},[898,74034,1749],{},[3018,74036,3707],{},[898,74038,2930],{"mathvariant":2124},[898,74040,1904],{},[902,74042,74043],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,74045,74047],{"className":74046},[886],[888,74048,74049],{"xmlns":890},[892,74050,74051,74071],{},[895,74052,74053,74055,74057,74059,74061,74063,74065,74067,74069],{},[898,74054,3611],{"mathvariant":2124},[898,74056,1754],{},[898,74058,1721],{},[1723,74060,3456],{},[898,74062,1728],{},[898,74064,1721],{},[3018,74066,3707],{},[898,74068,2930],{"mathvariant":2124},[898,74070,1904],{},[902,74072,74073],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,74075,74076,2628,74078,1664],{},[38,74077,59293],{},[883,74079,74081],{"className":74080},[886],[888,74082,74083],{"xmlns":890},[892,74084,74085,74111],{},[895,74086,74087,74089,74091,74093,74095,74097,74099,74101,74103,74105,74107,74109],{},[898,74088,1754],{},[898,74090,1721],{},[1723,74092,1725],{},[898,74094,11136],{},[898,74096,1721],{},[1723,74098,2087],{},[898,74100,1754],{},[898,74102,41031],{},[898,74104,1721],{},[1723,74106,1908],{"stretchy":1907},[898,74108,1904],{},[1723,74110,1914],{"stretchy":1907},[902,74112,74113],{"encoding":904},"TC = FC + TVC(Q)",[123,74115,74116,2628,74119,1343,74134,2628,74136,1343,74159,2628,74162,1664],{},[38,74117,74118],{},"Fixní náklady",[883,74120,74122],{"className":74121},[886],[888,74123,74124],{"xmlns":890},[892,74125,74126,74132],{},[895,74127,74128,74130],{},[898,74129,11136],{},[898,74131,1721],{},[902,74133,56178],{"encoding":904},[38,74135,59446],{},[883,74137,74139],{"className":74138},[886],[888,74140,74141],{"xmlns":890},[892,74142,74143,74157],{},[895,74144,74145,74147,74149,74151,74153,74155],{},[898,74146,1754],{},[898,74148,41031],{},[898,74150,1721],{},[1723,74152,1908],{"stretchy":1907},[898,74154,1904],{},[1723,74156,1914],{"stretchy":1907},[902,74158,59443],{"encoding":904},[38,74160,74161],{},"variabilní náklady na jednotku",[883,74163,74165],{"className":74164},[886],[888,74166,74167],{"xmlns":890},[892,74168,74169,74203],{},[895,74170,74171,74173,74175,74177,74179,74181,74183],{},[898,74172,41031],{},[898,74174,1721],{},[1723,74176,1908],{"stretchy":1907},[898,74178,1904],{},[1723,74180,1914],{"stretchy":1907},[1723,74182,1725],{},[3055,74184,74185],{"scriptlevel":2256,"displaystyle":1907},[3058,74186,74187,74201],{},[895,74188,74189,74191,74193,74195,74197,74199],{},[898,74190,1754],{},[898,74192,41031],{},[898,74194,1721],{},[1723,74196,1908],{"stretchy":1907},[898,74198,1904],{},[1723,74200,1914],{"stretchy":1907},[898,74202,1904],{},[902,74204,74205],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,74207,74208,2628,74210,1343,74240,2628,74243,1343,74275,2628,74278,1664],{},[38,74209,59454],{},[883,74211,74213],{"className":74212},[886],[888,74214,74215],{"xmlns":890},[892,74216,74217,74237],{},[895,74218,74219,74221,74223,74225],{},[898,74220,1718],{},[898,74222,1721],{},[1723,74224,1725],{},[3055,74226,74227],{"scriptlevel":2256,"displaystyle":1907},[3058,74228,74229,74235],{},[895,74230,74231,74233],{},[898,74232,1754],{},[898,74234,1721],{},[898,74236,1904],{},[902,74238,74239],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,74241,74242],{},"průměrné fixní",[883,74244,74246],{"className":74245},[886],[888,74247,74248],{"xmlns":890},[892,74249,74250,74272],{},[895,74251,74252,74254,74256,74258,74260],{},[898,74253,1718],{},[898,74255,11136],{},[898,74257,1721],{},[1723,74259,1725],{},[3055,74261,74262],{"scriptlevel":2256,"displaystyle":1907},[3058,74263,74264,74270],{},[895,74265,74266,74268],{},[898,74267,11136],{},[898,74269,1721],{},[898,74271,1904],{},[902,74273,74274],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,74276,74277],{},"průměrné variabilní",[883,74279,74281],{"className":74280},[886],[888,74282,74283],{"xmlns":890},[892,74284,74285,74309],{},[895,74286,74287,74289,74291,74293,74295],{},[898,74288,1718],{},[898,74290,41031],{},[898,74292,1721],{},[1723,74294,1725],{},[3055,74296,74297],{"scriptlevel":2256,"displaystyle":1907},[3058,74298,74299,74307],{},[895,74300,74301,74303,74305],{},[898,74302,1754],{},[898,74304,41031],{},[898,74306,1721],{},[898,74308,1904],{},[902,74310,74311],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,74313,74314,2628,74316,1664],{},[38,74315,60641],{},[883,74317,74319],{"className":74318},[886],[888,74320,74321],{"xmlns":890},[892,74322,74323,74349],{},[895,74324,74325,74327,74329,74331],{},[898,74326,1728],{},[898,74328,1721],{},[1723,74330,1725],{},[3055,74332,74333],{"scriptlevel":2256,"displaystyle":1907},[3058,74334,74335,74343],{},[895,74336,74337,74339,74341],{},[898,74338,2930],{"mathvariant":2124},[898,74340,1754],{},[898,74342,1721],{},[895,74344,74345,74347],{},[898,74346,2930],{"mathvariant":2124},[898,74348,1904],{},[902,74350,74351],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,74353,74354,2628,74356,74404,74405,74418,74419,1343,74434,1343,74451,1664],{},[38,74355,61539],{},[883,74357,74359],{"className":74358},[886],[888,74360,74361],{"xmlns":890},[892,74362,74363,74401],{},[895,74364,74365,74367,74369,74371,74373,74375,74377,74379,74381,74383,74385,74391,74393,74395],{},[898,74366,1754],{},[898,74368,1721],{},[1723,74370,1725],{},[898,74372,11136],{},[898,74374,1721],{},[1723,74376,2087],{},[898,74378,207],{},[898,74380,1904],{},[1723,74382,2087],{},[898,74384,2069],{},[2057,74386,74387,74389],{},[898,74388,1904],{},[1864,74390,2331],{},[1723,74392,2087],{},[898,74394,2878],{},[2057,74396,74397,74399],{},[898,74398,1904],{},[1864,74400,2909],{},[902,74402,74403],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,74406,74408],{"className":74407},[886],[888,74409,74410],{"xmlns":890},[892,74411,74412,74416],{},[895,74413,74414],{},[898,74415,900],{},[902,74417,900],{"encoding":904},"-průběhem ",[883,74420,74422],{"className":74421},[886],[888,74423,74424],{"xmlns":890},[892,74425,74426,74432],{},[895,74427,74428,74430],{},[898,74429,1718],{},[898,74431,1721],{},[902,74433,56247],{"encoding":904},[883,74435,74437],{"className":74436},[886],[888,74438,74439],{"xmlns":890},[892,74440,74441,74449],{},[895,74442,74443,74445,74447],{},[898,74444,1718],{},[898,74446,41031],{},[898,74448,1721],{},[902,74450,55998],{"encoding":904},[883,74452,74454],{"className":74453},[886],[888,74455,74456],{"xmlns":890},[892,74457,74458,74464],{},[895,74459,74460,74462],{},[898,74461,1728],{},[898,74463,1721],{},[902,74465,55979],{"encoding":904},[123,74467,74468,74470,74471,11094,74486,74527,74528,62184,74543,74558],{},[38,74469,62621],{},": v bodě minima ",[883,74472,74474],{"className":74473},[886],[888,74475,74476],{"xmlns":890},[892,74477,74478,74484],{},[895,74479,74480,74482],{},[898,74481,1718],{},[898,74483,1721],{},[902,74485,56247],{"encoding":904},[883,74487,74489],{"className":74488},[886],[888,74490,74491],{"xmlns":890},[892,74492,74493,74525],{},[895,74494,74495,74497,74499,74501,74507,74509,74511,74513,74515,74517,74523],{},[898,74496,1718],{},[898,74498,1721],{},[1723,74500,1908],{"stretchy":1907},[1931,74502,74503,74505],{},[898,74504,1904],{},[1864,74506,2256],{},[1723,74508,1914],{"stretchy":1907},[1723,74510,1725],{},[898,74512,1728],{},[898,74514,1721],{},[1723,74516,1908],{"stretchy":1907},[1931,74518,74519,74521],{},[898,74520,1904],{},[1864,74522,2256],{},[1723,74524,1914],{"stretchy":1907},[902,74526,63256],{"encoding":904},"; geometricky ",[883,74529,74531],{"className":74530},[886],[888,74532,74533],{"xmlns":890},[892,74534,74535,74541],{},[895,74536,74537,74539],{},[898,74538,1728],{},[898,74540,1721],{},[902,74542,55979],{"encoding":904},[883,74544,74546],{"className":74545},[886],[888,74547,74548],{"xmlns":890},[892,74549,74550,74556],{},[895,74551,74552,74554],{},[898,74553,1718],{},[898,74555,1721],{},[902,74557,56247],{"encoding":904}," v jejím minimu.",[123,74560,74561,74470,74563,11094,74580,1664],{},[38,74562,63971],{},[883,74564,74566],{"className":74565},[886],[888,74567,74568],{"xmlns":890},[892,74569,74570,74578],{},[895,74571,74572,74574,74576],{},[898,74573,1718],{},[898,74575,41031],{},[898,74577,1721],{},[902,74579,55998],{"encoding":904},[883,74581,74583],{"className":74582},[886],[888,74584,74585],{"xmlns":890},[892,74586,74587,74621],{},[895,74588,74589,74591,74593,74595,74597,74603,74605,74607,74609,74611,74613,74619],{},[898,74590,1718],{},[898,74592,41031],{},[898,74594,1721],{},[1723,74596,1908],{"stretchy":1907},[1931,74598,74599,74601],{},[898,74600,1904],{},[1864,74602,2256],{},[1723,74604,1914],{"stretchy":1907},[1723,74606,1725],{},[898,74608,1728],{},[898,74610,1721],{},[1723,74612,1908],{"stretchy":1907},[1931,74614,74615,74617],{},[898,74616,1904],{},[1864,74618,2256],{},[1723,74620,1914],{"stretchy":1907},[902,74622,69705],{"encoding":904},[123,74624,74625,2628,74627,74654],{},[38,74626,64150],{},[883,74628,74630],{"className":74629},[886],[888,74631,74632],{"xmlns":890},[892,74633,74634,74652],{},[895,74635,74636,74638,74640,74642,74644,74646,74648,74650],{},[898,74637,1746],{},[898,74639,1749],{},[1723,74641,1725],{},[898,74643,1754],{},[898,74645,1749],{},[1723,74647,1759],{},[898,74649,1754],{},[898,74651,1721],{},[902,74653,1766],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,74656,74657,1981,74659,74661,74662,74688,74689,74714],{},[38,74658,65012],{},[614,74660,64275],{},") — hodnoty ",[883,74663,74665],{"className":74664},[886],[888,74666,74667],{"xmlns":890},[892,74668,74669,74685],{},[895,74670,74671,74677,74679],{},[1931,74672,74673,74675],{},[898,74674,1904],{},[898,74676,1718],{},[1723,74678,2031],{"separator":2030},[1931,74680,74681,74683],{},[898,74682,1904],{},[898,74684,23946],{},[902,74686,74687],{"encoding":904},"Q_A, Q_B"," splňující ",[883,74690,74692],{"className":74691},[886],[888,74693,74694],{"xmlns":890},[892,74695,74696,74712],{},[895,74697,74698,74700,74702,74704,74706,74708,74710],{},[898,74699,1746],{},[898,74701,1749],{},[1723,74703,1908],{"stretchy":1907},[898,74705,1904],{},[1723,74707,1914],{"stretchy":1907},[1723,74709,1725],{},[1864,74711,2256],{},[902,74713,64552],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,74716,74717,74720],{},[38,74718,74719],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,74722,74723,74725,74726,11094,74743,74784],{},[38,74724,66066],{}," — v bodě maxima zisku ",[883,74727,74729],{"className":74728},[886],[888,74730,74731],{"xmlns":890},[892,74732,74733,74741],{},[895,74734,74735],{},[1931,74736,74737,74739],{},[898,74738,1904],{},[1864,74740,2256],{},[902,74742,39000],{"encoding":904},[883,74744,74746],{"className":74745},[886],[888,74747,74748],{"xmlns":890},[892,74749,74750,74782],{},[895,74751,74752,74754,74756,74758,74764,74766,74768,74770,74772,74774,74780],{},[898,74753,1728],{},[898,74755,1749],{},[1723,74757,1908],{"stretchy":1907},[1931,74759,74760,74762],{},[898,74761,1904],{},[1864,74763,2256],{},[1723,74765,1914],{"stretchy":1907},[1723,74767,1725],{},[898,74769,1728],{},[898,74771,1721],{},[1723,74773,1908],{"stretchy":1907},[1931,74775,74776,74778],{},[898,74777,1904],{},[1864,74779,2256],{},[1723,74781,1914],{"stretchy":1907},[902,74783,66332],{"encoding":904}," (3.13).",[123,74786,74787,20994,74789,11094,74808,74833],{},[38,74788,67359],{},[883,74790,74792],{"className":74791},[886],[888,74793,74794],{"xmlns":890},[892,74795,74796,74805],{},[895,74797,74798,74800,74802],{},[898,74799,1746],{},[1723,74801,1725],{},[3018,74803,74804],{},"konst",[902,74806,74807],{"encoding":904},"P = \\text{konst}",[883,74809,74811],{"className":74810},[886],[888,74812,74813],{"xmlns":890},[892,74814,74815,74831],{},[895,74816,74817,74819,74821,74823,74825,74827,74829],{},[898,74818,1746],{},[1723,74820,1725],{},[898,74822,1728],{},[898,74824,1721],{},[1723,74826,1908],{"stretchy":1907},[898,74828,1904],{},[1723,74830,1914],{"stretchy":1907},[902,74832,68053],{"encoding":904}," (3.14).",[123,74835,74836,74839,74840,74869,74870,74887],{},[38,74837,74838],{},"Shutdown point"," — bod ",[883,74841,74843],{"className":74842},[886],[888,74844,74845],{"xmlns":890},[892,74846,74847,74867],{},[895,74848,74849,74851,74857,74859,74865],{},[1723,74850,1908],{"stretchy":1907},[2057,74852,74853,74855],{},[898,74854,1904],{},[1723,74856,5066],{},[1723,74858,2031],{"separator":2030},[2057,74860,74861,74863],{},[898,74862,1746],{},[1723,74864,5066],{},[1723,74866,1914],{"stretchy":1907},[902,74868,68342],{"encoding":904}," v minimu ",[883,74871,74873],{"className":74872},[886],[888,74874,74875],{"xmlns":890},[892,74876,74877,74885],{},[895,74878,74879,74881,74883],{},[898,74880,1718],{},[898,74882,41031],{},[898,74884,1721],{},[902,74886,55998],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,74889,74890,2628,74893,7183,74928,68612,74949,74962,74963,74978,74979,1664],{},[38,74891,74892],{},"Funkce nabídky firmy",[883,74894,74896],{"className":74895},[886],[888,74897,74898],{"xmlns":890},[892,74899,74900,74926],{},[895,74901,74902,74904,74906,74908,74910,74912,74914,74916,74918,74920,74922,74924],{},[898,74903,1746],{},[1723,74905,1725],{},[898,74907,2111],{},[1723,74909,1908],{"stretchy":1907},[898,74911,1904],{},[1723,74913,1914],{"stretchy":1907},[1723,74915,1725],{},[898,74917,1728],{},[898,74919,1721],{},[1723,74921,1908],{"stretchy":1907},[898,74923,1904],{},[1723,74925,1914],{"stretchy":1907},[902,74927,69808],{"encoding":904},[883,74929,74931],{"className":74930},[886],[888,74932,74933],{"xmlns":890},[892,74934,74935,74947],{},[895,74936,74937,74939,74941],{},[898,74938,1904],{},[1723,74940,5197],{},[2057,74942,74943,74945],{},[898,74944,1904],{},[1723,74946,5066],{},[902,74948,68611],{"encoding":904},[883,74950,74952],{"className":74951},[886],[888,74953,74954],{"xmlns":890},[892,74955,74956,74960],{},[895,74957,74958],{},[1864,74959,2256],{},[902,74961,2256],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,74964,74966],{"className":74965},[886],[888,74967,74968],{"xmlns":890},[892,74969,74970,74976],{},[895,74971,74972,74974],{},[898,74973,1728],{},[898,74975,1721],{},[902,74977,55979],{"encoding":904}," nad minimem ",[883,74980,74982],{"className":74981},[886],[888,74983,74984],{"xmlns":890},[892,74985,74986,74994],{},[895,74987,74988,74990,74992],{},[898,74989,1718],{},[898,74991,41031],{},[898,74993,1721],{},[902,74995,55998],{"encoding":904},[123,74997,74998,7725,75000,75021,75022,1664],{},[38,74999,50769],{},[883,75001,75003],{"className":75002},[886],[888,75004,75005],{"xmlns":890},[892,75006,75007,75019],{},[895,75008,75009,75011,75013],{},[898,75010,1746],{},[1723,75012,1725],{},[2057,75014,75015,75017],{},[898,75016,1746],{},[1723,75018,5066],{},[902,75020,5069],{"encoding":904}," konstantní ⇒ ",[883,75023,75025],{"className":75024},[886],[888,75026,75027],{"xmlns":890},[892,75028,75029,75049],{},[895,75030,75031,75033,75035,75037,75039,75041,75043],{},[898,75032,1718],{},[898,75034,1749],{},[1723,75036,1725],{},[898,75038,1728],{},[898,75040,1749],{},[1723,75042,1725],{},[2057,75044,75045,75047],{},[898,75046,1746],{},[1723,75048,5066],{},[902,75050,59285],{"encoding":904},[123,75052,75053,75056],{},[38,75054,75055],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,75058,2620],{"id":2619},[120,75060,75061,75080,75092],{},[123,75062,75063,2628,75065,1343,75068,1343,75071,1343,75074,1343,75077],{},[38,75064,51413],{},[207,75066,12642],{"className":75067,"dataFsResolvedFilePath":800,"href":801},[210],[207,75069,4544],{"className":75070,"dataFsResolvedFilePath":848,"href":849},[210],[207,75072,3086],{"className":75073,"dataFsResolvedFilePath":764,"href":765},[210],[207,75075,775],{"className":75076,"dataFsResolvedFilePath":773,"href":774},[210],[207,75078,859],{"className":75079,"dataFsResolvedFilePath":857,"href":858},[210],[123,75081,75082,2628,75084,1343,75088],{},[38,75083,37396],{},[207,75085,75087],{"className":75086,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,75089,75091],{"className":75090,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,75093,75094,2628,75096],{},[38,75095,2627],{},[207,75097,1646],{"className":75098,"dataFsResolvedFilePath":1645,"href":1644},[210],{"title":641,"searchDepth":642,"depth":642,"links":75100},[75101,75102,75109,75115,75119,75120,75124,75125,75126,75127,75133,75134],{"id":51644,"depth":642,"text":1241},{"id":56425,"depth":642,"text":56426,"children":75103},[75104,75105,75106,75107,75108],{"id":56436,"depth":649,"text":56437},{"id":57022,"depth":649,"text":57023},{"id":57170,"depth":649,"text":57171},{"id":57912,"depth":649,"text":57913},{"id":58567,"depth":649,"text":58568},{"id":59288,"depth":642,"text":59289,"children":75110},[75111,75112,75113,75114],{"id":59292,"depth":649,"text":59293},{"id":59453,"depth":649,"text":59454},{"id":60640,"depth":649,"text":60641},{"id":61538,"depth":649,"text":61539},{"id":62620,"depth":642,"text":62621,"children":75116},[75117,75118],{"id":17107,"depth":649,"text":17108},{"id":63970,"depth":649,"text":63971},{"id":64144,"depth":642,"text":64145},{"id":66065,"depth":642,"text":66066,"children":75121},[75122,75123],{"id":66079,"depth":649,"text":17108},{"id":67358,"depth":649,"text":67359},{"id":67990,"depth":642,"text":67991},{"id":69455,"depth":642,"text":69456},{"id":50572,"depth":642,"text":2615},{"id":69916,"depth":642,"text":1817,"children":75128},[75129,75130,75131,75132],{"id":69919,"depth":649,"text":69920},{"id":70771,"depth":649,"text":70772},{"id":72317,"depth":649,"text":72318},{"id":73693,"depth":649,"text":73694},{"id":16420,"depth":642,"text":16421},{"id":2619,"depth":642,"text":2620},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":55810,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,75141,75142,55862,75143,75144,75145],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":75148,"title":75149,"body":75150,"course":1128,"courses":659,"created":2676,"description":641,"extension":661,"meta":87242,"navigation":664,"path":87243,"seo":87244,"sources":87245,"stem":87246,"tags":87247,"type":4573,"updated":677,"__hash__":87253},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":75151,"toc":87199},[75152,75155,75507,75511,75514,75582,75634,75644,75648,75682,75723,75747,75770,75799,75866,75973,76016,76073,76148,76193,76197,76205,76213,76216,76481,76532,76612,76682,76705,76733,76778,76800,76804,76811,76860,76886,77037,77040,77077,77240,77348,77352,77389,77464,77533,77652,77774,77855,77861,77902,77975,78068,78072,78108,78196,78310,78415,78500,78640,78644,78692,78737,78743,78747,78750,78801,78851,78858,78924,79057,79102,79106,79127,79506,79601,79618,79672,79676,79758,79842,80012,80015,80058,80125,80199,80203,80208,80277,80285,80294,80372,80438,80443,80538,80581,80586,80634,80639,80687,80805,80888,80926,81029,81088,81229,81233,81276,81349,81373,81427,81434,81436,81481,81526,81537,81542,81578,81640,81663,81672,81773,81840,81913,81920,82011,82073,82109,82166,82225,82410,82506,82510,82514,82593,82598,82722,82808,82814,82924,82961,83052,83150,83153,83157,83223,83260,83382,83434,83438,83466,83518,83592,83697,83721,83780,83784,83802,83945,84093,84095,84130,84133,84135,84225,84355,84481,84573,84648,84652,84768,84872,85062,85098,85192,85198,85311,85614,85620,85738,85837,85913,85915,87077,87079],[12,75153,75149],{"id":75154},"produkce-produkční-funkce-cobb-douglas-mrts",[4584,75156,75157],{},[724,75158,75159,4591,75161,75163,75164,37588,75177,75190,75191,17072,75204,1981,75206,75230,75231,2628,75233,1682,75267,2628,75270,75298,75299,11094,75318,75347,75348,1981,75351,75379,75380,75383,75384,75413,75414,75444,75445,2628,75448,75487,75488,75506],{},[883,75160,4590],{},[38,75162,859],{}," popisuje vztah mezi vstupy (práce ",[883,75165,75167],{"className":75166},[886],[888,75168,75169],{"xmlns":890},[892,75170,75171,75175],{},[895,75172,75173],{},[898,75174,1911],{},[902,75176,1911],{"encoding":904},[883,75178,75180],{"className":75179},[886],[888,75181,75182],{"xmlns":890},[892,75183,75184,75188],{},[895,75185,75186],{},[898,75187,2034],{},[902,75189,2034],{"encoding":904},") a výstupem ",[883,75192,75194],{"className":75193},[886],[888,75195,75196],{"xmlns":890},[892,75197,75198,75202],{},[895,75199,75200],{},[898,75201,1904],{},[902,75203,1904],{"encoding":904},[38,75205,37656],{},[883,75207,75209],{"className":75208},[886],[888,75210,75211],{"xmlns":890},[892,75212,75213,75227],{},[895,75214,75215,75217,75219,75221,75223,75225],{},[898,75216,1904],{},[1723,75218,1725],{},[898,75220,1904],{},[1723,75222,1908],{"stretchy":1907},[898,75224,1911],{},[1723,75226,1914],{"stretchy":1907},[902,75228,75229],{"encoding":904},"Q = Q(L)",") studujeme ",[614,75232,10726],{},[883,75234,75236],{"className":75235},[886],[888,75237,75238],{"xmlns":890},[892,75239,75240,75264],{},[895,75241,75242,75244,75250,75252,75258,75260,75262],{},[898,75243,1728],{},[1931,75245,75246,75248],{},[898,75247,1746],{},[898,75249,1911],{},[1723,75251,1725],{},[2057,75253,75254,75256],{},[898,75255,1904],{},[1723,75257,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,75259,1908],{"stretchy":1907},[898,75261,1911],{},[1723,75263,1914],{"stretchy":1907},[902,75265,75266],{"encoding":904},"MP_L = Q'(L)",[614,75268,75269],{},"průměrný produkt",[883,75271,75273],{"className":75272},[886],[888,75274,75275],{"xmlns":890},[892,75276,75277,75295],{},[895,75278,75279,75281,75287,75289,75291,75293],{},[898,75280,1718],{},[1931,75282,75283,75285],{},[898,75284,1746],{},[898,75286,1911],{},[1723,75288,1725],{},[898,75290,1904],{},[898,75292,2125],{"mathvariant":2124},[898,75294,1911],{},[902,75296,75297],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,75300,75302],{"className":75301},[886],[888,75303,75304],{"xmlns":890},[892,75305,75306,75316],{},[895,75307,75308,75310],{},[898,75309,1718],{},[1931,75311,75312,75314],{},[898,75313,1746],{},[898,75315,1911],{},[902,75317,1960],{"encoding":904},[883,75319,75321],{"className":75320},[886],[888,75322,75323],{"xmlns":890},[892,75324,75325,75345],{},[895,75326,75327,75329,75335,75337,75339],{},[898,75328,1728],{},[1931,75330,75331,75333],{},[898,75332,1746],{},[898,75334,1911],{},[1723,75336,1725],{},[898,75338,1718],{},[1931,75340,75341,75343],{},[898,75342,1746],{},[898,75344,1911],{},[902,75346,2011],{"encoding":904},". Ve ",[38,75349,75350],{},"dvoufaktorovém modelu",[883,75352,75354],{"className":75353},[886],[888,75355,75356],{"xmlns":890},[892,75357,75358,75376],{},[895,75359,75360,75362,75364,75366,75368,75370,75372,75374],{},[898,75361,1904],{},[1723,75363,1725],{},[898,75365,1904],{},[1723,75367,1908],{"stretchy":1907},[898,75369,1911],{},[1723,75371,2031],{"separator":2030},[898,75373,2034],{},[1723,75375,1914],{"stretchy":1907},[902,75377,75378],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,75381,75382],{},"Cobb-Douglasovy"," funkce ",[883,75385,75387],{"className":75386},[886],[888,75388,75389],{"xmlns":890},[892,75390,75391,75411],{},[895,75392,75393,75395,75397,75399,75405],{},[898,75394,1904],{},[1723,75396,1725],{},[898,75398,1718],{},[2057,75400,75401,75403],{},[898,75402,1911],{},[898,75404,207],{},[2057,75406,75407,75409],{},[898,75408,2034],{},[898,75410,2069],{},[902,75412,2072],{"encoding":904},"; mezní produkty ",[883,75415,75417],{"className":75416},[886],[888,75418,75419],{"xmlns":890},[892,75420,75421,75441],{},[895,75422,75423,75425,75431,75433,75435],{},[898,75424,1728],{},[1931,75426,75427,75429],{},[898,75428,1746],{},[898,75430,1911],{},[1723,75432,2031],{"separator":2030},[898,75434,1728],{},[1931,75436,75437,75439],{},[898,75438,1746],{},[898,75440,2034],{},[902,75442,75443],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,75446,75447],{},"mezní míru technické substituce",[883,75449,75451],{"className":75450},[886],[888,75452,75453],{"xmlns":890},[892,75454,75455,75485],{},[895,75456,75457,75459,75461,75463,75465,75467,75469,75475,75477,75479],{},[898,75458,1728],{},[898,75460,1749],{},[898,75462,1754],{},[898,75464,2111],{},[1723,75466,1725],{},[898,75468,1728],{},[1931,75470,75471,75473],{},[898,75472,1746],{},[898,75474,1911],{},[898,75476,2125],{"mathvariant":2124},[898,75478,1728],{},[1931,75480,75481,75483],{},[898,75482,1746],{},[898,75484,2034],{},[902,75486,2136],{"encoding":904}," — sklon izokvanty. Součet exponentů ",[883,75489,75491],{"className":75490},[886],[888,75492,75493],{"xmlns":890},[892,75494,75495,75503],{},[895,75496,75497,75499,75501],{},[898,75498,207],{},[1723,75500,2087],{},[898,75502,2069],{},[902,75504,75505],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,75508,75510],{"id":75509},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,75512,75513],{},"Po prostudování kapitoly 5 student umí:",[120,75515,75516,75522,75532,75538,75544,75549,75555,75565,75570,75576],{},[123,75517,75518,75519,2031],{},"popsat ",[38,75520,75521],{},"jednofaktorový model produkce",[123,75523,75524,75525,1682,75528,75531],{},"vypočítat ",[38,75526,75527],{},"mezní",[38,75529,75530],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,75533,75534,75535,2031],{},"charakterizovat průběh ",[38,75536,75537],{},"křivky produkce",[123,75539,75540,75541,2031],{},"formulovat ",[38,75542,75543],{},"princip maximalizace průměrného produktu práce",[123,75545,75518,75546,2031],{},[38,75547,75548],{},"dvoufaktorový model produkce",[123,75550,75551,75552,2031],{},"uvést tvar ",[38,75553,75554],{},"Cobb–Douglasových produkčních funkcí",[123,75556,75557,75558,1343,75560,1343,75562,2031],{},"vyložit, co jsou ",[38,75559,25306],{},[38,75561,14358],{},[38,75563,75564],{},"klesající výnosy z rozsahu",[123,75566,75524,75567,75531],{},[38,75568,75569],{},"mezní produkty práce a kapitálu",[123,75571,75572,75573,2031],{},"najít ",[38,75574,75575],{},"izokvanty",[123,75577,75524,75578,75581],{},[38,75579,75580],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,75583,75584,75585,75588,75589,75592,75593,2628,75596,1343,75609,2628,75612,1682,75625,75628,75629,75631,75632,1664],{},"Každý proces produkce je určován ",[38,75586,75587],{},"faktory"," (též ",[38,75590,75591],{},"vstupy",") produkce. K hlavním patří ",[38,75594,75595],{},"práce",[883,75597,75599],{"className":75598},[886],[888,75600,75601],{"xmlns":890},[892,75602,75603,75607],{},[895,75604,75605],{},[898,75606,1911],{},[902,75608,1911],{"encoding":904},[38,75610,75611],{},"kapitál",[883,75613,75615],{"className":75614},[886],[888,75616,75617],{"xmlns":890},[892,75618,75619,75623],{},[895,75620,75621],{},[898,75622,2034],{},[902,75624,2034],{"encoding":904},[38,75626,75627],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,75630,37656],{}," (produkce závisí jen na práci); v opačném případě o ",[38,75633,75350],{},[724,75635,75636,75637,1343,75640,75643],{},"Související matematický aparát: ",[207,75638,3086],{"className":75639,"dataFsResolvedFilePath":764,"href":765},[210],[207,75641,784],{"className":75642,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,75645,75647],{"id":75646},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,75649,75650,75651,75664,75665,75678,75679],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,75652,75654],{"className":75653},[886],[888,75655,75656],{"xmlns":890},[892,75657,75658,75662],{},[895,75659,75660],{},[898,75661,1904],{},[902,75663,1904],{"encoding":904}," na práci ",[883,75666,75668],{"className":75667},[886],[888,75669,75670],{"xmlns":890},[892,75671,75672,75676],{},[895,75673,75674],{},[898,75675,1911],{},[902,75677,1911],{"encoding":904}," vyjadřuje ",[38,75680,75681],{},"produkční funkce",[883,75683,75685],{"className":75684},[886],[888,75686,75687],{"xmlns":890,"display":28759},[892,75688,75689,75720],{},[21447,75690,75691],{"width":28764},[21452,75692,75693,75695,75713,75715],{},[21455,75694],{"width":28769},[21455,75696,75697],{},[895,75698,75699,75701,75703,75705,75707,75709,75711],{},[898,75700,1904],{},[1723,75702,1725],{},[898,75704,1904],{},[1723,75706,1908],{"stretchy":1907},[898,75708,1911],{},[1723,75710,1914],{"stretchy":1907},[1723,75712,2031],{"separator":2030},[21455,75714],{"width":28769},[21455,75716,75717],{},[3018,75718,75719],{},"(5.1)",[902,75721,75722],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,75724,75725,75726,1981,75729,75732,75733,75746],{},"jejíž graf se nazývá ",[38,75727,75728],{},"křivka produkce",[614,75730,75731],{},"production curve","). Práce ",[883,75734,75736],{"className":75735},[886],[888,75737,75738],{"xmlns":890},[892,75739,75740,75744],{},[895,75741,75742],{},[898,75743,1911],{},[902,75745,1911],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,75748,75750,75751,1914],{"id":75749},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,75752,75754],{"className":75753},[886],[888,75755,75756],{"xmlns":890},[892,75757,75758,75768],{},[895,75759,75760,75762],{},[898,75761,1728],{},[1931,75763,75764,75766],{},[898,75765,1746],{},[898,75767,1911],{},[902,75769,1939],{"encoding":904},[724,75771,75772,1981,75775,75778,75779,75798],{},[38,75773,75774],{},"Mezní produkt práce",[614,75776,75777],{},"marginal product of labour",") ",[883,75780,75782],{"className":75781},[886],[888,75783,75784],{"xmlns":890},[892,75785,75786,75796],{},[895,75787,75788,75790],{},[898,75789,1728],{},[1931,75791,75792,75794],{},[898,75793,1746],{},[898,75795,1911],{},[902,75797,1939],{"encoding":904}," je derivace produkce podle práce:",[883,75800,75802],{"className":75801},[886],[888,75803,75804],{"xmlns":890,"display":28759},[892,75805,75806,75863],{},[21447,75807,75808],{"width":28764},[21452,75809,75810,75812,75856,75858],{},[21455,75811],{"width":28769},[21455,75813,75814],{},[895,75815,75816,75818,75824,75826,75840,75842,75848,75850,75852,75854],{},[898,75817,1728],{},[1931,75819,75820,75822],{},[898,75821,1746],{},[898,75823,1911],{},[1723,75825,1725],{},[3058,75827,75828,75834],{},[895,75829,75830,75832],{},[898,75831,2930],{},[898,75833,1904],{},[895,75835,75836,75838],{},[898,75837,2930],{},[898,75839,1911],{},[1723,75841,1725],{},[2057,75843,75844,75846],{},[898,75845,1904],{},[1723,75847,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,75849,1908],{"stretchy":1907},[898,75851,1911],{},[1723,75853,1914],{"stretchy":1907},[898,75855,1664],{"mathvariant":2124},[21455,75857],{"width":28769},[21455,75859,75860],{},[3018,75861,75862],{},"(5.2)",[902,75864,75865],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,75867,75868,75869,20638,75887,75915,75916,75933,75934,3411,75951,4634],{},"Pro pevnou hodnotu ",[883,75870,75872],{"className":75871},[886],[888,75873,75874],{"xmlns":890},[892,75875,75876,75884],{},[895,75877,75878],{},[2057,75879,75880,75882],{},[898,75881,1911],{},[1723,75883,5066],{},[902,75885,75886],{"encoding":904},"L^*",[883,75888,75890],{"className":75889},[886],[888,75891,75892],{"xmlns":890},[892,75893,75894,75912],{},[895,75895,75896,75902,75904,75910],{},[2057,75897,75898,75900],{},[898,75899,1904],{},[1723,75901,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,75903,1908],{"stretchy":1907},[2057,75905,75906,75908],{},[898,75907,1911],{},[1723,75909,5066],{},[1723,75911,1914],{"stretchy":1907},[902,75913,75914],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,75917,75919],{"className":75918},[886],[888,75920,75921],{"xmlns":890},[892,75922,75923,75931],{},[895,75924,75925],{},[2057,75926,75927,75929],{},[898,75928,1911],{},[1723,75930,5066],{},[902,75932,75886],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,75935,75937],{"className":75936},[886],[888,75938,75939],{"xmlns":890},[892,75940,75941,75949],{},[895,75942,75943],{},[2057,75944,75945,75947],{},[898,75946,1911],{},[1723,75948,5066],{},[902,75950,75886],{"encoding":904},[883,75952,75954],{"className":75953},[886],[888,75955,75956],{"xmlns":890},[892,75957,75958,75970],{},[895,75959,75960,75966,75968],{},[2057,75961,75962,75964],{},[898,75963,1911],{},[1723,75965,5066],{},[1723,75967,2087],{},[1864,75969,1866],{},[902,75971,75972],{"encoding":904},"L^*+1",[4584,75974,75975],{},[724,75976,75977,18718,75979,75998,75999,76002,76003,1664],{},[883,75978,4869],{},[883,75980,75982],{"className":75981},[886],[888,75983,75984],{"xmlns":890},[892,75985,75986,75996],{},[895,75987,75988,75990],{},[898,75989,1728],{},[1931,75991,75992,75994],{},[898,75993,1746],{},[898,75995,1911],{},[902,75997,1939],{"encoding":904}," odpovídá na otázku „",[38,76000,76001],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,76004,76006],{"className":76005},[886],[888,76007,76008],{"xmlns":890},[892,76009,76010,76014],{},[895,76011,76012],{},[898,76013,1911],{},[902,76015,1911],{"encoding":904},[724,76017,76018,76021,76022,76038,76039,3411,76052,76072],{},[38,76019,76020],{},"Přibližná změna produkce"," pro změnu práce o ",[883,76023,76025],{"className":76024},[886],[888,76026,76027],{"xmlns":890},[892,76028,76029,76035],{},[895,76030,76031,76033],{},[898,76032,2930],{},[898,76034,1911],{},[902,76036,76037],{"encoding":904},"dL"," (z ",[883,76040,76042],{"className":76041},[886],[888,76043,76044],{"xmlns":890},[892,76045,76046,76050],{},[895,76047,76048],{},[898,76049,1911],{},[902,76051,1911],{"encoding":904},[883,76053,76055],{"className":76054},[886],[888,76056,76057],{"xmlns":890},[892,76058,76059,76069],{},[895,76060,76061,76063,76065,76067],{},[898,76062,1911],{},[1723,76064,2087],{},[898,76066,2930],{},[898,76068,1911],{},[902,76070,76071],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,76074,76076],{"className":76075},[886],[888,76077,76078],{"xmlns":890,"display":28759},[892,76079,76080,76145],{},[21447,76081,76082],{"width":28764},[21452,76083,76084,76086,76138,76140],{},[21455,76085],{"width":28769},[21455,76087,76088],{},[895,76089,76090,76092,76094,76096,76098,76100,76102,76108,76110,76112,76114,76116,76118,76120,76122,76124,76130,76132,76134,76136],{},[898,76091,3611],{"mathvariant":2124},[898,76093,1904],{},[1723,76095,3456],{},[898,76097,2930],{},[898,76099,1904],{},[1723,76101,1725],{},[2057,76103,76104,76106],{},[898,76105,1904],{},[1723,76107,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,76109,1908],{"stretchy":1907},[898,76111,1911],{},[1723,76113,1914],{"stretchy":1907},[3018,76115,3707],{},[898,76117,2930],{},[898,76119,1911],{},[1723,76121,1725],{},[898,76123,1728],{},[1931,76125,76126,76128],{},[898,76127,1746],{},[898,76129,1911],{},[3018,76131,3707],{},[898,76133,2930],{},[898,76135,1911],{},[898,76137,1664],{"mathvariant":2124},[21455,76139],{"width":28769},[21455,76141,76142],{},[3018,76143,76144],{},"(5.3)",[902,76146,76147],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,76149,76150,76151,1664],{},"Skutečná změna je ",[883,76152,76154],{"className":76153},[886],[888,76155,76156],{"xmlns":890},[892,76157,76158,76190],{},[895,76159,76160,76162,76164,76166,76168,76170,76172,76174,76176,76178,76180,76182,76184,76186,76188],{},[898,76161,3611],{"mathvariant":2124},[898,76163,1904],{},[1723,76165,1725],{},[898,76167,1904],{},[1723,76169,1908],{"stretchy":1907},[898,76171,1911],{},[1723,76173,2087],{},[898,76175,2930],{},[898,76177,1911],{},[1723,76179,1914],{"stretchy":1907},[1723,76181,1759],{},[898,76183,1904],{},[1723,76185,1908],{"stretchy":1907},[898,76187,1911],{},[1723,76189,1914],{"stretchy":1907},[902,76191,76192],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,76194,76196],{"id":76195},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,76198,76199,1981,76202,3871],{},[38,76200,76201],{},"Zákon klesajících výnosů",[614,76203,76204],{},"law of diminishing marginal productivity",[4584,76206,76207],{},[724,76208,76209,76210,76212],{},"Roste-li postupně některý ze vstupů (",[614,76211,37652],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,76214,76215],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,76217,76218,76219,2628,76240,76259,76260,76310,76311,76313,76314,2628,76334,76353,76354,76310,76386,2137,76388,76407,76408,22287,76425,76459,76460,8812,76477,76480],{},"1° ",[38,76220,76221,76222,3430],{},"Do bodu ",[883,76223,76225],{"className":76224},[886],[888,76226,76227],{"xmlns":890},[892,76228,76229,76237],{},[895,76230,76231],{},[1931,76232,76233,76235],{},[898,76234,1911],{},[1864,76236,2256],{},[902,76238,76239],{"encoding":904},"L_0",[883,76241,76243],{"className":76242},[886],[888,76244,76245],{"xmlns":890},[892,76246,76247,76257],{},[895,76248,76249,76251],{},[898,76250,1728],{},[1931,76252,76253,76255],{},[898,76254,1746],{},[898,76256,1911],{},[902,76258,1939],{"encoding":904}," roste, tj. ",[883,76261,76263],{"className":76262},[886],[888,76264,76265],{"xmlns":890},[892,76266,76267,76307],{},[895,76268,76269,76271,76273,76279,76285,76287,76297,76299,76301,76303,76305],{},[1723,76270,1908],{"stretchy":1907},[898,76272,1728],{},[1931,76274,76275,76277],{},[898,76276,1746],{},[898,76278,1911],{},[2057,76280,76281,76283],{},[1723,76282,1914],{"stretchy":1907},[1723,76284,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,76286,1725],{},[2057,76288,76289,76291],{},[898,76290,1904],{},[895,76292,76293,76295],{},[1723,76294,2229],{"mathvariant":2124},[1723,76296,2229],{"mathvariant":2124},[1723,76298,1908],{"stretchy":1907},[898,76300,1911],{},[1723,76302,1914],{"stretchy":1907},[1723,76304,2253],{},[1864,76306,2256],{},[902,76308,76309],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,76312,38356],{},".\n2° ",[38,76315,76316,76317,3430],{},"Od bodu ",[883,76318,76320],{"className":76319},[886],[888,76321,76322],{"xmlns":890},[892,76323,76324,76332],{},[895,76325,76326],{},[1931,76327,76328,76330],{},[898,76329,1911],{},[1864,76331,2256],{},[902,76333,76239],{"encoding":904},[883,76335,76337],{"className":76336},[886],[888,76338,76339],{"xmlns":890},[892,76340,76341,76351],{},[895,76342,76343,76345],{},[898,76344,1728],{},[1931,76346,76347,76349],{},[898,76348,1746],{},[898,76350,1911],{},[902,76352,1939],{"encoding":904}," klesá, ",[883,76355,76357],{"className":76356},[886],[888,76358,76359],{"xmlns":890},[892,76360,76361,76383],{},[895,76362,76363,76373,76375,76377,76379,76381],{},[2057,76364,76365,76367],{},[898,76366,1904],{},[895,76368,76369,76371],{},[1723,76370,2229],{"mathvariant":2124},[1723,76372,2229],{"mathvariant":2124},[1723,76374,1908],{"stretchy":1907},[898,76376,1911],{},[1723,76378,1914],{"stretchy":1907},[1723,76380,2287],{},[1864,76382,2256],{},[902,76384,76385],{"encoding":904},"Q''(L) \u003C 0",[38,76387,39180],{},[883,76389,76391],{"className":76390},[886],[888,76392,76393],{"xmlns":890},[892,76394,76395,76405],{},[895,76396,76397,76399],{},[898,76398,1728],{},[1931,76400,76401,76403],{},[898,76402,1746],{},[898,76404,1911],{},[902,76406,1939],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,76409,76411],{"className":76410},[886],[888,76412,76413],{"xmlns":890},[892,76414,76415,76423],{},[895,76416,76417],{},[1931,76418,76419,76421],{},[898,76420,1911],{},[1864,76422,1866],{},[902,76424,13913],{"encoding":904},[883,76426,76428],{"className":76427},[886],[888,76429,76430],{"xmlns":890},[892,76431,76432,76456],{},[895,76433,76434,76436,76442,76444,76450,76452,76454],{},[898,76435,1728],{},[1931,76437,76438,76440],{},[898,76439,1746],{},[898,76441,1911],{},[1723,76443,1908],{"stretchy":1907},[1931,76445,76446,76448],{},[898,76447,1911],{},[1864,76449,1866],{},[1723,76451,1914],{"stretchy":1907},[1723,76453,1725],{},[1864,76455,2256],{},[902,76457,76458],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,76461,76463],{"className":76462},[886],[888,76464,76465],{"xmlns":890},[892,76466,76467,76475],{},[895,76468,76469],{},[1931,76470,76471,76473],{},[898,76472,1911],{},[1864,76474,2256],{},[902,76476,76239],{"encoding":904},[38,76478,76479],{},"inflexním bodem"," produkční funkce.",[724,76482,76483,76484,11094,76501,1664],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,76485,76487],{"className":76486},[886],[888,76488,76489],{"xmlns":890},[892,76490,76491,76499],{},[895,76492,76493],{},[1931,76494,76495,76497],{},[898,76496,1911],{},[1864,76498,2256],{},[902,76500,76239],{"encoding":904},[883,76502,76504],{"className":76503},[886],[888,76505,76506],{"xmlns":890},[892,76507,76508,76530],{},[895,76509,76510,76520,76522,76524,76526,76528],{},[2057,76511,76512,76514],{},[898,76513,1904],{},[895,76515,76516,76518],{},[1723,76517,2229],{"mathvariant":2124},[1723,76519,2229],{"mathvariant":2124},[1723,76521,1908],{"stretchy":1907},[898,76523,1911],{},[1723,76525,1914],{"stretchy":1907},[1723,76527,2287],{},[1864,76529,2256],{},[902,76531,76385],{"encoding":904},[724,76533,76534,2628,76537,6379,76577,1343,76594,76611],{},[38,76535,76536],{},"Typický polynom třetího stupně:",[883,76538,76540],{"className":76539},[886],[888,76541,76542],{"xmlns":890},[892,76543,76544,76574],{},[895,76545,76546,76548,76550,76552,76554,76556,76558,76564,76566,76568],{},[898,76547,1904],{},[1723,76549,1908],{"stretchy":1907},[898,76551,1911],{},[1723,76553,1914],{"stretchy":1907},[1723,76555,1725],{},[898,76557,207],{},[2057,76559,76560,76562],{},[898,76561,1911],{},[1864,76563,2909],{},[1723,76565,2087],{},[898,76567,2069],{},[2057,76569,76570,76572],{},[898,76571,1911],{},[1864,76573,2331],{},[902,76575,76576],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,76578,76580],{"className":76579},[886],[888,76581,76582],{"xmlns":890},[892,76583,76584,76592],{},[895,76585,76586,76588,76590],{},[898,76587,207],{},[1723,76589,2287],{},[1864,76591,2256],{},[902,76593,43777],{"encoding":904},[883,76595,76597],{"className":76596},[886],[888,76598,76599],{"xmlns":890},[892,76600,76601,76609],{},[895,76602,76603,76605,76607],{},[898,76604,2069],{},[1723,76606,2253],{},[1864,76608,2256],{},[902,76610,19508],{"encoding":904},". Pak",[883,76613,76615],{"className":76614},[886],[888,76616,76617],{"xmlns":890,"display":28759},[892,76618,76619,76679],{},[895,76620,76621,76627,76629,76631,76639,76647,76649,76651,76657,76659,76661,76669,76677],{},[1931,76622,76623,76625],{},[898,76624,1911],{},[1864,76626,2256],{},[1723,76628,1725],{},[1723,76630,1759],{},[3055,76632,76633],{"scriptlevel":2256,"displaystyle":1907},[3058,76634,76635,76637],{},[1864,76636,1866],{},[1864,76638,2909],{},[3055,76640,76641],{"scriptlevel":2256,"displaystyle":1907},[3058,76642,76643,76645],{},[898,76644,2069],{},[898,76646,207],{},[1723,76648,2031],{"separator":2030},[6588,76650],{"width":6590},[1931,76652,76653,76655],{},[898,76654,1911],{},[1864,76656,1866],{},[1723,76658,1725],{},[1723,76660,1759],{},[3055,76662,76663],{"scriptlevel":2256,"displaystyle":1907},[3058,76664,76665,76667],{},[1864,76666,2331],{},[1864,76668,2909],{},[3055,76670,76671],{"scriptlevel":2256,"displaystyle":1907},[3058,76672,76673,76675],{},[898,76674,2069],{},[898,76676,207],{},[898,76678,1664],{"mathvariant":2124},[902,76680,76681],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,76683,76685,76686,1914],{"id":76684},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,76687,76689],{"className":76688},[886],[888,76690,76691],{"xmlns":890},[892,76692,76693,76703],{},[895,76694,76695,76697],{},[898,76696,1718],{},[1931,76698,76699,76701],{},[898,76700,1746],{},[898,76702,1911],{},[902,76704,1960],{"encoding":904},[724,76706,76707,1981,76710,75778,76713,76732],{},[38,76708,76709],{},"Průměrný produkt práce",[614,76711,76712],{},"average product of labour",[883,76714,76716],{"className":76715},[886],[888,76717,76718],{"xmlns":890},[892,76719,76720,76730],{},[895,76721,76722,76724],{},[898,76723,1718],{},[1931,76725,76726,76728],{},[898,76727,1746],{},[898,76729,1911],{},[902,76731,1960],{"encoding":904}," je podíl produkce a práce:",[883,76734,76736],{"className":76735},[886],[888,76737,76738],{"xmlns":890,"display":28759},[892,76739,76740,76775],{},[21447,76741,76742],{"width":28764},[21452,76743,76744,76746,76768,76770],{},[21455,76745],{"width":28769},[21455,76747,76748],{},[895,76749,76750,76752,76758,76760,76766],{},[898,76751,1718],{},[1931,76753,76754,76756],{},[898,76755,1746],{},[898,76757,1911],{},[1723,76759,1725],{},[3058,76761,76762,76764],{},[898,76763,1904],{},[898,76765,1911],{},[898,76767,1664],{"mathvariant":2124},[21455,76769],{"width":28769},[21455,76771,76772],{},[3018,76773,76774],{},"(5.4)",[902,76776,76777],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,76779,76780,76781,1664],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,76782,76784],{"className":76783},[886],[888,76785,76786],{"xmlns":890},[892,76787,76788,76798],{},[895,76789,76790,76792],{},[898,76791,1718],{},[1931,76793,76794,76796],{},[898,76795,1746],{},[898,76797,1911],{},[902,76799,1960],{"encoding":904},[115,76801,76803],{"id":76802},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,76805,76806],{},[3285,76807],{"alt":76808,"className":76809,"src":76810},"imek-q-mpl-apl-tripanel",[210,3289],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[4584,76812,76813],{},[724,76814,76815,76818,76819,3350,76838,76855,76856],{},[38,76816,76817],{},"Princip:"," Má-li ",[883,76820,76822],{"className":76821},[886],[888,76823,76824],{"xmlns":890},[892,76825,76826,76836],{},[895,76827,76828,76830],{},[898,76829,1718],{},[1931,76831,76832,76834],{},[898,76833,1746],{},[898,76835,1911],{},[902,76837,1960],{"encoding":904},[883,76839,76841],{"className":76840},[886],[888,76842,76843],{"xmlns":890},[892,76844,76845,76853],{},[895,76846,76847],{},[1931,76848,76849,76851],{},[898,76850,1911],{},[1864,76852,2256],{},[902,76854,76239],{"encoding":904}," maximum, pak platí\n",[883,76857,76859],{"className":76858,"title":4914,"style":4915},[4913],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,76861,76862,76863,76866,76867,2628,76871,1664],{},"Slovně: ",[38,76864,76865],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,76868,76870],{"className":76869,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,76872,76874],{"className":76873},[886],[888,76875,76876],{"xmlns":890},[892,76877,76878,76884],{},[895,76879,76880,76882],{},[898,76881,1718],{},[898,76883,1721],{},[902,76885,56247],{"encoding":904},[4584,76887,76888,76912],{},[724,76889,76890,76892,76893],{},[883,76891,5283],{}," Postup — jak najít max ",[883,76894,76896],{"className":76895},[886],[888,76897,76898],{"xmlns":890},[892,76899,76900,76910],{},[895,76901,76902,76904],{},[898,76903,1718],{},[1931,76905,76906,76908],{},[898,76907,1746],{},[898,76909,1911],{},[902,76911,1960],{"encoding":904},[152,76913,76914,76952,77034],{},[123,76915,76916,76917,76951],{},"Napište ",[883,76918,76920],{"className":76919},[886],[888,76921,76922],{"xmlns":890},[892,76923,76924,76948],{},[895,76925,76926,76928,76934,76936,76938,76940,76942,76944,76946],{},[898,76927,1718],{},[1931,76929,76930,76932],{},[898,76931,1746],{},[898,76933,1911],{},[1723,76935,1725],{},[898,76937,1904],{},[1723,76939,1908],{"stretchy":1907},[898,76941,1911],{},[1723,76943,1914],{"stretchy":1907},[898,76945,2125],{"mathvariant":2124},[898,76947,1911],{},[902,76949,76950],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,76953,76954,76955,76987,76988,76991,76992,1664],{},"Položte ",[883,76956,76958],{"className":76957},[886],[888,76959,76960],{"xmlns":890},[892,76961,76962,76984],{},[895,76963,76964,76966,76968,76974,76980,76982],{},[1723,76965,1908],{"stretchy":1907},[898,76967,1718],{},[1931,76969,76970,76972],{},[898,76971,1746],{},[898,76973,1911],{},[2057,76975,76976,76978],{},[1723,76977,1914],{"stretchy":1907},[1723,76979,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,76981,1725],{},[1864,76983,2256],{},[902,76985,76986],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,76989,76990],{},"Zkratka:"," můžete rovnou řešit ",[883,76993,76995],{"className":76994},[886],[888,76996,76997],{"xmlns":890},[892,76998,76999,77031],{},[895,77000,77001,77003,77009,77011,77013,77015,77017,77019,77025,77027,77029],{},[898,77002,1728],{},[1931,77004,77005,77007],{},[898,77006,1746],{},[898,77008,1911],{},[1723,77010,1908],{"stretchy":1907},[898,77012,1911],{},[1723,77014,1914],{"stretchy":1907},[1723,77016,1725],{},[898,77018,1718],{},[1931,77020,77021,77023],{},[898,77022,1746],{},[898,77024,1911],{},[1723,77026,1908],{"stretchy":1907},[898,77028,1911],{},[1723,77030,1914],{"stretchy":1907},[902,77032,77033],{"encoding":904},"MP_L(L) = AP_L(L)",[123,77035,77036],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,77038,66188],{"id":77039},"odvození",[724,77041,77042,77043,77076],{},"Z ",[883,77044,77046],{"className":77045},[886],[888,77047,77048],{"xmlns":890},[892,77049,77050,77074],{},[895,77051,77052,77054,77060,77062,77064,77066,77068,77070,77072],{},[898,77053,1718],{},[1931,77055,77056,77058],{},[898,77057,1746],{},[898,77059,1911],{},[1723,77061,1725],{},[898,77063,1904],{},[1723,77065,1908],{"stretchy":1907},[898,77067,1911],{},[1723,77069,1914],{"stretchy":1907},[898,77071,2125],{"mathvariant":2124},[898,77073,1911],{},[902,77075,76950],{"encoding":904}," a derivace podílu:",[883,77078,77080],{"className":77079},[886],[888,77081,77082],{"xmlns":890,"display":28759},[892,77083,77084,77237],{},[895,77085,77086,77088,77090,77096,77102,77104,77106,77108,77110,77150,77152,77158,77192,77194,77200,77203,77205,77211,77213,77215,77217,77219,77221,77227,77229,77231,77233,77235],{},[1723,77087,1908],{"stretchy":1907},[898,77089,1718],{},[1931,77091,77092,77094],{},[898,77093,1746],{},[898,77095,1911],{},[2057,77097,77098,77100],{},[1723,77099,1914],{"stretchy":1907},[1723,77101,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,77103,1908],{"stretchy":1907},[898,77105,1911],{},[1723,77107,1914],{"stretchy":1907},[1723,77109,1725],{},[3058,77111,77112,77144],{},[895,77113,77114,77120,77122,77124,77126,77128,77130,77132,77134,77136,77138,77140,77142],{},[2057,77115,77116,77118],{},[898,77117,1904],{},[1723,77119,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,77121,1908],{"stretchy":1907},[898,77123,1911],{},[1723,77125,1914],{"stretchy":1907},[1723,77127,3897],{},[898,77129,1911],{},[1723,77131,1759],{},[898,77133,1904],{},[1723,77135,1908],{"stretchy":1907},[898,77137,1911],{},[1723,77139,1914],{"stretchy":1907},[1723,77141,3897],{},[1864,77143,1866],{},[2057,77145,77146,77148],{},[898,77147,1911],{},[1864,77149,2331],{},[1723,77151,1725],{},[3058,77153,77154,77156],{},[1864,77155,1866],{},[898,77157,1911],{},[895,77159,77160,77162,77168,77170,77172,77174,77176,77190],{},[1723,77161,1908],{"fence":2030},[2057,77163,77164,77166],{},[898,77165,1904],{},[1723,77167,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,77169,1908],{"stretchy":1907},[898,77171,1911],{},[1723,77173,1914],{"stretchy":1907},[1723,77175,1759],{},[3058,77177,77178,77188],{},[895,77179,77180,77182,77184,77186],{},[898,77181,1904],{},[1723,77183,1908],{"stretchy":1907},[898,77185,1911],{},[1723,77187,1914],{"stretchy":1907},[898,77189,1911],{},[1723,77191,1914],{"fence":2030},[1723,77193,1725],{},[3058,77195,77196,77198],{},[1864,77197,1866],{},[898,77199,1911],{},[1723,77201,1908],{"fence":2030,"stretchy":2030,"minsize":77202,"maxsize":77202},"1.2em",[898,77204,1728],{},[1931,77206,77207,77209],{},[898,77208,1746],{},[898,77210,1911],{},[1723,77212,1908],{"stretchy":1907},[898,77214,1911],{},[1723,77216,1914],{"stretchy":1907},[1723,77218,1759],{},[898,77220,1718],{},[1931,77222,77223,77225],{},[898,77224,1746],{},[898,77226,1911],{},[1723,77228,1908],{"stretchy":1907},[898,77230,1911],{},[1723,77232,1914],{"stretchy":1907},[1723,77234,1914],{"fence":2030,"stretchy":2030,"minsize":77202,"maxsize":77202},[898,77236,1664],{"mathvariant":2124},[902,77238,77239],{"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).",[724,77241,10369,77242,8812,77264,77347],{},[883,77243,77245],{"className":77244},[886],[888,77246,77247],{"xmlns":890},[892,77248,77249,77261],{},[895,77250,77251,77257,77259],{},[1931,77252,77253,77255],{},[898,77254,1911],{},[1864,77256,2256],{},[1723,77258,2253],{},[1864,77260,2256],{},[902,77262,77263],{"encoding":904},"L_0 > 0",[883,77265,77267],{"className":77266},[886],[888,77268,77269],{"xmlns":890},[892,77270,77271,77344],{},[895,77272,77273,77275,77277,77283,77289,77291,77297,77299,77301,77303,77306,77308,77314,77316,77322,77324,77326,77328,77334,77336,77342],{},[1723,77274,1908],{"stretchy":1907},[898,77276,1718],{},[1931,77278,77279,77281],{},[898,77280,1746],{},[898,77282,1911],{},[2057,77284,77285,77287],{},[1723,77286,1914],{"stretchy":1907},[1723,77288,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,77290,1908],{"stretchy":1907},[1931,77292,77293,77295],{},[898,77294,1911],{},[1864,77296,2256],{},[1723,77298,1914],{"stretchy":1907},[1723,77300,1725],{},[1864,77302,2256],{},[1723,77304,77305],{},"⇔",[898,77307,1728],{},[1931,77309,77310,77312],{},[898,77311,1746],{},[898,77313,1911],{},[1723,77315,1908],{"stretchy":1907},[1931,77317,77318,77320],{},[898,77319,1911],{},[1864,77321,2256],{},[1723,77323,1914],{"stretchy":1907},[1723,77325,1725],{},[898,77327,1718],{},[1931,77329,77330,77332],{},[898,77331,1746],{},[898,77333,1911],{},[1723,77335,1908],{"stretchy":1907},[1931,77337,77338,77340],{},[898,77339,1911],{},[1864,77341,2256],{},[1723,77343,1914],{"stretchy":1907},[902,77345,77346],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,77349,77351],{"id":77350},"příklad-51","Příklad 5.1",[724,77353,77354,77355,1664],{},"Je dána produkce ",[883,77356,77358],{"className":77357},[886],[888,77359,77360],{"xmlns":890},[892,77361,77362,77386],{},[895,77363,77364,77366,77368,77370,77376,77378,77380],{},[898,77365,1904],{},[1723,77367,1725],{},[1864,77369,2969],{},[2057,77371,77372,77374],{},[898,77373,1911],{},[1864,77375,2331],{},[1723,77377,1759],{},[1864,77379,3561],{},[2057,77381,77382,77384],{},[898,77383,1911],{},[1864,77385,2909],{},[902,77387,77388],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,77390,77391,58209,77394,77444,77445,1664],{},[38,77392,77393],{},"(a)",[883,77395,77397],{"className":77396},[886],[888,77398,77399],{"xmlns":890},[892,77400,77401,77441],{},[895,77402,77403,77405,77407,77409,77411,77413,77415,77417,77419,77421,77423,77425,77427,77429,77431,77433,77435,77437,77439],{},[898,77404,1911],{},[1723,77406,1725],{},[1864,77408,2331],{},[1723,77410,2031],{"separator":2030},[1864,77412,2962],{},[1723,77414,2031],{"separator":2030},[1864,77416,6295],{},[1723,77418,2031],{"separator":2030},[1864,77420,3585],{},[1723,77422,2031],{"separator":2030},[1864,77424,23639],{},[1723,77426,2031],{"separator":2030},[1864,77428,4425],{},[1723,77430,2031],{"separator":2030},[1864,77432,9744],{},[1723,77434,2031],{"separator":2030},[1864,77436,39038],{},[1723,77438,2031],{"separator":2030},[1864,77440,5714],{},[902,77442,77443],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,77446,77448],{"className":77447},[886],[888,77449,77450],{"xmlns":890},[892,77451,77452,77462],{},[895,77453,77454,77456],{},[898,77455,1728],{},[1931,77457,77458,77460],{},[898,77459,1746],{},[898,77461,1911],{},[902,77463,1939],{"encoding":904},[724,77465,77466,77467,35661],{},"Podle (5.2): ",[883,77468,77470],{"className":77469},[886],[888,77471,77472],{"xmlns":890},[892,77473,77474,77530],{},[895,77475,77476,77478,77484,77486,77492,77494,77496,77498,77500,77502,77504,77506,77508,77514,77516,77518,77520,77522,77524,77526,77528],{},[898,77477,1728],{},[1931,77479,77480,77482],{},[898,77481,1746],{},[898,77483,1911],{},[1723,77485,1725],{},[2057,77487,77488,77490],{},[898,77489,1904],{},[1723,77491,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,77493,1908],{"stretchy":1907},[898,77495,1911],{},[1723,77497,1914],{"stretchy":1907},[1723,77499,1725],{},[1864,77501,4227],{},[898,77503,1911],{},[1723,77505,1759],{},[1864,77507,20015],{},[2057,77509,77510,77512],{},[898,77511,1911],{},[1864,77513,2331],{},[1723,77515,1725],{},[898,77517,1911],{},[1723,77519,1908],{"stretchy":1907},[1864,77521,4227],{},[1723,77523,1759],{},[1864,77525,20015],{},[898,77527,1911],{},[1723,77529,1914],{"stretchy":1907},[902,77531,77532],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,77534,77535,77572],{},[19,77536,77537],{},[22,77538,77539,77554,77556,77558,77560,77562,77564,77566,77568,77570],{},[25,77540,77541],{},[883,77542,77544],{"className":77543},[886],[888,77545,77546],{"xmlns":890},[892,77547,77548,77552],{},[895,77549,77550],{},[898,77551,1911],{},[902,77553,1911],{"encoding":904},[25,77555,2331],{},[25,77557,2962],{},[25,77559,6295],{},[25,77561,3585],{},[25,77563,23639],{},[25,77565,4425],{},[25,77567,9744],{},[25,77569,39038],{},[25,77571,5714],{},[30,77573,77574],{},[22,77575,77576,77597,77600,77603,77606,77608,77611,77613,77615,77634],{},[35,77577,77578],{},[883,77579,77581],{"className":77580},[886],[888,77582,77583],{"xmlns":890},[892,77584,77585,77595],{},[895,77586,77587,77589],{},[898,77588,1728],{},[1931,77590,77591,77593],{},[898,77592,1746],{},[898,77594,1911],{},[902,77596,1939],{"encoding":904},[35,77598,77599],{},"21,6",[35,77601,77602],{},"45",[35,77604,77605],{},"57,6",[35,77607,3846],{},[35,77609,77610],{},"50,4",[35,77612,77599],{},[35,77614,2256],{},[35,77616,77617],{},[883,77618,77620],{"className":77619},[886],[888,77621,77622],{"xmlns":890},[892,77623,77624,77631],{},[895,77625,77626,77628],{},[1723,77627,1759],{},[1864,77629,77630],{},"12,6",[902,77632,77633],{"encoding":904},"-12{,}6",[35,77635,77636],{},[883,77637,77639],{"className":77638},[886],[888,77640,77641],{"xmlns":890},[892,77642,77643,77649],{},[895,77644,77645,77647],{},[1723,77646,1759],{},[1864,77648,46143],{},[902,77650,77651],{"encoding":904},"-75",[724,77653,77654,77673,77674,77692,77693,77710,77711,77729,77730,77754,77755,77773],{},[883,77655,77657],{"className":77656},[886],[888,77658,77659],{"xmlns":890},[892,77660,77661,77671],{},[895,77662,77663,77665],{},[898,77664,1728],{},[1931,77666,77667,77669],{},[898,77668,1746],{},[898,77670,1911],{},[902,77672,1939],{"encoding":904}," nabývá maxima pro ",[883,77675,77677],{"className":77676},[886],[888,77678,77679],{"xmlns":890},[892,77680,77681,77689],{},[895,77682,77683,77685,77687],{},[898,77684,1911],{},[1723,77686,1725],{},[1864,77688,3585],{},[902,77690,77691],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,77694,77696],{"className":77695},[886],[888,77697,77698],{"xmlns":890},[892,77699,77700,77708],{},[895,77701,77702,77704,77706],{},[898,77703,1911],{},[1723,77705,1725],{},[1864,77707,3585],{},[902,77709,77691],{"encoding":904}," přírůstky klesají, v ",[883,77712,77714],{"className":77713},[886],[888,77715,77716],{"xmlns":890},[892,77717,77718,77726],{},[895,77719,77720,77722,77724],{},[898,77721,1911],{},[1723,77723,1725],{},[1864,77725,9744],{},[902,77727,77728],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,77731,77733],{"className":77732},[886],[888,77734,77735],{"xmlns":890},[892,77736,77737,77751],{},[895,77738,77739,77741,77743,77745,77747,77749],{},[898,77740,1904],{},[1723,77742,1908],{"stretchy":1907},[1864,77744,9744],{},[1723,77746,1914],{"stretchy":1907},[1723,77748,1725],{},[1864,77750,24551],{},[902,77752,77753],{"encoding":904},"Q(20) = 800","), od ",[883,77756,77758],{"className":77757},[886],[888,77759,77760],{"xmlns":890},[892,77761,77762,77770],{},[895,77763,77764,77766,77768],{},[898,77765,1911],{},[1723,77767,2253],{},[1864,77769,9744],{},[902,77771,77772],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,77775,77776],{},[614,77777,77778,77779,77819,77820,3350,77838,1664],{},"Obrázek 5.1 — graf produkce ",[883,77780,77782],{"className":77781},[886],[888,77783,77784],{"xmlns":890},[892,77785,77786,77816],{},[895,77787,77788,77790,77792,77794,77796,77798,77800,77806,77808,77810],{},[898,77789,1904],{},[1723,77791,1908],{"stretchy":1907},[898,77793,1911],{},[1723,77795,1914],{"stretchy":1907},[1723,77797,1725],{},[1864,77799,2969],{},[2057,77801,77802,77804],{},[898,77803,1911],{},[1864,77805,2331],{},[1723,77807,1759],{},[1864,77809,3561],{},[2057,77811,77812,77814],{},[898,77813,1911],{},[1864,77815,2909],{},[902,77817,77818],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,77821,77823],{"className":77822},[886],[888,77824,77825],{"xmlns":890},[892,77826,77827,77835],{},[895,77828,77829,77831,77833],{},[898,77830,1904],{},[1723,77832,1725],{},[1864,77834,24551],{},[902,77836,77837],{"encoding":904},"Q = 800",[883,77839,77841],{"className":77840},[886],[888,77842,77843],{"xmlns":890},[892,77844,77845,77853],{},[895,77846,77847,77849,77851],{},[898,77848,1911],{},[1723,77850,1725],{},[1864,77852,9744],{},[902,77854,77728],{"encoding":904},[724,77856,77857,77860],{},[38,77858,77859],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,77862,77863,77864,1343,77882,3430],{},"Podle (5.3) s ",[883,77865,77867],{"className":77866},[886],[888,77868,77869],{"xmlns":890},[892,77870,77871,77879],{},[895,77872,77873,77875,77877],{},[898,77874,1911],{},[1723,77876,1725],{},[1864,77878,2969],{},[902,77880,77881],{"encoding":904},"L = 6",[883,77883,77885],{"className":77884},[886],[888,77886,77887],{"xmlns":890},[892,77888,77889,77899],{},[895,77890,77891,77893,77895,77897],{},[898,77892,2930],{},[898,77894,1911],{},[1723,77896,1725],{},[1864,77898,2909],{},[902,77900,77901],{"encoding":904},"dL = 3",[883,77903,77905],{"className":77904},[886],[888,77906,77907],{"xmlns":890,"display":28759},[892,77908,77909,77972],{},[895,77910,77911,77913,77915,77917,77919,77925,77927,77929,77931,77933,77935,77937,77939,77941,77943,77945,77947,77949,77951,77953,77955,77957,77959,77961,77963,77965,77967,77969],{},[898,77912,2930],{},[898,77914,1904],{},[1723,77916,1725],{},[898,77918,1728],{},[1931,77920,77921,77923],{},[898,77922,1746],{},[898,77924,1911],{},[1723,77926,1908],{"stretchy":1907},[1864,77928,2969],{},[1723,77930,1914],{"stretchy":1907},[1723,77932,3897],{},[1864,77934,2909],{},[1723,77936,1725],{},[1723,77938,1908],{"stretchy":1907},[1864,77940,4227],{},[1723,77942,3897],{},[1864,77944,2969],{},[1723,77946,1759],{},[1864,77948,20015],{},[1723,77950,3897],{},[1864,77952,6275],{},[1723,77954,1914],{"stretchy":1907},[1723,77956,3897],{},[1864,77958,2909],{},[1723,77960,1725],{},[1864,77962,77610],{},[1723,77964,3897],{},[1864,77966,2909],{},[1723,77968,1725],{},[1864,77970,77971],{},"151,2.",[902,77973,77974],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,77976,77977,77978,58439,78003,78017,78018,1664],{},"Produkce vzroste z ",[883,77979,77981],{"className":77980},[886],[888,77982,77983],{"xmlns":890},[892,77984,77985,78000],{},[895,77986,77987,77989,77991,77993,77995,77997],{},[898,77988,1904],{},[1723,77990,1908],{"stretchy":1907},[1864,77992,2969],{},[1723,77994,1914],{"stretchy":1907},[1723,77996,1725],{},[1864,77998,77999],{},"172,8",[902,78001,78002],{"encoding":904},"Q(6) = 172{,}8",[883,78004,78006],{"className":78005},[886],[888,78007,78008],{"xmlns":890},[892,78009,78010,78015],{},[895,78011,78012],{},[1864,78013,78014],{},"324",[902,78016,78014],{"encoding":904},". Skutečná hodnota: ",[883,78019,78021],{"className":78020},[886],[888,78022,78023],{"xmlns":890},[892,78024,78025,78065],{},[895,78026,78027,78029,78031,78033,78035,78037,78039,78041,78043,78045,78047,78049,78051,78053,78056,78058,78060,78062],{},[898,78028,3611],{"mathvariant":2124},[898,78030,1904],{},[1723,78032,1725],{},[898,78034,1904],{},[1723,78036,1908],{"stretchy":1907},[1864,78038,4713],{},[1723,78040,1914],{"stretchy":1907},[1723,78042,1759],{},[898,78044,1904],{},[1723,78046,1908],{"stretchy":1907},[1864,78048,2969],{},[1723,78050,1914],{"stretchy":1907},[1723,78052,1725],{},[1864,78054,78055],{},"340,2",[1723,78057,1759],{},[1864,78059,77999],{},[1723,78061,1725],{},[1864,78063,78064],{},"167,4",[902,78066,78067],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,78069,78071],{"id":78070},"příklad-52","Příklad 5.2",[724,78073,78074,78075,1664],{},"Ověříme princip (5.5) pro ",[883,78076,78078],{"className":78077},[886],[888,78079,78080],{"xmlns":890},[892,78081,78082,78106],{},[895,78083,78084,78086,78088,78090,78096,78098,78100],{},[898,78085,1904],{},[1723,78087,1725],{},[1864,78089,2969],{},[2057,78091,78092,78094],{},[898,78093,1911],{},[1864,78095,2331],{},[1723,78097,1759],{},[1864,78099,3561],{},[2057,78101,78102,78104],{},[898,78103,1911],{},[1864,78105,2909],{},[902,78107,77388],{"encoding":904},[883,78109,78111],{"className":78110},[886],[888,78112,78113],{"xmlns":890,"display":28759},[892,78114,78115,78193],{},[895,78116,78117,78119,78125,78127,78133,78135,78137,78139,78141,78143,78149,78151,78153,78155,78163,78165,78167,78169,78171,78173,78175,78177,78179,78181,78183,78189,78191],{},[898,78118,1718],{},[1931,78120,78121,78123],{},[898,78122,1746],{},[898,78124,1911],{},[1723,78126,1725],{},[3058,78128,78129,78131],{},[898,78130,1904],{},[898,78132,1911],{},[1723,78134,1725],{},[1864,78136,2969],{},[898,78138,1911],{},[1723,78140,1759],{},[1864,78142,3561],{},[2057,78144,78145,78147],{},[898,78146,1911],{},[1864,78148,2331],{},[1723,78150,2031],{"separator":2030},[6588,78152],{"width":15985},[898,78154,1718],{},[2220,78156,78157,78159,78161],{},[898,78158,1746],{},[898,78160,1911],{},[1723,78162,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,78164,1725],{},[1864,78166,2969],{},[1723,78168,1759],{},[1864,78170,19965],{},[898,78172,1911],{},[1723,78174,1725],{},[1864,78176,2256],{},[3018,78178,4699],{},[1723,78180,4702],{},[3018,78182,4699],{},[1931,78184,78185,78187],{},[898,78186,1911],{},[1864,78188,2256],{},[1723,78190,1725],{},[1864,78192,68969],{},[902,78194,78195],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,78197,78198,78234,78235,78253,78254,1664],{},[883,78199,78201],{"className":78200},[886],[888,78202,78203],{"xmlns":890},[892,78204,78205,78231],{},[895,78206,78207,78209,78221,78223,78225,78227,78229],{},[898,78208,1718],{},[2220,78210,78211,78213,78215],{},[898,78212,1746],{},[898,78214,1911],{},[895,78216,78217,78219],{},[1723,78218,2229],{"mathvariant":2124},[1723,78220,2229],{"mathvariant":2124},[1723,78222,1725],{},[1723,78224,1759],{},[1864,78226,19965],{},[1723,78228,2287],{},[1864,78230,2256],{},[902,78232,78233],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,78236,78238],{"className":78237},[886],[888,78239,78240],{"xmlns":890},[892,78241,78242,78250],{},[895,78243,78244,78246,78248],{},[898,78245,1911],{},[1723,78247,1725],{},[1864,78249,36937],{},[902,78251,78252],{"encoding":904},"L = 15"," je maximum, ",[883,78255,78257],{"className":78256},[886],[888,78258,78259],{"xmlns":890},[892,78260,78261,78307],{},[895,78262,78263,78265,78271,78273,78275,78277,78279,78281,78283,78285,78287,78289,78291,78294,78296,78299,78301,78303,78305],{},[898,78264,1718],{},[1931,78266,78267,78269],{},[898,78268,1746],{},[898,78270,1911],{},[1723,78272,1908],{"stretchy":1907},[1864,78274,36937],{},[1723,78276,1914],{"stretchy":1907},[1723,78278,1725],{},[1864,78280,2969],{},[1723,78282,3897],{},[1864,78284,36937],{},[1723,78286,1759],{},[1864,78288,3561],{},[1723,78290,3897],{},[1864,78292,78293],{},"225",[1723,78295,1725],{},[1864,78297,78298],{},"90",[1723,78300,1759],{},[1864,78302,77602],{},[1723,78304,1725],{},[1864,78306,77602],{},[902,78308,78309],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,78311,78312,42572,78368,78414],{},[883,78313,78315],{"className":78314},[886],[888,78316,78317],{"xmlns":890},[892,78318,78319,78365],{},[895,78320,78321,78323,78329,78331,78333,78335,78337,78339,78341,78343,78345,78347,78349,78351,78353,78356,78358,78361,78363],{},[898,78322,1728],{},[1931,78324,78325,78327],{},[898,78326,1746],{},[898,78328,1911],{},[1723,78330,1908],{"stretchy":1907},[1864,78332,36937],{},[1723,78334,1914],{"stretchy":1907},[1723,78336,1725],{},[1864,78338,4227],{},[1723,78340,3897],{},[1864,78342,36937],{},[1723,78344,1759],{},[1864,78346,20015],{},[1723,78348,3897],{},[1864,78350,78293],{},[1723,78352,1725],{},[1864,78354,78355],{},"180",[1723,78357,1759],{},[1864,78359,78360],{},"135",[1723,78362,1725],{},[1864,78364,77602],{},[902,78366,78367],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,78369,78371],{"className":78370},[886],[888,78372,78373],{"xmlns":890},[892,78374,78375,78411],{},[895,78376,78377,78379,78385,78387,78389,78391,78393,78395,78401,78403,78405,78407,78409],{},[898,78378,1728],{},[1931,78380,78381,78383],{},[898,78382,1746],{},[898,78384,1911],{},[1723,78386,1908],{"stretchy":1907},[1864,78388,36937],{},[1723,78390,1914],{"stretchy":1907},[1723,78392,1725],{},[898,78394,1718],{},[1931,78396,78397,78399],{},[898,78398,1746],{},[898,78400,1911],{},[1723,78402,1908],{"stretchy":1907},[1864,78404,36937],{},[1723,78406,1914],{"stretchy":1907},[1723,78408,1725],{},[1864,78410,77602],{},[902,78412,78413],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,78416,78417,78420,78421,18272,78450,1664],{},[38,78418,78419],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,78422,78424],{"className":78423},[886],[888,78425,78426],{"xmlns":890},[892,78427,78428,78448],{},[895,78429,78430,78432,78438,78440,78442],{},[898,78431,1728],{},[1931,78433,78434,78436],{},[898,78435,1746],{},[898,78437,1911],{},[1723,78439,1725],{},[898,78441,1718],{},[1931,78443,78444,78446],{},[898,78445,1746],{},[898,78447,1911],{},[902,78449,2011],{"encoding":904},[883,78451,78453],{"className":78452},[886],[888,78454,78455],{"xmlns":890},[892,78456,78457,78497],{},[895,78458,78459,78461,78463,78465,78467,78473,78475,78477,78479,78481,78483,78489,78491,78493,78495],{},[1864,78460,4227],{},[898,78462,1911],{},[1723,78464,1759],{},[1864,78466,20015],{},[2057,78468,78469,78471],{},[898,78470,1911],{},[1864,78472,2331],{},[1723,78474,1725],{},[1864,78476,2969],{},[898,78478,1911],{},[1723,78480,1759],{},[1864,78482,3561],{},[2057,78484,78485,78487],{},[898,78486,1911],{},[1864,78488,2331],{},[1723,78490,4702],{},[898,78492,1911],{},[1723,78494,1725],{},[1864,78496,36937],{},[902,78498,78499],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,78501,78502],{},[614,78503,78504,78505,78524,78525,12829,78543,78562,78563,78581,78582,78599,78600,78619,78620,78639],{},"Obrázek 5.3 — křivky ",[883,78506,78508],{"className":78507},[886],[888,78509,78510],{"xmlns":890},[892,78511,78512,78522],{},[895,78513,78514,78516],{},[898,78515,1728],{},[1931,78517,78518,78520],{},[898,78519,1746],{},[898,78521,1911],{},[902,78523,1939],{"encoding":904}," (max 60 při ",[883,78526,78528],{"className":78527},[886],[888,78529,78530],{"xmlns":890},[892,78531,78532,78540],{},[895,78533,78534,78536,78538],{},[898,78535,1911],{},[1723,78537,1725],{},[1864,78539,3585],{},[902,78541,78542],{"encoding":904},"L=10",[883,78544,78546],{"className":78545},[886],[888,78547,78548],{"xmlns":890},[892,78549,78550,78560],{},[895,78551,78552,78554],{},[898,78553,1718],{},[1931,78555,78556,78558],{},[898,78557,1746],{},[898,78559,1911],{},[902,78561,1960],{"encoding":904}," (max 45 při ",[883,78564,78566],{"className":78565},[886],[888,78567,78568],{"xmlns":890},[892,78569,78570,78578],{},[895,78571,78572,78574,78576],{},[898,78573,1911],{},[1723,78575,1725],{},[1864,78577,36937],{},[902,78579,78580],{"encoding":904},"L=15","), průsečík v ",[883,78583,78585],{"className":78584},[886],[888,78586,78587],{"xmlns":890},[892,78588,78589,78597],{},[895,78590,78591,78593,78595],{},[898,78592,1911],{},[1723,78594,1725],{},[1864,78596,36937],{},[902,78598,78252],{"encoding":904},". Nalevo od 15 leží ",[883,78601,78603],{"className":78602},[886],[888,78604,78605],{"xmlns":890},[892,78606,78607,78617],{},[895,78608,78609,78611],{},[898,78610,1728],{},[1931,78612,78613,78615],{},[898,78614,1746],{},[898,78616,1911],{},[902,78618,1939],{"encoding":904}," nad ",[883,78621,78623],{"className":78622},[886],[888,78624,78625],{"xmlns":890},[892,78626,78627,78637],{},[895,78628,78629,78631],{},[898,78630,1718],{},[1931,78632,78633,78635],{},[898,78634,1746],{},[898,78636,1911],{},[902,78638,1960],{"encoding":904},", napravo pod ní.",[115,78641,78643],{"id":78642},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,78645,78646,78647,3411,78660,2628,78663,6900,78676,2628,78679,3430],{},"V dvoufaktorovém modelu závisí produkce ",[883,78648,78650],{"className":78649},[886],[888,78651,78652],{"xmlns":890},[892,78653,78654,78658],{},[895,78655,78656],{},[898,78657,1904],{},[902,78659,1904],{"encoding":904},[38,78661,78662],{},"práci",[883,78664,78666],{"className":78665},[886],[888,78667,78668],{"xmlns":890},[892,78669,78670,78674],{},[895,78671,78672],{},[898,78673,1911],{},[902,78675,1911],{"encoding":904},[38,78677,78678],{},"kapitálu",[883,78680,78682],{"className":78681},[886],[888,78683,78684],{"xmlns":890},[892,78685,78686,78690],{},[895,78687,78688],{},[898,78689,2034],{},[902,78691,2034],{"encoding":904},[883,78693,78695],{"className":78694},[886],[888,78696,78697],{"xmlns":890,"display":28759},[892,78698,78699,78734],{},[21447,78700,78701],{"width":28764},[21452,78702,78703,78705,78727,78729],{},[21455,78704],{"width":28769},[21455,78706,78707],{},[895,78708,78709,78711,78713,78715,78717,78719,78721,78723,78725],{},[898,78710,1904],{},[1723,78712,1725],{},[898,78714,1904],{},[1723,78716,1908],{"stretchy":1907},[898,78718,1911],{},[1723,78720,2031],{"separator":2030},[898,78722,2034],{},[1723,78724,1914],{"stretchy":1907},[898,78726,1664],{"mathvariant":2124},[21455,78728],{"width":28769},[21455,78730,78731],{},[3018,78732,78733],{},"(5.6)",[902,78735,78736],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,78738,78739,78740,78742],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,78741,75681],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,78744,78746],{"id":78745},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,78748,78749],{},"Široce používané produkční funkce mají tvar",[883,78751,78753],{"className":78752},[886],[888,78754,78755],{"xmlns":890,"display":28759},[892,78756,78757,78798],{},[21447,78758,78759],{"width":28764},[21452,78760,78761,78763,78791,78793],{},[21455,78762],{"width":28769},[21455,78764,78765],{},[895,78766,78767,78769,78771,78773,78775,78781,78783,78789],{},[898,78768,1904],{},[1723,78770,1725],{},[898,78772,1718],{},[3018,78774,3707],{},[2057,78776,78777,78779],{},[898,78778,1911],{},[898,78780,207],{},[3018,78782,3707],{},[2057,78784,78785,78787],{},[898,78786,2034],{},[898,78788,2069],{},[1723,78790,2031],{"separator":2030},[21455,78792],{"width":28769},[21455,78794,78795],{},[3018,78796,78797],{},"(5.7)",[902,78799,78800],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,78802,5022,78803,78825,78826,78828,78829,1664],{},[883,78804,78806],{"className":78805},[886],[888,78807,78808],{"xmlns":890},[892,78809,78810,78822],{},[895,78811,78812,78814,78816,78818,78820],{},[898,78813,1718],{},[1723,78815,2031],{"separator":2030},[898,78817,207],{},[1723,78819,2031],{"separator":2030},[898,78821,2069],{},[902,78823,78824],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,78827,75382],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,78830,78832],{"className":78831},[886],[888,78833,78834],{"xmlns":890},[892,78835,78836,78848],{},[895,78837,78838,78840,78842,78844,78846],{},[898,78839,207],{},[1723,78841,2031],{"separator":2030},[898,78843,2069],{},[1723,78845,2287],{},[1864,78847,1866],{},[902,78849,78850],{"encoding":904},"a, b \u003C 1",[724,78852,78853],{},[3285,78854],{"alt":78855,"className":78856,"src":78857},"imek-vynosy-z-rozsahu-3typy",[210,3289],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,78859,78860,78861,78864,78865,3411,78878,78894,78895,3411,78908,3430],{},"Reflektují ekonomickou zákonitost, že ",[38,78862,78863],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,78866,78868],{"className":78867},[886],[888,78869,78870],{"xmlns":890},[892,78871,78872,78876],{},[895,78873,78874],{},[898,78875,1911],{},[902,78877,1911],{"encoding":904},[883,78879,78881],{"className":78880},[886],[888,78882,78883],{"xmlns":890},[892,78884,78885,78891],{},[895,78886,78887,78889],{},[898,78888,12742],{},[898,78890,1911],{},[902,78892,78893],{"encoding":904},"rL"," a kapitál z ",[883,78896,78898],{"className":78897},[886],[888,78899,78900],{"xmlns":890},[892,78901,78902,78906],{},[895,78903,78904],{},[898,78905,2034],{},[902,78907,2034],{"encoding":904},[883,78909,78911],{"className":78910},[886],[888,78912,78913],{"xmlns":890},[892,78914,78915,78921],{},[895,78916,78917,78919],{},[898,78918,12742],{},[898,78920,2034],{},[902,78922,78923],{"encoding":904},"rK",[883,78925,78927],{"className":78926},[886],[888,78928,78929],{"xmlns":890,"display":28759},[892,78930,78931,79054],{},[21447,78932,78933],{"width":28764},[21452,78934,78935,78937,79047,79049],{},[21455,78936],{"width":28769},[21455,78938,78939],{},[895,78940,78941,78943,78945,78947,78949,78951,78953,78955,78957,78959,78961,78963,78965,78967,78973,78975,78977,78979,78985,78987,78989,78991,79003,79005,79011,79017,79019,79031,79033,79035,79037,79039,79041,79043,79045],{},[898,78942,1904],{},[1723,78944,1908],{"stretchy":1907},[898,78946,12742],{},[898,78948,1911],{},[1723,78950,2031],{"separator":2030},[898,78952,12742],{},[898,78954,2034],{},[1723,78956,1914],{"stretchy":1907},[1723,78958,1725],{},[898,78960,1718],{},[1723,78962,1908],{"stretchy":1907},[898,78964,12742],{},[898,78966,1911],{},[2057,78968,78969,78971],{},[1723,78970,1914],{"stretchy":1907},[898,78972,207],{},[1723,78974,1908],{"stretchy":1907},[898,78976,12742],{},[898,78978,2034],{},[2057,78980,78981,78983],{},[1723,78982,1914],{"stretchy":1907},[898,78984,2069],{},[1723,78986,1725],{},[898,78988,1718],{},[3018,78990,3707],{},[2057,78992,78993,78995],{},[898,78994,12742],{},[895,78996,78997,78999,79001],{},[898,78998,207],{},[1723,79000,2087],{},[898,79002,2069],{},[3018,79004,3707],{},[2057,79006,79007,79009],{},[898,79008,1911],{},[898,79010,207],{},[2057,79012,79013,79015],{},[898,79014,2034],{},[898,79016,2069],{},[1723,79018,1725],{},[2057,79020,79021,79023],{},[898,79022,12742],{},[895,79024,79025,79027,79029],{},[898,79026,207],{},[1723,79028,2087],{},[898,79030,2069],{},[3018,79032,3707],{},[898,79034,1904],{},[1723,79036,1908],{"stretchy":1907},[898,79038,1911],{},[1723,79040,2031],{"separator":2030},[898,79042,2034],{},[1723,79044,1914],{"stretchy":1907},[898,79046,1664],{"mathvariant":2124},[21455,79048],{"width":28769},[21455,79050,79051],{},[3018,79052,79053],{},"(5.8)",[902,79055,79056],{"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}",[724,79058,79059,79060],{},"Volně: ",[38,79061,79062,79063,79076,79077,79101],{},"změní-li se vstupy ",[883,79064,79066],{"className":79065},[886],[888,79067,79068],{"xmlns":890},[892,79069,79070,79074],{},[895,79071,79072],{},[898,79073,12742],{},[902,79075,12742],{"encoding":904},"-krát, změní se výstup ",[883,79078,79080],{"className":79079},[886],[888,79081,79082],{"xmlns":890},[892,79083,79084,79098],{},[895,79085,79086],{},[2057,79087,79088,79090],{},[898,79089,12742],{},[895,79091,79092,79094,79096],{},[898,79093,207],{},[1723,79095,2087],{},[898,79097,2069],{},[902,79099,79100],{"encoding":904},"r^{a+b}","-krát.",[198,79103,79105],{"id":79104},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,79107,79108,79109,79126],{},"Součet exponentů ",[883,79110,79112],{"className":79111},[886],[888,79113,79114],{"xmlns":890},[892,79115,79116,79124],{},[895,79117,79118,79120,79122],{},[898,79119,207],{},[1723,79121,2087],{},[898,79123,2069],{},[902,79125,75505],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,79128,79129,79158],{},[19,79130,79131],{},[22,79132,79133,79136,79139,79156],{},[25,79134,79135],{},"Typ",[25,79137,79138],{},"Podmínka",[25,79140,79141,79142,79155],{},"Chování produkce při ",[883,79143,79145],{"className":79144},[886],[888,79146,79147],{"xmlns":890},[892,79148,79149,79153],{},[895,79150,79151],{},[898,79152,12742],{},[902,79154,12742],{"encoding":904},"-násobném zvýšení vstupů",[25,79157,3790],{},[30,79159,79160,79271,79386],{},[22,79161,79162,79170,79194,79227],{},[35,79163,76218,79164,1981,79167,1914],{},[38,79165,79166],{},"Konstantní",[614,79168,79169],{},"constant returns",[35,79171,79172],{},[883,79173,79175],{"className":79174},[886],[888,79176,79177],{"xmlns":890},[892,79178,79179,79191],{},[895,79180,79181,79183,79185,79187,79189],{},[898,79182,207],{},[1723,79184,2087],{},[898,79186,2069],{},[1723,79188,1725],{},[1864,79190,1866],{},[902,79192,79193],{"encoding":904},"a+b = 1",[35,79195,79196,79209,79210,2628,79213,79226],{},[883,79197,79199],{"className":79198},[886],[888,79200,79201],{"xmlns":890},[892,79202,79203,79207],{},[895,79204,79205],{},[898,79206,1904],{},[902,79208,1904],{"encoding":904}," vzroste ",[38,79211,79212],{},"přesně",[883,79214,79216],{"className":79215},[886],[888,79217,79218],{"xmlns":890},[892,79219,79220,79224],{},[895,79221,79222],{},[898,79223,12742],{},[902,79225,12742],{"encoding":904},"-krát",[35,79228,79229],{},[883,79230,79232],{"className":79231},[886],[888,79233,79234],{"xmlns":890},[892,79235,79236,79268],{},[895,79237,79238,79240,79242,79244,79256],{},[898,79239,1904],{},[1723,79241,1725],{},[1864,79243,2331],{},[2057,79245,79246,79248],{},[898,79247,1911],{},[895,79249,79250,79252,79254],{},[1864,79251,1866],{},[898,79253,2125],{"mathvariant":2124},[1864,79255,3080],{},[2057,79257,79258,79260],{},[898,79259,2034],{},[895,79261,79262,79264,79266],{},[1864,79263,2909],{},[898,79265,2125],{"mathvariant":2124},[1864,79267,3080],{},[902,79269,79270],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,79272,79273,79282,79306,79336],{},[35,79274,79275,79276,1981,79279,1914],{},"2° ",[38,79277,79278],{},"Rostoucí",[614,79280,79281],{},"increasing returns",[35,79283,79284],{},[883,79285,79287],{"className":79286},[886],[888,79288,79289],{"xmlns":890},[892,79290,79291,79303],{},[895,79292,79293,79295,79297,79299,79301],{},[898,79294,207],{},[1723,79296,2087],{},[898,79298,2069],{},[1723,79300,2253],{},[1864,79302,1866],{},[902,79304,79305],{"encoding":904},"a+b > 1",[35,79307,79308,79209,79321,51921,79323,79226],{},[883,79309,79311],{"className":79310},[886],[888,79312,79313],{"xmlns":890},[892,79314,79315,79319],{},[895,79316,79317],{},[898,79318,1904],{},[902,79320,1904],{"encoding":904},[38,79322,25963],{},[883,79324,79326],{"className":79325},[886],[888,79327,79328],{"xmlns":890},[892,79329,79330,79334],{},[895,79331,79332],{},[898,79333,12742],{},[902,79335,12742],{"encoding":904},[35,79337,79338,1981,79364,1914],{},[883,79339,79341],{"className":79340},[886],[888,79342,79343],{"xmlns":890},[892,79344,79345,79361],{},[895,79346,79347,79349,79351,79353,79355],{},[898,79348,1904],{},[1723,79350,1725],{},[1864,79352,24894],{},[898,79354,1911],{},[2057,79356,79357,79359],{},[898,79358,2034],{},[1864,79360,2331],{},[902,79362,79363],{"encoding":904},"Q = 7LK^2",[883,79365,79367],{"className":79366},[886],[888,79368,79369],{"xmlns":890},[892,79370,79371,79383],{},[895,79372,79373,79375,79377,79379,79381],{},[898,79374,207],{},[1723,79376,2087],{},[898,79378,2069],{},[1723,79380,1725],{},[1864,79382,2909],{},[902,79384,79385],{"encoding":904},"a+b = 3",[22,79387,79388,79397,79421,79452],{},[35,79389,79390,79391,1981,79394,1914],{},"3° ",[38,79392,79393],{},"Klesající",[614,79395,79396],{},"decreasing returns",[35,79398,79399],{},[883,79400,79402],{"className":79401},[886],[888,79403,79404],{"xmlns":890},[892,79405,79406,79418],{},[895,79407,79408,79410,79412,79414,79416],{},[898,79409,207],{},[1723,79411,2087],{},[898,79413,2069],{},[1723,79415,2287],{},[1864,79417,1866],{},[902,79419,79420],{"encoding":904},"a+b \u003C 1",[35,79422,79423,79209,79436,51921,79439,79226],{},[883,79424,79426],{"className":79425},[886],[888,79427,79428],{"xmlns":890},[892,79429,79430,79434],{},[895,79431,79432],{},[898,79433,1904],{},[902,79435,1904],{"encoding":904},[38,79437,79438],{},"méně",[883,79440,79442],{"className":79441},[886],[888,79443,79444],{"xmlns":890},[892,79445,79446,79450],{},[895,79447,79448],{},[898,79449,12742],{},[902,79451,12742],{"encoding":904},[35,79453,79454,1981,79484,1914],{},[883,79455,79457],{"className":79456},[886],[888,79458,79459],{"xmlns":890},[892,79460,79461,79481],{},[895,79462,79463,79465,79467,79469,79475],{},[898,79464,1904],{},[1723,79466,1725],{},[1864,79468,3585],{},[2057,79470,79471,79473],{},[898,79472,1911],{},[1864,79474,68898],{},[2057,79476,79477,79479],{},[898,79478,2034],{},[1864,79480,5719],{},[902,79482,79483],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,79485,79487],{"className":79486},[886],[888,79488,79489],{"xmlns":890},[892,79490,79491,79503],{},[895,79492,79493,79495,79497,79499,79501],{},[898,79494,207],{},[1723,79496,2087],{},[898,79498,2069],{},[1723,79500,1725],{},[1864,79502,15290],{},[902,79504,79505],{"encoding":904},"a+b = 0{,}8",[4584,79507,79508],{},[724,79509,79510,79512,79513,79530,79531,79534,79535,2628,79538,79574,79575,79597,79598,1664],{},[883,79511,5124],{}," Pozor\nSoučet ",[883,79514,79516],{"className":79515},[886],[888,79517,79518],{"xmlns":890},[892,79519,79520,79528],{},[895,79521,79522,79524,79526],{},[898,79523,207],{},[1723,79525,2087],{},[898,79527,2069],{},[902,79529,75505],{"encoding":904}," neudává velikost produkce, ale ",[38,79532,79533],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,79536,79537],{},"ryzí Cobb-Douglas",[883,79539,79541],{"className":79540},[886],[888,79542,79543],{"xmlns":890},[892,79544,79545,79571],{},[895,79546,79547,79549,79551,79553,79559],{},[898,79548,1904],{},[1723,79550,1725],{},[898,79552,1718],{},[2057,79554,79555,79557],{},[898,79556,1911],{},[898,79558,207],{},[2057,79560,79561,79563],{},[898,79562,2034],{},[895,79564,79565,79567,79569],{},[1864,79566,1866],{},[1723,79568,1759],{},[898,79570,207],{},[902,79572,79573],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,79576,79578],{"className":79577},[886],[888,79579,79580],{"xmlns":890},[892,79581,79582,79594],{},[895,79583,79584,79586,79588,79590,79592],{},[898,79585,2069],{},[1723,79587,1725],{},[1864,79589,1866],{},[1723,79591,1759],{},[898,79593,207],{},[902,79595,79596],{"encoding":904},"b = 1-a",", tedy vždy ",[38,79599,79600],{},"konstantní výnosy z rozsahu",[198,79602,79604,79605],{"id":79603},"parametr-efektivity-aa","Parametr efektivity ",[883,79606,79608],{"className":79607},[886],[888,79609,79610],{"xmlns":890},[892,79611,79612,79616],{},[895,79613,79614],{},[898,79615,1718],{},[902,79617,1718],{"encoding":904},[724,79619,79620,79621,79634,79635,79648,79649,79667,79668,79671],{},"Konstanta ",[883,79622,79624],{"className":79623},[886],[888,79625,79626],{"xmlns":890},[892,79627,79628,79632],{},[895,79629,79630],{},[898,79631,1718],{},[902,79633,1718],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,79636,79638],{"className":79637},[886],[888,79639,79640],{"xmlns":890},[892,79641,79642,79646],{},[895,79643,79644],{},[898,79645,1904],{},[902,79647,1904],{"encoding":904}," při pevně zadaných ",[883,79650,79652],{"className":79651},[886],[888,79653,79654],{"xmlns":890},[892,79655,79656,79664],{},[895,79657,79658,79660,79662],{},[898,79659,1911],{},[1723,79661,2031],{"separator":2030},[898,79663,2034],{},[902,79665,79666],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,79669,79670],{},"parametr efektivity"," — indikátor stavu technologie.",[198,79673,79675],{"id":79674},"příklad-53","Příklad 5.3",[724,79677,79678,79679,79574,79721,79723,79724,1664],{},"Produkční funkce ",[883,79680,79682],{"className":79681},[886],[888,79683,79684],{"xmlns":890},[892,79685,79686,79718],{},[895,79687,79688,79690,79692,79694,79706],{},[898,79689,1904],{},[1723,79691,1725],{},[1864,79693,2331],{},[2057,79695,79696,79698],{},[898,79697,1911],{},[895,79699,79700,79702,79704],{},[1864,79701,1866],{},[898,79703,2125],{"mathvariant":2124},[1864,79705,3080],{},[2057,79707,79708,79710],{},[898,79709,2034],{},[895,79711,79712,79714,79716],{},[1864,79713,2909],{},[898,79715,2125],{"mathvariant":2124},[1864,79717,3080],{},[902,79719,79720],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,79722,25306],{}," výnosy z rozsahu, neboť ",[883,79725,79727],{"className":79726},[886],[888,79728,79729],{"xmlns":890},[892,79730,79731,79755],{},[895,79732,79733,79741,79743,79751,79753],{},[3055,79734,79735],{"scriptlevel":2256,"displaystyle":1907},[3058,79736,79737,79739],{},[1864,79738,1866],{},[1864,79740,3080],{},[1723,79742,2087],{},[3055,79744,79745],{"scriptlevel":2256,"displaystyle":1907},[3058,79746,79747,79749],{},[1864,79748,2909],{},[1864,79750,3080],{},[1723,79752,1725],{},[1864,79754,1866],{},[902,79756,79757],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,79759,79760,79761,6900,79774,79787,79788,2628,79801,79841],{},"Změní-li se ",[883,79762,79764],{"className":79763},[886],[888,79765,79766],{"xmlns":890},[892,79767,79768,79772],{},[895,79769,79770],{},[898,79771,1911],{},[902,79773,1911],{"encoding":904},[883,79775,79777],{"className":79776},[886],[888,79778,79779],{"xmlns":890},[892,79780,79781,79785],{},[895,79782,79783],{},[898,79784,2034],{},[902,79786,2034],{"encoding":904}," čtyřnásobně, změní se ",[883,79789,79791],{"className":79790},[886],[888,79792,79793],{"xmlns":890},[892,79794,79795,79799],{},[895,79796,79797],{},[898,79798,1904],{},[902,79800,1904],{"encoding":904},[883,79802,79804],{"className":79803},[886],[888,79805,79806],{"xmlns":890},[892,79807,79808,79838],{},[895,79809,79810,79830,79832],{},[2057,79811,79812,79814],{},[1864,79813,3080],{},[895,79815,79816,79818,79820,79822,79824,79826,79828],{},[1864,79817,1866],{},[898,79819,2125],{"mathvariant":2124},[1864,79821,3080],{},[1723,79823,2087],{},[1864,79825,2909],{},[898,79827,2125],{"mathvariant":2124},[1864,79829,3080],{},[1723,79831,1725],{},[2057,79833,79834,79836],{},[1864,79835,3080],{},[1864,79837,1866],{},[902,79839,79840],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,79843,79845],{"className":79844},[886],[888,79846,79847],{"xmlns":890,"display":28759},[892,79848,79849,80009],{},[895,79850,79851,79853,79855,79857,79859,79861,79863,79865,79867,79869,79871,79873,79875,79877,79889,79891,79893,79895,79907,79909,79911,79913,79933,79945,79957,79959,79961,79963,79965,79977,79989,79991,79993,79995,79997,79999,80001,80003,80005,80007],{},[898,79852,1904],{},[1723,79854,1908],{"stretchy":1907},[1864,79856,3080],{},[898,79858,1911],{},[1723,79860,2031],{"separator":2030},[1864,79862,3080],{},[898,79864,2034],{},[1723,79866,1914],{"stretchy":1907},[1723,79868,1725],{},[1864,79870,2331],{},[1723,79872,1908],{"stretchy":1907},[1864,79874,3080],{},[898,79876,1911],{},[2057,79878,79879,79881],{},[1723,79880,1914],{"stretchy":1907},[895,79882,79883,79885,79887],{},[1864,79884,1866],{},[898,79886,2125],{"mathvariant":2124},[1864,79888,3080],{},[1723,79890,1908],{"stretchy":1907},[1864,79892,3080],{},[898,79894,2034],{},[2057,79896,79897,79899],{},[1723,79898,1914],{"stretchy":1907},[895,79900,79901,79903,79905],{},[1864,79902,2909],{},[898,79904,2125],{"mathvariant":2124},[1864,79906,3080],{},[1723,79908,1725],{},[1864,79910,2331],{},[1723,79912,3897],{},[2057,79914,79915,79917],{},[1864,79916,3080],{},[895,79918,79919,79921,79923,79925,79927,79929,79931],{},[1864,79920,1866],{},[898,79922,2125],{"mathvariant":2124},[1864,79924,3080],{},[1723,79926,2087],{},[1864,79928,2909],{},[898,79930,2125],{"mathvariant":2124},[1864,79932,3080],{},[2057,79934,79935,79937],{},[898,79936,1911],{},[895,79938,79939,79941,79943],{},[1864,79940,1866],{},[898,79942,2125],{"mathvariant":2124},[1864,79944,3080],{},[2057,79946,79947,79949],{},[898,79948,2034],{},[895,79950,79951,79953,79955],{},[1864,79952,2909],{},[898,79954,2125],{"mathvariant":2124},[1864,79956,3080],{},[1723,79958,1725],{},[1864,79960,3080],{},[1723,79962,3897],{},[1864,79964,2331],{},[2057,79966,79967,79969],{},[898,79968,1911],{},[895,79970,79971,79973,79975],{},[1864,79972,1866],{},[898,79974,2125],{"mathvariant":2124},[1864,79976,3080],{},[2057,79978,79979,79981],{},[898,79980,2034],{},[895,79982,79983,79985,79987],{},[1864,79984,2909],{},[898,79986,2125],{"mathvariant":2124},[1864,79988,3080],{},[1723,79990,1725],{},[1864,79992,3080],{},[3018,79994,3707],{},[898,79996,1904],{},[1723,79998,1908],{"stretchy":1907},[898,80000,1911],{},[1723,80002,2031],{"separator":2030},[898,80004,2034],{},[1723,80006,1914],{"stretchy":1907},[898,80008,1664],{"mathvariant":2124},[902,80010,80011],{"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).",[198,80013,80014],{"id":37871},"Homogenita",[724,80016,80017,80018,8812,80041,80057],{},"Funkce ",[883,80019,80021],{"className":80020},[886],[888,80022,80023],{"xmlns":890},[892,80024,80025,80039],{},[895,80026,80027,80029,80031,80033,80035,80037],{},[898,80028,1904],{},[1723,80030,1908],{"stretchy":1907},[898,80032,1911],{},[1723,80034,2031],{"separator":2030},[898,80036,2034],{},[1723,80038,1914],{"stretchy":1907},[902,80040,10699],{"encoding":904},[38,80042,80043,80044],{},"homogenní stupně ",[883,80045,80047],{"className":80046},[886],[888,80048,80049],{"xmlns":890},[892,80050,80051,80055],{},[895,80052,80053],{},[898,80054,2192],{},[902,80056,2192],{"encoding":904},", jestliže",[883,80059,80061],{"className":80060},[886],[888,80062,80063],{"xmlns":890,"display":28759},[892,80064,80065,80122],{},[21447,80066,80067],{"width":28764},[21452,80068,80069,80071,80115,80117],{},[21455,80070],{"width":28769},[21455,80072,80073],{},[895,80074,80075,80077,80079,80081,80083,80085,80087,80089,80091,80093,80099,80101,80103,80105,80107,80109,80111,80113],{},[898,80076,1904],{},[1723,80078,1908],{"stretchy":1907},[898,80080,12742],{},[898,80082,1911],{},[1723,80084,2031],{"separator":2030},[898,80086,12742],{},[898,80088,2034],{},[1723,80090,1914],{"stretchy":1907},[1723,80092,1725],{},[2057,80094,80095,80097],{},[898,80096,12742],{},[898,80098,2192],{},[3018,80100,3707],{},[898,80102,1904],{},[1723,80104,1908],{"stretchy":1907},[898,80106,1911],{},[1723,80108,2031],{"separator":2030},[898,80110,2034],{},[1723,80112,1914],{"stretchy":1907},[1723,80114,2031],{"separator":2030},[21455,80116],{"width":28769},[21455,80118,80119],{},[3018,80120,80121],{},"(5.10)",[902,80123,80124],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,80126,5022,80127,80145,80146,80164,80165,44328,80178,80181,80182,1664],{},[883,80128,80130],{"className":80129},[886],[888,80131,80132],{"xmlns":890},[892,80133,80134,80142],{},[895,80135,80136,80138,80140],{},[898,80137,2192],{},[1723,80139,5197],{},[1864,80141,2256],{},[902,80143,80144],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,80147,80149],{"className":80148},[886],[888,80150,80151],{"xmlns":890},[892,80152,80153,80161],{},[895,80154,80155,80157,80159],{},[898,80156,12742],{},[1723,80158,2253],{},[1864,80160,2256],{},[902,80162,80163],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,80166,80168],{"className":80167},[886],[888,80169,80170],{"xmlns":890},[892,80171,80172,80176],{},[895,80173,80174],{},[1864,80175,1866],{},[902,80177,1866],{"encoding":904},[38,80179,80180],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,80183,80185],{"className":80184},[886],[888,80186,80187],{"xmlns":890},[892,80188,80189,80197],{},[895,80190,80191,80193,80195],{},[898,80192,207],{},[1723,80194,2087],{},[898,80196,2069],{},[902,80198,75505],{"encoding":904},[115,80200,80202],{"id":80201},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,80204,80205],{},[38,80206,80207],{},"Ryzí Cobb-Douglasovy funkce:",[883,80209,80211],{"className":80210},[886],[888,80212,80213],{"xmlns":890,"display":28759},[892,80214,80215,80274],{},[21447,80216,80217],{"width":28764},[21452,80218,80219,80221,80267,80269],{},[21455,80220],{"width":28769},[21455,80222,80223],{},[895,80224,80225,80227,80229,80231,80233,80239,80241,80253,80255,80257,80259,80261,80263,80265],{},[898,80226,1904],{},[1723,80228,1725],{},[898,80230,1718],{},[3018,80232,3707],{},[2057,80234,80235,80237],{},[898,80236,1911],{},[898,80238,207],{},[3018,80240,3707],{},[2057,80242,80243,80245],{},[898,80244,2034],{},[895,80246,80247,80249,80251],{},[1864,80248,1866],{},[1723,80250,1759],{},[898,80252,207],{},[1723,80254,2031],{"separator":2030},[6588,80256],{"width":15985},[1864,80258,2256],{},[1723,80260,2287],{},[898,80262,207],{},[1723,80264,2287],{},[1864,80266,13961],{},[21455,80268],{"width":28769},[21455,80270,80271],{},[3018,80272,80273],{},"(5.9)",[902,80275,80276],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,80278,80279,80280,80282,80283,1664],{},"Mají vždy ",[38,80281,79600],{}," a jsou ",[38,80284,80180],{},[724,80286,80287,1981,80290,80293],{},[38,80288,80289],{},"CES produkční funkce",[614,80291,80292],{},"Constant Elasticity of Substitution",", 1961):",[883,80295,80297],{"className":80296},[886],[888,80298,80299],{"xmlns":890,"display":28759},[892,80300,80301,80369],{},[895,80302,80303,80305,80307,80309,80367],{},[898,80304,1904],{},[1723,80306,1725],{},[898,80308,1718],{},[2057,80310,80311,80355],{},[895,80312,80313,80315,80317,80319,80321,80323,80325,80327,80337,80339,80341,80343,80353],{},[1723,80314,3212],{"fence":2030},[1723,80316,1908],{"stretchy":1907},[1864,80318,1866],{},[1723,80320,1759],{},[898,80322,207],{},[1723,80324,1914],{"stretchy":1907},[3018,80326,3707],{},[2057,80328,80329,80331],{},[898,80330,1911],{},[895,80332,80333,80335],{},[1723,80334,1759],{},[898,80336,2069],{},[1723,80338,2087],{},[898,80340,207],{},[3018,80342,3707],{},[2057,80344,80345,80347],{},[898,80346,2034],{},[895,80348,80349,80351],{},[1723,80350,1759],{},[898,80352,2069],{},[1723,80354,3227],{"fence":2030},[895,80356,80357,80359],{},[1723,80358,1759],{},[3055,80360,80361],{"scriptlevel":2256,"displaystyle":1907},[3058,80362,80363,80365],{},[1864,80364,1866],{},[898,80366,2069],{},[1723,80368,2031],{"separator":2030},[902,80370,80371],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,80373,5022,80374,1343,80392,1343,80413,80437],{},[883,80375,80377],{"className":80376},[886],[888,80378,80379],{"xmlns":890},[892,80380,80381,80389],{},[895,80382,80383,80385,80387],{},[898,80384,1718],{},[1723,80386,2253],{},[1864,80388,2256],{},[902,80390,80391],{"encoding":904},"A > 0",[883,80393,80395],{"className":80394},[886],[888,80396,80397],{"xmlns":890},[892,80398,80399,80411],{},[895,80400,80401,80403,80405,80407,80409],{},[1864,80402,2256],{},[1723,80404,2287],{},[898,80406,207],{},[1723,80408,2287],{},[1864,80410,1866],{},[902,80412,19530],{"encoding":904},[883,80414,80416],{"className":80415},[886],[888,80417,80418],{"xmlns":890},[892,80419,80420,80434],{},[895,80421,80422,80424,80426,80428,80430,80432],{},[1723,80423,1759],{},[1864,80425,1866],{},[1723,80427,2287],{},[898,80429,2069],{},[1723,80431,4091],{"mathvariant":2124},[1864,80433,2256],{},[902,80435,80436],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,80439,80440],{},[38,80441,80442],{},"Další typy:",[120,80444,80445,80487],{},[123,80446,80447,2628,80450,80486],{},[38,80448,80449],{},"Lineární:",[883,80451,80453],{"className":80452},[886],[888,80454,80455],{"xmlns":890},[892,80456,80457,80483],{},[895,80458,80459,80461,80463,80465,80467,80469,80471,80473,80475,80477,80479,80481],{},[898,80460,1904],{},[1723,80462,1908],{"stretchy":1907},[898,80464,1911],{},[1723,80466,2031],{"separator":2030},[898,80468,2034],{},[1723,80470,1914],{"stretchy":1907},[1723,80472,1725],{},[898,80474,207],{},[898,80476,1911],{},[1723,80478,2087],{},[898,80480,2069],{},[898,80482,2034],{},[902,80484,80485],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,80488,80489,2628,80492,80537],{},[38,80490,80491],{},"Leontiefova:",[883,80493,80495],{"className":80494},[886],[888,80496,80497],{"xmlns":890},[892,80498,80499,80534],{},[895,80500,80501,80503,80505,80507,80509,80511,80513,80515,80518,80520,80522,80524,80526,80528,80530,80532],{},[898,80502,1904],{},[1723,80504,1908],{"stretchy":1907},[898,80506,1911],{},[1723,80508,2031],{"separator":2030},[898,80510,2034],{},[1723,80512,1914],{"stretchy":1907},[1723,80514,1725],{},[898,80516,80517],{},"min",[1723,80519,56887],{},[1723,80521,1908],{"stretchy":1907},[898,80523,207],{},[898,80525,1911],{},[1723,80527,2031],{"separator":2030},[898,80529,2069],{},[898,80531,2034],{},[1723,80533,1914],{"stretchy":1907},[902,80535,80536],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,80539,80541,80542,1343,80561,80580],{"id":80540},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,80543,80545],{"className":80544},[886],[888,80546,80547],{"xmlns":890},[892,80548,80549,80559],{},[895,80550,80551,80553],{},[898,80552,1728],{},[1931,80554,80555,80557],{},[898,80556,1746],{},[898,80558,1911],{},[902,80560,1939],{"encoding":904},[883,80562,80564],{"className":80563},[886],[888,80565,80566],{"xmlns":890},[892,80567,80568,80578],{},[895,80569,80570,80572],{},[898,80571,1728],{},[1931,80573,80574,80576],{},[898,80575,1746],{},[898,80577,2034],{},[902,80579,10790],{"encoding":904}," a totální diferenciál",[724,80582,80583],{},[38,80584,80585],{},"Mezní produkt práce:",[883,80587,80589],{"className":80588},[886],[888,80590,80591],{"xmlns":890,"display":28759},[892,80592,80593,80631],{},[895,80594,80595,80597,80603,80605,80613,80615,80629],{},[898,80596,1728],{},[1931,80598,80599,80601],{},[898,80600,1746],{},[898,80602,1911],{},[1723,80604,1725],{},[2220,80606,80607,80609,80611],{},[898,80608,1904],{},[898,80610,1911],{},[1723,80612,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,80614,1725],{},[3058,80616,80617,80623],{},[895,80618,80619,80621],{},[898,80620,10574],{"mathvariant":2124},[898,80622,1904],{},[895,80624,80625,80627],{},[898,80626,10574],{"mathvariant":2124},[898,80628,1911],{},[898,80630,1664],{"mathvariant":2124},[902,80632,80633],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,80635,80636],{},[38,80637,80638],{},"Mezní produkt kapitálu:",[883,80640,80642],{"className":80641},[886],[888,80643,80644],{"xmlns":890,"display":28759},[892,80645,80646,80684],{},[895,80647,80648,80650,80656,80658,80666,80668,80682],{},[898,80649,1728],{},[1931,80651,80652,80654],{},[898,80653,1746],{},[898,80655,2034],{},[1723,80657,1725],{},[2220,80659,80660,80662,80664],{},[898,80661,1904],{},[898,80663,2034],{},[1723,80665,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,80667,1725],{},[3058,80669,80670,80676],{},[895,80671,80672,80674],{},[898,80673,10574],{"mathvariant":2124},[898,80675,1904],{},[895,80677,80678,80680],{},[898,80679,10574],{"mathvariant":2124},[898,80681,2034],{},[898,80683,1664],{"mathvariant":2124},[902,80685,80686],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,80688,80689,80719,80720,80741,80742,80760,80761,80774,80775,1664],{},[883,80690,80692],{"className":80691},[886],[888,80693,80694],{"xmlns":890},[892,80695,80696,80716],{},[895,80697,80698,80700,80706,80708,80710,80712,80714],{},[898,80699,1728],{},[1931,80701,80702,80704],{},[898,80703,1746],{},[898,80705,1911],{},[1723,80707,1908],{"stretchy":1907},[898,80709,207],{},[1723,80711,2031],{"separator":2030},[898,80713,2069],{},[1723,80715,1914],{"stretchy":1907},[902,80717,80718],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,80721,80723],{"className":80722},[886],[888,80724,80725],{"xmlns":890},[892,80726,80727,80739],{},[895,80728,80729,80731,80733,80735,80737],{},[1723,80730,3212],{"stretchy":1907},[898,80732,207],{},[1723,80734,2031],{"separator":2030},[898,80736,2069],{},[1723,80738,3227],{"stretchy":1907},[902,80740,11524],{"encoding":904}," (na hladině ",[883,80743,80745],{"className":80744},[886],[888,80746,80747],{"xmlns":890},[892,80748,80749,80757],{},[895,80750,80751,80753,80755],{},[898,80752,2034],{},[1723,80754,1725],{},[898,80756,2069],{},[902,80758,80759],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,80762,80764],{"className":80763},[886],[888,80765,80766],{"xmlns":890},[892,80767,80768,80772],{},[895,80769,80770],{},[898,80771,1911],{},[902,80773,1911],{"encoding":904},". Analogicky ",[883,80776,80778],{"className":80777},[886],[888,80779,80780],{"xmlns":890},[892,80781,80782,80802],{},[895,80783,80784,80786,80792,80794,80796,80798,80800],{},[898,80785,1728],{},[1931,80787,80788,80790],{},[898,80789,1746],{},[898,80791,2034],{},[1723,80793,1908],{"stretchy":1907},[898,80795,207],{},[1723,80797,2031],{"separator":2030},[898,80799,2069],{},[1723,80801,1914],{"stretchy":1907},[902,80803,80804],{"encoding":904},"MP_K(a, b)",[4584,80806,80807,80811],{},[724,80808,80809,51909],{},[883,80810,4869],{},[120,80812,80813,80851],{},[123,80814,80815,26882,80834],{},[883,80816,80818],{"className":80817},[886],[888,80819,80820],{"xmlns":890},[892,80821,80822,80832],{},[895,80823,80824,80826],{},[898,80825,1728],{},[1931,80827,80828,80830],{},[898,80829,1746],{},[898,80831,1911],{},[902,80833,1939],{"encoding":904},[614,80835,80836,80837,80850],{},"„o kolik vzroste ",[883,80838,80840],{"className":80839},[886],[888,80841,80842],{"xmlns":890},[892,80843,80844,80848],{},[895,80845,80846],{},[898,80847,1904],{},[902,80849,1904],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,80852,80853,26882,80872],{},[883,80854,80856],{"className":80855},[886],[888,80857,80858],{"xmlns":890},[892,80859,80860,80870],{},[895,80861,80862,80864],{},[898,80863,1728],{},[1931,80865,80866,80868],{},[898,80867,1746],{},[898,80869,2034],{},[902,80871,10790],{"encoding":904},[614,80873,80836,80874,80887],{},[883,80875,80877],{"className":80876},[886],[888,80878,80879],{"xmlns":890},[892,80880,80881,80885],{},[895,80882,80883],{},[898,80884,1904],{},[902,80886,1904],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,80889,80890,80893,80894,80909,80910,3430],{},[38,80891,80892],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,80895,80897],{"className":80896},[886],[888,80898,80899],{"xmlns":890},[892,80900,80901,80907],{},[895,80902,80903,80905],{},[898,80904,2930],{},[898,80906,1911],{},[902,80908,76037],{"encoding":904}," a kapitálu o ",[883,80911,80913],{"className":80912},[886],[888,80914,80915],{"xmlns":890},[892,80916,80917,80923],{},[895,80918,80919,80921],{},[898,80920,2930],{},[898,80922,2034],{},[902,80924,80925],{"encoding":904},"dK",[883,80927,80929],{"className":80928},[886],[888,80930,80931],{"xmlns":890,"display":28759},[892,80932,80933,81026],{},[21447,80934,80935],{"width":28764},[21452,80936,80937,80939,81019,81021],{},[21455,80938],{"width":28769},[21455,80940,80941],{},[895,80942,80943,80945,80947,80949,80951,80953,80955,80963,80965,80967,80969,80971,80979,80981,80983,80985,80987,80989,80995,80997,80999,81001,81003,81005,81011,81013,81015,81017],{},[898,80944,3611],{"mathvariant":2124},[898,80946,1904],{},[1723,80948,3456],{},[898,80950,2930],{},[898,80952,1904],{},[1723,80954,1725],{},[2220,80956,80957,80959,80961],{},[898,80958,1904],{},[898,80960,1911],{},[1723,80962,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[3018,80964,3707],{},[898,80966,2930],{},[898,80968,1911],{},[1723,80970,2087],{},[2220,80972,80973,80975,80977],{},[898,80974,1904],{},[898,80976,2034],{},[1723,80978,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[3018,80980,3707],{},[898,80982,2930],{},[898,80984,2034],{},[1723,80986,1725],{},[898,80988,1728],{},[1931,80990,80991,80993],{},[898,80992,1746],{},[898,80994,1911],{},[3018,80996,3707],{},[898,80998,2930],{},[898,81000,1911],{},[1723,81002,2087],{},[898,81004,1728],{},[1931,81006,81007,81009],{},[898,81008,1746],{},[898,81010,2034],{},[3018,81012,3707],{},[898,81014,2930],{},[898,81016,2034],{},[898,81018,1664],{"mathvariant":2124},[21455,81020],{"width":28769},[21455,81022,81023],{},[3018,81024,81025],{},"(5.11)",[902,81027,81028],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,81030,81031,81032,1664],{},"Skutečná změna: ",[883,81033,81035],{"className":81034},[886],[888,81036,81037],{"xmlns":890},[892,81038,81039,81085],{},[895,81040,81041,81043,81045,81047,81049,81051,81053,81055,81057,81059,81061,81063,81065,81067,81069,81071,81073,81075,81077,81079,81081,81083],{},[898,81042,3611],{"mathvariant":2124},[898,81044,1904],{},[1723,81046,1725],{},[898,81048,1904],{},[1723,81050,1908],{"stretchy":1907},[898,81052,1911],{},[1723,81054,2087],{},[898,81056,2930],{},[898,81058,1911],{},[1723,81060,2031],{"separator":2030},[898,81062,2034],{},[1723,81064,2087],{},[898,81066,2930],{},[898,81068,2034],{},[1723,81070,1914],{"stretchy":1907},[1723,81072,1759],{},[898,81074,1904],{},[1723,81076,1908],{"stretchy":1907},[898,81078,1911],{},[1723,81080,2031],{"separator":2030},[898,81082,2034],{},[1723,81084,1914],{"stretchy":1907},[902,81086,81087],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,81089,81090,81092,81093,81111,81112,81125,81126,81145,81146,81178,81179,81211,81212,1664],{},[38,81091,76201],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,81094,81096],{"className":81095},[886],[888,81097,81098],{"xmlns":890},[892,81099,81100,81108],{},[895,81101,81102],{},[1931,81103,81104,81106],{},[898,81105,2034],{},[1864,81107,2256],{},[902,81109,81110],{"encoding":904},"K_0"," se od jistého ",[883,81113,81115],{"className":81114},[886],[888,81116,81117],{"xmlns":890},[892,81118,81119,81123],{},[895,81120,81121],{},[898,81122,1911],{},[902,81124,1911],{"encoding":904}," stane ",[883,81127,81129],{"className":81128},[886],[888,81130,81131],{"xmlns":890},[892,81132,81133,81143],{},[895,81134,81135,81137],{},[898,81136,1728],{},[1931,81138,81139,81141],{},[898,81140,1746],{},[898,81142,1911],{},[902,81144,1939],{"encoding":904}," klesající (",[883,81147,81149],{"className":81148},[886],[888,81150,81151],{"xmlns":890},[892,81152,81153,81175],{},[895,81154,81155,81171,81173],{},[2220,81156,81157,81159,81165],{},[898,81158,1904],{},[895,81160,81161,81163],{},[898,81162,1911],{},[898,81164,1911],{},[895,81166,81167,81169],{},[1723,81168,2229],{"mathvariant":2124},[1723,81170,2229],{"mathvariant":2124},[1723,81172,2287],{},[1864,81174,2256],{},[902,81176,81177],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,81180,81182],{"className":81181},[886],[888,81183,81184],{"xmlns":890},[892,81185,81186,81208],{},[895,81187,81188,81204,81206],{},[2220,81189,81190,81192,81198],{},[898,81191,1904],{},[895,81193,81194,81196],{},[898,81195,2034],{},[898,81197,2034],{},[895,81199,81200,81202],{},[1723,81201,2229],{"mathvariant":2124},[1723,81203,2229],{"mathvariant":2124},[1723,81205,2287],{},[1864,81207,2256],{},[902,81209,81210],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,81213,81215],{"className":81214},[886],[888,81216,81217],{"xmlns":890},[892,81218,81219,81227],{},[895,81220,81221],{},[1931,81222,81223,81225],{},[898,81224,1911],{},[1864,81226,2256],{},[902,81228,76239],{"encoding":904},[115,81230,81232],{"id":81231},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,81234,81235,81238,81239,81262,81263,30637],{},[38,81236,81237],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,81240,81242],{"className":81241},[886],[888,81243,81244],{"xmlns":890},[892,81245,81246,81260],{},[895,81247,81248,81250,81252,81254,81256,81258],{},[898,81249,1904],{},[1723,81251,1908],{"stretchy":1907},[898,81253,1911],{},[1723,81255,2031],{"separator":2030},[898,81257,2034],{},[1723,81259,1914],{"stretchy":1907},[902,81261,10699],{"encoding":904}," stupně ",[883,81264,81266],{"className":81265},[886],[888,81267,81268],{"xmlns":890},[892,81269,81270,81274],{},[895,81271,81272],{},[898,81273,2192],{},[902,81275,2192],{"encoding":904},[883,81277,81279],{"className":81278},[886],[888,81280,81281],{"xmlns":890,"display":28759},[892,81282,81283,81346],{},[21447,81284,81285],{"width":28764},[21452,81286,81287,81289,81339,81341],{},[21455,81288],{"width":28769},[21455,81290,81291],{},[895,81292,81293,81295,81297,81305,81307,81309,81311,81319,81321,81323,81325,81327,81329,81331,81333,81335,81337],{},[898,81294,1911],{},[3018,81296,3707],{},[2220,81298,81299,81301,81303],{},[898,81300,1904],{},[898,81302,1911],{},[1723,81304,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,81306,2087],{},[898,81308,2034],{},[3018,81310,3707],{},[2220,81312,81313,81315,81317],{},[898,81314,1904],{},[898,81316,2034],{},[1723,81318,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,81320,1725],{},[898,81322,2192],{},[3018,81324,3707],{},[898,81326,1904],{},[1723,81328,1908],{"stretchy":1907},[898,81330,1911],{},[1723,81332,2031],{"separator":2030},[898,81334,2034],{},[1723,81336,1914],{"stretchy":1907},[898,81338,1664],{"mathvariant":2124},[21455,81340],{"width":28769},[21455,81342,81343],{},[3018,81344,81345],{},"(5.12)",[902,81347,81348],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,81350,81351,81372],{},[38,81352,81353,81354],{},"Speciální případ ",[883,81355,81357],{"className":81356},[886],[888,81358,81359],{"xmlns":890},[892,81360,81361,81369],{},[895,81362,81363,81365,81367],{},[898,81364,2192],{},[1723,81366,1725],{},[1864,81368,1866],{},[902,81370,81371],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,81374,81376],{"className":81375},[886],[888,81377,81378],{"xmlns":890,"display":28759},[892,81379,81380,81424],{},[895,81381,81382,81384,81386,81388,81394,81396,81398,81400,81402,81408,81410,81412,81414,81416,81418,81420,81422],{},[898,81383,1911],{},[1723,81385,3897],{},[898,81387,1728],{},[1931,81389,81390,81392],{},[898,81391,1746],{},[898,81393,1911],{},[1723,81395,2087],{},[898,81397,2034],{},[1723,81399,3897],{},[898,81401,1728],{},[1931,81403,81404,81406],{},[898,81405,1746],{},[898,81407,2034],{},[1723,81409,1725],{},[898,81411,1904],{},[1723,81413,1908],{"stretchy":1907},[898,81415,1911],{},[1723,81417,2031],{"separator":2030},[898,81419,2034],{},[1723,81421,1914],{"stretchy":1907},[898,81423,1664],{"mathvariant":2124},[902,81425,81426],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,81428,81429,81430,81433],{},"Slovně — ",[38,81431,81432],{},"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).",[115,81435,10483],{"id":75575},[724,81437,81438,1981,81440,81443,81444,81466,81467,3430],{},[38,81439,10483],{},[614,81441,81442],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,81445,81447],{"className":81446},[886],[888,81448,81449],{"xmlns":890},[892,81450,81451,81463],{},[895,81452,81453,81455,81457,81459,81461],{},[1723,81454,3212],{"stretchy":1907},[898,81456,1911],{},[1723,81458,2031],{"separator":2030},[898,81460,2034],{},[1723,81462,3227],{"stretchy":1907},[902,81464,81465],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,81468,81470],{"className":81469},[886],[888,81471,81472],{"xmlns":890},[892,81473,81474,81479],{},[895,81475,81476],{},[898,81477,81478],{},"q",[902,81480,81478],{"encoding":904},[883,81482,81484],{"className":81483},[886],[888,81485,81486],{"xmlns":890,"display":28759},[892,81487,81488,81523],{},[21447,81489,81490],{"width":28764},[21452,81491,81492,81494,81516,81518],{},[21455,81493],{"width":28769},[21455,81495,81496],{},[895,81497,81498,81500,81502,81504,81506,81508,81510,81512,81514],{},[898,81499,1904],{},[1723,81501,1908],{"stretchy":1907},[898,81503,1911],{},[1723,81505,2031],{"separator":2030},[898,81507,2034],{},[1723,81509,1914],{"stretchy":1907},[1723,81511,1725],{},[898,81513,81478],{},[898,81515,1664],{"mathvariant":2124},[21455,81517],{"width":28769},[21455,81519,81520],{},[3018,81521,81522],{},"(5.13)",[902,81524,81525],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,81527,81528,81529,81532,81533,4634],{},"Jsou to ",[38,81530,81531],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,81534,81536],{"className":81535,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,81538,81539],{},[38,81540,81541],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,81543,81544,81549,81554,81559],{},[123,81545,81546,81548],{},[38,81547,13220],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,81550,81551,81553],{},[38,81552,38356],{}," (úloha 5.14);",[123,81555,81556,9135],{},[38,81557,81558],{},"neprotínají se",[123,81560,81561,81562,5070,81575,1664],{},"s rostoucím ",[883,81563,81565],{"className":81564},[886],[888,81566,81567],{"xmlns":890},[892,81568,81569,81573],{},[895,81570,81571],{},[898,81572,81478],{},[902,81574,81478],{"encoding":904},[38,81576,81577],{},"vzdalují od počátku",[724,81579,81580],{},[614,81581,81582,81583,81605,81606,1664],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,81584,81586],{"className":81585},[886],[888,81587,81588],{"xmlns":890},[892,81589,81590,81602],{},[895,81591,81592,81594,81596,81598,81600],{},[1723,81593,1908],{"stretchy":1907},[898,81595,1911],{},[1723,81597,2031],{"separator":2030},[898,81599,2034],{},[1723,81601,1914],{"stretchy":1907},[902,81603,81604],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,81607,81609],{"className":81608},[886],[888,81610,81611],{"xmlns":890},[892,81612,81613,81637],{},[895,81614,81615,81621,81623,81629,81631],{},[1931,81616,81617,81619],{},[898,81618,81478],{},[1864,81620,1866],{},[1723,81622,2287],{},[1931,81624,81625,81627],{},[898,81626,81478],{},[1864,81628,2256],{},[1723,81630,2287],{},[1931,81632,81633,81635],{},[898,81634,81478],{},[1864,81636,2331],{},[902,81638,81639],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,81641,81643,81644,1914],{"id":81642},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,81645,81647],{"className":81646},[886],[888,81648,81649],{"xmlns":890},[892,81650,81651,81661],{},[895,81652,81653,81655,81657,81659],{},[898,81654,1728],{},[898,81656,1749],{},[898,81658,1754],{},[898,81660,2111],{},[902,81662,11299],{"encoding":904},[724,81664,81665,1981,81668,81671],{},[38,81666,81667],{},"Mezní míra technické substituce",[614,81669,81670],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,81673,81675],{"className":81674},[886],[888,81676,81677],{"xmlns":890,"display":28759},[892,81678,81679,81770],{},[21447,81680,81681],{"width":28764},[21452,81682,81683,81685,81763,81765],{},[21455,81684],{"width":28769},[21455,81686,81687],{},[895,81688,81689,81691,81693,81695,81697,81699,81701,81703,81705,81707,81709,81711,81713,81715,81717,81719,81741,81743,81761],{},[898,81690,1728],{},[898,81692,1749],{},[898,81694,1754],{},[898,81696,2111],{},[1723,81698,1725],{},[898,81700,1728],{},[898,81702,1749],{},[898,81704,1754],{},[898,81706,2111],{},[1723,81708,1908],{"stretchy":1907},[898,81710,1911],{},[1723,81712,2031],{"separator":2030},[898,81714,2034],{},[1723,81716,1914],{"stretchy":1907},[1723,81718,1725],{},[3058,81720,81721,81731],{},[895,81722,81723,81725],{},[898,81724,1728],{},[1931,81726,81727,81729],{},[898,81728,1746],{},[898,81730,1911],{},[895,81732,81733,81735],{},[898,81734,1728],{},[1931,81736,81737,81739],{},[898,81738,1746],{},[898,81740,2034],{},[1723,81742,1725],{},[3058,81744,81745,81753],{},[2220,81746,81747,81749,81751],{},[898,81748,1904],{},[898,81750,1911],{},[1723,81752,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[2220,81754,81755,81757,81759],{},[898,81756,1904],{},[898,81758,2034],{},[1723,81760,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[898,81762,1664],{"mathvariant":2124},[21455,81764],{"width":28769},[21455,81766,81767],{},[3018,81768,81769],{},"(5.14)",[902,81771,81772],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,81774,81775,2628,81777,81807,81808,81839],{},[38,81776,9924],{},[883,81778,81780],{"className":81779},[886],[888,81781,81782],{"xmlns":890},[892,81783,81784,81804],{},[895,81785,81786,81788,81790,81792,81794,81796,81798,81800,81802],{},[898,81787,1728],{},[898,81789,1749],{},[898,81791,1754],{},[898,81793,2111],{},[1723,81795,1908],{"stretchy":1907},[898,81797,1911],{},[1723,81799,2031],{"separator":2030},[898,81801,2034],{},[1723,81803,1914],{"stretchy":1907},[902,81805,81806],{"encoding":904},"MRTS(L, K)"," udává, ",[38,81809,81810,81811,81824,81825,81838],{},"o kolik se musí přibližně změnit kapitál ",[883,81812,81814],{"className":81813},[886],[888,81815,81816],{"xmlns":890},[892,81817,81818,81822],{},[895,81819,81820],{},[898,81821,2034],{},[902,81823,2034],{"encoding":904},", jestliže se práce ",[883,81826,81828],{"className":81827},[886],[888,81829,81830],{"xmlns":890},[892,81831,81832,81836],{},[895,81833,81834],{},[898,81835,1911],{},[902,81837,1911],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[4584,81841,81842],{},[724,81843,81844,18718,81846,81865,81866,81903,81904,81907,81908,81912],{},[883,81845,4869],{},[883,81847,81849],{"className":81848},[886],[888,81850,81851],{"xmlns":890},[892,81852,81853,81863],{},[895,81854,81855,81857,81859,81861],{},[898,81856,1728],{},[898,81858,1749],{},[898,81860,1754],{},[898,81862,2111],{},[902,81864,11299],{"encoding":904}," říká: ",[614,81867,81868,81869,81888,81889,81902],{},"„jednu jednotku práce musím nahradit přibližně ",[883,81870,81872],{"className":81871},[886],[888,81873,81874],{"xmlns":890},[892,81875,81876,81886],{},[895,81877,81878,81880,81882,81884],{},[898,81879,1728],{},[898,81881,1749],{},[898,81883,1754],{},[898,81885,2111],{},[902,81887,11299],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,81890,81892],{"className":81891},[886],[888,81893,81894],{"xmlns":890},[892,81895,81896,81900],{},[895,81897,81898],{},[898,81899,1904],{},[902,81901,1904],{"encoding":904}," zůstala stejná.\""," Je to ",[38,81905,81906],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,81909,81911],{"className":81910,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,81914,81915],{},[3285,81916],{"alt":81917,"className":81918,"src":81919},"imek-izokvanty-mrts",[210,3289],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,81921,81922,81925,81926,8812,81956,81978,81979,3871],{},[38,81923,81924],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,81927,81929],{"className":81928},[886],[888,81930,81931],{"xmlns":890},[892,81932,81933,81953],{},[895,81934,81935,81937,81943,81945,81951],{},[1723,81936,3212],{"stretchy":1907},[1931,81938,81939,81941],{},[898,81940,1911],{},[1864,81942,2256],{},[1723,81944,2031],{"separator":2030},[1931,81946,81947,81949],{},[898,81948,2034],{},[1864,81950,2256],{},[1723,81952,3227],{"stretchy":1907},[902,81954,81955],{"encoding":904},"[L_0, K_0]",[883,81957,81959],{"className":81958},[886],[888,81960,81961],{"xmlns":890},[892,81962,81963,81975],{},[895,81964,81965,81967,81969,81971,81973],{},[1723,81966,1759],{},[898,81968,1728],{},[898,81970,1749],{},[898,81972,1754],{},[898,81974,2111],{},[902,81976,81977],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,81980,81982],{"className":81981},[886],[888,81983,81984],{"xmlns":890},[892,81985,81986,82008],{},[895,81987,81988,81990,81992,81994,81996,81998,82000,82002],{},[898,81989,1904],{},[1723,81991,1908],{"stretchy":1907},[898,81993,1911],{},[1723,81995,2031],{"separator":2030},[898,81997,2034],{},[1723,81999,1914],{"stretchy":1907},[1723,82001,1725],{},[1931,82003,82004,82006],{},[898,82005,81478],{},[1864,82007,2256],{},[902,82009,82010],{"encoding":904},"Q(L,K) = q_0",[883,82012,82014],{"className":82013},[886],[888,82015,82016],{"xmlns":890,"display":28759},[892,82017,82018,82070],{},[895,82019,82020,82034,82036,82038,82056,82058,82060,82062,82064,82066,82068],{},[3058,82021,82022,82028],{},[895,82023,82024,82026],{},[898,82025,2930],{},[898,82027,2034],{},[895,82029,82030,82032],{},[898,82031,2930],{},[898,82033,1911],{},[1723,82035,1725],{},[1723,82037,1759],{},[3058,82039,82040,82048],{},[2220,82041,82042,82044,82046],{},[898,82043,1904],{},[898,82045,1911],{},[1723,82047,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[2220,82049,82050,82052,82054],{},[898,82051,1904],{},[898,82053,2034],{},[1723,82055,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,82057,1725],{},[1723,82059,1759],{},[898,82061,1728],{},[898,82063,1749],{},[898,82065,1754],{},[898,82067,2111],{},[898,82069,1664],{"mathvariant":2124},[902,82071,82072],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,82074,82075,82076,82091,82092,82108],{},"Změní-li se práce o ",[883,82077,82079],{"className":82078},[886],[888,82080,82081],{"xmlns":890},[892,82082,82083,82089],{},[895,82084,82085,82087],{},[898,82086,2930],{},[898,82088,1911],{},[902,82090,76037],{"encoding":904},", lze pro odhad změny kapitálu ",[883,82093,82095],{"className":82094},[886],[888,82096,82097],{"xmlns":890},[892,82098,82099,82105],{},[895,82100,82101,82103],{},[898,82102,3611],{"mathvariant":2124},[898,82104,2034],{},[902,82106,82107],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,82110,82112],{"className":82111},[886],[888,82113,82114],{"xmlns":890,"display":28759},[892,82115,82116,82163],{},[21447,82117,82118],{"width":28764},[21452,82119,82120,82122,82156,82158],{},[21455,82121],{"width":28769},[21455,82123,82124],{},[895,82125,82126,82128,82130,82132,82134,82136,82138,82140,82142,82144,82146,82148,82150,82152,82154],{},[898,82127,3611],{"mathvariant":2124},[898,82129,2034],{},[1723,82131,3456],{},[898,82133,2930],{},[898,82135,2034],{},[1723,82137,1725],{},[1723,82139,1759],{},[898,82141,1728],{},[898,82143,1749],{},[898,82145,1754],{},[898,82147,2111],{},[3018,82149,3707],{},[898,82151,2930],{},[898,82153,1911],{},[1723,82155,2031],{"separator":2030},[21455,82157],{"width":28769},[21455,82159,82160],{},[3018,82161,82162],{},"(5.15)",[902,82164,82165],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,82167,82169],{"className":82168},[886],[888,82170,82171],{"xmlns":890,"display":28759},[892,82172,82173,82222],{},[21447,82174,82175],{"width":28764},[21452,82176,82177,82179,82215,82217],{},[21455,82178],{"width":28769},[21455,82180,82181],{},[895,82182,82183,82185,82187,82189,82207,82209,82211,82213],{},[898,82184,2930],{},[898,82186,1911],{},[1723,82188,1725],{},[3058,82190,82191,82197],{},[895,82192,82193,82195],{},[1723,82194,1759],{},[1864,82196,1866],{},[895,82198,82199,82201,82203,82205],{},[898,82200,1728],{},[898,82202,1749],{},[898,82204,1754],{},[898,82206,2111],{},[3018,82208,3707],{},[898,82210,2930],{},[898,82212,2034],{},[898,82214,1664],{"mathvariant":2124},[21455,82216],{"width":28769},[21455,82218,82219],{},[3018,82220,82221],{},"(5.16)",[902,82223,82224],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[4584,82226,82227,82251],{},[724,82228,82229,82231,82232],{},[883,82230,5283],{}," Postup — jak spočítat ",[883,82233,82235],{"className":82234},[886],[888,82236,82237],{"xmlns":890},[892,82238,82239,82249],{},[895,82240,82241,82243,82245,82247],{},[898,82242,1728],{},[898,82244,1749],{},[898,82246,1754],{},[898,82248,2111],{},[902,82250,11299],{"encoding":904},[152,82252,82253,82294,82337,82369],{},[123,82254,82255,82256,1682,82275,1664],{},"Vypočtěte parciální derivace ",[883,82257,82259],{"className":82258},[886],[888,82260,82261],{"xmlns":890},[892,82262,82263,82273],{},[895,82264,82265],{},[2220,82266,82267,82269,82271],{},[898,82268,1904],{},[898,82270,1911],{},[1723,82272,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,82274,10723],{"encoding":904},[883,82276,82278],{"className":82277},[886],[888,82279,82280],{"xmlns":890},[892,82281,82282,82292],{},[895,82283,82284],{},[2220,82285,82286,82288,82290],{},[898,82287,1904],{},[898,82289,2034],{},[1723,82291,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,82293,10767],{"encoding":904},[123,82295,66528,82296,82336],{},[883,82297,82299],{"className":82298},[886],[888,82300,82301],{"xmlns":890},[892,82302,82303,82333],{},[895,82304,82305,82307,82309,82311,82313,82315,82323,82325],{},[898,82306,1728],{},[898,82308,1749],{},[898,82310,1754],{},[898,82312,2111],{},[1723,82314,1725],{},[2220,82316,82317,82319,82321],{},[898,82318,1904],{},[898,82320,1911],{},[1723,82322,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[898,82324,2125],{"mathvariant":2124},[2220,82326,82327,82329,82331],{},[898,82328,1904],{},[898,82330,2034],{},[1723,82332,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,82334,82335],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,82338,82339,82340,1664],{},"Případně dosaďte konkrétní ",[883,82341,82343],{"className":82342},[886],[888,82344,82345],{"xmlns":890},[892,82346,82347,82367],{},[895,82348,82349,82351,82357,82359,82365],{},[1723,82350,3212],{"stretchy":1907},[1931,82352,82353,82355],{},[898,82354,1911],{},[1864,82356,2256],{},[1723,82358,2031],{"separator":2030},[1931,82360,82361,82363],{},[898,82362,2034],{},[1864,82364,2256],{},[1723,82366,3227],{"stretchy":1907},[902,82368,81955],{"encoding":904},[123,82370,82371,82372,82406,82407,82409],{},"Pro odhad substituce použijte ",[883,82373,82375],{"className":82374},[886],[888,82376,82377],{"xmlns":890},[892,82378,82379,82403],{},[895,82380,82381,82383,82385,82387,82389,82391,82393,82395,82397,82399,82401],{},[898,82382,3611],{"mathvariant":2124},[898,82384,2034],{},[1723,82386,3456],{},[1723,82388,1759],{},[898,82390,1728],{},[898,82392,1749],{},[898,82394,1754],{},[898,82396,2111],{},[1723,82398,3897],{},[898,82400,3611],{"mathvariant":2124},[898,82402,1911],{},[902,82404,82405],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,82408,53296],{}," — substituce, ne doplnění).",[724,82411,82412],{},[614,82413,82414,82415,82447,82448,3350,82461,16493,82490,82505],{},"Obrázek 5.7 — izokvanta ",[883,82416,82418],{"className":82417},[886],[888,82419,82420],{"xmlns":890},[892,82421,82422,82444],{},[895,82423,82424,82430,82432,82434,82436,82438,82440,82442],{},[1931,82425,82426,82428],{},[898,82427,81478],{},[1864,82429,2256],{},[1723,82431,1725],{},[898,82433,1904],{},[1723,82435,1908],{"stretchy":1907},[898,82437,1911],{},[1723,82439,2031],{"separator":2030},[898,82441,2034],{},[1723,82443,1914],{"stretchy":1907},[902,82445,82446],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,82449,82451],{"className":82450},[886],[888,82452,82453],{"xmlns":890},[892,82454,82455,82459],{},[895,82456,82457],{},[898,82458,19549],{},[902,82460,19549],{"encoding":904},[883,82462,82464],{"className":82463},[886],[888,82465,82466],{"xmlns":890},[892,82467,82468,82488],{},[895,82469,82470,82472,82478,82480,82486],{},[1723,82471,3212],{"stretchy":1907},[1931,82473,82474,82476],{},[898,82475,1911],{},[1864,82477,2256],{},[1723,82479,2031],{"separator":2030},[1931,82481,82482,82484],{},[898,82483,2034],{},[1864,82485,2256],{},[1723,82487,3227],{"stretchy":1907},[902,82489,81955],{"encoding":904},[883,82491,82493],{"className":82492},[886],[888,82494,82495],{"xmlns":890},[892,82496,82497,82503],{},[895,82498,82499,82501],{},[898,82500,3611],{"mathvariant":2124},[898,82502,2034],{},[902,82504,82107],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,82507,82509],{"id":82508},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,82511,82513],{"id":82512},"příklad-54","Příklad 5.4",[724,82515,77354,82516,1343,82558,1343,82575,1664],{},[883,82517,82519],{"className":82518},[886],[888,82520,82521],{"xmlns":890},[892,82522,82523,82555],{},[895,82524,82525,82527,82529,82531,82543],{},[898,82526,1904],{},[1723,82528,1725],{},[1864,82530,36937],{},[2057,82532,82533,82535],{},[898,82534,1911],{},[895,82536,82537,82539,82541],{},[1864,82538,1866],{},[898,82540,2125],{"mathvariant":2124},[1864,82542,2331],{},[2057,82544,82545,82547],{},[898,82546,2034],{},[895,82548,82549,82551,82553],{},[1864,82550,1866],{},[898,82552,2125],{"mathvariant":2124},[1864,82554,2909],{},[902,82556,82557],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,82559,82561],{"className":82560},[886],[888,82562,82563],{"xmlns":890},[892,82564,82565,82573],{},[895,82566,82567,82569,82571],{},[898,82568,1911],{},[1723,82570,1725],{},[1864,82572,9744],{},[902,82574,77728],{"encoding":904},[883,82576,82578],{"className":82577},[886],[888,82579,82580],{"xmlns":890},[892,82581,82582,82590],{},[895,82583,82584,82586,82588],{},[898,82585,2034],{},[1723,82587,1725],{},[1864,82589,3810],{},[902,82591,82592],{"encoding":904},"K = 100",[724,82594,82595],{},[38,82596,82597],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,82599,82601],{"className":82600},[886],[888,82602,82603],{"xmlns":890,"display":28759},[892,82604,82605,82719],{},[895,82606,82607,82609,82615,82617,82625,82627,82635,82649,82661,82663,82665,82667,82673,82675,82677,82679,82681,82683,82685,82693,82695,82705,82707,82714,82716],{},[898,82608,1728],{},[1931,82610,82611,82613],{},[898,82612,1746],{},[898,82614,1911],{},[1723,82616,1725],{},[2220,82618,82619,82621,82623],{},[898,82620,1904],{},[898,82622,1911],{},[1723,82624,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,82626,1725],{},[3055,82628,82629],{"scriptlevel":2256,"displaystyle":1907},[3058,82630,82631,82633],{},[1864,82632,36937],{},[1864,82634,2331],{},[2057,82636,82637,82639],{},[898,82638,1911],{},[895,82640,82641,82643,82645,82647],{},[1723,82642,1759],{},[1864,82644,1866],{},[898,82646,2125],{"mathvariant":2124},[1864,82648,2331],{},[2057,82650,82651,82653],{},[898,82652,2034],{},[895,82654,82655,82657,82659],{},[1864,82656,1866],{},[898,82658,2125],{"mathvariant":2124},[1864,82660,2909],{},[1723,82662,2031],{"separator":2030},[6588,82664],{"width":15985},[898,82666,1728],{},[1931,82668,82669,82671],{},[898,82670,1746],{},[898,82672,1911],{},[1723,82674,1908],{"stretchy":1907},[1864,82676,9744],{},[1723,82678,2031],{"separator":2030},[1864,82680,3810],{},[1723,82682,1914],{"stretchy":1907},[1723,82684,1725],{},[3055,82686,82687],{"scriptlevel":2256,"displaystyle":1907},[3058,82688,82689,82691],{},[1864,82690,36937],{},[1864,82692,2331],{},[1723,82694,3897],{},[3055,82696,82697],{"scriptlevel":2256,"displaystyle":1907},[3058,82698,82699,82701],{},[1864,82700,1866],{},[8827,82702,82703],{},[1864,82704,9744],{},[1723,82706,3897],{},[82708,82709,82710,82712],"mroot",{},[1864,82711,3810],{},[1864,82713,2909],{},[1723,82715,3456],{},[1864,82717,82718],{},"7,153.",[902,82720,82721],{"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.",[724,82723,82724,82725,44852,82747,10933,82764,82785,82786,82807],{},"Přibližná změna při ",[883,82726,82728],{"className":82727},[886],[888,82729,82730],{"xmlns":890},[892,82731,82732,82744],{},[895,82733,82734,82736,82738,82740,82742],{},[898,82735,1911],{},[1723,82737,3430],{},[1864,82739,9744],{},[1723,82741,3843],{},[1864,82743,39038],{},[902,82745,82746],{"encoding":904},"L: 20 \\to 21",[883,82748,82750],{"className":82749},[886],[888,82751,82752],{"xmlns":890},[892,82753,82754,82762],{},[895,82755,82756,82758,82760],{},[898,82757,2034],{},[1723,82759,1725],{},[1864,82761,3810],{},[902,82763,82592],{"encoding":904},[883,82765,82767],{"className":82766},[886],[888,82768,82769],{"xmlns":890},[892,82770,82771,82782],{},[895,82772,82773,82775,82777,82779],{},[898,82774,3611],{"mathvariant":2124},[898,82776,1904],{},[1723,82778,3456],{},[1864,82780,82781],{},"7,153",[902,82783,82784],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,82787,82789],{"className":82788},[886],[888,82790,82791],{"xmlns":890},[892,82792,82793,82804],{},[895,82794,82795,82797,82799,82801],{},[898,82796,3611],{"mathvariant":2124},[898,82798,1904],{},[1723,82800,3456],{},[1864,82802,82803],{},"26,888",[902,82805,82806],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,82809,82810,82813],{},[38,82811,82812],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,82815,82817],{"className":82816},[886],[888,82818,82819],{"xmlns":890,"display":28759},[892,82820,82821,82921],{},[895,82822,82823,82825,82831,82833,82841,82843,82845,82857,82871,82873,82875,82877,82883,82885,82887,82889,82891,82893,82895,82897,82901,82903,82916,82918],{},[898,82824,1728],{},[1931,82826,82827,82829],{},[898,82828,1746],{},[898,82830,2034],{},[1723,82832,1725],{},[2220,82834,82835,82837,82839],{},[898,82836,1904],{},[898,82838,2034],{},[1723,82840,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,82842,1725],{},[1864,82844,2962],{},[2057,82846,82847,82849],{},[898,82848,1911],{},[895,82850,82851,82853,82855],{},[1864,82852,1866],{},[898,82854,2125],{"mathvariant":2124},[1864,82856,2331],{},[2057,82858,82859,82861],{},[898,82860,2034],{},[895,82862,82863,82865,82867,82869],{},[1723,82864,1759],{},[1864,82866,2331],{},[898,82868,2125],{"mathvariant":2124},[1864,82870,2909],{},[1723,82872,2031],{"separator":2030},[6588,82874],{"width":15985},[898,82876,1728],{},[1931,82878,82879,82881],{},[898,82880,1746],{},[898,82882,2034],{},[1723,82884,1908],{"stretchy":1907},[1864,82886,9744],{},[1723,82888,2031],{"separator":2030},[1864,82890,3810],{},[1723,82892,1914],{"stretchy":1907},[1723,82894,1725],{},[1864,82896,2962],{},[8827,82898,82899],{},[1864,82900,9744],{},[1723,82902,3897],{},[3055,82904,82905],{"scriptlevel":2256,"displaystyle":1907},[3058,82906,82907,82909],{},[1864,82908,1866],{},[82708,82910,82911,82914],{},[1864,82912,82913],{},"10000",[1864,82915,2909],{},[1723,82917,3456],{},[1864,82919,82920],{},"4,525.",[902,82922,82923],{"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.",[724,82925,82926,82927,3411,82944,4634],{},"Produkce poklesne přibližně o 4,525 (z ",[883,82928,82930],{"className":82929},[886],[888,82931,82932],{"xmlns":890},[892,82933,82934,82941],{},[895,82935,82936,82938],{},[1723,82937,3456],{},[1864,82939,82940],{},"905,126",[902,82942,82943],{"encoding":904},"\\approx 905{,}126",[883,82945,82947],{"className":82946},[886],[888,82948,82949],{"xmlns":890},[892,82950,82951,82958],{},[895,82952,82953,82955],{},[1723,82954,3456],{},[1864,82956,82957],{},"900,601",[902,82959,82960],{"encoding":904},"\\approx 900{,}601",[724,82962,82963,3850,83010,1343,83032,4634],{},[38,82964,82965,82966,1682,82988],{},"(c) Změna ",[883,82967,82969],{"className":82968},[886],[888,82970,82971],{"xmlns":890},[892,82972,82973,82985],{},[895,82974,82975,82977,82979,82981,82983],{},[898,82976,1911],{},[1723,82978,3430],{},[1864,82980,9744],{},[1723,82982,3843],{},[1864,82984,36937],{},[902,82986,82987],{"encoding":904},"L: 20 \\to 15",[883,82989,82991],{"className":82990},[886],[888,82992,82993],{"xmlns":890},[892,82994,82995,83007],{},[895,82996,82997,82999,83001,83003,83005],{},[898,82998,2034],{},[1723,83000,3430],{},[1864,83002,3810],{},[1723,83004,3843],{},[1864,83006,9512],{},[902,83008,83009],{"encoding":904},"K: 100 \\to 150",[883,83011,83013],{"className":83012},[886],[888,83014,83015],{"xmlns":890},[892,83016,83017,83029],{},[895,83018,83019,83021,83023,83025,83027],{},[898,83020,2930],{},[898,83022,1911],{},[1723,83024,1725],{},[1723,83026,1759],{},[1864,83028,2962],{},[902,83030,83031],{"encoding":904},"dL = -5",[883,83033,83035],{"className":83034},[886],[888,83036,83037],{"xmlns":890},[892,83038,83039,83049],{},[895,83040,83041,83043,83045,83047],{},[898,83042,2930],{},[898,83044,2034],{},[1723,83046,1725],{},[1864,83048,3840],{},[902,83050,83051],{"encoding":904},"dK = 50",[883,83053,83055],{"className":83054},[886],[888,83056,83057],{"xmlns":890,"display":28759},[892,83058,83059,83147],{},[895,83060,83061,83063,83065,83067,83069,83075,83077,83079,83081,83083,83085,83087,83089,83091,83093,83095,83097,83099,83105,83107,83109,83111,83113,83115,83117,83119,83121,83123,83125,83127,83129,83131,83133,83135,83138,83140,83142,83144],{},[898,83062,2930],{},[898,83064,1904],{},[1723,83066,1725],{},[898,83068,1728],{},[1931,83070,83071,83073],{},[898,83072,1746],{},[898,83074,1911],{},[1723,83076,1908],{"stretchy":1907},[1864,83078,9744],{},[1723,83080,2031],{"separator":2030},[1864,83082,3810],{},[1723,83084,1914],{"stretchy":1907},[1723,83086,3897],{},[1723,83088,1908],{"stretchy":1907},[1723,83090,1759],{},[1864,83092,2962],{},[1723,83094,1914],{"stretchy":1907},[1723,83096,2087],{},[898,83098,1728],{},[1931,83100,83101,83103],{},[898,83102,1746],{},[898,83104,2034],{},[1723,83106,1908],{"stretchy":1907},[1864,83108,9744],{},[1723,83110,2031],{"separator":2030},[1864,83112,3810],{},[1723,83114,1914],{"stretchy":1907},[1723,83116,3897],{},[1864,83118,3840],{},[1723,83120,1725],{},[1864,83122,82781],{},[1723,83124,3897],{},[1723,83126,1908],{"stretchy":1907},[1723,83128,1759],{},[1864,83130,2962],{},[1723,83132,1914],{"stretchy":1907},[1723,83134,2087],{},[1864,83136,83137],{},"4,525",[1723,83139,3897],{},[1864,83141,3840],{},[1723,83143,3456],{},[1864,83145,83146],{},"190,485.",[902,83148,83149],{"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.",[724,83151,83152],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,83154,83156],{"id":83155},"příklad-55","Příklad 5.5",[724,83158,83159,83160,83196,83197,1664],{},"Pro produkci ",[883,83161,83163],{"className":83162},[886],[888,83164,83165],{"xmlns":890},[892,83166,83167,83193],{},[895,83168,83169,83171,83173,83175,83177,83179,83181,83183,83189],{},[898,83170,1904],{},[1723,83172,1908],{"stretchy":1907},[898,83174,1911],{},[1723,83176,2031],{"separator":2030},[898,83178,2034],{},[1723,83180,1914],{"stretchy":1907},[1723,83182,1725],{},[82708,83184,83185,83187],{},[898,83186,1911],{},[1864,83188,2909],{},[8827,83190,83191],{},[898,83192,2034],{},[902,83194,83195],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,83198,83200],{"className":83199},[886],[888,83201,83202],{"xmlns":890},[892,83203,83204,83220],{},[895,83205,83206,83212,83216,83218],{},[82708,83207,83208,83210],{},[898,83209,1911],{},[1864,83211,2909],{},[8827,83213,83214],{},[898,83215,2034],{},[1723,83217,1725],{},[898,83219,81478],{},[902,83221,83222],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,83224,83225,83226,1664],{},"Umocněním na druhou: ",[883,83227,83229],{"className":83228},[886],[888,83230,83231],{"xmlns":890},[892,83232,83233,83257],{},[895,83234,83235,83237,83239,83245,83247],{},[898,83236,2034],{},[1723,83238,1725],{},[2057,83240,83241,83243],{},[898,83242,81478],{},[1864,83244,2331],{},[898,83246,2125],{"mathvariant":2124},[82708,83248,83249,83255],{},[2057,83250,83251,83253],{},[898,83252,1911],{},[1864,83254,2331],{},[1864,83256,2909],{},[902,83258,83259],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,83261,83262,83302,83342],{},[123,83263,83264],{},[883,83265,83267],{"className":83266},[886],[888,83268,83269],{"xmlns":890},[892,83270,83271,83299],{},[895,83272,83273,83275,83277,83279,83281,83283,83285,83287,83289],{},[898,83274,81478],{},[1723,83276,1725],{},[1864,83278,1866],{},[1723,83280,4702],{},[898,83282,2034],{},[1723,83284,1725],{},[1864,83286,1866],{},[898,83288,2125],{"mathvariant":2124},[82708,83290,83291,83297],{},[2057,83292,83293,83295],{},[898,83294,1911],{},[1864,83296,2331],{},[1864,83298,2909],{},[902,83300,83301],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,83303,83304],{},[883,83305,83307],{"className":83306},[886],[888,83308,83309],{"xmlns":890},[892,83310,83311,83339],{},[895,83312,83313,83315,83317,83319,83321,83323,83325,83327,83329],{},[898,83314,81478],{},[1723,83316,1725],{},[1864,83318,2331],{},[1723,83320,4702],{},[898,83322,2034],{},[1723,83324,1725],{},[1864,83326,3080],{},[898,83328,2125],{"mathvariant":2124},[82708,83330,83331,83337],{},[2057,83332,83333,83335],{},[898,83334,1911],{},[1864,83336,2331],{},[1864,83338,2909],{},[902,83340,83341],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,83343,83344],{},[883,83345,83347],{"className":83346},[886],[888,83348,83349],{"xmlns":890},[892,83350,83351,83379],{},[895,83352,83353,83355,83357,83359,83361,83363,83365,83367,83369],{},[898,83354,81478],{},[1723,83356,1725],{},[1864,83358,2909],{},[1723,83360,4702],{},[898,83362,2034],{},[1723,83364,1725],{},[1864,83366,4713],{},[898,83368,2125],{"mathvariant":2124},[82708,83370,83371,83377],{},[2057,83372,83373,83375],{},[898,83374,1911],{},[1864,83376,2331],{},[1864,83378,2909],{},[902,83380,83381],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,83383,83384],{},[614,83385,83386,83387,7183,83408,1664],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,83388,83390],{"className":83389},[886],[888,83391,83392],{"xmlns":890},[892,83393,83394,83406],{},[895,83395,83396,83398,83400,83402,83404],{},[1723,83397,1908],{"stretchy":1907},[898,83399,1911],{},[1723,83401,2031],{"separator":2030},[898,83403,2034],{},[1723,83405,1914],{"stretchy":1907},[902,83407,81604],{"encoding":904},[883,83409,83411],{"className":83410},[886],[888,83412,83413],{"xmlns":890},[892,83414,83415,83431],{},[895,83416,83417,83419,83421,83423,83425,83427,83429],{},[898,83418,81478],{},[1723,83420,1725],{},[1864,83422,1866],{},[1723,83424,2031],{"separator":2030},[1864,83426,2331],{},[1723,83428,2031],{"separator":2030},[1864,83430,2909],{},[902,83432,83433],{"encoding":904},"q = 1, 2, 3",[198,83435,83437],{"id":83436},"příklad-56","Příklad 5.6",[724,83439,77354,83440,1664],{},[883,83441,83443],{"className":83442},[886],[888,83444,83445],{"xmlns":890},[892,83446,83447,83463],{},[895,83448,83449,83451,83453,83455,83457,83459],{},[898,83450,1904],{},[1723,83452,1725],{},[1864,83454,2331],{},[898,83456,1911],{},[1723,83458,2087],{},[8827,83460,83461],{},[898,83462,2034],{},[902,83464,83465],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,83467,83469],{"className":83468},[886],[888,83470,83471],{"xmlns":890,"display":28759},[892,83472,83473,83515],{},[895,83474,83475,83477,83483,83485,83487,83489,83491,83493,83499,83501,83513],{},[898,83476,1728],{},[1931,83478,83479,83481],{},[898,83480,1746],{},[898,83482,1911],{},[1723,83484,1725],{},[1864,83486,2331],{},[1723,83488,2031],{"separator":2030},[6588,83490],{"width":6590},[898,83492,1728],{},[1931,83494,83495,83497],{},[898,83496,1746],{},[898,83498,2034],{},[1723,83500,1725],{},[3058,83502,83503,83505],{},[1864,83504,1866],{},[895,83506,83507,83509],{},[1864,83508,2331],{},[8827,83510,83511],{},[898,83512,2034],{},[898,83514,1664],{"mathvariant":2124},[902,83516,83517],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,83519,83521],{"className":83520},[886],[888,83522,83523],{"xmlns":890,"display":28759},[892,83524,83525,83589],{},[895,83526,83527,83529,83531,83533,83535,83537,83559,83561,83579,83581,83583,83587],{},[898,83528,1728],{},[898,83530,1749],{},[898,83532,1754],{},[898,83534,2111],{},[1723,83536,1725],{},[3058,83538,83539,83549],{},[895,83540,83541,83543],{},[898,83542,1728],{},[1931,83544,83545,83547],{},[898,83546,1746],{},[898,83548,1911],{},[895,83550,83551,83553],{},[898,83552,1728],{},[1931,83554,83555,83557],{},[898,83556,1746],{},[898,83558,2034],{},[1723,83560,1725],{},[3058,83562,83563,83565],{},[1864,83564,2331],{},[3055,83566,83567],{"scriptlevel":2256,"displaystyle":1907},[3058,83568,83569,83571],{},[1864,83570,1866],{},[895,83572,83573,83575],{},[1864,83574,2331],{},[8827,83576,83577],{},[898,83578,2034],{},[1723,83580,1725],{},[1864,83582,3080],{},[8827,83584,83585],{},[898,83586,2034],{},[898,83588,1664],{"mathvariant":2124},[902,83590,83591],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,83593,83594,83595,83638,83639,83678,83679,1664],{},"Například ",[883,83596,83598],{"className":83597},[886],[888,83599,83600],{"xmlns":890},[892,83601,83602,83635],{},[895,83603,83604,83606,83608,83610,83612,83614,83616,83618,83620,83622,83624,83626,83630,83632],{},[898,83605,1728],{},[898,83607,1749],{},[898,83609,1754],{},[898,83611,2111],{},[1723,83613,1908],{"stretchy":1907},[1864,83615,3080],{},[1723,83617,2031],{"separator":2030},[1864,83619,24894],{},[1723,83621,1914],{"stretchy":1907},[1723,83623,1725],{},[1864,83625,3080],{},[8827,83627,83628],{},[1864,83629,24894],{},[1723,83631,3456],{},[1864,83633,83634],{},"10,58",[902,83636,83637],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,83640,83642],{"className":83641},[886],[888,83643,83644],{"xmlns":890},[892,83645,83646,83675],{},[895,83647,83648,83650,83652,83654,83656,83658,83660,83662,83664,83666,83670,83672],{},[898,83649,1904],{},[1723,83651,1908],{"stretchy":1907},[1864,83653,3080],{},[1723,83655,2031],{"separator":2030},[1864,83657,24894],{},[1723,83659,1914],{"stretchy":1907},[1723,83661,1725],{},[1864,83663,6295],{},[1723,83665,2087],{},[8827,83667,83668],{},[1864,83669,24894],{},[1723,83671,3456],{},[1864,83673,83674],{},"10,646",[902,83676,83677],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,83680,83682],{"className":83681},[886],[888,83683,83684],{"xmlns":890},[892,83685,83686,83694],{},[895,83687,83688,83690],{},[1864,83689,3080],{},[8827,83691,83692],{},[1864,83693,24894],{},[902,83695,83696],{"encoding":904},"4\\sqrt{7}",[724,83698,83699,83700,83720],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,83701,83703],{"className":83702},[886],[888,83704,83705],{"xmlns":890},[892,83706,83707,83717],{},[895,83708,83709,83711,83713,83715],{},[898,83710,2930],{},[898,83712,1911],{},[1723,83714,1725],{},[1864,83716,2331],{},[902,83718,83719],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,83722,83724],{"className":83723},[886],[888,83725,83726],{"xmlns":890,"display":28759},[892,83727,83728,83777],{},[895,83729,83730,83732,83734,83736,83738,83740,83742,83744,83746,83748,83750,83752,83754,83756,83758,83760,83762,83764,83766,83770,83772,83774],{},[898,83731,2930],{},[898,83733,2034],{},[1723,83735,1725],{},[1723,83737,1759],{},[898,83739,1728],{},[898,83741,1749],{},[898,83743,1754],{},[898,83745,2111],{},[1723,83747,1908],{"stretchy":1907},[1864,83749,3080],{},[1723,83751,2031],{"separator":2030},[1864,83753,24894],{},[1723,83755,1914],{"stretchy":1907},[1723,83757,3897],{},[1864,83759,2331],{},[1723,83761,1725],{},[1723,83763,1759],{},[1864,83765,6295],{},[8827,83767,83768],{},[1864,83769,24894],{},[1723,83771,3456],{},[1723,83773,1759],{},[1864,83775,83776],{},"21,17.",[902,83778,83779],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,83781,83783],{"id":83782},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,83785,83786,83787,1343,83789,1682,83791,83793,83794,83797,83798,83801],{},"Hlavními faktory produkce jsou ",[38,83788,75595],{},[38,83790,75611],{},[38,83792,75627],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,83795,83796],{},"jednofaktorový"," (pouze práce) a ",[38,83799,83800],{},"dvoufaktorový"," (práce + kapitál) model.",[724,83803,83804,83805,83808,83809,83811,83812,83814,83815,26882,83818,83837,83838,83855,83856,83873,83874,83896,83897,5070,83916,1664],{},"V ",[38,83806,83807],{},"1F modelu"," se definuje ",[38,83810,10726],{}," (derivace produkce podle práce) a ",[38,83813,75530],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,83816,83817],{},"zákonu klesajících výnosů",[883,83819,83821],{"className":83820},[886],[888,83822,83823],{"xmlns":890},[892,83824,83825,83835],{},[895,83826,83827,83829],{},[898,83828,1728],{},[1931,83830,83831,83833],{},[898,83832,1746],{},[898,83834,1911],{},[902,83836,1939],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,83839,83841],{"className":83840},[886],[888,83842,83843],{"xmlns":890},[892,83844,83845,83853],{},[895,83846,83847],{},[1931,83848,83849,83851],{},[898,83850,1911],{},[1864,83852,2256],{},[902,83854,76239],{"encoding":904}," klesá a v bodě ",[883,83857,83859],{"className":83858},[886],[888,83860,83861],{"xmlns":890},[892,83862,83863,83871],{},[895,83864,83865],{},[1931,83866,83867,83869],{},[898,83868,1911],{},[1864,83870,1866],{},[902,83872,13913],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,83875,83876,83877],{},"princip maximalizace ",[883,83878,83880],{"className":83879},[886],[888,83881,83882],{"xmlns":890},[892,83883,83884,83894],{},[895,83885,83886,83888],{},[898,83887,1718],{},[1931,83889,83890,83892],{},[898,83891,1746],{},[898,83893,1911],{},[902,83895,1960],{"encoding":904},": v bodě maxima ",[883,83898,83900],{"className":83899},[886],[888,83901,83902],{"xmlns":890},[892,83903,83904,83914],{},[895,83905,83906,83908],{},[898,83907,1718],{},[1931,83909,83910,83912],{},[898,83911,1746],{},[898,83913,1911],{},[902,83915,1960],{"encoding":904},[883,83917,83919],{"className":83918},[886],[888,83920,83921],{"xmlns":890},[892,83922,83923,83943],{},[895,83924,83925,83927,83933,83935,83937],{},[898,83926,1728],{},[1931,83928,83929,83931],{},[898,83930,1746],{},[898,83932,1911],{},[1723,83934,1725],{},[898,83936,1718],{},[1931,83938,83939,83941],{},[898,83940,1746],{},[898,83942,1911],{},[902,83944,2011],{"encoding":904},[724,83946,83947,83948,83951,83952,2628,83955,83984,83985,84002,84003,84006,84007,84036,84037,84039,84040,8812,84070,84092],{},"Ve ",[38,83949,83950],{},"2F modelu"," se obvykle používají ",[38,83953,83954],{},"Cobb-Douglasovy funkce",[883,83956,83958],{"className":83957},[886],[888,83959,83960],{"xmlns":890},[892,83961,83962,83982],{},[895,83963,83964,83966,83968,83970,83976],{},[898,83965,1904],{},[1723,83967,1725],{},[898,83969,1718],{},[2057,83971,83972,83974],{},[898,83973,1911],{},[898,83975,207],{},[2057,83977,83978,83980],{},[898,83979,2034],{},[898,83981,2069],{},[902,83983,2072],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,83986,83988],{"className":83987},[886],[888,83989,83990],{"xmlns":890},[892,83991,83992,84000],{},[895,83993,83994,83996,83998],{},[898,83995,207],{},[1723,83997,2087],{},[898,83999,2069],{},[902,84001,75505],{"encoding":904}," rozlišujeme ",[38,84004,84005],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,84008,84010],{"className":84009},[886],[888,84011,84012],{"xmlns":890},[892,84013,84014,84034],{},[895,84015,84016,84018,84024,84026,84028],{},[898,84017,1728],{},[1931,84019,84020,84022],{},[898,84021,1746],{},[898,84023,1911],{},[1723,84025,2031],{"separator":2030},[898,84027,1728],{},[1931,84029,84030,84032],{},[898,84031,1746],{},[898,84033,2034],{},[902,84035,75443],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,84038,10483],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,84041,84043],{"className":84042},[886],[888,84044,84045],{"xmlns":890},[892,84046,84047,84067],{},[895,84048,84049,84051,84057,84059,84061],{},[898,84050,1728],{},[1931,84052,84053,84055],{},[898,84054,1746],{},[898,84056,1911],{},[898,84058,2125],{"mathvariant":2124},[898,84060,1728],{},[1931,84062,84063,84065],{},[898,84064,1746],{},[898,84066,2034],{},[902,84068,84069],{"encoding":904},"MP_L\u002FMP_K",[38,84071,84072,84073,1914],{},"mezní míra technické substituce (",[883,84074,84076],{"className":84075},[886],[888,84077,84078],{"xmlns":890},[892,84079,84080,84090],{},[895,84081,84082,84084,84086,84088],{},[898,84083,1728],{},[898,84085,1749],{},[898,84087,1754],{},[898,84089,2111],{},[902,84091,11299],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,84094,2615],{"id":50572},[152,84096,84097,84100,84103,84106,84109,84112,84115,84118,84121,84124,84127],{},[123,84098,84099],{},"Jaké jsou faktory produkce?",[123,84101,84102],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,84104,84105],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,84107,84108],{},"Co udává mezní produkt práce?",[123,84110,84111],{},"Co musí respektovat průběh křivky produkce?",[123,84113,84114],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,84116,84117],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,84119,84120],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,84122,84123],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,84125,84126],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,84128,84129],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,84131,2143],{"id":84132},"úlohy-51517",[198,84134,41143],{"id":41142},[724,84136,84137,84140,84141,84163,84164,1343,84184,1343,84204,84224],{},[38,84138,84139],{},"5.1"," Je dána produkce ",[883,84142,84144],{"className":84143},[886],[888,84145,84146],{"xmlns":890},[892,84147,84148,84160],{},[895,84149,84150,84152,84154,84156],{},[898,84151,1904],{},[1723,84153,1725],{},[1864,84155,3585],{},[8827,84157,84158],{},[898,84159,1911],{},[902,84161,84162],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,84165,84167],{"className":84166},[886],[888,84168,84169],{"xmlns":890},[892,84170,84171,84181],{},[895,84172,84173,84175,84177,84179],{},[898,84174,1904],{},[1723,84176,1908],{"stretchy":1907},[1864,84178,1866],{},[1723,84180,1914],{"stretchy":1907},[902,84182,84183],{"encoding":904},"Q(1)",[883,84185,84187],{"className":84186},[886],[888,84188,84189],{"xmlns":890},[892,84190,84191,84201],{},[895,84192,84193,84195,84197,84199],{},[898,84194,1904],{},[1723,84196,1908],{"stretchy":1907},[1864,84198,3080],{},[1723,84200,1914],{"stretchy":1907},[902,84202,84203],{"encoding":904},"Q(4)",[883,84205,84207],{"className":84206},[886],[888,84208,84209],{"xmlns":890},[892,84210,84211,84221],{},[895,84212,84213,84215,84217,84219],{},[898,84214,1904],{},[1723,84216,1908],{"stretchy":1907},[1864,84218,4713],{},[1723,84220,1914],{"stretchy":1907},[902,84222,84223],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,84226,84227,84140,84230,84266,84267,84280,84281,84300,84301,84327,84328,3411,84341,84354],{},[38,84228,84229],{},"5.2",[883,84231,84233],{"className":84232},[886],[888,84234,84235],{"xmlns":890},[892,84236,84237,84263],{},[895,84238,84239,84241,84243,84245,84247,84253,84255,84257],{},[898,84240,1904],{},[1723,84242,1725],{},[1723,84244,1759],{},[1864,84246,3517],{},[2057,84248,84249,84251],{},[898,84250,1911],{},[1864,84252,2909],{},[1723,84254,2087],{},[1864,84256,4713],{},[2057,84258,84259,84261],{},[898,84260,1911],{},[1864,84262,2331],{},[902,84264,84265],{"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 ",[883,84268,84270],{"className":84269},[886],[888,84271,84272],{"xmlns":890},[892,84273,84274,84278],{},[895,84275,84276],{},[898,84277,1911],{},[902,84279,1911],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,84282,84284],{"className":84283},[886],[888,84285,84286],{"xmlns":890},[892,84287,84288,84298],{},[895,84289,84290,84292],{},[898,84291,1728],{},[1931,84293,84294,84296],{},[898,84295,1746],{},[898,84297,1911],{},[902,84299,1939],{"encoding":904},". (f) Vypočtěte ",[883,84302,84304],{"className":84303},[886],[888,84305,84306],{"xmlns":890},[892,84307,84308,84324],{},[895,84309,84310,84312,84318,84320,84322],{},[898,84311,1728],{},[1931,84313,84314,84316],{},[898,84315,1746],{},[898,84317,1911],{},[1723,84319,1908],{"stretchy":1907},[1864,84321,3585],{},[1723,84323,1914],{"stretchy":1907},[902,84325,84326],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,84329,84331],{"className":84330},[886],[888,84332,84333],{"xmlns":890},[892,84334,84335,84339],{},[895,84336,84337],{},[1864,84338,3585],{},[902,84340,3585],{"encoding":904},[883,84342,84344],{"className":84343},[886],[888,84345,84346],{"xmlns":890},[892,84347,84348,84352],{},[895,84349,84350],{},[1864,84351,42979],{},[902,84353,42979],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,84356,84357,84360,84361,84383,84384,84412,84413,84444,84445,1664],{},[38,84358,84359],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,84362,84364],{"className":84363},[886],[888,84365,84366],{"xmlns":890},[892,84367,84368,84380],{},[895,84369,84370,84372,84374,84376],{},[898,84371,1904],{},[1723,84373,1725],{},[1864,84375,15811],{},[8827,84377,84378],{},[898,84379,1911],{},[902,84381,84382],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,84385,84387],{"className":84386},[886],[888,84388,84389],{"xmlns":890},[892,84390,84391,84409],{},[895,84392,84393,84395,84397,84399,84403,84405,84407],{},[898,84394,1904],{},[1723,84396,1725],{},[1864,84398,30774],{},[8827,84400,84401],{},[898,84402,1911],{},[1723,84404,1759],{},[1864,84406,3080],{},[898,84408,1911],{},[902,84410,84411],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,84414,84416],{"className":84415},[886],[888,84417,84418],{"xmlns":890},[892,84419,84420,84441],{},[895,84421,84422,84424,84426,84428,84430,84432,84435],{},[898,84423,1904],{},[1723,84425,1725],{},[1864,84427,3840],{},[898,84429,1911],{},[1723,84431,1759],{},[1864,84433,84434],{},"0,01",[2057,84436,84437,84439],{},[898,84438,1911],{},[1864,84440,2331],{},[902,84442,84443],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,84446,84448],{"className":84447},[886],[888,84449,84450],{"xmlns":890},[892,84451,84452,84478],{},[895,84453,84454,84456,84458,84460,84462,84468,84470,84472],{},[898,84455,1904],{},[1723,84457,1725],{},[1723,84459,1759],{},[1864,84461,68898],{},[2057,84463,84464,84466],{},[898,84465,1911],{},[1864,84467,2909],{},[1723,84469,2087],{},[1864,84471,4713],{},[2057,84473,84474,84476],{},[898,84475,1911],{},[1864,84477,2331],{},[902,84479,84480],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,84482,84483,84486,84487,3350,84506,72883,84523,1664],{},[38,84484,84485],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,84488,84490],{"className":84489},[886],[888,84491,84492],{"xmlns":890},[892,84493,84494,84504],{},[895,84495,84496,84498],{},[898,84497,1718],{},[1931,84499,84500,84502],{},[898,84501,1746],{},[898,84503,1911],{},[902,84505,1960],{"encoding":904},[883,84507,84509],{"className":84508},[886],[888,84510,84511],{"xmlns":890},[892,84512,84513,84521],{},[895,84514,84515],{},[1931,84516,84517,84519],{},[898,84518,1911],{},[1864,84520,2256],{},[902,84522,76239],{"encoding":904},[883,84524,84526],{"className":84525},[886],[888,84527,84528],{"xmlns":890},[892,84529,84530,84570],{},[895,84531,84532,84534,84540,84542,84548,84550,84552,84554,84560,84562,84568],{},[898,84533,1718],{},[1931,84535,84536,84538],{},[898,84537,1746],{},[898,84539,1911],{},[1723,84541,1908],{"stretchy":1907},[1931,84543,84544,84546],{},[898,84545,1911],{},[1864,84547,2256],{},[1723,84549,1914],{"stretchy":1907},[1723,84551,1725],{},[898,84553,1728],{},[1931,84555,84556,84558],{},[898,84557,1746],{},[898,84559,1911],{},[1723,84561,1908],{"stretchy":1907},[1931,84563,84564,84566],{},[898,84565,1911],{},[1864,84567,2256],{},[1723,84569,1914],{"stretchy":1907},[902,84571,84572],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,84574,84575,84140,84578,22287,84614,84627,84628,84647],{},[38,84576,84577],{},"5.5",[883,84579,84581],{"className":84580},[886],[888,84582,84583],{"xmlns":890},[892,84584,84585,84611],{},[895,84586,84587,84589,84591,84593,84595,84601,84603,84605],{},[898,84588,1904],{},[1723,84590,1725],{},[1723,84592,1759],{},[1864,84594,3561],{},[2057,84596,84597,84599],{},[898,84598,1911],{},[1864,84600,2909],{},[1723,84602,2087],{},[1864,84604,4227],{},[2057,84606,84607,84609],{},[898,84608,1911],{},[1864,84610,2331],{},[902,84612,84613],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,84615,84617],{"className":84616},[886],[888,84618,84619],{"xmlns":890},[892,84620,84621,84625],{},[895,84622,84623],{},[898,84624,1911],{},[902,84626,1911],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,84629,84631],{"className":84630},[886],[888,84632,84633],{"xmlns":890},[892,84634,84635,84645],{},[895,84636,84637,84639],{},[898,84638,1718],{},[1931,84640,84641,84643],{},[898,84642,1746],{},[898,84644,1911],{},[902,84646,1960],{"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.",[198,84649,84651],{"id":84650},"dvoufaktorový-model","Dvoufaktorový model",[724,84653,84654,84657,84658,84383,84684,84412,84726,1664],{},[38,84655,84656],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,84659,84661],{"className":84660},[886],[888,84662,84663],{"xmlns":890},[892,84664,84665,84681],{},[895,84666,84667,84669,84671,84673,84675],{},[898,84668,1904],{},[1723,84670,1725],{},[1864,84672,24894],{},[898,84674,1911],{},[2057,84676,84677,84679],{},[898,84678,2034],{},[1864,84680,2331],{},[902,84682,84683],{"encoding":904},"Q = 7 L K^{2}",[883,84685,84687],{"className":84686},[886],[888,84688,84689],{"xmlns":890},[892,84690,84691,84723],{},[895,84692,84693,84695,84697,84699,84711],{},[898,84694,1904],{},[1723,84696,1725],{},[1864,84698,3840],{},[2057,84700,84701,84703],{},[898,84702,1911],{},[895,84704,84705,84707,84709],{},[1864,84706,2331],{},[898,84708,2125],{"mathvariant":2124},[1864,84710,2909],{},[2057,84712,84713,84715],{},[898,84714,2034],{},[895,84716,84717,84719,84721],{},[1864,84718,1866],{},[898,84720,2125],{"mathvariant":2124},[1864,84722,2909],{},[902,84724,84725],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,84727,84729],{"className":84728},[886],[888,84730,84731],{"xmlns":890},[892,84732,84733,84765],{},[895,84734,84735,84737,84739,84741,84753],{},[898,84736,1904],{},[1723,84738,1725],{},[1864,84740,4425],{},[2057,84742,84743,84745],{},[898,84744,1911],{},[895,84746,84747,84749,84751],{},[1864,84748,2909],{},[898,84750,2125],{"mathvariant":2124},[1864,84752,2962],{},[2057,84754,84755,84757],{},[898,84756,2034],{},[895,84758,84759,84761,84763],{},[1864,84760,2331],{},[898,84762,2125],{"mathvariant":2124},[1864,84764,2962],{},[902,84766,84767],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,84769,84770,84140,84773,84815,84816,1343,84834,84853,84854,84871],{},[38,84771,84772],{},"5.7",[883,84774,84776],{"className":84775},[886],[888,84777,84778],{"xmlns":890},[892,84779,84780,84812],{},[895,84781,84782,84784,84786,84788,84800],{},[898,84783,1904],{},[1723,84785,1725],{},[1864,84787,3585],{},[2057,84789,84790,84792],{},[898,84791,1911],{},[895,84793,84794,84796,84798],{},[1864,84795,1866],{},[898,84797,2125],{"mathvariant":2124},[1864,84799,2331],{},[2057,84801,84802,84804],{},[898,84803,2034],{},[895,84805,84806,84808,84810],{},[1864,84807,1866],{},[898,84809,2125],{"mathvariant":2124},[1864,84811,2331],{},[902,84813,84814],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,84817,84819],{"className":84818},[886],[888,84820,84821],{"xmlns":890},[892,84822,84823,84831],{},[895,84824,84825,84827,84829],{},[898,84826,1911],{},[1723,84828,1725],{},[1864,84830,20835],{},[902,84832,84833],{"encoding":904},"L = 400",[883,84835,84837],{"className":84836},[886],[888,84838,84839],{"xmlns":890},[892,84840,84841,84850],{},[895,84842,84843,84845,84847],{},[898,84844,2034],{},[1723,84846,1725],{},[1864,84848,84849],{},"17576",[902,84851,84852],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,84855,84857],{"className":84856},[886],[888,84858,84859],{"xmlns":890},[892,84860,84861,84869],{},[895,84862,84863,84865,84867],{},[898,84864,1911],{},[1723,84866,2031],{"separator":2030},[898,84868,2034],{},[902,84870,79666],{"encoding":904}," zdvojnásobí.",[724,84873,84874,84877,84878,84815,84909,1343,84927,70269,84945,84975,84976,85006,85007,3411,85020,85034,85035,3411,85048,85061],{},[38,84875,84876],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,84879,84881],{"className":84880},[886],[888,84882,84883],{"xmlns":890},[892,84884,84885,84906],{},[895,84886,84887,84889,84891,84894,84900],{},[898,84888,1904],{},[1723,84890,1725],{},[1864,84892,84893],{},"1,01",[2057,84895,84896,84898],{},[898,84897,1911],{},[1864,84899,24423],{},[2057,84901,84902,84904],{},[898,84903,2034],{},[1864,84905,24482],{},[902,84907,84908],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,84910,84912],{"className":84911},[886],[888,84913,84914],{"xmlns":890},[892,84915,84916,84924],{},[895,84917,84918,84920,84922],{},[898,84919,1911],{},[1723,84921,1725],{},[1864,84923,31436],{},[902,84925,84926],{"encoding":904},"L = 250",[883,84928,84930],{"className":84929},[886],[888,84931,84932],{"xmlns":890},[892,84933,84934,84942],{},[895,84935,84936,84938,84940],{},[898,84937,2034],{},[1723,84939,1725],{},[1864,84941,3506],{},[902,84943,84944],{"encoding":904},"K = 1000",[883,84946,84948],{"className":84947},[886],[888,84949,84950],{"xmlns":890},[892,84951,84952,84972],{},[895,84953,84954,84956,84962,84964,84966,84968,84970],{},[898,84955,1728],{},[1931,84957,84958,84960],{},[898,84959,1746],{},[898,84961,1911],{},[1723,84963,1908],{"stretchy":1907},[1864,84965,31436],{},[1723,84967,2031],{"separator":2030},[1864,84969,3506],{},[1723,84971,1914],{"stretchy":1907},[902,84973,84974],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,84977,84979],{"className":84978},[886],[888,84980,84981],{"xmlns":890},[892,84982,84983,85003],{},[895,84984,84985,84987,84993,84995,84997,84999,85001],{},[898,84986,1728],{},[1931,84988,84989,84991],{},[898,84990,1746],{},[898,84992,2034],{},[1723,84994,1908],{"stretchy":1907},[1864,84996,31436],{},[1723,84998,2031],{"separator":2030},[1864,85000,3506],{},[1723,85002,1914],{"stretchy":1907},[902,85004,85005],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,85008,85010],{"className":85009},[886],[888,85011,85012],{"xmlns":890},[892,85013,85014,85018],{},[895,85015,85016],{},[898,85017,1911],{},[902,85019,1911],{"encoding":904},[883,85021,85023],{"className":85022},[886],[888,85024,85025],{"xmlns":890},[892,85026,85027,85032],{},[895,85028,85029],{},[1864,85030,85031],{},"260",[902,85033,85031],{"encoding":904}," a současném poklesu ",[883,85036,85038],{"className":85037},[886],[888,85039,85040],{"xmlns":890},[892,85041,85042,85046],{},[895,85043,85044],{},[898,85045,2034],{},[902,85047,2034],{"encoding":904},[883,85049,85051],{"className":85050},[886],[888,85052,85053],{"xmlns":890},[892,85054,85055,85059],{},[895,85056,85057],{},[1864,85058,15892],{},[902,85060,15892],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,85063,85064,85067,85068,1664],{},[38,85065,85066],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,85069,85071],{"className":85070},[886],[888,85072,85073],{"xmlns":890},[892,85074,85075,85095],{},[895,85076,85077,85079,85081,85083,85089],{},[898,85078,1904],{},[1723,85080,1725],{},[1864,85082,3585],{},[2057,85084,85085,85087],{},[898,85086,1911],{},[1864,85088,68898],{},[2057,85090,85091,85093],{},[898,85092,2034],{},[1864,85094,5719],{},[902,85096,85097],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,85099,85100,85103,85104,81262,85127,11094,85140,1981,85190,4634],{},[38,85101,85102],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,85105,85107],{"className":85106},[886],[888,85108,85109],{"xmlns":890},[892,85110,85111,85125],{},[895,85112,85113,85115,85117,85119,85121,85123],{},[898,85114,1904],{},[1723,85116,1908],{"stretchy":1907},[898,85118,1911],{},[1723,85120,2031],{"separator":2030},[898,85122,2034],{},[1723,85124,1914],{"stretchy":1907},[902,85126,10699],{"encoding":904},[883,85128,85130],{"className":85129},[886],[888,85131,85132],{"xmlns":890},[892,85133,85134,85138],{},[895,85135,85136],{},[898,85137,2192],{},[902,85139,2192],{"encoding":904},[883,85141,85143],{"className":85142},[886],[888,85144,85145],{"xmlns":890},[892,85146,85147,85187],{},[895,85148,85149,85151,85159,85161,85163,85171,85173,85175,85177,85179,85181,85183,85185],{},[898,85150,1911],{},[2220,85152,85153,85155,85157],{},[898,85154,1904],{},[898,85156,1911],{},[1723,85158,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,85160,2087],{},[898,85162,2034],{},[2220,85164,85165,85167,85169],{},[898,85166,1904],{},[898,85168,2034],{},[1723,85170,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,85172,1725],{},[898,85174,2192],{},[898,85176,1904],{},[1723,85178,1908],{"stretchy":1907},[898,85180,1911],{},[1723,85182,2031],{"separator":2030},[898,85184,2034],{},[1723,85186,1914],{"stretchy":1907},[902,85188,85189],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,85191,81237],{},[724,85193,85194,85197],{},[38,85195,85196],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,85199,85200,84140,85203,85243,85244,1343,85266,1343,85288,85310],{},[38,85201,85202],{},"5.12",[883,85204,85206],{"className":85205},[886],[888,85207,85208],{"xmlns":890},[892,85209,85210,85240],{},[895,85211,85212,85214,85216,85228],{},[898,85213,1904],{},[1723,85215,1725],{},[2057,85217,85218,85220],{},[898,85219,1911],{},[895,85221,85222,85224,85226],{},[1864,85223,1866],{},[898,85225,2125],{"mathvariant":2124},[1864,85227,2909],{},[2057,85229,85230,85232],{},[898,85231,2034],{},[895,85233,85234,85236,85238],{},[1864,85235,1866],{},[898,85237,2125],{"mathvariant":2124},[1864,85239,3080],{},[902,85241,85242],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,85245,85247],{"className":85246},[886],[888,85248,85249],{"xmlns":890},[892,85250,85251,85263],{},[895,85252,85253,85259,85261],{},[1931,85254,85255,85257],{},[898,85256,81478],{},[1864,85258,2256],{},[1723,85260,1725],{},[1864,85262,1866],{},[902,85264,85265],{"encoding":904},"q_0 = 1",[883,85267,85269],{"className":85268},[886],[888,85270,85271],{"xmlns":890},[892,85272,85273,85285],{},[895,85274,85275,85281,85283],{},[1931,85276,85277,85279],{},[898,85278,81478],{},[1864,85280,1866],{},[1723,85282,1725],{},[1864,85284,2331],{},[902,85286,85287],{"encoding":904},"q_1 = 2",[883,85289,85291],{"className":85290},[886],[888,85292,85293],{"xmlns":890},[892,85294,85295,85307],{},[895,85296,85297,85303,85305],{},[1931,85298,85299,85301],{},[898,85300,81478],{},[1864,85302,2331],{},[1723,85304,1725],{},[1864,85306,2909],{},[902,85308,85309],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,85312,85313,84140,85316,85356,85357,1343,85385,1343,85413,1343,85441,1343,85470,1343,85499,1343,85528,1343,85557,1343,85586,1664],{},[38,85314,85315],{},"5.13",[883,85317,85319],{"className":85318},[886],[888,85320,85321],{"xmlns":890},[892,85322,85323,85353],{},[895,85324,85325,85327,85329,85341],{},[898,85326,1904],{},[1723,85328,1725],{},[2057,85330,85331,85333],{},[898,85332,1911],{},[895,85334,85335,85337,85339],{},[1864,85336,1866],{},[898,85338,2125],{"mathvariant":2124},[1864,85340,2909],{},[2057,85342,85343,85345],{},[898,85344,2034],{},[895,85346,85347,85349,85351],{},[1864,85348,1866],{},[898,85350,2125],{"mathvariant":2124},[1864,85352,2331],{},[902,85354,85355],{"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): ",[883,85358,85360],{"className":85359},[886],[888,85361,85362],{"xmlns":890},[892,85363,85364,85382],{},[895,85365,85366,85372,85374,85376,85378,85380],{},[1931,85367,85368,85370],{},[898,85369,1718],{},[1864,85371,1866],{},[1723,85373,3212],{"stretchy":1907},[1864,85375,1866],{},[1723,85377,9135],{"separator":2030},[1864,85379,1866],{},[1723,85381,3227],{"stretchy":1907},[902,85383,85384],{"encoding":904},"A_1[1; 1]",[883,85386,85388],{"className":85387},[886],[888,85389,85390],{"xmlns":890},[892,85391,85392,85410],{},[895,85393,85394,85400,85402,85404,85406,85408],{},[1931,85395,85396,85398],{},[898,85397,1718],{},[1864,85399,2331],{},[1723,85401,3212],{"stretchy":1907},[1864,85403,1866],{},[1723,85405,9135],{"separator":2030},[1864,85407,6295],{},[1723,85409,3227],{"stretchy":1907},[902,85411,85412],{"encoding":904},"A_2[1; 8]",[883,85414,85416],{"className":85415},[886],[888,85417,85418],{"xmlns":890},[892,85419,85420,85438],{},[895,85421,85422,85428,85430,85432,85434,85436],{},[1931,85423,85424,85426],{},[898,85425,1718],{},[1864,85427,2909],{},[1723,85429,3212],{"stretchy":1907},[1864,85431,1866],{},[1723,85433,9135],{"separator":2030},[1864,85435,67284],{},[1723,85437,3227],{"stretchy":1907},[902,85439,85440],{"encoding":904},"A_3[1; 27]",[883,85442,85444],{"className":85443},[886],[888,85445,85446],{"xmlns":890},[892,85447,85448,85467],{},[895,85449,85450,85456,85458,85460,85462,85465],{},[1931,85451,85452,85454],{},[898,85453,1718],{},[1864,85455,3080],{},[1723,85457,3212],{"stretchy":1907},[1864,85459,2331],{},[1723,85461,9135],{"separator":2030},[1864,85463,85464],{},"0,353",[1723,85466,3227],{"stretchy":1907},[902,85468,85469],{"encoding":904},"A_4[2; 0{,}353]",[883,85471,85473],{"className":85472},[886],[888,85474,85475],{"xmlns":890},[892,85476,85477,85496],{},[895,85478,85479,85485,85487,85489,85491,85494],{},[1931,85480,85481,85483],{},[898,85482,1718],{},[1864,85484,2962],{},[1723,85486,3212],{"stretchy":1907},[1864,85488,2331],{},[1723,85490,9135],{"separator":2030},[1864,85492,85493],{},"2,828",[1723,85495,3227],{"stretchy":1907},[902,85497,85498],{"encoding":904},"A_5[2; 2{,}828]",[883,85500,85502],{"className":85501},[886],[888,85503,85504],{"xmlns":890},[892,85505,85506,85525],{},[895,85507,85508,85514,85516,85518,85520,85523],{},[1931,85509,85510,85512],{},[898,85511,1718],{},[1864,85513,2969],{},[1723,85515,3212],{"stretchy":1907},[1864,85517,2331],{},[1723,85519,9135],{"separator":2030},[1864,85521,85522],{},"9,545",[1723,85524,3227],{"stretchy":1907},[902,85526,85527],{"encoding":904},"A_6[2; 9{,}545]",[883,85529,85531],{"className":85530},[886],[888,85532,85533],{"xmlns":890},[892,85534,85535,85554],{},[895,85536,85537,85543,85545,85547,85549,85552],{},[1931,85538,85539,85541],{},[898,85540,1718],{},[1864,85542,24894],{},[1723,85544,3212],{"stretchy":1907},[1864,85546,65246],{},[1723,85548,9135],{"separator":2030},[1864,85550,85551],{},"0,544",[1723,85553,3227],{"stretchy":1907},[902,85555,85556],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,85558,85560],{"className":85559},[886],[888,85561,85562],{"xmlns":890},[892,85563,85564,85583],{},[895,85565,85566,85572,85574,85576,85578,85581],{},[1931,85567,85568,85570],{},[898,85569,1718],{},[1864,85571,6295],{},[1723,85573,3212],{"stretchy":1907},[1864,85575,65246],{},[1723,85577,9135],{"separator":2030},[1864,85579,85580],{},"14,696",[1723,85582,3227],{"stretchy":1907},[902,85584,85585],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,85587,85589],{"className":85588},[886],[888,85590,85591],{"xmlns":890},[892,85592,85593,85611],{},[895,85594,85595,85601,85603,85605,85607,85609],{},[1931,85596,85597,85599],{},[898,85598,1718],{},[1864,85600,4713],{},[1723,85602,3212],{"stretchy":1907},[1864,85604,2331],{},[1723,85606,9135],{"separator":2030},[1864,85608,2962],{},[1723,85610,3227],{"stretchy":1907},[902,85612,85613],{"encoding":904},"A_9[2; 5]",[724,85615,85616,85619],{},[38,85617,85618],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,85621,85622,85625,85626,85656,85657,85670,85671,85684,85685,70002,85704,85723,85724,1664],{},[38,85623,85624],{},"5.15"," Produkce firmy je dána vztahem ",[883,85627,85629],{"className":85628},[886],[888,85630,85631],{"xmlns":890},[892,85632,85633,85653],{},[895,85634,85635,85637,85639,85641,85647],{},[898,85636,1904],{},[1723,85638,1725],{},[1864,85640,2331],{},[2057,85642,85643,85645],{},[898,85644,1911],{},[1864,85646,5719],{},[2057,85648,85649,85651],{},[898,85650,2034],{},[1864,85652,24482],{},[902,85654,85655],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,85658,85660],{"className":85659},[886],[888,85661,85662],{"xmlns":890},[892,85663,85664,85668],{},[895,85665,85666],{},[1864,85667,3810],{},[902,85669,3810],{"encoding":904}," pracovníků a disponuje-li ",[883,85672,85674],{"className":85673},[886],[888,85675,85676],{"xmlns":890},[892,85677,85678,85682],{},[895,85679,85680],{},[1864,85681,65122],{},[902,85683,65122],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,85686,85688],{"className":85687},[886],[888,85689,85690],{"xmlns":890},[892,85691,85692,85702],{},[895,85693,85694,85696,85698,85700],{},[898,85695,1728],{},[898,85697,1749],{},[898,85699,1754],{},[898,85701,2111],{},[902,85703,11299],{"encoding":904},[883,85705,85707],{"className":85706},[886],[888,85708,85709],{"xmlns":890},[892,85710,85711,85721],{},[895,85712,85713,85715,85717,85719],{},[898,85714,1728],{},[898,85716,1749],{},[898,85718,1754],{},[898,85720,2111],{},[902,85722,11299],{"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 ",[883,85725,85727],{"className":85726},[886],[888,85728,85729],{"xmlns":890},[892,85730,85731,85736],{},[895,85732,85733],{},[1864,85734,85735],{},"95",[902,85737,85735],{"encoding":904},[724,85739,85740,84140,85743,71676,85775,85794,85795,85808,85809,85822,85823,85836],{},[38,85741,85742],{},"5.16",[883,85744,85746],{"className":85745},[886],[888,85747,85748],{"xmlns":890},[892,85749,85750,85772],{},[895,85751,85752,85754,85756,85762,85764,85766],{},[898,85753,1904],{},[1723,85755,1725],{},[2057,85757,85758,85760],{},[898,85759,2034],{},[1864,85761,2331],{},[1723,85763,2087],{},[1864,85765,2331],{},[2057,85767,85768,85770],{},[898,85769,1911],{},[1864,85771,2331],{},[902,85773,85774],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,85776,85778],{"className":85777},[886],[888,85779,85780],{"xmlns":890},[892,85781,85782,85792],{},[895,85783,85784,85786,85788,85790],{},[898,85785,1728],{},[898,85787,1749],{},[898,85789,1754],{},[898,85791,2111],{},[902,85793,11299],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,85796,85798],{"className":85797},[886],[888,85799,85800],{"xmlns":890},[892,85801,85802,85806],{},[895,85803,85804],{},[1864,85805,3840],{},[902,85807,3840],{"encoding":904}," pracovníky a ",[883,85810,85812],{"className":85811},[886],[888,85813,85814],{"xmlns":890},[892,85815,85816,85820],{},[895,85817,85818],{},[1864,85819,78298],{},[902,85821,78298],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,85824,85826],{"className":85825},[886],[888,85827,85828],{"xmlns":890},[892,85829,85830,85834],{},[895,85831,85832],{},[1864,85833,47394],{},[902,85835,47394],{"encoding":904}," jednotek.",[724,85838,85839,85842,85843,11094,85873,1664],{},[38,85840,85841],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,85844,85846],{"className":85845},[886],[888,85847,85848],{"xmlns":890},[892,85849,85850,85870],{},[895,85851,85852,85854,85856,85858,85864],{},[898,85853,1904],{},[1723,85855,1725],{},[898,85857,1718],{},[2057,85859,85860,85862],{},[898,85861,1911],{},[898,85863,207],{},[2057,85865,85866,85868],{},[898,85867,2034],{},[898,85869,2069],{},[902,85871,85872],{"encoding":904},"Q = A L^{a} K^{b}",[883,85874,85876],{"className":85875},[886],[888,85877,85878],{"xmlns":890},[892,85879,85880,85910],{},[895,85881,85882,85884,85886,85888,85890,85892,85900,85902],{},[898,85883,1728],{},[898,85885,1749],{},[898,85887,1754],{},[898,85889,2111],{},[1723,85891,1725],{},[3055,85893,85894],{"scriptlevel":2256,"displaystyle":1907},[3058,85895,85896,85898],{},[898,85897,207],{},[898,85899,2069],{},[1723,85901,3897],{},[3055,85903,85904],{"scriptlevel":2256,"displaystyle":1907},[3058,85905,85906,85908],{},[898,85907,2034],{},[898,85909,1911],{},[902,85911,85912],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,85914,16421],{"id":16420},[120,85916,85917,85950,85977,85986,86036,86067,86120,86143,86198,86271,86349,86392,86424,86457,86498,86570,86631,86697,86714,86787,86853,86905,86961,86995,87038],{},[123,85918,85919,85922,85923,37588,85936,85949],{},[38,85920,85921],{},"Faktory (vstupy) produkce:"," práce ",[883,85924,85926],{"className":85925},[886],[888,85927,85928],{"xmlns":890},[892,85929,85930,85934],{},[895,85931,85932],{},[898,85933,1911],{},[902,85935,1911],{"encoding":904},[883,85937,85939],{"className":85938},[886],[888,85940,85941],{"xmlns":890},[892,85942,85943,85947],{},[895,85944,85945],{},[898,85946,2034],{},[902,85948,2034],{"encoding":904},", půda.",[123,85951,85952,7725,85954,1664],{},[38,85953,41143],{},[883,85955,85957],{"className":85956},[886],[888,85958,85959],{"xmlns":890},[892,85960,85961,85975],{},[895,85962,85963,85965,85967,85969,85971,85973],{},[898,85964,1904],{},[1723,85966,1725],{},[898,85968,1904],{},[1723,85970,1908],{"stretchy":1907},[898,85972,1911],{},[1723,85974,1914],{"stretchy":1907},[902,85976,75229],{"encoding":904},[123,85978,85979,1981,85981,12829,85984,1664],{},[38,85980,859],{},[614,85982,85983],{},"production function",[38,85985,75728],{},[123,85987,85988,2628,85990,1664],{},[38,85989,75774],{},[883,85991,85993],{"className":85992},[886],[888,85994,85995],{"xmlns":890},[892,85996,85997,86033],{},[895,85998,85999,86001,86007,86009,86011,86013,86015,86017,86019,86021,86027,86029,86031],{},[898,86000,1728],{},[1931,86002,86003,86005],{},[898,86004,1746],{},[898,86006,1911],{},[1723,86008,1725],{},[898,86010,2930],{},[898,86012,1904],{},[898,86014,2125],{"mathvariant":2124},[898,86016,2930],{},[898,86018,1911],{},[1723,86020,1725],{},[2057,86022,86023,86025],{},[898,86024,1904],{},[1723,86026,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,86028,1908],{"stretchy":1907},[898,86030,1911],{},[1723,86032,1914],{"stretchy":1907},[902,86034,86035],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,86037,86038,2628,86040,1664],{},[38,86039,76709],{},[883,86041,86043],{"className":86042},[886],[888,86044,86045],{"xmlns":890},[892,86046,86047,86065],{},[895,86048,86049,86051,86057,86059,86061,86063],{},[898,86050,1718],{},[1931,86052,86053,86055],{},[898,86054,1746],{},[898,86056,1911],{},[1723,86058,1725],{},[898,86060,1904],{},[898,86062,2125],{"mathvariant":2124},[898,86064,1911],{},[902,86066,75297],{"encoding":904},[123,86068,86069,86071,86072,11094,86089,1664],{},[38,86070,76196],{}," — od určitého ",[883,86073,86075],{"className":86074},[886],[888,86076,86077],{"xmlns":890},[892,86078,86079,86087],{},[895,86080,86081],{},[1931,86082,86083,86085],{},[898,86084,1911],{},[1864,86086,2256],{},[902,86088,76239],{"encoding":904},[883,86090,86092],{"className":86091},[886],[888,86093,86094],{"xmlns":890},[892,86095,86096,86118],{},[895,86097,86098,86108,86110,86112,86114,86116],{},[2057,86099,86100,86102],{},[898,86101,1904],{},[895,86103,86104,86106],{},[1723,86105,2229],{"mathvariant":2124},[1723,86107,2229],{"mathvariant":2124},[1723,86109,1908],{"stretchy":1907},[898,86111,1911],{},[1723,86113,1914],{"stretchy":1907},[1723,86115,2287],{},[1864,86117,2256],{},[902,86119,76385],{"encoding":904},[123,86121,86122,2628,86125,86142],{},[38,86123,86124],{},"Inflexní bod",[883,86126,86128],{"className":86127},[886],[888,86129,86130],{"xmlns":890},[892,86131,86132,86140],{},[895,86133,86134],{},[1931,86135,86136,86138],{},[898,86137,1911],{},[1864,86139,2256],{},[902,86141,76239],{"encoding":904}," — přechod z konvexity do konkavity.",[123,86144,86145,2628,86148,7725,86165,1664],{},[38,86146,86147],{},"Bod maxima produkce",[883,86149,86151],{"className":86150},[886],[888,86152,86153],{"xmlns":890},[892,86154,86155,86163],{},[895,86156,86157],{},[1931,86158,86159,86161],{},[898,86160,1911],{},[1864,86162,1866],{},[902,86164,13913],{"encoding":904},[883,86166,86168],{"className":86167},[886],[888,86169,86170],{"xmlns":890},[892,86171,86172,86196],{},[895,86173,86174,86176,86182,86184,86190,86192,86194],{},[898,86175,1728],{},[1931,86177,86178,86180],{},[898,86179,1746],{},[898,86181,1911],{},[1723,86183,1908],{"stretchy":1907},[1931,86185,86186,86188],{},[898,86187,1911],{},[1864,86189,1866],{},[1723,86191,1914],{"stretchy":1907},[1723,86193,1725],{},[1864,86195,2256],{},[902,86197,76458],{"encoding":904},[123,86199,86200,86222,86223,11094,86242,1664],{},[38,86201,86202,86203],{},"Princip maximalizace ",[883,86204,86206],{"className":86205},[886],[888,86207,86208],{"xmlns":890},[892,86209,86210,86220],{},[895,86211,86212,86214],{},[898,86213,1718],{},[1931,86215,86216,86218],{},[898,86217,1746],{},[898,86219,1911],{},[902,86221,1960],{"encoding":904}," — v bodě maxima ",[883,86224,86226],{"className":86225},[886],[888,86227,86228],{"xmlns":890},[892,86229,86230,86240],{},[895,86231,86232,86234],{},[898,86233,1718],{},[1931,86235,86236,86238],{},[898,86237,1746],{},[898,86239,1911],{},[902,86241,1960],{"encoding":904},[883,86243,86245],{"className":86244},[886],[888,86246,86247],{"xmlns":890},[892,86248,86249,86269],{},[895,86250,86251,86253,86259,86261,86263],{},[898,86252,1728],{},[1931,86254,86255,86257],{},[898,86256,1746],{},[898,86258,1911],{},[1723,86260,1725],{},[898,86262,1718],{},[1931,86264,86265,86267],{},[898,86266,1746],{},[898,86268,1911],{},[902,86270,2011],{"encoding":904},[123,86272,86273,2628,86276,1343,86315,1343,86332,1664],{},[38,86274,86275],{},"Polynomiální produkční funkce",[883,86277,86279],{"className":86278},[886],[888,86280,86281],{"xmlns":890},[892,86282,86283,86313],{},[895,86284,86285,86287,86289,86291,86293,86295,86297,86303,86305,86307],{},[898,86286,1904],{},[1723,86288,1908],{"stretchy":1907},[898,86290,1911],{},[1723,86292,1914],{"stretchy":1907},[1723,86294,1725],{},[898,86296,207],{},[2057,86298,86299,86301],{},[898,86300,1911],{},[1864,86302,2909],{},[1723,86304,2087],{},[898,86306,2069],{},[2057,86308,86309,86311],{},[898,86310,1911],{},[1864,86312,2331],{},[902,86314,76576],{"encoding":904},[883,86316,86318],{"className":86317},[886],[888,86319,86320],{"xmlns":890},[892,86321,86322,86330],{},[895,86323,86324,86326,86328],{},[898,86325,207],{},[1723,86327,2287],{},[1864,86329,2256],{},[902,86331,43777],{"encoding":904},[883,86333,86335],{"className":86334},[886],[888,86336,86337],{"xmlns":890},[892,86338,86339,86347],{},[895,86340,86341,86343,86345],{},[898,86342,2069],{},[1723,86344,2253],{},[1864,86346,2256],{},[902,86348,19508],{"encoding":904},[123,86350,86351,2628,86354,1664],{},[38,86352,86353],{},"Diferenciál produkce",[883,86355,86357],{"className":86356},[886],[888,86358,86359],{"xmlns":890},[892,86360,86361,86389],{},[895,86362,86363,86365,86367,86369,86371,86373,86375,86377,86383,86385,86387],{},[898,86364,3611],{"mathvariant":2124},[898,86366,1904],{},[1723,86368,3456],{},[898,86370,2930],{},[898,86372,1904],{},[1723,86374,1725],{},[898,86376,1728],{},[1931,86378,86379,86381],{},[898,86380,1746],{},[898,86382,1911],{},[3018,86384,3707],{},[898,86386,2930],{},[898,86388,1911],{},[902,86390,86391],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,86393,86394,7725,86396,1664],{},[38,86395,84651],{},[883,86397,86399],{"className":86398},[886],[888,86400,86401],{"xmlns":890},[892,86402,86403,86421],{},[895,86404,86405,86407,86409,86411,86413,86415,86417,86419],{},[898,86406,1904],{},[1723,86408,1725],{},[898,86410,1904],{},[1723,86412,1908],{"stretchy":1907},[898,86414,1911],{},[1723,86416,2031],{"separator":2030},[898,86418,2034],{},[1723,86420,1914],{"stretchy":1907},[902,86422,86423],{"encoding":904},"Q = Q(L, K)",[123,86425,86426,7725,86428,1664],{},[38,86427,78746],{},[883,86429,86431],{"className":86430},[886],[888,86432,86433],{"xmlns":890},[892,86434,86435,86455],{},[895,86436,86437,86439,86441,86443,86449],{},[898,86438,1904],{},[1723,86440,1725],{},[898,86442,1718],{},[2057,86444,86445,86447],{},[898,86446,1911],{},[898,86448,207],{},[2057,86450,86451,86453],{},[898,86452,2034],{},[898,86454,2069],{},[902,86456,2072],{"encoding":904},[123,86458,86459,7725,86462,86497],{},[38,86460,86461],{},"Ryzí Cobb-Douglas",[883,86463,86465],{"className":86464},[886],[888,86466,86467],{"xmlns":890},[892,86468,86469,86495],{},[895,86470,86471,86473,86475,86477,86483],{},[898,86472,1904],{},[1723,86474,1725],{},[898,86476,1718],{},[2057,86478,86479,86481],{},[898,86480,1911],{},[898,86482,207],{},[2057,86484,86485,86487],{},[898,86486,2034],{},[895,86488,86489,86491,86493],{},[1864,86490,1866],{},[1723,86492,1759],{},[898,86494,207],{},[902,86496,79573],{"encoding":904}," (konstantní výnosy).",[123,86499,86500,7725,86502,1664],{},[38,86501,80289],{},[883,86503,86505],{"className":86504},[886],[888,86506,86507],{"xmlns":890},[892,86508,86509,86567],{},[895,86510,86511,86513,86515,86517,86519,86521,86523,86525,86527,86529,86539,86541,86543,86553],{},[898,86512,1904],{},[1723,86514,1725],{},[898,86516,1718],{},[1723,86518,3212],{"stretchy":1907},[1723,86520,1908],{"stretchy":1907},[1864,86522,1866],{},[1723,86524,1759],{},[898,86526,207],{},[1723,86528,1914],{"stretchy":1907},[2057,86530,86531,86533],{},[898,86532,1911],{},[895,86534,86535,86537],{},[1723,86536,1759],{},[898,86538,2069],{},[1723,86540,2087],{},[898,86542,207],{},[2057,86544,86545,86547],{},[898,86546,2034],{},[895,86548,86549,86551],{},[1723,86550,1759],{},[898,86552,2069],{},[2057,86554,86555,86557],{},[1723,86556,3227],{"stretchy":1907},[895,86558,86559,86561,86563,86565],{},[1723,86560,1759],{},[1864,86562,1866],{},[898,86564,2125],{"mathvariant":2124},[898,86566,2069],{},[902,86568,86569],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,86571,86572,1981,86575,12829,86597,1981,86600,86630],{},[38,86573,86574],{},"Lineární",[883,86576,86578],{"className":86577},[886],[888,86579,86580],{"xmlns":890},[892,86581,86582,86594],{},[895,86583,86584,86586,86588,86590,86592],{},[898,86585,207],{},[898,86587,1911],{},[1723,86589,2087],{},[898,86591,2069],{},[898,86593,2034],{},[902,86595,86596],{"encoding":904},"aL + bK",[38,86598,86599],{},"Leontiefova",[883,86601,86603],{"className":86602},[886],[888,86604,86605],{"xmlns":890},[892,86606,86607,86627],{},[895,86608,86609,86611,86613,86615,86617,86619,86621,86623,86625],{},[898,86610,80517],{},[1723,86612,56887],{},[1723,86614,1908],{"stretchy":1907},[898,86616,207],{},[898,86618,1911],{},[1723,86620,2031],{"separator":2030},[898,86622,2069],{},[898,86624,2034],{},[1723,86626,1914],{"stretchy":1907},[902,86628,86629],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,86632,86633,7725,86649,1664],{},[38,86634,86635,86636],{},"Homogenita stupně ",[883,86637,86639],{"className":86638},[886],[888,86640,86641],{"xmlns":890},[892,86642,86643,86647],{},[895,86644,86645],{},[898,86646,2192],{},[902,86648,2192],{"encoding":904},[883,86650,86652],{"className":86651},[886],[888,86653,86654],{"xmlns":890},[892,86655,86656,86694],{},[895,86657,86658,86660,86662,86664,86666,86668,86670,86672,86674,86676,86682,86684,86686,86688,86690,86692],{},[898,86659,1904],{},[1723,86661,1908],{"stretchy":1907},[898,86663,12742],{},[898,86665,1911],{},[1723,86667,2031],{"separator":2030},[898,86669,12742],{},[898,86671,2034],{},[1723,86673,1914],{"stretchy":1907},[1723,86675,1725],{},[2057,86677,86678,86680],{},[898,86679,12742],{},[898,86681,2192],{},[898,86683,1904],{},[1723,86685,1908],{"stretchy":1907},[898,86687,1911],{},[1723,86689,2031],{"separator":2030},[898,86691,2034],{},[1723,86693,1914],{"stretchy":1907},[902,86695,86696],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,86698,86699,79671],{},[38,86700,79604,86701],{},[883,86702,86704],{"className":86703},[886],[888,86705,86706],{"xmlns":890},[892,86707,86708,86712],{},[895,86709,86710],{},[898,86711,1718],{},[902,86713,1718],{"encoding":904},[123,86715,86716,86718,86719,86741,86742,86764,86765,4634],{},[38,86717,79105],{}," — konstantní (",[883,86720,86722],{"className":86721},[886],[888,86723,86724],{"xmlns":890},[892,86725,86726,86738],{},[895,86727,86728,86730,86732,86734,86736],{},[898,86729,207],{},[1723,86731,2087],{},[898,86733,2069],{},[1723,86735,1725],{},[1864,86737,1866],{},[902,86739,86740],{"encoding":904},"a+b=1","), rostoucí (",[883,86743,86745],{"className":86744},[886],[888,86746,86747],{"xmlns":890},[892,86748,86749,86761],{},[895,86750,86751,86753,86755,86757,86759],{},[898,86752,207],{},[1723,86754,2087],{},[898,86756,2069],{},[1723,86758,2253],{},[1864,86760,1866],{},[902,86762,86763],{"encoding":904},"a+b>1","), klesající (",[883,86766,86768],{"className":86767},[886],[888,86769,86770],{"xmlns":890},[892,86771,86772,86784],{},[895,86773,86774,86776,86778,86780,86782],{},[898,86775,207],{},[1723,86777,2087],{},[898,86779,2069],{},[1723,86781,2287],{},[1864,86783,1866],{},[902,86785,86786],{"encoding":904},"a+b\u003C1",[123,86788,86789,2628,86791,1343,86821,2628,86823,1664],{},[38,86790,75774],{},[883,86792,86794],{"className":86793},[886],[888,86795,86796],{"xmlns":890},[892,86797,86798,86818],{},[895,86799,86800,86802,86808,86810],{},[898,86801,1728],{},[1931,86803,86804,86806],{},[898,86805,1746],{},[898,86807,1911],{},[1723,86809,1725],{},[2220,86811,86812,86814,86816],{},[898,86813,1904],{},[898,86815,1911],{},[1723,86817,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,86819,86820],{"encoding":904},"MP_L = Q'_L",[38,86822,78678],{},[883,86824,86826],{"className":86825},[886],[888,86827,86828],{"xmlns":890},[892,86829,86830,86850],{},[895,86831,86832,86834,86840,86842],{},[898,86833,1728],{},[1931,86835,86836,86838],{},[898,86837,1746],{},[898,86839,2034],{},[1723,86841,1725],{},[2220,86843,86844,86846,86848],{},[898,86845,1904],{},[898,86847,2034],{},[1723,86849,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,86851,86852],{"encoding":904},"MP_K = Q'_K",[123,86854,86855,2628,86857,1664],{},[38,86856,80892],{},[883,86858,86860],{"className":86859},[886],[888,86861,86862],{"xmlns":890},[892,86863,86864,86902],{},[895,86865,86866,86868,86870,86872,86874,86880,86882,86884,86886,86888,86890,86896,86898,86900],{},[898,86867,2930],{},[898,86869,1904],{},[1723,86871,1725],{},[898,86873,1728],{},[1931,86875,86876,86878],{},[898,86877,1746],{},[898,86879,1911],{},[3018,86881,3707],{},[898,86883,2930],{},[898,86885,1911],{},[1723,86887,2087],{},[898,86889,1728],{},[1931,86891,86892,86894],{},[898,86893,1746],{},[898,86895,2034],{},[3018,86897,3707],{},[898,86899,2930],{},[898,86901,2034],{},[902,86903,86904],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,86906,86907,7725,86909,1664],{},[38,86908,81237],{},[883,86910,86912],{"className":86911},[886],[888,86913,86914],{"xmlns":890},[892,86915,86916,86958],{},[895,86917,86918,86920,86928,86930,86932,86940,86942,86944,86946,86948,86950,86952,86954,86956],{},[898,86919,1911],{},[2220,86921,86922,86924,86926],{},[898,86923,1904],{},[898,86925,1911],{},[1723,86927,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,86929,2087],{},[898,86931,2034],{},[2220,86933,86934,86936,86938],{},[898,86935,1904],{},[898,86937,2034],{},[1723,86939,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,86941,1725],{},[898,86943,2192],{},[3018,86945,3707],{},[898,86947,1904],{},[1723,86949,1908],{"stretchy":1907},[898,86951,1911],{},[1723,86953,2031],{"separator":2030},[898,86955,2034],{},[1723,86957,1914],{"stretchy":1907},[902,86959,86960],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,86962,86963,86966,86967,1664],{},[38,86964,86965],{},"Izokvanta"," — křivka ",[883,86968,86970],{"className":86969},[886],[888,86971,86972],{"xmlns":890},[892,86973,86974,86992],{},[895,86975,86976,86978,86980,86982,86984,86986,86988,86990],{},[898,86977,1904],{},[1723,86979,1908],{"stretchy":1907},[898,86981,1911],{},[1723,86983,2031],{"separator":2030},[898,86985,2034],{},[1723,86987,1914],{"stretchy":1907},[1723,86989,1725],{},[898,86991,81478],{},[902,86993,86994],{"encoding":904},"Q(L, K) = q",[123,86996,86997,2628,86999,1664],{},[38,86998,81667],{},[883,87000,87002],{"className":87001},[886],[888,87003,87004],{"xmlns":890},[892,87005,87006,87036],{},[895,87007,87008,87010,87012,87014,87016,87018,87020,87026,87028,87030],{},[898,87009,1728],{},[898,87011,1749],{},[898,87013,1754],{},[898,87015,2111],{},[1723,87017,1725],{},[898,87019,1728],{},[1931,87021,87022,87024],{},[898,87023,1746],{},[898,87025,1911],{},[898,87027,2125],{"mathvariant":2124},[898,87029,1728],{},[1931,87031,87032,87034],{},[898,87033,1746],{},[898,87035,2034],{},[902,87037,2136],{"encoding":904},[123,87039,87040,2628,87043,1664],{},[38,87041,87042],{},"Substituční vztah",[883,87044,87046],{"className":87045},[886],[888,87047,87048],{"xmlns":890},[892,87049,87050,87074],{},[895,87051,87052,87054,87056,87058,87060,87062,87064,87066,87068,87070,87072],{},[898,87053,3611],{"mathvariant":2124},[898,87055,2034],{},[1723,87057,3456],{},[1723,87059,1759],{},[898,87061,1728],{},[898,87063,1749],{},[898,87065,1754],{},[898,87067,2111],{},[3018,87069,3707],{},[898,87071,2930],{},[898,87073,1911],{},[902,87075,87076],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,87078,2620],{"id":2619},[120,87080,87081,87178,87185,87192],{},[123,87082,87083,2628,87085,87088,87089,1343,87092,87095,87096,87099,87100,87119,87120,19342,87139,87142,87143,87162,87163,4634],{},[38,87084,51413],{},[207,87086,784],{"className":87087,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,87090,3086],{"className":87091,"dataFsResolvedFilePath":764,"href":765},[210],[207,87093,793],{"className":87094,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,87097,880],{"className":87098,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,87101,87103],{"className":87102},[886],[888,87104,87105],{"xmlns":890},[892,87106,87107,87117],{},[895,87108,87109,87111,87113,87115],{},[898,87110,1728],{},[898,87112,1749],{},[898,87114,1754],{},[898,87116,2111],{},[902,87118,11299],{"encoding":904}," ↔ ",[883,87121,87123],{"className":87122},[886],[888,87124,87125],{"xmlns":890},[892,87126,87127,87137],{},[895,87128,87129,87131,87133,87135],{},[898,87130,1728],{},[898,87132,1749],{},[898,87134,1721],{},[898,87136,2111],{},[902,87138,11303],{"encoding":904},[207,87140,4539],{"className":87141,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,87144,87146],{"className":87145},[886],[888,87147,87148],{"xmlns":890},[892,87149,87150,87160],{},[895,87151,87152,87154],{},[898,87153,1718],{},[1931,87155,87156,87158],{},[898,87157,1746],{},[898,87159,1911],{},[902,87161,1960],{"encoding":904}," ↔ min ",[883,87164,87166],{"className":87165},[886],[888,87167,87168],{"xmlns":890},[892,87169,87170,87176],{},[895,87171,87172,87174],{},[898,87173,1718],{},[898,87175,1721],{},[902,87177,56247],{"encoding":904},[123,87179,87180,2628,87182,1664],{},[38,87181,4515],{},[207,87183,4544],{"className":87184,"dataFsResolvedFilePath":848,"href":849},[210],[123,87186,87187,2628,87189,1664],{},[38,87188,16912],{},[207,87190,1094],{"className":87191,"dataFsResolvedFilePath":838,"href":839},[210],[123,87193,87194,2628,87196,1664],{},[38,87195,2627],{},[207,87197,1646],{"className":87198,"dataFsResolvedFilePath":1645,"href":1644},[210],{"title":641,"searchDepth":642,"depth":642,"links":87200},[87201,87202,87203,87207,87209,87214,87215,87222,87223,87225,87226,87227,87229,87234,87235,87236,87240,87241],{"id":75509,"depth":642,"text":75510},{"id":75646,"depth":642,"text":75647},{"id":75749,"depth":642,"text":87204,"children":87205},"Mezní produkt práce (MPLMP_L)",[87206],{"id":76195,"depth":649,"text":76196},{"id":76684,"depth":642,"text":87208},"Průměrný produkt práce (APLAP_L)",{"id":76802,"depth":642,"text":76803,"children":87210},[87211,87212,87213],{"id":77039,"depth":649,"text":66188},{"id":77350,"depth":649,"text":77351},{"id":78070,"depth":649,"text":78071},{"id":78642,"depth":642,"text":78643},{"id":78745,"depth":642,"text":78746,"children":87216},[87217,87218,87220,87221],{"id":79104,"depth":649,"text":79105},{"id":79603,"depth":649,"text":87219},"Parametr efektivity AA",{"id":79674,"depth":649,"text":79675},{"id":37871,"depth":649,"text":80014},{"id":80201,"depth":642,"text":80202},{"id":80540,"depth":642,"text":87224},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":81231,"depth":642,"text":81232},{"id":75575,"depth":642,"text":10483},{"id":81642,"depth":642,"text":87228},"Mezní míra technické substituce (MRTSMRTS)",{"id":82508,"depth":642,"text":82509,"children":87230},[87231,87232,87233],{"id":82512,"depth":649,"text":82513},{"id":83155,"depth":649,"text":83156},{"id":83436,"depth":649,"text":83437},{"id":83782,"depth":642,"text":83783},{"id":50572,"depth":642,"text":2615},{"id":84132,"depth":642,"text":2143,"children":87237},[87238,87239],{"id":41142,"depth":649,"text":41143},{"id":84650,"depth":649,"text":84651},{"id":16420,"depth":642,"text":16421},{"id":2619,"depth":642,"text":2620},{},"\u002Ftopics\u002Fprodukce",{"title":75149,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,2149,87248,87249,87250,75575,87251,87252],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":87255,"title":87256,"body":87257,"course":1128,"courses":659,"created":2676,"description":641,"extension":661,"meta":96200,"navigation":664,"path":96201,"seo":96202,"sources":96203,"stem":96204,"tags":96205,"type":4573,"updated":677,"__hash__":96208},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":87258,"toc":96174},[87259,87262,87264,87459,87468,87472,87475,87528,87532,87544,87548,87551,87568,87691,87697,87841,87851,87855,87890,87928,87976,88033,88093,88135,88711,88715,88798,88907,89000,89258,89261,89314,89425,89507,89511,89522,89755,89810,89816,89856,89919,89930,90121,90227,90380,90428,90433,90547,90585,90711,90757,90784,90861,90936,91016,91146,91207,91295,91299,91302,91371,91454,91461,91521,91831,91835,91841,91894,91910,91961,92099,92175,92288,92605,92609,92616,92776,92835,92839,92861,92958,93079,93193,93216,93279,93336,93588,93596,93600,93607,93861,93911,93967,93970,94134,94138,94236,94238,94270,94274,94407,94649,94833,95001,95308,95441,95628,95640,95642,96075,96077],[12,87260,87256],{"id":87261},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,87263,12707],{"id":12706},[724,87265,87266,2628,87268,87299,87300,87303,87304,87333,87334,87352,87353,87392,87393,87396,87397,87410,87411,28946,87414,87427,87428,87441,87442,87455,87456,1664],{},[38,87267,880],{},[883,87269,87271],{"className":87270},[886],[888,87272,87273],{"xmlns":890},[892,87274,87275,87297],{},[895,87276,87277,87279,87281,87287,87289,87295],{},[898,87278,900],{},[1723,87280,1908],{"stretchy":1907},[1931,87282,87283,87285],{},[898,87284,1904],{},[1864,87286,1866],{},[1723,87288,2031],{"separator":2030},[1931,87290,87291,87293],{},[898,87292,1904],{},[1864,87294,2331],{},[1723,87296,1914],{"stretchy":1907},[902,87298,17039],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,87301,87302],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,87305,87307],{"className":87306},[886],[888,87308,87309],{"xmlns":890},[892,87310,87311,87331],{},[895,87312,87313,87315,87321,87323],{},[898,87314,1728],{},[1931,87316,87317,87319],{},[898,87318,900],{},[898,87320,2216],{},[1723,87322,1725],{},[2220,87324,87325,87327,87329],{},[898,87326,900],{},[898,87328,2216],{},[1723,87330,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,87332,2232],{"encoding":904},", indiferenční křivky ",[883,87335,87337],{"className":87336},[886],[888,87338,87339],{"xmlns":890},[892,87340,87341,87349],{},[895,87342,87343,87345,87347],{},[898,87344,900],{},[1723,87346,1725],{},[898,87348,2878],{},[902,87350,87351],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,87354,87356],{"className":87355},[886],[888,87357,87358],{"xmlns":890},[892,87359,87360,87390],{},[895,87361,87362,87364,87366,87368,87370,87372,87374,87380,87382,87384],{},[898,87363,1728],{},[898,87365,1749],{},[898,87367,1721],{},[898,87369,2111],{},[1723,87371,1725],{},[898,87373,1728],{},[1931,87375,87376,87378],{},[898,87377,900],{},[1864,87379,1866],{},[898,87381,2125],{"mathvariant":2124},[898,87383,1728],{},[1931,87385,87386,87388],{},[898,87387,900],{},[1864,87389,2331],{},[902,87391,2334],{"encoding":904},". Tato stránka pokrývá ",[38,87394,87395],{},"teorii užitečnosti"," — funkce ",[883,87398,87400],{"className":87399},[886],[888,87401,87402],{"xmlns":890},[892,87403,87404,87408],{},[895,87405,87406],{},[898,87407,900],{},[902,87409,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,87412,87413],{},"Optimalizaci spotřebitele",[883,87415,87417],{"className":87416},[886],[888,87418,87419],{"xmlns":890},[892,87420,87421,87425],{},[895,87422,87423],{},[898,87424,900],{},[902,87426,900],{"encoding":904}," při rozpočtu, min ",[883,87429,87431],{"className":87430},[886],[888,87432,87433],{"xmlns":890},[892,87434,87435,87439],{},[895,87436,87437],{},[898,87438,1846],{},[902,87440,1846],{"encoding":904}," při dané ",[883,87443,87445],{"className":87444},[886],[888,87446,87447],{"xmlns":890},[892,87448,87449,87453],{},[895,87450,87451],{},[898,87452,900],{},[902,87454,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,87457,913],{"className":87458,"dataFsResolvedFilePath":911,"href":912},[210],[724,87460,87461,87462,87464,87465,1664],{},"Kapitola 6 knihy ",[614,87463,1646],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,87466,37447],{"className":87467,"dataFsResolvedFilePath":911,"href":912},[210],[115,87469,87471],{"id":87470},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,87473,87474],{},"Po prostudování této kapitoly byste měli umět:",[120,87476,87477,87483,87492,87497,87500,87506,87512,87515,87521],{},[123,87478,87479,87480,2031],{},"vyložit, co se rozumí termínem ",[38,87481,87482],{},"užitečnost",[123,87484,87485,87486,1682,87489,2031],{},"definovat pojmy ",[38,87487,87488],{},"svazek zboží",[38,87490,87491],{},"funkce užitečnosti",[123,87493,75524,87494,75531],{},[38,87495,87496],{},"mezní užitečnosti",[123,87498,87499],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,87501,75551,87502,87505],{},[38,87503,87504],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,87507,75572,87508,87511],{},[38,87509,87510],{},"křivky užitečnosti"," (indiferenční křivky),",[123,87513,87514],{},"vyjmenovat jejich základní vlastnosti,",[123,87516,75524,87517,87520],{},[38,87518,87519],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,87522,87523,87524,87527],{},"řešit ",[38,87525,87526],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,87529,87531],{"id":87530},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,87533,87534,87535,87539,87540,87543],{},"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 ",[207,87536,87538],{"className":87537,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,87541,87542],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,87545,87547],{"id":87546},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,87549,87550],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,87552,87553,87559],{},[123,87554,87555,87558],{},[38,87556,87557],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,87560,87561,87564,87565,87567],{},[38,87562,87563],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,87566,87302],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[4584,87569,87570],{},[724,87571,87572,87574,87575,87578,87579,2628,87592,87595,87596,1682,87609,87628,87629,1343,87655,87682,87683,87686,87687,87690],{},[883,87573,5124],{}," Pozor — ordinalisté užitečnost ",[38,87576,87577],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,87580,87582],{"className":87581},[886],[888,87583,87584],{"xmlns":890},[892,87585,87586,87590],{},[895,87587,87588],{},[898,87589,900],{},[902,87591,900],{"encoding":904},[38,87593,87594],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,87597,87599],{"className":87598},[886],[888,87600,87601],{"xmlns":890},[892,87602,87603,87607],{},[895,87604,87605],{},[898,87606,900],{},[902,87608,900],{"encoding":904},[883,87610,87612],{"className":87611},[886],[888,87613,87614],{"xmlns":890},[892,87615,87616,87625],{},[895,87617,87618],{},[9096,87619,87620,87622],{"accent":2030},[898,87621,900],{},[1723,87623,87624],{},"~",[902,87626,87627],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,87630,87632],{"className":87631},[886],[888,87633,87634],{"xmlns":890},[892,87635,87636,87652],{},[895,87637,87638,87644,87646],{},[9096,87639,87640,87642],{"accent":2030},[898,87641,900],{},[1723,87643,87624],{},[1723,87645,1725],{},[2057,87647,87648,87650],{},[898,87649,900],{},[1864,87651,2331],{},[902,87653,87654],{"encoding":904},"\\tilde U = U^2",[883,87656,87658],{"className":87657},[886],[888,87659,87660],{"xmlns":890},[892,87661,87662,87679],{},[895,87663,87664,87670,87672,87675,87677],{},[9096,87665,87666,87668],{"accent":2030},[898,87667,900],{},[1723,87669,87624],{},[1723,87671,1725],{},[898,87673,87674],{},"ln",[1723,87676,56887],{},[898,87678,900],{},[902,87680,87681],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,87684,87685],{},"porovnání"," mezi svazky a ",[38,87688,87689],{},"poměry"," mezních veličin.",[724,87692,87693,87694,3430],{},"Ordinalistický přístup vychází z ",[38,87695,87696],{},"pěti hlavních předpokladů",[152,87698,87699,87705,87711,87829,87835],{},[123,87700,87701,87704],{},[38,87702,87703],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,87706,87707,87710],{},[38,87708,87709],{},"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.",[123,87712,87713,87716,87717,62428,87730,87743,87744,62428,87757,2137,87770,87773,87774,1682,87793,63257,87811,1664],{},[38,87714,87715],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,87718,87720],{"className":87719},[886],[888,87721,87722],{"xmlns":890},[892,87723,87724,87728],{},[895,87725,87726],{},[898,87727,1718],{},[902,87729,1718],{"encoding":904},[883,87731,87733],{"className":87732},[886],[888,87734,87735],{"xmlns":890},[892,87736,87737,87741],{},[895,87738,87739],{},[898,87740,23946],{},[902,87742,23946],{"encoding":904},", nebude jindy preferovat ",[883,87745,87747],{"className":87746},[886],[888,87748,87749],{"xmlns":890},[892,87750,87751,87755],{},[895,87752,87753],{},[898,87754,23946],{},[902,87756,23946],{"encoding":904},[883,87758,87760],{"className":87759},[886],[888,87761,87762],{"xmlns":890},[892,87763,87764,87768],{},[895,87765,87766],{},[898,87767,1718],{},[902,87769,1718],{"encoding":904},[38,87771,87772],{},"Tranzitivita",": pokud ",[883,87775,87777],{"className":87776},[886],[888,87778,87779],{"xmlns":890},[892,87780,87781,87790],{},[895,87782,87783,87785,87788],{},[898,87784,1718],{},[1723,87786,87787],{},"≻",[898,87789,23946],{},[902,87791,87792],{"encoding":904},"A \\succ B",[883,87794,87796],{"className":87795},[886],[888,87797,87798],{"xmlns":890},[892,87799,87800,87808],{},[895,87801,87802,87804,87806],{},[898,87803,23946],{},[1723,87805,87787],{},[898,87807,1721],{},[902,87809,87810],{"encoding":904},"B \\succ C",[883,87812,87814],{"className":87813},[886],[888,87815,87816],{"xmlns":890},[892,87817,87818,87826],{},[895,87819,87820,87822,87824],{},[898,87821,1718],{},[1723,87823,87787],{},[898,87825,1721],{},[902,87827,87828],{"encoding":904},"A \\succ C",[123,87830,87831,87834],{},[38,87832,87833],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,87836,87837,87840],{},[38,87838,87839],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,87842,87843,87844,87847,87848,1664],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,87845,87846],{},"preference"," a na příbuzné ",[614,87849,87850],{},"funkci užitečnosti",[115,87852,87854],{"id":87853},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,87856,87857,87858,87871,87872,87875,87876,87889],{},"Uvažujme ",[883,87859,87861],{"className":87860},[886],[888,87862,87863],{"xmlns":890},[892,87864,87865,87869],{},[895,87866,87867],{},[898,87868,2192],{},[902,87870,2192],{"encoding":904}," různých zboží. ",[38,87873,87874],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,87877,87879],{"className":87878},[886],[888,87880,87881],{"xmlns":890},[892,87882,87883,87887],{},[895,87884,87885],{},[898,87886,2192],{},[902,87888,2192],{"encoding":904},"-tice",[724,87891,87892],{},[883,87893,87895],{"className":87894},[886],[888,87896,87897],{"xmlns":890},[892,87898,87899,87925],{},[895,87900,87901,87903,87909,87911,87913,87915,87921,87923],{},[1723,87902,1908],{"stretchy":1907},[1931,87904,87905,87907],{},[898,87906,1904],{},[1864,87908,1866],{},[1723,87910,2031],{"separator":2030},[1723,87912,2183],{},[1723,87914,2031],{"separator":2030},[1931,87916,87917,87919],{},[898,87918,1904],{},[898,87920,2192],{},[1723,87922,1914],{"stretchy":1907},[1723,87924,2031],{"separator":2030},[902,87926,87927],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,87929,5022,87930,87947,87948,87961,87962,87965,87966,87969,87970,87973,87974,3430],{},[883,87931,87933],{"className":87932},[886],[888,87934,87935],{"xmlns":890},[892,87936,87937,87945],{},[895,87938,87939],{},[1931,87940,87941,87943],{},[898,87942,1904],{},[898,87944,2216],{},[902,87946,48229],{"encoding":904}," značí množství ",[883,87949,87951],{"className":87950},[886],[888,87952,87953],{"xmlns":890},[892,87954,87955,87959],{},[895,87956,87957],{},[898,87958,2216],{},[902,87960,2216],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,87963,87964],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,87967,87968],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,87971,87972],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,87975,87850],{},[883,87977,87979],{"className":87978},[886],[888,87980,87981],{"xmlns":890,"display":28759},[892,87982,87983,88030],{},[21447,87984,87985],{"width":28764},[21452,87986,87987,87989,88023,88025],{},[21455,87988],{"width":28769},[21455,87990,87991],{},[895,87992,87993,87995,87997,87999,88001,88007,88009,88011,88013,88019,88021],{},[898,87994,900],{},[1723,87996,1725],{},[898,87998,900],{},[1723,88000,1908],{"stretchy":1907},[1931,88002,88003,88005],{},[898,88004,1904],{},[1864,88006,1866],{},[1723,88008,2031],{"separator":2030},[1723,88010,2183],{},[1723,88012,2031],{"separator":2030},[1931,88014,88015,88017],{},[898,88016,1904],{},[898,88018,2192],{},[1723,88020,1914],{"stretchy":1907},[1723,88022,2031],{"separator":2030},[21455,88024],{"width":28769},[21455,88026,88027],{},[3018,88028,88029],{},"(6.1)",[902,88031,88032],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,88034,5022,88035,88065,88066,88088,88089,88092],{},[883,88036,88038],{"className":88037},[886],[888,88039,88040],{"xmlns":890},[892,88041,88042,88062],{},[895,88043,88044,88050,88052,88054,88056],{},[1931,88045,88046,88048],{},[898,88047,1904],{},[1864,88049,1866],{},[1723,88051,2031],{"separator":2030},[1723,88053,2183],{},[1723,88055,2031],{"separator":2030},[1931,88057,88058,88060],{},[898,88059,1904],{},[898,88061,2192],{},[902,88063,88064],{"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 ",[883,88067,88069],{"className":88068},[886],[888,88070,88071],{"xmlns":890},[892,88072,88073,88085],{},[895,88074,88075,88077,88079],{},[898,88076,900],{},[1723,88078,2031],{"separator":2030},[9096,88080,88081,88083],{"accent":2030},[898,88082,900],{},[1723,88084,87624],{},[902,88086,88087],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,88090,88091],{},"monotónní transformace"," zachovávající pořadí.",[724,88094,88095,88096,7725,88099,1664],{},"Dále se omezíme na funkce pro ",[38,88097,88098],{},"dvě zboží",[883,88100,88102],{"className":88101},[886],[888,88103,88104],{"xmlns":890},[892,88105,88106,88132],{},[895,88107,88108,88110,88112,88114,88116,88122,88124,88130],{},[898,88109,900],{},[1723,88111,1725],{},[898,88113,900],{},[1723,88115,1908],{"stretchy":1907},[1931,88117,88118,88120],{},[898,88119,1904],{},[1864,88121,1866],{},[1723,88123,2031],{"separator":2030},[1931,88125,88126,88128],{},[898,88127,1904],{},[1864,88129,2331],{},[1723,88131,1914],{"stretchy":1907},[902,88133,88134],{"encoding":904},"U = U(Q_1, Q_2)",[4584,88136,88137,88212],{},[724,88138,88139,88141,88142,3430],{},[883,88140,53385],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,88143,88145],{"className":88144},[886],[888,88146,88147],{"xmlns":890},[892,88148,88149,88209],{},[895,88150,88151,88153,88155,88157,88159,88165,88167,88173,88175,88181,88183,88185,88187],{},[898,88152,900],{},[1723,88154,1725],{},[898,88156,900],{},[1723,88158,1908],{"stretchy":1907},[1931,88160,88161,88163],{},[898,88162,1904],{},[1864,88164,1866],{},[1723,88166,2031],{"separator":2030},[1931,88168,88169,88171],{},[898,88170,1904],{},[1864,88172,2331],{},[1723,88174,2031],{"separator":2030},[1931,88176,88177,88179],{},[898,88178,1904],{},[1864,88180,2909],{},[1723,88182,1914],{"stretchy":1907},[1723,88184,1725],{},[1864,88186,2331],{},[8827,88188,88189],{},[895,88190,88191,88197,88203],{},[1931,88192,88193,88195],{},[898,88194,1904],{},[1864,88196,1866],{},[1931,88198,88199,88201],{},[898,88200,1904],{},[1864,88202,2331],{},[1931,88204,88205,88207],{},[898,88206,1904],{},[1864,88208,2909],{},[902,88210,88211],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,88213,88214,88407],{},[123,88215,88216,88217,88243,88244,13639,88270,1682,88329,6299,88389,9135],{},"svazek ",[883,88218,88220],{"className":88219},[886],[888,88221,88222],{"xmlns":890},[892,88223,88224,88240],{},[895,88225,88226,88228,88230,88232,88234,88236,88238],{},[1723,88227,1908],{"stretchy":1907},[1864,88229,42554],{},[1723,88231,2031],{"separator":2030},[1864,88233,3080],{},[1723,88235,2031],{"separator":2030},[1864,88237,42532],{},[1723,88239,1914],{"stretchy":1907},[902,88241,88242],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,88245,88247],{"className":88246},[886],[888,88248,88249],{"xmlns":890},[892,88250,88251,88267],{},[895,88252,88253,88255,88257,88259,88261,88263,88265],{},[1723,88254,1908],{"stretchy":1907},[1864,88256,4713],{},[1723,88258,2031],{"separator":2030},[1864,88260,4713],{},[1723,88262,2031],{"separator":2030},[1864,88264,67284],{},[1723,88266,1914],{"stretchy":1907},[902,88268,88269],{"encoding":904},"(9, 9, 27)",[883,88271,88273],{"className":88272},[886],[888,88274,88275],{"xmlns":890},[892,88276,88277,88326],{},[895,88278,88279,88281,88283,88285,88287,88289,88291,88293,88295,88297,88299,88313,88315,88317,88322,88324],{},[898,88280,900],{},[1723,88282,1908],{"stretchy":1907},[1864,88284,42554],{},[1723,88286,2031],{"separator":2030},[1864,88288,3080],{},[1723,88290,2031],{"separator":2030},[1864,88292,42532],{},[1723,88294,1914],{"stretchy":1907},[1723,88296,1725],{},[1864,88298,2331],{},[8827,88300,88301],{},[895,88302,88303,88305,88307,88309,88311],{},[1864,88304,42554],{},[1723,88306,3897],{},[1864,88308,3080],{},[1723,88310,3897],{},[1864,88312,42532],{},[1723,88314,1725],{},[1864,88316,2331],{},[8827,88318,88319],{},[1864,88320,88321],{},"4096",[1723,88323,1725],{},[1864,88325,6327],{},[902,88327,88328],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,88330,88332],{"className":88331},[886],[888,88333,88334],{"xmlns":890},[892,88335,88336,88386],{},[895,88337,88338,88340,88342,88344,88346,88348,88350,88352,88354,88356,88358,88372,88374,88376,88381,88383],{},[898,88339,900],{},[1723,88341,1908],{"stretchy":1907},[1864,88343,4713],{},[1723,88345,2031],{"separator":2030},[1864,88347,4713],{},[1723,88349,2031],{"separator":2030},[1864,88351,67284],{},[1723,88353,1914],{"stretchy":1907},[1723,88355,1725],{},[1864,88357,2331],{},[8827,88359,88360],{},[895,88361,88362,88364,88366,88368,88370],{},[1864,88363,4713],{},[1723,88365,3897],{},[1864,88367,4713],{},[1723,88369,3897],{},[1864,88371,67284],{},[1723,88373,1725],{},[1864,88375,2331],{},[8827,88377,88378],{},[1864,88379,88380],{},"2187",[1723,88382,6610],{},[1864,88384,88385],{},"93,53",[902,88387,88388],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,88390,88392],{"className":88391},[886],[888,88393,88394],{"xmlns":890},[892,88395,88396,88404],{},[895,88397,88398,88400,88402],{},[1864,88399,6327],{},[1723,88401,2253],{},[1864,88403,88385],{},[902,88405,88406],{"encoding":904},"128 > 93{,}53",[123,88408,88409,88410,1682,88436,88462,88463,1682,88503,88544,88545,88591,88592,1682,88618,3567,88644,1682,88662,88680,88681,1664],{},"svazky ",[883,88411,88413],{"className":88412},[886],[888,88414,88415],{"xmlns":890},[892,88416,88417,88433],{},[895,88418,88419,88421,88423,88425,88427,88429,88431],{},[1723,88420,1908],{"stretchy":1907},[1864,88422,3080],{},[1723,88424,2031],{"separator":2030},[1864,88426,6295],{},[1723,88428,2031],{"separator":2030},[1864,88430,2331],{},[1723,88432,1914],{"stretchy":1907},[902,88434,88435],{"encoding":904},"(4, 8, 2)",[883,88437,88439],{"className":88438},[886],[888,88440,88441],{"xmlns":890},[892,88442,88443,88459],{},[895,88444,88445,88447,88449,88451,88453,88455,88457],{},[1723,88446,1908],{"stretchy":1907},[1864,88448,42532],{},[1723,88450,2031],{"separator":2030},[1864,88452,1866],{},[1723,88454,2031],{"separator":2030},[1864,88456,3080],{},[1723,88458,1914],{"stretchy":1907},[902,88460,88461],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,88464,88466],{"className":88465},[886],[888,88467,88468],{"xmlns":890},[892,88469,88470,88500],{},[895,88471,88472,88474,88476,88478,88480,88482,88484,88486,88488,88490,88492,88496,88498],{},[898,88473,900],{},[1723,88475,1908],{"stretchy":1907},[1864,88477,3080],{},[1723,88479,2031],{"separator":2030},[1864,88481,6295],{},[1723,88483,2031],{"separator":2030},[1864,88485,2331],{},[1723,88487,1914],{"stretchy":1907},[1723,88489,1725],{},[1864,88491,2331],{},[8827,88493,88494],{},[1864,88495,42532],{},[1723,88497,1725],{},[1864,88499,42554],{},[902,88501,88502],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,88504,88506],{"className":88505},[886],[888,88507,88508],{"xmlns":890},[892,88509,88510,88541],{},[895,88511,88512,88514,88516,88518,88520,88522,88524,88526,88528,88530,88532,88537,88539],{},[898,88513,900],{},[1723,88515,1908],{"stretchy":1907},[1864,88517,42532],{},[1723,88519,2031],{"separator":2030},[1864,88521,1866],{},[1723,88523,2031],{"separator":2030},[1864,88525,3080],{},[1723,88527,1914],{"stretchy":1907},[1723,88529,1725],{},[1864,88531,2331],{},[8827,88533,88534],{},[1864,88535,88536],{},"256",[1723,88538,1725],{},[1864,88540,73044],{},[902,88542,88543],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,88546,88548],{"className":88547},[886],[888,88549,88550],{"xmlns":890},[892,88551,88552,88588],{},[895,88553,88554,88556,88558,88560,88562,88564,88566,88568,88570,88572,88574,88576,88578,88580,88582,88584,88586],{},[898,88555,900],{},[1723,88557,1908],{"stretchy":1907},[1864,88559,3080],{},[1723,88561,2031],{"separator":2030},[1864,88563,6295],{},[1723,88565,2031],{"separator":2030},[1864,88567,2331],{},[1723,88569,1914],{"stretchy":1907},[1723,88571,1725],{},[898,88573,900],{},[1723,88575,1908],{"stretchy":1907},[1864,88577,42532],{},[1723,88579,2031],{"separator":2030},[1864,88581,1866],{},[1723,88583,2031],{"separator":2030},[1864,88585,3080],{},[1723,88587,1914],{"stretchy":1907},[902,88589,88590],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,88593,88595],{"className":88594},[886],[888,88596,88597],{"xmlns":890},[892,88598,88599,88615],{},[895,88600,88601,88603,88605,88607,88609,88611,88613],{},[1864,88602,3080],{},[1723,88604,3897],{},[1864,88606,6295],{},[1723,88608,3897],{},[1864,88610,2331],{},[1723,88612,1725],{},[1864,88614,42532],{},[902,88616,88617],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,88619,88621],{"className":88620},[886],[888,88622,88623],{"xmlns":890},[892,88624,88625,88641],{},[895,88626,88627,88629,88631,88633,88635,88637,88639],{},[1864,88628,42532],{},[1723,88630,3897],{},[1864,88632,1866],{},[1723,88634,3897],{},[1864,88636,3080],{},[1723,88638,1725],{},[1864,88640,88536],{},[902,88642,88643],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,88645,88647],{"className":88646},[886],[888,88648,88649],{"xmlns":890},[892,88650,88651,88659],{},[895,88652,88653,88655,88657],{},[898,88654,900],{},[1723,88656,1725],{},[1864,88658,42554],{},[902,88660,88661],{"encoding":904},"U = 16",[883,88663,88665],{"className":88664},[886],[888,88666,88667],{"xmlns":890},[892,88668,88669,88677],{},[895,88670,88671,88673,88675],{},[898,88672,900],{},[1723,88674,1725],{},[1864,88676,73044],{},[902,88678,88679],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,88682,88684],{"className":88683},[886],[888,88685,88686],{"xmlns":890},[892,88687,88688,88708],{},[895,88689,88690,88696,88702],{},[1931,88691,88692,88694],{},[898,88693,1904],{},[1864,88695,1866],{},[1931,88697,88698,88700],{},[898,88699,1904],{},[1864,88701,2331],{},[1931,88703,88704,88706],{},[898,88705,1904],{},[1864,88707,2909],{},[902,88709,88710],{"encoding":904},"Q_1 Q_2 Q_3",[115,88712,88714],{"id":88713},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,88716,88717,88718,8812,88753,2628,88756,42506,88773,1981,88790,88793,88794,88797],{},"Pro funkci užitečnosti ",[883,88719,88721],{"className":88720},[886],[888,88722,88723],{"xmlns":890},[892,88724,88725,88751],{},[895,88726,88727,88729,88731,88733,88735,88741,88743,88749],{},[898,88728,900],{},[1723,88730,1725],{},[898,88732,900],{},[1723,88734,1908],{"stretchy":1907},[1931,88736,88737,88739],{},[898,88738,1904],{},[1864,88740,1866],{},[1723,88742,2031],{"separator":2030},[1931,88744,88745,88747],{},[898,88746,1904],{},[1864,88748,2331],{},[1723,88750,1914],{"stretchy":1907},[902,88752,88134],{"encoding":904},[38,88754,88755],{},"mezní užitečnost",[883,88757,88759],{"className":88758},[886],[888,88760,88761],{"xmlns":890},[892,88762,88763,88771],{},[895,88764,88765],{},[1931,88766,88767,88769],{},[898,88768,1904],{},[1864,88770,1866],{},[902,88772,29695],{"encoding":904},[883,88774,88776],{"className":88775},[886],[888,88777,88778],{"xmlns":890},[892,88779,88780,88788],{},[895,88781,88782],{},[1931,88783,88784,88786],{},[898,88785,1904],{},[1864,88787,2331],{},[902,88789,29714],{"encoding":904},[38,88791,88792],{},"marginal utility",") parciální ",[207,88795,1145],{"className":88796,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,88799,88801],{"className":88800},[886],[888,88802,88803],{"xmlns":890,"display":28759},[892,88804,88805,88904],{},[21447,88806,88807],{"width":28764},[21452,88808,88809,88811,88897,88899],{},[21455,88810],{"width":28769},[21455,88812,88813],{},[895,88814,88815,88817,88823,88825,88833,88835,88853,88855,88857,88859,88865,88867,88875,88877,88895],{},[898,88816,1728],{},[1931,88818,88819,88821],{},[898,88820,900],{},[1864,88822,1866],{},[1723,88824,1725],{},[2220,88826,88827,88829,88831],{},[898,88828,900],{},[1864,88830,1866],{},[1723,88832,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,88834,1725],{},[3058,88836,88837,88843],{},[895,88838,88839,88841],{},[898,88840,10574],{"mathvariant":2124},[898,88842,900],{},[895,88844,88845,88847],{},[898,88846,10574],{"mathvariant":2124},[1931,88848,88849,88851],{},[898,88850,1904],{},[1864,88852,1866],{},[1723,88854,2031],{"separator":2030},[6588,88856],{"width":15985},[898,88858,1728],{},[1931,88860,88861,88863],{},[898,88862,900],{},[1864,88864,2331],{},[1723,88866,1725],{},[2220,88868,88869,88871,88873],{},[898,88870,900],{},[1864,88872,2331],{},[1723,88874,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,88876,1725],{},[3058,88878,88879,88885],{},[895,88880,88881,88883],{},[898,88882,10574],{"mathvariant":2124},[898,88884,900],{},[895,88886,88887,88889],{},[898,88888,10574],{"mathvariant":2124},[1931,88890,88891,88893],{},[898,88892,1904],{},[1864,88894,2331],{},[898,88896,1664],{"mathvariant":2124},[21455,88898],{"width":28769},[21455,88900,88901],{},[3018,88902,88903],{},"(6.2)",[902,88905,88906],{"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}",[724,88908,88909,88910,88944,88945,88975,88976,2628,88979,1664],{},"Pro pevné ",[883,88911,88913],{"className":88912},[886],[888,88914,88915],{"xmlns":890},[892,88916,88917,88941],{},[895,88918,88919,88925,88927,88929,88931,88937,88939],{},[1931,88920,88921,88923],{},[898,88922,1904],{},[1864,88924,1866],{},[1723,88926,1725],{},[898,88928,207],{},[1723,88930,2031],{"separator":2030},[1931,88932,88933,88935],{},[898,88934,1904],{},[1864,88936,2331],{},[1723,88938,1725],{},[898,88940,2069],{},[902,88942,88943],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,88946,88948],{"className":88947},[886],[888,88949,88950],{"xmlns":890},[892,88951,88952,88972],{},[895,88953,88954,88956,88962,88964,88966,88968,88970],{},[898,88955,1728],{},[1931,88957,88958,88960],{},[898,88959,900],{},[1864,88961,1866],{},[1723,88963,1908],{"stretchy":1907},[898,88965,207],{},[1723,88967,2031],{"separator":2030},[898,88969,2069],{},[1723,88971,1914],{"stretchy":1907},[902,88973,88974],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,88977,88978],{},"v bodě (na hladině)",[883,88980,88982],{"className":88981},[886],[888,88983,88984],{"xmlns":890},[892,88985,88986,88998],{},[895,88987,88988,88990,88992,88994,88996],{},[1723,88989,3212],{"stretchy":1907},[898,88991,207],{},[1723,88993,2031],{"separator":2030},[898,88995,2069],{},[1723,88997,3227],{"stretchy":1907},[902,88999,11524],{"encoding":904},[4584,89001,89002],{},[724,89003,89004,89006,89007,89037,89066,89067,3336,89080,3350,89097,89118,89119,3397,89136,3411,89149,89166,89167,89189,89190,89219,89220,7183,89240,89257],{},[883,89005,4869],{}," Intuice — co říká ",[883,89008,89010],{"className":89009},[886],[888,89011,89012],{"xmlns":890},[892,89013,89014,89034],{},[895,89015,89016,89018,89024,89026,89028,89030,89032],{},[898,89017,1728],{},[1931,89019,89020,89022],{},[898,89021,900],{},[1864,89023,1866],{},[1723,89025,1908],{"stretchy":1907},[898,89027,207],{},[1723,89029,2031],{"separator":2030},[898,89031,2069],{},[1723,89033,1914],{"stretchy":1907},[902,89035,89036],{"encoding":904},"MU_1(a,b)",[883,89038,89040],{"className":89039},[886],[888,89041,89042],{"xmlns":890},[892,89043,89044,89064],{},[895,89045,89046,89048,89054,89056,89058,89060,89062],{},[898,89047,1728],{},[1931,89049,89050,89052],{},[898,89051,900],{},[1864,89053,1866],{},[1723,89055,1908],{"stretchy":1907},[898,89057,207],{},[1723,89059,2031],{"separator":2030},[898,89061,2069],{},[1723,89063,1914],{"stretchy":1907},[902,89065,88974],{"encoding":904}," je rychlost změny ",[883,89068,89070],{"className":89069},[886],[888,89071,89072],{"xmlns":890},[892,89073,89074,89078],{},[895,89075,89076],{},[898,89077,900],{},[902,89079,900],{"encoding":904},[883,89081,89083],{"className":89082},[886],[888,89084,89085],{"xmlns":890},[892,89086,89087,89095],{},[895,89088,89089],{},[1931,89090,89091,89093],{},[898,89092,1904],{},[1864,89094,1866],{},[902,89096,29695],{"encoding":904},[883,89098,89100],{"className":89099},[886],[888,89101,89102],{"xmlns":890},[892,89103,89104,89116],{},[895,89105,89106,89108,89110,89112,89114],{},[1723,89107,3212],{"stretchy":1907},[898,89109,207],{},[1723,89111,2031],{"separator":2030},[898,89113,2069],{},[1723,89115,3227],{"stretchy":1907},[902,89117,11524],{"encoding":904},". Přibližně: změní-li se ",[883,89120,89122],{"className":89121},[886],[888,89123,89124],{"xmlns":890},[892,89125,89126,89134],{},[895,89127,89128],{},[1931,89129,89130,89132],{},[898,89131,1904],{},[1864,89133,1866],{},[902,89135,29695],{"encoding":904},[883,89137,89139],{"className":89138},[886],[888,89140,89141],{"xmlns":890},[892,89142,89143,89147],{},[895,89144,89145],{},[898,89146,207],{},[902,89148,207],{"encoding":904},[883,89150,89152],{"className":89151},[886],[888,89153,89154],{"xmlns":890},[892,89155,89156,89164],{},[895,89157,89158,89160,89162],{},[898,89159,207],{},[1723,89161,2087],{},[1864,89163,1866],{},[902,89165,3429],{"encoding":904}," při pevném ",[883,89168,89170],{"className":89169},[886],[888,89171,89172],{"xmlns":890},[892,89173,89174,89186],{},[895,89175,89176,89182,89184],{},[1931,89177,89178,89180],{},[898,89179,1904],{},[1864,89181,2331],{},[1723,89183,1725],{},[898,89185,2069],{},[902,89187,89188],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,89191,89193],{"className":89192},[886],[888,89194,89195],{"xmlns":890},[892,89196,89197,89217],{},[895,89198,89199,89201,89207,89209,89211,89213,89215],{},[898,89200,1728],{},[1931,89202,89203,89205],{},[898,89204,900],{},[1864,89206,1866],{},[1723,89208,1908],{"stretchy":1907},[898,89210,207],{},[1723,89212,2031],{"separator":2030},[898,89214,2069],{},[1723,89216,1914],{"stretchy":1907},[902,89218,88974],{"encoding":904},". Stejně tak ",[883,89221,89223],{"className":89222},[886],[888,89224,89225],{"xmlns":890},[892,89226,89227,89237],{},[895,89228,89229,89231],{},[898,89230,1728],{},[1931,89232,89233,89235],{},[898,89234,900],{},[1864,89236,2331],{},[902,89238,89239],{"encoding":904},"MU_2",[883,89241,89243],{"className":89242},[886],[888,89244,89245],{"xmlns":890},[892,89246,89247,89255],{},[895,89248,89249],{},[1931,89250,89251,89253],{},[898,89252,1904],{},[1864,89254,2331],{},[902,89256,29714],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,89259,80892],{"id":89260},"totální-diferenciál",[724,89262,89263,89264,49031,89280,89310,89311,3430],{},"Přibližnou změnu užitečnosti ",[883,89265,89267],{"className":89266},[886],[888,89268,89269],{"xmlns":890},[892,89270,89271,89277],{},[895,89272,89273,89275],{},[898,89274,3611],{"mathvariant":2124},[898,89276,900],{},[902,89278,89279],{"encoding":904},"\\Delta U",[883,89281,89283],{"className":89282},[886],[888,89284,89285],{"xmlns":890},[892,89286,89287,89307],{},[895,89288,89289,89291,89297,89299,89301],{},[898,89290,2930],{"mathvariant":2124},[1931,89292,89293,89295],{},[898,89294,1904],{},[1864,89296,1866],{},[1723,89298,2031],{"separator":2030},[898,89300,2930],{"mathvariant":2124},[1931,89302,89303,89305],{},[898,89304,1904],{},[1864,89306,2331],{},[902,89308,89309],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,89312,89313],{},"totálního diferenciálu",[883,89315,89317],{"className":89316},[886],[888,89318,89319],{"xmlns":890,"display":28759},[892,89320,89321,89422],{},[21447,89322,89323],{"width":28764},[21452,89324,89325,89327,89415,89417],{},[21455,89326],{"width":28769},[21455,89328,89329],{},[895,89330,89331,89333,89335,89337,89339,89341,89343,89351,89353,89359,89361,89369,89371,89377,89379,89381,89387,89389,89395,89397,89399,89405,89407,89413],{},[898,89332,3611],{"mathvariant":2124},[898,89334,900],{},[1723,89336,3456],{},[898,89338,2930],{"mathvariant":2124},[898,89340,900],{},[1723,89342,1725],{},[2220,89344,89345,89347,89349],{},[898,89346,900],{},[1864,89348,1866],{},[1723,89350,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[898,89352,2930],{"mathvariant":2124},[1931,89354,89355,89357],{},[898,89356,1904],{},[1864,89358,1866],{},[1723,89360,2087],{},[2220,89362,89363,89365,89367],{},[898,89364,900],{},[1864,89366,2331],{},[1723,89368,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[898,89370,2930],{"mathvariant":2124},[1931,89372,89373,89375],{},[898,89374,1904],{},[1864,89376,2331],{},[1723,89378,1725],{},[898,89380,1728],{},[1931,89382,89383,89385],{},[898,89384,900],{},[1864,89386,1866],{},[898,89388,2930],{"mathvariant":2124},[1931,89390,89391,89393],{},[898,89392,1904],{},[1864,89394,1866],{},[1723,89396,2087],{},[898,89398,1728],{},[1931,89400,89401,89403],{},[898,89402,900],{},[1864,89404,2331],{},[898,89406,2930],{"mathvariant":2124},[1931,89408,89409,89411],{},[898,89410,1904],{},[1864,89412,2331],{},[898,89414,1664],{"mathvariant":2124},[21455,89416],{"width":28769},[21455,89418,89419],{},[3018,89420,89421],{},"(6.3)",[902,89423,89424],{"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}",[724,89426,76150,89427,1664],{},[883,89428,89430],{"className":89429},[886],[888,89431,89432],{"xmlns":890},[892,89433,89434,89504],{},[895,89435,89436,89438,89440,89442,89444,89446,89452,89454,89456,89462,89464,89470,89472,89474,89480,89482,89484,89486,89488,89494,89496,89502],{},[898,89437,3611],{"mathvariant":2124},[898,89439,900],{},[1723,89441,1725],{},[898,89443,900],{},[1723,89445,1908],{"stretchy":1907},[1931,89447,89448,89450],{},[898,89449,1904],{},[1864,89451,1866],{},[1723,89453,2087],{},[898,89455,2930],{"mathvariant":2124},[1931,89457,89458,89460],{},[898,89459,1904],{},[1864,89461,1866],{},[1723,89463,2031],{"separator":2030},[1931,89465,89466,89468],{},[898,89467,1904],{},[1864,89469,2331],{},[1723,89471,2087],{},[898,89473,2930],{"mathvariant":2124},[1931,89475,89476,89478],{},[898,89477,1904],{},[1864,89479,2331],{},[1723,89481,1914],{"stretchy":1907},[1723,89483,1759],{},[898,89485,900],{},[1723,89487,1908],{"stretchy":1907},[1931,89489,89490,89492],{},[898,89491,1904],{},[1864,89493,1866],{},[1723,89495,2031],{"separator":2030},[1931,89497,89498,89500],{},[898,89499,1904],{},[1864,89501,2331],{},[1723,89503,1914],{"stretchy":1907},[902,89505,89506],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,89508,89510],{"id":89509},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,89512,89513,89514,89517,89518,89521],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,89515,89516],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,89519,89520],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,89523,89524,89527,89528,42506,89554,89580,89581,1343,89613,89645,89646,1682,89700,89754],{},[38,89525,89526],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,89529,89531],{"className":89530},[886],[888,89532,89533],{"xmlns":890},[892,89534,89535,89551],{},[895,89536,89537,89543,89545],{},[1931,89538,89539,89541],{},[898,89540,1904],{},[1864,89542,2331],{},[1723,89544,1725],{},[1931,89546,89547,89549],{},[898,89548,207],{},[1864,89550,2256],{},[902,89552,89553],{"encoding":904},"Q_2 = a_0",[883,89555,89557],{"className":89556},[886],[888,89558,89559],{"xmlns":890},[892,89560,89561,89577],{},[895,89562,89563,89569,89571],{},[1931,89564,89565,89567],{},[898,89566,1904],{},[1864,89568,1866],{},[1723,89570,1725],{},[1931,89572,89573,89575],{},[898,89574,2069],{},[1864,89576,2256],{},[902,89578,89579],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,89582,89584],{"className":89583},[886],[888,89585,89586],{"xmlns":890},[892,89587,89588,89610],{},[895,89589,89590,89592,89594,89600,89602,89608],{},[898,89591,900],{},[1723,89593,1908],{"stretchy":1907},[1931,89595,89596,89598],{},[898,89597,1904],{},[1864,89599,1866],{},[1723,89601,2031],{"separator":2030},[1931,89603,89604,89606],{},[898,89605,207],{},[1864,89607,2256],{},[1723,89609,1914],{"stretchy":1907},[902,89611,89612],{"encoding":904},"U(Q_1, a_0)",[883,89614,89616],{"className":89615},[886],[888,89617,89618],{"xmlns":890},[892,89619,89620,89642],{},[895,89621,89622,89624,89626,89632,89634,89640],{},[898,89623,900],{},[1723,89625,1908],{"stretchy":1907},[1931,89627,89628,89630],{},[898,89629,2069],{},[1864,89631,2256],{},[1723,89633,2031],{"separator":2030},[1931,89635,89636,89638],{},[898,89637,1904],{},[1864,89639,2331],{},[1723,89641,1914],{"stretchy":1907},[902,89643,89644],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,89647,89649],{"className":89648},[886],[888,89650,89651],{"xmlns":890},[892,89652,89653,89697],{},[895,89654,89655,89693,89695],{},[3055,89656,89657],{"scriptlevel":2256,"displaystyle":2030},[3058,89658,89659,89683],{},[895,89660,89661,89663,89665,89667,89673,89675,89681],{},[898,89662,2930],{"mathvariant":2124},[898,89664,900],{},[1723,89666,1908],{"stretchy":1907},[1931,89668,89669,89671],{},[898,89670,1904],{},[1864,89672,1866],{},[1723,89674,2031],{"separator":2030},[1931,89676,89677,89679],{},[898,89678,207],{},[1864,89680,2256],{},[1723,89682,1914],{"stretchy":1907},[895,89684,89685,89687],{},[898,89686,2930],{"mathvariant":2124},[1931,89688,89689,89691],{},[898,89690,1904],{},[1864,89692,1866],{},[1723,89694,2253],{},[1864,89696,2256],{},[902,89698,89699],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,89701,89703],{"className":89702},[886],[888,89704,89705],{"xmlns":890},[892,89706,89707,89751],{},[895,89708,89709,89747,89749],{},[3055,89710,89711],{"scriptlevel":2256,"displaystyle":2030},[3058,89712,89713,89737],{},[895,89714,89715,89717,89719,89721,89727,89729,89735],{},[898,89716,2930],{"mathvariant":2124},[898,89718,900],{},[1723,89720,1908],{"stretchy":1907},[1931,89722,89723,89725],{},[898,89724,2069],{},[1864,89726,2256],{},[1723,89728,2031],{"separator":2030},[1931,89730,89731,89733],{},[898,89732,1904],{},[1864,89734,2331],{},[1723,89736,1914],{"stretchy":1907},[895,89738,89739,89741],{},[898,89740,2930],{"mathvariant":2124},[1931,89742,89743,89745],{},[898,89744,1904],{},[1864,89746,2331],{},[1723,89748,2253],{},[1864,89750,2256],{},[902,89752,89753],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,89756,89758],{"className":89757},[886],[888,89759,89760],{"xmlns":890,"display":28759},[892,89761,89762,89807],{},[21447,89763,89764],{"width":28764},[21452,89765,89766,89768,89800,89802],{},[21455,89767],{"width":28769},[21455,89769,89770],{},[895,89771,89772,89780,89782,89784,89786,89788,89796,89798],{},[2220,89773,89774,89776,89778],{},[898,89775,900],{},[1864,89777,1866],{},[1723,89779,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,89781,2253],{},[1864,89783,2256],{},[1723,89785,2031],{"separator":2030},[6588,89787],{"width":15985},[2220,89789,89790,89792,89794],{},[898,89791,900],{},[1864,89793,2331],{},[1723,89795,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,89797,2253],{},[1864,89799,13161],{},[21455,89801],{"width":28769},[21455,89803,89804],{},[3018,89805,89806],{},"(6.4)",[902,89808,89809],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,89811,89812,89813,89815],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,89814,53367],{}," — užitečnost roste s množstvím každého zboží.",[724,89817,89818,89821,89822,89852,89853,3430],{},[38,89819,89820],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,89823,89825],{"className":89824},[886],[888,89826,89827],{"xmlns":890},[892,89828,89829,89849],{},[895,89830,89831,89839,89841],{},[2220,89832,89833,89835,89837],{},[898,89834,900],{},[1864,89836,1866],{},[1723,89838,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,89840,2031],{"separator":2030},[2220,89842,89843,89845,89847],{},[898,89844,900],{},[1864,89846,2331],{},[1723,89848,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,89850,89851],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,89854,89855],{},"záporné",[883,89857,89859],{"className":89858},[886],[888,89860,89861],{"xmlns":890,"display":28759},[892,89862,89863,89916],{},[21447,89864,89865],{"width":28764},[21452,89866,89867,89869,89909,89911],{},[21455,89868],{"width":28769},[21455,89870,89871],{},[895,89872,89873,89885,89887,89889,89891,89893,89905,89907],{},[2220,89874,89875,89877,89879],{},[898,89876,900],{},[1864,89878,3626],{},[895,89880,89881,89883],{},[1723,89882,2229],{"mathvariant":2124},[1723,89884,2229],{"mathvariant":2124},[1723,89886,2287],{},[1864,89888,2256],{},[1723,89890,2031],{"separator":2030},[6588,89892],{"width":15985},[2220,89894,89895,89897,89899],{},[898,89896,900],{},[1864,89898,33239],{},[895,89900,89901,89903],{},[1723,89902,2229],{"mathvariant":2124},[1723,89904,2229],{"mathvariant":2124},[1723,89906,2287],{},[1864,89908,13161],{},[21455,89910],{"width":28769},[21455,89912,89913],{},[3018,89914,89915],{},"(6.5)",[902,89917,89918],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,89920,89921,89922,89925,89926,1664],{},"Podmínka (6.5) je známa jako ",[38,89923,89924],{},"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 ",[207,89927,89929],{"className":89928,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,89931,89932,89933,1682,89965,89997,89998,1682,90024,90050,90051,90079,90080,1682,90082,90084,90085,90120],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,89934,89936],{"className":89935},[886],[888,89937,89938],{"xmlns":890},[892,89939,89940,89962],{},[895,89941,89942,89944,89946,89952,89954,89960],{},[898,89943,900],{},[1723,89945,1908],{"stretchy":1907},[1931,89947,89948,89950],{},[898,89949,1904],{},[1864,89951,1866],{},[1723,89953,2031],{"separator":2030},[1931,89955,89956,89958],{},[898,89957,2069],{},[1864,89959,2256],{},[1723,89961,1914],{"stretchy":1907},[902,89963,89964],{"encoding":904},"U(Q_1, b_0)",[883,89966,89968],{"className":89967},[886],[888,89969,89970],{"xmlns":890},[892,89971,89972,89994],{},[895,89973,89974,89976,89978,89984,89986,89992],{},[898,89975,900],{},[1723,89977,1908],{"stretchy":1907},[1931,89979,89980,89982],{},[898,89981,207],{},[1864,89983,2256],{},[1723,89985,2031],{"separator":2030},[1931,89987,89988,89990],{},[898,89989,1904],{},[1864,89991,2331],{},[1723,89993,1914],{"stretchy":1907},[902,89995,89996],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,89999,90001],{"className":90000},[886],[888,90002,90003],{"xmlns":890},[892,90004,90005,90021],{},[895,90006,90007,90009,90011,90013,90019],{},[1723,90008,1908],{"stretchy":1907},[898,90010,900],{},[1723,90012,2031],{"separator":2030},[1931,90014,90015,90017],{},[898,90016,1904],{},[1864,90018,1866],{},[1723,90020,1914],{"stretchy":1907},[902,90022,90023],{"encoding":904},"(U, Q_1)",[883,90025,90027],{"className":90026},[886],[888,90028,90029],{"xmlns":890},[892,90030,90031,90047],{},[895,90032,90033,90035,90037,90039,90045],{},[1723,90034,1908],{"stretchy":1907},[898,90036,900],{},[1723,90038,2031],{"separator":2030},[1931,90040,90041,90043],{},[898,90042,1904],{},[1864,90044,2331],{},[1723,90046,1914],{"stretchy":1907},[902,90048,90049],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,90052,90054],{"className":90053},[886],[888,90055,90056],{"xmlns":890},[892,90057,90058,90076],{},[895,90059,90060,90062,90064,90066,90068,90070,90072,90074],{},[898,90061,900],{},[1723,90063,1908],{"stretchy":1907},[1864,90065,2256],{},[1723,90067,2031],{"separator":2030},[1864,90069,2256],{},[1723,90071,1914],{"stretchy":1907},[1723,90073,1725],{},[1864,90075,2256],{},[902,90077,90078],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,90081,14358],{},[38,90083,39180],{},". Typický tvar grafu ",[883,90086,90088],{"className":90087},[886],[888,90089,90090],{"xmlns":890},[892,90091,90092,90118],{},[895,90093,90094,90096,90098,90100,90102,90108,90110,90116],{},[898,90095,900],{},[1723,90097,1725],{},[898,90099,900],{},[1723,90101,1908],{"stretchy":1907},[1931,90103,90104,90106],{},[898,90105,1904],{},[1864,90107,1866],{},[1723,90109,2031],{"separator":2030},[1931,90111,90112,90114],{},[898,90113,1904],{},[1864,90115,2331],{},[1723,90117,1914],{"stretchy":1907},[902,90119,88134],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,90122,90123],{},[614,90124,90125,90126,89166,90154,90175,90176,89166,90204,90226],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,90127,90129],{"className":90128},[886],[888,90130,90131],{"xmlns":890},[892,90132,90133,90151],{},[895,90134,90135,90137,90139,90145,90147,90149],{},[898,90136,900],{},[1723,90138,1908],{"stretchy":1907},[1931,90140,90141,90143],{},[898,90142,1904],{},[1864,90144,1866],{},[1723,90146,2031],{"separator":2030},[898,90148,2069],{},[1723,90150,1914],{"stretchy":1907},[902,90152,90153],{"encoding":904},"U(Q_1, b)",[883,90155,90157],{"className":90156},[886],[888,90158,90159],{"xmlns":890},[892,90160,90161,90173],{},[895,90162,90163,90169,90171],{},[1931,90164,90165,90167],{},[898,90166,1904],{},[1864,90168,2331],{},[1723,90170,1725],{},[898,90172,2069],{},[902,90174,89188],{"encoding":904}," (vlevo) a ",[883,90177,90179],{"className":90178},[886],[888,90180,90181],{"xmlns":890},[892,90182,90183,90201],{},[895,90184,90185,90187,90189,90191,90193,90199],{},[898,90186,900],{},[1723,90188,1908],{"stretchy":1907},[898,90190,207],{},[1723,90192,2031],{"separator":2030},[1931,90194,90195,90197],{},[898,90196,1904],{},[1864,90198,2331],{},[1723,90200,1914],{"stretchy":1907},[902,90202,90203],{"encoding":904},"U(a, Q_2)",[883,90205,90207],{"className":90206},[886],[888,90208,90209],{"xmlns":890},[892,90210,90211,90223],{},[895,90212,90213,90219,90221],{},[1931,90214,90215,90217],{},[898,90216,1904],{},[1864,90218,1866],{},[1723,90220,1725],{},[898,90222,207],{},[902,90224,90225],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,90228,90229],{},[614,90230,90231,90232,90267,90268,90298,90299,1682,90322,90344,90345,1664],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,90233,90235],{"className":90234},[886],[888,90236,90237],{"xmlns":890},[892,90238,90239,90265],{},[895,90240,90241,90243,90245,90247,90249,90255,90257,90263],{},[898,90242,900],{},[1723,90244,1725],{},[898,90246,900],{},[1723,90248,1908],{"stretchy":1907},[1931,90250,90251,90253],{},[898,90252,1904],{},[1864,90254,1866],{},[1723,90256,2031],{"separator":2030},[1931,90258,90259,90261],{},[898,90260,1904],{},[1864,90262,2331],{},[1723,90264,1914],{"stretchy":1907},[902,90266,88134],{"encoding":904}," nad rovinou ",[883,90269,90271],{"className":90270},[886],[888,90272,90273],{"xmlns":890},[892,90274,90275,90295],{},[895,90276,90277,90279,90285,90287,90293],{},[1723,90278,1908],{"stretchy":1907},[1931,90280,90281,90283],{},[898,90282,1904],{},[1864,90284,1866],{},[1723,90286,2031],{"separator":2030},[1931,90288,90289,90291],{},[898,90290,1904],{},[1864,90292,2331],{},[1723,90294,1914],{"stretchy":1907},[902,90296,90297],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,90300,90302],{"className":90301},[886],[888,90303,90304],{"xmlns":890},[892,90305,90306,90319],{},[895,90307,90308,90314,90316],{},[1931,90309,90310,90312],{},[898,90311,1904],{},[1864,90313,1866],{},[1723,90315,1725],{},[3018,90317,90318],{},"const",[902,90320,90321],{"encoding":904},"Q_1 = \\text{const}",[883,90323,90325],{"className":90324},[886],[888,90326,90327],{"xmlns":890},[892,90328,90329,90341],{},[895,90330,90331,90337,90339],{},[1931,90332,90333,90335],{},[898,90334,1904],{},[1864,90336,2331],{},[1723,90338,1725],{},[3018,90340,90318],{},[902,90342,90343],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,90346,90348],{"className":90347},[886],[888,90349,90350],{"xmlns":890},[892,90351,90352,90378],{},[895,90353,90354,90356,90358,90364,90366,90372,90374,90376],{},[898,90355,900],{},[1723,90357,1908],{"stretchy":1907},[1931,90359,90360,90362],{},[898,90361,1904],{},[1864,90363,1866],{},[1723,90365,2031],{"separator":2030},[1931,90367,90368,90370],{},[898,90369,1904],{},[1864,90371,2331],{},[1723,90373,1914],{"stretchy":1907},[1723,90375,1725],{},[898,90377,2878],{},[902,90379,10474],{"encoding":904},[198,90381,90383,90384],{"id":90382},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,90385,90387],{"className":90386},[886],[888,90388,90389],{"xmlns":890},[892,90390,90391,90425],{},[895,90392,90393,90395,90397,90411],{},[898,90394,900],{},[1723,90396,1725],{},[2220,90398,90399,90401,90403],{},[898,90400,1904],{},[1864,90402,1866],{},[895,90404,90405,90407,90409],{},[1864,90406,1866],{},[898,90408,2125],{"mathvariant":2124},[1864,90410,2331],{},[2220,90412,90413,90415,90417],{},[898,90414,1904],{},[1864,90416,2331],{},[895,90418,90419,90421,90423],{},[1864,90420,1866],{},[898,90422,2125],{"mathvariant":2124},[1864,90424,2909],{},[902,90426,90427],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,90429,90430],{},[38,90431,90432],{},"Ověření (6.4) a (6.5).",[883,90434,90436],{"className":90435},[886],[888,90437,90438],{"xmlns":890,"display":28759},[892,90439,90440,90544],{},[895,90441,90442,90450,90452,90460,90476,90490,90492,90494,90502,90504,90512,90526,90542],{},[2220,90443,90444,90446,90448],{},[898,90445,900],{},[1864,90447,1866],{},[1723,90449,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,90451,1725],{},[3055,90453,90454],{"scriptlevel":2256,"displaystyle":1907},[3058,90455,90456,90458],{},[1864,90457,1866],{},[1864,90459,2331],{},[2220,90461,90462,90464,90466],{},[898,90463,1904],{},[1864,90465,1866],{},[895,90467,90468,90470,90472,90474],{},[1723,90469,1759],{},[1864,90471,1866],{},[898,90473,2125],{"mathvariant":2124},[1864,90475,2331],{},[2220,90477,90478,90480,90482],{},[898,90479,1904],{},[1864,90481,2331],{},[895,90483,90484,90486,90488],{},[1864,90485,1866],{},[898,90487,2125],{"mathvariant":2124},[1864,90489,2909],{},[1723,90491,2031],{"separator":2030},[6588,90493],{"width":15985},[2220,90495,90496,90498,90500],{},[898,90497,900],{},[1864,90499,2331],{},[1723,90501,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,90503,1725],{},[3055,90505,90506],{"scriptlevel":2256,"displaystyle":1907},[3058,90507,90508,90510],{},[1864,90509,1866],{},[1864,90511,2909],{},[2220,90513,90514,90516,90518],{},[898,90515,1904],{},[1864,90517,1866],{},[895,90519,90520,90522,90524],{},[1864,90521,1866],{},[898,90523,2125],{"mathvariant":2124},[1864,90525,2331],{},[2220,90527,90528,90530,90532],{},[898,90529,1904],{},[1864,90531,2331],{},[895,90533,90534,90536,90538,90540],{},[1723,90535,1759],{},[1864,90537,2331],{},[898,90539,2125],{"mathvariant":2124},[1864,90541,2909],{},[1723,90543,2031],{"separator":2030},[902,90545,90546],{"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},",[724,90548,90549,90550,90584],{},"zřejmě ",[883,90551,90553],{"className":90552},[886],[888,90554,90555],{"xmlns":890},[892,90556,90557,90581],{},[895,90558,90559,90567,90569,90577,90579],{},[2220,90560,90561,90563,90565],{},[898,90562,900],{},[1864,90564,1866],{},[1723,90566,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,90568,2031],{"separator":2030},[2220,90570,90571,90573,90575],{},[898,90572,900],{},[1864,90574,2331],{},[1723,90576,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,90578,2253],{},[1864,90580,2256],{},[902,90582,90583],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,90586,90588],{"className":90587},[886],[888,90589,90590],{"xmlns":890,"display":28759},[892,90591,90592,90708],{},[895,90593,90594,90606,90608,90610,90618,90634,90648,90650,90652,90664,90666,90668,90676,90690,90706],{},[2220,90595,90596,90598,90600],{},[898,90597,900],{},[1864,90599,3626],{},[895,90601,90602,90604],{},[1723,90603,2229],{"mathvariant":2124},[1723,90605,2229],{"mathvariant":2124},[1723,90607,1725],{},[1723,90609,1759],{},[3055,90611,90612],{"scriptlevel":2256,"displaystyle":1907},[3058,90613,90614,90616],{},[1864,90615,1866],{},[1864,90617,3080],{},[2220,90619,90620,90622,90624],{},[898,90621,1904],{},[1864,90623,1866],{},[895,90625,90626,90628,90630,90632],{},[1723,90627,1759],{},[1864,90629,2909],{},[898,90631,2125],{"mathvariant":2124},[1864,90633,2331],{},[2220,90635,90636,90638,90640],{},[898,90637,1904],{},[1864,90639,2331],{},[895,90641,90642,90644,90646],{},[1864,90643,1866],{},[898,90645,2125],{"mathvariant":2124},[1864,90647,2909],{},[1723,90649,2031],{"separator":2030},[6588,90651],{"width":15985},[2220,90653,90654,90656,90658],{},[898,90655,900],{},[1864,90657,33239],{},[895,90659,90660,90662],{},[1723,90661,2229],{"mathvariant":2124},[1723,90663,2229],{"mathvariant":2124},[1723,90665,1725],{},[1723,90667,1759],{},[3055,90669,90670],{"scriptlevel":2256,"displaystyle":1907},[3058,90671,90672,90674],{},[1864,90673,2331],{},[1864,90675,4713],{},[2220,90677,90678,90680,90682],{},[898,90679,1904],{},[1864,90681,1866],{},[895,90683,90684,90686,90688],{},[1864,90685,1866],{},[898,90687,2125],{"mathvariant":2124},[1864,90689,2331],{},[2220,90691,90692,90694,90696],{},[898,90693,1904],{},[1864,90695,2331],{},[895,90697,90698,90700,90702,90704],{},[1723,90699,1759],{},[1864,90701,2962],{},[898,90703,2125],{"mathvariant":2124},[1864,90705,2909],{},[1723,90707,2031],{"separator":2030},[902,90709,90710],{"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},",[724,90712,90713,90714,90756],{},"opět ",[883,90715,90717],{"className":90716},[886],[888,90718,90719],{"xmlns":890},[892,90720,90721,90753],{},[895,90722,90723,90735,90737,90749,90751],{},[2220,90724,90725,90727,90729],{},[898,90726,900],{},[1864,90728,3626],{},[895,90730,90731,90733],{},[1723,90732,2229],{"mathvariant":2124},[1723,90734,2229],{"mathvariant":2124},[1723,90736,2031],{"separator":2030},[2220,90738,90739,90741,90743],{},[898,90740,900],{},[1864,90742,33239],{},[895,90744,90745,90747],{},[1723,90746,2229],{"mathvariant":2124},[1723,90748,2229],{"mathvariant":2124},[1723,90750,2287],{},[1864,90752,2256],{},[902,90754,90755],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,90758,90759],{},[38,90760,90761,90762,1664],{},"(a) Mezní užitečnosti v bodě ",[883,90763,90765],{"className":90764},[886],[888,90766,90767],{"xmlns":890},[892,90768,90769,90781],{},[895,90770,90771,90773,90775,90777,90779],{},[1723,90772,3212],{"stretchy":1907},[1864,90774,3810],{},[1723,90776,2031],{"separator":2030},[1864,90778,9087],{},[1723,90780,3227],{"stretchy":1907},[902,90782,90783],{"encoding":904},"[100, 200]",[883,90785,90787],{"className":90786},[886],[888,90788,90789],{"xmlns":890,"display":28759},[892,90790,90791,90858],{},[895,90792,90793,90795,90801,90803,90805,90807,90809,90811,90813,90821,90823,90837,90839,90851,90853,90856],{},[898,90794,1728],{},[1931,90796,90797,90799],{},[898,90798,900],{},[1864,90800,1866],{},[1723,90802,1908],{"stretchy":1907},[1864,90804,3810],{},[1723,90806,2031],{"separator":2030},[1864,90808,9087],{},[1723,90810,1914],{"stretchy":1907},[1723,90812,1725],{},[3055,90814,90815],{"scriptlevel":2256,"displaystyle":1907},[3058,90816,90817,90819],{},[1864,90818,1866],{},[1864,90820,2331],{},[1723,90822,3897],{},[2057,90824,90825,90827],{},[1864,90826,3810],{},[895,90828,90829,90831,90833,90835],{},[1723,90830,1759],{},[1864,90832,1866],{},[898,90834,2125],{"mathvariant":2124},[1864,90836,2331],{},[1723,90838,3897],{},[2057,90840,90841,90843],{},[1864,90842,9087],{},[895,90844,90845,90847,90849],{},[1864,90846,1866],{},[898,90848,2125],{"mathvariant":2124},[1864,90850,2909],{},[1723,90852,6610],{},[1864,90854,90855],{},"0,4204",[1723,90857,2031],{"separator":2030},[902,90859,90860],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,90862,90864],{"className":90863},[886],[888,90865,90866],{"xmlns":890,"display":28759},[892,90867,90868,90933],{},[895,90869,90870,90872,90878,90880,90882,90884,90886,90888,90890,90898,90900,90912,90914,90928,90930],{},[898,90871,1728],{},[1931,90873,90874,90876],{},[898,90875,900],{},[1864,90877,2331],{},[1723,90879,1908],{"stretchy":1907},[1864,90881,3810],{},[1723,90883,2031],{"separator":2030},[1864,90885,9087],{},[1723,90887,1914],{"stretchy":1907},[1723,90889,1725],{},[3055,90891,90892],{"scriptlevel":2256,"displaystyle":1907},[3058,90893,90894,90896],{},[1864,90895,1866],{},[1864,90897,2909],{},[1723,90899,3897],{},[2057,90901,90902,90904],{},[1864,90903,3810],{},[895,90905,90906,90908,90910],{},[1864,90907,1866],{},[898,90909,2125],{"mathvariant":2124},[1864,90911,2331],{},[1723,90913,3897],{},[2057,90915,90916,90918],{},[1864,90917,9087],{},[895,90919,90920,90922,90924,90926],{},[1723,90921,1759],{},[1864,90923,2331],{},[898,90925,2125],{"mathvariant":2124},[1864,90927,2909],{},[1723,90929,6610],{},[1864,90931,90932],{},"0,63067.",[902,90934,90935],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,90937,90938,2628,90940,90975,90976,90997,90998,91015],{},[614,90939,9924],{},[883,90941,90943],{"className":90942},[886],[888,90944,90945],{"xmlns":890},[892,90946,90947,90972],{},[895,90948,90949,90951,90957,90959,90961,90963,90965,90967,90969],{},[898,90950,1728],{},[1931,90952,90953,90955],{},[898,90954,900],{},[1864,90956,2331],{},[1723,90958,1908],{"stretchy":1907},[1864,90960,3810],{},[1723,90962,2031],{"separator":2030},[1864,90964,9087],{},[1723,90966,1914],{"stretchy":1907},[1723,90968,6610],{},[1864,90970,90971],{},"0,63067",[902,90973,90974],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,90977,90979],{"className":90978},[886],[888,90980,90981],{"xmlns":890},[892,90982,90983,90995],{},[895,90984,90985,90987,90989,90991,90993],{},[1723,90986,3212],{"stretchy":1907},[1864,90988,3810],{},[1723,90990,2031],{"separator":2030},[1864,90992,9087],{},[1723,90994,3227],{"stretchy":1907},[902,90996,90783],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,90999,91001],{"className":91000},[886],[888,91002,91003],{"xmlns":890},[892,91004,91005,91013],{},[895,91006,91007],{},[1931,91008,91009,91011],{},[898,91010,1904],{},[1864,91012,2331],{},[902,91014,29714],{"encoding":904}," přibližně o 0,63067.",[724,91017,91018,91037,91038,39876,91059,91076,91077,91103,91104,91121,91122,3871],{},[38,91019,91020,91021,91036],{},"(b) Odhad změny ",[883,91022,91024],{"className":91023},[886],[888,91025,91026],{"xmlns":890},[892,91027,91028,91034],{},[895,91029,91030,91032],{},[898,91031,3611],{"mathvariant":2124},[898,91033,900],{},[902,91035,89279],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,91039,91041],{"className":91040},[886],[888,91042,91043],{"xmlns":890},[892,91044,91045,91057],{},[895,91046,91047,91049,91051,91053,91055],{},[1723,91048,3212],{"stretchy":1907},[1864,91050,3810],{},[1723,91052,2031],{"separator":2030},[1864,91054,9087],{},[1723,91056,3227],{"stretchy":1907},[902,91058,90783],{"encoding":904},[883,91060,91062],{"className":91061},[886],[888,91063,91064],{"xmlns":890},[892,91065,91066,91074],{},[895,91067,91068],{},[1931,91069,91070,91072],{},[898,91071,1904],{},[1864,91073,1866],{},[902,91075,29695],{"encoding":904}," na 98 (tj. ",[883,91078,91080],{"className":91079},[886],[888,91081,91082],{"xmlns":890},[892,91083,91084,91100],{},[895,91085,91086,91088,91094,91096,91098],{},[898,91087,2930],{"mathvariant":2124},[1931,91089,91090,91092],{},[898,91091,1904],{},[1864,91093,1866],{},[1723,91095,1725],{},[1723,91097,1759],{},[1864,91099,2331],{},[902,91101,91102],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,91105,91107],{"className":91106},[886],[888,91108,91109],{"xmlns":890},[892,91110,91111,91119],{},[895,91112,91113],{},[1931,91114,91115,91117],{},[898,91116,1904],{},[1864,91118,2331],{},[902,91120,29714],{"encoding":904}," o 3 (tj. ",[883,91123,91125],{"className":91124},[886],[888,91126,91127],{"xmlns":890},[892,91128,91129,91143],{},[895,91130,91131,91133,91139,91141],{},[898,91132,2930],{"mathvariant":2124},[1931,91134,91135,91137],{},[898,91136,1904],{},[1864,91138,2331],{},[1723,91140,1725],{},[1864,91142,2909],{},[902,91144,91145],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,91147,91149],{"className":91148},[886],[888,91150,91151],{"xmlns":890,"display":28759},[892,91152,91153,91204],{},[895,91154,91155,91157,91159,91161,91163,91165,91167,91169,91171,91173,91175,91177,91179,91181,91183,91185,91187,91189,91191,91194,91196,91199,91201],{},[898,91156,3611],{"mathvariant":2124},[898,91158,900],{},[1723,91160,3456],{},[898,91162,2930],{"mathvariant":2124},[898,91164,900],{},[1723,91166,1725],{},[1864,91168,90855],{},[1723,91170,3897],{},[1723,91172,1908],{"stretchy":1907},[1723,91174,1759],{},[1864,91176,2331],{},[1723,91178,1914],{"stretchy":1907},[1723,91180,2087],{},[1864,91182,90971],{},[1723,91184,3897],{},[1864,91186,2909],{},[1723,91188,1725],{},[1723,91190,1759],{},[1864,91192,91193],{},"0,8408",[1723,91195,2087],{},[1864,91197,91198],{},"1,89201",[1723,91200,6610],{},[1864,91202,91203],{},"1,05.",[902,91205,91206],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,91208,91209,91210,91213,91214,91265,91266,1664],{},"Užitečnost se tedy zvýší přibližně o ",[38,91211,91212],{},"1,05",". Skutečná změna je ",[883,91215,91217],{"className":91216},[886],[888,91218,91219],{"xmlns":890},[892,91220,91221,91262],{},[895,91222,91223,91225,91227,91229,91231,91233,91236,91238,91241,91243,91245,91247,91249,91251,91253,91255,91257,91259],{},[898,91224,3611],{"mathvariant":2124},[898,91226,900],{},[1723,91228,1725],{},[898,91230,900],{},[1723,91232,1908],{"stretchy":1907},[1864,91234,91235],{},"98",[1723,91237,2031],{"separator":2030},[1864,91239,91240],{},"203",[1723,91242,1914],{"stretchy":1907},[1723,91244,1759],{},[898,91246,900],{},[1723,91248,1908],{"stretchy":1907},[1864,91250,3810],{},[1723,91252,2031],{"separator":2030},[1864,91254,9087],{},[1723,91256,1914],{"stretchy":1907},[1723,91258,6610],{},[1864,91260,91261],{},"1,031",[902,91263,91264],{"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 ",[883,91267,91269],{"className":91268},[886],[888,91270,91271],{"xmlns":890},[892,91272,91273,91293],{},[895,91274,91275,91277,91283,91285,91287],{},[898,91276,2930],{"mathvariant":2124},[1931,91278,91279,91281],{},[898,91280,1904],{},[1864,91282,1866],{},[1723,91284,2031],{"separator":2030},[898,91286,2930],{"mathvariant":2124},[1931,91288,91289,91291],{},[898,91290,1904],{},[1864,91292,2331],{},[902,91294,89309],{"encoding":904},[115,91296,91298],{"id":91297},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,91300,91301],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,91303,91305],{"className":91304},[886],[888,91306,91307],{"xmlns":890,"display":28759},[892,91308,91309,91368],{},[21447,91310,91311],{"width":28764},[21452,91312,91313,91315,91361,91363],{},[21455,91314],{"width":28769},[21455,91316,91317],{},[895,91318,91319,91321,91323,91329,91331,91337,91339,91341,91349,91351,91359],{},[898,91320,900],{},[1723,91322,1908],{"stretchy":1907},[1931,91324,91325,91327],{},[898,91326,1904],{},[1864,91328,1866],{},[1723,91330,2031],{"separator":2030},[1931,91332,91333,91335],{},[898,91334,1904],{},[1864,91336,2331],{},[1723,91338,1914],{"stretchy":1907},[1723,91340,1725],{},[2220,91342,91343,91345,91347],{},[898,91344,1904],{},[1864,91346,1866],{},[898,91348,207],{},[1723,91350,3897],{},[2220,91352,91353,91355,91357],{},[898,91354,1904],{},[1864,91356,2331],{},[898,91358,2069],{},[1723,91360,2031],{"separator":2030},[21455,91362],{"width":28769},[21455,91364,91365],{},[3018,91366,91367],{},"(6.6)",[902,91369,91370],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,91372,5022,91373,91391,91392,91394,91395,91399,91400,91430,91431,91453],{},[883,91374,91376],{"className":91375},[886],[888,91377,91378],{"xmlns":890},[892,91379,91380,91388],{},[895,91381,91382,91384,91386],{},[898,91383,207],{},[1723,91385,2031],{"separator":2030},[898,91387,2069],{},[902,91389,91390],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,91393,75382],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,91396,91398],{"className":91397,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,91401,91403],{"className":91402},[886],[888,91404,91405],{"xmlns":890},[892,91406,91407,91427],{},[895,91408,91409,91411,91413,91415,91417,91419,91421,91423,91425],{},[898,91410,207],{},[1723,91412,2031],{"separator":2030},[898,91414,2069],{},[1723,91416,7216],{},[1723,91418,1908],{"stretchy":1907},[1864,91420,2256],{},[1723,91422,2031],{"separator":2030},[1864,91424,1866],{},[1723,91426,1914],{"stretchy":1907},[902,91428,91429],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,91432,91434],{"className":91433},[886],[888,91435,91436],{"xmlns":890},[892,91437,91438,91450],{},[895,91439,91440,91442,91444,91446,91448],{},[898,91441,2069],{},[1723,91443,1725],{},[1864,91445,1866],{},[1723,91447,1759],{},[898,91449,207],{},[902,91451,91452],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,91455,91456],{},[3285,91457],{"alt":91458,"className":91459,"src":91460},"imek-cobb-douglas-3d-plus-ic",[210,3289],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,91462,91464],{"className":91463},[886],[888,91465,91466],{"xmlns":890,"display":28759},[892,91467,91468,91518],{},[895,91469,91470,91472,91474,91480,91482,91488,91490,91492,91500,91502,91516],{},[898,91471,900],{},[1723,91473,1908],{"stretchy":1907},[1931,91475,91476,91478],{},[898,91477,1904],{},[1864,91479,1866],{},[1723,91481,2031],{"separator":2030},[1931,91483,91484,91486],{},[898,91485,1904],{},[1864,91487,2331],{},[1723,91489,1914],{"stretchy":1907},[1723,91491,1725],{},[2220,91493,91494,91496,91498],{},[898,91495,1904],{},[1864,91497,1866],{},[898,91499,207],{},[1723,91501,3897],{},[2220,91503,91504,91506,91508],{},[898,91505,1904],{},[1864,91507,2331],{},[895,91509,91510,91512,91514],{},[1864,91511,1866],{},[1723,91513,1759],{},[898,91515,207],{},[898,91517,1664],{"mathvariant":2124},[902,91519,91520],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[4584,91522,91523,91572,91694,91828],{},[724,91524,91525,91527,91528],{},[883,91526,53385],{}," Příklad 6.3 — ověření vlastností pro ",[883,91529,91531],{"className":91530},[886],[888,91532,91533],{"xmlns":890},[892,91534,91535,91569],{},[895,91536,91537,91539,91541,91555],{},[898,91538,900],{},[1723,91540,1725],{},[2220,91542,91543,91545,91547],{},[898,91544,1904],{},[1864,91546,1866],{},[895,91548,91549,91551,91553],{},[1864,91550,1866],{},[898,91552,2125],{"mathvariant":2124},[1864,91554,3080],{},[2220,91556,91557,91559,91561],{},[898,91558,1904],{},[1864,91560,2331],{},[895,91562,91563,91565,91567],{},[1864,91564,2909],{},[898,91566,2125],{"mathvariant":2124},[1864,91568,3080],{},[902,91570,91571],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,91573,91575],{"className":91574},[886],[888,91576,91577],{"xmlns":890,"display":28759},[892,91578,91579,91691],{},[895,91580,91581,91589,91591,91599,91615,91629,91631,91633,91635,91637,91645,91647,91655,91669,91685,91687,91689],{},[2220,91582,91583,91585,91587],{},[898,91584,900],{},[1864,91586,1866],{},[1723,91588,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,91590,1725],{},[3055,91592,91593],{"scriptlevel":2256,"displaystyle":1907},[3058,91594,91595,91597],{},[1864,91596,1866],{},[1864,91598,3080],{},[2220,91600,91601,91603,91605],{},[898,91602,1904],{},[1864,91604,1866],{},[895,91606,91607,91609,91611,91613],{},[1723,91608,1759],{},[1864,91610,2909],{},[898,91612,2125],{"mathvariant":2124},[1864,91614,3080],{},[2220,91616,91617,91619,91621],{},[898,91618,1904],{},[1864,91620,2331],{},[895,91622,91623,91625,91627],{},[1864,91624,2909],{},[898,91626,2125],{"mathvariant":2124},[1864,91628,3080],{},[1723,91630,2253],{},[1864,91632,2256],{},[1723,91634,2031],{"separator":2030},[6588,91636],{"width":15985},[2220,91638,91639,91641,91643],{},[898,91640,900],{},[1864,91642,2331],{},[1723,91644,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,91646,1725],{},[3055,91648,91649],{"scriptlevel":2256,"displaystyle":1907},[3058,91650,91651,91653],{},[1864,91652,2909],{},[1864,91654,3080],{},[2220,91656,91657,91659,91661],{},[898,91658,1904],{},[1864,91660,1866],{},[895,91662,91663,91665,91667],{},[1864,91664,1866],{},[898,91666,2125],{"mathvariant":2124},[1864,91668,3080],{},[2220,91670,91671,91673,91675],{},[898,91672,1904],{},[1864,91674,2331],{},[895,91676,91677,91679,91681,91683],{},[1723,91678,1759],{},[1864,91680,1866],{},[898,91682,2125],{"mathvariant":2124},[1864,91684,3080],{},[1723,91686,2253],{},[1864,91688,2256],{},[1723,91690,2031],{"separator":2030},[902,91692,91693],{"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,",[883,91695,91697],{"className":91696},[886],[888,91698,91699],{"xmlns":890,"display":28759},[892,91700,91701,91825],{},[895,91702,91703,91715,91717,91719,91727,91743,91757,91759,91761,91763,91765,91777,91779,91781,91789,91803,91819,91821,91823],{},[2220,91704,91705,91707,91709],{},[898,91706,900],{},[1864,91708,3626],{},[895,91710,91711,91713],{},[1723,91712,2229],{"mathvariant":2124},[1723,91714,2229],{"mathvariant":2124},[1723,91716,1725],{},[1723,91718,1759],{},[3055,91720,91721],{"scriptlevel":2256,"displaystyle":1907},[3058,91722,91723,91725],{},[1864,91724,2909],{},[1864,91726,42554],{},[2220,91728,91729,91731,91733],{},[898,91730,1904],{},[1864,91732,1866],{},[895,91734,91735,91737,91739,91741],{},[1723,91736,1759],{},[1864,91738,24894],{},[898,91740,2125],{"mathvariant":2124},[1864,91742,3080],{},[2220,91744,91745,91747,91749],{},[898,91746,1904],{},[1864,91748,2331],{},[895,91750,91751,91753,91755],{},[1864,91752,2909],{},[898,91754,2125],{"mathvariant":2124},[1864,91756,3080],{},[1723,91758,2287],{},[1864,91760,2256],{},[1723,91762,2031],{"separator":2030},[6588,91764],{"width":15985},[2220,91766,91767,91769,91771],{},[898,91768,900],{},[1864,91770,33239],{},[895,91772,91773,91775],{},[1723,91774,2229],{"mathvariant":2124},[1723,91776,2229],{"mathvariant":2124},[1723,91778,1725],{},[1723,91780,1759],{},[3055,91782,91783],{"scriptlevel":2256,"displaystyle":1907},[3058,91784,91785,91787],{},[1864,91786,2909],{},[1864,91788,42554],{},[2220,91790,91791,91793,91795],{},[898,91792,1904],{},[1864,91794,1866],{},[895,91796,91797,91799,91801],{},[1864,91798,1866],{},[898,91800,2125],{"mathvariant":2124},[1864,91802,3080],{},[2220,91804,91805,91807,91809],{},[898,91806,1904],{},[1864,91808,2331],{},[895,91810,91811,91813,91815,91817],{},[1723,91812,1759],{},[1864,91814,2962],{},[898,91816,2125],{"mathvariant":2124},[1864,91818,3080],{},[1723,91820,2287],{},[1864,91822,2256],{},[1723,91824,2031],{"separator":2030},[902,91826,91827],{"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,",[724,91829,91830],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,91832,91834],{"id":91833},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,91836,91837,91840],{},[38,91838,91839],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,91842,91844],{"className":91843},[886],[888,91845,91846],{"xmlns":890,"display":28759},[892,91847,91848,91891],{},[21447,91849,91850],{"width":28764},[21452,91851,91852,91854,91884,91886],{},[21455,91853],{"width":28769},[21455,91855,91856],{},[895,91857,91858,91860,91862,91868,91870,91876,91878,91880,91882],{},[898,91859,900],{},[1723,91861,1908],{"stretchy":1907},[1931,91863,91864,91866],{},[898,91865,1904],{},[1864,91867,1866],{},[1723,91869,2031],{"separator":2030},[1931,91871,91872,91874],{},[898,91873,1904],{},[1864,91875,2331],{},[1723,91877,1914],{"stretchy":1907},[1723,91879,1725],{},[898,91881,2878],{},[1723,91883,2031],{"separator":2030},[21455,91885],{"width":28769},[21455,91887,91888],{},[3018,91889,91890],{},"(6.7)",[902,91892,91893],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,91895,5022,91896,91909],{},[883,91897,91899],{"className":91898},[886],[888,91900,91901],{"xmlns":890},[892,91902,91903,91907],{},[895,91904,91905],{},[898,91906,2878],{},[902,91908,2878],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,91911,91913],{"className":91912},[886],[888,91914,91915],{"xmlns":890,"display":28759},[892,91916,91917,91958],{},[21447,91918,91919],{"width":28764},[21452,91920,91921,91923,91951,91953],{},[21455,91922],{"width":28769},[21455,91924,91925],{},[895,91926,91927,91935,91937,91945,91947,91949],{},[2220,91928,91929,91931,91933],{},[898,91930,1904],{},[1864,91932,1866],{},[898,91934,207],{},[1723,91936,3897],{},[2220,91938,91939,91941,91943],{},[898,91940,1904],{},[1864,91942,2331],{},[898,91944,2069],{},[1723,91946,1725],{},[898,91948,2878],{},[898,91950,1664],{"mathvariant":2124},[21455,91952],{"width":28769},[21455,91954,91955],{},[3018,91956,91957],{},"(6.8)",[902,91959,91960],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,91962,91963,91964,5070,91994,2628,91997,92010,92011,92046,92047,92064,92065,92094,92095,92098],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,91965,91967],{"className":91966},[886],[888,91968,91969],{"xmlns":890},[892,91970,91971,91991],{},[895,91972,91973,91975,91981,91983,91989],{},[1723,91974,3212],{"stretchy":1907},[1931,91976,91977,91979],{},[898,91978,1904],{},[1864,91980,1866],{},[1723,91982,2031],{"separator":2030},[1931,91984,91985,91987],{},[898,91986,1904],{},[1864,91988,2331],{},[1723,91990,3227],{"stretchy":1907},[902,91992,91993],{"encoding":904},"[Q_1, Q_2]",[38,91995,91996],{},"stejnou úrovní uspokojení",[883,91998,92000],{"className":91999},[886],[888,92001,92002],{"xmlns":890},[892,92003,92004,92008],{},[895,92005,92006],{},[898,92007,2878],{},[902,92009,2878],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,92012,92014],{"className":92013},[886],[888,92015,92016],{"xmlns":890},[892,92017,92018,92044],{},[895,92019,92020,92022,92024,92026,92028,92034,92036,92042],{},[898,92021,900],{},[1723,92023,1725],{},[898,92025,900],{},[1723,92027,1908],{"stretchy":1907},[1931,92029,92030,92032],{},[898,92031,1904],{},[1864,92033,1866],{},[1723,92035,2031],{"separator":2030},[1931,92037,92038,92040],{},[898,92039,1904],{},[1864,92041,2331],{},[1723,92043,1914],{"stretchy":1907},[902,92045,88134],{"encoding":904}," s rovinami ",[883,92048,92050],{"className":92049},[886],[888,92051,92052],{"xmlns":890},[892,92053,92054,92062],{},[895,92055,92056,92058,92060],{},[898,92057,900],{},[1723,92059,1725],{},[898,92061,2878],{},[902,92063,87351],{"encoding":904}," rovnoběžnými s rovinou ",[883,92066,92068],{"className":92067},[886],[888,92069,92070],{"xmlns":890},[892,92071,92072,92092],{},[895,92073,92074,92076,92082,92084,92090],{},[1723,92075,1908],{"stretchy":1907},[1931,92077,92078,92080],{},[898,92079,1904],{},[1864,92081,1866],{},[1723,92083,2031],{"separator":2030},[1931,92085,92086,92088],{},[898,92087,1904],{},[1864,92089,2331],{},[1723,92091,1914],{"stretchy":1907},[902,92093,90297],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,92096,92097],{},"izokvantami"," produkčních funkcí.",[724,92100,92101],{},[614,92102,92103,92104,90175,92122,92140,92141,1664],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,92105,92107],{"className":92106},[886],[888,92108,92109],{"xmlns":890},[892,92110,92111,92119],{},[895,92112,92113,92115,92117],{},[898,92114,207],{},[1723,92116,2287],{},[898,92118,2069],{},[902,92120,92121],{"encoding":904},"a \u003C b",[883,92123,92125],{"className":92124},[886],[888,92126,92127],{"xmlns":890},[892,92128,92129,92137],{},[895,92130,92131,92133,92135],{},[898,92132,207],{},[1723,92134,2253],{},[898,92136,2069],{},[902,92138,92139],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,92142,92144],{"className":92143},[886],[888,92145,92146],{"xmlns":890},[892,92147,92148,92172],{},[895,92149,92150,92156,92158,92164,92166],{},[1931,92151,92152,92154],{},[898,92153,2878],{},[1864,92155,2256],{},[1723,92157,2287],{},[1931,92159,92160,92162],{},[898,92161,2878],{},[1864,92163,1866],{},[1723,92165,2287],{},[1931,92167,92168,92170],{},[898,92169,2878],{},[1864,92171,2331],{},[902,92173,92174],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,92176,92177],{},[614,92178,92179,92180,92209,92210,92268,92269,92287],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,92181,92183],{"className":92182},[886],[888,92184,92185],{"xmlns":890},[892,92186,92187,92207],{},[895,92188,92189,92191,92197,92199,92205],{},[1723,92190,1908],{"stretchy":1907},[1931,92192,92193,92195],{},[898,92194,1904],{},[1864,92196,1866],{},[1723,92198,2031],{"separator":2030},[1931,92200,92201,92203],{},[898,92202,1904],{},[1864,92204,2331],{},[1723,92206,1914],{"stretchy":1907},[902,92208,90297],{"encoding":904},"; body ",[883,92211,92213],{"className":92212},[886],[888,92214,92215],{"xmlns":890},[892,92216,92217,92265],{},[895,92218,92219,92221,92223,92225,92231,92233,92239,92241,92243,92245,92247,92249,92255,92257,92263],{},[898,92220,1718],{},[1723,92222,1725],{},[1723,92224,3212],{"stretchy":1907},[1931,92226,92227,92229],{},[898,92228,207],{},[1864,92230,1866],{},[1723,92232,2031],{"separator":2030},[1931,92234,92235,92237],{},[898,92236,207],{},[1864,92238,2331],{},[1723,92240,3227],{"stretchy":1907},[1723,92242,2031],{"separator":2030},[898,92244,23946],{},[1723,92246,1725],{},[1723,92248,3212],{"stretchy":1907},[1931,92250,92251,92253],{},[898,92252,2069],{},[1864,92254,1866],{},[1723,92256,2031],{"separator":2030},[1931,92258,92259,92261],{},[898,92260,2069],{},[1864,92262,2331],{},[1723,92264,3227],{"stretchy":1907},[902,92266,92267],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,92270,92272],{"className":92271},[886],[888,92273,92274],{"xmlns":890},[892,92275,92276,92284],{},[895,92277,92278,92280,92282],{},[898,92279,1721],{},[1723,92281,2031],{"separator":2030},[898,92283,4897],{},[902,92285,92286],{"encoding":904},"C, D"," na vyšší hladině.",[4584,92289,92290],{},[724,92291,92292,92294,92295,92357,92358,92402,92403,92437,92438,26882,92456,92437,92510,26882,92528,92604],{},[883,92293,53385],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,92296,92298],{"className":92297},[886],[888,92299,92300],{"xmlns":890},[892,92301,92302,92354],{},[895,92303,92304,92306,92308,92314,92316,92322,92324,92326,92340],{},[898,92305,900],{},[1723,92307,1908],{"stretchy":1907},[1931,92309,92310,92312],{},[898,92311,1904],{},[1864,92313,1866],{},[1723,92315,2031],{"separator":2030},[1931,92317,92318,92320],{},[898,92319,1904],{},[1864,92321,2331],{},[1723,92323,1914],{"stretchy":1907},[1723,92325,1725],{},[2220,92327,92328,92330,92332],{},[898,92329,1904],{},[1864,92331,1866],{},[895,92333,92334,92336,92338],{},[1864,92335,1866],{},[898,92337,2125],{"mathvariant":2124},[1864,92339,3080],{},[2220,92341,92342,92344,92346],{},[898,92343,1904],{},[1864,92345,2331],{},[895,92347,92348,92350,92352],{},[1864,92349,2909],{},[898,92351,2125],{"mathvariant":2124},[1864,92353,3080],{},[902,92355,92356],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,92359,92361],{"className":92360},[886],[888,92362,92363],{"xmlns":890},[892,92364,92365,92399],{},[895,92366,92367,92381,92395,92397],{},[2220,92368,92369,92371,92373],{},[898,92370,1904],{},[1864,92372,1866],{},[895,92374,92375,92377,92379],{},[1864,92376,1866],{},[898,92378,2125],{"mathvariant":2124},[1864,92380,3080],{},[2220,92382,92383,92385,92387],{},[898,92384,1904],{},[1864,92386,2331],{},[895,92388,92389,92391,92393],{},[1864,92390,2909],{},[898,92392,2125],{"mathvariant":2124},[1864,92394,3080],{},[1723,92396,1725],{},[898,92398,2878],{},[902,92400,92401],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,92404,92406],{"className":92405},[886],[888,92407,92408],{"xmlns":890},[892,92409,92410,92434],{},[895,92411,92412,92418,92426,92428],{},[1931,92413,92414,92416],{},[898,92415,1904],{},[1864,92417,1866],{},[2220,92419,92420,92422,92424],{},[898,92421,1904],{},[1864,92423,2331],{},[1864,92425,2909],{},[1723,92427,1725],{},[2057,92429,92430,92432],{},[898,92431,2878],{},[1864,92433,3080],{},[902,92435,92436],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,92439,92441],{"className":92440},[886],[888,92442,92443],{"xmlns":890},[892,92444,92445,92453],{},[895,92446,92447,92449,92451],{},[898,92448,2878],{},[1723,92450,1725],{},[1864,92452,1866],{},[902,92454,92455],{"encoding":904},"c = 1",[883,92457,92459],{"className":92458},[886],[888,92460,92461],{"xmlns":890},[892,92462,92463,92507],{},[895,92464,92465,92471,92473,92489,92491],{},[1931,92466,92467,92469],{},[898,92468,1904],{},[1864,92470,2331],{},[1723,92472,1725],{},[2220,92474,92475,92477,92479],{},[898,92476,1904],{},[1864,92478,1866],{},[895,92480,92481,92483,92485,92487],{},[1723,92482,1759],{},[1864,92484,1866],{},[898,92486,2125],{"mathvariant":2124},[1864,92488,2909],{},[1723,92490,1725],{},[3055,92492,92493],{"scriptlevel":2256,"displaystyle":2030},[3058,92494,92495,92497],{},[1864,92496,1866],{},[82708,92498,92499,92505],{},[1931,92500,92501,92503],{},[898,92502,1904],{},[1864,92504,1866],{},[1864,92506,2909],{},[902,92508,92509],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,92511,92513],{"className":92512},[886],[888,92514,92515],{"xmlns":890},[892,92516,92517,92525],{},[895,92518,92519,92521,92523],{},[898,92520,2878],{},[1723,92522,1725],{},[1864,92524,2331],{},[902,92526,92527],{"encoding":904},"c = 2",[883,92529,92531],{"className":92530},[886],[888,92532,92533],{"xmlns":890},[892,92534,92535,92601],{},[895,92536,92537,92543,92545,92557,92559,92575,92577],{},[1931,92538,92539,92541],{},[898,92540,1904],{},[1864,92542,2331],{},[1723,92544,1725],{},[2057,92546,92547,92549],{},[1864,92548,2331],{},[895,92550,92551,92553,92555],{},[1864,92552,3080],{},[898,92554,2125],{"mathvariant":2124},[1864,92556,2909],{},[1723,92558,3897],{},[2220,92560,92561,92563,92565],{},[898,92562,1904],{},[1864,92564,1866],{},[895,92566,92567,92569,92571,92573],{},[1723,92568,1759],{},[1864,92570,1866],{},[898,92572,2125],{"mathvariant":2124},[1864,92574,2909],{},[1723,92576,1725],{},[3055,92578,92579],{"scriptlevel":2256,"displaystyle":2030},[3058,92580,92581,92591],{},[895,92582,92583,92585],{},[1864,92584,2331],{},[82708,92586,92587,92589],{},[1864,92588,2331],{},[1864,92590,2909],{},[82708,92592,92593,92599],{},[1931,92594,92595,92597],{},[898,92596,1904],{},[1864,92598,1866],{},[1864,92600,2909],{},[902,92602,92603],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,92606,92608],{"id":92607},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,92610,92611],{},[3285,92612],{"alt":92613,"className":92614,"src":92615},"imek-ic-4vlastnosti-anotovane",[210,3289],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[4584,92617,92618,92627,92674,92718,92724,92730],{},[724,92619,92620,92622,92623,92626],{},[883,92621,5124],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,92624,92625],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,92628,92629],{},[883,92630,92632],{"className":92631},[886],[888,92633,92634],{"xmlns":890},[892,92635,92636,92671],{},[895,92637,92638,92641,92643,92645,92647,92649,92667,92669],{},[898,92639,92640],{"mathvariant":2124},"tg",[1723,92642,56887],{},[898,92644,19556],{},[1723,92646,1725],{},[1723,92648,1759],{},[3058,92650,92651,92659],{},[2220,92652,92653,92655,92657],{},[898,92654,900],{},[1864,92656,1866],{},[1723,92658,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[2220,92660,92661,92663,92665],{},[898,92662,900],{},[1864,92664,2331],{},[1723,92666,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,92668,2287],{},[1864,92670,2256],{},[902,92672,92673],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,92675,92676,92677,92717],{},"(derivace implicitně zadané funkce ",[883,92678,92680],{"className":92679},[886],[888,92681,92682],{"xmlns":890},[892,92683,92684,92714],{},[895,92685,92686,92688,92690,92696,92698,92704,92706,92708,92710,92712],{},[898,92687,900],{},[1723,92689,1908],{"stretchy":1907},[1931,92691,92692,92694],{},[898,92693,1904],{},[1864,92695,1866],{},[1723,92697,2031],{"separator":2030},[1931,92699,92700,92702],{},[898,92701,1904],{},[1864,92703,2331],{},[1723,92705,1914],{"stretchy":1907},[1723,92707,1759],{},[898,92709,2878],{},[1723,92711,1725],{},[1864,92713,2256],{},[902,92715,92716],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,92719,92720,92723],{},[38,92721,92722],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,92725,92726,92729],{},[38,92727,92728],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,92731,92732,92735,92736,92754,92755,92771,92772,92775],{},[38,92733,92734],{},"4° Konvexní."," Pro každé dva body ",[883,92737,92739],{"className":92738},[886],[888,92740,92741],{"xmlns":890},[892,92742,92743,92751],{},[895,92744,92745,92747,92749],{},[898,92746,1718],{},[1723,92748,2031],{"separator":2030},[898,92750,23946],{},[902,92752,92753],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,92756,92758],{"className":92757},[886],[888,92759,92760],{"xmlns":890},[892,92761,92762,92768],{},[895,92763,92764,92766],{},[898,92765,1718],{},[898,92767,23946],{},[902,92769,92770],{"encoding":904},"AB"," ve ",[38,92773,92774],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,92777,92778],{},[614,92779,92780,92781,92816,92817,1664],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,92782,92784],{"className":92783},[886],[888,92785,92786],{"xmlns":890},[892,92787,92788,92814],{},[895,92789,92790,92792,92794,92800,92802,92808,92810,92812],{},[898,92791,900],{},[1723,92793,1908],{"stretchy":1907},[1931,92795,92796,92798],{},[898,92797,1904],{},[1864,92799,1866],{},[1723,92801,2031],{"separator":2030},[1931,92803,92804,92806],{},[898,92805,1904],{},[1864,92807,2331],{},[1723,92809,1914],{"stretchy":1907},[1723,92811,1725],{},[898,92813,2878],{},[902,92815,10474],{"encoding":904}," s tečnou se sklonem ",[883,92818,92820],{"className":92819},[886],[888,92821,92822],{"xmlns":890},[892,92823,92824,92832],{},[895,92825,92826,92828,92830],{},[898,92827,92640],{"mathvariant":2124},[1723,92829,56887],{},[898,92831,19556],{},[902,92833,92834],{"encoding":904},"\\operatorname{tg}\\alpha",[115,92836,92838],{"id":92837},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,92840,92841,2628,92844,1981,92857,92860],{},[38,92842,92843],{},"Mezní míra komoditní substituce",[883,92845,92847],{"className":92846},[886],[888,92848,92849],{"xmlns":890},[892,92850,92851,92855],{},[895,92852,92853],{},[3018,92854,11303],{},[902,92856,28931],{"encoding":904},[38,92858,92859],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,92862,92864],{"className":92863},[886],[888,92865,92866],{"xmlns":890,"display":28759},[892,92867,92868,92955],{},[21447,92869,92870],{"width":28764},[21452,92871,92872,92874,92948,92950],{},[21455,92873],{"width":28769},[21455,92875,92876],{},[895,92877,92878,92880,92882,92884,92886,92892,92894,92900,92902,92904,92926,92928,92946],{},[3018,92879,11303],{},[1723,92881,1725],{},[3018,92883,11303],{},[1723,92885,1908],{"stretchy":1907},[1931,92887,92888,92890],{},[898,92889,1904],{},[1864,92891,1866],{},[1723,92893,2031],{"separator":2030},[1931,92895,92896,92898],{},[898,92897,1904],{},[1864,92899,2331],{},[1723,92901,1914],{"stretchy":1907},[1723,92903,1725],{},[3058,92905,92906,92916],{},[895,92907,92908,92910],{},[898,92909,1728],{},[1931,92911,92912,92914],{},[898,92913,900],{},[1864,92915,1866],{},[895,92917,92918,92920],{},[898,92919,1728],{},[1931,92921,92922,92924],{},[898,92923,900],{},[1864,92925,2331],{},[1723,92927,1725],{},[3058,92929,92930,92938],{},[2220,92931,92932,92934,92936],{},[898,92933,900],{},[1864,92935,1866],{},[1723,92937,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[2220,92939,92940,92942,92944],{},[898,92941,900],{},[1864,92943,2331],{},[1723,92945,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[898,92947,1664],{"mathvariant":2124},[21455,92949],{"width":28769},[21455,92951,92952],{},[3018,92953,92954],{},"(6.9)",[902,92956,92957],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,92959,92960,92961,92995,92996,93028,93029,93064,93065,93078],{},"Geometricky: ",[883,92962,92964],{"className":92963},[886],[888,92965,92966],{"xmlns":890},[892,92967,92968,92992],{},[895,92969,92970,92972],{},[1723,92971,1759],{},[3055,92973,92974],{"scriptlevel":2256,"displaystyle":1907},[3058,92975,92976,92984],{},[2220,92977,92978,92980,92982],{},[898,92979,900],{},[1864,92981,1866],{},[1723,92983,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[2220,92985,92986,92988,92990],{},[898,92987,900],{},[1864,92989,2331],{},[1723,92991,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,92993,92994],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,92997,92999],{"className":92998},[886],[888,93000,93001],{"xmlns":890},[892,93002,93003,93025],{},[895,93004,93005,93011,93013,93015,93017,93023],{},[1931,93006,93007,93009],{},[898,93008,1904],{},[1864,93010,2331],{},[1723,93012,1725],{},[898,93014,2745],{},[1723,93016,1908],{"stretchy":1907},[1931,93018,93019,93021],{},[898,93020,1904],{},[1864,93022,1866],{},[1723,93024,1914],{"stretchy":1907},[902,93026,93027],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,93030,93032],{"className":93031},[886],[888,93033,93034],{"xmlns":890},[892,93035,93036,93062],{},[895,93037,93038,93040,93042,93048,93050,93056,93058,93060],{},[898,93039,900],{},[1723,93041,1908],{"stretchy":1907},[1931,93043,93044,93046],{},[898,93045,1904],{},[1864,93047,1866],{},[1723,93049,2031],{"separator":2030},[1931,93051,93052,93054],{},[898,93053,1904],{},[1864,93055,2331],{},[1723,93057,1914],{"stretchy":1907},[1723,93059,1725],{},[898,93061,2878],{},[902,93063,10474],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,93066,93068],{"className":93067},[886],[888,93069,93070],{"xmlns":890},[892,93071,93072,93076],{},[895,93073,93074],{},[3018,93075,11303],{},[902,93077,28931],{"encoding":904}," chápeme jako velikost kompenzace.",[4584,93080,93081],{},[724,93082,93083,93085,93086,8812,93118,93156,93157,93174,93175,93192],{},[883,93084,4869],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,93087,93089],{"className":93088},[886],[888,93090,93091],{"xmlns":890},[892,93092,93093,93115],{},[895,93094,93095,93097,93099,93105,93107,93113],{},[3018,93096,11303],{},[1723,93098,1908],{"stretchy":1907},[1931,93100,93101,93103],{},[898,93102,1904],{},[1864,93104,1866],{},[1723,93106,2031],{"separator":2030},[1931,93108,93109,93111],{},[898,93110,1904],{},[1864,93112,2331],{},[1723,93114,1914],{"stretchy":1907},[902,93116,93117],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,93119,93120,93121,29696,93138,93155],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,93122,93124],{"className":93123},[886],[888,93125,93126],{"xmlns":890},[892,93127,93128,93136],{},[895,93129,93130],{},[1931,93131,93132,93134],{},[898,93133,1904],{},[1864,93135,1866],{},[902,93137,29695],{"encoding":904},[883,93139,93141],{"className":93140},[886],[888,93142,93143],{"xmlns":890},[892,93144,93145,93153],{},[895,93146,93147],{},[1931,93148,93149,93151],{},[898,93150,1904],{},[1864,93152,2331],{},[902,93154,29714],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,93158,93160],{"className":93159},[886],[888,93161,93162],{"xmlns":890},[892,93163,93164,93172],{},[895,93165,93166],{},[1931,93167,93168,93170],{},[898,93169,1904],{},[1864,93171,2331],{},[902,93173,29714],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,93176,93178],{"className":93177},[886],[888,93179,93180],{"xmlns":890},[892,93181,93182,93190],{},[895,93183,93184],{},[1931,93185,93186,93188],{},[898,93187,1904],{},[1864,93189,1866],{},[902,93191,29695],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,93194,93195,93196,30637],{},"Pro obecnou změnu ",[883,93197,93199],{"className":93198},[886],[888,93200,93201],{"xmlns":890},[892,93202,93203,93213],{},[895,93204,93205,93207],{},[898,93206,2930],{"mathvariant":2124},[1931,93208,93209,93211],{},[898,93210,1904],{},[1864,93212,1866],{},[902,93214,93215],{"encoding":904},"\\mathrm{d} Q_1",[883,93217,93219],{"className":93218},[886],[888,93220,93221],{"xmlns":890,"display":28759},[892,93222,93223,93276],{},[21447,93224,93225],{"width":28764},[21452,93226,93227,93229,93269,93271],{},[21455,93228],{"width":28769},[21455,93230,93231],{},[895,93232,93233,93235,93241,93243,93245,93251,93253,93255,93257,93259,93261,93267],{},[898,93234,3611],{"mathvariant":2124},[1931,93236,93237,93239],{},[898,93238,1904],{},[1864,93240,2331],{},[1723,93242,3456],{},[898,93244,2930],{"mathvariant":2124},[1931,93246,93247,93249],{},[898,93248,1904],{},[1864,93250,2331],{},[1723,93252,1725],{},[1723,93254,1759],{},[3018,93256,11303],{},[1723,93258,3897],{},[898,93260,2930],{"mathvariant":2124},[1931,93262,93263,93265],{},[898,93264,1904],{},[1864,93266,1866],{},[1723,93268,2031],{"separator":2030},[21455,93270],{"width":28769},[21455,93272,93273],{},[3018,93274,93275],{},"(6.10)",[902,93277,93278],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,93280,93282],{"className":93281},[886],[888,93283,93284],{"xmlns":890,"display":28759},[892,93285,93286,93333],{},[21447,93287,93288],{"width":28764},[21452,93289,93290,93292,93326,93328],{},[21455,93291],{"width":28769},[21455,93293,93294],{},[895,93295,93296,93298,93304,93306,93308,93314,93316,93318,93324],{},[898,93297,2930],{"mathvariant":2124},[1931,93299,93300,93302],{},[898,93301,1904],{},[1864,93303,1866],{},[1723,93305,1725],{},[1723,93307,1759],{},[3058,93309,93310,93312],{},[1864,93311,1866],{},[3018,93313,11303],{},[3018,93315,3707],{},[898,93317,2930],{"mathvariant":2124},[1931,93319,93320,93322],{},[898,93321,1904],{},[1864,93323,2331],{},[898,93325,1664],{"mathvariant":2124},[21455,93327],{"width":28769},[21455,93329,93330],{},[3018,93331,93332],{},"(6.11)",[902,93334,93335],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[4584,93337,93338,93404,93521],{},[724,93339,93340,93342,93343,30637],{},[883,93341,53385],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,93344,93346],{"className":93345},[886],[888,93347,93348],{"xmlns":890},[892,93349,93350,93402],{},[895,93351,93352,93354,93356,93362,93364,93370,93372,93374,93388],{},[898,93353,900],{},[1723,93355,1908],{"stretchy":1907},[1931,93357,93358,93360],{},[898,93359,1904],{},[1864,93361,1866],{},[1723,93363,2031],{"separator":2030},[1931,93365,93366,93368],{},[898,93367,1904],{},[1864,93369,2331],{},[1723,93371,1914],{"stretchy":1907},[1723,93373,1725],{},[2220,93375,93376,93378,93380],{},[898,93377,1904],{},[1864,93379,1866],{},[895,93381,93382,93384,93386],{},[1864,93383,1866],{},[898,93385,2125],{"mathvariant":2124},[1864,93387,2331],{},[2220,93389,93390,93392,93394],{},[898,93391,1904],{},[1864,93393,2331],{},[895,93395,93396,93398,93400],{},[1864,93397,1866],{},[898,93399,2125],{"mathvariant":2124},[1864,93401,2331],{},[902,93403,30636],{"encoding":904},[724,93405,93406],{},[883,93407,93409],{"className":93408},[886],[888,93410,93411],{"xmlns":890},[892,93412,93413,93519],{},[895,93414,93415,93417,93419,93501,93503,93517],{},[3018,93416,11303],{},[1723,93418,1725],{},[3058,93420,93421,93461],{},[895,93422,93423,93431,93447],{},[3055,93424,93425],{"scriptlevel":2256,"displaystyle":1907},[3058,93426,93427,93429],{},[1864,93428,1866],{},[1864,93430,2331],{},[2220,93432,93433,93435,93437],{},[898,93434,1904],{},[1864,93436,1866],{},[895,93438,93439,93441,93443,93445],{},[1723,93440,1759],{},[1864,93442,1866],{},[898,93444,2125],{"mathvariant":2124},[1864,93446,2331],{},[2220,93448,93449,93451,93453],{},[898,93450,1904],{},[1864,93452,2331],{},[895,93454,93455,93457,93459],{},[1864,93456,1866],{},[898,93458,2125],{"mathvariant":2124},[1864,93460,2331],{},[895,93462,93463,93471,93485],{},[3055,93464,93465],{"scriptlevel":2256,"displaystyle":1907},[3058,93466,93467,93469],{},[1864,93468,1866],{},[1864,93470,2331],{},[2220,93472,93473,93475,93477],{},[898,93474,1904],{},[1864,93476,1866],{},[895,93478,93479,93481,93483],{},[1864,93480,1866],{},[898,93482,2125],{"mathvariant":2124},[1864,93484,2331],{},[2220,93486,93487,93489,93491],{},[898,93488,1904],{},[1864,93490,2331],{},[895,93492,93493,93495,93497,93499],{},[1723,93494,1759],{},[1864,93496,1866],{},[898,93498,2125],{"mathvariant":2124},[1864,93500,2331],{},[1723,93502,1725],{},[3058,93504,93505,93511],{},[1931,93506,93507,93509],{},[898,93508,1904],{},[1864,93510,2331],{},[1931,93512,93513,93515],{},[898,93514,1904],{},[1864,93516,1866],{},[898,93518,1664],{"mathvariant":2124},[902,93520,30755],{"encoding":904},[724,93522,30758,93523,2137,93566,30806,93568,93587],{},[883,93524,93526],{"className":93525},[886],[888,93527,93528],{"xmlns":890},[892,93529,93530,93564],{},[895,93531,93532,93534,93536,93538,93540,93542,93544,93546,93554,93556],{},[3018,93533,11303],{},[1723,93535,1908],{"stretchy":1907},[1864,93537,30774],{},[1723,93539,2031],{"separator":2030},[1864,93541,15811],{},[1723,93543,1914],{"stretchy":1907},[1723,93545,1725],{},[3055,93547,93548],{"scriptlevel":2256,"displaystyle":1907},[3058,93549,93550,93552],{},[1864,93551,15811],{},[1864,93553,30774],{},[1723,93555,1725],{},[3055,93557,93558],{"scriptlevel":2256,"displaystyle":1907},[3058,93559,93560,93562],{},[1864,93561,2962],{},[1864,93563,2909],{},[902,93565,30803],{"encoding":904},[614,93567,9924],{},[883,93569,93571],{"className":93570},[886],[888,93572,93573],{"xmlns":890},[892,93574,93575,93585],{},[895,93576,93577],{},[3055,93578,93579],{"scriptlevel":2256,"displaystyle":1907},[3058,93580,93581,93583],{},[1864,93582,2962],{},[1864,93584,2909],{},[902,93586,30826],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,93589,93590,93591,93595],{},"(Paralelou je ",[207,93592,93594],{"className":93593,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,93597,93599],{"id":93598},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,93601,93602,93603,93606],{},"Rámcově se v kapitole 6 studují ",[38,93604,93605],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,93608,93609,93745],{},[123,93610,93611,93613,93614,10857,93645,2628,93648,93697,93698,1664],{},[38,93612,28945],{}," — maximalizace ",[883,93615,93617],{"className":93616},[886],[888,93618,93619],{"xmlns":890},[892,93620,93621,93643],{},[895,93622,93623,93625,93627,93633,93635,93641],{},[898,93624,900],{},[1723,93626,1908],{"stretchy":1907},[1931,93628,93629,93631],{},[898,93630,1904],{},[1864,93632,1866],{},[1723,93634,2031],{"separator":2030},[1931,93636,93637,93639],{},[898,93638,1904],{},[1864,93640,2331],{},[1723,93642,1914],{"stretchy":1907},[902,93644,17039],{"encoding":904},[38,93646,93647],{},"rozpočtovém omezení",[883,93649,93651],{"className":93650},[886],[888,93652,93653],{"xmlns":890},[892,93654,93655,93695],{},[895,93656,93657,93663,93665,93673,93679,93681,93689],{},[2057,93658,93659,93661],{},[898,93660,9837],{},[1723,93662,5066],{},[1723,93664,1725],{},[2220,93666,93667,93669,93671],{},[898,93668,1746],{},[1864,93670,1866],{},[1723,93672,5066],{},[1931,93674,93675,93677],{},[898,93676,1904],{},[1864,93678,1866],{},[1723,93680,2087],{},[2220,93682,93683,93685,93687],{},[898,93684,1746],{},[1864,93686,2331],{},[1723,93688,5066],{},[1931,93690,93691,93693],{},[898,93692,1904],{},[1864,93694,2331],{},[902,93696,17994],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,93699,93701],{"className":93700},[886],[888,93702,93703],{"xmlns":890},[892,93704,93705,93743],{},[895,93706,93707,93713,93715,93721,93723,93729,93731,93737,93739,93741],{},[1931,93708,93709,93711],{},[898,93710,1904],{},[898,93712,2216],{},[1723,93714,1725],{},[1931,93716,93717,93719],{},[898,93718,4897],{},[898,93720,2216],{},[1723,93722,1908],{"stretchy":1907},[1931,93724,93725,93727],{},[898,93726,1746],{},[1864,93728,1866],{},[1723,93730,2031],{"separator":2030},[1931,93732,93733,93735],{},[898,93734,1746],{},[1864,93736,2331],{},[1723,93738,2031],{"separator":2030},[898,93740,9837],{},[1723,93742,1914],{"stretchy":1907},[902,93744,37148],{"encoding":904},[123,93746,93747,28594,93750,28637,93796,93813,93814,1664],{},[38,93748,93749],{},"Duální úloha",[883,93751,93753],{"className":93752},[886],[888,93754,93755],{"xmlns":890},[892,93756,93757,93793],{},[895,93758,93759,93761,93763,93771,93777,93779,93787],{},[898,93760,1846],{},[1723,93762,1725],{},[2220,93764,93765,93767,93769],{},[898,93766,1746],{},[1864,93768,1866],{},[1723,93770,5066],{},[1931,93772,93773,93775],{},[898,93774,1904],{},[1864,93776,1866],{},[1723,93778,2087],{},[2220,93780,93781,93783,93785],{},[898,93782,1746],{},[1864,93784,2331],{},[1723,93786,5066],{},[1931,93788,93789,93791],{},[898,93790,1904],{},[1864,93792,2331],{},[902,93794,93795],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,93797,93799],{"className":93798},[886],[888,93800,93801],{"xmlns":890},[892,93802,93803,93811],{},[895,93804,93805],{},[2057,93806,93807,93809],{},[898,93808,900],{},[1723,93810,5066],{},[902,93812,28655],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,93815,93817],{"className":93816},[886],[888,93818,93819],{"xmlns":890},[892,93820,93821,93859],{},[895,93822,93823,93829,93831,93837,93839,93845,93847,93853,93855,93857],{},[1931,93824,93825,93827],{},[898,93826,1904],{},[898,93828,2216],{},[1723,93830,1725],{},[1931,93832,93833,93835],{},[898,93834,4897],{},[898,93836,2216],{},[1723,93838,1908],{"stretchy":1907},[1931,93840,93841,93843],{},[898,93842,1746],{},[1864,93844,1866],{},[1723,93846,2031],{"separator":2030},[1931,93848,93849,93851],{},[898,93850,1746],{},[1864,93852,2331],{},[1723,93854,2031],{"separator":2030},[898,93856,900],{},[1723,93858,1914],{"stretchy":1907},[902,93860,18518],{"encoding":904},[724,93862,93863,93864,93867,93868,2628,93871,93910],{},"Obě úlohy se řeší ",[207,93865,28660],{"className":93866,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,93869,93870],{},"tentýž bod dotyku",[883,93872,93874],{"className":93873},[886],[888,93875,93876],{"xmlns":890},[892,93877,93878,93908],{},[895,93879,93880,93886,93888,93896,93898,93906],{},[2057,93881,93882,93884],{},[898,93883,1904],{},[1723,93885,5066],{},[1723,93887,3212],{"stretchy":1907},[2220,93889,93890,93892,93894],{},[898,93891,1904],{},[1864,93893,1866],{},[1723,93895,5066],{},[1723,93897,2031],{"separator":2030},[2220,93899,93900,93902,93904],{},[898,93901,1904],{},[1864,93903,2331],{},[1723,93905,5066],{},[1723,93907,3227],{"stretchy":1907},[902,93909,29020],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,93912,93914],{"className":93913},[886],[888,93915,93916],{"xmlns":890,"display":28759},[892,93917,93918,93964],{},[895,93919,93920,93922,93924,93942,93944,93962],{},[3018,93921,11303],{},[1723,93923,1725],{},[3058,93925,93926,93934],{},[2220,93927,93928,93930,93932],{},[898,93929,900],{},[1864,93931,1866],{},[1723,93933,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[2220,93935,93936,93938,93940],{},[898,93937,900],{},[1864,93939,2331],{},[1723,93941,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,93943,1725],{},[3058,93945,93946,93954],{},[2220,93947,93948,93950,93952],{},[898,93949,1746],{},[1864,93951,1866],{},[1723,93953,5066],{},[2220,93955,93956,93958,93960],{},[898,93957,1746],{},[1864,93959,2331],{},[1723,93961,5066],{},[898,93963,1664],{"mathvariant":2124},[902,93965,93966],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,93968,93969],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[4584,93971,93972],{},[724,93973,93974,93976,93977,93980,93981,93984,93985,94012,94013,94047,94048,94082,94083,94126,94127,94130,94131,1664],{},[883,93975,4869],{}," Pro detailní postup viz ",[207,93978,37447],{"className":93979,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,93982,93983],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,93986,93988],{"className":93987},[886],[888,93989,93990],{"xmlns":890},[892,93991,93992,94010],{},[895,93993,93994,93996,93998,94004],{},[898,93995,900],{},[1723,93997,1725],{},[1931,93999,94000,94002],{},[898,94001,1904],{},[1864,94003,1866],{},[1931,94005,94006,94008],{},[898,94007,1904],{},[1864,94009,2331],{},[902,94011,30919],{"encoding":904}," s výsledkem ",[883,94014,94016],{"className":94015},[886],[888,94017,94018],{"xmlns":890},[892,94019,94020,94044],{},[895,94021,94022,94028,94030,94032,94034,94040,94042],{},[1931,94023,94024,94026],{},[898,94025,1904],{},[1864,94027,1866],{},[1723,94029,1725],{},[1864,94031,5714],{},[1723,94033,2031],{"separator":2030},[1931,94035,94036,94038],{},[898,94037,1904],{},[1864,94039,2331],{},[1723,94041,1725],{},[1864,94043,3585],{},[902,94045,94046],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,94049,94051],{"className":94050},[886],[888,94052,94053],{"xmlns":890},[892,94054,94055,94079],{},[895,94056,94057,94063,94065,94067,94069,94075,94077],{},[1931,94058,94059,94061],{},[898,94060,1904],{},[1864,94062,1866],{},[1723,94064,1725],{},[1864,94066,3080],{},[1723,94068,2031],{"separator":2030},[1931,94070,94071,94073],{},[898,94072,1904],{},[1864,94074,2331],{},[1723,94076,1725],{},[1864,94078,1866],{},[902,94080,94081],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,94084,94086],{"className":94085},[886],[888,94087,94088],{"xmlns":890},[892,94089,94090,94124],{},[895,94091,94092,94094,94096,94110],{},[898,94093,900],{},[1723,94095,1725],{},[2220,94097,94098,94100,94102],{},[898,94099,1904],{},[1864,94101,1866],{},[895,94103,94104,94106,94108],{},[1864,94105,1866],{},[898,94107,2125],{"mathvariant":2124},[1864,94109,2331],{},[2220,94111,94112,94114,94116],{},[898,94113,1904],{},[1864,94115,2331],{},[895,94117,94118,94120,94122],{},[1864,94119,1866],{},[898,94121,2125],{"mathvariant":2124},[1864,94123,2331],{},[902,94125,33852],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,94128,94129],{},"6.8–6.13"," jsou na stránce ",[207,94132,28460],{"className":94133,"dataFsResolvedFilePath":911,"href":912},[210],[115,94135,94137],{"id":94136},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,94139,94140,94141,94154,94155,94157,94158,94160,94161,94163,94164,94166,94167,94169,94170,94172,94173,2628,94175,94210,94211,94224,94225,94228,94229,94232,94233,1664],{},"Každá ",[883,94142,94144],{"className":94143},[886],[888,94145,94146],{"xmlns":890},[892,94147,94148,94152],{},[895,94149,94150],{},[898,94151,2192],{},[902,94153,2192],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,94156,87488],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,94159,87972],{}," a současně ",[38,94162,87491],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,94165,87496],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,94168,53367],{}," (6.4) a druhé parciální derivace ",[38,94171,89855],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,94174,10437],{},[883,94176,94178],{"className":94177},[886],[888,94179,94180],{"xmlns":890},[892,94181,94182,94208],{},[895,94183,94184,94186,94188,94194,94196,94202,94204,94206],{},[898,94185,900],{},[1723,94187,1908],{"stretchy":1907},[1931,94189,94190,94192],{},[898,94191,1904],{},[1864,94193,1866],{},[1723,94195,2031],{"separator":2030},[1931,94197,94198,94200],{},[898,94199,1904],{},[1864,94201,2331],{},[1723,94203,1914],{"stretchy":1907},[1723,94205,1725],{},[898,94207,2878],{},[902,94209,10474],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,94212,94214],{"className":94213},[886],[888,94215,94216],{"xmlns":890},[892,94217,94218,94222],{},[895,94219,94220],{},[3018,94221,11303],{},[902,94223,28931],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,94226,94227],{},"maximalizace užitečnosti"," a duální ",[38,94230,94231],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,94234,37447],{"className":94235,"dataFsResolvedFilePath":911,"href":912},[210],[115,94237,2615],{"id":50572},[152,94239,94240,94243,94246,94249,94252,94255,94258,94261,94264,94267],{},[123,94241,94242],{},"Co se zahrnuje pod termín užitečnost?",[123,94244,94245],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,94247,94248],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,94250,94251],{},"Jak se vypočítá mezní užitečnost?",[123,94253,94254],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,94256,94257],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,94259,94260],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,94262,94263],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,94265,94266],{},"Proč mají křivky užitečnosti záporný sklon?",[123,94268,94269],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,94271,94273],{"id":94272},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,94275,94276,94279,94280,84163,94322,1343,94350,1343,94378,94406],{},[38,94277,94278],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,94281,94283],{"className":94282},[886],[888,94284,94285],{"xmlns":890},[892,94286,94287,94319],{},[895,94288,94289,94291,94293,94299,94301,94303,94309,94311,94313],{},[898,94290,900],{},[1723,94292,1725],{},[1931,94294,94295,94297],{},[898,94296,1904],{},[1864,94298,1866],{},[1723,94300,2087],{},[1864,94302,65246],{},[1931,94304,94305,94307],{},[898,94306,1904],{},[1864,94308,2331],{},[1723,94310,2087],{},[1864,94312,2331],{},[1931,94314,94315,94317],{},[898,94316,1904],{},[1864,94318,2909],{},[902,94320,94321],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,94323,94325],{"className":94324},[886],[888,94326,94327],{"xmlns":890},[892,94328,94329,94347],{},[895,94330,94331,94333,94335,94337,94339,94341,94343,94345],{},[898,94332,900],{},[1723,94334,1908],{"stretchy":1907},[1864,94336,3080],{},[1723,94338,2031],{"separator":2030},[1864,94340,2331],{},[1723,94342,2031],{"separator":2030},[1864,94344,2331],{},[1723,94346,1914],{"stretchy":1907},[902,94348,94349],{"encoding":904},"U(4, 2, 2)",[883,94351,94353],{"className":94352},[886],[888,94354,94355],{"xmlns":890},[892,94356,94357,94375],{},[895,94358,94359,94361,94363,94365,94367,94369,94371,94373],{},[898,94360,900],{},[1723,94362,1908],{"stretchy":1907},[1864,94364,1866],{},[1723,94366,2031],{"separator":2030},[1864,94368,3080],{},[1723,94370,2031],{"separator":2030},[1864,94372,2331],{},[1723,94374,1914],{"stretchy":1907},[902,94376,94377],{"encoding":904},"U(1, 4, 2)",[883,94379,94381],{"className":94380},[886],[888,94382,94383],{"xmlns":890},[892,94384,94385,94403],{},[895,94386,94387,94389,94391,94393,94395,94397,94399,94401],{},[898,94388,900],{},[1723,94390,1908],{"stretchy":1907},[1864,94392,2331],{},[1723,94394,2031],{"separator":2030},[1864,94396,2909],{},[1723,94398,2031],{"separator":2030},[1864,94400,1866],{},[1723,94402,1914],{"stretchy":1907},[902,94404,94405],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,94408,94409,94412,94413,94465,94466,1343,94492,1343,94518,1343,94544,1343,94570,1343,94596,1343,94622,94648],{},[38,94410,94411],{},"6.2"," Je dána užitečnost ",[883,94414,94416],{"className":94415},[886],[888,94417,94418],{"xmlns":890},[892,94419,94420,94462],{},[895,94421,94422,94424,94426,94428,94442,94456],{},[898,94423,900],{},[1723,94425,1725],{},[1864,94427,2331],{},[2220,94429,94430,94432,94434],{},[898,94431,1904],{},[1864,94433,1866],{},[895,94435,94436,94438,94440],{},[1864,94437,1866],{},[898,94439,2125],{"mathvariant":2124},[1864,94441,2909],{},[2220,94443,94444,94446,94448],{},[898,94445,1904],{},[1864,94447,2331],{},[895,94449,94450,94452,94454],{},[1864,94451,1866],{},[898,94453,2125],{"mathvariant":2124},[1864,94455,2331],{},[1931,94457,94458,94460],{},[898,94459,1904],{},[1864,94461,2909],{},[902,94463,94464],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,94467,94469],{"className":94468},[886],[888,94470,94471],{"xmlns":890},[892,94472,94473,94489],{},[895,94474,94475,94477,94479,94481,94483,94485,94487],{},[1723,94476,1908],{"stretchy":1907},[1864,94478,6275],{},[1723,94480,2031],{"separator":2030},[1864,94482,67284],{},[1723,94484,2031],{"separator":2030},[1864,94486,3585],{},[1723,94488,1914],{"stretchy":1907},[902,94490,94491],{"encoding":904},"(36, 27, 10)",[883,94493,94495],{"className":94494},[886],[888,94496,94497],{"xmlns":890},[892,94498,94499,94515],{},[895,94500,94501,94503,94505,94507,94509,94511,94513],{},[1723,94502,1908],{"stretchy":1907},[1864,94504,42532],{},[1723,94506,2031],{"separator":2030},[1864,94508,6295],{},[1723,94510,2031],{"separator":2030},[1864,94512,9744],{},[1723,94514,1914],{"stretchy":1907},[902,94516,94517],{"encoding":904},"(64, 8, 20)",[883,94519,94521],{"className":94520},[886],[888,94522,94523],{"xmlns":890},[892,94524,94525,94541],{},[895,94526,94527,94529,94531,94533,94535,94537,94539],{},[1723,94528,1908],{"stretchy":1907},[1864,94530,5714],{},[1723,94532,2031],{"separator":2030},[1864,94534,42532],{},[1723,94536,2031],{"separator":2030},[1864,94538,6295],{},[1723,94540,1914],{"stretchy":1907},[902,94542,94543],{"encoding":904},"(25, 64, 8)",[883,94545,94547],{"className":94546},[886],[888,94548,94549],{"xmlns":890},[892,94550,94551,94567],{},[895,94552,94553,94555,94557,94559,94561,94563,94565],{},[1723,94554,1908],{"stretchy":1907},[1864,94556,3080],{},[1723,94558,2031],{"separator":2030},[1864,94560,73214],{},[1723,94562,2031],{"separator":2030},[1864,94564,2969],{},[1723,94566,1914],{"stretchy":1907},[902,94568,94569],{"encoding":904},"(4, 125, 6)",[883,94571,94573],{"className":94572},[886],[888,94574,94575],{"xmlns":890},[892,94576,94577,94593],{},[895,94578,94579,94581,94583,94585,94587,94589,94591],{},[1723,94580,1908],{"stretchy":1907},[1864,94582,4713],{},[1723,94584,2031],{"separator":2030},[1864,94586,5921],{},[1723,94588,2031],{"separator":2030},[1864,94590,4227],{},[1723,94592,1914],{"stretchy":1907},[902,94594,94595],{"encoding":904},"(9, 40, 12)",[883,94597,94599],{"className":94598},[886],[888,94600,94601],{"xmlns":890},[892,94602,94603,94619],{},[895,94604,94605,94607,94609,94611,94613,94615,94617],{},[1723,94606,1908],{"stretchy":1907},[1864,94608,4713],{},[1723,94610,2031],{"separator":2030},[1864,94612,42532],{},[1723,94614,2031],{"separator":2030},[1864,94616,2962],{},[1723,94618,1914],{"stretchy":1907},[902,94620,94621],{"encoding":904},"(9, 64, 5)",[883,94623,94625],{"className":94624},[886],[888,94626,94627],{"xmlns":890},[892,94628,94629,94645],{},[895,94630,94631,94633,94635,94637,94639,94641,94643],{},[1723,94632,1908],{"stretchy":1907},[1864,94634,42532],{},[1723,94636,2031],{"separator":2030},[1864,94638,6295],{},[1723,94640,2031],{"separator":2030},[1864,94642,3585],{},[1723,94644,1914],{"stretchy":1907},[902,94646,94647],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,94650,94651,94412,94654,94697,94698,94732,94733,7183,94763,94796,94797,94814,94815,94832],{},[38,94652,94653],{},"6.3",[883,94655,94657],{"className":94656},[886],[888,94658,94659],{"xmlns":890},[892,94660,94661,94695],{},[895,94662,94663,94665,94667,94681],{},[898,94664,900],{},[1723,94666,1725],{},[2220,94668,94669,94671,94673],{},[898,94670,1904],{},[1864,94672,1866],{},[895,94674,94675,94677,94679],{},[1864,94676,1866],{},[898,94678,2125],{"mathvariant":2124},[1864,94680,2331],{},[2220,94682,94683,94685,94687],{},[898,94684,1904],{},[1864,94686,2331],{},[895,94688,94689,94691,94693],{},[1864,94690,1866],{},[898,94692,2125],{"mathvariant":2124},[1864,94694,2331],{},[902,94696,33852],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,94699,94701],{"className":94700},[886],[888,94702,94703],{"xmlns":890},[892,94704,94705,94729],{},[895,94706,94707,94713,94715,94717,94719,94725,94727],{},[1931,94708,94709,94711],{},[898,94710,1904],{},[1864,94712,1866],{},[1723,94714,1725],{},[1864,94716,3840],{},[1723,94718,2031],{"separator":2030},[1931,94720,94721,94723],{},[898,94722,1904],{},[1864,94724,2331],{},[1723,94726,1725],{},[1864,94728,47394],{},[902,94730,94731],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,94734,94736],{"className":94735},[886],[888,94737,94738],{"xmlns":890},[892,94739,94740,94760],{},[895,94741,94742,94744,94750,94752,94754],{},[898,94743,1728],{},[1931,94745,94746,94748],{},[898,94747,900],{},[1864,94749,1866],{},[1723,94751,2031],{"separator":2030},[898,94753,1728],{},[1931,94755,94756,94758],{},[898,94757,900],{},[1864,94759,2331],{},[902,94761,94762],{"encoding":904},"MU_1, MU_2",[883,94764,94766],{"className":94765},[886],[888,94767,94768],{"xmlns":890},[892,94769,94770,94794],{},[895,94771,94772,94778,94780,94782,94784,94790,94792],{},[1931,94773,94774,94776],{},[898,94775,1904],{},[1864,94777,1866],{},[1723,94779,1725],{},[1864,94781,3840],{},[1723,94783,2031],{"separator":2030},[1931,94785,94786,94788],{},[898,94787,1904],{},[1864,94789,2331],{},[1723,94791,1725],{},[1864,94793,47394],{},[902,94795,94731],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,94798,94800],{"className":94799},[886],[888,94801,94802],{"xmlns":890},[892,94803,94804,94812],{},[895,94805,94806],{},[1931,94807,94808,94810],{},[898,94809,1904],{},[1864,94811,1866],{},[902,94813,29695],{"encoding":904}," na 60 a poklesu ",[883,94816,94818],{"className":94817},[886],[888,94819,94820],{"xmlns":890},[892,94821,94822,94830],{},[895,94823,94824],{},[1931,94825,94826,94828],{},[898,94827,1904],{},[1864,94829,2331],{},[902,94831,29714],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,94834,94835,94838,94839,94900,94901,1664],{},[38,94836,94837],{},"6.4"," Je dána funkce ",[883,94840,94842],{"className":94841},[886],[888,94843,94844],{"xmlns":890},[892,94845,94846,94898],{},[895,94847,94848,94850,94852,94858,94860,94866,94868,94870,94884],{},[898,94849,900],{},[1723,94851,1908],{"stretchy":1907},[1931,94853,94854,94856],{},[898,94855,1904],{},[1864,94857,1866],{},[1723,94859,2031],{"separator":2030},[1931,94861,94862,94864],{},[898,94863,1904],{},[1864,94865,2331],{},[1723,94867,1914],{"stretchy":1907},[1723,94869,1725],{},[2220,94871,94872,94874,94876],{},[898,94873,1904],{},[1864,94875,1866],{},[895,94877,94878,94880,94882],{},[1864,94879,1866],{},[898,94881,2125],{"mathvariant":2124},[1864,94883,2331],{},[2220,94885,94886,94888,94890],{},[898,94887,1904],{},[1864,94889,2331],{},[895,94891,94892,94894,94896],{},[1864,94893,1866],{},[898,94895,2125],{"mathvariant":2124},[1864,94897,2331],{},[902,94899,30636],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,94902,94904],{"className":94903},[886],[888,94905,94906],{"xmlns":890},[892,94907,94908,94998],{},[895,94909,94910,94912,94914,94920,94922,94924,94926,94928,94930,94932,94938,94940,94942,94944,94946,94948,94950,94952,94954,94960,94962,94964,94966,94968,94970,94972,94978,94980,94982,94984,94986,94988,94990,94996],{},[898,94911,900],{},[1723,94913,1908],{"stretchy":1907},[1931,94915,94916,94918],{},[898,94917,1904],{},[1864,94919,1866],{},[1723,94921,2031],{"separator":2030},[1864,94923,1866],{},[1723,94925,1914],{"stretchy":1907},[1723,94927,2031],{"separator":2030},[898,94929,900],{},[1723,94931,1908],{"stretchy":1907},[1931,94933,94934,94936],{},[898,94935,1904],{},[1864,94937,1866],{},[1723,94939,2031],{"separator":2030},[1864,94941,2331],{},[1723,94943,1914],{"stretchy":1907},[1723,94945,2031],{"separator":2030},[898,94947,900],{},[1723,94949,1908],{"stretchy":1907},[1864,94951,1866],{},[1723,94953,2031],{"separator":2030},[1931,94955,94956,94958],{},[898,94957,1904],{},[1864,94959,2331],{},[1723,94961,1914],{"stretchy":1907},[1723,94963,2031],{"separator":2030},[898,94965,900],{},[1723,94967,1908],{"stretchy":1907},[1864,94969,2331],{},[1723,94971,2031],{"separator":2030},[1931,94973,94974,94976],{},[898,94975,1904],{},[1864,94977,2331],{},[1723,94979,1914],{"stretchy":1907},[1723,94981,2031],{"separator":2030},[898,94983,900],{},[1723,94985,1908],{"stretchy":1907},[1864,94987,2909],{},[1723,94989,2031],{"separator":2030},[1931,94991,94992,94994],{},[898,94993,1904],{},[1864,94995,2331],{},[1723,94997,1914],{"stretchy":1907},[902,94999,95000],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,95002,95003,94412,95006,95050,95051,95159,95160,1343,95185,1343,95210,95252,95253,1343,95282,95307],{},[38,95004,95005],{},"6.5",[883,95007,95009],{"className":95008},[886],[888,95010,95011],{"xmlns":890},[892,95012,95013,95047],{},[895,95014,95015,95017,95019,95033],{},[898,95016,900],{},[1723,95018,1725],{},[2220,95020,95021,95023,95025],{},[898,95022,1904],{},[1864,95024,1866],{},[895,95026,95027,95029,95031],{},[1864,95028,2331],{},[898,95030,2125],{"mathvariant":2124},[1864,95032,2909],{},[2220,95034,95035,95037,95039],{},[898,95036,1904],{},[1864,95038,2331],{},[895,95040,95041,95043,95045],{},[1864,95042,1866],{},[898,95044,2125],{"mathvariant":2124},[1864,95046,2909],{},[902,95048,95049],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,95052,95054],{"className":95053},[886],[888,95055,95056],{"xmlns":890},[892,95057,95058,95156],{},[895,95059,95060,95062,95064,95070,95072,95078,95080,95082,95084,95086,95088,95090,95096,95098,95100,95102,95104,95106,95108,95114,95116,95118,95120,95122,95124,95126,95128,95130,95136,95138,95140,95142,95144,95146,95148,95154],{},[898,95061,900],{},[1723,95063,1908],{"stretchy":1907},[1931,95065,95066,95068],{},[898,95067,1904],{},[1864,95069,1866],{},[1723,95071,2031],{"separator":2030},[1931,95073,95074,95076],{},[898,95075,1904],{},[1864,95077,2331],{},[1723,95079,1914],{"stretchy":1907},[1723,95081,1725],{},[1864,95083,2331],{},[1723,95085,2031],{"separator":2030},[898,95087,900],{},[1723,95089,1908],{"stretchy":1907},[1931,95091,95092,95094],{},[898,95093,1904],{},[1864,95095,1866],{},[1723,95097,2031],{"separator":2030},[1864,95099,2909],{},[1723,95101,1914],{"stretchy":1907},[1723,95103,2031],{"separator":2030},[898,95105,900],{},[1723,95107,1908],{"stretchy":1907},[1931,95109,95110,95112],{},[898,95111,1904],{},[1864,95113,1866],{},[1723,95115,2031],{"separator":2030},[1864,95117,2331],{},[1723,95119,1914],{"stretchy":1907},[1723,95121,2031],{"separator":2030},[898,95123,900],{},[1723,95125,1908],{"stretchy":1907},[1864,95127,2331],{},[1723,95129,2031],{"separator":2030},[1931,95131,95132,95134],{},[898,95133,1904],{},[1864,95135,2331],{},[1723,95137,1914],{"stretchy":1907},[1723,95139,2031],{"separator":2030},[898,95141,900],{},[1723,95143,1908],{"stretchy":1907},[1864,95145,2909],{},[1723,95147,2031],{"separator":2030},[1931,95149,95150,95152],{},[898,95151,1904],{},[1864,95153,2331],{},[1723,95155,1914],{"stretchy":1907},[902,95157,95158],{"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 ",[883,95161,95163],{"className":95162},[886],[888,95164,95165],{"xmlns":890},[892,95166,95167,95182],{},[895,95168,95169,95171,95173,95175,95177,95180],{},[898,95170,1718],{},[1723,95172,3212],{"stretchy":1907},[1864,95174,65246],{},[1723,95176,9135],{"separator":2030},[1864,95178,95179],{},"3,555",[1723,95181,3227],{"stretchy":1907},[902,95183,95184],{"encoding":904},"A[1{,}5; 3{,}555]",[883,95186,95188],{"className":95187},[886],[888,95189,95190],{"xmlns":890},[892,95191,95192,95207],{},[895,95193,95194,95196,95198,95200,95202,95205],{},[898,95195,23946],{},[1723,95197,3212],{"stretchy":1907},[1864,95199,53889],{},[1723,95201,9135],{"separator":2030},[1864,95203,95204],{},"1,28",[1723,95206,3227],{"stretchy":1907},[902,95208,95209],{"encoding":904},"B[2{,}5; 1{,}28]",[883,95211,95213],{"className":95212},[886],[888,95214,95215],{"xmlns":890},[892,95216,95217,95249],{},[895,95218,95219,95221,95223,95225,95227,95229,95231,95237,95239,95241,95243,95245,95247],{},[898,95220,1721],{},[1723,95222,3212],{"stretchy":1907},[1864,95224,2331],{},[1723,95226,9135],{"separator":2030},[898,95228,900],{},[1723,95230,1908],{"stretchy":1907},[1931,95232,95233,95235],{},[898,95234,1904],{},[1864,95236,1866],{},[1723,95238,2031],{"separator":2030},[1864,95240,2909],{},[1723,95242,1914],{"stretchy":1907},[1723,95244,1725],{},[1864,95246,2909],{},[1723,95248,3227],{"stretchy":1907},[902,95250,95251],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,95254,95256],{"className":95255},[886],[888,95257,95258],{"xmlns":890},[892,95259,95260,95279],{},[895,95261,95262,95264,95266,95268,95270,95272,95274,95277],{},[898,95263,4897],{},[1723,95265,3212],{"stretchy":1907},[1864,95267,2909],{},[1723,95269,9135],{"separator":2030},[1864,95271,1866],{},[1723,95273,9135],{"separator":2030},[1864,95275,95276],{},"0,832",[1723,95278,3227],{"stretchy":1907},[902,95280,95281],{"encoding":904},"D[3; 1; 0{,}832]",[883,95283,95285],{"className":95284},[886],[888,95286,95287],{"xmlns":890},[892,95288,95289,95304],{},[895,95290,95291,95293,95295,95297,95299,95302],{},[898,95292,1846],{},[1723,95294,3212],{"stretchy":1907},[1864,95296,53889],{},[1723,95298,9135],{"separator":2030},[1864,95300,95301],{},"4,32",[1723,95303,3227],{"stretchy":1907},[902,95305,95306],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,95309,95310,94412,95313,95356,95357,7183,95370,95404,95405,95422,95423,95440],{},[38,95311,95312],{},"6.6",[883,95314,95316],{"className":95315},[886],[888,95317,95318],{"xmlns":890},[892,95319,95320,95354],{},[895,95321,95322,95324,95326,95340],{},[898,95323,900],{},[1723,95325,1725],{},[2220,95327,95328,95330,95332],{},[898,95329,1904],{},[1864,95331,1866],{},[895,95333,95334,95336,95338],{},[1864,95335,2331],{},[898,95337,2125],{"mathvariant":2124},[1864,95339,2909],{},[2220,95341,95342,95344,95346],{},[898,95343,1904],{},[1864,95345,2331],{},[895,95347,95348,95350,95352],{},[1864,95349,1866],{},[898,95351,2125],{"mathvariant":2124},[1864,95353,2909],{},[902,95355,95049],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,95358,95360],{"className":95359},[886],[888,95361,95362],{"xmlns":890},[892,95363,95364,95368],{},[895,95365,95366],{},[3018,95367,11303],{},[902,95369,28931],{"encoding":904},[883,95371,95373],{"className":95372},[886],[888,95374,95375],{"xmlns":890},[892,95376,95377,95401],{},[895,95378,95379,95385,95387,95389,95391,95397,95399],{},[1931,95380,95381,95383],{},[898,95382,1904],{},[1864,95384,1866],{},[1723,95386,1725],{},[1864,95388,3810],{},[1723,95390,2031],{"separator":2030},[1931,95392,95393,95395],{},[898,95394,1904],{},[1864,95396,2331],{},[1723,95398,1725],{},[1864,95400,9087],{},[902,95402,95403],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,95406,95408],{"className":95407},[886],[888,95409,95410],{"xmlns":890},[892,95411,95412,95420],{},[895,95413,95414],{},[1931,95415,95416,95418],{},[898,95417,1904],{},[1864,95419,1866],{},[902,95421,29695],{"encoding":904},", poklesne-li ",[883,95424,95426],{"className":95425},[886],[888,95427,95428],{"xmlns":890},[892,95429,95430,95438],{},[895,95431,95432],{},[1931,95433,95434,95436],{},[898,95435,1904],{},[1864,95437,2331],{},[902,95439,29714],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,95442,95443,95446,95447,95464,95465,95482,95483,95515,95516,95541,95542,95555,95556,1343,95580,1343,95604,1664],{},[38,95444,95445],{},"6.7"," Míra uspokojení z nákupu množství ",[883,95448,95450],{"className":95449},[886],[888,95451,95452],{"xmlns":890},[892,95453,95454,95462],{},[895,95455,95456],{},[1931,95457,95458,95460],{},[898,95459,1904],{},[1864,95461,1866],{},[902,95463,29695],{"encoding":904}," nealko nápojů a množství ",[883,95466,95468],{"className":95467},[886],[888,95469,95470],{"xmlns":890},[892,95471,95472,95480],{},[895,95473,95474],{},[1931,95475,95476,95478],{},[898,95477,1904],{},[1864,95479,2331],{},[902,95481,29714],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,95484,95486],{"className":95485},[886],[888,95487,95488],{"xmlns":890},[892,95489,95490,95512],{},[895,95491,95492,95494,95496],{},[898,95493,900],{},[1723,95495,1725],{},[8827,95497,95498],{},[895,95499,95500,95506],{},[1931,95501,95502,95504],{},[898,95503,1904],{},[1864,95505,1866],{},[1931,95507,95508,95510],{},[898,95509,1904],{},[1864,95511,2331],{},[902,95513,95514],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,95517,95519],{"className":95518},[886],[888,95520,95521],{"xmlns":890},[892,95522,95523,95539],{},[895,95524,95525,95531,95533],{},[1931,95526,95527,95529],{},[898,95528,1904],{},[1864,95530,1866],{},[1723,95532,2031],{"separator":2030},[1931,95534,95535,95537],{},[898,95536,1904],{},[1864,95538,2331],{},[902,95540,36315],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,95543,95545],{"className":95544},[886],[888,95546,95547],{"xmlns":890},[892,95548,95549,95553],{},[895,95550,95551],{},[3018,95552,11303],{},[902,95554,28931],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,95557,95559],{"className":95558},[886],[888,95560,95561],{"xmlns":890},[892,95562,95563,95577],{},[895,95564,95565,95567,95569,95571,95573,95575],{},[3018,95566,11303],{},[1723,95568,1908],{"stretchy":1907},[1864,95570,2962],{},[1723,95572,2031],{"separator":2030},[1864,95574,9744],{},[1723,95576,1914],{"stretchy":1907},[902,95578,95579],{"encoding":904},"\\text{MRCS}(5, 20)",[883,95581,95583],{"className":95582},[886],[888,95584,95585],{"xmlns":890},[892,95586,95587,95601],{},[895,95588,95589,95591,95593,95595,95597,95599],{},[3018,95590,11303],{},[1723,95592,1908],{"stretchy":1907},[1864,95594,9744],{},[1723,95596,2031],{"separator":2030},[1864,95598,2962],{},[1723,95600,1914],{"stretchy":1907},[902,95602,95603],{"encoding":904},"\\text{MRCS}(20, 5)",[883,95605,95607],{"className":95606},[886],[888,95608,95609],{"xmlns":890},[892,95610,95611,95625],{},[895,95612,95613,95615,95617,95619,95621,95623],{},[3018,95614,11303],{},[1723,95616,1908],{"stretchy":1907},[1864,95618,2331],{},[1723,95620,2031],{"separator":2030},[1864,95622,3840],{},[1723,95624,1914],{"stretchy":1907},[902,95626,95627],{"encoding":904},"\\text{MRCS}(2, 50)",[4584,95629,95630],{},[724,95631,95632,95634,95635,1664],{},[883,95633,5283],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,95636,95639],{"className":95637,"dataFsResolvedFilePath":911,"href":95638},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,95641,16421],{"id":16420},[120,95643,95644,95650,95655,95661,95714,95724,95770,95825,95886,95943,95998,96037],{},[123,95645,95646,95649],{},[38,95647,95648],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,95651,95652,95654],{},[38,95653,87547],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,95656,95657,95660],{},[38,95658,95659],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,95662,95663,95665,95666,95679,95680,1664],{},[38,95664,87874],{}," — uspořádaná ",[883,95667,95669],{"className":95668},[886],[888,95670,95671],{"xmlns":890},[892,95672,95673,95677],{},[895,95674,95675],{},[898,95676,2192],{},[902,95678,2192],{"encoding":904},"-tice ",[883,95681,95683],{"className":95682},[886],[888,95684,95685],{"xmlns":890},[892,95686,95687,95711],{},[895,95688,95689,95691,95697,95699,95701,95703,95709],{},[1723,95690,1908],{"stretchy":1907},[1931,95692,95693,95695],{},[898,95694,1904],{},[1864,95696,1866],{},[1723,95698,2031],{"separator":2030},[1723,95700,2183],{},[1723,95702,2031],{"separator":2030},[1931,95704,95705,95707],{},[898,95706,1904],{},[898,95708,2192],{},[1723,95710,1914],{"stretchy":1907},[902,95712,95713],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,95715,95716,95719,95720,95723],{},[38,95717,95718],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,95721,95722],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,95725,95726,2628,95729,95769],{},[38,95727,95728],{},"Funkce užitečnosti",[883,95730,95732],{"className":95731},[886],[888,95733,95734],{"xmlns":890},[892,95735,95736,95766],{},[895,95737,95738,95740,95742,95744,95746,95752,95754,95756,95758,95764],{},[898,95739,900],{},[1723,95741,1725],{},[898,95743,900],{},[1723,95745,1908],{"stretchy":1907},[1931,95747,95748,95750],{},[898,95749,1904],{},[1864,95751,1866],{},[1723,95753,2031],{"separator":2030},[1723,95755,2183],{},[1723,95757,2031],{"separator":2030},[1931,95759,95760,95762],{},[898,95761,1904],{},[898,95763,2192],{},[1723,95765,1914],{"stretchy":1907},[902,95767,95768],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,95771,95772,2628,95775,95804,95805,2628,95808,95824],{},[38,95773,95774],{},"Mezní užitečnost",[883,95776,95778],{"className":95777},[886],[888,95779,95780],{"xmlns":890},[892,95781,95782,95802],{},[895,95783,95784,95786,95792,95794],{},[898,95785,1728],{},[1931,95787,95788,95790],{},[898,95789,900],{},[898,95791,2216],{},[1723,95793,1725],{},[2220,95795,95796,95798,95800],{},[898,95797,900],{},[898,95799,2216],{},[1723,95801,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[902,95803,2232],{"encoding":904}," — vzorec (6.2); ",[38,95806,95807],{},"totální diferenciál",[883,95809,95811],{"className":95810},[886],[888,95812,95813],{"xmlns":890},[892,95814,95815,95821],{},[895,95816,95817,95819],{},[898,95818,2930],{"mathvariant":2124},[898,95820,900],{},[902,95822,95823],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,95826,95827,95829,95830,95853,95854,95885],{},[38,95828,89510],{}," — (6.4) ",[883,95831,95833],{"className":95832},[886],[888,95834,95835],{"xmlns":890},[892,95836,95837,95851],{},[895,95838,95839,95847,95849],{},[2220,95840,95841,95843,95845],{},[898,95842,900],{},[898,95844,2216],{},[1723,95846,2229],{"mathvariant":2124,"lspace":2228,"rspace":2228},[1723,95848,2253],{},[1864,95850,2256],{},[902,95852,2259],{"encoding":904},", (6.5) ",[883,95855,95857],{"className":95856},[886],[888,95858,95859],{"xmlns":890},[892,95860,95861,95883],{},[895,95862,95863,95879,95881],{},[2220,95864,95865,95867,95873],{},[898,95866,900],{},[895,95868,95869,95871],{},[898,95870,2216],{},[898,95872,2216],{},[895,95874,95875,95877],{},[1723,95876,2229],{"mathvariant":2124},[1723,95878,2229],{"mathvariant":2124},[1723,95880,2287],{},[1864,95882,2256],{},[902,95884,2292],{"encoding":904}," (zákon klesající mezní užitečnosti).",[123,95887,95888,2628,95890,95921,95922,1664],{},[38,95889,91298],{},[883,95891,95893],{"className":95892},[886],[888,95894,95895],{"xmlns":890},[892,95896,95897,95919],{},[895,95898,95899,95901,95903,95911],{},[898,95900,900],{},[1723,95902,1725],{},[2220,95904,95905,95907,95909],{},[898,95906,1904],{},[1864,95908,1866],{},[898,95910,207],{},[2220,95912,95913,95915,95917],{},[898,95914,1904],{},[1864,95916,2331],{},[898,95918,2069],{},[902,95920,36496],{"encoding":904}," — (6.6), speciálně ",[883,95923,95925],{"className":95924},[886],[888,95926,95927],{"xmlns":890},[892,95928,95929,95941],{},[895,95930,95931,95933,95935,95937,95939],{},[898,95932,2069],{},[1723,95934,1725],{},[1864,95936,1866],{},[1723,95938,1759],{},[898,95940,207],{},[902,95942,91452],{"encoding":904},[123,95944,95945,2628,95948,95983,95984,95997],{},[38,95946,95947],{},"Křivky užitečnosti (indiferenční)",[883,95949,95951],{"className":95950},[886],[888,95952,95953],{"xmlns":890},[892,95954,95955,95981],{},[895,95956,95957,95959,95961,95967,95969,95975,95977,95979],{},[898,95958,900],{},[1723,95960,1908],{"stretchy":1907},[1931,95962,95963,95965],{},[898,95964,1904],{},[1864,95966,1866],{},[1723,95968,2031],{"separator":2030},[1931,95970,95971,95973],{},[898,95972,1904],{},[1864,95974,2331],{},[1723,95976,1914],{"stretchy":1907},[1723,95978,1725],{},[898,95980,2878],{},[902,95982,10474],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,95985,95987],{"className":95986},[886],[888,95988,95989],{"xmlns":890},[892,95990,95991,95995],{},[895,95992,95993],{},[898,95994,900],{},[902,95996,900],{"encoding":904},", konvexní.",[123,95999,96000,2628,96002,96036],{},[38,96001,92843],{},[883,96003,96005],{"className":96004},[886],[888,96006,96007],{"xmlns":890},[892,96008,96009,96033],{},[895,96010,96011,96013,96015,96017,96023,96025,96027],{},[3018,96012,11303],{},[1723,96014,1725],{},[898,96016,1728],{},[1931,96018,96019,96021],{},[898,96020,900],{},[1864,96022,1866],{},[898,96024,2125],{"mathvariant":2124},[898,96026,1728],{},[1931,96028,96029,96031],{},[898,96030,900],{},[1864,96032,2331],{},[902,96034,96035],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,96038,96039,2628,96042,10475,96071,96074],{},[38,96040,96041],{},"Podmínka optimality",[883,96043,96045],{"className":96044},[886],[888,96046,96047],{"xmlns":890},[892,96048,96049,96069],{},[895,96050,96051,96053,96055,96061,96063],{},[3018,96052,11303],{},[1723,96054,1725],{},[1931,96056,96057,96059],{},[898,96058,1746],{},[1864,96060,1866],{},[898,96062,2125],{"mathvariant":2124},[1931,96064,96065,96067],{},[898,96066,1746],{},[1864,96068,2331],{},[902,96070,28691],{"encoding":904},[207,96072,37447],{"className":96073,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,96076,2620],{"id":2619},[120,96078,96079,96116,96157,96167],{},[123,96080,96081,2628,96084,96087,96088,96101,96102,96115],{},[38,96082,96083],{},"Navazující téma:",[207,96085,913],{"className":96086,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,96089,96091],{"className":96090},[886],[888,96092,96093],{"xmlns":890},[892,96094,96095,96099],{},[895,96096,96097],{},[898,96098,900],{},[902,96100,900],{"encoding":904},", min ",[883,96103,96105],{"className":96104},[886],[888,96106,96107],{"xmlns":890},[892,96108,96109,96113],{},[895,96110,96111],{},[898,96112,1846],{},[902,96114,1846],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,96117,96118,2628,96121,11793,96124,87088,96127,96130,96131,96134,96135,19342,96153,96156],{},[38,96119,96120],{},"Související pojmy:",[207,96122,784],{"className":96123,"dataFsResolvedFilePath":782,"href":783},[210],[207,96125,3086],{"className":96126,"dataFsResolvedFilePath":764,"href":765},[210],[207,96128,11788],{"className":96129,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,96132,12642],{"className":96133,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,96136,96138],{"className":96137},[886],[888,96139,96140],{"xmlns":890},[892,96141,96142,96150],{},[895,96143,96144],{},[1931,96145,96146,96148],{},[898,96147,4897],{},[898,96149,2216],{},[902,96151,96152],{"encoding":904},"D_i",[207,96154,793],{"className":96155,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,96158,96159,2628,96161,1343,96164],{},[38,96160,37396],{},[207,96162,1094],{"className":96163,"dataFsResolvedFilePath":838,"href":839},[210],[207,96165,1101],{"className":96166,"dataFsResolvedFilePath":868,"href":869},[210],[123,96168,96169,2628,96171],{},[38,96170,2627],{},[207,96172,1646],{"className":96173,"dataFsResolvedFilePath":1645,"href":1644},[210],{"title":641,"searchDepth":642,"depth":642,"links":96175},[96176,96177,96178,96181,96182,96185,96189,96190,96193,96194,96195,96196,96197,96198,96199],{"id":12706,"depth":642,"text":12707},{"id":87470,"depth":642,"text":87471},{"id":87530,"depth":642,"text":87531,"children":96179},[96180],{"id":87546,"depth":649,"text":87547},{"id":87853,"depth":642,"text":87854},{"id":88713,"depth":642,"text":88714,"children":96183},[96184],{"id":89260,"depth":649,"text":80892},{"id":89509,"depth":642,"text":89510,"children":96186},[96187],{"id":90382,"depth":649,"text":96188},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":91297,"depth":642,"text":91298},{"id":91833,"depth":642,"text":91834,"children":96191},[96192],{"id":92607,"depth":649,"text":92608},{"id":92837,"depth":642,"text":92838},{"id":93598,"depth":642,"text":93599},{"id":94136,"depth":642,"text":94137},{"id":50572,"depth":642,"text":2615},{"id":94272,"depth":642,"text":94273},{"id":16420,"depth":642,"text":16421},{"id":2619,"depth":642,"text":2620},{},"\u002Ftopics\u002Fuzitecnost",{"title":87256,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,2361,96206,87250,11823,96207],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":96210,"title":757,"body":96211,"course":1128,"courses":659,"created":1129,"description":96482,"extension":661,"meta":96483,"navigation":664,"path":96484,"seo":96485,"sources":96486,"stem":96487,"tags":96488,"type":4573,"updated":677,"__hash__":96494},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":96212,"toc":96474},[96213,96216,96223,96230,96234,96244,96246,96280,96284,96327,96330,96388,96392,96421,96425,96445,96447],[12,96214,757],{"id":96215},"základy-matematické-ekonomie",[724,96217,96218,96219,96222],{},"Úvodní pojmy a princip modelování v ",[207,96220,17076],{"className":96221,"dataFsResolvedFilePath":1645,"href":1644},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,96224,96225],{},[3285,96226],{"alt":96227,"className":96228,"src":96229},"imek-model-promenne",[210,3289],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,96231,96233],{"id":96232},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,96235,96236,96239,96240,96243],{},[38,96237,96238],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,96241,96242],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,96245,16421],{"id":16420},[120,96247,96248,96254,96260,96266,96275],{},[123,96249,96250,96253],{},[38,96251,96252],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,96255,96256,96259],{},[38,96257,96258],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,96261,96262,96265],{},[38,96263,96264],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,96267,96268,7725,96271,96274],{},[38,96269,96270],{},"Ceteris paribus",[614,96272,96273],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,96276,96277,96279],{},[38,96278,51325],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,96281,96283],{"id":96282},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,96285,96286,96326],{},[883,96287,96289],{"className":96288},[886],[888,96290,96291],{"xmlns":890},[892,96292,96293,96323],{},[895,96294,96295,96297,96299,96301,96303,96305,96307,96309,96311,96313,96315,96317,96319,96321],{},[898,96296,1904],{},[1723,96298,1725],{},[898,96300,4897],{},[1723,96302,1908],{"stretchy":1907},[898,96304,1746],{},[1723,96306,2031],{"separator":2030},[898,96308,9837],{},[1723,96310,2031],{"separator":2030},[898,96312,18988],{},[1723,96314,2031],{"separator":2030},[898,96316,900],{},[1723,96318,2031],{"separator":2030},[1723,96320,2183],{},[1723,96322,1914],{"stretchy":1907},[902,96324,96325],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,96328,96329],{},"Zjednodušení:",[120,96331,96332,96360],{},[123,96333,96334,2628,96337],{},[38,96335,96336],{},"Jednofaktorový model:",[883,96338,96340],{"className":96339},[886],[888,96341,96342],{"xmlns":890},[892,96343,96344,96358],{},[895,96345,96346,96348,96350,96352,96354,96356],{},[898,96347,1904],{},[1723,96349,1725],{},[898,96351,4897],{},[1723,96353,1908],{"stretchy":1907},[898,96355,1746],{},[1723,96357,1914],{"stretchy":1907},[902,96359,4906],{"encoding":904},[123,96361,96362,2628,96365],{},[38,96363,96364],{},"Inverzní zápis:",[883,96366,96368],{"className":96367},[886],[888,96369,96370],{"xmlns":890},[892,96371,96372,96386],{},[895,96373,96374,96376,96378,96380,96382,96384],{},[898,96375,1746],{},[1723,96377,1725],{},[898,96379,4897],{},[1723,96381,1908],{"stretchy":1907},[898,96383,1904],{},[1723,96385,1914],{"stretchy":1907},[902,96387,5351],{"encoding":904},[115,96389,96391],{"id":96390},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,96393,96394,96403],{},[123,96395,96396,96399,96400,4634],{},[38,96397,96398],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,96401,1692],{"className":96402,"dataFsResolvedFilePath":800,"href":801},[210],[123,96404,96405,96408,96409,96412,96413,96416,96417,96420],{},[38,96406,96407],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,96410,1145],{"className":96411,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,96414,2575],{"className":96415,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,96418,2579],{"className":96419,"dataFsResolvedFilePath":791,"href":792},[210]," pro vázané extrémy).",[115,96422,96424],{"id":96423},"konvence-z-přednášek","Konvence z přednášek",[120,96426,96427,96433,96439],{},[123,96428,96429,96430,96432],{},"Symbol ",[2638,96431,3456],{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,96434,96435,96436,1664],{},"Numerické výsledky ",[38,96437,96438],{},"na 3 desetinná místa",[123,96440,4611,96441,96444],{},[614,96442,96443],{},"jednotková změna"," má standardní význam (změna o 1).",[115,96446,2620],{"id":2619},[120,96448,96449,96454,96462],{},[123,96450,96451,96453],{},[38,96452,4515],{}," —",[123,96455,96456,2628,96458],{},[38,96457,4523],{},[207,96459,96461],{"className":96460,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,96463,96464,2628,96466,1343,96470],{},[38,96465,4531],{},[207,96467,96469],{"className":96468,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,96471,96473],{"className":96472,"dataFsResolvedFilePath":1645,"href":1644},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":96475},[96476,96477,96478,96479,96480,96481],{"id":96232,"depth":642,"text":96233},{"id":16420,"depth":642,"text":16421},{"id":96282,"depth":642,"text":96283},{"id":96390,"depth":642,"text":96391},{"id":96423,"depth":642,"text":96424},{"id":2619,"depth":642,"text":2620},"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":96482},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,96489,96490,96491,96492,96493],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":96496,"title":96497,"body":96498,"course":1128,"courses":659,"created":2676,"description":641,"extension":661,"meta":100770,"navigation":664,"path":100771,"seo":100772,"sources":100773,"stem":100774,"tags":100775,"type":4573,"updated":677,"__hash__":100779},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":96499,"toc":100753},[96500,96503,96597,96601,96623,96637,96689,96691,96695,96758,96801,96820,96983,97082,97085,97152,97156,97285,97324,97354,97466,97511,97577,97630,97706,97762,97764,97768,97832,97876,97896,98057,98060,98144,98241,98244,98310,98314,98363,98389,98494,98558,98563,98659,98706,98708,98711,98733,98775,98782,98815,98817,98888,98942,99051,99055,99144,99220,99484,99522,99524,99528,99531,99538,99849,99852,99910,100090,100119,100121,100125,100131,100269,100278,100280,100282,100707,100709,100711],[12,96501,96497],{"id":96502},"zdanění-trhu-dopady-daně-na-rovnováhu",[4584,96504,96505],{},[724,96506,96507,43320,96509,96522,96523,96526,96527,96529,96530,96533,96534,96555,96556,96579,96580,96583,96584,1664],{},[883,96508,4869],{},[883,96510,96512],{"className":96511},[886],[888,96513,96514],{"xmlns":890},[892,96515,96516,96520],{},[895,96517,96518],{},[898,96519,1754],{},[902,96521,1754],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,96524,96525],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,96528,87538],{}," (je-li uložena spotřebiteli). Výsledné ",[38,96531,96532],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,96535,96537],{"className":96536},[886],[888,96538,96539],{"xmlns":890},[892,96540,96541,96553],{},[895,96542,96543],{},[1931,96544,96545,96547],{},[898,96546,1754],{},[895,96548,96549,96551],{},[898,96550,43369],{},[898,96552,724],{},[902,96554,43374],{"encoding":904}," (spotřebitel) a ",[883,96557,96559],{"className":96558},[886],[888,96560,96561],{"xmlns":890},[892,96562,96563,96577],{},[895,96564,96565],{},[1931,96566,96567,96569],{},[898,96568,1754],{},[895,96570,96571,96573,96575],{},[898,96572,43392],{},[898,96574,2740],{},[898,96576,12742],{},[902,96578,43399],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,96581,96582],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,96585,96587],{"className":96586},[886],[888,96588,96589],{"xmlns":890},[892,96590,96591,96595],{},[895,96592,96593],{},[898,96594,1754],{},[902,96596,1754],{"encoding":904},[115,96598,96600],{"id":96599},"dvě-formy-zdanění","Dvě formy zdanění",[724,96602,96603,96604,96622],{},"Uvažujme jednotkovou daň ",[883,96605,96607],{"className":96606},[886],[888,96608,96609],{"xmlns":890},[892,96610,96611,96619],{},[895,96612,96613,96615,96617],{},[898,96614,1754],{},[1723,96616,2253],{},[1864,96618,2256],{},[902,96620,96621],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,96624,96625,96631],{},[123,96626,96627,96630],{},[38,96628,96629],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,96632,96633,96636],{},[38,96634,96635],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,96638,96639,96640,96653,96654,96657,96658,1664],{},"V obou případech dochází k posunu jedné z křivek o ",[883,96641,96643],{"className":96642},[886],[888,96644,96645],{"xmlns":890},[892,96646,96647,96651],{},[895,96648,96649],{},[898,96650,1754],{},[902,96652,1754],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,96655,96656],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,96659,96661],{"className":96660},[886],[888,96662,96663],{"xmlns":890},[892,96664,96665,96687],{},[895,96666,96667,96669,96671,96677,96679,96685],{},[898,96668,1846],{},[1723,96670,3212],{"stretchy":1907},[2057,96672,96673,96675],{},[898,96674,1904],{},[898,96676,1846],{},[1723,96678,2031],{"separator":2030},[2057,96680,96681,96683],{},[898,96682,1746],{},[898,96684,1846],{},[1723,96686,3227],{"stretchy":1907},[902,96688,42059],{"encoding":904},[37662,96690],{},[115,96692,96694],{"id":96693},"daň-uložená-výrobci","Daň uložená výrobci",[724,96696,96697,96698,96711,96712,96729,96730,96757],{},"Je-li daň ",[883,96699,96701],{"className":96700},[886],[888,96702,96703],{"xmlns":890},[892,96704,96705,96709],{},[895,96706,96707],{},[898,96708,1754],{},[902,96710,1754],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,96713,96715],{"className":96714},[886],[888,96716,96717],{"xmlns":890},[892,96718,96719,96727],{},[895,96720,96721,96723,96725],{},[898,96722,1746],{},[1723,96724,1759],{},[898,96726,1754],{},[902,96728,41814],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,96731,96733],{"className":96732},[886],[888,96734,96735],{"xmlns":890},[892,96736,96737,96755],{},[895,96738,96739,96741,96743,96745,96747,96749,96751,96753],{},[898,96740,1746],{},[1723,96742,1759],{},[898,96744,1754],{},[1723,96746,1725],{},[898,96748,2111],{},[1723,96750,1908],{"stretchy":1907},[898,96752,1904],{},[1723,96754,1914],{"stretchy":1907},[902,96756,41843],{"encoding":904}," nová funkce nabídky:",[883,96759,96761],{"className":96760},[886],[888,96762,96763],{"xmlns":890,"display":28759},[892,96764,96765,96799],{},[895,96766,96767,96769,96771,96777,96779,96781,96783,96785,96787,96789,96791,96793,96795,96797],{},[898,96768,1746],{},[1723,96770,1725],{},[1931,96772,96773,96775],{},[898,96774,2111],{},[1864,96776,1866],{},[1723,96778,1908],{"stretchy":1907},[898,96780,1904],{},[1723,96782,1914],{"stretchy":1907},[1723,96784,1725],{},[898,96786,2111],{},[1723,96788,1908],{"stretchy":1907},[898,96790,1904],{},[1723,96792,1914],{"stretchy":1907},[1723,96794,2087],{},[898,96796,1754],{},[898,96798,1664],{"mathvariant":2124},[902,96800,41888],{"encoding":904},[724,96802,96803,96804,2628,96817,96819],{},"Nabídka se tedy posouvá o ",[883,96805,96807],{"className":96806},[886],[888,96808,96809],{"xmlns":890},[892,96810,96811,96815],{},[895,96812,96813],{},[898,96814,1754],{},[902,96816,1754],{"encoding":904},[38,96818,41921],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,96821,96822,96823,96863,96864,1682,96892,96920,96921,96940,96941,96965,96966,4634],{},"Nový rovnovážný bod ",[883,96824,96826],{"className":96825},[886],[888,96827,96828],{"xmlns":890},[892,96829,96830,96860],{},[895,96831,96832,96838,96840,96848,96850,96858],{},[1931,96833,96834,96836],{},[898,96835,1846],{},[1864,96837,1866],{},[1723,96839,3212],{"stretchy":1907},[2220,96841,96842,96844,96846],{},[898,96843,1904],{},[1864,96845,1866],{},[898,96847,1846],{},[1723,96849,2031],{"separator":2030},[2220,96851,96852,96854,96856],{},[898,96853,1746],{},[1864,96855,1866],{},[898,96857,1846],{},[1723,96859,3227],{"stretchy":1907},[902,96861,96862],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,96865,96867],{"className":96866},[886],[888,96868,96869],{"xmlns":890},[892,96870,96871,96889],{},[895,96872,96873,96881,96883],{},[2220,96874,96875,96877,96879],{},[898,96876,1904],{},[1864,96878,1866],{},[898,96880,1846],{},[1723,96882,2287],{},[2057,96884,96885,96887],{},[898,96886,1904],{},[898,96888,1846],{},[902,96890,96891],{"encoding":904},"Q_1^E \u003C Q^E",[883,96893,96895],{"className":96894},[886],[888,96896,96897],{"xmlns":890},[892,96898,96899,96917],{},[895,96900,96901,96909,96911],{},[2220,96902,96903,96905,96907],{},[898,96904,1746],{},[1864,96906,1866],{},[898,96908,1846],{},[1723,96910,2253],{},[2057,96912,96913,96915],{},[898,96914,1746],{},[898,96916,1846],{},[902,96918,96919],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,96922,96924],{"className":96923},[886],[888,96925,96926],{"xmlns":890},[892,96927,96928,96938],{},[895,96929,96930],{},[2220,96931,96932,96934,96936],{},[898,96933,1746],{},[1864,96935,1866],{},[898,96937,1846],{},[902,96939,48548],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,96942,96944],{"className":96943},[886],[888,96945,96946],{"xmlns":890},[892,96947,96948,96962],{},[895,96949,96950,96958,96960],{},[2220,96951,96952,96954,96956],{},[898,96953,1746],{},[1864,96955,1866],{},[898,96957,1846],{},[1723,96959,1759],{},[898,96961,1754],{},[902,96963,96964],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,96967,96969],{"className":96968},[886],[888,96970,96971],{"xmlns":890},[892,96972,96973,96981],{},[895,96974,96975],{},[2057,96976,96977,96979],{},[898,96978,1746],{},[898,96980,1846],{},[902,96982,42158],{"encoding":904},[724,96984,96985],{},[614,96986,96987,96988,97018,97019,97032,97033,6379,97050,97063,97064,1664],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,96989,96991],{"className":96990},[886],[888,96992,96993],{"xmlns":890},[892,96994,96995,97015],{},[895,96996,96997,96999,97001,97007,97009,97011,97013],{},[898,96998,2111],{},[1723,97000,3843],{},[1931,97002,97003,97005],{},[898,97004,2111],{},[1864,97006,1866],{},[1723,97008,1725],{},[898,97010,2111],{},[1723,97012,2087],{},[898,97014,1754],{},[902,97016,97017],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,97020,97022],{"className":97021},[886],[888,97023,97024],{"xmlns":890},[892,97025,97026,97030],{},[895,97027,97028],{},[898,97029,1754],{},[902,97031,1754],{"encoding":904},". Průsečík ",[883,97034,97036],{"className":97035},[886],[888,97037,97038],{"xmlns":890},[892,97039,97040,97048],{},[895,97041,97042],{},[1931,97043,97044,97046],{},[898,97045,2111],{},[1864,97047,1866],{},[902,97049,41689],{"encoding":904},[883,97051,97053],{"className":97052},[886],[888,97054,97055],{"xmlns":890},[892,97056,97057,97061],{},[895,97058,97059],{},[898,97060,4897],{},[902,97062,4897],{"encoding":904}," je nový rovnovážný bod ",[883,97065,97067],{"className":97066},[886],[888,97068,97069],{"xmlns":890},[892,97070,97071,97079],{},[895,97072,97073],{},[1931,97074,97075,97077],{},[898,97076,1846],{},[1864,97078,1866],{},[902,97080,97081],{"encoding":904},"E_1",[198,97083,45994],{"id":97084},"příklad-29",[724,97086,97087,42347,97089,42382,97113,97133,97134,97151],{},[38,97088,38625],{},[883,97090,97092],{"className":97091},[886],[888,97093,97094],{"xmlns":890},[892,97095,97096,97110],{},[895,97097,97098,97100,97102,97104,97106,97108],{},[898,97099,1746],{},[1723,97101,1725],{},[1864,97103,4227],{},[1723,97105,1759],{},[1864,97107,2331],{},[898,97109,1904],{},[902,97111,97112],{"encoding":904},"P = 12 - 2Q",[883,97114,97116],{"className":97115},[886],[888,97117,97118],{"xmlns":890},[892,97119,97120,97130],{},[895,97121,97122,97124,97126,97128],{},[898,97123,1746],{},[1723,97125,1725],{},[1864,97127,3080],{},[898,97129,1904],{},[902,97131,97132],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,97135,97137],{"className":97136},[886],[888,97138,97139],{"xmlns":890},[892,97140,97141,97149],{},[895,97142,97143,97145,97147],{},[898,97144,1754],{},[1723,97146,1725],{},[1864,97148,2969],{},[902,97150,41960],{"encoding":904}," Kč.",[724,97153,97154],{},[38,97155,38657],{},[724,97157,97158,97161,97162,6279,97188,6299,97208,1343,97230,97260,97261,1664],{},[614,97159,97160],{},"Bez daně."," Z rovnosti ",[883,97163,97165],{"className":97164},[886],[888,97166,97167],{"xmlns":890},[892,97168,97169,97185],{},[895,97170,97171,97173,97175,97177,97179,97181,97183],{},[1864,97172,4227],{},[1723,97174,1759],{},[1864,97176,2331],{},[898,97178,1904],{},[1723,97180,1725],{},[1864,97182,3080],{},[898,97184,1904],{},[902,97186,97187],{"encoding":904},"12 - 2Q = 4Q",[883,97189,97191],{"className":97190},[886],[888,97192,97193],{"xmlns":890},[892,97194,97195,97205],{},[895,97196,97197,97199,97201,97203],{},[1864,97198,2969],{},[898,97200,1904],{},[1723,97202,1725],{},[1864,97204,4227],{},[902,97206,97207],{"encoding":904},"6Q = 12",[883,97209,97211],{"className":97210},[886],[888,97212,97213],{"xmlns":890},[892,97214,97215,97227],{},[895,97216,97217,97223,97225],{},[2057,97218,97219,97221],{},[898,97220,1904],{},[898,97222,1846],{},[1723,97224,1725],{},[1864,97226,2331],{},[902,97228,97229],{"encoding":904},"Q^E = 2",[883,97231,97233],{"className":97232},[886],[888,97234,97235],{"xmlns":890},[892,97236,97237,97257],{},[895,97238,97239,97245,97247,97249,97251,97253,97255],{},[2057,97240,97241,97243],{},[898,97242,1746],{},[898,97244,1846],{},[1723,97246,1725],{},[1864,97248,3080],{},[1723,97250,3897],{},[1864,97252,2331],{},[1723,97254,1725],{},[1864,97256,6295],{},[902,97258,97259],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,97262,97264],{"className":97263},[886],[888,97265,97266],{"xmlns":890},[892,97267,97268,97282],{},[895,97269,97270,97272,97274,97276,97278,97280],{},[898,97271,1846],{},[1723,97273,3212],{"stretchy":1907},[1864,97275,2331],{},[1723,97277,2031],{"separator":2030},[1864,97279,6295],{},[1723,97281,3227],{"stretchy":1907},[902,97283,97284],{"encoding":904},"E[2, 8]",[724,97286,97287,97290,97291,97323],{},[614,97288,97289],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,97292,97294],{"className":97293},[886],[888,97295,97296],{"xmlns":890},[892,97297,97298,97320],{},[895,97299,97300,97306,97308,97310,97312,97314,97316,97318],{},[1931,97301,97302,97304],{},[898,97303,2111],{},[1864,97305,1866],{},[1723,97307,3430],{},[898,97309,1746],{},[1723,97311,1725],{},[1864,97313,3080],{},[898,97315,1904],{},[1723,97317,2087],{},[1864,97319,2969],{},[902,97321,97322],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,97325,97327],{"className":97326},[886],[888,97328,97329],{"xmlns":890,"display":28759},[892,97330,97331,97351],{},[895,97332,97333,97335,97337,97339,97341,97343,97345,97347,97349],{},[1864,97334,4227],{},[1723,97336,1759],{},[1864,97338,2331],{},[898,97340,1904],{},[1723,97342,1725],{},[1864,97344,3080],{},[898,97346,1904],{},[1723,97348,2087],{},[1864,97350,2969],{},[902,97352,97353],{"encoding":904},"12 - 2Q = 4Q + 6",[724,97355,97356,97357,6299,97377,1343,97401,97437,97438,1664],{},"plyne ",[883,97358,97360],{"className":97359},[886],[888,97361,97362],{"xmlns":890},[892,97363,97364,97374],{},[895,97365,97366,97368,97370,97372],{},[1864,97367,2969],{},[898,97369,1904],{},[1723,97371,1725],{},[1864,97373,2969],{},[902,97375,97376],{"encoding":904},"6Q = 6",[883,97378,97380],{"className":97379},[886],[888,97381,97382],{"xmlns":890},[892,97383,97384,97398],{},[895,97385,97386,97394,97396],{},[2220,97387,97388,97390,97392],{},[898,97389,1904],{},[1864,97391,1866],{},[898,97393,1846],{},[1723,97395,1725],{},[1864,97397,1866],{},[902,97399,97400],{"encoding":904},"Q_1^E = 1",[883,97402,97404],{"className":97403},[886],[888,97405,97406],{"xmlns":890},[892,97407,97408,97434],{},[895,97409,97410,97418,97420,97422,97424,97426,97428,97430,97432],{},[2220,97411,97412,97414,97416],{},[898,97413,1746],{},[1864,97415,1866],{},[898,97417,1846],{},[1723,97419,1725],{},[1864,97421,3080],{},[1723,97423,3897],{},[1864,97425,1866],{},[1723,97427,2087],{},[1864,97429,2969],{},[1723,97431,1725],{},[1864,97433,3585],{},[902,97435,97436],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,97439,97441],{"className":97440},[886],[888,97442,97443],{"xmlns":890},[892,97444,97445,97463],{},[895,97446,97447,97453,97455,97457,97459,97461],{},[1931,97448,97449,97451],{},[898,97450,1846],{},[1864,97452,1866],{},[1723,97454,3212],{"stretchy":1907},[1864,97456,1866],{},[1723,97458,2031],{"separator":2030},[1864,97460,3585],{},[1723,97462,3227],{"stretchy":1907},[902,97464,97465],{"encoding":904},"E_1[1, 10]",[724,97467,97468,97471,97472,97496,97497,97510],{},[614,97469,97470],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,97473,97475],{"className":97474},[886],[888,97476,97477],{"xmlns":890},[892,97478,97479,97493],{},[895,97480,97481,97489,97491],{},[2220,97482,97483,97485,97487],{},[898,97484,1746],{},[1864,97486,1866],{},[898,97488,1846],{},[1723,97490,1725],{},[1864,97492,3585],{},[902,97494,97495],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,97498,97500],{"className":97499},[886],[888,97501,97502],{"xmlns":890},[892,97503,97504,97508],{},[895,97505,97506],{},[1864,97507,6295],{},[902,97509,6295],{"encoding":904},", navýšení je",[883,97512,97514],{"className":97513},[886],[888,97515,97516],{"xmlns":890,"display":28759},[892,97517,97518,97574],{},[895,97519,97520,97530,97532,97540,97542,97548,97550,97552,97554,97556,97558,97560,97562,97572],{},[1931,97521,97522,97524],{},[898,97523,1754],{},[895,97525,97526,97528],{},[898,97527,43369],{},[898,97529,724],{},[1723,97531,1725],{},[2220,97533,97534,97536,97538],{},[898,97535,1746],{},[1864,97537,1866],{},[898,97539,1846],{},[1723,97541,1759],{},[2057,97543,97544,97546],{},[898,97545,1746],{},[898,97547,1846],{},[1723,97549,1725],{},[1864,97551,3585],{},[1723,97553,1759],{},[1864,97555,6295],{},[1723,97557,1725],{},[1864,97559,2331],{},[3018,97561,3020],{},[895,97563,97564,97566],{},[3018,97565,2034],{},[9096,97567,97568,97570],{"accent":2030},[3018,97569,2878],{},[1723,97571,25751],{},[898,97573,1664],{"mathvariant":2124},[902,97575,97576],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,97578,97579,97580,97496,97616,97629],{},"Výrobci zůstává čistá cena ",[883,97581,97583],{"className":97582},[886],[888,97584,97585],{"xmlns":890},[892,97586,97587,97613],{},[895,97588,97589,97597,97599,97601,97603,97605,97607,97609,97611],{},[2220,97590,97591,97593,97595],{},[898,97592,1746],{},[1864,97594,1866],{},[898,97596,1846],{},[1723,97598,1759],{},[898,97600,1754],{},[1723,97602,1725],{},[1864,97604,3585],{},[1723,97606,1759],{},[1864,97608,2969],{},[1723,97610,1725],{},[1864,97612,3080],{},[902,97614,97615],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,97617,97619],{"className":97618},[886],[888,97620,97621],{"xmlns":890},[892,97622,97623,97627],{},[895,97624,97625],{},[1864,97626,6295],{},[902,97628,6295],{"encoding":904},", pokles je",[883,97631,97633],{"className":97632},[886],[888,97634,97635],{"xmlns":890,"display":28759},[892,97636,97637,97703],{},[895,97638,97639,97651,97653,97659,97661,97663,97671,97673,97675,97677,97679,97681,97683,97685,97687,97689,97691,97701],{},[1931,97640,97641,97643],{},[898,97642,1754],{},[895,97644,97645,97647,97649],{},[898,97646,43392],{},[898,97648,2740],{},[898,97650,12742],{},[1723,97652,1725],{},[2057,97654,97655,97657],{},[898,97656,1746],{},[898,97658,1846],{},[1723,97660,1759],{},[1723,97662,1908],{"stretchy":1907},[2220,97664,97665,97667,97669],{},[898,97666,1746],{},[1864,97668,1866],{},[898,97670,1846],{},[1723,97672,1759],{},[898,97674,1754],{},[1723,97676,1914],{"stretchy":1907},[1723,97678,1725],{},[1864,97680,6295],{},[1723,97682,1759],{},[1864,97684,3080],{},[1723,97686,1725],{},[1864,97688,3080],{},[3018,97690,3020],{},[895,97692,97693,97695],{},[3018,97694,2034],{},[9096,97696,97697,97699],{"accent":2030},[3018,97698,2878],{},[1723,97700,25751],{},[898,97702,1664],{"mathvariant":2124},[902,97704,97705],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,97707,97708,97709,97761],{},"Kontrola: ",[883,97710,97712],{"className":97711},[886],[888,97713,97714],{"xmlns":890},[892,97715,97716,97758],{},[895,97717,97718,97728,97730,97742,97744,97746,97748,97750,97752,97754,97756],{},[1931,97719,97720,97722],{},[898,97721,1754],{},[895,97723,97724,97726],{},[898,97725,43369],{},[898,97727,724],{},[1723,97729,2087],{},[1931,97731,97732,97734],{},[898,97733,1754],{},[895,97735,97736,97738,97740],{},[898,97737,43392],{},[898,97739,2740],{},[898,97741,12742],{},[1723,97743,1725],{},[1864,97745,2331],{},[1723,97747,2087],{},[1864,97749,3080],{},[1723,97751,1725],{},[1864,97753,2969],{},[1723,97755,1725],{},[898,97757,1754],{},[902,97759,97760],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[37662,97763],{},[115,97765,97767],{"id":97766},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,97769,96697,97770,97783,97784,97802,97803,97831],{},[883,97771,97773],{"className":97772},[886],[888,97774,97775],{"xmlns":890},[892,97776,97777,97781],{},[895,97778,97779],{},[898,97780,1754],{},[902,97782,1754],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,97785,97787],{"className":97786},[886],[888,97788,97789],{"xmlns":890},[892,97790,97791,97799],{},[895,97792,97793,97795,97797],{},[898,97794,1746],{},[1723,97796,2087],{},[898,97798,1754],{},[902,97800,97801],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,97804,97806],{"className":97805},[886],[888,97807,97808],{"xmlns":890},[892,97809,97810,97828],{},[895,97811,97812,97814,97816,97818,97820,97822,97824,97826],{},[898,97813,1746],{},[1723,97815,2087],{},[898,97817,1754],{},[1723,97819,1725],{},[898,97821,4897],{},[1723,97823,1908],{"stretchy":1907},[898,97825,1904],{},[1723,97827,1914],{"stretchy":1907},[902,97829,97830],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,97833,97835],{"className":97834},[886],[888,97836,97837],{"xmlns":890,"display":28759},[892,97838,97839,97873],{},[895,97840,97841,97843,97845,97851,97853,97855,97857,97859,97861,97863,97865,97867,97869,97871],{},[898,97842,1746],{},[1723,97844,1725],{},[1931,97846,97847,97849],{},[898,97848,4897],{},[1864,97850,2331],{},[1723,97852,1908],{"stretchy":1907},[898,97854,1904],{},[1723,97856,1914],{"stretchy":1907},[1723,97858,1725],{},[898,97860,4897],{},[1723,97862,1908],{"stretchy":1907},[898,97864,1904],{},[1723,97866,1914],{"stretchy":1907},[1723,97868,1759],{},[898,97870,1754],{},[898,97872,1664],{"mathvariant":2124},[902,97874,97875],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,97877,97878,97879,2628,97892,97895],{},"Poptávka se tedy posouvá o ",[883,97880,97882],{"className":97881},[886],[888,97883,97884],{"xmlns":890},[892,97885,97886,97890],{},[895,97887,97888],{},[898,97889,1754],{},[902,97891,1754],{"encoding":904},[38,97893,97894],{},"svisle dolů",". Nabídka se nemění.",[724,97897,96822,97898,96863,97938,1682,97966,97994,97995,98014,98015,98039,98040,4634],{},[883,97899,97901],{"className":97900},[886],[888,97902,97903],{"xmlns":890},[892,97904,97905,97935],{},[895,97906,97907,97913,97915,97923,97925,97933],{},[1931,97908,97909,97911],{},[898,97910,1846],{},[1864,97912,2331],{},[1723,97914,3212],{"stretchy":1907},[2220,97916,97917,97919,97921],{},[898,97918,1904],{},[1864,97920,2331],{},[898,97922,1846],{},[1723,97924,2031],{"separator":2030},[2220,97926,97927,97929,97931],{},[898,97928,1746],{},[1864,97930,2331],{},[898,97932,1846],{},[1723,97934,3227],{"stretchy":1907},[902,97936,97937],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,97939,97941],{"className":97940},[886],[888,97942,97943],{"xmlns":890},[892,97944,97945,97963],{},[895,97946,97947,97955,97957],{},[2220,97948,97949,97951,97953],{},[898,97950,1904],{},[1864,97952,2331],{},[898,97954,1846],{},[1723,97956,2287],{},[2057,97958,97959,97961],{},[898,97960,1904],{},[898,97962,1846],{},[902,97964,97965],{"encoding":904},"Q_2^E \u003C Q^E",[883,97967,97969],{"className":97968},[886],[888,97970,97971],{"xmlns":890},[892,97972,97973,97991],{},[895,97974,97975,97983,97985],{},[2220,97976,97977,97979,97981],{},[898,97978,1746],{},[1864,97980,2331],{},[898,97982,1846],{},[1723,97984,2287],{},[2057,97986,97987,97989],{},[898,97988,1746],{},[898,97990,1846],{},[902,97992,97993],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,97996,97998],{"className":97997},[886],[888,97999,98000],{"xmlns":890},[892,98001,98002,98012],{},[895,98003,98004],{},[2220,98005,98006,98008,98010],{},[898,98007,1746],{},[1864,98009,2331],{},[898,98011,1846],{},[902,98013,48609],{"encoding":904},", spotřebitel platí celkem ",[883,98016,98018],{"className":98017},[886],[888,98019,98020],{"xmlns":890},[892,98021,98022,98036],{},[895,98023,98024,98032,98034],{},[2220,98025,98026,98028,98030],{},[898,98027,1746],{},[1864,98029,2331],{},[898,98031,1846],{},[1723,98033,2087],{},[898,98035,1754],{},[902,98037,98038],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,98041,98043],{"className":98042},[886],[888,98044,98045],{"xmlns":890},[892,98046,98047,98055],{},[895,98048,98049],{},[2057,98050,98051,98053],{},[898,98052,1746],{},[898,98054,1846],{},[902,98056,42158],{"encoding":904},[724,98058,98059],{},"Daňové břemeno:",[883,98061,98063],{"className":98062},[886],[888,98064,98065],{"xmlns":890,"display":28759},[892,98066,98067,98141],{},[895,98068,98069,98079,98081,98083,98091,98093,98095,98097,98099,98105,98107,98109,98121,98123,98129,98131,98139],{},[1931,98070,98071,98073],{},[898,98072,1754],{},[895,98074,98075,98077],{},[898,98076,43369],{},[898,98078,724],{},[1723,98080,1725],{},[1723,98082,1908],{"stretchy":1907},[2220,98084,98085,98087,98089],{},[898,98086,1746],{},[1864,98088,2331],{},[898,98090,1846],{},[1723,98092,2087],{},[898,98094,1754],{},[1723,98096,1914],{"stretchy":1907},[1723,98098,1759],{},[2057,98100,98101,98103],{},[898,98102,1746],{},[898,98104,1846],{},[1723,98106,2031],{"separator":2030},[6588,98108],{"width":6590},[1931,98110,98111,98113],{},[898,98112,1754],{},[895,98114,98115,98117,98119],{},[898,98116,43392],{},[898,98118,2740],{},[898,98120,12742],{},[1723,98122,1725],{},[2057,98124,98125,98127],{},[898,98126,1746],{},[898,98128,1846],{},[1723,98130,1759],{},[2220,98132,98133,98135,98137],{},[898,98134,1746],{},[1864,98136,2331],{},[898,98138,1846],{},[898,98140,1664],{"mathvariant":2124},[902,98142,98143],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,98145,98146],{},[614,98147,98148,98149,98179,98180,97032,98193,6379,98210,97063,98223,1664],{},"Obrázek 2.19: Posun ",[883,98150,98152],{"className":98151},[886],[888,98153,98154],{"xmlns":890},[892,98155,98156,98176],{},[895,98157,98158,98160,98162,98168,98170,98172,98174],{},[898,98159,4897],{},[1723,98161,3843],{},[1931,98163,98164,98166],{},[898,98165,4897],{},[1864,98167,2331],{},[1723,98169,1725],{},[898,98171,4897],{},[1723,98173,1759],{},[898,98175,1754],{},[902,98177,98178],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,98181,98183],{"className":98182},[886],[888,98184,98185],{"xmlns":890},[892,98186,98187,98191],{},[895,98188,98189],{},[898,98190,1754],{},[902,98192,1754],{"encoding":904},[883,98194,98196],{"className":98195},[886],[888,98197,98198],{"xmlns":890},[892,98199,98200,98208],{},[895,98201,98202],{},[1931,98203,98204,98206],{},[898,98205,4897],{},[1864,98207,2331],{},[902,98209,39019],{"encoding":904},[883,98211,98213],{"className":98212},[886],[888,98214,98215],{"xmlns":890},[892,98216,98217,98221],{},[895,98218,98219],{},[898,98220,2111],{},[902,98222,2111],{"encoding":904},[883,98224,98226],{"className":98225},[886],[888,98227,98228],{"xmlns":890},[892,98229,98230,98238],{},[895,98231,98232],{},[1931,98233,98234,98236],{},[898,98235,1846],{},[1864,98237,2331],{},[902,98239,98240],{"encoding":904},"E_2",[198,98242,46074],{"id":98243},"příklad-210",[724,98245,98246,98248,98249,42382,98272,98291,98292,98309],{},[38,98247,38625],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,98250,98252],{"className":98251},[886],[888,98253,98254],{"xmlns":890},[892,98255,98256,98270],{},[895,98257,98258,98260,98262,98264,98266,98268],{},[898,98259,1746],{},[1723,98261,1725],{},[1864,98263,4227],{},[1723,98265,1759],{},[1864,98267,2331],{},[898,98269,1904],{},[902,98271,97112],{"encoding":904},[883,98273,98275],{"className":98274},[886],[888,98276,98277],{"xmlns":890},[892,98278,98279,98289],{},[895,98280,98281,98283,98285,98287],{},[898,98282,1746],{},[1723,98284,1725],{},[1864,98286,3080],{},[898,98288,1904],{},[902,98290,97132],{"encoding":904},". Daň ",[883,98293,98295],{"className":98294},[886],[888,98296,98297],{"xmlns":890},[892,98298,98299,98307],{},[895,98300,98301,98303,98305],{},[898,98302,1754],{},[1723,98304,1725],{},[1864,98306,2969],{},[902,98308,41960],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,98311,98312],{},[38,98313,38657],{},[724,98315,98316,98317,97323],{},"Nová poptávka je ",[883,98318,98320],{"className":98319},[886],[888,98321,98322],{"xmlns":890},[892,98323,98324,98360],{},[895,98325,98326,98332,98334,98336,98338,98340,98342,98344,98346,98348,98350,98352,98354,98356,98358],{},[1931,98327,98328,98330],{},[898,98329,4897],{},[1864,98331,2331],{},[1723,98333,3430],{},[898,98335,1746],{},[1723,98337,1725],{},[1864,98339,4227],{},[1723,98341,1759],{},[1864,98343,2331],{},[898,98345,1904],{},[1723,98347,1759],{},[1864,98349,2969],{},[1723,98351,1725],{},[1864,98353,2969],{},[1723,98355,1759],{},[1864,98357,2331],{},[898,98359,1904],{},[902,98361,98362],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,98364,98366],{"className":98365},[886],[888,98367,98368],{"xmlns":890,"display":28759},[892,98369,98370,98386],{},[895,98371,98372,98374,98376,98378,98380,98382,98384],{},[1864,98373,2969],{},[1723,98375,1759],{},[1864,98377,2331],{},[898,98379,1904],{},[1723,98381,1725],{},[1864,98383,3080],{},[898,98385,1904],{},[902,98387,98388],{"encoding":904},"6 - 2Q = 4Q",[724,98390,97356,98391,6299,98410,1343,98434,97437,98466,1664],{},[883,98392,98394],{"className":98393},[886],[888,98395,98396],{"xmlns":890},[892,98397,98398,98408],{},[895,98399,98400,98402,98404,98406],{},[1864,98401,2969],{},[898,98403,1904],{},[1723,98405,1725],{},[1864,98407,2969],{},[902,98409,97376],{"encoding":904},[883,98411,98413],{"className":98412},[886],[888,98414,98415],{"xmlns":890},[892,98416,98417,98431],{},[895,98418,98419,98427,98429],{},[2220,98420,98421,98423,98425],{},[898,98422,1904],{},[1864,98424,2331],{},[898,98426,1846],{},[1723,98428,1725],{},[1864,98430,1866],{},[902,98432,98433],{"encoding":904},"Q_2^E = 1",[883,98435,98437],{"className":98436},[886],[888,98438,98439],{"xmlns":890},[892,98440,98441,98463],{},[895,98442,98443,98451,98453,98455,98457,98459,98461],{},[2220,98444,98445,98447,98449],{},[898,98446,1746],{},[1864,98448,2331],{},[898,98450,1846],{},[1723,98452,1725],{},[1864,98454,3080],{},[1723,98456,3897],{},[1864,98458,1866],{},[1723,98460,1725],{},[1864,98462,3080],{},[902,98464,98465],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,98467,98469],{"className":98468},[886],[888,98470,98471],{"xmlns":890},[892,98472,98473,98491],{},[895,98474,98475,98481,98483,98485,98487,98489],{},[1931,98476,98477,98479],{},[898,98478,1846],{},[1864,98480,2331],{},[1723,98482,3212],{"stretchy":1907},[1864,98484,1866],{},[1723,98486,2031],{"separator":2030},[1864,98488,3080],{},[1723,98490,3227],{"stretchy":1907},[902,98492,98493],{"encoding":904},"E_2[1, 4]",[724,98495,98496,98497,98533,98534,97151],{},"Spotřebitel platí celkem ",[883,98498,98500],{"className":98499},[886],[888,98501,98502],{"xmlns":890},[892,98503,98504,98530],{},[895,98505,98506,98514,98516,98518,98520,98522,98524,98526,98528],{},[2220,98507,98508,98510,98512],{},[898,98509,1746],{},[1864,98511,2331],{},[898,98513,1846],{},[1723,98515,2087],{},[898,98517,1754],{},[1723,98519,1725],{},[1864,98521,3080],{},[1723,98523,2087],{},[1864,98525,2969],{},[1723,98527,1725],{},[1864,98529,3585],{},[902,98531,98532],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,98535,98537],{"className":98536},[886],[888,98538,98539],{"xmlns":890},[892,98540,98541,98555],{},[895,98542,98543,98551,98553],{},[2220,98544,98545,98547,98549],{},[898,98546,1746],{},[1864,98548,2331],{},[898,98550,1846],{},[1723,98552,1725],{},[1864,98554,3080],{},[902,98556,98557],{"encoding":904},"P_2^E = 4",[724,98559,98560],{},[614,98561,98562],{},"Rozklad daňového břemene:",[883,98564,98566],{"className":98565},[886],[888,98567,98568],{"xmlns":890,"display":28759},[892,98569,98570,98656],{},[895,98571,98572,98582,98584,98586,98588,98590,98592,98594,98596,98598,98600,98602,98604,98614,98616,98618,98630,98632,98634,98636,98638,98640,98642,98644,98654],{},[1931,98573,98574,98576],{},[898,98575,1754],{},[895,98577,98578,98580],{},[898,98579,43369],{},[898,98581,724],{},[1723,98583,1725],{},[1723,98585,1908],{"stretchy":1907},[1864,98587,3080],{},[1723,98589,2087],{},[1864,98591,2969],{},[1723,98593,1914],{"stretchy":1907},[1723,98595,1759],{},[1864,98597,6295],{},[1723,98599,1725],{},[1864,98601,2331],{},[3018,98603,3020],{},[895,98605,98606,98608],{},[3018,98607,2034],{},[9096,98609,98610,98612],{"accent":2030},[3018,98611,2878],{},[1723,98613,25751],{},[1723,98615,2031],{"separator":2030},[6588,98617],{"width":6590},[1931,98619,98620,98622],{},[898,98621,1754],{},[895,98623,98624,98626,98628],{},[898,98625,43392],{},[898,98627,2740],{},[898,98629,12742],{},[1723,98631,1725],{},[1864,98633,6295],{},[1723,98635,1759],{},[1864,98637,3080],{},[1723,98639,1725],{},[1864,98641,3080],{},[3018,98643,3020],{},[895,98645,98646,98648],{},[3018,98647,2034],{},[9096,98649,98650,98652],{"accent":2030},[3018,98651,2878],{},[1723,98653,25751],{},[898,98655,1664],{"mathvariant":2124},[902,98657,98658],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,98660,98661,98662,1664],{},"Opět ",[883,98663,98665],{"className":98664},[886],[888,98666,98667],{"xmlns":890},[892,98668,98669,98703],{},[895,98670,98671,98681,98683,98695,98697,98699,98701],{},[1931,98672,98673,98675],{},[898,98674,1754],{},[895,98676,98677,98679],{},[898,98678,43369],{},[898,98680,724],{},[1723,98682,2087],{},[1931,98684,98685,98687],{},[898,98686,1754],{},[895,98688,98689,98691,98693],{},[898,98690,43392],{},[898,98692,2740],{},[898,98694,12742],{},[1723,98696,1725],{},[1864,98698,2969],{},[1723,98700,1725],{},[898,98702,1754],{},[902,98704,98705],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[37662,98707],{},[115,98709,43350],{"id":98710},"daňové-břemeno",[724,98712,98713,1981,98715,98718,98719,98732],{},[38,98714,43350],{},[614,98716,98717],{},"tax burden",") je rozdělení zaplacené daně ",[883,98720,98722],{"className":98721},[886],[888,98723,98724],{"xmlns":890},[892,98725,98726,98730],{},[895,98727,98728],{},[898,98729,1754],{},[902,98731,1754],{"encoding":904}," mezi spotřebitele a výrobce:",[883,98734,98736],{"className":98735},[886],[888,98737,98738],{"xmlns":890,"display":28759},[892,98739,98740,98772],{},[895,98741,98742,98744,98746,98756,98758,98770],{},[898,98743,1754],{},[1723,98745,1725],{},[1931,98747,98748,98750],{},[898,98749,1754],{},[895,98751,98752,98754],{},[898,98753,43369],{},[898,98755,724],{},[1723,98757,2087],{},[1931,98759,98760,98762],{},[898,98761,1754],{},[895,98763,98764,98766,98768],{},[898,98765,43392],{},[898,98767,2740],{},[898,98769,12742],{},[898,98771,1664],{"mathvariant":2124},[902,98773,98774],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,98776,98777],{},[3285,98778],{"alt":98779,"className":98780,"src":98781},"imek-dan-rozklad-bremene-sklony",[210,3289],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[4584,98783,98784],{},[724,98785,98786,98788,98789,1682,98802,1664],{},[883,98787,4869],{}," 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 ",[883,98790,98792],{"className":98791},[886],[888,98793,98794],{"xmlns":890},[892,98795,98796,98800],{},[895,98797,98798],{},[898,98799,4897],{},[902,98801,4897],{"encoding":904},[883,98803,98805],{"className":98804},[886],[888,98806,98807],{"xmlns":890},[892,98808,98809,98813],{},[895,98810,98811],{},[898,98812,2111],{},[902,98814,2111],{"encoding":904},[198,98816,3170],{"id":3169},[724,98818,98819,98820,98841,98842,98855,98856,98873,98874,98887],{},"V grafu ",[883,98821,98823],{"className":98822},[886],[888,98824,98825],{"xmlns":890},[892,98826,98827,98839],{},[895,98828,98829,98831,98833,98835,98837],{},[1723,98830,1908],{"stretchy":1907},[898,98832,1904],{},[1723,98834,2031],{"separator":2030},[898,98836,1746],{},[1723,98838,1914],{"stretchy":1907},[902,98840,38383],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,98843,98845],{"className":98844},[886],[888,98846,98847],{"xmlns":890},[892,98848,98849,98853],{},[895,98850,98851],{},[898,98852,1754],{},[902,98854,1754],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,98857,98859],{"className":98858},[886],[888,98860,98861],{"xmlns":890},[892,98862,98863,98871],{},[895,98864,98865],{},[2057,98866,98867,98869],{},[898,98868,1746],{},[898,98870,1846],{},[902,98872,42158],{"encoding":904},", rozdělí se úsečka ",[883,98875,98877],{"className":98876},[886],[888,98878,98879],{"xmlns":890},[892,98880,98881,98885],{},[895,98882,98883],{},[898,98884,1754],{},[902,98886,1754],{"encoding":904}," na dvě části:",[120,98889,98890,98915],{},[123,98891,98892,98893,98914],{},"horní část odpovídá ",[883,98894,98896],{"className":98895},[886],[888,98897,98898],{"xmlns":890},[892,98899,98900,98912],{},[895,98901,98902],{},[1931,98903,98904,98906],{},[898,98905,1754],{},[895,98907,98908,98910],{},[898,98909,43369],{},[898,98911,724],{},[902,98913,43374],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,98916,98917,98918,98941],{},"dolní část odpovídá ",[883,98919,98921],{"className":98920},[886],[888,98922,98923],{"xmlns":890},[892,98924,98925,98939],{},[895,98926,98927],{},[1931,98928,98929,98931],{},[898,98930,1754],{},[895,98932,98933,98935,98937],{},[898,98934,43392],{},[898,98936,2740],{},[898,98938,12742],{},[902,98940,43399],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,98943,98944],{},[614,98945,98946,98947,3411,98960,98981,98982,99005,99006,1682,99027,99050],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,98948,98950],{"className":98949},[886],[888,98951,98952],{"xmlns":890},[892,98953,98954,98958],{},[895,98955,98956],{},[898,98957,1754],{},[902,98959,1754],{"encoding":904},[883,98961,98963],{"className":98962},[886],[888,98964,98965],{"xmlns":890},[892,98966,98967,98979],{},[895,98968,98969],{},[1931,98970,98971,98973],{},[898,98972,1754],{},[895,98974,98975,98977],{},[898,98976,43369],{},[898,98978,724],{},[902,98980,43374],{"encoding":904}," (nahoře) a ",[883,98983,98985],{"className":98984},[886],[888,98986,98987],{"xmlns":890},[892,98988,98989,99003],{},[895,98990,98991],{},[1931,98992,98993,98995],{},[898,98994,1754],{},[895,98996,98997,98999,99001],{},[898,98998,43392],{},[898,99000,2740],{},[898,99002,12742],{},[902,99004,43399],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,99007,99009],{"className":99008},[886],[888,99010,99011],{"xmlns":890},[892,99012,99013,99025],{},[895,99014,99015],{},[1931,99016,99017,99019],{},[898,99018,1754],{},[895,99020,99021,99023],{},[898,99022,43369],{},[898,99024,724],{},[902,99026,43374],{"encoding":904},[883,99028,99030],{"className":99029},[886],[888,99031,99032],{"xmlns":890},[892,99033,99034,99048],{},[895,99035,99036],{},[1931,99037,99038,99040],{},[898,99039,1754],{},[895,99041,99042,99044,99046],{},[898,99043,43392],{},[898,99045,2740],{},[898,99047,12742],{},[902,99049,43399],{"encoding":904}," je v obou případech stejná.",[198,99052,99054],{"id":99053},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,99056,99057,99058,99061,99062,1981,99085,99102,99103,1981,99126,99143],{},"Platí obecně: ",[38,99059,99060],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,99063,99065],{"className":99064},[886],[888,99066,99067],{"xmlns":890},[892,99068,99069,99083],{},[895,99070,99071,99073,99075,99077,99079,99081],{},[898,99072,1746],{},[1723,99074,1725],{},[898,99076,207],{},[898,99078,1904],{},[1723,99080,2087],{},[898,99082,2069],{},[902,99084,37752],{"encoding":904},[883,99086,99088],{"className":99087},[886],[888,99089,99090],{"xmlns":890},[892,99091,99092,99100],{},[895,99093,99094,99096,99098],{},[898,99095,207],{},[1723,99097,2287],{},[1864,99099,2256],{},[902,99101,43777],{"encoding":904},") a lineární nabídku ",[883,99104,99106],{"className":99105},[886],[888,99107,99108],{"xmlns":890},[892,99109,99110,99124],{},[895,99111,99112,99114,99116,99118,99120,99122],{},[898,99113,1746],{},[1723,99115,1725],{},[898,99117,2878],{},[898,99119,1904],{},[1723,99121,2087],{},[898,99123,2930],{},[902,99125,40934],{"encoding":904},[883,99127,99129],{"className":99128},[886],[888,99130,99131],{"xmlns":890},[892,99132,99133,99141],{},[895,99134,99135,99137,99139],{},[898,99136,2878],{},[1723,99138,2253],{},[1864,99140,2256],{},[902,99142,40952],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,99145,99147],{"className":99146},[886],[888,99148,99149],{"xmlns":890,"display":28759},[892,99150,99151,99217],{},[895,99152,99153,99177,99179,99189,99191,99215],{},[3058,99154,99155,99165],{},[1931,99156,99157,99159],{},[898,99158,1754],{},[895,99160,99161,99163],{},[898,99162,43369],{},[898,99164,724],{},[1931,99166,99167,99169],{},[898,99168,1754],{},[895,99170,99171,99173,99175],{},[898,99172,43392],{},[898,99174,2740],{},[898,99176,12742],{},[1723,99178,1725],{},[3058,99180,99181,99183],{},[898,99182,2878],{},[895,99184,99185,99187],{},[1723,99186,1759],{},[898,99188,207],{},[1723,99190,1725],{},[3058,99192,99193,99205],{},[895,99194,99195,99198,99201,99203],{},[898,99196,99197],{"mathvariant":2124},"∣",[3018,99199,99200],{},"sklon ",[898,99202,2111],{},[898,99204,99197],{"mathvariant":2124},[895,99206,99207,99209,99211,99213],{},[898,99208,99197],{"mathvariant":2124},[3018,99210,99200],{},[898,99212,4897],{},[898,99214,99197],{"mathvariant":2124},[898,99216,1664],{"mathvariant":2124},[902,99218,99219],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[4584,99221,99222,99227],{},[724,99223,99224,99226],{},[883,99225,5283],{}," Postup výpočtu rozkladu",[152,99228,99229,99264,99317,99396],{},[123,99230,99231,99232,99263],{},"Spočti rovnovážný bod ",[883,99233,99235],{"className":99234},[886],[888,99236,99237],{"xmlns":890},[892,99238,99239,99261],{},[895,99240,99241,99243,99245,99251,99253,99259],{},[898,99242,1846],{},[1723,99244,3212],{"stretchy":1907},[2057,99246,99247,99249],{},[898,99248,1904],{},[898,99250,1846],{},[1723,99252,2031],{"separator":2030},[2057,99254,99255,99257],{},[898,99256,1746],{},[898,99258,1846],{},[1723,99260,3227],{"stretchy":1907},[902,99262,42059],{"encoding":904}," bez daně.",[123,99265,99266,99267,1348,99292,4634],{},"Urči posunutou křivku (",[883,99268,99270],{"className":99269},[886],[888,99271,99272],{"xmlns":890},[892,99273,99274,99290],{},[895,99275,99276,99282,99284,99286,99288],{},[1931,99277,99278,99280],{},[898,99279,2111],{},[1864,99281,1866],{},[1723,99283,1725],{},[898,99285,2111],{},[1723,99287,2087],{},[898,99289,1754],{},[902,99291,43446],{"encoding":904},[883,99293,99295],{"className":99294},[886],[888,99296,99297],{"xmlns":890},[892,99298,99299,99315],{},[895,99300,99301,99307,99309,99311,99313],{},[1931,99302,99303,99305],{},[898,99304,4897],{},[1864,99306,2331],{},[1723,99308,1725],{},[898,99310,4897],{},[1723,99312,1759],{},[898,99314,1754],{},[902,99316,43477],{"encoding":904},[123,99318,99319,99320,4626,99339,12829,99358,4626,99377,4634],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,99321,99323],{"className":99322},[886],[888,99324,99325],{"xmlns":890},[892,99326,99327,99337],{},[895,99328,99329],{},[2220,99330,99331,99333,99335],{},[898,99332,1904],{},[1864,99334,1866],{},[898,99336,1846],{},[902,99338,48527],{"encoding":904},[883,99340,99342],{"className":99341},[886],[888,99343,99344],{"xmlns":890},[892,99345,99346,99356],{},[895,99347,99348],{},[2220,99349,99350,99352,99354],{},[898,99351,1904],{},[1864,99353,2331],{},[898,99355,1846],{},[902,99357,48589],{"encoding":904},[883,99359,99361],{"className":99360},[886],[888,99362,99363],{"xmlns":890},[892,99364,99365,99375],{},[895,99366,99367],{},[2220,99368,99369,99371,99373],{},[898,99370,1746],{},[1864,99372,1866],{},[898,99374,1846],{},[902,99376,48548],{"encoding":904},[883,99378,99380],{"className":99379},[886],[888,99381,99382],{"xmlns":890},[892,99383,99384,99394],{},[895,99385,99386],{},[2220,99387,99388,99390,99392],{},[898,99389,1746],{},[1864,99391,2331],{},[898,99393,1846],{},[902,99395,48609],{"encoding":904},[123,99397,99398,99399,1682,99420,99443,99444,1664],{},"Dopočítej ",[883,99400,99402],{"className":99401},[886],[888,99403,99404],{"xmlns":890},[892,99405,99406,99418],{},[895,99407,99408],{},[1931,99409,99410,99412],{},[898,99411,1754],{},[895,99413,99414,99416],{},[898,99415,43369],{},[898,99417,724],{},[902,99419,43374],{"encoding":904},[883,99421,99423],{"className":99422},[886],[888,99424,99425],{"xmlns":890},[892,99426,99427,99441],{},[895,99428,99429],{},[1931,99430,99431,99433],{},[898,99432,1754],{},[895,99434,99435,99437,99439],{},[898,99436,43392],{},[898,99438,2740],{},[898,99440,12742],{},[902,99442,43399],{"encoding":904}," z definice, vždy ověř ",[883,99445,99447],{"className":99446},[886],[888,99448,99449],{"xmlns":890},[892,99450,99451,99481],{},[895,99452,99453,99463,99465,99477,99479],{},[1931,99454,99455,99457],{},[898,99456,1754],{},[895,99458,99459,99461],{},[898,99460,43369],{},[898,99462,724],{},[1723,99464,2087],{},[1931,99466,99467,99469],{},[898,99468,1754],{},[895,99470,99471,99473,99475],{},[898,99472,43392],{},[898,99474,2740],{},[898,99476,12742],{},[1723,99478,1725],{},[898,99480,1754],{},[902,99482,99483],{"encoding":904},"T_{sp} + T_{vyr} = T",[4584,99485,99486],{},[724,99487,99488,99490,99491,99494,99495,1682,99508,99521],{},[883,99489,5124],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,99492,99493],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,99496,99498],{"className":99497},[886],[888,99499,99500],{"xmlns":890},[892,99501,99502,99506],{},[895,99503,99504],{},[898,99505,4897],{},[902,99507,4897],{"encoding":904},[883,99509,99511],{"className":99510},[886],[888,99512,99513],{"xmlns":890},[892,99514,99515,99519],{},[895,99516,99517],{},[898,99518,2111],{},[902,99520,2111],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[37662,99523],{},[115,99525,99527],{"id":99526},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,99529,99530],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,99532,99533],{},[3285,99534],{"alt":99535,"className":99536,"src":99537},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,3289],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,99539,99540,99552],{},[19,99541,99542],{},[22,99543,99544,99546,99549],{},[25,99545,54986],{},[25,99547,99548],{},"(a) daň výrobci",[25,99550,99551],{},"(b) daň spotřebiteli",[30,99553,99554,99609,99676,99736],{},[22,99555,99556,99559,99584],{},[35,99557,99558],{},"Rovnovážné množství",[35,99560,99561],{},[883,99562,99564],{"className":99563},[886],[888,99565,99566],{"xmlns":890},[892,99567,99568,99582],{},[895,99569,99570,99578,99580],{},[2220,99571,99572,99574,99576],{},[898,99573,1904],{},[1864,99575,1866],{},[898,99577,1846],{},[1723,99579,1725],{},[1864,99581,1866],{},[902,99583,97400],{"encoding":904},[35,99585,99586],{},[883,99587,99589],{"className":99588},[886],[888,99590,99591],{"xmlns":890},[892,99592,99593,99607],{},[895,99594,99595,99603,99605],{},[2220,99596,99597,99599,99601],{},[898,99598,1904],{},[1864,99600,2331],{},[898,99602,1846],{},[1723,99604,1725],{},[1864,99606,1866],{},[902,99608,98433],{"encoding":904},[22,99610,99611,99614,99639],{},[35,99612,99613],{},"Cena placená spotřebitelem",[35,99615,99616],{},[883,99617,99619],{"className":99618},[886],[888,99620,99621],{"xmlns":890},[892,99622,99623,99637],{},[895,99624,99625,99633,99635],{},[2220,99626,99627,99629,99631],{},[898,99628,1746],{},[1864,99630,1866],{},[898,99632,1846],{},[1723,99634,1725],{},[1864,99636,3585],{},[902,99638,97495],{"encoding":904},[35,99640,99641],{},[883,99642,99644],{"className":99643},[886],[888,99645,99646],{"xmlns":890},[892,99647,99648,99674],{},[895,99649,99650,99658,99660,99662,99664,99666,99668,99670,99672],{},[2220,99651,99652,99654,99656],{},[898,99653,1746],{},[1864,99655,2331],{},[898,99657,1846],{},[1723,99659,2087],{},[898,99661,1754],{},[1723,99663,1725],{},[1864,99665,3080],{},[1723,99667,2087],{},[1864,99669,2969],{},[1723,99671,1725],{},[1864,99673,3585],{},[902,99675,98532],{"encoding":904},[22,99677,99678,99681,99711],{},[35,99679,99680],{},"Cena přijímaná výrobcem",[35,99682,99683],{},[883,99684,99686],{"className":99685},[886],[888,99687,99688],{"xmlns":890},[892,99689,99690,99708],{},[895,99691,99692,99700,99702,99704,99706],{},[2220,99693,99694,99696,99698],{},[898,99695,1746],{},[1864,99697,1866],{},[898,99699,1846],{},[1723,99701,1759],{},[898,99703,1754],{},[1723,99705,1725],{},[1864,99707,3080],{},[902,99709,99710],{"encoding":904},"P_1^E - T = 4",[35,99712,99713],{},[883,99714,99716],{"className":99715},[886],[888,99717,99718],{"xmlns":890},[892,99719,99720,99734],{},[895,99721,99722,99730,99732],{},[2220,99723,99724,99726,99728],{},[898,99725,1746],{},[1864,99727,2331],{},[898,99729,1846],{},[1723,99731,1725],{},[1864,99733,3080],{},[902,99735,98557],{"encoding":904},[22,99737,99738,99741,99795],{},[35,99739,99740],{},"Rozklad břemene",[35,99742,99743,1343,99768],{},[883,99744,99746],{"className":99745},[886],[888,99747,99748],{"xmlns":890},[892,99749,99750,99766],{},[895,99751,99752,99762,99764],{},[1931,99753,99754,99756],{},[898,99755,1754],{},[895,99757,99758,99760],{},[898,99759,43369],{},[898,99761,724],{},[1723,99763,1725],{},[1864,99765,2331],{},[902,99767,43668],{"encoding":904},[883,99769,99771],{"className":99770},[886],[888,99772,99773],{"xmlns":890},[892,99774,99775,99793],{},[895,99776,99777,99789,99791],{},[1931,99778,99779,99781],{},[898,99780,1754],{},[895,99782,99783,99785,99787],{},[898,99784,43392],{},[898,99786,2740],{},[898,99788,12742],{},[1723,99790,1725],{},[1864,99792,3080],{},[902,99794,43697],{"encoding":904},[35,99796,99797,1343,99822],{},[883,99798,99800],{"className":99799},[886],[888,99801,99802],{"xmlns":890},[892,99803,99804,99820],{},[895,99805,99806,99816,99818],{},[1931,99807,99808,99810],{},[898,99809,1754],{},[895,99811,99812,99814],{},[898,99813,43369],{},[898,99815,724],{},[1723,99817,1725],{},[1864,99819,2331],{},[902,99821,43668],{"encoding":904},[883,99823,99825],{"className":99824},[886],[888,99826,99827],{"xmlns":890},[892,99828,99829,99847],{},[895,99830,99831,99843,99845],{},[1931,99832,99833,99835],{},[898,99834,1754],{},[895,99836,99837,99839,99841],{},[898,99838,43392],{},[898,99840,2740],{},[898,99842,12742],{},[1723,99844,1725],{},[1864,99846,3080],{},[902,99848,43697],{"encoding":904},[724,99850,99851],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,99853,99855],{"className":99854},[886],[888,99856,99857],{"xmlns":890,"display":28759},[892,99858,99859,99907],{},[895,99860,99861,99869,99871,99879,99881,99883,99891,99893,99895,99897,99905],{},[2220,99862,99863,99865,99867],{},[898,99864,1904],{},[1864,99866,1866],{},[898,99868,1846],{},[1723,99870,1725],{},[2220,99872,99873,99875,99877],{},[898,99874,1904],{},[1864,99876,2331],{},[898,99878,1846],{},[1723,99880,2031],{"separator":2030},[6588,99882],{"width":6590},[2220,99884,99885,99887,99889],{},[898,99886,1746],{},[1864,99888,1866],{},[898,99890,1846],{},[1723,99892,1759],{},[898,99894,1754],{},[1723,99896,1725],{},[2220,99898,99899,99901,99903],{},[898,99900,1746],{},[1864,99902,2331],{},[898,99904,1846],{},[898,99906,1664],{"mathvariant":2124},[902,99908,99909],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[4584,99911,99912,99931,100085],{},[724,99913,99914,99916,99917,99930],{},[883,99915,5283],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,99918,99920],{"className":99919},[886],[888,99921,99922],{"xmlns":890},[892,99923,99924,99928],{},[895,99925,99926],{},[898,99927,1754],{},[902,99929,1754],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,99932,99933,99965,100001,100038],{},[123,99934,99935,99936,2031],{},"rovnovážná množství obou režimů, ",[883,99937,99939],{"className":99938},[886],[888,99940,99941],{"xmlns":890},[892,99942,99943,99963],{},[895,99944,99945,99953,99955],{},[2220,99946,99947,99949,99951],{},[898,99948,1904],{},[1864,99950,1866],{},[898,99952,1846],{},[1723,99954,1725],{},[2220,99956,99957,99959,99961],{},[898,99958,1904],{},[1864,99960,2331],{},[898,99962,1846],{},[902,99964,43600],{"encoding":904},[123,99966,99967,99968,2031],{},"čistá cena přijímaná výrobcem, ",[883,99969,99971],{"className":99970},[886],[888,99972,99973],{"xmlns":890},[892,99974,99975,99999],{},[895,99976,99977,99985,99987,99989,99991],{},[2220,99978,99979,99981,99983],{},[898,99980,1746],{},[1864,99982,1866],{},[898,99984,1846],{},[1723,99986,1759],{},[898,99988,1754],{},[1723,99990,1725],{},[2220,99992,99993,99995,99997],{},[898,99994,1746],{},[1864,99996,2331],{},[898,99998,1846],{},[902,100000,43634],{"encoding":904},[123,100002,100003,100004,2031],{},"celková cena placená spotřebitelem, ",[883,100005,100007],{"className":100006},[886],[888,100008,100009],{"xmlns":890},[892,100010,100011,100035],{},[895,100012,100013,100021,100023,100031,100033],{},[2220,100014,100015,100017,100019],{},[898,100016,1746],{},[1864,100018,1866],{},[898,100020,1846],{},[1723,100022,1725],{},[2220,100024,100025,100027,100029],{},[898,100026,1746],{},[1864,100028,2331],{},[898,100030,1846],{},[1723,100032,2087],{},[898,100034,1754],{},[902,100036,100037],{"encoding":904},"P_1^E = P_2^E + T",[123,100039,100040,100041,1682,100062,1664],{},"rozklad daňového břemene ",[883,100042,100044],{"className":100043},[886],[888,100045,100046],{"xmlns":890},[892,100047,100048,100060],{},[895,100049,100050],{},[1931,100051,100052,100054],{},[898,100053,1754],{},[895,100055,100056,100058],{},[898,100057,43369],{},[898,100059,724],{},[902,100061,43374],{"encoding":904},[883,100063,100065],{"className":100064},[886],[888,100066,100067],{"xmlns":890},[892,100068,100069,100083],{},[895,100070,100071],{},[1931,100072,100073,100075],{},[898,100074,1754],{},[895,100076,100077,100079,100081],{},[898,100078,43392],{},[898,100080,2740],{},[898,100082,12742],{},[902,100084,43399],{"encoding":904},[724,100086,100087,100088,1664],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,100089,35890],{},[724,100091,100092,100093,1682,100106,4634],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,100094,100096],{"className":100095},[886],[888,100097,100098],{"xmlns":890},[892,100099,100100,100104],{},[895,100101,100102],{},[898,100103,4897],{},[902,100105,4897],{"encoding":904},[883,100107,100109],{"className":100108},[886],[888,100110,100111],{"xmlns":890},[892,100112,100113,100117],{},[895,100114,100115],{},[898,100116,2111],{},[902,100118,2111],{"encoding":904},[37662,100120],{},[115,100122,100124],{"id":100123},"úlohy","Úlohy",[724,100126,100127,100128,3871],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,100129,1692],{"className":100130,"dataFsResolvedFilePath":800,"href":801},[210],[120,100132,100133,100163,100194],{},[123,100134,100135,100138,100139,100162],{},[38,100136,100137],{},"Úloha 2.4"," — Poptávka ",[883,100140,100142],{"className":100141},[886],[888,100143,100144],{"xmlns":890},[892,100145,100146,100160],{},[895,100147,100148,100150,100152,100154,100156,100158],{},[898,100149,1746],{},[1723,100151,1725],{},[1864,100153,4227],{},[1723,100155,1759],{},[1864,100157,2331],{},[898,100159,1904],{},[902,100161,97112],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,100164,100165,100168,100169,100193],{},[38,100166,100167],{},"Úloha 2.9"," — Nabídka ",[883,100170,100172],{"className":100171},[886],[888,100173,100174],{"xmlns":890},[892,100175,100176,100190],{},[895,100177,100178,100180,100182,100184,100186,100188],{},[898,100179,1746],{},[1723,100181,1725],{},[1864,100183,5719],{},[898,100185,1904],{},[1723,100187,2087],{},[1864,100189,36937],{},[902,100191,100192],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,100195,100196,100199,100200,1682,100226,100250,100251,100268],{},[38,100197,100198],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,100201,100203],{"className":100202},[886],[888,100204,100205],{"xmlns":890},[892,100206,100207,100223],{},[895,100208,100209,100211,100213,100215,100217,100219,100221],{},[898,100210,1746],{},[1723,100212,1725],{},[1723,100214,1759],{},[1864,100216,3080],{},[898,100218,1904],{},[1723,100220,2087],{},[1864,100222,47394],{},[902,100224,100225],{"encoding":904},"P = -4Q + 80",[883,100227,100229],{"className":100228},[886],[888,100230,100231],{"xmlns":890},[892,100232,100233,100247],{},[895,100234,100235,100237,100239,100241,100243,100245],{},[898,100236,1746],{},[1723,100238,1725],{},[1864,100240,2909],{},[898,100242,1904],{},[1723,100244,2087],{},[1864,100246,3585],{},[902,100248,100249],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,100252,100254],{"className":100253},[886],[888,100255,100256],{"xmlns":890},[892,100257,100258,100266],{},[895,100259,100260,100262,100264],{},[898,100261,1754],{},[1723,100263,1725],{},[1864,100265,24894],{},[902,100267,48506],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,100270,100271,100272,100274,100275,100277],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,100273,45919],{}," (posun poptávky při zdanění kupujícího) a ",[38,100276,45953],{}," (posun nabídky při zdanění výrobce).",[37662,100279],{},[115,100281,16421],{"id":16420},[120,100283,100284,100303,100361,100418,100501,100547,100590,100635,100701],{},[123,100285,100286,2628,100289,100302],{},[38,100287,100288],{},"Jednotková daň",[883,100290,100292],{"className":100291},[886],[888,100293,100294],{"xmlns":890},[892,100295,100296,100300],{},[895,100297,100298],{},[898,100299,1754],{},[902,100301,1754],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,100304,100305,100307,100308,100346,100347,100360],{},[38,100306,96694],{}," — posun nabídky ",[883,100309,100311],{"className":100310},[886],[888,100312,100313],{"xmlns":890},[892,100314,100315,100343],{},[895,100316,100317,100323,100325,100327,100329,100331,100333,100335,100337,100339,100341],{},[1931,100318,100319,100321],{},[898,100320,2111],{},[1864,100322,1866],{},[1723,100324,1908],{"stretchy":1907},[898,100326,1904],{},[1723,100328,1914],{"stretchy":1907},[1723,100330,1725],{},[898,100332,2111],{},[1723,100334,1908],{"stretchy":1907},[898,100336,1904],{},[1723,100338,1914],{"stretchy":1907},[1723,100340,2087],{},[898,100342,1754],{},[902,100344,100345],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,100348,100350],{"className":100349},[886],[888,100351,100352],{"xmlns":890},[892,100353,100354,100358],{},[895,100355,100356],{},[898,100357,1754],{},[902,100359,1754],{"encoding":904}," svisle nahoru)",[123,100362,100363,100365,100366,100346,100404,100417],{},[38,100364,97767],{}," — posun poptávky ",[883,100367,100369],{"className":100368},[886],[888,100370,100371],{"xmlns":890},[892,100372,100373,100401],{},[895,100374,100375,100381,100383,100385,100387,100389,100391,100393,100395,100397,100399],{},[1931,100376,100377,100379],{},[898,100378,4897],{},[1864,100380,2331],{},[1723,100382,1908],{"stretchy":1907},[898,100384,1904],{},[1723,100386,1914],{"stretchy":1907},[1723,100388,1725],{},[898,100390,4897],{},[1723,100392,1908],{"stretchy":1907},[898,100394,1904],{},[1723,100396,1914],{"stretchy":1907},[1723,100398,1759],{},[898,100400,1754],{},[902,100402,100403],{"encoding":904},"D_2(Q) = D(Q) - T",[883,100405,100407],{"className":100406},[886],[888,100408,100409],{"xmlns":890},[892,100410,100411,100415],{},[895,100412,100413],{},[898,100414,1754],{},[902,100416,1754],{"encoding":904}," svisle dolů)",[123,100419,100420,7725,100423,42506,100462],{},[38,100421,100422],{},"Rovnovážný bod s daní",[883,100424,100426],{"className":100425},[886],[888,100427,100428],{"xmlns":890},[892,100429,100430,100460],{},[895,100431,100432,100438,100440,100448,100450,100458],{},[1931,100433,100434,100436],{},[898,100435,1846],{},[1864,100437,1866],{},[1723,100439,3212],{"stretchy":1907},[2220,100441,100442,100444,100446],{},[898,100443,1904],{},[1864,100445,1866],{},[898,100447,1846],{},[1723,100449,2031],{"separator":2030},[2220,100451,100452,100454,100456],{},[898,100453,1746],{},[1864,100455,1866],{},[898,100457,1846],{},[1723,100459,3227],{"stretchy":1907},[902,100461,96862],{"encoding":904},[883,100463,100465],{"className":100464},[886],[888,100466,100467],{"xmlns":890},[892,100468,100469,100499],{},[895,100470,100471,100477,100479,100487,100489,100497],{},[1931,100472,100473,100475],{},[898,100474,1846],{},[1864,100476,2331],{},[1723,100478,3212],{"stretchy":1907},[2220,100480,100481,100483,100485],{},[898,100482,1904],{},[1864,100484,2331],{},[898,100486,1846],{},[1723,100488,2031],{"separator":2030},[2220,100490,100491,100493,100495],{},[898,100492,1746],{},[1864,100494,2331],{},[898,100496,1846],{},[1723,100498,3227],{"stretchy":1907},[902,100500,97937],{"encoding":904},[123,100502,100503,1981,100505,100507,100508],{},[38,100504,43350],{},[614,100506,98717],{},") — rozklad ",[883,100509,100511],{"className":100510},[886],[888,100512,100513],{"xmlns":890},[892,100514,100515,100545],{},[895,100516,100517,100519,100521,100531,100533],{},[898,100518,1754],{},[1723,100520,1725],{},[1931,100522,100523,100525],{},[898,100524,1754],{},[895,100526,100527,100529],{},[898,100528,43369],{},[898,100530,724],{},[1723,100532,2087],{},[1931,100534,100535,100537],{},[898,100536,1754],{},[895,100538,100539,100541,100543],{},[898,100540,43392],{},[898,100542,2740],{},[898,100544,12742],{},[902,100546,43536],{"encoding":904},[123,100548,100549,100572,100573,1914],{},[38,100550,100551],{},[883,100552,100554],{"className":100553},[886],[888,100555,100556],{"xmlns":890},[892,100557,100558,100570],{},[895,100559,100560],{},[1931,100561,100562,100564],{},[898,100563,1754],{},[895,100565,100566,100568],{},[898,100567,43369],{},[898,100569,724],{},[902,100571,43374],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,100574,100576],{"className":100575},[886],[888,100577,100578],{"xmlns":890},[892,100579,100580,100588],{},[895,100581,100582],{},[2057,100583,100584,100586],{},[898,100585,1746],{},[898,100587,1846],{},[902,100589,42158],{"encoding":904},[123,100591,100592,100617,100618,1914],{},[38,100593,100594],{},[883,100595,100597],{"className":100596},[886],[888,100598,100599],{"xmlns":890},[892,100600,100601,100615],{},[895,100602,100603],{},[1931,100604,100605,100607],{},[898,100606,1754],{},[895,100608,100609,100611,100613],{},[898,100610,43392],{},[898,100612,2740],{},[898,100614,12742],{},[902,100616,43399],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,100619,100621],{"className":100620},[886],[888,100622,100623],{"xmlns":890},[892,100624,100625,100633],{},[895,100626,100627],{},[2057,100628,100629,100631],{},[898,100630,1746],{},[898,100632,1846],{},[902,100634,42158],{"encoding":904},[123,100636,100637,7725,100639,1343,100668],{},[38,100638,51164],{},[883,100640,100642],{"className":100641},[886],[888,100643,100644],{"xmlns":890},[892,100645,100646,100666],{},[895,100647,100648,100656,100658],{},[2220,100649,100650,100652,100654],{},[898,100651,1904],{},[1864,100653,1866],{},[898,100655,1846],{},[1723,100657,1725],{},[2220,100659,100660,100662,100664],{},[898,100661,1904],{},[1864,100663,2331],{},[898,100665,1846],{},[902,100667,43600],{"encoding":904},[883,100669,100671],{"className":100670},[886],[888,100672,100673],{"xmlns":890},[892,100674,100675,100699],{},[895,100676,100677,100685,100687,100689,100691],{},[2220,100678,100679,100681,100683],{},[898,100680,1746],{},[1864,100682,1866],{},[898,100684,1846],{},[1723,100686,1759],{},[898,100688,1754],{},[1723,100690,1725],{},[2220,100692,100693,100695,100697],{},[898,100694,1746],{},[1864,100696,2331],{},[898,100698,1846],{},[902,100700,43634],{"encoding":904},[123,100702,100703,100706],{},[38,100704,100705],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[37662,100708],{},[115,100710,2620],{"id":2619},[120,100712,100713,100721,100739,100746],{},[123,100714,100715,2628,100718],{},[38,100716,100717],{},"Kontext (hub):",[207,100719,802],{"className":100720,"dataFsResolvedFilePath":800,"href":801},[210],[123,100722,100723,2628,100725,100728,100729,19342,100731,100734,100735,100738],{},[38,100724,51413],{},[207,100726,820],{"className":100727,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,100730,55724],{},[207,100732,3086],{"className":100733,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,100736,4544],{"className":100737,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,100740,100741,2628,100743],{},[38,100742,51448],{},[207,100744,51452],{"className":100745,"dataFsResolvedFilePath":745,"href":746},[210],[123,100747,100748,2628,100750],{},[38,100749,2627],{},[207,100751,1646],{"className":100752,"dataFsResolvedFilePath":1645,"href":1644},[210],{"title":641,"searchDepth":642,"depth":642,"links":100754},[100755,100756,100759,100762,100766,100767,100768,100769],{"id":96599,"depth":642,"text":96600},{"id":96693,"depth":642,"text":96694,"children":100757},[100758],{"id":97084,"depth":649,"text":45994},{"id":97766,"depth":642,"text":97767,"children":100760},[100761],{"id":98243,"depth":649,"text":46074},{"id":98710,"depth":642,"text":43350,"children":100763},[100764,100765],{"id":3169,"depth":649,"text":3170},{"id":99053,"depth":649,"text":99054},{"id":99526,"depth":642,"text":99527},{"id":100123,"depth":642,"text":100124},{"id":16420,"depth":642,"text":16421},{"id":2619,"depth":642,"text":2620},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":96497,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,51513,100776,100777,100778,1692],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[100781,100783],{"slug":1128,"path":1644,"title":681,"snippet":100782},"… 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